From 8d435d44109e0bb4efde6b2d367c47a953ccb667 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E4=BA=8E=E7=BA=A2=E9=9B=A8?= <yuhongyu04@126.com>
Date: Fri, 21 Sep 2018 15:21:32 +0800
Subject: [PATCH 1/8] test order difficulty

---
 gateway/order_difficulty/difficulty.go      | 150 +++++++++++++++-----
 gateway/order_difficulty/difficulty_test.go |  84 +++++++++++
 gateway/wallet_service.go                   |  13 ++
 node/config.go                              |   2 +
 node/node.go                                |  45 +++---
 5 files changed, 242 insertions(+), 52 deletions(-)
 create mode 100644 gateway/order_difficulty/difficulty_test.go

diff --git a/gateway/order_difficulty/difficulty.go b/gateway/order_difficulty/difficulty.go
index 450ccad7..39bf6084 100644
--- a/gateway/order_difficulty/difficulty.go
+++ b/gateway/order_difficulty/difficulty.go
@@ -19,6 +19,7 @@
 package order_difficulty
 
 import (
+	"encoding/json"
 	"github.com/Loopring/relay-lib/cache"
 	"github.com/Loopring/relay-lib/eventemitter"
 	"github.com/Loopring/relay-lib/types"
@@ -33,32 +34,50 @@ import (
 
 const (
 	OrderCountPerSecond = "o_cnt_per_s_"
-	OrderDifficulty     = "order_diff"
+	OrderDifficultyKey  = "order_diff"
 	ZklockDifficulty    = "zklock_diff"
 )
 
 type OrderDifficultyEvaluator struct {
 	//currentDifficult *OrderDifficulty
 	//parentDifficult  *OrderDifficulty
-	evaluator        Evaluator
-	baseDifficulty   *big.Int
-	orderTraffic     int64
-	triggerThreshold float64
-	stopFuns         []func()
-	calCount         int64 //must be odd
+	evaluator Evaluator
+	stopFuns  []func()
+	calCount  int64 //must be odd
+	duration  int64
 }
 
 type OrderDifficulty struct {
-	difficulty *big.Int
-	ordersNum  int64
-	timeStamp  int64
+	Difficulty common.Hash
+	OrdersNum  int64
+	TimeStamp  int64
 }
 
-func (evaluator *OrderDifficultyEvaluator) getCacheKey(createTime int64) (key string, expireAt int64) {
+func (evaluator *OrderDifficultyEvaluator) getOrderCacheKey(createTime int64) (key string, expireAt int64) {
 	mod := createTime % evaluator.calCount
 	orderSection := createTime - mod
 	orderSectionStr := strconv.FormatInt(orderSection, 10)
-	return OrderCountPerSecond + orderSectionStr, createTime + evaluator.calCount
+	return OrderCountPerSecond + orderSectionStr, createTime + evaluator.calCount*evaluator.duration
+}
+
+func (evaluator *OrderDifficultyEvaluator) getDiffCacheKey(createTime int64) (key string, expireAt int64) {
+	mod := createTime % evaluator.calCount
+	orderSection := createTime - mod
+	orderSectionStr := strconv.FormatInt(orderSection, 10)
+	return OrderDifficultyKey + orderSectionStr, createTime + evaluator.calCount*evaluator.duration
+}
+
+func NewOrderDifficultyEvaluator(config OrderDifficultyConfig) *OrderDifficultyEvaluator {
+	evaluator := &OrderDifficultyEvaluator{calCount: config.CalCount, duration: config.Duration}
+	evaluator.evaluator = &LinearEvaluator{baseDifficulty: config.BaseDifficulty, threshold: config.Threshold}
+	return evaluator
+}
+
+type OrderDifficultyConfig struct {
+	BaseDifficulty *big.Int
+	Threshold      int64
+	CalCount       int64
+	Duration       int64
 }
 
 func (evaluator *OrderDifficultyEvaluator) Start() {
@@ -68,27 +87,50 @@ func (evaluator *OrderDifficultyEvaluator) Start() {
 			log.Errorf("erro:%s", err.Error())
 		} else {
 			now := time.Now().Unix()
-			orderCntList := []int64{}
+			orderCntList := []*OrderDifficulty{}
 			for i := evaluator.calCount; i > 0; i-- {
-				t := now - i
-				cacheKey, _ := evaluator.getCacheKey(t)
+				t := now - i*evaluator.duration
+				cacheKey, _ := evaluator.getDiffCacheKey(t)
+				orderDifficulty := &OrderDifficulty{}
 				if data, err := cache.Get(cacheKey); nil == err {
-					cnt, _ := strconv.ParseInt(string(data), 10, 0)
-					orderCntList = append(orderCntList, cnt)
+					json.Unmarshal(data, orderDifficulty)
 				}
+				orderCntList = append(orderCntList, orderDifficulty)
 			}
 			for {
 				select {
-				case <-time.After(2 * time.Second):
-					cacheKey, _ := evaluator.getCacheKey(time.Now().Unix() - 1)
-					if data, err := cache.Get(cacheKey); nil == err {
-						cnt, _ := strconv.ParseInt(string(data), 10, 0)
-						orderCntList = append(orderCntList, cnt)
+				case <-time.After(time.Duration(evaluator.duration) * time.Second):
+					now := time.Now().Unix()
+					if diffHash, err := GetDifficulty(); nil == err {
+						currentDiff := diffHash
+						orderDiff := &OrderDifficulty{}
+						cacheKey, _ := evaluator.getOrderCacheKey(now)
+						orderDiff.OrdersNum = 60
+						if data, err1 := cache.Get(cacheKey); nil == err1 {
+							if orderNum, err3 := strconv.Atoi(string(data)); nil == err3 {
+								orderDiff.OrdersNum = int64(orderNum)
+							}
+						}
+						diffCacheKey, _ := evaluator.getDiffCacheKey(now)
+						orderDiff.Difficulty = currentDiff
+						if data, err4 := json.Marshal(orderDiff); nil == err4 {
+							cache.Set(diffCacheKey, data, (evaluator.calCount+2)*evaluator.duration)
+						}
+					}
+					orderCntList := []*OrderDifficulty{}
+					for i := evaluator.calCount; i > 0; i-- {
+						t := now - i*evaluator.duration
+						diffCacheKey, _ := evaluator.getDiffCacheKey(t)
+						orderDifficulty := &OrderDifficulty{}
+						if data, err := cache.Get(diffCacheKey); nil == err {
+							json.Unmarshal(data, orderDifficulty)
+						}
+						orderCntList = append(orderCntList, orderDifficulty)
 					}
-					diff := evaluator.evaluator.CalcAndSaveDifficulty(orderCntList)
+					diff := evaluator.evaluator.CalcAndSaveDifficulty(orderCntList, evaluator.duration)
 					diffHash := common.BytesToHash(diff.Bytes())
-					cache.Set(OrderDifficulty, []byte(diffHash.Hex()), int64(0))
-					orderCntList = orderCntList[1:]
+					log.Infof("current order difficulty:%s", diff.String())
+					cache.Set(OrderDifficultyKey, []byte(diffHash.Hex()), int64(0))
 				}
 			}
 		}
@@ -101,12 +143,12 @@ func (evaluator *OrderDifficultyEvaluator) Stop() {
 	}
 }
 
-//add ordersNum
+//add OrdersNum
 func (evaluator *OrderDifficultyEvaluator) HandleNewOrder() {
 	watcher := &eventemitter.Watcher{
 		Concurrent: false, Handle: func(input eventemitter.EventData) error {
 			state := input.(*types.OrderState)
-			cacheKey, expireAt := evaluator.getCacheKey(state.RawOrder.CreateTime)
+			cacheKey, expireAt := evaluator.getOrderCacheKey(state.RawOrder.CreateTime)
 			_, err := cache.Incr(cacheKey)
 			if nil == err {
 				err = cache.ExpireAt(cacheKey, expireAt)
@@ -122,27 +164,69 @@ func (evaluator *OrderDifficultyEvaluator) HandleNewOrder() {
 }
 
 type Evaluator interface {
-	CalcAndSaveDifficulty(orderCntList []int64) *big.Int
+	CalcAndSaveDifficulty(orderCntList []*OrderDifficulty, duration int64) *big.Int
+	getBaseDifficulty() *big.Int
 }
 
 type LinearEvaluator struct {
+	baseDifficulty *big.Int
+	threshold      int64
 }
 
-//控制订单的提交速度，随着订单的流量增大而增大
-func (evaluator *LinearEvaluator) CalcAndSaveDifficulty(orderCntList []int64) *big.Int {
+func (evaluator *LinearEvaluator) getBaseDifficulty() *big.Int {
+	return new(big.Int).Set(evaluator.baseDifficulty)
+}
+
+func (evaluator *LinearEvaluator) CalNextOrderCnt(orderCntList []*OrderDifficulty, duration int64) int64 {
 	xes := []float64{}
 	yes := []float64{}
 	now := time.Now().Unix()
 	for idx, cnt := range orderCntList {
-		xes = append(xes, float64(idx))
-		yes = append(yes, float64(cnt))
+		//println("sum",cnt.OrdersNum)
+		xes = append(xes, float64(now-duration*int64(len(orderCntList)-idx)))
+		yes = append(yes, float64(cnt.OrdersNum))
 	}
 	alpha, beta := stat.LinearRegression(xes, yes, nil, false)
 	return int64(beta*float64(now) + alpha)
 }
 
+//控制订单的提交速度，随着订单的流量增大而增大
+func (evaluator *LinearEvaluator) CalcAndSaveDifficulty(orderCntList []*OrderDifficulty, duration int64) *big.Int {
+	nextCnt := evaluator.CalNextOrderCnt(orderCntList, duration)
+	log.Infof("next order count:%d", nextCnt)
+	orderList := append(orderCntList, &OrderDifficulty{OrdersNum: nextCnt})
+	return evaluator.nextDifficulty(orderList)
+}
+
+func NewOrderDiff(ordersNum int64, diff common.Hash) *OrderDifficulty {
+	return &OrderDifficulty{OrdersNum: ordersNum, Difficulty: diff}
+}
+
+func NewLinearEvaluator(baseDifficulty *big.Int, threshold int64) *LinearEvaluator {
+	return &LinearEvaluator{baseDifficulty: baseDifficulty, threshold: threshold}
+}
+
+func (evaluator *LinearEvaluator) nextDifficulty(orderCntList []*OrderDifficulty) *big.Int {
+	nextOrderDiff := orderCntList[len(orderCntList)-1]
+	if nextOrderDiff.OrdersNum < evaluator.threshold {
+		return evaluator.baseDifficulty
+	} else {
+		currentDiff := new(big.Int).Set(evaluator.baseDifficulty)
+		if currentDiffBytes, err := GetDifficulty(); nil == err {
+			currentDiff = new(big.Int).SetBytes(currentDiffBytes.Bytes())
+		}
+		addRatio := big.NewInt(3)
+		if nextOrderDiff.OrdersNum > int64(float64(evaluator.threshold)*1.5) {
+			addRatio = big.NewInt(1)
+		} else if nextOrderDiff.OrdersNum < int64(float64(evaluator.threshold)*1.2) {
+			addRatio = big.NewInt(5)
+		}
+		return new(big.Int).Add(currentDiff, new(big.Int).Quo(currentDiff, addRatio))
+	}
+}
+
 func GetDifficulty() (common.Hash, error) {
-	if data, err := cache.Get(OrderDifficulty); nil == err {
+	if data, err := cache.Get(OrderDifficultyKey); nil == err {
 		return common.HexToHash(string(data)), nil
 	} else {
 		return common.Hash{}, err
diff --git a/gateway/order_difficulty/difficulty_test.go b/gateway/order_difficulty/difficulty_test.go
new file mode 100644
index 00000000..19180cad
--- /dev/null
+++ b/gateway/order_difficulty/difficulty_test.go
@@ -0,0 +1,84 @@
+/*
+
+  Copyright 2017 Loopring Project Ltd (Loopring Foundation).
+
+  Licensed under the Apache License, Version 2.0 (the "License");
+  you may not use this file except in compliance with the License.
+  You may obtain a copy of the License at
+
+  http://www.apache.org/licenses/LICENSE-2.0
+
+  Unless required by applicable law or agreed to in writing, software
+  distributed under the License is distributed on an "AS IS" BASIS,
+  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+  See the License for the specific language governing permissions and
+  limitations under the License.
+
+*/
+
+package order_difficulty_test
+
+import (
+	"encoding/json"
+	"github.com/Loopring/relay-cluster/gateway/order_difficulty"
+	"github.com/Loopring/relay-lib/cache"
+	"github.com/Loopring/relay-lib/cache/redis"
+	"github.com/Loopring/relay-lib/log"
+	"github.com/Loopring/relay-lib/zklock"
+	"github.com/ethereum/go-ethereum/common"
+	"go.uber.org/zap"
+	"math/big"
+	"testing"
+	"time"
+)
+
+func init() {
+	logConfig := `{
+	  "level": "debug",
+	  "development": false,
+	  "encoding": "json",
+	  "outputPaths": ["stdout"],
+	  "errorOutputPaths": ["stderr"],
+	  "encoderConfig": {
+	    "messageKey": "message",
+	    "levelKey": "level",
+	    "levelEncoder": "lowercase"
+	  }
+	}`
+	rawJSON := []byte(logConfig)
+
+	var (
+		cfg zap.Config
+		err error
+	)
+	if err = json.Unmarshal(rawJSON, &cfg); err != nil {
+		panic(err)
+	}
+	log.Initialize(cfg)
+	cache.NewCache(redis.RedisOptions{Host: "127.0.0.1", Port: "6379"})
+	zklock.Initialize(zklock.ZkLockConfig{ZkServers: "127.0.0.1:2181", ConnectTimeOut: 10000})
+
+}
+
+func TestEvaluator(t *testing.T) {
+	config := order_difficulty.OrderDifficultyConfig{BaseDifficulty: big.NewInt(1000), Threshold: 100, Duration: 2, CalCount: 100}
+	evaluator := order_difficulty.NewOrderDifficultyEvaluator(config)
+	evaluator.Start()
+	time.Sleep(1000000 * time.Second)
+}
+
+func TestLinearEvaluator_CalcAndSaveDifficulty(t *testing.T) {
+	evaluator := order_difficulty.NewLinearEvaluator(big.NewInt(100), 200)
+	cntList := make([]*order_difficulty.OrderDifficulty, 0)
+	cntList = append(cntList, order_difficulty.NewOrderDiff(100, common.BytesToHash(big.NewInt(100).Bytes())))
+	cntList = append(cntList, order_difficulty.NewOrderDiff(900, common.BytesToHash(big.NewInt(200).Bytes())))
+	cntList = append(cntList, order_difficulty.NewOrderDiff(900, common.BytesToHash(big.NewInt(200).Bytes())))
+	cntList = append(cntList, order_difficulty.NewOrderDiff(400, common.BytesToHash(big.NewInt(200).Bytes())))
+	cntList = append(cntList, order_difficulty.NewOrderDiff(400, common.BytesToHash(big.NewInt(200).Bytes())))
+	cntList = append(cntList, order_difficulty.NewOrderDiff(400, common.BytesToHash(big.NewInt(200).Bytes())))
+	cntList = append(cntList, order_difficulty.NewOrderDiff(400, common.BytesToHash(big.NewInt(200).Bytes())))
+	cntList = append(cntList, order_difficulty.NewOrderDiff(600, common.BytesToHash(big.NewInt(200).Bytes())))
+	//cntList = append(cntList, order_difficulty.NewOrderDiff(700, common.BytesToHash(big.NewInt(200).Bytes())))
+	//cntList = append(cntList, order_difficulty.NewOrderDiff(700, common.BytesToHash(big.NewInt(200).Bytes())))
+	println(evaluator.CalcAndSaveDifficulty(cntList, 10).String())
+}
diff --git a/gateway/wallet_service.go b/gateway/wallet_service.go
index e5d4c7bc..efd2bfdb 100644
--- a/gateway/wallet_service.go
+++ b/gateway/wallet_service.go
@@ -24,6 +24,7 @@ import (
 	"fmt"
 	"github.com/Loopring/relay-cluster/accountmanager"
 	"github.com/Loopring/relay-cluster/dao"
+	"github.com/Loopring/relay-cluster/gateway/order_difficulty"
 	"github.com/Loopring/relay-cluster/market"
 	"github.com/Loopring/relay-cluster/ordermanager/manager"
 	"github.com/Loopring/relay-cluster/ordermanager/viewer"
@@ -411,6 +412,13 @@ type AddTokenReq struct {
 	Decimals             string `json:"decimals"`
 }
 
+type OrderDifficultyReq struct {
+}
+
+type OrderDifficultyRes struct {
+	Difficulty common.Hash `json:"difficulty"`
+}
+
 type WalletServiceImpl struct {
 	trendManager    market.TrendManager
 	orderViewer     viewer.OrderViewer
@@ -546,6 +554,11 @@ func (w *WalletServiceImpl) GetPriceQuote(query PriceQuoteQuery) (result PriceQu
 	return rst, nil
 }
 
+func (w *WalletServiceImpl) GetOrderDifficulty(req OrderDifficultyReq) (result OrderDifficultyRes, err error) {
+	diff, err1 := order_difficulty.GetDifficulty()
+	return OrderDifficultyRes{Difficulty: diff}, err1
+}
+
 func (w *WalletServiceImpl) GetTickers(mkt SingleMarket) (result map[string]market.Ticker, err error) {
 	result = make(map[string]market.Ticker)
 	loopringTicker, err := w.trendManager.GetTickerByMarket(mkt.Market)
diff --git a/node/config.go b/node/config.go
index bf39d082..b10d4ac1 100644
--- a/node/config.go
+++ b/node/config.go
@@ -25,6 +25,7 @@ import (
 
 	"github.com/Loopring/relay-cluster/accountmanager"
 	"github.com/Loopring/relay-cluster/gateway"
+	"github.com/Loopring/relay-cluster/gateway/order_difficulty"
 	"github.com/Loopring/relay-cluster/market"
 	ordermanager "github.com/Loopring/relay-cluster/ordermanager/common"
 	"github.com/Loopring/relay-cluster/usermanager"
@@ -84,6 +85,7 @@ type GlobalConfig struct {
 	AccountManager   accountmanager.AccountManagerOptions
 	MyToken          market.MyTokenConfig
 	CloudWatch       cloudwatch.CloudWatchConfig
+	OrderDifficulty  order_difficulty.OrderDifficultyConfig
 }
 
 func Validator(cv reflect.Value) (bool, error) {
diff --git a/node/node.go b/node/node.go
index ebf65f0e..be94a73f 100644
--- a/node/node.go
+++ b/node/node.go
@@ -25,9 +25,11 @@ import (
 	"github.com/Loopring/relay-cluster/accountmanager"
 	"github.com/Loopring/relay-cluster/dao"
 	"github.com/Loopring/relay-cluster/gateway"
+	"github.com/Loopring/relay-cluster/gateway/order_difficulty"
 	"github.com/Loopring/relay-cluster/market"
 	ordermanager "github.com/Loopring/relay-cluster/ordermanager/manager"
 	orderviewer "github.com/Loopring/relay-cluster/ordermanager/viewer"
+	ringtrackerviewer "github.com/Loopring/relay-cluster/ringtrackermanager/viewer"
 	txmanager "github.com/Loopring/relay-cluster/txmanager/manager"
 	txviewer "github.com/Loopring/relay-cluster/txmanager/viewer"
 	"github.com/Loopring/relay-cluster/usermanager"
@@ -46,31 +48,30 @@ import (
 	"github.com/Loopring/relay-lib/zklock"
 	"github.com/ethereum/go-ethereum/accounts/keystore"
 	"go.uber.org/zap"
-	ringtrackerviewer "github.com/Loopring/relay-cluster/ringtrackermanager/viewer"
 )
 
 type Node struct {
 	globalConfig *GlobalConfig
 	rdsService   *dao.RdsService
 	//ipfsSubService    gateway.IPFSSubService
-	orderManager      ordermanager.OrderManager
-	orderViewer       orderviewer.OrderViewer
-	userManager       usermanager.UserManager
-	marketCapProvider marketcap.MarketCapProvider
-	accountManager    accountmanager.AccountManager
-	trendManager      market.TrendManager
-	tickerCollector   market.CollectorImpl
-	tickerManager     market.GetTickerImpl
-	globalMarket      market.GlobalMarket
-	jsonRpcService    gateway.JsonrpcServiceImpl
-	websocketService  gateway.WebsocketServiceImpl
-	socketIOService   gateway.SocketIOServiceImpl
-	walletService     gateway.WalletServiceImpl
-	txManager         txmanager.TransactionManager
-	motanService      *gateway.MotanService
-
-	wg     *sync.WaitGroup
-	logger *zap.Logger
+	orderManager             ordermanager.OrderManager
+	orderViewer              orderviewer.OrderViewer
+	userManager              usermanager.UserManager
+	marketCapProvider        marketcap.MarketCapProvider
+	accountManager           accountmanager.AccountManager
+	trendManager             market.TrendManager
+	tickerCollector          market.CollectorImpl
+	tickerManager            market.GetTickerImpl
+	globalMarket             market.GlobalMarket
+	jsonRpcService           gateway.JsonrpcServiceImpl
+	websocketService         gateway.WebsocketServiceImpl
+	socketIOService          gateway.SocketIOServiceImpl
+	walletService            gateway.WalletServiceImpl
+	txManager                txmanager.TransactionManager
+	motanService             *gateway.MotanService
+	orderDifficultyEvaluator *order_difficulty.OrderDifficultyEvaluator
+	wg                       *sync.WaitGroup
+	logger                   *zap.Logger
 
 	ringTrackerViewer  ringtrackerviewer.RingTrackerViewer
 	ringTrackerService gateway.RingTrackerServiceImpl
@@ -118,6 +119,7 @@ func NewNode(logger *zap.Logger, globalConfig *GlobalConfig) *Node {
 
 	n.registerRingTrackerViewer()
 	n.registerRingTrackerService()
+	n.registerOrderDifficultyEvaluator()
 	return n
 }
 
@@ -135,6 +137,7 @@ func (n *Node) Start() {
 	//n.websocketService.Start()
 	go n.socketIOService.Start()
 	gateway.StartMotanService(n.globalConfig.MotanServer, n.accountManager, n.orderViewer)
+	n.orderDifficultyEvaluator.Start()
 
 	n.wg.Add(1)
 }
@@ -268,6 +271,10 @@ func (n *Node) registerCloudWatch() {
 	cloudwatch.Initialize(n.globalConfig.CloudWatch)
 }
 
+func (n *Node) registerOrderDifficultyEvaluator() {
+	n.orderDifficultyEvaluator = order_difficulty.NewOrderDifficultyEvaluator(n.globalConfig.OrderDifficulty)
+}
+
 func (n *Node) registerRingTrackerViewer() {
 	n.ringTrackerViewer = ringtrackerviewer.NewRingTrackerViewer(n.rdsService, n.marketCapProvider)
 }

From 999f996f7a275abc8d4bd31aa87b491e6091fbb5 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E4=BA=8E=E7=BA=A2=E9=9B=A8?= <yuhongyu04@126.com>
Date: Fri, 21 Sep 2018 15:36:42 +0800
Subject: [PATCH 2/8] test order difficulty

---
 gateway/order_difficulty/difficulty.go      | 39 +++++++++++++++------
 gateway/order_difficulty/difficulty_test.go |  2 +-
 2 files changed, 29 insertions(+), 12 deletions(-)

diff --git a/gateway/order_difficulty/difficulty.go b/gateway/order_difficulty/difficulty.go
index 39bf6084..e5f78039 100644
--- a/gateway/order_difficulty/difficulty.go
+++ b/gateway/order_difficulty/difficulty.go
@@ -68,6 +68,18 @@ func (evaluator *OrderDifficultyEvaluator) getDiffCacheKey(createTime int64) (ke
 }
 
 func NewOrderDifficultyEvaluator(config OrderDifficultyConfig) *OrderDifficultyEvaluator {
+	if nil == config.BaseDifficulty {
+		config.BaseDifficulty = big.NewInt(0)
+	}
+	if 0 == config.CalCount {
+		config.CalCount = 1000
+	}
+	if 0 == config.Duration {
+		config.Duration = 2
+	}
+	if 0 == config.Threshold {
+		config.Threshold = 10
+	}
 	evaluator := &OrderDifficultyEvaluator{calCount: config.CalCount, duration: config.Duration}
 	evaluator.evaluator = &LinearEvaluator{baseDifficulty: config.BaseDifficulty, threshold: config.Threshold}
 	return evaluator
@@ -86,17 +98,22 @@ func (evaluator *OrderDifficultyEvaluator) Start() {
 		if err := zklock.TryLock(ZklockDifficulty); nil != err {
 			log.Errorf("erro:%s", err.Error())
 		} else {
-			now := time.Now().Unix()
-			orderCntList := []*OrderDifficulty{}
-			for i := evaluator.calCount; i > 0; i-- {
-				t := now - i*evaluator.duration
-				cacheKey, _ := evaluator.getDiffCacheKey(t)
-				orderDifficulty := &OrderDifficulty{}
-				if data, err := cache.Get(cacheKey); nil == err {
-					json.Unmarshal(data, orderDifficulty)
-				}
-				orderCntList = append(orderCntList, orderDifficulty)
+			if _, err1 := GetDifficulty(); nil != err1 {
+				println("##########")
+				diff := common.BytesToHash(evaluator.evaluator.getBaseDifficulty().Bytes())
+				cache.Set(OrderDifficultyKey, []byte(diff.Hex()), int64(10000))
 			}
+			//now := time.Now().Unix()
+			//orderCntList := []*OrderDifficulty{}
+			//for i := evaluator.calCount; i > 0; i-- {
+			//	t := now - i*evaluator.duration
+			//	cacheKey, _ := evaluator.getDiffCacheKey(t)
+			//	orderDifficulty := &OrderDifficulty{}
+			//	if data, err := cache.Get(cacheKey); nil == err {
+			//		json.Unmarshal(data, orderDifficulty)
+			//	}
+			//	orderCntList = append(orderCntList, orderDifficulty)
+			//}
 			for {
 				select {
 				case <-time.After(time.Duration(evaluator.duration) * time.Second):
@@ -105,7 +122,7 @@ func (evaluator *OrderDifficultyEvaluator) Start() {
 						currentDiff := diffHash
 						orderDiff := &OrderDifficulty{}
 						cacheKey, _ := evaluator.getOrderCacheKey(now)
-						orderDiff.OrdersNum = 60
+						orderDiff.OrdersNum = 0
 						if data, err1 := cache.Get(cacheKey); nil == err1 {
 							if orderNum, err3 := strconv.Atoi(string(data)); nil == err3 {
 								orderDiff.OrdersNum = int64(orderNum)
diff --git a/gateway/order_difficulty/difficulty_test.go b/gateway/order_difficulty/difficulty_test.go
index 19180cad..9dd69d6d 100644
--- a/gateway/order_difficulty/difficulty_test.go
+++ b/gateway/order_difficulty/difficulty_test.go
@@ -61,7 +61,7 @@ func init() {
 }
 
 func TestEvaluator(t *testing.T) {
-	config := order_difficulty.OrderDifficultyConfig{BaseDifficulty: big.NewInt(1000), Threshold: 100, Duration: 2, CalCount: 100}
+	config := order_difficulty.OrderDifficultyConfig{}
 	evaluator := order_difficulty.NewOrderDifficultyEvaluator(config)
 	evaluator.Start()
 	time.Sleep(1000000 * time.Second)

From 5ceecbd39483334ca25e6b535d741cd23ea9b42b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E4=BA=8E=E7=BA=A2=E9=9B=A8?= <yuhongyu04@126.com>
Date: Fri, 21 Sep 2018 15:41:12 +0800
Subject: [PATCH 3/8] test order difficulty

---
 gateway/order_difficulty/difficulty.go | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/gateway/order_difficulty/difficulty.go b/gateway/order_difficulty/difficulty.go
index e5f78039..08c42f6a 100644
--- a/gateway/order_difficulty/difficulty.go
+++ b/gateway/order_difficulty/difficulty.go
@@ -22,12 +22,12 @@ import (
 	"encoding/json"
 	"github.com/Loopring/relay-lib/cache"
 	"github.com/Loopring/relay-lib/eventemitter"
+	"github.com/Loopring/relay-lib/log"
 	"github.com/Loopring/relay-lib/types"
 	"github.com/Loopring/relay-lib/zklock"
 	"github.com/ethereum/go-ethereum/common"
 	"gonum.org/v1/gonum/stat"
 	"math/big"
-	"qiniupkg.com/x/log.v7"
 	"strconv"
 	"time"
 )

From 165a4dcc3c565766c25a7fbe7883ea18eb68d69f Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E4=BA=8E=E7=BA=A2=E9=9B=A8?= <yuhongyu04@126.com>
Date: Fri, 21 Sep 2018 15:46:18 +0800
Subject: [PATCH 4/8] test order difficulty

---
 vendor/gonum.org/v1/gonum/LICENSE         |   23 +
 vendor/gonum.org/v1/gonum/stat/README.md  |    3 +
 vendor/gonum.org/v1/gonum/stat/doc.go     |    6 +
 vendor/gonum.org/v1/gonum/stat/pca_cca.go |  315 ++++++
 vendor/gonum.org/v1/gonum/stat/roc.go     |  121 +++
 vendor/gonum.org/v1/gonum/stat/stat.go    | 1160 +++++++++++++++++++++
 vendor/gonum.org/v1/gonum/stat/statmat.go |  146 +++
 vendor/vendor.json                        |    6 +
 8 files changed, 1780 insertions(+)
 create mode 100644 vendor/gonum.org/v1/gonum/LICENSE
 create mode 100644 vendor/gonum.org/v1/gonum/stat/README.md
 create mode 100644 vendor/gonum.org/v1/gonum/stat/doc.go
 create mode 100644 vendor/gonum.org/v1/gonum/stat/pca_cca.go
 create mode 100644 vendor/gonum.org/v1/gonum/stat/roc.go
 create mode 100644 vendor/gonum.org/v1/gonum/stat/stat.go
 create mode 100644 vendor/gonum.org/v1/gonum/stat/statmat.go

diff --git a/vendor/gonum.org/v1/gonum/LICENSE b/vendor/gonum.org/v1/gonum/LICENSE
new file mode 100644
index 00000000..76edf5ef
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/LICENSE
@@ -0,0 +1,23 @@
+Copyright ©2013 The gonum Authors. All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+    * Redistributions of source code must retain the above copyright
+      notice, this list of conditions and the following disclaimer.
+    * Redistributions in binary form must reproduce the above copyright
+      notice, this list of conditions and the following disclaimer in the
+      documentation and/or other materials provided with the distribution.
+    * Neither the name of the gonum project nor the names of its authors and
+      contributors may be used to endorse or promote products derived from this
+      software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
+FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
\ No newline at end of file
diff --git a/vendor/gonum.org/v1/gonum/stat/README.md b/vendor/gonum.org/v1/gonum/stat/README.md
new file mode 100644
index 00000000..31615b05
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/README.md
@@ -0,0 +1,3 @@
+# Gonum stat [![GoDoc](https://godoc.org/gonum.org/v1/gonum/stat?status.svg)](https://godoc.org/gonum.org/v1/gonum/stat)
+
+Package stat is a statistics package for the Go language.
diff --git a/vendor/gonum.org/v1/gonum/stat/doc.go b/vendor/gonum.org/v1/gonum/stat/doc.go
new file mode 100644
index 00000000..0225eef9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package stat provides generalized statistical functions.
+package stat // import "gonum.org/v1/gonum/stat"
diff --git a/vendor/gonum.org/v1/gonum/stat/pca_cca.go b/vendor/gonum.org/v1/gonum/stat/pca_cca.go
new file mode 100644
index 00000000..59e742eb
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/pca_cca.go
@@ -0,0 +1,315 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package stat
+
+import (
+	"errors"
+	"math"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+)
+
+// PC is a type for computing and extracting the principal components of a
+// matrix. The results of the principal components analysis are only valid
+// if the call to PrincipalComponents was successful.
+type PC struct {
+	n, d    int
+	weights []float64
+	svd     *mat.SVD
+	ok      bool
+}
+
+// PrincipalComponents performs a weighted principal components analysis on the
+// matrix of the input data which is represented as an n×d matrix a where each
+// row is an observation and each column is a variable.
+//
+// PrincipalComponents centers the variables but does not scale the variance.
+//
+// The weights slice is used to weight the observations. If weights is nil, each
+// weight is considered to have a value of one, otherwise the length of weights
+// must match the number of observations or PrincipalComponents will panic.
+//
+// PrincipalComponents returns whether the analysis was successful.
+func (c *PC) PrincipalComponents(a mat.Matrix, weights []float64) (ok bool) {
+	c.n, c.d = a.Dims()
+	if weights != nil && len(weights) != c.n {
+		panic("stat: len(weights) != observations")
+	}
+
+	c.svd, c.ok = svdFactorizeCentered(c.svd, a, weights)
+	if c.ok {
+		c.weights = append(c.weights[:0], weights...)
+	}
+	return c.ok
+}
+
+// VectorsTo returns the component direction vectors of a principal components
+// analysis. The vectors are returned in the columns of a d×min(n, d) matrix.
+// If dst is not nil it must either be zero-sized or be a d×min(n, d) matrix.
+// dst will  be used as the destination for the direction vector data. If dst
+// is nil, a new mat.Dense is allocated for the destination.
+func (c *PC) VectorsTo(dst *mat.Dense) *mat.Dense {
+	if !c.ok {
+		panic("stat: use of unsuccessful principal components analysis")
+	}
+
+	if dst != nil {
+		if d, n := dst.Dims(); !dst.IsZero() && (d != c.d || n != min(c.n, c.d)) {
+			panic(mat.ErrShape)
+		}
+	}
+	return c.svd.VTo(dst)
+}
+
+// VarsTo returns the column variances of the principal component scores,
+// b * vecs, where b is a matrix with centered columns. Variances are returned
+// in descending order.
+// If dst is not nil it is used to store the variances and returned.
+// Vars will panic if the receiver has not successfully performed a principal
+// components analysis or dst is not nil and the length of dst is not min(n, d).
+func (c *PC) VarsTo(dst []float64) []float64 {
+	if !c.ok {
+		panic("stat: use of unsuccessful principal components analysis")
+	}
+	if dst != nil && len(dst) != min(c.n, c.d) {
+		panic("stat: length of slice does not match analysis")
+	}
+
+	dst = c.svd.Values(dst)
+	var f float64
+	if c.weights == nil {
+		f = 1 / float64(c.n-1)
+	} else {
+		f = 1 / (floats.Sum(c.weights) - 1)
+	}
+	for i, v := range dst {
+		dst[i] = f * v * v
+	}
+	return dst
+}
+
+func min(a, b int) int {
+	if a < b {
+		return a
+	}
+	return b
+}
+
+// CC is a type for computing the canonical correlations of a pair of matrices.
+// The results of the canonical correlation analysis are only valid
+// if the call to CanonicalCorrelations was successful.
+type CC struct {
+	// n is the number of observations used to
+	// construct the canonical correlations.
+	n int
+
+	// xd and yd are used for size checks.
+	xd, yd int
+
+	x, y, c *mat.SVD
+	ok      bool
+}
+
+// CanonicalCorrelations returns a CC which can provide the results of canonical
+// correlation analysis of the input data x and y, columns of which should be
+// interpretable as two sets of measurements on the same observations (rows).
+// These observations are optionally weighted by weights.
+//
+// Canonical correlation analysis finds associations between two sets of
+// variables on the same observations by finding linear combinations of the two
+// sphered datasets that maximize the correlation between them.
+//
+// Some notation: let Xc and Yc denote the centered input data matrices x
+// and y (column means subtracted from each column), let Sx and Sy denote the
+// sample covariance matrices within x and y respectively, and let Sxy denote
+// the covariance matrix between x and y. The sphered data can then be expressed
+// as Xc * Sx^{-1/2} and Yc * Sy^{-1/2} respectively, and the correlation matrix
+// between the sphered data is called the canonical correlation matrix,
+// Sx^{-1/2} * Sxy * Sy^{-1/2}. In cases where S^{-1/2} is ambiguous for some
+// covariance matrix S, S^{-1/2} is taken to be E * D^{-1/2} * E^T where S can
+// be eigendecomposed as S = E * D * E^T.
+//
+// The canonical correlations are the correlations between the corresponding
+// pairs of canonical variables and can be obtained with c.Corrs(). Canonical
+// variables can be obtained by projecting the sphered data into the left and
+// right eigenvectors of the canonical correlation matrix, and these
+// eigenvectors can be obtained with c.Left(m, true) and c.Right(m, true)
+// respectively. The canonical variables can also be obtained directly from the
+// centered raw data by using the back-transformed eigenvectors which can be
+// obtained with c.Left(m, false) and c.Right(m, false) respectively.
+//
+// The first pair of left and right eigenvectors of the canonical correlation
+// matrix can be interpreted as directions into which the respective sphered
+// data can be projected such that the correlation between the two projections
+// is maximized. The second pair and onwards solve the same optimization but
+// under the constraint that they are uncorrelated (orthogonal in sphered space)
+// to previous projections.
+//
+// CanonicalCorrelations will panic if the inputs x and y do not have the same
+// number of rows.
+//
+// The slice weights is used to weight the observations. If weights is nil, each
+// weight is considered to have a value of one, otherwise the length of weights
+// must match the number of observations (rows of both x and y) or
+// CanonicalCorrelations will panic.
+//
+// More details can be found at
+// https://en.wikipedia.org/wiki/Canonical_correlation
+// or in Chapter 3 of
+// Koch, Inge. Analysis of multivariate and high-dimensional data.
+// Vol. 32. Cambridge University Press, 2013. ISBN: 9780521887939
+func (c *CC) CanonicalCorrelations(x, y mat.Matrix, weights []float64) error {
+	var yn int
+	c.n, c.xd = x.Dims()
+	yn, c.yd = y.Dims()
+	if c.n != yn {
+		panic("stat: unequal number of observations")
+	}
+	if weights != nil && len(weights) != c.n {
+		panic("stat: len(weights) != observations")
+	}
+
+	// Center and factorize x and y.
+	c.x, c.ok = svdFactorizeCentered(c.x, x, weights)
+	if !c.ok {
+		return errors.New("stat: failed to factorize x")
+	}
+	c.y, c.ok = svdFactorizeCentered(c.y, y, weights)
+	if !c.ok {
+		return errors.New("stat: failed to factorize y")
+	}
+	xu := c.x.UTo(nil)
+	xv := c.x.VTo(nil)
+	yu := c.y.UTo(nil)
+	yv := c.y.VTo(nil)
+
+	// Calculate and factorise the canonical correlation matrix.
+	var ccor mat.Dense
+	ccor.Product(xv, xu.T(), yu, yv.T())
+	if c.c == nil {
+		c.c = &mat.SVD{}
+	}
+	c.ok = c.c.Factorize(&ccor, mat.SVDThin)
+	if !c.ok {
+		return errors.New("stat: failed to factorize ccor")
+	}
+	return nil
+}
+
+// CorrsTo returns the canonical correlations, using dst if it is not nil.
+// If dst is not nil and len(dst) does not match the number of columns in
+// the y input matrix, Corrs will panic.
+func (c *CC) CorrsTo(dst []float64) []float64 {
+	if !c.ok {
+		panic("stat: canonical correlations missing or invalid")
+	}
+
+	if dst != nil && len(dst) != c.yd {
+		panic("stat: length of destination does not match input dimension")
+	}
+	return c.c.Values(dst)
+}
+
+// LeftTo returns the left eigenvectors of the canonical correlation matrix if
+// spheredSpace is true. If spheredSpace is false it returns these eigenvectors
+// back-transformed to the original data space.
+// If dst is not nil it must either be zero-sized or be an xd×yd matrix where xd
+// and yd are the number of variables in the input x and y matrices. dst will
+// be used as the destination for the vector data. If dst is nil, a new
+// mat.Dense is allocated for the destination.
+func (c *CC) LeftTo(dst *mat.Dense, spheredSpace bool) *mat.Dense {
+	if !c.ok || c.n < 2 {
+		panic("stat: canonical correlations missing or invalid")
+	}
+
+	if dst != nil {
+		if d, n := dst.Dims(); !dst.IsZero() && (n != c.yd || d != c.xd) {
+			panic(mat.ErrShape)
+		}
+	}
+	dst = c.c.UTo(dst)
+	if spheredSpace {
+		return dst
+	}
+
+	xs := c.x.Values(nil)
+	xv := c.x.VTo(nil)
+
+	scaleColsReciSqrt(xv, xs)
+
+	dst.Product(xv, xv.T(), dst)
+	dst.Scale(math.Sqrt(float64(c.n-1)), dst)
+	return dst
+}
+
+// RightTo returns the right eigenvectors of the canonical correlation matrix if
+// spheredSpace is true. If spheredSpace is false it returns these eigenvectors
+// back-transformed to the original data space.
+// If dst is not nil it must either be zero-sized or be an yd×yd matrix where yd
+// is the number of variables in the input y matrix. dst will
+// be used as the destination for the vector data. If dst is nil, a new
+// mat.Dense is allocated for the destination.
+func (c *CC) RightTo(dst *mat.Dense, spheredSpace bool) *mat.Dense {
+	if !c.ok || c.n < 2 {
+		panic("stat: canonical correlations missing or invalid")
+	}
+
+	if dst != nil {
+		if d, n := dst.Dims(); (n != 0 || d != 0) && (n != c.yd || d != c.yd) {
+			panic(mat.ErrShape)
+		}
+	}
+	dst = c.c.VTo(dst)
+	if spheredSpace {
+		return dst
+	}
+
+	ys := c.y.Values(nil)
+	yv := c.y.VTo(nil)
+
+	scaleColsReciSqrt(yv, ys)
+
+	dst.Product(yv, yv.T(), dst)
+	dst.Scale(math.Sqrt(float64(c.n-1)), dst)
+	return dst
+}
+
+func svdFactorizeCentered(work *mat.SVD, m mat.Matrix, weights []float64) (svd *mat.SVD, ok bool) {
+	n, d := m.Dims()
+	centered := mat.NewDense(n, d, nil)
+	col := make([]float64, n)
+	for j := 0; j < d; j++ {
+		mat.Col(col, j, m)
+		floats.AddConst(-Mean(col, weights), col)
+		centered.SetCol(j, col)
+	}
+	for i, w := range weights {
+		floats.Scale(math.Sqrt(w), centered.RawRowView(i))
+	}
+	if work == nil {
+		work = &mat.SVD{}
+	}
+	ok = work.Factorize(centered, mat.SVDThin)
+	return work, ok
+}
+
+// scaleColsReciSqrt scales the columns of cols
+// by the reciprocal square-root of vals.
+func scaleColsReciSqrt(cols *mat.Dense, vals []float64) {
+	if cols == nil {
+		panic("stat: input nil")
+	}
+	n, d := cols.Dims()
+	if len(vals) != d {
+		panic("stat: input length mismatch")
+	}
+	col := make([]float64, n)
+	for j := 0; j < d; j++ {
+		mat.Col(col, j, cols)
+		floats.Scale(math.Sqrt(1/vals[j]), col)
+		cols.SetCol(j, col)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/roc.go b/vendor/gonum.org/v1/gonum/stat/roc.go
new file mode 100644
index 00000000..73584b61
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/roc.go
@@ -0,0 +1,121 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package stat
+
+import "sort"
+
+// ROC returns paired false positive rate (FPR) and true positive rate
+// (TPR) values corresponding to n cutoffs spanning the relative
+// (or receiver) operator characteristic (ROC) curve obtained when y is
+// treated as a binary classifier for classes with weights.
+//
+// Cutoffs are equally spaced from eps less than the minimum value of y
+// to the maximum value of y, including both endpoints meaning that the
+// resulting ROC curve will always begin at (0,0) and end at (1,1).
+//
+// The input y must be sorted, and SortWeightedLabeled can be used in
+// order to sort y together with classes and weights.
+//
+// For a given cutoff value, observations corresponding to entries in y
+// greater than the cutoff value are classified as false, while those
+// below (or equal to) the cutoff value are classified as true. These
+// assigned class labels are compared with the true values in the classes
+// slice and used to calculate the FPR and TPR.
+//
+// If weights is nil, all weights are treated as 1.
+//
+// When n is zero all possible cutoffs are calculated, resulting
+// in fpr and tpr having length one greater than the number of unique
+// values in y. When n is greater than one fpr and tpr will be returned
+// with length n. ROC will panic if n is equal to one or less than 0.
+//
+// More details about ROC curves are available at
+// https://en.wikipedia.org/wiki/Receiver_operating_characteristic
+func ROC(n int, y []float64, classes []bool, weights []float64) (tpr, fpr []float64) {
+	if len(y) != len(classes) {
+		panic("stat: slice length mismatch")
+	}
+	if weights != nil && len(y) != len(weights) {
+		panic("stat: slice length mismatch")
+	}
+	if !sort.Float64sAreSorted(y) {
+		panic("stat: input must be sorted")
+	}
+
+	var incWidth, tol float64
+	if n == 0 {
+		if len(y) == 0 {
+			return nil, nil
+		}
+		tpr = make([]float64, len(y)+1)
+		fpr = make([]float64, len(y)+1)
+	} else {
+		if n < 2 {
+			panic("stat: cannot calculate fewer than 2 points on a ROC curve")
+		}
+		if len(y) == 0 {
+			return nil, nil
+		}
+		tpr = make([]float64, n)
+		fpr = make([]float64, n)
+		incWidth = (y[len(y)-1] - y[0]) / float64(n-1)
+		tol = y[0] + incWidth
+		if incWidth == 0 {
+			tpr[n-1] = 1
+			fpr[n-1] = 1
+			return
+		}
+	}
+
+	var bin int = 1 // the initial bin is known to have 0 fpr and 0 tpr
+	var nPos, nNeg float64
+	for i, u := range classes {
+		var posWeight, negWeight float64 = 0, 1
+		if weights != nil {
+			negWeight = weights[i]
+		}
+		if u {
+			posWeight, negWeight = negWeight, posWeight
+		}
+		nPos += posWeight
+		nNeg += negWeight
+		tpr[bin] += posWeight
+		fpr[bin] += negWeight
+
+		// Assess if the bin needs to be updated. If n is zero,
+		// the bin is always updated, unless consecutive y values
+		// are equal. Otherwise, the bin must be updated until it
+		// matches the next y value (skipping empty bins).
+		if n == 0 {
+			if i != (len(y)-1) && y[i] != y[i+1] {
+				bin++
+				tpr[bin] = tpr[bin-1]
+				fpr[bin] = fpr[bin-1]
+			}
+		} else {
+			for i != (len(y)-1) && y[i+1] > tol {
+				tol += incWidth
+				bin++
+				tpr[bin] = tpr[bin-1]
+				fpr[bin] = fpr[bin-1]
+			}
+		}
+	}
+	if n == 0 {
+		tpr = tpr[:(bin + 1)]
+		fpr = fpr[:(bin + 1)]
+	}
+
+	invNeg := 1 / nNeg
+	invPos := 1 / nPos
+	for i := range tpr {
+		tpr[i] *= invPos
+		fpr[i] *= invNeg
+	}
+	tpr[len(tpr)-1] = 1
+	fpr[len(fpr)-1] = 1
+
+	return tpr, fpr
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/stat.go b/vendor/gonum.org/v1/gonum/stat/stat.go
new file mode 100644
index 00000000..11b90e91
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/stat.go
@@ -0,0 +1,1160 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package stat
+
+import (
+	"math"
+	"sort"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+// CumulantKind specifies the behavior for calculating the empirical CDF or Quantile
+type CumulantKind int
+
+const (
+	// Constant values should match the R nomenclature. See
+	// https://en.wikipedia.org/wiki/Quantile#Estimating_the_quantiles_of_a_population
+
+	// Empirical treats the distribution as the actual empirical distribution.
+	Empirical CumulantKind = 1
+)
+
+// bhattacharyyaCoeff computes the Bhattacharyya Coefficient for probability distributions given by:
+//  \sum_i \sqrt{p_i q_i}
+//
+// It is assumed that p and q have equal length.
+func bhattacharyyaCoeff(p, q []float64) float64 {
+	var bc float64
+	for i, a := range p {
+		bc += math.Sqrt(a * q[i])
+	}
+	return bc
+}
+
+// Bhattacharyya computes the distance between the probability distributions p and q given by:
+//  -\ln ( \sum_i \sqrt{p_i q_i} )
+//
+// The lengths of p and q must be equal. It is assumed that p and q sum to 1.
+func Bhattacharyya(p, q []float64) float64 {
+	if len(p) != len(q) {
+		panic("stat: slice length mismatch")
+	}
+	bc := bhattacharyyaCoeff(p, q)
+	return -math.Log(bc)
+}
+
+// CDF returns the empirical cumulative distribution function value of x, that is
+// the fraction of the samples less than or equal to q. The
+// exact behavior is determined by the CumulantKind. CDF is theoretically
+// the inverse of the Quantile function, though it may not be the actual inverse
+// for all values q and CumulantKinds.
+//
+// The x data must be sorted in increasing order. If weights is nil then all
+// of the weights are 1. If weights is not nil, then len(x) must equal len(weights).
+//
+// CumulantKind behaviors:
+//  - Empirical: Returns the lowest fraction for which q is greater than or equal
+//  to that fraction of samples
+func CDF(q float64, c CumulantKind, x, weights []float64) float64 {
+	if weights != nil && len(x) != len(weights) {
+		panic("stat: slice length mismatch")
+	}
+	if floats.HasNaN(x) {
+		return math.NaN()
+	}
+	if !sort.Float64sAreSorted(x) {
+		panic("x data are not sorted")
+	}
+
+	if q < x[0] {
+		return 0
+	}
+	if q >= x[len(x)-1] {
+		return 1
+	}
+
+	var sumWeights float64
+	if weights == nil {
+		sumWeights = float64(len(x))
+	} else {
+		sumWeights = floats.Sum(weights)
+	}
+
+	// Calculate the index
+	switch c {
+	case Empirical:
+		// Find the smallest value that is greater than that percent of the samples
+		var w float64
+		for i, v := range x {
+			if v > q {
+				return w / sumWeights
+			}
+			if weights == nil {
+				w++
+			} else {
+				w += weights[i]
+			}
+		}
+		panic("impossible")
+	default:
+		panic("stat: bad cumulant kind")
+	}
+}
+
+// ChiSquare computes the chi-square distance between the observed frequences 'obs' and
+// expected frequences 'exp' given by:
+//  \sum_i (obs_i-exp_i)^2 / exp_i
+//
+// The lengths of obs and exp must be equal.
+func ChiSquare(obs, exp []float64) float64 {
+	if len(obs) != len(exp) {
+		panic("stat: slice length mismatch")
+	}
+	var result float64
+	for i, a := range obs {
+		b := exp[i]
+		if a == 0 && b == 0 {
+			continue
+		}
+		result += (a - b) * (a - b) / b
+	}
+	return result
+}
+
+// CircularMean returns the circular mean of the dataset.
+//	atan2(\sum_i w_i * sin(alpha_i), \sum_i w_i * cos(alpha_i))
+// If weights is nil then all of the weights are 1. If weights is not nil, then
+// len(x) must equal len(weights).
+func CircularMean(x, weights []float64) float64 {
+	if weights != nil && len(x) != len(weights) {
+		panic("stat: slice length mismatch")
+	}
+
+	var aX, aY float64
+	if weights != nil {
+		for i, v := range x {
+			aX += weights[i] * math.Cos(v)
+			aY += weights[i] * math.Sin(v)
+		}
+	} else {
+		for _, v := range x {
+			aX += math.Cos(v)
+			aY += math.Sin(v)
+		}
+	}
+
+	return math.Atan2(aY, aX)
+}
+
+// Correlation returns the weighted correlation between the samples of x and y
+// with the given means.
+//  sum_i {w_i (x_i - meanX) * (y_i - meanY)} / (stdX * stdY)
+// The lengths of x and y must be equal. If weights is nil then all of the
+// weights are 1. If weights is not nil, then len(x) must equal len(weights).
+func Correlation(x, y, weights []float64) float64 {
+	// This is a two-pass corrected implementation.  It is an adaptation of the
+	// algorithm used in the MeanVariance function, which applies a correction
+	// to the typical two pass approach.
+
+	if len(x) != len(y) {
+		panic("stat: slice length mismatch")
+	}
+	xu := Mean(x, weights)
+	yu := Mean(y, weights)
+	var (
+		sxx           float64
+		syy           float64
+		sxy           float64
+		xcompensation float64
+		ycompensation float64
+	)
+	if weights == nil {
+		for i, xv := range x {
+			yv := y[i]
+			xd := xv - xu
+			yd := yv - yu
+			sxx += xd * xd
+			syy += yd * yd
+			sxy += xd * yd
+			xcompensation += xd
+			ycompensation += yd
+		}
+		// xcompensation and ycompensation are from Chan, et. al.
+		// referenced in the MeanVariance function.  They are analogous
+		// to the second term in (1.7) in that paper.
+		sxx -= xcompensation * xcompensation / float64(len(x))
+		syy -= ycompensation * ycompensation / float64(len(x))
+
+		return (sxy - xcompensation*ycompensation/float64(len(x))) / math.Sqrt(sxx*syy)
+
+	}
+
+	var sumWeights float64
+	for i, xv := range x {
+		w := weights[i]
+		yv := y[i]
+		xd := xv - xu
+		wxd := w * xd
+		yd := yv - yu
+		wyd := w * yd
+		sxx += wxd * xd
+		syy += wyd * yd
+		sxy += wxd * yd
+		xcompensation += wxd
+		ycompensation += wyd
+		sumWeights += w
+	}
+	// xcompensation and ycompensation are from Chan, et. al.
+	// referenced in the MeanVariance function.  They are analogous
+	// to the second term in (1.7) in that paper, except they use
+	// the sumWeights instead of the sample count.
+	sxx -= xcompensation * xcompensation / sumWeights
+	syy -= ycompensation * ycompensation / sumWeights
+
+	return (sxy - xcompensation*ycompensation/sumWeights) / math.Sqrt(sxx*syy)
+}
+
+// Covariance returns the weighted covariance between the samples of x and y.
+//  sum_i {w_i (x_i - meanX) * (y_i - meanY)} / (sum_j {w_j} - 1)
+// The lengths of x and y must be equal. If weights is nil then all of the
+// weights are 1. If weights is not nil, then len(x) must equal len(weights).
+func Covariance(x, y, weights []float64) float64 {
+	// This is a two-pass corrected implementation.  It is an adaptation of the
+	// algorithm used in the MeanVariance function, which applies a correction
+	// to the typical two pass approach.
+
+	if len(x) != len(y) {
+		panic("stat: slice length mismatch")
+	}
+	xu := Mean(x, weights)
+	yu := Mean(y, weights)
+	var (
+		ss            float64
+		xcompensation float64
+		ycompensation float64
+	)
+	if weights == nil {
+		for i, xv := range x {
+			yv := y[i]
+			xd := xv - xu
+			yd := yv - yu
+			ss += xd * yd
+			xcompensation += xd
+			ycompensation += yd
+		}
+		// xcompensation and ycompensation are from Chan, et. al.
+		// referenced in the MeanVariance function.  They are analogous
+		// to the second term in (1.7) in that paper.
+		return (ss - xcompensation*ycompensation/float64(len(x))) / float64(len(x)-1)
+	}
+
+	var sumWeights float64
+
+	for i, xv := range x {
+		w := weights[i]
+		yv := y[i]
+		wxd := w * (xv - xu)
+		yd := (yv - yu)
+		ss += wxd * yd
+		xcompensation += wxd
+		ycompensation += w * yd
+		sumWeights += w
+	}
+	// xcompensation and ycompensation are from Chan, et. al.
+	// referenced in the MeanVariance function.  They are analogous
+	// to the second term in (1.7) in that paper, except they use
+	// the sumWeights instead of the sample count.
+	return (ss - xcompensation*ycompensation/sumWeights) / (sumWeights - 1)
+}
+
+// CrossEntropy computes the cross-entropy between the two distributions specified
+// in p and q.
+func CrossEntropy(p, q []float64) float64 {
+	if len(p) != len(q) {
+		panic("stat: slice length mismatch")
+	}
+	var ce float64
+	for i, v := range p {
+		if v != 0 {
+			ce -= v * math.Log(q[i])
+		}
+	}
+	return ce
+}
+
+// Entropy computes the Shannon entropy of a distribution or the distance between
+// two distributions. The natural logarithm is used.
+//  - sum_i (p_i * log_e(p_i))
+func Entropy(p []float64) float64 {
+	var e float64
+	for _, v := range p {
+		if v != 0 { // Entropy needs 0 * log(0) == 0
+			e -= v * math.Log(v)
+		}
+	}
+	return e
+}
+
+// ExKurtosis returns the population excess kurtosis of the sample.
+// The kurtosis is defined by the 4th moment of the mean divided by the squared
+// variance. The excess kurtosis subtracts 3.0 so that the excess kurtosis of
+// the normal distribution is zero.
+// If weights is nil then all of the weights are 1. If weights is not nil, then
+// len(x) must equal len(weights).
+func ExKurtosis(x, weights []float64) float64 {
+	mean, std := MeanStdDev(x, weights)
+	if weights == nil {
+		var e float64
+		for _, v := range x {
+			z := (v - mean) / std
+			e += z * z * z * z
+		}
+		mul, offset := kurtosisCorrection(float64(len(x)))
+		return e*mul - offset
+	}
+
+	var (
+		e          float64
+		sumWeights float64
+	)
+	for i, v := range x {
+		z := (v - mean) / std
+		e += weights[i] * z * z * z * z
+		sumWeights += weights[i]
+	}
+	mul, offset := kurtosisCorrection(sumWeights)
+	return e*mul - offset
+}
+
+// n is the number of samples
+// see https://en.wikipedia.org/wiki/Kurtosis
+func kurtosisCorrection(n float64) (mul, offset float64) {
+	return ((n + 1) / (n - 1)) * (n / (n - 2)) * (1 / (n - 3)), 3 * ((n - 1) / (n - 2)) * ((n - 1) / (n - 3))
+}
+
+// GeometricMean returns the weighted geometric mean of the dataset
+//  \prod_i {x_i ^ w_i}
+// This only applies with positive x and positive weights. If weights is nil
+// then all of the weights are 1. If weights is not nil, then len(x) must equal
+// len(weights).
+func GeometricMean(x, weights []float64) float64 {
+	if weights == nil {
+		var s float64
+		for _, v := range x {
+			s += math.Log(v)
+		}
+		s /= float64(len(x))
+		return math.Exp(s)
+	}
+	if len(x) != len(weights) {
+		panic("stat: slice length mismatch")
+	}
+	var (
+		s          float64
+		sumWeights float64
+	)
+	for i, v := range x {
+		s += weights[i] * math.Log(v)
+		sumWeights += weights[i]
+	}
+	s /= sumWeights
+	return math.Exp(s)
+}
+
+// HarmonicMean returns the weighted harmonic mean of the dataset
+//  \sum_i {w_i} / ( sum_i {w_i / x_i} )
+// This only applies with positive x and positive weights.
+// If weights is nil then all of the weights are 1. If weights is not nil, then
+// len(x) must equal len(weights).
+func HarmonicMean(x, weights []float64) float64 {
+	if weights != nil && len(x) != len(weights) {
+		panic("stat: slice length mismatch")
+	}
+	// TODO: Fix this to make it more efficient and avoid allocation
+
+	// This can be numerically unstable (for example if x is very small)
+	// W = \sum_i {w_i}
+	// hm = exp(log(W) - log(\sum_i w_i / x_i))
+
+	logs := make([]float64, len(x))
+	var W float64
+	for i := range x {
+		if weights == nil {
+			logs[i] = -math.Log(x[i])
+			W++
+			continue
+		}
+		logs[i] = math.Log(weights[i]) - math.Log(x[i])
+		W += weights[i]
+	}
+
+	// Sum all of the logs
+	v := floats.LogSumExp(logs) // this computes log(\sum_i { w_i / x_i})
+	return math.Exp(math.Log(W) - v)
+}
+
+// Hellinger computes the distance between the probability distributions p and q given by:
+//  \sqrt{ 1 - \sum_i \sqrt{p_i q_i} }
+//
+// The lengths of p and q must be equal. It is assumed that p and q sum to 1.
+func Hellinger(p, q []float64) float64 {
+	if len(p) != len(q) {
+		panic("stat: slice length mismatch")
+	}
+	bc := bhattacharyyaCoeff(p, q)
+	return math.Sqrt(1 - bc)
+}
+
+// Histogram sums up the weighted number of data points in each bin.
+// The weight of data point x[i] will be placed into count[j] if
+// dividers[j] <= x < dividers[j+1]. The "span" function in the floats package can assist
+// with bin creation.
+//
+// The following conditions on the inputs apply:
+//  - The count variable must either be nil or have length of one less than dividers.
+//  - The values in dividers must be sorted (use the sort package).
+//  - The x values must be sorted.
+//  - If weights is nil then all of the weights are 1.
+//  - If weights is not nil, then len(x) must equal len(weights).
+func Histogram(count, dividers, x, weights []float64) []float64 {
+	if weights != nil && len(x) != len(weights) {
+		panic("stat: slice length mismatch")
+	}
+	if count == nil {
+		count = make([]float64, len(dividers)-1)
+	}
+	if len(dividers) < 2 {
+		panic("histogram: fewer than two dividers")
+	}
+	if len(count) != len(dividers)-1 {
+		panic("histogram: bin count mismatch")
+	}
+	if !sort.Float64sAreSorted(dividers) {
+		panic("histogram: dividers are not sorted")
+	}
+	if !sort.Float64sAreSorted(x) {
+		panic("histogram: x data are not sorted")
+	}
+	for i := range count {
+		count[i] = 0
+	}
+	if len(x) == 0 {
+		return count
+	}
+	if x[0] < dividers[0] {
+		panic("histogram: minimum x value is less than lowest divider")
+	}
+	if x[len(x)-1] >= dividers[len(dividers)-1] {
+		panic("histogram: minimum x value is greater than highest divider")
+	}
+
+	idx := 0
+	comp := dividers[idx+1]
+	if weights == nil {
+		for _, v := range x {
+			if v < comp {
+				// Still in the current bucket
+				count[idx]++
+				continue
+			}
+			// Find the next divider where v is less than the divider
+			for j := idx + 1; j < len(dividers); j++ {
+				if v < dividers[j+1] {
+					idx = j
+					comp = dividers[j+1]
+					break
+				}
+			}
+			count[idx]++
+		}
+		return count
+	}
+
+	for i, v := range x {
+		if v < comp {
+			// Still in the current bucket
+			count[idx] += weights[i]
+			continue
+		}
+		// Need to find the next divider where v is less than the divider.
+		for j := idx + 1; j < len(count); j++ {
+			if v < dividers[j+1] {
+				idx = j
+				comp = dividers[j+1]
+				break
+			}
+		}
+		count[idx] += weights[i]
+	}
+	return count
+}
+
+// JensenShannon computes the JensenShannon divergence between the distributions
+// p and q. The Jensen-Shannon divergence is defined as
+//  m = 0.5 * (p + q)
+//  JS(p, q) = 0.5 ( KL(p, m) + KL(q, m) )
+// Unlike Kullback-Liebler, the Jensen-Shannon distance is symmetric. The value
+// is between 0 and ln(2).
+func JensenShannon(p, q []float64) float64 {
+	if len(p) != len(q) {
+		panic("stat: slice length mismatch")
+	}
+	var js float64
+	for i, v := range p {
+		qi := q[i]
+		m := 0.5 * (v + qi)
+		if v != 0 {
+			// add kl from p to m
+			js += 0.5 * v * (math.Log(v) - math.Log(m))
+		}
+		if qi != 0 {
+			// add kl from q to m
+			js += 0.5 * qi * (math.Log(qi) - math.Log(m))
+		}
+	}
+	return js
+}
+
+// KolmogorovSmirnov computes the largest distance between two empirical CDFs.
+// Each dataset x and y consists of sample locations and counts, xWeights and
+// yWeights, respectively.
+//
+// x and y may have different lengths, though len(x) must equal len(xWeights), and
+// len(y) must equal len(yWeights).  Both x and y must be sorted.
+//
+// Special cases are:
+//  = 0 if len(x) == len(y) == 0
+//  = 1 if len(x) == 0, len(y) != 0 or len(x) != 0 and len(y) == 0
+func KolmogorovSmirnov(x, xWeights, y, yWeights []float64) float64 {
+	if xWeights != nil && len(x) != len(xWeights) {
+		panic("stat: slice length mismatch")
+	}
+	if yWeights != nil && len(y) != len(yWeights) {
+		panic("stat: slice length mismatch")
+	}
+	if len(x) == 0 || len(y) == 0 {
+		if len(x) == 0 && len(y) == 0 {
+			return 0
+		}
+		return 1
+	}
+
+	if floats.HasNaN(x) {
+		return math.NaN()
+	}
+	if floats.HasNaN(y) {
+		return math.NaN()
+	}
+
+	if !sort.Float64sAreSorted(x) {
+		panic("x data are not sorted")
+	}
+	if !sort.Float64sAreSorted(y) {
+		panic("y data are not sorted")
+	}
+
+	xWeightsNil := xWeights == nil
+	yWeightsNil := yWeights == nil
+
+	var (
+		maxDist    float64
+		xSum, ySum float64
+		xCdf, yCdf float64
+		xIdx, yIdx int
+	)
+
+	if xWeightsNil {
+		xSum = float64(len(x))
+	} else {
+		xSum = floats.Sum(xWeights)
+	}
+
+	if yWeightsNil {
+		ySum = float64(len(y))
+	} else {
+		ySum = floats.Sum(yWeights)
+	}
+
+	xVal := x[0]
+	yVal := y[0]
+
+	// Algorithm description:
+	// The goal is to find the maximum difference in the empirical CDFs for the
+	// two datasets. The CDFs are piecewise-constant, and thus the distance
+	// between the CDFs will only change at the values themselves.
+	//
+	// To find the maximum distance, step through the data in ascending order
+	// of value between the two datasets. At each step, compute the empirical CDF
+	// and compare the local distance with the maximum distance.
+	// Due to some corner cases, equal data entries must be tallied simultaneously.
+	for {
+		switch {
+		case xVal < yVal:
+			xVal, xCdf, xIdx = updateKS(xIdx, xCdf, xSum, x, xWeights, xWeightsNil)
+		case yVal < xVal:
+			yVal, yCdf, yIdx = updateKS(yIdx, yCdf, ySum, y, yWeights, yWeightsNil)
+		case xVal == yVal:
+			newX := x[xIdx]
+			newY := y[yIdx]
+			if newX < newY {
+				xVal, xCdf, xIdx = updateKS(xIdx, xCdf, xSum, x, xWeights, xWeightsNil)
+			} else if newY < newX {
+				yVal, yCdf, yIdx = updateKS(yIdx, yCdf, ySum, y, yWeights, yWeightsNil)
+			} else {
+				// Update them both, they'll be equal next time and the right
+				// thing will happen
+				xVal, xCdf, xIdx = updateKS(xIdx, xCdf, xSum, x, xWeights, xWeightsNil)
+				yVal, yCdf, yIdx = updateKS(yIdx, yCdf, ySum, y, yWeights, yWeightsNil)
+			}
+		default:
+			panic("unreachable")
+		}
+
+		dist := math.Abs(xCdf - yCdf)
+		if dist > maxDist {
+			maxDist = dist
+		}
+
+		// Both xCdf and yCdf will equal 1 at the end, so if we have reached the
+		// end of either sample list, the distance is as large as it can be.
+		if xIdx == len(x) || yIdx == len(y) {
+			return maxDist
+		}
+	}
+}
+
+// updateKS gets the next data point from one of the set. In doing so, it combines
+// the weight of all the data points of equal value. Upon return, val is the new
+// value of the data set, newCdf is the total combined CDF up until this point,
+// and newIdx is the index of the next location in that sample to examine.
+func updateKS(idx int, cdf, sum float64, values, weights []float64, isNil bool) (val, newCdf float64, newIdx int) {
+	// Sum up all the weights of consecutive values that are equal
+	if isNil {
+		newCdf = cdf + 1/sum
+	} else {
+		newCdf = cdf + weights[idx]/sum
+	}
+	newIdx = idx + 1
+	for {
+		if newIdx == len(values) {
+			return values[newIdx-1], newCdf, newIdx
+		}
+		if values[newIdx-1] != values[newIdx] {
+			return values[newIdx], newCdf, newIdx
+		}
+		if isNil {
+			newCdf += 1 / sum
+		} else {
+			newCdf += weights[newIdx] / sum
+		}
+		newIdx++
+	}
+}
+
+// KullbackLeibler computes the Kullback-Leibler distance between the
+// distributions p and q. The natural logarithm is used.
+//  sum_i(p_i * log(p_i / q_i))
+// Note that the Kullback-Leibler distance is not symmetric;
+// KullbackLeibler(p,q) != KullbackLeibler(q,p)
+func KullbackLeibler(p, q []float64) float64 {
+	if len(p) != len(q) {
+		panic("stat: slice length mismatch")
+	}
+	var kl float64
+	for i, v := range p {
+		if v != 0 { // Entropy needs 0 * log(0) == 0
+			kl += v * (math.Log(v) - math.Log(q[i]))
+		}
+	}
+	return kl
+}
+
+// LinearRegression computes the best-fit line
+//  y = alpha + beta*x
+// to the data in x and y with the given weights. If origin is true, the
+// regression is forced to pass through the origin.
+//
+// Specifically, LinearRegression computes the values of alpha and
+// beta such that the total residual
+//  \sum_i w[i]*(y[i] - alpha - beta*x[i])^2
+// is minimized. If origin is true, then alpha is forced to be zero.
+//
+// The lengths of x and y must be equal. If weights is nil then all of the
+// weights are 1. If weights is not nil, then len(x) must equal len(weights).
+func LinearRegression(x, y, weights []float64, origin bool) (alpha, beta float64) {
+	if len(x) != len(y) {
+		panic("stat: slice length mismatch")
+	}
+	if weights != nil && len(weights) != len(x) {
+		panic("stat: slice length mismatch")
+	}
+
+	w := 1.0
+	if origin {
+		var x2Sum, xySum float64
+		for i, xi := range x {
+			if weights != nil {
+				w = weights[i]
+			}
+			yi := y[i]
+			xySum += w * xi * yi
+			x2Sum += w * xi * xi
+		}
+		beta = xySum / x2Sum
+
+		return 0, beta
+	}
+
+	beta = Covariance(x, y, weights) / Variance(x, weights)
+	alpha = Mean(y, weights) - beta*Mean(x, weights)
+	return alpha, beta
+}
+
+// RSquared returns the coefficient of determination defined as
+//  R^2 = 1 - \sum_i w[i]*(y[i] - alpha - beta*x[i])^2 / \sum_i w[i]*(y[i] - mean(y))^2
+// for the line
+//  y = alpha + beta*x
+// and the data in x and y with the given weights.
+//
+// The lengths of x and y must be equal. If weights is nil then all of the
+// weights are 1. If weights is not nil, then len(x) must equal len(weights).
+func RSquared(x, y, weights []float64, alpha, beta float64) float64 {
+	if len(x) != len(y) {
+		panic("stat: slice length mismatch")
+	}
+	if weights != nil && len(weights) != len(x) {
+		panic("stat: slice length mismatch")
+	}
+
+	w := 1.0
+	yMean := Mean(y, weights)
+	var res, tot, d float64
+	for i, xi := range x {
+		if weights != nil {
+			w = weights[i]
+		}
+		yi := y[i]
+		fi := alpha + beta*xi
+		d = yi - fi
+		res += w * d * d
+		d = yi - yMean
+		tot += w * d * d
+	}
+	return 1 - res/tot
+}
+
+// RSquaredFrom returns the coefficient of determination defined as
+//  R^2 = 1 - \sum_i w[i]*(estimate[i] - value[i])^2 / \sum_i w[i]*(value[i] - mean(values))^2
+// and the data in estimates and values with the given weights.
+//
+// The lengths of estimates and values must be equal. If weights is nil then
+// all of the weights are 1. If weights is not nil, then len(values) must
+// equal len(weights).
+func RSquaredFrom(estimates, values, weights []float64) float64 {
+	if len(estimates) != len(values) {
+		panic("stat: slice length mismatch")
+	}
+	if weights != nil && len(weights) != len(values) {
+		panic("stat: slice length mismatch")
+	}
+
+	w := 1.0
+	mean := Mean(values, weights)
+	var res, tot, d float64
+	for i, val := range values {
+		if weights != nil {
+			w = weights[i]
+		}
+		d = val - estimates[i]
+		res += w * d * d
+		d = val - mean
+		tot += w * d * d
+	}
+	return 1 - res/tot
+}
+
+// RNoughtSquared returns the coefficient of determination defined as
+//  R₀^2 = \sum_i w[i]*(beta*x[i])^2 / \sum_i w[i]*y[i]^2
+// for the line
+//  y = beta*x
+// and the data in x and y with the given weights. RNoughtSquared should
+// only be used for best-fit lines regressed through the origin.
+//
+// The lengths of x and y must be equal. If weights is nil then all of the
+// weights are 1. If weights is not nil, then len(x) must equal len(weights).
+func RNoughtSquared(x, y, weights []float64, beta float64) float64 {
+	if len(x) != len(y) {
+		panic("stat: slice length mismatch")
+	}
+	if weights != nil && len(weights) != len(x) {
+		panic("stat: slice length mismatch")
+	}
+
+	w := 1.0
+	var ssr, tot float64
+	for i, xi := range x {
+		if weights != nil {
+			w = weights[i]
+		}
+		fi := beta * xi
+		ssr += w * fi * fi
+		yi := y[i]
+		tot += w * yi * yi
+	}
+	return ssr / tot
+}
+
+// Mean computes the weighted mean of the data set.
+//  sum_i {w_i * x_i} / sum_i {w_i}
+// If weights is nil then all of the weights are 1. If weights is not nil, then
+// len(x) must equal len(weights).
+func Mean(x, weights []float64) float64 {
+	if weights == nil {
+		return floats.Sum(x) / float64(len(x))
+	}
+	if len(x) != len(weights) {
+		panic("stat: slice length mismatch")
+	}
+	var (
+		sumValues  float64
+		sumWeights float64
+	)
+	for i, w := range weights {
+		sumValues += w * x[i]
+		sumWeights += w
+	}
+	return sumValues / sumWeights
+}
+
+// Mode returns the most common value in the dataset specified by x and the
+// given weights. Strict float64 equality is used when comparing values, so users
+// should take caution. If several values are the mode, any of them may be returned.
+func Mode(x, weights []float64) (val float64, count float64) {
+	if weights != nil && len(x) != len(weights) {
+		panic("stat: slice length mismatch")
+	}
+	if len(x) == 0 {
+		return 0, 0
+	}
+	m := make(map[float64]float64)
+	if weights == nil {
+		for _, v := range x {
+			m[v]++
+		}
+	} else {
+		for i, v := range x {
+			m[v] += weights[i]
+		}
+	}
+	var (
+		maxCount float64
+		max      float64
+	)
+	for val, count := range m {
+		if count > maxCount {
+			maxCount = count
+			max = val
+		}
+	}
+	return max, maxCount
+}
+
+// Moment computes the weighted n^th moment of the samples,
+//  E[(x - μ)^N]
+// No degrees of freedom correction is done.
+// If weights is nil then all of the weights are 1. If weights is not nil, then
+// len(x) must equal len(weights).
+func Moment(moment float64, x, weights []float64) float64 {
+	mean := Mean(x, weights)
+	if weights == nil {
+		var m float64
+		for _, v := range x {
+			m += math.Pow(v-mean, moment)
+		}
+		return m / float64(len(x))
+	}
+	var (
+		m          float64
+		sumWeights float64
+	)
+	for i, v := range x {
+		m += weights[i] * math.Pow(v-mean, moment)
+		sumWeights += weights[i]
+	}
+	return m / sumWeights
+}
+
+// MomentAbout computes the weighted n^th weighted moment of the samples about
+// the given mean \mu,
+//  E[(x - μ)^N]
+// No degrees of freedom correction is done.
+// If weights is nil then all of the weights are 1. If weights is not nil, then
+// len(x) must equal len(weights).
+func MomentAbout(moment float64, x []float64, mean float64, weights []float64) float64 {
+	if weights == nil {
+		var m float64
+		for _, v := range x {
+			m += math.Pow(v-mean, moment)
+		}
+		m /= float64(len(x))
+		return m
+	}
+	if len(weights) != len(x) {
+		panic("stat: slice length mismatch")
+	}
+	var (
+		m          float64
+		sumWeights float64
+	)
+	for i, v := range x {
+		m += weights[i] * math.Pow(v-mean, moment)
+		sumWeights += weights[i]
+	}
+	return m / sumWeights
+}
+
+// Quantile returns the sample of x such that x is greater than or
+// equal to the fraction p of samples. The exact behavior is determined by the
+// CumulantKind, and p should be a number between 0 and 1. Quantile is theoretically
+// the inverse of the CDF function, though it may not be the actual inverse
+// for all values p and CumulantKinds.
+//
+// The x data must be sorted in increasing order. If weights is nil then all
+// of the weights are 1. If weights is not nil, then len(x) must equal len(weights).
+//
+// CumulantKind behaviors:
+//  - Empirical: Returns the lowest value q for which q is greater than or equal
+//  to the fraction p of samples
+func Quantile(p float64, c CumulantKind, x, weights []float64) float64 {
+	if !(p >= 0 && p <= 1) {
+		panic("stat: percentile out of bounds")
+	}
+
+	if weights != nil && len(x) != len(weights) {
+		panic("stat: slice length mismatch")
+	}
+	if floats.HasNaN(x) {
+		return math.NaN() // This is needed because the algorithm breaks otherwise
+	}
+	if !sort.Float64sAreSorted(x) {
+		panic("x data are not sorted")
+	}
+
+	var sumWeights float64
+	if weights == nil {
+		sumWeights = float64(len(x))
+	} else {
+		sumWeights = floats.Sum(weights)
+	}
+	switch c {
+	case Empirical:
+		var cumsum float64
+		fidx := p * sumWeights
+		for i := range x {
+			if weights == nil {
+				cumsum++
+			} else {
+				cumsum += weights[i]
+			}
+			if cumsum >= fidx {
+				return x[i]
+			}
+		}
+		panic("impossible")
+	default:
+		panic("stat: bad cumulant kind")
+	}
+}
+
+// Skew computes the skewness of the sample data.
+// If weights is nil then all of the weights are 1. If weights is not nil, then
+// len(x) must equal len(weights).
+func Skew(x, weights []float64) float64 {
+
+	mean, std := MeanStdDev(x, weights)
+	if weights == nil {
+		var s float64
+		for _, v := range x {
+			z := (v - mean) / std
+			s += z * z * z
+		}
+		return s * skewCorrection(float64(len(x)))
+	}
+	var (
+		s          float64
+		sumWeights float64
+	)
+	for i, v := range x {
+		z := (v - mean) / std
+		s += weights[i] * z * z * z
+		sumWeights += weights[i]
+	}
+	return s * skewCorrection(sumWeights)
+}
+
+// From: http://www.amstat.org/publications/jse/v19n2/doane.pdf page 7
+func skewCorrection(n float64) float64 {
+	return (n / (n - 1)) * (1 / (n - 2))
+}
+
+// SortWeighted rearranges the data in x along with their corresponding
+// weights so that the x data are sorted. The data is sorted in place.
+// Weights may be nil, but if weights is non-nil then it must have the same
+// length as x.
+func SortWeighted(x, weights []float64) {
+	if weights == nil {
+		sort.Float64s(x)
+		return
+	}
+	if len(x) != len(weights) {
+		panic("stat: slice length mismatch")
+	}
+	sort.Sort(weightSorter{
+		x: x,
+		w: weights,
+	})
+}
+
+type weightSorter struct {
+	x []float64
+	w []float64
+}
+
+func (w weightSorter) Len() int           { return len(w.x) }
+func (w weightSorter) Less(i, j int) bool { return w.x[i] < w.x[j] }
+func (w weightSorter) Swap(i, j int) {
+	w.x[i], w.x[j] = w.x[j], w.x[i]
+	w.w[i], w.w[j] = w.w[j], w.w[i]
+}
+
+// SortWeightedLabeled rearranges the data in x along with their
+// corresponding weights and boolean labels so that the x data are sorted.
+// The data is sorted in place. Weights and labels may be nil, if either
+// is non-nil it must have the same length as x.
+func SortWeightedLabeled(x []float64, labels []bool, weights []float64) {
+	if labels == nil {
+		SortWeighted(x, weights)
+		return
+	}
+	if weights == nil {
+		if len(x) != len(labels) {
+			panic("stat: slice length mismatch")
+		}
+		sort.Sort(labelSorter{
+			x: x,
+			l: labels,
+		})
+		return
+	}
+	if len(x) != len(labels) || len(x) != len(weights) {
+		panic("stat: slice length mismatch")
+	}
+	sort.Sort(weightLabelSorter{
+		x: x,
+		l: labels,
+		w: weights,
+	})
+}
+
+type labelSorter struct {
+	x []float64
+	l []bool
+}
+
+func (a labelSorter) Len() int           { return len(a.x) }
+func (a labelSorter) Less(i, j int) bool { return a.x[i] < a.x[j] }
+func (a labelSorter) Swap(i, j int) {
+	a.x[i], a.x[j] = a.x[j], a.x[i]
+	a.l[i], a.l[j] = a.l[j], a.l[i]
+}
+
+type weightLabelSorter struct {
+	x []float64
+	l []bool
+	w []float64
+}
+
+func (a weightLabelSorter) Len() int           { return len(a.x) }
+func (a weightLabelSorter) Less(i, j int) bool { return a.x[i] < a.x[j] }
+func (a weightLabelSorter) Swap(i, j int) {
+	a.x[i], a.x[j] = a.x[j], a.x[i]
+	a.l[i], a.l[j] = a.l[j], a.l[i]
+	a.w[i], a.w[j] = a.w[j], a.w[i]
+}
+
+// StdDev returns the sample standard deviation.
+func StdDev(x, weights []float64) float64 {
+	_, std := MeanStdDev(x, weights)
+	return std
+}
+
+// MeanStdDev returns the sample mean and standard deviation
+func MeanStdDev(x, weights []float64) (mean, std float64) {
+	mean, variance := MeanVariance(x, weights)
+	return mean, math.Sqrt(variance)
+}
+
+// StdErr returns the standard error in the mean with the given values.
+func StdErr(std, sampleSize float64) float64 {
+	return std / math.Sqrt(sampleSize)
+}
+
+// StdScore returns the standard score (a.k.a. z-score, z-value) for the value x
+// with the givem mean and standard deviation, i.e.
+//  (x - mean) / std
+func StdScore(x, mean, std float64) float64 {
+	return (x - mean) / std
+}
+
+// Variance computes the weighted sample variance:
+//  \sum_i w_i (x_i - mean)^2 / (sum_i w_i - 1)
+// If weights is nil then all of the weights are 1. If weights is not nil, then
+// len(x) must equal len(weights).
+func Variance(x, weights []float64) float64 {
+	_, variance := MeanVariance(x, weights)
+	return variance
+}
+
+// MeanVariance computes the sample mean and variance, where the mean and variance are
+//  \sum_i w_i * x_i / (sum_i w_i)
+//  \sum_i w_i (x_i - mean)^2 / (sum_i w_i - 1)
+// respectively.
+// If weights is nil then all of the weights are 1. If weights is not nil, then
+// len(x) must equal len(weights).
+func MeanVariance(x, weights []float64) (mean, variance float64) {
+
+	// This uses the corrected two-pass algorithm (1.7), from "Algorithms for computing
+	// the sample variance: Analysis and recommendations" by Chan, Tony F., Gene H. Golub,
+	// and Randall J. LeVeque.
+
+	// note that this will panic if the slice lengths do not match
+	mean = Mean(x, weights)
+	var (
+		ss           float64
+		compensation float64
+	)
+	if weights == nil {
+		for _, v := range x {
+			d := v - mean
+			ss += d * d
+			compensation += d
+		}
+		variance = (ss - compensation*compensation/float64(len(x))) / float64(len(x)-1)
+		return
+	}
+
+	var sumWeights float64
+	for i, v := range x {
+		w := weights[i]
+		d := v - mean
+		wd := w * d
+		ss += wd * d
+		compensation += wd
+		sumWeights += w
+	}
+	variance = (ss - compensation*compensation/sumWeights) / (sumWeights - 1)
+	return
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/statmat.go b/vendor/gonum.org/v1/gonum/stat/statmat.go
new file mode 100644
index 00000000..1f9bd794
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/statmat.go
@@ -0,0 +1,146 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package stat
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+)
+
+// CovarianceMatrix returns the covariance matrix (also known as the
+// variance-covariance matrix) calculated from a matrix of data, x, using
+// a two-pass algorithm.
+//
+// If weights is not nil the weighted covariance of x is calculated. weights
+// must have length equal to the number of rows in input data matrix and
+// must not contain negative elements.
+// If cov is not nil it must either be zero-sized or have the same number of
+// columns as the input data matrix. cov will be used as the destination for
+// the covariance data. If cov is nil, a new mat.SymDense is allocated for
+// the destination.
+func CovarianceMatrix(cov *mat.SymDense, x mat.Matrix, weights []float64) *mat.SymDense {
+	// This is the matrix version of the two-pass algorithm. It doesn't use the
+	// additional floating point error correction that the Covariance function uses
+	// to reduce the impact of rounding during centering.
+
+	r, c := x.Dims()
+
+	if cov == nil {
+		cov = mat.NewSymDense(c, nil)
+	} else if n := cov.Symmetric(); n != c && n != 0 {
+		panic(mat.ErrShape)
+	}
+
+	var xt mat.Dense
+	xt.Clone(x.T())
+	// Subtract the mean of each of the columns.
+	for i := 0; i < c; i++ {
+		v := xt.RawRowView(i)
+		// This will panic with ErrShape if len(weights) != len(v), so
+		// we don't have to check the size later.
+		mean := Mean(v, weights)
+		floats.AddConst(-mean, v)
+	}
+
+	if weights == nil {
+		// Calculate the normalization factor
+		// scaled by the sample size.
+		cov.SymOuterK(1/(float64(r)-1), &xt)
+		return cov
+	}
+
+	// Multiply by the sqrt of the weights, so that multiplication is symmetric.
+	sqrtwts := make([]float64, r)
+	for i, w := range weights {
+		if w < 0 {
+			panic("stat: negative covariance matrix weights")
+		}
+		sqrtwts[i] = math.Sqrt(w)
+	}
+	// Weight the rows.
+	for i := 0; i < c; i++ {
+		v := xt.RawRowView(i)
+		floats.Mul(v, sqrtwts)
+	}
+
+	// Calculate the normalization factor
+	// scaled by the weighted sample size.
+	cov.SymOuterK(1/(floats.Sum(weights)-1), &xt)
+	return cov
+}
+
+// CorrelationMatrix returns the correlation matrix calculated from a matrix
+// of data, x, using a two-pass algorithm.
+//
+// If weights is not nil the weighted correlation of x is calculated. weights
+// must have length equal to the number of rows in input data matrix and
+// must not contain negative elements.
+// If corr is not nil it must either be zero-sized or have the same number of
+// columns as the input data matrix. corr will be used as the destination for
+// the correlation data. If corr is nil, a new mat.SymDense is allocated for
+// the destination.
+func CorrelationMatrix(corr *mat.SymDense, x mat.Matrix, weights []float64) *mat.SymDense {
+	// This will panic if the sizes don't match, or if weights is the wrong size.
+	corr = CovarianceMatrix(corr, x, weights)
+	covToCorr(corr)
+	return corr
+}
+
+// covToCorr converts a covariance matrix to a correlation matrix.
+func covToCorr(c *mat.SymDense) {
+	r := c.Symmetric()
+
+	s := make([]float64, r)
+	for i := 0; i < r; i++ {
+		s[i] = 1 / math.Sqrt(c.At(i, i))
+	}
+	for i, sx := range s {
+		// Ensure that the diagonal has exactly ones.
+		c.SetSym(i, i, 1)
+		for j := i + 1; j < r; j++ {
+			v := c.At(i, j)
+			c.SetSym(i, j, v*sx*s[j])
+		}
+	}
+}
+
+// corrToCov converts a correlation matrix to a covariance matrix.
+// The input sigma should be vector of standard deviations corresponding
+// to the covariance.  It will panic if len(sigma) is not equal to the
+// number of rows in the correlation matrix.
+func corrToCov(c *mat.SymDense, sigma []float64) {
+	r, _ := c.Dims()
+
+	if r != len(sigma) {
+		panic(mat.ErrShape)
+	}
+	for i, sx := range sigma {
+		// Ensure that the diagonal has exactly sigma squared.
+		c.SetSym(i, i, sx*sx)
+		for j := i + 1; j < r; j++ {
+			v := c.At(i, j)
+			c.SetSym(i, j, v*sx*sigma[j])
+		}
+	}
+}
+
+// Mahalanobis computes the Mahalanobis distance
+//  D = sqrt((x-y)^T * Σ^-1 * (x-y))
+// between the vectors x and y given the cholesky decomposition of Σ.
+// Mahalanobis returns NaN if the linear solve fails.
+//
+// See https://en.wikipedia.org/wiki/Mahalanobis_distance for more information.
+func Mahalanobis(x, y *mat.VecDense, chol *mat.Cholesky) float64 {
+	var diff mat.VecDense
+	diff.SubVec(x, y)
+	var tmp mat.VecDense
+	err := chol.SolveVec(&tmp, &diff)
+	if err != nil {
+		return math.NaN()
+	}
+	return math.Sqrt(mat.Dot(&tmp, &diff))
+}
diff --git a/vendor/vendor.json b/vendor/vendor.json
index 3fe19d2b..7067e25f 100644
--- a/vendor/vendor.json
+++ b/vendor/vendor.json
@@ -1113,6 +1113,12 @@
 			"revision": "505032a0737bf9d1007ff782db67a4e41eac71f7",
 			"revisionTime": "2018-06-28T04:47:44Z"
 		},
+		{
+			"checksumSHA1": "db1fjQUFM01O5HhI1zzREmB9ARQ=",
+			"path": "gonum.org/v1/gonum/stat",
+			"revision": "d7342e68fbbe64d7dbbdc0feb4ecf60500444cdc",
+			"revisionTime": "2017-08-28T20:52:35Z"
+		},
 		{
 			"checksumSHA1": "AvVpgwhxhJgjoSledwDtYrEKVE4=",
 			"origin": "github.com/Loopring/relay-lib/vendor/google.golang.org/genproto/googleapis/rpc/status",

From 29a9ba28462890238f0df0c22ae00828d2424e70 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E4=BA=8E=E7=BA=A2=E9=9B=A8?= <yuhongyu04@126.com>
Date: Fri, 21 Sep 2018 16:16:48 +0800
Subject: [PATCH 5/8] add vendor

---
 vendor/gonum.org/v1/gonum/LICENSE             |   23 -
 vendor/gonum.org/v1/gonum/blas/README.md      |   79 +
 vendor/gonum.org/v1/gonum/blas/blas.go        |  287 ++
 .../gonum.org/v1/gonum/blas/blas32/blas32.go  |  457 +++
 vendor/gonum.org/v1/gonum/blas/blas32/conv.go |  279 ++
 .../v1/gonum/blas/blas32/conv_symmetric.go    |  155 +
 .../gonum/blas/blas32/conv_symmetric_test.go  |  307 ++
 .../v1/gonum/blas/blas32/conv_test.go         |  620 ++++
 vendor/gonum.org/v1/gonum/blas/blas32/doc.go  |    6 +
 .../gonum.org/v1/gonum/blas/blas64/blas64.go  |  445 +++
 vendor/gonum.org/v1/gonum/blas/blas64/conv.go |  277 ++
 .../v1/gonum/blas/blas64/conv_symmetric.go    |  153 +
 .../gonum/blas/blas64/conv_symmetric_test.go  |  305 ++
 .../v1/gonum/blas/blas64/conv_test.go         |  618 ++++
 vendor/gonum.org/v1/gonum/blas/blas64/doc.go  |    6 +
 .../v1/gonum/blas/cblas128/cblas128.go        |  507 +++
 .../gonum.org/v1/gonum/blas/cblas128/conv.go  |  279 ++
 .../v1/gonum/blas/cblas128/conv_hermitian.go  |  155 +
 .../blas/cblas128/conv_hermitian_test.go      |  307 ++
 .../v1/gonum/blas/cblas128/conv_symmetric.go  |  155 +
 .../blas/cblas128/conv_symmetric_test.go      |  307 ++
 .../v1/gonum/blas/cblas128/conv_test.go       |  620 ++++
 .../gonum.org/v1/gonum/blas/cblas128/doc.go   |    6 +
 .../v1/gonum/blas/cblas64/cblas64.go          |  507 +++
 .../gonum.org/v1/gonum/blas/cblas64/conv.go   |  279 ++
 .../v1/gonum/blas/cblas64/conv_hermitian.go   |  155 +
 .../gonum/blas/cblas64/conv_hermitian_test.go |  307 ++
 .../v1/gonum/blas/cblas64/conv_test.go        |  620 ++++
 vendor/gonum.org/v1/gonum/blas/cblas64/doc.go |    6 +
 .../gonum.org/v1/gonum/blas/conversions.bash  |  159 +
 vendor/gonum.org/v1/gonum/blas/doc.go         |  108 +
 .../v1/gonum/blas/gonum/bench_test.go         |   22 +
 vendor/gonum.org/v1/gonum/blas/gonum/cmplx.go |  206 ++
 vendor/gonum.org/v1/gonum/blas/gonum/dgemm.go |  261 ++
 .../v1/gonum/blas/gonum/dgemmbench_test.go    |   51 +
 .../v1/gonum/blas/gonum/dgemvbench_test.go    |   91 +
 .../v1/gonum/blas/gonum/dgerbench_test.go     |   51 +
 vendor/gonum.org/v1/gonum/blas/gonum/doc.go   |   88 +
 .../v1/gonum/blas/gonum/dtrmvbench_test.go    |   54 +
 .../v1/gonum/blas/gonum/general_double.go     |   50 +
 .../v1/gonum/blas/gonum/general_single.go     |   52 +
 vendor/gonum.org/v1/gonum/blas/gonum/gonum.go |  133 +
 .../v1/gonum/blas/gonum/level1cmplx128.go     |  442 +++
 .../blas/gonum/level1cmplx128_bench_test.go   |   41 +
 .../gonum/blas/gonum/level1cmplx128_test.go   |   51 +
 .../v1/gonum/blas/gonum/level1double.go       |  595 ++++
 .../blas/gonum/level1doubleBench_auto_test.go | 1685 +++++++++
 .../v1/gonum/blas/gonum/level1double_ddot.go  |   49 +
 .../v1/gonum/blas/gonum/level1double_test.go  |   61 +
 .../v1/gonum/blas/gonum/level1single.go       |  619 ++++
 .../v1/gonum/blas/gonum/level1single_dsdot.go |   53 +
 .../v1/gonum/blas/gonum/level1single_sdot.go  |   53 +
 .../gonum/blas/gonum/level1single_sdsdot.go   |   53 +
 .../v1/gonum/blas/gonum/level2cmplx128.go     |  289 ++
 .../blas/gonum/level2cmplx128_bench_test.go   |   49 +
 .../gonum/blas/gonum/level2cmplx128_test.go   |   27 +
 .../v1/gonum/blas/gonum/level2double.go       | 2234 ++++++++++++
 .../v1/gonum/blas/gonum/level2double_test.go  |   79 +
 .../v1/gonum/blas/gonum/level2single.go       | 2268 ++++++++++++
 .../v1/gonum/blas/gonum/level3double.go       |  831 +++++
 .../v1/gonum/blas/gonum/level3double_test.go  |   35 +
 .../v1/gonum/blas/gonum/level3single.go       |  843 +++++
 .../v1/gonum/blas/gonum/pardgemm_test.go      |  181 +
 vendor/gonum.org/v1/gonum/blas/gonum/sgemm.go |  265 ++
 .../v1/gonum/blas/gonum/single_precision.bash |  158 +
 .../autogen_bench_level1double.go             |  292 ++
 .../v1/gonum/blas/testblas/benchsize.go       |    8 +
 .../v1/gonum/blas/testblas/common.go          |  316 ++
 .../v1/gonum/blas/testblas/common_test.go     |  187 +
 .../gonum.org/v1/gonum/blas/testblas/dgbmv.go |  131 +
 .../gonum.org/v1/gonum/blas/testblas/dgemm.go |  244 ++
 .../v1/gonum/blas/testblas/dgemmbench.go      |   39 +
 .../gonum.org/v1/gonum/blas/testblas/dgemv.go |  678 ++++
 .../gonum.org/v1/gonum/blas/testblas/dger.go  |  163 +
 .../gonum.org/v1/gonum/blas/testblas/doc.go   |    6 +
 .../gonum.org/v1/gonum/blas/testblas/dsbmv.go |   83 +
 .../gonum.org/v1/gonum/blas/testblas/dspmv.go |   73 +
 .../gonum.org/v1/gonum/blas/testblas/dspr.go  |   71 +
 .../gonum.org/v1/gonum/blas/testblas/dspr2.go |   76 +
 .../gonum.org/v1/gonum/blas/testblas/dsymm.go |  277 ++
 .../gonum.org/v1/gonum/blas/testblas/dsymv.go |   73 +
 .../gonum.org/v1/gonum/blas/testblas/dsyr.go  |   72 +
 .../gonum.org/v1/gonum/blas/testblas/dsyr2.go |   76 +
 .../v1/gonum/blas/testblas/dsyr2k.go          |  201 ++
 .../gonum.org/v1/gonum/blas/testblas/dsyrk.go |  171 +
 .../gonum.org/v1/gonum/blas/testblas/dtbmv.go |  123 +
 .../gonum.org/v1/gonum/blas/testblas/dtbsv.go |  255 ++
 .../gonum.org/v1/gonum/blas/testblas/dtpmv.go |  129 +
 .../gonum.org/v1/gonum/blas/testblas/dtpsv.go |  144 +
 .../gonum.org/v1/gonum/blas/testblas/dtrmm.go |  806 +++++
 .../gonum.org/v1/gonum/blas/testblas/dtrmv.go |  147 +
 .../v1/gonum/blas/testblas/dtrmvbench.go      |   30 +
 .../gonum.org/v1/gonum/blas/testblas/dtrsm.go |  811 +++++
 .../gonum.org/v1/gonum/blas/testblas/dtrsv.go |  144 +
 .../gonum.org/v1/gonum/blas/testblas/dtxmv.go |  145 +
 .../v1/gonum/blas/testblas/dzasum.go          |   58 +
 .../v1/gonum/blas/testblas/dznrm2.go          |  137 +
 .../v1/gonum/blas/testblas/izamax.go          |   47 +
 .../v1/gonum/blas/testblas/level1double.go    | 2048 +++++++++++
 .../v1/gonum/blas/testblas/level2bench.go     |   60 +
 .../gonum.org/v1/gonum/blas/testblas/zaxpy.go |  157 +
 .../gonum.org/v1/gonum/blas/testblas/zcopy.go |   71 +
 .../gonum.org/v1/gonum/blas/testblas/zdotc.go |  139 +
 .../gonum.org/v1/gonum/blas/testblas/zdotu.go |  139 +
 .../v1/gonum/blas/testblas/zdscal.go          |  119 +
 .../gonum.org/v1/gonum/blas/testblas/zgerc.go |  183 +
 .../gonum.org/v1/gonum/blas/testblas/zgeru.go |  257 ++
 .../gonum.org/v1/gonum/blas/testblas/zher.go  |  155 +
 .../gonum.org/v1/gonum/blas/testblas/zher2.go |  257 ++
 .../gonum.org/v1/gonum/blas/testblas/zscal.go |  119 +
 .../gonum.org/v1/gonum/blas/testblas/zswap.go |   68 +
 vendor/gonum.org/v1/gonum/diff/README.md      |    3 +
 .../v1/gonum/diff/fd/crosslaplacian.go        |  186 +
 .../v1/gonum/diff/fd/crosslaplacian_test.go   |  111 +
 .../gonum.org/v1/gonum/diff/fd/derivative.go  |   71 +
 .../v1/gonum/diff/fd/derivative_test.go       |  145 +
 vendor/gonum.org/v1/gonum/diff/fd/diff.go     |  148 +
 vendor/gonum.org/v1/gonum/diff/fd/doc.go      |    6 +
 .../v1/gonum/diff/fd/example_test.go          |   68 +
 vendor/gonum.org/v1/gonum/diff/fd/gradient.go |  145 +
 .../v1/gonum/diff/fd/gradient_test.go         |  187 +
 vendor/gonum.org/v1/gonum/diff/fd/hessian.go  |  193 +
 .../v1/gonum/diff/fd/hessian_test.go          |   94 +
 vendor/gonum.org/v1/gonum/diff/fd/jacobian.go |  200 ++
 .../v1/gonum/diff/fd/jacobian_test.go         |  268 ++
 .../gonum.org/v1/gonum/diff/fd/laplacian.go   |  158 +
 .../v1/gonum/diff/fd/laplacian_test.go        |   44 +
 .../v1/gonum/diff/fd/simplefunctions_test.go  |   87 +
 .../gonum.org/v1/gonum/diff/fd/watson_test.go |  132 +
 vendor/gonum.org/v1/gonum/floats/README.md    |    4 +
 vendor/gonum.org/v1/gonum/floats/doc.go       |   11 +
 .../v1/gonum/floats/examples_test.go          |  104 +
 vendor/gonum.org/v1/gonum/floats/floats.go    |  771 ++++
 .../gonum.org/v1/gonum/floats/floats_test.go  | 1403 ++++++++
 .../v1/gonum/floats/parse_example_test.go     |   43 +
 vendor/gonum.org/v1/gonum/graph/.gitignore    |    1 +
 vendor/gonum.org/v1/gonum/graph/README.md     |    3 +
 .../v1/gonum/graph/community/bisect.go        |  248 ++
 .../v1/gonum/graph/community/bisect_test.go   |  311 ++
 .../gonum.org/v1/gonum/graph/community/doc.go |    6 +
 .../v1/gonum/graph/community/louvain.tex      |  466 +++
 .../gonum/graph/community/louvain_common.go   |  415 +++
 .../gonum/graph/community/louvain_directed.go |  650 ++++
 .../community/louvain_directed_multiplex.go   |  888 +++++
 .../louvain_directed_multiplex_test.go        |  722 ++++
 .../graph/community/louvain_directed_test.go  |  719 ++++
 .../v1/gonum/graph/community/louvain_test.go  |  277 ++
 .../graph/community/louvain_undirected.go     |  590 ++++
 .../community/louvain_undirected_multiplex.go |  826 +++++
 .../louvain_undirected_multiplex_test.go      |  691 ++++
 .../community/louvain_undirected_test.go      |  778 +++++
 .../v1/gonum/graph/community/printgraphs.go   |  142 +
 vendor/gonum.org/v1/gonum/graph/doc.go        |   38 +
 .../gonum.org/v1/gonum/graph/encoding/doc.go  |    6 +
 .../v1/gonum/graph/encoding/dot/decode.go     |  278 ++
 .../gonum/graph/encoding/dot/decode_test.go   |  247 ++
 .../v1/gonum/graph/encoding/dot/doc.go        |   14 +
 .../v1/gonum/graph/encoding/dot/dot.go        |    5 +
 .../v1/gonum/graph/encoding/dot/encode.go     |  359 ++
 .../gonum/graph/encoding/dot/encode_test.go   | 1436 ++++++++
 .../v1/gonum/graph/encoding/encoding.go       |   30 +
 .../v1/gonum/graph/encoding/graphql/decode.go |  157 +
 .../graph/encoding/graphql/decode_test.go     |  221 ++
 .../v1/gonum/graph/encoding/graphql/doc.go    |    7 +
 .../gonum/graph/encoding/graphql/graphql.go   |    5 +
 .../graph/encoding/graphql/graphs_test.go     | 1013 ++++++
 .../v1/gonum/graph/ex/fdpclust/gn.go          |  278 ++
 .../v1/gonum/graph/ex/fdpclust/main.go        |   75 +
 .../v1/gonum/graph/formats/dot/README.md      |    9 +
 .../v1/gonum/graph/formats/dot/ast/ast.go     |  406 +++
 .../gonum/graph/formats/dot/ast/ast_test.go   |  101 +
 .../v1/gonum/graph/formats/dot/ast/doc.go     |    7 +
 .../v1/gonum/graph/formats/dot/doc.go         |    6 +
 .../v1/gonum/graph/formats/dot/dot.go         |   64 +
 .../gonum/graph/formats/dot/internal/Makefile |   33 +
 .../graph/formats/dot/internal/astx/astx.go   |  326 ++
 .../formats/dot/internal/astx/astx_test.go    |   90 +
 .../graph/formats/dot/internal/astx/doc.go    |    7 +
 .../gonum/graph/formats/dot/internal/dot.bnf  |  358 ++
 .../formats/dot/internal/errors/errors.go     |   66 +
 .../formats/dot/internal/lexer/acttab.go      |  597 ++++
 .../graph/formats/dot/internal/lexer/lexer.go |  310 ++
 .../formats/dot/internal/lexer/lexer_test.go  |   54 +
 .../dot/internal/lexer/testdata/tokens.dot    |   39 +
 .../dot/internal/lexer/testdata/tokens.golden |   37 +
 .../dot/internal/lexer/transitiontable.go     | 2741 +++++++++++++++
 .../formats/dot/internal/parser/action.go     |   61 +
 .../dot/internal/parser/actiontable.go        | 2199 ++++++++++++
 .../formats/dot/internal/parser/gototable.go  | 2807 +++++++++++++++
 .../formats/dot/internal/parser/parser.go     |  221 ++
 .../dot/internal/parser/parser_test.go        |  114 +
 .../dot/internal/parser/productionstable.go   |  586 ++++
 .../formats/dot/internal/paste_copyright.bash |   17 +
 .../formats/dot/internal/testdata/attr.dot    |    4 +
 .../dot/internal/testdata/attr_lists.dot      |    3 +
 .../dot/internal/testdata/attr_lists.golden   |    3 +
 .../dot/internal/testdata/attr_sep.dot        |    3 +
 .../dot/internal/testdata/attr_sep.golden     |    3 +
 .../dot/internal/testdata/attr_stmt.dot       |    6 +
 .../testdata/backslash_newline_id.dot         |    4 +
 .../testdata/backslash_newline_id.golden      |    3 +
 .../formats/dot/internal/testdata/digraph.dot |    3 +
 .../dot/internal/testdata/edge_stmt.dot       |    4 +
 .../formats/dot/internal/testdata/empty.dot   |    2 +
 .../dot/internal/testdata/empty_attr.dot      |    3 +
 .../dot/internal/testdata/empty_attr.golden   |    3 +
 .../formats/dot/internal/testdata/error.dot   |    3 +
 .../formats/dot/internal/testdata/graph.dot   |    3 +
 .../formats/dot/internal/testdata/multi.dot   |    6 +
 .../dot/internal/testdata/named_graph.dot     |    3 +
 .../dot/internal/testdata/node_stmt.dot       |    3 +
 .../formats/dot/internal/testdata/port.dot    |   11 +
 .../formats/dot/internal/testdata/port.golden |   11 +
 .../dot/internal/testdata/quoted_id.dot       |    3 +
 .../formats/dot/internal/testdata/semi.dot    |    3 +
 .../formats/dot/internal/testdata/semi.golden |    4 +
 .../formats/dot/internal/testdata/strict.dot  |    4 +
 .../dot/internal/testdata/subgraph.dot        |    5 +
 .../dot/internal/testdata/subgraph.golden     |    5 +
 .../dot/internal/testdata/subgraph_vertex.dot |    3 +
 .../graph/formats/dot/internal/token/token.go |  116 +
 .../formats/dot/internal/util/litconv.go      |  118 +
 .../graph/formats/dot/internal/util/rune.go   |   49 +
 .../gonum/graph/formats/dot/makeinternal.bash |    4 +
 .../v1/gonum/graph/formats/dot/sem.go         |  160 +
 .../graph/formats/dot/testdata/.gitignore     |    5 +
 .../gonum/graph/formats/dot/testdata/Makefile |  106 +
 vendor/gonum.org/v1/gonum/graph/graph.go      |  247 ++
 .../graph/graphs/gen/batagelj_brandes.go      |  357 ++
 .../graph/graphs/gen/batagelj_brandes_test.go |  174 +
 .../v1/gonum/graph/graphs/gen/doc.go          |    6 +
 .../v1/gonum/graph/graphs/gen/duplication.go  |  125 +
 .../graph/graphs/gen/duplication_test.go      |   58 +
 .../v1/gonum/graph/graphs/gen/gen.go          |   21 +
 .../v1/gonum/graph/graphs/gen/holme_kim.go    |  160 +
 .../gonum/graph/graphs/gen/holme_kim_test.go  |   55 +
 .../v1/gonum/graph/graphs/gen/small_world.go  |  204 ++
 .../graph/graphs/gen/small_world_test.go      |   72 +
 .../v1/gonum/graph/internal/linear/doc.go     |    6 +
 .../v1/gonum/graph/internal/linear/linear.go  |   73 +
 .../v1/gonum/graph/internal/ordered/doc.go    |    6 +
 .../v1/gonum/graph/internal/ordered/sort.go   |   69 +
 .../v1/gonum/graph/internal/set/doc.go        |    6 +
 .../v1/gonum/graph/internal/set/same.go       |   36 +
 .../graph/internal/set/same_appengine.go      |   36 +
 .../v1/gonum/graph/internal/set/set.go        |  256 ++
 .../v1/gonum/graph/internal/set/set_test.go   |  413 +++
 .../v1/gonum/graph/network/betweenness.go     |  250 ++
 .../gonum/graph/network/betweenness_test.go   |  338 ++
 .../v1/gonum/graph/network/distance.go        |  124 +
 .../v1/gonum/graph/network/distance_test.go   |  394 +++
 .../gonum.org/v1/gonum/graph/network/doc.go   |    6 +
 .../gonum.org/v1/gonum/graph/network/hits.go  |  101 +
 .../v1/gonum/graph/network/hits_test.go       |   98 +
 .../v1/gonum/graph/network/network.go         |   13 +
 .../v1/gonum/graph/network/network_test.go    |   33 +
 .../gonum.org/v1/gonum/graph/network/page.go  |  228 ++
 .../v1/gonum/graph/network/page_test.go       |  151 +
 .../gonum.org/v1/gonum/graph/path/a_star.go   |  151 +
 .../v1/gonum/graph/path/a_star_test.go        |  310 ++
 .../v1/gonum/graph/path/bellman_ford_moore.go |   67 +
 .../graph/path/bellman_ford_moore_test.go     |   70 +
 .../v1/gonum/graph/path/bench_test.go         |  141 +
 .../v1/gonum/graph/path/control_flow.go       |  118 +
 .../gonum.org/v1/gonum/graph/path/dijkstra.go |  147 +
 .../v1/gonum/graph/path/dijkstra_test.go      |  178 +
 .../gonum.org/v1/gonum/graph/path/disjoint.go |   87 +
 .../v1/gonum/graph/path/disjoint_test.go      |   63 +
 vendor/gonum.org/v1/gonum/graph/path/doc.go   |    6 +
 .../v1/gonum/graph/path/dynamic/doc.go        |    6 +
 .../v1/gonum/graph/path/dynamic/dstarlite.go  |  491 +++
 .../graph/path/dynamic/dstarlite_test.go      |  680 ++++
 .../gonum/graph/path/dynamic/dumper_test.go   |  153 +
 .../v1/gonum/graph/path/floydwarshall.go      |   59 +
 .../v1/gonum/graph/path/floydwarshall_test.go |  102 +
 .../v1/gonum/graph/path/internal/grid.go      |  296 ++
 .../v1/gonum/graph/path/internal/grid_test.go |  258 ++
 .../v1/gonum/graph/path/internal/limited.go   |  316 ++
 .../gonum/graph/path/internal/limited_test.go | 1242 +++++++
 .../path/internal/testgraphs/shortest.go      |  654 ++++
 .../v1/gonum/graph/path/johnson_apsp.go       |  142 +
 .../v1/gonum/graph/path/johnson_apsp_test.go  |  102 +
 .../gonum.org/v1/gonum/graph/path/shortest.go |  319 ++
 .../v1/gonum/graph/path/spanning_tree.go      |  187 +
 .../v1/gonum/graph/path/spanning_tree_test.go |  294 ++
 .../gonum.org/v1/gonum/graph/path/weight.go   |   40 +
 .../graph/simple/dense_directed_matrix.go     |  300 ++
 .../graph/simple/dense_undirected_matrix.go   |  261 ++
 .../v1/gonum/graph/simple/densegraph_test.go  |  149 +
 .../v1/gonum/graph/simple/directed.go         |  245 ++
 .../v1/gonum/graph/simple/directed_test.go    |   65 +
 vendor/gonum.org/v1/gonum/graph/simple/doc.go |    7 +
 .../gonum.org/v1/gonum/graph/simple/simple.go |   99 +
 .../v1/gonum/graph/simple/undirected.go       |  205 ++
 .../v1/gonum/graph/simple/undirected_test.go  |   67 +
 .../gonum/graph/simple/weighted_directed.go   |  285 ++
 .../graph/simple/weighted_directed_test.go    |   67 +
 .../gonum/graph/simple/weighted_undirected.go |  260 ++
 .../graph/simple/weighted_undirected_test.go  |   69 +
 .../v1/gonum/graph/topo/bench_test.go         |   57 +
 .../v1/gonum/graph/topo/bron_kerbosch.go      |  225 ++
 .../v1/gonum/graph/topo/bron_kerbosch_test.go |  163 +
 .../v1/gonum/graph/topo/common_test.go        |   47 +
 vendor/gonum.org/v1/gonum/graph/topo/doc.go   |    6 +
 .../v1/gonum/graph/topo/johnson_cycles.go     |  280 ++
 .../gonum/graph/topo/johnson_cycles_test.go   |  117 +
 .../v1/gonum/graph/topo/non_tomita_choice.go  |    9 +
 .../v1/gonum/graph/topo/paton_cycles.go       |   81 +
 .../v1/gonum/graph/topo/paton_cycles_test.go  |  143 +
 .../gonum.org/v1/gonum/graph/topo/tarjan.go   |  203 ++
 .../v1/gonum/graph/topo/tarjan_test.go        |  308 ++
 .../v1/gonum/graph/topo/tomita_choice.go      |    9 +
 vendor/gonum.org/v1/gonum/graph/topo/topo.go  |   68 +
 .../v1/gonum/graph/topo/topo_test.go          |  175 +
 .../gonum.org/v1/gonum/graph/traverse/doc.go  |    6 +
 .../v1/gonum/graph/traverse/traverse.go       |  180 +
 .../v1/gonum/graph/traverse/traverse_test.go  |  433 +++
 vendor/gonum.org/v1/gonum/graph/undirect.go   |  224 ++
 .../gonum.org/v1/gonum/graph/undirect_test.go |  175 +
 vendor/gonum.org/v1/gonum/integrate/README.md |    3 +
 vendor/gonum.org/v1/gonum/integrate/doc.go    |    7 +
 .../gonum.org/v1/gonum/integrate/quad/doc.go  |    7 +
 .../v1/gonum/integrate/quad/example_test.go   |   47 +
 .../v1/gonum/integrate/quad/hermite.go        |  314 ++
 .../v1/gonum/integrate/quad/hermite_data.go   |  413 +++
 .../v1/gonum/integrate/quad/hermite_test.go   |  251 ++
 .../integrate/quad/internal/PrintGoSlice.m    |   11 +
 .../gonum/integrate/quad/internal/genherm.m   |   32 +
 .../gonum/integrate/quad/internal/hermpts.m   |  609 ++++
 .../v1/gonum/integrate/quad/legendre.go       |  385 ++
 .../v1/gonum/integrate/quad/legendre_test.go  |   84 +
 .../gonum.org/v1/gonum/integrate/quad/quad.go |  157 +
 .../v1/gonum/integrate/quad/quad_test.go      |  126 +
 .../v1/gonum/integrate/trapezoidal.go         |   40 +
 .../v1/gonum/integrate/trapezoidal_test.go    |   82 +
 vendor/gonum.org/v1/gonum/internal/README.md  |    3 +
 .../v1/gonum/internal/asm/bench_gen.sh        |   30 +
 .../gonum/internal/asm/c128/axpyinc_amd64.s   |  134 +
 .../gonum/internal/asm/c128/axpyincto_amd64.s |  141 +
 .../internal/asm/c128/axpyunitary_amd64.s     |  122 +
 .../internal/asm/c128/axpyunitaryto_amd64.s   |  123 +
 .../v1/gonum/internal/asm/c128/bench_test.go  |  284 ++
 .../v1/gonum/internal/asm/c128/doc.go         |    6 +
 .../v1/gonum/internal/asm/c128/dotc.go        |   35 +
 .../v1/gonum/internal/asm/c128/dotu.go        |   33 +
 .../gonum/internal/asm/c128/dscalinc_amd64.s  |   69 +
 .../internal/asm/c128/dscalunitary_amd64.s    |   66 +
 .../v1/gonum/internal/asm/c128/scal.go        |   31 +
 .../internal/asm/c128/scalUnitary_amd64.s     |  116 +
 .../gonum/internal/asm/c128/scalinc_amd64.s   |  121 +
 .../v1/gonum/internal/asm/c128/stubs_amd64.go |   64 +
 .../v1/gonum/internal/asm/c128/stubs_noasm.go |  105 +
 .../v1/gonum/internal/asm/c128/stubs_test.go  |  335 ++
 .../v1/gonum/internal/asm/c128/util_test.go   |  123 +
 .../v1/gonum/internal/asm/c64/axpyinc_amd64.s |  151 +
 .../gonum/internal/asm/c64/axpyincto_amd64.s  |  156 +
 .../internal/asm/c64/axpyunitary_amd64.s      |  160 +
 .../internal/asm/c64/axpyunitaryto_amd64.s    |  157 +
 .../v1/gonum/internal/asm/c64/bench_test.go   |  282 ++
 .../v1/gonum/internal/asm/c64/conj.go         |    7 +
 .../v1/gonum/internal/asm/c64/doc.go          |    6 +
 .../v1/gonum/internal/asm/c64/dotc.go         |   33 +
 .../v1/gonum/internal/asm/c64/dotu.go         |   33 +
 .../v1/gonum/internal/asm/c64/scal.go         |   55 +
 .../v1/gonum/internal/asm/c64/stubs_amd64.go  |   36 +
 .../v1/gonum/internal/asm/c64/stubs_noasm.go  |   57 +
 .../v1/gonum/internal/asm/c64/stubs_test.go   |  231 ++
 .../v1/gonum/internal/asm/f32/axpyinc_amd64.s |   73 +
 .../gonum/internal/asm/f32/axpyincto_amd64.s  |   78 +
 .../internal/asm/f32/axpyunitary_amd64.s      |   97 +
 .../internal/asm/f32/axpyunitaryto_amd64.s    |   98 +
 .../v1/gonum/internal/asm/f32/bench_test.go   |  282 ++
 .../v1/gonum/internal/asm/f32/ddot.go         |   33 +
 .../v1/gonum/internal/asm/f32/doc.go          |    6 +
 .../v1/gonum/internal/asm/f32/dot.go          |   33 +
 .../v1/gonum/internal/asm/f32/scal.go         |   55 +
 .../v1/gonum/internal/asm/f32/stubs_amd64.go  |   36 +
 .../v1/gonum/internal/asm/f32/stubs_noasm.go  |   57 +
 .../v1/gonum/internal/asm/f32/stubs_test.go   |  217 ++
 .../v1/gonum/internal/asm/f64/abssum_amd64.s  |   82 +
 .../gonum/internal/asm/f64/abssuminc_amd64.s  |   90 +
 .../v1/gonum/internal/asm/f64/add_amd64.s     |   66 +
 .../gonum/internal/asm/f64/addconst_amd64.s   |   53 +
 .../v1/gonum/internal/asm/f64/asm_test.go     |  204 ++
 .../v1/gonum/internal/asm/f64/axpy.go         |   57 +
 .../v1/gonum/internal/asm/f64/axpy_test.go    |  274 ++
 .../v1/gonum/internal/asm/f64/axpyinc_amd64.s |  142 +
 .../gonum/internal/asm/f64/axpyincto_amd64.s  |  148 +
 .../internal/asm/f64/axpyunitary_amd64.s      |  134 +
 .../internal/asm/f64/axpyunitaryto_amd64.s    |  140 +
 .../gonum/internal/asm/f64/benchAxpy_test.go  |  167 +
 .../gonum/internal/asm/f64/benchScal_test.go  |   87 +
 .../internal/asm/f64/bench_other_test.go      |  443 +++
 .../v1/gonum/internal/asm/f64/bench_test.go   |  438 +++
 .../v1/gonum/internal/asm/f64/cumprod_amd64.s |   71 +
 .../v1/gonum/internal/asm/f64/cumsum_amd64.s  |   64 +
 .../v1/gonum/internal/asm/f64/div_amd64.s     |   67 +
 .../v1/gonum/internal/asm/f64/divto_amd64.s   |   73 +
 .../v1/gonum/internal/asm/f64/doc.go          |    6 +
 .../v1/gonum/internal/asm/f64/dot.go          |   35 +
 .../v1/gonum/internal/asm/f64/dot_amd64.s     |  145 +
 .../v1/gonum/internal/asm/f64/dot_test.go     |  280 ++
 .../v1/gonum/internal/asm/f64/l1norm_amd64.s  |   58 +
 .../gonum/internal/asm/f64/linfnorm_amd64.s   |   57 +
 .../v1/gonum/internal/asm/f64/scal.go         |   57 +
 .../v1/gonum/internal/asm/f64/scal_test.go    |  179 +
 .../v1/gonum/internal/asm/f64/scalinc_amd64.s |  113 +
 .../gonum/internal/asm/f64/scalincto_amd64.s  |  122 +
 .../internal/asm/f64/scalunitary_amd64.s      |  112 +
 .../internal/asm/f64/scalunitaryto_amd64.s    |  113 +
 .../v1/gonum/internal/asm/f64/stubs_amd64.go  |  165 +
 .../v1/gonum/internal/asm/f64/stubs_noasm.go  |  157 +
 .../v1/gonum/internal/asm/f64/stubs_test.go   |  574 +++
 .../v1/gonum/internal/cmplx64/abs.go          |   14 +
 .../v1/gonum/internal/cmplx64/cmath_test.go   |  240 ++
 .../v1/gonum/internal/cmplx64/conj.go         |   12 +
 .../v1/gonum/internal/cmplx64/doc.go          |    7 +
 .../v1/gonum/internal/cmplx64/isinf.go        |   25 +
 .../v1/gonum/internal/cmplx64/isnan.go        |   29 +
 .../v1/gonum/internal/cmplx64/sqrt.go         |  108 +
 .../gonum.org/v1/gonum/internal/math32/doc.go |    7 +
 .../v1/gonum/internal/math32/math.go          |  111 +
 .../v1/gonum/internal/math32/math_test.go     |  238 ++
 .../v1/gonum/internal/math32/signbit.go       |   16 +
 .../v1/gonum/internal/math32/sqrt.go          |   25 +
 .../v1/gonum/internal/math32/sqrt_amd64.go    |   20 +
 .../v1/gonum/internal/math32/sqrt_amd64.s     |   20 +
 vendor/gonum.org/v1/gonum/lapack/.gitignore   |    0
 vendor/gonum.org/v1/gonum/lapack/README.md    |   50 +
 .../v1/gonum/lapack/gonum/appengine_test.go   |    9 +
 .../v1/gonum/lapack/gonum/bench_test.go       |   15 +
 .../gonum.org/v1/gonum/lapack/gonum/dbdsqr.go |  488 +++
 .../gonum.org/v1/gonum/lapack/gonum/dgebak.go |   78 +
 .../gonum.org/v1/gonum/lapack/gonum/dgebal.go |  228 ++
 .../gonum.org/v1/gonum/lapack/gonum/dgebd2.go |   74 +
 .../gonum.org/v1/gonum/lapack/gonum/dgebrd.go |  150 +
 .../gonum.org/v1/gonum/lapack/gonum/dgecon.go |   81 +
 .../gonum.org/v1/gonum/lapack/gonum/dgeev.go  |  284 ++
 .../gonum.org/v1/gonum/lapack/gonum/dgehd2.go |   84 +
 .../gonum.org/v1/gonum/lapack/gonum/dgehrd.go |  183 +
 .../gonum.org/v1/gonum/lapack/gonum/dgelq2.go |   49 +
 .../gonum.org/v1/gonum/lapack/gonum/dgelqf.go |   84 +
 .../gonum.org/v1/gonum/lapack/gonum/dgels.go  |  200 ++
 .../gonum.org/v1/gonum/lapack/gonum/dgeql2.go |   45 +
 .../gonum.org/v1/gonum/lapack/gonum/dgeqp3.go |  174 +
 .../gonum.org/v1/gonum/lapack/gonum/dgeqr2.go |   59 +
 .../gonum.org/v1/gonum/lapack/gonum/dgeqrf.go |   99 +
 .../gonum.org/v1/gonum/lapack/gonum/dgerq2.go |   53 +
 .../gonum.org/v1/gonum/lapack/gonum/dgerqf.go |  128 +
 .../gonum.org/v1/gonum/lapack/gonum/dgesvd.go | 1356 +++++++
 .../gonum.org/v1/gonum/lapack/gonum/dgetf2.go |   69 +
 .../gonum.org/v1/gonum/lapack/gonum/dgetrf.go |   70 +
 .../gonum.org/v1/gonum/lapack/gonum/dgetri.go |   92 +
 .../gonum.org/v1/gonum/lapack/gonum/dgetrs.go |   55 +
 .../v1/gonum/lapack/gonum/dggsvd3.go          |  230 ++
 .../v1/gonum/lapack/gonum/dggsvp3.go          |  273 ++
 .../gonum.org/v1/gonum/lapack/gonum/dhseqr.go |  257 ++
 .../gonum.org/v1/gonum/lapack/gonum/dlabrd.go |  150 +
 .../gonum.org/v1/gonum/lapack/gonum/dlacn2.go |  134 +
 .../gonum.org/v1/gonum/lapack/gonum/dlacpy.go |   40 +
 .../gonum.org/v1/gonum/lapack/gonum/dlae2.go  |   49 +
 .../gonum.org/v1/gonum/lapack/gonum/dlaev2.go |   82 +
 .../gonum.org/v1/gonum/lapack/gonum/dlaexc.go |  261 ++
 .../gonum.org/v1/gonum/lapack/gonum/dlags2.go |  182 +
 .../gonum.org/v1/gonum/lapack/gonum/dlahqr.go |  423 +++
 .../gonum.org/v1/gonum/lapack/gonum/dlahr2.go |  169 +
 .../gonum.org/v1/gonum/lapack/gonum/dlaln2.go |  396 +++
 .../gonum.org/v1/gonum/lapack/gonum/dlange.go |   84 +
 .../gonum.org/v1/gonum/lapack/gonum/dlanst.go |   68 +
 .../gonum.org/v1/gonum/lapack/gonum/dlansy.go |  125 +
 .../gonum.org/v1/gonum/lapack/gonum/dlantr.go |  252 ++
 .../gonum.org/v1/gonum/lapack/gonum/dlanv2.go |  132 +
 .../gonum.org/v1/gonum/lapack/gonum/dlapll.go |   36 +
 .../gonum.org/v1/gonum/lapack/gonum/dlapmt.go |   72 +
 .../gonum.org/v1/gonum/lapack/gonum/dlapy2.go |   14 +
 .../gonum.org/v1/gonum/lapack/gonum/dlaqp2.go |  111 +
 .../gonum.org/v1/gonum/lapack/gonum/dlaqps.go |  217 ++
 .../v1/gonum/lapack/gonum/dlaqr04.go          |  475 +++
 .../gonum.org/v1/gonum/lapack/gonum/dlaqr1.go |   57 +
 .../v1/gonum/lapack/gonum/dlaqr23.go          |  403 +++
 .../gonum.org/v1/gonum/lapack/gonum/dlaqr5.go |  616 ++++
 .../gonum.org/v1/gonum/lapack/gonum/dlarf.go  |   83 +
 .../gonum.org/v1/gonum/lapack/gonum/dlarfb.go |  431 +++
 .../gonum.org/v1/gonum/lapack/gonum/dlarfg.go |   62 +
 .../gonum.org/v1/gonum/lapack/gonum/dlarft.go |  150 +
 .../gonum.org/v1/gonum/lapack/gonum/dlarfx.go |  535 +++
 .../gonum.org/v1/gonum/lapack/gonum/dlartg.go |   80 +
 .../gonum.org/v1/gonum/lapack/gonum/dlas2.go  |   43 +
 .../gonum.org/v1/gonum/lapack/gonum/dlascl.go |   89 +
 .../gonum.org/v1/gonum/lapack/gonum/dlaset.go |   40 +
 .../gonum.org/v1/gonum/lapack/gonum/dlasq1.go |   97 +
 .../gonum.org/v1/gonum/lapack/gonum/dlasq2.go |  368 ++
 .../gonum.org/v1/gonum/lapack/gonum/dlasq3.go |  161 +
 .../gonum.org/v1/gonum/lapack/gonum/dlasq4.go |  238 ++
 .../gonum.org/v1/gonum/lapack/gonum/dlasq5.go |  127 +
 .../gonum.org/v1/gonum/lapack/gonum/dlasq6.go |  109 +
 .../gonum.org/v1/gonum/lapack/gonum/dlasr.go  |  268 ++
 .../gonum.org/v1/gonum/lapack/gonum/dlasrt.go |   30 +
 .../gonum.org/v1/gonum/lapack/gonum/dlassq.go |   31 +
 .../gonum.org/v1/gonum/lapack/gonum/dlasv2.go |  115 +
 .../gonum.org/v1/gonum/lapack/gonum/dlaswp.go |   47 +
 .../gonum.org/v1/gonum/lapack/gonum/dlasy2.go |  290 ++
 .../gonum.org/v1/gonum/lapack/gonum/dlatrd.go |  145 +
 .../gonum.org/v1/gonum/lapack/gonum/dlatrs.go |  350 ++
 vendor/gonum.org/v1/gonum/lapack/gonum/doc.go |   28 +
 .../gonum.org/v1/gonum/lapack/gonum/dorg2l.go |   65 +
 .../gonum.org/v1/gonum/lapack/gonum/dorg2r.go |   65 +
 .../gonum.org/v1/gonum/lapack/gonum/dorgbr.go |  124 +
 .../gonum.org/v1/gonum/lapack/gonum/dorghr.go |   93 +
 .../gonum.org/v1/gonum/lapack/gonum/dorgl2.go |   63 +
 .../gonum.org/v1/gonum/lapack/gonum/dorglq.go |  117 +
 .../gonum.org/v1/gonum/lapack/gonum/dorgql.go |  130 +
 .../gonum.org/v1/gonum/lapack/gonum/dorgqr.go |  120 +
 .../gonum.org/v1/gonum/lapack/gonum/dorgtr.go |   99 +
 .../gonum.org/v1/gonum/lapack/gonum/dorm2r.go |   88 +
 .../gonum.org/v1/gonum/lapack/gonum/dormbr.go |  158 +
 .../gonum.org/v1/gonum/lapack/gonum/dormhr.go |  121 +
 .../gonum.org/v1/gonum/lapack/gonum/dorml2.go |   83 +
 .../gonum.org/v1/gonum/lapack/gonum/dormlq.go |  159 +
 .../gonum.org/v1/gonum/lapack/gonum/dormqr.go |  167 +
 .../gonum.org/v1/gonum/lapack/gonum/dormr2.go |   93 +
 .../gonum.org/v1/gonum/lapack/gonum/dpbtf2.go |   97 +
 .../gonum.org/v1/gonum/lapack/gonum/dpocon.go |   76 +
 .../gonum.org/v1/gonum/lapack/gonum/dpotf2.go |   72 +
 .../gonum.org/v1/gonum/lapack/gonum/dpotrf.go |   72 +
 .../gonum.org/v1/gonum/lapack/gonum/drscl.go  |   47 +
 .../gonum.org/v1/gonum/lapack/gonum/dsteqr.go |  373 ++
 .../gonum.org/v1/gonum/lapack/gonum/dsterf.go |  278 ++
 .../gonum.org/v1/gonum/lapack/gonum/dsyev.go  |  113 +
 .../gonum.org/v1/gonum/lapack/gonum/dsytd2.go |  123 +
 .../gonum.org/v1/gonum/lapack/gonum/dsytrd.go |  178 +
 .../gonum.org/v1/gonum/lapack/gonum/dtgsja.go |  357 ++
 .../gonum.org/v1/gonum/lapack/gonum/dtrcon.go |   82 +
 .../v1/gonum/lapack/gonum/dtrevc3.go          |  866 +++++
 .../gonum.org/v1/gonum/lapack/gonum/dtrexc.go |  221 ++
 .../gonum.org/v1/gonum/lapack/gonum/dtrti2.go |   57 +
 .../gonum.org/v1/gonum/lapack/gonum/dtrtri.go |   64 +
 .../gonum.org/v1/gonum/lapack/gonum/dtrtrs.go |   30 +
 .../v1/gonum/lapack/gonum/general.go          |  143 +
 .../gonum.org/v1/gonum/lapack/gonum/iladlc.go |   33 +
 .../gonum.org/v1/gonum/lapack/gonum/iladlr.go |   30 +
 .../gonum.org/v1/gonum/lapack/gonum/ilaenv.go |  387 ++
 .../gonum.org/v1/gonum/lapack/gonum/iparmq.go |  115 +
 .../v1/gonum/lapack/gonum/lapack_test.go      |  441 +++
 .../internal/testdata/dlahr2test/main.go      |  101 +
 .../internal/testdata/dlaqr5test/main.go      |  185 +
 .../internal/testdata/dlasqtest/Makefile      |   27 +
 .../internal/testdata/dlasqtest/Readme.md     |   23 +
 .../internal/testdata/dlasqtest/dcopy.f       |  115 +
 .../internal/testdata/dlasqtest/disnan.f      |   80 +
 .../internal/testdata/dlasqtest/dlaisnan.f    |   91 +
 .../internal/testdata/dlasqtest/dlamch.f      |  193 +
 .../internal/testdata/dlasqtest/dlas2.f       |  183 +
 .../internal/testdata/dlasqtest/dlascl.f      |  364 ++
 .../internal/testdata/dlasqtest/dlasq1.f      |  226 ++
 .../internal/testdata/dlasqtest/dlasq2.f      |  652 ++++
 .../internal/testdata/dlasqtest/dlasq3.f      |  498 +++
 .../internal/testdata/dlasqtest/dlasq4.f      |  427 +++
 .../internal/testdata/dlasqtest/dlasq5.f      |  413 +++
 .../internal/testdata/dlasqtest/dlasq6.f      |  258 ++
 .../internal/testdata/dlasqtest/dlasrt.f      |  303 ++
 .../internal/testdata/dlasqtest/ieeeck.f      |  203 ++
 .../internal/testdata/dlasqtest/ilaenv.f      |  624 ++++
 .../internal/testdata/dlasqtest/iparmq.f      |  322 ++
 .../internal/testdata/dlasqtest/lsame.f       |  125 +
 .../testdata/dlasqtest/testdlasq1.f90         |  626 ++++
 .../testdata/dlasqtest/testdlasq2.f90         |  171 +
 .../testdata/dlasqtest/testdlasq3.f90         |  132 +
 .../testdata/dlasqtest/testdlasq4.f90         |  435 +++
 .../internal/testdata/dlasqtest/xerbla.f      |   99 +
 .../internal/testdata/dsterftest/Makefile     |   20 +
 .../internal/testdata/dsterftest/disnan.f     |   80 +
 .../internal/testdata/dsterftest/dlae2.f      |  185 +
 .../internal/testdata/dsterftest/dlaisnan.f   |   91 +
 .../internal/testdata/dsterftest/dlamch.f     |  193 +
 .../internal/testdata/dsterftest/dlanst.f     |  186 +
 .../internal/testdata/dsterftest/dlapy2.f     |  104 +
 .../internal/testdata/dsterftest/dlascl.f     |  364 ++
 .../internal/testdata/dsterftest/dlasrt.f     |  303 ++
 .../internal/testdata/dsterftest/dlassq.f     |  155 +
 .../internal/testdata/dsterftest/dsterf.f     |  448 +++
 .../internal/testdata/dsterftest/lsame.f      |  125 +
 .../testdata/dsterftest/testdsterf.f90        |   15 +
 .../internal/testdata/dsterftest/xerbla.f     |   99 +
 .../lapack/internal/testdata/netlib/daxpy.f   |  115 +
 .../lapack/internal/testdata/netlib/dcopy.f   |  115 +
 .../lapack/internal/testdata/netlib/dgemm.f   |  384 ++
 .../lapack/internal/testdata/netlib/dgemv.f   |  330 ++
 .../lapack/internal/testdata/netlib/dlabad.f  |  105 +
 .../lapack/internal/testdata/netlib/dlacpy.f  |  156 +
 .../lapack/internal/testdata/netlib/dlahr2.f  |  326 ++
 .../lapack/internal/testdata/netlib/dlamch.f  |  189 +
 .../lapack/internal/testdata/netlib/dlapy2.f  |  104 +
 .../lapack/internal/testdata/netlib/dlaqr1.f  |  179 +
 .../lapack/internal/testdata/netlib/dlaqr5.f  |  921 +++++
 .../lapack/internal/testdata/netlib/dlarfg.f  |  196 ++
 .../lapack/internal/testdata/netlib/dlaset.f  |  184 +
 .../lapack/internal/testdata/netlib/dnrm2.f   |  112 +
 .../lapack/internal/testdata/netlib/dscal.f   |  110 +
 .../lapack/internal/testdata/netlib/dtrmm.f   |  415 +++
 .../lapack/internal/testdata/netlib/dtrmv.f   |  342 ++
 .../lapack/internal/testdata/netlib/lsame.f   |  125 +
 .../lapack/internal/testdata/netlib/netlib.go |   68 +
 .../lapack/internal/testdata/netlib/xerbla.f  |   89 +
 vendor/gonum.org/v1/gonum/lapack/lapack.go    |  188 +
 .../gonum.org/v1/gonum/lapack/lapack64/doc.go |   20 +
 .../v1/gonum/lapack/lapack64/lapack64.go      |  545 +++
 .../v1/gonum/lapack/testlapack/dbdsqr.go      |  198 ++
 .../v1/gonum/lapack/testlapack/dgebak.go      |  110 +
 .../v1/gonum/lapack/testlapack/dgebal.go      |  175 +
 .../v1/gonum/lapack/testlapack/dgebd2.go      |   54 +
 .../v1/gonum/lapack/testlapack/dgebrd.go      |  151 +
 .../v1/gonum/lapack/testlapack/dgecon.go      |   97 +
 .../v1/gonum/lapack/testlapack/dgeev.go       |  735 ++++
 .../v1/gonum/lapack/testlapack/dgeev_bench.go |   63 +
 .../v1/gonum/lapack/testlapack/dgehd2.go      |  196 ++
 .../v1/gonum/lapack/testlapack/dgehrd.go      |  209 ++
 .../v1/gonum/lapack/testlapack/dgelq2.go      |  113 +
 .../v1/gonum/lapack/testlapack/dgelqf.go      |   98 +
 .../v1/gonum/lapack/testlapack/dgels.go       |  182 +
 .../v1/gonum/lapack/testlapack/dgeql2.go      |   99 +
 .../v1/gonum/lapack/testlapack/dgeqp3.go      |  135 +
 .../v1/gonum/lapack/testlapack/dgeqr2.go      |  111 +
 .../v1/gonum/lapack/testlapack/dgeqrf.go      |   95 +
 .../v1/gonum/lapack/testlapack/dgerq2.go      |  117 +
 .../v1/gonum/lapack/testlapack/dgerqf.go      |  142 +
 .../v1/gonum/lapack/testlapack/dgesvd.go      |  286 ++
 .../v1/gonum/lapack/testlapack/dgetf2.go      |  195 ++
 .../v1/gonum/lapack/testlapack/dgetrf.go      |   65 +
 .../v1/gonum/lapack/testlapack/dgetri.go      |   89 +
 .../v1/gonum/lapack/testlapack/dgetrs.go      |  113 +
 .../v1/gonum/lapack/testlapack/dggsvd3.go     |  173 +
 .../v1/gonum/lapack/testlapack/dggsvp3.go     |  146 +
 .../v1/gonum/lapack/testlapack/dhseqr.go      |  861 +++++
 .../v1/gonum/lapack/testlapack/dlabrd.go      |  107 +
 .../v1/gonum/lapack/testlapack/dlacn2.go      |   72 +
 .../v1/gonum/lapack/testlapack/dlacpy.go      |   89 +
 .../v1/gonum/lapack/testlapack/dlae2.go       |   53 +
 .../v1/gonum/lapack/testlapack/dlaev2.go      |   46 +
 .../v1/gonum/lapack/testlapack/dlaexc.go      |  227 ++
 .../v1/gonum/lapack/testlapack/dlags2.go      |  100 +
 .../v1/gonum/lapack/testlapack/dlahqr.go      |  441 +++
 .../v1/gonum/lapack/testlapack/dlahr2.go      |  240 ++
 .../v1/gonum/lapack/testlapack/dlaln2.go      |  139 +
 .../v1/gonum/lapack/testlapack/dlange.go      |   93 +
 .../v1/gonum/lapack/testlapack/dlanst.go      |   53 +
 .../v1/gonum/lapack/testlapack/dlansy.go      |   80 +
 .../v1/gonum/lapack/testlapack/dlantr.go      |   89 +
 .../v1/gonum/lapack/testlapack/dlanv2.go      |   69 +
 .../v1/gonum/lapack/testlapack/dlapll.go      |   46 +
 .../v1/gonum/lapack/testlapack/dlapmt.go      |  113 +
 .../v1/gonum/lapack/testlapack/dlapy2.go      |   30 +
 .../v1/gonum/lapack/testlapack/dlaqp2.go      |  115 +
 .../v1/gonum/lapack/testlapack/dlaqps.go      |  112 +
 .../v1/gonum/lapack/testlapack/dlaqr04.go     |  449 +++
 .../v1/gonum/lapack/testlapack/dlaqr1.go      |   91 +
 .../v1/gonum/lapack/testlapack/dlaqr23.go     |  335 ++
 .../v1/gonum/lapack/testlapack/dlaqr5.go      |  214 ++
 .../v1/gonum/lapack/testlapack/dlarf.go       |  173 +
 .../v1/gonum/lapack/testlapack/dlarfb.go      |  161 +
 .../v1/gonum/lapack/testlapack/dlarfg.go      |  134 +
 .../v1/gonum/lapack/testlapack/dlarft.go      |  168 +
 .../v1/gonum/lapack/testlapack/dlarfx.go      |   82 +
 .../v1/gonum/lapack/testlapack/dlartg.go      |   98 +
 .../v1/gonum/lapack/testlapack/dlas2.go       |   34 +
 .../v1/gonum/lapack/testlapack/dlascl.go      |  106 +
 .../v1/gonum/lapack/testlapack/dlaset.go      |   76 +
 .../v1/gonum/lapack/testlapack/dlasq1.go      |   87 +
 .../v1/gonum/lapack/testlapack/dlasq2.go      |  714 ++++
 .../v1/gonum/lapack/testlapack/dlasq3.go      | 2703 ++++++++++++++
 .../v1/gonum/lapack/testlapack/dlasq4.go      | 3101 +++++++++++++++++
 .../v1/gonum/lapack/testlapack/dlasq5.go      | 1992 +++++++++++
 .../v1/gonum/lapack/testlapack/dlasr.go       |  148 +
 .../v1/gonum/lapack/testlapack/dlasrt.go      |   80 +
 .../v1/gonum/lapack/testlapack/dlasv2.go      |   48 +
 .../v1/gonum/lapack/testlapack/dlaswp.go      |  130 +
 .../v1/gonum/lapack/testlapack/dlasy2.go      |  104 +
 .../v1/gonum/lapack/testlapack/dlatrd.go      |  245 ++
 .../v1/gonum/lapack/testlapack/dlatrs.go      |  141 +
 .../v1/gonum/lapack/testlapack/doc.go         |    6 +
 .../v1/gonum/lapack/testlapack/dorg2l.go      |   75 +
 .../v1/gonum/lapack/testlapack/dorg2r.go      |   79 +
 .../v1/gonum/lapack/testlapack/dorgbr.go      |  156 +
 .../v1/gonum/lapack/testlapack/dorghr.go      |   99 +
 .../v1/gonum/lapack/testlapack/dorgl2.go      |   65 +
 .../v1/gonum/lapack/testlapack/dorglq.go      |   83 +
 .../v1/gonum/lapack/testlapack/dorgql.go      |  130 +
 .../v1/gonum/lapack/testlapack/dorgqr.go      |   83 +
 .../v1/gonum/lapack/testlapack/dorgtr.go      |  136 +
 .../v1/gonum/lapack/testlapack/dorm2r.go      |  139 +
 .../v1/gonum/lapack/testlapack/dormbr.go      |  164 +
 .../v1/gonum/lapack/testlapack/dormhr.go      |  132 +
 .../v1/gonum/lapack/testlapack/dorml2.go      |  144 +
 .../v1/gonum/lapack/testlapack/dormlq.go      |  130 +
 .../v1/gonum/lapack/testlapack/dormqr.go      |  154 +
 .../v1/gonum/lapack/testlapack/dormr2.go      |  137 +
 .../v1/gonum/lapack/testlapack/dpbtf2.go      |   47 +
 .../v1/gonum/lapack/testlapack/dpocon.go      |  157 +
 .../v1/gonum/lapack/testlapack/dpotf2.go      |  117 +
 .../v1/gonum/lapack/testlapack/dpotrf.go      |  135 +
 .../v1/gonum/lapack/testlapack/drscl.go       |   52 +
 .../v1/gonum/lapack/testlapack/dsteqr.go      |  171 +
 .../v1/gonum/lapack/testlapack/dsterf.go      |  126 +
 .../v1/gonum/lapack/testlapack/dsyev.go       |  115 +
 .../v1/gonum/lapack/testlapack/dsytd2.go      |  205 ++
 .../v1/gonum/lapack/testlapack/dsytrd.go      |  160 +
 .../v1/gonum/lapack/testlapack/dtgsja.go      |  165 +
 .../v1/gonum/lapack/testlapack/dtrcon.go      |  184 +
 .../v1/gonum/lapack/testlapack/dtrevc3.go     |  221 ++
 .../v1/gonum/lapack/testlapack/dtrexc.go      |  219 ++
 .../v1/gonum/lapack/testlapack/dtrti2.go      |  163 +
 .../v1/gonum/lapack/testlapack/dtrtri.go      |   95 +
 .../v1/gonum/lapack/testlapack/fortran.go     |   33 +
 .../v1/gonum/lapack/testlapack/general.go     | 1516 ++++++++
 .../v1/gonum/lapack/testlapack/iladlc.go      |   83 +
 .../v1/gonum/lapack/testlapack/iladlr.go      |   83 +
 .../v1/gonum/lapack/testlapack/matgen.go      |  655 ++++
 .../v1/gonum/lapack/testlapack/matgen_test.go |   90 +
 .../gonum/lapack/testlapack/test_matrices.go  |  615 ++++
 .../testlapack/testdata/dlahr2data.json.gz    |  Bin 0 -> 28251 bytes
 .../testlapack/testdata/dlaqr5data.json.gz    |  Bin 0 -> 1342926 bytes
 vendor/gonum.org/v1/gonum/mat/README.md       |    3 +
 vendor/gonum.org/v1/gonum/mat/band.go         |  228 ++
 vendor/gonum.org/v1/gonum/mat/band_test.go    |  377 ++
 vendor/gonum.org/v1/gonum/mat/cblas_test.go   |   16 +
 vendor/gonum.org/v1/gonum/mat/cholesky.go     |  479 +++
 .../v1/gonum/mat/cholesky_example_test.go     |  121 +
 .../gonum.org/v1/gonum/mat/cholesky_test.go   |  453 +++
 vendor/gonum.org/v1/gonum/mat/cmatrix.go      |   71 +
 vendor/gonum.org/v1/gonum/mat/consts.go       |   54 +
 vendor/gonum.org/v1/gonum/mat/dense.go        |  534 +++
 .../v1/gonum/mat/dense_arithmetic.go          |  719 ++++
 vendor/gonum.org/v1/gonum/mat/dense_test.go   | 2005 +++++++++++
 vendor/gonum.org/v1/gonum/mat/doc.go          |  173 +
 vendor/gonum.org/v1/gonum/mat/eigen.go        |  260 ++
 vendor/gonum.org/v1/gonum/mat/eigen_test.go   |  164 +
 vendor/gonum.org/v1/gonum/mat/errors.go       |  148 +
 vendor/gonum.org/v1/gonum/mat/errors_test.go  |   56 +
 .../gonum.org/v1/gonum/mat/fao_data_test.go   |  122 +
 vendor/gonum.org/v1/gonum/mat/format.go       |  238 ++
 .../v1/gonum/mat/format_example_test.go       |  112 +
 vendor/gonum.org/v1/gonum/mat/format_test.go  |  150 +
 vendor/gonum.org/v1/gonum/mat/gsvd.go         |  371 ++
 .../v1/gonum/mat/gsvd_example_test.go         |   85 +
 vendor/gonum.org/v1/gonum/mat/gsvd_test.go    |  117 +
 vendor/gonum.org/v1/gonum/mat/hogsvd.go       |  213 ++
 .../v1/gonum/mat/hogsvd_example_test.go       |  134 +
 vendor/gonum.org/v1/gonum/mat/hogsvd_test.go  |   87 +
 .../v1/gonum/mat/index_bound_checks.go        |  227 ++
 .../v1/gonum/mat/index_no_bound_checks.go     |  228 ++
 vendor/gonum.org/v1/gonum/mat/inner.go        |  102 +
 vendor/gonum.org/v1/gonum/mat/inner_test.go   |  181 +
 vendor/gonum.org/v1/gonum/mat/io.go           |  360 ++
 vendor/gonum.org/v1/gonum/mat/io_test.go      |  731 ++++
 vendor/gonum.org/v1/gonum/mat/list_test.go    | 1151 ++++++
 vendor/gonum.org/v1/gonum/mat/lq.go           |  225 ++
 vendor/gonum.org/v1/gonum/mat/lq_test.go      |  179 +
 vendor/gonum.org/v1/gonum/mat/lu.go           |  373 ++
 vendor/gonum.org/v1/gonum/mat/lu_test.go      |  189 +
 vendor/gonum.org/v1/gonum/mat/matrix.go       |  881 +++++
 vendor/gonum.org/v1/gonum/mat/matrix_test.go  |  624 ++++
 vendor/gonum.org/v1/gonum/mat/mul_test.go     |  283 ++
 vendor/gonum.org/v1/gonum/mat/offset.go       |   20 +
 .../v1/gonum/mat/offset_appengine.go          |   24 +
 vendor/gonum.org/v1/gonum/mat/pool.go         |  236 ++
 vendor/gonum.org/v1/gonum/mat/pool_test.go    |   81 +
 vendor/gonum.org/v1/gonum/mat/product.go      |  193 +
 vendor/gonum.org/v1/gonum/mat/product_test.go |  251 ++
 vendor/gonum.org/v1/gonum/mat/qr.go           |  221 ++
 vendor/gonum.org/v1/gonum/mat/qr_test.go      |  205 ++
 vendor/gonum.org/v1/gonum/mat/shadow.go       |  280 ++
 vendor/gonum.org/v1/gonum/mat/shadow_test.go  |  274 ++
 vendor/gonum.org/v1/gonum/mat/solve.go        |  127 +
 vendor/gonum.org/v1/gonum/mat/solve_test.go   |  296 ++
 vendor/gonum.org/v1/gonum/mat/svd.go          |  190 +
 vendor/gonum.org/v1/gonum/mat/svd_test.go     |  172 +
 vendor/gonum.org/v1/gonum/mat/symband.go      |  175 +
 vendor/gonum.org/v1/gonum/mat/symband_test.go |  230 ++
 vendor/gonum.org/v1/gonum/mat/symmetric.go    |  502 +++
 .../v1/gonum/mat/symmetric_example_test.go    |   54 +
 .../gonum.org/v1/gonum/mat/symmetric_test.go  |  694 ++++
 vendor/gonum.org/v1/gonum/mat/triangular.go   |  540 +++
 .../gonum.org/v1/gonum/mat/triangular_test.go |  438 +++
 vendor/gonum.org/v1/gonum/mat/vector.go       |  484 +++
 vendor/gonum.org/v1/gonum/mat/vector_test.go  |  530 +++
 vendor/gonum.org/v1/gonum/mathext/README.md   |    3 +
 vendor/gonum.org/v1/gonum/mathext/airy.go     |   37 +
 .../gonum.org/v1/gonum/mathext/airy_test.go   |   28 +
 vendor/gonum.org/v1/gonum/mathext/beta.go     |   34 +
 .../gonum.org/v1/gonum/mathext/beta_test.go   |  177 +
 vendor/gonum.org/v1/gonum/mathext/betainc.go  |   29 +
 .../v1/gonum/mathext/betainc_test.go          |   75 +
 vendor/gonum.org/v1/gonum/mathext/digamma.go  |   28 +
 .../v1/gonum/mathext/digamma_test.go          |   27 +
 vendor/gonum.org/v1/gonum/mathext/doc.go      |    7 +
 .../gonum.org/v1/gonum/mathext/ell_carlson.go |  156 +
 .../v1/gonum/mathext/ell_carlson_test.go      |  103 +
 .../v1/gonum/mathext/ell_complete.go          |  157 +
 .../v1/gonum/mathext/ell_complete_test.go     |   27 +
 vendor/gonum.org/v1/gonum/mathext/erf.go      |   91 +
 vendor/gonum.org/v1/gonum/mathext/erf_test.go |   69 +
 .../gonum.org/v1/gonum/mathext/gamma_inc.go   |   50 +
 .../v1/gonum/mathext/gamma_inc_inv.go         |   56 +
 .../v1/gonum/mathext/gamma_inc_test.go        |  138 +
 .../v1/gonum/mathext/internal/amos/amos.go    | 2154 ++++++++++++
 .../gonum/mathext/internal/amos/amos_test.go  |  521 +++
 .../mathext/internal/amos/amoslib/Make.files  |    5 +
 .../mathext/internal/amos/amoslib/d1mach.f    |   97 +
 .../mathext/internal/amos/amoslib/dgamln.f    |  189 +
 .../mathext/internal/amos/amoslib/fortran.go  |  366 ++
 .../mathext/internal/amos/amoslib/i1mach.f    |  113 +
 .../mathext/internal/amos/amoslib/myabs.f     |    5 +
 .../mathext/internal/amos/amoslib/myatan.f    |    5 +
 .../mathext/internal/amos/amoslib/mycos.f     |    5 +
 .../mathext/internal/amos/amoslib/myexp.f     |    5 +
 .../mathext/internal/amos/amoslib/mylog.f     |    5 +
 .../mathext/internal/amos/amoslib/mymax.f     |    5 +
 .../mathext/internal/amos/amoslib/mymin.f     |    5 +
 .../mathext/internal/amos/amoslib/mysin.f     |    5 +
 .../mathext/internal/amos/amoslib/mysqrt.f    |    5 +
 .../mathext/internal/amos/amoslib/mytan.f     |    5 +
 .../mathext/internal/amos/amoslib/xerror.f    |   22 +
 .../mathext/internal/amos/amoslib/zabs.f      |   34 +
 .../mathext/internal/amos/amoslib/zacai.f     |   99 +
 .../mathext/internal/amos/amoslib/zacon.f     |  203 ++
 .../mathext/internal/amos/amoslib/zairy.f     |  395 +++
 .../mathext/internal/amos/amoslib/zasyi.f     |  169 +
 .../mathext/internal/amos/amoslib/zbesh.f     |  348 ++
 .../mathext/internal/amos/amoslib/zbesi.f     |  269 ++
 .../mathext/internal/amos/amoslib/zbesj.f     |  266 ++
 .../mathext/internal/amos/amoslib/zbesk.f     |  281 ++
 .../mathext/internal/amos/amoslib/zbesy.f     |  244 ++
 .../mathext/internal/amos/amoslib/zbinu.f     |  110 +
 .../mathext/internal/amos/amoslib/zbiry.f     |  364 ++
 .../mathext/internal/amos/amoslib/zbknu.f     |  568 +++
 .../mathext/internal/amos/amoslib/zbuni.f     |  174 +
 .../mathext/internal/amos/amoslib/zbunk.f     |   35 +
 .../mathext/internal/amos/amoslib/zdiv.f      |   19 +
 .../mathext/internal/amos/amoslib/zexp.f      |   16 +
 .../mathext/internal/amos/amoslib/zkscl.f     |  121 +
 .../mathext/internal/amos/amoslib/zlog.f      |   41 +
 .../mathext/internal/amos/amoslib/zmlri.f     |  206 ++
 .../mathext/internal/amos/amoslib/zmlt.f      |   15 +
 .../mathext/internal/amos/amoslib/zrati.f     |  132 +
 .../mathext/internal/amos/amoslib/zs1s2.f     |   51 +
 .../mathext/internal/amos/amoslib/zseri.f     |  195 ++
 .../mathext/internal/amos/amoslib/zshch.f     |   22 +
 .../mathext/internal/amos/amoslib/zsqrt.f     |   45 +
 .../mathext/internal/amos/amoslib/zuchk.f     |   28 +
 .../mathext/internal/amos/amoslib/zunhj.f     |  714 ++++
 .../mathext/internal/amos/amoslib/zuni1.f     |  204 ++
 .../mathext/internal/amos/amoslib/zuni2.f     |  267 ++
 .../mathext/internal/amos/amoslib/zunik.f     |  211 ++
 .../mathext/internal/amos/amoslib/zunk1.f     |  426 +++
 .../mathext/internal/amos/amoslib/zunk2.f     |  505 +++
 .../mathext/internal/amos/amoslib/zuoik.f     |  194 ++
 .../mathext/internal/amos/amoslib/zwrsk.f     |   94 +
 .../v1/gonum/mathext/internal/amos/doc.go     |    6 +
 .../mathext/internal/amos/origcode_test.go    | 2276 ++++++++++++
 .../gonum/mathext/internal/cephes/cephes.go   |   28 +
 .../v1/gonum/mathext/internal/cephes/doc.go   |    6 +
 .../v1/gonum/mathext/internal/cephes/igam.go  |  311 ++
 .../v1/gonum/mathext/internal/cephes/igami.go |  153 +
 .../gonum/mathext/internal/cephes/incbeta.go  |  312 ++
 .../v1/gonum/mathext/internal/cephes/incbi.go |  248 ++
 .../gonum/mathext/internal/cephes/lanczos.go  |  153 +
 .../v1/gonum/mathext/internal/cephes/ndtri.go |  150 +
 .../gonum/mathext/internal/cephes/polevl.go   |   82 +
 .../v1/gonum/mathext/internal/cephes/unity.go |  170 +
 .../v1/gonum/mathext/internal/cephes/zeta.go  |  110 +
 .../v1/gonum/mathext/internal/gonum/beta.go   |   52 +
 .../v1/gonum/mathext/internal/gonum/doc.go    |    7 +
 .../v1/gonum/mathext/internal/gonum/gonum.go  |    5 +
 vendor/gonum.org/v1/gonum/mathext/mvgamma.go  |   32 +
 .../v1/gonum/mathext/mvgamma_test.go          |   27 +
 vendor/gonum.org/v1/gonum/mathext/roots.go    |  178 +
 vendor/gonum.org/v1/gonum/mathext/zeta.go     |   20 +
 .../gonum.org/v1/gonum/mathext/zeta_test.go   |   42 +
 vendor/gonum.org/v1/gonum/optimize/README.md  |    3 +
 .../v1/gonum/optimize/backtracking.go         |   82 +
 vendor/gonum.org/v1/gonum/optimize/bfgs.go    |  160 +
 .../gonum.org/v1/gonum/optimize/bisection.go  |  146 +
 vendor/gonum.org/v1/gonum/optimize/cg.go      |  313 ++
 .../v1/gonum/optimize/convex/lp/convert.go    |  137 +
 .../v1/gonum/optimize/convex/lp/doc.go        |    6 +
 .../v1/gonum/optimize/convex/lp/simplex.go    |  619 ++++
 .../gonum/optimize/convex/lp/simplex_test.go  |  269 ++
 .../optimize/convex/lp/simplexexample_test.go |   29 +
 vendor/gonum.org/v1/gonum/optimize/doc.go     |    6 +
 vendor/gonum.org/v1/gonum/optimize/errors.go  |   72 +
 .../v1/gonum/optimize/functionconvergence.go  |   40 +
 .../v1/gonum/optimize/functions/doc.go        |   15 +
 .../v1/gonum/optimize/functions/functions.go  | 1818 ++++++++++
 .../optimize/functions/functions_test.go      |  326 ++
 .../v1/gonum/optimize/functions/minsurf.go    |  252 ++
 .../gonum/optimize/functions/minsurf_test.go  |   48 +
 .../v1/gonum/optimize/functions/validate.go   |  127 +
 .../v1/gonum/optimize/functions/vlse.go       |  325 ++
 vendor/gonum.org/v1/gonum/optimize/global.go  |  239 ++
 .../v1/gonum/optimize/gradientdescent.go      |   63 +
 .../v1/gonum/optimize/guessandcheck.go        |   60 +
 .../v1/gonum/optimize/guessandcheck_test.go   |   34 +
 .../gonum.org/v1/gonum/optimize/interfaces.go |  130 +
 vendor/gonum.org/v1/gonum/optimize/lbfgs.go   |  167 +
 .../gonum.org/v1/gonum/optimize/linesearch.go |  218 ++
 .../v1/gonum/optimize/linesearcher_test.go    |  136 +
 vendor/gonum.org/v1/gonum/optimize/local.go   |  225 ++
 .../v1/gonum/optimize/local_example_test.go   |   43 +
 .../gonum.org/v1/gonum/optimize/minimize.go   |  202 ++
 .../v1/gonum/optimize/morethuente.go          |  385 ++
 .../gonum.org/v1/gonum/optimize/neldermead.go |  314 ++
 vendor/gonum.org/v1/gonum/optimize/newton.go  |  147 +
 vendor/gonum.org/v1/gonum/optimize/printer.go |  106 +
 .../gonum.org/v1/gonum/optimize/stepsizers.go |  185 +
 .../v1/gonum/optimize/termination.go          |  119 +
 vendor/gonum.org/v1/gonum/optimize/types.go   |  262 ++
 .../v1/gonum/optimize/unconstrained_test.go   | 1305 +++++++
 .../gonum.org/v1/gonum/stat/appengine_test.go |    9 +
 .../v1/gonum/stat/boston_data_test.go         |  531 +++
 .../gonum.org/v1/gonum/stat/car_data_test.go  |  406 +++
 .../v1/gonum/stat/cca_example_test.go         |  165 +
 vendor/gonum.org/v1/gonum/stat/cca_test.go    |  191 +
 .../gonum.org/v1/gonum/stat/combin/combin.go  |  181 +
 .../v1/gonum/stat/combin/combin_test.go       |  181 +
 vendor/gonum.org/v1/gonum/stat/combin/doc.go  |    7 +
 vendor/gonum.org/v1/gonum/stat/distmat/doc.go |    6 +
 .../v1/gonum/stat/distmat/general.go          |    7 +
 .../v1/gonum/stat/distmat/wishart.go          |  209 ++
 .../v1/gonum/stat/distmat/wishart_test.go     |  129 +
 .../v1/gonum/stat/distmv/dirichlet.go         |  144 +
 .../v1/gonum/stat/distmv/dirichlet_test.go    |   67 +
 vendor/gonum.org/v1/gonum/stat/distmv/doc.go  |    6 +
 .../gonum.org/v1/gonum/stat/distmv/general.go |   30 +
 .../v1/gonum/stat/distmv/general_test.go      |   96 +
 .../v1/gonum/stat/distmv/interfaces.go        |   33 +
 .../gonum.org/v1/gonum/stat/distmv/normal.go  |  345 ++
 .../v1/gonum/stat/distmv/normal_test.go       |  573 +++
 .../v1/gonum/stat/distmv/normalbench_test.go  |   73 +
 .../v1/gonum/stat/distmv/statdist.go          |  320 ++
 .../v1/gonum/stat/distmv/statdist_test.go     |  329 ++
 .../v1/gonum/stat/distmv/studentst.go         |  354 ++
 .../v1/gonum/stat/distmv/studentst_test.go    |  265 ++
 .../gonum.org/v1/gonum/stat/distmv/uniform.go |  196 ++
 .../v1/gonum/stat/distmv/uniform_test.go      |   31 +
 .../v1/gonum/stat/distuv/bernoulli.go         |  131 +
 .../v1/gonum/stat/distuv/bernoulli_test.go    |   23 +
 vendor/gonum.org/v1/gonum/stat/distuv/beta.go |  126 +
 .../v1/gonum/stat/distuv/beta_test.go         |   61 +
 .../v1/gonum/stat/distuv/categorical.go       |  184 +
 .../v1/gonum/stat/distuv/categorical_test.go  |  196 ++
 .../v1/gonum/stat/distuv/chisquared.go        |   99 +
 .../v1/gonum/stat/distuv/chisquared_test.go   |   78 +
 .../v1/gonum/stat/distuv/constants.go         |   24 +
 .../v1/gonum/stat/distuv/distribution_test.go |  293 ++
 vendor/gonum.org/v1/gonum/stat/distuv/doc.go  |    6 +
 .../v1/gonum/stat/distuv/exponential.go       |  259 ++
 .../v1/gonum/stat/distuv/exponential_test.go  |   71 +
 vendor/gonum.org/v1/gonum/stat/distuv/f.go    |  132 +
 .../gonum.org/v1/gonum/stat/distuv/f_test.go  |   89 +
 .../gonum.org/v1/gonum/stat/distuv/gamma.go   |  244 ++
 .../v1/gonum/stat/distuv/gamma_test.go        |   63 +
 .../gonum.org/v1/gonum/stat/distuv/general.go |   24 +
 .../v1/gonum/stat/distuv/general_test.go      |  204 ++
 .../v1/gonum/stat/distuv/interfaces.go        |   22 +
 .../gonum.org/v1/gonum/stat/distuv/laplace.go |  251 ++
 .../v1/gonum/stat/distuv/laplace_test.go      |   58 +
 .../v1/gonum/stat/distuv/lognormal.go         |  112 +
 .../v1/gonum/stat/distuv/lognormal_test.go    |   44 +
 vendor/gonum.org/v1/gonum/stat/distuv/norm.go |  254 ++
 .../v1/gonum/stat/distuv/norm_example_test.go |   35 +
 .../v1/gonum/stat/distuv/norm_test.go         |  171 +
 .../v1/gonum/stat/distuv/studentst.go         |  160 +
 .../v1/gonum/stat/distuv/studentst_test.go    |   83 +
 .../v1/gonum/stat/distuv/triangle.go          |  192 +
 .../v1/gonum/stat/distuv/triangle_test.go     |  101 +
 .../gonum.org/v1/gonum/stat/distuv/uniform.go |  158 +
 .../gonum.org/v1/gonum/stat/distuv/weibull.go |  247 ++
 .../v1/gonum/stat/distuv/weibull_test.go      |  209 ++
 .../gonum.org/v1/gonum/stat/faithful_test.go  |   81 +
 .../v1/gonum/stat/moments_bench_test.go       |  611 ++++
 .../v1/gonum/stat/pca_example_test.go         |   60 +
 vendor/gonum.org/v1/gonum/stat/pca_test.go    |  188 +
 .../v1/gonum/stat/roc_example_test.go         |   56 +
 vendor/gonum.org/v1/gonum/stat/roc_test.go    |  178 +
 .../gonum.org/v1/gonum/stat/samplemv/doc.go   |   11 +
 .../gonum/stat/samplemv/metropolishastings.go |  221 ++
 .../v1/gonum/stat/samplemv/sample_test.go     |  280 ++
 .../v1/gonum/stat/samplemv/samplemv.go        |  274 ++
 .../gonum.org/v1/gonum/stat/sampleuv/doc.go   |   11 +
 .../stat/sampleuv/example_burnin_test.go      |   39 +
 .../gonum/stat/sampleuv/example_rate_test.go  |   49 +
 .../v1/gonum/stat/sampleuv/sample.go          |  393 +++
 .../v1/gonum/stat/sampleuv/sample_test.go     |   99 +
 .../v1/gonum/stat/sampleuv/weighted.go        |  138 +
 .../v1/gonum/stat/sampleuv/weighted_test.go   |  267 ++
 .../gonum/stat/sampleuv/withoutreplacement.go |   59 +
 .../stat/sampleuv/withoutreplacement_test.go  |   65 +
 vendor/gonum.org/v1/gonum/stat/spatial/doc.go |    6 +
 .../v1/gonum/stat/spatial/spatial.go          |  162 +
 .../spatial/spatial_areal_example_test.go     |   74 +
 .../stat/spatial/spatial_example_test.go      |  142 +
 .../v1/gonum/stat/spatial/spatial_test.go     |  293 ++
 vendor/gonum.org/v1/gonum/stat/stat_test.go   | 1569 +++++++++
 .../gonum.org/v1/gonum/stat/statmat_test.go   |  463 +++
 vendor/gonum.org/v1/gonum/unit/autogen.go     |  363 ++
 vendor/gonum.org/v1/gonum/unit/consts.go      |   29 +
 vendor/gonum.org/v1/gonum/unit/dimless.go     |   66 +
 vendor/gonum.org/v1/gonum/unit/doc.go         |   83 +
 vendor/gonum.org/v1/gonum/unit/length.go      |   90 +
 vendor/gonum.org/v1/gonum/unit/mass.go        |   90 +
 vendor/gonum.org/v1/gonum/unit/time.go        |   93 +
 vendor/gonum.org/v1/gonum/unit/unit_test.go   |  352 ++
 .../v1/gonum/unit/unitexample_test.go         |   29 +
 vendor/gonum.org/v1/gonum/unit/unittype.go    |  342 ++
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diff --git a/vendor/gonum.org/v1/gonum/LICENSE b/vendor/gonum.org/v1/gonum/LICENSE
deleted file mode 100644
index 76edf5ef..00000000
--- a/vendor/gonum.org/v1/gonum/LICENSE
+++ /dev/null
@@ -1,23 +0,0 @@
-Copyright ©2013 The gonum Authors. All rights reserved.
-
-Redistribution and use in source and binary forms, with or without
-modification, are permitted provided that the following conditions are met:
-    * Redistributions of source code must retain the above copyright
-      notice, this list of conditions and the following disclaimer.
-    * Redistributions in binary form must reproduce the above copyright
-      notice, this list of conditions and the following disclaimer in the
-      documentation and/or other materials provided with the distribution.
-    * Neither the name of the gonum project nor the names of its authors and
-      contributors may be used to endorse or promote products derived from this
-      software without specific prior written permission.
-
-THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
-ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
-WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
-DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
-FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
-DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
-SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
-CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
-OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
-OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
\ No newline at end of file
diff --git a/vendor/gonum.org/v1/gonum/blas/README.md b/vendor/gonum.org/v1/gonum/blas/README.md
new file mode 100644
index 00000000..8d0af75f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/README.md
@@ -0,0 +1,79 @@
+# Gonum BLAS [![GoDoc](https://godoc.org/gonum.org/v1/gonum/blas?status.svg)](https://godoc.org/gonum.org/v1/gonum/blas)
+
+A collection of packages to provide BLAS functionality for the [Go programming
+language](http://golang.org)
+
+## Installation
+```sh
+  go get gonum.org/v1/gonum/blas/...
+```
+
+### BLAS C-bindings
+
+If you want to use OpenBLAS, install it in any directory:
+```sh
+  git clone https://github.com/xianyi/OpenBLAS
+  cd OpenBLAS
+  make
+```
+
+The blas/cgo package provides bindings to C-backed BLAS packages. blas/cgo needs the `CGO_LDFLAGS`
+environment variable to point to the blas installation. More information can be found in the
+[cgo command documentation](http://golang.org/cmd/cgo/).
+
+Then install the blas/cgo package:
+```sh
+  CGO_LDFLAGS="-L/path/to/OpenBLAS -lopenblas" go install gonum.org/v1/netlib/blas
+```
+
+For Windows you can download binary packages for OpenBLAS at
+[SourceForge](http://sourceforge.net/projects/openblas/files/).
+
+If you want to use a different BLAS package such as the Intel MKL you can
+adjust the `CGO_LDFLAGS` variable:
+```sh
+  CGO_LDFLAGS="-lmkl_rt" go install gonum.org/v1/netlib/blas
+```
+
+On OS X the easiest solution is to use the libraries provided by the system:
+```sh
+  CGO_LDFLAGS="-framework Accelerate" go install gonum.org/v1/netlib/blas
+```
+
+## Packages
+
+### blas
+
+Defines [BLAS API](http://www.netlib.org/blas/blast-forum/cinterface.pdf) split in several
+interfaces.
+
+### blas/gonum
+
+Go implementation of the BLAS API (incomplete, implements the `float32` and `float64` API).
+
+### blas/blas64 and blas/blas32
+
+Wrappers for an implementation of the double (i.e., `float64`) and single (`float32`)
+precision real parts of the BLAS API.
+
+```Go
+package main
+
+import (
+	"fmt"
+
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+func main() {
+	v := blas64.Vector{Inc: 1, Data: []float64{1, 1, 1}}
+	fmt.Println("v has length:", blas64.Nrm2(len(v.Data), v))
+}
+```
+
+### blas/cblas128 and blas/cblas64
+
+Wrappers for an implementation of the double (i.e., `complex128`) and single (`complex64`) 
+precision complex parts of the blas API.
+
+Currently blas/cblas64 and blas/cblas128 require gonum.org/v1/netlib/blas.
diff --git a/vendor/gonum.org/v1/gonum/blas/blas.go b/vendor/gonum.org/v1/gonum/blas/blas.go
new file mode 100644
index 00000000..3fda4ff8
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/blas.go
@@ -0,0 +1,287 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//go:generate ./conversions.bash
+
+package blas
+
+// Flag constants indicate Givens transformation H matrix state.
+type Flag int
+
+const (
+	Identity    Flag = iota - 2 // H is the identity matrix; no rotation is needed.
+	Rescaling                   // H specifies rescaling.
+	OffDiagonal                 // Off-diagonal elements of H are units.
+	Diagonal                    // Diagonal elements of H are units.
+)
+
+// SrotmParams contains Givens transformation parameters returned
+// by the Float32 Srotm method.
+type SrotmParams struct {
+	Flag
+	H [4]float32 // Column-major 2 by 2 matrix.
+}
+
+// DrotmParams contains Givens transformation parameters returned
+// by the Float64 Drotm method.
+type DrotmParams struct {
+	Flag
+	H [4]float64 // Column-major 2 by 2 matrix.
+}
+
+// Transpose is used to specify the transposition operation for a
+// routine.
+type Transpose int
+
+const (
+	NoTrans Transpose = 111 + iota
+	Trans
+	ConjTrans
+)
+
+// Uplo is used to specify whether the matrix is an upper or lower
+// triangular matrix.
+type Uplo int
+
+const (
+	All Uplo = 120 + iota
+	Upper
+	Lower
+)
+
+// Diag is used to specify whether the matrix is a unit or non-unit
+// triangular matrix.
+type Diag int
+
+const (
+	NonUnit Diag = 131 + iota
+	Unit
+)
+
+// Side is used to specify from which side a multiplication operation
+// is performed.
+type Side int
+
+const (
+	Left Side = 141 + iota
+	Right
+)
+
+// Float32 implements the single precision real BLAS routines.
+type Float32 interface {
+	Float32Level1
+	Float32Level2
+	Float32Level3
+}
+
+// Float32Level1 implements the single precision real BLAS Level 1 routines.
+type Float32Level1 interface {
+	Sdsdot(n int, alpha float32, x []float32, incX int, y []float32, incY int) float32
+	Dsdot(n int, x []float32, incX int, y []float32, incY int) float64
+	Sdot(n int, x []float32, incX int, y []float32, incY int) float32
+	Snrm2(n int, x []float32, incX int) float32
+	Sasum(n int, x []float32, incX int) float32
+	Isamax(n int, x []float32, incX int) int
+	Sswap(n int, x []float32, incX int, y []float32, incY int)
+	Scopy(n int, x []float32, incX int, y []float32, incY int)
+	Saxpy(n int, alpha float32, x []float32, incX int, y []float32, incY int)
+	Srotg(a, b float32) (c, s, r, z float32)
+	Srotmg(d1, d2, b1, b2 float32) (p SrotmParams, rd1, rd2, rb1 float32)
+	Srot(n int, x []float32, incX int, y []float32, incY int, c, s float32)
+	Srotm(n int, x []float32, incX int, y []float32, incY int, p SrotmParams)
+	Sscal(n int, alpha float32, x []float32, incX int)
+}
+
+// Float32Level2 implements the single precision real BLAS Level 2 routines.
+type Float32Level2 interface {
+	Sgemv(tA Transpose, m, n int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int)
+	Sgbmv(tA Transpose, m, n, kL, kU int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int)
+	Strmv(ul Uplo, tA Transpose, d Diag, n int, a []float32, lda int, x []float32, incX int)
+	Stbmv(ul Uplo, tA Transpose, d Diag, n, k int, a []float32, lda int, x []float32, incX int)
+	Stpmv(ul Uplo, tA Transpose, d Diag, n int, ap []float32, x []float32, incX int)
+	Strsv(ul Uplo, tA Transpose, d Diag, n int, a []float32, lda int, x []float32, incX int)
+	Stbsv(ul Uplo, tA Transpose, d Diag, n, k int, a []float32, lda int, x []float32, incX int)
+	Stpsv(ul Uplo, tA Transpose, d Diag, n int, ap []float32, x []float32, incX int)
+	Ssymv(ul Uplo, n int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int)
+	Ssbmv(ul Uplo, n, k int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int)
+	Sspmv(ul Uplo, n int, alpha float32, ap []float32, x []float32, incX int, beta float32, y []float32, incY int)
+	Sger(m, n int, alpha float32, x []float32, incX int, y []float32, incY int, a []float32, lda int)
+	Ssyr(ul Uplo, n int, alpha float32, x []float32, incX int, a []float32, lda int)
+	Sspr(ul Uplo, n int, alpha float32, x []float32, incX int, ap []float32)
+	Ssyr2(ul Uplo, n int, alpha float32, x []float32, incX int, y []float32, incY int, a []float32, lda int)
+	Sspr2(ul Uplo, n int, alpha float32, x []float32, incX int, y []float32, incY int, a []float32)
+}
+
+// Float32Level3 implements the single precision real BLAS Level 3 routines.
+type Float32Level3 interface {
+	Sgemm(tA, tB Transpose, m, n, k int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int)
+	Ssymm(s Side, ul Uplo, m, n int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int)
+	Ssyrk(ul Uplo, t Transpose, n, k int, alpha float32, a []float32, lda int, beta float32, c []float32, ldc int)
+	Ssyr2k(ul Uplo, t Transpose, n, k int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int)
+	Strmm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha float32, a []float32, lda int, b []float32, ldb int)
+	Strsm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha float32, a []float32, lda int, b []float32, ldb int)
+}
+
+// Float64 implements the single precision real BLAS routines.
+type Float64 interface {
+	Float64Level1
+	Float64Level2
+	Float64Level3
+}
+
+// Float64Level1 implements the double precision real BLAS Level 1 routines.
+type Float64Level1 interface {
+	Ddot(n int, x []float64, incX int, y []float64, incY int) float64
+	Dnrm2(n int, x []float64, incX int) float64
+	Dasum(n int, x []float64, incX int) float64
+	Idamax(n int, x []float64, incX int) int
+	Dswap(n int, x []float64, incX int, y []float64, incY int)
+	Dcopy(n int, x []float64, incX int, y []float64, incY int)
+	Daxpy(n int, alpha float64, x []float64, incX int, y []float64, incY int)
+	Drotg(a, b float64) (c, s, r, z float64)
+	Drotmg(d1, d2, b1, b2 float64) (p DrotmParams, rd1, rd2, rb1 float64)
+	Drot(n int, x []float64, incX int, y []float64, incY int, c float64, s float64)
+	Drotm(n int, x []float64, incX int, y []float64, incY int, p DrotmParams)
+	Dscal(n int, alpha float64, x []float64, incX int)
+}
+
+// Float64Level2 implements the double precision real BLAS Level 2 routines.
+type Float64Level2 interface {
+	Dgemv(tA Transpose, m, n int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int)
+	Dgbmv(tA Transpose, m, n, kL, kU int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int)
+	Dtrmv(ul Uplo, tA Transpose, d Diag, n int, a []float64, lda int, x []float64, incX int)
+	Dtbmv(ul Uplo, tA Transpose, d Diag, n, k int, a []float64, lda int, x []float64, incX int)
+	Dtpmv(ul Uplo, tA Transpose, d Diag, n int, ap []float64, x []float64, incX int)
+	Dtrsv(ul Uplo, tA Transpose, d Diag, n int, a []float64, lda int, x []float64, incX int)
+	Dtbsv(ul Uplo, tA Transpose, d Diag, n, k int, a []float64, lda int, x []float64, incX int)
+	Dtpsv(ul Uplo, tA Transpose, d Diag, n int, ap []float64, x []float64, incX int)
+	Dsymv(ul Uplo, n int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int)
+	Dsbmv(ul Uplo, n, k int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int)
+	Dspmv(ul Uplo, n int, alpha float64, ap []float64, x []float64, incX int, beta float64, y []float64, incY int)
+	Dger(m, n int, alpha float64, x []float64, incX int, y []float64, incY int, a []float64, lda int)
+	Dsyr(ul Uplo, n int, alpha float64, x []float64, incX int, a []float64, lda int)
+	Dspr(ul Uplo, n int, alpha float64, x []float64, incX int, ap []float64)
+	Dsyr2(ul Uplo, n int, alpha float64, x []float64, incX int, y []float64, incY int, a []float64, lda int)
+	Dspr2(ul Uplo, n int, alpha float64, x []float64, incX int, y []float64, incY int, a []float64)
+}
+
+// Float64Level3 implements the double precision real BLAS Level 3 routines.
+type Float64Level3 interface {
+	Dgemm(tA, tB Transpose, m, n, k int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int)
+	Dsymm(s Side, ul Uplo, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int)
+	Dsyrk(ul Uplo, t Transpose, n, k int, alpha float64, a []float64, lda int, beta float64, c []float64, ldc int)
+	Dsyr2k(ul Uplo, t Transpose, n, k int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int)
+	Dtrmm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int)
+	Dtrsm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int)
+}
+
+// Complex64 implements the single precision complex BLAS routines.
+type Complex64 interface {
+	Complex64Level1
+	Complex64Level2
+	Complex64Level3
+}
+
+// Complex64Level1 implements the single precision complex BLAS Level 1 routines.
+type Complex64Level1 interface {
+	Cdotu(n int, x []complex64, incX int, y []complex64, incY int) (dotu complex64)
+	Cdotc(n int, x []complex64, incX int, y []complex64, incY int) (dotc complex64)
+	Scnrm2(n int, x []complex64, incX int) float32
+	Scasum(n int, x []complex64, incX int) float32
+	Icamax(n int, x []complex64, incX int) int
+	Cswap(n int, x []complex64, incX int, y []complex64, incY int)
+	Ccopy(n int, x []complex64, incX int, y []complex64, incY int)
+	Caxpy(n int, alpha complex64, x []complex64, incX int, y []complex64, incY int)
+	Cscal(n int, alpha complex64, x []complex64, incX int)
+	Csscal(n int, alpha float32, x []complex64, incX int)
+}
+
+// Complex64Level2 implements the single precision complex BLAS routines Level 2 routines.
+type Complex64Level2 interface {
+	Cgemv(tA Transpose, m, n int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int)
+	Cgbmv(tA Transpose, m, n, kL, kU int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int)
+	Ctrmv(ul Uplo, tA Transpose, d Diag, n int, a []complex64, lda int, x []complex64, incX int)
+	Ctbmv(ul Uplo, tA Transpose, d Diag, n, k int, a []complex64, lda int, x []complex64, incX int)
+	Ctpmv(ul Uplo, tA Transpose, d Diag, n int, ap []complex64, x []complex64, incX int)
+	Ctrsv(ul Uplo, tA Transpose, d Diag, n int, a []complex64, lda int, x []complex64, incX int)
+	Ctbsv(ul Uplo, tA Transpose, d Diag, n, k int, a []complex64, lda int, x []complex64, incX int)
+	Ctpsv(ul Uplo, tA Transpose, d Diag, n int, ap []complex64, x []complex64, incX int)
+	Chemv(ul Uplo, n int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int)
+	Chbmv(ul Uplo, n, k int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int)
+	Chpmv(ul Uplo, n int, alpha complex64, ap []complex64, x []complex64, incX int, beta complex64, y []complex64, incY int)
+	Cgeru(m, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, a []complex64, lda int)
+	Cgerc(m, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, a []complex64, lda int)
+	Cher(ul Uplo, n int, alpha float32, x []complex64, incX int, a []complex64, lda int)
+	Chpr(ul Uplo, n int, alpha float32, x []complex64, incX int, a []complex64)
+	Cher2(ul Uplo, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, a []complex64, lda int)
+	Chpr2(ul Uplo, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, ap []complex64)
+}
+
+// Complex64Level3 implements the single precision complex BLAS Level 3 routines.
+type Complex64Level3 interface {
+	Cgemm(tA, tB Transpose, m, n, k int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int)
+	Csymm(s Side, ul Uplo, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int)
+	Csyrk(ul Uplo, t Transpose, n, k int, alpha complex64, a []complex64, lda int, beta complex64, c []complex64, ldc int)
+	Csyr2k(ul Uplo, t Transpose, n, k int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int)
+	Ctrmm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int)
+	Ctrsm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int)
+	Chemm(s Side, ul Uplo, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int)
+	Cherk(ul Uplo, t Transpose, n, k int, alpha float32, a []complex64, lda int, beta float32, c []complex64, ldc int)
+	Cher2k(ul Uplo, t Transpose, n, k int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta float32, c []complex64, ldc int)
+}
+
+// Complex128 implements the double precision complex BLAS routines.
+type Complex128 interface {
+	Complex128Level1
+	Complex128Level2
+	Complex128Level3
+}
+
+// Complex128Level1 implements the double precision complex BLAS Level 1 routines.
+type Complex128Level1 interface {
+	Zdotu(n int, x []complex128, incX int, y []complex128, incY int) (dotu complex128)
+	Zdotc(n int, x []complex128, incX int, y []complex128, incY int) (dotc complex128)
+	Dznrm2(n int, x []complex128, incX int) float64
+	Dzasum(n int, x []complex128, incX int) float64
+	Izamax(n int, x []complex128, incX int) int
+	Zswap(n int, x []complex128, incX int, y []complex128, incY int)
+	Zcopy(n int, x []complex128, incX int, y []complex128, incY int)
+	Zaxpy(n int, alpha complex128, x []complex128, incX int, y []complex128, incY int)
+	Zscal(n int, alpha complex128, x []complex128, incX int)
+	Zdscal(n int, alpha float64, x []complex128, incX int)
+}
+
+// Complex128Level2 implements the double precision complex BLAS Level 2 routines.
+type Complex128Level2 interface {
+	Zgemv(tA Transpose, m, n int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int)
+	Zgbmv(tA Transpose, m, n int, kL int, kU int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int)
+	Ztrmv(ul Uplo, tA Transpose, d Diag, n int, a []complex128, lda int, x []complex128, incX int)
+	Ztbmv(ul Uplo, tA Transpose, d Diag, n, k int, a []complex128, lda int, x []complex128, incX int)
+	Ztpmv(ul Uplo, tA Transpose, d Diag, n int, ap []complex128, x []complex128, incX int)
+	Ztrsv(ul Uplo, tA Transpose, d Diag, n int, a []complex128, lda int, x []complex128, incX int)
+	Ztbsv(ul Uplo, tA Transpose, d Diag, n, k int, a []complex128, lda int, x []complex128, incX int)
+	Ztpsv(ul Uplo, tA Transpose, d Diag, n int, ap []complex128, x []complex128, incX int)
+	Zhemv(ul Uplo, n int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int)
+	Zhbmv(ul Uplo, n, k int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int)
+	Zhpmv(ul Uplo, n int, alpha complex128, ap []complex128, x []complex128, incX int, beta complex128, y []complex128, incY int)
+	Zgeru(m, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, a []complex128, lda int)
+	Zgerc(m, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, a []complex128, lda int)
+	Zher(ul Uplo, n int, alpha float64, x []complex128, incX int, a []complex128, lda int)
+	Zhpr(ul Uplo, n int, alpha float64, x []complex128, incX int, a []complex128)
+	Zher2(ul Uplo, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, a []complex128, lda int)
+	Zhpr2(ul Uplo, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, ap []complex128)
+}
+
+// Complex128Level3 implements the double precision complex BLAS Level 3 routines.
+type Complex128Level3 interface {
+	Zgemm(tA, tB Transpose, m, n, k int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int)
+	Zsymm(s Side, ul Uplo, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int)
+	Zsyrk(ul Uplo, t Transpose, n, k int, alpha complex128, a []complex128, lda int, beta complex128, c []complex128, ldc int)
+	Zsyr2k(ul Uplo, t Transpose, n, k int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int)
+	Ztrmm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int)
+	Ztrsm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int)
+	Zhemm(s Side, ul Uplo, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int)
+	Zherk(ul Uplo, t Transpose, n, k int, alpha float64, a []complex128, lda int, beta float64, c []complex128, ldc int)
+	Zher2k(ul Uplo, t Transpose, n, k int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta float64, c []complex128, ldc int)
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/blas32/blas32.go b/vendor/gonum.org/v1/gonum/blas/blas32/blas32.go
new file mode 100644
index 00000000..fe5a144e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/blas32/blas32.go
@@ -0,0 +1,457 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package blas32
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/gonum"
+)
+
+var blas32 blas.Float32 = gonum.Implementation{}
+
+// Use sets the BLAS float32 implementation to be used by subsequent BLAS calls.
+// The default implementation is native.Implementation.
+func Use(b blas.Float32) {
+	blas32 = b
+}
+
+// Implementation returns the current BLAS float32 implementation.
+//
+// Implementation allows direct calls to the current the BLAS float32 implementation
+// giving finer control of parameters.
+func Implementation() blas.Float32 {
+	return blas32
+}
+
+// Vector represents a vector with an associated element increment.
+type Vector struct {
+	Inc  int
+	Data []float32
+}
+
+// General represents a matrix using the conventional storage scheme.
+type General struct {
+	Rows, Cols int
+	Stride     int
+	Data       []float32
+}
+
+// Band represents a band matrix using the band storage scheme.
+type Band struct {
+	Rows, Cols int
+	KL, KU     int
+	Stride     int
+	Data       []float32
+}
+
+// Triangular represents a triangular matrix using the conventional storage scheme.
+type Triangular struct {
+	N      int
+	Stride int
+	Data   []float32
+	Uplo   blas.Uplo
+	Diag   blas.Diag
+}
+
+// TriangularBand represents a triangular matrix using the band storage scheme.
+type TriangularBand struct {
+	N, K   int
+	Stride int
+	Data   []float32
+	Uplo   blas.Uplo
+	Diag   blas.Diag
+}
+
+// TriangularPacked represents a triangular matrix using the packed storage scheme.
+type TriangularPacked struct {
+	N    int
+	Data []float32
+	Uplo blas.Uplo
+	Diag blas.Diag
+}
+
+// Symmetric represents a symmetric matrix using the conventional storage scheme.
+type Symmetric struct {
+	N      int
+	Stride int
+	Data   []float32
+	Uplo   blas.Uplo
+}
+
+// SymmetricBand represents a symmetric matrix using the band storage scheme.
+type SymmetricBand struct {
+	N, K   int
+	Stride int
+	Data   []float32
+	Uplo   blas.Uplo
+}
+
+// SymmetricPacked represents a symmetric matrix using the packed storage scheme.
+type SymmetricPacked struct {
+	N    int
+	Data []float32
+	Uplo blas.Uplo
+}
+
+// Level 1
+
+const negInc = "blas32: negative vector increment"
+
+// Dot computes the dot product of the two vectors:
+//  \sum_i x[i]*y[i].
+func Dot(n int, x, y Vector) float32 {
+	return blas32.Sdot(n, x.Data, x.Inc, y.Data, y.Inc)
+}
+
+// DDot computes the dot product of the two vectors:
+//  \sum_i x[i]*y[i].
+func DDot(n int, x, y Vector) float64 {
+	return blas32.Dsdot(n, x.Data, x.Inc, y.Data, y.Inc)
+}
+
+// SDDot computes the dot product of the two vectors adding a constant:
+//  alpha + \sum_i x[i]*y[i].
+func SDDot(n int, alpha float32, x, y Vector) float32 {
+	return blas32.Sdsdot(n, alpha, x.Data, x.Inc, y.Data, y.Inc)
+}
+
+// Nrm2 computes the Euclidean norm of the vector x:
+//  sqrt(\sum_i x[i]*x[i]).
+//
+// Nrm2 will panic if the vector increment is negative.
+func Nrm2(n int, x Vector) float32 {
+	if x.Inc < 0 {
+		panic(negInc)
+	}
+	return blas32.Snrm2(n, x.Data, x.Inc)
+}
+
+// Asum computes the sum of the absolute values of the elements of x:
+//  \sum_i |x[i]|.
+//
+// Asum will panic if the vector increment is negative.
+func Asum(n int, x Vector) float32 {
+	if x.Inc < 0 {
+		panic(negInc)
+	}
+	return blas32.Sasum(n, x.Data, x.Inc)
+}
+
+// Iamax returns the index of an element of x with the largest absolute value.
+// If there are multiple such indices the earliest is returned.
+// Iamax returns -1 if n == 0.
+//
+// Iamax will panic if the vector increment is negative.
+func Iamax(n int, x Vector) int {
+	if x.Inc < 0 {
+		panic(negInc)
+	}
+	return blas32.Isamax(n, x.Data, x.Inc)
+}
+
+// Swap exchanges the elements of the two vectors:
+//  x[i], y[i] = y[i], x[i] for all i.
+func Swap(n int, x, y Vector) {
+	blas32.Sswap(n, x.Data, x.Inc, y.Data, y.Inc)
+}
+
+// Copy copies the elements of x into the elements of y:
+//  y[i] = x[i] for all i.
+func Copy(n int, x, y Vector) {
+	blas32.Scopy(n, x.Data, x.Inc, y.Data, y.Inc)
+}
+
+// Axpy adds x scaled by alpha to y:
+//  y[i] += alpha*x[i] for all i.
+func Axpy(n int, alpha float32, x, y Vector) {
+	blas32.Saxpy(n, alpha, x.Data, x.Inc, y.Data, y.Inc)
+}
+
+// Rotg computes the parameters of a Givens plane rotation so that
+//  ⎡ c s⎤   ⎡a⎤   ⎡r⎤
+//  ⎣-s c⎦ * ⎣b⎦ = ⎣0⎦
+// where a and b are the Cartesian coordinates of a given point.
+// c, s, and r are defined as
+//  r = ±Sqrt(a^2 + b^2),
+//  c = a/r, the cosine of the rotation angle,
+//  s = a/r, the sine of the rotation angle,
+// and z is defined such that
+//  if |a| > |b|,        z = s,
+//  otherwise if c != 0, z = 1/c,
+//  otherwise            z = 1.
+func Rotg(a, b float32) (c, s, r, z float32) {
+	return blas32.Srotg(a, b)
+}
+
+// Rotmg computes the modified Givens rotation. See
+// http://www.netlib.org/lapack/explore-html/df/deb/drotmg_8f.html
+// for more details.
+func Rotmg(d1, d2, b1, b2 float32) (p blas.SrotmParams, rd1, rd2, rb1 float32) {
+	return blas32.Srotmg(d1, d2, b1, b2)
+}
+
+// Rot applies a plane transformation to n points represented by the vectors x
+// and y:
+//  x[i] =  c*x[i] + s*y[i],
+//  y[i] = -s*x[i] + c*y[i], for all i.
+func Rot(n int, x, y Vector, c, s float32) {
+	blas32.Srot(n, x.Data, x.Inc, y.Data, y.Inc, c, s)
+}
+
+// Rotm applies the modified Givens rotation to n points represented by the
+// vectors x and y.
+func Rotm(n int, x, y Vector, p blas.SrotmParams) {
+	blas32.Srotm(n, x.Data, x.Inc, y.Data, y.Inc, p)
+}
+
+// Scal scales the vector x by alpha:
+//  x[i] *= alpha for all i.
+//
+// Scal will panic if the vector increment is negative.
+func Scal(n int, alpha float32, x Vector) {
+	if x.Inc < 0 {
+		panic(negInc)
+	}
+	blas32.Sscal(n, alpha, x.Data, x.Inc)
+}
+
+// Level 2
+
+// Gemv computes
+//  y = alpha * A * x + beta * y,   if t == blas.NoTrans,
+//  y = alpha * A^T * x + beta * y, if t == blas.Trans or blas.ConjTrans,
+// where A is an m×n dense matrix, x and y are vectors, and alpha and beta are scalars.
+func Gemv(t blas.Transpose, alpha float32, a General, x Vector, beta float32, y Vector) {
+	blas32.Sgemv(t, a.Rows, a.Cols, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
+}
+
+// Gbmv computes
+//  y = alpha * A * x + beta * y,   if t == blas.NoTrans,
+//  y = alpha * A^T * x + beta * y, if t == blas.Trans or blas.ConjTrans,
+// where A is an m×n band matrix, x and y are vectors, and alpha and beta are scalars.
+func Gbmv(t blas.Transpose, alpha float32, a Band, x Vector, beta float32, y Vector) {
+	blas32.Sgbmv(t, a.Rows, a.Cols, a.KL, a.KU, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
+}
+
+// Trmv computes
+//  x = A * x,   if t == blas.NoTrans,
+//  x = A^T * x, if t == blas.Trans or blas.ConjTrans,
+// where A is an n×n triangular matrix, and x is a vector.
+func Trmv(t blas.Transpose, a Triangular, x Vector) {
+	blas32.Strmv(a.Uplo, t, a.Diag, a.N, a.Data, a.Stride, x.Data, x.Inc)
+}
+
+// Tbmv computes
+//  x = A * x,   if t == blas.NoTrans,
+//  x = A^T * x, if t == blas.Trans or blas.ConjTrans,
+// where A is an n×n triangular band matrix, and x is a vector.
+func Tbmv(t blas.Transpose, a TriangularBand, x Vector) {
+	blas32.Stbmv(a.Uplo, t, a.Diag, a.N, a.K, a.Data, a.Stride, x.Data, x.Inc)
+}
+
+// Tpmv computes
+//  x = A * x,   if t == blas.NoTrans,
+//  x = A^T * x, if t == blas.Trans or blas.ConjTrans,
+// where A is an n×n triangular matrix in packed format, and x is a vector.
+func Tpmv(t blas.Transpose, a TriangularPacked, x Vector) {
+	blas32.Stpmv(a.Uplo, t, a.Diag, a.N, a.Data, x.Data, x.Inc)
+}
+
+// Trsv solves
+//  A * x = b,   if t == blas.NoTrans,
+//  A^T * x = b, if t == blas.Trans or blas.ConjTrans,
+// where A is an n×n triangular matrix, and x and b are vectors.
+//
+// At entry to the function, x contains the values of b, and the result is
+// stored in-place into x.
+//
+// No test for singularity or near-singularity is included in this
+// routine. Such tests must be performed before calling this routine.
+func Trsv(t blas.Transpose, a Triangular, x Vector) {
+	blas32.Strsv(a.Uplo, t, a.Diag, a.N, a.Data, a.Stride, x.Data, x.Inc)
+}
+
+// Tbsv solves
+//  A * x = b,   if t == blas.NoTrans,
+//  A^T * x = b, if t == blas.Trans or blas.ConjTrans,
+// where A is an n×n triangular band matrix, and x and b are vectors.
+//
+// At entry to the function, x contains the values of b, and the result is
+// stored in place into x.
+//
+// No test for singularity or near-singularity is included in this
+// routine. Such tests must be performed before calling this routine.
+func Tbsv(t blas.Transpose, a TriangularBand, x Vector) {
+	blas32.Stbsv(a.Uplo, t, a.Diag, a.N, a.K, a.Data, a.Stride, x.Data, x.Inc)
+}
+
+// Tpsv solves
+//  A * x = b,   if t == blas.NoTrans,
+//  A^T * x = b, if t == blas.Trans or blas.ConjTrans,
+// where A is an n×n triangular matrix in packed format, and x and b are
+// vectors.
+//
+// At entry to the function, x contains the values of b, and the result is
+// stored in place into x.
+//
+// No test for singularity or near-singularity is included in this
+// routine. Such tests must be performed before calling this routine.
+func Tpsv(t blas.Transpose, a TriangularPacked, x Vector) {
+	blas32.Stpsv(a.Uplo, t, a.Diag, a.N, a.Data, x.Data, x.Inc)
+}
+
+// Symv computes
+//    y = alpha * A * x + beta * y,
+// where A is an n×n symmetric matrix, x and y are vectors, and alpha and
+// beta are scalars.
+func Symv(alpha float32, a Symmetric, x Vector, beta float32, y Vector) {
+	blas32.Ssymv(a.Uplo, a.N, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
+}
+
+// Sbmv performs
+//  y = alpha * A * x + beta * y,
+// where A is an n×n symmetric band matrix, x and y are vectors, and alpha
+// and beta are scalars.
+func Sbmv(alpha float32, a SymmetricBand, x Vector, beta float32, y Vector) {
+	blas32.Ssbmv(a.Uplo, a.N, a.K, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
+}
+
+// Spmv performs
+//    y = alpha * A * x + beta * y,
+// where A is an n×n symmetric matrix in packed format, x and y are vectors,
+// and alpha and beta are scalars.
+func Spmv(alpha float32, a SymmetricPacked, x Vector, beta float32, y Vector) {
+	blas32.Sspmv(a.Uplo, a.N, alpha, a.Data, x.Data, x.Inc, beta, y.Data, y.Inc)
+}
+
+// Ger performs a rank-1 update
+//  A += alpha * x * y^T,
+// where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.
+func Ger(alpha float32, x, y Vector, a General) {
+	blas32.Sger(a.Rows, a.Cols, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
+}
+
+// Syr performs a rank-1 update
+//  A += alpha * x * x^T,
+// where A is an n×n symmetric matrix, x is a vector, and alpha is a scalar.
+func Syr(alpha float32, x Vector, a Symmetric) {
+	blas32.Ssyr(a.Uplo, a.N, alpha, x.Data, x.Inc, a.Data, a.Stride)
+}
+
+// Spr performs the rank-1 update
+//  A += alpha * x * x^T,
+// where A is an n×n symmetric matrix in packed format, x is a vector, and
+// alpha is a scalar.
+func Spr(alpha float32, x Vector, a SymmetricPacked) {
+	blas32.Sspr(a.Uplo, a.N, alpha, x.Data, x.Inc, a.Data)
+}
+
+// Syr2 performs a rank-2 update
+//  A += alpha * x * y^T + alpha * y * x^T,
+// where A is a symmetric n×n matrix, x and y are vectors, and alpha is a scalar.
+func Syr2(alpha float32, x, y Vector, a Symmetric) {
+	blas32.Ssyr2(a.Uplo, a.N, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
+}
+
+// Spr2 performs a rank-2 update
+//  A += alpha * x * y^T + alpha * y * x^T,
+// where A is an n×n symmetric matrix in packed format, x and y are vectors,
+// and alpha is a scalar.
+func Spr2(alpha float32, x, y Vector, a SymmetricPacked) {
+	blas32.Sspr2(a.Uplo, a.N, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data)
+}
+
+// Level 3
+
+// Gemm computes
+//  C = alpha * A * B + beta * C,
+// where A, B, and C are dense matrices, and alpha and beta are scalars.
+// tA and tB specify whether A or B are transposed.
+func Gemm(tA, tB blas.Transpose, alpha float32, a, b General, beta float32, c General) {
+	var m, n, k int
+	if tA == blas.NoTrans {
+		m, k = a.Rows, a.Cols
+	} else {
+		m, k = a.Cols, a.Rows
+	}
+	if tB == blas.NoTrans {
+		n = b.Cols
+	} else {
+		n = b.Rows
+	}
+	blas32.Sgemm(tA, tB, m, n, k, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
+}
+
+// Symm performs
+//  C = alpha * A * B + beta * C, if s == blas.Left,
+//  C = alpha * B * A + beta * C, if s == blas.Right,
+// where A is an n×n or m×m symmetric matrix, B and C are m×n matrices, and
+// alpha is a scalar.
+func Symm(s blas.Side, alpha float32, a Symmetric, b General, beta float32, c General) {
+	var m, n int
+	if s == blas.Left {
+		m, n = a.N, b.Cols
+	} else {
+		m, n = b.Rows, a.N
+	}
+	blas32.Ssymm(s, a.Uplo, m, n, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
+}
+
+// Syrk performs a symmetric rank-k update
+//  C = alpha * A * A^T + beta * C, if t == blas.NoTrans,
+//  C = alpha * A^T * A + beta * C, if t == blas.Trans or blas.ConjTrans,
+// where C is an n×n symmetric matrix, A is an n×k matrix if t == blas.NoTrans and
+// a k×n matrix otherwise, and alpha and beta are scalars.
+func Syrk(t blas.Transpose, alpha float32, a General, beta float32, c Symmetric) {
+	var n, k int
+	if t == blas.NoTrans {
+		n, k = a.Rows, a.Cols
+	} else {
+		n, k = a.Cols, a.Rows
+	}
+	blas32.Ssyrk(c.Uplo, t, n, k, alpha, a.Data, a.Stride, beta, c.Data, c.Stride)
+}
+
+// Syr2k performs a symmetric rank-2k update
+//  C = alpha * A * B^T + alpha * B * A^T + beta * C, if t == blas.NoTrans,
+//  C = alpha * A^T * B + alpha * B^T * A + beta * C, if t == blas.Trans or blas.ConjTrans,
+// where C is an n×n symmetric matrix, A and B are n×k matrices if t == NoTrans
+// and k×n matrices otherwise, and alpha and beta are scalars.
+func Syr2k(t blas.Transpose, alpha float32, a, b General, beta float32, c Symmetric) {
+	var n, k int
+	if t == blas.NoTrans {
+		n, k = a.Rows, a.Cols
+	} else {
+		n, k = a.Cols, a.Rows
+	}
+	blas32.Ssyr2k(c.Uplo, t, n, k, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
+}
+
+// Trmm performs
+//  B = alpha * A * B,   if tA == blas.NoTrans and s == blas.Left,
+//  B = alpha * A^T * B, if tA == blas.Trans or blas.ConjTrans, and s == blas.Left,
+//  B = alpha * B * A,   if tA == blas.NoTrans and s == blas.Right,
+//  B = alpha * B * A^T, if tA == blas.Trans or blas.ConjTrans, and s == blas.Right,
+// where A is an n×n or m×m triangular matrix, B is an m×n matrix, and alpha is
+// a scalar.
+func Trmm(s blas.Side, tA blas.Transpose, alpha float32, a Triangular, b General) {
+	blas32.Strmm(s, a.Uplo, tA, a.Diag, b.Rows, b.Cols, alpha, a.Data, a.Stride, b.Data, b.Stride)
+}
+
+// Trsm solves
+//  A * X = alpha * B,   if tA == blas.NoTrans and s == blas.Left,
+//  A^T * X = alpha * B, if tA == blas.Trans or blas.ConjTrans, and s == blas.Left,
+//  X * A = alpha * B,   if tA == blas.NoTrans and s == blas.Right,
+//  X * A^T = alpha * B, if tA == blas.Trans or blas.ConjTrans, and s == blas.Right,
+// where A is an n×n or m×m triangular matrix, X and B are m×n matrices, and
+// alpha is a scalar.
+//
+// At entry to the function, X contains the values of B, and the result is
+// stored in-place into X.
+//
+// No check is made that A is invertible.
+func Trsm(s blas.Side, tA blas.Transpose, alpha float32, a Triangular, b General) {
+	blas32.Strsm(s, a.Uplo, tA, a.Diag, b.Rows, b.Cols, alpha, a.Data, a.Stride, b.Data, b.Stride)
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/blas32/conv.go b/vendor/gonum.org/v1/gonum/blas/blas32/conv.go
new file mode 100644
index 00000000..24107906
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/blas32/conv.go
@@ -0,0 +1,279 @@
+// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.
+
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package blas32
+
+import "gonum.org/v1/gonum/blas"
+
+// GeneralCols represents a matrix using the conventional column-major storage scheme.
+type GeneralCols General
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions as a and have adequate backing
+// data storage.
+func (t GeneralCols) From(a General) {
+	if t.Rows != a.Rows || t.Cols != a.Cols {
+		panic("blas32: mismatched dimension")
+	}
+	if len(t.Data) < (t.Cols-1)*t.Stride+t.Rows {
+		panic("blas32: short data slice")
+	}
+	for i := 0; i < a.Rows; i++ {
+		for j, v := range a.Data[i*a.Stride : i*a.Stride+a.Cols] {
+			t.Data[i+j*t.Stride] = v
+		}
+	}
+}
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions as a and have adequate backing
+// data storage.
+func (t General) From(a GeneralCols) {
+	if t.Rows != a.Rows || t.Cols != a.Cols {
+		panic("blas32: mismatched dimension")
+	}
+	if len(t.Data) < (t.Rows-1)*t.Stride+t.Cols {
+		panic("blas32: short data slice")
+	}
+	for j := 0; j < a.Cols; j++ {
+		for i, v := range a.Data[j*a.Stride : j*a.Stride+a.Rows] {
+			t.Data[i*t.Stride+j] = v
+		}
+	}
+}
+
+// TriangularCols represents a matrix using the conventional column-major storage scheme.
+type TriangularCols Triangular
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions, uplo and diag as a and have
+// adequate backing data storage.
+func (t TriangularCols) From(a Triangular) {
+	if t.N != a.N {
+		panic("blas32: mismatched dimension")
+	}
+	if t.Uplo != a.Uplo {
+		panic("blas32: mismatched BLAS uplo")
+	}
+	if t.Diag != a.Diag {
+		panic("blas32: mismatched BLAS diag")
+	}
+	switch a.Uplo {
+	default:
+		panic("blas32: bad BLAS uplo")
+	case blas.Upper:
+		for i := 0; i < a.N; i++ {
+			for j := i; j < a.N; j++ {
+				t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
+			}
+		}
+	case blas.Lower:
+		for i := 0; i < a.N; i++ {
+			for j := 0; j <= i; j++ {
+				t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
+			}
+		}
+	case blas.All:
+		for i := 0; i < a.N; i++ {
+			for j := 0; j < a.N; j++ {
+				t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
+			}
+		}
+	}
+}
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions, uplo and diag as a and have
+// adequate backing data storage.
+func (t Triangular) From(a TriangularCols) {
+	if t.N != a.N {
+		panic("blas32: mismatched dimension")
+	}
+	if t.Uplo != a.Uplo {
+		panic("blas32: mismatched BLAS uplo")
+	}
+	if t.Diag != a.Diag {
+		panic("blas32: mismatched BLAS diag")
+	}
+	switch a.Uplo {
+	default:
+		panic("blas32: bad BLAS uplo")
+	case blas.Upper:
+		for i := 0; i < a.N; i++ {
+			for j := i; j < a.N; j++ {
+				t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
+			}
+		}
+	case blas.Lower:
+		for i := 0; i < a.N; i++ {
+			for j := 0; j <= i; j++ {
+				t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
+			}
+		}
+	case blas.All:
+		for i := 0; i < a.N; i++ {
+			for j := 0; j < a.N; j++ {
+				t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
+			}
+		}
+	}
+}
+
+// BandCols represents a matrix using the band column-major storage scheme.
+type BandCols Band
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions and bandwidth as a and have
+// adequate backing data storage.
+func (t BandCols) From(a Band) {
+	if t.Rows != a.Rows || t.Cols != a.Cols {
+		panic("blas32: mismatched dimension")
+	}
+	if t.KL != a.KL || t.KU != a.KU {
+		panic("blas32: mismatched bandwidth")
+	}
+	if a.Stride < a.KL+a.KU+1 {
+		panic("blas32: short stride for source")
+	}
+	if t.Stride < t.KL+t.KU+1 {
+		panic("blas32: short stride for destination")
+	}
+	for i := 0; i < a.Rows; i++ {
+		for j := max(0, i-a.KL); j < min(i+a.KU+1, a.Cols); j++ {
+			t.Data[i+t.KU-j+j*t.Stride] = a.Data[j+a.KL-i+i*a.Stride]
+		}
+	}
+}
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions and bandwidth as a and have
+// adequate backing data storage.
+func (t Band) From(a BandCols) {
+	if t.Rows != a.Rows || t.Cols != a.Cols {
+		panic("blas32: mismatched dimension")
+	}
+	if t.KL != a.KL || t.KU != a.KU {
+		panic("blas32: mismatched bandwidth")
+	}
+	if a.Stride < a.KL+a.KU+1 {
+		panic("blas32: short stride for source")
+	}
+	if t.Stride < t.KL+t.KU+1 {
+		panic("blas32: short stride for destination")
+	}
+	for j := 0; j < a.Cols; j++ {
+		for i := max(0, j-a.KU); i < min(j+a.KL+1, a.Rows); i++ {
+			t.Data[j+a.KL-i+i*a.Stride] = a.Data[i+t.KU-j+j*t.Stride]
+		}
+	}
+}
+
+// TriangularBandCols represents a symmetric matrix using the band column-major storage scheme.
+type TriangularBandCols TriangularBand
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions, bandwidth and uplo as a and
+// have adequate backing data storage.
+func (t TriangularBandCols) From(a TriangularBand) {
+	if t.N != a.N {
+		panic("blas32: mismatched dimension")
+	}
+	if t.K != a.K {
+		panic("blas32: mismatched bandwidth")
+	}
+	if a.Stride < a.K+1 {
+		panic("blas32: short stride for source")
+	}
+	if t.Stride < t.K+1 {
+		panic("blas32: short stride for destination")
+	}
+	if t.Uplo != a.Uplo {
+		panic("blas32: mismatched BLAS uplo")
+	}
+	if t.Diag != a.Diag {
+		panic("blas32: mismatched BLAS diag")
+	}
+	dst := BandCols{
+		Rows: t.N, Cols: t.N,
+		Stride: t.Stride,
+		Data:   t.Data,
+	}
+	src := Band{
+		Rows: a.N, Cols: a.N,
+		Stride: a.Stride,
+		Data:   a.Data,
+	}
+	switch a.Uplo {
+	default:
+		panic("blas32: bad BLAS uplo")
+	case blas.Upper:
+		dst.KU = t.K
+		src.KU = a.K
+	case blas.Lower:
+		dst.KL = t.K
+		src.KL = a.K
+	}
+	dst.From(src)
+}
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions, bandwidth and uplo as a and
+// have adequate backing data storage.
+func (t TriangularBand) From(a TriangularBandCols) {
+	if t.N != a.N {
+		panic("blas32: mismatched dimension")
+	}
+	if t.K != a.K {
+		panic("blas32: mismatched bandwidth")
+	}
+	if a.Stride < a.K+1 {
+		panic("blas32: short stride for source")
+	}
+	if t.Stride < t.K+1 {
+		panic("blas32: short stride for destination")
+	}
+	if t.Uplo != a.Uplo {
+		panic("blas32: mismatched BLAS uplo")
+	}
+	if t.Diag != a.Diag {
+		panic("blas32: mismatched BLAS diag")
+	}
+	dst := Band{
+		Rows: t.N, Cols: t.N,
+		Stride: t.Stride,
+		Data:   t.Data,
+	}
+	src := BandCols{
+		Rows: a.N, Cols: a.N,
+		Stride: a.Stride,
+		Data:   a.Data,
+	}
+	switch a.Uplo {
+	default:
+		panic("blas32: bad BLAS uplo")
+	case blas.Upper:
+		dst.KU = t.K
+		src.KU = a.K
+	case blas.Lower:
+		dst.KL = t.K
+		src.KL = a.K
+	}
+	dst.From(src)
+}
+
+func min(a, b int) int {
+	if a < b {
+		return a
+	}
+	return b
+}
+
+func max(a, b int) int {
+	if a > b {
+		return a
+	}
+	return b
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/blas32/conv_symmetric.go b/vendor/gonum.org/v1/gonum/blas/blas32/conv_symmetric.go
new file mode 100644
index 00000000..e385a641
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/blas32/conv_symmetric.go
@@ -0,0 +1,155 @@
+// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.
+
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package blas32
+
+import "gonum.org/v1/gonum/blas"
+
+// SymmetricCols represents a matrix using the conventional column-major storage scheme.
+type SymmetricCols Symmetric
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions and uplo as a and have adequate
+// backing data storage.
+func (t SymmetricCols) From(a Symmetric) {
+	if t.N != a.N {
+		panic("blas32: mismatched dimension")
+	}
+	if t.Uplo != a.Uplo {
+		panic("blas32: mismatched BLAS uplo")
+	}
+	switch a.Uplo {
+	default:
+		panic("blas32: bad BLAS uplo")
+	case blas.Upper:
+		for i := 0; i < a.N; i++ {
+			for j := i; j < a.N; j++ {
+				t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
+			}
+		}
+	case blas.Lower:
+		for i := 0; i < a.N; i++ {
+			for j := 0; j <= i; j++ {
+				t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
+			}
+		}
+	}
+}
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions and uplo as a and have adequate
+// backing data storage.
+func (t Symmetric) From(a SymmetricCols) {
+	if t.N != a.N {
+		panic("blas32: mismatched dimension")
+	}
+	if t.Uplo != a.Uplo {
+		panic("blas32: mismatched BLAS uplo")
+	}
+	switch a.Uplo {
+	default:
+		panic("blas32: bad BLAS uplo")
+	case blas.Upper:
+		for i := 0; i < a.N; i++ {
+			for j := i; j < a.N; j++ {
+				t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
+			}
+		}
+	case blas.Lower:
+		for i := 0; i < a.N; i++ {
+			for j := 0; j <= i; j++ {
+				t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
+			}
+		}
+	}
+}
+
+// SymmetricBandCols represents a symmetric matrix using the band column-major storage scheme.
+type SymmetricBandCols SymmetricBand
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions, bandwidth and uplo as a and
+// have adequate backing data storage.
+func (t SymmetricBandCols) From(a SymmetricBand) {
+	if t.N != a.N {
+		panic("blas32: mismatched dimension")
+	}
+	if t.K != a.K {
+		panic("blas32: mismatched bandwidth")
+	}
+	if a.Stride < a.K+1 {
+		panic("blas32: short stride for source")
+	}
+	if t.Stride < t.K+1 {
+		panic("blas32: short stride for destination")
+	}
+	if t.Uplo != a.Uplo {
+		panic("blas32: mismatched BLAS uplo")
+	}
+	dst := BandCols{
+		Rows: t.N, Cols: t.N,
+		Stride: t.Stride,
+		Data:   t.Data,
+	}
+	src := Band{
+		Rows: a.N, Cols: a.N,
+		Stride: a.Stride,
+		Data:   a.Data,
+	}
+	switch a.Uplo {
+	default:
+		panic("blas32: bad BLAS uplo")
+	case blas.Upper:
+		dst.KU = t.K
+		src.KU = a.K
+	case blas.Lower:
+		dst.KL = t.K
+		src.KL = a.K
+	}
+	dst.From(src)
+}
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions, bandwidth and uplo as a and
+// have adequate backing data storage.
+func (t SymmetricBand) From(a SymmetricBandCols) {
+	if t.N != a.N {
+		panic("blas32: mismatched dimension")
+	}
+	if t.K != a.K {
+		panic("blas32: mismatched bandwidth")
+	}
+	if a.Stride < a.K+1 {
+		panic("blas32: short stride for source")
+	}
+	if t.Stride < t.K+1 {
+		panic("blas32: short stride for destination")
+	}
+	if t.Uplo != a.Uplo {
+		panic("blas32: mismatched BLAS uplo")
+	}
+	dst := Band{
+		Rows: t.N, Cols: t.N,
+		Stride: t.Stride,
+		Data:   t.Data,
+	}
+	src := BandCols{
+		Rows: a.N, Cols: a.N,
+		Stride: a.Stride,
+		Data:   a.Data,
+	}
+	switch a.Uplo {
+	default:
+		panic("blas32: bad BLAS uplo")
+	case blas.Upper:
+		dst.KU = t.K
+		src.KU = a.K
+	case blas.Lower:
+		dst.KL = t.K
+		src.KL = a.K
+	}
+	dst.From(src)
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/blas32/conv_symmetric_test.go b/vendor/gonum.org/v1/gonum/blas/blas32/conv_symmetric_test.go
new file mode 100644
index 00000000..335f0fa0
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/blas32/conv_symmetric_test.go
@@ -0,0 +1,307 @@
+// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.
+
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package blas32
+
+import (
+	math "gonum.org/v1/gonum/internal/math32"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+func newSymmetricFrom(a SymmetricCols) Symmetric {
+	t := Symmetric{
+		N:      a.N,
+		Stride: a.N,
+		Data:   make([]float32, a.N*a.N),
+		Uplo:   a.Uplo,
+	}
+	t.From(a)
+	return t
+}
+
+func (m Symmetric) n() int { return m.N }
+func (m Symmetric) at(i, j int) float32 {
+	if m.Uplo == blas.Lower && i < j && j < m.N {
+		i, j = j, i
+	}
+	if m.Uplo == blas.Upper && i > j {
+		i, j = j, i
+	}
+	return m.Data[i*m.Stride+j]
+}
+func (m Symmetric) uplo() blas.Uplo { return m.Uplo }
+
+func newSymmetricColsFrom(a Symmetric) SymmetricCols {
+	t := SymmetricCols{
+		N:      a.N,
+		Stride: a.N,
+		Data:   make([]float32, a.N*a.N),
+		Uplo:   a.Uplo,
+	}
+	t.From(a)
+	return t
+}
+
+func (m SymmetricCols) n() int { return m.N }
+func (m SymmetricCols) at(i, j int) float32 {
+	if m.Uplo == blas.Lower && i < j {
+		i, j = j, i
+	}
+	if m.Uplo == blas.Upper && i > j && i < m.N {
+		i, j = j, i
+	}
+	return m.Data[i+j*m.Stride]
+}
+func (m SymmetricCols) uplo() blas.Uplo { return m.Uplo }
+
+type symmetric interface {
+	n() int
+	at(i, j int) float32
+	uplo() blas.Uplo
+}
+
+func sameSymmetric(a, b symmetric) bool {
+	an := a.n()
+	bn := b.n()
+	if an != bn {
+		return false
+	}
+	if a.uplo() != b.uplo() {
+		return false
+	}
+	for i := 0; i < an; i++ {
+		for j := 0; j < an; j++ {
+			if a.at(i, j) != b.at(i, j) || math.IsNaN(a.at(i, j)) != math.IsNaN(b.at(i, j)) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+var symmetricTests = []Symmetric{
+	{N: 3, Stride: 3, Data: []float32{
+		1, 2, 3,
+		4, 5, 6,
+		7, 8, 9,
+	}},
+	{N: 3, Stride: 5, Data: []float32{
+		1, 2, 3, 0, 0,
+		4, 5, 6, 0, 0,
+		7, 8, 9, 0, 0,
+	}},
+}
+
+func TestConvertSymmetric(t *testing.T) {
+	for _, test := range symmetricTests {
+		for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
+			test.Uplo = uplo
+			colmajor := newSymmetricColsFrom(test)
+			if !sameSymmetric(colmajor, test) {
+				t.Errorf("unexpected result for row major to col major conversion:\n\tgot: %#v\n\tfrom:%#v",
+					colmajor, test)
+			}
+			rowmajor := newSymmetricFrom(colmajor)
+			if !sameSymmetric(rowmajor, test) {
+				t.Errorf("unexpected result for col major to row major conversion:\n\tgot: %#v\n\twant:%#v",
+					rowmajor, test)
+			}
+		}
+	}
+}
+func newSymmetricBandFrom(a SymmetricBandCols) SymmetricBand {
+	t := SymmetricBand{
+		N:      a.N,
+		K:      a.K,
+		Stride: a.K + 1,
+		Data:   make([]float32, a.N*(a.K+1)),
+		Uplo:   a.Uplo,
+	}
+	for i := range t.Data {
+		t.Data[i] = math.NaN()
+	}
+	t.From(a)
+	return t
+}
+
+func (m SymmetricBand) n() (n int) { return m.N }
+func (m SymmetricBand) at(i, j int) float32 {
+	b := Band{
+		Rows: m.N, Cols: m.N,
+		Stride: m.Stride,
+		Data:   m.Data,
+	}
+	switch m.Uplo {
+	default:
+		panic("blas32: bad BLAS uplo")
+	case blas.Upper:
+		b.KU = m.K
+		if i > j {
+			i, j = j, i
+		}
+	case blas.Lower:
+		b.KL = m.K
+		if i < j {
+			i, j = j, i
+		}
+	}
+	return b.at(i, j)
+}
+func (m SymmetricBand) bandwidth() (k int) { return m.K }
+func (m SymmetricBand) uplo() blas.Uplo    { return m.Uplo }
+
+func newSymmetricBandColsFrom(a SymmetricBand) SymmetricBandCols {
+	t := SymmetricBandCols{
+		N:      a.N,
+		K:      a.K,
+		Stride: a.K + 1,
+		Data:   make([]float32, a.N*(a.K+1)),
+		Uplo:   a.Uplo,
+	}
+	for i := range t.Data {
+		t.Data[i] = math.NaN()
+	}
+	t.From(a)
+	return t
+}
+
+func (m SymmetricBandCols) n() (n int) { return m.N }
+func (m SymmetricBandCols) at(i, j int) float32 {
+	b := BandCols{
+		Rows: m.N, Cols: m.N,
+		Stride: m.Stride,
+		Data:   m.Data,
+	}
+	switch m.Uplo {
+	default:
+		panic("blas32: bad BLAS uplo")
+	case blas.Upper:
+		b.KU = m.K
+		if i > j {
+			i, j = j, i
+		}
+	case blas.Lower:
+		b.KL = m.K
+		if i < j {
+			i, j = j, i
+		}
+	}
+	return b.at(i, j)
+}
+func (m SymmetricBandCols) bandwidth() (k int) { return m.K }
+func (m SymmetricBandCols) uplo() blas.Uplo    { return m.Uplo }
+
+type symmetricBand interface {
+	n() (n int)
+	at(i, j int) float32
+	bandwidth() (k int)
+	uplo() blas.Uplo
+}
+
+func sameSymmetricBand(a, b symmetricBand) bool {
+	an := a.n()
+	bn := b.n()
+	if an != bn {
+		return false
+	}
+	if a.uplo() != b.uplo() {
+		return false
+	}
+	ak := a.bandwidth()
+	bk := b.bandwidth()
+	if ak != bk {
+		return false
+	}
+	for i := 0; i < an; i++ {
+		for j := 0; j < an; j++ {
+			if a.at(i, j) != b.at(i, j) || math.IsNaN(a.at(i, j)) != math.IsNaN(b.at(i, j)) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+var symmetricBandTests = []SymmetricBand{
+	{N: 3, K: 0, Stride: 1, Uplo: blas.Upper, Data: []float32{
+		1,
+		2,
+		3,
+	}},
+	{N: 3, K: 0, Stride: 1, Uplo: blas.Lower, Data: []float32{
+		1,
+		2,
+		3,
+	}},
+	{N: 3, K: 1, Stride: 2, Uplo: blas.Upper, Data: []float32{
+		1, 2,
+		3, 4,
+		5, -1,
+	}},
+	{N: 3, K: 1, Stride: 2, Uplo: blas.Lower, Data: []float32{
+		-1, 1,
+		2, 3,
+		4, 5,
+	}},
+	{N: 3, K: 2, Stride: 3, Uplo: blas.Upper, Data: []float32{
+		1, 2, 3,
+		4, 5, -1,
+		6, -2, -3,
+	}},
+	{N: 3, K: 2, Stride: 3, Uplo: blas.Lower, Data: []float32{
+		-2, -1, 1,
+		-3, 2, 4,
+		3, 5, 6,
+	}},
+
+	{N: 3, K: 0, Stride: 5, Uplo: blas.Upper, Data: []float32{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{N: 3, K: 0, Stride: 5, Uplo: blas.Lower, Data: []float32{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{N: 3, K: 1, Stride: 5, Uplo: blas.Upper, Data: []float32{
+		1, 2, 0, 0, 0,
+		3, 4, 0, 0, 0,
+		5, -1, 0, 0, 0,
+	}},
+	{N: 3, K: 1, Stride: 5, Uplo: blas.Lower, Data: []float32{
+		-1, 1, 0, 0, 0,
+		2, 3, 0, 0, 0,
+		4, 5, 0, 0, 0,
+	}},
+	{N: 3, K: 2, Stride: 5, Uplo: blas.Upper, Data: []float32{
+		1, 2, 3, 0, 0,
+		4, 5, -1, 0, 0,
+		6, -2, -3, 0, 0,
+	}},
+	{N: 3, K: 2, Stride: 5, Uplo: blas.Lower, Data: []float32{
+		-2, -1, 1, 0, 0,
+		-3, 2, 4, 0, 0,
+		3, 5, 6, 0, 0,
+	}},
+}
+
+func TestConvertSymBand(t *testing.T) {
+	for _, test := range symmetricBandTests {
+		colmajor := newSymmetricBandColsFrom(test)
+		if !sameSymmetricBand(colmajor, test) {
+			t.Errorf("unexpected result for row major to col major conversion:\n\tgot: %#v\n\tfrom:%#v",
+				colmajor, test)
+		}
+		rowmajor := newSymmetricBandFrom(colmajor)
+		if !sameSymmetricBand(rowmajor, test) {
+			t.Errorf("unexpected result for col major to row major conversion:\n\tgot: %#v\n\twant:%#v",
+				rowmajor, test)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/blas32/conv_test.go b/vendor/gonum.org/v1/gonum/blas/blas32/conv_test.go
new file mode 100644
index 00000000..9cff493e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/blas32/conv_test.go
@@ -0,0 +1,620 @@
+// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.
+
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package blas32
+
+import (
+	math "gonum.org/v1/gonum/internal/math32"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+func newGeneralFrom(a GeneralCols) General {
+	t := General{
+		Rows:   a.Rows,
+		Cols:   a.Cols,
+		Stride: a.Cols,
+		Data:   make([]float32, a.Rows*a.Cols),
+	}
+	t.From(a)
+	return t
+}
+
+func (m General) dims() (r, c int)    { return m.Rows, m.Cols }
+func (m General) at(i, j int) float32 { return m.Data[i*m.Stride+j] }
+
+func newGeneralColsFrom(a General) GeneralCols {
+	t := GeneralCols{
+		Rows:   a.Rows,
+		Cols:   a.Cols,
+		Stride: a.Rows,
+		Data:   make([]float32, a.Rows*a.Cols),
+	}
+	t.From(a)
+	return t
+}
+
+func (m GeneralCols) dims() (r, c int)    { return m.Rows, m.Cols }
+func (m GeneralCols) at(i, j int) float32 { return m.Data[i+j*m.Stride] }
+
+type general interface {
+	dims() (r, c int)
+	at(i, j int) float32
+}
+
+func sameGeneral(a, b general) bool {
+	ar, ac := a.dims()
+	br, bc := b.dims()
+	if ar != br || ac != bc {
+		return false
+	}
+	for i := 0; i < ar; i++ {
+		for j := 0; j < ac; j++ {
+			if a.at(i, j) != b.at(i, j) || math.IsNaN(a.at(i, j)) != math.IsNaN(b.at(i, j)) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+var generalTests = []General{
+	{Rows: 2, Cols: 3, Stride: 3, Data: []float32{
+		1, 2, 3,
+		4, 5, 6,
+	}},
+	{Rows: 3, Cols: 2, Stride: 2, Data: []float32{
+		1, 2,
+		3, 4,
+		5, 6,
+	}},
+	{Rows: 3, Cols: 3, Stride: 3, Data: []float32{
+		1, 2, 3,
+		4, 5, 6,
+		7, 8, 9,
+	}},
+	{Rows: 2, Cols: 3, Stride: 5, Data: []float32{
+		1, 2, 3, 0, 0,
+		4, 5, 6, 0, 0,
+	}},
+	{Rows: 3, Cols: 2, Stride: 5, Data: []float32{
+		1, 2, 0, 0, 0,
+		3, 4, 0, 0, 0,
+		5, 6, 0, 0, 0,
+	}},
+	{Rows: 3, Cols: 3, Stride: 5, Data: []float32{
+		1, 2, 3, 0, 0,
+		4, 5, 6, 0, 0,
+		7, 8, 9, 0, 0,
+	}},
+}
+
+func TestConvertGeneral(t *testing.T) {
+	for _, test := range generalTests {
+		colmajor := newGeneralColsFrom(test)
+		if !sameGeneral(colmajor, test) {
+			t.Errorf("unexpected result for row major to col major conversion:\n\tgot: %#v\n\tfrom:%#v",
+				colmajor, test)
+		}
+		rowmajor := newGeneralFrom(colmajor)
+		if !sameGeneral(rowmajor, test) {
+			t.Errorf("unexpected result for col major to row major conversion:\n\tgot: %#v\n\twant:%#v",
+				rowmajor, test)
+		}
+	}
+}
+
+func newTriangularFrom(a TriangularCols) Triangular {
+	t := Triangular{
+		N:      a.N,
+		Stride: a.N,
+		Data:   make([]float32, a.N*a.N),
+		Diag:   a.Diag,
+		Uplo:   a.Uplo,
+	}
+	t.From(a)
+	return t
+}
+
+func (m Triangular) n() int { return m.N }
+func (m Triangular) at(i, j int) float32 {
+	if m.Diag == blas.Unit && i == j {
+		return 1
+	}
+	if m.Uplo == blas.Lower && i < j && j < m.N {
+		return 0
+	}
+	if m.Uplo == blas.Upper && i > j {
+		return 0
+	}
+	return m.Data[i*m.Stride+j]
+}
+func (m Triangular) uplo() blas.Uplo { return m.Uplo }
+func (m Triangular) diag() blas.Diag { return m.Diag }
+
+func newTriangularColsFrom(a Triangular) TriangularCols {
+	t := TriangularCols{
+		N:      a.N,
+		Stride: a.N,
+		Data:   make([]float32, a.N*a.N),
+		Diag:   a.Diag,
+		Uplo:   a.Uplo,
+	}
+	t.From(a)
+	return t
+}
+
+func (m TriangularCols) n() int { return m.N }
+func (m TriangularCols) at(i, j int) float32 {
+	if m.Diag == blas.Unit && i == j {
+		return 1
+	}
+	if m.Uplo == blas.Lower && i < j {
+		return 0
+	}
+	if m.Uplo == blas.Upper && i > j && i < m.N {
+		return 0
+	}
+	return m.Data[i+j*m.Stride]
+}
+func (m TriangularCols) uplo() blas.Uplo { return m.Uplo }
+func (m TriangularCols) diag() blas.Diag { return m.Diag }
+
+type triangular interface {
+	n() int
+	at(i, j int) float32
+	uplo() blas.Uplo
+	diag() blas.Diag
+}
+
+func sameTriangular(a, b triangular) bool {
+	an := a.n()
+	bn := b.n()
+	if an != bn {
+		return false
+	}
+	for i := 0; i < an; i++ {
+		for j := 0; j < an; j++ {
+			if a.at(i, j) != b.at(i, j) || math.IsNaN(a.at(i, j)) != math.IsNaN(b.at(i, j)) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+var triangularTests = []Triangular{
+	{N: 3, Stride: 3, Data: []float32{
+		1, 2, 3,
+		4, 5, 6,
+		7, 8, 9,
+	}},
+	{N: 3, Stride: 5, Data: []float32{
+		1, 2, 3, 0, 0,
+		4, 5, 6, 0, 0,
+		7, 8, 9, 0, 0,
+	}},
+}
+
+func TestConvertTriangular(t *testing.T) {
+	for _, test := range triangularTests {
+		for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower, blas.All} {
+			for _, diag := range []blas.Diag{blas.Unit, blas.NonUnit} {
+				test.Uplo = uplo
+				test.Diag = diag
+				colmajor := newTriangularColsFrom(test)
+				if !sameTriangular(colmajor, test) {
+					t.Errorf("unexpected result for row major to col major conversion:\n\tgot: %#v\n\tfrom:%#v",
+						colmajor, test)
+				}
+				rowmajor := newTriangularFrom(colmajor)
+				if !sameTriangular(rowmajor, test) {
+					t.Errorf("unexpected result for col major to row major conversion:\n\tgot: %#v\n\twant:%#v",
+						rowmajor, test)
+				}
+			}
+		}
+	}
+}
+
+func newBandFrom(a BandCols) Band {
+	t := Band{
+		Rows:   a.Rows,
+		Cols:   a.Cols,
+		KL:     a.KL,
+		KU:     a.KU,
+		Stride: a.KL + a.KU + 1,
+		Data:   make([]float32, a.Rows*(a.KL+a.KU+1)),
+	}
+	for i := range t.Data {
+		t.Data[i] = math.NaN()
+	}
+	t.From(a)
+	return t
+}
+
+func (m Band) dims() (r, c int) { return m.Rows, m.Cols }
+func (m Band) at(i, j int) float32 {
+	pj := j + m.KL - i
+	if pj < 0 || m.KL+m.KU+1 <= pj {
+		return 0
+	}
+	return m.Data[i*m.Stride+pj]
+}
+func (m Band) bandwidth() (kl, ku int) { return m.KL, m.KU }
+
+func newBandColsFrom(a Band) BandCols {
+	t := BandCols{
+		Rows:   a.Rows,
+		Cols:   a.Cols,
+		KL:     a.KL,
+		KU:     a.KU,
+		Stride: a.KL + a.KU + 1,
+		Data:   make([]float32, a.Cols*(a.KL+a.KU+1)),
+	}
+	for i := range t.Data {
+		t.Data[i] = math.NaN()
+	}
+	t.From(a)
+	return t
+}
+
+func (m BandCols) dims() (r, c int) { return m.Rows, m.Cols }
+func (m BandCols) at(i, j int) float32 {
+	pj := i + m.KU - j
+	if pj < 0 || m.KL+m.KU+1 <= pj {
+		return 0
+	}
+	return m.Data[j*m.Stride+pj]
+}
+func (m BandCols) bandwidth() (kl, ku int) { return m.KL, m.KU }
+
+type band interface {
+	dims() (r, c int)
+	at(i, j int) float32
+	bandwidth() (kl, ku int)
+}
+
+func sameBand(a, b band) bool {
+	ar, ac := a.dims()
+	br, bc := b.dims()
+	if ar != br || ac != bc {
+		return false
+	}
+	akl, aku := a.bandwidth()
+	bkl, bku := b.bandwidth()
+	if akl != bkl || aku != bku {
+		return false
+	}
+	for i := 0; i < ar; i++ {
+		for j := 0; j < ac; j++ {
+			if a.at(i, j) != b.at(i, j) || math.IsNaN(a.at(i, j)) != math.IsNaN(b.at(i, j)) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+var bandTests = []Band{
+	{Rows: 3, Cols: 4, KL: 0, KU: 0, Stride: 1, Data: []float32{
+		1,
+		2,
+		3,
+	}},
+	{Rows: 3, Cols: 3, KL: 0, KU: 0, Stride: 1, Data: []float32{
+		1,
+		2,
+		3,
+	}},
+	{Rows: 4, Cols: 3, KL: 0, KU: 0, Stride: 1, Data: []float32{
+		1,
+		2,
+		3,
+	}},
+	{Rows: 4, Cols: 3, KL: 0, KU: 1, Stride: 2, Data: []float32{
+		1, 2,
+		3, 4,
+		5, 6,
+	}},
+	{Rows: 3, Cols: 4, KL: 0, KU: 1, Stride: 2, Data: []float32{
+		1, 2,
+		3, 4,
+		5, 6,
+	}},
+	{Rows: 3, Cols: 4, KL: 1, KU: 1, Stride: 3, Data: []float32{
+		-1, 2, 3,
+		4, 5, 6,
+		7, 8, 9,
+	}},
+	{Rows: 4, Cols: 3, KL: 1, KU: 1, Stride: 3, Data: []float32{
+		-1, 2, 3,
+		4, 5, 6,
+		7, 8, -2,
+		9, -3, -4,
+	}},
+	{Rows: 3, Cols: 4, KL: 2, KU: 1, Stride: 4, Data: []float32{
+		-2, -1, 3, 4,
+		-3, 5, 6, 7,
+		8, 9, 10, 11,
+	}},
+	{Rows: 4, Cols: 3, KL: 2, KU: 1, Stride: 4, Data: []float32{
+		-2, -1, 2, 3,
+		-3, 4, 5, 6,
+		7, 8, 9, -4,
+		10, 11, -5, -6,
+	}},
+
+	{Rows: 3, Cols: 4, KL: 0, KU: 0, Stride: 5, Data: []float32{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{Rows: 3, Cols: 3, KL: 0, KU: 0, Stride: 5, Data: []float32{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{Rows: 4, Cols: 3, KL: 0, KU: 0, Stride: 5, Data: []float32{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{Rows: 4, Cols: 3, KL: 0, KU: 1, Stride: 5, Data: []float32{
+		1, 2, 0, 0, 0,
+		3, 4, 0, 0, 0,
+		5, 6, 0, 0, 0,
+	}},
+	{Rows: 3, Cols: 4, KL: 0, KU: 1, Stride: 5, Data: []float32{
+		1, 2, 0, 0, 0,
+		3, 4, 0, 0, 0,
+		5, 6, 0, 0, 0,
+	}},
+	{Rows: 3, Cols: 4, KL: 1, KU: 1, Stride: 5, Data: []float32{
+		-1, 2, 3, 0, 0,
+		4, 5, 6, 0, 0,
+		7, 8, 9, 0, 0,
+	}},
+	{Rows: 4, Cols: 3, KL: 1, KU: 1, Stride: 5, Data: []float32{
+		-1, 2, 3, 0, 0,
+		4, 5, 6, 0, 0,
+		7, 8, -2, 0, 0,
+		9, -3, -4, 0, 0,
+	}},
+	{Rows: 3, Cols: 4, KL: 2, KU: 1, Stride: 5, Data: []float32{
+		-2, -1, 3, 4, 0,
+		-3, 5, 6, 7, 0,
+		8, 9, 10, 11, 0,
+	}},
+	{Rows: 4, Cols: 3, KL: 2, KU: 1, Stride: 5, Data: []float32{
+		-2, -1, 2, 3, 0,
+		-3, 4, 5, 6, 0,
+		7, 8, 9, -4, 0,
+		10, 11, -5, -6, 0,
+	}},
+}
+
+func TestConvertBand(t *testing.T) {
+	for _, test := range bandTests {
+		colmajor := newBandColsFrom(test)
+		if !sameBand(colmajor, test) {
+			t.Errorf("unexpected result for row major to col major conversion:\n\tgot: %#v\n\tfrom:%#v",
+				colmajor, test)
+		}
+		rowmajor := newBandFrom(colmajor)
+		if !sameBand(rowmajor, test) {
+			t.Errorf("unexpected result for col major to row major conversion:\n\tgot: %#v\n\twant:%#v",
+				rowmajor, test)
+		}
+	}
+}
+
+func newTriangularBandFrom(a TriangularBandCols) TriangularBand {
+	t := TriangularBand{
+		N:      a.N,
+		K:      a.K,
+		Stride: a.K + 1,
+		Data:   make([]float32, a.N*(a.K+1)),
+		Uplo:   a.Uplo,
+		Diag:   a.Diag,
+	}
+	for i := range t.Data {
+		t.Data[i] = math.NaN()
+	}
+	t.From(a)
+	return t
+}
+
+func (m TriangularBand) n() (n int) { return m.N }
+func (m TriangularBand) at(i, j int) float32 {
+	if m.Diag == blas.Unit && i == j {
+		return 1
+	}
+	b := Band{
+		Rows: m.N, Cols: m.N,
+		Stride: m.Stride,
+		Data:   m.Data,
+	}
+	switch m.Uplo {
+	default:
+		panic("blas32: bad BLAS uplo")
+	case blas.Upper:
+		if i > j {
+			return 0
+		}
+		b.KU = m.K
+	case blas.Lower:
+		if i < j {
+			return 0
+		}
+		b.KL = m.K
+	}
+	return b.at(i, j)
+}
+func (m TriangularBand) bandwidth() (k int) { return m.K }
+func (m TriangularBand) uplo() blas.Uplo    { return m.Uplo }
+func (m TriangularBand) diag() blas.Diag    { return m.Diag }
+
+func newTriangularBandColsFrom(a TriangularBand) TriangularBandCols {
+	t := TriangularBandCols{
+		N:      a.N,
+		K:      a.K,
+		Stride: a.K + 1,
+		Data:   make([]float32, a.N*(a.K+1)),
+		Uplo:   a.Uplo,
+		Diag:   a.Diag,
+	}
+	for i := range t.Data {
+		t.Data[i] = math.NaN()
+	}
+	t.From(a)
+	return t
+}
+
+func (m TriangularBandCols) n() (n int) { return m.N }
+func (m TriangularBandCols) at(i, j int) float32 {
+	if m.Diag == blas.Unit && i == j {
+		return 1
+	}
+	b := BandCols{
+		Rows: m.N, Cols: m.N,
+		Stride: m.Stride,
+		Data:   m.Data,
+	}
+	switch m.Uplo {
+	default:
+		panic("blas32: bad BLAS uplo")
+	case blas.Upper:
+		if i > j {
+			return 0
+		}
+		b.KU = m.K
+	case blas.Lower:
+		if i < j {
+			return 0
+		}
+		b.KL = m.K
+	}
+	return b.at(i, j)
+}
+func (m TriangularBandCols) bandwidth() (k int) { return m.K }
+func (m TriangularBandCols) uplo() blas.Uplo    { return m.Uplo }
+func (m TriangularBandCols) diag() blas.Diag    { return m.Diag }
+
+type triangularBand interface {
+	n() (n int)
+	at(i, j int) float32
+	bandwidth() (k int)
+	uplo() blas.Uplo
+	diag() blas.Diag
+}
+
+func sameTriangularBand(a, b triangularBand) bool {
+	an := a.n()
+	bn := b.n()
+	if an != bn {
+		return false
+	}
+	if a.uplo() != b.uplo() {
+		return false
+	}
+	if a.diag() != b.diag() {
+		return false
+	}
+	ak := a.bandwidth()
+	bk := b.bandwidth()
+	if ak != bk {
+		return false
+	}
+	for i := 0; i < an; i++ {
+		for j := 0; j < an; j++ {
+			if a.at(i, j) != b.at(i, j) || math.IsNaN(a.at(i, j)) != math.IsNaN(b.at(i, j)) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+var triangularBandTests = []TriangularBand{
+	{N: 3, K: 0, Stride: 1, Uplo: blas.Upper, Data: []float32{
+		1,
+		2,
+		3,
+	}},
+	{N: 3, K: 0, Stride: 1, Uplo: blas.Lower, Data: []float32{
+		1,
+		2,
+		3,
+	}},
+	{N: 3, K: 1, Stride: 2, Uplo: blas.Upper, Data: []float32{
+		1, 2,
+		3, 4,
+		5, -1,
+	}},
+	{N: 3, K: 1, Stride: 2, Uplo: blas.Lower, Data: []float32{
+		-1, 1,
+		2, 3,
+		4, 5,
+	}},
+	{N: 3, K: 2, Stride: 3, Uplo: blas.Upper, Data: []float32{
+		1, 2, 3,
+		4, 5, -1,
+		6, -2, -3,
+	}},
+	{N: 3, K: 2, Stride: 3, Uplo: blas.Lower, Data: []float32{
+		-2, -1, 1,
+		-3, 2, 4,
+		3, 5, 6,
+	}},
+
+	{N: 3, K: 0, Stride: 5, Uplo: blas.Upper, Data: []float32{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{N: 3, K: 0, Stride: 5, Uplo: blas.Lower, Data: []float32{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{N: 3, K: 1, Stride: 5, Uplo: blas.Upper, Data: []float32{
+		1, 2, 0, 0, 0,
+		3, 4, 0, 0, 0,
+		5, -1, 0, 0, 0,
+	}},
+	{N: 3, K: 1, Stride: 5, Uplo: blas.Lower, Data: []float32{
+		-1, 1, 0, 0, 0,
+		2, 3, 0, 0, 0,
+		4, 5, 0, 0, 0,
+	}},
+	{N: 3, K: 2, Stride: 5, Uplo: blas.Upper, Data: []float32{
+		1, 2, 3, 0, 0,
+		4, 5, -1, 0, 0,
+		6, -2, -3, 0, 0,
+	}},
+	{N: 3, K: 2, Stride: 5, Uplo: blas.Lower, Data: []float32{
+		-2, -1, 1, 0, 0,
+		-3, 2, 4, 0, 0,
+		3, 5, 6, 0, 0,
+	}},
+}
+
+func TestConvertTriBand(t *testing.T) {
+	for _, test := range triangularBandTests {
+		colmajor := newTriangularBandColsFrom(test)
+		if !sameTriangularBand(colmajor, test) {
+			t.Errorf("unexpected result for row major to col major conversion:\n\tgot: %#v\n\tfrom:%#v",
+				colmajor, test)
+		}
+		rowmajor := newTriangularBandFrom(colmajor)
+		if !sameTriangularBand(rowmajor, test) {
+			t.Errorf("unexpected result for col major to row major conversion:\n\tgot: %#v\n\twant:%#v",
+				rowmajor, test)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/blas32/doc.go b/vendor/gonum.org/v1/gonum/blas/blas32/doc.go
new file mode 100644
index 00000000..d01a5162
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/blas32/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package blas32 provides a simple interface to the float32 BLAS API.
+package blas32 // import "gonum.org/v1/gonum/blas/blas32"
diff --git a/vendor/gonum.org/v1/gonum/blas/blas64/blas64.go b/vendor/gonum.org/v1/gonum/blas/blas64/blas64.go
new file mode 100644
index 00000000..88e746bb
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/blas64/blas64.go
@@ -0,0 +1,445 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package blas64
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/gonum"
+)
+
+var blas64 blas.Float64 = gonum.Implementation{}
+
+// Use sets the BLAS float64 implementation to be used by subsequent BLAS calls.
+// The default implementation is native.Implementation.
+func Use(b blas.Float64) {
+	blas64 = b
+}
+
+// Implementation returns the current BLAS float64 implementation.
+//
+// Implementation allows direct calls to the current the BLAS float64 implementation
+// giving finer control of parameters.
+func Implementation() blas.Float64 {
+	return blas64
+}
+
+// Vector represents a vector with an associated element increment.
+type Vector struct {
+	Inc  int
+	Data []float64
+}
+
+// General represents a matrix using the conventional storage scheme.
+type General struct {
+	Rows, Cols int
+	Stride     int
+	Data       []float64
+}
+
+// Band represents a band matrix using the band storage scheme.
+type Band struct {
+	Rows, Cols int
+	KL, KU     int
+	Stride     int
+	Data       []float64
+}
+
+// Triangular represents a triangular matrix using the conventional storage scheme.
+type Triangular struct {
+	N      int
+	Stride int
+	Data   []float64
+	Uplo   blas.Uplo
+	Diag   blas.Diag
+}
+
+// TriangularBand represents a triangular matrix using the band storage scheme.
+type TriangularBand struct {
+	N, K   int
+	Stride int
+	Data   []float64
+	Uplo   blas.Uplo
+	Diag   blas.Diag
+}
+
+// TriangularPacked represents a triangular matrix using the packed storage scheme.
+type TriangularPacked struct {
+	N    int
+	Data []float64
+	Uplo blas.Uplo
+	Diag blas.Diag
+}
+
+// Symmetric represents a symmetric matrix using the conventional storage scheme.
+type Symmetric struct {
+	N      int
+	Stride int
+	Data   []float64
+	Uplo   blas.Uplo
+}
+
+// SymmetricBand represents a symmetric matrix using the band storage scheme.
+type SymmetricBand struct {
+	N, K   int
+	Stride int
+	Data   []float64
+	Uplo   blas.Uplo
+}
+
+// SymmetricPacked represents a symmetric matrix using the packed storage scheme.
+type SymmetricPacked struct {
+	N    int
+	Data []float64
+	Uplo blas.Uplo
+}
+
+// Level 1
+
+const negInc = "blas64: negative vector increment"
+
+// Dot computes the dot product of the two vectors:
+//  \sum_i x[i]*y[i].
+func Dot(n int, x, y Vector) float64 {
+	return blas64.Ddot(n, x.Data, x.Inc, y.Data, y.Inc)
+}
+
+// Nrm2 computes the Euclidean norm of the vector x:
+//  sqrt(\sum_i x[i]*x[i]).
+//
+// Nrm2 will panic if the vector increment is negative.
+func Nrm2(n int, x Vector) float64 {
+	if x.Inc < 0 {
+		panic(negInc)
+	}
+	return blas64.Dnrm2(n, x.Data, x.Inc)
+}
+
+// Asum computes the sum of the absolute values of the elements of x:
+//  \sum_i |x[i]|.
+//
+// Asum will panic if the vector increment is negative.
+func Asum(n int, x Vector) float64 {
+	if x.Inc < 0 {
+		panic(negInc)
+	}
+	return blas64.Dasum(n, x.Data, x.Inc)
+}
+
+// Iamax returns the index of an element of x with the largest absolute value.
+// If there are multiple such indices the earliest is returned.
+// Iamax returns -1 if n == 0.
+//
+// Iamax will panic if the vector increment is negative.
+func Iamax(n int, x Vector) int {
+	if x.Inc < 0 {
+		panic(negInc)
+	}
+	return blas64.Idamax(n, x.Data, x.Inc)
+}
+
+// Swap exchanges the elements of the two vectors:
+//  x[i], y[i] = y[i], x[i] for all i.
+func Swap(n int, x, y Vector) {
+	blas64.Dswap(n, x.Data, x.Inc, y.Data, y.Inc)
+}
+
+// Copy copies the elements of x into the elements of y:
+//  y[i] = x[i] for all i.
+func Copy(n int, x, y Vector) {
+	blas64.Dcopy(n, x.Data, x.Inc, y.Data, y.Inc)
+}
+
+// Axpy adds x scaled by alpha to y:
+//  y[i] += alpha*x[i] for all i.
+func Axpy(n int, alpha float64, x, y Vector) {
+	blas64.Daxpy(n, alpha, x.Data, x.Inc, y.Data, y.Inc)
+}
+
+// Rotg computes the parameters of a Givens plane rotation so that
+//  ⎡ c s⎤   ⎡a⎤   ⎡r⎤
+//  ⎣-s c⎦ * ⎣b⎦ = ⎣0⎦
+// where a and b are the Cartesian coordinates of a given point.
+// c, s, and r are defined as
+//  r = ±Sqrt(a^2 + b^2),
+//  c = a/r, the cosine of the rotation angle,
+//  s = a/r, the sine of the rotation angle,
+// and z is defined such that
+//  if |a| > |b|,        z = s,
+//  otherwise if c != 0, z = 1/c,
+//  otherwise            z = 1.
+func Rotg(a, b float64) (c, s, r, z float64) {
+	return blas64.Drotg(a, b)
+}
+
+// Rotmg computes the modified Givens rotation. See
+// http://www.netlib.org/lapack/explore-html/df/deb/drotmg_8f.html
+// for more details.
+func Rotmg(d1, d2, b1, b2 float64) (p blas.DrotmParams, rd1, rd2, rb1 float64) {
+	return blas64.Drotmg(d1, d2, b1, b2)
+}
+
+// Rot applies a plane transformation to n points represented by the vectors x
+// and y:
+//  x[i] =  c*x[i] + s*y[i],
+//  y[i] = -s*x[i] + c*y[i], for all i.
+func Rot(n int, x, y Vector, c, s float64) {
+	blas64.Drot(n, x.Data, x.Inc, y.Data, y.Inc, c, s)
+}
+
+// Rotm applies the modified Givens rotation to n points represented by the
+// vectors x and y.
+func Rotm(n int, x, y Vector, p blas.DrotmParams) {
+	blas64.Drotm(n, x.Data, x.Inc, y.Data, y.Inc, p)
+}
+
+// Scal scales the vector x by alpha:
+//  x[i] *= alpha for all i.
+//
+// Scal will panic if the vector increment is negative.
+func Scal(n int, alpha float64, x Vector) {
+	if x.Inc < 0 {
+		panic(negInc)
+	}
+	blas64.Dscal(n, alpha, x.Data, x.Inc)
+}
+
+// Level 2
+
+// Gemv computes
+//  y = alpha * A * x + beta * y,   if t == blas.NoTrans,
+//  y = alpha * A^T * x + beta * y, if t == blas.Trans or blas.ConjTrans,
+// where A is an m×n dense matrix, x and y are vectors, and alpha and beta are scalars.
+func Gemv(t blas.Transpose, alpha float64, a General, x Vector, beta float64, y Vector) {
+	blas64.Dgemv(t, a.Rows, a.Cols, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
+}
+
+// Gbmv computes
+//  y = alpha * A * x + beta * y,   if t == blas.NoTrans,
+//  y = alpha * A^T * x + beta * y, if t == blas.Trans or blas.ConjTrans,
+// where A is an m×n band matrix, x and y are vectors, and alpha and beta are scalars.
+func Gbmv(t blas.Transpose, alpha float64, a Band, x Vector, beta float64, y Vector) {
+	blas64.Dgbmv(t, a.Rows, a.Cols, a.KL, a.KU, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
+}
+
+// Trmv computes
+//  x = A * x,   if t == blas.NoTrans,
+//  x = A^T * x, if t == blas.Trans or blas.ConjTrans,
+// where A is an n×n triangular matrix, and x is a vector.
+func Trmv(t blas.Transpose, a Triangular, x Vector) {
+	blas64.Dtrmv(a.Uplo, t, a.Diag, a.N, a.Data, a.Stride, x.Data, x.Inc)
+}
+
+// Tbmv computes
+//  x = A * x,   if t == blas.NoTrans,
+//  x = A^T * x, if t == blas.Trans or blas.ConjTrans,
+// where A is an n×n triangular band matrix, and x is a vector.
+func Tbmv(t blas.Transpose, a TriangularBand, x Vector) {
+	blas64.Dtbmv(a.Uplo, t, a.Diag, a.N, a.K, a.Data, a.Stride, x.Data, x.Inc)
+}
+
+// Tpmv computes
+//  x = A * x,   if t == blas.NoTrans,
+//  x = A^T * x, if t == blas.Trans or blas.ConjTrans,
+// where A is an n×n triangular matrix in packed format, and x is a vector.
+func Tpmv(t blas.Transpose, a TriangularPacked, x Vector) {
+	blas64.Dtpmv(a.Uplo, t, a.Diag, a.N, a.Data, x.Data, x.Inc)
+}
+
+// Trsv solves
+//  A * x = b,   if t == blas.NoTrans,
+//  A^T * x = b, if t == blas.Trans or blas.ConjTrans,
+// where A is an n×n triangular matrix, and x and b are vectors.
+//
+// At entry to the function, x contains the values of b, and the result is
+// stored in-place into x.
+//
+// No test for singularity or near-singularity is included in this
+// routine. Such tests must be performed before calling this routine.
+func Trsv(t blas.Transpose, a Triangular, x Vector) {
+	blas64.Dtrsv(a.Uplo, t, a.Diag, a.N, a.Data, a.Stride, x.Data, x.Inc)
+}
+
+// Tbsv solves
+//  A * x = b,   if t == blas.NoTrans,
+//  A^T * x = b, if t == blas.Trans or blas.ConjTrans,
+// where A is an n×n triangular band matrix, and x and b are vectors.
+//
+// At entry to the function, x contains the values of b, and the result is
+// stored in place into x.
+//
+// No test for singularity or near-singularity is included in this
+// routine. Such tests must be performed before calling this routine.
+func Tbsv(t blas.Transpose, a TriangularBand, x Vector) {
+	blas64.Dtbsv(a.Uplo, t, a.Diag, a.N, a.K, a.Data, a.Stride, x.Data, x.Inc)
+}
+
+// Tpsv solves
+//  A * x = b,   if t == blas.NoTrans,
+//  A^T * x = b, if t == blas.Trans or blas.ConjTrans,
+// where A is an n×n triangular matrix in packed format, and x and b are
+// vectors.
+//
+// At entry to the function, x contains the values of b, and the result is
+// stored in place into x.
+//
+// No test for singularity or near-singularity is included in this
+// routine. Such tests must be performed before calling this routine.
+func Tpsv(t blas.Transpose, a TriangularPacked, x Vector) {
+	blas64.Dtpsv(a.Uplo, t, a.Diag, a.N, a.Data, x.Data, x.Inc)
+}
+
+// Symv computes
+//    y = alpha * A * x + beta * y,
+// where A is an n×n symmetric matrix, x and y are vectors, and alpha and
+// beta are scalars.
+func Symv(alpha float64, a Symmetric, x Vector, beta float64, y Vector) {
+	blas64.Dsymv(a.Uplo, a.N, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
+}
+
+// Sbmv performs
+//  y = alpha * A * x + beta * y,
+// where A is an n×n symmetric band matrix, x and y are vectors, and alpha
+// and beta are scalars.
+func Sbmv(alpha float64, a SymmetricBand, x Vector, beta float64, y Vector) {
+	blas64.Dsbmv(a.Uplo, a.N, a.K, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
+}
+
+// Spmv performs
+//    y = alpha * A * x + beta * y,
+// where A is an n×n symmetric matrix in packed format, x and y are vectors,
+// and alpha and beta are scalars.
+func Spmv(alpha float64, a SymmetricPacked, x Vector, beta float64, y Vector) {
+	blas64.Dspmv(a.Uplo, a.N, alpha, a.Data, x.Data, x.Inc, beta, y.Data, y.Inc)
+}
+
+// Ger performs a rank-1 update
+//  A += alpha * x * y^T,
+// where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.
+func Ger(alpha float64, x, y Vector, a General) {
+	blas64.Dger(a.Rows, a.Cols, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
+}
+
+// Syr performs a rank-1 update
+//  A += alpha * x * x^T,
+// where A is an n×n symmetric matrix, x is a vector, and alpha is a scalar.
+func Syr(alpha float64, x Vector, a Symmetric) {
+	blas64.Dsyr(a.Uplo, a.N, alpha, x.Data, x.Inc, a.Data, a.Stride)
+}
+
+// Spr performs the rank-1 update
+//  A += alpha * x * x^T,
+// where A is an n×n symmetric matrix in packed format, x is a vector, and
+// alpha is a scalar.
+func Spr(alpha float64, x Vector, a SymmetricPacked) {
+	blas64.Dspr(a.Uplo, a.N, alpha, x.Data, x.Inc, a.Data)
+}
+
+// Syr2 performs a rank-2 update
+//  A += alpha * x * y^T + alpha * y * x^T,
+// where A is a symmetric n×n matrix, x and y are vectors, and alpha is a scalar.
+func Syr2(alpha float64, x, y Vector, a Symmetric) {
+	blas64.Dsyr2(a.Uplo, a.N, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
+}
+
+// Spr2 performs a rank-2 update
+//  A += alpha * x * y^T + alpha * y * x^T,
+// where A is an n×n symmetric matrix in packed format, x and y are vectors,
+// and alpha is a scalar.
+func Spr2(alpha float64, x, y Vector, a SymmetricPacked) {
+	blas64.Dspr2(a.Uplo, a.N, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data)
+}
+
+// Level 3
+
+// Gemm computes
+//  C = alpha * A * B + beta * C,
+// where A, B, and C are dense matrices, and alpha and beta are scalars.
+// tA and tB specify whether A or B are transposed.
+func Gemm(tA, tB blas.Transpose, alpha float64, a, b General, beta float64, c General) {
+	var m, n, k int
+	if tA == blas.NoTrans {
+		m, k = a.Rows, a.Cols
+	} else {
+		m, k = a.Cols, a.Rows
+	}
+	if tB == blas.NoTrans {
+		n = b.Cols
+	} else {
+		n = b.Rows
+	}
+	blas64.Dgemm(tA, tB, m, n, k, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
+}
+
+// Symm performs
+//  C = alpha * A * B + beta * C, if s == blas.Left,
+//  C = alpha * B * A + beta * C, if s == blas.Right,
+// where A is an n×n or m×m symmetric matrix, B and C are m×n matrices, and
+// alpha is a scalar.
+func Symm(s blas.Side, alpha float64, a Symmetric, b General, beta float64, c General) {
+	var m, n int
+	if s == blas.Left {
+		m, n = a.N, b.Cols
+	} else {
+		m, n = b.Rows, a.N
+	}
+	blas64.Dsymm(s, a.Uplo, m, n, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
+}
+
+// Syrk performs a symmetric rank-k update
+//  C = alpha * A * A^T + beta * C, if t == blas.NoTrans,
+//  C = alpha * A^T * A + beta * C, if t == blas.Trans or blas.ConjTrans,
+// where C is an n×n symmetric matrix, A is an n×k matrix if t == blas.NoTrans and
+// a k×n matrix otherwise, and alpha and beta are scalars.
+func Syrk(t blas.Transpose, alpha float64, a General, beta float64, c Symmetric) {
+	var n, k int
+	if t == blas.NoTrans {
+		n, k = a.Rows, a.Cols
+	} else {
+		n, k = a.Cols, a.Rows
+	}
+	blas64.Dsyrk(c.Uplo, t, n, k, alpha, a.Data, a.Stride, beta, c.Data, c.Stride)
+}
+
+// Syr2k performs a symmetric rank-2k update
+//  C = alpha * A * B^T + alpha * B * A^T + beta * C, if t == blas.NoTrans,
+//  C = alpha * A^T * B + alpha * B^T * A + beta * C, if t == blas.Trans or blas.ConjTrans,
+// where C is an n×n symmetric matrix, A and B are n×k matrices if t == NoTrans
+// and k×n matrices otherwise, and alpha and beta are scalars.
+func Syr2k(t blas.Transpose, alpha float64, a, b General, beta float64, c Symmetric) {
+	var n, k int
+	if t == blas.NoTrans {
+		n, k = a.Rows, a.Cols
+	} else {
+		n, k = a.Cols, a.Rows
+	}
+	blas64.Dsyr2k(c.Uplo, t, n, k, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
+}
+
+// Trmm performs
+//  B = alpha * A * B,   if tA == blas.NoTrans and s == blas.Left,
+//  B = alpha * A^T * B, if tA == blas.Trans or blas.ConjTrans, and s == blas.Left,
+//  B = alpha * B * A,   if tA == blas.NoTrans and s == blas.Right,
+//  B = alpha * B * A^T, if tA == blas.Trans or blas.ConjTrans, and s == blas.Right,
+// where A is an n×n or m×m triangular matrix, B is an m×n matrix, and alpha is
+// a scalar.
+func Trmm(s blas.Side, tA blas.Transpose, alpha float64, a Triangular, b General) {
+	blas64.Dtrmm(s, a.Uplo, tA, a.Diag, b.Rows, b.Cols, alpha, a.Data, a.Stride, b.Data, b.Stride)
+}
+
+// Trsm solves
+//  A * X = alpha * B,   if tA == blas.NoTrans and s == blas.Left,
+//  A^T * X = alpha * B, if tA == blas.Trans or blas.ConjTrans, and s == blas.Left,
+//  X * A = alpha * B,   if tA == blas.NoTrans and s == blas.Right,
+//  X * A^T = alpha * B, if tA == blas.Trans or blas.ConjTrans, and s == blas.Right,
+// where A is an n×n or m×m triangular matrix, X and B are m×n matrices, and
+// alpha is a scalar.
+//
+// At entry to the function, X contains the values of B, and the result is
+// stored in-place into X.
+//
+// No check is made that A is invertible.
+func Trsm(s blas.Side, tA blas.Transpose, alpha float64, a Triangular, b General) {
+	blas64.Dtrsm(s, a.Uplo, tA, a.Diag, b.Rows, b.Cols, alpha, a.Data, a.Stride, b.Data, b.Stride)
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/blas64/conv.go b/vendor/gonum.org/v1/gonum/blas/blas64/conv.go
new file mode 100644
index 00000000..17de0943
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/blas64/conv.go
@@ -0,0 +1,277 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package blas64
+
+import "gonum.org/v1/gonum/blas"
+
+// GeneralCols represents a matrix using the conventional column-major storage scheme.
+type GeneralCols General
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions as a and have adequate backing
+// data storage.
+func (t GeneralCols) From(a General) {
+	if t.Rows != a.Rows || t.Cols != a.Cols {
+		panic("blas64: mismatched dimension")
+	}
+	if len(t.Data) < (t.Cols-1)*t.Stride+t.Rows {
+		panic("blas64: short data slice")
+	}
+	for i := 0; i < a.Rows; i++ {
+		for j, v := range a.Data[i*a.Stride : i*a.Stride+a.Cols] {
+			t.Data[i+j*t.Stride] = v
+		}
+	}
+}
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions as a and have adequate backing
+// data storage.
+func (t General) From(a GeneralCols) {
+	if t.Rows != a.Rows || t.Cols != a.Cols {
+		panic("blas64: mismatched dimension")
+	}
+	if len(t.Data) < (t.Rows-1)*t.Stride+t.Cols {
+		panic("blas64: short data slice")
+	}
+	for j := 0; j < a.Cols; j++ {
+		for i, v := range a.Data[j*a.Stride : j*a.Stride+a.Rows] {
+			t.Data[i*t.Stride+j] = v
+		}
+	}
+}
+
+// TriangularCols represents a matrix using the conventional column-major storage scheme.
+type TriangularCols Triangular
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions, uplo and diag as a and have
+// adequate backing data storage.
+func (t TriangularCols) From(a Triangular) {
+	if t.N != a.N {
+		panic("blas64: mismatched dimension")
+	}
+	if t.Uplo != a.Uplo {
+		panic("blas64: mismatched BLAS uplo")
+	}
+	if t.Diag != a.Diag {
+		panic("blas64: mismatched BLAS diag")
+	}
+	switch a.Uplo {
+	default:
+		panic("blas64: bad BLAS uplo")
+	case blas.Upper:
+		for i := 0; i < a.N; i++ {
+			for j := i; j < a.N; j++ {
+				t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
+			}
+		}
+	case blas.Lower:
+		for i := 0; i < a.N; i++ {
+			for j := 0; j <= i; j++ {
+				t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
+			}
+		}
+	case blas.All:
+		for i := 0; i < a.N; i++ {
+			for j := 0; j < a.N; j++ {
+				t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
+			}
+		}
+	}
+}
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions, uplo and diag as a and have
+// adequate backing data storage.
+func (t Triangular) From(a TriangularCols) {
+	if t.N != a.N {
+		panic("blas64: mismatched dimension")
+	}
+	if t.Uplo != a.Uplo {
+		panic("blas64: mismatched BLAS uplo")
+	}
+	if t.Diag != a.Diag {
+		panic("blas64: mismatched BLAS diag")
+	}
+	switch a.Uplo {
+	default:
+		panic("blas64: bad BLAS uplo")
+	case blas.Upper:
+		for i := 0; i < a.N; i++ {
+			for j := i; j < a.N; j++ {
+				t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
+			}
+		}
+	case blas.Lower:
+		for i := 0; i < a.N; i++ {
+			for j := 0; j <= i; j++ {
+				t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
+			}
+		}
+	case blas.All:
+		for i := 0; i < a.N; i++ {
+			for j := 0; j < a.N; j++ {
+				t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
+			}
+		}
+	}
+}
+
+// BandCols represents a matrix using the band column-major storage scheme.
+type BandCols Band
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions and bandwidth as a and have
+// adequate backing data storage.
+func (t BandCols) From(a Band) {
+	if t.Rows != a.Rows || t.Cols != a.Cols {
+		panic("blas64: mismatched dimension")
+	}
+	if t.KL != a.KL || t.KU != a.KU {
+		panic("blas64: mismatched bandwidth")
+	}
+	if a.Stride < a.KL+a.KU+1 {
+		panic("blas64: short stride for source")
+	}
+	if t.Stride < t.KL+t.KU+1 {
+		panic("blas64: short stride for destination")
+	}
+	for i := 0; i < a.Rows; i++ {
+		for j := max(0, i-a.KL); j < min(i+a.KU+1, a.Cols); j++ {
+			t.Data[i+t.KU-j+j*t.Stride] = a.Data[j+a.KL-i+i*a.Stride]
+		}
+	}
+}
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions and bandwidth as a and have
+// adequate backing data storage.
+func (t Band) From(a BandCols) {
+	if t.Rows != a.Rows || t.Cols != a.Cols {
+		panic("blas64: mismatched dimension")
+	}
+	if t.KL != a.KL || t.KU != a.KU {
+		panic("blas64: mismatched bandwidth")
+	}
+	if a.Stride < a.KL+a.KU+1 {
+		panic("blas64: short stride for source")
+	}
+	if t.Stride < t.KL+t.KU+1 {
+		panic("blas64: short stride for destination")
+	}
+	for j := 0; j < a.Cols; j++ {
+		for i := max(0, j-a.KU); i < min(j+a.KL+1, a.Rows); i++ {
+			t.Data[j+a.KL-i+i*a.Stride] = a.Data[i+t.KU-j+j*t.Stride]
+		}
+	}
+}
+
+// TriangularBandCols represents a symmetric matrix using the band column-major storage scheme.
+type TriangularBandCols TriangularBand
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions, bandwidth and uplo as a and
+// have adequate backing data storage.
+func (t TriangularBandCols) From(a TriangularBand) {
+	if t.N != a.N {
+		panic("blas64: mismatched dimension")
+	}
+	if t.K != a.K {
+		panic("blas64: mismatched bandwidth")
+	}
+	if a.Stride < a.K+1 {
+		panic("blas64: short stride for source")
+	}
+	if t.Stride < t.K+1 {
+		panic("blas64: short stride for destination")
+	}
+	if t.Uplo != a.Uplo {
+		panic("blas64: mismatched BLAS uplo")
+	}
+	if t.Diag != a.Diag {
+		panic("blas64: mismatched BLAS diag")
+	}
+	dst := BandCols{
+		Rows: t.N, Cols: t.N,
+		Stride: t.Stride,
+		Data:   t.Data,
+	}
+	src := Band{
+		Rows: a.N, Cols: a.N,
+		Stride: a.Stride,
+		Data:   a.Data,
+	}
+	switch a.Uplo {
+	default:
+		panic("blas64: bad BLAS uplo")
+	case blas.Upper:
+		dst.KU = t.K
+		src.KU = a.K
+	case blas.Lower:
+		dst.KL = t.K
+		src.KL = a.K
+	}
+	dst.From(src)
+}
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions, bandwidth and uplo as a and
+// have adequate backing data storage.
+func (t TriangularBand) From(a TriangularBandCols) {
+	if t.N != a.N {
+		panic("blas64: mismatched dimension")
+	}
+	if t.K != a.K {
+		panic("blas64: mismatched bandwidth")
+	}
+	if a.Stride < a.K+1 {
+		panic("blas64: short stride for source")
+	}
+	if t.Stride < t.K+1 {
+		panic("blas64: short stride for destination")
+	}
+	if t.Uplo != a.Uplo {
+		panic("blas64: mismatched BLAS uplo")
+	}
+	if t.Diag != a.Diag {
+		panic("blas64: mismatched BLAS diag")
+	}
+	dst := Band{
+		Rows: t.N, Cols: t.N,
+		Stride: t.Stride,
+		Data:   t.Data,
+	}
+	src := BandCols{
+		Rows: a.N, Cols: a.N,
+		Stride: a.Stride,
+		Data:   a.Data,
+	}
+	switch a.Uplo {
+	default:
+		panic("blas64: bad BLAS uplo")
+	case blas.Upper:
+		dst.KU = t.K
+		src.KU = a.K
+	case blas.Lower:
+		dst.KL = t.K
+		src.KL = a.K
+	}
+	dst.From(src)
+}
+
+func min(a, b int) int {
+	if a < b {
+		return a
+	}
+	return b
+}
+
+func max(a, b int) int {
+	if a > b {
+		return a
+	}
+	return b
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/blas64/conv_symmetric.go b/vendor/gonum.org/v1/gonum/blas/blas64/conv_symmetric.go
new file mode 100644
index 00000000..a43b2304
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/blas64/conv_symmetric.go
@@ -0,0 +1,153 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package blas64
+
+import "gonum.org/v1/gonum/blas"
+
+// SymmetricCols represents a matrix using the conventional column-major storage scheme.
+type SymmetricCols Symmetric
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions and uplo as a and have adequate
+// backing data storage.
+func (t SymmetricCols) From(a Symmetric) {
+	if t.N != a.N {
+		panic("blas64: mismatched dimension")
+	}
+	if t.Uplo != a.Uplo {
+		panic("blas64: mismatched BLAS uplo")
+	}
+	switch a.Uplo {
+	default:
+		panic("blas64: bad BLAS uplo")
+	case blas.Upper:
+		for i := 0; i < a.N; i++ {
+			for j := i; j < a.N; j++ {
+				t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
+			}
+		}
+	case blas.Lower:
+		for i := 0; i < a.N; i++ {
+			for j := 0; j <= i; j++ {
+				t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
+			}
+		}
+	}
+}
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions and uplo as a and have adequate
+// backing data storage.
+func (t Symmetric) From(a SymmetricCols) {
+	if t.N != a.N {
+		panic("blas64: mismatched dimension")
+	}
+	if t.Uplo != a.Uplo {
+		panic("blas64: mismatched BLAS uplo")
+	}
+	switch a.Uplo {
+	default:
+		panic("blas64: bad BLAS uplo")
+	case blas.Upper:
+		for i := 0; i < a.N; i++ {
+			for j := i; j < a.N; j++ {
+				t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
+			}
+		}
+	case blas.Lower:
+		for i := 0; i < a.N; i++ {
+			for j := 0; j <= i; j++ {
+				t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
+			}
+		}
+	}
+}
+
+// SymmetricBandCols represents a symmetric matrix using the band column-major storage scheme.
+type SymmetricBandCols SymmetricBand
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions, bandwidth and uplo as a and
+// have adequate backing data storage.
+func (t SymmetricBandCols) From(a SymmetricBand) {
+	if t.N != a.N {
+		panic("blas64: mismatched dimension")
+	}
+	if t.K != a.K {
+		panic("blas64: mismatched bandwidth")
+	}
+	if a.Stride < a.K+1 {
+		panic("blas64: short stride for source")
+	}
+	if t.Stride < t.K+1 {
+		panic("blas64: short stride for destination")
+	}
+	if t.Uplo != a.Uplo {
+		panic("blas64: mismatched BLAS uplo")
+	}
+	dst := BandCols{
+		Rows: t.N, Cols: t.N,
+		Stride: t.Stride,
+		Data:   t.Data,
+	}
+	src := Band{
+		Rows: a.N, Cols: a.N,
+		Stride: a.Stride,
+		Data:   a.Data,
+	}
+	switch a.Uplo {
+	default:
+		panic("blas64: bad BLAS uplo")
+	case blas.Upper:
+		dst.KU = t.K
+		src.KU = a.K
+	case blas.Lower:
+		dst.KL = t.K
+		src.KL = a.K
+	}
+	dst.From(src)
+}
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions, bandwidth and uplo as a and
+// have adequate backing data storage.
+func (t SymmetricBand) From(a SymmetricBandCols) {
+	if t.N != a.N {
+		panic("blas64: mismatched dimension")
+	}
+	if t.K != a.K {
+		panic("blas64: mismatched bandwidth")
+	}
+	if a.Stride < a.K+1 {
+		panic("blas64: short stride for source")
+	}
+	if t.Stride < t.K+1 {
+		panic("blas64: short stride for destination")
+	}
+	if t.Uplo != a.Uplo {
+		panic("blas64: mismatched BLAS uplo")
+	}
+	dst := Band{
+		Rows: t.N, Cols: t.N,
+		Stride: t.Stride,
+		Data:   t.Data,
+	}
+	src := BandCols{
+		Rows: a.N, Cols: a.N,
+		Stride: a.Stride,
+		Data:   a.Data,
+	}
+	switch a.Uplo {
+	default:
+		panic("blas64: bad BLAS uplo")
+	case blas.Upper:
+		dst.KU = t.K
+		src.KU = a.K
+	case blas.Lower:
+		dst.KL = t.K
+		src.KL = a.K
+	}
+	dst.From(src)
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/blas64/conv_symmetric_test.go b/vendor/gonum.org/v1/gonum/blas/blas64/conv_symmetric_test.go
new file mode 100644
index 00000000..167de52d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/blas64/conv_symmetric_test.go
@@ -0,0 +1,305 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package blas64
+
+import (
+	"math"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+func newSymmetricFrom(a SymmetricCols) Symmetric {
+	t := Symmetric{
+		N:      a.N,
+		Stride: a.N,
+		Data:   make([]float64, a.N*a.N),
+		Uplo:   a.Uplo,
+	}
+	t.From(a)
+	return t
+}
+
+func (m Symmetric) n() int { return m.N }
+func (m Symmetric) at(i, j int) float64 {
+	if m.Uplo == blas.Lower && i < j && j < m.N {
+		i, j = j, i
+	}
+	if m.Uplo == blas.Upper && i > j {
+		i, j = j, i
+	}
+	return m.Data[i*m.Stride+j]
+}
+func (m Symmetric) uplo() blas.Uplo { return m.Uplo }
+
+func newSymmetricColsFrom(a Symmetric) SymmetricCols {
+	t := SymmetricCols{
+		N:      a.N,
+		Stride: a.N,
+		Data:   make([]float64, a.N*a.N),
+		Uplo:   a.Uplo,
+	}
+	t.From(a)
+	return t
+}
+
+func (m SymmetricCols) n() int { return m.N }
+func (m SymmetricCols) at(i, j int) float64 {
+	if m.Uplo == blas.Lower && i < j {
+		i, j = j, i
+	}
+	if m.Uplo == blas.Upper && i > j && i < m.N {
+		i, j = j, i
+	}
+	return m.Data[i+j*m.Stride]
+}
+func (m SymmetricCols) uplo() blas.Uplo { return m.Uplo }
+
+type symmetric interface {
+	n() int
+	at(i, j int) float64
+	uplo() blas.Uplo
+}
+
+func sameSymmetric(a, b symmetric) bool {
+	an := a.n()
+	bn := b.n()
+	if an != bn {
+		return false
+	}
+	if a.uplo() != b.uplo() {
+		return false
+	}
+	for i := 0; i < an; i++ {
+		for j := 0; j < an; j++ {
+			if a.at(i, j) != b.at(i, j) || math.IsNaN(a.at(i, j)) != math.IsNaN(b.at(i, j)) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+var symmetricTests = []Symmetric{
+	{N: 3, Stride: 3, Data: []float64{
+		1, 2, 3,
+		4, 5, 6,
+		7, 8, 9,
+	}},
+	{N: 3, Stride: 5, Data: []float64{
+		1, 2, 3, 0, 0,
+		4, 5, 6, 0, 0,
+		7, 8, 9, 0, 0,
+	}},
+}
+
+func TestConvertSymmetric(t *testing.T) {
+	for _, test := range symmetricTests {
+		for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
+			test.Uplo = uplo
+			colmajor := newSymmetricColsFrom(test)
+			if !sameSymmetric(colmajor, test) {
+				t.Errorf("unexpected result for row major to col major conversion:\n\tgot: %#v\n\tfrom:%#v",
+					colmajor, test)
+			}
+			rowmajor := newSymmetricFrom(colmajor)
+			if !sameSymmetric(rowmajor, test) {
+				t.Errorf("unexpected result for col major to row major conversion:\n\tgot: %#v\n\twant:%#v",
+					rowmajor, test)
+			}
+		}
+	}
+}
+func newSymmetricBandFrom(a SymmetricBandCols) SymmetricBand {
+	t := SymmetricBand{
+		N:      a.N,
+		K:      a.K,
+		Stride: a.K + 1,
+		Data:   make([]float64, a.N*(a.K+1)),
+		Uplo:   a.Uplo,
+	}
+	for i := range t.Data {
+		t.Data[i] = math.NaN()
+	}
+	t.From(a)
+	return t
+}
+
+func (m SymmetricBand) n() (n int) { return m.N }
+func (m SymmetricBand) at(i, j int) float64 {
+	b := Band{
+		Rows: m.N, Cols: m.N,
+		Stride: m.Stride,
+		Data:   m.Data,
+	}
+	switch m.Uplo {
+	default:
+		panic("blas64: bad BLAS uplo")
+	case blas.Upper:
+		b.KU = m.K
+		if i > j {
+			i, j = j, i
+		}
+	case blas.Lower:
+		b.KL = m.K
+		if i < j {
+			i, j = j, i
+		}
+	}
+	return b.at(i, j)
+}
+func (m SymmetricBand) bandwidth() (k int) { return m.K }
+func (m SymmetricBand) uplo() blas.Uplo    { return m.Uplo }
+
+func newSymmetricBandColsFrom(a SymmetricBand) SymmetricBandCols {
+	t := SymmetricBandCols{
+		N:      a.N,
+		K:      a.K,
+		Stride: a.K + 1,
+		Data:   make([]float64, a.N*(a.K+1)),
+		Uplo:   a.Uplo,
+	}
+	for i := range t.Data {
+		t.Data[i] = math.NaN()
+	}
+	t.From(a)
+	return t
+}
+
+func (m SymmetricBandCols) n() (n int) { return m.N }
+func (m SymmetricBandCols) at(i, j int) float64 {
+	b := BandCols{
+		Rows: m.N, Cols: m.N,
+		Stride: m.Stride,
+		Data:   m.Data,
+	}
+	switch m.Uplo {
+	default:
+		panic("blas64: bad BLAS uplo")
+	case blas.Upper:
+		b.KU = m.K
+		if i > j {
+			i, j = j, i
+		}
+	case blas.Lower:
+		b.KL = m.K
+		if i < j {
+			i, j = j, i
+		}
+	}
+	return b.at(i, j)
+}
+func (m SymmetricBandCols) bandwidth() (k int) { return m.K }
+func (m SymmetricBandCols) uplo() blas.Uplo    { return m.Uplo }
+
+type symmetricBand interface {
+	n() (n int)
+	at(i, j int) float64
+	bandwidth() (k int)
+	uplo() blas.Uplo
+}
+
+func sameSymmetricBand(a, b symmetricBand) bool {
+	an := a.n()
+	bn := b.n()
+	if an != bn {
+		return false
+	}
+	if a.uplo() != b.uplo() {
+		return false
+	}
+	ak := a.bandwidth()
+	bk := b.bandwidth()
+	if ak != bk {
+		return false
+	}
+	for i := 0; i < an; i++ {
+		for j := 0; j < an; j++ {
+			if a.at(i, j) != b.at(i, j) || math.IsNaN(a.at(i, j)) != math.IsNaN(b.at(i, j)) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+var symmetricBandTests = []SymmetricBand{
+	{N: 3, K: 0, Stride: 1, Uplo: blas.Upper, Data: []float64{
+		1,
+		2,
+		3,
+	}},
+	{N: 3, K: 0, Stride: 1, Uplo: blas.Lower, Data: []float64{
+		1,
+		2,
+		3,
+	}},
+	{N: 3, K: 1, Stride: 2, Uplo: blas.Upper, Data: []float64{
+		1, 2,
+		3, 4,
+		5, -1,
+	}},
+	{N: 3, K: 1, Stride: 2, Uplo: blas.Lower, Data: []float64{
+		-1, 1,
+		2, 3,
+		4, 5,
+	}},
+	{N: 3, K: 2, Stride: 3, Uplo: blas.Upper, Data: []float64{
+		1, 2, 3,
+		4, 5, -1,
+		6, -2, -3,
+	}},
+	{N: 3, K: 2, Stride: 3, Uplo: blas.Lower, Data: []float64{
+		-2, -1, 1,
+		-3, 2, 4,
+		3, 5, 6,
+	}},
+
+	{N: 3, K: 0, Stride: 5, Uplo: blas.Upper, Data: []float64{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{N: 3, K: 0, Stride: 5, Uplo: blas.Lower, Data: []float64{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{N: 3, K: 1, Stride: 5, Uplo: blas.Upper, Data: []float64{
+		1, 2, 0, 0, 0,
+		3, 4, 0, 0, 0,
+		5, -1, 0, 0, 0,
+	}},
+	{N: 3, K: 1, Stride: 5, Uplo: blas.Lower, Data: []float64{
+		-1, 1, 0, 0, 0,
+		2, 3, 0, 0, 0,
+		4, 5, 0, 0, 0,
+	}},
+	{N: 3, K: 2, Stride: 5, Uplo: blas.Upper, Data: []float64{
+		1, 2, 3, 0, 0,
+		4, 5, -1, 0, 0,
+		6, -2, -3, 0, 0,
+	}},
+	{N: 3, K: 2, Stride: 5, Uplo: blas.Lower, Data: []float64{
+		-2, -1, 1, 0, 0,
+		-3, 2, 4, 0, 0,
+		3, 5, 6, 0, 0,
+	}},
+}
+
+func TestConvertSymBand(t *testing.T) {
+	for _, test := range symmetricBandTests {
+		colmajor := newSymmetricBandColsFrom(test)
+		if !sameSymmetricBand(colmajor, test) {
+			t.Errorf("unexpected result for row major to col major conversion:\n\tgot: %#v\n\tfrom:%#v",
+				colmajor, test)
+		}
+		rowmajor := newSymmetricBandFrom(colmajor)
+		if !sameSymmetricBand(rowmajor, test) {
+			t.Errorf("unexpected result for col major to row major conversion:\n\tgot: %#v\n\twant:%#v",
+				rowmajor, test)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/blas64/conv_test.go b/vendor/gonum.org/v1/gonum/blas/blas64/conv_test.go
new file mode 100644
index 00000000..61645317
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/blas64/conv_test.go
@@ -0,0 +1,618 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package blas64
+
+import (
+	"math"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+func newGeneralFrom(a GeneralCols) General {
+	t := General{
+		Rows:   a.Rows,
+		Cols:   a.Cols,
+		Stride: a.Cols,
+		Data:   make([]float64, a.Rows*a.Cols),
+	}
+	t.From(a)
+	return t
+}
+
+func (m General) dims() (r, c int)    { return m.Rows, m.Cols }
+func (m General) at(i, j int) float64 { return m.Data[i*m.Stride+j] }
+
+func newGeneralColsFrom(a General) GeneralCols {
+	t := GeneralCols{
+		Rows:   a.Rows,
+		Cols:   a.Cols,
+		Stride: a.Rows,
+		Data:   make([]float64, a.Rows*a.Cols),
+	}
+	t.From(a)
+	return t
+}
+
+func (m GeneralCols) dims() (r, c int)    { return m.Rows, m.Cols }
+func (m GeneralCols) at(i, j int) float64 { return m.Data[i+j*m.Stride] }
+
+type general interface {
+	dims() (r, c int)
+	at(i, j int) float64
+}
+
+func sameGeneral(a, b general) bool {
+	ar, ac := a.dims()
+	br, bc := b.dims()
+	if ar != br || ac != bc {
+		return false
+	}
+	for i := 0; i < ar; i++ {
+		for j := 0; j < ac; j++ {
+			if a.at(i, j) != b.at(i, j) || math.IsNaN(a.at(i, j)) != math.IsNaN(b.at(i, j)) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+var generalTests = []General{
+	{Rows: 2, Cols: 3, Stride: 3, Data: []float64{
+		1, 2, 3,
+		4, 5, 6,
+	}},
+	{Rows: 3, Cols: 2, Stride: 2, Data: []float64{
+		1, 2,
+		3, 4,
+		5, 6,
+	}},
+	{Rows: 3, Cols: 3, Stride: 3, Data: []float64{
+		1, 2, 3,
+		4, 5, 6,
+		7, 8, 9,
+	}},
+	{Rows: 2, Cols: 3, Stride: 5, Data: []float64{
+		1, 2, 3, 0, 0,
+		4, 5, 6, 0, 0,
+	}},
+	{Rows: 3, Cols: 2, Stride: 5, Data: []float64{
+		1, 2, 0, 0, 0,
+		3, 4, 0, 0, 0,
+		5, 6, 0, 0, 0,
+	}},
+	{Rows: 3, Cols: 3, Stride: 5, Data: []float64{
+		1, 2, 3, 0, 0,
+		4, 5, 6, 0, 0,
+		7, 8, 9, 0, 0,
+	}},
+}
+
+func TestConvertGeneral(t *testing.T) {
+	for _, test := range generalTests {
+		colmajor := newGeneralColsFrom(test)
+		if !sameGeneral(colmajor, test) {
+			t.Errorf("unexpected result for row major to col major conversion:\n\tgot: %#v\n\tfrom:%#v",
+				colmajor, test)
+		}
+		rowmajor := newGeneralFrom(colmajor)
+		if !sameGeneral(rowmajor, test) {
+			t.Errorf("unexpected result for col major to row major conversion:\n\tgot: %#v\n\twant:%#v",
+				rowmajor, test)
+		}
+	}
+}
+
+func newTriangularFrom(a TriangularCols) Triangular {
+	t := Triangular{
+		N:      a.N,
+		Stride: a.N,
+		Data:   make([]float64, a.N*a.N),
+		Diag:   a.Diag,
+		Uplo:   a.Uplo,
+	}
+	t.From(a)
+	return t
+}
+
+func (m Triangular) n() int { return m.N }
+func (m Triangular) at(i, j int) float64 {
+	if m.Diag == blas.Unit && i == j {
+		return 1
+	}
+	if m.Uplo == blas.Lower && i < j && j < m.N {
+		return 0
+	}
+	if m.Uplo == blas.Upper && i > j {
+		return 0
+	}
+	return m.Data[i*m.Stride+j]
+}
+func (m Triangular) uplo() blas.Uplo { return m.Uplo }
+func (m Triangular) diag() blas.Diag { return m.Diag }
+
+func newTriangularColsFrom(a Triangular) TriangularCols {
+	t := TriangularCols{
+		N:      a.N,
+		Stride: a.N,
+		Data:   make([]float64, a.N*a.N),
+		Diag:   a.Diag,
+		Uplo:   a.Uplo,
+	}
+	t.From(a)
+	return t
+}
+
+func (m TriangularCols) n() int { return m.N }
+func (m TriangularCols) at(i, j int) float64 {
+	if m.Diag == blas.Unit && i == j {
+		return 1
+	}
+	if m.Uplo == blas.Lower && i < j {
+		return 0
+	}
+	if m.Uplo == blas.Upper && i > j && i < m.N {
+		return 0
+	}
+	return m.Data[i+j*m.Stride]
+}
+func (m TriangularCols) uplo() blas.Uplo { return m.Uplo }
+func (m TriangularCols) diag() blas.Diag { return m.Diag }
+
+type triangular interface {
+	n() int
+	at(i, j int) float64
+	uplo() blas.Uplo
+	diag() blas.Diag
+}
+
+func sameTriangular(a, b triangular) bool {
+	an := a.n()
+	bn := b.n()
+	if an != bn {
+		return false
+	}
+	for i := 0; i < an; i++ {
+		for j := 0; j < an; j++ {
+			if a.at(i, j) != b.at(i, j) || math.IsNaN(a.at(i, j)) != math.IsNaN(b.at(i, j)) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+var triangularTests = []Triangular{
+	{N: 3, Stride: 3, Data: []float64{
+		1, 2, 3,
+		4, 5, 6,
+		7, 8, 9,
+	}},
+	{N: 3, Stride: 5, Data: []float64{
+		1, 2, 3, 0, 0,
+		4, 5, 6, 0, 0,
+		7, 8, 9, 0, 0,
+	}},
+}
+
+func TestConvertTriangular(t *testing.T) {
+	for _, test := range triangularTests {
+		for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower, blas.All} {
+			for _, diag := range []blas.Diag{blas.Unit, blas.NonUnit} {
+				test.Uplo = uplo
+				test.Diag = diag
+				colmajor := newTriangularColsFrom(test)
+				if !sameTriangular(colmajor, test) {
+					t.Errorf("unexpected result for row major to col major conversion:\n\tgot: %#v\n\tfrom:%#v",
+						colmajor, test)
+				}
+				rowmajor := newTriangularFrom(colmajor)
+				if !sameTriangular(rowmajor, test) {
+					t.Errorf("unexpected result for col major to row major conversion:\n\tgot: %#v\n\twant:%#v",
+						rowmajor, test)
+				}
+			}
+		}
+	}
+}
+
+func newBandFrom(a BandCols) Band {
+	t := Band{
+		Rows:   a.Rows,
+		Cols:   a.Cols,
+		KL:     a.KL,
+		KU:     a.KU,
+		Stride: a.KL + a.KU + 1,
+		Data:   make([]float64, a.Rows*(a.KL+a.KU+1)),
+	}
+	for i := range t.Data {
+		t.Data[i] = math.NaN()
+	}
+	t.From(a)
+	return t
+}
+
+func (m Band) dims() (r, c int) { return m.Rows, m.Cols }
+func (m Band) at(i, j int) float64 {
+	pj := j + m.KL - i
+	if pj < 0 || m.KL+m.KU+1 <= pj {
+		return 0
+	}
+	return m.Data[i*m.Stride+pj]
+}
+func (m Band) bandwidth() (kl, ku int) { return m.KL, m.KU }
+
+func newBandColsFrom(a Band) BandCols {
+	t := BandCols{
+		Rows:   a.Rows,
+		Cols:   a.Cols,
+		KL:     a.KL,
+		KU:     a.KU,
+		Stride: a.KL + a.KU + 1,
+		Data:   make([]float64, a.Cols*(a.KL+a.KU+1)),
+	}
+	for i := range t.Data {
+		t.Data[i] = math.NaN()
+	}
+	t.From(a)
+	return t
+}
+
+func (m BandCols) dims() (r, c int) { return m.Rows, m.Cols }
+func (m BandCols) at(i, j int) float64 {
+	pj := i + m.KU - j
+	if pj < 0 || m.KL+m.KU+1 <= pj {
+		return 0
+	}
+	return m.Data[j*m.Stride+pj]
+}
+func (m BandCols) bandwidth() (kl, ku int) { return m.KL, m.KU }
+
+type band interface {
+	dims() (r, c int)
+	at(i, j int) float64
+	bandwidth() (kl, ku int)
+}
+
+func sameBand(a, b band) bool {
+	ar, ac := a.dims()
+	br, bc := b.dims()
+	if ar != br || ac != bc {
+		return false
+	}
+	akl, aku := a.bandwidth()
+	bkl, bku := b.bandwidth()
+	if akl != bkl || aku != bku {
+		return false
+	}
+	for i := 0; i < ar; i++ {
+		for j := 0; j < ac; j++ {
+			if a.at(i, j) != b.at(i, j) || math.IsNaN(a.at(i, j)) != math.IsNaN(b.at(i, j)) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+var bandTests = []Band{
+	{Rows: 3, Cols: 4, KL: 0, KU: 0, Stride: 1, Data: []float64{
+		1,
+		2,
+		3,
+	}},
+	{Rows: 3, Cols: 3, KL: 0, KU: 0, Stride: 1, Data: []float64{
+		1,
+		2,
+		3,
+	}},
+	{Rows: 4, Cols: 3, KL: 0, KU: 0, Stride: 1, Data: []float64{
+		1,
+		2,
+		3,
+	}},
+	{Rows: 4, Cols: 3, KL: 0, KU: 1, Stride: 2, Data: []float64{
+		1, 2,
+		3, 4,
+		5, 6,
+	}},
+	{Rows: 3, Cols: 4, KL: 0, KU: 1, Stride: 2, Data: []float64{
+		1, 2,
+		3, 4,
+		5, 6,
+	}},
+	{Rows: 3, Cols: 4, KL: 1, KU: 1, Stride: 3, Data: []float64{
+		-1, 2, 3,
+		4, 5, 6,
+		7, 8, 9,
+	}},
+	{Rows: 4, Cols: 3, KL: 1, KU: 1, Stride: 3, Data: []float64{
+		-1, 2, 3,
+		4, 5, 6,
+		7, 8, -2,
+		9, -3, -4,
+	}},
+	{Rows: 3, Cols: 4, KL: 2, KU: 1, Stride: 4, Data: []float64{
+		-2, -1, 3, 4,
+		-3, 5, 6, 7,
+		8, 9, 10, 11,
+	}},
+	{Rows: 4, Cols: 3, KL: 2, KU: 1, Stride: 4, Data: []float64{
+		-2, -1, 2, 3,
+		-3, 4, 5, 6,
+		7, 8, 9, -4,
+		10, 11, -5, -6,
+	}},
+
+	{Rows: 3, Cols: 4, KL: 0, KU: 0, Stride: 5, Data: []float64{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{Rows: 3, Cols: 3, KL: 0, KU: 0, Stride: 5, Data: []float64{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{Rows: 4, Cols: 3, KL: 0, KU: 0, Stride: 5, Data: []float64{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{Rows: 4, Cols: 3, KL: 0, KU: 1, Stride: 5, Data: []float64{
+		1, 2, 0, 0, 0,
+		3, 4, 0, 0, 0,
+		5, 6, 0, 0, 0,
+	}},
+	{Rows: 3, Cols: 4, KL: 0, KU: 1, Stride: 5, Data: []float64{
+		1, 2, 0, 0, 0,
+		3, 4, 0, 0, 0,
+		5, 6, 0, 0, 0,
+	}},
+	{Rows: 3, Cols: 4, KL: 1, KU: 1, Stride: 5, Data: []float64{
+		-1, 2, 3, 0, 0,
+		4, 5, 6, 0, 0,
+		7, 8, 9, 0, 0,
+	}},
+	{Rows: 4, Cols: 3, KL: 1, KU: 1, Stride: 5, Data: []float64{
+		-1, 2, 3, 0, 0,
+		4, 5, 6, 0, 0,
+		7, 8, -2, 0, 0,
+		9, -3, -4, 0, 0,
+	}},
+	{Rows: 3, Cols: 4, KL: 2, KU: 1, Stride: 5, Data: []float64{
+		-2, -1, 3, 4, 0,
+		-3, 5, 6, 7, 0,
+		8, 9, 10, 11, 0,
+	}},
+	{Rows: 4, Cols: 3, KL: 2, KU: 1, Stride: 5, Data: []float64{
+		-2, -1, 2, 3, 0,
+		-3, 4, 5, 6, 0,
+		7, 8, 9, -4, 0,
+		10, 11, -5, -6, 0,
+	}},
+}
+
+func TestConvertBand(t *testing.T) {
+	for _, test := range bandTests {
+		colmajor := newBandColsFrom(test)
+		if !sameBand(colmajor, test) {
+			t.Errorf("unexpected result for row major to col major conversion:\n\tgot: %#v\n\tfrom:%#v",
+				colmajor, test)
+		}
+		rowmajor := newBandFrom(colmajor)
+		if !sameBand(rowmajor, test) {
+			t.Errorf("unexpected result for col major to row major conversion:\n\tgot: %#v\n\twant:%#v",
+				rowmajor, test)
+		}
+	}
+}
+
+func newTriangularBandFrom(a TriangularBandCols) TriangularBand {
+	t := TriangularBand{
+		N:      a.N,
+		K:      a.K,
+		Stride: a.K + 1,
+		Data:   make([]float64, a.N*(a.K+1)),
+		Uplo:   a.Uplo,
+		Diag:   a.Diag,
+	}
+	for i := range t.Data {
+		t.Data[i] = math.NaN()
+	}
+	t.From(a)
+	return t
+}
+
+func (m TriangularBand) n() (n int) { return m.N }
+func (m TriangularBand) at(i, j int) float64 {
+	if m.Diag == blas.Unit && i == j {
+		return 1
+	}
+	b := Band{
+		Rows: m.N, Cols: m.N,
+		Stride: m.Stride,
+		Data:   m.Data,
+	}
+	switch m.Uplo {
+	default:
+		panic("blas64: bad BLAS uplo")
+	case blas.Upper:
+		if i > j {
+			return 0
+		}
+		b.KU = m.K
+	case blas.Lower:
+		if i < j {
+			return 0
+		}
+		b.KL = m.K
+	}
+	return b.at(i, j)
+}
+func (m TriangularBand) bandwidth() (k int) { return m.K }
+func (m TriangularBand) uplo() blas.Uplo    { return m.Uplo }
+func (m TriangularBand) diag() blas.Diag    { return m.Diag }
+
+func newTriangularBandColsFrom(a TriangularBand) TriangularBandCols {
+	t := TriangularBandCols{
+		N:      a.N,
+		K:      a.K,
+		Stride: a.K + 1,
+		Data:   make([]float64, a.N*(a.K+1)),
+		Uplo:   a.Uplo,
+		Diag:   a.Diag,
+	}
+	for i := range t.Data {
+		t.Data[i] = math.NaN()
+	}
+	t.From(a)
+	return t
+}
+
+func (m TriangularBandCols) n() (n int) { return m.N }
+func (m TriangularBandCols) at(i, j int) float64 {
+	if m.Diag == blas.Unit && i == j {
+		return 1
+	}
+	b := BandCols{
+		Rows: m.N, Cols: m.N,
+		Stride: m.Stride,
+		Data:   m.Data,
+	}
+	switch m.Uplo {
+	default:
+		panic("blas64: bad BLAS uplo")
+	case blas.Upper:
+		if i > j {
+			return 0
+		}
+		b.KU = m.K
+	case blas.Lower:
+		if i < j {
+			return 0
+		}
+		b.KL = m.K
+	}
+	return b.at(i, j)
+}
+func (m TriangularBandCols) bandwidth() (k int) { return m.K }
+func (m TriangularBandCols) uplo() blas.Uplo    { return m.Uplo }
+func (m TriangularBandCols) diag() blas.Diag    { return m.Diag }
+
+type triangularBand interface {
+	n() (n int)
+	at(i, j int) float64
+	bandwidth() (k int)
+	uplo() blas.Uplo
+	diag() blas.Diag
+}
+
+func sameTriangularBand(a, b triangularBand) bool {
+	an := a.n()
+	bn := b.n()
+	if an != bn {
+		return false
+	}
+	if a.uplo() != b.uplo() {
+		return false
+	}
+	if a.diag() != b.diag() {
+		return false
+	}
+	ak := a.bandwidth()
+	bk := b.bandwidth()
+	if ak != bk {
+		return false
+	}
+	for i := 0; i < an; i++ {
+		for j := 0; j < an; j++ {
+			if a.at(i, j) != b.at(i, j) || math.IsNaN(a.at(i, j)) != math.IsNaN(b.at(i, j)) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+var triangularBandTests = []TriangularBand{
+	{N: 3, K: 0, Stride: 1, Uplo: blas.Upper, Data: []float64{
+		1,
+		2,
+		3,
+	}},
+	{N: 3, K: 0, Stride: 1, Uplo: blas.Lower, Data: []float64{
+		1,
+		2,
+		3,
+	}},
+	{N: 3, K: 1, Stride: 2, Uplo: blas.Upper, Data: []float64{
+		1, 2,
+		3, 4,
+		5, -1,
+	}},
+	{N: 3, K: 1, Stride: 2, Uplo: blas.Lower, Data: []float64{
+		-1, 1,
+		2, 3,
+		4, 5,
+	}},
+	{N: 3, K: 2, Stride: 3, Uplo: blas.Upper, Data: []float64{
+		1, 2, 3,
+		4, 5, -1,
+		6, -2, -3,
+	}},
+	{N: 3, K: 2, Stride: 3, Uplo: blas.Lower, Data: []float64{
+		-2, -1, 1,
+		-3, 2, 4,
+		3, 5, 6,
+	}},
+
+	{N: 3, K: 0, Stride: 5, Uplo: blas.Upper, Data: []float64{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{N: 3, K: 0, Stride: 5, Uplo: blas.Lower, Data: []float64{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{N: 3, K: 1, Stride: 5, Uplo: blas.Upper, Data: []float64{
+		1, 2, 0, 0, 0,
+		3, 4, 0, 0, 0,
+		5, -1, 0, 0, 0,
+	}},
+	{N: 3, K: 1, Stride: 5, Uplo: blas.Lower, Data: []float64{
+		-1, 1, 0, 0, 0,
+		2, 3, 0, 0, 0,
+		4, 5, 0, 0, 0,
+	}},
+	{N: 3, K: 2, Stride: 5, Uplo: blas.Upper, Data: []float64{
+		1, 2, 3, 0, 0,
+		4, 5, -1, 0, 0,
+		6, -2, -3, 0, 0,
+	}},
+	{N: 3, K: 2, Stride: 5, Uplo: blas.Lower, Data: []float64{
+		-2, -1, 1, 0, 0,
+		-3, 2, 4, 0, 0,
+		3, 5, 6, 0, 0,
+	}},
+}
+
+func TestConvertTriBand(t *testing.T) {
+	for _, test := range triangularBandTests {
+		colmajor := newTriangularBandColsFrom(test)
+		if !sameTriangularBand(colmajor, test) {
+			t.Errorf("unexpected result for row major to col major conversion:\n\tgot: %#v\n\tfrom:%#v",
+				colmajor, test)
+		}
+		rowmajor := newTriangularBandFrom(colmajor)
+		if !sameTriangularBand(rowmajor, test) {
+			t.Errorf("unexpected result for col major to row major conversion:\n\tgot: %#v\n\twant:%#v",
+				rowmajor, test)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/blas64/doc.go b/vendor/gonum.org/v1/gonum/blas/blas64/doc.go
new file mode 100644
index 00000000..92e588f8
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/blas64/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package blas64 provides a simple interface to the float64 BLAS API.
+package blas64 // import "gonum.org/v1/gonum/blas/blas64"
diff --git a/vendor/gonum.org/v1/gonum/blas/cblas128/cblas128.go b/vendor/gonum.org/v1/gonum/blas/cblas128/cblas128.go
new file mode 100644
index 00000000..9b463504
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/cblas128/cblas128.go
@@ -0,0 +1,507 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package cblas128
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/gonum"
+)
+
+var cblas128 blas.Complex128 = gonum.Implementation{}
+
+// Use sets the BLAS complex128 implementation to be used by subsequent BLAS calls.
+// The default implementation is cgo.Implementation.
+func Use(b blas.Complex128) {
+	cblas128 = b
+}
+
+// Implementation returns the current BLAS complex128 implementation.
+//
+// Implementation allows direct calls to the current the BLAS complex128 implementation
+// giving finer control of parameters.
+func Implementation() blas.Complex128 {
+	return cblas128
+}
+
+// Vector represents a vector with an associated element increment.
+type Vector struct {
+	Inc  int
+	Data []complex128
+}
+
+// General represents a matrix using the conventional storage scheme.
+type General struct {
+	Rows, Cols int
+	Stride     int
+	Data       []complex128
+}
+
+// Band represents a band matrix using the band storage scheme.
+type Band struct {
+	Rows, Cols int
+	KL, KU     int
+	Stride     int
+	Data       []complex128
+}
+
+// Triangular represents a triangular matrix using the conventional storage scheme.
+type Triangular struct {
+	N      int
+	Stride int
+	Data   []complex128
+	Uplo   blas.Uplo
+	Diag   blas.Diag
+}
+
+// TriangularBand represents a triangular matrix using the band storage scheme.
+type TriangularBand struct {
+	N, K   int
+	Stride int
+	Data   []complex128
+	Uplo   blas.Uplo
+	Diag   blas.Diag
+}
+
+// TriangularPacked represents a triangular matrix using the packed storage scheme.
+type TriangularPacked struct {
+	N    int
+	Data []complex128
+	Uplo blas.Uplo
+	Diag blas.Diag
+}
+
+// Symmetric represents a symmetric matrix using the conventional storage scheme.
+type Symmetric struct {
+	N      int
+	Stride int
+	Data   []complex128
+	Uplo   blas.Uplo
+}
+
+// SymmetricBand represents a symmetric matrix using the band storage scheme.
+type SymmetricBand struct {
+	N, K   int
+	Stride int
+	Data   []complex128
+	Uplo   blas.Uplo
+}
+
+// SymmetricPacked represents a symmetric matrix using the packed storage scheme.
+type SymmetricPacked struct {
+	N    int
+	Data []complex128
+	Uplo blas.Uplo
+}
+
+// Hermitian represents an Hermitian matrix using the conventional storage scheme.
+type Hermitian Symmetric
+
+// HermitianBand represents an Hermitian matrix using the band storage scheme.
+type HermitianBand SymmetricBand
+
+// HermitianPacked represents an Hermitian matrix using the packed storage scheme.
+type HermitianPacked SymmetricPacked
+
+// Level 1
+
+const negInc = "cblas128: negative vector increment"
+
+// Dotu computes the dot product of the two vectors without
+// complex conjugation:
+//  x^T * y.
+func Dotu(n int, x, y Vector) complex128 {
+	return cblas128.Zdotu(n, x.Data, x.Inc, y.Data, y.Inc)
+}
+
+// Dotc computes the dot product of the two vectors with
+// complex conjugation:
+//  x^H * y.
+func Dotc(n int, x, y Vector) complex128 {
+	return cblas128.Zdotc(n, x.Data, x.Inc, y.Data, y.Inc)
+}
+
+// Nrm2 computes the Euclidean norm of the vector x:
+//  sqrt(\sum_i x[i] * x[i]).
+//
+// Nrm2 will panic if the vector increment is negative.
+func Nrm2(n int, x Vector) float64 {
+	if x.Inc < 0 {
+		panic(negInc)
+	}
+	return cblas128.Dznrm2(n, x.Data, x.Inc)
+}
+
+// Asum computes the sum of magnitudes of the real and imaginary parts of
+// elements of the vector x:
+//  \sum_i (|Re x[i]| + |Im x[i]|).
+//
+// Asum will panic if the vector increment is negative.
+func Asum(n int, x Vector) float64 {
+	if x.Inc < 0 {
+		panic(negInc)
+	}
+	return cblas128.Dzasum(n, x.Data, x.Inc)
+}
+
+// Iamax returns the index of an element of x with the largest sum of
+// magnitudes of the real and imaginary parts (|Re x[i]|+|Im x[i]|).
+// If there are multiple such indices, the earliest is returned.
+//
+// Iamax returns -1 if n == 0.
+//
+// Iamax will panic if the vector increment is negative.
+func Iamax(n int, x Vector) int {
+	if x.Inc < 0 {
+		panic(negInc)
+	}
+	return cblas128.Izamax(n, x.Data, x.Inc)
+}
+
+// Swap exchanges the elements of two vectors:
+//  x[i], y[i] = y[i], x[i] for all i.
+func Swap(n int, x, y Vector) {
+	cblas128.Zswap(n, x.Data, x.Inc, y.Data, y.Inc)
+}
+
+// Copy copies the elements of x into the elements of y:
+//  y[i] = x[i] for all i.
+func Copy(n int, x, y Vector) {
+	cblas128.Zcopy(n, x.Data, x.Inc, y.Data, y.Inc)
+}
+
+// Axpy computes
+//  y = alpha * x + y,
+// where x and y are vectors, and alpha is a scalar.
+func Axpy(n int, alpha complex128, x, y Vector) {
+	cblas128.Zaxpy(n, alpha, x.Data, x.Inc, y.Data, y.Inc)
+}
+
+// Scal computes
+//  x = alpha * x,
+// where x is a vector, and alpha is a scalar.
+//
+// Scal will panic if the vector increment is negative.
+func Scal(n int, alpha complex128, x Vector) {
+	if x.Inc < 0 {
+		panic(negInc)
+	}
+	cblas128.Zscal(n, alpha, x.Data, x.Inc)
+}
+
+// Dscal computes
+//  x = alpha * x,
+// where x is a vector, and alpha is a real scalar.
+//
+// Dscal will panic if the vector increment is negative.
+func Dscal(n int, alpha float64, x Vector) {
+	if x.Inc < 0 {
+		panic(negInc)
+	}
+	cblas128.Zdscal(n, alpha, x.Data, x.Inc)
+}
+
+// Level 2
+
+// Gemv computes
+//  y = alpha * A * x + beta * y,   if t == blas.NoTrans,
+//  y = alpha * A^T * x + beta * y, if t == blas.Trans,
+//  y = alpha * A^H * x + beta * y, if t == blas.ConjTrans,
+// where A is an m×n dense matrix, x and y are vectors, and alpha and beta are
+// scalars.
+func Gemv(t blas.Transpose, alpha complex128, a General, x Vector, beta complex128, y Vector) {
+	cblas128.Zgemv(t, a.Rows, a.Cols, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
+}
+
+// Gbmv computes
+//  y = alpha * A * x + beta * y,   if t == blas.NoTrans,
+//  y = alpha * A^T * x + beta * y, if t == blas.Trans,
+//  y = alpha * A^H * x + beta * y, if t == blas.ConjTrans,
+// where A is an m×n band matrix, x and y are vectors, and alpha and beta are
+// scalars.
+func Gbmv(t blas.Transpose, alpha complex128, a Band, x Vector, beta complex128, y Vector) {
+	cblas128.Zgbmv(t, a.Rows, a.Cols, a.KL, a.KU, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
+}
+
+// Trmv computes
+//  x = A * x,   if t == blas.NoTrans,
+//  x = A^T * x, if t == blas.Trans,
+//  x = A^H * x, if t == blas.ConjTrans,
+// where A is an n×n triangular matrix, and x is a vector.
+func Trmv(t blas.Transpose, a Triangular, x Vector) {
+	cblas128.Ztrmv(a.Uplo, t, a.Diag, a.N, a.Data, a.Stride, x.Data, x.Inc)
+}
+
+// Tbmv computes
+//  x = A * x,   if t == blas.NoTrans,
+//  x = A^T * x, if t == blas.Trans,
+//  x = A^H * x, if t == blas.ConjTrans,
+// where A is an n×n triangular band matrix, and x is a vector.
+func Tbmv(t blas.Transpose, a TriangularBand, x Vector) {
+	cblas128.Ztbmv(a.Uplo, t, a.Diag, a.N, a.K, a.Data, a.Stride, x.Data, x.Inc)
+}
+
+// Tpmv computes
+//  x = A * x,   if t == blas.NoTrans,
+//  x = A^T * x, if t == blas.Trans,
+//  x = A^H * x, if t == blas.ConjTrans,
+// where A is an n×n triangular matrix in packed format, and x is a vector.
+func Tpmv(t blas.Transpose, a TriangularPacked, x Vector) {
+	cblas128.Ztpmv(a.Uplo, t, a.Diag, a.N, a.Data, x.Data, x.Inc)
+}
+
+// Trsv solves
+//  A * x = b,   if t == blas.NoTrans,
+//  A^T * x = b, if t == blas.Trans,
+//  A^H * x = b, if t == blas.ConjTrans,
+// where A is an n×n triangular matrix and x is a vector.
+//
+// At entry to the function, x contains the values of b, and the result is
+// stored in-place into x.
+//
+// No test for singularity or near-singularity is included in this
+// routine. Such tests must be performed before calling this routine.
+func Trsv(t blas.Transpose, a Triangular, x Vector) {
+	cblas128.Ztrsv(a.Uplo, t, a.Diag, a.N, a.Data, a.Stride, x.Data, x.Inc)
+}
+
+// Tbsv solves
+//  A * x = b,   if t == blas.NoTrans,
+//  A^T * x = b, if t == blas.Trans,
+//  A^H * x = b, if t == blas.ConjTrans,
+// where A is an n×n triangular band matrix, and x is a vector.
+//
+// At entry to the function, x contains the values of b, and the result is
+// stored in-place into x.
+//
+// No test for singularity or near-singularity is included in this
+// routine. Such tests must be performed before calling this routine.
+func Tbsv(t blas.Transpose, a TriangularBand, x Vector) {
+	cblas128.Ztbsv(a.Uplo, t, a.Diag, a.N, a.K, a.Data, a.Stride, x.Data, x.Inc)
+}
+
+// Tpsv solves
+//  A * x = b,   if t == blas.NoTrans,
+//  A^T * x = b, if t == blas.Trans,
+//  A^H * x = b, if t == blas.ConjTrans,
+// where A is an n×n triangular matrix in packed format and x is a vector.
+//
+// At entry to the function, x contains the values of b, and the result is
+// stored in-place into x.
+//
+// No test for singularity or near-singularity is included in this
+// routine. Such tests must be performed before calling this routine.
+func Tpsv(t blas.Transpose, a TriangularPacked, x Vector) {
+	cblas128.Ztpsv(a.Uplo, t, a.Diag, a.N, a.Data, x.Data, x.Inc)
+}
+
+// Hemv computes
+//  y = alpha * A * x + beta * y,
+// where A is an n×n Hermitian matrix, x and y are vectors, and alpha and
+// beta are scalars.
+func Hemv(alpha complex128, a Hermitian, x Vector, beta complex128, y Vector) {
+	cblas128.Zhemv(a.Uplo, a.N, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
+}
+
+// Hbmv performs
+//  y = alpha * A * x + beta * y,
+// where A is an n×n Hermitian band matrix, x and y are vectors, and alpha
+// and beta are scalars.
+func Hbmv(alpha complex128, a HermitianBand, x Vector, beta complex128, y Vector) {
+	cblas128.Zhbmv(a.Uplo, a.N, a.K, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
+}
+
+// Hpmv performs
+//  y = alpha * A * x + beta * y,
+// where A is an n×n Hermitian matrix in packed format, x and y are vectors,
+// and alpha and beta are scalars.
+func Hpmv(alpha complex128, a HermitianPacked, x Vector, beta complex128, y Vector) {
+	cblas128.Zhpmv(a.Uplo, a.N, alpha, a.Data, x.Data, x.Inc, beta, y.Data, y.Inc)
+}
+
+// Geru performs a rank-1 update
+//  A += alpha * x * y^T,
+// where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.
+func Geru(alpha complex128, x, y Vector, a General) {
+	cblas128.Zgeru(a.Rows, a.Cols, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
+}
+
+// Gerc performs a rank-1 update
+//  A += alpha * x * y^H,
+// where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.
+func Gerc(alpha complex128, x, y Vector, a General) {
+	cblas128.Zgerc(a.Rows, a.Cols, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
+}
+
+// Her performs a rank-1 update
+//  A += alpha * x * y^T,
+// where A is an m×n Hermitian matrix, x and y are vectors, and alpha is a scalar.
+func Her(alpha float64, x Vector, a Hermitian) {
+	cblas128.Zher(a.Uplo, a.N, alpha, x.Data, x.Inc, a.Data, a.Stride)
+}
+
+// Hpr performs a rank-1 update
+//  A += alpha * x * x^H,
+// where A is an n×n Hermitian matrix in packed format, x is a vector, and
+// alpha is a scalar.
+func Hpr(alpha float64, x Vector, a HermitianPacked) {
+	cblas128.Zhpr(a.Uplo, a.N, alpha, x.Data, x.Inc, a.Data)
+}
+
+// Her2 performs a rank-2 update
+//  A += alpha * x * y^H + conj(alpha) * y * x^H,
+// where A is an n×n Hermitian matrix, x and y are vectors, and alpha is a scalar.
+func Her2(alpha complex128, x, y Vector, a Hermitian) {
+	cblas128.Zher2(a.Uplo, a.N, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
+}
+
+// Hpr2 performs a rank-2 update
+//  A += alpha * x * y^H + conj(alpha) * y * x^H,
+// where A is an n×n Hermitian matrix in packed format, x and y are vectors,
+// and alpha is a scalar.
+func Hpr2(alpha complex128, x, y Vector, a HermitianPacked) {
+	cblas128.Zhpr2(a.Uplo, a.N, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data)
+}
+
+// Level 3
+
+// Gemm computes
+//  C = alpha * A * B + beta * C,
+// where A, B, and C are dense matrices, and alpha and beta are scalars.
+// tA and tB specify whether A or B are transposed or conjugated.
+func Gemm(tA, tB blas.Transpose, alpha complex128, a, b General, beta complex128, c General) {
+	var m, n, k int
+	if tA == blas.NoTrans {
+		m, k = a.Rows, a.Cols
+	} else {
+		m, k = a.Cols, a.Rows
+	}
+	if tB == blas.NoTrans {
+		n = b.Cols
+	} else {
+		n = b.Rows
+	}
+	cblas128.Zgemm(tA, tB, m, n, k, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
+}
+
+// Symm performs
+//  C = alpha * A * B + beta * C, if s == blas.Left,
+//  C = alpha * B * A + beta * C, if s == blas.Right,
+// where A is an n×n or m×m symmetric matrix, B and C are m×n matrices, and
+// alpha and beta are scalars.
+func Symm(s blas.Side, alpha complex128, a Symmetric, b General, beta complex128, c General) {
+	var m, n int
+	if s == blas.Left {
+		m, n = a.N, b.Cols
+	} else {
+		m, n = b.Rows, a.N
+	}
+	cblas128.Zsymm(s, a.Uplo, m, n, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
+}
+
+// Syrk performs a symmetric rank-k update
+//  C = alpha * A * A^T + beta * C, if t == blas.NoTrans,
+//  C = alpha * A^T * A + beta * C, if t == blas.Trans,
+// where C is an n×n symmetric matrix, A is an n×k matrix if t == blas.NoTrans
+// and a k×n matrix otherwise, and alpha and beta are scalars.
+func Syrk(t blas.Transpose, alpha complex128, a General, beta complex128, c Symmetric) {
+	var n, k int
+	if t == blas.NoTrans {
+		n, k = a.Rows, a.Cols
+	} else {
+		n, k = a.Cols, a.Rows
+	}
+	cblas128.Zsyrk(c.Uplo, t, n, k, alpha, a.Data, a.Stride, beta, c.Data, c.Stride)
+}
+
+// Syr2k performs a symmetric rank-2k update
+//  C = alpha * A * B^T + alpha * B * A^T + beta * C, if t == blas.NoTrans,
+//  C = alpha * A^T * B + alpha * B^T * A + beta * C, if t == blas.Trans,
+// where C is an n×n symmetric matrix, A and B are n×k matrices if
+// t == blas.NoTrans and k×n otherwise, and alpha and beta are scalars.
+func Syr2k(t blas.Transpose, alpha complex128, a, b General, beta complex128, c Symmetric) {
+	var n, k int
+	if t == blas.NoTrans {
+		n, k = a.Rows, a.Cols
+	} else {
+		n, k = a.Cols, a.Rows
+	}
+	cblas128.Zsyr2k(c.Uplo, t, n, k, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
+}
+
+// Trmm performs
+//  B = alpha * A * B,   if tA == blas.NoTrans and s == blas.Left,
+//  B = alpha * A^T * B, if tA == blas.Trans and s == blas.Left,
+//  B = alpha * A^H * B, if tA == blas.ConjTrans and s == blas.Left,
+//  B = alpha * B * A,   if tA == blas.NoTrans and s == blas.Right,
+//  B = alpha * B * A^T, if tA == blas.Trans and s == blas.Right,
+//  B = alpha * B * A^H, if tA == blas.ConjTrans and s == blas.Right,
+// where A is an n×n or m×m triangular matrix, B is an m×n matrix, and alpha is
+// a scalar.
+func Trmm(s blas.Side, tA blas.Transpose, alpha complex128, a Triangular, b General) {
+	cblas128.Ztrmm(s, a.Uplo, tA, a.Diag, b.Rows, b.Cols, alpha, a.Data, a.Stride, b.Data, b.Stride)
+}
+
+// Trsm solves
+//  A * X = alpha * B,   if tA == blas.NoTrans and s == blas.Left,
+//  A^T * X = alpha * B, if tA == blas.Trans and s == blas.Left,
+//  A^H * X = alpha * B, if tA == blas.ConjTrans and s == blas.Left,
+//  X * A = alpha * B,   if tA == blas.NoTrans and s == blas.Right,
+//  X * A^T = alpha * B, if tA == blas.Trans and s == blas.Right,
+//  X * A^H = alpha * B, if tA == blas.ConjTrans and s == blas.Right,
+// where A is an n×n or m×m triangular matrix, X and B are m×n matrices, and
+// alpha is a scalar.
+//
+// At entry to the function, b contains the values of B, and the result is
+// stored in-place into b.
+//
+// No check is made that A is invertible.
+func Trsm(s blas.Side, tA blas.Transpose, alpha complex128, a Triangular, b General) {
+	cblas128.Ztrsm(s, a.Uplo, tA, a.Diag, b.Rows, b.Cols, alpha, a.Data, a.Stride, b.Data, b.Stride)
+}
+
+// Hemm performs
+//  C = alpha * A * B + beta * C, if s == blas.Left,
+//  C = alpha * B * A + beta * C, if s == blas.Right,
+// where A is an n×n or m×m Hermitian matrix, B and C are m×n matrices, and
+// alpha and beta are scalars.
+func Hemm(s blas.Side, alpha complex128, a Hermitian, b General, beta complex128, c General) {
+	var m, n int
+	if s == blas.Left {
+		m, n = a.N, b.Cols
+	} else {
+		m, n = b.Rows, a.N
+	}
+	cblas128.Zhemm(s, a.Uplo, m, n, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
+}
+
+// Herk performs the Hermitian rank-k update
+//  C = alpha * A * A^H + beta*C, if t == blas.NoTrans,
+//  C = alpha * A^H * A + beta*C, if t == blas.ConjTrans,
+// where C is an n×n Hermitian matrix, A is an n×k matrix if t == blas.NoTrans
+// and a k×n matrix otherwise, and alpha and beta are scalars.
+func Herk(t blas.Transpose, alpha float64, a General, beta float64, c Hermitian) {
+	var n, k int
+	if t == blas.NoTrans {
+		n, k = a.Rows, a.Cols
+	} else {
+		n, k = a.Cols, a.Rows
+	}
+	cblas128.Zherk(c.Uplo, t, n, k, alpha, a.Data, a.Stride, beta, c.Data, c.Stride)
+}
+
+// Her2k performs the Hermitian rank-2k update
+//  C = alpha * A * B^H + conj(alpha) * B * A^H + beta * C, if t == blas.NoTrans,
+//  C = alpha * A^H * B + conj(alpha) * B^H * A + beta * C, if t == blas.ConjTrans,
+// where C is an n×n Hermitian matrix, A and B are n×k matrices if t == NoTrans
+// and k×n matrices otherwise, and alpha and beta are scalars.
+func Her2k(t blas.Transpose, alpha complex128, a, b General, beta float64, c Hermitian) {
+	var n, k int
+	if t == blas.NoTrans {
+		n, k = a.Rows, a.Cols
+	} else {
+		n, k = a.Cols, a.Rows
+	}
+	cblas128.Zher2k(c.Uplo, t, n, k, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/cblas128/conv.go b/vendor/gonum.org/v1/gonum/blas/cblas128/conv.go
new file mode 100644
index 00000000..cb62b7be
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/cblas128/conv.go
@@ -0,0 +1,279 @@
+// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.
+
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package cblas128
+
+import "gonum.org/v1/gonum/blas"
+
+// GeneralCols represents a matrix using the conventional column-major storage scheme.
+type GeneralCols General
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions as a and have adequate backing
+// data storage.
+func (t GeneralCols) From(a General) {
+	if t.Rows != a.Rows || t.Cols != a.Cols {
+		panic("cblas128: mismatched dimension")
+	}
+	if len(t.Data) < (t.Cols-1)*t.Stride+t.Rows {
+		panic("cblas128: short data slice")
+	}
+	for i := 0; i < a.Rows; i++ {
+		for j, v := range a.Data[i*a.Stride : i*a.Stride+a.Cols] {
+			t.Data[i+j*t.Stride] = v
+		}
+	}
+}
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions as a and have adequate backing
+// data storage.
+func (t General) From(a GeneralCols) {
+	if t.Rows != a.Rows || t.Cols != a.Cols {
+		panic("cblas128: mismatched dimension")
+	}
+	if len(t.Data) < (t.Rows-1)*t.Stride+t.Cols {
+		panic("cblas128: short data slice")
+	}
+	for j := 0; j < a.Cols; j++ {
+		for i, v := range a.Data[j*a.Stride : j*a.Stride+a.Rows] {
+			t.Data[i*t.Stride+j] = v
+		}
+	}
+}
+
+// TriangularCols represents a matrix using the conventional column-major storage scheme.
+type TriangularCols Triangular
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions, uplo and diag as a and have
+// adequate backing data storage.
+func (t TriangularCols) From(a Triangular) {
+	if t.N != a.N {
+		panic("cblas128: mismatched dimension")
+	}
+	if t.Uplo != a.Uplo {
+		panic("cblas128: mismatched BLAS uplo")
+	}
+	if t.Diag != a.Diag {
+		panic("cblas128: mismatched BLAS diag")
+	}
+	switch a.Uplo {
+	default:
+		panic("cblas128: bad BLAS uplo")
+	case blas.Upper:
+		for i := 0; i < a.N; i++ {
+			for j := i; j < a.N; j++ {
+				t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
+			}
+		}
+	case blas.Lower:
+		for i := 0; i < a.N; i++ {
+			for j := 0; j <= i; j++ {
+				t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
+			}
+		}
+	case blas.All:
+		for i := 0; i < a.N; i++ {
+			for j := 0; j < a.N; j++ {
+				t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
+			}
+		}
+	}
+}
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions, uplo and diag as a and have
+// adequate backing data storage.
+func (t Triangular) From(a TriangularCols) {
+	if t.N != a.N {
+		panic("cblas128: mismatched dimension")
+	}
+	if t.Uplo != a.Uplo {
+		panic("cblas128: mismatched BLAS uplo")
+	}
+	if t.Diag != a.Diag {
+		panic("cblas128: mismatched BLAS diag")
+	}
+	switch a.Uplo {
+	default:
+		panic("cblas128: bad BLAS uplo")
+	case blas.Upper:
+		for i := 0; i < a.N; i++ {
+			for j := i; j < a.N; j++ {
+				t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
+			}
+		}
+	case blas.Lower:
+		for i := 0; i < a.N; i++ {
+			for j := 0; j <= i; j++ {
+				t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
+			}
+		}
+	case blas.All:
+		for i := 0; i < a.N; i++ {
+			for j := 0; j < a.N; j++ {
+				t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
+			}
+		}
+	}
+}
+
+// BandCols represents a matrix using the band column-major storage scheme.
+type BandCols Band
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions and bandwidth as a and have
+// adequate backing data storage.
+func (t BandCols) From(a Band) {
+	if t.Rows != a.Rows || t.Cols != a.Cols {
+		panic("cblas128: mismatched dimension")
+	}
+	if t.KL != a.KL || t.KU != a.KU {
+		panic("cblas128: mismatched bandwidth")
+	}
+	if a.Stride < a.KL+a.KU+1 {
+		panic("cblas128: short stride for source")
+	}
+	if t.Stride < t.KL+t.KU+1 {
+		panic("cblas128: short stride for destination")
+	}
+	for i := 0; i < a.Rows; i++ {
+		for j := max(0, i-a.KL); j < min(i+a.KU+1, a.Cols); j++ {
+			t.Data[i+t.KU-j+j*t.Stride] = a.Data[j+a.KL-i+i*a.Stride]
+		}
+	}
+}
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions and bandwidth as a and have
+// adequate backing data storage.
+func (t Band) From(a BandCols) {
+	if t.Rows != a.Rows || t.Cols != a.Cols {
+		panic("cblas128: mismatched dimension")
+	}
+	if t.KL != a.KL || t.KU != a.KU {
+		panic("cblas128: mismatched bandwidth")
+	}
+	if a.Stride < a.KL+a.KU+1 {
+		panic("cblas128: short stride for source")
+	}
+	if t.Stride < t.KL+t.KU+1 {
+		panic("cblas128: short stride for destination")
+	}
+	for j := 0; j < a.Cols; j++ {
+		for i := max(0, j-a.KU); i < min(j+a.KL+1, a.Rows); i++ {
+			t.Data[j+a.KL-i+i*a.Stride] = a.Data[i+t.KU-j+j*t.Stride]
+		}
+	}
+}
+
+// TriangularBandCols represents a symmetric matrix using the band column-major storage scheme.
+type TriangularBandCols TriangularBand
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions, bandwidth and uplo as a and
+// have adequate backing data storage.
+func (t TriangularBandCols) From(a TriangularBand) {
+	if t.N != a.N {
+		panic("cblas128: mismatched dimension")
+	}
+	if t.K != a.K {
+		panic("cblas128: mismatched bandwidth")
+	}
+	if a.Stride < a.K+1 {
+		panic("cblas128: short stride for source")
+	}
+	if t.Stride < t.K+1 {
+		panic("cblas128: short stride for destination")
+	}
+	if t.Uplo != a.Uplo {
+		panic("cblas128: mismatched BLAS uplo")
+	}
+	if t.Diag != a.Diag {
+		panic("cblas128: mismatched BLAS diag")
+	}
+	dst := BandCols{
+		Rows: t.N, Cols: t.N,
+		Stride: t.Stride,
+		Data:   t.Data,
+	}
+	src := Band{
+		Rows: a.N, Cols: a.N,
+		Stride: a.Stride,
+		Data:   a.Data,
+	}
+	switch a.Uplo {
+	default:
+		panic("cblas128: bad BLAS uplo")
+	case blas.Upper:
+		dst.KU = t.K
+		src.KU = a.K
+	case blas.Lower:
+		dst.KL = t.K
+		src.KL = a.K
+	}
+	dst.From(src)
+}
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions, bandwidth and uplo as a and
+// have adequate backing data storage.
+func (t TriangularBand) From(a TriangularBandCols) {
+	if t.N != a.N {
+		panic("cblas128: mismatched dimension")
+	}
+	if t.K != a.K {
+		panic("cblas128: mismatched bandwidth")
+	}
+	if a.Stride < a.K+1 {
+		panic("cblas128: short stride for source")
+	}
+	if t.Stride < t.K+1 {
+		panic("cblas128: short stride for destination")
+	}
+	if t.Uplo != a.Uplo {
+		panic("cblas128: mismatched BLAS uplo")
+	}
+	if t.Diag != a.Diag {
+		panic("cblas128: mismatched BLAS diag")
+	}
+	dst := Band{
+		Rows: t.N, Cols: t.N,
+		Stride: t.Stride,
+		Data:   t.Data,
+	}
+	src := BandCols{
+		Rows: a.N, Cols: a.N,
+		Stride: a.Stride,
+		Data:   a.Data,
+	}
+	switch a.Uplo {
+	default:
+		panic("cblas128: bad BLAS uplo")
+	case blas.Upper:
+		dst.KU = t.K
+		src.KU = a.K
+	case blas.Lower:
+		dst.KL = t.K
+		src.KL = a.K
+	}
+	dst.From(src)
+}
+
+func min(a, b int) int {
+	if a < b {
+		return a
+	}
+	return b
+}
+
+func max(a, b int) int {
+	if a > b {
+		return a
+	}
+	return b
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/cblas128/conv_hermitian.go b/vendor/gonum.org/v1/gonum/blas/cblas128/conv_hermitian.go
new file mode 100644
index 00000000..455668a3
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/cblas128/conv_hermitian.go
@@ -0,0 +1,155 @@
+// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.
+
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package cblas128
+
+import "gonum.org/v1/gonum/blas"
+
+// HermitianCols represents a matrix using the conventional column-major storage scheme.
+type HermitianCols Hermitian
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions and uplo as a and have adequate
+// backing data storage.
+func (t HermitianCols) From(a Hermitian) {
+	if t.N != a.N {
+		panic("cblas128: mismatched dimension")
+	}
+	if t.Uplo != a.Uplo {
+		panic("cblas128: mismatched BLAS uplo")
+	}
+	switch a.Uplo {
+	default:
+		panic("cblas128: bad BLAS uplo")
+	case blas.Upper:
+		for i := 0; i < a.N; i++ {
+			for j := i; j < a.N; j++ {
+				t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
+			}
+		}
+	case blas.Lower:
+		for i := 0; i < a.N; i++ {
+			for j := 0; j <= i; j++ {
+				t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
+			}
+		}
+	}
+}
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions and uplo as a and have adequate
+// backing data storage.
+func (t Hermitian) From(a HermitianCols) {
+	if t.N != a.N {
+		panic("cblas128: mismatched dimension")
+	}
+	if t.Uplo != a.Uplo {
+		panic("cblas128: mismatched BLAS uplo")
+	}
+	switch a.Uplo {
+	default:
+		panic("cblas128: bad BLAS uplo")
+	case blas.Upper:
+		for i := 0; i < a.N; i++ {
+			for j := i; j < a.N; j++ {
+				t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
+			}
+		}
+	case blas.Lower:
+		for i := 0; i < a.N; i++ {
+			for j := 0; j <= i; j++ {
+				t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
+			}
+		}
+	}
+}
+
+// HermitianBandCols represents an Hermitian matrix using the band column-major storage scheme.
+type HermitianBandCols HermitianBand
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions, bandwidth and uplo as a and
+// have adequate backing data storage.
+func (t HermitianBandCols) From(a HermitianBand) {
+	if t.N != a.N {
+		panic("cblas128: mismatched dimension")
+	}
+	if t.K != a.K {
+		panic("cblas128: mismatched bandwidth")
+	}
+	if a.Stride < a.K+1 {
+		panic("cblas128: short stride for source")
+	}
+	if t.Stride < t.K+1 {
+		panic("cblas128: short stride for destination")
+	}
+	if t.Uplo != a.Uplo {
+		panic("cblas128: mismatched BLAS uplo")
+	}
+	dst := BandCols{
+		Rows: t.N, Cols: t.N,
+		Stride: t.Stride,
+		Data:   t.Data,
+	}
+	src := Band{
+		Rows: a.N, Cols: a.N,
+		Stride: a.Stride,
+		Data:   a.Data,
+	}
+	switch a.Uplo {
+	default:
+		panic("cblas128: bad BLAS uplo")
+	case blas.Upper:
+		dst.KU = t.K
+		src.KU = a.K
+	case blas.Lower:
+		dst.KL = t.K
+		src.KL = a.K
+	}
+	dst.From(src)
+}
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions, bandwidth and uplo as a and
+// have adequate backing data storage.
+func (t HermitianBand) From(a HermitianBandCols) {
+	if t.N != a.N {
+		panic("cblas128: mismatched dimension")
+	}
+	if t.K != a.K {
+		panic("cblas128: mismatched bandwidth")
+	}
+	if a.Stride < a.K+1 {
+		panic("cblas128: short stride for source")
+	}
+	if t.Stride < t.K+1 {
+		panic("cblas128: short stride for destination")
+	}
+	if t.Uplo != a.Uplo {
+		panic("cblas128: mismatched BLAS uplo")
+	}
+	dst := Band{
+		Rows: t.N, Cols: t.N,
+		Stride: t.Stride,
+		Data:   t.Data,
+	}
+	src := BandCols{
+		Rows: a.N, Cols: a.N,
+		Stride: a.Stride,
+		Data:   a.Data,
+	}
+	switch a.Uplo {
+	default:
+		panic("cblas128: bad BLAS uplo")
+	case blas.Upper:
+		dst.KU = t.K
+		src.KU = a.K
+	case blas.Lower:
+		dst.KL = t.K
+		src.KL = a.K
+	}
+	dst.From(src)
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/cblas128/conv_hermitian_test.go b/vendor/gonum.org/v1/gonum/blas/cblas128/conv_hermitian_test.go
new file mode 100644
index 00000000..21bd3cbf
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/cblas128/conv_hermitian_test.go
@@ -0,0 +1,307 @@
+// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.
+
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package cblas128
+
+import (
+	math "math/cmplx"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+func newHermitianFrom(a HermitianCols) Hermitian {
+	t := Hermitian{
+		N:      a.N,
+		Stride: a.N,
+		Data:   make([]complex128, a.N*a.N),
+		Uplo:   a.Uplo,
+	}
+	t.From(a)
+	return t
+}
+
+func (m Hermitian) n() int { return m.N }
+func (m Hermitian) at(i, j int) complex128 {
+	if m.Uplo == blas.Lower && i < j && j < m.N {
+		i, j = j, i
+	}
+	if m.Uplo == blas.Upper && i > j {
+		i, j = j, i
+	}
+	return m.Data[i*m.Stride+j]
+}
+func (m Hermitian) uplo() blas.Uplo { return m.Uplo }
+
+func newHermitianColsFrom(a Hermitian) HermitianCols {
+	t := HermitianCols{
+		N:      a.N,
+		Stride: a.N,
+		Data:   make([]complex128, a.N*a.N),
+		Uplo:   a.Uplo,
+	}
+	t.From(a)
+	return t
+}
+
+func (m HermitianCols) n() int { return m.N }
+func (m HermitianCols) at(i, j int) complex128 {
+	if m.Uplo == blas.Lower && i < j {
+		i, j = j, i
+	}
+	if m.Uplo == blas.Upper && i > j && i < m.N {
+		i, j = j, i
+	}
+	return m.Data[i+j*m.Stride]
+}
+func (m HermitianCols) uplo() blas.Uplo { return m.Uplo }
+
+type hermitian interface {
+	n() int
+	at(i, j int) complex128
+	uplo() blas.Uplo
+}
+
+func sameHermitian(a, b hermitian) bool {
+	an := a.n()
+	bn := b.n()
+	if an != bn {
+		return false
+	}
+	if a.uplo() != b.uplo() {
+		return false
+	}
+	for i := 0; i < an; i++ {
+		for j := 0; j < an; j++ {
+			if a.at(i, j) != b.at(i, j) || math.IsNaN(a.at(i, j)) != math.IsNaN(b.at(i, j)) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+var hermitianTests = []Hermitian{
+	{N: 3, Stride: 3, Data: []complex128{
+		1, 2, 3,
+		4, 5, 6,
+		7, 8, 9,
+	}},
+	{N: 3, Stride: 5, Data: []complex128{
+		1, 2, 3, 0, 0,
+		4, 5, 6, 0, 0,
+		7, 8, 9, 0, 0,
+	}},
+}
+
+func TestConvertHermitian(t *testing.T) {
+	for _, test := range hermitianTests {
+		for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
+			test.Uplo = uplo
+			colmajor := newHermitianColsFrom(test)
+			if !sameHermitian(colmajor, test) {
+				t.Errorf("unexpected result for row major to col major conversion:\n\tgot: %#v\n\tfrom:%#v",
+					colmajor, test)
+			}
+			rowmajor := newHermitianFrom(colmajor)
+			if !sameHermitian(rowmajor, test) {
+				t.Errorf("unexpected result for col major to row major conversion:\n\tgot: %#v\n\twant:%#v",
+					rowmajor, test)
+			}
+		}
+	}
+}
+func newHermitianBandFrom(a HermitianBandCols) HermitianBand {
+	t := HermitianBand{
+		N:      a.N,
+		K:      a.K,
+		Stride: a.K + 1,
+		Data:   make([]complex128, a.N*(a.K+1)),
+		Uplo:   a.Uplo,
+	}
+	for i := range t.Data {
+		t.Data[i] = math.NaN()
+	}
+	t.From(a)
+	return t
+}
+
+func (m HermitianBand) n() (n int) { return m.N }
+func (m HermitianBand) at(i, j int) complex128 {
+	b := Band{
+		Rows: m.N, Cols: m.N,
+		Stride: m.Stride,
+		Data:   m.Data,
+	}
+	switch m.Uplo {
+	default:
+		panic("cblas128: bad BLAS uplo")
+	case blas.Upper:
+		b.KU = m.K
+		if i > j {
+			i, j = j, i
+		}
+	case blas.Lower:
+		b.KL = m.K
+		if i < j {
+			i, j = j, i
+		}
+	}
+	return b.at(i, j)
+}
+func (m HermitianBand) bandwidth() (k int) { return m.K }
+func (m HermitianBand) uplo() blas.Uplo    { return m.Uplo }
+
+func newHermitianBandColsFrom(a HermitianBand) HermitianBandCols {
+	t := HermitianBandCols{
+		N:      a.N,
+		K:      a.K,
+		Stride: a.K + 1,
+		Data:   make([]complex128, a.N*(a.K+1)),
+		Uplo:   a.Uplo,
+	}
+	for i := range t.Data {
+		t.Data[i] = math.NaN()
+	}
+	t.From(a)
+	return t
+}
+
+func (m HermitianBandCols) n() (n int) { return m.N }
+func (m HermitianBandCols) at(i, j int) complex128 {
+	b := BandCols{
+		Rows: m.N, Cols: m.N,
+		Stride: m.Stride,
+		Data:   m.Data,
+	}
+	switch m.Uplo {
+	default:
+		panic("cblas128: bad BLAS uplo")
+	case blas.Upper:
+		b.KU = m.K
+		if i > j {
+			i, j = j, i
+		}
+	case blas.Lower:
+		b.KL = m.K
+		if i < j {
+			i, j = j, i
+		}
+	}
+	return b.at(i, j)
+}
+func (m HermitianBandCols) bandwidth() (k int) { return m.K }
+func (m HermitianBandCols) uplo() blas.Uplo    { return m.Uplo }
+
+type hermitianBand interface {
+	n() (n int)
+	at(i, j int) complex128
+	bandwidth() (k int)
+	uplo() blas.Uplo
+}
+
+func sameHermitianBand(a, b hermitianBand) bool {
+	an := a.n()
+	bn := b.n()
+	if an != bn {
+		return false
+	}
+	if a.uplo() != b.uplo() {
+		return false
+	}
+	ak := a.bandwidth()
+	bk := b.bandwidth()
+	if ak != bk {
+		return false
+	}
+	for i := 0; i < an; i++ {
+		for j := 0; j < an; j++ {
+			if a.at(i, j) != b.at(i, j) || math.IsNaN(a.at(i, j)) != math.IsNaN(b.at(i, j)) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+var hermitianBandTests = []HermitianBand{
+	{N: 3, K: 0, Stride: 1, Uplo: blas.Upper, Data: []complex128{
+		1,
+		2,
+		3,
+	}},
+	{N: 3, K: 0, Stride: 1, Uplo: blas.Lower, Data: []complex128{
+		1,
+		2,
+		3,
+	}},
+	{N: 3, K: 1, Stride: 2, Uplo: blas.Upper, Data: []complex128{
+		1, 2,
+		3, 4,
+		5, -1,
+	}},
+	{N: 3, K: 1, Stride: 2, Uplo: blas.Lower, Data: []complex128{
+		-1, 1,
+		2, 3,
+		4, 5,
+	}},
+	{N: 3, K: 2, Stride: 3, Uplo: blas.Upper, Data: []complex128{
+		1, 2, 3,
+		4, 5, -1,
+		6, -2, -3,
+	}},
+	{N: 3, K: 2, Stride: 3, Uplo: blas.Lower, Data: []complex128{
+		-2, -1, 1,
+		-3, 2, 4,
+		3, 5, 6,
+	}},
+
+	{N: 3, K: 0, Stride: 5, Uplo: blas.Upper, Data: []complex128{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{N: 3, K: 0, Stride: 5, Uplo: blas.Lower, Data: []complex128{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{N: 3, K: 1, Stride: 5, Uplo: blas.Upper, Data: []complex128{
+		1, 2, 0, 0, 0,
+		3, 4, 0, 0, 0,
+		5, -1, 0, 0, 0,
+	}},
+	{N: 3, K: 1, Stride: 5, Uplo: blas.Lower, Data: []complex128{
+		-1, 1, 0, 0, 0,
+		2, 3, 0, 0, 0,
+		4, 5, 0, 0, 0,
+	}},
+	{N: 3, K: 2, Stride: 5, Uplo: blas.Upper, Data: []complex128{
+		1, 2, 3, 0, 0,
+		4, 5, -1, 0, 0,
+		6, -2, -3, 0, 0,
+	}},
+	{N: 3, K: 2, Stride: 5, Uplo: blas.Lower, Data: []complex128{
+		-2, -1, 1, 0, 0,
+		-3, 2, 4, 0, 0,
+		3, 5, 6, 0, 0,
+	}},
+}
+
+func TestConvertHermBand(t *testing.T) {
+	for _, test := range hermitianBandTests {
+		colmajor := newHermitianBandColsFrom(test)
+		if !sameHermitianBand(colmajor, test) {
+			t.Errorf("unexpected result for row major to col major conversion:\n\tgot: %#v\n\tfrom:%#v",
+				colmajor, test)
+		}
+		rowmajor := newHermitianBandFrom(colmajor)
+		if !sameHermitianBand(rowmajor, test) {
+			t.Errorf("unexpected result for col major to row major conversion:\n\tgot: %#v\n\twant:%#v",
+				rowmajor, test)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/cblas128/conv_symmetric.go b/vendor/gonum.org/v1/gonum/blas/cblas128/conv_symmetric.go
new file mode 100644
index 00000000..ad5e0a65
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/cblas128/conv_symmetric.go
@@ -0,0 +1,155 @@
+// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.
+
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package cblas128
+
+import "gonum.org/v1/gonum/blas"
+
+// SymmetricCols represents a matrix using the conventional column-major storage scheme.
+type SymmetricCols Symmetric
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions and uplo as a and have adequate
+// backing data storage.
+func (t SymmetricCols) From(a Symmetric) {
+	if t.N != a.N {
+		panic("cblas128: mismatched dimension")
+	}
+	if t.Uplo != a.Uplo {
+		panic("cblas128: mismatched BLAS uplo")
+	}
+	switch a.Uplo {
+	default:
+		panic("cblas128: bad BLAS uplo")
+	case blas.Upper:
+		for i := 0; i < a.N; i++ {
+			for j := i; j < a.N; j++ {
+				t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
+			}
+		}
+	case blas.Lower:
+		for i := 0; i < a.N; i++ {
+			for j := 0; j <= i; j++ {
+				t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
+			}
+		}
+	}
+}
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions and uplo as a and have adequate
+// backing data storage.
+func (t Symmetric) From(a SymmetricCols) {
+	if t.N != a.N {
+		panic("cblas128: mismatched dimension")
+	}
+	if t.Uplo != a.Uplo {
+		panic("cblas128: mismatched BLAS uplo")
+	}
+	switch a.Uplo {
+	default:
+		panic("cblas128: bad BLAS uplo")
+	case blas.Upper:
+		for i := 0; i < a.N; i++ {
+			for j := i; j < a.N; j++ {
+				t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
+			}
+		}
+	case blas.Lower:
+		for i := 0; i < a.N; i++ {
+			for j := 0; j <= i; j++ {
+				t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
+			}
+		}
+	}
+}
+
+// SymmetricBandCols represents a symmetric matrix using the band column-major storage scheme.
+type SymmetricBandCols SymmetricBand
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions, bandwidth and uplo as a and
+// have adequate backing data storage.
+func (t SymmetricBandCols) From(a SymmetricBand) {
+	if t.N != a.N {
+		panic("cblas128: mismatched dimension")
+	}
+	if t.K != a.K {
+		panic("cblas128: mismatched bandwidth")
+	}
+	if a.Stride < a.K+1 {
+		panic("cblas128: short stride for source")
+	}
+	if t.Stride < t.K+1 {
+		panic("cblas128: short stride for destination")
+	}
+	if t.Uplo != a.Uplo {
+		panic("cblas128: mismatched BLAS uplo")
+	}
+	dst := BandCols{
+		Rows: t.N, Cols: t.N,
+		Stride: t.Stride,
+		Data:   t.Data,
+	}
+	src := Band{
+		Rows: a.N, Cols: a.N,
+		Stride: a.Stride,
+		Data:   a.Data,
+	}
+	switch a.Uplo {
+	default:
+		panic("cblas128: bad BLAS uplo")
+	case blas.Upper:
+		dst.KU = t.K
+		src.KU = a.K
+	case blas.Lower:
+		dst.KL = t.K
+		src.KL = a.K
+	}
+	dst.From(src)
+}
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions, bandwidth and uplo as a and
+// have adequate backing data storage.
+func (t SymmetricBand) From(a SymmetricBandCols) {
+	if t.N != a.N {
+		panic("cblas128: mismatched dimension")
+	}
+	if t.K != a.K {
+		panic("cblas128: mismatched bandwidth")
+	}
+	if a.Stride < a.K+1 {
+		panic("cblas128: short stride for source")
+	}
+	if t.Stride < t.K+1 {
+		panic("cblas128: short stride for destination")
+	}
+	if t.Uplo != a.Uplo {
+		panic("cblas128: mismatched BLAS uplo")
+	}
+	dst := Band{
+		Rows: t.N, Cols: t.N,
+		Stride: t.Stride,
+		Data:   t.Data,
+	}
+	src := BandCols{
+		Rows: a.N, Cols: a.N,
+		Stride: a.Stride,
+		Data:   a.Data,
+	}
+	switch a.Uplo {
+	default:
+		panic("cblas128: bad BLAS uplo")
+	case blas.Upper:
+		dst.KU = t.K
+		src.KU = a.K
+	case blas.Lower:
+		dst.KL = t.K
+		src.KL = a.K
+	}
+	dst.From(src)
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/cblas128/conv_symmetric_test.go b/vendor/gonum.org/v1/gonum/blas/cblas128/conv_symmetric_test.go
new file mode 100644
index 00000000..eef76f4a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/cblas128/conv_symmetric_test.go
@@ -0,0 +1,307 @@
+// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.
+
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package cblas128
+
+import (
+	math "math/cmplx"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+func newSymmetricFrom(a SymmetricCols) Symmetric {
+	t := Symmetric{
+		N:      a.N,
+		Stride: a.N,
+		Data:   make([]complex128, a.N*a.N),
+		Uplo:   a.Uplo,
+	}
+	t.From(a)
+	return t
+}
+
+func (m Symmetric) n() int { return m.N }
+func (m Symmetric) at(i, j int) complex128 {
+	if m.Uplo == blas.Lower && i < j && j < m.N {
+		i, j = j, i
+	}
+	if m.Uplo == blas.Upper && i > j {
+		i, j = j, i
+	}
+	return m.Data[i*m.Stride+j]
+}
+func (m Symmetric) uplo() blas.Uplo { return m.Uplo }
+
+func newSymmetricColsFrom(a Symmetric) SymmetricCols {
+	t := SymmetricCols{
+		N:      a.N,
+		Stride: a.N,
+		Data:   make([]complex128, a.N*a.N),
+		Uplo:   a.Uplo,
+	}
+	t.From(a)
+	return t
+}
+
+func (m SymmetricCols) n() int { return m.N }
+func (m SymmetricCols) at(i, j int) complex128 {
+	if m.Uplo == blas.Lower && i < j {
+		i, j = j, i
+	}
+	if m.Uplo == blas.Upper && i > j && i < m.N {
+		i, j = j, i
+	}
+	return m.Data[i+j*m.Stride]
+}
+func (m SymmetricCols) uplo() blas.Uplo { return m.Uplo }
+
+type symmetric interface {
+	n() int
+	at(i, j int) complex128
+	uplo() blas.Uplo
+}
+
+func sameSymmetric(a, b symmetric) bool {
+	an := a.n()
+	bn := b.n()
+	if an != bn {
+		return false
+	}
+	if a.uplo() != b.uplo() {
+		return false
+	}
+	for i := 0; i < an; i++ {
+		for j := 0; j < an; j++ {
+			if a.at(i, j) != b.at(i, j) || math.IsNaN(a.at(i, j)) != math.IsNaN(b.at(i, j)) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+var symmetricTests = []Symmetric{
+	{N: 3, Stride: 3, Data: []complex128{
+		1, 2, 3,
+		4, 5, 6,
+		7, 8, 9,
+	}},
+	{N: 3, Stride: 5, Data: []complex128{
+		1, 2, 3, 0, 0,
+		4, 5, 6, 0, 0,
+		7, 8, 9, 0, 0,
+	}},
+}
+
+func TestConvertSymmetric(t *testing.T) {
+	for _, test := range symmetricTests {
+		for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
+			test.Uplo = uplo
+			colmajor := newSymmetricColsFrom(test)
+			if !sameSymmetric(colmajor, test) {
+				t.Errorf("unexpected result for row major to col major conversion:\n\tgot: %#v\n\tfrom:%#v",
+					colmajor, test)
+			}
+			rowmajor := newSymmetricFrom(colmajor)
+			if !sameSymmetric(rowmajor, test) {
+				t.Errorf("unexpected result for col major to row major conversion:\n\tgot: %#v\n\twant:%#v",
+					rowmajor, test)
+			}
+		}
+	}
+}
+func newSymmetricBandFrom(a SymmetricBandCols) SymmetricBand {
+	t := SymmetricBand{
+		N:      a.N,
+		K:      a.K,
+		Stride: a.K + 1,
+		Data:   make([]complex128, a.N*(a.K+1)),
+		Uplo:   a.Uplo,
+	}
+	for i := range t.Data {
+		t.Data[i] = math.NaN()
+	}
+	t.From(a)
+	return t
+}
+
+func (m SymmetricBand) n() (n int) { return m.N }
+func (m SymmetricBand) at(i, j int) complex128 {
+	b := Band{
+		Rows: m.N, Cols: m.N,
+		Stride: m.Stride,
+		Data:   m.Data,
+	}
+	switch m.Uplo {
+	default:
+		panic("cblas128: bad BLAS uplo")
+	case blas.Upper:
+		b.KU = m.K
+		if i > j {
+			i, j = j, i
+		}
+	case blas.Lower:
+		b.KL = m.K
+		if i < j {
+			i, j = j, i
+		}
+	}
+	return b.at(i, j)
+}
+func (m SymmetricBand) bandwidth() (k int) { return m.K }
+func (m SymmetricBand) uplo() blas.Uplo    { return m.Uplo }
+
+func newSymmetricBandColsFrom(a SymmetricBand) SymmetricBandCols {
+	t := SymmetricBandCols{
+		N:      a.N,
+		K:      a.K,
+		Stride: a.K + 1,
+		Data:   make([]complex128, a.N*(a.K+1)),
+		Uplo:   a.Uplo,
+	}
+	for i := range t.Data {
+		t.Data[i] = math.NaN()
+	}
+	t.From(a)
+	return t
+}
+
+func (m SymmetricBandCols) n() (n int) { return m.N }
+func (m SymmetricBandCols) at(i, j int) complex128 {
+	b := BandCols{
+		Rows: m.N, Cols: m.N,
+		Stride: m.Stride,
+		Data:   m.Data,
+	}
+	switch m.Uplo {
+	default:
+		panic("cblas128: bad BLAS uplo")
+	case blas.Upper:
+		b.KU = m.K
+		if i > j {
+			i, j = j, i
+		}
+	case blas.Lower:
+		b.KL = m.K
+		if i < j {
+			i, j = j, i
+		}
+	}
+	return b.at(i, j)
+}
+func (m SymmetricBandCols) bandwidth() (k int) { return m.K }
+func (m SymmetricBandCols) uplo() blas.Uplo    { return m.Uplo }
+
+type symmetricBand interface {
+	n() (n int)
+	at(i, j int) complex128
+	bandwidth() (k int)
+	uplo() blas.Uplo
+}
+
+func sameSymmetricBand(a, b symmetricBand) bool {
+	an := a.n()
+	bn := b.n()
+	if an != bn {
+		return false
+	}
+	if a.uplo() != b.uplo() {
+		return false
+	}
+	ak := a.bandwidth()
+	bk := b.bandwidth()
+	if ak != bk {
+		return false
+	}
+	for i := 0; i < an; i++ {
+		for j := 0; j < an; j++ {
+			if a.at(i, j) != b.at(i, j) || math.IsNaN(a.at(i, j)) != math.IsNaN(b.at(i, j)) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+var symmetricBandTests = []SymmetricBand{
+	{N: 3, K: 0, Stride: 1, Uplo: blas.Upper, Data: []complex128{
+		1,
+		2,
+		3,
+	}},
+	{N: 3, K: 0, Stride: 1, Uplo: blas.Lower, Data: []complex128{
+		1,
+		2,
+		3,
+	}},
+	{N: 3, K: 1, Stride: 2, Uplo: blas.Upper, Data: []complex128{
+		1, 2,
+		3, 4,
+		5, -1,
+	}},
+	{N: 3, K: 1, Stride: 2, Uplo: blas.Lower, Data: []complex128{
+		-1, 1,
+		2, 3,
+		4, 5,
+	}},
+	{N: 3, K: 2, Stride: 3, Uplo: blas.Upper, Data: []complex128{
+		1, 2, 3,
+		4, 5, -1,
+		6, -2, -3,
+	}},
+	{N: 3, K: 2, Stride: 3, Uplo: blas.Lower, Data: []complex128{
+		-2, -1, 1,
+		-3, 2, 4,
+		3, 5, 6,
+	}},
+
+	{N: 3, K: 0, Stride: 5, Uplo: blas.Upper, Data: []complex128{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{N: 3, K: 0, Stride: 5, Uplo: blas.Lower, Data: []complex128{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{N: 3, K: 1, Stride: 5, Uplo: blas.Upper, Data: []complex128{
+		1, 2, 0, 0, 0,
+		3, 4, 0, 0, 0,
+		5, -1, 0, 0, 0,
+	}},
+	{N: 3, K: 1, Stride: 5, Uplo: blas.Lower, Data: []complex128{
+		-1, 1, 0, 0, 0,
+		2, 3, 0, 0, 0,
+		4, 5, 0, 0, 0,
+	}},
+	{N: 3, K: 2, Stride: 5, Uplo: blas.Upper, Data: []complex128{
+		1, 2, 3, 0, 0,
+		4, 5, -1, 0, 0,
+		6, -2, -3, 0, 0,
+	}},
+	{N: 3, K: 2, Stride: 5, Uplo: blas.Lower, Data: []complex128{
+		-2, -1, 1, 0, 0,
+		-3, 2, 4, 0, 0,
+		3, 5, 6, 0, 0,
+	}},
+}
+
+func TestConvertSymBand(t *testing.T) {
+	for _, test := range symmetricBandTests {
+		colmajor := newSymmetricBandColsFrom(test)
+		if !sameSymmetricBand(colmajor, test) {
+			t.Errorf("unexpected result for row major to col major conversion:\n\tgot: %#v\n\tfrom:%#v",
+				colmajor, test)
+		}
+		rowmajor := newSymmetricBandFrom(colmajor)
+		if !sameSymmetricBand(rowmajor, test) {
+			t.Errorf("unexpected result for col major to row major conversion:\n\tgot: %#v\n\twant:%#v",
+				rowmajor, test)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/cblas128/conv_test.go b/vendor/gonum.org/v1/gonum/blas/cblas128/conv_test.go
new file mode 100644
index 00000000..8d25fd28
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/cblas128/conv_test.go
@@ -0,0 +1,620 @@
+// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.
+
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package cblas128
+
+import (
+	math "math/cmplx"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+func newGeneralFrom(a GeneralCols) General {
+	t := General{
+		Rows:   a.Rows,
+		Cols:   a.Cols,
+		Stride: a.Cols,
+		Data:   make([]complex128, a.Rows*a.Cols),
+	}
+	t.From(a)
+	return t
+}
+
+func (m General) dims() (r, c int)       { return m.Rows, m.Cols }
+func (m General) at(i, j int) complex128 { return m.Data[i*m.Stride+j] }
+
+func newGeneralColsFrom(a General) GeneralCols {
+	t := GeneralCols{
+		Rows:   a.Rows,
+		Cols:   a.Cols,
+		Stride: a.Rows,
+		Data:   make([]complex128, a.Rows*a.Cols),
+	}
+	t.From(a)
+	return t
+}
+
+func (m GeneralCols) dims() (r, c int)       { return m.Rows, m.Cols }
+func (m GeneralCols) at(i, j int) complex128 { return m.Data[i+j*m.Stride] }
+
+type general interface {
+	dims() (r, c int)
+	at(i, j int) complex128
+}
+
+func sameGeneral(a, b general) bool {
+	ar, ac := a.dims()
+	br, bc := b.dims()
+	if ar != br || ac != bc {
+		return false
+	}
+	for i := 0; i < ar; i++ {
+		for j := 0; j < ac; j++ {
+			if a.at(i, j) != b.at(i, j) || math.IsNaN(a.at(i, j)) != math.IsNaN(b.at(i, j)) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+var generalTests = []General{
+	{Rows: 2, Cols: 3, Stride: 3, Data: []complex128{
+		1, 2, 3,
+		4, 5, 6,
+	}},
+	{Rows: 3, Cols: 2, Stride: 2, Data: []complex128{
+		1, 2,
+		3, 4,
+		5, 6,
+	}},
+	{Rows: 3, Cols: 3, Stride: 3, Data: []complex128{
+		1, 2, 3,
+		4, 5, 6,
+		7, 8, 9,
+	}},
+	{Rows: 2, Cols: 3, Stride: 5, Data: []complex128{
+		1, 2, 3, 0, 0,
+		4, 5, 6, 0, 0,
+	}},
+	{Rows: 3, Cols: 2, Stride: 5, Data: []complex128{
+		1, 2, 0, 0, 0,
+		3, 4, 0, 0, 0,
+		5, 6, 0, 0, 0,
+	}},
+	{Rows: 3, Cols: 3, Stride: 5, Data: []complex128{
+		1, 2, 3, 0, 0,
+		4, 5, 6, 0, 0,
+		7, 8, 9, 0, 0,
+	}},
+}
+
+func TestConvertGeneral(t *testing.T) {
+	for _, test := range generalTests {
+		colmajor := newGeneralColsFrom(test)
+		if !sameGeneral(colmajor, test) {
+			t.Errorf("unexpected result for row major to col major conversion:\n\tgot: %#v\n\tfrom:%#v",
+				colmajor, test)
+		}
+		rowmajor := newGeneralFrom(colmajor)
+		if !sameGeneral(rowmajor, test) {
+			t.Errorf("unexpected result for col major to row major conversion:\n\tgot: %#v\n\twant:%#v",
+				rowmajor, test)
+		}
+	}
+}
+
+func newTriangularFrom(a TriangularCols) Triangular {
+	t := Triangular{
+		N:      a.N,
+		Stride: a.N,
+		Data:   make([]complex128, a.N*a.N),
+		Diag:   a.Diag,
+		Uplo:   a.Uplo,
+	}
+	t.From(a)
+	return t
+}
+
+func (m Triangular) n() int { return m.N }
+func (m Triangular) at(i, j int) complex128 {
+	if m.Diag == blas.Unit && i == j {
+		return 1
+	}
+	if m.Uplo == blas.Lower && i < j && j < m.N {
+		return 0
+	}
+	if m.Uplo == blas.Upper && i > j {
+		return 0
+	}
+	return m.Data[i*m.Stride+j]
+}
+func (m Triangular) uplo() blas.Uplo { return m.Uplo }
+func (m Triangular) diag() blas.Diag { return m.Diag }
+
+func newTriangularColsFrom(a Triangular) TriangularCols {
+	t := TriangularCols{
+		N:      a.N,
+		Stride: a.N,
+		Data:   make([]complex128, a.N*a.N),
+		Diag:   a.Diag,
+		Uplo:   a.Uplo,
+	}
+	t.From(a)
+	return t
+}
+
+func (m TriangularCols) n() int { return m.N }
+func (m TriangularCols) at(i, j int) complex128 {
+	if m.Diag == blas.Unit && i == j {
+		return 1
+	}
+	if m.Uplo == blas.Lower && i < j {
+		return 0
+	}
+	if m.Uplo == blas.Upper && i > j && i < m.N {
+		return 0
+	}
+	return m.Data[i+j*m.Stride]
+}
+func (m TriangularCols) uplo() blas.Uplo { return m.Uplo }
+func (m TriangularCols) diag() blas.Diag { return m.Diag }
+
+type triangular interface {
+	n() int
+	at(i, j int) complex128
+	uplo() blas.Uplo
+	diag() blas.Diag
+}
+
+func sameTriangular(a, b triangular) bool {
+	an := a.n()
+	bn := b.n()
+	if an != bn {
+		return false
+	}
+	for i := 0; i < an; i++ {
+		for j := 0; j < an; j++ {
+			if a.at(i, j) != b.at(i, j) || math.IsNaN(a.at(i, j)) != math.IsNaN(b.at(i, j)) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+var triangularTests = []Triangular{
+	{N: 3, Stride: 3, Data: []complex128{
+		1, 2, 3,
+		4, 5, 6,
+		7, 8, 9,
+	}},
+	{N: 3, Stride: 5, Data: []complex128{
+		1, 2, 3, 0, 0,
+		4, 5, 6, 0, 0,
+		7, 8, 9, 0, 0,
+	}},
+}
+
+func TestConvertTriangular(t *testing.T) {
+	for _, test := range triangularTests {
+		for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower, blas.All} {
+			for _, diag := range []blas.Diag{blas.Unit, blas.NonUnit} {
+				test.Uplo = uplo
+				test.Diag = diag
+				colmajor := newTriangularColsFrom(test)
+				if !sameTriangular(colmajor, test) {
+					t.Errorf("unexpected result for row major to col major conversion:\n\tgot: %#v\n\tfrom:%#v",
+						colmajor, test)
+				}
+				rowmajor := newTriangularFrom(colmajor)
+				if !sameTriangular(rowmajor, test) {
+					t.Errorf("unexpected result for col major to row major conversion:\n\tgot: %#v\n\twant:%#v",
+						rowmajor, test)
+				}
+			}
+		}
+	}
+}
+
+func newBandFrom(a BandCols) Band {
+	t := Band{
+		Rows:   a.Rows,
+		Cols:   a.Cols,
+		KL:     a.KL,
+		KU:     a.KU,
+		Stride: a.KL + a.KU + 1,
+		Data:   make([]complex128, a.Rows*(a.KL+a.KU+1)),
+	}
+	for i := range t.Data {
+		t.Data[i] = math.NaN()
+	}
+	t.From(a)
+	return t
+}
+
+func (m Band) dims() (r, c int) { return m.Rows, m.Cols }
+func (m Band) at(i, j int) complex128 {
+	pj := j + m.KL - i
+	if pj < 0 || m.KL+m.KU+1 <= pj {
+		return 0
+	}
+	return m.Data[i*m.Stride+pj]
+}
+func (m Band) bandwidth() (kl, ku int) { return m.KL, m.KU }
+
+func newBandColsFrom(a Band) BandCols {
+	t := BandCols{
+		Rows:   a.Rows,
+		Cols:   a.Cols,
+		KL:     a.KL,
+		KU:     a.KU,
+		Stride: a.KL + a.KU + 1,
+		Data:   make([]complex128, a.Cols*(a.KL+a.KU+1)),
+	}
+	for i := range t.Data {
+		t.Data[i] = math.NaN()
+	}
+	t.From(a)
+	return t
+}
+
+func (m BandCols) dims() (r, c int) { return m.Rows, m.Cols }
+func (m BandCols) at(i, j int) complex128 {
+	pj := i + m.KU - j
+	if pj < 0 || m.KL+m.KU+1 <= pj {
+		return 0
+	}
+	return m.Data[j*m.Stride+pj]
+}
+func (m BandCols) bandwidth() (kl, ku int) { return m.KL, m.KU }
+
+type band interface {
+	dims() (r, c int)
+	at(i, j int) complex128
+	bandwidth() (kl, ku int)
+}
+
+func sameBand(a, b band) bool {
+	ar, ac := a.dims()
+	br, bc := b.dims()
+	if ar != br || ac != bc {
+		return false
+	}
+	akl, aku := a.bandwidth()
+	bkl, bku := b.bandwidth()
+	if akl != bkl || aku != bku {
+		return false
+	}
+	for i := 0; i < ar; i++ {
+		for j := 0; j < ac; j++ {
+			if a.at(i, j) != b.at(i, j) || math.IsNaN(a.at(i, j)) != math.IsNaN(b.at(i, j)) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+var bandTests = []Band{
+	{Rows: 3, Cols: 4, KL: 0, KU: 0, Stride: 1, Data: []complex128{
+		1,
+		2,
+		3,
+	}},
+	{Rows: 3, Cols: 3, KL: 0, KU: 0, Stride: 1, Data: []complex128{
+		1,
+		2,
+		3,
+	}},
+	{Rows: 4, Cols: 3, KL: 0, KU: 0, Stride: 1, Data: []complex128{
+		1,
+		2,
+		3,
+	}},
+	{Rows: 4, Cols: 3, KL: 0, KU: 1, Stride: 2, Data: []complex128{
+		1, 2,
+		3, 4,
+		5, 6,
+	}},
+	{Rows: 3, Cols: 4, KL: 0, KU: 1, Stride: 2, Data: []complex128{
+		1, 2,
+		3, 4,
+		5, 6,
+	}},
+	{Rows: 3, Cols: 4, KL: 1, KU: 1, Stride: 3, Data: []complex128{
+		-1, 2, 3,
+		4, 5, 6,
+		7, 8, 9,
+	}},
+	{Rows: 4, Cols: 3, KL: 1, KU: 1, Stride: 3, Data: []complex128{
+		-1, 2, 3,
+		4, 5, 6,
+		7, 8, -2,
+		9, -3, -4,
+	}},
+	{Rows: 3, Cols: 4, KL: 2, KU: 1, Stride: 4, Data: []complex128{
+		-2, -1, 3, 4,
+		-3, 5, 6, 7,
+		8, 9, 10, 11,
+	}},
+	{Rows: 4, Cols: 3, KL: 2, KU: 1, Stride: 4, Data: []complex128{
+		-2, -1, 2, 3,
+		-3, 4, 5, 6,
+		7, 8, 9, -4,
+		10, 11, -5, -6,
+	}},
+
+	{Rows: 3, Cols: 4, KL: 0, KU: 0, Stride: 5, Data: []complex128{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{Rows: 3, Cols: 3, KL: 0, KU: 0, Stride: 5, Data: []complex128{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{Rows: 4, Cols: 3, KL: 0, KU: 0, Stride: 5, Data: []complex128{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{Rows: 4, Cols: 3, KL: 0, KU: 1, Stride: 5, Data: []complex128{
+		1, 2, 0, 0, 0,
+		3, 4, 0, 0, 0,
+		5, 6, 0, 0, 0,
+	}},
+	{Rows: 3, Cols: 4, KL: 0, KU: 1, Stride: 5, Data: []complex128{
+		1, 2, 0, 0, 0,
+		3, 4, 0, 0, 0,
+		5, 6, 0, 0, 0,
+	}},
+	{Rows: 3, Cols: 4, KL: 1, KU: 1, Stride: 5, Data: []complex128{
+		-1, 2, 3, 0, 0,
+		4, 5, 6, 0, 0,
+		7, 8, 9, 0, 0,
+	}},
+	{Rows: 4, Cols: 3, KL: 1, KU: 1, Stride: 5, Data: []complex128{
+		-1, 2, 3, 0, 0,
+		4, 5, 6, 0, 0,
+		7, 8, -2, 0, 0,
+		9, -3, -4, 0, 0,
+	}},
+	{Rows: 3, Cols: 4, KL: 2, KU: 1, Stride: 5, Data: []complex128{
+		-2, -1, 3, 4, 0,
+		-3, 5, 6, 7, 0,
+		8, 9, 10, 11, 0,
+	}},
+	{Rows: 4, Cols: 3, KL: 2, KU: 1, Stride: 5, Data: []complex128{
+		-2, -1, 2, 3, 0,
+		-3, 4, 5, 6, 0,
+		7, 8, 9, -4, 0,
+		10, 11, -5, -6, 0,
+	}},
+}
+
+func TestConvertBand(t *testing.T) {
+	for _, test := range bandTests {
+		colmajor := newBandColsFrom(test)
+		if !sameBand(colmajor, test) {
+			t.Errorf("unexpected result for row major to col major conversion:\n\tgot: %#v\n\tfrom:%#v",
+				colmajor, test)
+		}
+		rowmajor := newBandFrom(colmajor)
+		if !sameBand(rowmajor, test) {
+			t.Errorf("unexpected result for col major to row major conversion:\n\tgot: %#v\n\twant:%#v",
+				rowmajor, test)
+		}
+	}
+}
+
+func newTriangularBandFrom(a TriangularBandCols) TriangularBand {
+	t := TriangularBand{
+		N:      a.N,
+		K:      a.K,
+		Stride: a.K + 1,
+		Data:   make([]complex128, a.N*(a.K+1)),
+		Uplo:   a.Uplo,
+		Diag:   a.Diag,
+	}
+	for i := range t.Data {
+		t.Data[i] = math.NaN()
+	}
+	t.From(a)
+	return t
+}
+
+func (m TriangularBand) n() (n int) { return m.N }
+func (m TriangularBand) at(i, j int) complex128 {
+	if m.Diag == blas.Unit && i == j {
+		return 1
+	}
+	b := Band{
+		Rows: m.N, Cols: m.N,
+		Stride: m.Stride,
+		Data:   m.Data,
+	}
+	switch m.Uplo {
+	default:
+		panic("cblas128: bad BLAS uplo")
+	case blas.Upper:
+		if i > j {
+			return 0
+		}
+		b.KU = m.K
+	case blas.Lower:
+		if i < j {
+			return 0
+		}
+		b.KL = m.K
+	}
+	return b.at(i, j)
+}
+func (m TriangularBand) bandwidth() (k int) { return m.K }
+func (m TriangularBand) uplo() blas.Uplo    { return m.Uplo }
+func (m TriangularBand) diag() blas.Diag    { return m.Diag }
+
+func newTriangularBandColsFrom(a TriangularBand) TriangularBandCols {
+	t := TriangularBandCols{
+		N:      a.N,
+		K:      a.K,
+		Stride: a.K + 1,
+		Data:   make([]complex128, a.N*(a.K+1)),
+		Uplo:   a.Uplo,
+		Diag:   a.Diag,
+	}
+	for i := range t.Data {
+		t.Data[i] = math.NaN()
+	}
+	t.From(a)
+	return t
+}
+
+func (m TriangularBandCols) n() (n int) { return m.N }
+func (m TriangularBandCols) at(i, j int) complex128 {
+	if m.Diag == blas.Unit && i == j {
+		return 1
+	}
+	b := BandCols{
+		Rows: m.N, Cols: m.N,
+		Stride: m.Stride,
+		Data:   m.Data,
+	}
+	switch m.Uplo {
+	default:
+		panic("cblas128: bad BLAS uplo")
+	case blas.Upper:
+		if i > j {
+			return 0
+		}
+		b.KU = m.K
+	case blas.Lower:
+		if i < j {
+			return 0
+		}
+		b.KL = m.K
+	}
+	return b.at(i, j)
+}
+func (m TriangularBandCols) bandwidth() (k int) { return m.K }
+func (m TriangularBandCols) uplo() blas.Uplo    { return m.Uplo }
+func (m TriangularBandCols) diag() blas.Diag    { return m.Diag }
+
+type triangularBand interface {
+	n() (n int)
+	at(i, j int) complex128
+	bandwidth() (k int)
+	uplo() blas.Uplo
+	diag() blas.Diag
+}
+
+func sameTriangularBand(a, b triangularBand) bool {
+	an := a.n()
+	bn := b.n()
+	if an != bn {
+		return false
+	}
+	if a.uplo() != b.uplo() {
+		return false
+	}
+	if a.diag() != b.diag() {
+		return false
+	}
+	ak := a.bandwidth()
+	bk := b.bandwidth()
+	if ak != bk {
+		return false
+	}
+	for i := 0; i < an; i++ {
+		for j := 0; j < an; j++ {
+			if a.at(i, j) != b.at(i, j) || math.IsNaN(a.at(i, j)) != math.IsNaN(b.at(i, j)) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+var triangularBandTests = []TriangularBand{
+	{N: 3, K: 0, Stride: 1, Uplo: blas.Upper, Data: []complex128{
+		1,
+		2,
+		3,
+	}},
+	{N: 3, K: 0, Stride: 1, Uplo: blas.Lower, Data: []complex128{
+		1,
+		2,
+		3,
+	}},
+	{N: 3, K: 1, Stride: 2, Uplo: blas.Upper, Data: []complex128{
+		1, 2,
+		3, 4,
+		5, -1,
+	}},
+	{N: 3, K: 1, Stride: 2, Uplo: blas.Lower, Data: []complex128{
+		-1, 1,
+		2, 3,
+		4, 5,
+	}},
+	{N: 3, K: 2, Stride: 3, Uplo: blas.Upper, Data: []complex128{
+		1, 2, 3,
+		4, 5, -1,
+		6, -2, -3,
+	}},
+	{N: 3, K: 2, Stride: 3, Uplo: blas.Lower, Data: []complex128{
+		-2, -1, 1,
+		-3, 2, 4,
+		3, 5, 6,
+	}},
+
+	{N: 3, K: 0, Stride: 5, Uplo: blas.Upper, Data: []complex128{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{N: 3, K: 0, Stride: 5, Uplo: blas.Lower, Data: []complex128{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{N: 3, K: 1, Stride: 5, Uplo: blas.Upper, Data: []complex128{
+		1, 2, 0, 0, 0,
+		3, 4, 0, 0, 0,
+		5, -1, 0, 0, 0,
+	}},
+	{N: 3, K: 1, Stride: 5, Uplo: blas.Lower, Data: []complex128{
+		-1, 1, 0, 0, 0,
+		2, 3, 0, 0, 0,
+		4, 5, 0, 0, 0,
+	}},
+	{N: 3, K: 2, Stride: 5, Uplo: blas.Upper, Data: []complex128{
+		1, 2, 3, 0, 0,
+		4, 5, -1, 0, 0,
+		6, -2, -3, 0, 0,
+	}},
+	{N: 3, K: 2, Stride: 5, Uplo: blas.Lower, Data: []complex128{
+		-2, -1, 1, 0, 0,
+		-3, 2, 4, 0, 0,
+		3, 5, 6, 0, 0,
+	}},
+}
+
+func TestConvertTriBand(t *testing.T) {
+	for _, test := range triangularBandTests {
+		colmajor := newTriangularBandColsFrom(test)
+		if !sameTriangularBand(colmajor, test) {
+			t.Errorf("unexpected result for row major to col major conversion:\n\tgot: %#v\n\tfrom:%#v",
+				colmajor, test)
+		}
+		rowmajor := newTriangularBandFrom(colmajor)
+		if !sameTriangularBand(rowmajor, test) {
+			t.Errorf("unexpected result for col major to row major conversion:\n\tgot: %#v\n\twant:%#v",
+				rowmajor, test)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/cblas128/doc.go b/vendor/gonum.org/v1/gonum/blas/cblas128/doc.go
new file mode 100644
index 00000000..15398184
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/cblas128/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package cblas128 provides a simple interface to the complex128 BLAS API.
+package cblas128 // import "gonum.org/v1/gonum/blas/cblas128"
diff --git a/vendor/gonum.org/v1/gonum/blas/cblas64/cblas64.go b/vendor/gonum.org/v1/gonum/blas/cblas64/cblas64.go
new file mode 100644
index 00000000..6164d479
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/cblas64/cblas64.go
@@ -0,0 +1,507 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package cblas64
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/gonum"
+)
+
+var cblas64 blas.Complex64 = gonum.Implementation{}
+
+// Use sets the BLAS complex64 implementation to be used by subsequent BLAS calls.
+// The default implementation is cgo.Implementation.
+func Use(b blas.Complex64) {
+	cblas64 = b
+}
+
+// Implementation returns the current BLAS complex64 implementation.
+//
+// Implementation allows direct calls to the current the BLAS complex64 implementation
+// giving finer control of parameters.
+func Implementation() blas.Complex64 {
+	return cblas64
+}
+
+// Vector represents a vector with an associated element increment.
+type Vector struct {
+	Inc  int
+	Data []complex64
+}
+
+// General represents a matrix using the conventional storage scheme.
+type General struct {
+	Rows, Cols int
+	Stride     int
+	Data       []complex64
+}
+
+// Band represents a band matrix using the band storage scheme.
+type Band struct {
+	Rows, Cols int
+	KL, KU     int
+	Stride     int
+	Data       []complex64
+}
+
+// Triangular represents a triangular matrix using the conventional storage scheme.
+type Triangular struct {
+	N      int
+	Stride int
+	Data   []complex64
+	Uplo   blas.Uplo
+	Diag   blas.Diag
+}
+
+// TriangularBand represents a triangular matrix using the band storage scheme.
+type TriangularBand struct {
+	N, K   int
+	Stride int
+	Data   []complex64
+	Uplo   blas.Uplo
+	Diag   blas.Diag
+}
+
+// TriangularPacked represents a triangular matrix using the packed storage scheme.
+type TriangularPacked struct {
+	N    int
+	Data []complex64
+	Uplo blas.Uplo
+	Diag blas.Diag
+}
+
+// Symmetric represents a symmetric matrix using the conventional storage scheme.
+type Symmetric struct {
+	N      int
+	Stride int
+	Data   []complex64
+	Uplo   blas.Uplo
+}
+
+// SymmetricBand represents a symmetric matrix using the band storage scheme.
+type SymmetricBand struct {
+	N, K   int
+	Stride int
+	Data   []complex64
+	Uplo   blas.Uplo
+}
+
+// SymmetricPacked represents a symmetric matrix using the packed storage scheme.
+type SymmetricPacked struct {
+	N    int
+	Data []complex64
+	Uplo blas.Uplo
+}
+
+// Hermitian represents an Hermitian matrix using the conventional storage scheme.
+type Hermitian Symmetric
+
+// HermitianBand represents an Hermitian matrix using the band storage scheme.
+type HermitianBand SymmetricBand
+
+// HermitianPacked represents an Hermitian matrix using the packed storage scheme.
+type HermitianPacked SymmetricPacked
+
+// Level 1
+
+const negInc = "cblas64: negative vector increment"
+
+// Dotu computes the dot product of the two vectors without
+// complex conjugation:
+//  x^T * y
+func Dotu(n int, x, y Vector) complex64 {
+	return cblas64.Cdotu(n, x.Data, x.Inc, y.Data, y.Inc)
+}
+
+// Dotc computes the dot product of the two vectors with
+// complex conjugation:
+//  x^H * y.
+func Dotc(n int, x, y Vector) complex64 {
+	return cblas64.Cdotc(n, x.Data, x.Inc, y.Data, y.Inc)
+}
+
+// Nrm2 computes the Euclidean norm of the vector x:
+//  sqrt(\sum_i x[i] * x[i]).
+//
+// Nrm2 will panic if the vector increment is negative.
+func Nrm2(n int, x Vector) float32 {
+	if x.Inc < 0 {
+		panic(negInc)
+	}
+	return cblas64.Scnrm2(n, x.Data, x.Inc)
+}
+
+// Asum computes the sum of magnitudes of the real and imaginary parts of
+// elements of the vector x:
+//  \sum_i (|Re x[i]| + |Im x[i]|).
+//
+// Asum will panic if the vector increment is negative.
+func Asum(n int, x Vector) float32 {
+	if x.Inc < 0 {
+		panic(negInc)
+	}
+	return cblas64.Scasum(n, x.Data, x.Inc)
+}
+
+// Iamax returns the index of an element of x with the largest sum of
+// magnitudes of the real and imaginary parts (|Re x[i]|+|Im x[i]|).
+// If there are multiple such indices, the earliest is returned.
+//
+// Iamax returns -1 if n == 0.
+//
+// Iamax will panic if the vector increment is negative.
+func Iamax(n int, x Vector) int {
+	if x.Inc < 0 {
+		panic(negInc)
+	}
+	return cblas64.Icamax(n, x.Data, x.Inc)
+}
+
+// Swap exchanges the elements of two vectors:
+//  x[i], y[i] = y[i], x[i] for all i.
+func Swap(n int, x, y Vector) {
+	cblas64.Cswap(n, x.Data, x.Inc, y.Data, y.Inc)
+}
+
+// Copy copies the elements of x into the elements of y:
+//  y[i] = x[i] for all i.
+func Copy(n int, x, y Vector) {
+	cblas64.Ccopy(n, x.Data, x.Inc, y.Data, y.Inc)
+}
+
+// Axpy computes
+//  y = alpha * x + y,
+// where x and y are vectors, and alpha is a scalar.
+func Axpy(n int, alpha complex64, x, y Vector) {
+	cblas64.Caxpy(n, alpha, x.Data, x.Inc, y.Data, y.Inc)
+}
+
+// Scal computes
+//  x = alpha * x,
+// where x is a vector, and alpha is a scalar.
+//
+// Scal will panic if the vector increment is negative.
+func Scal(n int, alpha complex64, x Vector) {
+	if x.Inc < 0 {
+		panic(negInc)
+	}
+	cblas64.Cscal(n, alpha, x.Data, x.Inc)
+}
+
+// Dscal computes
+//  x = alpha * x,
+// where x is a vector, and alpha is a real scalar.
+//
+// Dscal will panic if the vector increment is negative.
+func Dscal(n int, alpha float32, x Vector) {
+	if x.Inc < 0 {
+		panic(negInc)
+	}
+	cblas64.Csscal(n, alpha, x.Data, x.Inc)
+}
+
+// Level 2
+
+// Gemv computes
+//  y = alpha * A * x + beta * y,   if t == blas.NoTrans,
+//  y = alpha * A^T * x + beta * y, if t == blas.Trans,
+//  y = alpha * A^H * x + beta * y, if t == blas.ConjTrans,
+// where A is an m×n dense matrix, x and y are vectors, and alpha and beta are
+// scalars.
+func Gemv(t blas.Transpose, alpha complex64, a General, x Vector, beta complex64, y Vector) {
+	cblas64.Cgemv(t, a.Rows, a.Cols, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
+}
+
+// Gbmv computes
+//  y = alpha * A * x + beta * y,   if t == blas.NoTrans,
+//  y = alpha * A^T * x + beta * y, if t == blas.Trans,
+//  y = alpha * A^H * x + beta * y, if t == blas.ConjTrans,
+// where A is an m×n band matrix, x and y are vectors, and alpha and beta are
+// scalars.
+func Gbmv(t blas.Transpose, alpha complex64, a Band, x Vector, beta complex64, y Vector) {
+	cblas64.Cgbmv(t, a.Rows, a.Cols, a.KL, a.KU, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
+}
+
+// Trmv computes
+//  x = A * x,   if t == blas.NoTrans,
+//  x = A^T * x, if t == blas.Trans,
+//  x = A^H * x, if t == blas.ConjTrans,
+// where A is an n×n triangular matrix, and x is a vector.
+func Trmv(t blas.Transpose, a Triangular, x Vector) {
+	cblas64.Ctrmv(a.Uplo, t, a.Diag, a.N, a.Data, a.Stride, x.Data, x.Inc)
+}
+
+// Tbmv computes
+//  x = A * x,   if t == blas.NoTrans,
+//  x = A^T * x, if t == blas.Trans,
+//  x = A^H * x, if t == blas.ConjTrans,
+// where A is an n×n triangular band matrix, and x is a vector.
+func Tbmv(t blas.Transpose, a TriangularBand, x Vector) {
+	cblas64.Ctbmv(a.Uplo, t, a.Diag, a.N, a.K, a.Data, a.Stride, x.Data, x.Inc)
+}
+
+// Tpmv computes
+//  x = A * x,   if t == blas.NoTrans,
+//  x = A^T * x, if t == blas.Trans,
+//  x = A^H * x, if t == blas.ConjTrans,
+// where A is an n×n triangular matrix in packed format, and x is a vector.
+func Tpmv(t blas.Transpose, a TriangularPacked, x Vector) {
+	cblas64.Ctpmv(a.Uplo, t, a.Diag, a.N, a.Data, x.Data, x.Inc)
+}
+
+// Trsv solves
+//  A * x = b,   if t == blas.NoTrans,
+//  A^T * x = b, if t == blas.Trans,
+//  A^H * x = b, if t == blas.ConjTrans,
+// where A is an n×n triangular matrix and x is a vector.
+//
+// At entry to the function, x contains the values of b, and the result is
+// stored in-place into x.
+//
+// No test for singularity or near-singularity is included in this
+// routine. Such tests must be performed before calling this routine.
+func Trsv(t blas.Transpose, a Triangular, x Vector) {
+	cblas64.Ctrsv(a.Uplo, t, a.Diag, a.N, a.Data, a.Stride, x.Data, x.Inc)
+}
+
+// Tbsv solves
+//  A * x = b,   if t == blas.NoTrans,
+//  A^T * x = b, if t == blas.Trans,
+//  A^H * x = b, if t == blas.ConjTrans,
+// where A is an n×n triangular band matrix, and x is a vector.
+//
+// At entry to the function, x contains the values of b, and the result is
+// stored in-place into x.
+//
+// No test for singularity or near-singularity is included in this
+// routine. Such tests must be performed before calling this routine.
+func Tbsv(t blas.Transpose, a TriangularBand, x Vector) {
+	cblas64.Ctbsv(a.Uplo, t, a.Diag, a.N, a.K, a.Data, a.Stride, x.Data, x.Inc)
+}
+
+// Tpsv solves
+//  A * x = b,   if t == blas.NoTrans,
+//  A^T * x = b, if t == blas.Trans,
+//  A^H * x = b, if t == blas.ConjTrans,
+// where A is an n×n triangular matrix in packed format and x is a vector.
+//
+// At entry to the function, x contains the values of b, and the result is
+// stored in-place into x.
+//
+// No test for singularity or near-singularity is included in this
+// routine. Such tests must be performed before calling this routine.
+func Tpsv(t blas.Transpose, a TriangularPacked, x Vector) {
+	cblas64.Ctpsv(a.Uplo, t, a.Diag, a.N, a.Data, x.Data, x.Inc)
+}
+
+// Hemv computes
+//  y = alpha * A * x + beta * y,
+// where A is an n×n Hermitian matrix, x and y are vectors, and alpha and
+// beta are scalars.
+func Hemv(alpha complex64, a Hermitian, x Vector, beta complex64, y Vector) {
+	cblas64.Chemv(a.Uplo, a.N, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
+}
+
+// Hbmv performs
+//  y = alpha * A * x + beta * y,
+// where A is an n×n Hermitian band matrix, x and y are vectors, and alpha
+// and beta are scalars.
+func Hbmv(alpha complex64, a HermitianBand, x Vector, beta complex64, y Vector) {
+	cblas64.Chbmv(a.Uplo, a.N, a.K, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
+}
+
+// Hpmv performs
+//  y = alpha * A * x + beta * y,
+// where A is an n×n Hermitian matrix in packed format, x and y are vectors,
+// and alpha and beta are scalars.
+func Hpmv(alpha complex64, a HermitianPacked, x Vector, beta complex64, y Vector) {
+	cblas64.Chpmv(a.Uplo, a.N, alpha, a.Data, x.Data, x.Inc, beta, y.Data, y.Inc)
+}
+
+// Geru performs a rank-1 update
+//  A += alpha * x * y^T,
+// where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.
+func Geru(alpha complex64, x, y Vector, a General) {
+	cblas64.Cgeru(a.Rows, a.Cols, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
+}
+
+// Gerc performs a rank-1 update
+//  A += alpha * x * y^H,
+// where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.
+func Gerc(alpha complex64, x, y Vector, a General) {
+	cblas64.Cgerc(a.Rows, a.Cols, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
+}
+
+// Her performs a rank-1 update
+//  A += alpha * x * y^T,
+// where A is an m×n Hermitian matrix, x and y are vectors, and alpha is a scalar.
+func Her(alpha float32, x Vector, a Hermitian) {
+	cblas64.Cher(a.Uplo, a.N, alpha, x.Data, x.Inc, a.Data, a.Stride)
+}
+
+// Hpr performs a rank-1 update
+//  A += alpha * x * x^H,
+// where A is an n×n Hermitian matrix in packed format, x is a vector, and
+// alpha is a scalar.
+func Hpr(alpha float32, x Vector, a HermitianPacked) {
+	cblas64.Chpr(a.Uplo, a.N, alpha, x.Data, x.Inc, a.Data)
+}
+
+// Her2 performs a rank-2 update
+//  A += alpha * x * y^H + conj(alpha) * y * x^H,
+// where A is an n×n Hermitian matrix, x and y are vectors, and alpha is a scalar.
+func Her2(alpha complex64, x, y Vector, a Hermitian) {
+	cblas64.Cher2(a.Uplo, a.N, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
+}
+
+// Hpr2 performs a rank-2 update
+//  A += alpha * x * y^H + conj(alpha) * y * x^H,
+// where A is an n×n Hermitian matrix in packed format, x and y are vectors,
+// and alpha is a scalar.
+func Hpr2(alpha complex64, x, y Vector, a HermitianPacked) {
+	cblas64.Chpr2(a.Uplo, a.N, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data)
+}
+
+// Level 3
+
+// Gemm computes
+//  C = alpha * A * B + beta * C,
+// where A, B, and C are dense matrices, and alpha and beta are scalars.
+// tA and tB specify whether A or B are transposed or conjugated.
+func Gemm(tA, tB blas.Transpose, alpha complex64, a, b General, beta complex64, c General) {
+	var m, n, k int
+	if tA == blas.NoTrans {
+		m, k = a.Rows, a.Cols
+	} else {
+		m, k = a.Cols, a.Rows
+	}
+	if tB == blas.NoTrans {
+		n = b.Cols
+	} else {
+		n = b.Rows
+	}
+	cblas64.Cgemm(tA, tB, m, n, k, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
+}
+
+// Symm performs
+//  C = alpha * A * B + beta * C, if s == blas.Left,
+//  C = alpha * B * A + beta * C, if s == blas.Right,
+// where A is an n×n or m×m symmetric matrix, B and C are m×n matrices, and
+// alpha and beta are scalars.
+func Symm(s blas.Side, alpha complex64, a Symmetric, b General, beta complex64, c General) {
+	var m, n int
+	if s == blas.Left {
+		m, n = a.N, b.Cols
+	} else {
+		m, n = b.Rows, a.N
+	}
+	cblas64.Csymm(s, a.Uplo, m, n, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
+}
+
+// Syrk performs a symmetric rank-k update
+//  C = alpha * A * A^T + beta * C, if t == blas.NoTrans,
+//  C = alpha * A^T * A + beta * C, if t == blas.Trans,
+// where C is an n×n symmetric matrix, A is an n×k matrix if t == blas.NoTrans
+// and a k×n matrix otherwise, and alpha and beta are scalars.
+func Syrk(t blas.Transpose, alpha complex64, a General, beta complex64, c Symmetric) {
+	var n, k int
+	if t == blas.NoTrans {
+		n, k = a.Rows, a.Cols
+	} else {
+		n, k = a.Cols, a.Rows
+	}
+	cblas64.Csyrk(c.Uplo, t, n, k, alpha, a.Data, a.Stride, beta, c.Data, c.Stride)
+}
+
+// Syr2k performs a symmetric rank-2k update
+//  C = alpha * A * B^T + alpha * B * A^T + beta * C, if t == blas.NoTrans,
+//  C = alpha * A^T * B + alpha * B^T * A + beta * C, if t == blas.Trans,
+// where C is an n×n symmetric matrix, A and B are n×k matrices if
+// t == blas.NoTrans and k×n otherwise, and alpha and beta are scalars.
+func Syr2k(t blas.Transpose, alpha complex64, a, b General, beta complex64, c Symmetric) {
+	var n, k int
+	if t == blas.NoTrans {
+		n, k = a.Rows, a.Cols
+	} else {
+		n, k = a.Cols, a.Rows
+	}
+	cblas64.Csyr2k(c.Uplo, t, n, k, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
+}
+
+// Trmm performs
+//  B = alpha * A * B,   if tA == blas.NoTrans and s == blas.Left,
+//  B = alpha * A^T * B, if tA == blas.Trans and s == blas.Left,
+//  B = alpha * A^H * B, if tA == blas.ConjTrans and s == blas.Left,
+//  B = alpha * B * A,   if tA == blas.NoTrans and s == blas.Right,
+//  B = alpha * B * A^T, if tA == blas.Trans and s == blas.Right,
+//  B = alpha * B * A^H, if tA == blas.ConjTrans and s == blas.Right,
+// where A is an n×n or m×m triangular matrix, B is an m×n matrix, and alpha is
+// a scalar.
+func Trmm(s blas.Side, tA blas.Transpose, alpha complex64, a Triangular, b General) {
+	cblas64.Ctrmm(s, a.Uplo, tA, a.Diag, b.Rows, b.Cols, alpha, a.Data, a.Stride, b.Data, b.Stride)
+}
+
+// Trsm solves
+//  A * X = alpha * B,   if tA == blas.NoTrans and s == blas.Left,
+//  A^T * X = alpha * B, if tA == blas.Trans and s == blas.Left,
+//  A^H * X = alpha * B, if tA == blas.ConjTrans and s == blas.Left,
+//  X * A = alpha * B,   if tA == blas.NoTrans and s == blas.Right,
+//  X * A^T = alpha * B, if tA == blas.Trans and s == blas.Right,
+//  X * A^H = alpha * B, if tA == blas.ConjTrans and s == blas.Right,
+// where A is an n×n or m×m triangular matrix, X and B are m×n matrices, and
+// alpha is a scalar.
+//
+// At entry to the function, b contains the values of B, and the result is
+// stored in-place into b.
+//
+// No check is made that A is invertible.
+func Trsm(s blas.Side, tA blas.Transpose, alpha complex64, a Triangular, b General) {
+	cblas64.Ctrsm(s, a.Uplo, tA, a.Diag, b.Rows, b.Cols, alpha, a.Data, a.Stride, b.Data, b.Stride)
+}
+
+// Hemm performs
+//  C = alpha * A * B + beta * C, if s == blas.Left,
+//  C = alpha * B * A + beta * C, if s == blas.Right,
+// where A is an n×n or m×m Hermitian matrix, B and C are m×n matrices, and
+// alpha and beta are scalars.
+func Hemm(s blas.Side, alpha complex64, a Hermitian, b General, beta complex64, c General) {
+	var m, n int
+	if s == blas.Left {
+		m, n = a.N, b.Cols
+	} else {
+		m, n = b.Rows, a.N
+	}
+	cblas64.Chemm(s, a.Uplo, m, n, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
+}
+
+// Herk performs the Hermitian rank-k update
+//  C = alpha * A * A^H + beta*C, if t == blas.NoTrans,
+//  C = alpha * A^H * A + beta*C, if t == blas.ConjTrans,
+// where C is an n×n Hermitian matrix, A is an n×k matrix if t == blas.NoTrans
+// and a k×n matrix otherwise, and alpha and beta are scalars.
+func Herk(t blas.Transpose, alpha float32, a General, beta float32, c Hermitian) {
+	var n, k int
+	if t == blas.NoTrans {
+		n, k = a.Rows, a.Cols
+	} else {
+		n, k = a.Cols, a.Rows
+	}
+	cblas64.Cherk(c.Uplo, t, n, k, alpha, a.Data, a.Stride, beta, c.Data, c.Stride)
+}
+
+// Her2k performs the Hermitian rank-2k update
+//  C = alpha * A * B^H + conj(alpha) * B * A^H + beta * C, if t == blas.NoTrans,
+//  C = alpha * A^H * B + conj(alpha) * B^H * A + beta * C, if t == blas.ConjTrans,
+// where C is an n×n Hermitian matrix, A and B are n×k matrices if t == NoTrans
+// and k×n matrices otherwise, and alpha and beta are scalars.
+func Her2k(t blas.Transpose, alpha complex64, a, b General, beta float32, c Hermitian) {
+	var n, k int
+	if t == blas.NoTrans {
+		n, k = a.Rows, a.Cols
+	} else {
+		n, k = a.Cols, a.Rows
+	}
+	cblas64.Cher2k(c.Uplo, t, n, k, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/cblas64/conv.go b/vendor/gonum.org/v1/gonum/blas/cblas64/conv.go
new file mode 100644
index 00000000..fa5c9780
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/cblas64/conv.go
@@ -0,0 +1,279 @@
+// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.
+
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package cblas64
+
+import "gonum.org/v1/gonum/blas"
+
+// GeneralCols represents a matrix using the conventional column-major storage scheme.
+type GeneralCols General
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions as a and have adequate backing
+// data storage.
+func (t GeneralCols) From(a General) {
+	if t.Rows != a.Rows || t.Cols != a.Cols {
+		panic("cblas64: mismatched dimension")
+	}
+	if len(t.Data) < (t.Cols-1)*t.Stride+t.Rows {
+		panic("cblas64: short data slice")
+	}
+	for i := 0; i < a.Rows; i++ {
+		for j, v := range a.Data[i*a.Stride : i*a.Stride+a.Cols] {
+			t.Data[i+j*t.Stride] = v
+		}
+	}
+}
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions as a and have adequate backing
+// data storage.
+func (t General) From(a GeneralCols) {
+	if t.Rows != a.Rows || t.Cols != a.Cols {
+		panic("cblas64: mismatched dimension")
+	}
+	if len(t.Data) < (t.Rows-1)*t.Stride+t.Cols {
+		panic("cblas64: short data slice")
+	}
+	for j := 0; j < a.Cols; j++ {
+		for i, v := range a.Data[j*a.Stride : j*a.Stride+a.Rows] {
+			t.Data[i*t.Stride+j] = v
+		}
+	}
+}
+
+// TriangularCols represents a matrix using the conventional column-major storage scheme.
+type TriangularCols Triangular
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions, uplo and diag as a and have
+// adequate backing data storage.
+func (t TriangularCols) From(a Triangular) {
+	if t.N != a.N {
+		panic("cblas64: mismatched dimension")
+	}
+	if t.Uplo != a.Uplo {
+		panic("cblas64: mismatched BLAS uplo")
+	}
+	if t.Diag != a.Diag {
+		panic("cblas64: mismatched BLAS diag")
+	}
+	switch a.Uplo {
+	default:
+		panic("cblas64: bad BLAS uplo")
+	case blas.Upper:
+		for i := 0; i < a.N; i++ {
+			for j := i; j < a.N; j++ {
+				t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
+			}
+		}
+	case blas.Lower:
+		for i := 0; i < a.N; i++ {
+			for j := 0; j <= i; j++ {
+				t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
+			}
+		}
+	case blas.All:
+		for i := 0; i < a.N; i++ {
+			for j := 0; j < a.N; j++ {
+				t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
+			}
+		}
+	}
+}
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions, uplo and diag as a and have
+// adequate backing data storage.
+func (t Triangular) From(a TriangularCols) {
+	if t.N != a.N {
+		panic("cblas64: mismatched dimension")
+	}
+	if t.Uplo != a.Uplo {
+		panic("cblas64: mismatched BLAS uplo")
+	}
+	if t.Diag != a.Diag {
+		panic("cblas64: mismatched BLAS diag")
+	}
+	switch a.Uplo {
+	default:
+		panic("cblas64: bad BLAS uplo")
+	case blas.Upper:
+		for i := 0; i < a.N; i++ {
+			for j := i; j < a.N; j++ {
+				t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
+			}
+		}
+	case blas.Lower:
+		for i := 0; i < a.N; i++ {
+			for j := 0; j <= i; j++ {
+				t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
+			}
+		}
+	case blas.All:
+		for i := 0; i < a.N; i++ {
+			for j := 0; j < a.N; j++ {
+				t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
+			}
+		}
+	}
+}
+
+// BandCols represents a matrix using the band column-major storage scheme.
+type BandCols Band
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions and bandwidth as a and have
+// adequate backing data storage.
+func (t BandCols) From(a Band) {
+	if t.Rows != a.Rows || t.Cols != a.Cols {
+		panic("cblas64: mismatched dimension")
+	}
+	if t.KL != a.KL || t.KU != a.KU {
+		panic("cblas64: mismatched bandwidth")
+	}
+	if a.Stride < a.KL+a.KU+1 {
+		panic("cblas64: short stride for source")
+	}
+	if t.Stride < t.KL+t.KU+1 {
+		panic("cblas64: short stride for destination")
+	}
+	for i := 0; i < a.Rows; i++ {
+		for j := max(0, i-a.KL); j < min(i+a.KU+1, a.Cols); j++ {
+			t.Data[i+t.KU-j+j*t.Stride] = a.Data[j+a.KL-i+i*a.Stride]
+		}
+	}
+}
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions and bandwidth as a and have
+// adequate backing data storage.
+func (t Band) From(a BandCols) {
+	if t.Rows != a.Rows || t.Cols != a.Cols {
+		panic("cblas64: mismatched dimension")
+	}
+	if t.KL != a.KL || t.KU != a.KU {
+		panic("cblas64: mismatched bandwidth")
+	}
+	if a.Stride < a.KL+a.KU+1 {
+		panic("cblas64: short stride for source")
+	}
+	if t.Stride < t.KL+t.KU+1 {
+		panic("cblas64: short stride for destination")
+	}
+	for j := 0; j < a.Cols; j++ {
+		for i := max(0, j-a.KU); i < min(j+a.KL+1, a.Rows); i++ {
+			t.Data[j+a.KL-i+i*a.Stride] = a.Data[i+t.KU-j+j*t.Stride]
+		}
+	}
+}
+
+// TriangularBandCols represents a symmetric matrix using the band column-major storage scheme.
+type TriangularBandCols TriangularBand
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions, bandwidth and uplo as a and
+// have adequate backing data storage.
+func (t TriangularBandCols) From(a TriangularBand) {
+	if t.N != a.N {
+		panic("cblas64: mismatched dimension")
+	}
+	if t.K != a.K {
+		panic("cblas64: mismatched bandwidth")
+	}
+	if a.Stride < a.K+1 {
+		panic("cblas64: short stride for source")
+	}
+	if t.Stride < t.K+1 {
+		panic("cblas64: short stride for destination")
+	}
+	if t.Uplo != a.Uplo {
+		panic("cblas64: mismatched BLAS uplo")
+	}
+	if t.Diag != a.Diag {
+		panic("cblas64: mismatched BLAS diag")
+	}
+	dst := BandCols{
+		Rows: t.N, Cols: t.N,
+		Stride: t.Stride,
+		Data:   t.Data,
+	}
+	src := Band{
+		Rows: a.N, Cols: a.N,
+		Stride: a.Stride,
+		Data:   a.Data,
+	}
+	switch a.Uplo {
+	default:
+		panic("cblas64: bad BLAS uplo")
+	case blas.Upper:
+		dst.KU = t.K
+		src.KU = a.K
+	case blas.Lower:
+		dst.KL = t.K
+		src.KL = a.K
+	}
+	dst.From(src)
+}
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions, bandwidth and uplo as a and
+// have adequate backing data storage.
+func (t TriangularBand) From(a TriangularBandCols) {
+	if t.N != a.N {
+		panic("cblas64: mismatched dimension")
+	}
+	if t.K != a.K {
+		panic("cblas64: mismatched bandwidth")
+	}
+	if a.Stride < a.K+1 {
+		panic("cblas64: short stride for source")
+	}
+	if t.Stride < t.K+1 {
+		panic("cblas64: short stride for destination")
+	}
+	if t.Uplo != a.Uplo {
+		panic("cblas64: mismatched BLAS uplo")
+	}
+	if t.Diag != a.Diag {
+		panic("cblas64: mismatched BLAS diag")
+	}
+	dst := Band{
+		Rows: t.N, Cols: t.N,
+		Stride: t.Stride,
+		Data:   t.Data,
+	}
+	src := BandCols{
+		Rows: a.N, Cols: a.N,
+		Stride: a.Stride,
+		Data:   a.Data,
+	}
+	switch a.Uplo {
+	default:
+		panic("cblas64: bad BLAS uplo")
+	case blas.Upper:
+		dst.KU = t.K
+		src.KU = a.K
+	case blas.Lower:
+		dst.KL = t.K
+		src.KL = a.K
+	}
+	dst.From(src)
+}
+
+func min(a, b int) int {
+	if a < b {
+		return a
+	}
+	return b
+}
+
+func max(a, b int) int {
+	if a > b {
+		return a
+	}
+	return b
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/cblas64/conv_hermitian.go b/vendor/gonum.org/v1/gonum/blas/cblas64/conv_hermitian.go
new file mode 100644
index 00000000..76598b96
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/cblas64/conv_hermitian.go
@@ -0,0 +1,155 @@
+// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.
+
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package cblas64
+
+import "gonum.org/v1/gonum/blas"
+
+// HermitianCols represents a matrix using the conventional column-major storage scheme.
+type HermitianCols Hermitian
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions and uplo as a and have adequate
+// backing data storage.
+func (t HermitianCols) From(a Hermitian) {
+	if t.N != a.N {
+		panic("cblas64: mismatched dimension")
+	}
+	if t.Uplo != a.Uplo {
+		panic("cblas64: mismatched BLAS uplo")
+	}
+	switch a.Uplo {
+	default:
+		panic("cblas64: bad BLAS uplo")
+	case blas.Upper:
+		for i := 0; i < a.N; i++ {
+			for j := i; j < a.N; j++ {
+				t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
+			}
+		}
+	case blas.Lower:
+		for i := 0; i < a.N; i++ {
+			for j := 0; j <= i; j++ {
+				t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
+			}
+		}
+	}
+}
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions and uplo as a and have adequate
+// backing data storage.
+func (t Hermitian) From(a HermitianCols) {
+	if t.N != a.N {
+		panic("cblas64: mismatched dimension")
+	}
+	if t.Uplo != a.Uplo {
+		panic("cblas64: mismatched BLAS uplo")
+	}
+	switch a.Uplo {
+	default:
+		panic("cblas64: bad BLAS uplo")
+	case blas.Upper:
+		for i := 0; i < a.N; i++ {
+			for j := i; j < a.N; j++ {
+				t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
+			}
+		}
+	case blas.Lower:
+		for i := 0; i < a.N; i++ {
+			for j := 0; j <= i; j++ {
+				t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
+			}
+		}
+	}
+}
+
+// HermitianBandCols represents an Hermitian matrix using the band column-major storage scheme.
+type HermitianBandCols HermitianBand
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions, bandwidth and uplo as a and
+// have adequate backing data storage.
+func (t HermitianBandCols) From(a HermitianBand) {
+	if t.N != a.N {
+		panic("cblas64: mismatched dimension")
+	}
+	if t.K != a.K {
+		panic("cblas64: mismatched bandwidth")
+	}
+	if a.Stride < a.K+1 {
+		panic("cblas64: short stride for source")
+	}
+	if t.Stride < t.K+1 {
+		panic("cblas64: short stride for destination")
+	}
+	if t.Uplo != a.Uplo {
+		panic("cblas64: mismatched BLAS uplo")
+	}
+	dst := BandCols{
+		Rows: t.N, Cols: t.N,
+		Stride: t.Stride,
+		Data:   t.Data,
+	}
+	src := Band{
+		Rows: a.N, Cols: a.N,
+		Stride: a.Stride,
+		Data:   a.Data,
+	}
+	switch a.Uplo {
+	default:
+		panic("cblas64: bad BLAS uplo")
+	case blas.Upper:
+		dst.KU = t.K
+		src.KU = a.K
+	case blas.Lower:
+		dst.KL = t.K
+		src.KL = a.K
+	}
+	dst.From(src)
+}
+
+// From fills the receiver with elements from a. The receiver
+// must have the same dimensions, bandwidth and uplo as a and
+// have adequate backing data storage.
+func (t HermitianBand) From(a HermitianBandCols) {
+	if t.N != a.N {
+		panic("cblas64: mismatched dimension")
+	}
+	if t.K != a.K {
+		panic("cblas64: mismatched bandwidth")
+	}
+	if a.Stride < a.K+1 {
+		panic("cblas64: short stride for source")
+	}
+	if t.Stride < t.K+1 {
+		panic("cblas64: short stride for destination")
+	}
+	if t.Uplo != a.Uplo {
+		panic("cblas64: mismatched BLAS uplo")
+	}
+	dst := Band{
+		Rows: t.N, Cols: t.N,
+		Stride: t.Stride,
+		Data:   t.Data,
+	}
+	src := BandCols{
+		Rows: a.N, Cols: a.N,
+		Stride: a.Stride,
+		Data:   a.Data,
+	}
+	switch a.Uplo {
+	default:
+		panic("cblas64: bad BLAS uplo")
+	case blas.Upper:
+		dst.KU = t.K
+		src.KU = a.K
+	case blas.Lower:
+		dst.KL = t.K
+		src.KL = a.K
+	}
+	dst.From(src)
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/cblas64/conv_hermitian_test.go b/vendor/gonum.org/v1/gonum/blas/cblas64/conv_hermitian_test.go
new file mode 100644
index 00000000..5f412647
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/cblas64/conv_hermitian_test.go
@@ -0,0 +1,307 @@
+// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.
+
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package cblas64
+
+import (
+	math "gonum.org/v1/gonum/internal/cmplx64"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+func newHermitianFrom(a HermitianCols) Hermitian {
+	t := Hermitian{
+		N:      a.N,
+		Stride: a.N,
+		Data:   make([]complex64, a.N*a.N),
+		Uplo:   a.Uplo,
+	}
+	t.From(a)
+	return t
+}
+
+func (m Hermitian) n() int { return m.N }
+func (m Hermitian) at(i, j int) complex64 {
+	if m.Uplo == blas.Lower && i < j && j < m.N {
+		i, j = j, i
+	}
+	if m.Uplo == blas.Upper && i > j {
+		i, j = j, i
+	}
+	return m.Data[i*m.Stride+j]
+}
+func (m Hermitian) uplo() blas.Uplo { return m.Uplo }
+
+func newHermitianColsFrom(a Hermitian) HermitianCols {
+	t := HermitianCols{
+		N:      a.N,
+		Stride: a.N,
+		Data:   make([]complex64, a.N*a.N),
+		Uplo:   a.Uplo,
+	}
+	t.From(a)
+	return t
+}
+
+func (m HermitianCols) n() int { return m.N }
+func (m HermitianCols) at(i, j int) complex64 {
+	if m.Uplo == blas.Lower && i < j {
+		i, j = j, i
+	}
+	if m.Uplo == blas.Upper && i > j && i < m.N {
+		i, j = j, i
+	}
+	return m.Data[i+j*m.Stride]
+}
+func (m HermitianCols) uplo() blas.Uplo { return m.Uplo }
+
+type hermitian interface {
+	n() int
+	at(i, j int) complex64
+	uplo() blas.Uplo
+}
+
+func sameHermitian(a, b hermitian) bool {
+	an := a.n()
+	bn := b.n()
+	if an != bn {
+		return false
+	}
+	if a.uplo() != b.uplo() {
+		return false
+	}
+	for i := 0; i < an; i++ {
+		for j := 0; j < an; j++ {
+			if a.at(i, j) != b.at(i, j) || math.IsNaN(a.at(i, j)) != math.IsNaN(b.at(i, j)) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+var hermitianTests = []Hermitian{
+	{N: 3, Stride: 3, Data: []complex64{
+		1, 2, 3,
+		4, 5, 6,
+		7, 8, 9,
+	}},
+	{N: 3, Stride: 5, Data: []complex64{
+		1, 2, 3, 0, 0,
+		4, 5, 6, 0, 0,
+		7, 8, 9, 0, 0,
+	}},
+}
+
+func TestConvertHermitian(t *testing.T) {
+	for _, test := range hermitianTests {
+		for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
+			test.Uplo = uplo
+			colmajor := newHermitianColsFrom(test)
+			if !sameHermitian(colmajor, test) {
+				t.Errorf("unexpected result for row major to col major conversion:\n\tgot: %#v\n\tfrom:%#v",
+					colmajor, test)
+			}
+			rowmajor := newHermitianFrom(colmajor)
+			if !sameHermitian(rowmajor, test) {
+				t.Errorf("unexpected result for col major to row major conversion:\n\tgot: %#v\n\twant:%#v",
+					rowmajor, test)
+			}
+		}
+	}
+}
+func newHermitianBandFrom(a HermitianBandCols) HermitianBand {
+	t := HermitianBand{
+		N:      a.N,
+		K:      a.K,
+		Stride: a.K + 1,
+		Data:   make([]complex64, a.N*(a.K+1)),
+		Uplo:   a.Uplo,
+	}
+	for i := range t.Data {
+		t.Data[i] = math.NaN()
+	}
+	t.From(a)
+	return t
+}
+
+func (m HermitianBand) n() (n int) { return m.N }
+func (m HermitianBand) at(i, j int) complex64 {
+	b := Band{
+		Rows: m.N, Cols: m.N,
+		Stride: m.Stride,
+		Data:   m.Data,
+	}
+	switch m.Uplo {
+	default:
+		panic("cblas64: bad BLAS uplo")
+	case blas.Upper:
+		b.KU = m.K
+		if i > j {
+			i, j = j, i
+		}
+	case blas.Lower:
+		b.KL = m.K
+		if i < j {
+			i, j = j, i
+		}
+	}
+	return b.at(i, j)
+}
+func (m HermitianBand) bandwidth() (k int) { return m.K }
+func (m HermitianBand) uplo() blas.Uplo    { return m.Uplo }
+
+func newHermitianBandColsFrom(a HermitianBand) HermitianBandCols {
+	t := HermitianBandCols{
+		N:      a.N,
+		K:      a.K,
+		Stride: a.K + 1,
+		Data:   make([]complex64, a.N*(a.K+1)),
+		Uplo:   a.Uplo,
+	}
+	for i := range t.Data {
+		t.Data[i] = math.NaN()
+	}
+	t.From(a)
+	return t
+}
+
+func (m HermitianBandCols) n() (n int) { return m.N }
+func (m HermitianBandCols) at(i, j int) complex64 {
+	b := BandCols{
+		Rows: m.N, Cols: m.N,
+		Stride: m.Stride,
+		Data:   m.Data,
+	}
+	switch m.Uplo {
+	default:
+		panic("cblas64: bad BLAS uplo")
+	case blas.Upper:
+		b.KU = m.K
+		if i > j {
+			i, j = j, i
+		}
+	case blas.Lower:
+		b.KL = m.K
+		if i < j {
+			i, j = j, i
+		}
+	}
+	return b.at(i, j)
+}
+func (m HermitianBandCols) bandwidth() (k int) { return m.K }
+func (m HermitianBandCols) uplo() blas.Uplo    { return m.Uplo }
+
+type hermitianBand interface {
+	n() (n int)
+	at(i, j int) complex64
+	bandwidth() (k int)
+	uplo() blas.Uplo
+}
+
+func sameHermitianBand(a, b hermitianBand) bool {
+	an := a.n()
+	bn := b.n()
+	if an != bn {
+		return false
+	}
+	if a.uplo() != b.uplo() {
+		return false
+	}
+	ak := a.bandwidth()
+	bk := b.bandwidth()
+	if ak != bk {
+		return false
+	}
+	for i := 0; i < an; i++ {
+		for j := 0; j < an; j++ {
+			if a.at(i, j) != b.at(i, j) || math.IsNaN(a.at(i, j)) != math.IsNaN(b.at(i, j)) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+var hermitianBandTests = []HermitianBand{
+	{N: 3, K: 0, Stride: 1, Uplo: blas.Upper, Data: []complex64{
+		1,
+		2,
+		3,
+	}},
+	{N: 3, K: 0, Stride: 1, Uplo: blas.Lower, Data: []complex64{
+		1,
+		2,
+		3,
+	}},
+	{N: 3, K: 1, Stride: 2, Uplo: blas.Upper, Data: []complex64{
+		1, 2,
+		3, 4,
+		5, -1,
+	}},
+	{N: 3, K: 1, Stride: 2, Uplo: blas.Lower, Data: []complex64{
+		-1, 1,
+		2, 3,
+		4, 5,
+	}},
+	{N: 3, K: 2, Stride: 3, Uplo: blas.Upper, Data: []complex64{
+		1, 2, 3,
+		4, 5, -1,
+		6, -2, -3,
+	}},
+	{N: 3, K: 2, Stride: 3, Uplo: blas.Lower, Data: []complex64{
+		-2, -1, 1,
+		-3, 2, 4,
+		3, 5, 6,
+	}},
+
+	{N: 3, K: 0, Stride: 5, Uplo: blas.Upper, Data: []complex64{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{N: 3, K: 0, Stride: 5, Uplo: blas.Lower, Data: []complex64{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{N: 3, K: 1, Stride: 5, Uplo: blas.Upper, Data: []complex64{
+		1, 2, 0, 0, 0,
+		3, 4, 0, 0, 0,
+		5, -1, 0, 0, 0,
+	}},
+	{N: 3, K: 1, Stride: 5, Uplo: blas.Lower, Data: []complex64{
+		-1, 1, 0, 0, 0,
+		2, 3, 0, 0, 0,
+		4, 5, 0, 0, 0,
+	}},
+	{N: 3, K: 2, Stride: 5, Uplo: blas.Upper, Data: []complex64{
+		1, 2, 3, 0, 0,
+		4, 5, -1, 0, 0,
+		6, -2, -3, 0, 0,
+	}},
+	{N: 3, K: 2, Stride: 5, Uplo: blas.Lower, Data: []complex64{
+		-2, -1, 1, 0, 0,
+		-3, 2, 4, 0, 0,
+		3, 5, 6, 0, 0,
+	}},
+}
+
+func TestConvertHermBand(t *testing.T) {
+	for _, test := range hermitianBandTests {
+		colmajor := newHermitianBandColsFrom(test)
+		if !sameHermitianBand(colmajor, test) {
+			t.Errorf("unexpected result for row major to col major conversion:\n\tgot: %#v\n\tfrom:%#v",
+				colmajor, test)
+		}
+		rowmajor := newHermitianBandFrom(colmajor)
+		if !sameHermitianBand(rowmajor, test) {
+			t.Errorf("unexpected result for col major to row major conversion:\n\tgot: %#v\n\twant:%#v",
+				rowmajor, test)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/cblas64/conv_test.go b/vendor/gonum.org/v1/gonum/blas/cblas64/conv_test.go
new file mode 100644
index 00000000..da8d736e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/cblas64/conv_test.go
@@ -0,0 +1,620 @@
+// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.
+
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package cblas64
+
+import (
+	math "gonum.org/v1/gonum/internal/cmplx64"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+func newGeneralFrom(a GeneralCols) General {
+	t := General{
+		Rows:   a.Rows,
+		Cols:   a.Cols,
+		Stride: a.Cols,
+		Data:   make([]complex64, a.Rows*a.Cols),
+	}
+	t.From(a)
+	return t
+}
+
+func (m General) dims() (r, c int)      { return m.Rows, m.Cols }
+func (m General) at(i, j int) complex64 { return m.Data[i*m.Stride+j] }
+
+func newGeneralColsFrom(a General) GeneralCols {
+	t := GeneralCols{
+		Rows:   a.Rows,
+		Cols:   a.Cols,
+		Stride: a.Rows,
+		Data:   make([]complex64, a.Rows*a.Cols),
+	}
+	t.From(a)
+	return t
+}
+
+func (m GeneralCols) dims() (r, c int)      { return m.Rows, m.Cols }
+func (m GeneralCols) at(i, j int) complex64 { return m.Data[i+j*m.Stride] }
+
+type general interface {
+	dims() (r, c int)
+	at(i, j int) complex64
+}
+
+func sameGeneral(a, b general) bool {
+	ar, ac := a.dims()
+	br, bc := b.dims()
+	if ar != br || ac != bc {
+		return false
+	}
+	for i := 0; i < ar; i++ {
+		for j := 0; j < ac; j++ {
+			if a.at(i, j) != b.at(i, j) || math.IsNaN(a.at(i, j)) != math.IsNaN(b.at(i, j)) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+var generalTests = []General{
+	{Rows: 2, Cols: 3, Stride: 3, Data: []complex64{
+		1, 2, 3,
+		4, 5, 6,
+	}},
+	{Rows: 3, Cols: 2, Stride: 2, Data: []complex64{
+		1, 2,
+		3, 4,
+		5, 6,
+	}},
+	{Rows: 3, Cols: 3, Stride: 3, Data: []complex64{
+		1, 2, 3,
+		4, 5, 6,
+		7, 8, 9,
+	}},
+	{Rows: 2, Cols: 3, Stride: 5, Data: []complex64{
+		1, 2, 3, 0, 0,
+		4, 5, 6, 0, 0,
+	}},
+	{Rows: 3, Cols: 2, Stride: 5, Data: []complex64{
+		1, 2, 0, 0, 0,
+		3, 4, 0, 0, 0,
+		5, 6, 0, 0, 0,
+	}},
+	{Rows: 3, Cols: 3, Stride: 5, Data: []complex64{
+		1, 2, 3, 0, 0,
+		4, 5, 6, 0, 0,
+		7, 8, 9, 0, 0,
+	}},
+}
+
+func TestConvertGeneral(t *testing.T) {
+	for _, test := range generalTests {
+		colmajor := newGeneralColsFrom(test)
+		if !sameGeneral(colmajor, test) {
+			t.Errorf("unexpected result for row major to col major conversion:\n\tgot: %#v\n\tfrom:%#v",
+				colmajor, test)
+		}
+		rowmajor := newGeneralFrom(colmajor)
+		if !sameGeneral(rowmajor, test) {
+			t.Errorf("unexpected result for col major to row major conversion:\n\tgot: %#v\n\twant:%#v",
+				rowmajor, test)
+		}
+	}
+}
+
+func newTriangularFrom(a TriangularCols) Triangular {
+	t := Triangular{
+		N:      a.N,
+		Stride: a.N,
+		Data:   make([]complex64, a.N*a.N),
+		Diag:   a.Diag,
+		Uplo:   a.Uplo,
+	}
+	t.From(a)
+	return t
+}
+
+func (m Triangular) n() int { return m.N }
+func (m Triangular) at(i, j int) complex64 {
+	if m.Diag == blas.Unit && i == j {
+		return 1
+	}
+	if m.Uplo == blas.Lower && i < j && j < m.N {
+		return 0
+	}
+	if m.Uplo == blas.Upper && i > j {
+		return 0
+	}
+	return m.Data[i*m.Stride+j]
+}
+func (m Triangular) uplo() blas.Uplo { return m.Uplo }
+func (m Triangular) diag() blas.Diag { return m.Diag }
+
+func newTriangularColsFrom(a Triangular) TriangularCols {
+	t := TriangularCols{
+		N:      a.N,
+		Stride: a.N,
+		Data:   make([]complex64, a.N*a.N),
+		Diag:   a.Diag,
+		Uplo:   a.Uplo,
+	}
+	t.From(a)
+	return t
+}
+
+func (m TriangularCols) n() int { return m.N }
+func (m TriangularCols) at(i, j int) complex64 {
+	if m.Diag == blas.Unit && i == j {
+		return 1
+	}
+	if m.Uplo == blas.Lower && i < j {
+		return 0
+	}
+	if m.Uplo == blas.Upper && i > j && i < m.N {
+		return 0
+	}
+	return m.Data[i+j*m.Stride]
+}
+func (m TriangularCols) uplo() blas.Uplo { return m.Uplo }
+func (m TriangularCols) diag() blas.Diag { return m.Diag }
+
+type triangular interface {
+	n() int
+	at(i, j int) complex64
+	uplo() blas.Uplo
+	diag() blas.Diag
+}
+
+func sameTriangular(a, b triangular) bool {
+	an := a.n()
+	bn := b.n()
+	if an != bn {
+		return false
+	}
+	for i := 0; i < an; i++ {
+		for j := 0; j < an; j++ {
+			if a.at(i, j) != b.at(i, j) || math.IsNaN(a.at(i, j)) != math.IsNaN(b.at(i, j)) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+var triangularTests = []Triangular{
+	{N: 3, Stride: 3, Data: []complex64{
+		1, 2, 3,
+		4, 5, 6,
+		7, 8, 9,
+	}},
+	{N: 3, Stride: 5, Data: []complex64{
+		1, 2, 3, 0, 0,
+		4, 5, 6, 0, 0,
+		7, 8, 9, 0, 0,
+	}},
+}
+
+func TestConvertTriangular(t *testing.T) {
+	for _, test := range triangularTests {
+		for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower, blas.All} {
+			for _, diag := range []blas.Diag{blas.Unit, blas.NonUnit} {
+				test.Uplo = uplo
+				test.Diag = diag
+				colmajor := newTriangularColsFrom(test)
+				if !sameTriangular(colmajor, test) {
+					t.Errorf("unexpected result for row major to col major conversion:\n\tgot: %#v\n\tfrom:%#v",
+						colmajor, test)
+				}
+				rowmajor := newTriangularFrom(colmajor)
+				if !sameTriangular(rowmajor, test) {
+					t.Errorf("unexpected result for col major to row major conversion:\n\tgot: %#v\n\twant:%#v",
+						rowmajor, test)
+				}
+			}
+		}
+	}
+}
+
+func newBandFrom(a BandCols) Band {
+	t := Band{
+		Rows:   a.Rows,
+		Cols:   a.Cols,
+		KL:     a.KL,
+		KU:     a.KU,
+		Stride: a.KL + a.KU + 1,
+		Data:   make([]complex64, a.Rows*(a.KL+a.KU+1)),
+	}
+	for i := range t.Data {
+		t.Data[i] = math.NaN()
+	}
+	t.From(a)
+	return t
+}
+
+func (m Band) dims() (r, c int) { return m.Rows, m.Cols }
+func (m Band) at(i, j int) complex64 {
+	pj := j + m.KL - i
+	if pj < 0 || m.KL+m.KU+1 <= pj {
+		return 0
+	}
+	return m.Data[i*m.Stride+pj]
+}
+func (m Band) bandwidth() (kl, ku int) { return m.KL, m.KU }
+
+func newBandColsFrom(a Band) BandCols {
+	t := BandCols{
+		Rows:   a.Rows,
+		Cols:   a.Cols,
+		KL:     a.KL,
+		KU:     a.KU,
+		Stride: a.KL + a.KU + 1,
+		Data:   make([]complex64, a.Cols*(a.KL+a.KU+1)),
+	}
+	for i := range t.Data {
+		t.Data[i] = math.NaN()
+	}
+	t.From(a)
+	return t
+}
+
+func (m BandCols) dims() (r, c int) { return m.Rows, m.Cols }
+func (m BandCols) at(i, j int) complex64 {
+	pj := i + m.KU - j
+	if pj < 0 || m.KL+m.KU+1 <= pj {
+		return 0
+	}
+	return m.Data[j*m.Stride+pj]
+}
+func (m BandCols) bandwidth() (kl, ku int) { return m.KL, m.KU }
+
+type band interface {
+	dims() (r, c int)
+	at(i, j int) complex64
+	bandwidth() (kl, ku int)
+}
+
+func sameBand(a, b band) bool {
+	ar, ac := a.dims()
+	br, bc := b.dims()
+	if ar != br || ac != bc {
+		return false
+	}
+	akl, aku := a.bandwidth()
+	bkl, bku := b.bandwidth()
+	if akl != bkl || aku != bku {
+		return false
+	}
+	for i := 0; i < ar; i++ {
+		for j := 0; j < ac; j++ {
+			if a.at(i, j) != b.at(i, j) || math.IsNaN(a.at(i, j)) != math.IsNaN(b.at(i, j)) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+var bandTests = []Band{
+	{Rows: 3, Cols: 4, KL: 0, KU: 0, Stride: 1, Data: []complex64{
+		1,
+		2,
+		3,
+	}},
+	{Rows: 3, Cols: 3, KL: 0, KU: 0, Stride: 1, Data: []complex64{
+		1,
+		2,
+		3,
+	}},
+	{Rows: 4, Cols: 3, KL: 0, KU: 0, Stride: 1, Data: []complex64{
+		1,
+		2,
+		3,
+	}},
+	{Rows: 4, Cols: 3, KL: 0, KU: 1, Stride: 2, Data: []complex64{
+		1, 2,
+		3, 4,
+		5, 6,
+	}},
+	{Rows: 3, Cols: 4, KL: 0, KU: 1, Stride: 2, Data: []complex64{
+		1, 2,
+		3, 4,
+		5, 6,
+	}},
+	{Rows: 3, Cols: 4, KL: 1, KU: 1, Stride: 3, Data: []complex64{
+		-1, 2, 3,
+		4, 5, 6,
+		7, 8, 9,
+	}},
+	{Rows: 4, Cols: 3, KL: 1, KU: 1, Stride: 3, Data: []complex64{
+		-1, 2, 3,
+		4, 5, 6,
+		7, 8, -2,
+		9, -3, -4,
+	}},
+	{Rows: 3, Cols: 4, KL: 2, KU: 1, Stride: 4, Data: []complex64{
+		-2, -1, 3, 4,
+		-3, 5, 6, 7,
+		8, 9, 10, 11,
+	}},
+	{Rows: 4, Cols: 3, KL: 2, KU: 1, Stride: 4, Data: []complex64{
+		-2, -1, 2, 3,
+		-3, 4, 5, 6,
+		7, 8, 9, -4,
+		10, 11, -5, -6,
+	}},
+
+	{Rows: 3, Cols: 4, KL: 0, KU: 0, Stride: 5, Data: []complex64{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{Rows: 3, Cols: 3, KL: 0, KU: 0, Stride: 5, Data: []complex64{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{Rows: 4, Cols: 3, KL: 0, KU: 0, Stride: 5, Data: []complex64{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{Rows: 4, Cols: 3, KL: 0, KU: 1, Stride: 5, Data: []complex64{
+		1, 2, 0, 0, 0,
+		3, 4, 0, 0, 0,
+		5, 6, 0, 0, 0,
+	}},
+	{Rows: 3, Cols: 4, KL: 0, KU: 1, Stride: 5, Data: []complex64{
+		1, 2, 0, 0, 0,
+		3, 4, 0, 0, 0,
+		5, 6, 0, 0, 0,
+	}},
+	{Rows: 3, Cols: 4, KL: 1, KU: 1, Stride: 5, Data: []complex64{
+		-1, 2, 3, 0, 0,
+		4, 5, 6, 0, 0,
+		7, 8, 9, 0, 0,
+	}},
+	{Rows: 4, Cols: 3, KL: 1, KU: 1, Stride: 5, Data: []complex64{
+		-1, 2, 3, 0, 0,
+		4, 5, 6, 0, 0,
+		7, 8, -2, 0, 0,
+		9, -3, -4, 0, 0,
+	}},
+	{Rows: 3, Cols: 4, KL: 2, KU: 1, Stride: 5, Data: []complex64{
+		-2, -1, 3, 4, 0,
+		-3, 5, 6, 7, 0,
+		8, 9, 10, 11, 0,
+	}},
+	{Rows: 4, Cols: 3, KL: 2, KU: 1, Stride: 5, Data: []complex64{
+		-2, -1, 2, 3, 0,
+		-3, 4, 5, 6, 0,
+		7, 8, 9, -4, 0,
+		10, 11, -5, -6, 0,
+	}},
+}
+
+func TestConvertBand(t *testing.T) {
+	for _, test := range bandTests {
+		colmajor := newBandColsFrom(test)
+		if !sameBand(colmajor, test) {
+			t.Errorf("unexpected result for row major to col major conversion:\n\tgot: %#v\n\tfrom:%#v",
+				colmajor, test)
+		}
+		rowmajor := newBandFrom(colmajor)
+		if !sameBand(rowmajor, test) {
+			t.Errorf("unexpected result for col major to row major conversion:\n\tgot: %#v\n\twant:%#v",
+				rowmajor, test)
+		}
+	}
+}
+
+func newTriangularBandFrom(a TriangularBandCols) TriangularBand {
+	t := TriangularBand{
+		N:      a.N,
+		K:      a.K,
+		Stride: a.K + 1,
+		Data:   make([]complex64, a.N*(a.K+1)),
+		Uplo:   a.Uplo,
+		Diag:   a.Diag,
+	}
+	for i := range t.Data {
+		t.Data[i] = math.NaN()
+	}
+	t.From(a)
+	return t
+}
+
+func (m TriangularBand) n() (n int) { return m.N }
+func (m TriangularBand) at(i, j int) complex64 {
+	if m.Diag == blas.Unit && i == j {
+		return 1
+	}
+	b := Band{
+		Rows: m.N, Cols: m.N,
+		Stride: m.Stride,
+		Data:   m.Data,
+	}
+	switch m.Uplo {
+	default:
+		panic("cblas64: bad BLAS uplo")
+	case blas.Upper:
+		if i > j {
+			return 0
+		}
+		b.KU = m.K
+	case blas.Lower:
+		if i < j {
+			return 0
+		}
+		b.KL = m.K
+	}
+	return b.at(i, j)
+}
+func (m TriangularBand) bandwidth() (k int) { return m.K }
+func (m TriangularBand) uplo() blas.Uplo    { return m.Uplo }
+func (m TriangularBand) diag() blas.Diag    { return m.Diag }
+
+func newTriangularBandColsFrom(a TriangularBand) TriangularBandCols {
+	t := TriangularBandCols{
+		N:      a.N,
+		K:      a.K,
+		Stride: a.K + 1,
+		Data:   make([]complex64, a.N*(a.K+1)),
+		Uplo:   a.Uplo,
+		Diag:   a.Diag,
+	}
+	for i := range t.Data {
+		t.Data[i] = math.NaN()
+	}
+	t.From(a)
+	return t
+}
+
+func (m TriangularBandCols) n() (n int) { return m.N }
+func (m TriangularBandCols) at(i, j int) complex64 {
+	if m.Diag == blas.Unit && i == j {
+		return 1
+	}
+	b := BandCols{
+		Rows: m.N, Cols: m.N,
+		Stride: m.Stride,
+		Data:   m.Data,
+	}
+	switch m.Uplo {
+	default:
+		panic("cblas64: bad BLAS uplo")
+	case blas.Upper:
+		if i > j {
+			return 0
+		}
+		b.KU = m.K
+	case blas.Lower:
+		if i < j {
+			return 0
+		}
+		b.KL = m.K
+	}
+	return b.at(i, j)
+}
+func (m TriangularBandCols) bandwidth() (k int) { return m.K }
+func (m TriangularBandCols) uplo() blas.Uplo    { return m.Uplo }
+func (m TriangularBandCols) diag() blas.Diag    { return m.Diag }
+
+type triangularBand interface {
+	n() (n int)
+	at(i, j int) complex64
+	bandwidth() (k int)
+	uplo() blas.Uplo
+	diag() blas.Diag
+}
+
+func sameTriangularBand(a, b triangularBand) bool {
+	an := a.n()
+	bn := b.n()
+	if an != bn {
+		return false
+	}
+	if a.uplo() != b.uplo() {
+		return false
+	}
+	if a.diag() != b.diag() {
+		return false
+	}
+	ak := a.bandwidth()
+	bk := b.bandwidth()
+	if ak != bk {
+		return false
+	}
+	for i := 0; i < an; i++ {
+		for j := 0; j < an; j++ {
+			if a.at(i, j) != b.at(i, j) || math.IsNaN(a.at(i, j)) != math.IsNaN(b.at(i, j)) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+var triangularBandTests = []TriangularBand{
+	{N: 3, K: 0, Stride: 1, Uplo: blas.Upper, Data: []complex64{
+		1,
+		2,
+		3,
+	}},
+	{N: 3, K: 0, Stride: 1, Uplo: blas.Lower, Data: []complex64{
+		1,
+		2,
+		3,
+	}},
+	{N: 3, K: 1, Stride: 2, Uplo: blas.Upper, Data: []complex64{
+		1, 2,
+		3, 4,
+		5, -1,
+	}},
+	{N: 3, K: 1, Stride: 2, Uplo: blas.Lower, Data: []complex64{
+		-1, 1,
+		2, 3,
+		4, 5,
+	}},
+	{N: 3, K: 2, Stride: 3, Uplo: blas.Upper, Data: []complex64{
+		1, 2, 3,
+		4, 5, -1,
+		6, -2, -3,
+	}},
+	{N: 3, K: 2, Stride: 3, Uplo: blas.Lower, Data: []complex64{
+		-2, -1, 1,
+		-3, 2, 4,
+		3, 5, 6,
+	}},
+
+	{N: 3, K: 0, Stride: 5, Uplo: blas.Upper, Data: []complex64{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{N: 3, K: 0, Stride: 5, Uplo: blas.Lower, Data: []complex64{
+		1, 0, 0, 0, 0,
+		2, 0, 0, 0, 0,
+		3, 0, 0, 0, 0,
+	}},
+	{N: 3, K: 1, Stride: 5, Uplo: blas.Upper, Data: []complex64{
+		1, 2, 0, 0, 0,
+		3, 4, 0, 0, 0,
+		5, -1, 0, 0, 0,
+	}},
+	{N: 3, K: 1, Stride: 5, Uplo: blas.Lower, Data: []complex64{
+		-1, 1, 0, 0, 0,
+		2, 3, 0, 0, 0,
+		4, 5, 0, 0, 0,
+	}},
+	{N: 3, K: 2, Stride: 5, Uplo: blas.Upper, Data: []complex64{
+		1, 2, 3, 0, 0,
+		4, 5, -1, 0, 0,
+		6, -2, -3, 0, 0,
+	}},
+	{N: 3, K: 2, Stride: 5, Uplo: blas.Lower, Data: []complex64{
+		-2, -1, 1, 0, 0,
+		-3, 2, 4, 0, 0,
+		3, 5, 6, 0, 0,
+	}},
+}
+
+func TestConvertTriBand(t *testing.T) {
+	for _, test := range triangularBandTests {
+		colmajor := newTriangularBandColsFrom(test)
+		if !sameTriangularBand(colmajor, test) {
+			t.Errorf("unexpected result for row major to col major conversion:\n\tgot: %#v\n\tfrom:%#v",
+				colmajor, test)
+		}
+		rowmajor := newTriangularBandFrom(colmajor)
+		if !sameTriangularBand(rowmajor, test) {
+			t.Errorf("unexpected result for col major to row major conversion:\n\tgot: %#v\n\twant:%#v",
+				rowmajor, test)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/cblas64/doc.go b/vendor/gonum.org/v1/gonum/blas/cblas64/doc.go
new file mode 100644
index 00000000..bb9c70b1
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/cblas64/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package cblas64 provides a simple interface to the complex64 BLAS API.
+package cblas64 // import "gonum.org/v1/gonum/blas/cblas64"
diff --git a/vendor/gonum.org/v1/gonum/blas/conversions.bash b/vendor/gonum.org/v1/gonum/blas/conversions.bash
new file mode 100755
index 00000000..96ff2272
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/conversions.bash
@@ -0,0 +1,159 @@
+#!/usr/bin/env bash
+
+# Copyright ©2017 The gonum Authors. All rights reserved.
+# Use of this source code is governed by a BSD-style
+# license that can be found in the LICENSE file.
+
+# Generate code for blas32.
+echo Generating blas32/conv.go
+echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > blas32/conv.go
+cat blas64/conv.go \
+| gofmt -r 'float64 -> float32' \
+\
+| sed -e 's/blas64/blas32/' \
+\
+>> blas32/conv.go
+
+echo Generating blas32/conv_test.go
+echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > blas32/conv_test.go
+cat blas64/conv_test.go \
+| gofmt -r 'float64 -> float32' \
+\
+| sed -e 's/blas64/blas32/' \
+      -e 's_"math"_math "gonum.org/v1/gonum/internal/math32"_' \
+\
+>> blas32/conv_test.go
+
+echo Generating blas32/conv_symmetric.go
+echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > blas32/conv_symmetric.go
+cat blas64/conv_symmetric.go \
+| gofmt -r 'float64 -> float32' \
+\
+| sed -e 's/blas64/blas32/' \
+\
+>> blas32/conv_symmetric.go
+
+echo Generating blas32/conv_symmetric_test.go
+echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > blas32/conv_symmetric_test.go
+cat blas64/conv_symmetric_test.go \
+| gofmt -r 'float64 -> float32' \
+\
+| sed -e 's/blas64/blas32/' \
+      -e 's_"math"_math "gonum.org/v1/gonum/internal/math32"_' \
+\
+>> blas32/conv_symmetric_test.go
+
+
+# Generate code for cblas128.
+echo Generating cblas128/conv.go
+echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > cblas128/conv.go
+cat blas64/conv.go \
+| gofmt -r 'float64 -> complex128' \
+\
+| sed -e 's/blas64/cblas128/' \
+\
+>> cblas128/conv.go
+
+echo Generating cblas128/conv_test.go
+echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > cblas128/conv_test.go
+cat blas64/conv_test.go \
+| gofmt -r 'float64 -> complex128' \
+\
+| sed -e 's/blas64/cblas128/' \
+      -e 's_"math"_math "math/cmplx"_' \
+\
+>> cblas128/conv_test.go
+
+echo Generating cblas128/conv_symmetric.go
+echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > cblas128/conv_symmetric.go
+cat blas64/conv_symmetric.go \
+| gofmt -r 'float64 -> complex128' \
+\
+| sed -e 's/blas64/cblas128/' \
+\
+>> cblas128/conv_symmetric.go
+
+echo Generating cblas128/conv_symmetric_test.go
+echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > cblas128/conv_symmetric_test.go
+cat blas64/conv_symmetric_test.go \
+| gofmt -r 'float64 -> complex128' \
+\
+| sed -e 's/blas64/cblas128/' \
+      -e 's_"math"_math "math/cmplx"_' \
+\
+>> cblas128/conv_symmetric_test.go
+
+echo Generating cblas128/conv_hermitian.go
+echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > cblas128/conv_hermitian.go
+cat blas64/conv_symmetric.go \
+| gofmt -r 'float64 -> complex128' \
+\
+| sed -e 's/blas64/cblas128/' \
+      -e 's/Symmetric/Hermitian/g' \
+      -e 's/a symmetric/an Hermitian/g' \
+      -e 's/symmetric/hermitian/g' \
+      -e 's/Sym/Herm/g' \
+\
+>> cblas128/conv_hermitian.go
+
+echo Generating cblas128/conv_hermitian_test.go
+echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > cblas128/conv_hermitian_test.go
+cat blas64/conv_symmetric_test.go \
+| gofmt -r 'float64 -> complex128' \
+\
+| sed -e 's/blas64/cblas128/' \
+      -e 's/Symmetric/Hermitian/g' \
+      -e 's/a symmetric/an Hermitian/g' \
+      -e 's/symmetric/hermitian/g' \
+      -e 's/Sym/Herm/g' \
+      -e 's_"math"_math "math/cmplx"_' \
+\
+>> cblas128/conv_hermitian_test.go
+
+
+# Generate code for cblas64.
+echo Generating cblas64/conv.go
+echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > cblas64/conv.go
+cat blas64/conv.go \
+| gofmt -r 'float64 -> complex64' \
+\
+| sed -e 's/blas64/cblas64/' \
+\
+>> cblas64/conv.go
+
+echo Generating cblas64/conv_test.go
+echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > cblas64/conv_test.go
+cat blas64/conv_test.go \
+| gofmt -r 'float64 -> complex64' \
+\
+| sed -e 's/blas64/cblas64/' \
+      -e 's_"math"_math "gonum.org/v1/gonum/internal/cmplx64"_' \
+\
+>> cblas64/conv_test.go
+
+echo Generating cblas64/conv_hermitian.go
+echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > cblas64/conv_hermitian.go
+cat blas64/conv_symmetric.go \
+| gofmt -r 'float64 -> complex64' \
+\
+| sed -e 's/blas64/cblas64/' \
+      -e 's/Symmetric/Hermitian/g' \
+      -e 's/a symmetric/an Hermitian/g' \
+      -e 's/symmetric/hermitian/g' \
+      -e 's/Sym/Herm/g' \
+\
+>> cblas64/conv_hermitian.go
+
+echo Generating cblas64/conv_hermitian_test.go
+echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > cblas64/conv_hermitian_test.go
+cat blas64/conv_symmetric_test.go \
+| gofmt -r 'float64 -> complex64' \
+\
+| sed -e 's/blas64/cblas64/' \
+      -e 's/Symmetric/Hermitian/g' \
+      -e 's/a symmetric/an Hermitian/g' \
+      -e 's/symmetric/hermitian/g' \
+      -e 's/Sym/Herm/g' \
+      -e 's_"math"_math "gonum.org/v1/gonum/internal/cmplx64"_' \
+\
+>> cblas64/conv_hermitian_test.go
diff --git a/vendor/gonum.org/v1/gonum/blas/doc.go b/vendor/gonum.org/v1/gonum/blas/doc.go
new file mode 100644
index 00000000..99231c46
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/doc.go
@@ -0,0 +1,108 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+/*
+Package blas provides interfaces for the BLAS linear algebra standard.
+
+All methods must perform appropriate parameter checking and panic if
+provided parameters that do not conform to the requirements specified
+by the BLAS standard.
+
+Quick Reference Guide to the BLAS from http://www.netlib.org/lapack/lug/node145.html
+
+This version is modified to remove the "order" option. All matrix operations are
+on row-order matrices.
+
+Level 1 BLAS
+
+	        dim scalar vector   vector   scalars              5-element prefixes
+	                                                          struct
+
+	_rotg (                                      a, b )                S, D
+	_rotmg(                              d1, d2, a, b )                S, D
+	_rot  ( n,         x, incX, y, incY,               c, s )          S, D
+	_rotm ( n,         x, incX, y, incY,                      param )  S, D
+	_swap ( n,         x, incX, y, incY )                              S, D, C, Z
+	_scal ( n,  alpha, x, incX )                                       S, D, C, Z, Cs, Zd
+	_copy ( n,         x, incX, y, incY )                              S, D, C, Z
+	_axpy ( n,  alpha, x, incX, y, incY )                              S, D, C, Z
+	_dot  ( n,         x, incX, y, incY )                              S, D, Ds
+	_dotu ( n,         x, incX, y, incY )                              C, Z
+	_dotc ( n,         x, incX, y, incY )                              C, Z
+	__dot ( n,  alpha, x, incX, y, incY )                              Sds
+	_nrm2 ( n,         x, incX )                                       S, D, Sc, Dz
+	_asum ( n,         x, incX )                                       S, D, Sc, Dz
+	I_amax( n,         x, incX )                                       s, d, c, z
+
+Level 2 BLAS
+
+	        options                   dim   b-width scalar matrix  vector   scalar vector   prefixes
+
+	_gemv (        trans,      m, n,         alpha, a, lda, x, incX, beta,  y, incY ) S, D, C, Z
+	_gbmv (        trans,      m, n, kL, kU, alpha, a, lda, x, incX, beta,  y, incY ) S, D, C, Z
+	_hemv ( uplo,                 n,         alpha, a, lda, x, incX, beta,  y, incY ) C, Z
+	_hbmv ( uplo,                 n, k,      alpha, a, lda, x, incX, beta,  y, incY ) C, Z
+	_hpmv ( uplo,                 n,         alpha, ap,     x, incX, beta,  y, incY ) C, Z
+	_symv ( uplo,                 n,         alpha, a, lda, x, incX, beta,  y, incY ) S, D
+	_sbmv ( uplo,                 n, k,      alpha, a, lda, x, incX, beta,  y, incY ) S, D
+	_spmv ( uplo,                 n,         alpha, ap,     x, incX, beta,  y, incY ) S, D
+	_trmv ( uplo, trans, diag,    n,                a, lda, x, incX )                 S, D, C, Z
+	_tbmv ( uplo, trans, diag,    n, k,             a, lda, x, incX )                 S, D, C, Z
+	_tpmv ( uplo, trans, diag,    n,                ap,     x, incX )                 S, D, C, Z
+	_trsv ( uplo, trans, diag,    n,                a, lda, x, incX )                 S, D, C, Z
+	_tbsv ( uplo, trans, diag,    n, k,             a, lda, x, incX )                 S, D, C, Z
+	_tpsv ( uplo, trans, diag,    n,                ap,     x, incX )                 S, D, C, Z
+
+	        options                   dim   scalar vector   vector   matrix  prefixes
+
+	_ger  (                    m, n, alpha, x, incX, y, incY, a, lda ) S, D
+	_geru (                    m, n, alpha, x, incX, y, incY, a, lda ) C, Z
+	_gerc (                    m, n, alpha, x, incX, y, incY, a, lda ) C, Z
+	_her  ( uplo,                 n, alpha, x, incX,          a, lda ) C, Z
+	_hpr  ( uplo,                 n, alpha, x, incX,          ap )     C, Z
+	_her2 ( uplo,                 n, alpha, x, incX, y, incY, a, lda ) C, Z
+	_hpr2 ( uplo,                 n, alpha, x, incX, y, incY, ap )     C, Z
+	_syr  ( uplo,                 n, alpha, x, incX,          a, lda ) S, D
+	_spr  ( uplo,                 n, alpha, x, incX,          ap )     S, D
+	_syr2 ( uplo,                 n, alpha, x, incX, y, incY, a, lda ) S, D
+	_spr2 ( uplo,                 n, alpha, x, incX, y, incY, ap )     S, D
+
+Level 3 BLAS
+
+	        options                                 dim      scalar matrix  matrix  scalar matrix  prefixes
+
+	_gemm (             transA, transB,      m, n, k, alpha, a, lda, b, ldb, beta,  c, ldc ) S, D, C, Z
+	_symm ( side, uplo,                      m, n,    alpha, a, lda, b, ldb, beta,  c, ldc ) S, D, C, Z
+	_hemm ( side, uplo,                      m, n,    alpha, a, lda, b, ldb, beta,  c, ldc ) C, Z
+	_syrk (       uplo, trans,                  n, k, alpha, a, lda,         beta,  c, ldc ) S, D, C, Z
+	_herk (       uplo, trans,                  n, k, alpha, a, lda,         beta,  c, ldc ) C, Z
+	_syr2k(       uplo, trans,                  n, k, alpha, a, lda, b, ldb, beta,  c, ldc ) S, D, C, Z
+	_her2k(       uplo, trans,                  n, k, alpha, a, lda, b, ldb, beta,  c, ldc ) C, Z
+	_trmm ( side, uplo, transA,        diag, m, n,    alpha, a, lda, b, ldb )                S, D, C, Z
+	_trsm ( side, uplo, transA,        diag, m, n,    alpha, a, lda, b, ldb )                S, D, C, Z
+
+Meaning of prefixes
+
+	S - float32	C - complex64
+	D - float64	Z - complex128
+
+Matrix types
+
+	GE - GEneral 		GB - General Band
+	SY - SYmmetric 		SB - Symmetric Band 	SP - Symmetric Packed
+	HE - HErmitian 		HB - Hermitian Band 	HP - Hermitian Packed
+	TR - TRiangular 	TB - Triangular Band 	TP - Triangular Packed
+
+Options
+
+	trans 	= NoTrans, Trans, ConjTrans
+	uplo 	= Upper, Lower
+	diag 	= Nonunit, Unit
+	side 	= Left, Right (A or op(A) on the left, or A or op(A) on the right)
+
+For real matrices, Trans and ConjTrans have the same meaning.
+For Hermitian matrices, trans = Trans is not allowed.
+For complex symmetric matrices, trans = ConjTrans is not allowed.
+*/
+package blas // import "gonum.org/v1/gonum/blas"
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/bench_test.go b/vendor/gonum.org/v1/gonum/blas/gonum/bench_test.go
new file mode 100644
index 00000000..81124fea
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/bench_test.go
@@ -0,0 +1,22 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/testblas"
+)
+
+const (
+	Sm  = testblas.SmallMat
+	Med = testblas.MediumMat
+	Lg  = testblas.LargeMat
+	Hg  = testblas.HugeMat
+)
+
+const (
+	T  = blas.Trans
+	NT = blas.NoTrans
+)
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/cmplx.go b/vendor/gonum.org/v1/gonum/blas/gonum/cmplx.go
new file mode 100644
index 00000000..24ff57c9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/cmplx.go
@@ -0,0 +1,206 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "gonum.org/v1/gonum/blas"
+
+var (
+	_ blas.Complex64  = Implementation{}
+	_ blas.Complex128 = Implementation{}
+)
+
+// TODO(btracey): Replace this as complex routines are added, and instead
+// automatically generate the complex64 routines from the complex128 ones.
+
+var noComplex = "native: implementation does not implement this routine, see the cgo wrapper in gonum.org/v1/netlib/blas"
+
+// Level 1 complex64 routines.
+
+func (Implementation) Cdotu(n int, x []complex64, incX int, y []complex64, incY int) (dotu complex64) {
+	panic(noComplex)
+}
+func (Implementation) Cdotc(n int, x []complex64, incX int, y []complex64, incY int) (dotc complex64) {
+	panic(noComplex)
+}
+func (Implementation) Scnrm2(n int, x []complex64, incX int) float32 {
+	panic(noComplex)
+}
+func (Implementation) Scasum(n int, x []complex64, incX int) float32 {
+	panic(noComplex)
+}
+func (Implementation) Icamax(n int, x []complex64, incX int) int {
+	panic(noComplex)
+}
+func (Implementation) Cswap(n int, x []complex64, incX int, y []complex64, incY int) {
+	panic(noComplex)
+}
+func (Implementation) Ccopy(n int, x []complex64, incX int, y []complex64, incY int) {
+	panic(noComplex)
+}
+func (Implementation) Caxpy(n int, alpha complex64, x []complex64, incX int, y []complex64, incY int) {
+	panic(noComplex)
+}
+func (Implementation) Cscal(n int, alpha complex64, x []complex64, incX int) {
+	panic(noComplex)
+}
+func (Implementation) Csscal(n int, alpha float32, x []complex64, incX int) {
+	panic(noComplex)
+}
+
+// Level 2 complex64 routines.
+
+func (Implementation) Cgemv(tA blas.Transpose, m, n int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int) {
+	panic(noComplex)
+}
+func (Implementation) Cgbmv(tA blas.Transpose, m, n, kL, kU int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int) {
+	panic(noComplex)
+}
+func (Implementation) Ctrmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, a []complex64, lda int, x []complex64, incX int) {
+	panic(noComplex)
+}
+func (Implementation) Ctbmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n, k int, a []complex64, lda int, x []complex64, incX int) {
+	panic(noComplex)
+}
+func (Implementation) Ctpmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, ap []complex64, x []complex64, incX int) {
+	panic(noComplex)
+}
+func (Implementation) Ctrsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, a []complex64, lda int, x []complex64, incX int) {
+	panic(noComplex)
+}
+func (Implementation) Ctbsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n, k int, a []complex64, lda int, x []complex64, incX int) {
+	panic(noComplex)
+}
+func (Implementation) Ctpsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, ap []complex64, x []complex64, incX int) {
+	panic(noComplex)
+}
+func (Implementation) Chemv(ul blas.Uplo, n int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int) {
+	panic(noComplex)
+}
+func (Implementation) Chbmv(ul blas.Uplo, n, k int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int) {
+	panic(noComplex)
+}
+func (Implementation) Chpmv(ul blas.Uplo, n int, alpha complex64, ap []complex64, x []complex64, incX int, beta complex64, y []complex64, incY int) {
+	panic(noComplex)
+}
+func (Implementation) Cgeru(m, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, a []complex64, lda int) {
+	panic(noComplex)
+}
+func (Implementation) Cgerc(m, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, a []complex64, lda int) {
+	panic(noComplex)
+}
+func (Implementation) Cher(ul blas.Uplo, n int, alpha float32, x []complex64, incX int, a []complex64, lda int) {
+	panic(noComplex)
+}
+func (Implementation) Chpr(ul blas.Uplo, n int, alpha float32, x []complex64, incX int, a []complex64) {
+	panic(noComplex)
+}
+func (Implementation) Cher2(ul blas.Uplo, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, a []complex64, lda int) {
+	panic(noComplex)
+}
+func (Implementation) Chpr2(ul blas.Uplo, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, ap []complex64) {
+	panic(noComplex)
+}
+
+// Level 3 complex64 routines.
+
+func (Implementation) Cgemm(tA, tB blas.Transpose, m, n, k int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int) {
+	panic(noComplex)
+}
+func (Implementation) Csymm(s blas.Side, ul blas.Uplo, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int) {
+	panic(noComplex)
+}
+func (Implementation) Csyrk(ul blas.Uplo, t blas.Transpose, n, k int, alpha complex64, a []complex64, lda int, beta complex64, c []complex64, ldc int) {
+	panic(noComplex)
+}
+func (Implementation) Csyr2k(ul blas.Uplo, t blas.Transpose, n, k int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int) {
+	panic(noComplex)
+}
+func (Implementation) Ctrmm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int) {
+	panic(noComplex)
+}
+func (Implementation) Ctrsm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int) {
+	panic(noComplex)
+}
+func (Implementation) Chemm(s blas.Side, ul blas.Uplo, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int) {
+	panic(noComplex)
+}
+func (Implementation) Cherk(ul blas.Uplo, t blas.Transpose, n, k int, alpha float32, a []complex64, lda int, beta float32, c []complex64, ldc int) {
+	panic(noComplex)
+}
+func (Implementation) Cher2k(ul blas.Uplo, t blas.Transpose, n, k int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta float32, c []complex64, ldc int) {
+	panic(noComplex)
+}
+
+// Level 2 complex128 routines.
+
+func (Implementation) Zgemv(tA blas.Transpose, m, n int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int) {
+	panic(noComplex)
+}
+func (Implementation) Zgbmv(tA blas.Transpose, m, n int, kL int, kU int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int) {
+	panic(noComplex)
+}
+func (Implementation) Ztrmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, a []complex128, lda int, x []complex128, incX int) {
+	panic(noComplex)
+}
+func (Implementation) Ztbmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n, k int, a []complex128, lda int, x []complex128, incX int) {
+	panic(noComplex)
+}
+func (Implementation) Ztpmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, ap []complex128, x []complex128, incX int) {
+	panic(noComplex)
+}
+func (Implementation) Ztrsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, a []complex128, lda int, x []complex128, incX int) {
+	panic(noComplex)
+}
+func (Implementation) Ztbsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n, k int, a []complex128, lda int, x []complex128, incX int) {
+	panic(noComplex)
+}
+func (Implementation) Ztpsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, ap []complex128, x []complex128, incX int) {
+	panic(noComplex)
+}
+func (Implementation) Zhemv(ul blas.Uplo, n int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int) {
+	panic(noComplex)
+}
+func (Implementation) Zhbmv(ul blas.Uplo, n, k int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int) {
+	panic(noComplex)
+}
+func (Implementation) Zhpmv(ul blas.Uplo, n int, alpha complex128, ap []complex128, x []complex128, incX int, beta complex128, y []complex128, incY int) {
+	panic(noComplex)
+}
+func (Implementation) Zhpr(ul blas.Uplo, n int, alpha float64, x []complex128, incX int, a []complex128) {
+	panic(noComplex)
+}
+func (Implementation) Zhpr2(ul blas.Uplo, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, ap []complex128) {
+	panic(noComplex)
+}
+
+// Level 3 complex128 routines.
+
+func (Implementation) Zgemm(tA, tB blas.Transpose, m, n, k int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int) {
+	panic(noComplex)
+}
+func (Implementation) Zsymm(s blas.Side, ul blas.Uplo, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int) {
+	panic(noComplex)
+}
+func (Implementation) Zsyrk(ul blas.Uplo, t blas.Transpose, n, k int, alpha complex128, a []complex128, lda int, beta complex128, c []complex128, ldc int) {
+	panic(noComplex)
+}
+func (Implementation) Zsyr2k(ul blas.Uplo, t blas.Transpose, n, k int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int) {
+	panic(noComplex)
+}
+func (Implementation) Ztrmm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int) {
+	panic(noComplex)
+}
+func (Implementation) Ztrsm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int) {
+	panic(noComplex)
+}
+func (Implementation) Zhemm(s blas.Side, ul blas.Uplo, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int) {
+	panic(noComplex)
+}
+func (Implementation) Zherk(ul blas.Uplo, t blas.Transpose, n, k int, alpha float64, a []complex128, lda int, beta float64, c []complex128, ldc int) {
+	panic(noComplex)
+}
+func (Implementation) Zher2k(ul blas.Uplo, t blas.Transpose, n, k int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta float64, c []complex128, ldc int) {
+	panic(noComplex)
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/dgemm.go b/vendor/gonum.org/v1/gonum/blas/gonum/dgemm.go
new file mode 100644
index 00000000..a9291d9b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/dgemm.go
@@ -0,0 +1,261 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"runtime"
+	"sync"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/internal/asm/f64"
+)
+
+// Dgemm computes
+//  C = beta * C + alpha * A * B,
+// where A, B, and C are dense matrices, and alpha and beta are scalars.
+// tA and tB specify whether A or B are transposed.
+func (Implementation) Dgemm(tA, tB blas.Transpose, m, n, k int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int) {
+	if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	if tB != blas.NoTrans && tB != blas.Trans && tB != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	aTrans := tA == blas.Trans || tA == blas.ConjTrans
+	if aTrans {
+		checkDMatrix('a', k, m, a, lda)
+	} else {
+		checkDMatrix('a', m, k, a, lda)
+	}
+	bTrans := tB == blas.Trans || tB == blas.ConjTrans
+	if bTrans {
+		checkDMatrix('b', n, k, b, ldb)
+	} else {
+		checkDMatrix('b', k, n, b, ldb)
+	}
+	checkDMatrix('c', m, n, c, ldc)
+
+	// scale c
+	if beta != 1 {
+		if beta == 0 {
+			for i := 0; i < m; i++ {
+				ctmp := c[i*ldc : i*ldc+n]
+				for j := range ctmp {
+					ctmp[j] = 0
+				}
+			}
+		} else {
+			for i := 0; i < m; i++ {
+				ctmp := c[i*ldc : i*ldc+n]
+				for j := range ctmp {
+					ctmp[j] *= beta
+				}
+			}
+		}
+	}
+
+	dgemmParallel(aTrans, bTrans, m, n, k, a, lda, b, ldb, c, ldc, alpha)
+}
+
+func dgemmParallel(aTrans, bTrans bool, m, n, k int, a []float64, lda int, b []float64, ldb int, c []float64, ldc int, alpha float64) {
+	// dgemmParallel computes a parallel matrix multiplication by partitioning
+	// a and b into sub-blocks, and updating c with the multiplication of the sub-block
+	// In all cases,
+	// A = [ 	A_11	A_12 ... 	A_1j
+	//			A_21	A_22 ...	A_2j
+	//				...
+	//			A_i1	A_i2 ...	A_ij]
+	//
+	// and same for B. All of the submatrix sizes are blockSize×blockSize except
+	// at the edges.
+	//
+	// In all cases, there is one dimension for each matrix along which
+	// C must be updated sequentially.
+	// Cij = \sum_k Aik Bki,	(A * B)
+	// Cij = \sum_k Aki Bkj,	(A^T * B)
+	// Cij = \sum_k Aik Bjk,	(A * B^T)
+	// Cij = \sum_k Aki Bjk,	(A^T * B^T)
+	//
+	// This code computes one {i, j} block sequentially along the k dimension,
+	// and computes all of the {i, j} blocks concurrently. This
+	// partitioning allows Cij to be updated in-place without race-conditions.
+	// Instead of launching a goroutine for each possible concurrent computation,
+	// a number of worker goroutines are created and channels are used to pass
+	// available and completed cases.
+	//
+	// http://alexkr.com/docs/matrixmult.pdf is a good reference on matrix-matrix
+	// multiplies, though this code does not copy matrices to attempt to eliminate
+	// cache misses.
+
+	maxKLen := k
+	parBlocks := blocks(m, blockSize) * blocks(n, blockSize)
+	if parBlocks < minParBlock {
+		// The matrix multiplication is small in the dimensions where it can be
+		// computed concurrently. Just do it in serial.
+		dgemmSerial(aTrans, bTrans, m, n, k, a, lda, b, ldb, c, ldc, alpha)
+		return
+	}
+
+	nWorkers := runtime.GOMAXPROCS(0)
+	if parBlocks < nWorkers {
+		nWorkers = parBlocks
+	}
+	// There is a tradeoff between the workers having to wait for work
+	// and a large buffer making operations slow.
+	buf := buffMul * nWorkers
+	if buf > parBlocks {
+		buf = parBlocks
+	}
+
+	sendChan := make(chan subMul, buf)
+
+	// Launch workers. A worker receives an {i, j} submatrix of c, and computes
+	// A_ik B_ki (or the transposed version) storing the result in c_ij. When the
+	// channel is finally closed, it signals to the waitgroup that it has finished
+	// computing.
+	var wg sync.WaitGroup
+	for i := 0; i < nWorkers; i++ {
+		wg.Add(1)
+		go func() {
+			defer wg.Done()
+			// Make local copies of otherwise global variables to reduce shared memory.
+			// This has a noticeable effect on benchmarks in some cases.
+			alpha := alpha
+			aTrans := aTrans
+			bTrans := bTrans
+			m := m
+			n := n
+			for sub := range sendChan {
+				i := sub.i
+				j := sub.j
+				leni := blockSize
+				if i+leni > m {
+					leni = m - i
+				}
+				lenj := blockSize
+				if j+lenj > n {
+					lenj = n - j
+				}
+
+				cSub := sliceView64(c, ldc, i, j, leni, lenj)
+
+				// Compute A_ik B_kj for all k
+				for k := 0; k < maxKLen; k += blockSize {
+					lenk := blockSize
+					if k+lenk > maxKLen {
+						lenk = maxKLen - k
+					}
+					var aSub, bSub []float64
+					if aTrans {
+						aSub = sliceView64(a, lda, k, i, lenk, leni)
+					} else {
+						aSub = sliceView64(a, lda, i, k, leni, lenk)
+					}
+					if bTrans {
+						bSub = sliceView64(b, ldb, j, k, lenj, lenk)
+					} else {
+						bSub = sliceView64(b, ldb, k, j, lenk, lenj)
+					}
+					dgemmSerial(aTrans, bTrans, leni, lenj, lenk, aSub, lda, bSub, ldb, cSub, ldc, alpha)
+				}
+			}
+		}()
+	}
+
+	// Send out all of the {i, j} subblocks for computation.
+	for i := 0; i < m; i += blockSize {
+		for j := 0; j < n; j += blockSize {
+			sendChan <- subMul{
+				i: i,
+				j: j,
+			}
+		}
+	}
+	close(sendChan)
+	wg.Wait()
+}
+
+// dgemmSerial is serial matrix multiply
+func dgemmSerial(aTrans, bTrans bool, m, n, k int, a []float64, lda int, b []float64, ldb int, c []float64, ldc int, alpha float64) {
+	switch {
+	case !aTrans && !bTrans:
+		dgemmSerialNotNot(m, n, k, a, lda, b, ldb, c, ldc, alpha)
+		return
+	case aTrans && !bTrans:
+		dgemmSerialTransNot(m, n, k, a, lda, b, ldb, c, ldc, alpha)
+		return
+	case !aTrans && bTrans:
+		dgemmSerialNotTrans(m, n, k, a, lda, b, ldb, c, ldc, alpha)
+		return
+	case aTrans && bTrans:
+		dgemmSerialTransTrans(m, n, k, a, lda, b, ldb, c, ldc, alpha)
+		return
+	default:
+		panic("unreachable")
+	}
+}
+
+// dgemmSerial where neither a nor b are transposed
+func dgemmSerialNotNot(m, n, k int, a []float64, lda int, b []float64, ldb int, c []float64, ldc int, alpha float64) {
+	// This style is used instead of the literal [i*stride +j]) is used because
+	// approximately 5 times faster as of go 1.3.
+	for i := 0; i < m; i++ {
+		ctmp := c[i*ldc : i*ldc+n]
+		for l, v := range a[i*lda : i*lda+k] {
+			tmp := alpha * v
+			if tmp != 0 {
+				f64.AxpyUnitaryTo(ctmp, tmp, b[l*ldb:l*ldb+n], ctmp)
+			}
+		}
+	}
+}
+
+// dgemmSerial where neither a is transposed and b is not
+func dgemmSerialTransNot(m, n, k int, a []float64, lda int, b []float64, ldb int, c []float64, ldc int, alpha float64) {
+	// This style is used instead of the literal [i*stride +j]) is used because
+	// approximately 5 times faster as of go 1.3.
+	for l := 0; l < k; l++ {
+		btmp := b[l*ldb : l*ldb+n]
+		for i, v := range a[l*lda : l*lda+m] {
+			tmp := alpha * v
+			if tmp != 0 {
+				ctmp := c[i*ldc : i*ldc+n]
+				f64.AxpyUnitaryTo(ctmp, tmp, btmp, ctmp)
+			}
+		}
+	}
+}
+
+// dgemmSerial where neither a is not transposed and b is
+func dgemmSerialNotTrans(m, n, k int, a []float64, lda int, b []float64, ldb int, c []float64, ldc int, alpha float64) {
+	// This style is used instead of the literal [i*stride +j]) is used because
+	// approximately 5 times faster as of go 1.3.
+	for i := 0; i < m; i++ {
+		atmp := a[i*lda : i*lda+k]
+		ctmp := c[i*ldc : i*ldc+n]
+		for j := 0; j < n; j++ {
+			ctmp[j] += alpha * f64.DotUnitary(atmp, b[j*ldb:j*ldb+k])
+		}
+	}
+}
+
+// dgemmSerial where both are transposed
+func dgemmSerialTransTrans(m, n, k int, a []float64, lda int, b []float64, ldb int, c []float64, ldc int, alpha float64) {
+	// This style is used instead of the literal [i*stride +j]) is used because
+	// approximately 5 times faster as of go 1.3.
+	for l := 0; l < k; l++ {
+		for i, v := range a[l*lda : l*lda+m] {
+			tmp := alpha * v
+			if tmp != 0 {
+				ctmp := c[i*ldc : i*ldc+n]
+				f64.AxpyInc(tmp, b[l:], ctmp, uintptr(n), uintptr(ldb), 1, 0, 0)
+			}
+		}
+	}
+}
+
+func sliceView64(a []float64, lda, i, j, r, c int) []float64 {
+	return a[i*lda+j : (i+r-1)*lda+j+c]
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/dgemmbench_test.go b/vendor/gonum.org/v1/gonum/blas/gonum/dgemmbench_test.go
new file mode 100644
index 00000000..55a44997
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/dgemmbench_test.go
@@ -0,0 +1,51 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas/testblas"
+)
+
+func BenchmarkDgemmSmSmSm(b *testing.B) {
+	testblas.DgemmBenchmark(b, impl, Sm, Sm, Sm, NT, NT)
+}
+
+func BenchmarkDgemmMedMedMed(b *testing.B) {
+	testblas.DgemmBenchmark(b, impl, Med, Med, Med, NT, NT)
+}
+
+func BenchmarkDgemmMedLgMed(b *testing.B) {
+	testblas.DgemmBenchmark(b, impl, Med, Lg, Med, NT, NT)
+}
+
+func BenchmarkDgemmLgLgLg(b *testing.B) {
+	testblas.DgemmBenchmark(b, impl, Lg, Lg, Lg, NT, NT)
+}
+
+func BenchmarkDgemmLgSmLg(b *testing.B) {
+	testblas.DgemmBenchmark(b, impl, Lg, Sm, Lg, NT, NT)
+}
+
+func BenchmarkDgemmLgLgSm(b *testing.B) {
+	testblas.DgemmBenchmark(b, impl, Lg, Lg, Sm, NT, NT)
+}
+
+func BenchmarkDgemmHgHgSm(b *testing.B) {
+	testblas.DgemmBenchmark(b, impl, Hg, Hg, Sm, NT, NT)
+}
+
+func BenchmarkDgemmMedMedMedTNT(b *testing.B) {
+	testblas.DgemmBenchmark(b, impl, Med, Med, Med, T, NT)
+}
+
+func BenchmarkDgemmMedMedMedNTT(b *testing.B) {
+	testblas.DgemmBenchmark(b, impl, Med, Med, Med, NT, T)
+}
+
+func BenchmarkDgemmMedMedMedTT(b *testing.B) {
+	testblas.DgemmBenchmark(b, impl, Med, Med, Med, T, T)
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/dgemvbench_test.go b/vendor/gonum.org/v1/gonum/blas/gonum/dgemvbench_test.go
new file mode 100644
index 00000000..97899809
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/dgemvbench_test.go
@@ -0,0 +1,91 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas/testblas"
+)
+
+func BenchmarkDgemvSmSmNoTransInc1(b *testing.B) {
+	testblas.DgemvBenchmark(b, impl, NT, Sm, Sm, 1, 1)
+}
+
+func BenchmarkDgemvSmSmNoTransIncN(b *testing.B) {
+	testblas.DgemvBenchmark(b, impl, NT, Sm, Sm, 2, 3)
+}
+
+func BenchmarkDgemvSmSmTransInc1(b *testing.B) {
+	testblas.DgemvBenchmark(b, impl, T, Sm, Sm, 1, 1)
+}
+
+func BenchmarkDgemvSmSmTransIncN(b *testing.B) {
+	testblas.DgemvBenchmark(b, impl, T, Sm, Sm, 2, 3)
+}
+
+func BenchmarkDgemvMedMedNoTransInc1(b *testing.B) {
+	testblas.DgemvBenchmark(b, impl, NT, Med, Med, 1, 1)
+}
+
+func BenchmarkDgemvMedMedNoTransIncN(b *testing.B) {
+	testblas.DgemvBenchmark(b, impl, NT, Med, Med, 2, 3)
+}
+
+func BenchmarkDgemvMedMedTransInc1(b *testing.B) {
+	testblas.DgemvBenchmark(b, impl, T, Med, Med, 1, 1)
+}
+
+func BenchmarkDgemvMedMedTransIncN(b *testing.B) {
+	testblas.DgemvBenchmark(b, impl, T, Med, Med, 2, 3)
+}
+
+func BenchmarkDgemvLgLgNoTransInc1(b *testing.B) {
+	testblas.DgemvBenchmark(b, impl, NT, Lg, Lg, 1, 1)
+}
+
+func BenchmarkDgemvLgLgNoTransIncN(b *testing.B) {
+	testblas.DgemvBenchmark(b, impl, NT, Lg, Lg, 2, 3)
+}
+
+func BenchmarkDgemvLgLgTransInc1(b *testing.B) {
+	testblas.DgemvBenchmark(b, impl, T, Lg, Lg, 1, 1)
+}
+
+func BenchmarkDgemvLgLgTransIncN(b *testing.B) {
+	testblas.DgemvBenchmark(b, impl, T, Lg, Lg, 2, 3)
+}
+
+func BenchmarkDgemvLgSmNoTransInc1(b *testing.B) {
+	testblas.DgemvBenchmark(b, impl, NT, Lg, Sm, 1, 1)
+}
+
+func BenchmarkDgemvLgSmNoTransIncN(b *testing.B) {
+	testblas.DgemvBenchmark(b, impl, NT, Lg, Sm, 2, 3)
+}
+
+func BenchmarkDgemvLgSmTransInc1(b *testing.B) {
+	testblas.DgemvBenchmark(b, impl, T, Lg, Sm, 1, 1)
+}
+
+func BenchmarkDgemvLgSmTransIncN(b *testing.B) {
+	testblas.DgemvBenchmark(b, impl, T, Lg, Sm, 2, 3)
+}
+
+func BenchmarkDgemvSmLgNoTransInc1(b *testing.B) {
+	testblas.DgemvBenchmark(b, impl, NT, Sm, Lg, 1, 1)
+}
+
+func BenchmarkDgemvSmLgNoTransIncN(b *testing.B) {
+	testblas.DgemvBenchmark(b, impl, NT, Sm, Lg, 2, 3)
+}
+
+func BenchmarkDgemvSmLgTransInc1(b *testing.B) {
+	testblas.DgemvBenchmark(b, impl, T, Sm, Lg, 1, 1)
+}
+
+func BenchmarkDgemvSmLgTransIncN(b *testing.B) {
+	testblas.DgemvBenchmark(b, impl, T, Sm, Lg, 2, 3)
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/dgerbench_test.go b/vendor/gonum.org/v1/gonum/blas/gonum/dgerbench_test.go
new file mode 100644
index 00000000..e1f85939
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/dgerbench_test.go
@@ -0,0 +1,51 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas/testblas"
+)
+
+func BenchmarkDgerSmSmInc1(b *testing.B) {
+	testblas.DgerBenchmark(b, impl, Sm, Sm, 1, 1)
+}
+
+func BenchmarkDgerSmSmIncN(b *testing.B) {
+	testblas.DgerBenchmark(b, impl, Sm, Sm, 2, 3)
+}
+
+func BenchmarkDgerMedMedInc1(b *testing.B) {
+	testblas.DgerBenchmark(b, impl, Med, Med, 1, 1)
+}
+
+func BenchmarkDgerMedMedIncN(b *testing.B) {
+	testblas.DgerBenchmark(b, impl, Med, Med, 2, 3)
+}
+
+func BenchmarkDgerLgLgInc1(b *testing.B) {
+	testblas.DgerBenchmark(b, impl, Lg, Lg, 1, 1)
+}
+
+func BenchmarkDgerLgLgIncN(b *testing.B) {
+	testblas.DgerBenchmark(b, impl, Lg, Lg, 2, 3)
+}
+
+func BenchmarkDgerLgSmInc1(b *testing.B) {
+	testblas.DgerBenchmark(b, impl, Lg, Sm, 1, 1)
+}
+
+func BenchmarkDgerLgSmIncN(b *testing.B) {
+	testblas.DgerBenchmark(b, impl, Lg, Sm, 2, 3)
+}
+
+func BenchmarkDgerSmLgInc1(b *testing.B) {
+	testblas.DgerBenchmark(b, impl, Sm, Lg, 1, 1)
+}
+
+func BenchmarkDgerSmLgIncN(b *testing.B) {
+	testblas.DgerBenchmark(b, impl, Sm, Lg, 2, 3)
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/doc.go b/vendor/gonum.org/v1/gonum/blas/gonum/doc.go
new file mode 100644
index 00000000..3b6b4077
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/doc.go
@@ -0,0 +1,88 @@
+// Copyright ©2015 The Gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Ensure changes made to blas/native are reflected in blas/cgo where relevant.
+
+/*
+Package native is a Go implementation of the BLAS API. This implementation
+panics when the input arguments are invalid as per the standard, for example
+if a vector increment is zero. Please note that the treatment of NaN values
+is not specified, and differs among the BLAS implementations.
+gonum.org/v1/gonum/blas/blas64 provides helpful wrapper functions to the BLAS
+interface. The rest of this text describes the layout of the data for the input types.
+
+Please note that in the function documentation, x[i] refers to the i^th element
+of the vector, which will be different from the i^th element of the slice if
+incX != 1.
+
+See http://www.netlib.org/lapack/explore-html/d4/de1/_l_i_c_e_n_s_e_source.html
+for more license information.
+
+Vector arguments are effectively strided slices. They have two input arguments,
+a number of elements, n, and an increment, incX. The increment specifies the
+distance between elements of the vector. The actual Go slice may be longer
+than necessary.
+The increment may be positive or negative, except in functions with only
+a single vector argument where the increment may only be positive. If the increment
+is negative, s[0] is the last element in the slice. Note that this is not the same
+as counting backward from the end of the slice, as len(s) may be longer than
+necessary. So, for example, if n = 5 and incX = 3, the elements of s are
+	[0 * * 1 * * 2 * * 3 * * 4 * * * ...]
+where ∗ elements are never accessed. If incX = -3, the same elements are
+accessed, just in reverse order (4, 3, 2, 1, 0).
+
+Dense matrices are specified by a number of rows, a number of columns, and a stride.
+The stride specifies the number of entries in the slice between the first element
+of successive rows. The stride must be at least as large as the number of columns
+but may be longer.
+	[a00 ... a0n a0* ... a1stride-1 a21 ... amn am* ... amstride-1]
+Thus, dense[i*ld + j] refers to the {i, j}th element of the matrix.
+
+Symmetric and triangular matrices (non-packed) are stored identically to Dense,
+except that only elements in one triangle of the matrix are accessed.
+
+Packed symmetric and packed triangular matrices are laid out with the entries
+condensed such that all of the unreferenced elements are removed. So, the upper triangular
+matrix
+  [
+    1  2  3
+    0  4  5
+    0  0  6
+  ]
+and the lower-triangular matrix
+  [
+    1  0  0
+    2  3  0
+    4  5  6
+  ]
+will both be compacted as [1 2 3 4 5 6]. The (i, j) element of the original
+dense matrix can be found at element i*n - (i-1)*i/2 + j for upper triangular,
+and at element i * (i+1) /2 + j for lower triangular.
+
+Banded matrices are laid out in a compact format, constructed by removing the
+zeros in the rows and aligning the diagonals. For example, the matrix
+  [
+    1  2  3  0  0  0
+    4  5  6  7  0  0
+    0  8  9 10 11  0
+    0  0 12 13 14 15
+    0  0  0 16 17 18
+    0  0  0  0 19 20
+  ]
+
+implicitly becomes (∗ entries are never accessed)
+  [
+     *  1  2  3
+     4  5  6  7
+     8  9 10 11
+    12 13 14 15
+    16 17 18  *
+    19 20  *  *
+  ]
+which is given to the BLAS routine as [∗ 1 2 3 4 ...].
+
+See http://www.crest.iu.edu/research/mtl/reference/html/banded.html
+for more information
+*/
+package gonum // import "gonum.org/v1/gonum/blas/gonum"
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/dtrmvbench_test.go b/vendor/gonum.org/v1/gonum/blas/gonum/dtrmvbench_test.go
new file mode 100644
index 00000000..371c0192
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/dtrmvbench_test.go
@@ -0,0 +1,54 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build go1.7
+
+package gonum
+
+import (
+	"strconv"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/testblas"
+)
+
+func BenchmarkDtrmv(b *testing.B) {
+	for _, n := range []int{testblas.MediumMat, testblas.LargeMat} {
+		for _, incX := range []int{1, 5} {
+			for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
+				for _, trans := range []blas.Transpose{blas.NoTrans, blas.Trans} {
+					for _, unit := range []blas.Diag{blas.NonUnit, blas.Unit} {
+						var str string
+						if n == testblas.MediumMat {
+							str += "Med"
+						} else if n == testblas.LargeMat {
+							str += "Large"
+						}
+						str += "_Inc" + strconv.Itoa(incX)
+						if uplo == blas.Upper {
+							str += "_UP"
+						} else {
+							str += "_LO"
+						}
+						if trans == blas.NoTrans {
+							str += "_NT"
+						} else {
+							str += "_TR"
+						}
+						if unit == blas.NonUnit {
+							str += "_NU"
+						} else {
+							str += "_UN"
+						}
+						lda := n
+						b.Run(str, func(b *testing.B) {
+							testblas.DtrmvBenchmark(b, Implementation{}, n, lda, incX, uplo, trans, unit)
+						})
+					}
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/general_double.go b/vendor/gonum.org/v1/gonum/blas/gonum/general_double.go
new file mode 100644
index 00000000..58ded80c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/general_double.go
@@ -0,0 +1,50 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+)
+
+type general64 struct {
+	data       []float64
+	rows, cols int
+	stride     int
+}
+
+func (g general64) clone() general64 {
+	data := make([]float64, len(g.data))
+	copy(data, g.data)
+	return general64{
+		data:   data,
+		rows:   g.rows,
+		cols:   g.cols,
+		stride: g.stride,
+	}
+}
+
+func (g general64) equal(a general64) bool {
+	if g.rows != a.rows || g.cols != a.cols || g.stride != a.stride {
+		return false
+	}
+	for i, v := range g.data {
+		if a.data[i] != v {
+			return false
+		}
+	}
+	return true
+}
+
+func (g general64) equalWithinAbs(a general64, tol float64) bool {
+	if g.rows != a.rows || g.cols != a.cols || g.stride != a.stride {
+		return false
+	}
+	for i, v := range g.data {
+		if math.Abs(a.data[i]-v) > tol {
+			return false
+		}
+	}
+	return true
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/general_single.go b/vendor/gonum.org/v1/gonum/blas/gonum/general_single.go
new file mode 100644
index 00000000..ca360a72
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/general_single.go
@@ -0,0 +1,52 @@
+// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.
+
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	math "gonum.org/v1/gonum/internal/math32"
+)
+
+type general32 struct {
+	data       []float32
+	rows, cols int
+	stride     int
+}
+
+func (g general32) clone() general32 {
+	data := make([]float32, len(g.data))
+	copy(data, g.data)
+	return general32{
+		data:   data,
+		rows:   g.rows,
+		cols:   g.cols,
+		stride: g.stride,
+	}
+}
+
+func (g general32) equal(a general32) bool {
+	if g.rows != a.rows || g.cols != a.cols || g.stride != a.stride {
+		return false
+	}
+	for i, v := range g.data {
+		if a.data[i] != v {
+			return false
+		}
+	}
+	return true
+}
+
+func (g general32) equalWithinAbs(a general32, tol float32) bool {
+	if g.rows != a.rows || g.cols != a.cols || g.stride != a.stride {
+		return false
+	}
+	for i, v := range g.data {
+		if math.Abs(a.data[i]-v) > tol {
+			return false
+		}
+	}
+	return true
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/gonum.go b/vendor/gonum.org/v1/gonum/blas/gonum/gonum.go
new file mode 100644
index 00000000..e65f745a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/gonum.go
@@ -0,0 +1,133 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//go:generate ./single_precision.bash
+
+package gonum
+
+import "math"
+
+type Implementation struct{}
+
+// The following are panic strings used during parameter checks.
+const (
+	negativeN = "blas: n < 0"
+	zeroIncX  = "blas: zero x index increment"
+	zeroIncY  = "blas: zero y index increment"
+	badLenX   = "blas: x index out of range"
+	badLenY   = "blas: y index out of range"
+
+	mLT0  = "blas: m < 0"
+	nLT0  = "blas: n < 0"
+	kLT0  = "blas: k < 0"
+	kLLT0 = "blas: kL < 0"
+	kULT0 = "blas: kU < 0"
+
+	badUplo      = "blas: illegal triangle"
+	badTranspose = "blas: illegal transpose"
+	badDiag      = "blas: illegal diagonal"
+	badSide      = "blas: illegal side"
+
+	badLdA = "blas: index of a out of range"
+	badLdB = "blas: index of b out of range"
+	badLdC = "blas: index of c out of range"
+
+	badX = "blas: x index out of range"
+	badY = "blas: y index out of range"
+)
+
+// [SD]gemm behavior constants. These are kept here to keep them out of the
+// way during single precision code genration.
+const (
+	blockSize   = 64 // b x b matrix
+	minParBlock = 4  // minimum number of blocks needed to go parallel
+	buffMul     = 4  // how big is the buffer relative to the number of workers
+)
+
+// subMul is a common type shared by [SD]gemm.
+type subMul struct {
+	i, j int // index of block
+}
+
+func max(a, b int) int {
+	if a > b {
+		return a
+	}
+	return b
+}
+
+func min(a, b int) int {
+	if a > b {
+		return b
+	}
+	return a
+}
+
+func checkSMatrix(name byte, m, n int, a []float32, lda int) {
+	if m < 0 {
+		panic(mLT0)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if lda < n {
+		panic("blas: illegal stride of " + string(name))
+	}
+	if len(a) < (m-1)*lda+n {
+		panic("blas: index of " + string(name) + " out of range")
+	}
+}
+
+func checkDMatrix(name byte, m, n int, a []float64, lda int) {
+	if m < 0 {
+		panic(mLT0)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if lda < n {
+		panic("blas: illegal stride of " + string(name))
+	}
+	if len(a) < (m-1)*lda+n {
+		panic("blas: index of " + string(name) + " out of range")
+	}
+}
+
+func checkZMatrix(name byte, m, n int, a []complex128, lda int) {
+	if m < 0 {
+		panic(mLT0)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if lda < max(1, n) {
+		panic("blas: illegal stride of " + string(name))
+	}
+	if len(a) < (m-1)*lda+n {
+		panic("blas: insufficient " + string(name) + " matrix slice length")
+	}
+}
+
+func checkZVector(name byte, n int, x []complex128, incX int) {
+	if n < 0 {
+		panic(nLT0)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic("blas: insufficient " + string(name) + " vector slice length")
+	}
+}
+
+// blocks returns the number of divisions of the dimension length with the given
+// block size.
+func blocks(dim, bsize int) int {
+	return (dim + bsize - 1) / bsize
+}
+
+// dcabs1 returns |real(z)|+|imag(z)|.
+func dcabs1(z complex128) float64 {
+	return math.Abs(real(z)) + math.Abs(imag(z))
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/level1cmplx128.go b/vendor/gonum.org/v1/gonum/blas/gonum/level1cmplx128.go
new file mode 100644
index 00000000..b759c902
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/level1cmplx128.go
@@ -0,0 +1,442 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/internal/asm/c128"
+)
+
+// Dzasum returns the sum of the absolute values of the elements of x
+//  \sum_i |Re(x[i])| + |Im(x[i])|
+// Dzasum returns 0 if incX is negative.
+func (Implementation) Dzasum(n int, x []complex128, incX int) float64 {
+	if n < 0 {
+		panic(negativeN)
+	}
+	if incX < 1 {
+		if incX == 0 {
+			panic(zeroIncX)
+		}
+		return 0
+	}
+	var sum float64
+	if incX == 1 {
+		if len(x) < n {
+			panic(badX)
+		}
+		for _, v := range x[:n] {
+			sum += dcabs1(v)
+		}
+		return sum
+	}
+	if (n-1)*incX >= len(x) {
+		panic(badX)
+	}
+	for i := 0; i < n; i++ {
+		v := x[i*incX]
+		sum += dcabs1(v)
+	}
+	return sum
+}
+
+// Dznrm2 computes the Euclidean norm of the complex vector x,
+//  ‖x‖_2 = sqrt(\sum_i x[i] * conj(x[i])).
+// This function returns 0 if incX is negative.
+func (Implementation) Dznrm2(n int, x []complex128, incX int) float64 {
+	if incX < 1 {
+		if incX == 0 {
+			panic(zeroIncX)
+		}
+		return 0
+	}
+	if n < 1 {
+		if n == 0 {
+			return 0
+		}
+		panic(negativeN)
+	}
+	if (n-1)*incX >= len(x) {
+		panic(badX)
+	}
+	var (
+		scale float64
+		ssq   float64 = 1
+	)
+	if incX == 1 {
+		for _, v := range x[:n] {
+			re, im := math.Abs(real(v)), math.Abs(imag(v))
+			if re != 0 {
+				if re > scale {
+					ssq = 1 + ssq*(scale/re)*(scale/re)
+					scale = re
+				} else {
+					ssq += (re / scale) * (re / scale)
+				}
+			}
+			if im != 0 {
+				if im > scale {
+					ssq = 1 + ssq*(scale/im)*(scale/im)
+					scale = im
+				} else {
+					ssq += (im / scale) * (im / scale)
+				}
+			}
+		}
+		if math.IsInf(scale, 1) {
+			return math.Inf(1)
+		}
+		return scale * math.Sqrt(ssq)
+	}
+	for ix := 0; ix < n*incX; ix += incX {
+		re, im := math.Abs(real(x[ix])), math.Abs(imag(x[ix]))
+		if re != 0 {
+			if re > scale {
+				ssq = 1 + ssq*(scale/re)*(scale/re)
+				scale = re
+			} else {
+				ssq += (re / scale) * (re / scale)
+			}
+		}
+		if im != 0 {
+			if im > scale {
+				ssq = 1 + ssq*(scale/im)*(scale/im)
+				scale = im
+			} else {
+				ssq += (im / scale) * (im / scale)
+			}
+		}
+	}
+	if math.IsInf(scale, 1) {
+		return math.Inf(1)
+	}
+	return scale * math.Sqrt(ssq)
+}
+
+// Izamax returns the index of the first element of x having largest |Re(·)|+|Im(·)|.
+// Izamax returns -1 if n is 0 or incX is negative.
+func (Implementation) Izamax(n int, x []complex128, incX int) int {
+	if incX < 1 {
+		if incX == 0 {
+			panic(zeroIncX)
+		}
+		// Return invalid index.
+		return -1
+	}
+	if n < 1 {
+		if n == 0 {
+			// Return invalid index.
+			return -1
+		}
+		panic(negativeN)
+	}
+	if len(x) <= (n-1)*incX {
+		panic(badX)
+	}
+	idx := 0
+	max := dcabs1(x[0])
+	if incX == 1 {
+		for i, v := range x[1:n] {
+			absV := dcabs1(v)
+			if absV > max {
+				max = absV
+				idx = i + 1
+			}
+		}
+		return idx
+	}
+	ix := incX
+	for i := 1; i < n; i++ {
+		absV := dcabs1(x[ix])
+		if absV > max {
+			max = absV
+			idx = i
+		}
+		ix += incX
+	}
+	return idx
+}
+
+// Zaxpy adds alpha times x to y:
+//  y[i] += alpha * x[i] for all i
+func (Implementation) Zaxpy(n int, alpha complex128, x []complex128, incX int, y []complex128, incY int) {
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if n < 1 {
+		if n == 0 {
+			return
+		}
+		panic(negativeN)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
+		panic(badY)
+	}
+	if alpha == 0 {
+		return
+	}
+	if incX == 1 && incY == 1 {
+		c128.AxpyUnitary(alpha, x[:n], y[:n])
+		return
+	}
+	var ix, iy int
+	if incX < 0 {
+		ix = (1 - n) * incX
+	}
+	if incY < 0 {
+		iy = (1 - n) * incY
+	}
+	c128.AxpyInc(alpha, x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
+}
+
+// Zcopy copies the vector x to vector y.
+func (Implementation) Zcopy(n int, x []complex128, incX int, y []complex128, incY int) {
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if n < 1 {
+		if n == 0 {
+			return
+		}
+		panic(negativeN)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
+		panic(badY)
+	}
+	if incX == 1 && incY == 1 {
+		copy(y[:n], x[:n])
+		return
+	}
+	var ix, iy int
+	if incX < 0 {
+		ix = (-n + 1) * incX
+	}
+	if incY < 0 {
+		iy = (-n + 1) * incY
+	}
+	for i := 0; i < n; i++ {
+		y[iy] = x[ix]
+		ix += incX
+		iy += incY
+	}
+}
+
+// Zdotc computes the dot product
+//  x^H · y
+// of two complex vectors x and y.
+func (Implementation) Zdotc(n int, x []complex128, incX int, y []complex128, incY int) complex128 {
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if n <= 0 {
+		if n == 0 {
+			return 0
+		}
+		panic(negativeN)
+	}
+	if incX == 1 && incY == 1 {
+		if len(x) < n {
+			panic(badX)
+		}
+		if len(y) < n {
+			panic(badY)
+		}
+		return c128.DotcUnitary(x[:n], y[:n])
+	}
+	var ix, iy int
+	if incX < 0 {
+		ix = (-n + 1) * incX
+	}
+	if incY < 0 {
+		iy = (-n + 1) * incY
+	}
+	if ix >= len(x) || (n-1)*incX >= len(x) {
+		panic(badX)
+	}
+	if iy >= len(y) || (n-1)*incY >= len(y) {
+		panic(badY)
+	}
+	return c128.DotcInc(x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
+}
+
+// Zdotu computes the dot product
+//  x^T · y
+// of two complex vectors x and y.
+func (Implementation) Zdotu(n int, x []complex128, incX int, y []complex128, incY int) complex128 {
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if n <= 0 {
+		if n == 0 {
+			return 0
+		}
+		panic(negativeN)
+	}
+	if incX == 1 && incY == 1 {
+		if len(x) < n {
+			panic(badX)
+		}
+		if len(y) < n {
+			panic(badY)
+		}
+		return c128.DotuUnitary(x[:n], y[:n])
+	}
+	var ix, iy int
+	if incX < 0 {
+		ix = (-n + 1) * incX
+	}
+	if incY < 0 {
+		iy = (-n + 1) * incY
+	}
+	if ix >= len(x) || (n-1)*incX >= len(x) {
+		panic(badX)
+	}
+	if iy >= len(y) || (n-1)*incY >= len(y) {
+		panic(badY)
+	}
+	return c128.DotuInc(x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
+}
+
+// Zdscal scales the vector x by a real scalar alpha.
+// Zdscal has no effect if incX < 0.
+func (Implementation) Zdscal(n int, alpha float64, x []complex128, incX int) {
+	if incX < 1 {
+		if incX == 0 {
+			panic(zeroIncX)
+		}
+		return
+	}
+	if (n-1)*incX >= len(x) {
+		panic(badX)
+	}
+	if n < 1 {
+		if n == 0 {
+			return
+		}
+		panic(negativeN)
+	}
+	if alpha == 0 {
+		if incX == 1 {
+			x = x[:n]
+			for i := range x {
+				x[i] = 0
+			}
+			return
+		}
+		for ix := 0; ix < n*incX; ix += incX {
+			x[ix] = 0
+		}
+		return
+	}
+	if incX == 1 {
+		x = x[:n]
+		for i, v := range x {
+			x[i] = complex(alpha*real(v), alpha*imag(v))
+		}
+		return
+	}
+	for ix := 0; ix < n*incX; ix += incX {
+		v := x[ix]
+		x[ix] = complex(alpha*real(v), alpha*imag(v))
+	}
+}
+
+// Zscal scales the vector x by a complex scalar alpha.
+// Zscal has no effect if incX < 0.
+func (Implementation) Zscal(n int, alpha complex128, x []complex128, incX int) {
+	if incX < 1 {
+		if incX == 0 {
+			panic(zeroIncX)
+		}
+		return
+	}
+	if (n-1)*incX >= len(x) {
+		panic(badX)
+	}
+	if n < 1 {
+		if n == 0 {
+			return
+		}
+		panic(negativeN)
+	}
+	if alpha == 0 {
+		if incX == 1 {
+			x = x[:n]
+			for i := range x {
+				x[i] = 0
+			}
+			return
+		}
+		for ix := 0; ix < n*incX; ix += incX {
+			x[ix] = 0
+		}
+		return
+	}
+	if incX == 1 {
+		c128.ScalUnitary(alpha, x[:n])
+		return
+	}
+	c128.ScalInc(alpha, x, uintptr(n), uintptr(incX))
+}
+
+// Zswap exchanges the elements of two complex vectors x and y.
+func (Implementation) Zswap(n int, x []complex128, incX int, y []complex128, incY int) {
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if n < 1 {
+		if n == 0 {
+			return
+		}
+		panic(negativeN)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
+		panic(badY)
+	}
+	if incX == 1 && incY == 1 {
+		x = x[:n]
+		for i, v := range x {
+			x[i], y[i] = y[i], v
+		}
+		return
+	}
+	var ix, iy int
+	if incX < 0 {
+		ix = (-n + 1) * incX
+	}
+	if incY < 0 {
+		iy = (-n + 1) * incY
+	}
+	for i := 0; i < n; i++ {
+		x[ix], y[iy] = y[iy], x[ix]
+		ix += incX
+		iy += incY
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/level1cmplx128_bench_test.go b/vendor/gonum.org/v1/gonum/blas/gonum/level1cmplx128_bench_test.go
new file mode 100644
index 00000000..af536365
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/level1cmplx128_bench_test.go
@@ -0,0 +1,41 @@
+// Copyright ©2017 The Gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math/rand"
+	"testing"
+)
+
+func benchmarkZdscal(b *testing.B, n, inc int) {
+	rnd := rand.New(rand.NewSource(1))
+	alpha := rnd.NormFloat64()
+	x := make([]complex128, (n-1)*inc+1)
+	for i := range x {
+		x[i] = complex(rnd.NormFloat64(), rnd.NormFloat64())
+	}
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		impl.Zdscal(n, alpha, x, inc)
+	}
+}
+
+func BenchmarkZdscalN10Inc1(b *testing.B)     { benchmarkZdscal(b, 10, 1) }
+func BenchmarkZdscalN100Inc1(b *testing.B)    { benchmarkZdscal(b, 100, 1) }
+func BenchmarkZdscalN1000Inc1(b *testing.B)   { benchmarkZdscal(b, 1000, 1) }
+func BenchmarkZdscalN10000Inc1(b *testing.B)  { benchmarkZdscal(b, 10000, 1) }
+func BenchmarkZdscalN100000Inc1(b *testing.B) { benchmarkZdscal(b, 100000, 1) }
+
+func BenchmarkZdscalN10Inc10(b *testing.B)     { benchmarkZdscal(b, 10, 10) }
+func BenchmarkZdscalN100Inc10(b *testing.B)    { benchmarkZdscal(b, 100, 10) }
+func BenchmarkZdscalN1000Inc10(b *testing.B)   { benchmarkZdscal(b, 1000, 10) }
+func BenchmarkZdscalN10000Inc10(b *testing.B)  { benchmarkZdscal(b, 10000, 10) }
+func BenchmarkZdscalN100000Inc10(b *testing.B) { benchmarkZdscal(b, 100000, 10) }
+
+func BenchmarkZdscalN10Inc1000(b *testing.B)     { benchmarkZdscal(b, 10, 1000) }
+func BenchmarkZdscalN100Inc1000(b *testing.B)    { benchmarkZdscal(b, 100, 1000) }
+func BenchmarkZdscalN1000Inc1000(b *testing.B)   { benchmarkZdscal(b, 1000, 1000) }
+func BenchmarkZdscalN10000Inc1000(b *testing.B)  { benchmarkZdscal(b, 10000, 1000) }
+func BenchmarkZdscalN100000Inc1000(b *testing.B) { benchmarkZdscal(b, 100000, 1000) }
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/level1cmplx128_test.go b/vendor/gonum.org/v1/gonum/blas/gonum/level1cmplx128_test.go
new file mode 100644
index 00000000..1755e9e6
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/level1cmplx128_test.go
@@ -0,0 +1,51 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas/testblas"
+)
+
+func TestDzasum(t *testing.T) {
+	testblas.DzasumTest(t, impl)
+}
+
+func TestDznrm2(t *testing.T) {
+	testblas.Dznrm2Test(t, impl)
+}
+
+func TestIzamax(t *testing.T) {
+	testblas.IzamaxTest(t, impl)
+}
+
+func TestZaxpy(t *testing.T) {
+	testblas.ZaxpyTest(t, impl)
+}
+
+func TestZcopy(t *testing.T) {
+	testblas.ZcopyTest(t, impl)
+}
+
+func TestZdotc(t *testing.T) {
+	testblas.ZdotcTest(t, impl)
+}
+
+func TestZdotu(t *testing.T) {
+	testblas.ZdotuTest(t, impl)
+}
+
+func TestZdscal(t *testing.T) {
+	testblas.ZdscalTest(t, impl)
+}
+
+func TestZscal(t *testing.T) {
+	testblas.ZscalTest(t, impl)
+}
+
+func TestZswap(t *testing.T) {
+	testblas.ZswapTest(t, impl)
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/level1double.go b/vendor/gonum.org/v1/gonum/blas/gonum/level1double.go
new file mode 100644
index 00000000..e433fddf
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/level1double.go
@@ -0,0 +1,595 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/internal/asm/f64"
+)
+
+var _ blas.Float64Level1 = Implementation{}
+
+// Dnrm2 computes the Euclidean norm of a vector,
+//  sqrt(\sum_i x[i] * x[i]).
+// This function returns 0 if incX is negative.
+func (Implementation) Dnrm2(n int, x []float64, incX int) float64 {
+	if incX < 1 {
+		if incX == 0 {
+			panic(zeroIncX)
+		}
+		return 0
+	}
+	if incX > 0 && (n-1)*incX >= len(x) {
+		panic(badX)
+	}
+	if n < 2 {
+		if n == 1 {
+			return math.Abs(x[0])
+		}
+		if n == 0 {
+			return 0
+		}
+		if n < 1 {
+			panic(negativeN)
+		}
+	}
+	var (
+		scale      float64 = 0
+		sumSquares float64 = 1
+	)
+	if incX == 1 {
+		x = x[:n]
+		for _, v := range x {
+			if v == 0 {
+				continue
+			}
+			absxi := math.Abs(v)
+			if math.IsNaN(absxi) {
+				return math.NaN()
+			}
+			if scale < absxi {
+				sumSquares = 1 + sumSquares*(scale/absxi)*(scale/absxi)
+				scale = absxi
+			} else {
+				sumSquares = sumSquares + (absxi/scale)*(absxi/scale)
+			}
+		}
+		if math.IsInf(scale, 1) {
+			return math.Inf(1)
+		}
+		return scale * math.Sqrt(sumSquares)
+	}
+	for ix := 0; ix < n*incX; ix += incX {
+		val := x[ix]
+		if val == 0 {
+			continue
+		}
+		absxi := math.Abs(val)
+		if math.IsNaN(absxi) {
+			return math.NaN()
+		}
+		if scale < absxi {
+			sumSquares = 1 + sumSquares*(scale/absxi)*(scale/absxi)
+			scale = absxi
+		} else {
+			sumSquares = sumSquares + (absxi/scale)*(absxi/scale)
+		}
+	}
+	if math.IsInf(scale, 1) {
+		return math.Inf(1)
+	}
+	return scale * math.Sqrt(sumSquares)
+}
+
+// Dasum computes the sum of the absolute values of the elements of x.
+//  \sum_i |x[i]|
+// Dasum returns 0 if incX is negative.
+func (Implementation) Dasum(n int, x []float64, incX int) float64 {
+	var sum float64
+	if n < 0 {
+		panic(negativeN)
+	}
+	if incX < 1 {
+		if incX == 0 {
+			panic(zeroIncX)
+		}
+		return 0
+	}
+	if incX > 0 && (n-1)*incX >= len(x) {
+		panic(badX)
+	}
+	if incX == 1 {
+		x = x[:n]
+		for _, v := range x {
+			sum += math.Abs(v)
+		}
+		return sum
+	}
+	for i := 0; i < n; i++ {
+		sum += math.Abs(x[i*incX])
+	}
+	return sum
+}
+
+// Idamax returns the index of an element of x with the largest absolute value.
+// If there are multiple such indices the earliest is returned.
+// Idamax returns -1 if n == 0.
+func (Implementation) Idamax(n int, x []float64, incX int) int {
+	if incX < 1 {
+		if incX == 0 {
+			panic(zeroIncX)
+		}
+		return -1
+	}
+	if incX > 0 && (n-1)*incX >= len(x) {
+		panic(badX)
+	}
+	if n < 2 {
+		if n == 1 {
+			return 0
+		}
+		if n == 0 {
+			return -1 // Netlib returns invalid index when n == 0
+		}
+		if n < 1 {
+			panic(negativeN)
+		}
+	}
+	idx := 0
+	max := math.Abs(x[0])
+	if incX == 1 {
+		for i, v := range x[:n] {
+			absV := math.Abs(v)
+			if absV > max {
+				max = absV
+				idx = i
+			}
+		}
+		return idx
+	}
+	ix := incX
+	for i := 1; i < n; i++ {
+		v := x[ix]
+		absV := math.Abs(v)
+		if absV > max {
+			max = absV
+			idx = i
+		}
+		ix += incX
+	}
+	return idx
+}
+
+// Dswap exchanges the elements of two vectors.
+//  x[i], y[i] = y[i], x[i] for all i
+func (Implementation) Dswap(n int, x []float64, incX int, y []float64, incY int) {
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if n < 1 {
+		if n == 0 {
+			return
+		}
+		panic(negativeN)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
+		panic(badY)
+	}
+	if incX == 1 && incY == 1 {
+		x = x[:n]
+		for i, v := range x {
+			x[i], y[i] = y[i], v
+		}
+		return
+	}
+	var ix, iy int
+	if incX < 0 {
+		ix = (-n + 1) * incX
+	}
+	if incY < 0 {
+		iy = (-n + 1) * incY
+	}
+	for i := 0; i < n; i++ {
+		x[ix], y[iy] = y[iy], x[ix]
+		ix += incX
+		iy += incY
+	}
+}
+
+// Dcopy copies the elements of x into the elements of y.
+//  y[i] = x[i] for all i
+func (Implementation) Dcopy(n int, x []float64, incX int, y []float64, incY int) {
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if n < 1 {
+		if n == 0 {
+			return
+		}
+		panic(negativeN)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
+		panic(badY)
+	}
+	if incX == 1 && incY == 1 {
+		copy(y[:n], x[:n])
+		return
+	}
+	var ix, iy int
+	if incX < 0 {
+		ix = (-n + 1) * incX
+	}
+	if incY < 0 {
+		iy = (-n + 1) * incY
+	}
+	for i := 0; i < n; i++ {
+		y[iy] = x[ix]
+		ix += incX
+		iy += incY
+	}
+}
+
+// Daxpy adds alpha times x to y
+//  y[i] += alpha * x[i] for all i
+func (Implementation) Daxpy(n int, alpha float64, x []float64, incX int, y []float64, incY int) {
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if n < 1 {
+		if n == 0 {
+			return
+		}
+		panic(negativeN)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
+		panic(badY)
+	}
+	if alpha == 0 {
+		return
+	}
+	if incX == 1 && incY == 1 {
+		f64.AxpyUnitary(alpha, x[:n], y[:n])
+		return
+	}
+	var ix, iy int
+	if incX < 0 {
+		ix = (-n + 1) * incX
+	}
+	if incY < 0 {
+		iy = (-n + 1) * incY
+	}
+	f64.AxpyInc(alpha, x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
+}
+
+// Drotg computes the plane rotation
+//   _    _      _ _       _ _
+//  |  c s |    | a |     | r |
+//  | -s c |  * | b |   = | 0 |
+//   ‾    ‾      ‾ ‾       ‾ ‾
+// where
+//  r = ±√(a^2 + b^2)
+//  c = a/r, the cosine of the plane rotation
+//  s = b/r, the sine of the plane rotation
+//
+// NOTE: There is a discrepancy between the refence implementation and the BLAS
+// technical manual regarding the sign for r when a or b are zero.
+// Drotg agrees with the definition in the manual and other
+// common BLAS implementations.
+func (Implementation) Drotg(a, b float64) (c, s, r, z float64) {
+	if b == 0 && a == 0 {
+		return 1, 0, a, 0
+	}
+	absA := math.Abs(a)
+	absB := math.Abs(b)
+	aGTb := absA > absB
+	r = math.Hypot(a, b)
+	if aGTb {
+		r = math.Copysign(r, a)
+	} else {
+		r = math.Copysign(r, b)
+	}
+	c = a / r
+	s = b / r
+	if aGTb {
+		z = s
+	} else if c != 0 { // r == 0 case handled above
+		z = 1 / c
+	} else {
+		z = 1
+	}
+	return
+}
+
+// Drotmg computes the modified Givens rotation. See
+// http://www.netlib.org/lapack/explore-html/df/deb/drotmg_8f.html
+// for more details.
+func (Implementation) Drotmg(d1, d2, x1, y1 float64) (p blas.DrotmParams, rd1, rd2, rx1 float64) {
+	var p1, p2, q1, q2, u float64
+
+	const (
+		gam    = 4096.0
+		gamsq  = 16777216.0
+		rgamsq = 5.9604645e-8
+	)
+
+	if d1 < 0 {
+		p.Flag = blas.Rescaling
+		return
+	}
+
+	p2 = d2 * y1
+	if p2 == 0 {
+		p.Flag = blas.Identity
+		rd1 = d1
+		rd2 = d2
+		rx1 = x1
+		return
+	}
+	p1 = d1 * x1
+	q2 = p2 * y1
+	q1 = p1 * x1
+
+	absQ1 := math.Abs(q1)
+	absQ2 := math.Abs(q2)
+
+	if absQ1 < absQ2 && q2 < 0 {
+		p.Flag = blas.Rescaling
+		return
+	}
+
+	if d1 == 0 {
+		p.Flag = blas.Diagonal
+		p.H[0] = p1 / p2
+		p.H[3] = x1 / y1
+		u = 1 + p.H[0]*p.H[3]
+		rd1, rd2 = d2/u, d1/u
+		rx1 = y1 / u
+		return
+	}
+
+	// Now we know that d1 != 0, and d2 != 0. If d2 == 0, it would be caught
+	// when p2 == 0, and if d1 == 0, then it is caught above
+
+	if absQ1 > absQ2 {
+		p.H[1] = -y1 / x1
+		p.H[2] = p2 / p1
+		u = 1 - p.H[2]*p.H[1]
+		rd1 = d1
+		rd2 = d2
+		rx1 = x1
+		p.Flag = blas.OffDiagonal
+		// u must be greater than zero because |q1| > |q2|, so check from netlib
+		// is unnecessary
+		// This is left in for ease of comparison with complex routines
+		//if u > 0 {
+		rd1 /= u
+		rd2 /= u
+		rx1 *= u
+		//}
+	} else {
+		p.Flag = blas.Diagonal
+		p.H[0] = p1 / p2
+		p.H[3] = x1 / y1
+		u = 1 + p.H[0]*p.H[3]
+		rd1 = d2 / u
+		rd2 = d1 / u
+		rx1 = y1 * u
+	}
+
+	for rd1 <= rgamsq || rd1 >= gamsq {
+		if p.Flag == blas.OffDiagonal {
+			p.H[0] = 1
+			p.H[3] = 1
+			p.Flag = blas.Rescaling
+		} else if p.Flag == blas.Diagonal {
+			p.H[1] = -1
+			p.H[2] = 1
+			p.Flag = blas.Rescaling
+		}
+		if rd1 <= rgamsq {
+			rd1 *= gam * gam
+			rx1 /= gam
+			p.H[0] /= gam
+			p.H[2] /= gam
+		} else {
+			rd1 /= gam * gam
+			rx1 *= gam
+			p.H[0] *= gam
+			p.H[2] *= gam
+		}
+	}
+
+	for math.Abs(rd2) <= rgamsq || math.Abs(rd2) >= gamsq {
+		if p.Flag == blas.OffDiagonal {
+			p.H[0] = 1
+			p.H[3] = 1
+			p.Flag = blas.Rescaling
+		} else if p.Flag == blas.Diagonal {
+			p.H[1] = -1
+			p.H[2] = 1
+			p.Flag = blas.Rescaling
+		}
+		if math.Abs(rd2) <= rgamsq {
+			rd2 *= gam * gam
+			p.H[1] /= gam
+			p.H[3] /= gam
+		} else {
+			rd2 /= gam * gam
+			p.H[1] *= gam
+			p.H[3] *= gam
+		}
+	}
+	return
+}
+
+// Drot applies a plane transformation.
+//  x[i] = c * x[i] + s * y[i]
+//  y[i] = c * y[i] - s * x[i]
+func (Implementation) Drot(n int, x []float64, incX int, y []float64, incY int, c float64, s float64) {
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if n < 1 {
+		if n == 0 {
+			return
+		}
+		panic(negativeN)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
+		panic(badY)
+	}
+	if incX == 1 && incY == 1 {
+		x = x[:n]
+		for i, vx := range x {
+			vy := y[i]
+			x[i], y[i] = c*vx+s*vy, c*vy-s*vx
+		}
+		return
+	}
+	var ix, iy int
+	if incX < 0 {
+		ix = (-n + 1) * incX
+	}
+	if incY < 0 {
+		iy = (-n + 1) * incY
+	}
+	for i := 0; i < n; i++ {
+		vx := x[ix]
+		vy := y[iy]
+		x[ix], y[iy] = c*vx+s*vy, c*vy-s*vx
+		ix += incX
+		iy += incY
+	}
+}
+
+// Drotm applies the modified Givens rotation to the 2×n matrix.
+func (Implementation) Drotm(n int, x []float64, incX int, y []float64, incY int, p blas.DrotmParams) {
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if n <= 0 {
+		if n == 0 {
+			return
+		}
+		panic(negativeN)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
+		panic(badY)
+	}
+
+	var h11, h12, h21, h22 float64
+	var ix, iy int
+	switch p.Flag {
+	case blas.Identity:
+		return
+	case blas.Rescaling:
+		h11 = p.H[0]
+		h12 = p.H[2]
+		h21 = p.H[1]
+		h22 = p.H[3]
+	case blas.OffDiagonal:
+		h11 = 1
+		h12 = p.H[2]
+		h21 = p.H[1]
+		h22 = 1
+	case blas.Diagonal:
+		h11 = p.H[0]
+		h12 = 1
+		h21 = -1
+		h22 = p.H[3]
+	}
+	if incX < 0 {
+		ix = (-n + 1) * incX
+	}
+	if incY < 0 {
+		iy = (-n + 1) * incY
+	}
+	if incX == 1 && incY == 1 {
+		x = x[:n]
+		for i, vx := range x {
+			vy := y[i]
+			x[i], y[i] = vx*h11+vy*h12, vx*h21+vy*h22
+		}
+		return
+	}
+	for i := 0; i < n; i++ {
+		vx := x[ix]
+		vy := y[iy]
+		x[ix], y[iy] = vx*h11+vy*h12, vx*h21+vy*h22
+		ix += incX
+		iy += incY
+	}
+}
+
+// Dscal scales x by alpha.
+//  x[i] *= alpha
+// Dscal has no effect if incX < 0.
+func (Implementation) Dscal(n int, alpha float64, x []float64, incX int) {
+	if incX < 1 {
+		if incX == 0 {
+			panic(zeroIncX)
+		}
+		return
+	}
+	if (n-1)*incX >= len(x) {
+		panic(badX)
+	}
+	if n < 1 {
+		if n == 0 {
+			return
+		}
+		panic(negativeN)
+	}
+	if alpha == 0 {
+		if incX == 1 {
+			x = x[:n]
+			for i := range x {
+				x[i] = 0
+			}
+			return
+		}
+		for ix := 0; ix < n*incX; ix += incX {
+			x[ix] = 0
+		}
+		return
+	}
+	if incX == 1 {
+		f64.ScalUnitary(alpha, x[:n])
+		return
+	}
+	f64.ScalInc(alpha, x, uintptr(n), uintptr(incX))
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/level1doubleBench_auto_test.go b/vendor/gonum.org/v1/gonum/blas/gonum/level1doubleBench_auto_test.go
new file mode 100644
index 00000000..08296957
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/level1doubleBench_auto_test.go
@@ -0,0 +1,1685 @@
+// Code generated by "go run github.com/gonum/blas/testblas/benchautogen/autogen_bench_level1double.go"; DO NOT EDIT.
+
+// Copyright 2014 The Gonum Authors. All rights reserved.
+// Use of this code is governed by a BSD-style
+// license that can be found in the LICENSE file
+
+package gonum
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+const (
+	posInc1      = 5
+	posInc2      = 3
+	negInc1      = -3
+	negInc2      = -4
+	SMALL_SLICE  = 10
+	MEDIUM_SLICE = 1000
+	LARGE_SLICE  = 100000
+	HUGE_SLICE   = 10000000
+)
+
+func randomSlice(l, idx int) []float64 {
+	if idx < 0 {
+		idx = -idx
+	}
+	s := make([]float64, l*idx)
+	for i := range s {
+		s[i] = rand.Float64()
+	}
+	return s
+}
+
+func benchmarkDdot(b *testing.B, n int, x []float64, incX int, y []float64, incY int) {
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		impl.Ddot(n, x, incX, y, incY)
+	}
+}
+
+func BenchmarkDdotSmallBothUnitary(b *testing.B) {
+	n := SMALL_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+
+	benchmarkDdot(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDdotSmallIncUni(b *testing.B) {
+	n := SMALL_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+
+	benchmarkDdot(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDdotSmallUniInc(b *testing.B) {
+	n := SMALL_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+
+	benchmarkDdot(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDdotSmallBothInc(b *testing.B) {
+	n := SMALL_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+
+	benchmarkDdot(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDdotMediumBothUnitary(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+
+	benchmarkDdot(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDdotMediumIncUni(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+
+	benchmarkDdot(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDdotMediumUniInc(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+
+	benchmarkDdot(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDdotMediumBothInc(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+
+	benchmarkDdot(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDdotLargeBothUnitary(b *testing.B) {
+	n := LARGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+
+	benchmarkDdot(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDdotLargeIncUni(b *testing.B) {
+	n := LARGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+
+	benchmarkDdot(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDdotLargeUniInc(b *testing.B) {
+	n := LARGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+
+	benchmarkDdot(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDdotLargeBothInc(b *testing.B) {
+	n := LARGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+
+	benchmarkDdot(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDdotHugeBothUnitary(b *testing.B) {
+	n := HUGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+
+	benchmarkDdot(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDdotHugeIncUni(b *testing.B) {
+	n := HUGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+
+	benchmarkDdot(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDdotHugeUniInc(b *testing.B) {
+	n := HUGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+
+	benchmarkDdot(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDdotHugeBothInc(b *testing.B) {
+	n := HUGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+
+	benchmarkDdot(b, n, x, incX, y, incY)
+}
+
+/* ------------------ */
+func benchmarkDnrm2(b *testing.B, n int, x []float64, incX int) {
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		impl.Dnrm2(n, x, incX)
+	}
+}
+
+func BenchmarkDnrm2SmallUnitaryInc(b *testing.B) {
+	n := SMALL_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+
+	benchmarkDnrm2(b, n, x, incX)
+}
+
+func BenchmarkDnrm2SmallPosInc(b *testing.B) {
+	n := SMALL_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+
+	benchmarkDnrm2(b, n, x, incX)
+}
+
+func BenchmarkDnrm2MediumUnitaryInc(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+
+	benchmarkDnrm2(b, n, x, incX)
+}
+
+func BenchmarkDnrm2MediumPosInc(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+
+	benchmarkDnrm2(b, n, x, incX)
+}
+
+func BenchmarkDnrm2LargeUnitaryInc(b *testing.B) {
+	n := LARGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+
+	benchmarkDnrm2(b, n, x, incX)
+}
+
+func BenchmarkDnrm2LargePosInc(b *testing.B) {
+	n := LARGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+
+	benchmarkDnrm2(b, n, x, incX)
+}
+
+func BenchmarkDnrm2HugeUnitaryInc(b *testing.B) {
+	n := HUGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+
+	benchmarkDnrm2(b, n, x, incX)
+}
+
+func BenchmarkDnrm2HugePosInc(b *testing.B) {
+	n := HUGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+
+	benchmarkDnrm2(b, n, x, incX)
+}
+
+/* ------------------ */
+func benchmarkDasum(b *testing.B, n int, x []float64, incX int) {
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		impl.Dasum(n, x, incX)
+	}
+}
+
+func BenchmarkDasumSmallUnitaryInc(b *testing.B) {
+	n := SMALL_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+
+	benchmarkDasum(b, n, x, incX)
+}
+
+func BenchmarkDasumSmallPosInc(b *testing.B) {
+	n := SMALL_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+
+	benchmarkDasum(b, n, x, incX)
+}
+
+func BenchmarkDasumMediumUnitaryInc(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+
+	benchmarkDasum(b, n, x, incX)
+}
+
+func BenchmarkDasumMediumPosInc(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+
+	benchmarkDasum(b, n, x, incX)
+}
+
+func BenchmarkDasumLargeUnitaryInc(b *testing.B) {
+	n := LARGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+
+	benchmarkDasum(b, n, x, incX)
+}
+
+func BenchmarkDasumLargePosInc(b *testing.B) {
+	n := LARGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+
+	benchmarkDasum(b, n, x, incX)
+}
+
+func BenchmarkDasumHugeUnitaryInc(b *testing.B) {
+	n := HUGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+
+	benchmarkDasum(b, n, x, incX)
+}
+
+func BenchmarkDasumHugePosInc(b *testing.B) {
+	n := HUGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+
+	benchmarkDasum(b, n, x, incX)
+}
+
+/* ------------------ */
+func benchmarkIdamax(b *testing.B, n int, x []float64, incX int) {
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		impl.Idamax(n, x, incX)
+	}
+}
+
+func BenchmarkIdamaxSmallUnitaryInc(b *testing.B) {
+	n := SMALL_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+
+	benchmarkIdamax(b, n, x, incX)
+}
+
+func BenchmarkIdamaxSmallPosInc(b *testing.B) {
+	n := SMALL_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+
+	benchmarkIdamax(b, n, x, incX)
+}
+
+func BenchmarkIdamaxMediumUnitaryInc(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+
+	benchmarkIdamax(b, n, x, incX)
+}
+
+func BenchmarkIdamaxMediumPosInc(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+
+	benchmarkIdamax(b, n, x, incX)
+}
+
+func BenchmarkIdamaxLargeUnitaryInc(b *testing.B) {
+	n := LARGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+
+	benchmarkIdamax(b, n, x, incX)
+}
+
+func BenchmarkIdamaxLargePosInc(b *testing.B) {
+	n := LARGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+
+	benchmarkIdamax(b, n, x, incX)
+}
+
+func BenchmarkIdamaxHugeUnitaryInc(b *testing.B) {
+	n := HUGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+
+	benchmarkIdamax(b, n, x, incX)
+}
+
+func BenchmarkIdamaxHugePosInc(b *testing.B) {
+	n := HUGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+
+	benchmarkIdamax(b, n, x, incX)
+}
+
+/* ------------------ */
+func benchmarkDswap(b *testing.B, n int, x []float64, incX int, y []float64, incY int) {
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		impl.Dswap(n, x, incX, y, incY)
+	}
+}
+
+func BenchmarkDswapSmallBothUnitary(b *testing.B) {
+	n := SMALL_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+
+	benchmarkDswap(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDswapSmallIncUni(b *testing.B) {
+	n := SMALL_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+
+	benchmarkDswap(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDswapSmallUniInc(b *testing.B) {
+	n := SMALL_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+
+	benchmarkDswap(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDswapSmallBothInc(b *testing.B) {
+	n := SMALL_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+
+	benchmarkDswap(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDswapMediumBothUnitary(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+
+	benchmarkDswap(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDswapMediumIncUni(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+
+	benchmarkDswap(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDswapMediumUniInc(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+
+	benchmarkDswap(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDswapMediumBothInc(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+
+	benchmarkDswap(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDswapLargeBothUnitary(b *testing.B) {
+	n := LARGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+
+	benchmarkDswap(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDswapLargeIncUni(b *testing.B) {
+	n := LARGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+
+	benchmarkDswap(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDswapLargeUniInc(b *testing.B) {
+	n := LARGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+
+	benchmarkDswap(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDswapLargeBothInc(b *testing.B) {
+	n := LARGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+
+	benchmarkDswap(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDswapHugeBothUnitary(b *testing.B) {
+	n := HUGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+
+	benchmarkDswap(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDswapHugeIncUni(b *testing.B) {
+	n := HUGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+
+	benchmarkDswap(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDswapHugeUniInc(b *testing.B) {
+	n := HUGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+
+	benchmarkDswap(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDswapHugeBothInc(b *testing.B) {
+	n := HUGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+
+	benchmarkDswap(b, n, x, incX, y, incY)
+}
+
+/* ------------------ */
+func benchmarkDcopy(b *testing.B, n int, x []float64, incX int, y []float64, incY int) {
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		impl.Dcopy(n, x, incX, y, incY)
+	}
+}
+
+func BenchmarkDcopySmallBothUnitary(b *testing.B) {
+	n := SMALL_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+
+	benchmarkDcopy(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDcopySmallIncUni(b *testing.B) {
+	n := SMALL_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+
+	benchmarkDcopy(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDcopySmallUniInc(b *testing.B) {
+	n := SMALL_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+
+	benchmarkDcopy(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDcopySmallBothInc(b *testing.B) {
+	n := SMALL_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+
+	benchmarkDcopy(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDcopyMediumBothUnitary(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+
+	benchmarkDcopy(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDcopyMediumIncUni(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+
+	benchmarkDcopy(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDcopyMediumUniInc(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+
+	benchmarkDcopy(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDcopyMediumBothInc(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+
+	benchmarkDcopy(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDcopyLargeBothUnitary(b *testing.B) {
+	n := LARGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+
+	benchmarkDcopy(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDcopyLargeIncUni(b *testing.B) {
+	n := LARGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+
+	benchmarkDcopy(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDcopyLargeUniInc(b *testing.B) {
+	n := LARGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+
+	benchmarkDcopy(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDcopyLargeBothInc(b *testing.B) {
+	n := LARGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+
+	benchmarkDcopy(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDcopyHugeBothUnitary(b *testing.B) {
+	n := HUGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+
+	benchmarkDcopy(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDcopyHugeIncUni(b *testing.B) {
+	n := HUGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+
+	benchmarkDcopy(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDcopyHugeUniInc(b *testing.B) {
+	n := HUGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+
+	benchmarkDcopy(b, n, x, incX, y, incY)
+}
+
+func BenchmarkDcopyHugeBothInc(b *testing.B) {
+	n := HUGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+
+	benchmarkDcopy(b, n, x, incX, y, incY)
+}
+
+/* ------------------ */
+func benchmarkDaxpy(b *testing.B, n int, alpha float64, x []float64, incX int, y []float64, incY int) {
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		impl.Daxpy(n, alpha, x, incX, y, incY)
+	}
+}
+
+func BenchmarkDaxpySmallBothUnitary(b *testing.B) {
+	n := SMALL_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	alpha := 2.4
+	benchmarkDaxpy(b, n, alpha, x, incX, y, incY)
+}
+
+func BenchmarkDaxpySmallIncUni(b *testing.B) {
+	n := SMALL_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	alpha := 2.4
+	benchmarkDaxpy(b, n, alpha, x, incX, y, incY)
+}
+
+func BenchmarkDaxpySmallUniInc(b *testing.B) {
+	n := SMALL_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	alpha := 2.4
+	benchmarkDaxpy(b, n, alpha, x, incX, y, incY)
+}
+
+func BenchmarkDaxpySmallBothInc(b *testing.B) {
+	n := SMALL_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	alpha := 2.4
+	benchmarkDaxpy(b, n, alpha, x, incX, y, incY)
+}
+
+func BenchmarkDaxpyMediumBothUnitary(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	alpha := 2.4
+	benchmarkDaxpy(b, n, alpha, x, incX, y, incY)
+}
+
+func BenchmarkDaxpyMediumIncUni(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	alpha := 2.4
+	benchmarkDaxpy(b, n, alpha, x, incX, y, incY)
+}
+
+func BenchmarkDaxpyMediumUniInc(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	alpha := 2.4
+	benchmarkDaxpy(b, n, alpha, x, incX, y, incY)
+}
+
+func BenchmarkDaxpyMediumBothInc(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	alpha := 2.4
+	benchmarkDaxpy(b, n, alpha, x, incX, y, incY)
+}
+
+func BenchmarkDaxpyLargeBothUnitary(b *testing.B) {
+	n := LARGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	alpha := 2.4
+	benchmarkDaxpy(b, n, alpha, x, incX, y, incY)
+}
+
+func BenchmarkDaxpyLargeIncUni(b *testing.B) {
+	n := LARGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	alpha := 2.4
+	benchmarkDaxpy(b, n, alpha, x, incX, y, incY)
+}
+
+func BenchmarkDaxpyLargeUniInc(b *testing.B) {
+	n := LARGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	alpha := 2.4
+	benchmarkDaxpy(b, n, alpha, x, incX, y, incY)
+}
+
+func BenchmarkDaxpyLargeBothInc(b *testing.B) {
+	n := LARGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	alpha := 2.4
+	benchmarkDaxpy(b, n, alpha, x, incX, y, incY)
+}
+
+func BenchmarkDaxpyHugeBothUnitary(b *testing.B) {
+	n := HUGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	alpha := 2.4
+	benchmarkDaxpy(b, n, alpha, x, incX, y, incY)
+}
+
+func BenchmarkDaxpyHugeIncUni(b *testing.B) {
+	n := HUGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	alpha := 2.4
+	benchmarkDaxpy(b, n, alpha, x, incX, y, incY)
+}
+
+func BenchmarkDaxpyHugeUniInc(b *testing.B) {
+	n := HUGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	alpha := 2.4
+	benchmarkDaxpy(b, n, alpha, x, incX, y, incY)
+}
+
+func BenchmarkDaxpyHugeBothInc(b *testing.B) {
+	n := HUGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	alpha := 2.4
+	benchmarkDaxpy(b, n, alpha, x, incX, y, incY)
+}
+
+/* ------------------ */
+func benchmarkDrot(b *testing.B, n int, x []float64, incX int, y []float64, incY int, c, s float64) {
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		impl.Drot(n, x, incX, y, incY, c, s)
+	}
+}
+
+func BenchmarkDrotSmallBothUnitary(b *testing.B) {
+	n := SMALL_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	c := 0.89725836967
+	s := 0.44150585279
+	benchmarkDrot(b, n, x, incX, y, incY, c, s)
+}
+
+func BenchmarkDrotSmallIncUni(b *testing.B) {
+	n := SMALL_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	c := 0.89725836967
+	s := 0.44150585279
+	benchmarkDrot(b, n, x, incX, y, incY, c, s)
+}
+
+func BenchmarkDrotSmallUniInc(b *testing.B) {
+	n := SMALL_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	c := 0.89725836967
+	s := 0.44150585279
+	benchmarkDrot(b, n, x, incX, y, incY, c, s)
+}
+
+func BenchmarkDrotSmallBothInc(b *testing.B) {
+	n := SMALL_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	c := 0.89725836967
+	s := 0.44150585279
+	benchmarkDrot(b, n, x, incX, y, incY, c, s)
+}
+
+func BenchmarkDrotMediumBothUnitary(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	c := 0.89725836967
+	s := 0.44150585279
+	benchmarkDrot(b, n, x, incX, y, incY, c, s)
+}
+
+func BenchmarkDrotMediumIncUni(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	c := 0.89725836967
+	s := 0.44150585279
+	benchmarkDrot(b, n, x, incX, y, incY, c, s)
+}
+
+func BenchmarkDrotMediumUniInc(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	c := 0.89725836967
+	s := 0.44150585279
+	benchmarkDrot(b, n, x, incX, y, incY, c, s)
+}
+
+func BenchmarkDrotMediumBothInc(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	c := 0.89725836967
+	s := 0.44150585279
+	benchmarkDrot(b, n, x, incX, y, incY, c, s)
+}
+
+func BenchmarkDrotLargeBothUnitary(b *testing.B) {
+	n := LARGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	c := 0.89725836967
+	s := 0.44150585279
+	benchmarkDrot(b, n, x, incX, y, incY, c, s)
+}
+
+func BenchmarkDrotLargeIncUni(b *testing.B) {
+	n := LARGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	c := 0.89725836967
+	s := 0.44150585279
+	benchmarkDrot(b, n, x, incX, y, incY, c, s)
+}
+
+func BenchmarkDrotLargeUniInc(b *testing.B) {
+	n := LARGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	c := 0.89725836967
+	s := 0.44150585279
+	benchmarkDrot(b, n, x, incX, y, incY, c, s)
+}
+
+func BenchmarkDrotLargeBothInc(b *testing.B) {
+	n := LARGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	c := 0.89725836967
+	s := 0.44150585279
+	benchmarkDrot(b, n, x, incX, y, incY, c, s)
+}
+
+func BenchmarkDrotHugeBothUnitary(b *testing.B) {
+	n := HUGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	c := 0.89725836967
+	s := 0.44150585279
+	benchmarkDrot(b, n, x, incX, y, incY, c, s)
+}
+
+func BenchmarkDrotHugeIncUni(b *testing.B) {
+	n := HUGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	c := 0.89725836967
+	s := 0.44150585279
+	benchmarkDrot(b, n, x, incX, y, incY, c, s)
+}
+
+func BenchmarkDrotHugeUniInc(b *testing.B) {
+	n := HUGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	c := 0.89725836967
+	s := 0.44150585279
+	benchmarkDrot(b, n, x, incX, y, incY, c, s)
+}
+
+func BenchmarkDrotHugeBothInc(b *testing.B) {
+	n := HUGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	c := 0.89725836967
+	s := 0.44150585279
+	benchmarkDrot(b, n, x, incX, y, incY, c, s)
+}
+
+/* ------------------ */
+func benchmarkDrotmOffDia(b *testing.B, n int, x []float64, incX int, y []float64, incY int, p blas.DrotmParams) {
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		impl.Drotm(n, x, incX, y, incY, p)
+	}
+}
+
+func BenchmarkDrotmOffDiaSmallBothUnitary(b *testing.B) {
+	n := SMALL_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{0, -0.625, 0.9375, 0}}
+	benchmarkDrotmOffDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmOffDiaSmallIncUni(b *testing.B) {
+	n := SMALL_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{0, -0.625, 0.9375, 0}}
+	benchmarkDrotmOffDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmOffDiaSmallUniInc(b *testing.B) {
+	n := SMALL_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{0, -0.625, 0.9375, 0}}
+	benchmarkDrotmOffDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmOffDiaSmallBothInc(b *testing.B) {
+	n := SMALL_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{0, -0.625, 0.9375, 0}}
+	benchmarkDrotmOffDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmOffDiaMediumBothUnitary(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{0, -0.625, 0.9375, 0}}
+	benchmarkDrotmOffDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmOffDiaMediumIncUni(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{0, -0.625, 0.9375, 0}}
+	benchmarkDrotmOffDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmOffDiaMediumUniInc(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{0, -0.625, 0.9375, 0}}
+	benchmarkDrotmOffDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmOffDiaMediumBothInc(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{0, -0.625, 0.9375, 0}}
+	benchmarkDrotmOffDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmOffDiaLargeBothUnitary(b *testing.B) {
+	n := LARGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{0, -0.625, 0.9375, 0}}
+	benchmarkDrotmOffDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmOffDiaLargeIncUni(b *testing.B) {
+	n := LARGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{0, -0.625, 0.9375, 0}}
+	benchmarkDrotmOffDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmOffDiaLargeUniInc(b *testing.B) {
+	n := LARGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{0, -0.625, 0.9375, 0}}
+	benchmarkDrotmOffDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmOffDiaLargeBothInc(b *testing.B) {
+	n := LARGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{0, -0.625, 0.9375, 0}}
+	benchmarkDrotmOffDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmOffDiaHugeBothUnitary(b *testing.B) {
+	n := HUGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{0, -0.625, 0.9375, 0}}
+	benchmarkDrotmOffDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmOffDiaHugeIncUni(b *testing.B) {
+	n := HUGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{0, -0.625, 0.9375, 0}}
+	benchmarkDrotmOffDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmOffDiaHugeUniInc(b *testing.B) {
+	n := HUGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{0, -0.625, 0.9375, 0}}
+	benchmarkDrotmOffDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmOffDiaHugeBothInc(b *testing.B) {
+	n := HUGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{0, -0.625, 0.9375, 0}}
+	benchmarkDrotmOffDia(b, n, x, incX, y, incY, p)
+}
+
+/* ------------------ */
+func benchmarkDrotmDia(b *testing.B, n int, x []float64, incX int, y []float64, incY int, p blas.DrotmParams) {
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		impl.Drotm(n, x, incX, y, incY, p)
+	}
+}
+
+func BenchmarkDrotmDiaSmallBothUnitary(b *testing.B) {
+	n := SMALL_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{5.0 / 12, 0, 0, 0.625}}
+	benchmarkDrotmDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmDiaSmallIncUni(b *testing.B) {
+	n := SMALL_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{5.0 / 12, 0, 0, 0.625}}
+	benchmarkDrotmDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmDiaSmallUniInc(b *testing.B) {
+	n := SMALL_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{5.0 / 12, 0, 0, 0.625}}
+	benchmarkDrotmDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmDiaSmallBothInc(b *testing.B) {
+	n := SMALL_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{5.0 / 12, 0, 0, 0.625}}
+	benchmarkDrotmDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmDiaMediumBothUnitary(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{5.0 / 12, 0, 0, 0.625}}
+	benchmarkDrotmDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmDiaMediumIncUni(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{5.0 / 12, 0, 0, 0.625}}
+	benchmarkDrotmDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmDiaMediumUniInc(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{5.0 / 12, 0, 0, 0.625}}
+	benchmarkDrotmDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmDiaMediumBothInc(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{5.0 / 12, 0, 0, 0.625}}
+	benchmarkDrotmDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmDiaLargeBothUnitary(b *testing.B) {
+	n := LARGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{5.0 / 12, 0, 0, 0.625}}
+	benchmarkDrotmDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmDiaLargeIncUni(b *testing.B) {
+	n := LARGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{5.0 / 12, 0, 0, 0.625}}
+	benchmarkDrotmDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmDiaLargeUniInc(b *testing.B) {
+	n := LARGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{5.0 / 12, 0, 0, 0.625}}
+	benchmarkDrotmDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmDiaLargeBothInc(b *testing.B) {
+	n := LARGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{5.0 / 12, 0, 0, 0.625}}
+	benchmarkDrotmDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmDiaHugeBothUnitary(b *testing.B) {
+	n := HUGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{5.0 / 12, 0, 0, 0.625}}
+	benchmarkDrotmDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmDiaHugeIncUni(b *testing.B) {
+	n := HUGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{5.0 / 12, 0, 0, 0.625}}
+	benchmarkDrotmDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmDiaHugeUniInc(b *testing.B) {
+	n := HUGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{5.0 / 12, 0, 0, 0.625}}
+	benchmarkDrotmDia(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmDiaHugeBothInc(b *testing.B) {
+	n := HUGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{5.0 / 12, 0, 0, 0.625}}
+	benchmarkDrotmDia(b, n, x, incX, y, incY, p)
+}
+
+/* ------------------ */
+func benchmarkDrotmResc(b *testing.B, n int, x []float64, incX int, y []float64, incY int, p blas.DrotmParams) {
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		impl.Drotm(n, x, incX, y, incY, p)
+	}
+}
+
+func BenchmarkDrotmRescSmallBothUnitary(b *testing.B) {
+	n := SMALL_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{4096, -3584, 1792, 4096}}
+	benchmarkDrotmResc(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmRescSmallIncUni(b *testing.B) {
+	n := SMALL_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{4096, -3584, 1792, 4096}}
+	benchmarkDrotmResc(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmRescSmallUniInc(b *testing.B) {
+	n := SMALL_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{4096, -3584, 1792, 4096}}
+	benchmarkDrotmResc(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmRescSmallBothInc(b *testing.B) {
+	n := SMALL_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{4096, -3584, 1792, 4096}}
+	benchmarkDrotmResc(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmRescMediumBothUnitary(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{4096, -3584, 1792, 4096}}
+	benchmarkDrotmResc(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmRescMediumIncUni(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{4096, -3584, 1792, 4096}}
+	benchmarkDrotmResc(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmRescMediumUniInc(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{4096, -3584, 1792, 4096}}
+	benchmarkDrotmResc(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmRescMediumBothInc(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{4096, -3584, 1792, 4096}}
+	benchmarkDrotmResc(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmRescLargeBothUnitary(b *testing.B) {
+	n := LARGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{4096, -3584, 1792, 4096}}
+	benchmarkDrotmResc(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmRescLargeIncUni(b *testing.B) {
+	n := LARGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{4096, -3584, 1792, 4096}}
+	benchmarkDrotmResc(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmRescLargeUniInc(b *testing.B) {
+	n := LARGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{4096, -3584, 1792, 4096}}
+	benchmarkDrotmResc(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmRescLargeBothInc(b *testing.B) {
+	n := LARGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{4096, -3584, 1792, 4096}}
+	benchmarkDrotmResc(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmRescHugeBothUnitary(b *testing.B) {
+	n := HUGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{4096, -3584, 1792, 4096}}
+	benchmarkDrotmResc(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmRescHugeIncUni(b *testing.B) {
+	n := HUGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := 1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{4096, -3584, 1792, 4096}}
+	benchmarkDrotmResc(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmRescHugeUniInc(b *testing.B) {
+	n := HUGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{4096, -3584, 1792, 4096}}
+	benchmarkDrotmResc(b, n, x, incX, y, incY, p)
+}
+
+func BenchmarkDrotmRescHugeBothInc(b *testing.B) {
+	n := HUGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	incY := negInc1
+	y := randomSlice(n, incY)
+	p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{4096, -3584, 1792, 4096}}
+	benchmarkDrotmResc(b, n, x, incX, y, incY, p)
+}
+
+/* ------------------ */
+func benchmarkDscal(b *testing.B, n int, alpha float64, x []float64, incX int) {
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		impl.Dscal(n, alpha, x, incX)
+	}
+}
+
+func BenchmarkDscalSmallUnitaryInc(b *testing.B) {
+	n := SMALL_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	alpha := 2.4
+	benchmarkDscal(b, n, alpha, x, incX)
+}
+
+func BenchmarkDscalSmallPosInc(b *testing.B) {
+	n := SMALL_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	alpha := 2.4
+	benchmarkDscal(b, n, alpha, x, incX)
+}
+
+func BenchmarkDscalMediumUnitaryInc(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	alpha := 2.4
+	benchmarkDscal(b, n, alpha, x, incX)
+}
+
+func BenchmarkDscalMediumPosInc(b *testing.B) {
+	n := MEDIUM_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	alpha := 2.4
+	benchmarkDscal(b, n, alpha, x, incX)
+}
+
+func BenchmarkDscalLargeUnitaryInc(b *testing.B) {
+	n := LARGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	alpha := 2.4
+	benchmarkDscal(b, n, alpha, x, incX)
+}
+
+func BenchmarkDscalLargePosInc(b *testing.B) {
+	n := LARGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	alpha := 2.4
+	benchmarkDscal(b, n, alpha, x, incX)
+}
+
+func BenchmarkDscalHugeUnitaryInc(b *testing.B) {
+	n := HUGE_SLICE
+	incX := 1
+	x := randomSlice(n, incX)
+	alpha := 2.4
+	benchmarkDscal(b, n, alpha, x, incX)
+}
+
+func BenchmarkDscalHugePosInc(b *testing.B) {
+	n := HUGE_SLICE
+	incX := posInc1
+	x := randomSlice(n, incX)
+	alpha := 2.4
+	benchmarkDscal(b, n, alpha, x, incX)
+}
+
+/* ------------------ */
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/level1double_ddot.go b/vendor/gonum.org/v1/gonum/blas/gonum/level1double_ddot.go
new file mode 100644
index 00000000..30c01100
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/level1double_ddot.go
@@ -0,0 +1,49 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/internal/asm/f64"
+)
+
+// Ddot computes the dot product of the two vectors
+//  \sum_i x[i]*y[i]
+func (Implementation) Ddot(n int, x []float64, incX int, y []float64, incY int) float64 {
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if n <= 0 {
+		if n == 0 {
+			return 0
+		}
+		panic(negativeN)
+	}
+	if incX == 1 && incY == 1 {
+		if len(x) < n {
+			panic(badLenX)
+		}
+		if len(y) < n {
+			panic(badLenY)
+		}
+		return f64.DotUnitary(x[:n], y)
+	}
+	var ix, iy int
+	if incX < 0 {
+		ix = (-n + 1) * incX
+	}
+	if incY < 0 {
+		iy = (-n + 1) * incY
+	}
+	if ix >= len(x) || ix+(n-1)*incX >= len(x) {
+		panic(badLenX)
+	}
+	if iy >= len(y) || iy+(n-1)*incY >= len(y) {
+		panic(badLenY)
+	}
+	return f64.DotInc(x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/level1double_test.go b/vendor/gonum.org/v1/gonum/blas/gonum/level1double_test.go
new file mode 100644
index 00000000..45adc85f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/level1double_test.go
@@ -0,0 +1,61 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas/testblas"
+)
+
+var impl Implementation
+
+func TestDasum(t *testing.T) {
+	testblas.DasumTest(t, impl)
+}
+
+func TestDaxpy(t *testing.T) {
+	testblas.DaxpyTest(t, impl)
+}
+
+func TestDdot(t *testing.T) {
+	testblas.DdotTest(t, impl)
+}
+
+func TestDnrm2(t *testing.T) {
+	testblas.Dnrm2Test(t, impl)
+}
+
+func TestIdamax(t *testing.T) {
+	testblas.IdamaxTest(t, impl)
+}
+
+func TestDswap(t *testing.T) {
+	testblas.DswapTest(t, impl)
+}
+
+func TestDcopy(t *testing.T) {
+	testblas.DcopyTest(t, impl)
+}
+
+func TestDrotg(t *testing.T) {
+	testblas.DrotgTest(t, impl)
+}
+
+func TestDrotmg(t *testing.T) {
+	testblas.DrotmgTest(t, impl)
+}
+
+func TestDrot(t *testing.T) {
+	testblas.DrotTest(t, impl)
+}
+
+func TestDrotm(t *testing.T) {
+	testblas.DrotmTest(t, impl)
+}
+
+func TestDscal(t *testing.T) {
+	testblas.DscalTest(t, impl)
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/level1single.go b/vendor/gonum.org/v1/gonum/blas/gonum/level1single.go
new file mode 100644
index 00000000..8081c814
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/level1single.go
@@ -0,0 +1,619 @@
+// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.
+
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	math "gonum.org/v1/gonum/internal/math32"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/internal/asm/f32"
+)
+
+var _ blas.Float32Level1 = Implementation{}
+
+// Snrm2 computes the Euclidean norm of a vector,
+//  sqrt(\sum_i x[i] * x[i]).
+// This function returns 0 if incX is negative.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Snrm2(n int, x []float32, incX int) float32 {
+	if incX < 1 {
+		if incX == 0 {
+			panic(zeroIncX)
+		}
+		return 0
+	}
+	if incX > 0 && (n-1)*incX >= len(x) {
+		panic(badX)
+	}
+	if n < 2 {
+		if n == 1 {
+			return math.Abs(x[0])
+		}
+		if n == 0 {
+			return 0
+		}
+		if n < 1 {
+			panic(negativeN)
+		}
+	}
+	var (
+		scale      float32 = 0
+		sumSquares float32 = 1
+	)
+	if incX == 1 {
+		x = x[:n]
+		for _, v := range x {
+			if v == 0 {
+				continue
+			}
+			absxi := math.Abs(v)
+			if math.IsNaN(absxi) {
+				return math.NaN()
+			}
+			if scale < absxi {
+				sumSquares = 1 + sumSquares*(scale/absxi)*(scale/absxi)
+				scale = absxi
+			} else {
+				sumSquares = sumSquares + (absxi/scale)*(absxi/scale)
+			}
+		}
+		if math.IsInf(scale, 1) {
+			return math.Inf(1)
+		}
+		return scale * math.Sqrt(sumSquares)
+	}
+	for ix := 0; ix < n*incX; ix += incX {
+		val := x[ix]
+		if val == 0 {
+			continue
+		}
+		absxi := math.Abs(val)
+		if math.IsNaN(absxi) {
+			return math.NaN()
+		}
+		if scale < absxi {
+			sumSquares = 1 + sumSquares*(scale/absxi)*(scale/absxi)
+			scale = absxi
+		} else {
+			sumSquares = sumSquares + (absxi/scale)*(absxi/scale)
+		}
+	}
+	if math.IsInf(scale, 1) {
+		return math.Inf(1)
+	}
+	return scale * math.Sqrt(sumSquares)
+}
+
+// Sasum computes the sum of the absolute values of the elements of x.
+//  \sum_i |x[i]|
+// Sasum returns 0 if incX is negative.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Sasum(n int, x []float32, incX int) float32 {
+	var sum float32
+	if n < 0 {
+		panic(negativeN)
+	}
+	if incX < 1 {
+		if incX == 0 {
+			panic(zeroIncX)
+		}
+		return 0
+	}
+	if incX > 0 && (n-1)*incX >= len(x) {
+		panic(badX)
+	}
+	if incX == 1 {
+		x = x[:n]
+		for _, v := range x {
+			sum += math.Abs(v)
+		}
+		return sum
+	}
+	for i := 0; i < n; i++ {
+		sum += math.Abs(x[i*incX])
+	}
+	return sum
+}
+
+// Isamax returns the index of an element of x with the largest absolute value.
+// If there are multiple such indices the earliest is returned.
+// Isamax returns -1 if n == 0.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Isamax(n int, x []float32, incX int) int {
+	if incX < 1 {
+		if incX == 0 {
+			panic(zeroIncX)
+		}
+		return -1
+	}
+	if incX > 0 && (n-1)*incX >= len(x) {
+		panic(badX)
+	}
+	if n < 2 {
+		if n == 1 {
+			return 0
+		}
+		if n == 0 {
+			return -1 // Netlib returns invalid index when n == 0
+		}
+		if n < 1 {
+			panic(negativeN)
+		}
+	}
+	idx := 0
+	max := math.Abs(x[0])
+	if incX == 1 {
+		for i, v := range x[:n] {
+			absV := math.Abs(v)
+			if absV > max {
+				max = absV
+				idx = i
+			}
+		}
+		return idx
+	}
+	ix := incX
+	for i := 1; i < n; i++ {
+		v := x[ix]
+		absV := math.Abs(v)
+		if absV > max {
+			max = absV
+			idx = i
+		}
+		ix += incX
+	}
+	return idx
+}
+
+// Sswap exchanges the elements of two vectors.
+//  x[i], y[i] = y[i], x[i] for all i
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Sswap(n int, x []float32, incX int, y []float32, incY int) {
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if n < 1 {
+		if n == 0 {
+			return
+		}
+		panic(negativeN)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
+		panic(badY)
+	}
+	if incX == 1 && incY == 1 {
+		x = x[:n]
+		for i, v := range x {
+			x[i], y[i] = y[i], v
+		}
+		return
+	}
+	var ix, iy int
+	if incX < 0 {
+		ix = (-n + 1) * incX
+	}
+	if incY < 0 {
+		iy = (-n + 1) * incY
+	}
+	for i := 0; i < n; i++ {
+		x[ix], y[iy] = y[iy], x[ix]
+		ix += incX
+		iy += incY
+	}
+}
+
+// Scopy copies the elements of x into the elements of y.
+//  y[i] = x[i] for all i
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Scopy(n int, x []float32, incX int, y []float32, incY int) {
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if n < 1 {
+		if n == 0 {
+			return
+		}
+		panic(negativeN)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
+		panic(badY)
+	}
+	if incX == 1 && incY == 1 {
+		copy(y[:n], x[:n])
+		return
+	}
+	var ix, iy int
+	if incX < 0 {
+		ix = (-n + 1) * incX
+	}
+	if incY < 0 {
+		iy = (-n + 1) * incY
+	}
+	for i := 0; i < n; i++ {
+		y[iy] = x[ix]
+		ix += incX
+		iy += incY
+	}
+}
+
+// Saxpy adds alpha times x to y
+//  y[i] += alpha * x[i] for all i
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Saxpy(n int, alpha float32, x []float32, incX int, y []float32, incY int) {
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if n < 1 {
+		if n == 0 {
+			return
+		}
+		panic(negativeN)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
+		panic(badY)
+	}
+	if alpha == 0 {
+		return
+	}
+	if incX == 1 && incY == 1 {
+		f32.AxpyUnitary(alpha, x[:n], y[:n])
+		return
+	}
+	var ix, iy int
+	if incX < 0 {
+		ix = (-n + 1) * incX
+	}
+	if incY < 0 {
+		iy = (-n + 1) * incY
+	}
+	f32.AxpyInc(alpha, x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
+}
+
+// Srotg computes the plane rotation
+//   _    _      _ _       _ _
+//  |  c s |    | a |     | r |
+//  | -s c |  * | b |   = | 0 |
+//   ‾    ‾      ‾ ‾       ‾ ‾
+// where
+//  r = ±√(a^2 + b^2)
+//  c = a/r, the cosine of the plane rotation
+//  s = b/r, the sine of the plane rotation
+//
+// NOTE: There is a discrepancy between the refence implementation and the BLAS
+// technical manual regarding the sign for r when a or b are zero.
+// Srotg agrees with the definition in the manual and other
+// common BLAS implementations.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Srotg(a, b float32) (c, s, r, z float32) {
+	if b == 0 && a == 0 {
+		return 1, 0, a, 0
+	}
+	absA := math.Abs(a)
+	absB := math.Abs(b)
+	aGTb := absA > absB
+	r = math.Hypot(a, b)
+	if aGTb {
+		r = math.Copysign(r, a)
+	} else {
+		r = math.Copysign(r, b)
+	}
+	c = a / r
+	s = b / r
+	if aGTb {
+		z = s
+	} else if c != 0 { // r == 0 case handled above
+		z = 1 / c
+	} else {
+		z = 1
+	}
+	return
+}
+
+// Srotmg computes the modified Givens rotation. See
+// http://www.netlib.org/lapack/explore-html/df/deb/drotmg_8f.html
+// for more details.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Srotmg(d1, d2, x1, y1 float32) (p blas.SrotmParams, rd1, rd2, rx1 float32) {
+	var p1, p2, q1, q2, u float32
+
+	const (
+		gam    = 4096.0
+		gamsq  = 16777216.0
+		rgamsq = 5.9604645e-8
+	)
+
+	if d1 < 0 {
+		p.Flag = blas.Rescaling
+		return
+	}
+
+	p2 = d2 * y1
+	if p2 == 0 {
+		p.Flag = blas.Identity
+		rd1 = d1
+		rd2 = d2
+		rx1 = x1
+		return
+	}
+	p1 = d1 * x1
+	q2 = p2 * y1
+	q1 = p1 * x1
+
+	absQ1 := math.Abs(q1)
+	absQ2 := math.Abs(q2)
+
+	if absQ1 < absQ2 && q2 < 0 {
+		p.Flag = blas.Rescaling
+		return
+	}
+
+	if d1 == 0 {
+		p.Flag = blas.Diagonal
+		p.H[0] = p1 / p2
+		p.H[3] = x1 / y1
+		u = 1 + p.H[0]*p.H[3]
+		rd1, rd2 = d2/u, d1/u
+		rx1 = y1 / u
+		return
+	}
+
+	// Now we know that d1 != 0, and d2 != 0. If d2 == 0, it would be caught
+	// when p2 == 0, and if d1 == 0, then it is caught above
+
+	if absQ1 > absQ2 {
+		p.H[1] = -y1 / x1
+		p.H[2] = p2 / p1
+		u = 1 - p.H[2]*p.H[1]
+		rd1 = d1
+		rd2 = d2
+		rx1 = x1
+		p.Flag = blas.OffDiagonal
+		// u must be greater than zero because |q1| > |q2|, so check from netlib
+		// is unnecessary
+		// This is left in for ease of comparison with complex routines
+		//if u > 0 {
+		rd1 /= u
+		rd2 /= u
+		rx1 *= u
+		//}
+	} else {
+		p.Flag = blas.Diagonal
+		p.H[0] = p1 / p2
+		p.H[3] = x1 / y1
+		u = 1 + p.H[0]*p.H[3]
+		rd1 = d2 / u
+		rd2 = d1 / u
+		rx1 = y1 * u
+	}
+
+	for rd1 <= rgamsq || rd1 >= gamsq {
+		if p.Flag == blas.OffDiagonal {
+			p.H[0] = 1
+			p.H[3] = 1
+			p.Flag = blas.Rescaling
+		} else if p.Flag == blas.Diagonal {
+			p.H[1] = -1
+			p.H[2] = 1
+			p.Flag = blas.Rescaling
+		}
+		if rd1 <= rgamsq {
+			rd1 *= gam * gam
+			rx1 /= gam
+			p.H[0] /= gam
+			p.H[2] /= gam
+		} else {
+			rd1 /= gam * gam
+			rx1 *= gam
+			p.H[0] *= gam
+			p.H[2] *= gam
+		}
+	}
+
+	for math.Abs(rd2) <= rgamsq || math.Abs(rd2) >= gamsq {
+		if p.Flag == blas.OffDiagonal {
+			p.H[0] = 1
+			p.H[3] = 1
+			p.Flag = blas.Rescaling
+		} else if p.Flag == blas.Diagonal {
+			p.H[1] = -1
+			p.H[2] = 1
+			p.Flag = blas.Rescaling
+		}
+		if math.Abs(rd2) <= rgamsq {
+			rd2 *= gam * gam
+			p.H[1] /= gam
+			p.H[3] /= gam
+		} else {
+			rd2 /= gam * gam
+			p.H[1] *= gam
+			p.H[3] *= gam
+		}
+	}
+	return
+}
+
+// Srot applies a plane transformation.
+//  x[i] = c * x[i] + s * y[i]
+//  y[i] = c * y[i] - s * x[i]
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Srot(n int, x []float32, incX int, y []float32, incY int, c float32, s float32) {
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if n < 1 {
+		if n == 0 {
+			return
+		}
+		panic(negativeN)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
+		panic(badY)
+	}
+	if incX == 1 && incY == 1 {
+		x = x[:n]
+		for i, vx := range x {
+			vy := y[i]
+			x[i], y[i] = c*vx+s*vy, c*vy-s*vx
+		}
+		return
+	}
+	var ix, iy int
+	if incX < 0 {
+		ix = (-n + 1) * incX
+	}
+	if incY < 0 {
+		iy = (-n + 1) * incY
+	}
+	for i := 0; i < n; i++ {
+		vx := x[ix]
+		vy := y[iy]
+		x[ix], y[iy] = c*vx+s*vy, c*vy-s*vx
+		ix += incX
+		iy += incY
+	}
+}
+
+// Srotm applies the modified Givens rotation to the 2×n matrix.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Srotm(n int, x []float32, incX int, y []float32, incY int, p blas.SrotmParams) {
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if n <= 0 {
+		if n == 0 {
+			return
+		}
+		panic(negativeN)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
+		panic(badY)
+	}
+
+	var h11, h12, h21, h22 float32
+	var ix, iy int
+	switch p.Flag {
+	case blas.Identity:
+		return
+	case blas.Rescaling:
+		h11 = p.H[0]
+		h12 = p.H[2]
+		h21 = p.H[1]
+		h22 = p.H[3]
+	case blas.OffDiagonal:
+		h11 = 1
+		h12 = p.H[2]
+		h21 = p.H[1]
+		h22 = 1
+	case blas.Diagonal:
+		h11 = p.H[0]
+		h12 = 1
+		h21 = -1
+		h22 = p.H[3]
+	}
+	if incX < 0 {
+		ix = (-n + 1) * incX
+	}
+	if incY < 0 {
+		iy = (-n + 1) * incY
+	}
+	if incX == 1 && incY == 1 {
+		x = x[:n]
+		for i, vx := range x {
+			vy := y[i]
+			x[i], y[i] = vx*h11+vy*h12, vx*h21+vy*h22
+		}
+		return
+	}
+	for i := 0; i < n; i++ {
+		vx := x[ix]
+		vy := y[iy]
+		x[ix], y[iy] = vx*h11+vy*h12, vx*h21+vy*h22
+		ix += incX
+		iy += incY
+	}
+}
+
+// Sscal scales x by alpha.
+//  x[i] *= alpha
+// Sscal has no effect if incX < 0.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Sscal(n int, alpha float32, x []float32, incX int) {
+	if incX < 1 {
+		if incX == 0 {
+			panic(zeroIncX)
+		}
+		return
+	}
+	if (n-1)*incX >= len(x) {
+		panic(badX)
+	}
+	if n < 1 {
+		if n == 0 {
+			return
+		}
+		panic(negativeN)
+	}
+	if alpha == 0 {
+		if incX == 1 {
+			x = x[:n]
+			for i := range x {
+				x[i] = 0
+			}
+			return
+		}
+		for ix := 0; ix < n*incX; ix += incX {
+			x[ix] = 0
+		}
+		return
+	}
+	if incX == 1 {
+		f32.ScalUnitary(alpha, x[:n])
+		return
+	}
+	f32.ScalInc(alpha, x, uintptr(n), uintptr(incX))
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/level1single_dsdot.go b/vendor/gonum.org/v1/gonum/blas/gonum/level1single_dsdot.go
new file mode 100644
index 00000000..cfe6e75b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/level1single_dsdot.go
@@ -0,0 +1,53 @@
+// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.
+
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/internal/asm/f32"
+)
+
+// Dsdot computes the dot product of the two vectors
+//  \sum_i x[i]*y[i]
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Dsdot(n int, x []float32, incX int, y []float32, incY int) float64 {
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if n <= 0 {
+		if n == 0 {
+			return 0
+		}
+		panic(negativeN)
+	}
+	if incX == 1 && incY == 1 {
+		if len(x) < n {
+			panic(badLenX)
+		}
+		if len(y) < n {
+			panic(badLenY)
+		}
+		return f32.DdotUnitary(x[:n], y)
+	}
+	var ix, iy int
+	if incX < 0 {
+		ix = (-n + 1) * incX
+	}
+	if incY < 0 {
+		iy = (-n + 1) * incY
+	}
+	if ix >= len(x) || ix+(n-1)*incX >= len(x) {
+		panic(badLenX)
+	}
+	if iy >= len(y) || iy+(n-1)*incY >= len(y) {
+		panic(badLenY)
+	}
+	return f32.DdotInc(x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/level1single_sdot.go b/vendor/gonum.org/v1/gonum/blas/gonum/level1single_sdot.go
new file mode 100644
index 00000000..cf930ecf
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/level1single_sdot.go
@@ -0,0 +1,53 @@
+// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.
+
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/internal/asm/f32"
+)
+
+// Sdot computes the dot product of the two vectors
+//  \sum_i x[i]*y[i]
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Sdot(n int, x []float32, incX int, y []float32, incY int) float32 {
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if n <= 0 {
+		if n == 0 {
+			return 0
+		}
+		panic(negativeN)
+	}
+	if incX == 1 && incY == 1 {
+		if len(x) < n {
+			panic(badLenX)
+		}
+		if len(y) < n {
+			panic(badLenY)
+		}
+		return f32.DotUnitary(x[:n], y)
+	}
+	var ix, iy int
+	if incX < 0 {
+		ix = (-n + 1) * incX
+	}
+	if incY < 0 {
+		iy = (-n + 1) * incY
+	}
+	if ix >= len(x) || ix+(n-1)*incX >= len(x) {
+		panic(badLenX)
+	}
+	if iy >= len(y) || iy+(n-1)*incY >= len(y) {
+		panic(badLenY)
+	}
+	return f32.DotInc(x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/level1single_sdsdot.go b/vendor/gonum.org/v1/gonum/blas/gonum/level1single_sdsdot.go
new file mode 100644
index 00000000..600c2f99
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/level1single_sdsdot.go
@@ -0,0 +1,53 @@
+// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.
+
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/internal/asm/f32"
+)
+
+// Sdsdot computes the dot product of the two vectors plus a constant
+//  alpha + \sum_i x[i]*y[i]
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Sdsdot(n int, alpha float32, x []float32, incX int, y []float32, incY int) float32 {
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if n <= 0 {
+		if n == 0 {
+			return 0
+		}
+		panic(negativeN)
+	}
+	if incX == 1 && incY == 1 {
+		if len(x) < n {
+			panic(badLenX)
+		}
+		if len(y) < n {
+			panic(badLenY)
+		}
+		return alpha + float32(f32.DdotUnitary(x[:n], y))
+	}
+	var ix, iy int
+	if incX < 0 {
+		ix = (-n + 1) * incX
+	}
+	if incY < 0 {
+		iy = (-n + 1) * incY
+	}
+	if ix >= len(x) || ix+(n-1)*incX >= len(x) {
+		panic(badLenX)
+	}
+	if iy >= len(y) || iy+(n-1)*incY >= len(y) {
+		panic(badLenY)
+	}
+	return alpha + float32(f32.DdotInc(x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy)))
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/level2cmplx128.go b/vendor/gonum.org/v1/gonum/blas/gonum/level2cmplx128.go
new file mode 100644
index 00000000..ca241752
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/level2cmplx128.go
@@ -0,0 +1,289 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math/cmplx"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/internal/asm/c128"
+)
+
+// Zgerc performs the rank-one operation
+//  A += alpha * x * y^H
+// where A is an m×n dense matrix, alpha is a scalar, x is an m element vector,
+// and y is an n element vector.
+func (Implementation) Zgerc(m, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, a []complex128, lda int) {
+	checkZMatrix('A', m, n, a, lda)
+	checkZVector('x', m, x, incX)
+	checkZVector('y', n, y, incY)
+
+	if m == 0 || n == 0 || alpha == 0 {
+		return
+	}
+
+	var kx, jy int
+	if incX < 0 {
+		kx = (1 - m) * incX
+	}
+	if incY < 0 {
+		jy = (1 - n) * incY
+	}
+	for j := 0; j < n; j++ {
+		if y[jy] != 0 {
+			tmp := alpha * cmplx.Conj(y[jy])
+			c128.AxpyInc(tmp, x, a[j:], uintptr(m), uintptr(incX), uintptr(lda), uintptr(kx), 0)
+		}
+		jy += incY
+	}
+}
+
+// Zgeru performs the rank-one operation
+//  A += alpha * x * y^T
+// where A is an m×n dense matrix, alpha is a scalar, x is an m element vector,
+// and y is an n element vector.
+func (Implementation) Zgeru(m, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, a []complex128, lda int) {
+	checkZMatrix('A', m, n, a, lda)
+	checkZVector('x', m, x, incX)
+	checkZVector('y', n, y, incY)
+
+	if m == 0 || n == 0 || alpha == 0 {
+		return
+	}
+
+	var kx int
+	if incX < 0 {
+		kx = (1 - m) * incX
+	}
+	if incY == 1 {
+		for i := 0; i < m; i++ {
+			if x[kx] != 0 {
+				tmp := alpha * x[kx]
+				c128.AxpyUnitary(tmp, y[:n], a[i*lda:i*lda+n])
+			}
+			kx += incX
+		}
+		return
+	}
+	var jy int
+	if incY < 0 {
+		jy = (1 - n) * incY
+	}
+	for i := 0; i < m; i++ {
+		if x[kx] != 0 {
+			tmp := alpha * x[kx]
+			c128.AxpyInc(tmp, y, a[i*lda:i*lda+n], uintptr(n), uintptr(incY), 1, uintptr(jy), 0)
+		}
+		kx += incX
+	}
+}
+
+// Zher performs the Hermitian rank-one operation
+//  A += alpha * x * x^H
+// where A is an n×n Hermitian matrix, alpha is a real scalar, and x is an n
+// element vector. On entry, the imaginary parts of the diagonal elements of A
+// are ignored and assumed to be zero, on return they will be set to zero.
+func (Implementation) Zher(uplo blas.Uplo, n int, alpha float64, x []complex128, incX int, a []complex128, lda int) {
+	if uplo != blas.Upper && uplo != blas.Lower {
+		panic(badUplo)
+	}
+	checkZMatrix('A', n, n, a, lda)
+	checkZVector('x', n, x, incX)
+
+	if n == 0 || alpha == 0 {
+		return
+	}
+
+	var kx int
+	if incX < 0 {
+		kx = (1 - n) * incX
+	}
+	if uplo == blas.Upper {
+		if incX == 1 {
+			for i := 0; i < n; i++ {
+				if x[i] != 0 {
+					tmp := complex(alpha*real(x[i]), alpha*imag(x[i]))
+					aii := real(a[i*lda+i])
+					xtmp := real(tmp * cmplx.Conj(x[i]))
+					a[i*lda+i] = complex(aii+xtmp, 0)
+					for j := i + 1; j < n; j++ {
+						a[i*lda+j] += tmp * cmplx.Conj(x[j])
+					}
+				} else {
+					aii := real(a[i*lda+i])
+					a[i*lda+i] = complex(aii, 0)
+				}
+			}
+			return
+		}
+
+		ix := kx
+		for i := 0; i < n; i++ {
+			if x[ix] != 0 {
+				tmp := complex(alpha*real(x[ix]), alpha*imag(x[ix]))
+				aii := real(a[i*lda+i])
+				xtmp := real(tmp * cmplx.Conj(x[ix]))
+				a[i*lda+i] = complex(aii+xtmp, 0)
+				jx := ix + incX
+				for j := i + 1; j < n; j++ {
+					a[i*lda+j] += tmp * cmplx.Conj(x[jx])
+					jx += incX
+				}
+			} else {
+				aii := real(a[i*lda+i])
+				a[i*lda+i] = complex(aii, 0)
+			}
+			ix += incX
+		}
+		return
+	}
+
+	if incX == 1 {
+		for i := 0; i < n; i++ {
+			if x[i] != 0 {
+				tmp := complex(alpha*real(x[i]), alpha*imag(x[i]))
+				for j := 0; j < i; j++ {
+					a[i*lda+j] += tmp * cmplx.Conj(x[j])
+				}
+				aii := real(a[i*lda+i])
+				xtmp := real(tmp * cmplx.Conj(x[i]))
+				a[i*lda+i] = complex(aii+xtmp, 0)
+			} else {
+				aii := real(a[i*lda+i])
+				a[i*lda+i] = complex(aii, 0)
+			}
+		}
+		return
+	}
+
+	ix := kx
+	for i := 0; i < n; i++ {
+		if x[ix] != 0 {
+			tmp := complex(alpha*real(x[ix]), alpha*imag(x[ix]))
+			jx := kx
+			for j := 0; j < i; j++ {
+				a[i*lda+j] += tmp * cmplx.Conj(x[jx])
+				jx += incX
+			}
+			aii := real(a[i*lda+i])
+			xtmp := real(tmp * cmplx.Conj(x[ix]))
+			a[i*lda+i] = complex(aii+xtmp, 0)
+
+		} else {
+			aii := real(a[i*lda+i])
+			a[i*lda+i] = complex(aii, 0)
+		}
+		ix += incX
+	}
+}
+
+// Zher2 performs the Hermitian rank-two operation
+//  A += alpha*x*y^H + conj(alpha)*y*x^H
+// where alpha is a scalar, x and y are n element vectors and A is an n×n
+// Hermitian matrix. On entry, the imaginary parts of the diagonal elements are
+// ignored and assumed to be zero. On return they will be set to zero.
+func (Implementation) Zher2(uplo blas.Uplo, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, a []complex128, lda int) {
+	if uplo != blas.Upper && uplo != blas.Lower {
+		panic(badUplo)
+	}
+	checkZMatrix('A', n, n, a, lda)
+	checkZVector('x', n, x, incX)
+	checkZVector('y', n, y, incY)
+
+	if n == 0 || alpha == 0 {
+		return
+	}
+
+	var kx, ky int
+	var ix, iy int
+	if incX != 1 || incY != 1 {
+		if incX < 0 {
+			kx = (1 - n) * incX
+		}
+		if incY < 0 {
+			ky = (1 - n) * incY
+		}
+		ix = kx
+		iy = ky
+	}
+	if uplo == blas.Upper {
+		if incX == 1 && incY == 1 {
+			for i := 0; i < n; i++ {
+				if x[i] != 0 || y[i] != 0 {
+					tmp1 := alpha * x[i]
+					tmp2 := cmplx.Conj(alpha) * y[i]
+					aii := real(a[i*lda+i]) + real(tmp1*cmplx.Conj(y[i])) + real(tmp2*cmplx.Conj(x[i]))
+					a[i*lda+i] = complex(aii, 0)
+					for j := i + 1; j < n; j++ {
+						a[i*lda+j] += tmp1*cmplx.Conj(y[j]) + tmp2*cmplx.Conj(x[j])
+					}
+				} else {
+					aii := real(a[i*lda+i])
+					a[i*lda+i] = complex(aii, 0)
+				}
+			}
+			return
+		}
+		for i := 0; i < n; i++ {
+			if x[i] != 0 || y[i] != 0 {
+				tmp1 := alpha * x[ix]
+				tmp2 := cmplx.Conj(alpha) * y[iy]
+				aii := real(a[i*lda+i]) + real(tmp1*cmplx.Conj(y[iy])) + real(tmp2*cmplx.Conj(x[ix]))
+				a[i*lda+i] = complex(aii, 0)
+				jx := ix + incX
+				jy := iy + incY
+				for j := i + 1; j < n; j++ {
+					a[i*lda+j] += tmp1*cmplx.Conj(y[jy]) + tmp2*cmplx.Conj(x[jx])
+					jx += incX
+					jy += incY
+				}
+			} else {
+				aii := real(a[i*lda+i])
+				a[i*lda+i] = complex(aii, 0)
+			}
+			ix += incX
+			iy += incY
+		}
+		return
+	}
+
+	if incX == 1 && incY == 1 {
+		for i := 0; i < n; i++ {
+			if x[i] != 0 || y[i] != 0 {
+				tmp1 := alpha * x[i]
+				tmp2 := cmplx.Conj(alpha) * y[i]
+				for j := 0; j < i; j++ {
+					a[i*lda+j] += tmp1*cmplx.Conj(y[j]) + tmp2*cmplx.Conj(x[j])
+				}
+				aii := real(a[i*lda+i]) + real(tmp1*cmplx.Conj(y[i])) + real(tmp2*cmplx.Conj(x[i]))
+				a[i*lda+i] = complex(aii, 0)
+			} else {
+				aii := real(a[i*lda+i])
+				a[i*lda+i] = complex(aii, 0)
+			}
+		}
+		return
+	}
+	for i := 0; i < n; i++ {
+		if x[i] != 0 || y[i] != 0 {
+			tmp1 := alpha * x[ix]
+			tmp2 := cmplx.Conj(alpha) * y[iy]
+			jx := kx
+			jy := ky
+			for j := 0; j < i; j++ {
+				a[i*lda+j] += tmp1*cmplx.Conj(y[jy]) + tmp2*cmplx.Conj(x[jx])
+				jx += incX
+				jy += incY
+			}
+			aii := real(a[i*lda+i]) + real(tmp1*cmplx.Conj(y[iy])) + real(tmp2*cmplx.Conj(x[ix]))
+			a[i*lda+i] = complex(aii, 0)
+		} else {
+			aii := real(a[i*lda+i])
+			a[i*lda+i] = complex(aii, 0)
+		}
+		ix += incX
+		iy += incY
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/level2cmplx128_bench_test.go b/vendor/gonum.org/v1/gonum/blas/gonum/level2cmplx128_bench_test.go
new file mode 100644
index 00000000..915a1918
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/level2cmplx128_bench_test.go
@@ -0,0 +1,49 @@
+// Copyright ©2017 The Gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build go1.7
+
+package gonum
+
+import (
+	"fmt"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+var benchSinkZ []complex128
+
+func BenchmarkZher(b *testing.B) {
+	for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
+		for _, n := range []int{10, 100, 1000, 10000} {
+			for _, inc := range []int{1, 10, 1000} {
+				benchmarkZher(b, uplo, n, inc)
+			}
+		}
+	}
+}
+
+func benchmarkZher(b *testing.B, uplo blas.Uplo, n, inc int) {
+	b.Run(fmt.Sprintf("Uplo%d-N%d-Inc%d", uplo, n, inc), func(b *testing.B) {
+		rnd := rand.New(rand.NewSource(1))
+		alpha := rnd.NormFloat64()
+		x := make([]complex128, (n-1)*inc+1)
+		for i := range x {
+			x[i] = complex(rnd.NormFloat64(), rnd.NormFloat64())
+		}
+		a := make([]complex128, len(benchSinkZ))
+		for i := range a {
+			a[i] = complex(rnd.NormFloat64(), rnd.NormFloat64())
+		}
+		benchSinkZ = make([]complex128, n*n)
+		copy(benchSinkZ, a)
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			impl.Zher(uplo, n, alpha, x, inc, benchSinkZ, n)
+			copy(benchSinkZ, a)
+		}
+	})
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/level2cmplx128_test.go b/vendor/gonum.org/v1/gonum/blas/gonum/level2cmplx128_test.go
new file mode 100644
index 00000000..0649675a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/level2cmplx128_test.go
@@ -0,0 +1,27 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas/testblas"
+)
+
+func TestZgerc(t *testing.T) {
+	testblas.ZgercTest(t, impl)
+}
+
+func TestZgeru(t *testing.T) {
+	testblas.ZgeruTest(t, impl)
+}
+
+func TestZher(t *testing.T) {
+	testblas.ZherTest(t, impl)
+}
+
+func TestZher2(t *testing.T) {
+	testblas.Zher2Test(t, impl)
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/level2double.go b/vendor/gonum.org/v1/gonum/blas/gonum/level2double.go
new file mode 100644
index 00000000..9b828c2e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/level2double.go
@@ -0,0 +1,2234 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/internal/asm/f64"
+)
+
+var _ blas.Float64Level2 = Implementation{}
+
+// Dgemv computes
+//  y = alpha * a * x + beta * y if tA = blas.NoTrans
+//  y = alpha * A^T * x + beta * y if tA = blas.Trans or blas.ConjTrans
+// where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.
+func (Implementation) Dgemv(tA blas.Transpose, m, n int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int) {
+	if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	if m < 0 {
+		panic(mLT0)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if lda < max(1, n) {
+		panic(badLdA)
+	}
+
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	// Set up indexes
+	lenX := m
+	lenY := n
+	if tA == blas.NoTrans {
+		lenX = n
+		lenY = m
+	}
+	if (incX > 0 && (lenX-1)*incX >= len(x)) || (incX < 0 && (1-lenX)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (lenY-1)*incY >= len(y)) || (incY < 0 && (1-lenY)*incY >= len(y)) {
+		panic(badY)
+	}
+	if lda*(m-1)+n > len(a) || lda < max(1, n) {
+		panic(badLdA)
+	}
+
+	// Quick return if possible
+	if m == 0 || n == 0 || (alpha == 0 && beta == 1) {
+		return
+	}
+
+	var kx, ky int
+	if incX > 0 {
+		kx = 0
+	} else {
+		kx = -(lenX - 1) * incX
+	}
+	if incY > 0 {
+		ky = 0
+	} else {
+		ky = -(lenY - 1) * incY
+	}
+
+	// First form y := beta * y
+	if incY > 0 {
+		Implementation{}.Dscal(lenY, beta, y, incY)
+	} else {
+		Implementation{}.Dscal(lenY, beta, y, -incY)
+	}
+
+	if alpha == 0 {
+		return
+	}
+
+	// Form y := alpha * A * x + y
+	if tA == blas.NoTrans {
+		if incX == 1 && incY == 1 {
+			for i := 0; i < m; i++ {
+				y[i] += alpha * f64.DotUnitary(a[lda*i:lda*i+n], x)
+			}
+			return
+		}
+		iy := ky
+		for i := 0; i < m; i++ {
+			y[iy] += alpha * f64.DotInc(x, a[lda*i:lda*i+n], uintptr(n), uintptr(incX), 1, uintptr(kx), 0)
+			iy += incY
+		}
+		return
+	}
+	// Cases where a is transposed.
+	if incX == 1 && incY == 1 {
+		for i := 0; i < m; i++ {
+			tmp := alpha * x[i]
+			if tmp != 0 {
+				f64.AxpyUnitaryTo(y, tmp, a[lda*i:lda*i+n], y)
+			}
+		}
+		return
+	}
+	ix := kx
+	for i := 0; i < m; i++ {
+		tmp := alpha * x[ix]
+		if tmp != 0 {
+			f64.AxpyInc(tmp, a[lda*i:lda*i+n], y, uintptr(n), 1, uintptr(incY), 0, uintptr(ky))
+		}
+		ix += incX
+	}
+}
+
+// Dger performs the rank-one operation
+//  A += alpha * x * y^T
+// where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.
+func (Implementation) Dger(m, n int, alpha float64, x []float64, incX int, y []float64, incY int, a []float64, lda int) {
+	// Check inputs
+	if m < 0 {
+		panic("m < 0")
+	}
+	if n < 0 {
+		panic(negativeN)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if (incX > 0 && (m-1)*incX >= len(x)) || (incX < 0 && (1-m)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
+		panic(badY)
+	}
+	if lda*(m-1)+n > len(a) || lda < max(1, n) {
+		panic(badLdA)
+	}
+	if lda < max(1, n) {
+		panic(badLdA)
+	}
+
+	// Quick return if possible
+	if m == 0 || n == 0 || alpha == 0 {
+		return
+	}
+
+	var ky, kx int
+	if incY > 0 {
+		ky = 0
+	} else {
+		ky = -(n - 1) * incY
+	}
+
+	if incX > 0 {
+		kx = 0
+	} else {
+		kx = -(m - 1) * incX
+	}
+
+	if incX == 1 && incY == 1 {
+		x = x[:m]
+		y = y[:n]
+		for i, xv := range x {
+			tmp := alpha * xv
+			if tmp != 0 {
+				atmp := a[i*lda : i*lda+n]
+				f64.AxpyUnitaryTo(atmp, tmp, y, atmp)
+			}
+		}
+		return
+	}
+
+	ix := kx
+	for i := 0; i < m; i++ {
+		tmp := alpha * x[ix]
+		if tmp != 0 {
+			f64.AxpyInc(tmp, y, a[i*lda:i*lda+n], uintptr(n), uintptr(incY), 1, uintptr(ky), 0)
+		}
+		ix += incX
+	}
+}
+
+// Dgbmv computes
+//  y = alpha * A * x + beta * y if tA == blas.NoTrans
+//  y = alpha * A^T * x + beta * y if tA == blas.Trans or blas.ConjTrans
+// where a is an m×n band matrix kL subdiagonals and kU super-diagonals, and
+// m and n refer to the size of the full dense matrix it represents.
+// x and y are vectors, and alpha and beta are scalars.
+func (Implementation) Dgbmv(tA blas.Transpose, m, n, kL, kU int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int) {
+	if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	if m < 0 {
+		panic(mLT0)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if kL < 0 {
+		panic(kLLT0)
+	}
+	if kL < 0 {
+		panic(kULT0)
+	}
+	if lda < kL+kU+1 {
+		panic(badLdA)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	// Set up indexes
+	lenX := m
+	lenY := n
+	if tA == blas.NoTrans {
+		lenX = n
+		lenY = m
+	}
+	if (incX > 0 && (lenX-1)*incX >= len(x)) || (incX < 0 && (1-lenX)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (lenY-1)*incY >= len(y)) || (incY < 0 && (1-lenY)*incY >= len(y)) {
+		panic(badY)
+	}
+	if lda*(min(m, n+kL)-1)+kL+kU+1 > len(a) || lda < kL+kU+1 {
+		panic(badLdA)
+	}
+
+	// Quick return if possible
+	if m == 0 || n == 0 || (alpha == 0 && beta == 1) {
+		return
+	}
+
+	var kx, ky int
+	if incX > 0 {
+		kx = 0
+	} else {
+		kx = -(lenX - 1) * incX
+	}
+	if incY > 0 {
+		ky = 0
+	} else {
+		ky = -(lenY - 1) * incY
+	}
+
+	// First form y := beta * y
+	if incY > 0 {
+		Implementation{}.Dscal(lenY, beta, y, incY)
+	} else {
+		Implementation{}.Dscal(lenY, beta, y, -incY)
+	}
+
+	if alpha == 0 {
+		return
+	}
+
+	// i and j are indices of the compacted banded matrix.
+	// off is the offset into the dense matrix (off + j = densej)
+	ld := min(m, n)
+	nCol := kU + 1 + kL
+	if tA == blas.NoTrans {
+		iy := ky
+		if incX == 1 {
+			for i := 0; i < min(m, n+kL); i++ {
+				l := max(0, kL-i)
+				u := min(nCol, ld+kL-i)
+				off := max(0, i-kL)
+				atmp := a[i*lda+l : i*lda+u]
+				xtmp := x[off : off+u-l]
+				var sum float64
+				for j, v := range atmp {
+					sum += xtmp[j] * v
+				}
+				y[iy] += sum * alpha
+				iy += incY
+			}
+			return
+		}
+		for i := 0; i < min(m, n+kL); i++ {
+			l := max(0, kL-i)
+			u := min(nCol, ld+kL-i)
+			off := max(0, i-kL)
+			atmp := a[i*lda+l : i*lda+u]
+			jx := kx
+			var sum float64
+			for _, v := range atmp {
+				sum += x[off*incX+jx] * v
+				jx += incX
+			}
+			y[iy] += sum * alpha
+			iy += incY
+		}
+		return
+	}
+	if incX == 1 {
+		for i := 0; i < min(m, n+kL); i++ {
+			l := max(0, kL-i)
+			u := min(nCol, ld+kL-i)
+			off := max(0, i-kL)
+			atmp := a[i*lda+l : i*lda+u]
+			tmp := alpha * x[i]
+			jy := ky
+			for _, v := range atmp {
+				y[jy+off*incY] += tmp * v
+				jy += incY
+			}
+		}
+		return
+	}
+	ix := kx
+	for i := 0; i < min(m, n+kL); i++ {
+		l := max(0, kL-i)
+		u := min(nCol, ld+kL-i)
+		off := max(0, i-kL)
+		atmp := a[i*lda+l : i*lda+u]
+		tmp := alpha * x[ix]
+		jy := ky
+		for _, v := range atmp {
+			y[jy+off*incY] += tmp * v
+			jy += incY
+		}
+		ix += incX
+	}
+}
+
+// Dtrmv computes
+//  x = A * x if tA == blas.NoTrans
+//  x = A^T * x if tA == blas.Trans or blas.ConjTrans
+// A is an n×n Triangular matrix and x is a vector.
+func (Implementation) Dtrmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, a []float64, lda int, x []float64, incX int) {
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	if d != blas.NonUnit && d != blas.Unit {
+		panic(badDiag)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if lda < n {
+		panic(badLdA)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if lda*(n-1)+n > len(a) || lda < max(1, n) {
+		panic(badLdA)
+	}
+	if n == 0 {
+		return
+	}
+	nonUnit := d != blas.Unit
+	if n == 1 {
+		if nonUnit {
+			x[0] *= a[0]
+		}
+		return
+	}
+	var kx int
+	if incX <= 0 {
+		kx = -(n - 1) * incX
+	}
+	if tA == blas.NoTrans {
+		if ul == blas.Upper {
+			if incX == 1 {
+				for i := 0; i < n; i++ {
+					ilda := i * lda
+					var tmp float64
+					if nonUnit {
+						tmp = a[ilda+i] * x[i]
+					} else {
+						tmp = x[i]
+					}
+					xtmp := x[i+1:]
+					x[i] = tmp + f64.DotUnitary(a[ilda+i+1:ilda+n], xtmp)
+				}
+				return
+			}
+			ix := kx
+			for i := 0; i < n; i++ {
+				ilda := i * lda
+				var tmp float64
+				if nonUnit {
+					tmp = a[ilda+i] * x[ix]
+				} else {
+					tmp = x[ix]
+				}
+				x[ix] = tmp + f64.DotInc(x, a[ilda+i+1:ilda+n], uintptr(n-i-1), uintptr(incX), 1, uintptr(ix+incX), 0)
+				ix += incX
+			}
+			return
+		}
+		if incX == 1 {
+			for i := n - 1; i >= 0; i-- {
+				ilda := i * lda
+				var tmp float64
+				if nonUnit {
+					tmp += a[ilda+i] * x[i]
+				} else {
+					tmp = x[i]
+				}
+				x[i] = tmp + f64.DotUnitary(a[ilda:ilda+i], x)
+			}
+			return
+		}
+		ix := kx + (n-1)*incX
+		for i := n - 1; i >= 0; i-- {
+			ilda := i * lda
+			var tmp float64
+			if nonUnit {
+				tmp = a[ilda+i] * x[ix]
+			} else {
+				tmp = x[ix]
+			}
+			x[ix] = tmp + f64.DotInc(x, a[ilda:ilda+i], uintptr(i), uintptr(incX), 1, uintptr(kx), 0)
+			ix -= incX
+		}
+		return
+	}
+	// Cases where a is transposed.
+	if ul == blas.Upper {
+		if incX == 1 {
+			for i := n - 1; i >= 0; i-- {
+				ilda := i * lda
+				xi := x[i]
+				f64.AxpyUnitary(xi, a[ilda+i+1:ilda+n], x[i+1:n])
+				if nonUnit {
+					x[i] *= a[ilda+i]
+				}
+			}
+			return
+		}
+		ix := kx + (n-1)*incX
+		for i := n - 1; i >= 0; i-- {
+			ilda := i * lda
+			xi := x[ix]
+			f64.AxpyInc(xi, a[ilda+i+1:ilda+n], x, uintptr(n-i-1), 1, uintptr(incX), 0, uintptr(kx+(i+1)*incX))
+			if nonUnit {
+				x[ix] *= a[ilda+i]
+			}
+			ix -= incX
+		}
+		return
+	}
+	if incX == 1 {
+		for i := 0; i < n; i++ {
+			ilda := i * lda
+			xi := x[i]
+			f64.AxpyUnitary(xi, a[ilda:ilda+i], x)
+			if nonUnit {
+				x[i] *= a[i*lda+i]
+			}
+		}
+		return
+	}
+	ix := kx
+	for i := 0; i < n; i++ {
+		ilda := i * lda
+		xi := x[ix]
+		f64.AxpyInc(xi, a[ilda:ilda+i], x, uintptr(i), 1, uintptr(incX), 0, uintptr(kx))
+		if nonUnit {
+			x[ix] *= a[ilda+i]
+		}
+		ix += incX
+	}
+}
+
+// Dtrsv solves
+//  A * x = b if tA == blas.NoTrans
+//  A^T * x = b if tA == blas.Trans or blas.ConjTrans
+// A is an n×n triangular matrix and x is a vector.
+// At entry to the function, x contains the values of b, and the result is
+// stored in place into x.
+//
+// No test for singularity or near-singularity is included in this
+// routine. Such tests must be performed before calling this routine.
+func (Implementation) Dtrsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, a []float64, lda int, x []float64, incX int) {
+	// Test the input parameters
+	// Verify inputs
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	if d != blas.NonUnit && d != blas.Unit {
+		panic(badDiag)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if lda*(n-1)+n > len(a) || lda < max(1, n) {
+		panic(badLdA)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	// Quick return if possible
+	if n == 0 {
+		return
+	}
+	if n == 1 {
+		if d == blas.NonUnit {
+			x[0] /= a[0]
+		}
+		return
+	}
+
+	var kx int
+	if incX < 0 {
+		kx = -(n - 1) * incX
+	}
+	nonUnit := d == blas.NonUnit
+	if tA == blas.NoTrans {
+		if ul == blas.Upper {
+			if incX == 1 {
+				for i := n - 1; i >= 0; i-- {
+					var sum float64
+					atmp := a[i*lda+i+1 : i*lda+n]
+					for j, v := range atmp {
+						jv := i + j + 1
+						sum += x[jv] * v
+					}
+					x[i] -= sum
+					if nonUnit {
+						x[i] /= a[i*lda+i]
+					}
+				}
+				return
+			}
+			ix := kx + (n-1)*incX
+			for i := n - 1; i >= 0; i-- {
+				var sum float64
+				jx := ix + incX
+				atmp := a[i*lda+i+1 : i*lda+n]
+				for _, v := range atmp {
+					sum += x[jx] * v
+					jx += incX
+				}
+				x[ix] -= sum
+				if nonUnit {
+					x[ix] /= a[i*lda+i]
+				}
+				ix -= incX
+			}
+			return
+		}
+		if incX == 1 {
+			for i := 0; i < n; i++ {
+				var sum float64
+				atmp := a[i*lda : i*lda+i]
+				for j, v := range atmp {
+					sum += x[j] * v
+				}
+				x[i] -= sum
+				if nonUnit {
+					x[i] /= a[i*lda+i]
+				}
+			}
+			return
+		}
+		ix := kx
+		for i := 0; i < n; i++ {
+			jx := kx
+			var sum float64
+			atmp := a[i*lda : i*lda+i]
+			for _, v := range atmp {
+				sum += x[jx] * v
+				jx += incX
+			}
+			x[ix] -= sum
+			if nonUnit {
+				x[ix] /= a[i*lda+i]
+			}
+			ix += incX
+		}
+		return
+	}
+	// Cases where a is transposed.
+	if ul == blas.Upper {
+		if incX == 1 {
+			for i := 0; i < n; i++ {
+				if nonUnit {
+					x[i] /= a[i*lda+i]
+				}
+				xi := x[i]
+				atmp := a[i*lda+i+1 : i*lda+n]
+				for j, v := range atmp {
+					jv := j + i + 1
+					x[jv] -= v * xi
+				}
+			}
+			return
+		}
+		ix := kx
+		for i := 0; i < n; i++ {
+			if nonUnit {
+				x[ix] /= a[i*lda+i]
+			}
+			xi := x[ix]
+			jx := kx + (i+1)*incX
+			atmp := a[i*lda+i+1 : i*lda+n]
+			for _, v := range atmp {
+				x[jx] -= v * xi
+				jx += incX
+			}
+			ix += incX
+		}
+		return
+	}
+	if incX == 1 {
+		for i := n - 1; i >= 0; i-- {
+			if nonUnit {
+				x[i] /= a[i*lda+i]
+			}
+			xi := x[i]
+			atmp := a[i*lda : i*lda+i]
+			for j, v := range atmp {
+				x[j] -= v * xi
+			}
+		}
+		return
+	}
+	ix := kx + (n-1)*incX
+	for i := n - 1; i >= 0; i-- {
+		if nonUnit {
+			x[ix] /= a[i*lda+i]
+		}
+		xi := x[ix]
+		jx := kx
+		atmp := a[i*lda : i*lda+i]
+		for _, v := range atmp {
+			x[jx] -= v * xi
+			jx += incX
+		}
+		ix -= incX
+	}
+}
+
+// Dsymv computes
+//    y = alpha * A * x + beta * y,
+// where a is an n×n symmetric matrix, x and y are vectors, and alpha and
+// beta are scalars.
+func (Implementation) Dsymv(ul blas.Uplo, n int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int) {
+	// Check inputs
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if n < 0 {
+		panic(negativeN)
+	}
+	if lda > 1 && lda < n {
+		panic(badLdA)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
+		panic(badY)
+	}
+	if lda*(n-1)+n > len(a) || lda < max(1, n) {
+		panic(badLdA)
+	}
+	// Quick return if possible
+	if n == 0 || (alpha == 0 && beta == 1) {
+		return
+	}
+
+	// Set up start points
+	var kx, ky int
+	if incX > 0 {
+		kx = 0
+	} else {
+		kx = -(n - 1) * incX
+	}
+	if incY > 0 {
+		ky = 0
+	} else {
+		ky = -(n - 1) * incY
+	}
+
+	// Form y = beta * y
+	if beta != 1 {
+		if incY > 0 {
+			Implementation{}.Dscal(n, beta, y, incY)
+		} else {
+			Implementation{}.Dscal(n, beta, y, -incY)
+		}
+	}
+
+	if alpha == 0 {
+		return
+	}
+
+	if n == 1 {
+		y[0] += alpha * a[0] * x[0]
+		return
+	}
+
+	if ul == blas.Upper {
+		if incX == 1 {
+			iy := ky
+			for i := 0; i < n; i++ {
+				xv := x[i] * alpha
+				sum := x[i] * a[i*lda+i]
+				jy := ky + (i+1)*incY
+				atmp := a[i*lda+i+1 : i*lda+n]
+				for j, v := range atmp {
+					jp := j + i + 1
+					sum += x[jp] * v
+					y[jy] += xv * v
+					jy += incY
+				}
+				y[iy] += alpha * sum
+				iy += incY
+			}
+			return
+		}
+		ix := kx
+		iy := ky
+		for i := 0; i < n; i++ {
+			xv := x[ix] * alpha
+			sum := x[ix] * a[i*lda+i]
+			jx := kx + (i+1)*incX
+			jy := ky + (i+1)*incY
+			atmp := a[i*lda+i+1 : i*lda+n]
+			for _, v := range atmp {
+				sum += x[jx] * v
+				y[jy] += xv * v
+				jx += incX
+				jy += incY
+			}
+			y[iy] += alpha * sum
+			ix += incX
+			iy += incY
+		}
+		return
+	}
+	// Cases where a is lower triangular.
+	if incX == 1 {
+		iy := ky
+		for i := 0; i < n; i++ {
+			jy := ky
+			xv := alpha * x[i]
+			atmp := a[i*lda : i*lda+i]
+			var sum float64
+			for j, v := range atmp {
+				sum += x[j] * v
+				y[jy] += xv * v
+				jy += incY
+			}
+			sum += x[i] * a[i*lda+i]
+			sum *= alpha
+			y[iy] += sum
+			iy += incY
+		}
+		return
+	}
+	ix := kx
+	iy := ky
+	for i := 0; i < n; i++ {
+		jx := kx
+		jy := ky
+		xv := alpha * x[ix]
+		atmp := a[i*lda : i*lda+i]
+		var sum float64
+		for _, v := range atmp {
+			sum += x[jx] * v
+			y[jy] += xv * v
+			jx += incX
+			jy += incY
+		}
+		sum += x[ix] * a[i*lda+i]
+		sum *= alpha
+		y[iy] += sum
+		ix += incX
+		iy += incY
+	}
+}
+
+// Dtbmv computes
+//  x = A * x if tA == blas.NoTrans
+//  x = A^T * x if tA == blas.Trans or blas.ConjTrans
+// where A is an n×n triangular banded matrix with k diagonals, and x is a vector.
+func (Implementation) Dtbmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n, k int, a []float64, lda int, x []float64, incX int) {
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	if d != blas.NonUnit && d != blas.Unit {
+		panic(badDiag)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if k < 0 {
+		panic(kLT0)
+	}
+	if lda*(n-1)+k+1 > len(a) || lda < k+1 {
+		panic(badLdA)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if n == 0 {
+		return
+	}
+	var kx int
+	if incX <= 0 {
+		kx = -(n - 1) * incX
+	} else if incX != 1 {
+		kx = 0
+	}
+
+	nonunit := d != blas.Unit
+
+	if tA == blas.NoTrans {
+		if ul == blas.Upper {
+			if incX == 1 {
+				for i := 0; i < n; i++ {
+					u := min(1+k, n-i)
+					var sum float64
+					atmp := a[i*lda:]
+					xtmp := x[i:]
+					for j := 1; j < u; j++ {
+						sum += xtmp[j] * atmp[j]
+					}
+					if nonunit {
+						sum += xtmp[0] * atmp[0]
+					} else {
+						sum += xtmp[0]
+					}
+					x[i] = sum
+				}
+				return
+			}
+			ix := kx
+			for i := 0; i < n; i++ {
+				u := min(1+k, n-i)
+				var sum float64
+				atmp := a[i*lda:]
+				jx := incX
+				for j := 1; j < u; j++ {
+					sum += x[ix+jx] * atmp[j]
+					jx += incX
+				}
+				if nonunit {
+					sum += x[ix] * atmp[0]
+				} else {
+					sum += x[ix]
+				}
+				x[ix] = sum
+				ix += incX
+			}
+			return
+		}
+		if incX == 1 {
+			for i := n - 1; i >= 0; i-- {
+				l := max(0, k-i)
+				atmp := a[i*lda:]
+				var sum float64
+				for j := l; j < k; j++ {
+					sum += x[i-k+j] * atmp[j]
+				}
+				if nonunit {
+					sum += x[i] * atmp[k]
+				} else {
+					sum += x[i]
+				}
+				x[i] = sum
+			}
+			return
+		}
+		ix := kx + (n-1)*incX
+		for i := n - 1; i >= 0; i-- {
+			l := max(0, k-i)
+			atmp := a[i*lda:]
+			var sum float64
+			jx := l * incX
+			for j := l; j < k; j++ {
+				sum += x[ix-k*incX+jx] * atmp[j]
+				jx += incX
+			}
+			if nonunit {
+				sum += x[ix] * atmp[k]
+			} else {
+				sum += x[ix]
+			}
+			x[ix] = sum
+			ix -= incX
+		}
+		return
+	}
+	if ul == blas.Upper {
+		if incX == 1 {
+			for i := n - 1; i >= 0; i-- {
+				u := k + 1
+				if i < u {
+					u = i + 1
+				}
+				var sum float64
+				for j := 1; j < u; j++ {
+					sum += x[i-j] * a[(i-j)*lda+j]
+				}
+				if nonunit {
+					sum += x[i] * a[i*lda]
+				} else {
+					sum += x[i]
+				}
+				x[i] = sum
+			}
+			return
+		}
+		ix := kx + (n-1)*incX
+		for i := n - 1; i >= 0; i-- {
+			u := k + 1
+			if i < u {
+				u = i + 1
+			}
+			var sum float64
+			jx := incX
+			for j := 1; j < u; j++ {
+				sum += x[ix-jx] * a[(i-j)*lda+j]
+				jx += incX
+			}
+			if nonunit {
+				sum += x[ix] * a[i*lda]
+			} else {
+				sum += x[ix]
+			}
+			x[ix] = sum
+			ix -= incX
+		}
+		return
+	}
+	if incX == 1 {
+		for i := 0; i < n; i++ {
+			u := k
+			if i+k >= n {
+				u = n - i - 1
+			}
+			var sum float64
+			for j := 0; j < u; j++ {
+				sum += x[i+j+1] * a[(i+j+1)*lda+k-j-1]
+			}
+			if nonunit {
+				sum += x[i] * a[i*lda+k]
+			} else {
+				sum += x[i]
+			}
+			x[i] = sum
+		}
+		return
+	}
+	ix := kx
+	for i := 0; i < n; i++ {
+		u := k
+		if i+k >= n {
+			u = n - i - 1
+		}
+		var (
+			sum float64
+			jx  int
+		)
+		for j := 0; j < u; j++ {
+			sum += x[ix+jx+incX] * a[(i+j+1)*lda+k-j-1]
+			jx += incX
+		}
+		if nonunit {
+			sum += x[ix] * a[i*lda+k]
+		} else {
+			sum += x[ix]
+		}
+		x[ix] = sum
+		ix += incX
+	}
+}
+
+// Dtpmv computes
+//  x = A * x if tA == blas.NoTrans
+//  x = A^T * x if tA == blas.Trans or blas.ConjTrans
+// where A is an n×n unit triangular matrix in packed format, and x is a vector.
+func (Implementation) Dtpmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, ap []float64, x []float64, incX int) {
+	// Verify inputs
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	if d != blas.NonUnit && d != blas.Unit {
+		panic(badDiag)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if len(ap) < (n*(n+1))/2 {
+		panic(badLdA)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if n == 0 {
+		return
+	}
+	var kx int
+	if incX <= 0 {
+		kx = -(n - 1) * incX
+	}
+
+	nonUnit := d == blas.NonUnit
+	var offset int // Offset is the index of (i,i)
+	if tA == blas.NoTrans {
+		if ul == blas.Upper {
+			if incX == 1 {
+				for i := 0; i < n; i++ {
+					xi := x[i]
+					if nonUnit {
+						xi *= ap[offset]
+					}
+					atmp := ap[offset+1 : offset+n-i]
+					xtmp := x[i+1:]
+					for j, v := range atmp {
+						xi += v * xtmp[j]
+					}
+					x[i] = xi
+					offset += n - i
+				}
+				return
+			}
+			ix := kx
+			for i := 0; i < n; i++ {
+				xix := x[ix]
+				if nonUnit {
+					xix *= ap[offset]
+				}
+				atmp := ap[offset+1 : offset+n-i]
+				jx := kx + (i+1)*incX
+				for _, v := range atmp {
+					xix += v * x[jx]
+					jx += incX
+				}
+				x[ix] = xix
+				offset += n - i
+				ix += incX
+			}
+			return
+		}
+		if incX == 1 {
+			offset = n*(n+1)/2 - 1
+			for i := n - 1; i >= 0; i-- {
+				xi := x[i]
+				if nonUnit {
+					xi *= ap[offset]
+				}
+				atmp := ap[offset-i : offset]
+				for j, v := range atmp {
+					xi += v * x[j]
+				}
+				x[i] = xi
+				offset -= i + 1
+			}
+			return
+		}
+		ix := kx + (n-1)*incX
+		offset = n*(n+1)/2 - 1
+		for i := n - 1; i >= 0; i-- {
+			xix := x[ix]
+			if nonUnit {
+				xix *= ap[offset]
+			}
+			atmp := ap[offset-i : offset]
+			jx := kx
+			for _, v := range atmp {
+				xix += v * x[jx]
+				jx += incX
+			}
+			x[ix] = xix
+			offset -= i + 1
+			ix -= incX
+		}
+		return
+	}
+	// Cases where ap is transposed.
+	if ul == blas.Upper {
+		if incX == 1 {
+			offset = n*(n+1)/2 - 1
+			for i := n - 1; i >= 0; i-- {
+				xi := x[i]
+				atmp := ap[offset+1 : offset+n-i]
+				xtmp := x[i+1:]
+				for j, v := range atmp {
+					xtmp[j] += v * xi
+				}
+				if nonUnit {
+					x[i] *= ap[offset]
+				}
+				offset -= n - i + 1
+			}
+			return
+		}
+		ix := kx + (n-1)*incX
+		offset = n*(n+1)/2 - 1
+		for i := n - 1; i >= 0; i-- {
+			xix := x[ix]
+			jx := kx + (i+1)*incX
+			atmp := ap[offset+1 : offset+n-i]
+			for _, v := range atmp {
+				x[jx] += v * xix
+				jx += incX
+			}
+			if nonUnit {
+				x[ix] *= ap[offset]
+			}
+			offset -= n - i + 1
+			ix -= incX
+		}
+		return
+	}
+	if incX == 1 {
+		for i := 0; i < n; i++ {
+			xi := x[i]
+			atmp := ap[offset-i : offset]
+			for j, v := range atmp {
+				x[j] += v * xi
+			}
+			if nonUnit {
+				x[i] *= ap[offset]
+			}
+			offset += i + 2
+		}
+		return
+	}
+	ix := kx
+	for i := 0; i < n; i++ {
+		xix := x[ix]
+		jx := kx
+		atmp := ap[offset-i : offset]
+		for _, v := range atmp {
+			x[jx] += v * xix
+			jx += incX
+		}
+		if nonUnit {
+			x[ix] *= ap[offset]
+		}
+		ix += incX
+		offset += i + 2
+	}
+}
+
+// Dtbsv solves
+//  A * x = b
+// where A is an n×n triangular banded matrix with k diagonals in packed format,
+// and x is a vector.
+// At entry to the function, x contains the values of b, and the result is
+// stored in place into x.
+//
+// No test for singularity or near-singularity is included in this
+// routine. Such tests must be performed before calling this routine.
+func (Implementation) Dtbsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n, k int, a []float64, lda int, x []float64, incX int) {
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	if d != blas.NonUnit && d != blas.Unit {
+		panic(badDiag)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if lda*(n-1)+k+1 > len(a) || lda < k+1 {
+		panic(badLdA)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if n == 0 {
+		return
+	}
+	var kx int
+	if incX < 0 {
+		kx = -(n - 1) * incX
+	} else {
+		kx = 0
+	}
+	nonUnit := d == blas.NonUnit
+	// Form x = A^-1 x.
+	// Several cases below use subslices for speed improvement.
+	// The incX != 1 cases usually do not because incX may be negative.
+	if tA == blas.NoTrans {
+		if ul == blas.Upper {
+			if incX == 1 {
+				for i := n - 1; i >= 0; i-- {
+					bands := k
+					if i+bands >= n {
+						bands = n - i - 1
+					}
+					atmp := a[i*lda+1:]
+					xtmp := x[i+1 : i+bands+1]
+					var sum float64
+					for j, v := range xtmp {
+						sum += v * atmp[j]
+					}
+					x[i] -= sum
+					if nonUnit {
+						x[i] /= a[i*lda]
+					}
+				}
+				return
+			}
+			ix := kx + (n-1)*incX
+			for i := n - 1; i >= 0; i-- {
+				max := k + 1
+				if i+max > n {
+					max = n - i
+				}
+				atmp := a[i*lda:]
+				var (
+					jx  int
+					sum float64
+				)
+				for j := 1; j < max; j++ {
+					jx += incX
+					sum += x[ix+jx] * atmp[j]
+				}
+				x[ix] -= sum
+				if nonUnit {
+					x[ix] /= atmp[0]
+				}
+				ix -= incX
+			}
+			return
+		}
+		if incX == 1 {
+			for i := 0; i < n; i++ {
+				bands := k
+				if i-k < 0 {
+					bands = i
+				}
+				atmp := a[i*lda+k-bands:]
+				xtmp := x[i-bands : i]
+				var sum float64
+				for j, v := range xtmp {
+					sum += v * atmp[j]
+				}
+				x[i] -= sum
+				if nonUnit {
+					x[i] /= atmp[bands]
+				}
+			}
+			return
+		}
+		ix := kx
+		for i := 0; i < n; i++ {
+			bands := k
+			if i-k < 0 {
+				bands = i
+			}
+			atmp := a[i*lda+k-bands:]
+			var (
+				sum float64
+				jx  int
+			)
+			for j := 0; j < bands; j++ {
+				sum += x[ix-bands*incX+jx] * atmp[j]
+				jx += incX
+			}
+			x[ix] -= sum
+			if nonUnit {
+				x[ix] /= atmp[bands]
+			}
+			ix += incX
+		}
+		return
+	}
+	// Cases where a is transposed.
+	if ul == blas.Upper {
+		if incX == 1 {
+			for i := 0; i < n; i++ {
+				bands := k
+				if i-k < 0 {
+					bands = i
+				}
+				var sum float64
+				for j := 0; j < bands; j++ {
+					sum += x[i-bands+j] * a[(i-bands+j)*lda+bands-j]
+				}
+				x[i] -= sum
+				if nonUnit {
+					x[i] /= a[i*lda]
+				}
+			}
+			return
+		}
+		ix := kx
+		for i := 0; i < n; i++ {
+			bands := k
+			if i-k < 0 {
+				bands = i
+			}
+			var (
+				sum float64
+				jx  int
+			)
+			for j := 0; j < bands; j++ {
+				sum += x[ix-bands*incX+jx] * a[(i-bands+j)*lda+bands-j]
+				jx += incX
+			}
+			x[ix] -= sum
+			if nonUnit {
+				x[ix] /= a[i*lda]
+			}
+			ix += incX
+		}
+		return
+	}
+	if incX == 1 {
+		for i := n - 1; i >= 0; i-- {
+			bands := k
+			if i+bands >= n {
+				bands = n - i - 1
+			}
+			var sum float64
+			xtmp := x[i+1 : i+1+bands]
+			for j, v := range xtmp {
+				sum += v * a[(i+j+1)*lda+k-j-1]
+			}
+			x[i] -= sum
+			if nonUnit {
+				x[i] /= a[i*lda+k]
+			}
+		}
+		return
+	}
+	ix := kx + (n-1)*incX
+	for i := n - 1; i >= 0; i-- {
+		bands := k
+		if i+bands >= n {
+			bands = n - i - 1
+		}
+		var (
+			sum float64
+			jx  int
+		)
+		for j := 0; j < bands; j++ {
+			sum += x[ix+jx+incX] * a[(i+j+1)*lda+k-j-1]
+			jx += incX
+		}
+		x[ix] -= sum
+		if nonUnit {
+			x[ix] /= a[i*lda+k]
+		}
+		ix -= incX
+	}
+}
+
+// Dsbmv performs
+//  y = alpha * A * x + beta * y
+// where A is an n×n symmetric banded matrix, x and y are vectors, and alpha
+// and beta are scalars.
+func (Implementation) Dsbmv(ul blas.Uplo, n, k int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int) {
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
+		panic(badY)
+	}
+	if lda*(n-1)+k+1 > len(a) || lda < k+1 {
+		panic(badLdA)
+	}
+
+	// Quick return if possible
+	if n == 0 || (alpha == 0 && beta == 1) {
+		return
+	}
+
+	// Set up indexes
+	lenX := n
+	lenY := n
+	var kx, ky int
+	if incX > 0 {
+		kx = 0
+	} else {
+		kx = -(lenX - 1) * incX
+	}
+	if incY > 0 {
+		ky = 0
+	} else {
+		ky = -(lenY - 1) * incY
+	}
+
+	// First form y := beta * y
+	if incY > 0 {
+		Implementation{}.Dscal(lenY, beta, y, incY)
+	} else {
+		Implementation{}.Dscal(lenY, beta, y, -incY)
+	}
+
+	if alpha == 0 {
+		return
+	}
+
+	if ul == blas.Upper {
+		if incX == 1 {
+			iy := ky
+			for i := 0; i < n; i++ {
+				atmp := a[i*lda:]
+				tmp := alpha * x[i]
+				sum := tmp * atmp[0]
+				u := min(k, n-i-1)
+				jy := incY
+				for j := 1; j <= u; j++ {
+					v := atmp[j]
+					sum += alpha * x[i+j] * v
+					y[iy+jy] += tmp * v
+					jy += incY
+				}
+				y[iy] += sum
+				iy += incY
+			}
+			return
+		}
+		ix := kx
+		iy := ky
+		for i := 0; i < n; i++ {
+			atmp := a[i*lda:]
+			tmp := alpha * x[ix]
+			sum := tmp * atmp[0]
+			u := min(k, n-i-1)
+			jx := incX
+			jy := incY
+			for j := 1; j <= u; j++ {
+				v := atmp[j]
+				sum += alpha * x[ix+jx] * v
+				y[iy+jy] += tmp * v
+				jx += incX
+				jy += incY
+			}
+			y[iy] += sum
+			ix += incX
+			iy += incY
+		}
+		return
+	}
+
+	// Casses where a has bands below the diagonal.
+	if incX == 1 {
+		iy := ky
+		for i := 0; i < n; i++ {
+			l := max(0, k-i)
+			tmp := alpha * x[i]
+			jy := l * incY
+			atmp := a[i*lda:]
+			for j := l; j < k; j++ {
+				v := atmp[j]
+				y[iy] += alpha * v * x[i-k+j]
+				y[iy-k*incY+jy] += tmp * v
+				jy += incY
+			}
+			y[iy] += tmp * atmp[k]
+			iy += incY
+		}
+		return
+	}
+	ix := kx
+	iy := ky
+	for i := 0; i < n; i++ {
+		l := max(0, k-i)
+		tmp := alpha * x[ix]
+		jx := l * incX
+		jy := l * incY
+		atmp := a[i*lda:]
+		for j := l; j < k; j++ {
+			v := atmp[j]
+			y[iy] += alpha * v * x[ix-k*incX+jx]
+			y[iy-k*incY+jy] += tmp * v
+			jx += incX
+			jy += incY
+		}
+		y[iy] += tmp * atmp[k]
+		ix += incX
+		iy += incY
+	}
+}
+
+// Dsyr performs the rank-one update
+//  a += alpha * x * x^T
+// where a is an n×n symmetric matrix, and x is a vector.
+func (Implementation) Dsyr(ul blas.Uplo, n int, alpha float64, x []float64, incX int, a []float64, lda int) {
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if lda*(n-1)+n > len(a) || lda < max(1, n) {
+		panic(badLdA)
+	}
+	if alpha == 0 || n == 0 {
+		return
+	}
+
+	lenX := n
+	var kx int
+	if incX > 0 {
+		kx = 0
+	} else {
+		kx = -(lenX - 1) * incX
+	}
+	if ul == blas.Upper {
+		if incX == 1 {
+			for i := 0; i < n; i++ {
+				tmp := x[i] * alpha
+				if tmp != 0 {
+					atmp := a[i*lda+i : i*lda+n]
+					xtmp := x[i:n]
+					for j, v := range xtmp {
+						atmp[j] += v * tmp
+					}
+				}
+			}
+			return
+		}
+		ix := kx
+		for i := 0; i < n; i++ {
+			tmp := x[ix] * alpha
+			if tmp != 0 {
+				jx := ix
+				atmp := a[i*lda:]
+				for j := i; j < n; j++ {
+					atmp[j] += x[jx] * tmp
+					jx += incX
+				}
+			}
+			ix += incX
+		}
+		return
+	}
+	// Cases where a is lower triangular.
+	if incX == 1 {
+		for i := 0; i < n; i++ {
+			tmp := x[i] * alpha
+			if tmp != 0 {
+				atmp := a[i*lda:]
+				xtmp := x[:i+1]
+				for j, v := range xtmp {
+					atmp[j] += tmp * v
+				}
+			}
+		}
+		return
+	}
+	ix := kx
+	for i := 0; i < n; i++ {
+		tmp := x[ix] * alpha
+		if tmp != 0 {
+			atmp := a[i*lda:]
+			jx := kx
+			for j := 0; j < i+1; j++ {
+				atmp[j] += tmp * x[jx]
+				jx += incX
+			}
+		}
+		ix += incX
+	}
+}
+
+// Dsyr2 performs the symmetric rank-two update
+//  A += alpha * x * y^T + alpha * y * x^T
+// where A is a symmetric n×n matrix, x and y are vectors, and alpha is a scalar.
+func (Implementation) Dsyr2(ul blas.Uplo, n int, alpha float64, x []float64, incX int, y []float64, incY int, a []float64, lda int) {
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
+		panic(badY)
+	}
+	if lda*(n-1)+n > len(a) || lda < max(1, n) {
+		panic(badLdA)
+	}
+	if alpha == 0 {
+		return
+	}
+
+	var ky, kx int
+	if incY > 0 {
+		ky = 0
+	} else {
+		ky = -(n - 1) * incY
+	}
+	if incX > 0 {
+		kx = 0
+	} else {
+		kx = -(n - 1) * incX
+	}
+	if ul == blas.Upper {
+		if incX == 1 && incY == 1 {
+			for i := 0; i < n; i++ {
+				xi := x[i]
+				yi := y[i]
+				atmp := a[i*lda:]
+				for j := i; j < n; j++ {
+					atmp[j] += alpha * (xi*y[j] + x[j]*yi)
+				}
+			}
+			return
+		}
+		ix := kx
+		iy := ky
+		for i := 0; i < n; i++ {
+			jx := kx + i*incX
+			jy := ky + i*incY
+			xi := x[ix]
+			yi := y[iy]
+			atmp := a[i*lda:]
+			for j := i; j < n; j++ {
+				atmp[j] += alpha * (xi*y[jy] + x[jx]*yi)
+				jx += incX
+				jy += incY
+			}
+			ix += incX
+			iy += incY
+		}
+		return
+	}
+	if incX == 1 && incY == 1 {
+		for i := 0; i < n; i++ {
+			xi := x[i]
+			yi := y[i]
+			atmp := a[i*lda:]
+			for j := 0; j <= i; j++ {
+				atmp[j] += alpha * (xi*y[j] + x[j]*yi)
+			}
+		}
+		return
+	}
+	ix := kx
+	iy := ky
+	for i := 0; i < n; i++ {
+		jx := kx
+		jy := ky
+		xi := x[ix]
+		yi := y[iy]
+		atmp := a[i*lda:]
+		for j := 0; j <= i; j++ {
+			atmp[j] += alpha * (xi*y[jy] + x[jx]*yi)
+			jx += incX
+			jy += incY
+		}
+		ix += incX
+		iy += incY
+	}
+}
+
+// Dtpsv solves
+//  A * x = b if tA == blas.NoTrans
+//  A^T * x = b if tA == blas.Trans or blas.ConjTrans
+// where A is an n×n triangular matrix in packed format and x is a vector.
+// At entry to the function, x contains the values of b, and the result is
+// stored in place into x.
+//
+// No test for singularity or near-singularity is included in this
+// routine. Such tests must be performed before calling this routine.
+func (Implementation) Dtpsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, ap []float64, x []float64, incX int) {
+	// Verify inputs
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	if d != blas.NonUnit && d != blas.Unit {
+		panic(badDiag)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if len(ap) < (n*(n+1))/2 {
+		panic(badLdA)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if n == 0 {
+		return
+	}
+	var kx int
+	if incX <= 0 {
+		kx = -(n - 1) * incX
+	}
+
+	nonUnit := d == blas.NonUnit
+	var offset int // Offset is the index of (i,i)
+	if tA == blas.NoTrans {
+		if ul == blas.Upper {
+			offset = n*(n+1)/2 - 1
+			if incX == 1 {
+				for i := n - 1; i >= 0; i-- {
+					atmp := ap[offset+1 : offset+n-i]
+					xtmp := x[i+1:]
+					var sum float64
+					for j, v := range atmp {
+						sum += v * xtmp[j]
+					}
+					x[i] -= sum
+					if nonUnit {
+						x[i] /= ap[offset]
+					}
+					offset -= n - i + 1
+				}
+				return
+			}
+			ix := kx + (n-1)*incX
+			for i := n - 1; i >= 0; i-- {
+				atmp := ap[offset+1 : offset+n-i]
+				jx := kx + (i+1)*incX
+				var sum float64
+				for _, v := range atmp {
+					sum += v * x[jx]
+					jx += incX
+				}
+				x[ix] -= sum
+				if nonUnit {
+					x[ix] /= ap[offset]
+				}
+				ix -= incX
+				offset -= n - i + 1
+			}
+			return
+		}
+		if incX == 1 {
+			for i := 0; i < n; i++ {
+				atmp := ap[offset-i : offset]
+				var sum float64
+				for j, v := range atmp {
+					sum += v * x[j]
+				}
+				x[i] -= sum
+				if nonUnit {
+					x[i] /= ap[offset]
+				}
+				offset += i + 2
+			}
+			return
+		}
+		ix := kx
+		for i := 0; i < n; i++ {
+			jx := kx
+			atmp := ap[offset-i : offset]
+			var sum float64
+			for _, v := range atmp {
+				sum += v * x[jx]
+				jx += incX
+			}
+			x[ix] -= sum
+			if nonUnit {
+				x[ix] /= ap[offset]
+			}
+			ix += incX
+			offset += i + 2
+		}
+		return
+	}
+	// Cases where ap is transposed.
+	if ul == blas.Upper {
+		if incX == 1 {
+			for i := 0; i < n; i++ {
+				if nonUnit {
+					x[i] /= ap[offset]
+				}
+				xi := x[i]
+				atmp := ap[offset+1 : offset+n-i]
+				xtmp := x[i+1:]
+				for j, v := range atmp {
+					xtmp[j] -= v * xi
+				}
+				offset += n - i
+			}
+			return
+		}
+		ix := kx
+		for i := 0; i < n; i++ {
+			if nonUnit {
+				x[ix] /= ap[offset]
+			}
+			xix := x[ix]
+			atmp := ap[offset+1 : offset+n-i]
+			jx := kx + (i+1)*incX
+			for _, v := range atmp {
+				x[jx] -= v * xix
+				jx += incX
+			}
+			ix += incX
+			offset += n - i
+		}
+		return
+	}
+	if incX == 1 {
+		offset = n*(n+1)/2 - 1
+		for i := n - 1; i >= 0; i-- {
+			if nonUnit {
+				x[i] /= ap[offset]
+			}
+			xi := x[i]
+			atmp := ap[offset-i : offset]
+			for j, v := range atmp {
+				x[j] -= v * xi
+			}
+			offset -= i + 1
+		}
+		return
+	}
+	ix := kx + (n-1)*incX
+	offset = n*(n+1)/2 - 1
+	for i := n - 1; i >= 0; i-- {
+		if nonUnit {
+			x[ix] /= ap[offset]
+		}
+		xix := x[ix]
+		atmp := ap[offset-i : offset]
+		jx := kx
+		for _, v := range atmp {
+			x[jx] -= v * xix
+			jx += incX
+		}
+		ix -= incX
+		offset -= i + 1
+	}
+}
+
+// Dspmv performs
+//    y = alpha * A * x + beta * y,
+// where A is an n×n symmetric matrix in packed format, x and y are vectors
+// and alpha and beta are scalars.
+func (Implementation) Dspmv(ul blas.Uplo, n int, alpha float64, a []float64, x []float64, incX int, beta float64, y []float64, incY int) {
+	// Verify inputs
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if len(a) < (n*(n+1))/2 {
+		panic(badLdA)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
+		panic(badY)
+	}
+	// Quick return if possible
+	if n == 0 || (alpha == 0 && beta == 1) {
+		return
+	}
+
+	// Set up start points
+	var kx, ky int
+	if incX > 0 {
+		kx = 0
+	} else {
+		kx = -(n - 1) * incX
+	}
+	if incY > 0 {
+		ky = 0
+	} else {
+		ky = -(n - 1) * incY
+	}
+
+	// Form y = beta * y
+	if beta != 1 {
+		if incY > 0 {
+			Implementation{}.Dscal(n, beta, y, incY)
+		} else {
+			Implementation{}.Dscal(n, beta, y, -incY)
+		}
+	}
+
+	if alpha == 0 {
+		return
+	}
+
+	if n == 1 {
+		y[0] += alpha * a[0] * x[0]
+		return
+	}
+	var offset int // Offset is the index of (i,i).
+	if ul == blas.Upper {
+		if incX == 1 {
+			iy := ky
+			for i := 0; i < n; i++ {
+				xv := x[i] * alpha
+				sum := a[offset] * x[i]
+				atmp := a[offset+1 : offset+n-i]
+				xtmp := x[i+1:]
+				jy := ky + (i+1)*incY
+				for j, v := range atmp {
+					sum += v * xtmp[j]
+					y[jy] += v * xv
+					jy += incY
+				}
+				y[iy] += alpha * sum
+				iy += incY
+				offset += n - i
+			}
+			return
+		}
+		ix := kx
+		iy := ky
+		for i := 0; i < n; i++ {
+			xv := x[ix] * alpha
+			sum := a[offset] * x[ix]
+			atmp := a[offset+1 : offset+n-i]
+			jx := kx + (i+1)*incX
+			jy := ky + (i+1)*incY
+			for _, v := range atmp {
+				sum += v * x[jx]
+				y[jy] += v * xv
+				jx += incX
+				jy += incY
+			}
+			y[iy] += alpha * sum
+			ix += incX
+			iy += incY
+			offset += n - i
+		}
+		return
+	}
+	if incX == 1 {
+		iy := ky
+		for i := 0; i < n; i++ {
+			xv := x[i] * alpha
+			atmp := a[offset-i : offset]
+			jy := ky
+			var sum float64
+			for j, v := range atmp {
+				sum += v * x[j]
+				y[jy] += v * xv
+				jy += incY
+			}
+			sum += a[offset] * x[i]
+			y[iy] += alpha * sum
+			iy += incY
+			offset += i + 2
+		}
+		return
+	}
+	ix := kx
+	iy := ky
+	for i := 0; i < n; i++ {
+		xv := x[ix] * alpha
+		atmp := a[offset-i : offset]
+		jx := kx
+		jy := ky
+		var sum float64
+		for _, v := range atmp {
+			sum += v * x[jx]
+			y[jy] += v * xv
+			jx += incX
+			jy += incY
+		}
+
+		sum += a[offset] * x[ix]
+		y[iy] += alpha * sum
+		ix += incX
+		iy += incY
+		offset += i + 2
+	}
+}
+
+// Dspr computes the rank-one operation
+//  a += alpha * x * x^T
+// where a is an n×n symmetric matrix in packed format, x is a vector, and
+// alpha is a scalar.
+func (Implementation) Dspr(ul blas.Uplo, n int, alpha float64, x []float64, incX int, a []float64) {
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if len(a) < (n*(n+1))/2 {
+		panic(badLdA)
+	}
+	if alpha == 0 || n == 0 {
+		return
+	}
+	lenX := n
+	var kx int
+	if incX > 0 {
+		kx = 0
+	} else {
+		kx = -(lenX - 1) * incX
+	}
+	var offset int // Offset is the index of (i,i).
+	if ul == blas.Upper {
+		if incX == 1 {
+			for i := 0; i < n; i++ {
+				atmp := a[offset:]
+				xv := alpha * x[i]
+				xtmp := x[i:n]
+				for j, v := range xtmp {
+					atmp[j] += xv * v
+				}
+				offset += n - i
+			}
+			return
+		}
+		ix := kx
+		for i := 0; i < n; i++ {
+			jx := kx + i*incX
+			atmp := a[offset:]
+			xv := alpha * x[ix]
+			for j := 0; j < n-i; j++ {
+				atmp[j] += xv * x[jx]
+				jx += incX
+			}
+			ix += incX
+			offset += n - i
+		}
+		return
+	}
+	if incX == 1 {
+		for i := 0; i < n; i++ {
+			atmp := a[offset-i:]
+			xv := alpha * x[i]
+			xtmp := x[:i+1]
+			for j, v := range xtmp {
+				atmp[j] += xv * v
+			}
+			offset += i + 2
+		}
+		return
+	}
+	ix := kx
+	for i := 0; i < n; i++ {
+		jx := kx
+		atmp := a[offset-i:]
+		xv := alpha * x[ix]
+		for j := 0; j <= i; j++ {
+			atmp[j] += xv * x[jx]
+			jx += incX
+		}
+		ix += incX
+		offset += i + 2
+	}
+}
+
+// Dspr2 performs the symmetric rank-2 update
+//  A += alpha * x * y^T + alpha * y * x^T,
+// where A is an n×n symmetric matrix in packed format, x and y are vectors,
+// and alpha is a scalar.
+func (Implementation) Dspr2(ul blas.Uplo, n int, alpha float64, x []float64, incX int, y []float64, incY int, ap []float64) {
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
+		panic(badY)
+	}
+	if len(ap) < (n*(n+1))/2 {
+		panic(badLdA)
+	}
+	if alpha == 0 {
+		return
+	}
+	var ky, kx int
+	if incY > 0 {
+		ky = 0
+	} else {
+		ky = -(n - 1) * incY
+	}
+	if incX > 0 {
+		kx = 0
+	} else {
+		kx = -(n - 1) * incX
+	}
+	var offset int // Offset is the index of (i,i).
+	if ul == blas.Upper {
+		if incX == 1 && incY == 1 {
+			for i := 0; i < n; i++ {
+				atmp := ap[offset:]
+				xi := x[i]
+				yi := y[i]
+				xtmp := x[i:n]
+				ytmp := y[i:n]
+				for j, v := range xtmp {
+					atmp[j] += alpha * (xi*ytmp[j] + v*yi)
+				}
+				offset += n - i
+			}
+			return
+		}
+		ix := kx
+		iy := ky
+		for i := 0; i < n; i++ {
+			jx := kx + i*incX
+			jy := ky + i*incY
+			atmp := ap[offset:]
+			xi := x[ix]
+			yi := y[iy]
+			for j := 0; j < n-i; j++ {
+				atmp[j] += alpha * (xi*y[jy] + x[jx]*yi)
+				jx += incX
+				jy += incY
+			}
+			ix += incX
+			iy += incY
+			offset += n - i
+		}
+		return
+	}
+	if incX == 1 && incY == 1 {
+		for i := 0; i < n; i++ {
+			atmp := ap[offset-i:]
+			xi := x[i]
+			yi := y[i]
+			xtmp := x[:i+1]
+			for j, v := range xtmp {
+				atmp[j] += alpha * (xi*y[j] + v*yi)
+			}
+			offset += i + 2
+		}
+		return
+	}
+	ix := kx
+	iy := ky
+	for i := 0; i < n; i++ {
+		jx := kx
+		jy := ky
+		atmp := ap[offset-i:]
+		for j := 0; j <= i; j++ {
+			atmp[j] += alpha * (x[ix]*y[jy] + x[jx]*y[iy])
+			jx += incX
+			jy += incY
+		}
+		ix += incX
+		iy += incY
+		offset += i + 2
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/level2double_test.go b/vendor/gonum.org/v1/gonum/blas/gonum/level2double_test.go
new file mode 100644
index 00000000..42ac4798
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/level2double_test.go
@@ -0,0 +1,79 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas/testblas"
+)
+
+func TestDgemv(t *testing.T) {
+	testblas.DgemvTest(t, impl)
+}
+
+func TestDger(t *testing.T) {
+	testblas.DgerTest(t, impl)
+}
+
+func TestDtxmv(t *testing.T) {
+	testblas.DtxmvTest(t, impl)
+}
+
+func TestDgbmv(t *testing.T) {
+	testblas.DgbmvTest(t, impl)
+}
+
+func TestDtbsv(t *testing.T) {
+	testblas.DtbsvTest(t, impl)
+}
+
+func TestDsbmv(t *testing.T) {
+	testblas.DsbmvTest(t, impl)
+}
+
+func TestDtbmv(t *testing.T) {
+	testblas.DtbmvTest(t, impl)
+}
+
+func TestDtrsv(t *testing.T) {
+	testblas.DtrsvTest(t, impl)
+}
+
+func TestDtrmv(t *testing.T) {
+	testblas.DtrmvTest(t, impl)
+}
+
+func TestDsymv(t *testing.T) {
+	testblas.DsymvTest(t, impl)
+}
+
+func TestDsyr(t *testing.T) {
+	testblas.DsyrTest(t, impl)
+}
+
+func TestDsyr2(t *testing.T) {
+	testblas.Dsyr2Test(t, impl)
+}
+
+func TestDspr2(t *testing.T) {
+	testblas.Dspr2Test(t, impl)
+}
+
+func TestDspr(t *testing.T) {
+	testblas.DsprTest(t, impl)
+}
+
+func TestDspmv(t *testing.T) {
+	testblas.DspmvTest(t, impl)
+}
+
+func TestDtpsv(t *testing.T) {
+	testblas.DtpsvTest(t, impl)
+}
+
+func TestDtpmv(t *testing.T) {
+	testblas.DtpmvTest(t, impl)
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/level2single.go b/vendor/gonum.org/v1/gonum/blas/gonum/level2single.go
new file mode 100644
index 00000000..84ca967b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/level2single.go
@@ -0,0 +1,2268 @@
+// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.
+
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/internal/asm/f32"
+)
+
+var _ blas.Float32Level2 = Implementation{}
+
+// Sgemv computes
+//  y = alpha * a * x + beta * y if tA = blas.NoTrans
+//  y = alpha * A^T * x + beta * y if tA = blas.Trans or blas.ConjTrans
+// where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Sgemv(tA blas.Transpose, m, n int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int) {
+	if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	if m < 0 {
+		panic(mLT0)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if lda < max(1, n) {
+		panic(badLdA)
+	}
+
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	// Set up indexes
+	lenX := m
+	lenY := n
+	if tA == blas.NoTrans {
+		lenX = n
+		lenY = m
+	}
+	if (incX > 0 && (lenX-1)*incX >= len(x)) || (incX < 0 && (1-lenX)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (lenY-1)*incY >= len(y)) || (incY < 0 && (1-lenY)*incY >= len(y)) {
+		panic(badY)
+	}
+	if lda*(m-1)+n > len(a) || lda < max(1, n) {
+		panic(badLdA)
+	}
+
+	// Quick return if possible
+	if m == 0 || n == 0 || (alpha == 0 && beta == 1) {
+		return
+	}
+
+	var kx, ky int
+	if incX > 0 {
+		kx = 0
+	} else {
+		kx = -(lenX - 1) * incX
+	}
+	if incY > 0 {
+		ky = 0
+	} else {
+		ky = -(lenY - 1) * incY
+	}
+
+	// First form y := beta * y
+	if incY > 0 {
+		Implementation{}.Sscal(lenY, beta, y, incY)
+	} else {
+		Implementation{}.Sscal(lenY, beta, y, -incY)
+	}
+
+	if alpha == 0 {
+		return
+	}
+
+	// Form y := alpha * A * x + y
+	if tA == blas.NoTrans {
+		if incX == 1 && incY == 1 {
+			for i := 0; i < m; i++ {
+				y[i] += alpha * f32.DotUnitary(a[lda*i:lda*i+n], x)
+			}
+			return
+		}
+		iy := ky
+		for i := 0; i < m; i++ {
+			y[iy] += alpha * f32.DotInc(x, a[lda*i:lda*i+n], uintptr(n), uintptr(incX), 1, uintptr(kx), 0)
+			iy += incY
+		}
+		return
+	}
+	// Cases where a is transposed.
+	if incX == 1 && incY == 1 {
+		for i := 0; i < m; i++ {
+			tmp := alpha * x[i]
+			if tmp != 0 {
+				f32.AxpyUnitaryTo(y, tmp, a[lda*i:lda*i+n], y)
+			}
+		}
+		return
+	}
+	ix := kx
+	for i := 0; i < m; i++ {
+		tmp := alpha * x[ix]
+		if tmp != 0 {
+			f32.AxpyInc(tmp, a[lda*i:lda*i+n], y, uintptr(n), 1, uintptr(incY), 0, uintptr(ky))
+		}
+		ix += incX
+	}
+}
+
+// Sger performs the rank-one operation
+//  A += alpha * x * y^T
+// where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Sger(m, n int, alpha float32, x []float32, incX int, y []float32, incY int, a []float32, lda int) {
+	// Check inputs
+	if m < 0 {
+		panic("m < 0")
+	}
+	if n < 0 {
+		panic(negativeN)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if (incX > 0 && (m-1)*incX >= len(x)) || (incX < 0 && (1-m)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
+		panic(badY)
+	}
+	if lda*(m-1)+n > len(a) || lda < max(1, n) {
+		panic(badLdA)
+	}
+	if lda < max(1, n) {
+		panic(badLdA)
+	}
+
+	// Quick return if possible
+	if m == 0 || n == 0 || alpha == 0 {
+		return
+	}
+
+	var ky, kx int
+	if incY > 0 {
+		ky = 0
+	} else {
+		ky = -(n - 1) * incY
+	}
+
+	if incX > 0 {
+		kx = 0
+	} else {
+		kx = -(m - 1) * incX
+	}
+
+	if incX == 1 && incY == 1 {
+		x = x[:m]
+		y = y[:n]
+		for i, xv := range x {
+			tmp := alpha * xv
+			if tmp != 0 {
+				atmp := a[i*lda : i*lda+n]
+				f32.AxpyUnitaryTo(atmp, tmp, y, atmp)
+			}
+		}
+		return
+	}
+
+	ix := kx
+	for i := 0; i < m; i++ {
+		tmp := alpha * x[ix]
+		if tmp != 0 {
+			f32.AxpyInc(tmp, y, a[i*lda:i*lda+n], uintptr(n), uintptr(incY), 1, uintptr(ky), 0)
+		}
+		ix += incX
+	}
+}
+
+// Sgbmv computes
+//  y = alpha * A * x + beta * y if tA == blas.NoTrans
+//  y = alpha * A^T * x + beta * y if tA == blas.Trans or blas.ConjTrans
+// where a is an m×n band matrix kL subdiagonals and kU super-diagonals, and
+// m and n refer to the size of the full dense matrix it represents.
+// x and y are vectors, and alpha and beta are scalars.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Sgbmv(tA blas.Transpose, m, n, kL, kU int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int) {
+	if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	if m < 0 {
+		panic(mLT0)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if kL < 0 {
+		panic(kLLT0)
+	}
+	if kL < 0 {
+		panic(kULT0)
+	}
+	if lda < kL+kU+1 {
+		panic(badLdA)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	// Set up indexes
+	lenX := m
+	lenY := n
+	if tA == blas.NoTrans {
+		lenX = n
+		lenY = m
+	}
+	if (incX > 0 && (lenX-1)*incX >= len(x)) || (incX < 0 && (1-lenX)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (lenY-1)*incY >= len(y)) || (incY < 0 && (1-lenY)*incY >= len(y)) {
+		panic(badY)
+	}
+	if lda*(min(m, n+kL)-1)+kL+kU+1 > len(a) || lda < kL+kU+1 {
+		panic(badLdA)
+	}
+
+	// Quick return if possible
+	if m == 0 || n == 0 || (alpha == 0 && beta == 1) {
+		return
+	}
+
+	var kx, ky int
+	if incX > 0 {
+		kx = 0
+	} else {
+		kx = -(lenX - 1) * incX
+	}
+	if incY > 0 {
+		ky = 0
+	} else {
+		ky = -(lenY - 1) * incY
+	}
+
+	// First form y := beta * y
+	if incY > 0 {
+		Implementation{}.Sscal(lenY, beta, y, incY)
+	} else {
+		Implementation{}.Sscal(lenY, beta, y, -incY)
+	}
+
+	if alpha == 0 {
+		return
+	}
+
+	// i and j are indices of the compacted banded matrix.
+	// off is the offset into the dense matrix (off + j = densej)
+	ld := min(m, n)
+	nCol := kU + 1 + kL
+	if tA == blas.NoTrans {
+		iy := ky
+		if incX == 1 {
+			for i := 0; i < min(m, n+kL); i++ {
+				l := max(0, kL-i)
+				u := min(nCol, ld+kL-i)
+				off := max(0, i-kL)
+				atmp := a[i*lda+l : i*lda+u]
+				xtmp := x[off : off+u-l]
+				var sum float32
+				for j, v := range atmp {
+					sum += xtmp[j] * v
+				}
+				y[iy] += sum * alpha
+				iy += incY
+			}
+			return
+		}
+		for i := 0; i < min(m, n+kL); i++ {
+			l := max(0, kL-i)
+			u := min(nCol, ld+kL-i)
+			off := max(0, i-kL)
+			atmp := a[i*lda+l : i*lda+u]
+			jx := kx
+			var sum float32
+			for _, v := range atmp {
+				sum += x[off*incX+jx] * v
+				jx += incX
+			}
+			y[iy] += sum * alpha
+			iy += incY
+		}
+		return
+	}
+	if incX == 1 {
+		for i := 0; i < min(m, n+kL); i++ {
+			l := max(0, kL-i)
+			u := min(nCol, ld+kL-i)
+			off := max(0, i-kL)
+			atmp := a[i*lda+l : i*lda+u]
+			tmp := alpha * x[i]
+			jy := ky
+			for _, v := range atmp {
+				y[jy+off*incY] += tmp * v
+				jy += incY
+			}
+		}
+		return
+	}
+	ix := kx
+	for i := 0; i < min(m, n+kL); i++ {
+		l := max(0, kL-i)
+		u := min(nCol, ld+kL-i)
+		off := max(0, i-kL)
+		atmp := a[i*lda+l : i*lda+u]
+		tmp := alpha * x[ix]
+		jy := ky
+		for _, v := range atmp {
+			y[jy+off*incY] += tmp * v
+			jy += incY
+		}
+		ix += incX
+	}
+}
+
+// Strmv computes
+//  x = A * x if tA == blas.NoTrans
+//  x = A^T * x if tA == blas.Trans or blas.ConjTrans
+// A is an n×n Triangular matrix and x is a vector.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Strmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, a []float32, lda int, x []float32, incX int) {
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	if d != blas.NonUnit && d != blas.Unit {
+		panic(badDiag)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if lda < n {
+		panic(badLdA)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if lda*(n-1)+n > len(a) || lda < max(1, n) {
+		panic(badLdA)
+	}
+	if n == 0 {
+		return
+	}
+	nonUnit := d != blas.Unit
+	if n == 1 {
+		if nonUnit {
+			x[0] *= a[0]
+		}
+		return
+	}
+	var kx int
+	if incX <= 0 {
+		kx = -(n - 1) * incX
+	}
+	if tA == blas.NoTrans {
+		if ul == blas.Upper {
+			if incX == 1 {
+				for i := 0; i < n; i++ {
+					ilda := i * lda
+					var tmp float32
+					if nonUnit {
+						tmp = a[ilda+i] * x[i]
+					} else {
+						tmp = x[i]
+					}
+					xtmp := x[i+1:]
+					x[i] = tmp + f32.DotUnitary(a[ilda+i+1:ilda+n], xtmp)
+				}
+				return
+			}
+			ix := kx
+			for i := 0; i < n; i++ {
+				ilda := i * lda
+				var tmp float32
+				if nonUnit {
+					tmp = a[ilda+i] * x[ix]
+				} else {
+					tmp = x[ix]
+				}
+				x[ix] = tmp + f32.DotInc(x, a[ilda+i+1:ilda+n], uintptr(n-i-1), uintptr(incX), 1, uintptr(ix+incX), 0)
+				ix += incX
+			}
+			return
+		}
+		if incX == 1 {
+			for i := n - 1; i >= 0; i-- {
+				ilda := i * lda
+				var tmp float32
+				if nonUnit {
+					tmp += a[ilda+i] * x[i]
+				} else {
+					tmp = x[i]
+				}
+				x[i] = tmp + f32.DotUnitary(a[ilda:ilda+i], x)
+			}
+			return
+		}
+		ix := kx + (n-1)*incX
+		for i := n - 1; i >= 0; i-- {
+			ilda := i * lda
+			var tmp float32
+			if nonUnit {
+				tmp = a[ilda+i] * x[ix]
+			} else {
+				tmp = x[ix]
+			}
+			x[ix] = tmp + f32.DotInc(x, a[ilda:ilda+i], uintptr(i), uintptr(incX), 1, uintptr(kx), 0)
+			ix -= incX
+		}
+		return
+	}
+	// Cases where a is transposed.
+	if ul == blas.Upper {
+		if incX == 1 {
+			for i := n - 1; i >= 0; i-- {
+				ilda := i * lda
+				xi := x[i]
+				f32.AxpyUnitary(xi, a[ilda+i+1:ilda+n], x[i+1:n])
+				if nonUnit {
+					x[i] *= a[ilda+i]
+				}
+			}
+			return
+		}
+		ix := kx + (n-1)*incX
+		for i := n - 1; i >= 0; i-- {
+			ilda := i * lda
+			xi := x[ix]
+			f32.AxpyInc(xi, a[ilda+i+1:ilda+n], x, uintptr(n-i-1), 1, uintptr(incX), 0, uintptr(kx+(i+1)*incX))
+			if nonUnit {
+				x[ix] *= a[ilda+i]
+			}
+			ix -= incX
+		}
+		return
+	}
+	if incX == 1 {
+		for i := 0; i < n; i++ {
+			ilda := i * lda
+			xi := x[i]
+			f32.AxpyUnitary(xi, a[ilda:ilda+i], x)
+			if nonUnit {
+				x[i] *= a[i*lda+i]
+			}
+		}
+		return
+	}
+	ix := kx
+	for i := 0; i < n; i++ {
+		ilda := i * lda
+		xi := x[ix]
+		f32.AxpyInc(xi, a[ilda:ilda+i], x, uintptr(i), 1, uintptr(incX), 0, uintptr(kx))
+		if nonUnit {
+			x[ix] *= a[ilda+i]
+		}
+		ix += incX
+	}
+}
+
+// Strsv solves
+//  A * x = b if tA == blas.NoTrans
+//  A^T * x = b if tA == blas.Trans or blas.ConjTrans
+// A is an n×n triangular matrix and x is a vector.
+// At entry to the function, x contains the values of b, and the result is
+// stored in place into x.
+//
+// No test for singularity or near-singularity is included in this
+// routine. Such tests must be performed before calling this routine.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Strsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, a []float32, lda int, x []float32, incX int) {
+	// Test the input parameters
+	// Verify inputs
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	if d != blas.NonUnit && d != blas.Unit {
+		panic(badDiag)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if lda*(n-1)+n > len(a) || lda < max(1, n) {
+		panic(badLdA)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	// Quick return if possible
+	if n == 0 {
+		return
+	}
+	if n == 1 {
+		if d == blas.NonUnit {
+			x[0] /= a[0]
+		}
+		return
+	}
+
+	var kx int
+	if incX < 0 {
+		kx = -(n - 1) * incX
+	}
+	nonUnit := d == blas.NonUnit
+	if tA == blas.NoTrans {
+		if ul == blas.Upper {
+			if incX == 1 {
+				for i := n - 1; i >= 0; i-- {
+					var sum float32
+					atmp := a[i*lda+i+1 : i*lda+n]
+					for j, v := range atmp {
+						jv := i + j + 1
+						sum += x[jv] * v
+					}
+					x[i] -= sum
+					if nonUnit {
+						x[i] /= a[i*lda+i]
+					}
+				}
+				return
+			}
+			ix := kx + (n-1)*incX
+			for i := n - 1; i >= 0; i-- {
+				var sum float32
+				jx := ix + incX
+				atmp := a[i*lda+i+1 : i*lda+n]
+				for _, v := range atmp {
+					sum += x[jx] * v
+					jx += incX
+				}
+				x[ix] -= sum
+				if nonUnit {
+					x[ix] /= a[i*lda+i]
+				}
+				ix -= incX
+			}
+			return
+		}
+		if incX == 1 {
+			for i := 0; i < n; i++ {
+				var sum float32
+				atmp := a[i*lda : i*lda+i]
+				for j, v := range atmp {
+					sum += x[j] * v
+				}
+				x[i] -= sum
+				if nonUnit {
+					x[i] /= a[i*lda+i]
+				}
+			}
+			return
+		}
+		ix := kx
+		for i := 0; i < n; i++ {
+			jx := kx
+			var sum float32
+			atmp := a[i*lda : i*lda+i]
+			for _, v := range atmp {
+				sum += x[jx] * v
+				jx += incX
+			}
+			x[ix] -= sum
+			if nonUnit {
+				x[ix] /= a[i*lda+i]
+			}
+			ix += incX
+		}
+		return
+	}
+	// Cases where a is transposed.
+	if ul == blas.Upper {
+		if incX == 1 {
+			for i := 0; i < n; i++ {
+				if nonUnit {
+					x[i] /= a[i*lda+i]
+				}
+				xi := x[i]
+				atmp := a[i*lda+i+1 : i*lda+n]
+				for j, v := range atmp {
+					jv := j + i + 1
+					x[jv] -= v * xi
+				}
+			}
+			return
+		}
+		ix := kx
+		for i := 0; i < n; i++ {
+			if nonUnit {
+				x[ix] /= a[i*lda+i]
+			}
+			xi := x[ix]
+			jx := kx + (i+1)*incX
+			atmp := a[i*lda+i+1 : i*lda+n]
+			for _, v := range atmp {
+				x[jx] -= v * xi
+				jx += incX
+			}
+			ix += incX
+		}
+		return
+	}
+	if incX == 1 {
+		for i := n - 1; i >= 0; i-- {
+			if nonUnit {
+				x[i] /= a[i*lda+i]
+			}
+			xi := x[i]
+			atmp := a[i*lda : i*lda+i]
+			for j, v := range atmp {
+				x[j] -= v * xi
+			}
+		}
+		return
+	}
+	ix := kx + (n-1)*incX
+	for i := n - 1; i >= 0; i-- {
+		if nonUnit {
+			x[ix] /= a[i*lda+i]
+		}
+		xi := x[ix]
+		jx := kx
+		atmp := a[i*lda : i*lda+i]
+		for _, v := range atmp {
+			x[jx] -= v * xi
+			jx += incX
+		}
+		ix -= incX
+	}
+}
+
+// Ssymv computes
+//    y = alpha * A * x + beta * y,
+// where a is an n×n symmetric matrix, x and y are vectors, and alpha and
+// beta are scalars.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Ssymv(ul blas.Uplo, n int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int) {
+	// Check inputs
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if n < 0 {
+		panic(negativeN)
+	}
+	if lda > 1 && lda < n {
+		panic(badLdA)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
+		panic(badY)
+	}
+	if lda*(n-1)+n > len(a) || lda < max(1, n) {
+		panic(badLdA)
+	}
+	// Quick return if possible
+	if n == 0 || (alpha == 0 && beta == 1) {
+		return
+	}
+
+	// Set up start points
+	var kx, ky int
+	if incX > 0 {
+		kx = 0
+	} else {
+		kx = -(n - 1) * incX
+	}
+	if incY > 0 {
+		ky = 0
+	} else {
+		ky = -(n - 1) * incY
+	}
+
+	// Form y = beta * y
+	if beta != 1 {
+		if incY > 0 {
+			Implementation{}.Sscal(n, beta, y, incY)
+		} else {
+			Implementation{}.Sscal(n, beta, y, -incY)
+		}
+	}
+
+	if alpha == 0 {
+		return
+	}
+
+	if n == 1 {
+		y[0] += alpha * a[0] * x[0]
+		return
+	}
+
+	if ul == blas.Upper {
+		if incX == 1 {
+			iy := ky
+			for i := 0; i < n; i++ {
+				xv := x[i] * alpha
+				sum := x[i] * a[i*lda+i]
+				jy := ky + (i+1)*incY
+				atmp := a[i*lda+i+1 : i*lda+n]
+				for j, v := range atmp {
+					jp := j + i + 1
+					sum += x[jp] * v
+					y[jy] += xv * v
+					jy += incY
+				}
+				y[iy] += alpha * sum
+				iy += incY
+			}
+			return
+		}
+		ix := kx
+		iy := ky
+		for i := 0; i < n; i++ {
+			xv := x[ix] * alpha
+			sum := x[ix] * a[i*lda+i]
+			jx := kx + (i+1)*incX
+			jy := ky + (i+1)*incY
+			atmp := a[i*lda+i+1 : i*lda+n]
+			for _, v := range atmp {
+				sum += x[jx] * v
+				y[jy] += xv * v
+				jx += incX
+				jy += incY
+			}
+			y[iy] += alpha * sum
+			ix += incX
+			iy += incY
+		}
+		return
+	}
+	// Cases where a is lower triangular.
+	if incX == 1 {
+		iy := ky
+		for i := 0; i < n; i++ {
+			jy := ky
+			xv := alpha * x[i]
+			atmp := a[i*lda : i*lda+i]
+			var sum float32
+			for j, v := range atmp {
+				sum += x[j] * v
+				y[jy] += xv * v
+				jy += incY
+			}
+			sum += x[i] * a[i*lda+i]
+			sum *= alpha
+			y[iy] += sum
+			iy += incY
+		}
+		return
+	}
+	ix := kx
+	iy := ky
+	for i := 0; i < n; i++ {
+		jx := kx
+		jy := ky
+		xv := alpha * x[ix]
+		atmp := a[i*lda : i*lda+i]
+		var sum float32
+		for _, v := range atmp {
+			sum += x[jx] * v
+			y[jy] += xv * v
+			jx += incX
+			jy += incY
+		}
+		sum += x[ix] * a[i*lda+i]
+		sum *= alpha
+		y[iy] += sum
+		ix += incX
+		iy += incY
+	}
+}
+
+// Stbmv computes
+//  x = A * x if tA == blas.NoTrans
+//  x = A^T * x if tA == blas.Trans or blas.ConjTrans
+// where A is an n×n triangular banded matrix with k diagonals, and x is a vector.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Stbmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n, k int, a []float32, lda int, x []float32, incX int) {
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	if d != blas.NonUnit && d != blas.Unit {
+		panic(badDiag)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if k < 0 {
+		panic(kLT0)
+	}
+	if lda*(n-1)+k+1 > len(a) || lda < k+1 {
+		panic(badLdA)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if n == 0 {
+		return
+	}
+	var kx int
+	if incX <= 0 {
+		kx = -(n - 1) * incX
+	} else if incX != 1 {
+		kx = 0
+	}
+
+	nonunit := d != blas.Unit
+
+	if tA == blas.NoTrans {
+		if ul == blas.Upper {
+			if incX == 1 {
+				for i := 0; i < n; i++ {
+					u := min(1+k, n-i)
+					var sum float32
+					atmp := a[i*lda:]
+					xtmp := x[i:]
+					for j := 1; j < u; j++ {
+						sum += xtmp[j] * atmp[j]
+					}
+					if nonunit {
+						sum += xtmp[0] * atmp[0]
+					} else {
+						sum += xtmp[0]
+					}
+					x[i] = sum
+				}
+				return
+			}
+			ix := kx
+			for i := 0; i < n; i++ {
+				u := min(1+k, n-i)
+				var sum float32
+				atmp := a[i*lda:]
+				jx := incX
+				for j := 1; j < u; j++ {
+					sum += x[ix+jx] * atmp[j]
+					jx += incX
+				}
+				if nonunit {
+					sum += x[ix] * atmp[0]
+				} else {
+					sum += x[ix]
+				}
+				x[ix] = sum
+				ix += incX
+			}
+			return
+		}
+		if incX == 1 {
+			for i := n - 1; i >= 0; i-- {
+				l := max(0, k-i)
+				atmp := a[i*lda:]
+				var sum float32
+				for j := l; j < k; j++ {
+					sum += x[i-k+j] * atmp[j]
+				}
+				if nonunit {
+					sum += x[i] * atmp[k]
+				} else {
+					sum += x[i]
+				}
+				x[i] = sum
+			}
+			return
+		}
+		ix := kx + (n-1)*incX
+		for i := n - 1; i >= 0; i-- {
+			l := max(0, k-i)
+			atmp := a[i*lda:]
+			var sum float32
+			jx := l * incX
+			for j := l; j < k; j++ {
+				sum += x[ix-k*incX+jx] * atmp[j]
+				jx += incX
+			}
+			if nonunit {
+				sum += x[ix] * atmp[k]
+			} else {
+				sum += x[ix]
+			}
+			x[ix] = sum
+			ix -= incX
+		}
+		return
+	}
+	if ul == blas.Upper {
+		if incX == 1 {
+			for i := n - 1; i >= 0; i-- {
+				u := k + 1
+				if i < u {
+					u = i + 1
+				}
+				var sum float32
+				for j := 1; j < u; j++ {
+					sum += x[i-j] * a[(i-j)*lda+j]
+				}
+				if nonunit {
+					sum += x[i] * a[i*lda]
+				} else {
+					sum += x[i]
+				}
+				x[i] = sum
+			}
+			return
+		}
+		ix := kx + (n-1)*incX
+		for i := n - 1; i >= 0; i-- {
+			u := k + 1
+			if i < u {
+				u = i + 1
+			}
+			var sum float32
+			jx := incX
+			for j := 1; j < u; j++ {
+				sum += x[ix-jx] * a[(i-j)*lda+j]
+				jx += incX
+			}
+			if nonunit {
+				sum += x[ix] * a[i*lda]
+			} else {
+				sum += x[ix]
+			}
+			x[ix] = sum
+			ix -= incX
+		}
+		return
+	}
+	if incX == 1 {
+		for i := 0; i < n; i++ {
+			u := k
+			if i+k >= n {
+				u = n - i - 1
+			}
+			var sum float32
+			for j := 0; j < u; j++ {
+				sum += x[i+j+1] * a[(i+j+1)*lda+k-j-1]
+			}
+			if nonunit {
+				sum += x[i] * a[i*lda+k]
+			} else {
+				sum += x[i]
+			}
+			x[i] = sum
+		}
+		return
+	}
+	ix := kx
+	for i := 0; i < n; i++ {
+		u := k
+		if i+k >= n {
+			u = n - i - 1
+		}
+		var (
+			sum float32
+			jx  int
+		)
+		for j := 0; j < u; j++ {
+			sum += x[ix+jx+incX] * a[(i+j+1)*lda+k-j-1]
+			jx += incX
+		}
+		if nonunit {
+			sum += x[ix] * a[i*lda+k]
+		} else {
+			sum += x[ix]
+		}
+		x[ix] = sum
+		ix += incX
+	}
+}
+
+// Stpmv computes
+//  x = A * x if tA == blas.NoTrans
+//  x = A^T * x if tA == blas.Trans or blas.ConjTrans
+// where A is an n×n unit triangular matrix in packed format, and x is a vector.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Stpmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, ap []float32, x []float32, incX int) {
+	// Verify inputs
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	if d != blas.NonUnit && d != blas.Unit {
+		panic(badDiag)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if len(ap) < (n*(n+1))/2 {
+		panic(badLdA)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if n == 0 {
+		return
+	}
+	var kx int
+	if incX <= 0 {
+		kx = -(n - 1) * incX
+	}
+
+	nonUnit := d == blas.NonUnit
+	var offset int // Offset is the index of (i,i)
+	if tA == blas.NoTrans {
+		if ul == blas.Upper {
+			if incX == 1 {
+				for i := 0; i < n; i++ {
+					xi := x[i]
+					if nonUnit {
+						xi *= ap[offset]
+					}
+					atmp := ap[offset+1 : offset+n-i]
+					xtmp := x[i+1:]
+					for j, v := range atmp {
+						xi += v * xtmp[j]
+					}
+					x[i] = xi
+					offset += n - i
+				}
+				return
+			}
+			ix := kx
+			for i := 0; i < n; i++ {
+				xix := x[ix]
+				if nonUnit {
+					xix *= ap[offset]
+				}
+				atmp := ap[offset+1 : offset+n-i]
+				jx := kx + (i+1)*incX
+				for _, v := range atmp {
+					xix += v * x[jx]
+					jx += incX
+				}
+				x[ix] = xix
+				offset += n - i
+				ix += incX
+			}
+			return
+		}
+		if incX == 1 {
+			offset = n*(n+1)/2 - 1
+			for i := n - 1; i >= 0; i-- {
+				xi := x[i]
+				if nonUnit {
+					xi *= ap[offset]
+				}
+				atmp := ap[offset-i : offset]
+				for j, v := range atmp {
+					xi += v * x[j]
+				}
+				x[i] = xi
+				offset -= i + 1
+			}
+			return
+		}
+		ix := kx + (n-1)*incX
+		offset = n*(n+1)/2 - 1
+		for i := n - 1; i >= 0; i-- {
+			xix := x[ix]
+			if nonUnit {
+				xix *= ap[offset]
+			}
+			atmp := ap[offset-i : offset]
+			jx := kx
+			for _, v := range atmp {
+				xix += v * x[jx]
+				jx += incX
+			}
+			x[ix] = xix
+			offset -= i + 1
+			ix -= incX
+		}
+		return
+	}
+	// Cases where ap is transposed.
+	if ul == blas.Upper {
+		if incX == 1 {
+			offset = n*(n+1)/2 - 1
+			for i := n - 1; i >= 0; i-- {
+				xi := x[i]
+				atmp := ap[offset+1 : offset+n-i]
+				xtmp := x[i+1:]
+				for j, v := range atmp {
+					xtmp[j] += v * xi
+				}
+				if nonUnit {
+					x[i] *= ap[offset]
+				}
+				offset -= n - i + 1
+			}
+			return
+		}
+		ix := kx + (n-1)*incX
+		offset = n*(n+1)/2 - 1
+		for i := n - 1; i >= 0; i-- {
+			xix := x[ix]
+			jx := kx + (i+1)*incX
+			atmp := ap[offset+1 : offset+n-i]
+			for _, v := range atmp {
+				x[jx] += v * xix
+				jx += incX
+			}
+			if nonUnit {
+				x[ix] *= ap[offset]
+			}
+			offset -= n - i + 1
+			ix -= incX
+		}
+		return
+	}
+	if incX == 1 {
+		for i := 0; i < n; i++ {
+			xi := x[i]
+			atmp := ap[offset-i : offset]
+			for j, v := range atmp {
+				x[j] += v * xi
+			}
+			if nonUnit {
+				x[i] *= ap[offset]
+			}
+			offset += i + 2
+		}
+		return
+	}
+	ix := kx
+	for i := 0; i < n; i++ {
+		xix := x[ix]
+		jx := kx
+		atmp := ap[offset-i : offset]
+		for _, v := range atmp {
+			x[jx] += v * xix
+			jx += incX
+		}
+		if nonUnit {
+			x[ix] *= ap[offset]
+		}
+		ix += incX
+		offset += i + 2
+	}
+}
+
+// Stbsv solves
+//  A * x = b
+// where A is an n×n triangular banded matrix with k diagonals in packed format,
+// and x is a vector.
+// At entry to the function, x contains the values of b, and the result is
+// stored in place into x.
+//
+// No test for singularity or near-singularity is included in this
+// routine. Such tests must be performed before calling this routine.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Stbsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n, k int, a []float32, lda int, x []float32, incX int) {
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	if d != blas.NonUnit && d != blas.Unit {
+		panic(badDiag)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if lda*(n-1)+k+1 > len(a) || lda < k+1 {
+		panic(badLdA)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if n == 0 {
+		return
+	}
+	var kx int
+	if incX < 0 {
+		kx = -(n - 1) * incX
+	} else {
+		kx = 0
+	}
+	nonUnit := d == blas.NonUnit
+	// Form x = A^-1 x.
+	// Several cases below use subslices for speed improvement.
+	// The incX != 1 cases usually do not because incX may be negative.
+	if tA == blas.NoTrans {
+		if ul == blas.Upper {
+			if incX == 1 {
+				for i := n - 1; i >= 0; i-- {
+					bands := k
+					if i+bands >= n {
+						bands = n - i - 1
+					}
+					atmp := a[i*lda+1:]
+					xtmp := x[i+1 : i+bands+1]
+					var sum float32
+					for j, v := range xtmp {
+						sum += v * atmp[j]
+					}
+					x[i] -= sum
+					if nonUnit {
+						x[i] /= a[i*lda]
+					}
+				}
+				return
+			}
+			ix := kx + (n-1)*incX
+			for i := n - 1; i >= 0; i-- {
+				max := k + 1
+				if i+max > n {
+					max = n - i
+				}
+				atmp := a[i*lda:]
+				var (
+					jx  int
+					sum float32
+				)
+				for j := 1; j < max; j++ {
+					jx += incX
+					sum += x[ix+jx] * atmp[j]
+				}
+				x[ix] -= sum
+				if nonUnit {
+					x[ix] /= atmp[0]
+				}
+				ix -= incX
+			}
+			return
+		}
+		if incX == 1 {
+			for i := 0; i < n; i++ {
+				bands := k
+				if i-k < 0 {
+					bands = i
+				}
+				atmp := a[i*lda+k-bands:]
+				xtmp := x[i-bands : i]
+				var sum float32
+				for j, v := range xtmp {
+					sum += v * atmp[j]
+				}
+				x[i] -= sum
+				if nonUnit {
+					x[i] /= atmp[bands]
+				}
+			}
+			return
+		}
+		ix := kx
+		for i := 0; i < n; i++ {
+			bands := k
+			if i-k < 0 {
+				bands = i
+			}
+			atmp := a[i*lda+k-bands:]
+			var (
+				sum float32
+				jx  int
+			)
+			for j := 0; j < bands; j++ {
+				sum += x[ix-bands*incX+jx] * atmp[j]
+				jx += incX
+			}
+			x[ix] -= sum
+			if nonUnit {
+				x[ix] /= atmp[bands]
+			}
+			ix += incX
+		}
+		return
+	}
+	// Cases where a is transposed.
+	if ul == blas.Upper {
+		if incX == 1 {
+			for i := 0; i < n; i++ {
+				bands := k
+				if i-k < 0 {
+					bands = i
+				}
+				var sum float32
+				for j := 0; j < bands; j++ {
+					sum += x[i-bands+j] * a[(i-bands+j)*lda+bands-j]
+				}
+				x[i] -= sum
+				if nonUnit {
+					x[i] /= a[i*lda]
+				}
+			}
+			return
+		}
+		ix := kx
+		for i := 0; i < n; i++ {
+			bands := k
+			if i-k < 0 {
+				bands = i
+			}
+			var (
+				sum float32
+				jx  int
+			)
+			for j := 0; j < bands; j++ {
+				sum += x[ix-bands*incX+jx] * a[(i-bands+j)*lda+bands-j]
+				jx += incX
+			}
+			x[ix] -= sum
+			if nonUnit {
+				x[ix] /= a[i*lda]
+			}
+			ix += incX
+		}
+		return
+	}
+	if incX == 1 {
+		for i := n - 1; i >= 0; i-- {
+			bands := k
+			if i+bands >= n {
+				bands = n - i - 1
+			}
+			var sum float32
+			xtmp := x[i+1 : i+1+bands]
+			for j, v := range xtmp {
+				sum += v * a[(i+j+1)*lda+k-j-1]
+			}
+			x[i] -= sum
+			if nonUnit {
+				x[i] /= a[i*lda+k]
+			}
+		}
+		return
+	}
+	ix := kx + (n-1)*incX
+	for i := n - 1; i >= 0; i-- {
+		bands := k
+		if i+bands >= n {
+			bands = n - i - 1
+		}
+		var (
+			sum float32
+			jx  int
+		)
+		for j := 0; j < bands; j++ {
+			sum += x[ix+jx+incX] * a[(i+j+1)*lda+k-j-1]
+			jx += incX
+		}
+		x[ix] -= sum
+		if nonUnit {
+			x[ix] /= a[i*lda+k]
+		}
+		ix -= incX
+	}
+}
+
+// Ssbmv performs
+//  y = alpha * A * x + beta * y
+// where A is an n×n symmetric banded matrix, x and y are vectors, and alpha
+// and beta are scalars.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Ssbmv(ul blas.Uplo, n, k int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int) {
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
+		panic(badY)
+	}
+	if lda*(n-1)+k+1 > len(a) || lda < k+1 {
+		panic(badLdA)
+	}
+
+	// Quick return if possible
+	if n == 0 || (alpha == 0 && beta == 1) {
+		return
+	}
+
+	// Set up indexes
+	lenX := n
+	lenY := n
+	var kx, ky int
+	if incX > 0 {
+		kx = 0
+	} else {
+		kx = -(lenX - 1) * incX
+	}
+	if incY > 0 {
+		ky = 0
+	} else {
+		ky = -(lenY - 1) * incY
+	}
+
+	// First form y := beta * y
+	if incY > 0 {
+		Implementation{}.Sscal(lenY, beta, y, incY)
+	} else {
+		Implementation{}.Sscal(lenY, beta, y, -incY)
+	}
+
+	if alpha == 0 {
+		return
+	}
+
+	if ul == blas.Upper {
+		if incX == 1 {
+			iy := ky
+			for i := 0; i < n; i++ {
+				atmp := a[i*lda:]
+				tmp := alpha * x[i]
+				sum := tmp * atmp[0]
+				u := min(k, n-i-1)
+				jy := incY
+				for j := 1; j <= u; j++ {
+					v := atmp[j]
+					sum += alpha * x[i+j] * v
+					y[iy+jy] += tmp * v
+					jy += incY
+				}
+				y[iy] += sum
+				iy += incY
+			}
+			return
+		}
+		ix := kx
+		iy := ky
+		for i := 0; i < n; i++ {
+			atmp := a[i*lda:]
+			tmp := alpha * x[ix]
+			sum := tmp * atmp[0]
+			u := min(k, n-i-1)
+			jx := incX
+			jy := incY
+			for j := 1; j <= u; j++ {
+				v := atmp[j]
+				sum += alpha * x[ix+jx] * v
+				y[iy+jy] += tmp * v
+				jx += incX
+				jy += incY
+			}
+			y[iy] += sum
+			ix += incX
+			iy += incY
+		}
+		return
+	}
+
+	// Casses where a has bands below the diagonal.
+	if incX == 1 {
+		iy := ky
+		for i := 0; i < n; i++ {
+			l := max(0, k-i)
+			tmp := alpha * x[i]
+			jy := l * incY
+			atmp := a[i*lda:]
+			for j := l; j < k; j++ {
+				v := atmp[j]
+				y[iy] += alpha * v * x[i-k+j]
+				y[iy-k*incY+jy] += tmp * v
+				jy += incY
+			}
+			y[iy] += tmp * atmp[k]
+			iy += incY
+		}
+		return
+	}
+	ix := kx
+	iy := ky
+	for i := 0; i < n; i++ {
+		l := max(0, k-i)
+		tmp := alpha * x[ix]
+		jx := l * incX
+		jy := l * incY
+		atmp := a[i*lda:]
+		for j := l; j < k; j++ {
+			v := atmp[j]
+			y[iy] += alpha * v * x[ix-k*incX+jx]
+			y[iy-k*incY+jy] += tmp * v
+			jx += incX
+			jy += incY
+		}
+		y[iy] += tmp * atmp[k]
+		ix += incX
+		iy += incY
+	}
+}
+
+// Ssyr performs the rank-one update
+//  a += alpha * x * x^T
+// where a is an n×n symmetric matrix, and x is a vector.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Ssyr(ul blas.Uplo, n int, alpha float32, x []float32, incX int, a []float32, lda int) {
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if lda*(n-1)+n > len(a) || lda < max(1, n) {
+		panic(badLdA)
+	}
+	if alpha == 0 || n == 0 {
+		return
+	}
+
+	lenX := n
+	var kx int
+	if incX > 0 {
+		kx = 0
+	} else {
+		kx = -(lenX - 1) * incX
+	}
+	if ul == blas.Upper {
+		if incX == 1 {
+			for i := 0; i < n; i++ {
+				tmp := x[i] * alpha
+				if tmp != 0 {
+					atmp := a[i*lda+i : i*lda+n]
+					xtmp := x[i:n]
+					for j, v := range xtmp {
+						atmp[j] += v * tmp
+					}
+				}
+			}
+			return
+		}
+		ix := kx
+		for i := 0; i < n; i++ {
+			tmp := x[ix] * alpha
+			if tmp != 0 {
+				jx := ix
+				atmp := a[i*lda:]
+				for j := i; j < n; j++ {
+					atmp[j] += x[jx] * tmp
+					jx += incX
+				}
+			}
+			ix += incX
+		}
+		return
+	}
+	// Cases where a is lower triangular.
+	if incX == 1 {
+		for i := 0; i < n; i++ {
+			tmp := x[i] * alpha
+			if tmp != 0 {
+				atmp := a[i*lda:]
+				xtmp := x[:i+1]
+				for j, v := range xtmp {
+					atmp[j] += tmp * v
+				}
+			}
+		}
+		return
+	}
+	ix := kx
+	for i := 0; i < n; i++ {
+		tmp := x[ix] * alpha
+		if tmp != 0 {
+			atmp := a[i*lda:]
+			jx := kx
+			for j := 0; j < i+1; j++ {
+				atmp[j] += tmp * x[jx]
+				jx += incX
+			}
+		}
+		ix += incX
+	}
+}
+
+// Ssyr2 performs the symmetric rank-two update
+//  A += alpha * x * y^T + alpha * y * x^T
+// where A is a symmetric n×n matrix, x and y are vectors, and alpha is a scalar.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Ssyr2(ul blas.Uplo, n int, alpha float32, x []float32, incX int, y []float32, incY int, a []float32, lda int) {
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
+		panic(badY)
+	}
+	if lda*(n-1)+n > len(a) || lda < max(1, n) {
+		panic(badLdA)
+	}
+	if alpha == 0 {
+		return
+	}
+
+	var ky, kx int
+	if incY > 0 {
+		ky = 0
+	} else {
+		ky = -(n - 1) * incY
+	}
+	if incX > 0 {
+		kx = 0
+	} else {
+		kx = -(n - 1) * incX
+	}
+	if ul == blas.Upper {
+		if incX == 1 && incY == 1 {
+			for i := 0; i < n; i++ {
+				xi := x[i]
+				yi := y[i]
+				atmp := a[i*lda:]
+				for j := i; j < n; j++ {
+					atmp[j] += alpha * (xi*y[j] + x[j]*yi)
+				}
+			}
+			return
+		}
+		ix := kx
+		iy := ky
+		for i := 0; i < n; i++ {
+			jx := kx + i*incX
+			jy := ky + i*incY
+			xi := x[ix]
+			yi := y[iy]
+			atmp := a[i*lda:]
+			for j := i; j < n; j++ {
+				atmp[j] += alpha * (xi*y[jy] + x[jx]*yi)
+				jx += incX
+				jy += incY
+			}
+			ix += incX
+			iy += incY
+		}
+		return
+	}
+	if incX == 1 && incY == 1 {
+		for i := 0; i < n; i++ {
+			xi := x[i]
+			yi := y[i]
+			atmp := a[i*lda:]
+			for j := 0; j <= i; j++ {
+				atmp[j] += alpha * (xi*y[j] + x[j]*yi)
+			}
+		}
+		return
+	}
+	ix := kx
+	iy := ky
+	for i := 0; i < n; i++ {
+		jx := kx
+		jy := ky
+		xi := x[ix]
+		yi := y[iy]
+		atmp := a[i*lda:]
+		for j := 0; j <= i; j++ {
+			atmp[j] += alpha * (xi*y[jy] + x[jx]*yi)
+			jx += incX
+			jy += incY
+		}
+		ix += incX
+		iy += incY
+	}
+}
+
+// Stpsv solves
+//  A * x = b if tA == blas.NoTrans
+//  A^T * x = b if tA == blas.Trans or blas.ConjTrans
+// where A is an n×n triangular matrix in packed format and x is a vector.
+// At entry to the function, x contains the values of b, and the result is
+// stored in place into x.
+//
+// No test for singularity or near-singularity is included in this
+// routine. Such tests must be performed before calling this routine.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Stpsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, ap []float32, x []float32, incX int) {
+	// Verify inputs
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	if d != blas.NonUnit && d != blas.Unit {
+		panic(badDiag)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if len(ap) < (n*(n+1))/2 {
+		panic(badLdA)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if n == 0 {
+		return
+	}
+	var kx int
+	if incX <= 0 {
+		kx = -(n - 1) * incX
+	}
+
+	nonUnit := d == blas.NonUnit
+	var offset int // Offset is the index of (i,i)
+	if tA == blas.NoTrans {
+		if ul == blas.Upper {
+			offset = n*(n+1)/2 - 1
+			if incX == 1 {
+				for i := n - 1; i >= 0; i-- {
+					atmp := ap[offset+1 : offset+n-i]
+					xtmp := x[i+1:]
+					var sum float32
+					for j, v := range atmp {
+						sum += v * xtmp[j]
+					}
+					x[i] -= sum
+					if nonUnit {
+						x[i] /= ap[offset]
+					}
+					offset -= n - i + 1
+				}
+				return
+			}
+			ix := kx + (n-1)*incX
+			for i := n - 1; i >= 0; i-- {
+				atmp := ap[offset+1 : offset+n-i]
+				jx := kx + (i+1)*incX
+				var sum float32
+				for _, v := range atmp {
+					sum += v * x[jx]
+					jx += incX
+				}
+				x[ix] -= sum
+				if nonUnit {
+					x[ix] /= ap[offset]
+				}
+				ix -= incX
+				offset -= n - i + 1
+			}
+			return
+		}
+		if incX == 1 {
+			for i := 0; i < n; i++ {
+				atmp := ap[offset-i : offset]
+				var sum float32
+				for j, v := range atmp {
+					sum += v * x[j]
+				}
+				x[i] -= sum
+				if nonUnit {
+					x[i] /= ap[offset]
+				}
+				offset += i + 2
+			}
+			return
+		}
+		ix := kx
+		for i := 0; i < n; i++ {
+			jx := kx
+			atmp := ap[offset-i : offset]
+			var sum float32
+			for _, v := range atmp {
+				sum += v * x[jx]
+				jx += incX
+			}
+			x[ix] -= sum
+			if nonUnit {
+				x[ix] /= ap[offset]
+			}
+			ix += incX
+			offset += i + 2
+		}
+		return
+	}
+	// Cases where ap is transposed.
+	if ul == blas.Upper {
+		if incX == 1 {
+			for i := 0; i < n; i++ {
+				if nonUnit {
+					x[i] /= ap[offset]
+				}
+				xi := x[i]
+				atmp := ap[offset+1 : offset+n-i]
+				xtmp := x[i+1:]
+				for j, v := range atmp {
+					xtmp[j] -= v * xi
+				}
+				offset += n - i
+			}
+			return
+		}
+		ix := kx
+		for i := 0; i < n; i++ {
+			if nonUnit {
+				x[ix] /= ap[offset]
+			}
+			xix := x[ix]
+			atmp := ap[offset+1 : offset+n-i]
+			jx := kx + (i+1)*incX
+			for _, v := range atmp {
+				x[jx] -= v * xix
+				jx += incX
+			}
+			ix += incX
+			offset += n - i
+		}
+		return
+	}
+	if incX == 1 {
+		offset = n*(n+1)/2 - 1
+		for i := n - 1; i >= 0; i-- {
+			if nonUnit {
+				x[i] /= ap[offset]
+			}
+			xi := x[i]
+			atmp := ap[offset-i : offset]
+			for j, v := range atmp {
+				x[j] -= v * xi
+			}
+			offset -= i + 1
+		}
+		return
+	}
+	ix := kx + (n-1)*incX
+	offset = n*(n+1)/2 - 1
+	for i := n - 1; i >= 0; i-- {
+		if nonUnit {
+			x[ix] /= ap[offset]
+		}
+		xix := x[ix]
+		atmp := ap[offset-i : offset]
+		jx := kx
+		for _, v := range atmp {
+			x[jx] -= v * xix
+			jx += incX
+		}
+		ix -= incX
+		offset -= i + 1
+	}
+}
+
+// Sspmv performs
+//    y = alpha * A * x + beta * y,
+// where A is an n×n symmetric matrix in packed format, x and y are vectors
+// and alpha and beta are scalars.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Sspmv(ul blas.Uplo, n int, alpha float32, a []float32, x []float32, incX int, beta float32, y []float32, incY int) {
+	// Verify inputs
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if len(a) < (n*(n+1))/2 {
+		panic(badLdA)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
+		panic(badY)
+	}
+	// Quick return if possible
+	if n == 0 || (alpha == 0 && beta == 1) {
+		return
+	}
+
+	// Set up start points
+	var kx, ky int
+	if incX > 0 {
+		kx = 0
+	} else {
+		kx = -(n - 1) * incX
+	}
+	if incY > 0 {
+		ky = 0
+	} else {
+		ky = -(n - 1) * incY
+	}
+
+	// Form y = beta * y
+	if beta != 1 {
+		if incY > 0 {
+			Implementation{}.Sscal(n, beta, y, incY)
+		} else {
+			Implementation{}.Sscal(n, beta, y, -incY)
+		}
+	}
+
+	if alpha == 0 {
+		return
+	}
+
+	if n == 1 {
+		y[0] += alpha * a[0] * x[0]
+		return
+	}
+	var offset int // Offset is the index of (i,i).
+	if ul == blas.Upper {
+		if incX == 1 {
+			iy := ky
+			for i := 0; i < n; i++ {
+				xv := x[i] * alpha
+				sum := a[offset] * x[i]
+				atmp := a[offset+1 : offset+n-i]
+				xtmp := x[i+1:]
+				jy := ky + (i+1)*incY
+				for j, v := range atmp {
+					sum += v * xtmp[j]
+					y[jy] += v * xv
+					jy += incY
+				}
+				y[iy] += alpha * sum
+				iy += incY
+				offset += n - i
+			}
+			return
+		}
+		ix := kx
+		iy := ky
+		for i := 0; i < n; i++ {
+			xv := x[ix] * alpha
+			sum := a[offset] * x[ix]
+			atmp := a[offset+1 : offset+n-i]
+			jx := kx + (i+1)*incX
+			jy := ky + (i+1)*incY
+			for _, v := range atmp {
+				sum += v * x[jx]
+				y[jy] += v * xv
+				jx += incX
+				jy += incY
+			}
+			y[iy] += alpha * sum
+			ix += incX
+			iy += incY
+			offset += n - i
+		}
+		return
+	}
+	if incX == 1 {
+		iy := ky
+		for i := 0; i < n; i++ {
+			xv := x[i] * alpha
+			atmp := a[offset-i : offset]
+			jy := ky
+			var sum float32
+			for j, v := range atmp {
+				sum += v * x[j]
+				y[jy] += v * xv
+				jy += incY
+			}
+			sum += a[offset] * x[i]
+			y[iy] += alpha * sum
+			iy += incY
+			offset += i + 2
+		}
+		return
+	}
+	ix := kx
+	iy := ky
+	for i := 0; i < n; i++ {
+		xv := x[ix] * alpha
+		atmp := a[offset-i : offset]
+		jx := kx
+		jy := ky
+		var sum float32
+		for _, v := range atmp {
+			sum += v * x[jx]
+			y[jy] += v * xv
+			jx += incX
+			jy += incY
+		}
+
+		sum += a[offset] * x[ix]
+		y[iy] += alpha * sum
+		ix += incX
+		iy += incY
+		offset += i + 2
+	}
+}
+
+// Sspr computes the rank-one operation
+//  a += alpha * x * x^T
+// where a is an n×n symmetric matrix in packed format, x is a vector, and
+// alpha is a scalar.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Sspr(ul blas.Uplo, n int, alpha float32, x []float32, incX int, a []float32) {
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if len(a) < (n*(n+1))/2 {
+		panic(badLdA)
+	}
+	if alpha == 0 || n == 0 {
+		return
+	}
+	lenX := n
+	var kx int
+	if incX > 0 {
+		kx = 0
+	} else {
+		kx = -(lenX - 1) * incX
+	}
+	var offset int // Offset is the index of (i,i).
+	if ul == blas.Upper {
+		if incX == 1 {
+			for i := 0; i < n; i++ {
+				atmp := a[offset:]
+				xv := alpha * x[i]
+				xtmp := x[i:n]
+				for j, v := range xtmp {
+					atmp[j] += xv * v
+				}
+				offset += n - i
+			}
+			return
+		}
+		ix := kx
+		for i := 0; i < n; i++ {
+			jx := kx + i*incX
+			atmp := a[offset:]
+			xv := alpha * x[ix]
+			for j := 0; j < n-i; j++ {
+				atmp[j] += xv * x[jx]
+				jx += incX
+			}
+			ix += incX
+			offset += n - i
+		}
+		return
+	}
+	if incX == 1 {
+		for i := 0; i < n; i++ {
+			atmp := a[offset-i:]
+			xv := alpha * x[i]
+			xtmp := x[:i+1]
+			for j, v := range xtmp {
+				atmp[j] += xv * v
+			}
+			offset += i + 2
+		}
+		return
+	}
+	ix := kx
+	for i := 0; i < n; i++ {
+		jx := kx
+		atmp := a[offset-i:]
+		xv := alpha * x[ix]
+		for j := 0; j <= i; j++ {
+			atmp[j] += xv * x[jx]
+			jx += incX
+		}
+		ix += incX
+		offset += i + 2
+	}
+}
+
+// Sspr2 performs the symmetric rank-2 update
+//  A += alpha * x * y^T + alpha * y * x^T,
+// where A is an n×n symmetric matrix in packed format, x and y are vectors,
+// and alpha is a scalar.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Sspr2(ul blas.Uplo, n int, alpha float32, x []float32, incX int, y []float32, incY int, ap []float32) {
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if incX == 0 {
+		panic(zeroIncX)
+	}
+	if incY == 0 {
+		panic(zeroIncY)
+	}
+	if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
+		panic(badX)
+	}
+	if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
+		panic(badY)
+	}
+	if len(ap) < (n*(n+1))/2 {
+		panic(badLdA)
+	}
+	if alpha == 0 {
+		return
+	}
+	var ky, kx int
+	if incY > 0 {
+		ky = 0
+	} else {
+		ky = -(n - 1) * incY
+	}
+	if incX > 0 {
+		kx = 0
+	} else {
+		kx = -(n - 1) * incX
+	}
+	var offset int // Offset is the index of (i,i).
+	if ul == blas.Upper {
+		if incX == 1 && incY == 1 {
+			for i := 0; i < n; i++ {
+				atmp := ap[offset:]
+				xi := x[i]
+				yi := y[i]
+				xtmp := x[i:n]
+				ytmp := y[i:n]
+				for j, v := range xtmp {
+					atmp[j] += alpha * (xi*ytmp[j] + v*yi)
+				}
+				offset += n - i
+			}
+			return
+		}
+		ix := kx
+		iy := ky
+		for i := 0; i < n; i++ {
+			jx := kx + i*incX
+			jy := ky + i*incY
+			atmp := ap[offset:]
+			xi := x[ix]
+			yi := y[iy]
+			for j := 0; j < n-i; j++ {
+				atmp[j] += alpha * (xi*y[jy] + x[jx]*yi)
+				jx += incX
+				jy += incY
+			}
+			ix += incX
+			iy += incY
+			offset += n - i
+		}
+		return
+	}
+	if incX == 1 && incY == 1 {
+		for i := 0; i < n; i++ {
+			atmp := ap[offset-i:]
+			xi := x[i]
+			yi := y[i]
+			xtmp := x[:i+1]
+			for j, v := range xtmp {
+				atmp[j] += alpha * (xi*y[j] + v*yi)
+			}
+			offset += i + 2
+		}
+		return
+	}
+	ix := kx
+	iy := ky
+	for i := 0; i < n; i++ {
+		jx := kx
+		jy := ky
+		atmp := ap[offset-i:]
+		for j := 0; j <= i; j++ {
+			atmp[j] += alpha * (x[ix]*y[jy] + x[jx]*y[iy])
+			jx += incX
+			jy += incY
+		}
+		ix += incX
+		iy += incY
+		offset += i + 2
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/level3double.go b/vendor/gonum.org/v1/gonum/blas/gonum/level3double.go
new file mode 100644
index 00000000..b5001dcb
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/level3double.go
@@ -0,0 +1,831 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/internal/asm/f64"
+)
+
+var _ blas.Float64Level3 = Implementation{}
+
+// Dtrsm solves
+//  A * X = alpha * B,   if tA == blas.NoTrans side == blas.Left,
+//  A^T * X = alpha * B, if tA == blas.Trans or blas.ConjTrans, and side == blas.Left,
+//  X * A = alpha * B,   if tA == blas.NoTrans side == blas.Right,
+//  X * A^T = alpha * B, if tA == blas.Trans or blas.ConjTrans, and side == blas.Right,
+// where A is an n×n or m×m triangular matrix, X is an m×n matrix, and alpha is a
+// scalar.
+//
+// At entry to the function, X contains the values of B, and the result is
+// stored in place into X.
+//
+// No check is made that A is invertible.
+func (Implementation) Dtrsm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int) {
+	if s != blas.Left && s != blas.Right {
+		panic(badSide)
+	}
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	if d != blas.NonUnit && d != blas.Unit {
+		panic(badDiag)
+	}
+	if m < 0 {
+		panic(mLT0)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if ldb < n {
+		panic(badLdB)
+	}
+	var k int
+	if s == blas.Left {
+		k = m
+	} else {
+		k = n
+	}
+	if lda*(k-1)+k > len(a) || lda < max(1, k) {
+		panic(badLdA)
+	}
+	if ldb*(m-1)+n > len(b) || ldb < max(1, n) {
+		panic(badLdB)
+	}
+
+	if m == 0 || n == 0 {
+		return
+	}
+
+	if alpha == 0 {
+		for i := 0; i < m; i++ {
+			btmp := b[i*ldb : i*ldb+n]
+			for j := range btmp {
+				btmp[j] = 0
+			}
+		}
+		return
+	}
+	nonUnit := d == blas.NonUnit
+	if s == blas.Left {
+		if tA == blas.NoTrans {
+			if ul == blas.Upper {
+				for i := m - 1; i >= 0; i-- {
+					btmp := b[i*ldb : i*ldb+n]
+					if alpha != 1 {
+						for j := range btmp {
+							btmp[j] *= alpha
+						}
+					}
+					for ka, va := range a[i*lda+i+1 : i*lda+m] {
+						k := ka + i + 1
+						if va != 0 {
+							f64.AxpyUnitaryTo(btmp, -va, b[k*ldb:k*ldb+n], btmp)
+						}
+					}
+					if nonUnit {
+						tmp := 1 / a[i*lda+i]
+						for j := 0; j < n; j++ {
+							btmp[j] *= tmp
+						}
+					}
+				}
+				return
+			}
+			for i := 0; i < m; i++ {
+				btmp := b[i*ldb : i*ldb+n]
+				if alpha != 1 {
+					for j := 0; j < n; j++ {
+						btmp[j] *= alpha
+					}
+				}
+				for k, va := range a[i*lda : i*lda+i] {
+					if va != 0 {
+						f64.AxpyUnitaryTo(btmp, -va, b[k*ldb:k*ldb+n], btmp)
+					}
+				}
+				if nonUnit {
+					tmp := 1 / a[i*lda+i]
+					for j := 0; j < n; j++ {
+						btmp[j] *= tmp
+					}
+				}
+			}
+			return
+		}
+		// Cases where a is transposed
+		if ul == blas.Upper {
+			for k := 0; k < m; k++ {
+				btmpk := b[k*ldb : k*ldb+n]
+				if nonUnit {
+					tmp := 1 / a[k*lda+k]
+					for j := 0; j < n; j++ {
+						btmpk[j] *= tmp
+					}
+				}
+				for ia, va := range a[k*lda+k+1 : k*lda+m] {
+					i := ia + k + 1
+					if va != 0 {
+						btmp := b[i*ldb : i*ldb+n]
+						f64.AxpyUnitaryTo(btmp, -va, btmpk, btmp)
+					}
+				}
+				if alpha != 1 {
+					for j := 0; j < n; j++ {
+						btmpk[j] *= alpha
+					}
+				}
+			}
+			return
+		}
+		for k := m - 1; k >= 0; k-- {
+			btmpk := b[k*ldb : k*ldb+n]
+			if nonUnit {
+				tmp := 1 / a[k*lda+k]
+				for j := 0; j < n; j++ {
+					btmpk[j] *= tmp
+				}
+			}
+			for i, va := range a[k*lda : k*lda+k] {
+				if va != 0 {
+					btmp := b[i*ldb : i*ldb+n]
+					f64.AxpyUnitaryTo(btmp, -va, btmpk, btmp)
+				}
+			}
+			if alpha != 1 {
+				for j := 0; j < n; j++ {
+					btmpk[j] *= alpha
+				}
+			}
+		}
+		return
+	}
+	// Cases where a is to the right of X.
+	if tA == blas.NoTrans {
+		if ul == blas.Upper {
+			for i := 0; i < m; i++ {
+				btmp := b[i*ldb : i*ldb+n]
+				if alpha != 1 {
+					for j := 0; j < n; j++ {
+						btmp[j] *= alpha
+					}
+				}
+				for k, vb := range btmp {
+					if vb != 0 {
+						if btmp[k] != 0 {
+							if nonUnit {
+								btmp[k] /= a[k*lda+k]
+							}
+							btmpk := btmp[k+1 : n]
+							f64.AxpyUnitaryTo(btmpk, -btmp[k], a[k*lda+k+1:k*lda+n], btmpk)
+						}
+					}
+				}
+			}
+			return
+		}
+		for i := 0; i < m; i++ {
+			btmp := b[i*lda : i*lda+n]
+			if alpha != 1 {
+				for j := 0; j < n; j++ {
+					btmp[j] *= alpha
+				}
+			}
+			for k := n - 1; k >= 0; k-- {
+				if btmp[k] != 0 {
+					if nonUnit {
+						btmp[k] /= a[k*lda+k]
+					}
+					f64.AxpyUnitaryTo(btmp, -btmp[k], a[k*lda:k*lda+k], btmp)
+				}
+			}
+		}
+		return
+	}
+	// Cases where a is transposed.
+	if ul == blas.Upper {
+		for i := 0; i < m; i++ {
+			btmp := b[i*lda : i*lda+n]
+			for j := n - 1; j >= 0; j-- {
+				tmp := alpha*btmp[j] - f64.DotUnitary(a[j*lda+j+1:j*lda+n], btmp[j+1:])
+				if nonUnit {
+					tmp /= a[j*lda+j]
+				}
+				btmp[j] = tmp
+			}
+		}
+		return
+	}
+	for i := 0; i < m; i++ {
+		btmp := b[i*lda : i*lda+n]
+		for j := 0; j < n; j++ {
+			tmp := alpha*btmp[j] - f64.DotUnitary(a[j*lda:j*lda+j], btmp)
+			if nonUnit {
+				tmp /= a[j*lda+j]
+			}
+			btmp[j] = tmp
+		}
+	}
+}
+
+// Dsymm performs one of
+//  C = alpha * A * B + beta * C, if side == blas.Left,
+//  C = alpha * B * A + beta * C, if side == blas.Right,
+// where A is an n×n or m×m symmetric matrix, B and C are m×n matrices, and alpha
+// is a scalar.
+func (Implementation) Dsymm(s blas.Side, ul blas.Uplo, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int) {
+	if s != blas.Right && s != blas.Left {
+		panic("goblas: bad side")
+	}
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if m < 0 {
+		panic(mLT0)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	var k int
+	if s == blas.Left {
+		k = m
+	} else {
+		k = n
+	}
+	if lda*(k-1)+k > len(a) || lda < max(1, k) {
+		panic(badLdA)
+	}
+	if ldb*(m-1)+n > len(b) || ldb < max(1, n) {
+		panic(badLdB)
+	}
+	if ldc*(m-1)+n > len(c) || ldc < max(1, n) {
+		panic(badLdC)
+	}
+	if m == 0 || n == 0 {
+		return
+	}
+	if alpha == 0 && beta == 1 {
+		return
+	}
+	if alpha == 0 {
+		if beta == 0 {
+			for i := 0; i < m; i++ {
+				ctmp := c[i*ldc : i*ldc+n]
+				for j := range ctmp {
+					ctmp[j] = 0
+				}
+			}
+			return
+		}
+		for i := 0; i < m; i++ {
+			ctmp := c[i*ldc : i*ldc+n]
+			for j := 0; j < n; j++ {
+				ctmp[j] *= beta
+			}
+		}
+		return
+	}
+
+	isUpper := ul == blas.Upper
+	if s == blas.Left {
+		for i := 0; i < m; i++ {
+			atmp := alpha * a[i*lda+i]
+			btmp := b[i*ldb : i*ldb+n]
+			ctmp := c[i*ldc : i*ldc+n]
+			for j, v := range btmp {
+				ctmp[j] *= beta
+				ctmp[j] += atmp * v
+			}
+
+			for k := 0; k < i; k++ {
+				var atmp float64
+				if isUpper {
+					atmp = a[k*lda+i]
+				} else {
+					atmp = a[i*lda+k]
+				}
+				atmp *= alpha
+				ctmp := c[i*ldc : i*ldc+n]
+				f64.AxpyUnitaryTo(ctmp, atmp, b[k*ldb:k*ldb+n], ctmp)
+			}
+			for k := i + 1; k < m; k++ {
+				var atmp float64
+				if isUpper {
+					atmp = a[i*lda+k]
+				} else {
+					atmp = a[k*lda+i]
+				}
+				atmp *= alpha
+				ctmp := c[i*ldc : i*ldc+n]
+				f64.AxpyUnitaryTo(ctmp, atmp, b[k*ldb:k*ldb+n], ctmp)
+			}
+		}
+		return
+	}
+	if isUpper {
+		for i := 0; i < m; i++ {
+			for j := n - 1; j >= 0; j-- {
+				tmp := alpha * b[i*ldb+j]
+				var tmp2 float64
+				atmp := a[j*lda+j+1 : j*lda+n]
+				btmp := b[i*ldb+j+1 : i*ldb+n]
+				ctmp := c[i*ldc+j+1 : i*ldc+n]
+				for k, v := range atmp {
+					ctmp[k] += tmp * v
+					tmp2 += btmp[k] * v
+				}
+				c[i*ldc+j] *= beta
+				c[i*ldc+j] += tmp*a[j*lda+j] + alpha*tmp2
+			}
+		}
+		return
+	}
+	for i := 0; i < m; i++ {
+		for j := 0; j < n; j++ {
+			tmp := alpha * b[i*ldb+j]
+			var tmp2 float64
+			atmp := a[j*lda : j*lda+j]
+			btmp := b[i*ldb : i*ldb+j]
+			ctmp := c[i*ldc : i*ldc+j]
+			for k, v := range atmp {
+				ctmp[k] += tmp * v
+				tmp2 += btmp[k] * v
+			}
+			c[i*ldc+j] *= beta
+			c[i*ldc+j] += tmp*a[j*lda+j] + alpha*tmp2
+		}
+	}
+}
+
+// Dsyrk performs the symmetric rank-k operation
+//  C = alpha * A * A^T + beta*C
+// C is an n×n symmetric matrix. A is an n×k matrix if tA == blas.NoTrans, and
+// a k×n matrix otherwise. alpha and beta are scalars.
+func (Implementation) Dsyrk(ul blas.Uplo, tA blas.Transpose, n, k int, alpha float64, a []float64, lda int, beta float64, c []float64, ldc int) {
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if tA != blas.Trans && tA != blas.NoTrans && tA != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if k < 0 {
+		panic(kLT0)
+	}
+	if ldc < n {
+		panic(badLdC)
+	}
+	var row, col int
+	if tA == blas.NoTrans {
+		row, col = n, k
+	} else {
+		row, col = k, n
+	}
+	if lda*(row-1)+col > len(a) || lda < max(1, col) {
+		panic(badLdA)
+	}
+	if ldc*(n-1)+n > len(c) || ldc < max(1, n) {
+		panic(badLdC)
+	}
+	if alpha == 0 {
+		if beta == 0 {
+			if ul == blas.Upper {
+				for i := 0; i < n; i++ {
+					ctmp := c[i*ldc+i : i*ldc+n]
+					for j := range ctmp {
+						ctmp[j] = 0
+					}
+				}
+				return
+			}
+			for i := 0; i < n; i++ {
+				ctmp := c[i*ldc : i*ldc+i+1]
+				for j := range ctmp {
+					ctmp[j] = 0
+				}
+			}
+			return
+		}
+		if ul == blas.Upper {
+			for i := 0; i < n; i++ {
+				ctmp := c[i*ldc+i : i*ldc+n]
+				for j := range ctmp {
+					ctmp[j] *= beta
+				}
+			}
+			return
+		}
+		for i := 0; i < n; i++ {
+			ctmp := c[i*ldc : i*ldc+i+1]
+			for j := range ctmp {
+				ctmp[j] *= beta
+			}
+		}
+		return
+	}
+	if tA == blas.NoTrans {
+		if ul == blas.Upper {
+			for i := 0; i < n; i++ {
+				ctmp := c[i*ldc+i : i*ldc+n]
+				atmp := a[i*lda : i*lda+k]
+				for jc, vc := range ctmp {
+					j := jc + i
+					ctmp[jc] = vc*beta + alpha*f64.DotUnitary(atmp, a[j*lda:j*lda+k])
+				}
+			}
+			return
+		}
+		for i := 0; i < n; i++ {
+			atmp := a[i*lda : i*lda+k]
+			for j, vc := range c[i*ldc : i*ldc+i+1] {
+				c[i*ldc+j] = vc*beta + alpha*f64.DotUnitary(a[j*lda:j*lda+k], atmp)
+			}
+		}
+		return
+	}
+	// Cases where a is transposed.
+	if ul == blas.Upper {
+		for i := 0; i < n; i++ {
+			ctmp := c[i*ldc+i : i*ldc+n]
+			if beta != 1 {
+				for j := range ctmp {
+					ctmp[j] *= beta
+				}
+			}
+			for l := 0; l < k; l++ {
+				tmp := alpha * a[l*lda+i]
+				if tmp != 0 {
+					f64.AxpyUnitaryTo(ctmp, tmp, a[l*lda+i:l*lda+n], ctmp)
+				}
+			}
+		}
+		return
+	}
+	for i := 0; i < n; i++ {
+		ctmp := c[i*ldc : i*ldc+i+1]
+		if beta != 0 {
+			for j := range ctmp {
+				ctmp[j] *= beta
+			}
+		}
+		for l := 0; l < k; l++ {
+			tmp := alpha * a[l*lda+i]
+			if tmp != 0 {
+				f64.AxpyUnitaryTo(ctmp, tmp, a[l*lda:l*lda+i+1], ctmp)
+			}
+		}
+	}
+}
+
+// Dsyr2k performs the symmetric rank 2k operation
+//  C = alpha * A * B^T + alpha * B * A^T + beta * C
+// where C is an n×n symmetric matrix. A and B are n×k matrices if
+// tA == NoTrans and k×n otherwise. alpha and beta are scalars.
+func (Implementation) Dsyr2k(ul blas.Uplo, tA blas.Transpose, n, k int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int) {
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if tA != blas.Trans && tA != blas.NoTrans && tA != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if k < 0 {
+		panic(kLT0)
+	}
+	if ldc < n {
+		panic(badLdC)
+	}
+	var row, col int
+	if tA == blas.NoTrans {
+		row, col = n, k
+	} else {
+		row, col = k, n
+	}
+	if lda*(row-1)+col > len(a) || lda < max(1, col) {
+		panic(badLdA)
+	}
+	if ldb*(row-1)+col > len(b) || ldb < max(1, col) {
+		panic(badLdB)
+	}
+	if ldc*(n-1)+n > len(c) || ldc < max(1, n) {
+		panic(badLdC)
+	}
+	if alpha == 0 {
+		if beta == 0 {
+			if ul == blas.Upper {
+				for i := 0; i < n; i++ {
+					ctmp := c[i*ldc+i : i*ldc+n]
+					for j := range ctmp {
+						ctmp[j] = 0
+					}
+				}
+				return
+			}
+			for i := 0; i < n; i++ {
+				ctmp := c[i*ldc : i*ldc+i+1]
+				for j := range ctmp {
+					ctmp[j] = 0
+				}
+			}
+			return
+		}
+		if ul == blas.Upper {
+			for i := 0; i < n; i++ {
+				ctmp := c[i*ldc+i : i*ldc+n]
+				for j := range ctmp {
+					ctmp[j] *= beta
+				}
+			}
+			return
+		}
+		for i := 0; i < n; i++ {
+			ctmp := c[i*ldc : i*ldc+i+1]
+			for j := range ctmp {
+				ctmp[j] *= beta
+			}
+		}
+		return
+	}
+	if tA == blas.NoTrans {
+		if ul == blas.Upper {
+			for i := 0; i < n; i++ {
+				atmp := a[i*lda : i*lda+k]
+				btmp := b[i*ldb : i*ldb+k]
+				ctmp := c[i*ldc+i : i*ldc+n]
+				for jc := range ctmp {
+					j := i + jc
+					var tmp1, tmp2 float64
+					binner := b[j*ldb : j*ldb+k]
+					for l, v := range a[j*lda : j*lda+k] {
+						tmp1 += v * btmp[l]
+						tmp2 += atmp[l] * binner[l]
+					}
+					ctmp[jc] *= beta
+					ctmp[jc] += alpha * (tmp1 + tmp2)
+				}
+			}
+			return
+		}
+		for i := 0; i < n; i++ {
+			atmp := a[i*lda : i*lda+k]
+			btmp := b[i*ldb : i*ldb+k]
+			ctmp := c[i*ldc : i*ldc+i+1]
+			for j := 0; j <= i; j++ {
+				var tmp1, tmp2 float64
+				binner := b[j*ldb : j*ldb+k]
+				for l, v := range a[j*lda : j*lda+k] {
+					tmp1 += v * btmp[l]
+					tmp2 += atmp[l] * binner[l]
+				}
+				ctmp[j] *= beta
+				ctmp[j] += alpha * (tmp1 + tmp2)
+			}
+		}
+		return
+	}
+	if ul == blas.Upper {
+		for i := 0; i < n; i++ {
+			ctmp := c[i*ldc+i : i*ldc+n]
+			if beta != 1 {
+				for j := range ctmp {
+					ctmp[j] *= beta
+				}
+			}
+			for l := 0; l < k; l++ {
+				tmp1 := alpha * b[l*lda+i]
+				tmp2 := alpha * a[l*lda+i]
+				btmp := b[l*ldb+i : l*ldb+n]
+				if tmp1 != 0 || tmp2 != 0 {
+					for j, v := range a[l*lda+i : l*lda+n] {
+						ctmp[j] += v*tmp1 + btmp[j]*tmp2
+					}
+				}
+			}
+		}
+		return
+	}
+	for i := 0; i < n; i++ {
+		ctmp := c[i*ldc : i*ldc+i+1]
+		if beta != 1 {
+			for j := range ctmp {
+				ctmp[j] *= beta
+			}
+		}
+		for l := 0; l < k; l++ {
+			tmp1 := alpha * b[l*lda+i]
+			tmp2 := alpha * a[l*lda+i]
+			btmp := b[l*ldb : l*ldb+i+1]
+			if tmp1 != 0 || tmp2 != 0 {
+				for j, v := range a[l*lda : l*lda+i+1] {
+					ctmp[j] += v*tmp1 + btmp[j]*tmp2
+				}
+			}
+		}
+	}
+}
+
+// Dtrmm performs
+//  B = alpha * A * B,   if tA == blas.NoTrans and side == blas.Left,
+//  B = alpha * A^T * B, if tA == blas.Trans or blas.ConjTrans, and side == blas.Left,
+//  B = alpha * B * A,   if tA == blas.NoTrans and side == blas.Right,
+//  B = alpha * B * A^T, if tA == blas.Trans or blas.ConjTrans, and side == blas.Right,
+// where A is an n×n or m×m triangular matrix, and B is an m×n matrix.
+func (Implementation) Dtrmm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int) {
+	if s != blas.Left && s != blas.Right {
+		panic(badSide)
+	}
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	if d != blas.NonUnit && d != blas.Unit {
+		panic(badDiag)
+	}
+	if m < 0 {
+		panic(mLT0)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	var k int
+	if s == blas.Left {
+		k = m
+	} else {
+		k = n
+	}
+	if lda*(k-1)+k > len(a) || lda < max(1, k) {
+		panic(badLdA)
+	}
+	if ldb*(m-1)+n > len(b) || ldb < max(1, n) {
+		panic(badLdB)
+	}
+	if alpha == 0 {
+		for i := 0; i < m; i++ {
+			btmp := b[i*ldb : i*ldb+n]
+			for j := range btmp {
+				btmp[j] = 0
+			}
+		}
+		return
+	}
+
+	nonUnit := d == blas.NonUnit
+	if s == blas.Left {
+		if tA == blas.NoTrans {
+			if ul == blas.Upper {
+				for i := 0; i < m; i++ {
+					tmp := alpha
+					if nonUnit {
+						tmp *= a[i*lda+i]
+					}
+					btmp := b[i*ldb : i*ldb+n]
+					for j := range btmp {
+						btmp[j] *= tmp
+					}
+					for ka, va := range a[i*lda+i+1 : i*lda+m] {
+						k := ka + i + 1
+						tmp := alpha * va
+						if tmp != 0 {
+							f64.AxpyUnitaryTo(btmp, tmp, b[k*ldb:k*ldb+n], btmp)
+						}
+					}
+				}
+				return
+			}
+			for i := m - 1; i >= 0; i-- {
+				tmp := alpha
+				if nonUnit {
+					tmp *= a[i*lda+i]
+				}
+				btmp := b[i*ldb : i*ldb+n]
+				for j := range btmp {
+					btmp[j] *= tmp
+				}
+				for k, va := range a[i*lda : i*lda+i] {
+					tmp := alpha * va
+					if tmp != 0 {
+						f64.AxpyUnitaryTo(btmp, tmp, b[k*ldb:k*ldb+n], btmp)
+					}
+				}
+			}
+			return
+		}
+		// Cases where a is transposed.
+		if ul == blas.Upper {
+			for k := m - 1; k >= 0; k-- {
+				btmpk := b[k*ldb : k*ldb+n]
+				for ia, va := range a[k*lda+k+1 : k*lda+m] {
+					i := ia + k + 1
+					btmp := b[i*ldb : i*ldb+n]
+					tmp := alpha * va
+					if tmp != 0 {
+						f64.AxpyUnitaryTo(btmp, tmp, btmpk, btmp)
+					}
+				}
+				tmp := alpha
+				if nonUnit {
+					tmp *= a[k*lda+k]
+				}
+				if tmp != 1 {
+					for j := 0; j < n; j++ {
+						btmpk[j] *= tmp
+					}
+				}
+			}
+			return
+		}
+		for k := 0; k < m; k++ {
+			btmpk := b[k*ldb : k*ldb+n]
+			for i, va := range a[k*lda : k*lda+k] {
+				btmp := b[i*ldb : i*ldb+n]
+				tmp := alpha * va
+				if tmp != 0 {
+					f64.AxpyUnitaryTo(btmp, tmp, btmpk, btmp)
+				}
+			}
+			tmp := alpha
+			if nonUnit {
+				tmp *= a[k*lda+k]
+			}
+			if tmp != 1 {
+				for j := 0; j < n; j++ {
+					btmpk[j] *= tmp
+				}
+			}
+		}
+		return
+	}
+	// Cases where a is on the right
+	if tA == blas.NoTrans {
+		if ul == blas.Upper {
+			for i := 0; i < m; i++ {
+				btmp := b[i*ldb : i*ldb+n]
+				for k := n - 1; k >= 0; k-- {
+					tmp := alpha * btmp[k]
+					if tmp != 0 {
+						btmp[k] = tmp
+						if nonUnit {
+							btmp[k] *= a[k*lda+k]
+						}
+						for ja, v := range a[k*lda+k+1 : k*lda+n] {
+							j := ja + k + 1
+							btmp[j] += tmp * v
+						}
+					}
+				}
+			}
+			return
+		}
+		for i := 0; i < m; i++ {
+			btmp := b[i*ldb : i*ldb+n]
+			for k := 0; k < n; k++ {
+				tmp := alpha * btmp[k]
+				if tmp != 0 {
+					btmp[k] = tmp
+					if nonUnit {
+						btmp[k] *= a[k*lda+k]
+					}
+					f64.AxpyUnitaryTo(btmp, tmp, a[k*lda:k*lda+k], btmp)
+				}
+			}
+		}
+		return
+	}
+	// Cases where a is transposed.
+	if ul == blas.Upper {
+		for i := 0; i < m; i++ {
+			btmp := b[i*ldb : i*ldb+n]
+			for j, vb := range btmp {
+				tmp := vb
+				if nonUnit {
+					tmp *= a[j*lda+j]
+				}
+				tmp += f64.DotUnitary(a[j*lda+j+1:j*lda+n], btmp[j+1:n])
+				btmp[j] = alpha * tmp
+			}
+		}
+		return
+	}
+	for i := 0; i < m; i++ {
+		btmp := b[i*ldb : i*ldb+n]
+		for j := n - 1; j >= 0; j-- {
+			tmp := btmp[j]
+			if nonUnit {
+				tmp *= a[j*lda+j]
+			}
+			tmp += f64.DotUnitary(a[j*lda:j*lda+j], btmp[:j])
+			btmp[j] = alpha * tmp
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/level3double_test.go b/vendor/gonum.org/v1/gonum/blas/gonum/level3double_test.go
new file mode 100644
index 00000000..70459803
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/level3double_test.go
@@ -0,0 +1,35 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas/testblas"
+)
+
+func TestDgemm(t *testing.T) {
+	testblas.TestDgemm(t, impl)
+}
+
+func TestDsymm(t *testing.T) {
+	testblas.DsymmTest(t, impl)
+}
+
+func TestDtrsm(t *testing.T) {
+	testblas.DtrsmTest(t, impl)
+}
+
+func TestDsyrk(t *testing.T) {
+	testblas.DsyrkTest(t, impl)
+}
+
+func TestDsyr2k(t *testing.T) {
+	testblas.Dsyr2kTest(t, impl)
+}
+
+func TestDtrmm(t *testing.T) {
+	testblas.DtrmmTest(t, impl)
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/level3single.go b/vendor/gonum.org/v1/gonum/blas/gonum/level3single.go
new file mode 100644
index 00000000..ba158498
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/level3single.go
@@ -0,0 +1,843 @@
+// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.
+
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/internal/asm/f32"
+)
+
+var _ blas.Float32Level3 = Implementation{}
+
+// Strsm solves
+//  A * X = alpha * B,   if tA == blas.NoTrans side == blas.Left,
+//  A^T * X = alpha * B, if tA == blas.Trans or blas.ConjTrans, and side == blas.Left,
+//  X * A = alpha * B,   if tA == blas.NoTrans side == blas.Right,
+//  X * A^T = alpha * B, if tA == blas.Trans or blas.ConjTrans, and side == blas.Right,
+// where A is an n×n or m×m triangular matrix, X is an m×n matrix, and alpha is a
+// scalar.
+//
+// At entry to the function, X contains the values of B, and the result is
+// stored in place into X.
+//
+// No check is made that A is invertible.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Strsm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha float32, a []float32, lda int, b []float32, ldb int) {
+	if s != blas.Left && s != blas.Right {
+		panic(badSide)
+	}
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	if d != blas.NonUnit && d != blas.Unit {
+		panic(badDiag)
+	}
+	if m < 0 {
+		panic(mLT0)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if ldb < n {
+		panic(badLdB)
+	}
+	var k int
+	if s == blas.Left {
+		k = m
+	} else {
+		k = n
+	}
+	if lda*(k-1)+k > len(a) || lda < max(1, k) {
+		panic(badLdA)
+	}
+	if ldb*(m-1)+n > len(b) || ldb < max(1, n) {
+		panic(badLdB)
+	}
+
+	if m == 0 || n == 0 {
+		return
+	}
+
+	if alpha == 0 {
+		for i := 0; i < m; i++ {
+			btmp := b[i*ldb : i*ldb+n]
+			for j := range btmp {
+				btmp[j] = 0
+			}
+		}
+		return
+	}
+	nonUnit := d == blas.NonUnit
+	if s == blas.Left {
+		if tA == blas.NoTrans {
+			if ul == blas.Upper {
+				for i := m - 1; i >= 0; i-- {
+					btmp := b[i*ldb : i*ldb+n]
+					if alpha != 1 {
+						for j := range btmp {
+							btmp[j] *= alpha
+						}
+					}
+					for ka, va := range a[i*lda+i+1 : i*lda+m] {
+						k := ka + i + 1
+						if va != 0 {
+							f32.AxpyUnitaryTo(btmp, -va, b[k*ldb:k*ldb+n], btmp)
+						}
+					}
+					if nonUnit {
+						tmp := 1 / a[i*lda+i]
+						for j := 0; j < n; j++ {
+							btmp[j] *= tmp
+						}
+					}
+				}
+				return
+			}
+			for i := 0; i < m; i++ {
+				btmp := b[i*ldb : i*ldb+n]
+				if alpha != 1 {
+					for j := 0; j < n; j++ {
+						btmp[j] *= alpha
+					}
+				}
+				for k, va := range a[i*lda : i*lda+i] {
+					if va != 0 {
+						f32.AxpyUnitaryTo(btmp, -va, b[k*ldb:k*ldb+n], btmp)
+					}
+				}
+				if nonUnit {
+					tmp := 1 / a[i*lda+i]
+					for j := 0; j < n; j++ {
+						btmp[j] *= tmp
+					}
+				}
+			}
+			return
+		}
+		// Cases where a is transposed
+		if ul == blas.Upper {
+			for k := 0; k < m; k++ {
+				btmpk := b[k*ldb : k*ldb+n]
+				if nonUnit {
+					tmp := 1 / a[k*lda+k]
+					for j := 0; j < n; j++ {
+						btmpk[j] *= tmp
+					}
+				}
+				for ia, va := range a[k*lda+k+1 : k*lda+m] {
+					i := ia + k + 1
+					if va != 0 {
+						btmp := b[i*ldb : i*ldb+n]
+						f32.AxpyUnitaryTo(btmp, -va, btmpk, btmp)
+					}
+				}
+				if alpha != 1 {
+					for j := 0; j < n; j++ {
+						btmpk[j] *= alpha
+					}
+				}
+			}
+			return
+		}
+		for k := m - 1; k >= 0; k-- {
+			btmpk := b[k*ldb : k*ldb+n]
+			if nonUnit {
+				tmp := 1 / a[k*lda+k]
+				for j := 0; j < n; j++ {
+					btmpk[j] *= tmp
+				}
+			}
+			for i, va := range a[k*lda : k*lda+k] {
+				if va != 0 {
+					btmp := b[i*ldb : i*ldb+n]
+					f32.AxpyUnitaryTo(btmp, -va, btmpk, btmp)
+				}
+			}
+			if alpha != 1 {
+				for j := 0; j < n; j++ {
+					btmpk[j] *= alpha
+				}
+			}
+		}
+		return
+	}
+	// Cases where a is to the right of X.
+	if tA == blas.NoTrans {
+		if ul == blas.Upper {
+			for i := 0; i < m; i++ {
+				btmp := b[i*ldb : i*ldb+n]
+				if alpha != 1 {
+					for j := 0; j < n; j++ {
+						btmp[j] *= alpha
+					}
+				}
+				for k, vb := range btmp {
+					if vb != 0 {
+						if btmp[k] != 0 {
+							if nonUnit {
+								btmp[k] /= a[k*lda+k]
+							}
+							btmpk := btmp[k+1 : n]
+							f32.AxpyUnitaryTo(btmpk, -btmp[k], a[k*lda+k+1:k*lda+n], btmpk)
+						}
+					}
+				}
+			}
+			return
+		}
+		for i := 0; i < m; i++ {
+			btmp := b[i*lda : i*lda+n]
+			if alpha != 1 {
+				for j := 0; j < n; j++ {
+					btmp[j] *= alpha
+				}
+			}
+			for k := n - 1; k >= 0; k-- {
+				if btmp[k] != 0 {
+					if nonUnit {
+						btmp[k] /= a[k*lda+k]
+					}
+					f32.AxpyUnitaryTo(btmp, -btmp[k], a[k*lda:k*lda+k], btmp)
+				}
+			}
+		}
+		return
+	}
+	// Cases where a is transposed.
+	if ul == blas.Upper {
+		for i := 0; i < m; i++ {
+			btmp := b[i*lda : i*lda+n]
+			for j := n - 1; j >= 0; j-- {
+				tmp := alpha*btmp[j] - f32.DotUnitary(a[j*lda+j+1:j*lda+n], btmp[j+1:])
+				if nonUnit {
+					tmp /= a[j*lda+j]
+				}
+				btmp[j] = tmp
+			}
+		}
+		return
+	}
+	for i := 0; i < m; i++ {
+		btmp := b[i*lda : i*lda+n]
+		for j := 0; j < n; j++ {
+			tmp := alpha*btmp[j] - f32.DotUnitary(a[j*lda:j*lda+j], btmp)
+			if nonUnit {
+				tmp /= a[j*lda+j]
+			}
+			btmp[j] = tmp
+		}
+	}
+}
+
+// Ssymm performs one of
+//  C = alpha * A * B + beta * C, if side == blas.Left,
+//  C = alpha * B * A + beta * C, if side == blas.Right,
+// where A is an n×n or m×m symmetric matrix, B and C are m×n matrices, and alpha
+// is a scalar.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Ssymm(s blas.Side, ul blas.Uplo, m, n int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int) {
+	if s != blas.Right && s != blas.Left {
+		panic("goblas: bad side")
+	}
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if m < 0 {
+		panic(mLT0)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	var k int
+	if s == blas.Left {
+		k = m
+	} else {
+		k = n
+	}
+	if lda*(k-1)+k > len(a) || lda < max(1, k) {
+		panic(badLdA)
+	}
+	if ldb*(m-1)+n > len(b) || ldb < max(1, n) {
+		panic(badLdB)
+	}
+	if ldc*(m-1)+n > len(c) || ldc < max(1, n) {
+		panic(badLdC)
+	}
+	if m == 0 || n == 0 {
+		return
+	}
+	if alpha == 0 && beta == 1 {
+		return
+	}
+	if alpha == 0 {
+		if beta == 0 {
+			for i := 0; i < m; i++ {
+				ctmp := c[i*ldc : i*ldc+n]
+				for j := range ctmp {
+					ctmp[j] = 0
+				}
+			}
+			return
+		}
+		for i := 0; i < m; i++ {
+			ctmp := c[i*ldc : i*ldc+n]
+			for j := 0; j < n; j++ {
+				ctmp[j] *= beta
+			}
+		}
+		return
+	}
+
+	isUpper := ul == blas.Upper
+	if s == blas.Left {
+		for i := 0; i < m; i++ {
+			atmp := alpha * a[i*lda+i]
+			btmp := b[i*ldb : i*ldb+n]
+			ctmp := c[i*ldc : i*ldc+n]
+			for j, v := range btmp {
+				ctmp[j] *= beta
+				ctmp[j] += atmp * v
+			}
+
+			for k := 0; k < i; k++ {
+				var atmp float32
+				if isUpper {
+					atmp = a[k*lda+i]
+				} else {
+					atmp = a[i*lda+k]
+				}
+				atmp *= alpha
+				ctmp := c[i*ldc : i*ldc+n]
+				f32.AxpyUnitaryTo(ctmp, atmp, b[k*ldb:k*ldb+n], ctmp)
+			}
+			for k := i + 1; k < m; k++ {
+				var atmp float32
+				if isUpper {
+					atmp = a[i*lda+k]
+				} else {
+					atmp = a[k*lda+i]
+				}
+				atmp *= alpha
+				ctmp := c[i*ldc : i*ldc+n]
+				f32.AxpyUnitaryTo(ctmp, atmp, b[k*ldb:k*ldb+n], ctmp)
+			}
+		}
+		return
+	}
+	if isUpper {
+		for i := 0; i < m; i++ {
+			for j := n - 1; j >= 0; j-- {
+				tmp := alpha * b[i*ldb+j]
+				var tmp2 float32
+				atmp := a[j*lda+j+1 : j*lda+n]
+				btmp := b[i*ldb+j+1 : i*ldb+n]
+				ctmp := c[i*ldc+j+1 : i*ldc+n]
+				for k, v := range atmp {
+					ctmp[k] += tmp * v
+					tmp2 += btmp[k] * v
+				}
+				c[i*ldc+j] *= beta
+				c[i*ldc+j] += tmp*a[j*lda+j] + alpha*tmp2
+			}
+		}
+		return
+	}
+	for i := 0; i < m; i++ {
+		for j := 0; j < n; j++ {
+			tmp := alpha * b[i*ldb+j]
+			var tmp2 float32
+			atmp := a[j*lda : j*lda+j]
+			btmp := b[i*ldb : i*ldb+j]
+			ctmp := c[i*ldc : i*ldc+j]
+			for k, v := range atmp {
+				ctmp[k] += tmp * v
+				tmp2 += btmp[k] * v
+			}
+			c[i*ldc+j] *= beta
+			c[i*ldc+j] += tmp*a[j*lda+j] + alpha*tmp2
+		}
+	}
+}
+
+// Ssyrk performs the symmetric rank-k operation
+//  C = alpha * A * A^T + beta*C
+// C is an n×n symmetric matrix. A is an n×k matrix if tA == blas.NoTrans, and
+// a k×n matrix otherwise. alpha and beta are scalars.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Ssyrk(ul blas.Uplo, tA blas.Transpose, n, k int, alpha float32, a []float32, lda int, beta float32, c []float32, ldc int) {
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if tA != blas.Trans && tA != blas.NoTrans && tA != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if k < 0 {
+		panic(kLT0)
+	}
+	if ldc < n {
+		panic(badLdC)
+	}
+	var row, col int
+	if tA == blas.NoTrans {
+		row, col = n, k
+	} else {
+		row, col = k, n
+	}
+	if lda*(row-1)+col > len(a) || lda < max(1, col) {
+		panic(badLdA)
+	}
+	if ldc*(n-1)+n > len(c) || ldc < max(1, n) {
+		panic(badLdC)
+	}
+	if alpha == 0 {
+		if beta == 0 {
+			if ul == blas.Upper {
+				for i := 0; i < n; i++ {
+					ctmp := c[i*ldc+i : i*ldc+n]
+					for j := range ctmp {
+						ctmp[j] = 0
+					}
+				}
+				return
+			}
+			for i := 0; i < n; i++ {
+				ctmp := c[i*ldc : i*ldc+i+1]
+				for j := range ctmp {
+					ctmp[j] = 0
+				}
+			}
+			return
+		}
+		if ul == blas.Upper {
+			for i := 0; i < n; i++ {
+				ctmp := c[i*ldc+i : i*ldc+n]
+				for j := range ctmp {
+					ctmp[j] *= beta
+				}
+			}
+			return
+		}
+		for i := 0; i < n; i++ {
+			ctmp := c[i*ldc : i*ldc+i+1]
+			for j := range ctmp {
+				ctmp[j] *= beta
+			}
+		}
+		return
+	}
+	if tA == blas.NoTrans {
+		if ul == blas.Upper {
+			for i := 0; i < n; i++ {
+				ctmp := c[i*ldc+i : i*ldc+n]
+				atmp := a[i*lda : i*lda+k]
+				for jc, vc := range ctmp {
+					j := jc + i
+					ctmp[jc] = vc*beta + alpha*f32.DotUnitary(atmp, a[j*lda:j*lda+k])
+				}
+			}
+			return
+		}
+		for i := 0; i < n; i++ {
+			atmp := a[i*lda : i*lda+k]
+			for j, vc := range c[i*ldc : i*ldc+i+1] {
+				c[i*ldc+j] = vc*beta + alpha*f32.DotUnitary(a[j*lda:j*lda+k], atmp)
+			}
+		}
+		return
+	}
+	// Cases where a is transposed.
+	if ul == blas.Upper {
+		for i := 0; i < n; i++ {
+			ctmp := c[i*ldc+i : i*ldc+n]
+			if beta != 1 {
+				for j := range ctmp {
+					ctmp[j] *= beta
+				}
+			}
+			for l := 0; l < k; l++ {
+				tmp := alpha * a[l*lda+i]
+				if tmp != 0 {
+					f32.AxpyUnitaryTo(ctmp, tmp, a[l*lda+i:l*lda+n], ctmp)
+				}
+			}
+		}
+		return
+	}
+	for i := 0; i < n; i++ {
+		ctmp := c[i*ldc : i*ldc+i+1]
+		if beta != 0 {
+			for j := range ctmp {
+				ctmp[j] *= beta
+			}
+		}
+		for l := 0; l < k; l++ {
+			tmp := alpha * a[l*lda+i]
+			if tmp != 0 {
+				f32.AxpyUnitaryTo(ctmp, tmp, a[l*lda:l*lda+i+1], ctmp)
+			}
+		}
+	}
+}
+
+// Ssyr2k performs the symmetric rank 2k operation
+//  C = alpha * A * B^T + alpha * B * A^T + beta * C
+// where C is an n×n symmetric matrix. A and B are n×k matrices if
+// tA == NoTrans and k×n otherwise. alpha and beta are scalars.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Ssyr2k(ul blas.Uplo, tA blas.Transpose, n, k int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int) {
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if tA != blas.Trans && tA != blas.NoTrans && tA != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	if k < 0 {
+		panic(kLT0)
+	}
+	if ldc < n {
+		panic(badLdC)
+	}
+	var row, col int
+	if tA == blas.NoTrans {
+		row, col = n, k
+	} else {
+		row, col = k, n
+	}
+	if lda*(row-1)+col > len(a) || lda < max(1, col) {
+		panic(badLdA)
+	}
+	if ldb*(row-1)+col > len(b) || ldb < max(1, col) {
+		panic(badLdB)
+	}
+	if ldc*(n-1)+n > len(c) || ldc < max(1, n) {
+		panic(badLdC)
+	}
+	if alpha == 0 {
+		if beta == 0 {
+			if ul == blas.Upper {
+				for i := 0; i < n; i++ {
+					ctmp := c[i*ldc+i : i*ldc+n]
+					for j := range ctmp {
+						ctmp[j] = 0
+					}
+				}
+				return
+			}
+			for i := 0; i < n; i++ {
+				ctmp := c[i*ldc : i*ldc+i+1]
+				for j := range ctmp {
+					ctmp[j] = 0
+				}
+			}
+			return
+		}
+		if ul == blas.Upper {
+			for i := 0; i < n; i++ {
+				ctmp := c[i*ldc+i : i*ldc+n]
+				for j := range ctmp {
+					ctmp[j] *= beta
+				}
+			}
+			return
+		}
+		for i := 0; i < n; i++ {
+			ctmp := c[i*ldc : i*ldc+i+1]
+			for j := range ctmp {
+				ctmp[j] *= beta
+			}
+		}
+		return
+	}
+	if tA == blas.NoTrans {
+		if ul == blas.Upper {
+			for i := 0; i < n; i++ {
+				atmp := a[i*lda : i*lda+k]
+				btmp := b[i*ldb : i*ldb+k]
+				ctmp := c[i*ldc+i : i*ldc+n]
+				for jc := range ctmp {
+					j := i + jc
+					var tmp1, tmp2 float32
+					binner := b[j*ldb : j*ldb+k]
+					for l, v := range a[j*lda : j*lda+k] {
+						tmp1 += v * btmp[l]
+						tmp2 += atmp[l] * binner[l]
+					}
+					ctmp[jc] *= beta
+					ctmp[jc] += alpha * (tmp1 + tmp2)
+				}
+			}
+			return
+		}
+		for i := 0; i < n; i++ {
+			atmp := a[i*lda : i*lda+k]
+			btmp := b[i*ldb : i*ldb+k]
+			ctmp := c[i*ldc : i*ldc+i+1]
+			for j := 0; j <= i; j++ {
+				var tmp1, tmp2 float32
+				binner := b[j*ldb : j*ldb+k]
+				for l, v := range a[j*lda : j*lda+k] {
+					tmp1 += v * btmp[l]
+					tmp2 += atmp[l] * binner[l]
+				}
+				ctmp[j] *= beta
+				ctmp[j] += alpha * (tmp1 + tmp2)
+			}
+		}
+		return
+	}
+	if ul == blas.Upper {
+		for i := 0; i < n; i++ {
+			ctmp := c[i*ldc+i : i*ldc+n]
+			if beta != 1 {
+				for j := range ctmp {
+					ctmp[j] *= beta
+				}
+			}
+			for l := 0; l < k; l++ {
+				tmp1 := alpha * b[l*lda+i]
+				tmp2 := alpha * a[l*lda+i]
+				btmp := b[l*ldb+i : l*ldb+n]
+				if tmp1 != 0 || tmp2 != 0 {
+					for j, v := range a[l*lda+i : l*lda+n] {
+						ctmp[j] += v*tmp1 + btmp[j]*tmp2
+					}
+				}
+			}
+		}
+		return
+	}
+	for i := 0; i < n; i++ {
+		ctmp := c[i*ldc : i*ldc+i+1]
+		if beta != 1 {
+			for j := range ctmp {
+				ctmp[j] *= beta
+			}
+		}
+		for l := 0; l < k; l++ {
+			tmp1 := alpha * b[l*lda+i]
+			tmp2 := alpha * a[l*lda+i]
+			btmp := b[l*ldb : l*ldb+i+1]
+			if tmp1 != 0 || tmp2 != 0 {
+				for j, v := range a[l*lda : l*lda+i+1] {
+					ctmp[j] += v*tmp1 + btmp[j]*tmp2
+				}
+			}
+		}
+	}
+}
+
+// Strmm performs
+//  B = alpha * A * B,   if tA == blas.NoTrans and side == blas.Left,
+//  B = alpha * A^T * B, if tA == blas.Trans or blas.ConjTrans, and side == blas.Left,
+//  B = alpha * B * A,   if tA == blas.NoTrans and side == blas.Right,
+//  B = alpha * B * A^T, if tA == blas.Trans or blas.ConjTrans, and side == blas.Right,
+// where A is an n×n or m×m triangular matrix, and B is an m×n matrix.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Strmm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha float32, a []float32, lda int, b []float32, ldb int) {
+	if s != blas.Left && s != blas.Right {
+		panic(badSide)
+	}
+	if ul != blas.Lower && ul != blas.Upper {
+		panic(badUplo)
+	}
+	if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	if d != blas.NonUnit && d != blas.Unit {
+		panic(badDiag)
+	}
+	if m < 0 {
+		panic(mLT0)
+	}
+	if n < 0 {
+		panic(nLT0)
+	}
+	var k int
+	if s == blas.Left {
+		k = m
+	} else {
+		k = n
+	}
+	if lda*(k-1)+k > len(a) || lda < max(1, k) {
+		panic(badLdA)
+	}
+	if ldb*(m-1)+n > len(b) || ldb < max(1, n) {
+		panic(badLdB)
+	}
+	if alpha == 0 {
+		for i := 0; i < m; i++ {
+			btmp := b[i*ldb : i*ldb+n]
+			for j := range btmp {
+				btmp[j] = 0
+			}
+		}
+		return
+	}
+
+	nonUnit := d == blas.NonUnit
+	if s == blas.Left {
+		if tA == blas.NoTrans {
+			if ul == blas.Upper {
+				for i := 0; i < m; i++ {
+					tmp := alpha
+					if nonUnit {
+						tmp *= a[i*lda+i]
+					}
+					btmp := b[i*ldb : i*ldb+n]
+					for j := range btmp {
+						btmp[j] *= tmp
+					}
+					for ka, va := range a[i*lda+i+1 : i*lda+m] {
+						k := ka + i + 1
+						tmp := alpha * va
+						if tmp != 0 {
+							f32.AxpyUnitaryTo(btmp, tmp, b[k*ldb:k*ldb+n], btmp)
+						}
+					}
+				}
+				return
+			}
+			for i := m - 1; i >= 0; i-- {
+				tmp := alpha
+				if nonUnit {
+					tmp *= a[i*lda+i]
+				}
+				btmp := b[i*ldb : i*ldb+n]
+				for j := range btmp {
+					btmp[j] *= tmp
+				}
+				for k, va := range a[i*lda : i*lda+i] {
+					tmp := alpha * va
+					if tmp != 0 {
+						f32.AxpyUnitaryTo(btmp, tmp, b[k*ldb:k*ldb+n], btmp)
+					}
+				}
+			}
+			return
+		}
+		// Cases where a is transposed.
+		if ul == blas.Upper {
+			for k := m - 1; k >= 0; k-- {
+				btmpk := b[k*ldb : k*ldb+n]
+				for ia, va := range a[k*lda+k+1 : k*lda+m] {
+					i := ia + k + 1
+					btmp := b[i*ldb : i*ldb+n]
+					tmp := alpha * va
+					if tmp != 0 {
+						f32.AxpyUnitaryTo(btmp, tmp, btmpk, btmp)
+					}
+				}
+				tmp := alpha
+				if nonUnit {
+					tmp *= a[k*lda+k]
+				}
+				if tmp != 1 {
+					for j := 0; j < n; j++ {
+						btmpk[j] *= tmp
+					}
+				}
+			}
+			return
+		}
+		for k := 0; k < m; k++ {
+			btmpk := b[k*ldb : k*ldb+n]
+			for i, va := range a[k*lda : k*lda+k] {
+				btmp := b[i*ldb : i*ldb+n]
+				tmp := alpha * va
+				if tmp != 0 {
+					f32.AxpyUnitaryTo(btmp, tmp, btmpk, btmp)
+				}
+			}
+			tmp := alpha
+			if nonUnit {
+				tmp *= a[k*lda+k]
+			}
+			if tmp != 1 {
+				for j := 0; j < n; j++ {
+					btmpk[j] *= tmp
+				}
+			}
+		}
+		return
+	}
+	// Cases where a is on the right
+	if tA == blas.NoTrans {
+		if ul == blas.Upper {
+			for i := 0; i < m; i++ {
+				btmp := b[i*ldb : i*ldb+n]
+				for k := n - 1; k >= 0; k-- {
+					tmp := alpha * btmp[k]
+					if tmp != 0 {
+						btmp[k] = tmp
+						if nonUnit {
+							btmp[k] *= a[k*lda+k]
+						}
+						for ja, v := range a[k*lda+k+1 : k*lda+n] {
+							j := ja + k + 1
+							btmp[j] += tmp * v
+						}
+					}
+				}
+			}
+			return
+		}
+		for i := 0; i < m; i++ {
+			btmp := b[i*ldb : i*ldb+n]
+			for k := 0; k < n; k++ {
+				tmp := alpha * btmp[k]
+				if tmp != 0 {
+					btmp[k] = tmp
+					if nonUnit {
+						btmp[k] *= a[k*lda+k]
+					}
+					f32.AxpyUnitaryTo(btmp, tmp, a[k*lda:k*lda+k], btmp)
+				}
+			}
+		}
+		return
+	}
+	// Cases where a is transposed.
+	if ul == blas.Upper {
+		for i := 0; i < m; i++ {
+			btmp := b[i*ldb : i*ldb+n]
+			for j, vb := range btmp {
+				tmp := vb
+				if nonUnit {
+					tmp *= a[j*lda+j]
+				}
+				tmp += f32.DotUnitary(a[j*lda+j+1:j*lda+n], btmp[j+1:n])
+				btmp[j] = alpha * tmp
+			}
+		}
+		return
+	}
+	for i := 0; i < m; i++ {
+		btmp := b[i*ldb : i*ldb+n]
+		for j := n - 1; j >= 0; j-- {
+			tmp := btmp[j]
+			if nonUnit {
+				tmp *= a[j*lda+j]
+			}
+			tmp += f32.DotUnitary(a[j*lda:j*lda+j], btmp[:j])
+			btmp[j] = alpha * tmp
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/pardgemm_test.go b/vendor/gonum.org/v1/gonum/blas/gonum/pardgemm_test.go
new file mode 100644
index 00000000..b88cd606
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/pardgemm_test.go
@@ -0,0 +1,181 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+func TestDgemmParallel(t *testing.T) {
+	for i, test := range []struct {
+		m     int
+		n     int
+		k     int
+		alpha float64
+		tA    blas.Transpose
+		tB    blas.Transpose
+	}{
+		{
+			m:     3,
+			n:     4,
+			k:     2,
+			alpha: 2.5,
+			tA:    blas.NoTrans,
+			tB:    blas.NoTrans,
+		},
+		{
+			m:     blockSize*2 + 5,
+			n:     3,
+			k:     2,
+			alpha: 2.5,
+			tA:    blas.NoTrans,
+			tB:    blas.NoTrans,
+		},
+		{
+			m:     3,
+			n:     blockSize * 2,
+			k:     2,
+			alpha: 2.5,
+			tA:    blas.NoTrans,
+			tB:    blas.NoTrans,
+		},
+		{
+			m:     2,
+			n:     3,
+			k:     blockSize*3 - 2,
+			alpha: 2.5,
+			tA:    blas.NoTrans,
+			tB:    blas.NoTrans,
+		},
+		{
+			m:     blockSize * minParBlock,
+			n:     3,
+			k:     2,
+			alpha: 2.5,
+			tA:    blas.NoTrans,
+			tB:    blas.NoTrans,
+		},
+		{
+			m:     3,
+			n:     blockSize * minParBlock,
+			k:     2,
+			alpha: 2.5,
+			tA:    blas.NoTrans,
+			tB:    blas.NoTrans,
+		},
+		{
+			m:     2,
+			n:     3,
+			k:     blockSize * minParBlock,
+			alpha: 2.5,
+			tA:    blas.NoTrans,
+			tB:    blas.NoTrans,
+		},
+		{
+			m:     blockSize*minParBlock + 1,
+			n:     blockSize * minParBlock,
+			k:     3,
+			alpha: 2.5,
+			tA:    blas.NoTrans,
+			tB:    blas.NoTrans,
+		},
+		{
+			m:     3,
+			n:     blockSize*minParBlock + 2,
+			k:     blockSize * 3,
+			alpha: 2.5,
+			tA:    blas.NoTrans,
+			tB:    blas.NoTrans,
+		},
+		{
+			m:     blockSize * minParBlock,
+			n:     3,
+			k:     blockSize * minParBlock,
+			alpha: 2.5,
+			tA:    blas.NoTrans,
+			tB:    blas.NoTrans,
+		},
+		{
+			m:     blockSize * minParBlock,
+			n:     blockSize * minParBlock,
+			k:     blockSize * 3,
+			alpha: 2.5,
+			tA:    blas.NoTrans,
+			tB:    blas.NoTrans,
+		},
+		{
+			m:     blockSize + blockSize/2,
+			n:     blockSize + blockSize/2,
+			k:     blockSize + blockSize/2,
+			alpha: 2.5,
+			tA:    blas.NoTrans,
+			tB:    blas.NoTrans,
+		},
+	} {
+		testMatchParallelSerial(t, i, blas.NoTrans, blas.NoTrans, test.m, test.n, test.k, test.alpha)
+		testMatchParallelSerial(t, i, blas.Trans, blas.NoTrans, test.m, test.n, test.k, test.alpha)
+		testMatchParallelSerial(t, i, blas.NoTrans, blas.Trans, test.m, test.n, test.k, test.alpha)
+		testMatchParallelSerial(t, i, blas.Trans, blas.Trans, test.m, test.n, test.k, test.alpha)
+	}
+}
+
+func testMatchParallelSerial(t *testing.T, i int, tA, tB blas.Transpose, m, n, k int, alpha float64) {
+	var (
+		rowA, colA int
+		rowB, colB int
+	)
+	if tA == blas.NoTrans {
+		rowA = m
+		colA = k
+	} else {
+		rowA = k
+		colA = m
+	}
+	if tB == blas.NoTrans {
+		rowB = k
+		colB = n
+	} else {
+		rowB = n
+		colB = k
+	}
+	a := randmat(rowA, colA, colA)
+	b := randmat(rowB, colB, colB)
+	c := randmat(m, n, n)
+
+	aClone := a.clone()
+	bClone := b.clone()
+	cClone := c.clone()
+
+	lda := colA
+	ldb := colB
+	ldc := n
+	dgemmSerial(tA == blas.Trans, tB == blas.Trans, m, n, k, a.data, lda, b.data, ldb, cClone.data, ldc, alpha)
+	dgemmParallel(tA == blas.Trans, tB == blas.Trans, m, n, k, a.data, lda, b.data, ldb, c.data, ldc, alpha)
+	if !a.equal(aClone) {
+		t.Errorf("Case %v: a changed during call to dgemmParallel", i)
+	}
+	if !b.equal(bClone) {
+		t.Errorf("Case %v: b changed during call to dgemmParallel", i)
+	}
+	if !c.equalWithinAbs(cClone, 1e-12) {
+		t.Errorf("Case %v: answer not equal parallel and serial", i)
+	}
+}
+
+func randmat(r, c, stride int) general64 {
+	data := make([]float64, r*stride+c)
+	for i := range data {
+		data[i] = rand.Float64()
+	}
+	return general64{
+		data:   data,
+		rows:   r,
+		cols:   c,
+		stride: stride,
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/sgemm.go b/vendor/gonum.org/v1/gonum/blas/gonum/sgemm.go
new file mode 100644
index 00000000..06dd39bd
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/sgemm.go
@@ -0,0 +1,265 @@
+// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.
+
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"runtime"
+	"sync"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/internal/asm/f32"
+)
+
+// Sgemm computes
+//  C = beta * C + alpha * A * B,
+// where A, B, and C are dense matrices, and alpha and beta are scalars.
+// tA and tB specify whether A or B are transposed.
+//
+// Float32 implementations are autogenerated and not directly tested.
+func (Implementation) Sgemm(tA, tB blas.Transpose, m, n, k int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int) {
+	if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	if tB != blas.NoTrans && tB != blas.Trans && tB != blas.ConjTrans {
+		panic(badTranspose)
+	}
+	aTrans := tA == blas.Trans || tA == blas.ConjTrans
+	if aTrans {
+		checkSMatrix('a', k, m, a, lda)
+	} else {
+		checkSMatrix('a', m, k, a, lda)
+	}
+	bTrans := tB == blas.Trans || tB == blas.ConjTrans
+	if bTrans {
+		checkSMatrix('b', n, k, b, ldb)
+	} else {
+		checkSMatrix('b', k, n, b, ldb)
+	}
+	checkSMatrix('c', m, n, c, ldc)
+
+	// scale c
+	if beta != 1 {
+		if beta == 0 {
+			for i := 0; i < m; i++ {
+				ctmp := c[i*ldc : i*ldc+n]
+				for j := range ctmp {
+					ctmp[j] = 0
+				}
+			}
+		} else {
+			for i := 0; i < m; i++ {
+				ctmp := c[i*ldc : i*ldc+n]
+				for j := range ctmp {
+					ctmp[j] *= beta
+				}
+			}
+		}
+	}
+
+	sgemmParallel(aTrans, bTrans, m, n, k, a, lda, b, ldb, c, ldc, alpha)
+}
+
+func sgemmParallel(aTrans, bTrans bool, m, n, k int, a []float32, lda int, b []float32, ldb int, c []float32, ldc int, alpha float32) {
+	// dgemmParallel computes a parallel matrix multiplication by partitioning
+	// a and b into sub-blocks, and updating c with the multiplication of the sub-block
+	// In all cases,
+	// A = [ 	A_11	A_12 ... 	A_1j
+	//			A_21	A_22 ...	A_2j
+	//				...
+	//			A_i1	A_i2 ...	A_ij]
+	//
+	// and same for B. All of the submatrix sizes are blockSize×blockSize except
+	// at the edges.
+	//
+	// In all cases, there is one dimension for each matrix along which
+	// C must be updated sequentially.
+	// Cij = \sum_k Aik Bki,	(A * B)
+	// Cij = \sum_k Aki Bkj,	(A^T * B)
+	// Cij = \sum_k Aik Bjk,	(A * B^T)
+	// Cij = \sum_k Aki Bjk,	(A^T * B^T)
+	//
+	// This code computes one {i, j} block sequentially along the k dimension,
+	// and computes all of the {i, j} blocks concurrently. This
+	// partitioning allows Cij to be updated in-place without race-conditions.
+	// Instead of launching a goroutine for each possible concurrent computation,
+	// a number of worker goroutines are created and channels are used to pass
+	// available and completed cases.
+	//
+	// http://alexkr.com/docs/matrixmult.pdf is a good reference on matrix-matrix
+	// multiplies, though this code does not copy matrices to attempt to eliminate
+	// cache misses.
+
+	maxKLen := k
+	parBlocks := blocks(m, blockSize) * blocks(n, blockSize)
+	if parBlocks < minParBlock {
+		// The matrix multiplication is small in the dimensions where it can be
+		// computed concurrently. Just do it in serial.
+		sgemmSerial(aTrans, bTrans, m, n, k, a, lda, b, ldb, c, ldc, alpha)
+		return
+	}
+
+	nWorkers := runtime.GOMAXPROCS(0)
+	if parBlocks < nWorkers {
+		nWorkers = parBlocks
+	}
+	// There is a tradeoff between the workers having to wait for work
+	// and a large buffer making operations slow.
+	buf := buffMul * nWorkers
+	if buf > parBlocks {
+		buf = parBlocks
+	}
+
+	sendChan := make(chan subMul, buf)
+
+	// Launch workers. A worker receives an {i, j} submatrix of c, and computes
+	// A_ik B_ki (or the transposed version) storing the result in c_ij. When the
+	// channel is finally closed, it signals to the waitgroup that it has finished
+	// computing.
+	var wg sync.WaitGroup
+	for i := 0; i < nWorkers; i++ {
+		wg.Add(1)
+		go func() {
+			defer wg.Done()
+			// Make local copies of otherwise global variables to reduce shared memory.
+			// This has a noticeable effect on benchmarks in some cases.
+			alpha := alpha
+			aTrans := aTrans
+			bTrans := bTrans
+			m := m
+			n := n
+			for sub := range sendChan {
+				i := sub.i
+				j := sub.j
+				leni := blockSize
+				if i+leni > m {
+					leni = m - i
+				}
+				lenj := blockSize
+				if j+lenj > n {
+					lenj = n - j
+				}
+
+				cSub := sliceView32(c, ldc, i, j, leni, lenj)
+
+				// Compute A_ik B_kj for all k
+				for k := 0; k < maxKLen; k += blockSize {
+					lenk := blockSize
+					if k+lenk > maxKLen {
+						lenk = maxKLen - k
+					}
+					var aSub, bSub []float32
+					if aTrans {
+						aSub = sliceView32(a, lda, k, i, lenk, leni)
+					} else {
+						aSub = sliceView32(a, lda, i, k, leni, lenk)
+					}
+					if bTrans {
+						bSub = sliceView32(b, ldb, j, k, lenj, lenk)
+					} else {
+						bSub = sliceView32(b, ldb, k, j, lenk, lenj)
+					}
+					sgemmSerial(aTrans, bTrans, leni, lenj, lenk, aSub, lda, bSub, ldb, cSub, ldc, alpha)
+				}
+			}
+		}()
+	}
+
+	// Send out all of the {i, j} subblocks for computation.
+	for i := 0; i < m; i += blockSize {
+		for j := 0; j < n; j += blockSize {
+			sendChan <- subMul{
+				i: i,
+				j: j,
+			}
+		}
+	}
+	close(sendChan)
+	wg.Wait()
+}
+
+// sgemmSerial is serial matrix multiply
+func sgemmSerial(aTrans, bTrans bool, m, n, k int, a []float32, lda int, b []float32, ldb int, c []float32, ldc int, alpha float32) {
+	switch {
+	case !aTrans && !bTrans:
+		sgemmSerialNotNot(m, n, k, a, lda, b, ldb, c, ldc, alpha)
+		return
+	case aTrans && !bTrans:
+		sgemmSerialTransNot(m, n, k, a, lda, b, ldb, c, ldc, alpha)
+		return
+	case !aTrans && bTrans:
+		sgemmSerialNotTrans(m, n, k, a, lda, b, ldb, c, ldc, alpha)
+		return
+	case aTrans && bTrans:
+		sgemmSerialTransTrans(m, n, k, a, lda, b, ldb, c, ldc, alpha)
+		return
+	default:
+		panic("unreachable")
+	}
+}
+
+// sgemmSerial where neither a nor b are transposed
+func sgemmSerialNotNot(m, n, k int, a []float32, lda int, b []float32, ldb int, c []float32, ldc int, alpha float32) {
+	// This style is used instead of the literal [i*stride +j]) is used because
+	// approximately 5 times faster as of go 1.3.
+	for i := 0; i < m; i++ {
+		ctmp := c[i*ldc : i*ldc+n]
+		for l, v := range a[i*lda : i*lda+k] {
+			tmp := alpha * v
+			if tmp != 0 {
+				f32.AxpyUnitaryTo(ctmp, tmp, b[l*ldb:l*ldb+n], ctmp)
+			}
+		}
+	}
+}
+
+// sgemmSerial where neither a is transposed and b is not
+func sgemmSerialTransNot(m, n, k int, a []float32, lda int, b []float32, ldb int, c []float32, ldc int, alpha float32) {
+	// This style is used instead of the literal [i*stride +j]) is used because
+	// approximately 5 times faster as of go 1.3.
+	for l := 0; l < k; l++ {
+		btmp := b[l*ldb : l*ldb+n]
+		for i, v := range a[l*lda : l*lda+m] {
+			tmp := alpha * v
+			if tmp != 0 {
+				ctmp := c[i*ldc : i*ldc+n]
+				f32.AxpyUnitaryTo(ctmp, tmp, btmp, ctmp)
+			}
+		}
+	}
+}
+
+// sgemmSerial where neither a is not transposed and b is
+func sgemmSerialNotTrans(m, n, k int, a []float32, lda int, b []float32, ldb int, c []float32, ldc int, alpha float32) {
+	// This style is used instead of the literal [i*stride +j]) is used because
+	// approximately 5 times faster as of go 1.3.
+	for i := 0; i < m; i++ {
+		atmp := a[i*lda : i*lda+k]
+		ctmp := c[i*ldc : i*ldc+n]
+		for j := 0; j < n; j++ {
+			ctmp[j] += alpha * f32.DotUnitary(atmp, b[j*ldb:j*ldb+k])
+		}
+	}
+}
+
+// sgemmSerial where both are transposed
+func sgemmSerialTransTrans(m, n, k int, a []float32, lda int, b []float32, ldb int, c []float32, ldc int, alpha float32) {
+	// This style is used instead of the literal [i*stride +j]) is used because
+	// approximately 5 times faster as of go 1.3.
+	for l := 0; l < k; l++ {
+		for i, v := range a[l*lda : l*lda+m] {
+			tmp := alpha * v
+			if tmp != 0 {
+				ctmp := c[i*ldc : i*ldc+n]
+				f32.AxpyInc(tmp, b[l:], ctmp, uintptr(n), uintptr(ldb), 1, 0, 0)
+			}
+		}
+	}
+}
+
+func sliceView32(a []float32, lda, i, j, r, c int) []float32 {
+	return a[i*lda+j : (i+r-1)*lda+j+c]
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/gonum/single_precision.bash b/vendor/gonum.org/v1/gonum/blas/gonum/single_precision.bash
new file mode 100755
index 00000000..5213f0f2
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/gonum/single_precision.bash
@@ -0,0 +1,158 @@
+#!/usr/bin/env bash
+
+# Copyright ©2015 The gonum Authors. All rights reserved.
+# Use of this source code is governed by a BSD-style
+# license that can be found in the LICENSE file.
+
+WARNING='//\
+// Float32 implementations are autogenerated and not directly tested.\
+'
+
+# Level1 routines.
+
+echo Generating level1single.go
+echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > level1single.go
+cat level1double.go \
+| gofmt -r 'blas.Float64Level1 -> blas.Float32Level1' \
+\
+| gofmt -r 'float64 -> float32' \
+| gofmt -r 'blas.DrotmParams -> blas.SrotmParams' \
+\
+| gofmt -r 'f64.AxpyInc -> f32.AxpyInc' \
+| gofmt -r 'f64.AxpyIncTo -> f32.AxpyIncTo' \
+| gofmt -r 'f64.AxpyUnitary -> f32.AxpyUnitary' \
+| gofmt -r 'f64.AxpyUnitaryTo -> f32.AxpyUnitaryTo' \
+| gofmt -r 'f64.DotUnitary -> f32.DotUnitary' \
+| gofmt -r 'f64.ScalInc -> f32.ScalInc' \
+| gofmt -r 'f64.ScalUnitary -> f32.ScalUnitary' \
+\
+| sed -e "s_^\(func (Implementation) \)D\(.*\)\$_$WARNING\1S\2_" \
+      -e 's_^// D_// S_' \
+      -e "s_^\(func (Implementation) \)Id\(.*\)\$_$WARNING\1Is\2_" \
+      -e 's_^// Id_// Is_' \
+      -e 's_"gonum.org/v1/gonum/internal/asm/f64"_"gonum.org/v1/gonum/internal/asm/f32"_' \
+      -e 's_"math"_math "gonum.org/v1/gonum/internal/math32"_' \
+>> level1single.go
+
+echo Generating level1single_sdot.go
+echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > level1single_sdot.go
+cat level1double_ddot.go \
+| gofmt -r 'float64 -> float32' \
+\
+| gofmt -r 'f64.DotInc -> f32.DotInc' \
+| gofmt -r 'f64.DotUnitary -> f32.DotUnitary' \
+\
+| sed -e "s_^\(func (Implementation) \)D\(.*\)\$_$WARNING\1S\2_" \
+      -e 's_^// D_// S_' \
+      -e 's_"gonum.org/v1/gonum/internal/asm/f64"_"gonum.org/v1/gonum/internal/asm/f32"_' \
+>> level1single_sdot.go
+
+echo Generating level1single_dsdot.go
+echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > level1single_dsdot.go
+cat level1double_ddot.go \
+| gofmt -r '[]float64 -> []float32' \
+\
+| gofmt -r 'f64.DotInc -> f32.DdotInc' \
+| gofmt -r 'f64.DotUnitary -> f32.DdotUnitary' \
+\
+| sed -e "s_^\(func (Implementation) \)D\(.*\)\$_$WARNING\1Ds\2_" \
+      -e 's_^// D_// Ds_' \
+      -e 's_"gonum.org/v1/gonum/internal/asm/f64"_"gonum.org/v1/gonum/internal/asm/f32"_' \
+>> level1single_dsdot.go
+
+echo Generating level1single_sdsdot.go
+echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > level1single_sdsdot.go
+cat level1double_ddot.go \
+| gofmt -r 'float64 -> float32' \
+\
+| gofmt -r 'f64.DotInc(x, y, f(n), f(incX), f(incY), f(ix), f(iy)) -> alpha + float32(f32.DdotInc(x, y, f(n), f(incX), f(incY), f(ix), f(iy)))' \
+| gofmt -r 'f64.DotUnitary(a, b) -> alpha + float32(f32.DdotUnitary(a, b))' \
+\
+| sed -e "s_^\(func (Implementation) \)D\(.*\)\$_$WARNING\1Sds\2_" \
+      -e 's_^// D\(.*\)$_// Sds\1 plus a constant_' \
+      -e 's_\\sum_alpha + \\sum_' \
+      -e 's/n int/n int, alpha float32/' \
+      -e 's_"gonum.org/v1/gonum/internal/asm/f64"_"gonum.org/v1/gonum/internal/asm/f32"_' \
+>> level1single_sdsdot.go
+
+
+# Level2 routines.
+
+echo Generating level2single.go
+echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > level2single.go
+cat level2double.go \
+| gofmt -r 'blas.Float64Level2 -> blas.Float32Level2' \
+\
+| gofmt -r 'float64 -> float32' \
+\
+| gofmt -r 'Dscal -> Sscal' \
+\
+| gofmt -r 'f64.AxpyInc -> f32.AxpyInc' \
+| gofmt -r 'f64.AxpyIncTo -> f32.AxpyIncTo' \
+| gofmt -r 'f64.AxpyUnitary -> f32.AxpyUnitary' \
+| gofmt -r 'f64.AxpyUnitaryTo -> f32.AxpyUnitaryTo' \
+| gofmt -r 'f64.DotInc -> f32.DotInc' \
+| gofmt -r 'f64.DotUnitary -> f32.DotUnitary' \
+\
+| sed -e "s_^\(func (Implementation) \)D\(.*\)\$_$WARNING\1S\2_" \
+      -e 's_^// D_// S_' \
+      -e 's_"gonum.org/v1/gonum/internal/asm/f64"_"gonum.org/v1/gonum/internal/asm/f32"_' \
+>> level2single.go
+
+
+# Level3 routines.
+
+echo Generating level3single.go
+echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > level3single.go
+cat level3double.go \
+| gofmt -r 'blas.Float64Level3 -> blas.Float32Level3' \
+\
+| gofmt -r 'float64 -> float32' \
+\
+| gofmt -r 'f64.AxpyUnitaryTo -> f32.AxpyUnitaryTo' \
+| gofmt -r 'f64.DotUnitary -> f32.DotUnitary' \
+\
+| sed -e "s_^\(func (Implementation) \)D\(.*\)\$_$WARNING\1S\2_" \
+      -e 's_^// D_// S_' \
+      -e 's_"gonum.org/v1/gonum/internal/asm/f64"_"gonum.org/v1/gonum/internal/asm/f32"_' \
+>> level3single.go
+
+echo Generating general_single.go
+echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > general_single.go
+cat general_double.go \
+| gofmt -r 'float64 -> float32' \
+\
+| gofmt -r 'general64 -> general32' \
+| gofmt -r 'newGeneral64 -> newGeneral32' \
+\
+| sed -e 's/(g general64) print()/(g general32) print()/' \
+      -e 's_"math"_math "gonum.org/v1/gonum/internal/math32"_' \
+      -e 's_"gonum.org/v1/gonum/internal/asm/f64"_"gonum.org/v1/gonum/internal/asm/f32"_' \
+>> general_single.go
+
+echo Generating sgemm.go
+echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > sgemm.go
+cat dgemm.go \
+| gofmt -r 'float64 -> float32' \
+| gofmt -r 'general64 -> general32' \
+| gofmt -r 'sliceView64 -> sliceView32' \
+| gofmt -r 'checkDMatrix -> checkSMatrix' \
+\
+| gofmt -r 'dgemmParallel -> sgemmParallel' \
+| gofmt -r 'computeNumBlocks64 -> computeNumBlocks32' \
+| gofmt -r 'dgemmSerial -> sgemmSerial' \
+| gofmt -r 'dgemmSerialNotNot -> sgemmSerialNotNot' \
+| gofmt -r 'dgemmSerialTransNot -> sgemmSerialTransNot' \
+| gofmt -r 'dgemmSerialNotTrans -> sgemmSerialNotTrans' \
+| gofmt -r 'dgemmSerialTransTrans -> sgemmSerialTransTrans' \
+\
+| gofmt -r 'f64.AxpyInc -> f32.AxpyInc' \
+| gofmt -r 'f64.AxpyIncTo -> f32.AxpyIncTo' \
+| gofmt -r 'f64.AxpyUnitaryTo -> f32.AxpyUnitaryTo' \
+| gofmt -r 'f64.DotUnitary -> f32.DotUnitary' \
+\
+| sed -e "s_^\(func (Implementation) \)D\(.*\)\$_$WARNING\1S\2_" \
+      -e 's_^// D_// S_' \
+      -e 's_^// d_// s_' \
+      -e 's_"gonum.org/v1/gonum/internal/asm/f64"_"gonum.org/v1/gonum/internal/asm/f32"_' \
+>> sgemm.go
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/benchautogen/autogen_bench_level1double.go b/vendor/gonum.org/v1/gonum/blas/testblas/benchautogen/autogen_bench_level1double.go
new file mode 100644
index 00000000..35e08c1e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/benchautogen/autogen_bench_level1double.go
@@ -0,0 +1,292 @@
+// Copyright 2014 The Gonum Authors. All rights reserved.
+// Use of this code is governed by a BSD-style
+// license that can be found in the LICENSE file
+
+// Script for automatic code generation of the benchmark routines.
+package main
+
+import (
+	"fmt"
+	"os"
+	"os/exec"
+	"path"
+	"path/filepath"
+	"strconv"
+)
+
+var gopath string
+
+var copyrightnotice = []byte(`// Copyright 2014 The Gonum Authors. All rights reserved.
+// Use of this code is governed by a BSD-style
+// license that can be found in the LICENSE file`)
+
+var autogen = []byte("// Code generated by \"go run gonum.org/v1/gonum/blas/testblas/benchautogen/autogen_bench_level1double.go\"; DO NOT EDIT.\n")
+
+var imports = []byte(`import(
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)`)
+
+var randomSliceFunction = []byte(`func randomSlice(l, idx int) ([]float64) {
+	if idx < 0{
+		idx = -idx
+	}
+	s := make([]float64, l * idx)
+	for i := range s {
+		s[i] = rand.Float64()
+	}
+	return s
+}`)
+
+const (
+	posInc1 = 5
+	posInc2 = 3
+	negInc1 = -3
+	negInc2 = -4
+)
+
+var level1Sizes = []struct {
+	lower string
+	upper string
+	camel string
+	size  int
+}{
+	{
+		lower: "small",
+		upper: "SMALL_SLICE",
+		camel: "Small",
+		size:  10,
+	},
+	{
+		lower: "medium",
+		upper: "MEDIUM_SLICE",
+		camel: "Medium",
+		size:  1000,
+	},
+	{
+		lower: "large",
+		upper: "LARGE_SLICE",
+		camel: "Large",
+		size:  100000,
+	},
+	{
+		lower: "huge",
+		upper: "HUGE_SLICE",
+		camel: "Huge",
+		size:  10000000,
+	},
+}
+
+type level1functionStruct struct {
+	camel      string
+	sig        string
+	call       string
+	extraSetup string
+	oneInput   bool
+	extraName  string // if have a couple different cases for the same function
+}
+
+var level1Functions = []level1functionStruct{
+	{
+		camel:    "Ddot",
+		sig:      "n int, x []float64, incX int, y []float64, incY int",
+		call:     "n, x, incX, y, incY",
+		oneInput: false,
+	},
+	{
+		camel:    "Dnrm2",
+		sig:      "n int, x []float64, incX int",
+		call:     "n, x, incX",
+		oneInput: true,
+	},
+	{
+		camel:    "Dasum",
+		sig:      "n int, x []float64, incX int",
+		call:     "n, x, incX",
+		oneInput: true,
+	},
+	{
+		camel:    "Idamax",
+		sig:      "n int, x []float64, incX int",
+		call:     "n, x, incX",
+		oneInput: true,
+	},
+	{
+		camel:    "Dswap",
+		sig:      "n int, x []float64, incX int, y []float64, incY int",
+		call:     "n, x, incX, y, incY",
+		oneInput: false,
+	},
+	{
+		camel:    "Dcopy",
+		sig:      "n int, x []float64, incX int, y []float64, incY int",
+		call:     "n, x, incX, y, incY",
+		oneInput: false,
+	},
+	{
+		camel:      "Daxpy",
+		sig:        "n int, alpha float64, x []float64, incX int, y []float64, incY int",
+		call:       "n, alpha, x, incX, y, incY",
+		extraSetup: "alpha := 2.4",
+		oneInput:   false,
+	},
+	{
+		camel:      "Drot",
+		sig:        "n int, x []float64, incX int, y []float64, incY int, c, s float64",
+		call:       "n, x, incX, y, incY, c, s",
+		extraSetup: "c := 0.89725836967\ns:= 0.44150585279",
+		oneInput:   false,
+	},
+	{
+		camel:      "Drotm",
+		sig:        "n int, x []float64, incX int, y []float64, incY int, p blas.DrotmParams",
+		call:       "n, x, incX, y, incY, p",
+		extraSetup: "p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{0, -0.625, 0.9375,0}}",
+		oneInput:   false,
+		extraName:  "OffDia",
+	},
+	{
+		camel:      "Drotm",
+		sig:        "n int, x []float64, incX int, y []float64, incY int, p blas.DrotmParams",
+		call:       "n, x, incX, y, incY, p",
+		extraSetup: "p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{5.0 / 12, 0, 0, 0.625}}",
+		oneInput:   false,
+		extraName:  "Dia",
+	},
+	{
+		camel:      "Drotm",
+		sig:        "n int, x []float64, incX int, y []float64, incY int, p blas.DrotmParams",
+		call:       "n, x, incX, y, incY, p",
+		extraSetup: "p := blas.DrotmParams{Flag: blas.OffDiagonal, H: [4]float64{4096, -3584, 1792, 4096}}",
+		oneInput:   false,
+		extraName:  "Resc",
+	},
+	{
+		camel:      "Dscal",
+		sig:        "n int, alpha float64, x []float64, incX int",
+		call:       "n, alpha, x, incX",
+		extraSetup: "alpha := 2.4",
+		oneInput:   true,
+	},
+}
+
+func init() {
+	gopath = os.Getenv("GOPATH")
+	if gopath == "" {
+		panic("gopath not set")
+	}
+}
+
+func main() {
+	blasPath := filepath.Join(gopath, "src", "gonum.org", "v1", "gonum", "blas")
+
+	pkgs := []struct{ name string }{{name: "native"}, {name: "cgo"}}
+
+	for _, pkg := range pkgs {
+		err := level1(filepath.Join(blasPath, pkg.name), pkg.name)
+		if err != nil {
+			fmt.Println(err)
+			os.Exit(1)
+		}
+
+		err = exec.Command("go", "fmt", path.Join("gonum.org", "v1", "gonum", "blas", pkg.name)).Run()
+		if err != nil {
+			fmt.Println(err)
+			os.Exit(1)
+		}
+	}
+}
+
+func printHeader(f *os.File, name string) error {
+	if _, err := f.Write(autogen); err != nil {
+		return err
+	}
+	f.WriteString("\n\n")
+	f.Write(copyrightnotice)
+	f.WriteString("\n\n")
+	f.WriteString("package " + name)
+	f.WriteString("\n\n")
+	f.Write(imports)
+	f.WriteString("\n\n")
+	return nil
+}
+
+// Generate the benchmark scripts for level1
+func level1(benchPath string, pkgname string) error {
+	// Generate level 1 benchmarks
+	level1Filepath := filepath.Join(benchPath, "level1doubleBench_auto_test.go")
+	f, err := os.Create(level1Filepath)
+	if err != nil {
+		fmt.Println(err)
+		os.Exit(1)
+	}
+	defer f.Close()
+	printHeader(f, pkgname)
+
+	// Print all of the constants
+	f.WriteString("const (\n")
+	f.WriteString("\tposInc1 = " + strconv.Itoa(posInc1) + "\n")
+	f.WriteString("\tposInc2 = " + strconv.Itoa(posInc2) + "\n")
+	f.WriteString("\tnegInc1 = " + strconv.Itoa(negInc1) + "\n")
+	f.WriteString("\tnegInc2 = " + strconv.Itoa(negInc2) + "\n")
+	for _, con := range level1Sizes {
+		f.WriteString("\t" + con.upper + " = " + strconv.Itoa(con.size) + "\n")
+	}
+	f.WriteString(")\n")
+	f.WriteString("\n")
+
+	// Write the randomSlice function
+	f.Write(randomSliceFunction)
+	f.WriteString("\n\n")
+
+	// Start writing the benchmarks
+	for _, fun := range level1Functions {
+		writeLevel1Benchmark(fun, f)
+		f.WriteString("\n/* ------------------ */ \n")
+	}
+
+	return nil
+}
+
+func writeLevel1Benchmark(fun level1functionStruct, f *os.File) {
+	// First, write the base benchmark file
+	f.WriteString("func benchmark" + fun.camel + fun.extraName + "(b *testing.B, ")
+	f.WriteString(fun.sig)
+	f.WriteString(") {\n")
+
+	f.WriteString("b.ResetTimer()\n")
+	f.WriteString("for i := 0; i < b.N; i++{\n")
+	f.WriteString("\timpl." + fun.camel + "(")
+
+	f.WriteString(fun.call)
+	f.WriteString(")\n}\n}\n")
+	f.WriteString("\n")
+
+	// Write all of the benchmarks to call it
+	for _, sz := range level1Sizes {
+		lambda := func(incX, incY, name string, twoInput bool) {
+			f.WriteString("func Benchmark" + fun.camel + fun.extraName + sz.camel + name + "(b *testing.B){\n")
+			f.WriteString("n := " + sz.upper + "\n")
+			f.WriteString("incX := " + incX + "\n")
+			f.WriteString("x := randomSlice(n, incX)\n")
+			if twoInput {
+				f.WriteString("incY := " + incY + "\n")
+				f.WriteString("y := randomSlice(n, incY)\n")
+			}
+			f.WriteString(fun.extraSetup + "\n")
+			f.WriteString("benchmark" + fun.camel + fun.extraName + "(b, " + fun.call + ")\n")
+			f.WriteString("}\n\n")
+		}
+		if fun.oneInput {
+			lambda("1", "", "UnitaryInc", false)
+			lambda("posInc1", "", "PosInc", false)
+		} else {
+			lambda("1", "1", "BothUnitary", true)
+			lambda("posInc1", "1", "IncUni", true)
+			lambda("1", "negInc1", "UniInc", true)
+			lambda("posInc1", "negInc1", "BothInc", true)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/benchsize.go b/vendor/gonum.org/v1/gonum/blas/testblas/benchsize.go
new file mode 100644
index 00000000..41d132be
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/benchsize.go
@@ -0,0 +1,8 @@
+package testblas
+
+const (
+	SmallMat  = 10
+	MediumMat = 100
+	LargeMat  = 1000
+	HugeMat   = 10000
+)
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/common.go b/vendor/gonum.org/v1/gonum/blas/testblas/common.go
new file mode 100644
index 00000000..68a4c05a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/common.go
@@ -0,0 +1,316 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testblas
+
+import (
+	"math"
+	"math/cmplx"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+// throwPanic will throw unexpected panics if true, or will just report them as errors if false
+const throwPanic = true
+
+func dTolEqual(a, b float64) bool {
+	if math.IsNaN(a) && math.IsNaN(b) {
+		return true
+	}
+	if a == b {
+		return true
+	}
+	m := math.Max(math.Abs(a), math.Abs(b))
+	if m > 1 {
+		a /= m
+		b /= m
+	}
+	if math.Abs(a-b) < 1e-14 {
+		return true
+	}
+	return false
+}
+
+func dSliceTolEqual(a, b []float64) bool {
+	if len(a) != len(b) {
+		return false
+	}
+	for i := range a {
+		if !dTolEqual(a[i], b[i]) {
+			return false
+		}
+	}
+	return true
+}
+
+func dStridedSliceTolEqual(n int, a []float64, inca int, b []float64, incb int) bool {
+	ia := 0
+	ib := 0
+	if inca <= 0 {
+		ia = -(n - 1) * inca
+	}
+	if incb <= 0 {
+		ib = -(n - 1) * incb
+	}
+	for i := 0; i < n; i++ {
+		if !dTolEqual(a[ia], b[ib]) {
+			return false
+		}
+		ia += inca
+		ib += incb
+	}
+	return true
+}
+
+func dSliceEqual(a, b []float64) bool {
+	if len(a) != len(b) {
+		return false
+	}
+	for i := range a {
+		if !(a[i] == b[i]) {
+			return false
+		}
+	}
+	return true
+}
+
+func dCopyTwoTmp(x, xTmp, y, yTmp []float64) {
+	if len(x) != len(xTmp) {
+		panic("x size mismatch")
+	}
+	if len(y) != len(yTmp) {
+		panic("y size mismatch")
+	}
+	copy(xTmp, x)
+	copy(yTmp, y)
+}
+
+// returns true if the function panics
+func panics(f func()) (b bool) {
+	defer func() {
+		err := recover()
+		if err != nil {
+			b = true
+		}
+	}()
+	f()
+	return
+}
+
+func testpanics(f func(), name string, t *testing.T) {
+	b := panics(f)
+	if !b {
+		t.Errorf("%v should panic and does not", name)
+	}
+}
+
+func sliceOfSliceCopy(a [][]float64) [][]float64 {
+	n := make([][]float64, len(a))
+	for i := range a {
+		n[i] = make([]float64, len(a[i]))
+		copy(n[i], a[i])
+	}
+	return n
+}
+
+func sliceCopy(a []float64) []float64 {
+	n := make([]float64, len(a))
+	copy(n, a)
+	return n
+}
+
+func flatten(a [][]float64) []float64 {
+	if len(a) == 0 {
+		return nil
+	}
+	m := len(a)
+	n := len(a[0])
+	s := make([]float64, m*n)
+	for i := 0; i < m; i++ {
+		for j := 0; j < n; j++ {
+			s[i*n+j] = a[i][j]
+		}
+	}
+	return s
+}
+
+func unflatten(a []float64, m, n int) [][]float64 {
+	s := make([][]float64, m)
+	for i := 0; i < m; i++ {
+		s[i] = make([]float64, n)
+		for j := 0; j < n; j++ {
+			s[i][j] = a[i*n+j]
+		}
+	}
+	return s
+}
+
+// flattenTriangular turns the upper or lower triangle of a dense slice of slice
+// into a single slice with packed storage. a must be a square matrix.
+func flattenTriangular(a [][]float64, ul blas.Uplo) []float64 {
+	m := len(a)
+	aFlat := make([]float64, m*(m+1)/2)
+	var k int
+	if ul == blas.Upper {
+		for i := 0; i < m; i++ {
+			k += copy(aFlat[k:], a[i][i:])
+		}
+		return aFlat
+	}
+	for i := 0; i < m; i++ {
+		k += copy(aFlat[k:], a[i][:i+1])
+	}
+	return aFlat
+}
+
+// flattenBanded turns a dense banded slice of slice into the compact banded matrix format
+func flattenBanded(a [][]float64, ku, kl int) []float64 {
+	m := len(a)
+	n := len(a[0])
+	if ku < 0 || kl < 0 {
+		panic("testblas: negative band length")
+	}
+	nRows := m
+	nCols := (ku + kl + 1)
+	aflat := make([]float64, nRows*nCols)
+	for i := range aflat {
+		aflat[i] = math.NaN()
+	}
+	// loop over the rows, and then the bands
+	// elements in the ith row stay in the ith row
+	// order in bands is kept
+	for i := 0; i < nRows; i++ {
+		min := -kl
+		if i-kl < 0 {
+			min = -i
+		}
+		max := ku
+		if i+ku >= n {
+			max = n - i - 1
+		}
+		for j := min; j <= max; j++ {
+			col := kl + j
+			aflat[i*nCols+col] = a[i][i+j]
+		}
+	}
+	return aflat
+}
+
+// makeIncremented takes a slice with inc == 1 and makes an incremented version
+// and adds extra values on the end
+func makeIncremented(x []float64, inc int, extra int) []float64 {
+	if inc == 0 {
+		panic("zero inc")
+	}
+	absinc := inc
+	if absinc < 0 {
+		absinc = -inc
+	}
+	xcopy := make([]float64, len(x))
+	if inc > 0 {
+		copy(xcopy, x)
+	} else {
+		for i := 0; i < len(x); i++ {
+			xcopy[i] = x[len(x)-i-1]
+		}
+	}
+
+	// don't use NaN because it makes comparison hard
+	// Do use a weird unique value for easier debugging
+	counter := 100.0
+	var xnew []float64
+	for i, v := range xcopy {
+		xnew = append(xnew, v)
+		if i != len(x)-1 {
+			for j := 0; j < absinc-1; j++ {
+				xnew = append(xnew, counter)
+				counter++
+			}
+		}
+	}
+	for i := 0; i < extra; i++ {
+		xnew = append(xnew, counter)
+		counter++
+	}
+	return xnew
+}
+
+func abs(x int) int {
+	if x < 0 {
+		return -x
+	}
+	return x
+}
+
+func allPairs(x, y []int) [][2]int {
+	var p [][2]int
+	for _, v0 := range x {
+		for _, v1 := range y {
+			p = append(p, [2]int{v0, v1})
+		}
+	}
+	return p
+}
+
+func zsame(x, y []complex128) bool {
+	if len(x) != len(y) {
+		return false
+	}
+	for i, v := range x {
+		w := y[i]
+		if v != w && !math.IsNaN(real(v)) && !math.IsNaN(imag(v)) && !math.IsNaN(real(w)) && !math.IsNaN(imag(w)) {
+			return false
+		}
+	}
+	return true
+}
+
+func makeZVector(data []complex128, inc int) []complex128 {
+	if inc == 0 {
+		panic("bad test")
+	}
+	if len(data) == 0 {
+		return nil
+	}
+	inc = abs(inc)
+	x := make([]complex128, (len(data)-1)*inc+1)
+	for i := range x {
+		x[i] = cmplx.NaN()
+	}
+	for i, v := range data {
+		x[i*inc] = v
+	}
+	return x
+}
+
+func makeZGeneral(data []complex128, m, n int, ld int) []complex128 {
+	if m < 0 || n < 0 {
+		panic("bad test")
+	}
+	if len(data) != m*n {
+		panic("bad test")
+	}
+	if ld < max(1, n) {
+		panic("bad test")
+	}
+	if len(data) == 0 {
+		return nil
+	}
+	a := make([]complex128, (m-1)*ld+n)
+	for i := range a {
+		a[i] = cmplx.NaN()
+	}
+	for i := 0; i < m; i++ {
+		copy(a[i*ld:i*ld+n], data[i*n:i*n+n])
+	}
+	return a
+}
+
+func max(a, b int) int {
+	if a < b {
+		return b
+	}
+	return a
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/common_test.go b/vendor/gonum.org/v1/gonum/blas/testblas/common_test.go
new file mode 100644
index 00000000..852a939e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/common_test.go
@@ -0,0 +1,187 @@
+package testblas
+
+import (
+	"math"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/floats"
+)
+
+func TestFlattenBanded(t *testing.T) {
+	for i, test := range []struct {
+		dense     [][]float64
+		ku        int
+		kl        int
+		condensed [][]float64
+	}{
+		{
+			dense:     [][]float64{{3}},
+			ku:        0,
+			kl:        0,
+			condensed: [][]float64{{3}},
+		},
+		{
+			dense: [][]float64{
+				{3, 4, 0},
+			},
+			ku: 1,
+			kl: 0,
+			condensed: [][]float64{
+				{3, 4},
+			},
+		},
+		{
+			dense: [][]float64{
+				{3, 4, 0, 0, 0},
+			},
+			ku: 1,
+			kl: 0,
+			condensed: [][]float64{
+				{3, 4},
+			},
+		},
+		{
+			dense: [][]float64{
+				{3, 4, 0},
+				{0, 5, 8},
+				{0, 0, 2},
+				{0, 0, 0},
+				{0, 0, 0},
+			},
+			ku: 1,
+			kl: 0,
+			condensed: [][]float64{
+				{3, 4},
+				{5, 8},
+				{2, math.NaN()},
+				{math.NaN(), math.NaN()},
+				{math.NaN(), math.NaN()},
+			},
+		},
+		{
+			dense: [][]float64{
+				{3, 4, 6},
+				{0, 5, 8},
+				{0, 0, 2},
+				{0, 0, 0},
+				{0, 0, 0},
+			},
+			ku: 2,
+			kl: 0,
+			condensed: [][]float64{
+				{3, 4, 6},
+				{5, 8, math.NaN()},
+				{2, math.NaN(), math.NaN()},
+				{math.NaN(), math.NaN(), math.NaN()},
+				{math.NaN(), math.NaN(), math.NaN()},
+			},
+		},
+		{
+			dense: [][]float64{
+				{3, 4, 6},
+				{1, 5, 8},
+				{0, 6, 2},
+				{0, 0, 7},
+				{0, 0, 0},
+			},
+			ku: 2,
+			kl: 1,
+			condensed: [][]float64{
+				{math.NaN(), 3, 4, 6},
+				{1, 5, 8, math.NaN()},
+				{6, 2, math.NaN(), math.NaN()},
+				{7, math.NaN(), math.NaN(), math.NaN()},
+				{math.NaN(), math.NaN(), math.NaN(), math.NaN()},
+			},
+		},
+		{
+			dense: [][]float64{
+				{1, 2, 0},
+				{3, 4, 5},
+				{6, 7, 8},
+				{0, 9, 10},
+				{0, 0, 11},
+			},
+			ku: 1,
+			kl: 2,
+			condensed: [][]float64{
+				{math.NaN(), math.NaN(), 1, 2},
+				{math.NaN(), 3, 4, 5},
+				{6, 7, 8, math.NaN()},
+				{9, 10, math.NaN(), math.NaN()},
+				{11, math.NaN(), math.NaN(), math.NaN()},
+			},
+		},
+		{
+			dense: [][]float64{
+				{1, 0, 0},
+				{3, 4, 0},
+				{6, 7, 8},
+				{0, 9, 10},
+				{0, 0, 11},
+			},
+			ku: 0,
+			kl: 2,
+			condensed: [][]float64{
+				{math.NaN(), math.NaN(), 1},
+				{math.NaN(), 3, 4},
+				{6, 7, 8},
+				{9, 10, math.NaN()},
+				{11, math.NaN(), math.NaN()},
+			},
+		},
+		{
+			dense: [][]float64{
+				{1, 0, 0, 0, 0},
+				{3, 4, 0, 0, 0},
+				{1, 3, 5, 0, 0},
+			},
+			ku: 0,
+			kl: 2,
+			condensed: [][]float64{
+				{math.NaN(), math.NaN(), 1},
+				{math.NaN(), 3, 4},
+				{1, 3, 5},
+			},
+		},
+	} {
+		condensed := flattenBanded(test.dense, test.ku, test.kl)
+		correct := flatten(test.condensed)
+		if !floats.Same(condensed, correct) {
+			t.Errorf("Case %v mismatch. Want %v, got %v.", i, correct, condensed)
+		}
+	}
+}
+
+func TestFlattenTriangular(t *testing.T) {
+	for i, test := range []struct {
+		a   [][]float64
+		ans []float64
+		ul  blas.Uplo
+	}{
+		{
+			a: [][]float64{
+				{1, 2, 3},
+				{0, 4, 5},
+				{0, 0, 6},
+			},
+			ul:  blas.Upper,
+			ans: []float64{1, 2, 3, 4, 5, 6},
+		},
+		{
+			a: [][]float64{
+				{1, 0, 0},
+				{2, 3, 0},
+				{4, 5, 6},
+			},
+			ul:  blas.Lower,
+			ans: []float64{1, 2, 3, 4, 5, 6},
+		},
+	} {
+		a := flattenTriangular(test.a, test.ul)
+		if !floats.Equal(a, test.ans) {
+			t.Errorf("Case %v. Want %v, got %v.", i, test.ans, a)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/dgbmv.go b/vendor/gonum.org/v1/gonum/blas/testblas/dgbmv.go
new file mode 100644
index 00000000..1e0a5c18
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/dgbmv.go
@@ -0,0 +1,131 @@
+package testblas
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+type Dgbmver interface {
+	Dgbmv(tA blas.Transpose, m, n, kL, kU int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int)
+}
+
+func DgbmvTest(t *testing.T, blasser Dgbmver) {
+	for i, test := range []struct {
+		tA     blas.Transpose
+		m, n   int
+		kL, kU int
+		alpha  float64
+		a      [][]float64
+		lda    int
+		x      []float64
+		beta   float64
+		y      []float64
+		ans    []float64
+	}{
+		{
+			tA:    blas.NoTrans,
+			m:     9,
+			n:     6,
+			lda:   4,
+			kL:    2,
+			kU:    1,
+			alpha: 3.0,
+			beta:  2.0,
+			a: [][]float64{
+				{5, 3, 0, 0, 0, 0},
+				{-1, 2, 9, 0, 0, 0},
+				{4, 8, 3, 6, 0, 0},
+				{0, -1, 8, 2, 1, 0},
+				{0, 0, 9, 9, 9, 5},
+				{0, 0, 0, 2, -3, 2},
+				{0, 0, 0, 0, 1, 5},
+				{0, 0, 0, 0, 0, 6},
+			},
+			x:   []float64{1, 2, 3, 4, 5, 6},
+			y:   []float64{-1, -2, -3, -4, -5, -6, -7, -8, -9},
+			ans: []float64{31, 86, 153, 97, 404, 3, 91, 92, -18},
+		},
+		{
+			tA:    blas.Trans,
+			m:     9,
+			n:     6,
+			lda:   4,
+			kL:    2,
+			kU:    1,
+			alpha: 3.0,
+			beta:  2.0,
+			a: [][]float64{
+				{5, 3, 0, 0, 0, 0},
+				{-1, 2, 9, 0, 0, 0},
+				{4, 8, 3, 6, 0, 0},
+				{0, -1, 8, 2, 1, 0},
+				{0, 0, 9, 9, 9, 5},
+				{0, 0, 0, 2, -3, 2},
+				{0, 0, 0, 0, 1, 5},
+				{0, 0, 0, 0, 0, 6},
+			},
+			x:   []float64{1, 2, 3, 4, 5, 6, 7, 8, 9},
+			y:   []float64{-1, -2, -3, -4, -5, -6},
+			ans: []float64{43, 77, 306, 241, 104, 348},
+		},
+		{
+			tA:    blas.NoTrans,
+			m:     6,
+			n:     3,
+			lda:   1,
+			kL:    0,
+			kU:    0,
+			alpha: 2.0,
+			beta:  1.0,
+			a: [][]float64{
+				{1, 0, 0},
+				{0, 1, 0},
+				{0, 0, 1},
+			},
+			x:   []float64{1, 2, 3},
+			y:   []float64{-1, -2, -3, -4, -5, -6},
+			ans: []float64{1, 2, 3, -4, -5, -6},
+		},
+		{
+			tA:    blas.Trans,
+			m:     6,
+			n:     3,
+			lda:   1,
+			kL:    0,
+			kU:    0,
+			alpha: 2.0,
+			beta:  1.0,
+			a: [][]float64{
+				{1, 0, 0},
+				{0, 1, 0},
+				{0, 0, 1},
+				{0, 0, 0},
+				{0, 0, 0},
+				{0, 0, 0},
+			},
+			x:   []float64{1, 2, 3, 4, 5, 6},
+			y:   []float64{-1, -2, -3},
+			ans: []float64{1, 2, 3},
+		},
+	} {
+		extra := 3
+		aFlat := flattenBanded(test.a, test.kU, test.kL)
+		incTest := func(incX, incY, extra int) {
+			xnew := makeIncremented(test.x, incX, extra)
+			ynew := makeIncremented(test.y, incY, extra)
+			ans := makeIncremented(test.ans, incY, extra)
+			blasser.Dgbmv(test.tA, test.m, test.n, test.kL, test.kU, test.alpha, aFlat, test.lda, xnew, incX, test.beta, ynew, incY)
+			if !dSliceTolEqual(ans, ynew) {
+				t.Errorf("Case %v: Want %v, got %v", i, ans, ynew)
+			}
+		}
+		incTest(1, 1, extra)
+		incTest(1, 3, extra)
+		incTest(1, -3, extra)
+		incTest(2, 3, extra)
+		incTest(2, -3, extra)
+		incTest(3, 2, extra)
+		incTest(-3, 2, extra)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/dgemm.go b/vendor/gonum.org/v1/gonum/blas/testblas/dgemm.go
new file mode 100644
index 00000000..f4bcddd8
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/dgemm.go
@@ -0,0 +1,244 @@
+package testblas
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+type Dgemmer interface {
+	Dgemm(tA, tB blas.Transpose, m, n, k int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int)
+}
+
+type DgemmCase struct {
+	m, n, k     int
+	alpha, beta float64
+	a           [][]float64
+	b           [][]float64
+	c           [][]float64
+	ans         [][]float64
+}
+
+var DgemmCases = []DgemmCase{
+
+	{
+		m:     4,
+		n:     3,
+		k:     2,
+		alpha: 2,
+		beta:  0.5,
+		a: [][]float64{
+			{1, 2},
+			{4, 5},
+			{7, 8},
+			{10, 11},
+		},
+		b: [][]float64{
+			{1, 5, 6},
+			{5, -8, 8},
+		},
+		c: [][]float64{
+			{4, 8, -9},
+			{12, 16, -8},
+			{1, 5, 15},
+			{-3, -4, 7},
+		},
+		ans: [][]float64{
+			{24, -18, 39.5},
+			{64, -32, 124},
+			{94.5, -55.5, 219.5},
+			{128.5, -78, 299.5},
+		},
+	},
+	{
+		m:     4,
+		n:     2,
+		k:     3,
+		alpha: 2,
+		beta:  0.5,
+		a: [][]float64{
+			{1, 2, 3},
+			{4, 5, 6},
+			{7, 8, 9},
+			{10, 11, 12},
+		},
+		b: [][]float64{
+			{1, 5},
+			{5, -8},
+			{6, 2},
+		},
+		c: [][]float64{
+			{4, 8},
+			{12, 16},
+			{1, 5},
+			{-3, -4},
+		},
+		ans: [][]float64{
+			{60, -6},
+			{136, -8},
+			{202.5, -19.5},
+			{272.5, -30},
+		},
+	},
+	{
+		m:     3,
+		n:     2,
+		k:     4,
+		alpha: 2,
+		beta:  0.5,
+		a: [][]float64{
+			{1, 2, 3, 4},
+			{4, 5, 6, 7},
+			{8, 9, 10, 11},
+		},
+		b: [][]float64{
+			{1, 5},
+			{5, -8},
+			{6, 2},
+			{8, 10},
+		},
+		c: [][]float64{
+			{4, 8},
+			{12, 16},
+			{9, -10},
+		},
+		ans: [][]float64{
+			{124, 74},
+			{248, 132},
+			{406.5, 191},
+		},
+	},
+	{
+		m:     3,
+		n:     4,
+		k:     2,
+		alpha: 2,
+		beta:  0.5,
+		a: [][]float64{
+			{1, 2},
+			{4, 5},
+			{8, 9},
+		},
+		b: [][]float64{
+			{1, 5, 2, 1},
+			{5, -8, 2, 1},
+		},
+		c: [][]float64{
+			{4, 8, 2, 2},
+			{12, 16, 8, 9},
+			{9, -10, 10, 10},
+		},
+		ans: [][]float64{
+			{24, -18, 13, 7},
+			{64, -32, 40, 22.5},
+			{110.5, -69, 73, 39},
+		},
+	},
+	{
+		m:     2,
+		n:     4,
+		k:     3,
+		alpha: 2,
+		beta:  0.5,
+		a: [][]float64{
+			{1, 2, 3},
+			{4, 5, 6},
+		},
+		b: [][]float64{
+			{1, 5, 8, 8},
+			{5, -8, 9, 10},
+			{6, 2, -3, 2},
+		},
+		c: [][]float64{
+			{4, 8, 7, 8},
+			{12, 16, -2, 6},
+		},
+		ans: [][]float64{
+			{60, -6, 37.5, 72},
+			{136, -8, 117, 191},
+		},
+	},
+	{
+		m:     2,
+		n:     3,
+		k:     4,
+		alpha: 2,
+		beta:  0.5,
+		a: [][]float64{
+			{1, 2, 3, 4},
+			{4, 5, 6, 7},
+		},
+		b: [][]float64{
+			{1, 5, 8},
+			{5, -8, 9},
+			{6, 2, -3},
+			{8, 10, 2},
+		},
+		c: [][]float64{
+			{4, 8, 1},
+			{12, 16, 6},
+		},
+		ans: [][]float64{
+			{124, 74, 50.5},
+			{248, 132, 149},
+		},
+	},
+}
+
+// assumes [][]float64 is actually a matrix
+func transpose(a [][]float64) [][]float64 {
+	b := make([][]float64, len(a[0]))
+	for i := range b {
+		b[i] = make([]float64, len(a))
+		for j := range b[i] {
+			b[i][j] = a[j][i]
+		}
+	}
+	return b
+}
+
+func TestDgemm(t *testing.T, blasser Dgemmer) {
+	for i, test := range DgemmCases {
+		// Test that it passes row major
+		dgemmcomp(i, "RowMajorNoTrans", t, blasser, blas.NoTrans, blas.NoTrans,
+			test.m, test.n, test.k, test.alpha, test.beta, test.a, test.b, test.c, test.ans)
+		// Try with A transposed
+		dgemmcomp(i, "RowMajorTransA", t, blasser, blas.Trans, blas.NoTrans,
+			test.m, test.n, test.k, test.alpha, test.beta, transpose(test.a), test.b, test.c, test.ans)
+		// Try with B transposed
+		dgemmcomp(i, "RowMajorTransB", t, blasser, blas.NoTrans, blas.Trans,
+			test.m, test.n, test.k, test.alpha, test.beta, test.a, transpose(test.b), test.c, test.ans)
+		// Try with both transposed
+		dgemmcomp(i, "RowMajorTransBoth", t, blasser, blas.Trans, blas.Trans,
+			test.m, test.n, test.k, test.alpha, test.beta, transpose(test.a), transpose(test.b), test.c, test.ans)
+	}
+}
+
+func dgemmcomp(i int, name string, t *testing.T, blasser Dgemmer, tA, tB blas.Transpose, m, n, k int,
+	alpha, beta float64, a [][]float64, b [][]float64, c [][]float64, ans [][]float64) {
+
+	aFlat := flatten(a)
+	aCopy := flatten(a)
+	bFlat := flatten(b)
+	bCopy := flatten(b)
+	cFlat := flatten(c)
+	ansFlat := flatten(ans)
+	lda := len(a[0])
+	ldb := len(b[0])
+	ldc := len(c[0])
+
+	// Compute the matrix multiplication
+	blasser.Dgemm(tA, tB, m, n, k, alpha, aFlat, lda, bFlat, ldb, beta, cFlat, ldc)
+
+	if !dSliceEqual(aFlat, aCopy) {
+		t.Errorf("Test %v case %v: a changed during call to Dgemm", i, name)
+	}
+	if !dSliceEqual(bFlat, bCopy) {
+		t.Errorf("Test %v case %v: b changed during call to Dgemm", i, name)
+	}
+
+	if !dSliceTolEqual(ansFlat, cFlat) {
+		t.Errorf("Test %v case %v: answer mismatch. Expected %v, Found %v", i, name, ansFlat, cFlat)
+	}
+	// TODO: Need to add a sub-slice test where don't use up full matrix
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/dgemmbench.go b/vendor/gonum.org/v1/gonum/blas/testblas/dgemmbench.go
new file mode 100644
index 00000000..512f4eca
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/dgemmbench.go
@@ -0,0 +1,39 @@
+package testblas
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+func DgemmBenchmark(b *testing.B, dgemm Dgemmer, m, n, k int, tA, tB blas.Transpose) {
+	a := make([]float64, m*k)
+	for i := range a {
+		a[i] = rand.Float64()
+	}
+	bv := make([]float64, k*n)
+	for i := range bv {
+		bv[i] = rand.Float64()
+	}
+	c := make([]float64, m*n)
+	for i := range c {
+		c[i] = rand.Float64()
+	}
+	var lda, ldb int
+	if tA == blas.Trans {
+		lda = m
+	} else {
+		lda = k
+	}
+	if tB == blas.Trans {
+		ldb = k
+	} else {
+		ldb = n
+	}
+	ldc := n
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		dgemm.Dgemm(tA, tB, m, n, k, 3.0, a, lda, bv, ldb, 1.0, c, ldc)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/dgemv.go b/vendor/gonum.org/v1/gonum/blas/testblas/dgemv.go
new file mode 100644
index 00000000..d18dde2f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/dgemv.go
@@ -0,0 +1,678 @@
+package testblas
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+type DgemvCase struct {
+	Name string
+	m    int
+	n    int
+	A    [][]float64
+	tA   blas.Transpose
+	x    []float64
+	incX int
+	y    []float64
+	incY int
+
+	Subcases []DgemvSubcase
+}
+
+type DgemvSubcase struct {
+	mulXNeg1 bool
+	mulYNeg1 bool
+	alpha    float64
+	beta     float64
+	ans      []float64
+}
+
+var DgemvCases = []DgemvCase{
+	{
+		Name: "M_gt_N_Inc1_NoTrans",
+		tA:   blas.NoTrans,
+		m:    5,
+		n:    3,
+		A: [][]float64{
+			{4.1, 6.2, 8.1},
+			{9.6, 3.5, 9.1},
+			{10, 7, 3},
+			{1, 1, 2},
+			{9, 2, 5},
+		},
+		incX: 1,
+		incY: 1,
+		x:    []float64{1, 2, 3},
+		y:    []float64{7, 8, 9, 10, 11},
+
+		Subcases: []DgemvSubcase{
+			{
+				alpha: 0,
+				beta:  0,
+				ans:   []float64{0, 0, 0, 0, 0},
+			},
+			{
+				alpha: 0,
+				beta:  1,
+				ans:   []float64{7, 8, 9, 10, 11},
+			},
+			{
+				alpha: 1,
+				beta:  0,
+				ans:   []float64{40.8, 43.9, 33, 9, 28},
+			},
+			{
+				alpha: 8,
+				beta:  -6,
+				ans:   []float64{284.4, 303.2, 210, 12, 158},
+			},
+		},
+	},
+	{
+		Name: "M_gt_N_Inc1_Trans",
+		tA:   blas.Trans,
+		m:    5,
+		n:    3,
+		A: [][]float64{
+			{4.1, 6.2, 8.1},
+			{9.6, 3.5, 9.1},
+			{10, 7, 3},
+			{1, 1, 2},
+			{9, 2, 5},
+		},
+		incX: 1,
+		incY: 1,
+		x:    []float64{1, 2, 3, -4, 5},
+		y:    []float64{7, 8, 9},
+
+		Subcases: []DgemvSubcase{
+			{
+				alpha: 0,
+				beta:  0,
+				ans:   []float64{0, 0, 0},
+			},
+			{
+				alpha: 0,
+				beta:  1,
+				ans:   []float64{7, 8, 9},
+			},
+			{
+				alpha: 1,
+				beta:  0,
+				ans:   []float64{94.3, 40.2, 52.3},
+			},
+			{
+				alpha: 8,
+				beta:  -6,
+				ans:   []float64{712.4, 273.6, 364.4},
+			},
+		},
+	},
+	{
+		Name: "M_eq_N_Inc1_NoTrans",
+		tA:   blas.NoTrans,
+		m:    3,
+		n:    3,
+		A: [][]float64{
+			{4.1, 6.2, 8.1},
+			{9.6, 3.5, 9.1},
+			{10, 7, 3},
+		},
+		incX: 1,
+		incY: 1,
+		x:    []float64{1, 2, 3},
+		y:    []float64{7, 2, 2},
+
+		Subcases: []DgemvSubcase{
+			{
+				alpha: 0,
+				beta:  0,
+				ans:   []float64{0, 0, 0},
+			},
+			{
+				alpha: 0,
+				beta:  1,
+				ans:   []float64{7, 2, 2},
+			},
+			{
+				alpha: 1,
+				beta:  0,
+				ans:   []float64{40.8, 43.9, 33},
+			},
+			{
+				alpha: 8,
+				beta:  -6,
+				ans:   []float64{40.8*8 - 6*7, 43.9*8 - 6*2, 33*8 - 6*2},
+			},
+		},
+	},
+	{
+		Name: "M_eq_N_Inc1_Trans",
+		tA:   blas.Trans,
+		m:    3,
+		n:    3,
+		A: [][]float64{
+			{4.1, 6.2, 8.1},
+			{9.6, 3.5, 9.1},
+			{10, 7, 3},
+		},
+		incX: 1,
+		incY: 1,
+		x:    []float64{1, 2, 3},
+		y:    []float64{7, 2, 2},
+
+		Subcases: []DgemvSubcase{
+			{
+				alpha: 8,
+				beta:  -6,
+				ans:   []float64{384.4, 261.6, 270.4},
+			},
+		},
+	},
+	{
+		Name: "M_lt_N_Inc1_NoTrans",
+		tA:   blas.NoTrans,
+		m:    3,
+		n:    5,
+		A: [][]float64{
+			{4.1, 6.2, 8.1, 10, 7},
+			{9.6, 3.5, 9.1, -2, 9},
+			{10, 7, 3, 1, -5},
+		},
+		incX: 1,
+		incY: 1,
+		x:    []float64{1, 2, 3, -7.6, 8.1},
+		y:    []float64{7, 2, 2},
+
+		Subcases: []DgemvSubcase{
+			{
+				alpha: 0,
+				beta:  0,
+				ans:   []float64{0, 0, 0},
+			},
+			{
+				alpha: 0,
+				beta:  1,
+				ans:   []float64{7, 2, 2},
+			},
+			{
+				alpha: 1,
+				beta:  0,
+				ans:   []float64{21.5, 132, -15.1},
+			},
+
+			{
+				alpha: 8,
+				beta:  -6,
+				ans:   []float64{21.5*8 - 6*7, 132*8 - 6*2, -15.1*8 - 6*2},
+			},
+		},
+	},
+	{
+		Name: "M_lt_N_Inc1_Trans",
+		tA:   blas.Trans,
+		m:    3,
+		n:    5,
+		A: [][]float64{
+			{4.1, 6.2, 8.1, 10, 7},
+			{9.6, 3.5, 9.1, -2, 9},
+			{10, 7, 3, 1, -5},
+		},
+		incX: 1,
+		incY: 1,
+		x:    []float64{1, 2, 3},
+		y:    []float64{7, 2, 2, -3, 5},
+
+		Subcases: []DgemvSubcase{
+			{
+				alpha: 8,
+				beta:  -6,
+				ans:   []float64{384.4, 261.6, 270.4, 90, 50},
+			},
+		},
+	},
+	{
+		Name: "M_gt_N_Part1_NoTrans",
+		tA:   blas.NoTrans,
+		m:    5,
+		n:    3,
+		A: [][]float64{
+			{4.1, 6.2, 8.1},
+			{9.6, 3.5, 9.1},
+			{10, 7, 3},
+			{1, 1, 2},
+			{9, 2, 5},
+		},
+		incX: 1,
+		incY: 2,
+		x:    []float64{1, 2, 3},
+		y:    []float64{7, 100, 8, 101, 9, 102, 10, 103, 11},
+
+		Subcases: []DgemvSubcase{
+			{
+				alpha: 0,
+				beta:  0,
+				ans:   []float64{0, 100, 0, 101, 0, 102, 0, 103, 0},
+			},
+			{
+				alpha: 0,
+				beta:  1,
+				ans:   []float64{7, 100, 8, 101, 9, 102, 10, 103, 11},
+			},
+			{
+				alpha: 1,
+				beta:  0,
+				ans:   []float64{40.8, 100, 43.9, 101, 33, 102, 9, 103, 28},
+			},
+			{
+				alpha: 8,
+				beta:  -6,
+				ans:   []float64{284.4, 100, 303.2, 101, 210, 102, 12, 103, 158},
+			},
+		},
+	},
+	{
+		Name: "M_gt_N_Part1_Trans",
+		tA:   blas.Trans,
+		m:    5,
+		n:    3,
+		A: [][]float64{
+			{4.1, 6.2, 8.1},
+			{9.6, 3.5, 9.1},
+			{10, 7, 3},
+			{1, 1, 2},
+			{9, 2, 5},
+		},
+		incX: 1,
+		incY: 2,
+		x:    []float64{1, 2, 3, -4, 5},
+		y:    []float64{7, 100, 8, 101, 9},
+
+		Subcases: []DgemvSubcase{
+			{
+				alpha: 0,
+				beta:  0,
+				ans:   []float64{0, 100, 0, 101, 0},
+			},
+			{
+				alpha: 0,
+				beta:  1,
+				ans:   []float64{7, 100, 8, 101, 9},
+			},
+			{
+				alpha: 1,
+				beta:  0,
+				ans:   []float64{94.3, 100, 40.2, 101, 52.3},
+			},
+			{
+				alpha: 8,
+				beta:  -6,
+				ans:   []float64{712.4, 100, 273.6, 101, 364.4},
+			},
+		},
+	},
+	{
+		Name: "M_gt_N_IncNot1_NoTrans",
+		tA:   blas.NoTrans,
+		m:    5,
+		n:    3,
+
+		A: [][]float64{
+			{4.1, 6.2, 8.1},
+			{9.6, 3.5, 9.1},
+			{10, 7, 3},
+			{1, 1, 2},
+			{9, 2, 5},
+		},
+		incX: 2,
+		incY: 3,
+		x:    []float64{1, 15, 2, 150, 3},
+		y:    []float64{7, 2, 6, 8, -4, -5, 9, 1, 1, 10, 19, 22, 11},
+		Subcases: []DgemvSubcase{
+			{
+				alpha: 8,
+				beta:  -6,
+				ans:   []float64{284.4, 2, 6, 303.2, -4, -5, 210, 1, 1, 12, 19, 22, 158},
+			},
+			{
+				mulXNeg1: true,
+				alpha:    8,
+				beta:     -6,
+				ans:      []float64{220.4, 2, 6, 311.2, -4, -5, 322, 1, 1, -4, 19, 22, 222},
+			},
+			{
+				mulYNeg1: true,
+				alpha:    8,
+				beta:     -6,
+				ans:      []float64{182, 2, 6, 24, -4, -5, 210, 1, 1, 291.2, 19, 22, 260.4},
+			},
+			{
+				mulXNeg1: true,
+				mulYNeg1: true,
+				alpha:    8,
+				beta:     -6,
+				ans:      []float64{246, 2, 6, 8, -4, -5, 322, 1, 1, 299.2, 19, 22, 196.4},
+			},
+		},
+	},
+	{
+		Name: "M_gt_N_IncNot1_Trans",
+		tA:   blas.Trans,
+		m:    5,
+		n:    3,
+
+		A: [][]float64{
+			{4.1, 6.2, 8.1},
+			{9.6, 3.5, 9.1},
+			{10, 7, 3},
+			{1, 1, 2},
+			{9, 2, 5},
+		},
+		incX: 2,
+		incY: 3,
+		x:    []float64{1, 15, 2, 150, 3, 8, -3, 6, 5},
+		y:    []float64{7, 2, 6, 8, -4, -5, 9},
+		Subcases: []DgemvSubcase{
+			{
+				alpha: 8,
+				beta:  -6,
+				ans:   []float64{720.4, 2, 6, 281.6, -4, -5, 380.4},
+			},
+			{
+				mulXNeg1: true,
+				alpha:    8,
+				beta:     -6,
+				ans:      []float64{219.6, 2, 6, 316, -4, -5, 195.6},
+			},
+			{
+				mulYNeg1: true,
+				alpha:    8,
+				beta:     -6,
+				ans:      []float64{392.4, 2, 6, 281.6, -4, -5, 708.4},
+			},
+			{
+				mulXNeg1: true,
+				mulYNeg1: true,
+				alpha:    8,
+				beta:     -6,
+				ans:      []float64{207.6, 2, 6, 316, -4, -5, 207.6},
+			},
+		},
+	},
+	{
+		Name: "M_eq_N_IncNot1_NoTrans",
+		tA:   blas.NoTrans,
+		m:    3,
+		n:    3,
+		A: [][]float64{
+			{4.1, 6.2, 8.1},
+			{9.6, 3.5, 9.1},
+			{10, 7, 3},
+		},
+		incX: 2,
+		incY: 3,
+		x:    []float64{1, 15, 2, 150, 3},
+		y:    []float64{7, 2, 6, 8, -4, -5, 9},
+		Subcases: []DgemvSubcase{
+			{
+				alpha: 8,
+				beta:  -6,
+				ans:   []float64{284.4, 2, 6, 303.2, -4, -5, 210},
+			},
+			{
+				mulXNeg1: true,
+				alpha:    8,
+				beta:     -6,
+				ans:      []float64{220.4, 2, 6, 311.2, -4, -5, 322},
+			},
+			{
+				mulYNeg1: true,
+				alpha:    8,
+				beta:     -6,
+				ans:      []float64{222, 2, 6, 303.2, -4, -5, 272.4},
+			},
+			{
+				mulXNeg1: true,
+				mulYNeg1: true,
+				alpha:    8,
+				beta:     -6,
+				ans:      []float64{334, 2, 6, 311.2, -4, -5, 208.4},
+			},
+		},
+	},
+	{
+		Name: "M_eq_N_IncNot1_Trans",
+		tA:   blas.Trans,
+		m:    3,
+		n:    3,
+		A: [][]float64{
+			{4.1, 6.2, 8.1},
+			{9.6, 3.5, 9.1},
+			{10, 7, 3},
+		},
+		incX: 2,
+		incY: 3,
+		x:    []float64{1, 15, 2, 150, 3},
+		y:    []float64{7, 2, 6, 8, -4, -5, 9},
+
+		Subcases: []DgemvSubcase{
+			{
+				alpha: 8,
+				beta:  -6,
+				ans:   []float64{384.4, 2, 6, 225.6, -4, -5, 228.4},
+			},
+			{
+				mulXNeg1: true,
+				alpha:    8,
+				beta:     -6,
+				ans:      []float64{290, 2, 6, 212.8, -4, -5, 310},
+			},
+			{
+				mulYNeg1: true,
+				alpha:    8,
+				beta:     -6,
+				ans:      []float64{240.4, 2, 6, 225.6, -4, -5, 372.4},
+			},
+			{
+				mulXNeg1: true,
+				mulYNeg1: true,
+				alpha:    8,
+				beta:     -6,
+				ans:      []float64{322, 2, 6, 212.8, -4, -5, 278},
+			},
+		},
+	},
+	{
+		Name: "M_lt_N_IncNot1_NoTrans",
+		tA:   blas.NoTrans,
+		m:    3,
+		n:    5,
+		A: [][]float64{
+			{4.1, 6.2, 8.1, 10, 11},
+			{9.6, 3.5, 9.1, -3, -2},
+			{10, 7, 3, -7, -4},
+		},
+		incX: 2,
+		incY: 3,
+		x:    []float64{1, 15, 2, 150, 3, -2, -4, 8, -9},
+		y:    []float64{7, 2, 6, 8, -4, -5, 9},
+
+		Subcases: []DgemvSubcase{
+			{
+				alpha: 8,
+				beta:  -6,
+				ans:   []float64{-827.6, 2, 6, 543.2, -4, -5, 722},
+			},
+			{
+				mulXNeg1: true,
+				alpha:    8,
+				beta:     -6,
+				ans:      []float64{-93.2, 2, 6, -696.8, -4, -5, -1070},
+			},
+			{
+				mulYNeg1: true,
+				alpha:    8,
+				beta:     -6,
+				ans:      []float64{734, 2, 6, 543.2, -4, -5, -839.6},
+			},
+			{
+				mulXNeg1: true,
+				mulYNeg1: true,
+				alpha:    8,
+				beta:     -6,
+				ans:      []float64{-1058, 2, 6, -696.8, -4, -5, -105.2},
+			},
+		},
+	},
+	{
+		Name: "M_lt_N_IncNot1_Trans",
+		tA:   blas.Trans,
+		m:    3,
+		n:    5,
+		A: [][]float64{
+			{4.1, 6.2, 8.1, 10, 11},
+			{9.6, 3.5, 9.1, -3, -2},
+			{10, 7, 3, -7, -4},
+		},
+		incX: 2,
+		incY: 3,
+		x:    []float64{1, 15, 2, 150, 3},
+		y:    []float64{7, 2, 6, 8, -4, -5, 9, -4, -1, -9, 1, 1, 2},
+
+		Subcases: []DgemvSubcase{
+			{
+				alpha: 8,
+				beta:  -6,
+				ans:   []float64{384.4, 2, 6, 225.6, -4, -5, 228.4, -4, -1, -82, 1, 1, -52},
+			},
+			{
+				mulXNeg1: true,
+				alpha:    8,
+				beta:     -6,
+				ans:      []float64{290, 2, 6, 212.8, -4, -5, 310, -4, -1, 190, 1, 1, 188},
+			},
+			{
+				mulYNeg1: true,
+				alpha:    8,
+				beta:     -6,
+				ans:      []float64{-82, 2, 6, -184, -4, -5, 228.4, -4, -1, 327.6, 1, 1, 414.4},
+			},
+			{
+				mulXNeg1: true,
+				mulYNeg1: true,
+				alpha:    8,
+				beta:     -6,
+				ans:      []float64{158, 2, 6, 88, -4, -5, 310, -4, -1, 314.8, 1, 1, 320},
+			},
+		},
+	},
+
+	// TODO: A can be longer than mxn. Add cases where it is longer
+	// TODO: x and y can also be longer. Add tests for these
+	// TODO: Add tests for dimension mismatch
+	// TODO: Add places with a "submatrix view", where lda != m
+}
+
+type Dgemver interface {
+	Dgemv(tA blas.Transpose, m, n int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int)
+}
+
+func DgemvTest(t *testing.T, blasser Dgemver) {
+	for _, test := range DgemvCases {
+		for i, cas := range test.Subcases {
+			// Test that it passes with row-major
+			dgemvcomp(t, test, cas, i, blasser)
+
+			// Test the bad inputs
+			dgemvbad(t, test, cas, i, blasser)
+		}
+	}
+}
+
+func dgemvcomp(t *testing.T, test DgemvCase, cas DgemvSubcase, i int, blasser Dgemver) {
+	x := sliceCopy(test.x)
+	y := sliceCopy(test.y)
+	a := sliceOfSliceCopy(test.A)
+	aFlat := flatten(a)
+
+	lda := test.n
+
+	incX := test.incX
+	if cas.mulXNeg1 {
+		incX *= -1
+	}
+	incY := test.incY
+	if cas.mulYNeg1 {
+		incY *= -1
+	}
+
+	f := func() {
+		blasser.Dgemv(test.tA, test.m, test.n, cas.alpha, aFlat, lda, x, incX, cas.beta, y, incY)
+	}
+	if panics(f) {
+		t.Errorf("Test %v case %v: unexpected panic", test.Name, i)
+		if throwPanic {
+			blasser.Dgemv(test.tA, test.m, test.n, cas.alpha, aFlat, lda, x, incX, cas.beta, y, incY)
+		}
+		return
+	}
+	// Check that x and a are unchanged
+	if !dSliceEqual(x, test.x) {
+		t.Errorf("Test %v, case %v: x modified during call", test.Name, i)
+	}
+	aFlat2 := flatten(sliceOfSliceCopy(test.A))
+	if !dSliceEqual(aFlat2, aFlat) {
+		t.Errorf("Test %v, case %v: a modified during call", test.Name, i)
+	}
+
+	// Check that the answer matches
+	if !dSliceTolEqual(cas.ans, y) {
+		t.Errorf("Test %v, case %v: answer mismatch: Expected %v, Found %v", test.Name, i, cas.ans, y)
+	}
+}
+
+func dgemvbad(t *testing.T, test DgemvCase, cas DgemvSubcase, i int, blasser Dgemver) {
+	x := sliceCopy(test.x)
+	y := sliceCopy(test.y)
+	a := sliceOfSliceCopy(test.A)
+	aFlatRow := flatten(a)
+	ldaRow := test.n
+
+	f := func() {
+		blasser.Dgemv(312, test.m, test.n, cas.alpha, aFlatRow, ldaRow, x, test.incX, cas.beta, y, test.incY)
+	}
+	if !panics(f) {
+		t.Errorf("Test %v case %v: no panic for bad transpose", test.Name, i)
+	}
+	f = func() {
+		blasser.Dgemv(test.tA, -2, test.n, cas.alpha, aFlatRow, ldaRow, x, test.incX, cas.beta, y, test.incY)
+	}
+	if !panics(f) {
+		t.Errorf("Test %v case %v: no panic for m negative", test.Name, i)
+	}
+	f = func() {
+		blasser.Dgemv(test.tA, test.m, -4, cas.alpha, aFlatRow, ldaRow, x, test.incX, cas.beta, y, test.incY)
+	}
+	if !panics(f) {
+		t.Errorf("Test %v case %v: no panic for n negative", test.Name, i)
+	}
+	f = func() {
+		blasser.Dgemv(test.tA, test.m, test.n, cas.alpha, aFlatRow, ldaRow, x, 0, cas.beta, y, test.incY)
+	}
+	if !panics(f) {
+		t.Errorf("Test %v case %v: no panic for incX zero", test.Name, i)
+	}
+	f = func() {
+		blasser.Dgemv(test.tA, test.m, test.n, cas.alpha, aFlatRow, ldaRow, x, test.incX, cas.beta, y, 0)
+	}
+	if !panics(f) {
+		t.Errorf("Test %v case %v: no panic for incY zero", test.Name, i)
+	}
+	f = func() {
+		blasser.Dgemv(test.tA, test.m, test.n, cas.alpha, aFlatRow, ldaRow-1, x, test.incX, cas.beta, y, test.incY)
+	}
+	if !panics(f) {
+		t.Errorf("Test %v case %v: no panic for lda too small row major", test.Name, i)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/dger.go b/vendor/gonum.org/v1/gonum/blas/testblas/dger.go
new file mode 100644
index 00000000..0a905812
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/dger.go
@@ -0,0 +1,163 @@
+package testblas
+
+import "testing"
+
+type Dgerer interface {
+	Dger(m, n int, alpha float64, x []float64, incX int, y []float64, incY int, a []float64, lda int)
+}
+
+func DgerTest(t *testing.T, blasser Dgerer) {
+	for _, test := range []struct {
+		name string
+		a    [][]float64
+		m    int
+		n    int
+		x    []float64
+		y    []float64
+		incX int
+		incY int
+
+		trueAns [][]float64
+	}{
+		{
+			name: "M gt N inc 1",
+			m:    5,
+			n:    3,
+			a: [][]float64{
+				{1.3, 2.4, 3.5},
+				{2.6, 2.8, 3.3},
+				{-1.3, -4.3, -9.7},
+				{8, 9, -10},
+				{-12, -14, -6},
+			},
+			x:       []float64{-2, -3, 0, 1, 2},
+			y:       []float64{-1.1, 5, 0},
+			incX:    1,
+			incY:    1,
+			trueAns: [][]float64{{3.5, -7.6, 3.5}, {5.9, -12.2, 3.3}, {-1.3, -4.3, -9.7}, {6.9, 14, -10}, {-14.2, -4, -6}},
+		},
+		{
+			name: "M eq N inc 1",
+			m:    3,
+			n:    3,
+			a: [][]float64{
+				{1.3, 2.4, 3.5},
+				{2.6, 2.8, 3.3},
+				{-1.3, -4.3, -9.7},
+			},
+			x:       []float64{-2, -3, 0},
+			y:       []float64{-1.1, 5, 0},
+			incX:    1,
+			incY:    1,
+			trueAns: [][]float64{{3.5, -7.6, 3.5}, {5.9, -12.2, 3.3}, {-1.3, -4.3, -9.7}},
+		},
+
+		{
+			name: "M lt N inc 1",
+			m:    3,
+			n:    6,
+			a: [][]float64{
+				{1.3, 2.4, 3.5, 4.8, 1.11, -9},
+				{2.6, 2.8, 3.3, -3.4, 6.2, -8.7},
+				{-1.3, -4.3, -9.7, -3.1, 8.9, 8.9},
+			},
+			x:       []float64{-2, -3, 0},
+			y:       []float64{-1.1, 5, 0, 9, 19, 22},
+			incX:    1,
+			incY:    1,
+			trueAns: [][]float64{{3.5, -7.6, 3.5, -13.2, -36.89, -53}, {5.9, -12.2, 3.3, -30.4, -50.8, -74.7}, {-1.3, -4.3, -9.7, -3.1, 8.9, 8.9}},
+		},
+		{
+			name: "M gt N inc not 1",
+			m:    5,
+			n:    3,
+			a: [][]float64{
+				{1.3, 2.4, 3.5},
+				{2.6, 2.8, 3.3},
+				{-1.3, -4.3, -9.7},
+				{8, 9, -10},
+				{-12, -14, -6},
+			},
+			x:       []float64{-2, -3, 0, 1, 2, 6, 0, 9, 7},
+			y:       []float64{-1.1, 5, 0, 8, 7, -5, 7},
+			incX:    2,
+			incY:    3,
+			trueAns: [][]float64{{3.5, -13.6, -10.5}, {2.6, 2.8, 3.3}, {-3.5, 11.7, 4.3}, {8, 9, -10}, {-19.700000000000003, 42, 43}},
+		},
+		{
+			name: "M eq N inc not 1",
+			m:    3,
+			n:    3,
+			a: [][]float64{
+				{1.3, 2.4, 3.5},
+				{2.6, 2.8, 3.3},
+				{-1.3, -4.3, -9.7},
+			},
+			x:       []float64{-2, -3, 0, 8, 7, -9, 7, -6, 12, 6, 6, 6, -11},
+			y:       []float64{-1.1, 5, 0, 0, 9, 8, 6},
+			incX:    4,
+			incY:    3,
+			trueAns: [][]float64{{3.5, 2.4, -8.5}, {-5.1, 2.8, 45.3}, {-14.5, -4.3, 62.3}},
+		},
+		{
+			name: "M lt N inc not 1",
+			m:    3,
+			n:    6,
+			a: [][]float64{
+				{1.3, 2.4, 3.5, 4.8, 1.11, -9},
+				{2.6, 2.8, 3.3, -3.4, 6.2, -8.7},
+				{-1.3, -4.3, -9.7, -3.1, 8.9, 8.9},
+			},
+			x:       []float64{-2, -3, 0, 0, 8, 0, 9, -3},
+			y:       []float64{-1.1, 5, 0, 9, 19, 22, 11, -8.11, -9.22, 9.87, 7},
+			incX:    3,
+			incY:    2,
+			trueAns: [][]float64{{3.5, 2.4, -34.5, -17.2, 19.55, -23}, {2.6, 2.8, 3.3, -3.4, 6.2, -8.7}, {-11.2, -4.3, 161.3, 95.9, -74.08, 71.9}},
+		},
+	} {
+		// TODO: Add tests where a is longer
+		// TODO: Add panic tests
+		// TODO: Add negative increment tests
+
+		x := sliceCopy(test.x)
+		y := sliceCopy(test.y)
+
+		a := sliceOfSliceCopy(test.a)
+
+		// Test with row major
+		alpha := 1.0
+		aFlat := flatten(a)
+		blasser.Dger(test.m, test.n, alpha, x, test.incX, y, test.incY, aFlat, test.n)
+		ans := unflatten(aFlat, test.m, test.n)
+		dgercomp(t, x, test.x, y, test.y, ans, test.trueAns, test.name+" row maj")
+
+		// Test with different alpha
+		alpha = 4.0
+		aFlat = flatten(a)
+		blasser.Dger(test.m, test.n, alpha, x, test.incX, y, test.incY, aFlat, test.n)
+		ans = unflatten(aFlat, test.m, test.n)
+		trueCopy := sliceOfSliceCopy(test.trueAns)
+		for i := range trueCopy {
+			for j := range trueCopy[i] {
+				trueCopy[i][j] = alpha*(trueCopy[i][j]-a[i][j]) + a[i][j]
+			}
+		}
+		dgercomp(t, x, test.x, y, test.y, ans, trueCopy, test.name+" row maj alpha")
+	}
+}
+
+func dgercomp(t *testing.T, x, xCopy, y, yCopy []float64, ans [][]float64, trueAns [][]float64, name string) {
+	if !dSliceEqual(x, xCopy) {
+		t.Errorf("case %v: x modified during call to dger", name)
+	}
+	if !dSliceEqual(y, yCopy) {
+		t.Errorf("case %v: x modified during call to dger", name)
+	}
+
+	for i := range ans {
+		if !dSliceTolEqual(ans[i], trueAns[i]) {
+			t.Errorf("case %v: answer mismatch. Expected %v, Found %v", name, trueAns, ans)
+			break
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/doc.go b/vendor/gonum.org/v1/gonum/blas/testblas/doc.go
new file mode 100644
index 00000000..fc113147
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package testblas provides tests for blas implementations.
+package testblas // import "gonum.org/v1/gonum/blas/testblas"
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/dsbmv.go b/vendor/gonum.org/v1/gonum/blas/testblas/dsbmv.go
new file mode 100644
index 00000000..1a8c9c35
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/dsbmv.go
@@ -0,0 +1,83 @@
+package testblas
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+type Dsbmver interface {
+	Dsbmv(ul blas.Uplo, n, k int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int)
+}
+
+func DsbmvTest(t *testing.T, blasser Dsbmver) {
+	for i, test := range []struct {
+		ul    blas.Uplo
+		n     int
+		k     int
+		alpha float64
+		beta  float64
+		a     [][]float64
+		x     []float64
+		y     []float64
+
+		ans []float64
+	}{
+		{
+			ul:    blas.Upper,
+			n:     4,
+			k:     2,
+			alpha: 2,
+			beta:  3,
+			a: [][]float64{
+				{7, 8, 2, 0},
+				{0, 8, 2, -3},
+				{0, 0, 3, 6},
+				{0, 0, 0, 9},
+			},
+			x:   []float64{1, 2, 3, 4},
+			y:   []float64{-1, -2, -3, -4},
+			ans: []float64{55, 30, 69, 84},
+		},
+		{
+			ul:    blas.Lower,
+			n:     4,
+			k:     2,
+			alpha: 2,
+			beta:  3,
+			a: [][]float64{
+				{7, 0, 0, 0},
+				{8, 8, 0, 0},
+				{2, 2, 3, 0},
+				{0, -3, 6, 9},
+			},
+			x:   []float64{1, 2, 3, 4},
+			y:   []float64{-1, -2, -3, -4},
+			ans: []float64{55, 30, 69, 84},
+		},
+	} {
+		extra := 0
+		var aFlat []float64
+		if test.ul == blas.Upper {
+			aFlat = flattenBanded(test.a, test.k, 0)
+		} else {
+			aFlat = flattenBanded(test.a, 0, test.k)
+		}
+		incTest := func(incX, incY, extra int) {
+			xnew := makeIncremented(test.x, incX, extra)
+			ynew := makeIncremented(test.y, incY, extra)
+			ans := makeIncremented(test.ans, incY, extra)
+			blasser.Dsbmv(test.ul, test.n, test.k, test.alpha, aFlat, test.k+1, xnew, incX, test.beta, ynew, incY)
+			if !dSliceTolEqual(ans, ynew) {
+				t.Errorf("Case %v: Want %v, got %v", i, ans, ynew)
+			}
+		}
+		incTest(1, 1, extra)
+		incTest(1, 3, extra)
+		incTest(1, -3, extra)
+		incTest(2, 3, extra)
+		incTest(2, -3, extra)
+		incTest(3, 2, extra)
+		incTest(-3, 2, extra)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/dspmv.go b/vendor/gonum.org/v1/gonum/blas/testblas/dspmv.go
new file mode 100644
index 00000000..352bc4a9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/dspmv.go
@@ -0,0 +1,73 @@
+package testblas
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dspmver interface {
+	Dspmv(ul blas.Uplo, n int, alpha float64, ap []float64, x []float64, incX int, beta float64, y []float64, incY int)
+}
+
+func DspmvTest(t *testing.T, blasser Dspmver) {
+	for i, test := range []struct {
+		ul    blas.Uplo
+		n     int
+		a     [][]float64
+		x     []float64
+		y     []float64
+		alpha float64
+		beta  float64
+		ans   []float64
+	}{
+		{
+			ul: blas.Upper,
+			n:  3,
+			a: [][]float64{
+				{5, 6, 7},
+				{0, 8, 10},
+				{0, 0, 13},
+			},
+			x:     []float64{3, 4, 5},
+			y:     []float64{6, 7, 8},
+			alpha: 2.1,
+			beta:  -3,
+			ans:   []float64{137.4, 189, 240.6},
+		},
+		{
+			ul: blas.Lower,
+			n:  3,
+			a: [][]float64{
+				{5, 0, 0},
+				{6, 8, 0},
+				{7, 10, 13},
+			},
+			x:     []float64{3, 4, 5},
+			y:     []float64{6, 7, 8},
+			alpha: 2.1,
+			beta:  -3,
+			ans:   []float64{137.4, 189, 240.6},
+		},
+	} {
+		incTest := func(incX, incY, extra int) {
+			x := makeIncremented(test.x, incX, extra)
+			y := makeIncremented(test.y, incY, extra)
+			aFlat := flattenTriangular(test.a, test.ul)
+			ans := makeIncremented(test.ans, incY, extra)
+
+			blasser.Dspmv(test.ul, test.n, test.alpha, aFlat, x, incX, test.beta, y, incY)
+			if !floats.EqualApprox(ans, y, 1e-14) {
+				t.Errorf("Case %v, incX=%v, incY=%v: Want %v, got %v.", i, incX, incY, ans, y)
+			}
+		}
+		incTest(1, 1, 0)
+		incTest(2, 3, 0)
+		incTest(3, 2, 0)
+		incTest(-3, 2, 0)
+		incTest(-2, 4, 0)
+		incTest(2, -1, 0)
+		incTest(-3, -4, 3)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/dspr.go b/vendor/gonum.org/v1/gonum/blas/testblas/dspr.go
new file mode 100644
index 00000000..25e0ee40
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/dspr.go
@@ -0,0 +1,71 @@
+package testblas
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+type Dsprer interface {
+	Dspr(ul blas.Uplo, n int, alpha float64, x []float64, incX int, a []float64)
+}
+
+func DsprTest(t *testing.T, blasser Dsprer) {
+	for i, test := range []struct {
+		ul    blas.Uplo
+		n     int
+		a     [][]float64
+		x     []float64
+		alpha float64
+		ans   [][]float64
+	}{
+		{
+			ul: blas.Upper,
+			n:  4,
+			a: [][]float64{
+				{10, 2, 0, 1},
+				{0, 1, 2, 3},
+				{0, 0, 9, 15},
+				{0, 0, 0, -6},
+			},
+			x:     []float64{1, 2, 0, 5},
+			alpha: 8,
+			ans: [][]float64{
+				{18, 18, 0, 41},
+				{0, 33, 2, 83},
+				{0, 0, 9, 15},
+				{0, 0, 0, 194},
+			},
+		},
+		{
+			ul: blas.Lower,
+			n:  3,
+			a: [][]float64{
+				{10, 2, 0},
+				{4, 1, 2},
+				{2, 7, 9},
+			},
+			x:     []float64{3, 0, 5},
+			alpha: 8,
+			ans: [][]float64{
+				{82, 2, 0},
+				{4, 1, 2},
+				{122, 7, 209},
+			},
+		},
+	} {
+		incTest := func(incX, extra int) {
+			xnew := makeIncremented(test.x, incX, extra)
+			aFlat := flattenTriangular(test.a, test.ul)
+			ans := flattenTriangular(test.ans, test.ul)
+			blasser.Dspr(test.ul, test.n, test.alpha, xnew, incX, aFlat)
+			if !dSliceTolEqual(aFlat, ans) {
+				t.Errorf("Case %v, idx %v: Want %v, got %v.", i, incX, ans, aFlat)
+			}
+		}
+		incTest(1, 3)
+		incTest(1, 0)
+		incTest(3, 2)
+		incTest(-2, 2)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/dspr2.go b/vendor/gonum.org/v1/gonum/blas/testblas/dspr2.go
new file mode 100644
index 00000000..40b0cd32
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/dspr2.go
@@ -0,0 +1,76 @@
+package testblas
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dspr2er interface {
+	Dspr2(ul blas.Uplo, n int, alpha float64, x []float64, incX int, y []float64, incY int, a []float64)
+}
+
+func Dspr2Test(t *testing.T, blasser Dspr2er) {
+	for i, test := range []struct {
+		n     int
+		a     [][]float64
+		ul    blas.Uplo
+		x     []float64
+		y     []float64
+		alpha float64
+		ans   [][]float64
+	}{
+		{
+			n: 3,
+			a: [][]float64{
+				{7, 2, 4},
+				{0, 3, 5},
+				{0, 0, 6},
+			},
+			x:     []float64{2, 3, 4},
+			y:     []float64{5, 6, 7},
+			alpha: 2,
+			ul:    blas.Upper,
+			ans: [][]float64{
+				{47, 56, 72},
+				{0, 75, 95},
+				{0, 0, 118},
+			},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{7, 0, 0},
+				{2, 3, 0},
+				{4, 5, 6},
+			},
+			x:     []float64{2, 3, 4},
+			y:     []float64{5, 6, 7},
+			alpha: 2,
+			ul:    blas.Lower,
+			ans: [][]float64{
+				{47, 0, 0},
+				{56, 75, 0},
+				{72, 95, 118},
+			},
+		},
+	} {
+		incTest := func(incX, incY, extra int) {
+			aFlat := flattenTriangular(test.a, test.ul)
+			x := makeIncremented(test.x, incX, extra)
+			y := makeIncremented(test.y, incY, extra)
+			blasser.Dspr2(test.ul, test.n, test.alpha, x, incX, y, incY, aFlat)
+			ansFlat := flattenTriangular(test.ans, test.ul)
+			if !floats.EqualApprox(aFlat, ansFlat, 1e-14) {
+				t.Errorf("Case %v, incX = %v, incY = %v. Want %v, got %v.", i, incX, incY, ansFlat, aFlat)
+			}
+		}
+		incTest(1, 1, 0)
+		incTest(-2, 1, 0)
+		incTest(-2, 3, 0)
+		incTest(2, -3, 0)
+		incTest(3, -2, 0)
+		incTest(-3, -4, 0)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/dsymm.go b/vendor/gonum.org/v1/gonum/blas/testblas/dsymm.go
new file mode 100644
index 00000000..5e07e07d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/dsymm.go
@@ -0,0 +1,277 @@
+package testblas
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dsymmer interface {
+	Dsymm(s blas.Side, ul blas.Uplo, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int)
+}
+
+func DsymmTest(t *testing.T, blasser Dsymmer) {
+	for i, test := range []struct {
+		m     int
+		n     int
+		side  blas.Side
+		ul    blas.Uplo
+		a     [][]float64
+		b     [][]float64
+		c     [][]float64
+		alpha float64
+		beta  float64
+		ans   [][]float64
+	}{
+		{
+			side: blas.Left,
+			ul:   blas.Upper,
+			m:    3,
+			n:    4,
+			a: [][]float64{
+				{2, 3, 4},
+				{0, 6, 7},
+				{0, 0, 10},
+			},
+			b: [][]float64{
+				{2, 3, 4, 8},
+				{5, 6, 7, 15},
+				{8, 9, 10, 20},
+			},
+			c: [][]float64{
+				{8, 12, 2, 1},
+				{9, 12, 9, 9},
+				{12, 1, -1, 5},
+			},
+			alpha: 2,
+			beta:  3,
+			ans: [][]float64{
+				{126, 156, 144, 285},
+				{211, 252, 275, 535},
+				{282, 291, 327, 689},
+			},
+		},
+		{
+			side: blas.Left,
+			ul:   blas.Upper,
+			m:    4,
+			n:    3,
+			a: [][]float64{
+				{2, 3, 4, 8},
+				{0, 6, 7, 9},
+				{0, 0, 10, 10},
+				{0, 0, 0, 11},
+			},
+			b: [][]float64{
+				{2, 3, 4},
+				{5, 6, 7},
+				{8, 9, 10},
+				{2, 1, 1},
+			},
+			c: [][]float64{
+				{8, 12, 2},
+				{9, 12, 9},
+				{12, 1, -1},
+				{1, 9, 5},
+			},
+			alpha: 2,
+			beta:  3,
+			ans: [][]float64{
+				{158, 172, 160},
+				{247, 270, 293},
+				{322, 311, 347},
+				{329, 385, 427},
+			},
+		},
+		{
+			side: blas.Left,
+			ul:   blas.Lower,
+			m:    3,
+			n:    4,
+			a: [][]float64{
+				{2, 0, 0},
+				{3, 6, 0},
+				{4, 7, 10},
+			},
+			b: [][]float64{
+				{2, 3, 4, 8},
+				{5, 6, 7, 15},
+				{8, 9, 10, 20},
+			},
+			c: [][]float64{
+				{8, 12, 2, 1},
+				{9, 12, 9, 9},
+				{12, 1, -1, 5},
+			},
+			alpha: 2,
+			beta:  3,
+			ans: [][]float64{
+				{126, 156, 144, 285},
+				{211, 252, 275, 535},
+				{282, 291, 327, 689},
+			},
+		},
+		{
+			side: blas.Left,
+			ul:   blas.Lower,
+			m:    4,
+			n:    3,
+			a: [][]float64{
+				{2, 0, 0, 0},
+				{3, 6, 0, 0},
+				{4, 7, 10, 0},
+				{8, 9, 10, 11},
+			},
+			b: [][]float64{
+				{2, 3, 4},
+				{5, 6, 7},
+				{8, 9, 10},
+				{2, 1, 1},
+			},
+			c: [][]float64{
+				{8, 12, 2},
+				{9, 12, 9},
+				{12, 1, -1},
+				{1, 9, 5},
+			},
+			alpha: 2,
+			beta:  3,
+			ans: [][]float64{
+				{158, 172, 160},
+				{247, 270, 293},
+				{322, 311, 347},
+				{329, 385, 427},
+			},
+		},
+		{
+			side: blas.Right,
+			ul:   blas.Upper,
+			m:    3,
+			n:    4,
+			a: [][]float64{
+				{2, 0, 0, 0},
+				{3, 6, 0, 0},
+				{4, 7, 10, 0},
+				{3, 4, 5, 6},
+			},
+			b: [][]float64{
+				{2, 3, 4, 9},
+				{5, 6, 7, -3},
+				{8, 9, 10, -2},
+			},
+			c: [][]float64{
+				{8, 12, 2, 10},
+				{9, 12, 9, 10},
+				{12, 1, -1, 10},
+			},
+			alpha: 2,
+			beta:  3,
+			ans: [][]float64{
+				{32, 72, 86, 138},
+				{47, 108, 167, -6},
+				{68, 111, 197, 6},
+			},
+		},
+		{
+			side: blas.Right,
+			ul:   blas.Upper,
+			m:    4,
+			n:    3,
+			a: [][]float64{
+				{2, 0, 0},
+				{3, 6, 0},
+				{4, 7, 10},
+			},
+			b: [][]float64{
+				{2, 3, 4},
+				{5, 6, 7},
+				{8, 9, 10},
+				{2, 1, 1},
+			},
+			c: [][]float64{
+				{8, 12, 2},
+				{9, 12, 9},
+				{12, 1, -1},
+				{1, 9, 5},
+			},
+			alpha: 2,
+			beta:  3,
+			ans: [][]float64{
+				{32, 72, 86},
+				{47, 108, 167},
+				{68, 111, 197},
+				{11, 39, 35},
+			},
+		},
+		{
+			side: blas.Right,
+			ul:   blas.Lower,
+			m:    3,
+			n:    4,
+			a: [][]float64{
+				{2, 0, 0, 0},
+				{3, 6, 0, 0},
+				{4, 7, 10, 0},
+				{3, 4, 5, 6},
+			},
+			b: [][]float64{
+				{2, 3, 4, 2},
+				{5, 6, 7, 1},
+				{8, 9, 10, 1},
+			},
+			c: [][]float64{
+				{8, 12, 2, 1},
+				{9, 12, 9, 9},
+				{12, 1, -1, 5},
+			},
+			alpha: 2,
+			beta:  3,
+			ans: [][]float64{
+				{94, 156, 164, 103},
+				{145, 244, 301, 187},
+				{208, 307, 397, 247},
+			},
+		},
+		{
+			side: blas.Right,
+			ul:   blas.Lower,
+			m:    4,
+			n:    3,
+			a: [][]float64{
+				{2, 0, 0},
+				{3, 6, 0},
+				{4, 7, 10},
+			},
+			b: [][]float64{
+				{2, 3, 4},
+				{5, 6, 7},
+				{8, 9, 10},
+				{2, 1, 1},
+			},
+			c: [][]float64{
+				{8, 12, 2},
+				{9, 12, 9},
+				{12, 1, -1},
+				{1, 9, 5},
+			},
+			alpha: 2,
+			beta:  3,
+			ans: [][]float64{
+				{82, 140, 144},
+				{139, 236, 291},
+				{202, 299, 387},
+				{25, 65, 65},
+			},
+		},
+	} {
+		aFlat := flatten(test.a)
+		bFlat := flatten(test.b)
+		cFlat := flatten(test.c)
+		ansFlat := flatten(test.ans)
+		blasser.Dsymm(test.side, test.ul, test.m, test.n, test.alpha, aFlat, len(test.a[0]), bFlat, test.n, test.beta, cFlat, test.n)
+		if !floats.EqualApprox(cFlat, ansFlat, 1e-14) {
+			t.Errorf("Case %v: Want %v, got %v.", i, ansFlat, cFlat)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/dsymv.go b/vendor/gonum.org/v1/gonum/blas/testblas/dsymv.go
new file mode 100644
index 00000000..b3fd4ec2
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/dsymv.go
@@ -0,0 +1,73 @@
+package testblas
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dsymver interface {
+	Dsymv(ul blas.Uplo, n int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int)
+}
+
+func DsymvTest(t *testing.T, blasser Dsymver) {
+	for i, test := range []struct {
+		ul    blas.Uplo
+		n     int
+		a     [][]float64
+		x     []float64
+		y     []float64
+		alpha float64
+		beta  float64
+		ans   []float64
+	}{
+		{
+			ul: blas.Upper,
+			n:  3,
+			a: [][]float64{
+				{5, 6, 7},
+				{0, 8, 10},
+				{0, 0, 13},
+			},
+			x:     []float64{3, 4, 5},
+			y:     []float64{6, 7, 8},
+			alpha: 2.1,
+			beta:  -3,
+			ans:   []float64{137.4, 189, 240.6},
+		},
+		{
+			ul: blas.Lower,
+			n:  3,
+			a: [][]float64{
+				{5, 0, 0},
+				{6, 8, 0},
+				{7, 10, 13},
+			},
+			x:     []float64{3, 4, 5},
+			y:     []float64{6, 7, 8},
+			alpha: 2.1,
+			beta:  -3,
+			ans:   []float64{137.4, 189, 240.6},
+		},
+	} {
+		incTest := func(incX, incY, extra int) {
+			x := makeIncremented(test.x, incX, extra)
+			y := makeIncremented(test.y, incY, extra)
+			aFlat := flatten(test.a)
+			ans := makeIncremented(test.ans, incY, extra)
+
+			blasser.Dsymv(test.ul, test.n, test.alpha, aFlat, test.n, x, incX, test.beta, y, incY)
+			if !floats.EqualApprox(ans, y, 1e-14) {
+				t.Errorf("Case %v, incX=%v, incY=%v: Want %v, got %v.", i, incX, incY, ans, y)
+			}
+		}
+		incTest(1, 1, 0)
+		incTest(2, 3, 0)
+		incTest(3, 2, 0)
+		incTest(-3, 2, 0)
+		incTest(-2, 4, 0)
+		incTest(2, -1, 0)
+		incTest(-3, -4, 3)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/dsyr.go b/vendor/gonum.org/v1/gonum/blas/testblas/dsyr.go
new file mode 100644
index 00000000..4c404794
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/dsyr.go
@@ -0,0 +1,72 @@
+package testblas
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+type Dsyrer interface {
+	Dsyr(ul blas.Uplo, n int, alpha float64, x []float64, incX int, a []float64, lda int)
+}
+
+func DsyrTest(t *testing.T, blasser Dsyrer) {
+	for i, test := range []struct {
+		ul    blas.Uplo
+		n     int
+		a     [][]float64
+		x     []float64
+		alpha float64
+		ans   [][]float64
+	}{
+		{
+			ul: blas.Upper,
+			n:  4,
+			a: [][]float64{
+				{10, 2, 0, 1},
+				{0, 1, 2, 3},
+				{0, 0, 9, 15},
+				{0, 0, 0, -6},
+			},
+			x:     []float64{1, 2, 0, 5},
+			alpha: 8,
+			ans: [][]float64{
+				{18, 18, 0, 41},
+				{0, 33, 2, 83},
+				{0, 0, 9, 15},
+				{0, 0, 0, 194},
+			},
+		},
+		{
+			ul: blas.Lower,
+			n:  3,
+			a: [][]float64{
+				{10, 2, 0},
+				{4, 1, 2},
+				{2, 7, 9},
+			},
+			x:     []float64{3, 0, 5},
+			alpha: 8,
+			ans: [][]float64{
+				{82, 2, 0},
+				{4, 1, 2},
+				{122, 7, 209},
+			},
+		},
+	} {
+		incTest := func(incX, extra int) {
+			xnew := makeIncremented(test.x, incX, extra)
+			aFlat := flatten(test.a)
+			ans := flatten(test.ans)
+			lda := test.n
+			blasser.Dsyr(test.ul, test.n, test.alpha, xnew, incX, aFlat, lda)
+			if !dSliceTolEqual(aFlat, ans) {
+				t.Errorf("Case %v, idx %v: Want %v, got %v.", i, incX, ans, aFlat)
+			}
+		}
+		incTest(1, 3)
+		incTest(1, 0)
+		incTest(3, 2)
+		incTest(-2, 2)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/dsyr2.go b/vendor/gonum.org/v1/gonum/blas/testblas/dsyr2.go
new file mode 100644
index 00000000..e9069592
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/dsyr2.go
@@ -0,0 +1,76 @@
+package testblas
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dsyr2er interface {
+	Dsyr2(ul blas.Uplo, n int, alpha float64, x []float64, incX int, y []float64, incY int, a []float64, lda int)
+}
+
+func Dsyr2Test(t *testing.T, blasser Dsyr2er) {
+	for i, test := range []struct {
+		n     int
+		a     [][]float64
+		ul    blas.Uplo
+		x     []float64
+		y     []float64
+		alpha float64
+		ans   [][]float64
+	}{
+		{
+			n: 3,
+			a: [][]float64{
+				{7, 2, 4},
+				{0, 3, 5},
+				{0, 0, 6},
+			},
+			x:     []float64{2, 3, 4},
+			y:     []float64{5, 6, 7},
+			alpha: 2,
+			ul:    blas.Upper,
+			ans: [][]float64{
+				{47, 56, 72},
+				{0, 75, 95},
+				{0, 0, 118},
+			},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{7, 0, 0},
+				{2, 3, 0},
+				{4, 5, 6},
+			},
+			x:     []float64{2, 3, 4},
+			y:     []float64{5, 6, 7},
+			alpha: 2,
+			ul:    blas.Lower,
+			ans: [][]float64{
+				{47, 0, 0},
+				{56, 75, 0},
+				{72, 95, 118},
+			},
+		},
+	} {
+		incTest := func(incX, incY, extra int) {
+			aFlat := flatten(test.a)
+			x := makeIncremented(test.x, incX, extra)
+			y := makeIncremented(test.y, incY, extra)
+			blasser.Dsyr2(test.ul, test.n, test.alpha, x, incX, y, incY, aFlat, test.n)
+			ansFlat := flatten(test.ans)
+			if !floats.EqualApprox(aFlat, ansFlat, 1e-14) {
+				t.Errorf("Case %v, incX = %v, incY = %v. Want %v, got %v.", i, incX, incY, ansFlat, aFlat)
+			}
+		}
+		incTest(1, 1, 0)
+		incTest(-2, 1, 0)
+		incTest(-2, 3, 0)
+		incTest(2, -3, 0)
+		incTest(3, -2, 0)
+		incTest(-3, -4, 0)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/dsyr2k.go b/vendor/gonum.org/v1/gonum/blas/testblas/dsyr2k.go
new file mode 100644
index 00000000..7c8600b5
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/dsyr2k.go
@@ -0,0 +1,201 @@
+package testblas
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dsyr2ker interface {
+	Dsyr2k(ul blas.Uplo, tA blas.Transpose, n, k int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int)
+}
+
+func Dsyr2kTest(t *testing.T, blasser Dsyr2ker) {
+	for i, test := range []struct {
+		ul    blas.Uplo
+		tA    blas.Transpose
+		n     int
+		k     int
+		alpha float64
+		a     [][]float64
+		b     [][]float64
+		c     [][]float64
+		beta  float64
+		ans   [][]float64
+	}{
+		{
+			ul:    blas.Upper,
+			tA:    blas.NoTrans,
+			n:     3,
+			k:     2,
+			alpha: 0,
+			a: [][]float64{
+				{1, 2},
+				{3, 4},
+				{5, 6},
+			},
+			b: [][]float64{
+				{7, 8},
+				{9, 10},
+				{11, 12},
+			},
+			c: [][]float64{
+				{1, 2, 3},
+				{0, 5, 6},
+				{0, 0, 9},
+			},
+			beta: 2,
+			ans: [][]float64{
+				{2, 4, 6},
+				{0, 10, 12},
+				{0, 0, 18},
+			},
+		},
+		{
+			ul:    blas.Lower,
+			tA:    blas.NoTrans,
+			n:     3,
+			k:     2,
+			alpha: 0,
+			a: [][]float64{
+				{1, 2},
+				{3, 4},
+				{5, 6},
+			},
+			b: [][]float64{
+				{7, 8},
+				{9, 10},
+				{11, 12},
+			},
+			c: [][]float64{
+				{1, 0, 0},
+				{2, 3, 0},
+				{4, 5, 6},
+			},
+			beta: 2,
+			ans: [][]float64{
+				{2, 0, 0},
+				{4, 6, 0},
+				{8, 10, 12},
+			},
+		},
+		{
+			ul:    blas.Upper,
+			tA:    blas.NoTrans,
+			n:     3,
+			k:     2,
+			alpha: 3,
+			a: [][]float64{
+				{1, 2},
+				{3, 4},
+				{5, 6},
+			},
+			b: [][]float64{
+				{7, 8},
+				{9, 10},
+				{11, 12},
+			},
+			c: [][]float64{
+				{1, 2, 3},
+				{0, 4, 5},
+				{0, 0, 6},
+			},
+			beta: 2,
+			ans: [][]float64{
+				{140, 250, 360},
+				{0, 410, 568},
+				{0, 0, 774},
+			},
+		},
+		{
+			ul:    blas.Lower,
+			tA:    blas.NoTrans,
+			n:     3,
+			k:     2,
+			alpha: 3,
+			a: [][]float64{
+				{1, 2},
+				{3, 4},
+				{5, 6},
+			},
+			b: [][]float64{
+				{7, 8},
+				{9, 10},
+				{11, 12},
+			},
+			c: [][]float64{
+				{1, 0, 0},
+				{2, 4, 0},
+				{3, 5, 6},
+			},
+			beta: 2,
+			ans: [][]float64{
+				{140, 0, 0},
+				{250, 410, 0},
+				{360, 568, 774},
+			},
+		},
+		{
+			ul:    blas.Upper,
+			tA:    blas.Trans,
+			n:     3,
+			k:     2,
+			alpha: 3,
+			a: [][]float64{
+				{1, 3, 5},
+				{2, 4, 6},
+			},
+			b: [][]float64{
+				{7, 9, 11},
+				{8, 10, 12},
+			},
+			c: [][]float64{
+				{1, 2, 3},
+				{0, 4, 5},
+				{0, 0, 6},
+			},
+			beta: 2,
+			ans: [][]float64{
+				{140, 250, 360},
+				{0, 410, 568},
+				{0, 0, 774},
+			},
+		},
+		{
+			ul:    blas.Lower,
+			tA:    blas.Trans,
+			n:     3,
+			k:     2,
+			alpha: 3,
+			a: [][]float64{
+				{1, 3, 5},
+				{2, 4, 6},
+			},
+			b: [][]float64{
+				{7, 9, 11},
+				{8, 10, 12},
+			},
+			c: [][]float64{
+				{1, 0, 0},
+				{2, 4, 0},
+				{3, 5, 6},
+			},
+			beta: 2,
+			ans: [][]float64{
+				{140, 0, 0},
+				{250, 410, 0},
+				{360, 568, 774},
+			},
+		},
+	} {
+		aFlat := flatten(test.a)
+		bFlat := flatten(test.b)
+		cFlat := flatten(test.c)
+		ansFlat := flatten(test.ans)
+		blasser.Dsyr2k(test.ul, test.tA, test.n, test.k, test.alpha, aFlat, len(test.a[0]), bFlat, len(test.b[0]), test.beta, cFlat, len(test.c[0]))
+		if !floats.EqualApprox(ansFlat, cFlat, 1e-14) {
+			t.Errorf("Case %v. Want %v, got %v.", i, ansFlat, cFlat)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/dsyrk.go b/vendor/gonum.org/v1/gonum/blas/testblas/dsyrk.go
new file mode 100644
index 00000000..99e18ebb
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/dsyrk.go
@@ -0,0 +1,171 @@
+package testblas
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dsyker interface {
+	Dsyrk(ul blas.Uplo, tA blas.Transpose, n, k int, alpha float64, a []float64, lda int, beta float64, c []float64, ldc int)
+}
+
+func DsyrkTest(t *testing.T, blasser Dsyker) {
+	for i, test := range []struct {
+		ul    blas.Uplo
+		tA    blas.Transpose
+		n     int
+		k     int
+		alpha float64
+		a     [][]float64
+		c     [][]float64
+		beta  float64
+		ans   [][]float64
+	}{
+		{
+			ul:    blas.Upper,
+			tA:    blas.NoTrans,
+			n:     3,
+			k:     2,
+			alpha: 0,
+			a: [][]float64{
+				{1, 2},
+				{3, 4},
+				{5, 6},
+			},
+			c: [][]float64{
+				{1, 2, 3},
+				{0, 5, 6},
+				{0, 0, 9},
+			},
+			beta: 2,
+			ans: [][]float64{
+				{2, 4, 6},
+				{0, 10, 12},
+				{0, 0, 18},
+			},
+		},
+		{
+			ul:    blas.Lower,
+			tA:    blas.NoTrans,
+			n:     3,
+			k:     2,
+			alpha: 0,
+			a: [][]float64{
+				{1, 2},
+				{3, 4},
+				{5, 6},
+			},
+			c: [][]float64{
+				{1, 0, 0},
+				{2, 3, 0},
+				{4, 5, 6},
+			},
+			beta: 2,
+			ans: [][]float64{
+				{2, 0, 0},
+				{4, 6, 0},
+				{8, 10, 12},
+			},
+		},
+		{
+			ul:    blas.Upper,
+			tA:    blas.NoTrans,
+			n:     3,
+			k:     2,
+			alpha: 3,
+			a: [][]float64{
+				{1, 2},
+				{3, 4},
+				{5, 6},
+			},
+			c: [][]float64{
+				{1, 2, 3},
+				{0, 4, 5},
+				{0, 0, 6},
+			},
+			beta: 2,
+			ans: [][]float64{
+				{17, 37, 57},
+				{0, 83, 127},
+				{0, 0, 195},
+			},
+		},
+		{
+			ul:    blas.Lower,
+			tA:    blas.NoTrans,
+			n:     3,
+			k:     2,
+			alpha: 3,
+			a: [][]float64{
+				{1, 2},
+				{3, 4},
+				{5, 6},
+			},
+			c: [][]float64{
+				{1, 0, 0},
+				{2, 4, 0},
+				{3, 5, 6},
+			},
+			beta: 2,
+			ans: [][]float64{
+				{17, 0, 0},
+				{37, 83, 0},
+				{57, 127, 195},
+			},
+		},
+		{
+			ul:    blas.Upper,
+			tA:    blas.Trans,
+			n:     3,
+			k:     2,
+			alpha: 3,
+			a: [][]float64{
+				{1, 3, 5},
+				{2, 4, 6},
+			},
+			c: [][]float64{
+				{1, 2, 3},
+				{0, 4, 5},
+				{0, 0, 6},
+			},
+			beta: 2,
+			ans: [][]float64{
+				{17, 37, 57},
+				{0, 83, 127},
+				{0, 0, 195},
+			},
+		},
+		{
+			ul:    blas.Lower,
+			tA:    blas.Trans,
+			n:     3,
+			k:     2,
+			alpha: 3,
+			a: [][]float64{
+				{1, 3, 5},
+				{2, 4, 6},
+			},
+			c: [][]float64{
+				{1, 0, 0},
+				{2, 4, 0},
+				{3, 5, 6},
+			},
+			beta: 2,
+			ans: [][]float64{
+				{17, 0, 0},
+				{37, 83, 0},
+				{57, 127, 195},
+			},
+		},
+	} {
+		aFlat := flatten(test.a)
+		cFlat := flatten(test.c)
+		ansFlat := flatten(test.ans)
+		blasser.Dsyrk(test.ul, test.tA, test.n, test.k, test.alpha, aFlat, len(test.a[0]), test.beta, cFlat, len(test.c[0]))
+		if !floats.EqualApprox(ansFlat, cFlat, 1e-14) {
+			t.Errorf("Case %v. Want %v, got %v.", i, ansFlat, cFlat)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/dtbmv.go b/vendor/gonum.org/v1/gonum/blas/testblas/dtbmv.go
new file mode 100644
index 00000000..b0dee676
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/dtbmv.go
@@ -0,0 +1,123 @@
+package testblas
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+type Dtbmver interface {
+	Dtbmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n, k int, a []float64, lda int, x []float64, incX int)
+}
+
+func DtbmvTest(t *testing.T, blasser Dtbmver) {
+	for i, test := range []struct {
+		ul  blas.Uplo
+		tA  blas.Transpose
+		d   blas.Diag
+		n   int
+		k   int
+		a   [][]float64
+		x   []float64
+		ans []float64
+	}{
+		{
+			ul: blas.Upper,
+			tA: blas.NoTrans,
+			d:  blas.Unit,
+			n:  3,
+			k:  1,
+			a: [][]float64{
+				{1, 2, 0},
+				{0, 1, 4},
+				{0, 0, 1},
+			},
+			x:   []float64{2, 3, 4},
+			ans: []float64{8, 19, 4},
+		},
+		{
+			ul: blas.Upper,
+			tA: blas.NoTrans,
+			d:  blas.NonUnit,
+			n:  5,
+			k:  1,
+			a: [][]float64{
+				{1, 3, 0, 0, 0},
+				{0, 6, 7, 0, 0},
+				{0, 0, 2, 1, 0},
+				{0, 0, 0, 12, 3},
+				{0, 0, 0, 0, -1},
+			},
+			x:   []float64{1, 2, 3, 4, 5},
+			ans: []float64{7, 33, 10, 63, -5},
+		},
+		{
+			ul: blas.Lower,
+			tA: blas.NoTrans,
+			d:  blas.NonUnit,
+			n:  5,
+			k:  1,
+			a: [][]float64{
+				{7, 0, 0, 0, 0},
+				{3, 6, 0, 0, 0},
+				{0, 7, 2, 0, 0},
+				{0, 0, 1, 12, 0},
+				{0, 0, 0, 3, -1},
+			},
+			x:   []float64{1, 2, 3, 4, 5},
+			ans: []float64{7, 15, 20, 51, 7},
+		},
+		{
+			ul: blas.Upper,
+			tA: blas.Trans,
+			d:  blas.NonUnit,
+			n:  5,
+			k:  2,
+			a: [][]float64{
+				{7, 3, 9, 0, 0},
+				{0, 6, 7, 10, 0},
+				{0, 0, 2, 1, 11},
+				{0, 0, 0, 12, 3},
+				{0, 0, 0, 0, -1},
+			},
+			x:   []float64{1, 2, 3, 4, 5},
+			ans: []float64{7, 15, 29, 71, 40},
+		},
+		{
+			ul: blas.Lower,
+			tA: blas.Trans,
+			d:  blas.NonUnit,
+			n:  5,
+			k:  2,
+			a: [][]float64{
+				{7, 0, 0, 0, 0},
+				{3, 6, 0, 0, 0},
+				{9, 7, 2, 0, 0},
+				{0, 10, 1, 12, 0},
+				{0, 0, 11, 3, -1},
+			},
+			x:   []float64{1, 2, 3, 4, 5},
+			ans: []float64{40, 73, 65, 63, -5},
+		},
+	} {
+		extra := 0
+		var aFlat []float64
+		if test.ul == blas.Upper {
+			aFlat = flattenBanded(test.a, test.k, 0)
+		} else {
+			aFlat = flattenBanded(test.a, 0, test.k)
+		}
+		incTest := func(incX, extra int) {
+			xnew := makeIncremented(test.x, incX, extra)
+			ans := makeIncremented(test.ans, incX, extra)
+			lda := test.k + 1
+			blasser.Dtbmv(test.ul, test.tA, test.d, test.n, test.k, aFlat, lda, xnew, incX)
+			if !dSliceTolEqual(ans, xnew) {
+				t.Errorf("Case %v, Inc %v: Want %v, got %v", i, incX, ans, xnew)
+			}
+		}
+		incTest(1, extra)
+		incTest(3, extra)
+		incTest(-2, extra)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/dtbsv.go b/vendor/gonum.org/v1/gonum/blas/testblas/dtbsv.go
new file mode 100644
index 00000000..d3fad1ec
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/dtbsv.go
@@ -0,0 +1,255 @@
+package testblas
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+type Dtbsver interface {
+	Dtbsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n, k int, a []float64, lda int, x []float64, incX int)
+	Dtrsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, a []float64, lda int, x []float64, incX int)
+}
+
+func DtbsvTest(t *testing.T, blasser Dtbsver) {
+	for i, test := range []struct {
+		ul   blas.Uplo
+		tA   blas.Transpose
+		d    blas.Diag
+		n, k int
+		a    [][]float64
+		x    []float64
+		incX int
+		ans  []float64
+	}{
+		{
+			ul: blas.Upper,
+			tA: blas.NoTrans,
+			d:  blas.NonUnit,
+			n:  5,
+			k:  1,
+			a: [][]float64{
+				{1, 3, 0, 0, 0},
+				{0, 6, 7, 0, 0},
+				{0, 0, 2, 1, 0},
+				{0, 0, 0, 12, 3},
+				{0, 0, 0, 0, -1},
+			},
+			x:    []float64{1, 2, 3, 4, 5},
+			incX: 1,
+			ans:  []float64{2.479166666666667, -0.493055555555556, 0.708333333333333, 1.583333333333333, -5.000000000000000},
+		},
+		{
+			ul: blas.Upper,
+			tA: blas.NoTrans,
+			d:  blas.NonUnit,
+			n:  5,
+			k:  2,
+			a: [][]float64{
+				{1, 3, 5, 0, 0},
+				{0, 6, 7, 5, 0},
+				{0, 0, 2, 1, 5},
+				{0, 0, 0, 12, 3},
+				{0, 0, 0, 0, -1},
+			},
+			x:    []float64{1, 2, 3, 4, 5},
+			incX: 1,
+			ans:  []float64{-15.854166666666664, -16.395833333333336, 13.208333333333334, 1.583333333333333, -5.000000000000000},
+		},
+		{
+			ul: blas.Upper,
+			tA: blas.NoTrans,
+			d:  blas.NonUnit,
+			n:  5,
+			k:  1,
+			a: [][]float64{
+				{1, 3, 0, 0, 0},
+				{0, 6, 7, 0, 0},
+				{0, 0, 2, 1, 0},
+				{0, 0, 0, 12, 3},
+				{0, 0, 0, 0, -1},
+			},
+			x:    []float64{1, -101, 2, -201, 3, -301, 4, -401, 5, -501, -601, -701},
+			incX: 2,
+			ans:  []float64{2.479166666666667, -101, -0.493055555555556, -201, 0.708333333333333, -301, 1.583333333333333, -401, -5.000000000000000, -501, -601, -701},
+		},
+		{
+			ul: blas.Upper,
+			tA: blas.NoTrans,
+			d:  blas.NonUnit,
+			n:  5,
+			k:  2,
+			a: [][]float64{
+				{1, 3, 5, 0, 0},
+				{0, 6, 7, 5, 0},
+				{0, 0, 2, 1, 5},
+				{0, 0, 0, 12, 3},
+				{0, 0, 0, 0, -1},
+			},
+			x:    []float64{1, -101, 2, -201, 3, -301, 4, -401, 5, -501, -601, -701},
+			incX: 2,
+			ans:  []float64{-15.854166666666664, -101, -16.395833333333336, -201, 13.208333333333334, -301, 1.583333333333333, -401, -5.000000000000000, -501, -601, -701},
+		},
+		{
+			ul: blas.Lower,
+			tA: blas.NoTrans,
+			d:  blas.NonUnit,
+			n:  5,
+			k:  2,
+			a: [][]float64{
+				{1, 0, 0, 0, 0},
+				{3, 6, 0, 0, 0},
+				{5, 7, 2, 0, 0},
+				{0, 5, 1, 12, 0},
+				{0, 0, 5, 3, -1},
+			},
+			x:    []float64{1, 2, 3, 4, 5},
+			incX: 1,
+			ans:  []float64{1, -0.166666666666667, -0.416666666666667, 0.437500000000000, -5.770833333333334},
+		},
+		{
+			ul: blas.Lower,
+			tA: blas.NoTrans,
+			d:  blas.NonUnit,
+			n:  5,
+			k:  2,
+			a: [][]float64{
+				{1, 0, 0, 0, 0},
+				{3, 6, 0, 0, 0},
+				{5, 7, 2, 0, 0},
+				{0, 5, 1, 12, 0},
+				{0, 0, 5, 3, -1},
+			},
+			x:    []float64{1, -101, 2, -201, 3, -301, 4, -401, 5, -501, -601, -701},
+			incX: 2,
+			ans:  []float64{1, -101, -0.166666666666667, -201, -0.416666666666667, -301, 0.437500000000000, -401, -5.770833333333334, -501, -601, -701},
+		},
+		{
+			ul: blas.Upper,
+			tA: blas.Trans,
+			d:  blas.NonUnit,
+			n:  5,
+			k:  2,
+			a: [][]float64{
+				{1, 3, 5, 0, 0},
+				{0, 6, 7, 5, 0},
+				{0, 0, 2, 1, 5},
+				{0, 0, 0, 12, 3},
+				{0, 0, 0, 0, -1},
+			},
+			x:    []float64{1, 2, 3, 4, 5},
+			incX: 1,
+			ans:  []float64{1, -0.166666666666667, -0.416666666666667, 0.437500000000000, -5.770833333333334},
+		},
+		{
+			ul: blas.Upper,
+			tA: blas.Trans,
+			d:  blas.NonUnit,
+			n:  5,
+			k:  2,
+			a: [][]float64{
+				{1, 3, 5, 0, 0},
+				{0, 6, 7, 5, 0},
+				{0, 0, 2, 1, 5},
+				{0, 0, 0, 12, 3},
+				{0, 0, 0, 0, -1},
+			},
+			x:    []float64{1, -101, 2, -201, 3, -301, 4, -401, 5, -501, -601, -701},
+			incX: 2,
+			ans:  []float64{1, -101, -0.166666666666667, -201, -0.416666666666667, -301, 0.437500000000000, -401, -5.770833333333334, -501, -601, -701},
+		},
+		{
+			ul: blas.Lower,
+			tA: blas.Trans,
+			d:  blas.NonUnit,
+			n:  5,
+			k:  2,
+			a: [][]float64{
+				{1, 0, 0, 0, 0},
+				{3, 6, 0, 0, 0},
+				{5, 7, 2, 0, 0},
+				{0, 5, 1, 12, 0},
+				{0, 0, 5, 3, -1},
+			},
+			x:    []float64{1, 2, 3, 4, 5},
+			incX: 1,
+			ans:  []float64{-15.854166666666664, -16.395833333333336, 13.208333333333334, 1.583333333333333, -5.000000000000000},
+		},
+		{
+			ul: blas.Lower,
+			tA: blas.Trans,
+			d:  blas.NonUnit,
+			n:  5,
+			k:  2,
+			a: [][]float64{
+				{1, 0, 0, 0, 0},
+				{3, 6, 0, 0, 0},
+				{5, 7, 2, 0, 0},
+				{0, 5, 1, 12, 0},
+				{0, 0, 5, 3, -1},
+			},
+			x:    []float64{1, -101, 2, -201, 3, -301, 4, -401, 5, -501, -601, -701},
+			incX: 2,
+			ans:  []float64{-15.854166666666664, -101, -16.395833333333336, -201, 13.208333333333334, -301, 1.583333333333333, -401, -5.000000000000000, -501, -601, -701},
+		},
+	} {
+		var aFlat []float64
+		if test.ul == blas.Upper {
+			aFlat = flattenBanded(test.a, test.k, 0)
+		} else {
+			aFlat = flattenBanded(test.a, 0, test.k)
+		}
+		xCopy := sliceCopy(test.x)
+		// TODO: Have tests where the banded matrix is constructed explicitly
+		// to allow testing for lda =! k+1
+		blasser.Dtbsv(test.ul, test.tA, test.d, test.n, test.k, aFlat, test.k+1, xCopy, test.incX)
+		if !dSliceTolEqual(test.ans, xCopy) {
+			t.Errorf("Case %v: Want %v, got %v", i, test.ans, xCopy)
+		}
+	}
+
+	/*
+		// TODO: Uncomment when Dtrsv is fixed
+		// Compare with dense for larger matrices
+		for _, ul := range [...]blas.Uplo{blas.Upper, blas.Lower} {
+			for _, tA := range [...]blas.Transpose{blas.NoTrans, blas.Trans} {
+				for _, n := range [...]int{7, 8, 11} {
+					for _, d := range [...]blas.Diag{blas.NonUnit, blas.Unit} {
+						for _, k := range [...]int{0, 1, 3} {
+							for _, incX := range [...]int{1, 3} {
+								a := make([][]float64, n)
+								for i := range a {
+									a[i] = make([]float64, n)
+									for j := range a[i] {
+										a[i][j] = rand.Float64()
+									}
+								}
+								x := make([]float64, n)
+								for i := range x {
+									x[i] = rand.Float64()
+								}
+								extra := 3
+								xinc := makeIncremented(x, incX, extra)
+								bandX := sliceCopy(xinc)
+								var aFlatBand []float64
+								if ul == blas.Upper {
+									aFlatBand = flattenBanded(a, k, 0)
+								} else {
+									aFlatBand = flattenBanded(a, 0, k)
+								}
+								blasser.Dtbsv(ul, tA, d, n, k, aFlatBand, k+1, bandX, incX)
+
+								aFlatDense := flatten(a)
+								denseX := sliceCopy(xinc)
+								blasser.Dtrsv(ul, tA, d, n, aFlatDense, n, denseX, incX)
+								if !dSliceTolEqual(denseX, bandX) {
+									t.Errorf("Case %v: dense banded mismatch")
+								}
+							}
+						}
+					}
+				}
+			}
+		}
+	*/
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/dtpmv.go b/vendor/gonum.org/v1/gonum/blas/testblas/dtpmv.go
new file mode 100644
index 00000000..04af1641
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/dtpmv.go
@@ -0,0 +1,129 @@
+package testblas
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dtpmver interface {
+	Dtpmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, ap []float64, x []float64, incX int)
+}
+
+func DtpmvTest(t *testing.T, blasser Dtpmver) {
+	for i, test := range []struct {
+		n   int
+		a   [][]float64
+		x   []float64
+		d   blas.Diag
+		ul  blas.Uplo
+		tA  blas.Transpose
+		ans []float64
+	}{
+		{
+			n: 3,
+			a: [][]float64{
+				{5, 6, 7},
+				{0, 9, 10},
+				{0, 0, 13},
+			},
+			x:   []float64{3, 4, 5},
+			d:   blas.NonUnit,
+			ul:  blas.Upper,
+			tA:  blas.NoTrans,
+			ans: []float64{74, 86, 65},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{5, 6, 7},
+				{0, 9, 10},
+				{0, 0, 13},
+			},
+			x:   []float64{3, 4, 5},
+			d:   blas.Unit,
+			ul:  blas.Upper,
+			tA:  blas.NoTrans,
+			ans: []float64{62, 54, 5},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{5, 0, 0},
+				{6, 9, 0},
+				{7, 10, 13},
+			},
+			x:   []float64{3, 4, 5},
+			d:   blas.NonUnit,
+			ul:  blas.Lower,
+			tA:  blas.NoTrans,
+			ans: []float64{15, 54, 126},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{1, 0, 0},
+				{6, 1, 0},
+				{7, 10, 1},
+			},
+			x:   []float64{3, 4, 5},
+			d:   blas.Unit,
+			ul:  blas.Lower,
+			tA:  blas.NoTrans,
+			ans: []float64{3, 22, 66},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{5, 6, 7},
+				{0, 9, 10},
+				{0, 0, 13},
+			},
+			x:   []float64{3, 4, 5},
+			d:   blas.NonUnit,
+			ul:  blas.Upper,
+			tA:  blas.Trans,
+			ans: []float64{15, 54, 126},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{1, 6, 7},
+				{0, 1, 10},
+				{0, 0, 1},
+			},
+			x:   []float64{3, 4, 5},
+			d:   blas.Unit,
+			ul:  blas.Upper,
+			tA:  blas.Trans,
+			ans: []float64{3, 22, 66},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{5, 0, 0},
+				{6, 9, 0},
+				{7, 10, 13},
+			},
+			x:   []float64{3, 4, 5},
+			d:   blas.NonUnit,
+			ul:  blas.Lower,
+			tA:  blas.Trans,
+			ans: []float64{74, 86, 65},
+		},
+	} {
+		incTest := func(incX, extra int) {
+			aFlat := flattenTriangular(test.a, test.ul)
+			x := makeIncremented(test.x, incX, extra)
+			blasser.Dtpmv(test.ul, test.tA, test.d, test.n, aFlat, x, incX)
+			ans := makeIncremented(test.ans, incX, extra)
+			if !floats.EqualApprox(x, ans, 1e-14) {
+				t.Errorf("Case %v, idx %v: Want %v, got %v.", i, incX, ans, x)
+			}
+		}
+		incTest(1, 0)
+		incTest(-3, 3)
+		incTest(4, 3)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/dtpsv.go b/vendor/gonum.org/v1/gonum/blas/testblas/dtpsv.go
new file mode 100644
index 00000000..9fee545e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/dtpsv.go
@@ -0,0 +1,144 @@
+package testblas
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dtpsver interface {
+	Dtpsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, ap []float64, x []float64, incX int)
+}
+
+func DtpsvTest(t *testing.T, blasser Dtpsver) {
+	for i, test := range []struct {
+		n   int
+		a   [][]float64
+		ul  blas.Uplo
+		tA  blas.Transpose
+		d   blas.Diag
+		x   []float64
+		ans []float64
+	}{
+		{
+			n: 3,
+			a: [][]float64{
+				{1, 2, 3},
+				{0, 8, 15},
+				{0, 0, 8},
+			},
+			ul:  blas.Upper,
+			tA:  blas.NoTrans,
+			d:   blas.NonUnit,
+			x:   []float64{5, 6, 7},
+			ans: []float64{4.15625, -0.890625, 0.875},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{1, 2, 3},
+				{0, 1, 15},
+				{0, 0, 1},
+			},
+			ul:  blas.Upper,
+			tA:  blas.NoTrans,
+			d:   blas.Unit,
+			x:   []float64{5, 6, 7},
+			ans: []float64{182, -99, 7},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{1, 0, 0},
+				{2, 8, 0},
+				{3, 15, 8},
+			},
+			ul:  blas.Lower,
+			tA:  blas.NoTrans,
+			d:   blas.NonUnit,
+			x:   []float64{5, 6, 7},
+			ans: []float64{5, -0.5, -0.0625},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{1, 0, 0},
+				{2, 8, 0},
+				{3, 15, 8},
+			},
+			ul:  blas.Lower,
+			tA:  blas.NoTrans,
+			d:   blas.Unit,
+			x:   []float64{5, 6, 7},
+			ans: []float64{5, -4, 52},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{1, 2, 3},
+				{0, 8, 15},
+				{0, 0, 8},
+			},
+			ul:  blas.Upper,
+			tA:  blas.Trans,
+			d:   blas.NonUnit,
+			x:   []float64{5, 6, 7},
+			ans: []float64{5, -0.5, -0.0625},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{1, 2, 3},
+				{0, 8, 15},
+				{0, 0, 8},
+			},
+			ul:  blas.Upper,
+			tA:  blas.Trans,
+			d:   blas.Unit,
+			x:   []float64{5, 6, 7},
+			ans: []float64{5, -4, 52},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{1, 0, 0},
+				{2, 8, 0},
+				{3, 15, 8},
+			},
+			ul:  blas.Lower,
+			tA:  blas.Trans,
+			d:   blas.NonUnit,
+			x:   []float64{5, 6, 7},
+			ans: []float64{4.15625, -0.890625, 0.875},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{1, 0, 0},
+				{2, 1, 0},
+				{3, 15, 1},
+			},
+			ul:  blas.Lower,
+			tA:  blas.Trans,
+			d:   blas.Unit,
+			x:   []float64{5, 6, 7},
+			ans: []float64{182, -99, 7},
+		},
+	} {
+		incTest := func(incX, extra int) {
+			aFlat := flattenTriangular(test.a, test.ul)
+			x := makeIncremented(test.x, incX, extra)
+			blasser.Dtpsv(test.ul, test.tA, test.d, test.n, aFlat, x, incX)
+			ans := makeIncremented(test.ans, incX, extra)
+			if !floats.EqualApprox(x, ans, 1e-14) {
+				t.Errorf("Case %v, incX = %v: Want %v, got %v.", i, incX, ans, x)
+			}
+		}
+		incTest(1, 0)
+		incTest(-2, 0)
+		incTest(3, 0)
+		incTest(-3, 8)
+		incTest(4, 2)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/dtrmm.go b/vendor/gonum.org/v1/gonum/blas/testblas/dtrmm.go
new file mode 100644
index 00000000..95cccec5
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/dtrmm.go
@@ -0,0 +1,806 @@
+package testblas
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dtrmmer interface {
+	Dtrmm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int)
+}
+
+func DtrmmTest(t *testing.T, blasser Dtrmmer) {
+	for i, test := range []struct {
+		s     blas.Side
+		ul    blas.Uplo
+		tA    blas.Transpose
+		d     blas.Diag
+		m     int
+		n     int
+		alpha float64
+		a     [][]float64
+		b     [][]float64
+		ans   [][]float64
+	}{
+		{
+			s:     blas.Left,
+			ul:    blas.Upper,
+			tA:    blas.NoTrans,
+			d:     blas.NonUnit,
+			m:     4,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 2, 3, 4},
+				{0, 5, 6, 7},
+				{0, 0, 8, 9},
+				{0, 0, 0, 10},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+				{16, 17, 18},
+				{19, 20, 21},
+			},
+			ans: [][]float64{
+				{320, 340, 360},
+				{588, 624, 660},
+				{598, 632, 666},
+				{380, 400, 420},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Upper,
+			tA:    blas.NoTrans,
+			d:     blas.NonUnit,
+			m:     2,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 2},
+				{0, 5},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+			},
+			ans: [][]float64{
+				{72, 78, 84},
+				{130, 140, 150},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Upper,
+			tA:    blas.NoTrans,
+			d:     blas.Unit,
+			m:     4,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 2, 3, 4},
+				{0, 5, 6, 7},
+				{0, 0, 8, 9},
+				{0, 0, 0, 10},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+				{16, 17, 18},
+				{19, 20, 21},
+			},
+			ans: [][]float64{
+				{320, 340, 360},
+				{484, 512, 540},
+				{374, 394, 414},
+				{38, 40, 42},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Upper,
+			tA:    blas.NoTrans,
+			d:     blas.Unit,
+			m:     2,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 2},
+				{0, 5},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+			},
+			ans: [][]float64{
+				{72, 78, 84},
+				{26, 28, 30},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Lower,
+			tA:    blas.NoTrans,
+			d:     blas.NonUnit,
+			m:     4,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 0, 0, 0},
+				{2, 5, 0, 0},
+				{3, 6, 8, 0},
+				{4, 7, 9, 10},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+				{16, 17, 18},
+				{19, 20, 21},
+			},
+			ans: [][]float64{
+				{20, 22, 24},
+				{170, 184, 198},
+				{472, 506, 540},
+				{930, 990, 1050},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Lower,
+			tA:    blas.NoTrans,
+			d:     blas.NonUnit,
+			m:     2,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 0},
+				{2, 5},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+			},
+			ans: [][]float64{
+				{20, 22, 24},
+				{170, 184, 198},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Lower,
+			tA:    blas.NoTrans,
+			d:     blas.Unit,
+			m:     4,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 0, 0, 0},
+				{2, 5, 0, 0},
+				{3, 6, 8, 0},
+				{4, 7, 9, 10},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+				{16, 17, 18},
+				{19, 20, 21},
+			},
+			ans: [][]float64{
+				{20, 22, 24},
+				{66, 72, 78},
+				{248, 268, 288},
+				{588, 630, 672},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Lower,
+			tA:    blas.NoTrans,
+			d:     blas.Unit,
+			m:     2,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 0},
+				{2, 5},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+			},
+			ans: [][]float64{
+				{20, 22, 24},
+				{66, 72, 78},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Upper,
+			tA:    blas.Trans,
+			d:     blas.NonUnit,
+			m:     4,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 2, 3, 4},
+				{0, 5, 6, 7},
+				{0, 0, 8, 9},
+				{0, 0, 0, 10},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+				{16, 17, 18},
+				{19, 20, 21},
+			},
+			ans: [][]float64{
+				{20, 22, 24},
+				{170, 184, 198},
+				{472, 506, 540},
+				{930, 990, 1050},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Upper,
+			tA:    blas.Trans,
+			d:     blas.NonUnit,
+			m:     2,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 2},
+				{0, 5},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+			},
+			ans: [][]float64{
+				{20, 22, 24},
+				{170, 184, 198},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Upper,
+			tA:    blas.Trans,
+			d:     blas.Unit,
+			m:     4,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 2, 3, 4},
+				{0, 5, 6, 7},
+				{0, 0, 8, 9},
+				{0, 0, 0, 10},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+				{16, 17, 18},
+				{19, 20, 21},
+			},
+			ans: [][]float64{
+				{20, 22, 24},
+				{66, 72, 78},
+				{248, 268, 288},
+				{588, 630, 672},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Upper,
+			tA:    blas.Trans,
+			d:     blas.Unit,
+			m:     2,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 2},
+				{0, 5},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+			},
+			ans: [][]float64{
+				{20, 22, 24},
+				{66, 72, 78},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Lower,
+			tA:    blas.Trans,
+			d:     blas.NonUnit,
+			m:     4,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 0, 0, 0},
+				{2, 5, 0, 0},
+				{3, 6, 8, 0},
+				{4, 7, 9, 10},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+				{16, 17, 18},
+				{19, 20, 21},
+			},
+			ans: [][]float64{
+				{320, 340, 360},
+				{588, 624, 660},
+				{598, 632, 666},
+				{380, 400, 420},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Lower,
+			tA:    blas.Trans,
+			d:     blas.NonUnit,
+			m:     2,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 0},
+				{2, 5},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+			},
+			ans: [][]float64{
+				{72, 78, 84},
+				{130, 140, 150},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Lower,
+			tA:    blas.Trans,
+			d:     blas.Unit,
+			m:     4,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 0, 0, 0},
+				{2, 5, 0, 0},
+				{3, 6, 8, 0},
+				{4, 7, 9, 10},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+				{16, 17, 18},
+				{19, 20, 21},
+			},
+			ans: [][]float64{
+				{320, 340, 360},
+				{484, 512, 540},
+				{374, 394, 414},
+				{38, 40, 42},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Lower,
+			tA:    blas.Trans,
+			d:     blas.Unit,
+			m:     2,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 0},
+				{2, 5},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+			},
+			ans: [][]float64{
+				{72, 78, 84},
+				{26, 28, 30},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Upper,
+			tA:    blas.NoTrans,
+			d:     blas.NonUnit,
+			m:     4,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 2, 3},
+				{0, 4, 5},
+				{0, 0, 6},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+				{16, 17, 18},
+				{19, 20, 21},
+			},
+			ans: [][]float64{
+				{20, 128, 314},
+				{26, 164, 398},
+				{32, 200, 482},
+				{38, 236, 566},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Upper,
+			tA:    blas.NoTrans,
+			d:     blas.NonUnit,
+			m:     2,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 2, 3},
+				{0, 4, 5},
+				{0, 0, 6},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+			},
+			ans: [][]float64{
+				{20, 128, 314},
+				{26, 164, 398},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Upper,
+			tA:    blas.NoTrans,
+			d:     blas.Unit,
+			m:     4,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 2, 3},
+				{0, 4, 5},
+				{0, 0, 6},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+				{16, 17, 18},
+				{19, 20, 21},
+			},
+			ans: [][]float64{
+				{20, 62, 194},
+				{26, 80, 248},
+				{32, 98, 302},
+				{38, 116, 356},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Upper,
+			tA:    blas.NoTrans,
+			d:     blas.Unit,
+			m:     2,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 2, 3},
+				{0, 4, 5},
+				{0, 0, 6},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+			},
+			ans: [][]float64{
+				{20, 62, 194},
+				{26, 80, 248},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Lower,
+			tA:    blas.NoTrans,
+			d:     blas.NonUnit,
+			m:     4,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 0, 0},
+				{2, 4, 0},
+				{3, 5, 6},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+				{16, 17, 18},
+				{19, 20, 21},
+			},
+			ans: [][]float64{
+				{136, 208, 144},
+				{172, 262, 180},
+				{208, 316, 216},
+				{244, 370, 252},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Lower,
+			tA:    blas.NoTrans,
+			d:     blas.NonUnit,
+			m:     2,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 0, 0},
+				{2, 4, 0},
+				{3, 5, 6},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+			},
+			ans: [][]float64{
+				{136, 208, 144},
+				{172, 262, 180},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Lower,
+			tA:    blas.NoTrans,
+			d:     blas.Unit,
+			m:     4,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 0, 0},
+				{2, 4, 0},
+				{3, 5, 6},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+				{16, 17, 18},
+				{19, 20, 21},
+			},
+			ans: [][]float64{
+				{136, 142, 24},
+				{172, 178, 30},
+				{208, 214, 36},
+				{244, 250, 42},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Lower,
+			tA:    blas.NoTrans,
+			d:     blas.Unit,
+			m:     2,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 0, 0},
+				{2, 4, 0},
+				{3, 5, 6},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+			},
+			ans: [][]float64{
+				{136, 142, 24},
+				{172, 178, 30},
+			},
+		},
+
+		{
+			s:     blas.Right,
+			ul:    blas.Upper,
+			tA:    blas.Trans,
+			d:     blas.NonUnit,
+			m:     4,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 2, 3},
+				{0, 4, 5},
+				{0, 0, 6},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+				{16, 17, 18},
+				{19, 20, 21},
+			},
+			ans: [][]float64{
+				{136, 208, 144},
+				{172, 262, 180},
+				{208, 316, 216},
+				{244, 370, 252},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Upper,
+			tA:    blas.Trans,
+			d:     blas.NonUnit,
+			m:     2,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 2, 3},
+				{0, 4, 5},
+				{0, 0, 6},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+			},
+			ans: [][]float64{
+				{136, 208, 144},
+				{172, 262, 180},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Upper,
+			tA:    blas.Trans,
+			d:     blas.Unit,
+			m:     4,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 2, 3},
+				{0, 4, 5},
+				{0, 0, 6},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+				{16, 17, 18},
+				{19, 20, 21},
+			},
+			ans: [][]float64{
+				{136, 142, 24},
+				{172, 178, 30},
+				{208, 214, 36},
+				{244, 250, 42},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Upper,
+			tA:    blas.Trans,
+			d:     blas.Unit,
+			m:     2,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 2, 3},
+				{0, 4, 5},
+				{0, 0, 6},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+			},
+			ans: [][]float64{
+				{136, 142, 24},
+				{172, 178, 30},
+			},
+		},
+
+		{
+			s:     blas.Right,
+			ul:    blas.Lower,
+			tA:    blas.Trans,
+			d:     blas.NonUnit,
+			m:     4,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 0, 0},
+				{2, 4, 0},
+				{3, 5, 6},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+				{16, 17, 18},
+				{19, 20, 21},
+			},
+			ans: [][]float64{
+				{20, 128, 314},
+				{26, 164, 398},
+				{32, 200, 482},
+				{38, 236, 566},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Lower,
+			tA:    blas.Trans,
+			d:     blas.NonUnit,
+			m:     2,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 0, 0},
+				{2, 4, 0},
+				{3, 5, 6},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+			},
+			ans: [][]float64{
+				{20, 128, 314},
+				{26, 164, 398},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Lower,
+			tA:    blas.Trans,
+			d:     blas.Unit,
+			m:     4,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 0, 0},
+				{2, 4, 0},
+				{3, 5, 6},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+				{16, 17, 18},
+				{19, 20, 21},
+			},
+			ans: [][]float64{
+				{20, 62, 194},
+				{26, 80, 248},
+				{32, 98, 302},
+				{38, 116, 356},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Lower,
+			tA:    blas.Trans,
+			d:     blas.Unit,
+			m:     2,
+			n:     3,
+			alpha: 2,
+			a: [][]float64{
+				{1, 0, 0},
+				{2, 4, 0},
+				{3, 5, 6},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+			},
+			ans: [][]float64{
+				{20, 62, 194},
+				{26, 80, 248},
+			},
+		},
+	} {
+		aFlat := flatten(test.a)
+		bFlat := flatten(test.b)
+		ansFlat := flatten(test.ans)
+		blasser.Dtrmm(test.s, test.ul, test.tA, test.d, test.m, test.n, test.alpha, aFlat, len(test.a[0]), bFlat, len(test.b[0]))
+		if !floats.EqualApprox(ansFlat, bFlat, 1e-14) {
+			t.Errorf("Case %v. Want %v, got %v.", i, ansFlat, bFlat)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/dtrmv.go b/vendor/gonum.org/v1/gonum/blas/testblas/dtrmv.go
new file mode 100644
index 00000000..8f3b6d35
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/dtrmv.go
@@ -0,0 +1,147 @@
+package testblas
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dtrmver interface {
+	Dtrmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, a []float64, lda int, x []float64, incX int)
+}
+
+func DtrmvTest(t *testing.T, blasser Dtrmver) {
+	for i, test := range []struct {
+		n   int
+		a   [][]float64
+		x   []float64
+		d   blas.Diag
+		ul  blas.Uplo
+		tA  blas.Transpose
+		ans []float64
+	}{
+		{
+			n:   1,
+			a:   [][]float64{{5}},
+			x:   []float64{2},
+			d:   blas.NonUnit,
+			ul:  blas.Upper,
+			tA:  blas.NoTrans,
+			ans: []float64{10},
+		},
+		{
+			n:   1,
+			a:   [][]float64{{5}},
+			x:   []float64{2},
+			d:   blas.Unit,
+			ul:  blas.Upper,
+			tA:  blas.NoTrans,
+			ans: []float64{2},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{5, 6, 7},
+				{0, 9, 10},
+				{0, 0, 13},
+			},
+			x:   []float64{3, 4, 5},
+			d:   blas.NonUnit,
+			ul:  blas.Upper,
+			tA:  blas.NoTrans,
+			ans: []float64{74, 86, 65},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{5, 6, 7},
+				{0, 9, 10},
+				{0, 0, 13},
+			},
+			x:   []float64{3, 4, 5},
+			d:   blas.Unit,
+			ul:  blas.Upper,
+			tA:  blas.NoTrans,
+			ans: []float64{62, 54, 5},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{5, 0, 0},
+				{6, 9, 0},
+				{7, 10, 13},
+			},
+			x:   []float64{3, 4, 5},
+			d:   blas.NonUnit,
+			ul:  blas.Lower,
+			tA:  blas.NoTrans,
+			ans: []float64{15, 54, 126},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{1, 0, 0},
+				{6, 1, 0},
+				{7, 10, 1},
+			},
+			x:   []float64{3, 4, 5},
+			d:   blas.Unit,
+			ul:  blas.Lower,
+			tA:  blas.NoTrans,
+			ans: []float64{3, 22, 66},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{5, 6, 7},
+				{0, 9, 10},
+				{0, 0, 13},
+			},
+			x:   []float64{3, 4, 5},
+			d:   blas.NonUnit,
+			ul:  blas.Upper,
+			tA:  blas.Trans,
+			ans: []float64{15, 54, 126},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{1, 6, 7},
+				{0, 1, 10},
+				{0, 0, 1},
+			},
+			x:   []float64{3, 4, 5},
+			d:   blas.Unit,
+			ul:  blas.Upper,
+			tA:  blas.Trans,
+			ans: []float64{3, 22, 66},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{5, 0, 0},
+				{6, 9, 0},
+				{7, 10, 13},
+			},
+			x:   []float64{3, 4, 5},
+			d:   blas.NonUnit,
+			ul:  blas.Lower,
+			tA:  blas.Trans,
+			ans: []float64{74, 86, 65},
+		},
+	} {
+		incTest := func(incX, extra int) {
+			aFlat := flatten(test.a)
+			x := makeIncremented(test.x, incX, extra)
+			blasser.Dtrmv(test.ul, test.tA, test.d, test.n, aFlat, test.n, x, incX)
+			ans := makeIncremented(test.ans, incX, extra)
+			if !floats.EqualApprox(x, ans, 1e-14) {
+				t.Errorf("Case %v, idx %v: Want %v, got %v.", i, incX, ans, x)
+			}
+		}
+		incTest(1, 3)
+		incTest(-3, 3)
+		incTest(4, 3)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/dtrmvbench.go b/vendor/gonum.org/v1/gonum/blas/testblas/dtrmvbench.go
new file mode 100644
index 00000000..c6b439e9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/dtrmvbench.go
@@ -0,0 +1,30 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testblas
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+func DtrmvBenchmark(b *testing.B, dtrmv Dtrmver, n, lda, incX int, ul blas.Uplo, tA blas.Transpose, d blas.Diag) {
+	rnd := rand.New(rand.NewSource(0))
+	a := make([]float64, n*lda)
+	for i := range a {
+		a[i] = rnd.Float64()
+	}
+
+	x := make([]float64, n*incX)
+	for i := range x {
+		x[i] = rnd.Float64()
+	}
+
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		dtrmv.Dtrmv(ul, tA, d, n, a, lda, x, incX)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/dtrsm.go b/vendor/gonum.org/v1/gonum/blas/testblas/dtrsm.go
new file mode 100644
index 00000000..9623397c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/dtrsm.go
@@ -0,0 +1,811 @@
+package testblas
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dtrsmer interface {
+	Dtrsm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int,
+		alpha float64, a []float64, lda int, b []float64, ldb int)
+}
+
+func DtrsmTest(t *testing.T, blasser Dtrsmer) {
+	for i, test := range []struct {
+		s     blas.Side
+		ul    blas.Uplo
+		tA    blas.Transpose
+		d     blas.Diag
+		m     int
+		n     int
+		alpha float64
+		a     [][]float64
+		b     [][]float64
+		ans   [][]float64
+	}{
+		{
+			s:     blas.Left,
+			ul:    blas.Upper,
+			tA:    blas.NoTrans,
+			d:     blas.NonUnit,
+			m:     3,
+			n:     2,
+			alpha: 2,
+			a: [][]float64{
+				{1, 2, 3},
+				{0, 4, 5},
+				{0, 0, 5},
+			},
+			b: [][]float64{
+				{3, 6},
+				{4, 7},
+				{5, 8},
+			},
+			ans: [][]float64{
+				{1, 3.4},
+				{-0.5, -0.5},
+				{2, 3.2},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Upper,
+			tA:    blas.NoTrans,
+			d:     blas.Unit,
+			m:     3,
+			n:     2,
+			alpha: 2,
+			a: [][]float64{
+				{1, 2, 3},
+				{0, 4, 5},
+				{0, 0, 5},
+			},
+			b: [][]float64{
+				{3, 6},
+				{4, 7},
+				{5, 8},
+			},
+			ans: [][]float64{
+				{60, 96},
+				{-42, -66},
+				{10, 16},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Upper,
+			tA:    blas.NoTrans,
+			d:     blas.NonUnit,
+			m:     3,
+			n:     4,
+			alpha: 2,
+			a: [][]float64{
+				{1, 2, 3},
+				{0, 4, 5},
+				{0, 0, 5},
+			},
+			b: [][]float64{
+				{3, 6, 2, 9},
+				{4, 7, 1, 3},
+				{5, 8, 9, 10},
+			},
+			ans: [][]float64{
+				{1, 3.4, 1.2, 13},
+				{-0.5, -0.5, -4, -3.5},
+				{2, 3.2, 3.6, 4},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Upper,
+			tA:    blas.NoTrans,
+			d:     blas.Unit,
+			m:     3,
+			n:     4,
+			alpha: 2,
+			a: [][]float64{
+				{1, 2, 3},
+				{0, 4, 5},
+				{0, 0, 5},
+			},
+			b: [][]float64{
+				{3, 6, 2, 9},
+				{4, 7, 1, 3},
+				{5, 8, 9, 10},
+			},
+			ans: [][]float64{
+				{60, 96, 126, 146},
+				{-42, -66, -88, -94},
+				{10, 16, 18, 20},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Lower,
+			tA:    blas.NoTrans,
+			d:     blas.NonUnit,
+			m:     3,
+			n:     2,
+			alpha: 3,
+			a: [][]float64{
+				{2, 0, 0},
+				{3, 4, 0},
+				{5, 6, 7},
+			},
+			b: [][]float64{
+				{3, 6},
+				{4, 7},
+				{5, 8},
+			},
+			ans: [][]float64{
+				{4.5, 9},
+				{-0.375, -1.5},
+				{-0.75, -12.0 / 7},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Lower,
+			tA:    blas.NoTrans,
+			d:     blas.Unit,
+			m:     3,
+			n:     2,
+			alpha: 3,
+			a: [][]float64{
+				{2, 0, 0},
+				{3, 4, 0},
+				{5, 6, 7},
+			},
+			b: [][]float64{
+				{3, 6},
+				{4, 7},
+				{5, 8},
+			},
+			ans: [][]float64{
+				{9, 18},
+				{-15, -33},
+				{60, 132},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Lower,
+			tA:    blas.NoTrans,
+			d:     blas.NonUnit,
+			m:     3,
+			n:     4,
+			alpha: 3,
+			a: [][]float64{
+				{2, 0, 0},
+				{3, 4, 0},
+				{5, 6, 7},
+			},
+			b: [][]float64{
+				{3, 6, 2, 9},
+				{4, 7, 1, 3},
+				{5, 8, 9, 10},
+			},
+			ans: [][]float64{
+				{4.5, 9, 3, 13.5},
+				{-0.375, -1.5, -1.5, -63.0 / 8},
+				{-0.75, -12.0 / 7, 3, 39.0 / 28},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Lower,
+			tA:    blas.NoTrans,
+			d:     blas.Unit,
+			m:     3,
+			n:     4,
+			alpha: 3,
+			a: [][]float64{
+				{2, 0, 0},
+				{3, 4, 0},
+				{5, 6, 7},
+			},
+			b: [][]float64{
+				{3, 6, 2, 9},
+				{4, 7, 1, 3},
+				{5, 8, 9, 10},
+			},
+			ans: [][]float64{
+				{9, 18, 6, 27},
+				{-15, -33, -15, -72},
+				{60, 132, 87, 327},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Upper,
+			tA:    blas.Trans,
+			d:     blas.NonUnit,
+			m:     3,
+			n:     2,
+			alpha: 3,
+			a: [][]float64{
+				{2, 3, 4},
+				{0, 5, 6},
+				{0, 0, 7},
+			},
+			b: [][]float64{
+				{3, 6},
+				{4, 7},
+				{5, 8},
+			},
+			ans: [][]float64{
+				{4.5, 9},
+				{-0.30, -1.2},
+				{-6.0 / 35, -24.0 / 35},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Upper,
+			tA:    blas.Trans,
+			d:     blas.Unit,
+			m:     3,
+			n:     2,
+			alpha: 3,
+			a: [][]float64{
+				{2, 3, 4},
+				{0, 5, 6},
+				{0, 0, 7},
+			},
+			b: [][]float64{
+				{3, 6},
+				{4, 7},
+				{5, 8},
+			},
+			ans: [][]float64{
+				{9, 18},
+				{-15, -33},
+				{69, 150},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Upper,
+			tA:    blas.Trans,
+			d:     blas.NonUnit,
+			m:     3,
+			n:     4,
+			alpha: 3,
+			a: [][]float64{
+				{2, 3, 4},
+				{0, 5, 6},
+				{0, 0, 7},
+			},
+			b: [][]float64{
+				{3, 6, 6, 7},
+				{4, 7, 8, 9},
+				{5, 8, 10, 11},
+			},
+			ans: [][]float64{
+				{4.5, 9, 9, 10.5},
+				{-0.3, -1.2, -0.6, -0.9},
+				{-6.0 / 35, -24.0 / 35, -12.0 / 35, -18.0 / 35},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Upper,
+			tA:    blas.Trans,
+			d:     blas.Unit,
+			m:     3,
+			n:     4,
+			alpha: 3,
+			a: [][]float64{
+				{2, 3, 4},
+				{0, 5, 6},
+				{0, 0, 7},
+			},
+			b: [][]float64{
+				{3, 6, 6, 7},
+				{4, 7, 8, 9},
+				{5, 8, 10, 11},
+			},
+			ans: [][]float64{
+				{9, 18, 18, 21},
+				{-15, -33, -30, -36},
+				{69, 150, 138, 165},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Lower,
+			tA:    blas.Trans,
+			d:     blas.NonUnit,
+			m:     3,
+			n:     2,
+			alpha: 3,
+			a: [][]float64{
+				{2, 0, 0},
+				{3, 4, 0},
+				{5, 6, 8},
+			},
+			b: [][]float64{
+				{3, 6},
+				{4, 7},
+				{5, 8},
+			},
+			ans: [][]float64{
+				{-0.46875, 0.375},
+				{0.1875, 0.75},
+				{1.875, 3},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Lower,
+			tA:    blas.Trans,
+			d:     blas.Unit,
+			m:     3,
+			n:     2,
+			alpha: 3,
+			a: [][]float64{
+				{2, 0, 0},
+				{3, 4, 0},
+				{5, 6, 8},
+			},
+			b: [][]float64{
+				{3, 6},
+				{4, 7},
+				{5, 8},
+			},
+			ans: [][]float64{
+				{168, 267},
+				{-78, -123},
+				{15, 24},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Lower,
+			tA:    blas.Trans,
+			d:     blas.NonUnit,
+			m:     3,
+			n:     4,
+			alpha: 3,
+			a: [][]float64{
+				{2, 0, 0},
+				{3, 4, 0},
+				{5, 6, 8},
+			},
+			b: [][]float64{
+				{3, 6, 2, 3},
+				{4, 7, 4, 5},
+				{5, 8, 6, 7},
+			},
+			ans: [][]float64{
+				{-0.46875, 0.375, -2.0625, -1.78125},
+				{0.1875, 0.75, -0.375, -0.1875},
+				{1.875, 3, 2.25, 2.625},
+			},
+		},
+		{
+			s:     blas.Left,
+			ul:    blas.Lower,
+			tA:    blas.Trans,
+			d:     blas.Unit,
+			m:     3,
+			n:     4,
+			alpha: 3,
+			a: [][]float64{
+				{2, 0, 0},
+				{3, 4, 0},
+				{5, 6, 8},
+			},
+			b: [][]float64{
+				{3, 6, 2, 3},
+				{4, 7, 4, 5},
+				{5, 8, 6, 7},
+			},
+			ans: [][]float64{
+				{168, 267, 204, 237},
+				{-78, -123, -96, -111},
+				{15, 24, 18, 21},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Upper,
+			tA:    blas.NoTrans,
+			d:     blas.NonUnit,
+			m:     4,
+			n:     3,
+			alpha: 3,
+			a: [][]float64{
+				{2, 3, 4},
+				{0, 5, 6},
+				{0, 0, 7},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+				{16, 17, 18},
+				{19, 20, 21},
+			},
+			ans: [][]float64{
+				{15, -2.4, -48.0 / 35},
+				{19.5, -3.3, -66.0 / 35},
+				{24, -4.2, -2.4},
+				{28.5, -5.1, -102.0 / 35},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Upper,
+			tA:    blas.NoTrans,
+			d:     blas.Unit,
+			m:     4,
+			n:     3,
+			alpha: 3,
+			a: [][]float64{
+				{2, 3, 4},
+				{0, 5, 6},
+				{0, 0, 8},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+				{16, 17, 18},
+				{19, 20, 21},
+			},
+			ans: [][]float64{
+				{30, -57, 258},
+				{39, -75, 339},
+				{48, -93, 420},
+				{57, -111, 501},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Upper,
+			tA:    blas.NoTrans,
+			d:     blas.NonUnit,
+			m:     2,
+			n:     3,
+			alpha: 3,
+			a: [][]float64{
+				{2, 3, 4},
+				{0, 5, 6},
+				{0, 0, 7},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+			},
+			ans: [][]float64{
+				{15, -2.4, -48.0 / 35},
+				{19.5, -3.3, -66.0 / 35},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Upper,
+			tA:    blas.NoTrans,
+			d:     blas.Unit,
+			m:     2,
+			n:     3,
+			alpha: 3,
+			a: [][]float64{
+				{2, 3, 4},
+				{0, 5, 6},
+				{0, 0, 8},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+			},
+			ans: [][]float64{
+				{30, -57, 258},
+				{39, -75, 339},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Lower,
+			tA:    blas.NoTrans,
+			d:     blas.NonUnit,
+			m:     4,
+			n:     3,
+			alpha: 3,
+			a: [][]float64{
+				{2, 0, 0},
+				{3, 5, 0},
+				{4, 6, 8},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+				{16, 17, 18},
+				{19, 20, 21},
+			},
+			ans: [][]float64{
+				{4.2, 1.2, 4.5},
+				{5.775, 1.65, 5.625},
+				{7.35, 2.1, 6.75},
+				{8.925, 2.55, 7.875},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Lower,
+			tA:    blas.NoTrans,
+			d:     blas.Unit,
+			m:     4,
+			n:     3,
+			alpha: 3,
+			a: [][]float64{
+				{2, 0, 0},
+				{3, 5, 0},
+				{4, 6, 8},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+				{16, 17, 18},
+				{19, 20, 21},
+			},
+			ans: [][]float64{
+				{435, -183, 36},
+				{543, -228, 45},
+				{651, -273, 54},
+				{759, -318, 63},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Lower,
+			tA:    blas.NoTrans,
+			d:     blas.NonUnit,
+			m:     2,
+			n:     3,
+			alpha: 3,
+			a: [][]float64{
+				{2, 0, 0},
+				{3, 5, 0},
+				{4, 6, 8},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+			},
+			ans: [][]float64{
+				{4.2, 1.2, 4.5},
+				{5.775, 1.65, 5.625},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Lower,
+			tA:    blas.NoTrans,
+			d:     blas.Unit,
+			m:     2,
+			n:     3,
+			alpha: 3,
+			a: [][]float64{
+				{2, 0, 0},
+				{3, 5, 0},
+				{4, 6, 8},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+			},
+			ans: [][]float64{
+				{435, -183, 36},
+				{543, -228, 45},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Upper,
+			tA:    blas.Trans,
+			d:     blas.NonUnit,
+			m:     4,
+			n:     3,
+			alpha: 3,
+			a: [][]float64{
+				{2, 3, 4},
+				{0, 5, 6},
+				{0, 0, 8},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+				{16, 17, 18},
+				{19, 20, 21},
+			},
+			ans: [][]float64{
+				{4.2, 1.2, 4.5},
+				{5.775, 1.65, 5.625},
+				{7.35, 2.1, 6.75},
+				{8.925, 2.55, 7.875},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Upper,
+			tA:    blas.Trans,
+			d:     blas.Unit,
+			m:     4,
+			n:     3,
+			alpha: 3,
+			a: [][]float64{
+				{2, 3, 4},
+				{0, 5, 6},
+				{0, 0, 8},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+				{16, 17, 18},
+				{19, 20, 21},
+			},
+			ans: [][]float64{
+				{435, -183, 36},
+				{543, -228, 45},
+				{651, -273, 54},
+				{759, -318, 63},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Upper,
+			tA:    blas.Trans,
+			d:     blas.NonUnit,
+			m:     2,
+			n:     3,
+			alpha: 3,
+			a: [][]float64{
+				{2, 3, 4},
+				{0, 5, 6},
+				{0, 0, 8},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+			},
+			ans: [][]float64{
+				{4.2, 1.2, 4.5},
+				{5.775, 1.65, 5.625},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Upper,
+			tA:    blas.Trans,
+			d:     blas.Unit,
+			m:     2,
+			n:     3,
+			alpha: 3,
+			a: [][]float64{
+				{2, 3, 4},
+				{0, 5, 6},
+				{0, 0, 8},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+			},
+			ans: [][]float64{
+				{435, -183, 36},
+				{543, -228, 45},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Lower,
+			tA:    blas.Trans,
+			d:     blas.NonUnit,
+			m:     4,
+			n:     3,
+			alpha: 3,
+			a: [][]float64{
+				{2, 0, 0},
+				{3, 5, 0},
+				{4, 6, 8},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+				{16, 17, 18},
+				{19, 20, 21},
+			},
+			ans: [][]float64{
+				{15, -2.4, -1.2},
+				{19.5, -3.3, -1.65},
+				{24, -4.2, -2.1},
+				{28.5, -5.1, -2.55},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Lower,
+			tA:    blas.Trans,
+			d:     blas.Unit,
+			m:     4,
+			n:     3,
+			alpha: 3,
+			a: [][]float64{
+				{2, 0, 0},
+				{3, 5, 0},
+				{4, 6, 8},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+				{16, 17, 18},
+				{19, 20, 21},
+			},
+			ans: [][]float64{
+				{30, -57, 258},
+				{39, -75, 339},
+				{48, -93, 420},
+				{57, -111, 501},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Lower,
+			tA:    blas.Trans,
+			d:     blas.NonUnit,
+			m:     2,
+			n:     3,
+			alpha: 3,
+			a: [][]float64{
+				{2, 0, 0},
+				{3, 5, 0},
+				{4, 6, 8},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+			},
+			ans: [][]float64{
+				{15, -2.4, -1.2},
+				{19.5, -3.3, -1.65},
+			},
+		},
+		{
+			s:     blas.Right,
+			ul:    blas.Lower,
+			tA:    blas.Trans,
+			d:     blas.Unit,
+			m:     2,
+			n:     3,
+			alpha: 3,
+			a: [][]float64{
+				{2, 0, 0},
+				{3, 5, 0},
+				{4, 6, 8},
+			},
+			b: [][]float64{
+				{10, 11, 12},
+				{13, 14, 15},
+			},
+			ans: [][]float64{
+				{30, -57, 258},
+				{39, -75, 339},
+			},
+		},
+	} {
+		aFlat := flatten(test.a)
+		bFlat := flatten(test.b)
+		ansFlat := flatten(test.ans)
+		var lda int
+		if test.s == blas.Left {
+			lda = test.m
+		} else {
+			lda = test.n
+		}
+		blasser.Dtrsm(test.s, test.ul, test.tA, test.d, test.m, test.n, test.alpha, aFlat, lda, bFlat, test.n)
+		if !floats.EqualApprox(ansFlat, bFlat, 1e-13) {
+			t.Errorf("Case %v: Want %v, got %v.", i, ansFlat, bFlat)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/dtrsv.go b/vendor/gonum.org/v1/gonum/blas/testblas/dtrsv.go
new file mode 100644
index 00000000..1638177c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/dtrsv.go
@@ -0,0 +1,144 @@
+package testblas
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dtrsver interface {
+	Dtrsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, a []float64, lda int, x []float64, incX int)
+}
+
+func DtrsvTest(t *testing.T, blasser Dtrsver) {
+	for i, test := range []struct {
+		n   int
+		a   [][]float64
+		ul  blas.Uplo
+		tA  blas.Transpose
+		d   blas.Diag
+		x   []float64
+		ans []float64
+	}{
+		{
+			n: 3,
+			a: [][]float64{
+				{1, 2, 3},
+				{0, 8, 15},
+				{0, 0, 8},
+			},
+			ul:  blas.Upper,
+			tA:  blas.NoTrans,
+			d:   blas.NonUnit,
+			x:   []float64{5, 6, 7},
+			ans: []float64{4.15625, -0.890625, 0.875},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{1, 2, 3},
+				{0, 1, 15},
+				{0, 0, 1},
+			},
+			ul:  blas.Upper,
+			tA:  blas.NoTrans,
+			d:   blas.Unit,
+			x:   []float64{5, 6, 7},
+			ans: []float64{182, -99, 7},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{1, 0, 0},
+				{2, 8, 0},
+				{3, 15, 8},
+			},
+			ul:  blas.Lower,
+			tA:  blas.NoTrans,
+			d:   blas.NonUnit,
+			x:   []float64{5, 6, 7},
+			ans: []float64{5, -0.5, -0.0625},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{1, 0, 0},
+				{2, 8, 0},
+				{3, 15, 8},
+			},
+			ul:  blas.Lower,
+			tA:  blas.NoTrans,
+			d:   blas.Unit,
+			x:   []float64{5, 6, 7},
+			ans: []float64{5, -4, 52},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{1, 2, 3},
+				{0, 8, 15},
+				{0, 0, 8},
+			},
+			ul:  blas.Upper,
+			tA:  blas.Trans,
+			d:   blas.NonUnit,
+			x:   []float64{5, 6, 7},
+			ans: []float64{5, -0.5, -0.0625},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{1, 2, 3},
+				{0, 8, 15},
+				{0, 0, 8},
+			},
+			ul:  blas.Upper,
+			tA:  blas.Trans,
+			d:   blas.Unit,
+			x:   []float64{5, 6, 7},
+			ans: []float64{5, -4, 52},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{1, 0, 0},
+				{2, 8, 0},
+				{3, 15, 8},
+			},
+			ul:  blas.Lower,
+			tA:  blas.Trans,
+			d:   blas.NonUnit,
+			x:   []float64{5, 6, 7},
+			ans: []float64{4.15625, -0.890625, 0.875},
+		},
+		{
+			n: 3,
+			a: [][]float64{
+				{1, 0, 0},
+				{2, 1, 0},
+				{3, 15, 1},
+			},
+			ul:  blas.Lower,
+			tA:  blas.Trans,
+			d:   blas.Unit,
+			x:   []float64{5, 6, 7},
+			ans: []float64{182, -99, 7},
+		},
+	} {
+		incTest := func(incX, extra int) {
+			aFlat := flatten(test.a)
+			x := makeIncremented(test.x, incX, extra)
+			blasser.Dtrsv(test.ul, test.tA, test.d, test.n, aFlat, test.n, x, incX)
+			ans := makeIncremented(test.ans, incX, extra)
+			if !floats.EqualApprox(x, ans, 1e-14) {
+				t.Errorf("Case %v, incX = %v: Want %v, got %v.", i, incX, ans, x)
+			}
+		}
+		incTest(1, 0)
+		incTest(-2, 0)
+		incTest(3, 0)
+		incTest(-3, 8)
+		incTest(4, 2)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/dtxmv.go b/vendor/gonum.org/v1/gonum/blas/testblas/dtxmv.go
new file mode 100644
index 00000000..c55da3bd
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/dtxmv.go
@@ -0,0 +1,145 @@
+package testblas
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+type Dtxmver interface {
+	Dtrmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, a []float64, lda int, x []float64, incX int)
+	Dtbmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n, k int, a []float64, lda int, x []float64, incX int)
+	Dtpmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, a []float64, x []float64, incX int)
+}
+
+type vec struct {
+	data []float64
+	inc  int
+}
+
+var cases = []struct {
+	n, k       int
+	ul         blas.Uplo
+	d          blas.Diag
+	ldab       int
+	tr, tb, tp []float64
+	ins        []vec
+	solNoTrans []float64
+	solTrans   []float64
+}{
+	{
+		n:    3,
+		k:    1,
+		ul:   blas.Upper,
+		d:    blas.NonUnit,
+		tr:   []float64{1, 2, 0, 0, 3, 4, 0, 0, 5},
+		tb:   []float64{1, 2, 3, 4, 5, 0},
+		ldab: 2,
+		tp:   []float64{1, 2, 0, 3, 4, 5},
+		ins: []vec{
+			{[]float64{2, 3, 4}, 1},
+			{[]float64{2, 1, 3, 1, 4}, 2},
+			{[]float64{4, 1, 3, 1, 2}, -2},
+		},
+		solNoTrans: []float64{8, 25, 20},
+		solTrans:   []float64{2, 13, 32},
+	},
+	{
+		n:    3,
+		k:    1,
+		ul:   blas.Upper,
+		d:    blas.Unit,
+		tr:   []float64{1, 2, 0, 0, 3, 4, 0, 0, 5},
+		tb:   []float64{1, 2, 3, 4, 5, 0},
+		ldab: 2,
+		tp:   []float64{1, 2, 0, 3, 4, 5},
+		ins: []vec{
+			{[]float64{2, 3, 4}, 1},
+			{[]float64{2, 1, 3, 1, 4}, 2},
+			{[]float64{4, 1, 3, 1, 2}, -2},
+		},
+		solNoTrans: []float64{8, 19, 4},
+		solTrans:   []float64{2, 7, 16},
+	},
+	{
+		n:    3,
+		k:    1,
+		ul:   blas.Lower,
+		d:    blas.NonUnit,
+		tr:   []float64{1, 0, 0, 2, 3, 0, 0, 4, 5},
+		tb:   []float64{0, 1, 2, 3, 4, 5},
+		ldab: 2,
+		tp:   []float64{1, 2, 3, 0, 4, 5},
+		ins: []vec{
+			{[]float64{2, 3, 4}, 1},
+			{[]float64{2, 1, 3, 1, 4}, 2},
+			{[]float64{4, 1, 3, 1, 2}, -2},
+		},
+		solNoTrans: []float64{2, 13, 32},
+		solTrans:   []float64{8, 25, 20},
+	},
+	{
+		n:    3,
+		k:    1,
+		ul:   blas.Lower,
+		d:    blas.Unit,
+		tr:   []float64{1, 0, 0, 2, 3, 0, 0, 4, 5},
+		tb:   []float64{0, 1, 2, 3, 4, 5},
+		ldab: 2,
+		tp:   []float64{1, 2, 3, 0, 4, 5},
+		ins: []vec{
+			{[]float64{2, 3, 4}, 1},
+			{[]float64{2, 1, 3, 1, 4}, 2},
+			{[]float64{4, 1, 3, 1, 2}, -2},
+		},
+		solNoTrans: []float64{2, 7, 16},
+		solTrans:   []float64{8, 19, 4},
+	},
+}
+
+func DtxmvTest(t *testing.T, blasser Dtxmver) {
+
+	for nc, c := range cases {
+		for nx, x := range c.ins {
+			in := make([]float64, len(x.data))
+			copy(in, x.data)
+			blasser.Dtrmv(c.ul, blas.NoTrans, c.d, c.n, c.tr, c.n, in, x.inc)
+			if !dStridedSliceTolEqual(c.n, in, x.inc, c.solNoTrans, 1) {
+				t.Error("Wrong Dtrmv result for: NoTrans  in Case:", nc, "input:", nx)
+			}
+
+			in = make([]float64, len(x.data))
+			copy(in, x.data)
+			blasser.Dtrmv(c.ul, blas.Trans, c.d, c.n, c.tr, c.n, in, x.inc)
+			if !dStridedSliceTolEqual(c.n, in, x.inc, c.solTrans, 1) {
+				t.Error("Wrong Dtrmv result for: Trans in Case:", nc, "input:", nx)
+			}
+			in = make([]float64, len(x.data))
+			copy(in, x.data)
+			blasser.Dtbmv(c.ul, blas.NoTrans, c.d, c.n, c.k, c.tb, c.ldab, in, x.inc)
+			if !dStridedSliceTolEqual(c.n, in, x.inc, c.solNoTrans, 1) {
+				t.Error("Wrong Dtbmv result for: NoTrans  in Case:", nc, "input:", nx)
+			}
+
+			in = make([]float64, len(x.data))
+			copy(in, x.data)
+			blasser.Dtbmv(c.ul, blas.Trans, c.d, c.n, c.k, c.tb, c.ldab, in, x.inc)
+			if !dStridedSliceTolEqual(c.n, in, x.inc, c.solTrans, 1) {
+				t.Error("Wrong Dtbmv result for: Trans in Case:", nc, "input:", nx)
+			}
+			in = make([]float64, len(x.data))
+			copy(in, x.data)
+			blasser.Dtpmv(c.ul, blas.NoTrans, c.d, c.n, c.tp, in, x.inc)
+			if !dStridedSliceTolEqual(c.n, in, x.inc, c.solNoTrans, 1) {
+				t.Error("Wrong Dtpmv result for:  NoTrans  in Case:", nc, "input:", nx)
+			}
+
+			in = make([]float64, len(x.data))
+			copy(in, x.data)
+			blasser.Dtpmv(c.ul, blas.Trans, c.d, c.n, c.tp, in, x.inc)
+			if !dStridedSliceTolEqual(c.n, in, x.inc, c.solTrans, 1) {
+				t.Error("Wrong Dtpmv result for: Trans in Case:", nc, "input:", nx)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/dzasum.go b/vendor/gonum.org/v1/gonum/blas/testblas/dzasum.go
new file mode 100644
index 00000000..ab376a4c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/dzasum.go
@@ -0,0 +1,58 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testblas
+
+import (
+	"math/cmplx"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dzasumer interface {
+	Dzasum(n int, x []complex128, incX int) float64
+}
+
+func DzasumTest(t *testing.T, impl Dzasumer) {
+	const tol = 1e-14
+	rnd := rand.New(rand.NewSource(1))
+	for _, n := range []int{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 50, 100} {
+		for _, incX := range []int{-5, 1, 2, 10} {
+			aincX := abs(incX)
+			var x []complex128
+			if n > 0 {
+				x = make([]complex128, (n-1)*aincX+1)
+			}
+			for i := range x {
+				x[i] = cmplx.NaN()
+			}
+			for i := 0; i < n; i++ {
+				re := float64(2*i + 1)
+				if rnd.Intn(2) == 0 {
+					re *= -1
+				}
+				im := float64(2 * (i + 1))
+				if rnd.Intn(2) == 0 {
+					im *= -1
+				}
+				x[i*aincX] = complex(re, im)
+			}
+
+			want := float64(n * (2*n + 1))
+			got := impl.Dzasum(n, x, incX)
+
+			if incX < 0 {
+				if got != 0 {
+					t.Errorf("Case n=%v,incX=%v: non-zero result when incX < 0. got %v", n, incX, got)
+				}
+				continue
+			}
+			if !floats.EqualWithinAbsOrRel(got, want, tol, tol) {
+				t.Errorf("Case n=%v,incX=%v: unexpected result. want %v, got %v", n, incX, want, got)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/dznrm2.go b/vendor/gonum.org/v1/gonum/blas/testblas/dznrm2.go
new file mode 100644
index 00000000..3742347a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/dznrm2.go
@@ -0,0 +1,137 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testblas
+
+import (
+	"fmt"
+	"math"
+	"math/cmplx"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dznrm2er interface {
+	Dznrm2(n int, x []complex128, incX int) float64
+	Dnrm2er
+}
+
+func Dznrm2Test(t *testing.T, impl Dznrm2er) {
+	tol := 1e-12
+	for tc, test := range []struct {
+		x    []complex128
+		want float64
+	}{
+		{
+			x:    nil,
+			want: 0,
+		},
+		{
+			x:    []complex128{1 + 2i},
+			want: 2.2360679774998,
+		},
+		{
+			x:    []complex128{1 + 2i, 3 + 4i},
+			want: 5.4772255750517,
+		},
+		{
+			x:    []complex128{1 + 2i, 3 + 4i, 5 + 6i},
+			want: 9.5393920141695,
+		},
+		{
+			x:    []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i},
+			want: 1.4282856857086e+01,
+		},
+		{
+			x:    []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i},
+			want: 1.9621416870349e+01,
+		},
+		{
+			x:    []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i},
+			want: 2.5495097567964e+01,
+		},
+		{
+			x:    []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i},
+			want: 3.1859064644148e+01,
+		},
+		{
+			x:    []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i},
+			want: 3.8678159211627e+01,
+		},
+		{
+			x:    []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i},
+			want: 4.5923850012820e+01,
+		},
+		{
+			x:    []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i, 19 + 20i},
+			want: 5.3572380943915e+01,
+		},
+		{
+			x:    []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i, 19 + 20i, 21 + 22i},
+			want: 6.1603571325046e+01,
+		},
+		{
+			x:    []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i, 19 + 20i, 21 + 22i, 23 + 24i},
+			want: 70,
+		},
+	} {
+		n := len(test.x)
+		for _, incX := range []int{-10, -1, 1, 2, 9, 17} {
+			x := makeZVector(test.x, incX)
+			xCopy := make([]complex128, len(x))
+			copy(xCopy, x)
+
+			got := impl.Dznrm2(n, x, incX)
+
+			prefix := fmt.Sprintf("Case %v (n=%v,incX=%v):", tc, n, incX)
+
+			if !zsame(x, xCopy) {
+				t.Errorf("%v: unexpected modification of x", prefix)
+			}
+
+			if incX < 0 {
+				if got != 0 {
+					t.Errorf("%v: non-zero result when incX < 0. got %v", prefix, got)
+				}
+				continue
+			}
+
+			if !floats.EqualWithinAbsOrRel(test.want, got, tol, tol) {
+				t.Errorf("%v: unexpected result. want %v, got %v", prefix, test.want, got)
+			}
+		}
+	}
+
+	tol = 1e-14
+	rnd := rand.New(rand.NewSource(1))
+	for _, n := range []int{10, 50, 100} {
+		for _, incX := range []int{1, 2, 10} {
+			re := make([]float64, n)
+			for i := range re {
+				re[i] = rnd.NormFloat64()
+			}
+			im := make([]float64, n)
+			for i := range im {
+				im[i] = rnd.NormFloat64()
+			}
+			want := math.Hypot(impl.Dnrm2(n, re, 1), impl.Dnrm2(n, im, 1))
+
+			x := make([]complex128, (n-1)*incX+1)
+			for i := range x {
+				x[i] = cmplx.NaN()
+			}
+			for i := range re {
+				x[i*incX] = complex(re[i], im[i])
+			}
+
+			got := impl.Dznrm2(n, x, incX)
+
+			if !floats.EqualWithinAbsOrRel(want, got, tol, tol) {
+				t.Errorf("Case n=%v,incX=%v: unexpected result using Dnrm2. want %v, got %v", n, incX, want, got)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/izamax.go b/vendor/gonum.org/v1/gonum/blas/testblas/izamax.go
new file mode 100644
index 00000000..76798c7a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/izamax.go
@@ -0,0 +1,47 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testblas
+
+import (
+	"math/cmplx"
+	"math/rand"
+	"testing"
+)
+
+type Izamaxer interface {
+	Izamax(n int, x []complex128, incX int) int
+}
+
+func IzamaxTest(t *testing.T, impl Izamaxer) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, n := range []int{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 50, 100} {
+		for _, incX := range []int{-5, 1, 2, 10} {
+			aincX := abs(incX)
+			var x []complex128
+			if n > 0 {
+				x = make([]complex128, (n-1)*aincX+1)
+			}
+			for i := range x {
+				x[i] = cmplx.NaN()
+			}
+			for i := 0; i < n; i++ {
+				re := 2*rnd.Float64() - 1
+				im := 2*rnd.Float64() - 1
+				x[i*aincX] = complex(re, im)
+			}
+
+			want := -1
+			if incX > 0 && n > 0 {
+				want = rnd.Intn(n)
+				x[want*incX] = 10 + 10i
+			}
+			got := impl.Izamax(n, x, incX)
+
+			if got != want {
+				t.Errorf("Case n=%v,incX=%v: unexpected result. want %v, got %v", n, incX, want, got)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/level1double.go b/vendor/gonum.org/v1/gonum/blas/testblas/level1double.go
new file mode 100644
index 00000000..8673891f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/level1double.go
@@ -0,0 +1,2048 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testblas
+
+import (
+	"fmt"
+	"log"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/floats"
+
+	"math"
+	"testing"
+)
+
+type DoubleOneVectorCase struct {
+	Name       string
+	X          []float64
+	Incx       int
+	N          int
+	Panic      bool
+	Dasum      float64
+	Dnrm2      float64
+	Idamax     int
+	DscalCases []DScalCase
+}
+
+type DScalCase struct {
+	Alpha float64
+	Ans   []float64
+	Name  string
+}
+
+var DoubleOneVectorCases = []DoubleOneVectorCase{
+	{
+		Name:   "AllPositive",
+		X:      []float64{6, 5, 4, 2, 6},
+		Incx:   1,
+		N:      5,
+		Panic:  false,
+		Dasum:  23,
+		Dnrm2:  10.81665382639196787935766380241148783875388972153573863813135,
+		Idamax: 0,
+		DscalCases: []DScalCase{
+			{
+				Alpha: 0,
+				Ans:   []float64{0, 0, 0, 0, 0},
+			},
+			{
+				Alpha: 1,
+				Ans:   []float64{6, 5, 4, 2, 6},
+			},
+			{
+				Alpha: -2,
+				Ans:   []float64{-12, -10, -8, -4, -12},
+			},
+		},
+	},
+	{
+		Name:   "LeadingZero",
+		X:      []float64{0, 1},
+		Incx:   1,
+		N:      2,
+		Panic:  false,
+		Dasum:  1,
+		Dnrm2:  1,
+		Idamax: 1,
+		DscalCases: []DScalCase{
+			{
+				Alpha: 0,
+				Ans:   []float64{0, 0},
+			},
+			{
+				Alpha: 1,
+				Ans:   []float64{0, 1},
+			},
+			{
+				Alpha: -2,
+				Ans:   []float64{0, -2},
+			},
+		},
+	},
+	{
+		Name:   "MaxInMiddle",
+		X:      []float64{6, 5, 9, 0, 6},
+		Incx:   1,
+		N:      5,
+		Panic:  false,
+		Dasum:  26,
+		Dnrm2:  13.34166406412633371248943627250846646911846482744007727141318,
+		Idamax: 2,
+		DscalCases: []DScalCase{
+			{
+				Alpha: -2,
+				Ans:   []float64{-12, -10, -18, 0, -12},
+			},
+		},
+	},
+	{
+		Name:   "MaxAtEnd",
+		X:      []float64{6, 5, -9, 0, 10},
+		Incx:   1,
+		N:      5,
+		Panic:  false,
+		Dasum:  30,
+		Dnrm2:  15.55634918610404553681857596630667886426639062914642880494347,
+		Idamax: 4,
+		DscalCases: []DScalCase{
+			{
+				Alpha: -2,
+				Ans:   []float64{-12, -10, 18, 0, -20},
+			},
+		},
+	},
+	{
+		Name:   "AllNegative",
+		X:      []float64{-6, -5, -4, -2, -6},
+		Incx:   1,
+		N:      5,
+		Panic:  false,
+		Dasum:  23,
+		Dnrm2:  10.81665382639196787935766380241148783875388972153573863813135,
+		Idamax: 0,
+		DscalCases: []DScalCase{
+			{
+				Alpha: -2,
+				Ans:   []float64{12, 10, 8, 4, 12},
+			},
+		},
+	},
+	{
+		Name:   "AllMixed",
+		X:      []float64{-6, 5, 4, -2, -6},
+		Incx:   1,
+		N:      5,
+		Panic:  false,
+		Dasum:  23,
+		Dnrm2:  10.81665382639196787935766380241148783875388972153573863813135,
+		Idamax: 0,
+		DscalCases: []DScalCase{
+			{
+				Alpha: -2,
+				Ans:   []float64{12, -10, -8, 4, 12},
+			},
+		},
+	},
+	{
+		Name:   "ZeroN",
+		X:      []float64{-6, 5, 4, -2, -6},
+		Incx:   1,
+		N:      0,
+		Panic:  false,
+		Dasum:  0,
+		Dnrm2:  0,
+		Idamax: -1,
+		DscalCases: []DScalCase{
+			{
+				Alpha: -2,
+				Ans:   []float64{-6, 5, 4, -2, -6},
+			},
+		},
+	},
+	{
+		Name:   "OneN",
+		X:      []float64{-6, 5, 4, -2, -6},
+		Incx:   1,
+		N:      1,
+		Panic:  false,
+		Dasum:  6,
+		Dnrm2:  6,
+		Idamax: 0,
+		DscalCases: []DScalCase{
+			{
+				Alpha: -2,
+				Ans:   []float64{12, 5, 4, -2, -6},
+			},
+		},
+	},
+	{
+		Name:   "PositiveExactInc",
+		X:      []float64{-6, 5, 10, -2, -5},
+		Incx:   2,
+		N:      3,
+		Panic:  false,
+		Dasum:  21,
+		Dnrm2:  12.68857754044952038019377274608948979173952662752515253090272,
+		Idamax: 1,
+		DscalCases: []DScalCase{
+			{
+				Alpha: -2,
+				Ans:   []float64{12, 5, -20, -2, 10},
+			},
+		},
+	},
+	{
+		Name:   "PositiveOffInc",
+		X:      []float64{-6, 5, 4, -2, -6, 8, 10, 11},
+		Incx:   3,
+		N:      3,
+		Panic:  false,
+		Dasum:  18,
+		Dnrm2:  11.83215956619923208513465658312323409683100246158868064575943,
+		Idamax: 2,
+		DscalCases: []DScalCase{
+			{
+				Alpha: -2,
+				Ans:   []float64{12, 5, 4, 4, -6, 8, -20, 11},
+			},
+		},
+	},
+	{
+		Name:   "PositiveShortInc",
+		X:      []float64{-6, 5, 4, -2, -6, 8, 10, 11},
+		Incx:   3,
+		N:      2,
+		Panic:  false,
+		Dasum:  8,
+		Dnrm2:  6.324555320336758663997787088865437067439110278650433653715009,
+		Idamax: 0,
+		DscalCases: []DScalCase{
+			{
+				Alpha: -2,
+				Ans:   []float64{12, 5, 4, 4, -6, 8, 10, 11},
+			},
+		},
+	},
+	{
+		Name:   "NegativeInc",
+		X:      []float64{-6, 5, 4, -2, -6},
+		Incx:   -1,
+		N:      5,
+		Panic:  false,
+		Dasum:  0,
+		Dnrm2:  0,
+		Idamax: -1,
+		DscalCases: []DScalCase{
+			{
+				Alpha: -2,
+				Ans:   []float64{-6, 5, 4, -2, -6},
+			},
+		},
+	},
+	{
+		Name:   "NegativeExactInc",
+		X:      []float64{-6, 5, 4, -2, -6},
+		Incx:   -2,
+		N:      3,
+		Panic:  false,
+		Dasum:  0,
+		Dnrm2:  0,
+		Idamax: -1,
+		DscalCases: []DScalCase{
+			{
+				Alpha: -2,
+				Ans:   []float64{-6, 5, 4, -2, -6},
+			},
+		},
+	},
+	{
+		Name:   "NegativeOffInc",
+		X:      []float64{-6, 5, 4, -2, -6, 8, 10, 11},
+		Incx:   -3,
+		N:      2,
+		Panic:  false,
+		Dasum:  0,
+		Dnrm2:  0,
+		Idamax: -1,
+		DscalCases: []DScalCase{
+			{
+				Alpha: -2,
+				Ans:   []float64{-6, 5, 4, -2, -6, 8, 10, 11},
+			},
+		},
+	},
+	{
+		Name:   "NegativeShortInc",
+		X:      []float64{-6, 5, 4, -2, -6, 8, 10, 11},
+		Incx:   -3,
+		N:      2,
+		Panic:  false,
+		Dasum:  0,
+		Dnrm2:  0,
+		Idamax: -1,
+		DscalCases: []DScalCase{
+			{
+				Alpha: -2,
+				Ans:   []float64{-6, 5, 4, -2, -6, 8, 10, 11},
+			},
+		},
+	},
+	{
+		Name:  "NegativeN",
+		X:     []float64{-6, 5, 4, -2, -6},
+		Incx:  2,
+		N:     -5,
+		Panic: true,
+		DscalCases: []DScalCase{
+			{
+				Alpha: -2,
+				Ans:   []float64{-6, 5, 4, -2, -6},
+			},
+		},
+	},
+	{
+		Name:  "ZeroInc",
+		X:     []float64{-6, 5, 4, -2, -6},
+		Incx:  0,
+		N:     5,
+		Panic: true,
+		DscalCases: []DScalCase{
+			{
+				Alpha: -2,
+				Ans:   []float64{-6, 5, 4, -2, -6},
+			},
+		},
+	},
+	{
+		Name:  "OutOfBounds",
+		X:     []float64{-6, 5, 4, -2, -6},
+		Incx:  2,
+		N:     6,
+		Panic: true,
+		DscalCases: []DScalCase{
+			{
+				Alpha: -2,
+				Ans:   []float64{-6, 5, 4, -2, -6},
+			},
+		},
+	},
+	{
+		Name:   "NegativeOutOfBounds",
+		X:      []float64{-6, 5, 4, -2, -6},
+		Incx:   -2,
+		N:      6,
+		Panic:  false,
+		Dasum:  0,
+		Dnrm2:  0,
+		Idamax: -1,
+		DscalCases: []DScalCase{
+			{
+				Alpha: -2,
+				Ans:   []float64{-6, 5, 4, -2, -6},
+			},
+		},
+	},
+	{
+		Name:   "NaN",
+		X:      []float64{math.NaN(), 2.0},
+		Incx:   1,
+		N:      2,
+		Panic:  false,
+		Dasum:  math.NaN(),
+		Dnrm2:  math.NaN(),
+		Idamax: 0,
+		DscalCases: []DScalCase{
+			{
+				Alpha: -2,
+				Ans:   []float64{math.NaN(), -4.0},
+			},
+			{
+				Alpha: 0,
+				Ans:   []float64{0, 0},
+			},
+		},
+	},
+	{
+		Name:   "NaNInc",
+		X:      []float64{math.NaN(), math.NaN(), 2.0},
+		Incx:   2,
+		N:      2,
+		Panic:  false,
+		Dasum:  math.NaN(),
+		Dnrm2:  math.NaN(),
+		Idamax: 0,
+		DscalCases: []DScalCase{
+			{
+				Alpha: -2,
+				Ans:   []float64{math.NaN(), math.NaN(), -4.0},
+			},
+			{
+				Alpha: 0,
+				Ans:   []float64{0, math.NaN(), 0},
+			},
+		},
+	},
+	{
+		Name:   "Empty",
+		X:      []float64{},
+		Incx:   1,
+		N:      0,
+		Panic:  false,
+		Dasum:  0,
+		Dnrm2:  0,
+		Idamax: -1,
+		DscalCases: []DScalCase{
+			{
+				Alpha: -2,
+				Ans:   []float64{},
+			},
+			{
+				Alpha: 0,
+				Ans:   []float64{},
+			},
+		},
+	},
+	{
+		Name:   "EmptyZeroInc",
+		X:      []float64{},
+		Incx:   0,
+		N:      0,
+		Panic:  true,
+		Dasum:  0,
+		Dnrm2:  0,
+		Idamax: -1,
+		DscalCases: []DScalCase{
+			{
+				Alpha: -2,
+				Ans:   []float64{},
+			},
+			{
+				Alpha: 0,
+				Ans:   []float64{},
+			},
+		},
+	},
+	{
+		Name:   "EmptyReverse",
+		X:      []float64{},
+		Incx:   -1,
+		N:      0,
+		Panic:  false,
+		Dasum:  0,
+		Dnrm2:  0,
+		Idamax: -1,
+		DscalCases: []DScalCase{
+			{
+				Alpha: -2,
+				Ans:   []float64{},
+			},
+			{
+				Alpha: 0,
+				Ans:   []float64{},
+			},
+		},
+	},
+	{
+		Name:   "MultiInf",
+		X:      []float64{5, math.Inf(1), math.Inf(-1), 8, 9},
+		Incx:   1,
+		N:      5,
+		Panic:  false,
+		Dasum:  math.Inf(1),
+		Dnrm2:  math.Inf(1),
+		Idamax: 1,
+		DscalCases: []DScalCase{
+			{
+				Alpha: -2,
+				Ans:   []float64{-10, math.Inf(-1), math.Inf(1), -16, -18},
+			},
+			{
+				Alpha: 0,
+				Ans:   []float64{0, 0, 0, 0, 0},
+			},
+		},
+	},
+	{
+		Name:   "NaNInf",
+		X:      []float64{5, math.NaN(), math.Inf(-1), 8, 9},
+		Incx:   1,
+		N:      5,
+		Panic:  false,
+		Dasum:  math.NaN(),
+		Dnrm2:  math.NaN(),
+		Idamax: 2,
+		DscalCases: []DScalCase{
+			{
+				Alpha: -2,
+				Ans:   []float64{-10, math.NaN(), math.Inf(1), -16, -18},
+			},
+			{
+				Alpha: 0,
+				Ans:   []float64{0, 0, 0, 0, 0},
+			},
+		},
+	},
+	{
+		Name:   "InfNaN",
+		X:      []float64{5, math.Inf(1), math.NaN(), 8, 9},
+		Incx:   1,
+		N:      5,
+		Panic:  false,
+		Dasum:  math.NaN(),
+		Dnrm2:  math.NaN(),
+		Idamax: 1,
+		DscalCases: []DScalCase{
+			{
+				Alpha: -2,
+				Ans:   []float64{-10, math.Inf(-1), math.NaN(), -16, -18},
+			},
+			{
+				Alpha: 0,
+				Ans:   []float64{0, 0, 0, 0, 0},
+			},
+		},
+	},
+}
+
+type DoubleTwoVectorCase struct {
+	Name  string
+	X     []float64
+	Y     []float64
+	XTmp  []float64
+	YTmp  []float64
+	Incx  int
+	Incy  int
+	N     int
+	Panic bool
+	// For Daxpy
+	DaxpyCases []DaxpyCase
+	DdotAns    float64
+	DswapAns   DTwoVecAnswer
+	DcopyAns   DTwoVecAnswer
+	DrotCases  []DrotCase
+	DrotmCases []DrotmCase
+}
+
+type DaxpyCase struct {
+	Alpha float64
+	Ans   []float64
+}
+
+type DrotCase struct {
+	C    float64
+	S    float64
+	XAns []float64
+	YAns []float64
+}
+
+type DrotmCase struct {
+	P    blas.DrotmParams
+	XAns []float64
+	YAns []float64
+	Name string
+}
+
+type DTwoVecAnswer struct {
+	X []float64
+	Y []float64
+}
+
+var DoubleTwoVectorCases = []DoubleTwoVectorCase{
+	{
+		Name:  "UnitaryInc",
+		X:     []float64{10, 15, -6, 3, 14, 7},
+		Y:     []float64{8, -2, 4, 7, 6, -3},
+		XTmp:  []float64{0, 0, 0, 0, 0, 0},
+		YTmp:  []float64{0, 0, 0, 0, 0, 0},
+		Incx:  1,
+		Incy:  1,
+		N:     6,
+		Panic: false,
+		DaxpyCases: []DaxpyCase{
+			{
+				Alpha: 1,
+				Ans:   []float64{18, 13, -2, 10, 20, 4},
+			},
+			{
+				Alpha: 2,
+				Ans:   []float64{28, 28, -8, 13, 34, 11},
+			},
+			{
+				Alpha: -3,
+				Ans:   []float64{-22, -47, 22, -2, -36, -24},
+			},
+			{
+				Alpha: 0,
+				Ans:   []float64{8, -2, 4, 7, 6, -3},
+			},
+		},
+		DdotAns: 110,
+		DswapAns: DTwoVecAnswer{
+			X: []float64{8, -2, 4, 7, 6, -3},
+			Y: []float64{10, 15, -6, 3, 14, 7},
+		},
+		DcopyAns: DTwoVecAnswer{
+			X: []float64{10, 15, -6, 3, 14, 7},
+			Y: []float64{10, 15, -6, 3, 14, 7},
+		},
+		DrotCases: []DrotCase{
+			{
+				C:    math.Cos(0),
+				S:    math.Sin(0),
+				XAns: []float64{10, 15, -6, 3, 14, 7},
+				YAns: []float64{8, -2, 4, 7, 6, -3},
+			},
+			{
+				C:    math.Cos(25 * math.Pi / 180),
+				S:    math.Sin(25 * math.Pi / 180),
+				XAns: []float64{12.444023964292095, 12.749380282068351, -3.7473736752571014, 5.677251193294846, 15.224018588957296, 5.076299724034451},
+				YAns: []float64{3.024279678886205, -8.151889500183792, 6.160940718590796, 5.076299724034451, -0.4788089421498931, -5.677251193294846},
+			},
+			{
+				C:    math.Cos(0.5 * math.Pi),
+				S:    math.Sin(0.5 * math.Pi),
+				XAns: []float64{8, -2, 4, 7, 6, -3},
+				YAns: []float64{-10, -15, 6, -3, -14, -7},
+			},
+			{
+				C:    math.Cos(math.Pi),
+				S:    math.Sin(math.Pi),
+				XAns: []float64{-10, -15, 6, -3, -14, -7},
+				YAns: []float64{-8, 2, -4, -7, -6, 3},
+			},
+		},
+		DrotmCases: []DrotmCase{
+			{
+				P: blas.DrotmParams{
+					Flag: blas.Identity,
+					H:    [4]float64{0.9, 0.1, -0.1, 0.5},
+				},
+				XAns: []float64{10, 15, -6, 3, 14, 7},
+				YAns: []float64{8, -2, 4, 7, 6, -3},
+				Name: "Neg2Flag",
+			},
+			{
+				P: blas.DrotmParams{
+					Flag: blas.Rescaling,
+					H:    [4]float64{0.9, 0.1, -0.1, 0.5},
+				},
+				XAns: []float64{8.2, 13.7, -5.8, 2, 12, 6.6},
+				YAns: []float64{5, 0.5, 1.4, 3.8, 4.4, -0.8},
+				Name: "Neg1Flag",
+			},
+			{
+				P: blas.DrotmParams{
+					Flag: blas.OffDiagonal,
+					H:    [4]float64{1, 0.1, -0.1, 1},
+				},
+				XAns: []float64{9.2, 15.2, -6.4, 2.3, 13.4, 7.3},
+				YAns: []float64{9, -0.5, 3.4, 7.3, 7.4, -2.3},
+				Name: "ZeroFlag",
+			},
+			{
+				P: blas.DrotmParams{
+					Flag: blas.Diagonal,
+					H:    [4]float64{0.5, -1, 1, 0.7},
+				},
+				XAns: []float64{13, 5.5, 1, 8.5, 13, 0.5},
+				YAns: []float64{-4.4, -16.4, 8.8, 1.9, -9.8, -9.1},
+				Name: "OneFlag",
+			},
+		},
+	},
+	{
+		Name:  "UnitaryIncLong",
+		X:     []float64{10, 15, -6, 3, 14, 7, 8, -9, 10},
+		Y:     []float64{8, -2, 4, 7, 6, -3, 7, -6},
+		XTmp:  []float64{0, 0, 0, 0, 0, 0, 0, 0, 0},
+		YTmp:  []float64{0, 0, 0, 0, 0, 0, 0, 0},
+		Incx:  1,
+		Incy:  1,
+		N:     6,
+		Panic: false,
+		DaxpyCases: []DaxpyCase{
+			{
+				Alpha: 1,
+				Ans:   []float64{18, 13, -2, 10, 20, 4, 7, -6},
+			},
+			{
+				Alpha: 2,
+				Ans:   []float64{28, 28, -8, 13, 34, 11, 7, -6},
+			},
+			{
+				Alpha: -3,
+				Ans:   []float64{-22, -47, 22, -2, -36, -24, 7, -6},
+			},
+			{
+				Alpha: 0,
+				Ans:   []float64{8, -2, 4, 7, 6, -3, 7, -6},
+			},
+		},
+		DdotAns: 110,
+		DswapAns: DTwoVecAnswer{
+			X: []float64{8, -2, 4, 7, 6, -3, 8, -9, 10},
+			Y: []float64{10, 15, -6, 3, 14, 7, 7, -6},
+		},
+		DcopyAns: DTwoVecAnswer{
+			X: []float64{10, 15, -6, 3, 14, 7, 8, -9, 10},
+			Y: []float64{10, 15, -6, 3, 14, 7, 7, -6},
+		},
+		DrotCases: []DrotCase{
+			{
+				C:    math.Cos(0),
+				S:    math.Sin(0),
+				XAns: []float64{10, 15, -6, 3, 14, 7, 8, -9, 10},
+				YAns: []float64{8, -2, 4, 7, 6, -3, 7, -6},
+			},
+			{
+				C:    math.Cos(25 * math.Pi / 180),
+				S:    math.Sin(25 * math.Pi / 180),
+				XAns: []float64{12.444023964292095, 12.749380282068351, -3.7473736752571014, 5.677251193294846, 15.224018588957296, 5.076299724034451, 8, -9, 10},
+				YAns: []float64{3.024279678886205, -8.151889500183792, 6.160940718590796, 5.076299724034451, -0.4788089421498931, -5.677251193294846, 7, -6},
+			},
+			{
+				C:    math.Cos(0.5 * math.Pi),
+				S:    math.Sin(0.5 * math.Pi),
+				XAns: []float64{8, -2, 4, 7, 6, -3, 8, -9, 10},
+				YAns: []float64{-10, -15, 6, -3, -14, -7, 7, -6},
+			},
+			{
+				C:    math.Cos(math.Pi),
+				S:    math.Sin(math.Pi),
+				XAns: []float64{-10, -15, 6, -3, -14, -7, 8, -9, 10},
+				YAns: []float64{-8, 2, -4, -7, -6, 3, 7, -6},
+			},
+		},
+		DrotmCases: []DrotmCase{
+			{
+				P: blas.DrotmParams{
+					Flag: blas.Identity,
+					H:    [4]float64{0.9, 0.1, -0.1, 0.5},
+				},
+				XAns: []float64{10, 15, -6, 3, 14, 7, 8, -9, 10},
+				YAns: []float64{8, -2, 4, 7, 6, -3, 7, -6},
+				Name: "Neg2Flag",
+			},
+			{
+				P: blas.DrotmParams{
+					Flag: blas.Rescaling,
+					H:    [4]float64{0.9, 0.1, -0.1, 0.5},
+				},
+				XAns: []float64{8.2, 13.7, -5.8, 2, 12, 6.6, 8, -9, 10},
+				YAns: []float64{5, 0.5, 1.4, 3.8, 4.4, -0.8, 7, -6},
+				Name: "Neg1Flag",
+			},
+			{
+				P: blas.DrotmParams{
+					Flag: blas.OffDiagonal,
+					H:    [4]float64{1, 0.1, -0.1, 1},
+				},
+				XAns: []float64{9.2, 15.2, -6.4, 2.3, 13.4, 7.3, 8, -9, 10},
+				YAns: []float64{9, -0.5, 3.4, 7.3, 7.4, -2.3, 7, -6},
+				Name: "ZeroFlag",
+			},
+			{
+				P: blas.DrotmParams{
+					Flag: blas.Diagonal,
+					H:    [4]float64{0.5, -1, 1, 0.7},
+				},
+				XAns: []float64{13, 5.5, 1, 8.5, 13, 0.5, 8, -9, 10},
+				YAns: []float64{-4.4, -16.4, 8.8, 1.9, -9.8, -9.1, 7, -6},
+				Name: "OneFlag",
+			},
+		},
+	},
+	{
+		Name:  "PositiveInc",
+		X:     []float64{10, 15, -6, 3, 14, 7},
+		Y:     []float64{8, -2, 4, 7, 6, -3, -4, 10},
+		XTmp:  []float64{0, 0, 0, 0, 0, 0},
+		YTmp:  []float64{0, 0, 0, 0, 0, 0, 0, 0},
+		Incx:  2,
+		Incy:  3,
+		N:     3,
+		Panic: false,
+		DaxpyCases: []DaxpyCase{
+			{
+				Alpha: 2,
+				Ans:   []float64{28, -2, 4, -5, 6, -3, 24, 10},
+			},
+		},
+		DdotAns: -18,
+		DswapAns: DTwoVecAnswer{
+			X: []float64{8, 15, 7, 3, -4, 7},
+			Y: []float64{10, -2, 4, -6, 6, -3, 14, 10},
+		},
+		DcopyAns: DTwoVecAnswer{
+			X: []float64{10, 15, -6, 3, 14, 7},
+			Y: []float64{10, -2, 4, -6, 6, -3, 14, 10},
+		},
+		DrotCases: []DrotCase{
+			{
+				C:    math.Cos(25 * math.Pi / 180),
+				S:    math.Sin(25 * math.Pi / 180),
+				XAns: []float64{12.444023964292095, 15, -2.479518890035003, 3, 10.997835971550302, 7},
+				YAns: []float64{3.024279678886205, -2, 4, 8.879864079700745, 6, -3, -9.541886812516392, 10},
+			},
+		},
+		DrotmCases: []DrotmCase{
+			{
+				P: blas.DrotmParams{
+					Flag: blas.Rescaling,
+					H:    [4]float64{0.9, 0.1, -0.1, 0.5},
+				},
+				XAns: []float64{8.2, 15, -6.1, 3, 13, 7},
+				YAns: []float64{5, -2, 4, 2.9, 6, -3, -0.6, 10},
+			},
+			{
+				P: blas.DrotmParams{
+					Flag: blas.OffDiagonal,
+					H:    [4]float64{1, 0.1, -0.1, 1},
+				},
+				XAns: []float64{9.2, 15, -6.7, 3, 14.4, 7},
+				YAns: []float64{9, -2, 4, 6.4, 6, -3, -2.6, 10},
+			},
+			{
+				P: blas.DrotmParams{
+					Flag: blas.Diagonal,
+					H:    [4]float64{0.5, -1, 1, 0.7},
+				},
+				XAns: []float64{13, 15, 4, 3, 3, 7},
+				YAns: []float64{-4.4, -2, 4, 10.9, 6, -3, -16.8, 10},
+			},
+		},
+	},
+	{
+		Name:  "NegativeInc",
+		X:     []float64{10, 15, -6, 3, 14, 7},
+		Y:     []float64{8, -2, 4, 7, 6, -3, -4, 10},
+		XTmp:  []float64{0, 0, 0, 0, 0, 0},
+		YTmp:  []float64{0, 0, 0, 0, 0, 0, 0, 0},
+		Incx:  -2,
+		Incy:  -3,
+		N:     3,
+		Panic: false,
+		DaxpyCases: []DaxpyCase{
+			{
+				Alpha: 2,
+				Ans:   []float64{28, -2, 4, -5, 6, -3, 24, 10},
+			},
+		},
+		DdotAns: -18,
+		DswapAns: DTwoVecAnswer{
+			X: []float64{8, 15, 7, 3, -4, 7},
+			Y: []float64{10, -2, 4, -6, 6, -3, 14, 10},
+		},
+		DcopyAns: DTwoVecAnswer{
+			X: []float64{10, 15, -6, 3, 14, 7},
+			Y: []float64{10, -2, 4, -6, 6, -3, 14, 10},
+		},
+		DrotCases: []DrotCase{
+			{
+				C:    math.Cos(25 * math.Pi / 180),
+				S:    math.Sin(25 * math.Pi / 180),
+				XAns: []float64{12.444023964292095, 15, -2.479518890035003, 3, 10.997835971550302, 7},
+				YAns: []float64{3.024279678886205, -2, 4, 8.879864079700745, 6, -3, -9.541886812516392, 10},
+			},
+		},
+		DrotmCases: []DrotmCase{
+			{
+				P: blas.DrotmParams{
+					Flag: blas.Rescaling,
+					H:    [4]float64{0.9, 0.1, -0.1, 0.5},
+				},
+				XAns: []float64{8.2, 15, -6.1, 3, 13, 7},
+				YAns: []float64{5, -2, 4, 2.9, 6, -3, -0.6, 10},
+			},
+			{
+				P: blas.DrotmParams{
+					Flag: blas.OffDiagonal,
+					H:    [4]float64{1, 0.1, -0.1, 1},
+				},
+				XAns: []float64{9.2, 15, -6.7, 3, 14.4, 7},
+				YAns: []float64{9, -2, 4, 6.4, 6, -3, -2.6, 10},
+			},
+			{
+				P: blas.DrotmParams{
+					Flag: blas.Diagonal,
+					H:    [4]float64{0.5, -1, 1, 0.7},
+				},
+				XAns: []float64{13, 15, 4, 3, 3, 7},
+				YAns: []float64{-4.4, -2, 4, 10.9, 6, -3, -16.8, 10},
+			},
+		},
+	},
+	{
+		Name:  "MixedInc1",
+		X:     []float64{10, 15, -6, 3, 14, 7},
+		Y:     []float64{8, -2, 4, 7, 6, -3, -4, 10},
+		XTmp:  []float64{0, 0, 0, 0, 0, 0},
+		YTmp:  []float64{0, 0, 0, 0, 0, 0, 0, 0},
+		Incx:  2,
+		Incy:  -3,
+		N:     3,
+		Panic: false,
+		DaxpyCases: []DaxpyCase{
+			{
+				Alpha: 2,
+				Ans:   []float64{36, -2, 4, -5, 6, -3, 16, 10},
+			},
+		},
+		DdotAns: 30,
+		DswapAns: DTwoVecAnswer{
+			X: []float64{-4, 15, 7, 3, 8, 7},
+			Y: []float64{14, -2, 4, -6, 6, -3, 10, 10},
+		},
+		DcopyAns: DTwoVecAnswer{
+			X: []float64{10, 15, -6, 3, 14, 7},
+			Y: []float64{14, -2, 4, -6, 6, -3, 10, 10},
+		},
+		DrotCases: []DrotCase{
+			{
+				C:    math.Cos(25 * math.Pi / 180),
+				S:    math.Sin(25 * math.Pi / 180),
+				XAns: []float64{7.372604823403701, 15, -2.479518890035003, 3, 16.069255112438693, 7},
+				YAns: []float64{1.333806631923407, -2, 4, 8.879864079700745, 6, -3, -7.851413765553595, 10},
+			},
+		},
+		DrotmCases: []DrotmCase{
+			{
+				P: blas.DrotmParams{
+					Flag: blas.Rescaling,
+					H:    [4]float64{0.9, 0.1, -0.1, 0.5},
+				},
+				XAns: []float64{9.4, 15, -6.1, 3, 11.8, 7},
+				YAns: []float64{5.4, -2, 4, 2.9, 6, -3, -1, 10},
+			},
+			{
+				P: blas.DrotmParams{
+					Flag: blas.OffDiagonal,
+					H:    [4]float64{1, 0.1, -0.1, 1},
+				},
+				XAns: []float64{10.4, 15, -6.7, 3, 13.2, 7},
+				YAns: []float64{9.4, -2, 4, 6.4, 6, -3, -3, 10},
+			},
+			{
+				P: blas.DrotmParams{
+					Flag: blas.Diagonal,
+					H:    [4]float64{0.5, -1, 1, 0.7},
+				},
+				XAns: []float64{1, 15, 4, 3, 15, 7},
+				YAns: []float64{-8.4, -2, 4, 10.9, 6, -3, -12.8, 10},
+			},
+		},
+	},
+	{
+		Name:  "MixedInc2",
+		X:     []float64{10, 15, -6, 3, 14, 7},
+		Y:     []float64{8, -2, 4, 7, 6, -3, -4, 10},
+		XTmp:  []float64{0, 0, 0, 0, 0, 0},
+		YTmp:  []float64{0, 0, 0, 0, 0, 0, 0, 0},
+		Incx:  -2,
+		Incy:  3,
+		N:     3,
+		Panic: false,
+		DaxpyCases: []DaxpyCase{
+			{
+				Alpha: 2,
+				Ans:   []float64{36, -2, 4, -5, 6, -3, 16, 10},
+			},
+		},
+		DdotAns: 30,
+		DswapAns: DTwoVecAnswer{
+			X: []float64{-4, 15, 7, 3, 8, 7},
+			Y: []float64{14, -2, 4, -6, 6, -3, 10, 10},
+		},
+		DcopyAns: DTwoVecAnswer{
+			X: []float64{10, 15, -6, 3, 14, 7},
+			Y: []float64{14, -2, 4, -6, 6, -3, 10, 10},
+		},
+		DrotCases: []DrotCase{
+			{
+				C:    math.Cos(25 * math.Pi / 180),
+				S:    math.Sin(25 * math.Pi / 180),
+				XAns: []float64{7.372604823403701, 15, -2.479518890035003, 3, 16.069255112438693, 7},
+				YAns: []float64{1.333806631923407, -2, 4, 8.879864079700745, 6, -3, -7.851413765553595, 10},
+			},
+		},
+		DrotmCases: []DrotmCase{
+			{
+				P: blas.DrotmParams{
+					Flag: blas.Rescaling,
+					H:    [4]float64{0.9, 0.1, -0.1, 0.5},
+				},
+				XAns: []float64{9.4, 15, -6.1, 3, 11.8, 7},
+				YAns: []float64{5.4, -2, 4, 2.9, 6, -3, -1, 10},
+			},
+			{
+				P: blas.DrotmParams{
+					Flag: blas.OffDiagonal,
+					H:    [4]float64{1, 0.1, -0.1, 1},
+				},
+				XAns: []float64{10.4, 15, -6.7, 3, 13.2, 7},
+				YAns: []float64{9.4, -2, 4, 6.4, 6, -3, -3, 10},
+			},
+			{
+				P: blas.DrotmParams{
+					Flag: blas.Diagonal,
+					H:    [4]float64{0.5, -1, 1, 0.7},
+				},
+				XAns: []float64{1, 15, 4, 3, 15, 7},
+				YAns: []float64{-8.4, -2, 4, 10.9, 6, -3, -12.8, 10},
+			},
+		},
+	},
+	{
+		Name:  "ZeroN",
+		X:     []float64{10, 15, -6, 3, 14, 7},
+		Y:     []float64{8, -2, 4, 7, 6, -3, -4, 10},
+		XTmp:  []float64{0, 0, 0, 0, 0, 0},
+		YTmp:  []float64{0, 0, 0, 0, 0, 0, 0, 0},
+		Incx:  -2,
+		Incy:  3,
+		N:     0,
+		Panic: false,
+		DaxpyCases: []DaxpyCase{
+			{
+				Alpha: 2,
+				Ans:   []float64{8, -2, 4, 7, 6, -3, -4, 10},
+			},
+		},
+		DswapAns: DTwoVecAnswer{
+			X: []float64{10, 15, -6, 3, 14, 7},
+			Y: []float64{8, -2, 4, 7, 6, -3, -4, 10},
+		},
+		DcopyAns: DTwoVecAnswer{
+			X: []float64{10, 15, -6, 3, 14, 7},
+			Y: []float64{8, -2, 4, 7, 6, -3, -4, 10},
+		},
+		DrotCases: []DrotCase{
+			{
+				C:    math.Cos(25 * math.Pi / 180),
+				S:    math.Sin(25 * math.Pi / 180),
+				XAns: []float64{10, 15, -6, 3, 14, 7},
+				YAns: []float64{8, -2, 4, 7, 6, -3, -4, 10},
+			},
+		},
+		DrotmCases: []DrotmCase{
+			{
+				P: blas.DrotmParams{
+					Flag: blas.Rescaling,
+					H:    [4]float64{0.9, 0.1, -0.1, 0.5},
+				},
+				XAns: []float64{10, 15, -6, 3, 14, 7},
+				YAns: []float64{8, -2, 4, 7, 6, -3, -4, 10},
+			},
+		},
+	},
+	{
+		Name:  "NegativeN",
+		X:     []float64{10, 15, -6, 3, 14, 7},
+		Y:     []float64{8, -2, 4, 7, 6, -3, -4, 10},
+		XTmp:  []float64{0, 0, 0, 0, 0, 0},
+		YTmp:  []float64{0, 0, 0, 0, 0, 0, 0, 0},
+		Incx:  -2,
+		Incy:  3,
+		N:     -3,
+		Panic: true,
+		DaxpyCases: []DaxpyCase{
+			{
+				Alpha: 2,
+				Ans:   []float64{36, -2, 4, -5, 6, -3, 16, 10},
+			},
+		},
+		DrotCases: []DrotCase{
+			{
+				C:    math.Cos(25 * math.Pi / 180),
+				S:    math.Sin(25 * math.Pi / 180),
+				XAns: []float64{10, 15, -6, 3, 14, 7},
+				YAns: []float64{8, -2, 4, 7, 6, -3, -4, 10},
+			},
+		},
+		DrotmCases: []DrotmCase{
+			{
+				P: blas.DrotmParams{
+					Flag: blas.Rescaling,
+					H:    [4]float64{0.9, 0.1, -0.1, 0.5},
+				},
+				XAns: []float64{8.2, 13.7, -5.8, 2, 12, 6.6},
+				YAns: []float64{5, 0.5, 1.4, 3.8, 4.4, -0.8},
+			},
+		},
+	},
+	{
+		Name:  "ZeroIncX",
+		X:     []float64{10, 15, -6, 3, 14, 7},
+		Y:     []float64{8, -2, 4, 7, 6, -3, -4, 10},
+		XTmp:  []float64{0, 0, 0, 0, 0, 0},
+		YTmp:  []float64{0, 0, 0, 0, 0, 0, 0, 0},
+		Incx:  0,
+		Incy:  3,
+		N:     2,
+		Panic: true,
+		DaxpyCases: []DaxpyCase{
+			{
+				Alpha: 2,
+				Ans:   []float64{36, -2, 4, -5, 6, -3, 16, 10},
+			},
+		},
+		DrotCases: []DrotCase{
+			{
+				C:    math.Cos(25 * math.Pi / 180),
+				S:    math.Sin(25 * math.Pi / 180),
+				XAns: []float64{10, 15, -6, 3, 14, 7},
+				YAns: []float64{8, -2, 4, 7, 6, -3, -4, 10},
+			},
+		},
+		DrotmCases: []DrotmCase{
+			{
+				P: blas.DrotmParams{
+					Flag: blas.Rescaling,
+					H:    [4]float64{0.9, 0.1, -0.1, 0.5},
+				},
+				XAns: []float64{8.2, 13.7, -5.8, 2, 12, 6.6},
+				YAns: []float64{5, 0.5, 1.4, 3.8, 4.4, -0.8},
+			},
+		},
+	},
+	{
+		Name:  "ZeroIncY",
+		X:     []float64{10, 15, -6, 3, 14, 7},
+		Y:     []float64{8, -2, 4, 7, 6, -3, -4, 10},
+		XTmp:  []float64{0, 0, 0, 0, 0, 0},
+		YTmp:  []float64{0, 0, 0, 0, 0, 0, 0, 0},
+		Incx:  1,
+		Incy:  0,
+		N:     2,
+		Panic: true,
+		DaxpyCases: []DaxpyCase{
+			{
+				Alpha: 2,
+				Ans:   []float64{36, -2, 4, -5, 6, -3, 16, 10},
+			},
+		},
+		DrotCases: []DrotCase{
+			{
+				C:    math.Cos(25 * math.Pi / 180),
+				S:    math.Sin(25 * math.Pi / 180),
+				XAns: []float64{10, 15, -6, 3, 14, 7},
+				YAns: []float64{8, -2, 4, 7, 6, -3, -4, 10},
+			},
+		},
+		DrotmCases: []DrotmCase{
+			{
+				P: blas.DrotmParams{
+					Flag: blas.Rescaling,
+					H:    [4]float64{0.9, 0.1, -0.1, 0.5},
+				},
+				XAns: []float64{8.2, 13.7, -5.8, 2, 12, 6.6},
+				YAns: []float64{5, 0.5, 1.4, 3.8, 4.4, -0.8},
+			},
+		},
+	},
+	{
+		Name:  "OutOfBoundsX",
+		X:     []float64{10, 15, -6, 3, 14, 7},
+		Y:     []float64{8, -2, 4, 7, 6, -3, -4, 10},
+		XTmp:  []float64{0, 0, 0, 0, 0, 0},
+		YTmp:  []float64{0, 0, 0, 0, 0, 0, 0, 0},
+		Incx:  8,
+		Incy:  2,
+		N:     2,
+		Panic: true,
+		DaxpyCases: []DaxpyCase{
+			{
+				Alpha: 2,
+				Ans:   []float64{36, -2, 4, -5, 6, -3, 16, 10},
+			},
+		},
+		DrotCases: []DrotCase{
+			{
+				C:    math.Cos(25 * math.Pi / 180),
+				S:    math.Sin(25 * math.Pi / 180),
+				XAns: []float64{10, 15, -6, 3, 14, 7},
+				YAns: []float64{8, -2, 4, 7, 6, -3, -4, 10},
+			},
+		},
+		DrotmCases: []DrotmCase{
+			{
+				P: blas.DrotmParams{
+					Flag: blas.Rescaling,
+					H:    [4]float64{0.9, 0.1, -0.1, 0.5},
+				},
+				XAns: []float64{8.2, 13.7, -5.8, 2, 12, 6.6},
+				YAns: []float64{5, 0.5, 1.4, 3.8, 4.4, -0.8},
+			},
+		},
+	},
+	{
+		Name:  "OutOfBoundsY",
+		X:     []float64{10, 15, -6, 3, 14, 7},
+		Y:     []float64{8, -2, 4, 7, 6, -3, -4, 10},
+		XTmp:  []float64{0, 0, 0, 0, 0, 0},
+		YTmp:  []float64{0, 0, 0, 0, 0, 0, 0, 0},
+		Incx:  2,
+		Incy:  8,
+		N:     2,
+		Panic: true,
+		DaxpyCases: []DaxpyCase{
+			{
+				Alpha: 2,
+				Ans:   []float64{36, -2, 4, -5, 6, -3, 16, 10},
+			},
+		},
+		DrotCases: []DrotCase{
+			{
+				C:    math.Cos(25 * math.Pi / 180),
+				S:    math.Sin(25 * math.Pi / 180),
+				XAns: []float64{10, 15, -6, 3, 14, 7},
+				YAns: []float64{8, -2, 4, 7, 6, -3, -4, 10},
+			},
+		},
+		DrotmCases: []DrotmCase{
+			{
+				P: blas.DrotmParams{
+					Flag: blas.Rescaling,
+					H:    [4]float64{0.9, 0.1, -0.1, 0.5},
+				},
+				XAns: []float64{10, 15, -6, 3, 14, 7},
+				YAns: []float64{8, -2, 4, 7, 6, -3, -4, 10},
+			},
+		},
+	},
+	{
+		Name:  "Empty",
+		X:     []float64{},
+		Y:     []float64{},
+		Incx:  1,
+		Incy:  1,
+		N:     0,
+		Panic: false,
+		DaxpyCases: []DaxpyCase{
+			{
+				Alpha: 2,
+				Ans:   []float64{},
+			},
+		},
+		DrotCases: []DrotCase{
+			{
+				C:    math.Cos(25 * math.Pi / 180),
+				S:    math.Sin(25 * math.Pi / 180),
+				XAns: []float64{},
+				YAns: []float64{},
+			},
+		},
+		DrotmCases: []DrotmCase{
+			{
+				P: blas.DrotmParams{
+					Flag: blas.Rescaling,
+					H:    [4]float64{0.9, 0.1, -0.1, 0.5},
+				},
+				XAns: []float64{},
+				YAns: []float64{},
+			},
+		},
+	},
+	{
+		Name:  "EmptyZeroIncX",
+		X:     []float64{},
+		Y:     []float64{},
+		Incx:  0,
+		Incy:  1,
+		N:     0,
+		Panic: true,
+		DaxpyCases: []DaxpyCase{
+			{
+				Alpha: 2,
+				Ans:   []float64{},
+			},
+		},
+		DrotCases: []DrotCase{
+			{
+				C:    math.Cos(25 * math.Pi / 180),
+				S:    math.Sin(25 * math.Pi / 180),
+				XAns: []float64{},
+				YAns: []float64{},
+			},
+		},
+		DrotmCases: []DrotmCase{
+			{
+				P: blas.DrotmParams{
+					Flag: blas.Rescaling,
+					H:    [4]float64{0.9, 0.1, -0.1, 0.5},
+				},
+				XAns: []float64{},
+				YAns: []float64{},
+			},
+		},
+	},
+	{
+		Name:  "EmptyZeroIncY",
+		X:     []float64{},
+		Y:     []float64{},
+		Incx:  1,
+		Incy:  0,
+		N:     0,
+		Panic: true,
+		DaxpyCases: []DaxpyCase{
+			{
+				Alpha: 2,
+				Ans:   []float64{},
+			},
+		},
+		DrotCases: []DrotCase{
+			{
+				C:    math.Cos(25 * math.Pi / 180),
+				S:    math.Sin(25 * math.Pi / 180),
+				XAns: []float64{},
+				YAns: []float64{},
+			},
+		},
+		DrotmCases: []DrotmCase{
+			{
+				P: blas.DrotmParams{
+					Flag: blas.Rescaling,
+					H:    [4]float64{0.9, 0.1, -0.1, 0.5},
+				},
+				XAns: []float64{},
+				YAns: []float64{},
+			},
+		},
+	},
+	{
+		Name:  "EmptyReverse",
+		X:     []float64{},
+		Y:     []float64{},
+		Incx:  -1,
+		Incy:  -1,
+		N:     0,
+		Panic: false,
+		DaxpyCases: []DaxpyCase{
+			{
+				Alpha: 2,
+				Ans:   []float64{},
+			},
+		},
+		DrotCases: []DrotCase{
+			{
+				C:    math.Cos(25 * math.Pi / 180),
+				S:    math.Sin(25 * math.Pi / 180),
+				XAns: []float64{},
+				YAns: []float64{},
+			},
+		},
+		DrotmCases: []DrotmCase{
+			{
+				P: blas.DrotmParams{
+					Flag: blas.Rescaling,
+					H:    [4]float64{0.9, 0.1, -0.1, 0.5},
+				},
+				XAns: []float64{},
+				YAns: []float64{},
+			},
+		},
+	},
+}
+
+type Ddotter interface {
+	Ddot(n int, x []float64, incX int, y []float64, incY int) float64
+}
+
+func DdotTest(t *testing.T, d Ddotter) {
+	ddot := d.Ddot
+	for _, c := range DoubleTwoVectorCases {
+		dCopyTwoTmp(c.X, c.XTmp, c.Y, c.YTmp)
+		if c.Panic {
+			f := func() { ddot(c.N, c.XTmp, c.Incx, c.YTmp, c.Incy) }
+			testpanics(f, c.Name, t)
+			continue
+		}
+		dot := ddot(c.N, c.XTmp, c.Incx, c.YTmp, c.Incy)
+		if !dTolEqual(dot, c.DdotAns) {
+			t.Errorf("ddot: mismatch %v: expected %v, found %v", c.Name, c.DdotAns, dot)
+		}
+	}
+
+	// check it works for 16-byte unaligned slices
+	x := []float64{1, 1, 1, 1, 1}
+	if n := ddot(4, x[:4], 1, x[1:], 1); n != 4 {
+		t.Errorf("ddot: mismatch Unaligned: expected %v, found %v", 4, n)
+	}
+	if n := ddot(2, x[:4], 2, x[1:], 2); n != 2 {
+		t.Errorf("ddot: mismatch Unaligned: expected %v, found %v", 2, n)
+	}
+	if n := ddot(2, x[:4], 3, x[1:], 3); n != 2 {
+		t.Errorf("ddot: mismatch Unaligned: expected %v, found %v", 2, n)
+	}
+}
+
+type Dnrm2er interface {
+	Dnrm2(n int, x []float64, incX int) float64
+}
+
+func Dnrm2Test(t *testing.T, blasser Dnrm2er) {
+	dnrm2 := blasser.Dnrm2
+	for _, c := range DoubleOneVectorCases {
+		if c.Panic {
+			f := func() { dnrm2(c.N, c.X, c.Incx) }
+			testpanics(f, c.Name, t)
+			continue
+		}
+		v := dnrm2(c.N, c.X, c.Incx)
+		if !dTolEqual(v, c.Dnrm2) {
+			t.Errorf("dnrm2: mismatch %v: expected %v, found %v", c.Name, c.Dnrm2, v)
+		}
+	}
+}
+
+type Dasumer interface {
+	Dasum(n int, x []float64, incX int) float64
+}
+
+func DasumTest(t *testing.T, blasser Dasumer) {
+	dasum := blasser.Dasum
+	for _, c := range DoubleOneVectorCases {
+		if c.Panic {
+			f := func() { dasum(c.N, c.X, c.Incx) }
+			testpanics(f, c.Name, t)
+			continue
+		}
+		v := dasum(c.N, c.X, c.Incx)
+		if !dTolEqual(v, c.Dasum) {
+			t.Errorf("dasum: mismatch %v: expected %v, found %v", c.Name, c.Dasum, v)
+		}
+	}
+}
+
+type Idamaxer interface {
+	Idamax(n int, x []float64, incX int) int
+}
+
+func IdamaxTest(t *testing.T, blasser Idamaxer) {
+	idamax := blasser.Idamax
+	for _, c := range DoubleOneVectorCases {
+		if c.Panic {
+			f := func() { idamax(c.N, c.X, c.Incx) }
+			testpanics(f, c.Name, t)
+			continue
+		}
+		v := idamax(c.N, c.X, c.Incx)
+		if v != c.Idamax {
+			s := fmt.Sprintf("idamax: mismatch %v: expected %v, found %v", c.Name, c.Idamax, v)
+			if floats.HasNaN(c.X) {
+				log.Println(s)
+			} else {
+				t.Errorf(s)
+			}
+		}
+	}
+}
+
+type Dswapper interface {
+	Dswap(n int, x []float64, incX int, y []float64, incY int)
+}
+
+func DswapTest(t *testing.T, d Dswapper) {
+	dswap := d.Dswap
+	for _, c := range DoubleTwoVectorCases {
+		dCopyTwoTmp(c.X, c.XTmp, c.Y, c.YTmp)
+		if c.Panic {
+			f := func() { dswap(c.N, c.XTmp, c.Incx, c.YTmp, c.Incy) }
+			testpanics(f, c.Name, t)
+			continue
+		}
+		dswap(c.N, c.XTmp, c.Incx, c.YTmp, c.Incy)
+		if !dSliceTolEqual(c.XTmp, c.DswapAns.X) {
+			t.Errorf("dswap: x mismatch %v: expected %v, found %v", c.Name, c.DswapAns.X, c.XTmp)
+		}
+		if !dSliceTolEqual(c.YTmp, c.DswapAns.Y) {
+			t.Errorf("dswap: y mismatch %v: expected %v, found %v", c.Name, c.DswapAns.Y, c.YTmp)
+		}
+	}
+}
+
+type Dcopier interface {
+	Dcopy(n int, x []float64, incX int, y []float64, incY int)
+}
+
+func DcopyTest(t *testing.T, d Dcopier) {
+	dcopy := d.Dcopy
+	for _, c := range DoubleTwoVectorCases {
+		dCopyTwoTmp(c.X, c.XTmp, c.Y, c.YTmp)
+		if c.Panic {
+			f := func() { dcopy(c.N, c.XTmp, c.Incx, c.YTmp, c.Incy) }
+			testpanics(f, c.Name, t)
+			continue
+		}
+		dcopy(c.N, c.XTmp, c.Incx, c.YTmp, c.Incy)
+		if !dSliceTolEqual(c.XTmp, c.DcopyAns.X) {
+			t.Errorf("dswap: x mismatch %v: expected %v, found %v", c.Name, c.DcopyAns.X, c.XTmp)
+		}
+		if !dSliceTolEqual(c.YTmp, c.DcopyAns.Y) {
+			t.Errorf("dswap: y mismatch %v: expected %v, found %v", c.Name, c.DcopyAns.Y, c.YTmp)
+		}
+	}
+}
+
+type Daxpyer interface {
+	Daxpy(n int, alpha float64, x []float64, incX int, y []float64, incY int)
+}
+
+func DaxpyTest(t *testing.T, d Daxpyer) {
+	daxpy := d.Daxpy
+	for _, c := range DoubleTwoVectorCases {
+		for _, kind := range c.DaxpyCases {
+			dCopyTwoTmp(c.X, c.XTmp, c.Y, c.YTmp)
+			if c.Panic {
+				f := func() { daxpy(c.N, kind.Alpha, c.XTmp, c.Incx, c.YTmp, c.Incy) }
+				testpanics(f, c.Name, t)
+				continue
+			}
+			daxpy(c.N, kind.Alpha, c.XTmp, c.Incx, c.YTmp, c.Incy)
+			if !dSliceTolEqual(c.YTmp, kind.Ans) {
+				t.Errorf("daxpy: mismatch %v: expected %v, found %v", c.Name, kind.Ans, c.YTmp)
+			}
+		}
+	}
+}
+
+type DrotgTestStruct struct {
+	Name       string
+	A, B       float64
+	C, S, R, Z float64
+}
+
+var DrotgTests = []DrotgTestStruct{
+	{
+		Name: "ZeroAB",
+		C:    1,
+	},
+	{
+		Name: "PosA_ZeroB",
+		A:    0.5,
+		C:    1,
+		R:    0.5,
+	},
+	{
+		Name: "NegA_ZeroB",
+		A:    -4.6,
+		C:    1,
+		R:    -4.6,
+	},
+	{
+		Name: "ZeroA_PosB",
+		B:    3,
+		S:    1,
+		R:    3,
+		Z:    1,
+	},
+	{
+		Name: "ZeroA_NegB",
+		B:    -0.3,
+		S:    1,
+		R:    -0.3,
+		Z:    1,
+	},
+	{
+		Name: "PosA_PosB_AGTB",
+		A:    5,
+		B:    0.3,
+		C:    0.99820484546577868593549038000,
+		S:    0.05989229072794672115612942280,
+		R:    5.00899191454727744602429072688,
+		Z:    0.05989229072794672115612942280,
+	},
+	{
+		Name: "PosA_PosB_ALTB",
+		A:    3,
+		B:    4,
+		C:    3.0 / 5,
+		S:    4.0 / 5,
+		R:    5,
+		Z:    5.0 / 3.0,
+	},
+
+	{
+		Name: "PosA_NegB_AGTB",
+		A:    2.6,
+		B:    -0.9,
+		C:    0.94498607344025815971847507095,
+		S:    -0.32711056388316628605639521686,
+		R:    2.751363298439520872718790879655,
+		Z:    -0.3271105638831662860563952168,
+	},
+	{
+		Name: "PosA_NegB_ALTB",
+		A:    2.6,
+		B:    -2.9,
+		C:    -0.6675450157520258540548049558,
+		S:    0.7445694406464903756765132200,
+		R:    -3.8948684188300893100043812234,
+		Z:    1 / -0.6675450157520258540548049558,
+	},
+	{
+		Name: "NegA_PosB_AGTB",
+		A:    -11.4,
+		B:    10.3,
+		C:    0.7419981952497362418487847947,
+		S:    -0.6704018781642353764072353847,
+		R:    -15.363918770938617534070671122,
+		Z:    -0.6704018781642353764072353847,
+	},
+	{
+		Name: "NegA_PosB_ALTB",
+		A:    -1.4,
+		B:    10.3,
+		C:    -0.1346838895922121112404717523,
+		S:    0.9908886162855605326977564640,
+		R:    10.394710193170370442523552032,
+		Z:    1 / -0.1346838895922121112404717523,
+	},
+	{
+		Name: "NegA_NegB_AGTB",
+		A:    -11.4,
+		B:    10.3,
+		C:    0.7419981952497362418487847947,
+		S:    -0.6704018781642353764072353847,
+		R:    -15.363918770938617534070671122,
+		Z:    -0.6704018781642353764072353847,
+	},
+	{
+		Name: "NegA_NegB_ALTB",
+		A:    -1.4,
+		B:    -10.3,
+		C:    0.1346838895922121112404717523,
+		S:    0.9908886162855605326977564640,
+		R:    -10.394710193170370442523552032,
+		Z:    1 / 0.1346838895922121112404717523,
+	},
+}
+
+type Drotger interface {
+	Drotg(a, b float64) (c, s, r, z float64)
+}
+
+func DrotgTest(t *testing.T, d Drotger) {
+	drotg := d.Drotg
+	for _, test := range DrotgTests {
+		c, s, r, z := drotg(test.A, test.B)
+		if !dTolEqual(c, test.C) {
+			t.Errorf("drotg: c mismatch %v: expected %v, found %v", test.Name, test.C, c)
+		}
+		if !dTolEqual(s, test.S) {
+			t.Errorf("drotg: s mismatch %v: expected %v, found %v", test.Name, test.S, s)
+		}
+		if !dTolEqual(r, test.R) {
+			t.Errorf("drotg: r mismatch %v: expected %v, found %v", test.Name, test.R, r)
+		}
+		if !dTolEqual(z, test.Z) {
+			t.Errorf("drotg: z mismatch %v: expected %v, found %v", test.Name, test.Z, z)
+		}
+	}
+}
+
+type DrotmgTestStruct struct {
+	Name           string
+	D1, D2, X1, Y1 float64
+	P              *blas.DrotmParams
+	Rd1, Rd2, Rx1  float64
+}
+
+var DrotmgTests = []DrotmgTestStruct{
+	{
+		Name: "NegD1",
+		P: &blas.DrotmParams{
+			Flag: blas.Rescaling,
+		},
+		D1: -4,
+		D2: 6,
+		X1: 8,
+		Y1: -4,
+	},
+	{
+		Name: "ZeroD2",
+		P: &blas.DrotmParams{
+			Flag: blas.Identity,
+		},
+		D1:  4,
+		X1:  8,
+		Y1:  -5,
+		Rd1: 4,
+		Rx1: 8,
+	},
+	{
+		Name: "ZeroY1",
+		P: &blas.DrotmParams{
+			Flag: blas.Identity,
+		},
+		D1:  4,
+		D2:  -6,
+		X1:  8,
+		Rd1: 4,
+		Rd2: -6,
+		Rx1: 8,
+	},
+	{
+		Name: "NegQ2_and_AQ1_LT_AQ2",
+		P: &blas.DrotmParams{
+			Flag: blas.Rescaling,
+		},
+		D1:  8,
+		D2:  -6,
+		X1:  4,
+		Y1:  8,
+		Rd1: 0,
+		Rd2: 0,
+		Rx1: 0,
+	},
+	{
+		Name: "ZeroD1",
+		P: &blas.DrotmParams{
+			Flag: blas.Diagonal,
+			H:    [4]float64{0, 0, 0, 2},
+		},
+		D1:  0,
+		D2:  2,
+		X1:  8,
+		Y1:  4,
+		Rd1: 2,
+		Rd2: 0,
+		Rx1: 4,
+	},
+	{
+		Name: "AbsQ1_GT_AbsQU__D2_Pos",
+		P: &blas.DrotmParams{
+			Flag: blas.OffDiagonal,
+			H:    [4]float64{0, -0.625, 0.9375, 0},
+		},
+		D1:  2,
+		D2:  3,
+		X1:  8,
+		Y1:  5,
+		Rd1: 1.2610837438423645,
+		Rd2: 1.8916256157635467,
+		Rx1: 12.6875,
+	},
+	{
+		Name: "AbsQ1_GT_AbsQU__D2_Neg",
+		P: &blas.DrotmParams{
+			Flag: blas.OffDiagonal,
+			H:    [4]float64{0, -0.625, -0.9375, 0},
+		},
+		D1:  2,
+		D2:  -3,
+		X1:  8,
+		Y1:  5,
+		Rd1: 4.830188679245283,
+		Rd2: -7.245283018867925,
+		Rx1: 3.3125,
+	},
+	{
+		Name: "AbsQ1_LT_AbsQU__D2_Pos",
+		P: &blas.DrotmParams{
+			Flag: blas.Diagonal,
+			H:    [4]float64{5.0 / 12, 0, 0, 0.625},
+		},
+		D1:  2,
+		D2:  3,
+		X1:  5,
+		Y1:  8,
+		Rd1: 2.3801652892561984,
+		Rd2: 1.586776859504132,
+		Rx1: 121.0 / 12,
+	},
+	{
+		Name: "D1=D2_X1=X2",
+		P: &blas.DrotmParams{
+			Flag: blas.Diagonal,
+			H:    [4]float64{1, 0, 0, 1},
+		},
+		D1:  2,
+		D2:  2,
+		X1:  8,
+		Y1:  8,
+		Rd1: 1,
+		Rd2: 1,
+		Rx1: 16,
+	},
+	{
+		Name: "RD1_Big_RD2_Big_Flag_0",
+		P: &blas.DrotmParams{
+			Flag: blas.Rescaling,
+			H:    [4]float64{4096, -3584, 1792, 4096},
+		},
+		D1:  1600000000,
+		D2:  800000000,
+		X1:  8,
+		Y1:  7,
+		Rd1: 68.96627824858757,
+		Rd2: 34.483139124293785,
+		Rx1: 45312,
+	},
+	{
+		Name: "RD1_Big_RD2_Big_Flag_1",
+		P: &blas.DrotmParams{
+			Flag: blas.Rescaling,
+			H:    [4]float64{2340.5714285714284, -4096, 4096, 4681.142857142857},
+		},
+		D1:  800000000,
+		D2:  1600000000,
+		X1:  8,
+		Y1:  7,
+		Rd1: 57.6914092640818,
+		Rd2: 28.8457046320409,
+		Rx1: 47396.57142857142,
+	},
+	{
+		Name: "RD1_Big_RD2_Med_Flag_0",
+		P: &blas.DrotmParams{
+			Flag: blas.Rescaling,
+			H:    [4]float64{4096, -1, 0.0004096, 1},
+		},
+		D1:  20000000,
+		D2:  2,
+		X1:  8,
+		Y1:  8,
+		Rd1: 1.1920927762985347,
+		Rd2: 1.9999998000000199,
+		Rx1: 32768.0032768,
+	},
+	{
+		Name: "RD1_Big_RD2_Med_Flag_1",
+		P: &blas.DrotmParams{
+			Flag: blas.Rescaling,
+			H:    [4]float64{4.096e-17, -1, 4096, 1e-10},
+		},
+		D1:  2,
+		D2:  20000000000,
+		X1:  8,
+		Y1:  80000000000,
+		Rd1: 1192.0928955078125,
+		Rd2: 2,
+		Rx1: 3.2768e+14,
+	},
+
+	// TODO: Add D1 big, D2 small, Flag = 0
+	{
+		Name: "D1_Big_D2_Small_Flag_1",
+		P: &blas.DrotmParams{
+			Flag: blas.Rescaling,
+			H:    [4]float64{2.8671999999999997e-26, -0.000244140625, 4096, 2.44140625e-16},
+		},
+		D1:  0.000000014,
+		D2:  2000000000,
+		X1:  0.000008,
+		Y1:  8000000,
+		Rd1: 119.20928955078125,
+		Rd2: 0.234881024,
+		Rx1: 3.2768e+10,
+	},
+
+	{
+		Name: "RD1_Med_RD2_Big_Flag_0",
+		P: &blas.DrotmParams{
+			Flag: blas.Rescaling,
+			H:    [4]float64{1, -0.0004096, 1000, 4096},
+		},
+		D1:  2,
+		D2:  20000000000,
+		X1:  80000000,
+		Y1:  8,
+		Rd1: 1.9998000199980002,
+		Rd2: 1191.9736981379988,
+		Rx1: 8.0008e+07,
+	},
+	{
+		Name: "D1_Med_D2_Big_Flag_1",
+		P: &blas.DrotmParams{
+			Flag: blas.Rescaling,
+			H:    [4]float64{50, -4096, 1, 4.096e-06},
+		},
+		D1:  20000000000,
+		D2:  0.4,
+		X1:  80000000,
+		Y1:  80000000000000000,
+		Rd1: 0.39999998000000103,
+		Rd2: 1192.092835903171,
+		Rx1: 8.0000004e+16,
+	},
+	{
+		Name: "RD1_Med_RD2_Small_Flag_0",
+		P: &blas.DrotmParams{
+			Flag: blas.Rescaling,
+			H:    [4]float64{1, -0.0007233796296296296, 1.1111111111111111e-10, 0.000244140625},
+		},
+		D1:  1.2,
+		D2:  0.000000000045,
+		X1:  2.7,
+		Y1:  8,
+		Rd1: 1.1999999996049382,
+		Rd2: 0.0007549747197514486,
+		Rx1: 2.700000000888889,
+	},
+	{
+		Name: "RD1_Med_RD2_Small_Flag_1",
+		P: &blas.DrotmParams{
+			Flag: blas.Rescaling,
+			H:    [4]float64{0.0002197265625, -1, 0.000244140625, 3.375e-11},
+		},
+		D1:  1.2,
+		D2:  0.000000000045,
+		X1:  2.7,
+		Y1:  80000000000,
+		Rd1: 0.0007549747199770676,
+		Rd2: 1.19999999996355,
+		Rx1: 1.9531250000593264e+07,
+	},
+	// TODO: Add Small, Big, 0 case
+	{
+		Name: "D1_Small_D2_Big_Flag_1",
+		P: &blas.DrotmParams{
+			Flag: blas.Rescaling,
+			H:    [4]float64{2.3731773997569866e+10, -1.6777216e+07, 0.000244140625, 1.6777216e-07},
+		},
+		D1:  120000000000000000,
+		D2:  0.000000000012345,
+		X1:  0.08,
+		Y1:  8000000000000,
+		Rd1: 0.00010502490698765249,
+		Rd2: 216.1836123957717,
+		Rx1: 3.8516669198055897e+09,
+	},
+	{
+		Name: "RD1_Small_RD2_Med_Flag_0",
+		P: &blas.DrotmParams{
+			Flag: blas.Rescaling,
+			H:    [4]float64{0.000244140625, -1e-08, 0.24414062499999997, 1},
+		},
+		D1:  0.0000000002,
+		D2:  20,
+		X1:  0.8,
+		Y1:  0.000000008,
+		Rd1: 0.003355409645903541,
+		Rd2: 19.99980000199998,
+		Rx1: 0.000195314453125,
+	},
+	{
+		Name: "RD1_Small_RD2_Med_Flag_1",
+		P: &blas.DrotmParams{
+			Flag: blas.Rescaling,
+			H:    [4]float64{0.0012207031250000002, -1, 0.000244140625, 1e-09},
+		},
+		D1:  0.02,
+		D2:  0.000000000004,
+		X1:  0.008,
+		Y1:  8000000,
+		Rd1: 6.710886366445568e-05,
+		Rd2: 0.019999999900000003,
+		Rx1: 1953.125009765625,
+	},
+	// TODO: Add Small, Small, 0 case
+	// TODO: Add Small, Small, 1 case
+}
+
+type Drotmger interface {
+	Drotmg(d1, d2, x1, y1 float64) (p blas.DrotmParams, rd1, rd2, rx1 float64)
+}
+
+func DrotmgTest(t *testing.T, d Drotmger) {
+	for _, test := range DrotmgTests {
+
+		p, rd1, rd2, rx1 := d.Drotmg(test.D1, test.D2, test.X1, test.Y1)
+
+		if p.Flag != test.P.Flag {
+			t.Errorf("drotmg flag mismatch %v: expected %v, found %v", test.Name, test.P.Flag, p.Flag)
+		}
+		for i, val := range p.H {
+			if !dTolEqual(test.P.H[i], val) {
+				t.Errorf("drotmg H mismatch %v: expected %v, found %v", test.Name, test.P.H, p.H)
+				break
+			}
+		}
+		if !dTolEqual(rd1, test.Rd1) {
+			t.Errorf("drotmg rd1 mismatch %v: expected %v, found %v", test.Name, test.Rd1, rd1)
+		}
+		if !dTolEqual(rd2, test.Rd2) {
+			t.Errorf("drotmg rd2 mismatch %v: expected %v, found %v", test.Name, test.Rd2, rd2)
+		}
+		if !dTolEqual(rx1, test.Rx1) {
+			t.Errorf("drotmg rx1 mismatch %v: expected %v, found %v", test.Name, test.Rx1, rx1)
+		}
+	}
+}
+
+type Droter interface {
+	Drot(n int, x []float64, incX int, y []float64, incY int, c, s float64)
+}
+
+func DrotTest(t *testing.T, d Droter) {
+	drot := d.Drot
+	for _, c := range DoubleTwoVectorCases {
+		for _, kind := range c.DrotCases {
+			dCopyTwoTmp(c.X, c.XTmp, c.Y, c.YTmp)
+			if c.Panic {
+				f := func() { drot(c.N, c.XTmp, c.Incx, c.YTmp, c.Incy, kind.C, kind.S) }
+				testpanics(f, c.Name, t)
+				continue
+			}
+			drot(c.N, c.XTmp, c.Incx, c.YTmp, c.Incy, kind.C, kind.S)
+			if !dSliceTolEqual(c.XTmp, kind.XAns) {
+				t.Errorf("drot: x mismatch %v: expected %v, found %v", c.Name, kind.XAns, c.XTmp)
+			}
+			if !dSliceTolEqual(c.YTmp, kind.YAns) {
+				t.Errorf("drot: y mismatch %v: expected %v, found %v", c.Name, kind.YAns, c.YTmp)
+			}
+		}
+	}
+}
+
+type Drotmer interface {
+	Drotm(n int, x []float64, incX int, y []float64, incY int, p blas.DrotmParams)
+}
+
+func DrotmTest(t *testing.T, d Drotmer) {
+	drotm := d.Drotm
+	for _, c := range DoubleTwoVectorCases {
+		for _, kind := range c.DrotmCases {
+			dCopyTwoTmp(c.X, c.XTmp, c.Y, c.YTmp)
+			if c.Panic {
+				f := func() { drotm(c.N, c.XTmp, c.Incx, c.YTmp, c.Incy, kind.P) }
+				testpanics(f, c.Name+", "+kind.Name, t)
+				continue
+			}
+			drotm(c.N, c.XTmp, c.Incx, c.YTmp, c.Incy, kind.P)
+			if !dSliceTolEqual(c.XTmp, kind.XAns) {
+				t.Errorf("drotm: mismatch %v: expected %v, found %v", c.Name, kind.XAns, c.XTmp)
+			}
+			if !dSliceTolEqual(c.YTmp, kind.YAns) {
+				t.Errorf("drotm: mismatch %v: expected %v, found %v", c.Name, kind.YAns, c.YTmp)
+			}
+		}
+	}
+}
+
+type Dscaler interface {
+	Dscal(n int, alpha float64, x []float64, incX int)
+}
+
+func DscalTest(t *testing.T, blasser Dscaler) {
+	dscal := blasser.Dscal
+	for _, c := range DoubleOneVectorCases {
+		for _, kind := range c.DscalCases {
+			xTmp := make([]float64, len(c.X))
+			copy(xTmp, c.X)
+			if c.Panic {
+				f := func() { dscal(c.N, kind.Alpha, xTmp, c.Incx) }
+				testpanics(f, c.Name, t)
+				continue
+			}
+			dscal(c.N, kind.Alpha, xTmp, c.Incx)
+			if !dSliceTolEqual(xTmp, kind.Ans) {
+				t.Errorf("dscal: mismatch %v, %v: expected %v, found %v", c.Name, kind.Name, kind.Ans, xTmp)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/level2bench.go b/vendor/gonum.org/v1/gonum/blas/testblas/level2bench.go
new file mode 100644
index 00000000..387ffcce
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/level2bench.go
@@ -0,0 +1,60 @@
+package testblas
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+func DgemvBenchmark(b *testing.B, blasser Dgemver, tA blas.Transpose, m, n, incX, incY int) {
+	var lenX, lenY int
+	if tA == blas.NoTrans {
+		lenX = n
+		lenY = m
+	} else {
+		lenX = m
+		lenY = n
+	}
+	xr := make([]float64, lenX)
+	for i := range xr {
+		xr[i] = rand.Float64()
+	}
+	x := makeIncremented(xr, incX, 0)
+	yr := make([]float64, lenY)
+	for i := range yr {
+		yr[i] = rand.Float64()
+	}
+	y := makeIncremented(yr, incY, 0)
+	a := make([]float64, m*n)
+	for i := range a {
+		a[i] = rand.Float64()
+	}
+
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		blasser.Dgemv(tA, m, n, 2, a, n, x, incX, 3, y, incY)
+	}
+}
+
+func DgerBenchmark(b *testing.B, blasser Dgerer, m, n, incX, incY int) {
+	xr := make([]float64, m)
+	for i := range xr {
+		xr[i] = rand.Float64()
+	}
+	x := makeIncremented(xr, incX, 0)
+	yr := make([]float64, n)
+	for i := range yr {
+		yr[i] = rand.Float64()
+	}
+	y := makeIncremented(yr, incY, 0)
+	a := make([]float64, m*n)
+	for i := range a {
+		a[i] = rand.Float64()
+	}
+
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		blasser.Dger(m, n, 2, x, incX, y, incY, a, n)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/zaxpy.go b/vendor/gonum.org/v1/gonum/blas/testblas/zaxpy.go
new file mode 100644
index 00000000..9aeace52
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/zaxpy.go
@@ -0,0 +1,157 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testblas
+
+import (
+	"fmt"
+	"testing"
+)
+
+type Zaxpyer interface {
+	Zaxpy(n int, alpha complex128, x []complex128, incX int, y []complex128, incY int)
+}
+
+func ZaxpyTest(t *testing.T, impl Zaxpyer) {
+	for tc, test := range []struct {
+		alpha complex128
+		x, y  []complex128
+
+		want    []complex128 // Result when both increments have the same sign.
+		wantRev []complex128 // Result when the increments have opposite sign.
+	}{
+		{
+			alpha:   0,
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i, 19 + 20i, 21 + 22i, 23 + 24i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i, 45 + 46i, 48 + 49i, 51 + 52i, 54 + 55i, 57 + 58i, 60 + 61i, 63 + 64i},
+			want:    []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i, 45 + 46i, 48 + 49i, 51 + 52i, 54 + 55i, 57 + 58i, 60 + 61i, 63 + 64i},
+			wantRev: []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i, 45 + 46i, 48 + 49i, 51 + 52i, 54 + 55i, 57 + 58i, 60 + 61i, 63 + 64i},
+		},
+		{
+			alpha:   1,
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i, 19 + 20i, 21 + 22i, 23 + 24i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i, 45 + 46i, 48 + 49i, 51 + 52i, 54 + 55i, 57 + 58i, 60 + 61i, 63 + 64i},
+			want:    []complex128{31 + 33i, 36 + 38i, 41 + 43i, 46 + 48i, 51 + 53i, 56 + 58i, 61 + 63i, 66 + 68i, 71 + 73i, 76 + 78i, 81 + 83i, 86 + 88i},
+			wantRev: []complex128{53 + 55i, 54 + 56i, 55 + 57i, 56 + 58i, 57 + 59i, 58 + 60i, 59 + 61i, 60 + 62i, 61 + 63i, 62 + 64i, 63 + 65i, 64 + 66i},
+		},
+		{
+			alpha:   3 + 7i,
+			x:       []complex128{1 + 2i},
+			y:       []complex128{30 + 31i},
+			want:    []complex128{19 + 44i},
+			wantRev: []complex128{19 + 44i},
+		},
+		{
+			alpha:   3 + 7i,
+			x:       []complex128{1 + 2i, 3 + 4i},
+			y:       []complex128{30 + 31i, 33 + 34i},
+			want:    []complex128{19 + 44i, 14 + 67i},
+			wantRev: []complex128{11 + 64i, 22 + 47i},
+		},
+		{
+			alpha:   3 + 7i,
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i},
+			want:    []complex128{19 + 44i, 14 + 67i, 9 + 90i},
+			wantRev: []complex128{3 + 84i, 14 + 67i, 25 + 50i},
+		},
+		{
+			alpha:   3 + 7i,
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i},
+			want:    []complex128{19 + 44i, 14 + 67i, 9 + 90i, 4 + 113i},
+			wantRev: []complex128{-5 + 104i, 6 + 87i, 17 + 70i, 28 + 53i},
+		},
+		{
+			alpha:   3 + 7i,
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i},
+			want:    []complex128{19 + 44i, 14 + 67i, 9 + 90i, 4 + 113i, -1 + 136i},
+			wantRev: []complex128{-13 + 124i, -2 + 107i, 9 + 90i, 20 + 73i, 31 + 56i},
+		},
+		{
+			alpha:   3 + 7i,
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i, 45 + 46i},
+			want:    []complex128{19 + 44i, 14 + 67i, 9 + 90i, 4 + 113i, -1 + 136i, -6 + 159i},
+			wantRev: []complex128{-21 + 144i, -10 + 127i, 1 + 110i, 12 + 93i, 23 + 76i, 34 + 59i},
+		},
+		{
+			alpha:   3 + 7i,
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i, 45 + 46i, 48 + 49i},
+			want:    []complex128{19 + 44i, 14 + 67i, 9 + 90i, 4 + 113i, -1 + 136i, -6 + 159i, -11 + 182i},
+			wantRev: []complex128{-29 + 164i, -18 + 147i, -7 + 130i, 4 + 113i, 15 + 96i, 26 + 79i, 37 + 62i},
+		},
+		{
+			alpha:   3 + 7i,
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i, 45 + 46i, 48 + 49i, 51 + 52i},
+			want:    []complex128{19 + 44i, 14 + 67i, 9 + 90i, 4 + 113i, -1 + 136i, -6 + 159i, -11 + 182i, -16 + 205i},
+			wantRev: []complex128{-37 + 184i, -26 + 167i, -15 + 150i, -4 + 133i, 7 + 116i, 18 + 99i, 29 + 82i, 40 + 65i},
+		},
+		{
+			alpha:   3 + 7i,
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i, 45 + 46i, 48 + 49i, 51 + 52i, 54 + 55i},
+			want:    []complex128{19 + 44i, 14 + 67i, 9 + 90i, 4 + 113i, -1 + 136i, -6 + 159i, -11 + 182i, -16 + 205i, -21 + 228i},
+			wantRev: []complex128{-45 + 204i, -34 + 187i, -23 + 170i, -12 + 153i, -1 + 136i, 10 + 119i, 21 + 102i, 32 + 85i, 43 + 68i},
+		},
+		{
+			alpha:   3 + 7i,
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i, 19 + 20i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i, 45 + 46i, 48 + 49i, 51 + 52i, 54 + 55i, 57 + 58i},
+			want:    []complex128{19 + 44i, 14 + 67i, 9 + 90i, 4 + 113i, -1 + 136i, -6 + 159i, -11 + 182i, -16 + 205i, -21 + 228i, -26 + 251i},
+			wantRev: []complex128{-53 + 224i, -42 + 207i, -31 + 190i, -20 + 173i, -9 + 156i, 2 + 139i, 13 + 122i, 24 + 105i, 35 + 88i, 46 + 71i},
+		},
+		{
+			alpha:   3 + 7i,
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i, 19 + 20i, 21 + 22i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i, 45 + 46i, 48 + 49i, 51 + 52i, 54 + 55i, 57 + 58i, 60 + 61i},
+			want:    []complex128{19 + 44i, 14 + 67i, 9 + 90i, 4 + 113i, -1 + 136i, -6 + 159i, -11 + 182i, -16 + 205i, -21 + 228i, -26 + 251i, -31 + 274i},
+			wantRev: []complex128{-61 + 244i, -50 + 227i, -39 + 210i, -28 + 193i, -17 + 176i, -6 + 159i, 5 + 142i, 16 + 125i, 27 + 108i, 38 + 91i, 49 + 74i},
+		},
+		{
+			alpha:   3 + 7i,
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i, 19 + 20i, 21 + 22i, 23 + 24i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i, 45 + 46i, 48 + 49i, 51 + 52i, 54 + 55i, 57 + 58i, 60 + 61i, 63 + 64i},
+			want:    []complex128{19 + 44i, 14 + 67i, 9 + 90i, 4 + 113i, -1 + 136i, -6 + 159i, -11 + 182i, -16 + 205i, -21 + 228i, -26 + 251i, -31 + 274i, -36 + 297i},
+			wantRev: []complex128{-69 + 264i, -58 + 247i, -47 + 230i, -36 + 213i, -25 + 196i, -14 + 179i, -3 + 162i, 8 + 145i, 19 + 128i, 30 + 111i, 41 + 94i, 52 + 77i},
+		},
+	} {
+		n := len(test.x)
+		if len(test.y) != n || len(test.want) != n || len(test.wantRev) != n {
+			panic("bad test")
+		}
+		for _, inc := range allPairs([]int{-7, -3, 1, 13}, []int{-11, -5, 1, 17}) {
+			incX := inc[0]
+			incY := inc[1]
+
+			x := makeZVector(test.x, incX)
+			xCopy := make([]complex128, len(x))
+			copy(xCopy, x)
+
+			y := makeZVector(test.y, incY)
+
+			var want []complex128
+			if incX*incY > 0 {
+				want = makeZVector(test.want, incY)
+			} else {
+				want = makeZVector(test.wantRev, incY)
+			}
+
+			impl.Zaxpy(n, test.alpha, x, incX, y, incY)
+
+			prefix := fmt.Sprintf("Case %v (incX=%v,incY=%v):", tc, incX, incY)
+
+			if !zsame(x, xCopy) {
+				t.Errorf("%v: unexpected modification of x", prefix)
+			}
+
+			if !zsame(y, want) {
+				t.Errorf("%v: unexpected y:\nwant %v\ngot %v", prefix, want, y)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/zcopy.go b/vendor/gonum.org/v1/gonum/blas/testblas/zcopy.go
new file mode 100644
index 00000000..9aba717d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/zcopy.go
@@ -0,0 +1,71 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testblas
+
+import (
+	"fmt"
+	"math"
+	"math/rand"
+	"testing"
+)
+
+type Zcopyer interface {
+	Zcopy(n int, x []complex128, incX int, y []complex128, incY int)
+}
+
+func ZcopyTest(t *testing.T, impl Zcopyer) {
+	rnd := rand.New(rand.NewSource(1))
+	for n := 0; n <= 20; n++ {
+		for _, inc := range allPairs([]int{-7, -3, 1, 13}, []int{-11, -5, 1, 17}) {
+			incX := inc[0]
+			incY := inc[1]
+			aincX := abs(incX)
+			aincY := abs(incY)
+
+			var x []complex128
+			if n > 0 {
+				x = make([]complex128, (n-1)*aincX+1)
+			}
+			for i := range x {
+				x[i] = complex(math.NaN(), math.NaN())
+			}
+			for i := 0; i < n; i++ {
+				x[i*aincX] = complex(rnd.NormFloat64(), rnd.NormFloat64())
+			}
+			xCopy := make([]complex128, len(x))
+			copy(xCopy, x)
+
+			var y []complex128
+			if n > 0 {
+				y = make([]complex128, (n-1)*aincY+1)
+			}
+			for i := range y {
+				y[i] = complex(math.NaN(), math.NaN())
+			}
+
+			want := make([]complex128, len(y))
+			if incX*incY > 0 {
+				for i := 0; i < n; i++ {
+					want[i*aincY] = x[i*aincX]
+				}
+			} else {
+				for i := 0; i < n; i++ {
+					want[i*aincY] = x[(n-1-i)*aincX]
+				}
+			}
+
+			impl.Zcopy(n, x, incX, y, incY)
+
+			prefix := fmt.Sprintf("Case n=%v,incX=%v,incY=%v:", n, incX, incY)
+
+			if !zsame(x, xCopy) {
+				t.Errorf("%v: unexpected modification of x", prefix)
+			}
+			if !zsame(y, want) {
+				t.Errorf("%v: unexpected y:\nwant %v\ngot %v", prefix, want, y)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/zdotc.go b/vendor/gonum.org/v1/gonum/blas/testblas/zdotc.go
new file mode 100644
index 00000000..a28b0c1a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/zdotc.go
@@ -0,0 +1,139 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testblas
+
+import (
+	"fmt"
+	"testing"
+)
+
+type Zdotcer interface {
+	Zdotc(n int, x []complex128, incX int, y []complex128, incY int) complex128
+}
+
+func ZdotcTest(t *testing.T, impl Zdotcer) {
+	for tc, test := range []struct {
+		x, y []complex128
+
+		want    complex128 // Result when both increments have the same sign.
+		wantRev complex128 // Result when the increments have opposite sign.
+	}{
+		{
+			x:       nil,
+			y:       nil,
+			want:    0,
+			wantRev: 0,
+		},
+		{
+			x:       []complex128{1 + 2i},
+			y:       []complex128{30 + 31i},
+			want:    92 - 29i,
+			wantRev: 92 - 29i,
+		},
+		{
+			x:       []complex128{1 + 2i, 3 + 4i},
+			y:       []complex128{30 + 31i, 33 + 34i},
+			want:    327 - 59i,
+			wantRev: 315 - 59i,
+		},
+		{
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i},
+			want:    729 - 90i,
+			wantRev: 681 - 90i,
+		},
+		{
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i},
+			want:    1322 - 122i,
+			wantRev: 1202 - 122i,
+		},
+		{
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i},
+			want:    2130 - 155i,
+			wantRev: 1890 - 155i,
+		},
+		{
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i, 45 + 46i},
+			want:    3177 - 189i,
+			wantRev: 2757 - 189i,
+		},
+		{
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i, 45 + 46i, 48 + 49i},
+			want:    4487 - 224i,
+			wantRev: 3815 - 224i,
+		},
+		{
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i, 45 + 46i, 48 + 49i, 51 + 52i},
+			want:    6084 - 260i,
+			wantRev: 5076 - 260i,
+		},
+		{
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i, 45 + 46i, 48 + 49i, 51 + 52i, 54 + 55i},
+			want:    7992 - 297i,
+			wantRev: 6552 - 297i,
+		},
+		{
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i, 19 + 20i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i, 45 + 46i, 48 + 49i, 51 + 52i, 54 + 55i, 57 + 58i},
+			want:    10235 - 335i,
+			wantRev: 8255 - 335i,
+		},
+		{
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i, 19 + 20i, 21 + 22i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i, 45 + 46i, 48 + 49i, 51 + 52i, 54 + 55i, 57 + 58i, 60 + 61i},
+			want:    12837 - 374i,
+			wantRev: 10197 - 374i,
+		},
+		{
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i, 19 + 20i, 21 + 22i, 23 + 24i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i, 45 + 46i, 48 + 49i, 51 + 52i, 54 + 55i, 57 + 58i, 60 + 61i, 63 + 64i},
+			want:    15822 - 414i,
+			wantRev: 12390 - 414i,
+		},
+	} {
+		n := len(test.x)
+		if len(test.y) != n {
+			panic("bad test")
+		}
+		for _, inc := range allPairs([]int{-7, -3, 1, 13}, []int{-11, -5, 1, 17}) {
+			incX := inc[0]
+			incY := inc[1]
+
+			x := makeZVector(test.x, incX)
+			xCopy := make([]complex128, len(x))
+			copy(xCopy, x)
+
+			y := makeZVector(test.y, incY)
+			yCopy := make([]complex128, len(y))
+			copy(yCopy, y)
+
+			want := test.want
+			if incX*incY < 0 {
+				want = test.wantRev
+			}
+
+			got := impl.Zdotc(n, x, incX, y, incY)
+
+			prefix := fmt.Sprintf("Case %v (incX=%v,incY=%v):", tc, incX, incY)
+
+			if !zsame(x, xCopy) {
+				t.Errorf("%v: unexpected modification of x", prefix)
+			}
+			if !zsame(y, yCopy) {
+				t.Errorf("%v: unexpected modification of y", prefix)
+			}
+
+			if got != want {
+				t.Errorf("%v: unexpected result. want %v, got %v", prefix, want, got)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/zdotu.go b/vendor/gonum.org/v1/gonum/blas/testblas/zdotu.go
new file mode 100644
index 00000000..7b83b735
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/zdotu.go
@@ -0,0 +1,139 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testblas
+
+import (
+	"fmt"
+	"testing"
+)
+
+type Zdotuer interface {
+	Zdotu(n int, x []complex128, incX int, y []complex128, incY int) complex128
+}
+
+func ZdotuTest(t *testing.T, impl Zdotuer) {
+	for tc, test := range []struct {
+		x, y []complex128
+
+		want    complex128 // Result when both increments have the same sign.
+		wantRev complex128 // Result when the increments have opposite sign.
+	}{
+		{
+			x:       nil,
+			y:       nil,
+			want:    0,
+			wantRev: 0,
+		},
+		{
+			x:       []complex128{1 + 2i},
+			y:       []complex128{30 + 31i},
+			want:    -32 + 91i,
+			wantRev: -32 + 91i,
+		},
+		{
+			x:       []complex128{1 + 2i, 3 + 4i},
+			y:       []complex128{30 + 31i, 33 + 34i},
+			want:    -69 + 325i,
+			wantRev: -69 + 313i,
+		},
+		{
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i},
+			want:    -111 + 726i,
+			wantRev: -111 + 678i,
+		},
+		{
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i},
+			want:    -158 + 1318i,
+			wantRev: -158 + 1198i,
+		},
+		{
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i},
+			want:    -210 + 2125i,
+			wantRev: -210 + 1885i,
+		},
+		{
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i, 45 + 46i},
+			want:    -267 + 3171i,
+			wantRev: -267 + 2751i,
+		},
+		{
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i, 45 + 46i, 48 + 49i},
+			want:    -329 + 4480i,
+			wantRev: -329 + 3808i,
+		},
+		{
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i, 45 + 46i, 48 + 49i, 51 + 52i},
+			want:    -396 + 6076i,
+			wantRev: -396 + 5068i,
+		},
+		{
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i, 45 + 46i, 48 + 49i, 51 + 52i, 54 + 55i},
+			want:    -468 + 7983i,
+			wantRev: -468 + 6543i,
+		},
+		{
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i, 19 + 20i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i, 45 + 46i, 48 + 49i, 51 + 52i, 54 + 55i, 57 + 58i},
+			want:    -545 + 10225i,
+			wantRev: -545 + 8245i,
+		},
+		{
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i, 19 + 20i, 21 + 22i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i, 45 + 46i, 48 + 49i, 51 + 52i, 54 + 55i, 57 + 58i, 60 + 61i},
+			want:    -627 + 12826i,
+			wantRev: -627 + 10186i,
+		},
+		{
+			x:       []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i, 19 + 20i, 21 + 22i, 23 + 24i},
+			y:       []complex128{30 + 31i, 33 + 34i, 36 + 37i, 39 + 40i, 42 + 43i, 45 + 46i, 48 + 49i, 51 + 52i, 54 + 55i, 57 + 58i, 60 + 61i, 63 + 64i},
+			want:    -714 + 15810i,
+			wantRev: -714 + 12378i,
+		},
+	} {
+		n := len(test.x)
+		if len(test.y) != n {
+			panic("bad test")
+		}
+		for _, inc := range allPairs([]int{-7, -3, 1, 13}, []int{-11, -5, 1, 17}) {
+			incX := inc[0]
+			incY := inc[1]
+
+			x := makeZVector(test.x, incX)
+			xCopy := make([]complex128, len(x))
+			copy(xCopy, x)
+
+			y := makeZVector(test.y, incY)
+			yCopy := make([]complex128, len(y))
+			copy(yCopy, y)
+
+			want := test.want
+			if incX*incY < 0 {
+				want = test.wantRev
+			}
+
+			got := impl.Zdotu(n, x, incX, y, incY)
+
+			prefix := fmt.Sprintf("Case %v (incX=%v,incY=%v):", tc, incX, incY)
+
+			if !zsame(x, xCopy) {
+				t.Errorf("%v: unexpected modification of x", prefix)
+			}
+			if !zsame(y, yCopy) {
+				t.Errorf("%v: unexpected modification of y", prefix)
+			}
+
+			if got != want {
+				t.Errorf("%v: unexpected result. want %v, got %v", prefix, want, got)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/zdscal.go b/vendor/gonum.org/v1/gonum/blas/testblas/zdscal.go
new file mode 100644
index 00000000..9037d841
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/zdscal.go
@@ -0,0 +1,119 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testblas
+
+import (
+	"fmt"
+	"testing"
+)
+
+type Zdscaler interface {
+	Zdscal(n int, alpha float64, x []complex128, incX int)
+}
+
+func ZdscalTest(t *testing.T, impl Zdscaler) {
+	for tc, test := range []struct {
+		alpha float64
+		x     []complex128
+		want  []complex128
+	}{
+		{
+			alpha: 3,
+			x:     nil,
+			want:  nil,
+		},
+		{
+			alpha: 3,
+			x:     []complex128{1 + 2i},
+			want:  []complex128{3 + 6i},
+		},
+		{
+			alpha: 3,
+			x:     []complex128{1 + 2i, 3 + 4i},
+			want:  []complex128{3 + 6i, 9 + 12i},
+		},
+		{
+			alpha: 3,
+			x:     []complex128{1 + 2i, 3 + 4i, 5 + 6i},
+			want:  []complex128{3 + 6i, 9 + 12i, 15 + 18i},
+		},
+		{
+			alpha: 3,
+			x:     []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i},
+			want:  []complex128{3 + 6i, 9 + 12i, 15 + 18i, 21 + 24i},
+		},
+		{
+			alpha: 3,
+			x:     []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i},
+			want:  []complex128{3 + 6i, 9 + 12i, 15 + 18i, 21 + 24i, 27 + 30i},
+		},
+		{
+			alpha: 3,
+			x:     []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i},
+			want:  []complex128{3 + 6i, 9 + 12i, 15 + 18i, 21 + 24i, 27 + 30i, 33 + 36i},
+		},
+		{
+			alpha: 3,
+			x:     []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i},
+			want:  []complex128{3 + 6i, 9 + 12i, 15 + 18i, 21 + 24i, 27 + 30i, 33 + 36i, 39 + 42i},
+		},
+		{
+			alpha: 3,
+			x:     []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i},
+			want:  []complex128{3 + 6i, 9 + 12i, 15 + 18i, 21 + 24i, 27 + 30i, 33 + 36i, 39 + 42i, 45 + 48i},
+		},
+		{
+			alpha: 3,
+			x:     []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i},
+			want:  []complex128{3 + 6i, 9 + 12i, 15 + 18i, 21 + 24i, 27 + 30i, 33 + 36i, 39 + 42i, 45 + 48i, 51 + 54i},
+		},
+		{
+			alpha: 3,
+			x:     []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i, 19 + 20i},
+			want:  []complex128{3 + 6i, 9 + 12i, 15 + 18i, 21 + 24i, 27 + 30i, 33 + 36i, 39 + 42i, 45 + 48i, 51 + 54i, 57 + 60i},
+		},
+		{
+			alpha: 3,
+			x:     []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i, 19 + 20i, 21 + 22i},
+			want:  []complex128{3 + 6i, 9 + 12i, 15 + 18i, 21 + 24i, 27 + 30i, 33 + 36i, 39 + 42i, 45 + 48i, 51 + 54i, 57 + 60i, 63 + 66i},
+		},
+		{
+			alpha: 3,
+			x:     []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i, 19 + 20i, 21 + 22i, 23 + 24i},
+			want:  []complex128{3 + 6i, 9 + 12i, 15 + 18i, 21 + 24i, 27 + 30i, 33 + 36i, 39 + 42i, 45 + 48i, 51 + 54i, 57 + 60i, 63 + 66i, 69 + 72i},
+		},
+		{
+			alpha: 0,
+			x:     []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i, 19 + 20i, 21 + 22i, 23 + 24i},
+			want:  []complex128{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+		},
+	} {
+		n := len(test.x)
+		if len(test.want) != n {
+			panic("bad test")
+		}
+		for _, incX := range []int{-3, -1, 1, 2, 4, 7, 10} {
+			x := makeZVector(test.x, incX)
+			xCopy := make([]complex128, len(x))
+			copy(xCopy, x)
+
+			want := makeZVector(test.want, incX)
+
+			impl.Zdscal(n, test.alpha, x, incX)
+
+			prefix := fmt.Sprintf("Case %v (n=%v,incX=%v):", tc, n, incX)
+
+			if incX < 0 {
+				if !zsame(x, xCopy) {
+					t.Errorf("%v: unexpected modification of x\nwant %v\ngot %v", prefix, want, x)
+				}
+				continue
+			}
+			if !zsame(x, want) {
+				t.Errorf("%v: unexpected result:\nwant: %v\ngot: %v", prefix, want, x)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/zgerc.go b/vendor/gonum.org/v1/gonum/blas/testblas/zgerc.go
new file mode 100644
index 00000000..15a83745
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/zgerc.go
@@ -0,0 +1,183 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testblas
+
+import (
+	"testing"
+)
+
+type Zgercer interface {
+	Zgerc(m, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, a []complex128, lda int)
+}
+
+func ZgercTest(t *testing.T, impl Zgercer) {
+	for tc, test := range []struct {
+		alpha complex128
+		x     []complex128
+		incX  int
+		y     []complex128
+		incY  int
+		a     []complex128
+
+		want []complex128
+	}{
+		{
+			incX:  1,
+			incY:  1,
+			alpha: 1 + 2i,
+		},
+		{
+			incX:  1,
+			incY:  1,
+			alpha: 1 + 2i,
+			x:     []complex128{1 + 13i, 18 + 15i, 10 + 18i},
+			y:     []complex128{15 + 12i, 4 + 8i, 5 + 16i, 19 + 12i},
+			a: []complex128{
+				10 + 9i, 6 + 17i, 3 + 10i, 6 + 7i,
+				3 + 4i, 11 + 16i, 5 + 14i, 11 + 18i,
+				18 + 6i, 4 + 1i, 13 + 2i, 14 + 3i},
+			want: []complex128{
+				-185 + 534i, 26 + 277i, 118 + 485i, -289 + 592i,
+				435 + 913i, 371 + 316i, 761 + 461i, 395 + 1131i,
+				84 + 888i, 204 + 361i, 491 + 608i, -24 + 1037i},
+		},
+		{
+			incX:  7,
+			incY:  13,
+			alpha: 1 + 2i,
+			x:     []complex128{1 + 13i, 18 + 15i, 10 + 18i},
+			y:     []complex128{15 + 12i, 4 + 8i, 5 + 16i, 19 + 12i},
+			a: []complex128{
+				10 + 9i, 6 + 17i, 3 + 10i, 6 + 7i,
+				3 + 4i, 11 + 16i, 5 + 14i, 11 + 18i,
+				18 + 6i, 4 + 1i, 13 + 2i, 14 + 3i},
+			want: []complex128{
+				-185 + 534i, 26 + 277i, 118 + 485i, -289 + 592i,
+				435 + 913i, 371 + 316i, 761 + 461i, 395 + 1131i,
+				84 + 888i, 204 + 361i, 491 + 608i, -24 + 1037i},
+		},
+		{
+			incX:  -7,
+			incY:  -13,
+			alpha: 1 + 2i,
+			x:     []complex128{10 + 18i, 18 + 15i, 1 + 13i},
+			y:     []complex128{19 + 12i, 5 + 16i, 4 + 8i, 15 + 12i},
+			a: []complex128{
+				10 + 9i, 6 + 17i, 3 + 10i, 6 + 7i,
+				3 + 4i, 11 + 16i, 5 + 14i, 11 + 18i,
+				18 + 6i, 4 + 1i, 13 + 2i, 14 + 3i},
+			want: []complex128{
+				-185 + 534i, 26 + 277i, 118 + 485i, -289 + 592i,
+				435 + 913i, 371 + 316i, 761 + 461i, 395 + 1131i,
+				84 + 888i, 204 + 361i, 491 + 608i, -24 + 1037i},
+		},
+		{
+			incX:  1,
+			incY:  1,
+			alpha: 1 + 2i,
+			x:     []complex128{5 + 16i, 12 + 19i, 9 + 7i, 2 + 4i},
+			y:     []complex128{18 + 7i, 20 + 15i, 12 + 14i},
+			a: []complex128{
+				11 + 4i, 17 + 18i, 7 + 13i,
+				14 + 20i, 14 + 10i, 7 + 5i,
+				7 + 17i, 10 + 6i, 11 + 13i,
+				7 + 6i, 19 + 16i, 8 + 8i,
+			},
+			want: []complex128{
+				-293 + 661i, -133 + 943i, 47 + 703i,
+				-153 + 976i, 139 + 1260i, 297 + 885i,
+				92 + 502i, 285 + 581i, 301 + 383i,
+				-45 + 192i, 19 + 266i, 48 + 188i,
+			},
+		},
+		{
+			incX:  7,
+			incY:  13,
+			alpha: 1 + 2i,
+			x:     []complex128{5 + 16i, 12 + 19i, 9 + 7i, 2 + 4i},
+			y:     []complex128{18 + 7i, 20 + 15i, 12 + 14i},
+			a: []complex128{
+				11 + 4i, 17 + 18i, 7 + 13i,
+				14 + 20i, 14 + 10i, 7 + 5i,
+				7 + 17i, 10 + 6i, 11 + 13i,
+				7 + 6i, 19 + 16i, 8 + 8i,
+			},
+			want: []complex128{
+				-293 + 661i, -133 + 943i, 47 + 703i,
+				-153 + 976i, 139 + 1260i, 297 + 885i,
+				92 + 502i, 285 + 581i, 301 + 383i,
+				-45 + 192i, 19 + 266i, 48 + 188i,
+			},
+		},
+		{
+			incX:  -7,
+			incY:  -13,
+			alpha: 1 + 2i,
+			x:     []complex128{2 + 4i, 9 + 7i, 12 + 19i, 5 + 16i},
+			y:     []complex128{12 + 14i, 20 + 15i, 18 + 7i},
+			a: []complex128{
+				11 + 4i, 17 + 18i, 7 + 13i,
+				14 + 20i, 14 + 10i, 7 + 5i,
+				7 + 17i, 10 + 6i, 11 + 13i,
+				7 + 6i, 19 + 16i, 8 + 8i,
+			},
+			want: []complex128{
+				-293 + 661i, -133 + 943i, 47 + 703i,
+				-153 + 976i, 139 + 1260i, 297 + 885i,
+				92 + 502i, 285 + 581i, 301 + 383i,
+				-45 + 192i, 19 + 266i, 48 + 188i,
+			},
+		},
+		{
+			incX:  -7,
+			incY:  -13,
+			alpha: 0,
+			x:     []complex128{2 + 4i, 9 + 7i, 12 + 19i, 5 + 16i},
+			y:     []complex128{12 + 14i, 20 + 15i, 18 + 7i},
+			a: []complex128{
+				11 + 4i, 17 + 18i, 7 + 13i,
+				14 + 20i, 14 + 10i, 7 + 5i,
+				7 + 17i, 10 + 6i, 11 + 13i,
+				7 + 6i, 19 + 16i, 8 + 8i,
+			},
+			want: []complex128{
+				11 + 4i, 17 + 18i, 7 + 13i,
+				14 + 20i, 14 + 10i, 7 + 5i,
+				7 + 17i, 10 + 6i, 11 + 13i,
+				7 + 6i, 19 + 16i, 8 + 8i,
+			},
+		},
+	} {
+		m := len(test.x)
+		n := len(test.y)
+		incX := test.incX
+		incY := test.incY
+
+		for _, lda := range []int{max(1, n), n + 20} {
+			x := makeZVector(test.x, incX)
+			xCopy := make([]complex128, len(x))
+			copy(xCopy, x)
+
+			y := makeZVector(test.y, incY)
+			yCopy := make([]complex128, len(y))
+			copy(yCopy, y)
+
+			a := makeZGeneral(test.a, m, n, lda)
+			want := makeZGeneral(test.want, m, n, lda)
+
+			impl.Zgerc(m, n, test.alpha, x, incX, y, incY, a, lda)
+
+			if !zsame(x, xCopy) {
+				t.Errorf("Case %v: unexpected modification of x", tc)
+			}
+			if !zsame(y, yCopy) {
+				t.Errorf("Case %v: unexpected modification of y", tc)
+			}
+			if !zsame(want, a) {
+				t.Errorf("Case %v: unexpected result\nwant %v\ngot %v", tc, want, a)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/zgeru.go b/vendor/gonum.org/v1/gonum/blas/testblas/zgeru.go
new file mode 100644
index 00000000..09c66e71
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/zgeru.go
@@ -0,0 +1,257 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testblas
+
+import (
+	"testing"
+)
+
+type Zgeruer interface {
+	Zgeru(m, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, a []complex128, lda int)
+}
+
+func ZgeruTest(t *testing.T, impl Zgeruer) {
+	for tc, test := range []struct {
+		alpha complex128
+		x     []complex128
+		incX  int
+		y     []complex128
+		incY  int
+		a     []complex128
+
+		want []complex128
+	}{
+		{
+			incX:  1,
+			incY:  1,
+			alpha: 1 + 2i,
+		},
+		{
+			incX:  1,
+			incY:  1,
+			alpha: 1 + 2i,
+			x:     []complex128{1 + 13i, 18 + 15i, 10 + 18i},
+			y:     []complex128{15 + 12i, 4 + 8i, 5 + 16i, 19 + 12i},
+			a: []complex128{
+				4 + 7i, 4 + 7i, 12 + 3i, 9 + 10i,
+				3 + 3i, 1 + 2i, 17 + 17i, 9 + 18i,
+				14 + 12i, 9 + 16i, 1 + 1i, 9 + 1i,
+			},
+			want: []complex128{
+				-551 - 68i, -216 - 133i, -353 - 322i, -646 - 5i,
+				-789 + 624i, -455 + 110i, -859 + 80i, -831 + 843i,
+				-832 + 270i, -399 - 40i, -737 - 225i, -941 + 411i,
+			},
+		},
+		{
+			incX:  7,
+			incY:  13,
+			alpha: 1 + 2i,
+			x:     []complex128{1 + 13i, 18 + 15i, 10 + 18i},
+			y:     []complex128{15 + 12i, 4 + 8i, 5 + 16i, 19 + 12i},
+			a: []complex128{
+				4 + 7i, 4 + 7i, 12 + 3i, 9 + 10i,
+				3 + 3i, 1 + 2i, 17 + 17i, 9 + 18i,
+				14 + 12i, 9 + 16i, 1 + 1i, 9 + 1i,
+			},
+			want: []complex128{
+				-551 - 68i, -216 - 133i, -353 - 322i, -646 - 5i,
+				-789 + 624i, -455 + 110i, -859 + 80i, -831 + 843i,
+				-832 + 270i, -399 - 40i, -737 - 225i, -941 + 411i,
+			},
+		},
+		{
+			incX:  1,
+			incY:  13,
+			alpha: 1 + 2i,
+			x:     []complex128{1 + 13i, 18 + 15i, 10 + 18i},
+			y:     []complex128{15 + 12i, 4 + 8i, 5 + 16i, 19 + 12i},
+			a: []complex128{
+				4 + 7i, 4 + 7i, 12 + 3i, 9 + 10i,
+				3 + 3i, 1 + 2i, 17 + 17i, 9 + 18i,
+				14 + 12i, 9 + 16i, 1 + 1i, 9 + 1i,
+			},
+			want: []complex128{
+				-551 - 68i, -216 - 133i, -353 - 322i, -646 - 5i,
+				-789 + 624i, -455 + 110i, -859 + 80i, -831 + 843i,
+				-832 + 270i, -399 - 40i, -737 - 225i, -941 + 411i,
+			},
+		},
+		{
+			incX:  1,
+			incY:  -13,
+			alpha: 1 + 2i,
+			x:     []complex128{1 + 13i, 18 + 15i, 10 + 18i},
+			y:     []complex128{19 + 12i, 5 + 16i, 4 + 8i, 15 + 12i},
+			a: []complex128{
+				4 + 7i, 4 + 7i, 12 + 3i, 9 + 10i,
+				3 + 3i, 1 + 2i, 17 + 17i, 9 + 18i,
+				14 + 12i, 9 + 16i, 1 + 1i, 9 + 1i,
+			},
+			want: []complex128{
+				-551 - 68i, -216 - 133i, -353 - 322i, -646 - 5i,
+				-789 + 624i, -455 + 110i, -859 + 80i, -831 + 843i,
+				-832 + 270i, -399 - 40i, -737 - 225i, -941 + 411i,
+			},
+		},
+		{
+			incX:  7,
+			incY:  1,
+			alpha: 1 + 2i,
+			x:     []complex128{1 + 13i, 18 + 15i, 10 + 18i},
+			y:     []complex128{15 + 12i, 4 + 8i, 5 + 16i, 19 + 12i},
+			a: []complex128{
+				4 + 7i, 4 + 7i, 12 + 3i, 9 + 10i,
+				3 + 3i, 1 + 2i, 17 + 17i, 9 + 18i,
+				14 + 12i, 9 + 16i, 1 + 1i, 9 + 1i,
+			},
+			want: []complex128{
+				-551 - 68i, -216 - 133i, -353 - 322i, -646 - 5i,
+				-789 + 624i, -455 + 110i, -859 + 80i, -831 + 843i,
+				-832 + 270i, -399 - 40i, -737 - 225i, -941 + 411i,
+			},
+		},
+		{
+			incX:  -7,
+			incY:  1,
+			alpha: 1 + 2i,
+			x:     []complex128{10 + 18i, 18 + 15i, 1 + 13i},
+			y:     []complex128{15 + 12i, 4 + 8i, 5 + 16i, 19 + 12i},
+			a: []complex128{
+				4 + 7i, 4 + 7i, 12 + 3i, 9 + 10i,
+				3 + 3i, 1 + 2i, 17 + 17i, 9 + 18i,
+				14 + 12i, 9 + 16i, 1 + 1i, 9 + 1i,
+			},
+			want: []complex128{
+				-551 - 68i, -216 - 133i, -353 - 322i, -646 - 5i,
+				-789 + 624i, -455 + 110i, -859 + 80i, -831 + 843i,
+				-832 + 270i, -399 - 40i, -737 - 225i, -941 + 411i,
+			},
+		},
+		{
+			incX:  -7,
+			incY:  -13,
+			alpha: 1 + 2i,
+			x:     []complex128{10 + 18i, 18 + 15i, 1 + 13i},
+			y:     []complex128{19 + 12i, 5 + 16i, 4 + 8i, 15 + 12i},
+			a: []complex128{
+				4 + 7i, 4 + 7i, 12 + 3i, 9 + 10i,
+				3 + 3i, 1 + 2i, 17 + 17i, 9 + 18i,
+				14 + 12i, 9 + 16i, 1 + 1i, 9 + 1i,
+			},
+			want: []complex128{
+				-551 - 68i, -216 - 133i, -353 - 322i, -646 - 5i,
+				-789 + 624i, -455 + 110i, -859 + 80i, -831 + 843i,
+				-832 + 270i, -399 - 40i, -737 - 225i, -941 + 411i,
+			},
+		},
+		{
+			incX:  1,
+			incY:  1,
+			alpha: 1 + 2i,
+			x:     []complex128{5 + 16i, 12 + 19i, 9 + 7i, 2 + 4i},
+			y:     []complex128{18 + 7i, 20 + 15i, 12 + 14i},
+			a: []complex128{
+				8 + 17i, 2 + 2i, 8 + 17i,
+				1 + 10i, 10 + 15i, 4 + 18i,
+				11 + 3i, 15 + 7i, 12 + 15i,
+				20 + 10i, 8 + 13i, 19 + 10i,
+			},
+			want: []complex128{
+				-660 + 296i, -928 + 117i, -680 - 49i,
+				-768 + 602i, -1155 + 485i, -910 + 170i,
+				-254 + 418i, -460 + 432i, -398 + 245i,
+				-144 + 112i, -232 + 83i, -165 + 22i,
+			},
+		},
+		{
+			incX:  7,
+			incY:  13,
+			alpha: 1 + 2i,
+			x:     []complex128{5 + 16i, 12 + 19i, 9 + 7i, 2 + 4i},
+			y:     []complex128{18 + 7i, 20 + 15i, 12 + 14i},
+			a: []complex128{
+				8 + 17i, 2 + 2i, 8 + 17i,
+				1 + 10i, 10 + 15i, 4 + 18i,
+				11 + 3i, 15 + 7i, 12 + 15i,
+				20 + 10i, 8 + 13i, 19 + 10i,
+			},
+			want: []complex128{
+				-660 + 296i, -928 + 117i, -680 - 49i,
+				-768 + 602i, -1155 + 485i, -910 + 170i,
+				-254 + 418i, -460 + 432i, -398 + 245i,
+				-144 + 112i, -232 + 83i, -165 + 22i,
+			},
+		},
+		{
+			incX:  -7,
+			incY:  -13,
+			alpha: 1 + 2i,
+			x:     []complex128{2 + 4i, 9 + 7i, 12 + 19i, 5 + 16i},
+			y:     []complex128{12 + 14i, 20 + 15i, 18 + 7i},
+			a: []complex128{
+				8 + 17i, 2 + 2i, 8 + 17i,
+				1 + 10i, 10 + 15i, 4 + 18i,
+				11 + 3i, 15 + 7i, 12 + 15i,
+				20 + 10i, 8 + 13i, 19 + 10i,
+			},
+			want: []complex128{
+				-660 + 296i, -928 + 117i, -680 - 49i,
+				-768 + 602i, -1155 + 485i, -910 + 170i,
+				-254 + 418i, -460 + 432i, -398 + 245i,
+				-144 + 112i, -232 + 83i, -165 + 22i,
+			},
+		},
+		{
+			incX:  -7,
+			incY:  -13,
+			alpha: 0,
+			x:     []complex128{5 + 16i, 12 + 19i, 9 + 7i, 2 + 4i},
+			y:     []complex128{18 + 7i, 20 + 15i, 12 + 14i},
+			a: []complex128{
+				8 + 17i, 2 + 2i, 8 + 17i,
+				1 + 10i, 10 + 15i, 4 + 18i,
+				11 + 3i, 15 + 7i, 12 + 15i,
+				20 + 10i, 8 + 13i, 19 + 10i,
+			},
+			want: []complex128{
+				8 + 17i, 2 + 2i, 8 + 17i,
+				1 + 10i, 10 + 15i, 4 + 18i,
+				11 + 3i, 15 + 7i, 12 + 15i,
+				20 + 10i, 8 + 13i, 19 + 10i,
+			},
+		},
+	} {
+		m := len(test.x)
+		n := len(test.y)
+		incX := test.incX
+		incY := test.incY
+
+		for _, lda := range []int{max(1, n), n + 20} {
+			x := makeZVector(test.x, incX)
+			xCopy := make([]complex128, len(x))
+			copy(xCopy, x)
+
+			y := makeZVector(test.y, incY)
+			yCopy := make([]complex128, len(y))
+			copy(yCopy, y)
+
+			a := makeZGeneral(test.a, m, n, lda)
+			want := makeZGeneral(test.want, m, n, lda)
+
+			impl.Zgeru(m, n, test.alpha, x, incX, y, incY, a, lda)
+
+			if !zsame(x, xCopy) {
+				t.Errorf("Case %v: unexpected modification of x", tc)
+			}
+			if !zsame(y, yCopy) {
+				t.Errorf("Case %v: unexpected modification of y", tc)
+			}
+			if !zsame(want, a) {
+				t.Errorf("Case %v: unexpected result\nwant %v\ngot %v", tc, want, a)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/zher.go b/vendor/gonum.org/v1/gonum/blas/testblas/zher.go
new file mode 100644
index 00000000..fbd14b65
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/zher.go
@@ -0,0 +1,155 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testblas
+
+import (
+	"math"
+	"math/cmplx"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+type Zherer interface {
+	Zher(uplo blas.Uplo, n int, alpha float64, x []complex128, incX int, a []complex128, lda int)
+}
+
+func ZherTest(t *testing.T, impl Zherer) {
+	for tc, test := range []struct {
+		alpha float64
+		x     []complex128
+		a     []complex128
+
+		want    []complex128
+		wantRev []complex128 // Result when incX is negative.
+	}{
+		{
+			alpha: 1,
+		},
+		{
+			alpha: 3,
+			x: []complex128{
+				0 - 3i,
+				6 + 10i,
+				-2 - 7i,
+			},
+			a: []complex128{
+				-2 + 0i, -3 - 11i, 0 + 4i,
+				-3 + 11i, -6 + 0i, 7 + 2i,
+				0 - 4i, 7 - 2i, 18 + 0i,
+			},
+			want: []complex128{
+				25 + 0i, -93 - 65i, 63 + 22i,
+				-93 + 65i, 402 + 0i, -239 + 68i,
+				63 - 22i, -239 - 68i, 177 + 0i},
+			wantRev: []complex128{
+				157 + 0i, -249 - 77i, 63 - 14i,
+				-249 + 77i, 402 + 0i, -83 + 56i,
+				63 + 14i, -83 - 56i, 45 + 0i,
+			},
+		},
+		{
+			alpha: 3,
+			x: []complex128{
+				-6 + 2i,
+				-2 - 4i,
+				0 + 0i,
+				0 + 7i,
+			},
+			a: []complex128{
+				2 + 0i, -9 + 7i, 3 + 11i, 10 - 1i,
+				-9 - 7i, 16 + 0i, -5 + 2i, -7 - 5i,
+				3 - 11i, -5 - 2i, 14 + 0i, 2 - 1i,
+				10 + 1i, -7 + 5i, 2 + 1i, 18 + 0i,
+			},
+			want: []complex128{
+				122 + 0i, 3 - 77i, 3 + 11i, 52 + 125i,
+				3 + 77i, 76 + 0i, -5 + 2i, -91 + 37i,
+				3 - 11i, -5 - 2i, 14 + 0i, 2 - 1i,
+				52 - 125i, -91 - 37i, 2 + 1i, 165 + 0i,
+			},
+			wantRev: []complex128{
+				149 + 0i, -9 + 7i, -81 - 31i, 52 - 127i,
+				-9 - 7i, 16 + 0i, -5 + 2i, -7 - 5i,
+				-81 + 31i, -5 - 2i, 74 + 0i, 14 + 83i,
+				52 + 127i, -7 + 5i, 14 - 83i, 138 + 0i,
+			},
+		},
+		{
+			alpha: 0,
+			x: []complex128{
+				-6 + 2i,
+				-2 - 4i,
+				0 + 0i,
+				0 + 7i,
+			},
+			a: []complex128{
+				2 + 0i, -9 + 7i, 3 + 11i, 10 - 1i,
+				-9 - 7i, 16 + 0i, -5 + 2i, -7 - 5i,
+				3 - 11i, -5 - 2i, 14 + 0i, 2 - 1i,
+				10 + 1i, -7 + 5i, 2 + 1i, 18 + 0i,
+			},
+			want: []complex128{
+				2 + 0i, -9 + 7i, 3 + 11i, 10 - 1i,
+				-9 - 7i, 16 + 0i, -5 + 2i, -7 - 5i,
+				3 - 11i, -5 - 2i, 14 + 0i, 2 - 1i,
+				10 + 1i, -7 + 5i, 2 + 1i, 18 + 0i,
+			},
+			wantRev: []complex128{
+				2 + 0i, -9 + 7i, 3 + 11i, 10 - 1i,
+				-9 - 7i, 16 + 0i, -5 + 2i, -7 - 5i,
+				3 - 11i, -5 - 2i, 14 + 0i, 2 - 1i,
+				10 + 1i, -7 + 5i, 2 + 1i, 18 + 0i,
+			},
+		},
+	} {
+		n := len(test.x)
+		for _, uplo := range []blas.Uplo{blas.Lower, blas.Upper} {
+			for _, incX := range []int{-11, -2, -1, 1, 2, 7} {
+				for _, lda := range []int{max(1, n), n + 11} {
+					x := makeZVector(test.x, incX)
+					xCopy := make([]complex128, len(x))
+					copy(xCopy, x)
+
+					a := makeZGeneral(test.a, n, n, lda)
+
+					var want []complex128
+					if incX > 0 {
+						want = makeZGeneral(test.want, n, n, lda)
+					} else {
+						want = makeZGeneral(test.wantRev, n, n, lda)
+					}
+
+					if uplo == blas.Upper {
+						for i := 0; i < n; i++ {
+							for j := 0; j < i; j++ {
+								a[i*lda+j] = cmplx.NaN()
+								want[i*lda+j] = cmplx.NaN()
+							}
+							a[i*lda+i] = complex(real(a[i*lda+i]), math.NaN())
+						}
+					} else {
+						for i := 0; i < n; i++ {
+							for j := i + 1; j < n; j++ {
+								a[i*lda+j] = cmplx.NaN()
+								want[i*lda+j] = cmplx.NaN()
+							}
+							a[i*lda+i] = complex(real(a[i*lda+i]), math.NaN())
+						}
+					}
+
+					impl.Zher(uplo, n, test.alpha, x, incX, a, lda)
+
+					if !zsame(x, xCopy) {
+						t.Errorf("Case %v (uplo=%v,incX=%v,lda=%v: unexpected modification of x", tc, uplo, incX, lda)
+					}
+					if !zsame(want, a) {
+						t.Errorf("Case %v (uplo=%v,incX=%v,lda=%v: unexpected result\nwant: %v\ngot:  %v", tc, uplo, incX, lda, want, a)
+					}
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/zher2.go b/vendor/gonum.org/v1/gonum/blas/testblas/zher2.go
new file mode 100644
index 00000000..0a4c2435
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/zher2.go
@@ -0,0 +1,257 @@
+// Copyright ©2017 The Gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testblas
+
+import (
+	"math"
+	"math/cmplx"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+type Zher2er interface {
+	Zher2(uplo blas.Uplo, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, a []complex128, lda int)
+}
+
+func Zher2Test(t *testing.T, impl Zher2er) {
+	for tc, test := range []struct {
+		alpha      complex128
+		incX, incY int
+		x          []complex128
+		y          []complex128
+		a          []complex128
+
+		want []complex128
+	}{
+		{
+			alpha: 1 + 2i,
+			incX:  1,
+			incY:  1,
+		},
+		{
+			alpha: 1 + 2i,
+			incX:  1,
+			incY:  1,
+			x: []complex128{
+				-6 + 2i,
+				-2 - 4i,
+				0 + 0i,
+				0 + 7i,
+			},
+			y: []complex128{
+				2 - 5i,
+				0 + 0i,
+				-8 - 9i,
+				6 + 6i,
+			},
+			a: []complex128{
+				2 + 0i, -9 + 7i, 3 + 11i, 10 - 1i,
+				-9 - 7i, 16 + 0i, -5 + 2i, -7 - 5i,
+				3 - 11i, -5 - 2i, 14 + 0i, 2 - 1i,
+				10 + 1i, -7 + 5i, 2 + 1i, 18 + 0i,
+			},
+			want: []complex128{
+				62 + 0i, 43 - 7i, 173 + 1i, -173 + 55i,
+				43 + 7i, 16 + 0i, 19 + 120i, -19 - 89i,
+				173 - 1i, 19 - 120i, 14 + 0i, 51 + 181i,
+				-173 - 55i, -19 + 89i, 51 - 181i, -66 + 0i,
+			},
+		},
+		{
+			alpha: 1 + 2i,
+			incX:  3,
+			incY:  7,
+			x: []complex128{
+				-6 + 2i,
+				-2 - 4i,
+				0 + 0i,
+				0 + 7i,
+			},
+			y: []complex128{
+				2 - 5i,
+				0 + 0i,
+				-8 - 9i,
+				6 + 6i,
+			},
+			a: []complex128{
+				2 + 0i, -9 + 7i, 3 + 11i, 10 - 1i,
+				-9 - 7i, 16 + 0i, -5 + 2i, -7 - 5i,
+				3 - 11i, -5 - 2i, 14 + 0i, 2 - 1i,
+				10 + 1i, -7 + 5i, 2 + 1i, 18 + 0i,
+			},
+			want: []complex128{
+				62 + 0i, 43 - 7i, 173 + 1i, -173 + 55i,
+				43 + 7i, 16 + 0i, 19 + 120i, -19 - 89i,
+				173 - 1i, 19 - 120i, 14 + 0i, 51 + 181i,
+				-173 - 55i, -19 + 89i, 51 - 181i, -66 + 0i,
+			},
+		},
+		{
+			alpha: 1 + 2i,
+			incX:  -3,
+			incY:  7,
+			x: []complex128{
+				0 + 7i,
+				0 + 0i,
+				-2 - 4i,
+				-6 + 2i,
+			},
+			y: []complex128{
+				2 - 5i,
+				0 + 0i,
+				-8 - 9i,
+				6 + 6i,
+			},
+			a: []complex128{
+				2 + 0i, -9 + 7i, 3 + 11i, 10 - 1i,
+				-9 - 7i, 16 + 0i, -5 + 2i, -7 - 5i,
+				3 - 11i, -5 - 2i, 14 + 0i, 2 - 1i,
+				10 + 1i, -7 + 5i, 2 + 1i, 18 + 0i,
+			},
+			want: []complex128{
+				62 + 0i, 43 - 7i, 173 + 1i, -173 + 55i,
+				43 + 7i, 16 + 0i, 19 + 120i, -19 - 89i,
+				173 - 1i, 19 - 120i, 14 + 0i, 51 + 181i,
+				-173 - 55i, -19 + 89i, 51 - 181i, -66 + 0i,
+			},
+		},
+		{
+			alpha: 1 + 2i,
+			incX:  3,
+			incY:  -7,
+			x: []complex128{
+				-6 + 2i,
+				-2 - 4i,
+				0 + 0i,
+				0 + 7i,
+			},
+			y: []complex128{
+				6 + 6i,
+				-8 - 9i,
+				0 + 0i,
+				2 - 5i,
+			},
+			a: []complex128{
+				2 + 0i, -9 + 7i, 3 + 11i, 10 - 1i,
+				-9 - 7i, 16 + 0i, -5 + 2i, -7 - 5i,
+				3 - 11i, -5 - 2i, 14 + 0i, 2 - 1i,
+				10 + 1i, -7 + 5i, 2 + 1i, 18 + 0i,
+			},
+			want: []complex128{
+				62 + 0i, 43 - 7i, 173 + 1i, -173 + 55i,
+				43 + 7i, 16 + 0i, 19 + 120i, -19 - 89i,
+				173 - 1i, 19 - 120i, 14 + 0i, 51 + 181i,
+				-173 - 55i, -19 + 89i, 51 - 181i, -66 + 0i,
+			},
+		},
+		{
+			alpha: 1 + 2i,
+			incX:  -3,
+			incY:  -7,
+			x: []complex128{
+				0 + 7i,
+				0 + 0i,
+				-2 - 4i,
+				-6 + 2i,
+			},
+			y: []complex128{
+				6 + 6i,
+				-8 - 9i,
+				0 + 0i,
+				2 - 5i,
+			},
+			a: []complex128{
+				2 + 0i, -9 + 7i, 3 + 11i, 10 - 1i,
+				-9 - 7i, 16 + 0i, -5 + 2i, -7 - 5i,
+				3 - 11i, -5 - 2i, 14 + 0i, 2 - 1i,
+				10 + 1i, -7 + 5i, 2 + 1i, 18 + 0i,
+			},
+			want: []complex128{
+				62 + 0i, 43 - 7i, 173 + 1i, -173 + 55i,
+				43 + 7i, 16 + 0i, 19 + 120i, -19 - 89i,
+				173 - 1i, 19 - 120i, 14 + 0i, 51 + 181i,
+				-173 - 55i, -19 + 89i, 51 - 181i, -66 + 0i,
+			},
+		},
+		{
+			alpha: 0,
+			incX:  1,
+			incY:  1,
+			x: []complex128{
+				-6 + 2i,
+				-2 - 4i,
+				0 + 0i,
+				0 + 7i,
+			},
+			y: []complex128{
+				2 - 5i,
+				0 + 0i,
+				-8 - 9i,
+				6 + 6i,
+			},
+			a: []complex128{
+				2 + 0i, -9 + 7i, 3 + 11i, 10 - 1i,
+				-9 - 7i, 16 + 0i, -5 + 2i, -7 - 5i,
+				3 - 11i, -5 - 2i, 14 + 0i, 2 - 1i,
+				10 + 1i, -7 + 5i, 2 + 1i, 18 + 0i,
+			},
+			want: []complex128{
+				2 + 0i, -9 + 7i, 3 + 11i, 10 - 1i,
+				-9 - 7i, 16 + 0i, -5 + 2i, -7 - 5i,
+				3 - 11i, -5 - 2i, 14 + 0i, 2 - 1i,
+				10 + 1i, -7 + 5i, 2 + 1i, 18 + 0i,
+			},
+		},
+	} {
+		n := len(test.x)
+		incX := test.incX
+		incY := test.incY
+		for _, uplo := range []blas.Uplo{blas.Lower, blas.Upper} {
+			for _, lda := range []int{max(1, n), n + 11} {
+				x := makeZVector(test.x, incX)
+				xCopy := make([]complex128, len(x))
+				copy(xCopy, x)
+
+				y := makeZVector(test.y, incY)
+				yCopy := make([]complex128, len(y))
+				copy(yCopy, y)
+
+				a := makeZGeneral(test.a, n, n, lda)
+				want := makeZGeneral(test.want, n, n, lda)
+
+				if uplo == blas.Upper {
+					for i := 0; i < n; i++ {
+						for j := 0; j < i; j++ {
+							a[i*lda+j] = cmplx.NaN()
+							want[i*lda+j] = cmplx.NaN()
+						}
+						a[i*lda+i] = complex(real(a[i*lda+i]), math.NaN())
+					}
+				} else {
+					for i := 0; i < n; i++ {
+						for j := i + 1; j < n; j++ {
+							a[i*lda+j] = cmplx.NaN()
+							want[i*lda+j] = cmplx.NaN()
+						}
+						a[i*lda+i] = complex(real(a[i*lda+i]), math.NaN())
+					}
+				}
+
+				impl.Zher2(uplo, n, test.alpha, x, incX, y, incY, a, lda)
+
+				if !zsame(x, xCopy) {
+					t.Errorf("Case %v (uplo=%v,incX=%v,incY=%v,lda=%v: unexpected modification of x", tc, uplo, incX, incY, lda)
+				}
+				if !zsame(y, yCopy) {
+					t.Errorf("Case %v (uplo=%v,incX=%v,incY=%v,lda=%v: unexpected modification of y", tc, uplo, incX, incY, lda)
+				}
+				if !zsame(want, a) {
+					t.Errorf("Case %v (uplo=%v,incX=%v,incY=%v,lda=%v: unexpected result\nwant: %v\ngot:  %v", tc, uplo, incX, incY, lda, want, a)
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/zscal.go b/vendor/gonum.org/v1/gonum/blas/testblas/zscal.go
new file mode 100644
index 00000000..67210e1b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/zscal.go
@@ -0,0 +1,119 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testblas
+
+import (
+	"fmt"
+	"testing"
+)
+
+type Zscaler interface {
+	Zscal(n int, alpha complex128, x []complex128, incX int)
+}
+
+func ZscalTest(t *testing.T, impl Zscaler) {
+	for tc, test := range []struct {
+		alpha complex128
+		x     []complex128
+		want  []complex128
+	}{
+		{
+			alpha: 2 + 5i,
+			x:     nil,
+			want:  nil,
+		},
+		{
+			alpha: 2 + 5i,
+			x:     []complex128{1 + 2i},
+			want:  []complex128{-8 + 9i},
+		},
+		{
+			alpha: 2 + 5i,
+			x:     []complex128{1 + 2i, 3 + 4i},
+			want:  []complex128{-8 + 9i, -14 + 23i},
+		},
+		{
+			alpha: 2 + 5i,
+			x:     []complex128{1 + 2i, 3 + 4i, 5 + 6i},
+			want:  []complex128{-8 + 9i, -14 + 23i, -20 + 37i},
+		},
+		{
+			alpha: 2 + 5i,
+			x:     []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i},
+			want:  []complex128{-8 + 9i, -14 + 23i, -20 + 37i, -26 + 51i},
+		},
+		{
+			alpha: 2 + 5i,
+			x:     []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i},
+			want:  []complex128{-8 + 9i, -14 + 23i, -20 + 37i, -26 + 51i, -32 + 65i},
+		},
+		{
+			alpha: 2 + 5i,
+			x:     []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i},
+			want:  []complex128{-8 + 9i, -14 + 23i, -20 + 37i, -26 + 51i, -32 + 65i, -38 + 79i},
+		},
+		{
+			alpha: 2 + 5i,
+			x:     []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i},
+			want:  []complex128{-8 + 9i, -14 + 23i, -20 + 37i, -26 + 51i, -32 + 65i, -38 + 79i, -44 + 93i},
+		},
+		{
+			alpha: 2 + 5i,
+			x:     []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i},
+			want:  []complex128{-8 + 9i, -14 + 23i, -20 + 37i, -26 + 51i, -32 + 65i, -38 + 79i, -44 + 93i, -50 + 107i},
+		},
+		{
+			alpha: 2 + 5i,
+			x:     []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i},
+			want:  []complex128{-8 + 9i, -14 + 23i, -20 + 37i, -26 + 51i, -32 + 65i, -38 + 79i, -44 + 93i, -50 + 107i, -56 + 121i},
+		},
+		{
+			alpha: 2 + 5i,
+			x:     []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i, 19 + 20i},
+			want:  []complex128{-8 + 9i, -14 + 23i, -20 + 37i, -26 + 51i, -32 + 65i, -38 + 79i, -44 + 93i, -50 + 107i, -56 + 121i, -62 + 135i},
+		},
+		{
+			alpha: 2 + 5i,
+			x:     []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i, 19 + 20i, 21 + 22i},
+			want:  []complex128{-8 + 9i, -14 + 23i, -20 + 37i, -26 + 51i, -32 + 65i, -38 + 79i, -44 + 93i, -50 + 107i, -56 + 121i, -62 + 135i, -68 + 149i},
+		},
+		{
+			alpha: 2 + 5i,
+			x:     []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i, 19 + 20i, 21 + 22i, 23 + 24i},
+			want:  []complex128{-8 + 9i, -14 + 23i, -20 + 37i, -26 + 51i, -32 + 65i, -38 + 79i, -44 + 93i, -50 + 107i, -56 + 121i, -62 + 135i, -68 + 149i, -74 + 163i},
+		},
+		{
+			alpha: 0,
+			x:     []complex128{1 + 2i, 3 + 4i, 5 + 6i, 7 + 8i, 9 + 10i, 11 + 12i, 13 + 14i, 15 + 16i, 17 + 18i, 19 + 20i, 21 + 22i, 23 + 24i},
+			want:  []complex128{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+		},
+	} {
+		n := len(test.x)
+		if len(test.want) != n {
+			panic("bad test")
+		}
+		for _, incX := range []int{-3, -1, 1, 2, 4, 7, 10} {
+			x := makeZVector(test.x, incX)
+			xCopy := make([]complex128, len(x))
+			copy(xCopy, x)
+
+			want := makeZVector(test.want, incX)
+
+			impl.Zscal(n, test.alpha, x, incX)
+
+			prefix := fmt.Sprintf("Case %v (n=%v,incX=%v):", tc, n, incX)
+
+			if incX < 0 {
+				if !zsame(x, xCopy) {
+					t.Errorf("%v: unexpected modification of x\nwant %v\ngot %v", prefix, want, x)
+				}
+				continue
+			}
+			if !zsame(x, want) {
+				t.Errorf("%v: unexpected result:\nwant: %v\ngot: %v", prefix, want, x)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/blas/testblas/zswap.go b/vendor/gonum.org/v1/gonum/blas/testblas/zswap.go
new file mode 100644
index 00000000..1be1037e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/blas/testblas/zswap.go
@@ -0,0 +1,68 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testblas
+
+import (
+	"fmt"
+	"math/cmplx"
+	"math/rand"
+	"testing"
+)
+
+type Zswaper interface {
+	Zswap(n int, x []complex128, incX int, y []complex128, incY int)
+}
+
+func ZswapTest(t *testing.T, impl Zswaper) {
+	rnd := rand.New(rand.NewSource(1))
+	for n := 0; n < 20; n++ {
+		for _, inc := range allPairs([]int{-5, -1, 1, 2, 5, 10}, []int{-3, -1, 1, 3, 7, 12}) {
+			incX := inc[0]
+			incY := inc[1]
+			aincX := abs(incX)
+			aincY := abs(incY)
+
+			var x, y []complex128
+			if n > 0 {
+				x = make([]complex128, (n-1)*aincX+1)
+				y = make([]complex128, (n-1)*aincY+1)
+			}
+			for i := range x {
+				x[i] = cmplx.NaN()
+			}
+			for i := range y {
+				y[i] = cmplx.NaN()
+			}
+			for i := 0; i < n; i++ {
+				x[i*aincX] = complex(rnd.NormFloat64(), rnd.NormFloat64())
+				y[i*aincY] = complex(rnd.NormFloat64(), rnd.NormFloat64())
+			}
+
+			xWant := make([]complex128, len(x))
+			yWant := make([]complex128, len(y))
+			if incX*incY > 0 {
+				for i := 0; i < n; i++ {
+					xWant[i*aincX] = y[i*aincY]
+					yWant[i*aincY] = x[i*aincX]
+				}
+			} else {
+				for i := 0; i < n; i++ {
+					xWant[(n-i-1)*aincX] = y[i*aincY]
+					yWant[(n-i-1)*aincY] = x[i*aincX]
+				}
+			}
+
+			impl.Zswap(n, x, incX, y, incY)
+
+			prefix := fmt.Sprintf("Case n=%v,incX=%v,incY=%v:", n, incX, incY)
+			if !zsame(x, xWant) {
+				t.Errorf("%v: unexpected x:\nwant %v\ngot %v", prefix, xWant, x)
+			}
+			if !zsame(y, yWant) {
+				t.Errorf("%v: unexpected y:\nwant %v\ngot %v", prefix, yWant, y)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/diff/README.md b/vendor/gonum.org/v1/gonum/diff/README.md
new file mode 100644
index 00000000..6fbcf725
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/diff/README.md
@@ -0,0 +1,3 @@
+# Gonum diff [![GoDoc](https://godoc.org/gonum.org/v1/gonum/diff?status.svg)](https://godoc.org/gonum.org/v1/gonum/diff)
+
+Package diff is a package for computing derivatives of functions for the Go language.
diff --git a/vendor/gonum.org/v1/gonum/diff/fd/crosslaplacian.go b/vendor/gonum.org/v1/gonum/diff/fd/crosslaplacian.go
new file mode 100644
index 00000000..9b2f1d1f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/diff/fd/crosslaplacian.go
@@ -0,0 +1,186 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package fd
+
+import (
+	"math"
+	"sync"
+)
+
+// CrossLaplacian computes a Laplacian-like quantity for a function of two vectors
+// at the locations x and y.
+// It computes
+//  ∇_y · ∇_x f(x,y) = \sum_i ∂^2 f(x,y)/∂x_i ∂y_i
+// The two input vector lengths must be the same.
+//
+// Finite difference formula and other options are specified by settings. If
+// settings is nil, CrossLaplacian will be estimated using the Forward formula and
+// a default step size.
+//
+// CrossLaplacian panics if the two input vectors are not the same length, or if
+// the derivative order of the formula is not 1.
+func CrossLaplacian(f func(x, y []float64) float64, x, y []float64, settings *Settings) float64 {
+	n := len(x)
+	if n == 0 {
+		panic("crosslaplacian: x has zero length")
+	}
+	if len(x) != len(y) {
+		panic("crosslaplacian: input vector length mismatch")
+	}
+
+	// Default settings.
+	formula := Forward
+	step := math.Sqrt(formula.Step) // Use the sqrt because taking derivatives of derivatives.
+	var originValue float64
+	var originKnown, concurrent bool
+
+	// Use user settings if provided.
+	if settings != nil {
+		if !settings.Formula.isZero() {
+			formula = settings.Formula
+			step = math.Sqrt(formula.Step)
+			checkFormula(formula)
+			if formula.Derivative != 1 {
+				panic(badDerivOrder)
+			}
+		}
+		if settings.Step != 0 {
+			if settings.Step < 0 {
+				panic(negativeStep)
+			}
+			step = settings.Step
+		}
+		originKnown = settings.OriginKnown
+		originValue = settings.OriginValue
+		concurrent = settings.Concurrent
+	}
+
+	evals := n * len(formula.Stencil) * len(formula.Stencil)
+	if usesOrigin(formula.Stencil) {
+		evals -= n
+	}
+
+	nWorkers := computeWorkers(concurrent, evals)
+	if nWorkers == 1 {
+		return crossLaplacianSerial(f, x, y, formula.Stencil, step, originKnown, originValue)
+	}
+	return crossLaplacianConcurrent(nWorkers, evals, f, x, y, formula.Stencil, step, originKnown, originValue)
+}
+
+func crossLaplacianSerial(f func(x, y []float64) float64, x, y []float64, stencil []Point, step float64, originKnown bool, originValue float64) float64 {
+	n := len(x)
+	xCopy := make([]float64, len(x))
+	yCopy := make([]float64, len(y))
+	fo := func() float64 {
+		// Copy x and y in case they are modified during the call.
+		copy(xCopy, x)
+		copy(yCopy, y)
+		return f(x, y)
+	}
+	origin := getOrigin(originKnown, originValue, fo, stencil)
+
+	is2 := 1 / (step * step)
+	var laplacian float64
+	for i := 0; i < n; i++ {
+		for _, pty := range stencil {
+			for _, ptx := range stencil {
+				var v float64
+				if ptx.Loc == 0 && pty.Loc == 0 {
+					v = origin
+				} else {
+					// Copying the data anew has two benefits. First, it
+					// avoids floating point issues where adding and then
+					// subtracting the step don't return to the exact same
+					// location. Secondly, it protects against the function
+					// modifying the input data.
+					copy(yCopy, y)
+					copy(xCopy, x)
+					yCopy[i] += pty.Loc * step
+					xCopy[i] += ptx.Loc * step
+					v = f(xCopy, yCopy)
+				}
+				laplacian += v * ptx.Coeff * pty.Coeff * is2
+			}
+		}
+	}
+	return laplacian
+}
+
+func crossLaplacianConcurrent(nWorkers, evals int, f func(x, y []float64) float64, x, y []float64, stencil []Point, step float64, originKnown bool, originValue float64) float64 {
+	n := len(x)
+	type run struct {
+		i          int
+		xIdx, yIdx int
+		result     float64
+	}
+
+	send := make(chan run, evals)
+	ans := make(chan run, evals)
+
+	var originWG sync.WaitGroup
+	hasOrigin := usesOrigin(stencil)
+	if hasOrigin {
+		originWG.Add(1)
+		// Launch worker to compute the origin.
+		go func() {
+			defer originWG.Done()
+			xCopy := make([]float64, len(x))
+			yCopy := make([]float64, len(y))
+			copy(xCopy, x)
+			copy(yCopy, y)
+			originValue = f(xCopy, yCopy)
+		}()
+	}
+
+	var workerWG sync.WaitGroup
+	// Launch workers.
+	for i := 0; i < nWorkers; i++ {
+		workerWG.Add(1)
+		go func(send <-chan run, ans chan<- run) {
+			defer workerWG.Done()
+			xCopy := make([]float64, len(x))
+			yCopy := make([]float64, len(y))
+			for r := range send {
+				if stencil[r.xIdx].Loc == 0 && stencil[r.yIdx].Loc == 0 {
+					originWG.Wait()
+					r.result = originValue
+				} else {
+					// See crossLaplacianSerial for comment on the copy.
+					copy(xCopy, x)
+					copy(yCopy, y)
+					xCopy[r.i] += stencil[r.xIdx].Loc * step
+					yCopy[r.i] += stencil[r.yIdx].Loc * step
+					r.result = f(xCopy, yCopy)
+				}
+				ans <- r
+			}
+		}(send, ans)
+	}
+
+	// Launch the distributor, which sends all of runs.
+	go func(send chan<- run) {
+		for i := 0; i < n; i++ {
+			for xIdx := range stencil {
+				for yIdx := range stencil {
+					send <- run{
+						i: i, xIdx: xIdx, yIdx: yIdx,
+					}
+				}
+			}
+		}
+		close(send)
+		// Wait for all the workers to quit, then close the ans channel.
+		workerWG.Wait()
+		close(ans)
+	}(send)
+
+	// Read in the results.
+	is2 := 1 / (step * step)
+	var laplacian float64
+	for r := range ans {
+		laplacian += r.result * stencil[r.xIdx].Coeff * stencil[r.yIdx].Coeff * is2
+	}
+	return laplacian
+}
diff --git a/vendor/gonum.org/v1/gonum/diff/fd/crosslaplacian_test.go b/vendor/gonum.org/v1/gonum/diff/fd/crosslaplacian_test.go
new file mode 100644
index 00000000..e27a83fa
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/diff/fd/crosslaplacian_test.go
@@ -0,0 +1,111 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package fd
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+)
+
+type CrossLaplacianTester interface {
+	Func(x, y []float64) float64
+	CrossLaplacian(x, y []float64) float64
+}
+
+type WrapperCL struct {
+	Tester HessianTester
+}
+
+func (WrapperCL) constructZ(x, y []float64) []float64 {
+	z := make([]float64, len(x)+len(y))
+	copy(z, x)
+	copy(z[len(x):], y)
+	return z
+}
+
+func (w WrapperCL) Func(x, y []float64) float64 {
+	z := w.constructZ(x, y)
+	return w.Tester.Func(z)
+}
+
+func (w WrapperCL) CrossLaplacian(x, y []float64) float64 {
+	z := w.constructZ(x, y)
+	hess := mat.NewSymDense(len(z), nil)
+	w.Tester.Hess(hess, z)
+	// The CrossLaplacian is the trace of the off-diagonal block of the Hessian.
+	var l float64
+	for i := 0; i < len(x); i++ {
+		l += hess.At(i, i+len(x))
+	}
+	return l
+}
+
+func TestCrossLaplacian(t *testing.T) {
+	for cas, test := range []struct {
+		l        CrossLaplacianTester
+		x, y     []float64
+		settings *Settings
+		tol      float64
+	}{
+		{
+			l:   WrapperCL{Watson{}},
+			x:   []float64{0.2, 0.3},
+			y:   []float64{0.1, 0.4},
+			tol: 1e-3,
+		},
+		{
+			l:   WrapperCL{Watson{}},
+			x:   []float64{2, 3, 1},
+			y:   []float64{1, 4, 1},
+			tol: 1e-3,
+		},
+		{
+			l:   WrapperCL{ConstFunc(6)},
+			x:   []float64{2, -3, 1},
+			y:   []float64{1, 4, -5},
+			tol: 1e-6,
+		},
+		{
+			l:   WrapperCL{LinearFunc{w: []float64{10, 6, -1, 5}, c: 5}},
+			x:   []float64{3, 1},
+			y:   []float64{8, 6},
+			tol: 1e-6,
+		},
+		{
+			l: WrapperCL{QuadFunc{
+				a: mat.NewSymDense(4, []float64{
+					10, 2, 1, 9,
+					2, 5, -3, 4,
+					1, -3, 6, 2,
+					9, 4, 2, -14,
+				}),
+				b: mat.NewVecDense(4, []float64{3, -2, -1, 4}),
+				c: 5,
+			}},
+			x:   []float64{-1.6, -3},
+			y:   []float64{1.8, 3.4},
+			tol: 1e-6,
+		},
+	} {
+		got := CrossLaplacian(test.l.Func, test.x, test.y, test.settings)
+		want := test.l.CrossLaplacian(test.x, test.y)
+		if !floats.EqualWithinAbsOrRel(got, want, test.tol, test.tol) {
+			t.Errorf("Cas %d: CrossLaplacian mismatch serial. got %v, want %v", cas, got, want)
+		}
+
+		// Test that concurrency works.
+		settings := test.settings
+		if settings == nil {
+			settings = &Settings{}
+		}
+		settings.Concurrent = true
+		got2 := CrossLaplacian(test.l.Func, test.x, test.y, settings)
+		if !floats.EqualWithinAbsOrRel(got, got2, 1e-6, 1e-6) {
+			t.Errorf("Cas %d: Laplacian mismatch. got %v, want %v", cas, got2, got)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/diff/fd/derivative.go b/vendor/gonum.org/v1/gonum/diff/fd/derivative.go
new file mode 100644
index 00000000..e5aa9af3
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/diff/fd/derivative.go
@@ -0,0 +1,71 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package fd
+
+import (
+	"math"
+	"runtime"
+	"sync"
+)
+
+// Derivative estimates the derivative of the function f at the given location.
+// The finite difference formula, the step size, and other options are
+// specified by settings. If settings is nil, the first derivative will be
+// estimated using the Forward formula and a default step size.
+func Derivative(f func(float64) float64, x float64, settings *Settings) float64 {
+	// Default settings.
+	formula := Forward
+	step := formula.Step
+	var originValue float64
+	var originKnown, concurrent bool
+
+	// Use user settings if provided.
+	if settings != nil {
+		if !settings.Formula.isZero() {
+			formula = settings.Formula
+			step = formula.Step
+			checkFormula(formula)
+		}
+		if settings.Step != 0 {
+			step = settings.Step
+		}
+		originKnown = settings.OriginKnown
+		originValue = settings.OriginValue
+		concurrent = settings.Concurrent
+	}
+
+	var deriv float64
+	if !concurrent || runtime.GOMAXPROCS(0) == 1 {
+		for _, pt := range formula.Stencil {
+			if originKnown && pt.Loc == 0 {
+				deriv += pt.Coeff * originValue
+				continue
+			}
+			deriv += pt.Coeff * f(x+step*pt.Loc)
+		}
+		return deriv / math.Pow(step, float64(formula.Derivative))
+	}
+
+	wg := &sync.WaitGroup{}
+	mux := &sync.Mutex{}
+	for _, pt := range formula.Stencil {
+		if originKnown && pt.Loc == 0 {
+			mux.Lock()
+			deriv += pt.Coeff * originValue
+			mux.Unlock()
+			continue
+		}
+		wg.Add(1)
+		go func(pt Point) {
+			defer wg.Done()
+			fofx := f(x + step*pt.Loc)
+			mux.Lock()
+			defer mux.Unlock()
+			deriv += pt.Coeff * fofx
+		}(pt)
+	}
+	wg.Wait()
+	return deriv / math.Pow(step, float64(formula.Derivative))
+}
diff --git a/vendor/gonum.org/v1/gonum/diff/fd/derivative_test.go b/vendor/gonum.org/v1/gonum/diff/fd/derivative_test.go
new file mode 100644
index 00000000..35d4f0f3
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/diff/fd/derivative_test.go
@@ -0,0 +1,145 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package fd
+
+import (
+	"math"
+	"testing"
+)
+
+var xSquared = func(x float64) float64 { return x * x }
+
+type testPoint struct {
+	f    func(float64) float64
+	loc  float64
+	fofx float64
+	ans  float64
+}
+
+var testsFirst = []testPoint{
+	{
+		f:    xSquared,
+		loc:  0,
+		fofx: 0,
+		ans:  0,
+	},
+	{
+		f:    xSquared,
+		loc:  5,
+		fofx: 25,
+		ans:  10,
+	},
+	{
+		f:    xSquared,
+		loc:  2,
+		fofx: 4,
+		ans:  4,
+	},
+	{
+		f:    xSquared,
+		loc:  -5,
+		fofx: 25,
+		ans:  -10,
+	},
+}
+
+var testsSecond = []testPoint{
+	{
+		f:    xSquared,
+		loc:  0,
+		fofx: 0,
+		ans:  2,
+	},
+	{
+		f:    xSquared,
+		loc:  5,
+		fofx: 25,
+		ans:  2,
+	},
+	{
+		f:    xSquared,
+		loc:  2,
+		fofx: 4,
+		ans:  2,
+	},
+	{
+		f:    xSquared,
+		loc:  -5,
+		fofx: 25,
+		ans:  2,
+	},
+}
+
+func testDerivative(t *testing.T, formula Formula, tol float64, tests []testPoint) {
+	for i, test := range tests {
+
+		ans := Derivative(test.f, test.loc, &Settings{
+			Formula: formula,
+		})
+		if math.Abs(test.ans-ans) > tol {
+			t.Errorf("Case %v: ans mismatch serial: expected %v, found %v", i, test.ans, ans)
+		}
+
+		ans = Derivative(test.f, test.loc, &Settings{
+			Formula:     formula,
+			OriginKnown: true,
+			OriginValue: test.fofx,
+		})
+		if math.Abs(test.ans-ans) > tol {
+			t.Errorf("Case %v: ans mismatch serial origin known: expected %v, found %v", i, test.ans, ans)
+		}
+
+		ans = Derivative(test.f, test.loc, &Settings{
+			Formula:    formula,
+			Concurrent: true,
+		})
+		if math.Abs(test.ans-ans) > tol {
+			t.Errorf("Case %v: ans mismatch concurrent: expected %v, found %v", i, test.ans, ans)
+		}
+
+		ans = Derivative(test.f, test.loc, &Settings{
+			Formula:     formula,
+			OriginKnown: true,
+			OriginValue: test.fofx,
+			Concurrent:  true,
+		})
+		if math.Abs(test.ans-ans) > tol {
+			t.Errorf("Case %v: ans mismatch concurrent: expected %v, found %v", i, test.ans, ans)
+		}
+	}
+}
+
+func TestForward(t *testing.T) {
+	testDerivative(t, Forward, 2e-4, testsFirst)
+}
+
+func TestBackward(t *testing.T) {
+	testDerivative(t, Backward, 2e-4, testsFirst)
+}
+
+func TestCentral(t *testing.T) {
+	testDerivative(t, Central, 1e-6, testsFirst)
+}
+
+func TestCentralSecond(t *testing.T) {
+	testDerivative(t, Central2nd, 1e-3, testsSecond)
+}
+
+// TestDerivativeDefault checks that the derivative works when settings is nil
+// or zero value.
+func TestDerivativeDefault(t *testing.T) {
+	tol := 1e-6
+	for i, test := range testsFirst {
+		ans := Derivative(test.f, test.loc, nil)
+		if math.Abs(test.ans-ans) > tol {
+			t.Errorf("Case %v: ans mismatch default: expected %v, found %v", i, test.ans, ans)
+		}
+
+		ans = Derivative(test.f, test.loc, &Settings{})
+		if math.Abs(test.ans-ans) > tol {
+			t.Errorf("Case %v: ans mismatch zero value: expected %v, found %v", i, test.ans, ans)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/diff/fd/diff.go b/vendor/gonum.org/v1/gonum/diff/fd/diff.go
new file mode 100644
index 00000000..3bde48d9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/diff/fd/diff.go
@@ -0,0 +1,148 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package fd
+
+import (
+	"math"
+	"runtime"
+)
+
+// A Point is a stencil location in a finite difference formula.
+type Point struct {
+	Loc   float64
+	Coeff float64
+}
+
+// Formula represents a finite difference formula on a regularly spaced grid
+// that approximates the derivative of order k of a function f at x as
+//  d^k f(x) ≈ (1 / Step^k) * \sum_i Coeff_i * f(x + Step * Loc_i).
+// Step must be positive, or the finite difference formula will panic.
+type Formula struct {
+	// Stencil is the set of sampling Points which are used to estimate the
+	// derivative. The locations will be scaled by Step and are relative to x.
+	Stencil    []Point
+	Derivative int     // The order of the approximated derivative.
+	Step       float64 // Default step size for the formula.
+}
+
+func (f Formula) isZero() bool {
+	return f.Stencil == nil && f.Derivative == 0 && f.Step == 0
+}
+
+// Settings is the settings structure for computing finite differences.
+type Settings struct {
+	// Formula is the finite difference formula used
+	// for approximating the derivative.
+	// Zero value indicates a default formula.
+	Formula Formula
+	// Step is the distance between points of the stencil.
+	// If equal to 0, formula's default step will be used.
+	Step float64
+
+	OriginKnown bool    // Flag that the value at the origin x is known.
+	OriginValue float64 // Value at the origin (only used if OriginKnown is true).
+
+	Concurrent bool // Should the function calls be executed concurrently.
+}
+
+// Forward represents a first-order accurate forward approximation
+// to the first derivative.
+var Forward = Formula{
+	Stencil:    []Point{{Loc: 0, Coeff: -1}, {Loc: 1, Coeff: 1}},
+	Derivative: 1,
+	Step:       2e-8,
+}
+
+// Forward2nd represents a first-order accurate forward approximation
+// to the second derivative.
+var Forward2nd = Formula{
+	Stencil:    []Point{{Loc: 0, Coeff: 1}, {Loc: 1, Coeff: -2}, {Loc: 2, Coeff: 1}},
+	Derivative: 2,
+	Step:       1e-4,
+}
+
+// Backward represents a first-order accurate backward approximation
+// to the first derivative.
+var Backward = Formula{
+	Stencil:    []Point{{Loc: -1, Coeff: -1}, {Loc: 0, Coeff: 1}},
+	Derivative: 1,
+	Step:       2e-8,
+}
+
+// Backward2nd represents a first-order accurate forward approximation
+// to the second derivative.
+var Backward2nd = Formula{
+	Stencil:    []Point{{Loc: 0, Coeff: 1}, {Loc: -1, Coeff: -2}, {Loc: -2, Coeff: 1}},
+	Derivative: 2,
+	Step:       1e-4,
+}
+
+// Central represents a second-order accurate centered approximation
+// to the first derivative.
+var Central = Formula{
+	Stencil:    []Point{{Loc: -1, Coeff: -0.5}, {Loc: 1, Coeff: 0.5}},
+	Derivative: 1,
+	Step:       6e-6,
+}
+
+// Central2nd represents a secord-order accurate centered approximation
+// to the second derivative.
+var Central2nd = Formula{
+	Stencil:    []Point{{Loc: -1, Coeff: 1}, {Loc: 0, Coeff: -2}, {Loc: 1, Coeff: 1}},
+	Derivative: 2,
+	Step:       1e-4,
+}
+
+var negativeStep = "fd: negative step"
+
+// checkFormula checks if the formula is valid, and panics otherwise.
+func checkFormula(formula Formula) {
+	if formula.Derivative == 0 || formula.Stencil == nil || formula.Step <= 0 {
+		panic("fd: bad formula")
+	}
+}
+
+// computeWorkers returns the desired number of workers given the concurrency
+// level and number of evaluations.
+func computeWorkers(concurrent bool, evals int) int {
+	if !concurrent {
+		return 1
+	}
+	nWorkers := runtime.GOMAXPROCS(0)
+	if nWorkers > evals {
+		nWorkers = evals
+	}
+	return nWorkers
+}
+
+// usesOrigin returns whether the stencil uses the origin, which is true iff
+// one of the locations in the stencil equals 0.
+func usesOrigin(stencil []Point) bool {
+	for _, pt := range stencil {
+		if pt.Loc == 0 {
+			return true
+		}
+	}
+	return false
+}
+
+// getOrigin returns the value at the origin. It returns originValue if originKnown
+// is true. It returns the value returned by f if stencil contains a point with
+// zero location, and NaN otherwise.
+func getOrigin(originKnown bool, originValue float64, f func() float64, stencil []Point) float64 {
+	if originKnown {
+		return originValue
+	}
+	for _, pt := range stencil {
+		if pt.Loc == 0 {
+			return f()
+		}
+	}
+	return math.NaN()
+}
+
+const (
+	badDerivOrder = "fd: invalid derivative order"
+)
diff --git a/vendor/gonum.org/v1/gonum/diff/fd/doc.go b/vendor/gonum.org/v1/gonum/diff/fd/doc.go
new file mode 100644
index 00000000..ec6fbb10
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/diff/fd/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package fd provides functions to approximate derivatives using finite differences.
+package fd // import "gonum.org/v1/gonum/diff/fd"
diff --git a/vendor/gonum.org/v1/gonum/diff/fd/example_test.go b/vendor/gonum.org/v1/gonum/diff/fd/example_test.go
new file mode 100644
index 00000000..adc9db0f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/diff/fd/example_test.go
@@ -0,0 +1,68 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package fd_test
+
+import (
+	"fmt"
+	"math"
+
+	"gonum.org/v1/gonum/diff/fd"
+	"gonum.org/v1/gonum/mat"
+)
+
+func ExampleDerivative() {
+	f := func(x float64) float64 {
+		return math.Sin(x)
+	}
+	// Compute the first derivative of f at 0 using the default settings.
+	fmt.Println("f'(0) ≈", fd.Derivative(f, 0, nil))
+	// Compute the first derivative of f at 0 using the forward approximation
+	// with a custom step size.
+	df := fd.Derivative(f, 0, &fd.Settings{
+		Formula: fd.Forward,
+		Step:    1e-3,
+	})
+	fmt.Println("f'(0) ≈", df)
+
+	f = func(x float64) float64 {
+		return math.Pow(math.Cos(x), 3)
+	}
+	// Compute the second derivative of f at 0 using
+	// the centered approximation, concurrent evaluation,
+	// and a known function value at x.
+	df = fd.Derivative(f, 0, &fd.Settings{
+		Formula:     fd.Central2nd,
+		Concurrent:  true,
+		OriginKnown: true,
+		OriginValue: f(0),
+	})
+	fmt.Println("f''(0) ≈", df)
+
+	// Output:
+	// f'(0) ≈ 1
+	// f'(0) ≈ 0.9999998333333416
+	// f''(0) ≈ -2.999999981767587
+}
+
+func ExampleJacobian() {
+	f := func(dst, x []float64) {
+		dst[0] = x[0] + 1
+		dst[1] = 5 * x[2]
+		dst[2] = 4*x[1]*x[1] - 2*x[2]
+		dst[3] = x[2] * math.Sin(x[0])
+	}
+	jac := mat.NewDense(4, 3, nil)
+	fd.Jacobian(jac, f, []float64{1, 2, 3}, &fd.JacobianSettings{
+		Formula:    fd.Central,
+		Concurrent: true,
+	})
+	fmt.Printf("J ≈ %.6v\n", mat.Formatted(jac, mat.Prefix("    ")))
+
+	// Output:
+	// J ≈ ⎡       1         0         0⎤
+	//     ⎢       0         0         5⎥
+	//     ⎢       0        16        -2⎥
+	//     ⎣ 1.62091         0  0.841471⎦
+}
diff --git a/vendor/gonum.org/v1/gonum/diff/fd/gradient.go b/vendor/gonum.org/v1/gonum/diff/fd/gradient.go
new file mode 100644
index 00000000..79bb3d1a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/diff/fd/gradient.go
@@ -0,0 +1,145 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package fd
+
+import "gonum.org/v1/gonum/floats"
+
+// Gradient estimates the gradient of the multivariate function f at the
+// location x. If dst is not nil, the result will be stored in-place into dst
+// and returned, otherwise a new slice will be allocated first. Finite
+// difference formula and other options are specified by settings. If settings is
+// nil, the gradient will be estimated using the Forward formula and a default
+// step size.
+//
+// Gradient panics if the length of dst and x is not equal, or if the derivative
+// order of the formula is not 1.
+func Gradient(dst []float64, f func([]float64) float64, x []float64, settings *Settings) []float64 {
+	if dst == nil {
+		dst = make([]float64, len(x))
+	}
+	if len(dst) != len(x) {
+		panic("fd: slice length mismatch")
+	}
+
+	// Default settings.
+	formula := Forward
+	step := formula.Step
+	var originValue float64
+	var originKnown, concurrent bool
+
+	// Use user settings if provided.
+	if settings != nil {
+		if !settings.Formula.isZero() {
+			formula = settings.Formula
+			step = formula.Step
+			checkFormula(formula)
+			if formula.Derivative != 1 {
+				panic(badDerivOrder)
+			}
+		}
+		if settings.Step != 0 {
+			step = settings.Step
+		}
+		originKnown = settings.OriginKnown
+		originValue = settings.OriginValue
+		concurrent = settings.Concurrent
+	}
+
+	evals := len(formula.Stencil) * len(x)
+	nWorkers := computeWorkers(concurrent, evals)
+
+	hasOrigin := usesOrigin(formula.Stencil)
+	// Copy x in case it is modified during the call.
+	xcopy := make([]float64, len(x))
+	if hasOrigin && !originKnown {
+		copy(xcopy, x)
+		originValue = f(xcopy)
+	}
+
+	if nWorkers == 1 {
+		for i := range xcopy {
+			var deriv float64
+			for _, pt := range formula.Stencil {
+				if pt.Loc == 0 {
+					deriv += pt.Coeff * originValue
+					continue
+				}
+				// Copying the data anew has two benefits. First, it
+				// avoids floating point issues where adding and then
+				// subtracting the step don't return to the exact same
+				// location. Secondly, it protects against the function
+				// modifying the input data.
+				copy(xcopy, x)
+				xcopy[i] += pt.Loc * step
+				deriv += pt.Coeff * f(xcopy)
+			}
+			dst[i] = deriv / step
+		}
+		return dst
+	}
+
+	sendChan := make(chan fdrun, evals)
+	ansChan := make(chan fdrun, evals)
+	quit := make(chan struct{})
+	defer close(quit)
+
+	// Launch workers. Workers receive an index and a step, and compute the answer.
+	for i := 0; i < nWorkers; i++ {
+		go func(sendChan <-chan fdrun, ansChan chan<- fdrun, quit <-chan struct{}) {
+			xcopy := make([]float64, len(x))
+			for {
+				select {
+				case <-quit:
+					return
+				case run := <-sendChan:
+					// See above comment on the copy.
+					copy(xcopy, x)
+					xcopy[run.idx] += run.pt.Loc * step
+					run.result = f(xcopy)
+					ansChan <- run
+				}
+			}
+		}(sendChan, ansChan, quit)
+	}
+
+	// Launch the distributor. Distributor sends the cases to be computed.
+	go func(sendChan chan<- fdrun, ansChan chan<- fdrun) {
+		for i := range x {
+			for _, pt := range formula.Stencil {
+				if pt.Loc == 0 {
+					// Answer already known. Send the answer on the answer channel.
+					ansChan <- fdrun{
+						idx:    i,
+						pt:     pt,
+						result: originValue,
+					}
+					continue
+				}
+				// Answer not known, send the answer to be computed.
+				sendChan <- fdrun{
+					idx: i,
+					pt:  pt,
+				}
+			}
+		}
+	}(sendChan, ansChan)
+
+	for i := range dst {
+		dst[i] = 0
+	}
+	// Read in all of the results.
+	for i := 0; i < evals; i++ {
+		run := <-ansChan
+		dst[run.idx] += run.pt.Coeff * run.result
+	}
+	floats.Scale(1/step, dst)
+	return dst
+}
+
+type fdrun struct {
+	idx    int
+	pt     Point
+	result float64
+}
diff --git a/vendor/gonum.org/v1/gonum/diff/fd/gradient_test.go b/vendor/gonum.org/v1/gonum/diff/fd/gradient_test.go
new file mode 100644
index 00000000..0774ad73
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/diff/fd/gradient_test.go
@@ -0,0 +1,187 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package fd
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+type Rosenbrock struct {
+	nDim int
+}
+
+func (r Rosenbrock) F(x []float64) (sum float64) {
+	deriv := make([]float64, len(x))
+	return r.FDf(x, deriv)
+}
+
+func (r Rosenbrock) FDf(x []float64, deriv []float64) (sum float64) {
+	for i := range deriv {
+		deriv[i] = 0
+	}
+
+	for i := 0; i < len(x)-1; i++ {
+		sum += math.Pow(1-x[i], 2) + 100*math.Pow(x[i+1]-math.Pow(x[i], 2), 2)
+	}
+	for i := 0; i < len(x)-1; i++ {
+		deriv[i] += -1 * 2 * (1 - x[i])
+		deriv[i] += 2 * 100 * (x[i+1] - math.Pow(x[i], 2)) * (-2 * x[i])
+	}
+	for i := 1; i < len(x); i++ {
+		deriv[i] += 2 * 100 * (x[i] - math.Pow(x[i-1], 2))
+	}
+
+	return sum
+}
+
+func TestGradient(t *testing.T) {
+	rand.Seed(1)
+	for i, test := range []struct {
+		nDim    int
+		tol     float64
+		formula Formula
+	}{
+		{
+			nDim:    2,
+			tol:     2e-4,
+			formula: Forward,
+		},
+		{
+			nDim:    2,
+			tol:     1e-6,
+			formula: Central,
+		},
+		{
+			nDim:    40,
+			tol:     2e-4,
+			formula: Forward,
+		},
+		{
+			nDim:    40,
+			tol:     1e-6,
+			formula: Central,
+		},
+	} {
+		x := make([]float64, test.nDim)
+		for i := range x {
+			x[i] = rand.Float64()
+		}
+		xcopy := make([]float64, len(x))
+		copy(xcopy, x)
+
+		r := Rosenbrock{len(x)}
+		trueGradient := make([]float64, len(x))
+		r.FDf(x, trueGradient)
+
+		// Try with gradient nil.
+		gradient := Gradient(nil, r.F, x, &Settings{
+			Formula: test.formula,
+		})
+		if !floats.EqualApprox(gradient, trueGradient, test.tol) {
+			t.Errorf("Case %v: gradient mismatch in serial with nil. Want: %v, Got: %v.", i, trueGradient, gradient)
+		}
+		if !floats.Equal(x, xcopy) {
+			t.Errorf("Case %v: x modified during call to gradient in serial with nil.", i)
+		}
+
+		// Try with provided gradient.
+		for i := range gradient {
+			gradient[i] = rand.Float64()
+		}
+		Gradient(gradient, r.F, x, &Settings{
+			Formula: test.formula,
+		})
+		if !floats.EqualApprox(gradient, trueGradient, test.tol) {
+			t.Errorf("Case %v: gradient mismatch in serial. Want: %v, Got: %v.", i, trueGradient, gradient)
+		}
+		if !floats.Equal(x, xcopy) {
+			t.Errorf("Case %v: x modified during call to gradient in serial with non-nil.", i)
+		}
+
+		// Try with known value.
+		for i := range gradient {
+			gradient[i] = rand.Float64()
+		}
+		Gradient(gradient, r.F, x, &Settings{
+			Formula:     test.formula,
+			OriginKnown: true,
+			OriginValue: r.F(x),
+		})
+		if !floats.EqualApprox(gradient, trueGradient, test.tol) {
+			t.Errorf("Case %v: gradient mismatch with known origin in serial. Want: %v, Got: %v.", i, trueGradient, gradient)
+		}
+
+		// Try with concurrent evaluation.
+		for i := range gradient {
+			gradient[i] = rand.Float64()
+		}
+		Gradient(gradient, r.F, x, &Settings{
+			Formula:    test.formula,
+			Concurrent: true,
+		})
+		if !floats.EqualApprox(gradient, trueGradient, test.tol) {
+			t.Errorf("Case %v: gradient mismatch with unknown origin in parallel. Want: %v, Got: %v.", i, trueGradient, gradient)
+		}
+		if !floats.Equal(x, xcopy) {
+			t.Errorf("Case %v: x modified during call to gradient in parallel", i)
+		}
+
+		// Try with concurrent evaluation with origin known.
+		for i := range gradient {
+			gradient[i] = rand.Float64()
+		}
+		Gradient(gradient, r.F, x, &Settings{
+			Formula:     test.formula,
+			Concurrent:  true,
+			OriginKnown: true,
+			OriginValue: r.F(x),
+		})
+		if !floats.EqualApprox(gradient, trueGradient, test.tol) {
+			t.Errorf("Case %v: gradient mismatch with known origin in parallel. Want: %v, Got: %v.", i, trueGradient, gradient)
+		}
+
+		// Try with nil settings.
+		for i := range gradient {
+			gradient[i] = rand.Float64()
+		}
+		Gradient(gradient, r.F, x, nil)
+		if !floats.EqualApprox(gradient, trueGradient, test.tol) {
+			t.Errorf("Case %v: gradient mismatch with default settings. Want: %v, Got: %v.", i, trueGradient, gradient)
+		}
+
+		// Try with zero-valued settings.
+		for i := range gradient {
+			gradient[i] = rand.Float64()
+		}
+		Gradient(gradient, r.F, x, &Settings{})
+		if !floats.EqualApprox(gradient, trueGradient, test.tol) {
+			t.Errorf("Case %v: gradient mismatch with zero settings. Want: %v, Got: %v.", i, trueGradient, gradient)
+		}
+	}
+}
+
+func Panics(fun func()) (b bool) {
+	defer func() {
+		err := recover()
+		if err != nil {
+			b = true
+		}
+	}()
+	fun()
+	return
+}
+
+func TestGradientPanics(t *testing.T) {
+	// Test that it panics
+	if !Panics(func() {
+		Gradient([]float64{0.0}, func(x []float64) float64 { return x[0] * x[0] }, []float64{0.0, 0.0}, nil)
+	}) {
+		t.Errorf("Gradient did not panic with length mismatch")
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/diff/fd/hessian.go b/vendor/gonum.org/v1/gonum/diff/fd/hessian.go
new file mode 100644
index 00000000..871097ce
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/diff/fd/hessian.go
@@ -0,0 +1,193 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package fd
+
+import (
+	"math"
+	"sync"
+
+	"gonum.org/v1/gonum/mat"
+)
+
+// Hessian approximates the Hessian matrix of the multivariate function f
+// at the location x. That is
+//  H_{i,j} = ∂^2 f(x)/∂x_i ∂x_j
+// If dst is not nil, the resulting H will be stored in-place into dst
+// and returned, otherwise a new matrix will be allocated first. Finite difference
+// formula and other options are specified by settings. If settings is nil,
+// the Hessian will be estimated using the Forward formula and a default step size.
+//
+// Hessian panics if the size of dst and x is not equal, or if the derivative
+// order of the formula is not 1.
+func Hessian(dst *mat.SymDense, f func(x []float64) float64, x []float64, settings *Settings) *mat.SymDense {
+	n := len(x)
+	if dst == nil {
+		dst = mat.NewSymDense(n, nil)
+	} else {
+		if n2 := dst.Symmetric(); n2 != n {
+			panic("hessian: dst size mismatch")
+		}
+		for i := 0; i < n; i++ {
+			for j := i; j < n; j++ {
+				dst.SetSym(i, j, 0)
+			}
+		}
+	}
+
+	// Default settings.
+	formula := Forward
+	step := math.Sqrt(formula.Step) // Use the sqrt because taking derivatives of derivatives.
+	var originValue float64
+	var originKnown, concurrent bool
+
+	// Use user settings if provided.
+	if settings != nil {
+		if !settings.Formula.isZero() {
+			formula = settings.Formula
+			step = math.Sqrt(formula.Step)
+			checkFormula(formula)
+			if formula.Derivative != 1 {
+				panic(badDerivOrder)
+			}
+		}
+		if settings.Step != 0 {
+			if settings.Step < 0 {
+				panic(negativeStep)
+			}
+			step = settings.Step
+		}
+		originKnown = settings.OriginKnown
+		originValue = settings.OriginValue
+		concurrent = settings.Concurrent
+	}
+
+	evals := n * (n + 1) / 2 * len(formula.Stencil) * len(formula.Stencil)
+	for _, pt := range formula.Stencil {
+		if pt.Loc == 0 {
+			evals -= n * (n + 1) / 2
+			break
+		}
+	}
+
+	nWorkers := computeWorkers(concurrent, evals)
+	if nWorkers == 1 {
+		hessianSerial(dst, f, x, formula.Stencil, step, originKnown, originValue)
+		return dst
+	}
+	hessianConcurrent(dst, nWorkers, evals, f, x, formula.Stencil, step, originKnown, originValue)
+	return dst
+}
+
+func hessianSerial(dst *mat.SymDense, f func(x []float64) float64, x []float64, stencil []Point, step float64, originKnown bool, originValue float64) {
+	n := len(x)
+	xCopy := make([]float64, n)
+	fo := func() float64 {
+		// Copy x in case it is modified during the call.
+		copy(xCopy, x)
+		return f(x)
+	}
+	is2 := 1 / (step * step)
+	origin := getOrigin(originKnown, originValue, fo, stencil)
+	for i := 0; i < n; i++ {
+		for j := i; j < n; j++ {
+			var hess float64
+			for _, pti := range stencil {
+				for _, ptj := range stencil {
+					var v float64
+					if pti.Loc == 0 && ptj.Loc == 0 {
+						v = origin
+					} else {
+						// Copying the data anew has two benefits. First, it
+						// avoids floating point issues where adding and then
+						// subtracting the step don't return to the exact same
+						// location. Secondly, it protects against the function
+						// modifying the input data.
+						copy(xCopy, x)
+						xCopy[i] += pti.Loc * step
+						xCopy[j] += ptj.Loc * step
+						v = f(xCopy)
+					}
+					hess += v * pti.Coeff * ptj.Coeff * is2
+				}
+			}
+			dst.SetSym(i, j, hess)
+		}
+	}
+}
+
+func hessianConcurrent(dst *mat.SymDense, nWorkers, evals int, f func(x []float64) float64, x []float64, stencil []Point, step float64, originKnown bool, originValue float64) {
+	n := dst.Symmetric()
+	type run struct {
+		i, j       int
+		iIdx, jIdx int
+		result     float64
+	}
+
+	send := make(chan run, evals)
+	ans := make(chan run, evals)
+
+	var originWG sync.WaitGroup
+	hasOrigin := usesOrigin(stencil)
+	if hasOrigin {
+		originWG.Add(1)
+		// Launch worker to compute the origin.
+		go func() {
+			defer originWG.Done()
+			xCopy := make([]float64, len(x))
+			copy(xCopy, x)
+			originValue = f(xCopy)
+		}()
+	}
+
+	var workerWG sync.WaitGroup
+	// Launch workers.
+	for i := 0; i < nWorkers; i++ {
+		workerWG.Add(1)
+		go func(send <-chan run, ans chan<- run) {
+			defer workerWG.Done()
+			xCopy := make([]float64, len(x))
+			for r := range send {
+				if stencil[r.iIdx].Loc == 0 && stencil[r.jIdx].Loc == 0 {
+					originWG.Wait()
+					r.result = originValue
+				} else {
+					// See hessianSerial for comment on the copy.
+					copy(xCopy, x)
+					xCopy[r.i] += stencil[r.iIdx].Loc * step
+					xCopy[r.j] += stencil[r.jIdx].Loc * step
+					r.result = f(xCopy)
+				}
+				ans <- r
+			}
+		}(send, ans)
+	}
+
+	// Launch the distributor, which sends all of runs.
+	go func(send chan<- run) {
+		for i := 0; i < n; i++ {
+			for j := i; j < n; j++ {
+				for iIdx := range stencil {
+					for jIdx := range stencil {
+						send <- run{
+							i: i, j: j, iIdx: iIdx, jIdx: jIdx,
+						}
+					}
+				}
+			}
+		}
+		close(send)
+		// Wait for all the workers to quit, then close the ans channel.
+		workerWG.Wait()
+		close(ans)
+	}(send)
+
+	is2 := 1 / (step * step)
+	// Read in the results.
+	for r := range ans {
+		v := r.result * stencil[r.iIdx].Coeff * stencil[r.jIdx].Coeff * is2
+		v += dst.At(r.i, r.j)
+		dst.SetSym(r.i, r.j, v)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/diff/fd/hessian_test.go b/vendor/gonum.org/v1/gonum/diff/fd/hessian_test.go
new file mode 100644
index 00000000..f9ae8736
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/diff/fd/hessian_test.go
@@ -0,0 +1,94 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package fd
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/mat"
+)
+
+type HessianTester interface {
+	Func(x []float64) float64
+	Grad(grad, x []float64)
+	Hess(dst mat.MutableSymmetric, x []float64)
+}
+
+var hessianTestCases = []struct {
+	h        HessianTester
+	x        []float64
+	settings *Settings
+	tol      float64
+}{
+	{
+		h:   Watson{},
+		x:   []float64{0.2, 0.3, 0.1, 0.4},
+		tol: 1e-3,
+	},
+	{
+		h:   Watson{},
+		x:   []float64{2, 3, 1, 4},
+		tol: 1e-3,
+		settings: &Settings{
+			Step:    1e-5,
+			Formula: Central,
+		},
+	},
+	{
+		h:   Watson{},
+		x:   []float64{2, 3, 1},
+		tol: 1e-3,
+		settings: &Settings{
+			OriginKnown: true,
+			OriginValue: 7606.529501201192,
+		},
+	},
+	{
+		h:   ConstFunc(5),
+		x:   []float64{1, 9},
+		tol: 1e-16,
+	},
+	{
+		h:   LinearFunc{w: []float64{10, 6, -1}, c: 5},
+		x:   []float64{3, 1, 8},
+		tol: 1e-6,
+	},
+	{
+		h: QuadFunc{
+			a: mat.NewSymDense(3, []float64{
+				10, 2, 1,
+				2, 5, -3,
+				1, -3, 6,
+			}),
+			b: mat.NewVecDense(3, []float64{3, -2, -1}),
+			c: 5,
+		},
+		x:   []float64{-1.6, -3, 2},
+		tol: 1e-6,
+	},
+}
+
+func TestHessian(t *testing.T) {
+	for cas, test := range hessianTestCases {
+		n := len(test.x)
+		got := Hessian(nil, test.h.Func, test.x, test.settings)
+		want := mat.NewSymDense(n, nil)
+		test.h.Hess(want, test.x)
+		if !mat.EqualApprox(got, want, test.tol) {
+			t.Errorf("Cas %d: Hessian mismatch\ngot=\n%0.4v\nwant=\n%0.4v\n", cas, mat.Formatted(got), mat.Formatted(want))
+		}
+
+		// Test that concurrency works.
+		settings := test.settings
+		if settings == nil {
+			settings = &Settings{}
+		}
+		settings.Concurrent = true
+		got2 := Hessian(nil, test.h.Func, test.x, settings)
+		if !mat.EqualApprox(got, got2, 1e-5) {
+			t.Errorf("Cas %d: Hessian mismatch concurrent\ngot=\n%0.6v\nwant=\n%0.6v\n", cas, mat.Formatted(got2), mat.Formatted(got))
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/diff/fd/jacobian.go b/vendor/gonum.org/v1/gonum/diff/fd/jacobian.go
new file mode 100644
index 00000000..658d1183
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/diff/fd/jacobian.go
@@ -0,0 +1,200 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package fd
+
+import (
+	"sync"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+)
+
+type JacobianSettings struct {
+	Formula     Formula
+	OriginValue []float64
+	Step        float64
+	Concurrent  bool
+}
+
+// Jacobian approximates the Jacobian matrix of a vector-valued function f at
+// the location x and stores the result in-place into dst.
+//
+// Finite difference formula and other options are specified by settings. If
+// settings is nil, the Jacobian will be estimated using the Forward formula and
+// a default step size.
+//
+// The Jacobian matrix J is the matrix of all first-order partial derivatives of f.
+// If f maps an n-dimensional vector x to an m-dimensional vector y = f(x), J is
+// an m×n matrix whose elements are given as
+//  J_{i,j} = ∂f_i/∂x_j,
+// or expanded out
+//      [ ∂f_1/∂x_1 ... ∂f_1/∂x_n ]
+//      [     .  .          .     ]
+//  J = [     .      .      .     ]
+//      [     .          .  .     ]
+//      [ ∂f_m/∂x_1 ... ∂f_m/∂x_n ]
+//
+// dst must be non-nil, the number of its columns must equal the length of x, and
+// the derivative order of the formula must be 1, otherwise Jacobian will panic.
+func Jacobian(dst *mat.Dense, f func(y, x []float64), x []float64, settings *JacobianSettings) {
+	n := len(x)
+	if n == 0 {
+		panic("jacobian: x has zero length")
+	}
+	m, c := dst.Dims()
+	if c != n {
+		panic("jacobian: mismatched matrix size")
+	}
+
+	// Default settings.
+	formula := Forward
+	step := formula.Step
+	var originValue []float64
+	var concurrent bool
+
+	// Use user settings if provided.
+	if settings != nil {
+		if !settings.Formula.isZero() {
+			formula = settings.Formula
+			step = formula.Step
+			checkFormula(formula)
+			if formula.Derivative != 1 {
+				panic(badDerivOrder)
+			}
+		}
+		if settings.Step != 0 {
+			step = settings.Step
+		}
+		originValue = settings.OriginValue
+		if originValue != nil && len(originValue) != m {
+			panic("jacobian: mismatched OriginValue slice length")
+		}
+		concurrent = settings.Concurrent
+	}
+
+	evals := n * len(formula.Stencil)
+	for _, pt := range formula.Stencil {
+		if pt.Loc == 0 {
+			evals -= n - 1
+			break
+		}
+	}
+
+	nWorkers := computeWorkers(concurrent, evals)
+	if nWorkers == 1 {
+		jacobianSerial(dst, f, x, originValue, formula, step)
+		return
+	}
+	jacobianConcurrent(dst, f, x, originValue, formula, step, nWorkers)
+}
+
+func jacobianSerial(dst *mat.Dense, f func([]float64, []float64), x, origin []float64, formula Formula, step float64) {
+	m, n := dst.Dims()
+	xcopy := make([]float64, n)
+	y := make([]float64, m)
+	col := make([]float64, m)
+	for j := 0; j < n; j++ {
+		for i := range col {
+			col[i] = 0
+		}
+		for _, pt := range formula.Stencil {
+			if pt.Loc == 0 {
+				if origin == nil {
+					origin = make([]float64, m)
+					copy(xcopy, x)
+					f(origin, xcopy)
+				}
+				floats.AddScaled(col, pt.Coeff, origin)
+			} else {
+				copy(xcopy, x)
+				xcopy[j] += pt.Loc * step
+				f(y, xcopy)
+				floats.AddScaled(col, pt.Coeff, y)
+			}
+		}
+		dst.SetCol(j, col)
+	}
+	dst.Scale(1/step, dst)
+}
+
+func jacobianConcurrent(dst *mat.Dense, f func([]float64, []float64), x, origin []float64, formula Formula, step float64, nWorkers int) {
+	m, n := dst.Dims()
+	for i := 0; i < m; i++ {
+		for j := 0; j < n; j++ {
+			dst.Set(i, j, 0)
+		}
+	}
+
+	var (
+		wg sync.WaitGroup
+		mu = make([]sync.Mutex, n) // Guard access to individual columns.
+	)
+	worker := func(jobs <-chan jacJob) {
+		defer wg.Done()
+		xcopy := make([]float64, n)
+		y := make([]float64, m)
+		yVec := mat.NewVecDense(m, y)
+		for job := range jobs {
+			copy(xcopy, x)
+			xcopy[job.j] += job.pt.Loc * step
+			f(y, xcopy)
+			col := dst.ColView(job.j)
+			mu[job.j].Lock()
+			col.AddScaledVec(col, job.pt.Coeff, yVec)
+			mu[job.j].Unlock()
+		}
+	}
+	jobs := make(chan jacJob, nWorkers)
+	for i := 0; i < nWorkers; i++ {
+		wg.Add(1)
+		go worker(jobs)
+	}
+	var hasOrigin bool
+	for _, pt := range formula.Stencil {
+		if pt.Loc == 0 {
+			hasOrigin = true
+			continue
+		}
+		for j := 0; j < n; j++ {
+			jobs <- jacJob{j, pt}
+		}
+	}
+	close(jobs)
+	if hasOrigin && origin == nil {
+		wg.Add(1)
+		go func() {
+			defer wg.Done()
+			origin = make([]float64, m)
+			xcopy := make([]float64, n)
+			copy(xcopy, x)
+			f(origin, xcopy)
+		}()
+	}
+	wg.Wait()
+
+	if hasOrigin {
+		// The formula evaluated at x, we need to add scaled origin to
+		// all columns of dst. Iterate again over all Formula points
+		// because we don't forbid repeated locations.
+
+		originVec := mat.NewVecDense(m, origin)
+		for _, pt := range formula.Stencil {
+			if pt.Loc != 0 {
+				continue
+			}
+			for j := 0; j < n; j++ {
+				col := dst.ColView(j)
+				col.AddScaledVec(col, pt.Coeff, originVec)
+			}
+		}
+	}
+
+	dst.Scale(1/step, dst)
+}
+
+type jacJob struct {
+	j  int
+	pt Point
+}
diff --git a/vendor/gonum.org/v1/gonum/diff/fd/jacobian_test.go b/vendor/gonum.org/v1/gonum/diff/fd/jacobian_test.go
new file mode 100644
index 00000000..020f2c1b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/diff/fd/jacobian_test.go
@@ -0,0 +1,268 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package fd
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+)
+
+func vecFunc13(y, x []float64) {
+	y[0] = 5*x[0] + x[2]*math.Sin(x[1]) + 1
+}
+func vecFunc13Jac(jac *mat.Dense, x []float64) {
+	jac.Set(0, 0, 5)
+	jac.Set(0, 1, x[2]*math.Cos(x[1]))
+	jac.Set(0, 2, math.Sin(x[1]))
+}
+
+func vecFunc22(y, x []float64) {
+	y[0] = x[0]*x[0]*x[1] + 1
+	y[1] = 5*x[0] + math.Sin(x[1]) + 1
+}
+func vecFunc22Jac(jac *mat.Dense, x []float64) {
+	jac.Set(0, 0, 2*x[0]*x[1])
+	jac.Set(0, 1, x[0]*x[0])
+	jac.Set(1, 0, 5)
+	jac.Set(1, 1, math.Cos(x[1]))
+}
+
+func vecFunc43(y, x []float64) {
+	y[0] = x[0] + 1
+	y[1] = 5*x[2] + 1
+	y[2] = 4*x[1]*x[1] - 2*x[2] + 1
+	y[3] = x[2]*math.Sin(x[0]) + 1
+}
+func vecFunc43Jac(jac *mat.Dense, x []float64) {
+	jac.Set(0, 0, 1)
+	jac.Set(0, 1, 0)
+	jac.Set(0, 2, 0)
+	jac.Set(1, 0, 0)
+	jac.Set(1, 1, 0)
+	jac.Set(1, 2, 5)
+	jac.Set(2, 0, 0)
+	jac.Set(2, 1, 8*x[1])
+	jac.Set(2, 2, -2)
+	jac.Set(3, 0, x[2]*math.Cos(x[0]))
+	jac.Set(3, 1, 0)
+	jac.Set(3, 2, math.Sin(x[0]))
+}
+
+func TestJacobian(t *testing.T) {
+	rand.Seed(1)
+
+	// Test with default settings.
+	for tc, test := range []struct {
+		m, n int
+		f    func([]float64, []float64)
+		jac  func(*mat.Dense, []float64)
+	}{
+		{
+			m:   1,
+			n:   3,
+			f:   vecFunc13,
+			jac: vecFunc13Jac,
+		},
+		{
+			m:   2,
+			n:   2,
+			f:   vecFunc22,
+			jac: vecFunc22Jac,
+		},
+		{
+			m:   4,
+			n:   3,
+			f:   vecFunc43,
+			jac: vecFunc43Jac,
+		},
+	} {
+		const tol = 1e-6
+
+		x := randomSlice(test.n, 10)
+		xcopy := make([]float64, test.n)
+		copy(xcopy, x)
+
+		want := mat.NewDense(test.m, test.n, nil)
+		test.jac(want, x)
+
+		got := mat.NewDense(test.m, test.n, nil)
+		fillNaNDense(got)
+		Jacobian(got, test.f, x, nil)
+		if !mat.EqualApprox(want, got, tol) {
+			t.Errorf("Case %d (default settings): unexpected Jacobian.\nwant: %v\ngot:  %v",
+				tc, mat.Formatted(want, mat.Prefix("      ")), mat.Formatted(got, mat.Prefix("      ")))
+		}
+		if !floats.Equal(x, xcopy) {
+			t.Errorf("Case %d (default settings): x modified", tc)
+		}
+	}
+
+	// Test with non-default settings.
+	for tc, test := range []struct {
+		m, n    int
+		f       func([]float64, []float64)
+		jac     func(*mat.Dense, []float64)
+		tol     float64
+		formula Formula
+	}{
+		{
+			m:       1,
+			n:       3,
+			f:       vecFunc13,
+			jac:     vecFunc13Jac,
+			tol:     1e-6,
+			formula: Forward,
+		},
+		{
+			m:       1,
+			n:       3,
+			f:       vecFunc13,
+			jac:     vecFunc13Jac,
+			tol:     1e-6,
+			formula: Backward,
+		},
+		{
+			m:       1,
+			n:       3,
+			f:       vecFunc13,
+			jac:     vecFunc13Jac,
+			tol:     1e-9,
+			formula: Central,
+		},
+		{
+			m:       2,
+			n:       2,
+			f:       vecFunc22,
+			jac:     vecFunc22Jac,
+			tol:     1e-6,
+			formula: Forward,
+		},
+		{
+			m:       2,
+			n:       2,
+			f:       vecFunc22,
+			jac:     vecFunc22Jac,
+			tol:     1e-6,
+			formula: Backward,
+		},
+		{
+			m:       2,
+			n:       2,
+			f:       vecFunc22,
+			jac:     vecFunc22Jac,
+			tol:     1e-9,
+			formula: Central,
+		},
+		{
+			m:       4,
+			n:       3,
+			f:       vecFunc43,
+			jac:     vecFunc43Jac,
+			tol:     1e-6,
+			formula: Forward,
+		},
+		{
+			m:       4,
+			n:       3,
+			f:       vecFunc43,
+			jac:     vecFunc43Jac,
+			tol:     1e-6,
+			formula: Backward,
+		},
+		{
+			m:       4,
+			n:       3,
+			f:       vecFunc43,
+			jac:     vecFunc43Jac,
+			tol:     1e-9,
+			formula: Central,
+		},
+	} {
+		x := randomSlice(test.n, 10)
+		xcopy := make([]float64, test.n)
+		copy(xcopy, x)
+
+		want := mat.NewDense(test.m, test.n, nil)
+		test.jac(want, x)
+
+		got := mat.NewDense(test.m, test.n, nil)
+		fillNaNDense(got)
+		Jacobian(got, test.f, x, &JacobianSettings{
+			Formula: test.formula,
+		})
+		if !mat.EqualApprox(want, got, test.tol) {
+			t.Errorf("Case %d: unexpected Jacobian.\nwant: %v\ngot:  %v",
+				tc, mat.Formatted(want, mat.Prefix("      ")), mat.Formatted(got, mat.Prefix("      ")))
+		}
+		if !floats.Equal(x, xcopy) {
+			t.Errorf("Case %d: x modified", tc)
+		}
+
+		fillNaNDense(got)
+		Jacobian(got, test.f, x, &JacobianSettings{
+			Formula:    test.formula,
+			Concurrent: true,
+		})
+		if !mat.EqualApprox(want, got, test.tol) {
+			t.Errorf("Case %d (concurrent): unexpected Jacobian.\nwant: %v\ngot:  %v",
+				tc, mat.Formatted(want, mat.Prefix("      ")), mat.Formatted(got, mat.Prefix("      ")))
+		}
+		if !floats.Equal(x, xcopy) {
+			t.Errorf("Case %d (concurrent): x modified", tc)
+		}
+
+		fillNaNDense(got)
+		origin := make([]float64, test.m)
+		test.f(origin, x)
+		Jacobian(got, test.f, x, &JacobianSettings{
+			Formula:     test.formula,
+			OriginValue: origin,
+		})
+		if !mat.EqualApprox(want, got, test.tol) {
+			t.Errorf("Case %d (origin): unexpected Jacobian.\nwant: %v\ngot:  %v",
+				tc, mat.Formatted(want, mat.Prefix("      ")), mat.Formatted(got, mat.Prefix("      ")))
+		}
+		if !floats.Equal(x, xcopy) {
+			t.Errorf("Case %d (origin): x modified", tc)
+		}
+
+		fillNaNDense(got)
+		Jacobian(got, test.f, x, &JacobianSettings{
+			Formula:     test.formula,
+			OriginValue: origin,
+			Concurrent:  true,
+		})
+		if !mat.EqualApprox(want, got, test.tol) {
+			t.Errorf("Case %d (concurrent, origin): unexpected Jacobian.\nwant: %v\ngot:  %v",
+				tc, mat.Formatted(want, mat.Prefix("      ")), mat.Formatted(got, mat.Prefix("      ")))
+		}
+		if !floats.Equal(x, xcopy) {
+			t.Errorf("Case %d (concurrent, origin): x modified", tc)
+		}
+	}
+}
+
+// randomSlice returns a slice of n elements from the interval [-bound,bound).
+func randomSlice(n int, bound float64) []float64 {
+	x := make([]float64, n)
+	for i := range x {
+		x[i] = 2*bound*rand.Float64() - bound
+	}
+	return x
+}
+
+// fillNaNDense fills the matrix m with NaN values.
+func fillNaNDense(m *mat.Dense) {
+	r, c := m.Dims()
+	for i := 0; i < r; i++ {
+		for j := 0; j < c; j++ {
+			m.Set(i, j, math.NaN())
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/diff/fd/laplacian.go b/vendor/gonum.org/v1/gonum/diff/fd/laplacian.go
new file mode 100644
index 00000000..e5a8ca15
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/diff/fd/laplacian.go
@@ -0,0 +1,158 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package fd
+
+import "sync"
+
+// Laplacian computes the Laplacian of the multivariate function f at the location
+// x. That is, Laplacian returns
+//  ∆ f(x) = ∇ · ∇ f(x) = \sum_i ∂^2 f(x)/∂x_i^2
+// The finite difference formula and other options are specified by settings.
+// The order of the difference formula must be 2 or Laplacian will panic.
+func Laplacian(f func(x []float64) float64, x []float64, settings *Settings) float64 {
+	n := len(x)
+	if n == 0 {
+		panic("laplacian: x has zero length")
+	}
+
+	// Default settings.
+	formula := Central2nd
+	step := formula.Step
+	var originValue float64
+	var originKnown, concurrent bool
+
+	// Use user settings if provided.
+	if settings != nil {
+		if !settings.Formula.isZero() {
+			formula = settings.Formula
+			step = formula.Step
+			checkFormula(formula)
+			if formula.Derivative != 2 {
+				panic(badDerivOrder)
+			}
+		}
+		if settings.Step != 0 {
+			if settings.Step < 0 {
+				panic(negativeStep)
+			}
+			step = settings.Step
+		}
+		originKnown = settings.OriginKnown
+		originValue = settings.OriginValue
+		concurrent = settings.Concurrent
+	}
+
+	evals := n * len(formula.Stencil)
+	if usesOrigin(formula.Stencil) {
+		evals -= n
+	}
+
+	nWorkers := computeWorkers(concurrent, evals)
+	if nWorkers == 1 {
+		return laplacianSerial(f, x, formula.Stencil, step, originKnown, originValue)
+	}
+	return laplacianConcurrent(nWorkers, evals, f, x, formula.Stencil, step, originKnown, originValue)
+}
+
+func laplacianSerial(f func(x []float64) float64, x []float64, stencil []Point, step float64, originKnown bool, originValue float64) float64 {
+	n := len(x)
+	xCopy := make([]float64, n)
+	fo := func() float64 {
+		// Copy x in case it is modified during the call.
+		copy(xCopy, x)
+		return f(x)
+	}
+	is2 := 1 / (step * step)
+	origin := getOrigin(originKnown, originValue, fo, stencil)
+	var laplacian float64
+	for i := 0; i < n; i++ {
+		for _, pt := range stencil {
+			var v float64
+			if pt.Loc == 0 {
+				v = origin
+			} else {
+				// Copying the data anew has two benefits. First, it
+				// avoids floating point issues where adding and then
+				// subtracting the step don't return to the exact same
+				// location. Secondly, it protects against the function
+				// modifying the input data.
+				copy(xCopy, x)
+				xCopy[i] += pt.Loc * step
+				v = f(xCopy)
+			}
+			laplacian += v * pt.Coeff * is2
+		}
+	}
+	return laplacian
+}
+
+func laplacianConcurrent(nWorkers, evals int, f func(x []float64) float64, x []float64, stencil []Point, step float64, originKnown bool, originValue float64) float64 {
+	type run struct {
+		i      int
+		idx    int
+		result float64
+	}
+	n := len(x)
+	send := make(chan run, evals)
+	ans := make(chan run, evals)
+
+	var originWG sync.WaitGroup
+	hasOrigin := usesOrigin(stencil)
+	if hasOrigin {
+		originWG.Add(1)
+		// Launch worker to compute the origin.
+		go func() {
+			defer originWG.Done()
+			xCopy := make([]float64, len(x))
+			copy(xCopy, x)
+			originValue = f(xCopy)
+		}()
+	}
+
+	var workerWG sync.WaitGroup
+	// Launch workers.
+	for i := 0; i < nWorkers; i++ {
+		workerWG.Add(1)
+		go func(send <-chan run, ans chan<- run) {
+			defer workerWG.Done()
+			xCopy := make([]float64, len(x))
+			for r := range send {
+				if stencil[r.idx].Loc == 0 {
+					originWG.Wait()
+					r.result = originValue
+				} else {
+					// See laplacianSerial for comment on the copy.
+					copy(xCopy, x)
+					xCopy[r.i] += stencil[r.idx].Loc * step
+					r.result = f(xCopy)
+				}
+				ans <- r
+			}
+		}(send, ans)
+	}
+
+	// Launch the distributor, which sends all of runs.
+	go func(send chan<- run) {
+		for i := 0; i < n; i++ {
+			for idx := range stencil {
+				send <- run{
+					i: i, idx: idx,
+				}
+			}
+		}
+		close(send)
+		// Wait for all the workers to quit, then close the ans channel.
+		workerWG.Wait()
+		close(ans)
+	}(send)
+
+	// Read in the results.
+	is2 := 1 / (step * step)
+	var laplacian float64
+	for r := range ans {
+		laplacian += r.result * stencil[r.idx].Coeff * is2
+	}
+	return laplacian
+}
diff --git a/vendor/gonum.org/v1/gonum/diff/fd/laplacian_test.go b/vendor/gonum.org/v1/gonum/diff/fd/laplacian_test.go
new file mode 100644
index 00000000..75949d4a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/diff/fd/laplacian_test.go
@@ -0,0 +1,44 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package fd
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+)
+
+func TestLaplacian(t *testing.T) {
+	for cas, test := range hessianTestCases {
+		// Modify the test cases where the forumla is set.
+		settings := test.settings
+		if settings != nil && !settings.Formula.isZero() {
+			settings.Formula = Forward2nd
+		}
+
+		n := len(test.x)
+		got := Laplacian(test.h.Func, test.x, test.settings)
+		hess := mat.NewSymDense(n, nil)
+		test.h.Hess(hess, test.x)
+		var want float64
+		for i := 0; i < n; i++ {
+			want += hess.At(i, i)
+		}
+		if !floats.EqualWithinAbsOrRel(got, want, test.tol, test.tol) {
+			t.Errorf("Cas %d: Laplacian mismatch. got %v, want %v", cas, got, want)
+		}
+
+		// Test that concurrency works.
+		if settings == nil {
+			settings = &Settings{}
+		}
+		settings.Concurrent = true
+		got2 := Laplacian(test.h.Func, test.x, settings)
+		if !floats.EqualWithinAbsOrRel(got, got2, 1e-5, 1e-5) {
+			t.Errorf("Cas %d: Laplacian mismatch. got %v, want %v", cas, got2, got)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/diff/fd/simplefunctions_test.go b/vendor/gonum.org/v1/gonum/diff/fd/simplefunctions_test.go
new file mode 100644
index 00000000..1c1dd42e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/diff/fd/simplefunctions_test.go
@@ -0,0 +1,87 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package fd
+
+import (
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+)
+
+// ConstFunc is a constant function returning the value held by the type.
+type ConstFunc float64
+
+func (c ConstFunc) Func(x []float64) float64 {
+	return float64(c)
+}
+
+func (c ConstFunc) Grad(grad, x []float64) {
+	for i := range grad {
+		grad[i] = 0
+	}
+}
+
+func (c ConstFunc) Hess(dst mat.MutableSymmetric, x []float64) {
+	n := len(x)
+	for i := 0; i < n; i++ {
+		for j := i; j < n; j++ {
+			dst.SetSym(i, j, 0)
+		}
+	}
+}
+
+// LinearFunc is a linear function returning w*x+c.
+type LinearFunc struct {
+	w []float64
+	c float64
+}
+
+func (l LinearFunc) Func(x []float64) float64 {
+	return floats.Dot(l.w, x) + l.c
+}
+
+func (l LinearFunc) Grad(grad, x []float64) {
+	copy(grad, l.w)
+}
+
+func (l LinearFunc) Hess(dst mat.MutableSymmetric, x []float64) {
+	n := len(x)
+	for i := 0; i < n; i++ {
+		for j := i; j < n; j++ {
+			dst.SetSym(i, j, 0)
+		}
+	}
+}
+
+// QuadFunc is a quadratic function returning 0.5*x'*a*x + b*x + c.
+type QuadFunc struct {
+	a *mat.SymDense
+	b *mat.VecDense
+	c float64
+}
+
+func (q QuadFunc) Func(x []float64) float64 {
+	v := mat.NewVecDense(len(x), x)
+	var tmp mat.VecDense
+	tmp.MulVec(q.a, v)
+	return 0.5*mat.Dot(&tmp, v) + mat.Dot(q.b, v) + q.c
+}
+
+func (q QuadFunc) Grad(grad, x []float64) {
+	var tmp mat.VecDense
+	v := mat.NewVecDense(len(x), x)
+	tmp.MulVec(q.a, v)
+	for i := range grad {
+		grad[i] = tmp.At(i, 0) + q.b.At(i, 0)
+	}
+}
+
+func (q QuadFunc) Hess(dst mat.MutableSymmetric, x []float64) {
+	n := len(x)
+	for i := 0; i < n; i++ {
+		for j := i; j < n; j++ {
+			dst.SetSym(i, j, q.a.At(i, j))
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/diff/fd/watson_test.go b/vendor/gonum.org/v1/gonum/diff/fd/watson_test.go
new file mode 100644
index 00000000..62095e21
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/diff/fd/watson_test.go
@@ -0,0 +1,132 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package fd
+
+import "gonum.org/v1/gonum/mat"
+
+// Watson implements the Watson's function.
+// Dimension of the problem should be 2 <= dim <= 31. For dim == 9, the problem
+// of minimizing the function is very ill conditioned.
+//
+// This is copied from gonum.org/v1/optimize/functions for testing Hessian-like
+// derivative methods.
+//
+// References:
+//  - Kowalik, J.S., Osborne, M.R.: Methods for Unconstrained Optimization
+//    Problems. Elsevier North-Holland, New York, 1968
+//  - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
+//    optimization software. ACM Trans Math Softw 7 (1981), 17-41
+type Watson struct{}
+
+func (Watson) Func(x []float64) (sum float64) {
+	for i := 1; i <= 29; i++ {
+		d1 := float64(i) / 29
+
+		d2 := 1.0
+		var s1 float64
+		for j := 1; j < len(x); j++ {
+			s1 += float64(j) * d2 * x[j]
+			d2 *= d1
+		}
+
+		d2 = 1.0
+		var s2 float64
+		for _, v := range x {
+			s2 += d2 * v
+			d2 *= d1
+		}
+
+		t := s1 - s2*s2 - 1
+		sum += t * t
+	}
+	t := x[1] - x[0]*x[0] - 1
+	sum += x[0]*x[0] + t*t
+	return sum
+}
+
+func (Watson) Grad(grad, x []float64) {
+	if len(x) != len(grad) {
+		panic("incorrect size of the gradient")
+	}
+
+	for i := range grad {
+		grad[i] = 0
+	}
+	for i := 1; i <= 29; i++ {
+		d1 := float64(i) / 29
+
+		d2 := 1.0
+		var s1 float64
+		for j := 1; j < len(x); j++ {
+			s1 += float64(j) * d2 * x[j]
+			d2 *= d1
+		}
+
+		d2 = 1.0
+		var s2 float64
+		for _, v := range x {
+			s2 += d2 * v
+			d2 *= d1
+		}
+
+		t := s1 - s2*s2 - 1
+		s3 := 2 * d1 * s2
+		d2 = 2 / d1
+		for j := range x {
+			grad[j] += d2 * (float64(j) - s3) * t
+			d2 *= d1
+		}
+	}
+	t := x[1] - x[0]*x[0] - 1
+	grad[0] += x[0] * (2 - 4*t)
+	grad[1] += 2 * t
+}
+
+func (Watson) Hess(hess mat.MutableSymmetric, x []float64) {
+	dim := len(x)
+	if dim != hess.Symmetric() {
+		panic("incorrect size of the Hessian")
+	}
+
+	for j := 0; j < dim; j++ {
+		for k := j; k < dim; k++ {
+			hess.SetSym(j, k, 0)
+		}
+	}
+	for i := 1; i <= 29; i++ {
+		d1 := float64(i) / 29
+		d2 := 1.0
+		var s1 float64
+		for j := 1; j < dim; j++ {
+			s1 += float64(j) * d2 * x[j]
+			d2 *= d1
+		}
+
+		d2 = 1.0
+		var s2 float64
+		for _, v := range x {
+			s2 += d2 * v
+			d2 *= d1
+		}
+
+		t := s1 - s2*s2 - 1
+		s3 := 2 * d1 * s2
+		d2 = 2 / d1
+		th := 2 * d1 * d1 * t
+		for j := 0; j < dim; j++ {
+			v := float64(j) - s3
+			d3 := 1 / d1
+			for k := 0; k <= j; k++ {
+				hess.SetSym(k, j, hess.At(k, j)+d2*d3*(v*(float64(k)-s3)-th))
+				d3 *= d1
+			}
+			d2 *= d1
+		}
+	}
+	t1 := x[1] - x[0]*x[0] - 1
+	hess.SetSym(0, 0, hess.At(0, 0)+8*x[0]*x[0]+2-4*t1)
+	hess.SetSym(0, 1, hess.At(0, 1)-4*x[0])
+	hess.SetSym(1, 1, hess.At(1, 1)+2)
+}
diff --git a/vendor/gonum.org/v1/gonum/floats/README.md b/vendor/gonum.org/v1/gonum/floats/README.md
new file mode 100644
index 00000000..ee867bb7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/floats/README.md
@@ -0,0 +1,4 @@
+# Gonum floats [![GoDoc](https://godoc.org/gonum.org/v1/gonum/floats?status.svg)](https://godoc.org/gonum.org/v1/gonum/floats)
+
+Package floats provides a set of helper routines for dealing with slices of float64.
+The functions avoid allocations to allow for use within tight loops without garbage collection overhead.
diff --git a/vendor/gonum.org/v1/gonum/floats/doc.go b/vendor/gonum.org/v1/gonum/floats/doc.go
new file mode 100644
index 00000000..a9bd5742
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/floats/doc.go
@@ -0,0 +1,11 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package floats provides a set of helper routines for dealing with slices
+// of float64. The functions avoid allocations to allow for use within tight
+// loops without garbage collection overhead.
+//
+// The convention used is that when a slice is being modified in place, it has
+// the name dst.
+package floats // import "gonum.org/v1/gonum/floats"
diff --git a/vendor/gonum.org/v1/gonum/floats/examples_test.go b/vendor/gonum.org/v1/gonum/floats/examples_test.go
new file mode 100644
index 00000000..3bc59ad1
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/floats/examples_test.go
@@ -0,0 +1,104 @@
+// Copyright 2013 The Gonum Authors. All rights reserved.
+// Use of this code is governed by a BSD-style
+// license that can be found in the LICENSE file
+
+package floats
+
+import (
+	"fmt"
+)
+
+// Set of examples for all the functions
+
+func ExampleAdd_simple() {
+	// Adding three slices together. Note that
+	// the result is stored in the first slice
+	s1 := []float64{1, 2, 3, 4}
+	s2 := []float64{5, 6, 7, 8}
+	s3 := []float64{1, 1, 1, 1}
+	Add(s1, s2)
+	Add(s1, s3)
+
+	fmt.Println("s1 =", s1)
+	fmt.Println("s2 =", s2)
+	fmt.Println("s3 =", s3)
+	// Output:
+	// s1 = [7 9 11 13]
+	// s2 = [5 6 7 8]
+	// s3 = [1 1 1 1]
+}
+
+func ExampleAdd_newslice() {
+	// If one wants to store the result in a
+	// new container, just make a new slice
+	s1 := []float64{1, 2, 3, 4}
+	s2 := []float64{5, 6, 7, 8}
+	s3 := []float64{1, 1, 1, 1}
+	dst := make([]float64, len(s1))
+
+	AddTo(dst, s1, s2)
+	Add(dst, s3)
+
+	fmt.Println("dst =", dst)
+	fmt.Println("s1 =", s1)
+	fmt.Println("s2 =", s2)
+	fmt.Println("s3 =", s3)
+	// Output:
+	// dst = [7 9 11 13]
+	// s1 = [1 2 3 4]
+	// s2 = [5 6 7 8]
+	// s3 = [1 1 1 1]
+}
+
+func ExampleAdd_unequallengths() {
+	// If the lengths of the slices are unknown,
+	// use Eqlen to check
+	s1 := []float64{1, 2, 3}
+	s2 := []float64{5, 6, 7, 8}
+
+	eq := EqualLengths(s1, s2)
+	if eq {
+		Add(s1, s2)
+	} else {
+		fmt.Println("Unequal lengths")
+	}
+	// Output:
+	// Unequal lengths
+}
+
+func ExampleAddConst() {
+	s := []float64{1, -2, 3, -4}
+	c := 5.0
+
+	AddConst(c, s)
+
+	fmt.Println("s =", s)
+	// Output:
+	// s = [6 3 8 1]
+}
+
+func ExampleCumProd() {
+	s := []float64{1, -2, 3, -4}
+	dst := make([]float64, len(s))
+
+	CumProd(dst, s)
+
+	fmt.Println("dst =", dst)
+	fmt.Println("s =", s)
+	// Output:
+	// dst = [1 -2 -6 24]
+	// s = [1 -2 3 -4]
+}
+
+func ExampleCumSum() {
+	s := []float64{1, -2, 3, -4}
+	dst := make([]float64, len(s))
+
+	CumSum(dst, s)
+
+	fmt.Println("dst =", dst)
+	fmt.Println("s =", s)
+	// Output:
+	// dst = [1 -1 2 -2]
+	// s = [1 -2 3 -4]
+}
diff --git a/vendor/gonum.org/v1/gonum/floats/floats.go b/vendor/gonum.org/v1/gonum/floats/floats.go
new file mode 100644
index 00000000..6a582b70
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/floats/floats.go
@@ -0,0 +1,771 @@
+// Copyright 2013 The Gonum Authors. All rights reserved.
+// Use of this code is governed by a BSD-style
+// license that can be found in the LICENSE file
+
+package floats
+
+import (
+	"errors"
+	"math"
+	"sort"
+	"strconv"
+
+	"gonum.org/v1/gonum/internal/asm/f64"
+)
+
+// Add adds, element-wise, the elements of s and dst, and stores in dst.
+// Panics if the lengths of dst and s do not match.
+func Add(dst, s []float64) {
+	if len(dst) != len(s) {
+		panic("floats: length of the slices do not match")
+	}
+	f64.AxpyUnitaryTo(dst, 1, s, dst)
+}
+
+// AddTo adds, element-wise, the elements of s and t and
+// stores the result in dst. Panics if the lengths of s, t and dst do not match.
+func AddTo(dst, s, t []float64) []float64 {
+	if len(s) != len(t) {
+		panic("floats: length of adders do not match")
+	}
+	if len(dst) != len(s) {
+		panic("floats: length of destination does not match length of adder")
+	}
+	f64.AxpyUnitaryTo(dst, 1, s, t)
+	return dst
+}
+
+// AddConst adds the scalar c to all of the values in dst.
+func AddConst(c float64, dst []float64) {
+	for i := range dst {
+		dst[i] += c
+	}
+}
+
+// AddScaled performs dst = dst + alpha * s.
+// It panics if the lengths of dst and s are not equal.
+func AddScaled(dst []float64, alpha float64, s []float64) {
+	if len(dst) != len(s) {
+		panic("floats: length of destination and source to not match")
+	}
+	f64.AxpyUnitaryTo(dst, alpha, s, dst)
+}
+
+// AddScaledTo performs dst = y + alpha * s, where alpha is a scalar,
+// and dst, y and s are all slices.
+// It panics if the lengths of dst, y, and s are not equal.
+//
+// At the return of the function, dst[i] = y[i] + alpha * s[i]
+func AddScaledTo(dst, y []float64, alpha float64, s []float64) []float64 {
+	if len(dst) != len(s) || len(dst) != len(y) {
+		panic("floats: lengths of slices do not match")
+	}
+	f64.AxpyUnitaryTo(dst, alpha, s, y)
+	return dst
+}
+
+// argsort is a helper that implements sort.Interface, as used by
+// Argsort.
+type argsort struct {
+	s    []float64
+	inds []int
+}
+
+func (a argsort) Len() int {
+	return len(a.s)
+}
+
+func (a argsort) Less(i, j int) bool {
+	return a.s[i] < a.s[j]
+}
+
+func (a argsort) Swap(i, j int) {
+	a.s[i], a.s[j] = a.s[j], a.s[i]
+	a.inds[i], a.inds[j] = a.inds[j], a.inds[i]
+}
+
+// Argsort sorts the elements of s while tracking their original order.
+// At the conclusion of Argsort, s will contain the original elements of s
+// but sorted in increasing order, and inds will contain the original position
+// of the elements in the slice such that dst[i] = origDst[inds[i]].
+// It panics if the lengths of dst and inds do not match.
+func Argsort(dst []float64, inds []int) {
+	if len(dst) != len(inds) {
+		panic("floats: length of inds does not match length of slice")
+	}
+	for i := range dst {
+		inds[i] = i
+	}
+
+	a := argsort{s: dst, inds: inds}
+	sort.Sort(a)
+}
+
+// Count applies the function f to every element of s and returns the number
+// of times the function returned true.
+func Count(f func(float64) bool, s []float64) int {
+	var n int
+	for _, val := range s {
+		if f(val) {
+			n++
+		}
+	}
+	return n
+}
+
+// CumProd finds the cumulative product of the first i elements in
+// s and puts them in place into the ith element of the
+// destination dst. A panic will occur if the lengths of arguments
+// do not match.
+//
+// At the return of the function, dst[i] = s[i] * s[i-1] * s[i-2] * ...
+func CumProd(dst, s []float64) []float64 {
+	if len(dst) != len(s) {
+		panic("floats: length of destination does not match length of the source")
+	}
+	if len(dst) == 0 {
+		return dst
+	}
+	return f64.CumProd(dst, s)
+}
+
+// CumSum finds the cumulative sum of the first i elements in
+// s and puts them in place into the ith element of the
+// destination dst. A panic will occur if the lengths of arguments
+// do not match.
+//
+// At the return of the function, dst[i] = s[i] + s[i-1] + s[i-2] + ...
+func CumSum(dst, s []float64) []float64 {
+	if len(dst) != len(s) {
+		panic("floats: length of destination does not match length of the source")
+	}
+	if len(dst) == 0 {
+		return dst
+	}
+	return f64.CumSum(dst, s)
+}
+
+// Distance computes the L-norm of s - t. See Norm for special cases.
+// A panic will occur if the lengths of s and t do not match.
+func Distance(s, t []float64, L float64) float64 {
+	if len(s) != len(t) {
+		panic("floats: slice lengths do not match")
+	}
+	if len(s) == 0 {
+		return 0
+	}
+	var norm float64
+	if L == 2 {
+		for i, v := range s {
+			diff := t[i] - v
+			norm = math.Hypot(norm, diff)
+		}
+		return norm
+	}
+	if L == 1 {
+		for i, v := range s {
+			norm += math.Abs(t[i] - v)
+		}
+		return norm
+	}
+	if math.IsInf(L, 1) {
+		for i, v := range s {
+			absDiff := math.Abs(t[i] - v)
+			if absDiff > norm {
+				norm = absDiff
+			}
+		}
+		return norm
+	}
+	for i, v := range s {
+		norm += math.Pow(math.Abs(t[i]-v), L)
+	}
+	return math.Pow(norm, 1/L)
+}
+
+// Div performs element-wise division dst / s
+// and stores the value in dst. It panics if the
+// lengths of s and t are not equal.
+func Div(dst, s []float64) {
+	if len(dst) != len(s) {
+		panic("floats: slice lengths do not match")
+	}
+	f64.Div(dst, s)
+}
+
+// DivTo performs element-wise division s / t
+// and stores the value in dst. It panics if the
+// lengths of s, t, and dst are not equal.
+func DivTo(dst, s, t []float64) []float64 {
+	if len(s) != len(t) || len(dst) != len(t) {
+		panic("floats: slice lengths do not match")
+	}
+	return f64.DivTo(dst, s, t)
+}
+
+// Dot computes the dot product of s1 and s2, i.e.
+// sum_{i = 1}^N s1[i]*s2[i].
+// A panic will occur if lengths of arguments do not match.
+func Dot(s1, s2 []float64) float64 {
+	if len(s1) != len(s2) {
+		panic("floats: lengths of the slices do not match")
+	}
+	return f64.DotUnitary(s1, s2)
+}
+
+// Equal returns true if the slices have equal lengths and
+// all elements are numerically identical.
+func Equal(s1, s2 []float64) bool {
+	if len(s1) != len(s2) {
+		return false
+	}
+	for i, val := range s1 {
+		if s2[i] != val {
+			return false
+		}
+	}
+	return true
+}
+
+// EqualApprox returns true if the slices have equal lengths and
+// all element pairs have an absolute tolerance less than tol or a
+// relative tolerance less than tol.
+func EqualApprox(s1, s2 []float64, tol float64) bool {
+	if len(s1) != len(s2) {
+		return false
+	}
+	for i, a := range s1 {
+		if !EqualWithinAbsOrRel(a, s2[i], tol, tol) {
+			return false
+		}
+	}
+	return true
+}
+
+// EqualFunc returns true if the slices have the same lengths
+// and the function returns true for all element pairs.
+func EqualFunc(s1, s2 []float64, f func(float64, float64) bool) bool {
+	if len(s1) != len(s2) {
+		return false
+	}
+	for i, val := range s1 {
+		if !f(val, s2[i]) {
+			return false
+		}
+	}
+	return true
+}
+
+// EqualWithinAbs returns true if a and b have an absolute
+// difference of less than tol.
+func EqualWithinAbs(a, b, tol float64) bool {
+	return a == b || math.Abs(a-b) <= tol
+}
+
+const minNormalFloat64 = 2.2250738585072014e-308
+
+// EqualWithinRel returns true if the difference between a and b
+// is not greater than tol times the greater value.
+func EqualWithinRel(a, b, tol float64) bool {
+	if a == b {
+		return true
+	}
+	delta := math.Abs(a - b)
+	if delta <= minNormalFloat64 {
+		return delta <= tol*minNormalFloat64
+	}
+	// We depend on the division in this relationship to identify
+	// infinities (we rely on the NaN to fail the test) otherwise
+	// we compare Infs of the same sign and evaluate Infs as equal
+	// independent of sign.
+	return delta/math.Max(math.Abs(a), math.Abs(b)) <= tol
+}
+
+// EqualWithinAbsOrRel returns true if a and b are equal to within
+// the absolute tolerance.
+func EqualWithinAbsOrRel(a, b, absTol, relTol float64) bool {
+	if EqualWithinAbs(a, b, absTol) {
+		return true
+	}
+	return EqualWithinRel(a, b, relTol)
+}
+
+// EqualWithinULP returns true if a and b are equal to within
+// the specified number of floating point units in the last place.
+func EqualWithinULP(a, b float64, ulp uint) bool {
+	if a == b {
+		return true
+	}
+	if math.IsNaN(a) || math.IsNaN(b) {
+		return false
+	}
+	if math.Signbit(a) != math.Signbit(b) {
+		return math.Float64bits(math.Abs(a))+math.Float64bits(math.Abs(b)) <= uint64(ulp)
+	}
+	return ulpDiff(math.Float64bits(a), math.Float64bits(b)) <= uint64(ulp)
+}
+
+func ulpDiff(a, b uint64) uint64 {
+	if a > b {
+		return a - b
+	}
+	return b - a
+}
+
+// EqualLengths returns true if all of the slices have equal length,
+// and false otherwise. Returns true if there are no input slices.
+func EqualLengths(slices ...[]float64) bool {
+	// This length check is needed: http://play.golang.org/p/sdty6YiLhM
+	if len(slices) == 0 {
+		return true
+	}
+	l := len(slices[0])
+	for i := 1; i < len(slices); i++ {
+		if len(slices[i]) != l {
+			return false
+		}
+	}
+	return true
+}
+
+// Find applies f to every element of s and returns the indices of the first
+// k elements for which the f returns true, or all such elements
+// if k < 0.
+// Find will reslice inds to have 0 length, and will append
+// found indices to inds.
+// If k > 0 and there are fewer than k elements in s satisfying f,
+// all of the found elements will be returned along with an error.
+// At the return of the function, the input inds will be in an undetermined state.
+func Find(inds []int, f func(float64) bool, s []float64, k int) ([]int, error) {
+
+	// inds is also returned to allow for calling with nil
+
+	// Reslice inds to have zero length
+	inds = inds[:0]
+
+	// If zero elements requested, can just return
+	if k == 0 {
+		return inds, nil
+	}
+
+	// If k < 0, return all of the found indices
+	if k < 0 {
+		for i, val := range s {
+			if f(val) {
+				inds = append(inds, i)
+			}
+		}
+		return inds, nil
+	}
+
+	// Otherwise, find the first k elements
+	nFound := 0
+	for i, val := range s {
+		if f(val) {
+			inds = append(inds, i)
+			nFound++
+			if nFound == k {
+				return inds, nil
+			}
+		}
+	}
+	// Finished iterating over the loop, which means k elements were not found
+	return inds, errors.New("floats: insufficient elements found")
+}
+
+// HasNaN returns true if the slice s has any values that are NaN and false
+// otherwise.
+func HasNaN(s []float64) bool {
+	for _, v := range s {
+		if math.IsNaN(v) {
+			return true
+		}
+	}
+	return false
+}
+
+// LogSpan returns a set of n equally spaced points in log space between,
+// l and u where N is equal to len(dst). The first element of the
+// resulting dst will be l and the final element of dst will be u.
+// Panics if len(dst) < 2
+// Note that this call will return NaNs if either l or u are negative, and
+// will return all zeros if l or u is zero.
+// Also returns the mutated slice dst, so that it can be used in range, like:
+//
+//     for i, x := range LogSpan(dst, l, u) { ... }
+func LogSpan(dst []float64, l, u float64) []float64 {
+	Span(dst, math.Log(l), math.Log(u))
+	for i := range dst {
+		dst[i] = math.Exp(dst[i])
+	}
+	return dst
+}
+
+// LogSumExp returns the log of the sum of the exponentials of the values in s.
+// Panics if s is an empty slice.
+func LogSumExp(s []float64) float64 {
+	// Want to do this in a numerically stable way which avoids
+	// overflow and underflow
+	// First, find the maximum value in the slice.
+	maxval := Max(s)
+	if math.IsInf(maxval, 0) {
+		// If it's infinity either way, the logsumexp will be infinity as well
+		// returning now avoids NaNs
+		return maxval
+	}
+	var lse float64
+	// Compute the sumexp part
+	for _, val := range s {
+		lse += math.Exp(val - maxval)
+	}
+	// Take the log and add back on the constant taken out
+	return math.Log(lse) + maxval
+}
+
+// Max returns the maximum value in the input slice. If the slice is empty, Max will panic.
+func Max(s []float64) float64 {
+	return s[MaxIdx(s)]
+}
+
+// MaxIdx returns the index of the maximum value in the input slice. If several
+// entries have the maximum value, the first such index is returned. If the slice
+// is empty, MaxIdx will panic.
+func MaxIdx(s []float64) int {
+	if len(s) == 0 {
+		panic("floats: zero slice length")
+	}
+	max := s[0]
+	var ind int
+	for i, v := range s {
+		if v > max {
+			max = v
+			ind = i
+		}
+	}
+	return ind
+}
+
+// Min returns the maximum value in the input slice. If the slice is empty, Min will panic.
+func Min(s []float64) float64 {
+	return s[MinIdx(s)]
+}
+
+// MinIdx returns the index of the minimum value in the input slice. If several
+// entries have the maximum value, the first such index is returned. If the slice
+// is empty, MinIdx will panic.
+func MinIdx(s []float64) int {
+	min := s[0]
+	var ind int
+	for i, v := range s {
+		if v < min {
+			min = v
+			ind = i
+		}
+	}
+	return ind
+}
+
+// Mul performs element-wise multiplication between dst
+// and s and stores the value in dst. Panics if the
+// lengths of s and t are not equal.
+func Mul(dst, s []float64) {
+	if len(dst) != len(s) {
+		panic("floats: slice lengths do not match")
+	}
+	for i, val := range s {
+		dst[i] *= val
+	}
+}
+
+// MulTo performs element-wise multiplication between s
+// and t and stores the value in dst. Panics if the
+// lengths of s, t, and dst are not equal.
+func MulTo(dst, s, t []float64) []float64 {
+	if len(s) != len(t) || len(dst) != len(t) {
+		panic("floats: slice lengths do not match")
+	}
+	for i, val := range t {
+		dst[i] = val * s[i]
+	}
+	return dst
+}
+
+// Nearest returns the index of the element in s
+// whose value is nearest to v.  If several such
+// elements exist, the lowest index is returned.
+// Panics if len(s) == 0.
+func Nearest(s []float64, v float64) int {
+	var ind int
+	dist := math.Abs(v - s[0])
+	for i, val := range s {
+		newDist := math.Abs(v - val)
+		if newDist < dist {
+			dist = newDist
+			ind = i
+		}
+	}
+	return ind
+}
+
+// NearestWithinSpan return the index of a hypothetical vector created
+// by Span with length n and bounds l and u whose value is closest
+// to v. NearestWithinSpan panics if u < l. If the value is greater than u or
+// less than l, the function returns -1.
+func NearestWithinSpan(n int, l, u float64, v float64) int {
+	if u < l {
+		panic("floats: upper bound greater than lower bound")
+	}
+	if v < l || v > u {
+		return -1
+	}
+	// Can't guarantee anything about exactly halfway between
+	// because of floating point weirdness.
+	return int((float64(n)-1)/(u-l)*(v-l) + 0.5)
+}
+
+// Norm returns the L norm of the slice S, defined as
+// (sum_{i=1}^N s[i]^L)^{1/L}
+// Special cases:
+// L = math.Inf(1) gives the maximum absolute value.
+// Does not correctly compute the zero norm (use Count).
+func Norm(s []float64, L float64) float64 {
+	// Should this complain if L is not positive?
+	// Should this be done in log space for better numerical stability?
+	//	would be more cost
+	//	maybe only if L is high?
+	if len(s) == 0 {
+		return 0
+	}
+	if L == 2 {
+		twoNorm := math.Abs(s[0])
+		for i := 1; i < len(s); i++ {
+			twoNorm = math.Hypot(twoNorm, s[i])
+		}
+		return twoNorm
+	}
+	var norm float64
+	if L == 1 {
+		for _, val := range s {
+			norm += math.Abs(val)
+		}
+		return norm
+	}
+	if math.IsInf(L, 1) {
+		for _, val := range s {
+			norm = math.Max(norm, math.Abs(val))
+		}
+		return norm
+	}
+	for _, val := range s {
+		norm += math.Pow(math.Abs(val), L)
+	}
+	return math.Pow(norm, 1/L)
+}
+
+// ParseWithNA converts the string s to a float64 in v.
+// If s equals missing, w is returned as 0, otherwise 1.
+func ParseWithNA(s, missing string) (v, w float64, err error) {
+	if s == missing {
+		return 0, 0, nil
+	}
+	v, err = strconv.ParseFloat(s, 64)
+	if err == nil {
+		w = 1
+	}
+	return v, w, err
+}
+
+// Prod returns the product of the elements of the slice.
+// Returns 1 if len(s) = 0.
+func Prod(s []float64) float64 {
+	prod := 1.0
+	for _, val := range s {
+		prod *= val
+	}
+	return prod
+}
+
+// Reverse reverses the order of elements in the slice.
+func Reverse(s []float64) {
+	for i, j := 0, len(s)-1; i < j; i, j = i+1, j-1 {
+		s[i], s[j] = s[j], s[i]
+	}
+}
+
+// Round returns the half away from zero rounded value of x with prec precision.
+//
+// Special cases are:
+// 	Round(±0) = +0
+// 	Round(±Inf) = ±Inf
+// 	Round(NaN) = NaN
+func Round(x float64, prec int) float64 {
+	if x == 0 {
+		// Make sure zero is returned
+		// without the negative bit set.
+		return 0
+	}
+	// Fast path for positive precision on integers.
+	if prec >= 0 && x == math.Trunc(x) {
+		return x
+	}
+	pow := math.Pow10(prec)
+	intermed := x * pow
+	if math.IsInf(intermed, 0) {
+		return x
+	}
+	if x < 0 {
+		x = math.Ceil(intermed - 0.5)
+	} else {
+		x = math.Floor(intermed + 0.5)
+	}
+
+	if x == 0 {
+		return 0
+	}
+
+	return x / pow
+}
+
+// RoundEven returns the half even rounded value of x with prec precision.
+//
+// Special cases are:
+// 	RoundEven(±0) = +0
+// 	RoundEven(±Inf) = ±Inf
+// 	RoundEven(NaN) = NaN
+func RoundEven(x float64, prec int) float64 {
+	if x == 0 {
+		// Make sure zero is returned
+		// without the negative bit set.
+		return 0
+	}
+	// Fast path for positive precision on integers.
+	if prec >= 0 && x == math.Trunc(x) {
+		return x
+	}
+	pow := math.Pow10(prec)
+	intermed := x * pow
+	if math.IsInf(intermed, 0) {
+		return x
+	}
+	if isHalfway(intermed) {
+		correction, _ := math.Modf(math.Mod(intermed, 2))
+		intermed += correction
+		if intermed > 0 {
+			x = math.Floor(intermed)
+		} else {
+			x = math.Ceil(intermed)
+		}
+	} else {
+		if x < 0 {
+			x = math.Ceil(intermed - 0.5)
+		} else {
+			x = math.Floor(intermed + 0.5)
+		}
+	}
+
+	if x == 0 {
+		return 0
+	}
+
+	return x / pow
+}
+
+func isHalfway(x float64) bool {
+	_, frac := math.Modf(x)
+	frac = math.Abs(frac)
+	return frac == 0.5 || (math.Nextafter(frac, math.Inf(-1)) < 0.5 && math.Nextafter(frac, math.Inf(1)) > 0.5)
+}
+
+// Same returns true if the input slices have the same length and the all elements
+// have the same value with NaN treated as the same.
+func Same(s, t []float64) bool {
+	if len(s) != len(t) {
+		return false
+	}
+	for i, v := range s {
+		w := t[i]
+		if v != w && !math.IsNaN(v) && !math.IsNaN(w) {
+			return false
+		}
+	}
+	return true
+}
+
+// Scale multiplies every element in dst by the scalar c.
+func Scale(c float64, dst []float64) {
+	if len(dst) > 0 {
+		f64.ScalUnitary(c, dst)
+	}
+}
+
+// Span returns a set of N equally spaced points between l and u, where N
+// is equal to the length of the destination. The first element of the destination
+// is l, the final element of the destination is u.
+// Panics if len(dst) < 2.
+//
+// Also returns the mutated slice dst, so that it can be used in range expressions, like:
+//
+//     for i, x := range Span(dst, l, u) { ... }
+func Span(dst []float64, l, u float64) []float64 {
+	n := len(dst)
+	if n < 2 {
+		panic("floats: destination must have length >1")
+	}
+	step := (u - l) / float64(n-1)
+	for i := range dst {
+		dst[i] = l + step*float64(i)
+	}
+	return dst
+}
+
+// Sub subtracts, element-wise, the elements of s from dst. Panics if
+// the lengths of dst and s do not match.
+func Sub(dst, s []float64) {
+	if len(dst) != len(s) {
+		panic("floats: length of the slices do not match")
+	}
+	f64.AxpyUnitaryTo(dst, -1, s, dst)
+}
+
+// SubTo subtracts, element-wise, the elements of t from s and
+// stores the result in dst. Panics if the lengths of s, t and dst do not match.
+func SubTo(dst, s, t []float64) []float64 {
+	if len(s) != len(t) {
+		panic("floats: length of subtractor and subtractee do not match")
+	}
+	if len(dst) != len(s) {
+		panic("floats: length of destination does not match length of subtractor")
+	}
+	f64.AxpyUnitaryTo(dst, -1, t, s)
+	return dst
+}
+
+// Sum returns the sum of the elements of the slice.
+func Sum(s []float64) float64 {
+	var sum float64
+	for _, val := range s {
+		sum += val
+	}
+	return sum
+}
+
+// Within returns the first index i where s[i] <= v < s[i+1]. Within panics if:
+//  - len(s) < 2
+//  - s is not sorted
+func Within(s []float64, v float64) int {
+	if len(s) < 2 {
+		panic("floats: slice length less than 2")
+	}
+	if !sort.Float64sAreSorted(s) {
+		panic("floats: input slice not sorted")
+	}
+	if v < s[0] || v >= s[len(s)-1] || math.IsNaN(v) {
+		return -1
+	}
+	for i, f := range s[1:] {
+		if v < f {
+			return i
+		}
+	}
+	return -1
+}
diff --git a/vendor/gonum.org/v1/gonum/floats/floats_test.go b/vendor/gonum.org/v1/gonum/floats/floats_test.go
new file mode 100644
index 00000000..32e4a392
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/floats/floats_test.go
@@ -0,0 +1,1403 @@
+// Copyright 2013 The Gonum Authors. All rights reserved.
+// Use of this code is governed by a BSD-style
+// license that can be found in the LICENSE file
+
+package floats
+
+import (
+	"math"
+	"math/rand"
+	"strconv"
+	"testing"
+)
+
+const (
+	EqTolerance = 1E-14
+	Small       = 10
+	Medium      = 1000
+	Large       = 100000
+	Huge        = 10000000
+)
+
+func AreSlicesEqual(t *testing.T, truth, comp []float64, str string) {
+	if !EqualApprox(comp, truth, EqTolerance) {
+		t.Errorf(str+". Expected %v, returned %v", truth, comp)
+	}
+}
+
+func Panics(fun func()) (b bool) {
+	defer func() {
+		err := recover()
+		if err != nil {
+			b = true
+		}
+	}()
+	fun()
+	return
+}
+
+func TestAdd(t *testing.T) {
+	a := []float64{1, 2, 3}
+	b := []float64{4, 5, 6}
+	c := []float64{7, 8, 9}
+	truth := []float64{12, 15, 18}
+	n := make([]float64, len(a))
+
+	Add(n, a)
+	Add(n, b)
+	Add(n, c)
+	AreSlicesEqual(t, truth, n, "Wrong addition of slices new receiver")
+	Add(a, b)
+	Add(a, c)
+	AreSlicesEqual(t, truth, n, "Wrong addition of slices for no new receiver")
+
+	// Test that it panics
+	if !Panics(func() { Add(make([]float64, 2), make([]float64, 3)) }) {
+		t.Errorf("Did not panic with length mismatch")
+	}
+}
+
+func TestAddTo(t *testing.T) {
+	a := []float64{1, 2, 3}
+	b := []float64{4, 5, 6}
+	truth := []float64{5, 7, 9}
+	n1 := make([]float64, len(a))
+
+	n2 := AddTo(n1, a, b)
+	AreSlicesEqual(t, truth, n1, "Bad addition from mutator")
+	AreSlicesEqual(t, truth, n2, "Bad addition from returned slice")
+
+	// Test that it panics
+	if !Panics(func() { AddTo(make([]float64, 2), make([]float64, 3), make([]float64, 3)) }) {
+		t.Errorf("Did not panic with length mismatch")
+	}
+	if !Panics(func() { AddTo(make([]float64, 3), make([]float64, 3), make([]float64, 2)) }) {
+		t.Errorf("Did not panic with length mismatch")
+	}
+
+}
+
+func TestAddConst(t *testing.T) {
+	s := []float64{3, 4, 1, 7, 5}
+	c := 6.0
+	truth := []float64{9, 10, 7, 13, 11}
+	AddConst(c, s)
+	AreSlicesEqual(t, truth, s, "Wrong addition of constant")
+}
+
+func TestAddScaled(t *testing.T) {
+	s := []float64{3, 4, 1, 7, 5}
+	alpha := 6.0
+	dst := []float64{1, 2, 3, 4, 5}
+	ans := []float64{19, 26, 9, 46, 35}
+	AddScaled(dst, alpha, s)
+	if !EqualApprox(dst, ans, EqTolerance) {
+		t.Errorf("Adding scaled did not match")
+	}
+	short := []float64{1}
+	if !Panics(func() { AddScaled(dst, alpha, short) }) {
+		t.Errorf("Doesn't panic if s is smaller than dst")
+	}
+	if !Panics(func() { AddScaled(short, alpha, s) }) {
+		t.Errorf("Doesn't panic if dst is smaller than s")
+	}
+}
+
+func TestAddScaledTo(t *testing.T) {
+	s := []float64{3, 4, 1, 7, 5}
+	alpha := 6.0
+	y := []float64{1, 2, 3, 4, 5}
+	dst1 := make([]float64, 5)
+	ans := []float64{19, 26, 9, 46, 35}
+	dst2 := AddScaledTo(dst1, y, alpha, s)
+	if !EqualApprox(dst1, ans, EqTolerance) {
+		t.Errorf("AddScaledTo did not match for mutator")
+	}
+	if !EqualApprox(dst2, ans, EqTolerance) {
+		t.Errorf("AddScaledTo did not match for returned slice")
+	}
+	AddScaledTo(dst1, y, alpha, s)
+	if !EqualApprox(dst1, ans, EqTolerance) {
+		t.Errorf("Reusing dst did not match")
+	}
+	short := []float64{1}
+	if !Panics(func() { AddScaledTo(dst1, y, alpha, short) }) {
+		t.Errorf("Doesn't panic if s is smaller than dst")
+	}
+	if !Panics(func() { AddScaledTo(short, y, alpha, s) }) {
+		t.Errorf("Doesn't panic if dst is smaller than s")
+	}
+	if !Panics(func() { AddScaledTo(dst1, short, alpha, s) }) {
+		t.Errorf("Doesn't panic if y is smaller than dst")
+	}
+}
+
+func TestArgsort(t *testing.T) {
+	s := []float64{3, 4, 1, 7, 5}
+	inds := make([]int, len(s))
+
+	Argsort(s, inds)
+
+	sortedS := []float64{1, 3, 4, 5, 7}
+	trueInds := []int{2, 0, 1, 4, 3}
+
+	if !Equal(s, sortedS) {
+		t.Error("elements not sorted correctly")
+	}
+	for i := range trueInds {
+		if trueInds[i] != inds[i] {
+			t.Error("inds not correct")
+		}
+	}
+
+	inds = []int{1, 2}
+	if !Panics(func() { Argsort(s, inds) }) {
+		t.Error("does not panic if lengths do not match")
+	}
+}
+
+func TestCount(t *testing.T) {
+	s := []float64{3, 4, 1, 7, 5}
+	f := func(v float64) bool { return v > 3.5 }
+	truth := 3
+	n := Count(f, s)
+	if n != truth {
+		t.Errorf("Wrong number of elements counted")
+	}
+}
+
+func TestCumProd(t *testing.T) {
+	s := []float64{3, 4, 1, 7, 5}
+	receiver := make([]float64, len(s))
+	result := CumProd(receiver, s)
+	truth := []float64{3, 12, 12, 84, 420}
+	AreSlicesEqual(t, truth, receiver, "Wrong cumprod mutated with new receiver")
+	AreSlicesEqual(t, truth, result, "Wrong cumprod result with new receiver")
+	CumProd(receiver, s)
+	AreSlicesEqual(t, truth, receiver, "Wrong cumprod returned with reused receiver")
+
+	// Test that it panics
+	if !Panics(func() { CumProd(make([]float64, 2), make([]float64, 3)) }) {
+		t.Errorf("Did not panic with length mismatch")
+	}
+
+	// Test empty CumProd
+	emptyReceiver := make([]float64, 0)
+	truth = []float64{}
+	CumProd(emptyReceiver, emptyReceiver)
+	AreSlicesEqual(t, truth, emptyReceiver, "Wrong cumprod returned with empty receiver")
+
+}
+
+func TestCumSum(t *testing.T) {
+	s := []float64{3, 4, 1, 7, 5}
+	receiver := make([]float64, len(s))
+	result := CumSum(receiver, s)
+	truth := []float64{3, 7, 8, 15, 20}
+	AreSlicesEqual(t, truth, receiver, "Wrong cumsum mutated with new receiver")
+	AreSlicesEqual(t, truth, result, "Wrong cumsum returned with new receiver")
+	CumSum(receiver, s)
+	AreSlicesEqual(t, truth, receiver, "Wrong cumsum returned with reused receiver")
+
+	// Test that it panics
+	if !Panics(func() { CumSum(make([]float64, 2), make([]float64, 3)) }) {
+		t.Errorf("Did not panic with length mismatch")
+	}
+
+	// Test empty CumSum
+	emptyReceiver := make([]float64, 0)
+	truth = []float64{}
+	CumSum(emptyReceiver, emptyReceiver)
+	AreSlicesEqual(t, truth, emptyReceiver, "Wrong cumsum returned with empty receiver")
+
+}
+
+func TestDistance(t *testing.T) {
+	norms := []float64{1, 2, 4, math.Inf(1)}
+	slices := []struct {
+		s []float64
+		t []float64
+	}{
+		{
+			nil,
+			nil,
+		},
+		{
+			[]float64{8, 9, 10, -12},
+			[]float64{8, 9, 10, -12},
+		},
+		{
+			[]float64{1, 2, 3, -4, -5, 8},
+			[]float64{-9.2, -6.8, 9, -3, -2, 1},
+		},
+	}
+
+	for j, test := range slices {
+		tmp := make([]float64, len(test.s))
+		for i, L := range norms {
+			dist := Distance(test.s, test.t, L)
+			copy(tmp, test.s)
+			Sub(tmp, test.t)
+			norm := Norm(tmp, L)
+			if dist != norm { // Use equality because they should be identical
+				t.Errorf("Distance does not match norm for case %v, %v. Expected %v, Found %v.", i, j, norm, dist)
+			}
+		}
+	}
+
+	if !Panics(func() { Distance([]float64{}, norms, 1) }) {
+		t.Errorf("Did not panic with unequal lengths")
+	}
+
+}
+
+func TestDiv(t *testing.T) {
+	s1 := []float64{5, 12, 27}
+	s2 := []float64{1, 2, 3}
+	ans := []float64{5, 6, 9}
+	Div(s1, s2)
+	if !EqualApprox(s1, ans, EqTolerance) {
+		t.Errorf("Mul doesn't give correct answer")
+	}
+	s1short := []float64{1}
+	if !Panics(func() { Div(s1short, s2) }) {
+		t.Errorf("Did not panic with unequal lengths")
+	}
+	s2short := []float64{1}
+	if !Panics(func() { Div(s1, s2short) }) {
+		t.Errorf("Did not panic with unequal lengths")
+	}
+}
+
+func TestDivTo(t *testing.T) {
+	s1 := []float64{5, 12, 27}
+	s1orig := []float64{5, 12, 27}
+	s2 := []float64{1, 2, 3}
+	s2orig := []float64{1, 2, 3}
+	dst1 := make([]float64, 3)
+	ans := []float64{5, 6, 9}
+	dst2 := DivTo(dst1, s1, s2)
+	if !EqualApprox(dst1, ans, EqTolerance) {
+		t.Errorf("DivTo doesn't give correct answer in mutated slice")
+	}
+	if !EqualApprox(dst2, ans, EqTolerance) {
+		t.Errorf("DivTo doesn't give correct answer in returned slice")
+	}
+	if !EqualApprox(s1, s1orig, EqTolerance) {
+		t.Errorf("S1 changes during multo")
+	}
+	if !EqualApprox(s2, s2orig, EqTolerance) {
+		t.Errorf("s2 changes during multo")
+	}
+	DivTo(dst1, s1, s2)
+	if !EqualApprox(dst1, ans, EqTolerance) {
+		t.Errorf("DivTo doesn't give correct answer reusing dst")
+	}
+	dstShort := []float64{1}
+	if !Panics(func() { DivTo(dstShort, s1, s2) }) {
+		t.Errorf("Did not panic with s1 wrong length")
+	}
+	s1short := []float64{1}
+	if !Panics(func() { DivTo(dst1, s1short, s2) }) {
+		t.Errorf("Did not panic with s1 wrong length")
+	}
+	s2short := []float64{1}
+	if !Panics(func() { DivTo(dst1, s1, s2short) }) {
+		t.Errorf("Did not panic with s2 wrong length")
+	}
+}
+
+func TestDot(t *testing.T) {
+	s1 := []float64{1, 2, 3, 4}
+	s2 := []float64{-3, 4, 5, -6}
+	truth := -4.0
+	ans := Dot(s1, s2)
+	if ans != truth {
+		t.Errorf("Dot product computed incorrectly")
+	}
+
+	// Test that it panics
+	if !Panics(func() { Dot(make([]float64, 2), make([]float64, 3)) }) {
+		t.Errorf("Did not panic with length mismatch")
+	}
+}
+
+func TestEquals(t *testing.T) {
+	s1 := []float64{1, 2, 3, 4}
+	s2 := []float64{1, 2, 3, 4}
+	if !Equal(s1, s2) {
+		t.Errorf("Equal slices returned as unequal")
+	}
+	s2 = []float64{1, 2, 3, 4 + 1e-14}
+	if Equal(s1, s2) {
+		t.Errorf("Unequal slices returned as equal")
+	}
+	if Equal(s1, []float64{}) {
+		t.Errorf("Unequal slice lengths returned as equal")
+	}
+}
+
+func TestEqualApprox(t *testing.T) {
+	s1 := []float64{1, 2, 3, 4}
+	s2 := []float64{1, 2, 3, 4 + 1e-10}
+	if EqualApprox(s1, s2, 1e-13) {
+		t.Errorf("Unequal slices returned as equal for absolute")
+	}
+	if !EqualApprox(s1, s2, 1e-5) {
+		t.Errorf("Equal slices returned as unequal for absolute")
+	}
+	s1 = []float64{1, 2, 3, 1000}
+	s2 = []float64{1, 2, 3, 1000 * (1 + 1e-7)}
+	if EqualApprox(s1, s2, 1e-8) {
+		t.Errorf("Unequal slices returned as equal for relative")
+	}
+	if !EqualApprox(s1, s2, 1e-5) {
+		t.Errorf("Equal slices returned as unequal for relative")
+	}
+	if EqualApprox(s1, []float64{}, 1e-5) {
+		t.Errorf("Unequal slice lengths returned as equal")
+	}
+}
+
+func TestEqualFunc(t *testing.T) {
+	s1 := []float64{1, 2, 3, 4}
+	s2 := []float64{1, 2, 3, 4}
+	eq := func(x, y float64) bool { return x == y }
+	if !EqualFunc(s1, s2, eq) {
+		t.Errorf("Equal slices returned as unequal")
+	}
+	s2 = []float64{1, 2, 3, 4 + 1e-14}
+	if EqualFunc(s1, s2, eq) {
+		t.Errorf("Unequal slices returned as equal")
+	}
+	if EqualFunc(s1, []float64{}, eq) {
+		t.Errorf("Unequal slice lengths returned as equal")
+	}
+}
+
+func TestEqualsRelative(t *testing.T) {
+	var equalityTests = []struct {
+		a, b  float64
+		tol   float64
+		equal bool
+	}{
+		{1000000, 1000001, 0, true},
+		{1000001, 1000000, 0, true},
+		{10000, 10001, 0, false},
+		{10001, 10000, 0, false},
+		{-1000000, -1000001, 0, true},
+		{-1000001, -1000000, 0, true},
+		{-10000, -10001, 0, false},
+		{-10001, -10000, 0, false},
+		{1.0000001, 1.0000002, 0, true},
+		{1.0000002, 1.0000001, 0, true},
+		{1.0002, 1.0001, 0, false},
+		{1.0001, 1.0002, 0, false},
+		{-1.000001, -1.000002, 0, true},
+		{-1.000002, -1.000001, 0, true},
+		{-1.0001, -1.0002, 0, false},
+		{-1.0002, -1.0001, 0, false},
+		{0.000000001000001, 0.000000001000002, 0, true},
+		{0.000000001000002, 0.000000001000001, 0, true},
+		{0.000000000001002, 0.000000000001001, 0, false},
+		{0.000000000001001, 0.000000000001002, 0, false},
+		{-0.000000001000001, -0.000000001000002, 0, true},
+		{-0.000000001000002, -0.000000001000001, 0, true},
+		{-0.000000000001002, -0.000000000001001, 0, false},
+		{-0.000000000001001, -0.000000000001002, 0, false},
+		{0, 0, 0, true},
+		{0, -0, 0, true},
+		{-0, -0, 0, true},
+		{0.00000001, 0, 0, false},
+		{0, 0.00000001, 0, false},
+		{-0.00000001, 0, 0, false},
+		{0, -0.00000001, 0, false},
+		{0, 1e-310, 0.01, true},
+		{1e-310, 0, 0.01, true},
+		{1e-310, 0, 0.000001, false},
+		{0, 1e-310, 0.000001, false},
+		{0, -1e-310, 0.1, true},
+		{-1e-310, 0, 0.1, true},
+		{-1e-310, 0, 0.00000001, false},
+		{0, -1e-310, 0.00000001, false},
+		{math.Inf(1), math.Inf(1), 0, true},
+		{math.Inf(-1), math.Inf(-1), 0, true},
+		{math.Inf(-1), math.Inf(1), 0, false},
+		{math.Inf(1), math.MaxFloat64, 0, false},
+		{math.Inf(-1), -math.MaxFloat64, 0, false},
+		{math.NaN(), math.NaN(), 0, false},
+		{math.NaN(), 0, 0, false},
+		{-0, math.NaN(), 0, false},
+		{math.NaN(), -0, 0, false},
+		{0, math.NaN(), 0, false},
+		{math.NaN(), math.Inf(1), 0, false},
+		{math.Inf(1), math.NaN(), 0, false},
+		{math.NaN(), math.Inf(-1), 0, false},
+		{math.Inf(-1), math.NaN(), 0, false},
+		{math.NaN(), math.MaxFloat64, 0, false},
+		{math.MaxFloat64, math.NaN(), 0, false},
+		{math.NaN(), -math.MaxFloat64, 0, false},
+		{-math.MaxFloat64, math.NaN(), 0, false},
+		{math.NaN(), math.SmallestNonzeroFloat64, 0, false},
+		{math.SmallestNonzeroFloat64, math.NaN(), 0, false},
+		{math.NaN(), -math.SmallestNonzeroFloat64, 0, false},
+		{-math.SmallestNonzeroFloat64, math.NaN(), 0, false},
+		{1.000000001, -1.0, 0, false},
+		{-1.0, 1.000000001, 0, false},
+		{-1.000000001, 1.0, 0, false},
+		{1.0, -1.000000001, 0, false},
+		{10 * math.SmallestNonzeroFloat64, 10 * -math.SmallestNonzeroFloat64, 0, true},
+		{1e11 * math.SmallestNonzeroFloat64, 1e11 * -math.SmallestNonzeroFloat64, 0, false},
+		{math.SmallestNonzeroFloat64, -math.SmallestNonzeroFloat64, 0, true},
+		{-math.SmallestNonzeroFloat64, math.SmallestNonzeroFloat64, 0, true},
+		{math.SmallestNonzeroFloat64, 0, 0, true},
+		{0, math.SmallestNonzeroFloat64, 0, true},
+		{-math.SmallestNonzeroFloat64, 0, 0, true},
+		{0, -math.SmallestNonzeroFloat64, 0, true},
+		{0.000000001, -math.SmallestNonzeroFloat64, 0, false},
+		{0.000000001, math.SmallestNonzeroFloat64, 0, false},
+		{math.SmallestNonzeroFloat64, 0.000000001, 0, false},
+		{-math.SmallestNonzeroFloat64, 0.000000001, 0, false},
+	}
+	for _, ts := range equalityTests {
+		if ts.tol == 0 {
+			ts.tol = 1e-5
+		}
+		if equal := EqualWithinRel(ts.a, ts.b, ts.tol); equal != ts.equal {
+			t.Errorf("Relative equality of %g and %g with tolerance %g returned: %v. Expected: %v",
+				ts.a, ts.b, ts.tol, equal, ts.equal)
+		}
+	}
+}
+
+func nextAfterN(x, y float64, n int) float64 {
+	for i := 0; i < n; i++ {
+		x = math.Nextafter(x, y)
+	}
+	return x
+}
+
+func TestEqualsULP(t *testing.T) {
+	if f := 67329.242; !EqualWithinULP(f, nextAfterN(f, math.Inf(1), 10), 10) {
+		t.Errorf("Equal values returned as unequal")
+	}
+	if f := 67329.242; EqualWithinULP(f, nextAfterN(f, math.Inf(1), 5), 1) {
+		t.Errorf("Unequal values returned as equal")
+	}
+	if f := 67329.242; EqualWithinULP(nextAfterN(f, math.Inf(1), 5), f, 1) {
+		t.Errorf("Unequal values returned as equal")
+	}
+	if f := nextAfterN(0, math.Inf(1), 2); !EqualWithinULP(f, nextAfterN(f, math.Inf(-1), 5), 10) {
+		t.Errorf("Equal values returned as unequal")
+	}
+	if !EqualWithinULP(67329.242, 67329.242, 10) {
+		t.Errorf("Equal float64s not returned as equal")
+	}
+	if EqualWithinULP(1, math.NaN(), 10) {
+		t.Errorf("NaN returned as equal")
+	}
+
+}
+
+func TestEqualLengths(t *testing.T) {
+	s1 := []float64{1, 2, 3, 4}
+	s2 := []float64{1, 2, 3, 4}
+	s3 := []float64{1, 2, 3}
+	if !EqualLengths(s1, s2) {
+		t.Errorf("Equal lengths returned as unequal")
+	}
+	if EqualLengths(s1, s3) {
+		t.Errorf("Unequal lengths returned as equal")
+	}
+	if !EqualLengths(s1) {
+		t.Errorf("Single slice returned as unequal")
+	}
+	if !EqualLengths() {
+		t.Errorf("No slices returned as unequal")
+	}
+}
+
+func eqIntSlice(one, two []int) string {
+	if len(one) != len(two) {
+		return "Length mismatch"
+	}
+	for i, val := range one {
+		if val != two[i] {
+			return "Index " + strconv.Itoa(i) + " mismatch"
+		}
+	}
+	return ""
+}
+
+func TestFind(t *testing.T) {
+	s := []float64{3, 4, 1, 7, 5}
+	f := func(v float64) bool { return v > 3.5 }
+	allTrueInds := []int{1, 3, 4}
+
+	// Test finding first two elements
+	inds, err := Find(nil, f, s, 2)
+	if err != nil {
+		t.Errorf("Find first two: Improper error return")
+	}
+	trueInds := allTrueInds[:2]
+	str := eqIntSlice(inds, trueInds)
+	if str != "" {
+		t.Errorf("Find first two: " + str)
+	}
+
+	// Test finding no elements with non nil slice
+	inds = []int{1, 2, 3, 4, 5, 6}
+	inds, err = Find(inds, f, s, 0)
+	if err != nil {
+		t.Errorf("Find no elements: Improper error return")
+	}
+	str = eqIntSlice(inds, []int{})
+	if str != "" {
+		t.Errorf("Find no non-nil: " + str)
+	}
+
+	// Test finding first two elements with non nil slice
+	inds = []int{1, 2, 3, 4, 5, 6}
+	inds, err = Find(inds, f, s, 2)
+	if err != nil {
+		t.Errorf("Find first two non-nil: Improper error return")
+	}
+	str = eqIntSlice(inds, trueInds)
+	if str != "" {
+		t.Errorf("Find first two non-nil: " + str)
+	}
+
+	// Test finding too many elements
+	inds, err = Find(inds, f, s, 4)
+	if err == nil {
+		t.Errorf("Request too many: No error returned")
+	}
+	str = eqIntSlice(inds, allTrueInds)
+	if str != "" {
+		t.Errorf("Request too many: Does not match all of the inds: " + str)
+	}
+
+	// Test finding all elements
+	inds, err = Find(nil, f, s, -1)
+	if err != nil {
+		t.Errorf("Find all: Improper error returned")
+	}
+	str = eqIntSlice(inds, allTrueInds)
+	if str != "" {
+		t.Errorf("Find all: Does not match all of the inds: " + str)
+	}
+}
+
+func TestHasNaN(t *testing.T) {
+	for i, test := range []struct {
+		s   []float64
+		ans bool
+	}{
+		{},
+		{
+			s: []float64{1, 2, 3, 4},
+		},
+		{
+			s:   []float64{1, math.NaN(), 3, 4},
+			ans: true,
+		},
+		{
+			s:   []float64{1, 2, 3, math.NaN()},
+			ans: true,
+		},
+	} {
+		b := HasNaN(test.s)
+		if b != test.ans {
+			t.Errorf("HasNaN mismatch case %d. Expected %v, Found %v", i, test.ans, b)
+		}
+	}
+}
+
+func TestLogSpan(t *testing.T) {
+	receiver1 := make([]float64, 6)
+	truth := []float64{0.001, 0.01, 0.1, 1, 10, 100}
+	receiver2 := LogSpan(receiver1, 0.001, 100)
+	tst := make([]float64, 6)
+	for i := range truth {
+		tst[i] = receiver1[i] / truth[i]
+	}
+	comp := make([]float64, 6)
+	for i := range comp {
+		comp[i] = 1
+	}
+	AreSlicesEqual(t, comp, tst, "Improper logspace from mutator")
+
+	for i := range truth {
+		tst[i] = receiver2[i] / truth[i]
+	}
+	AreSlicesEqual(t, comp, tst, "Improper logspace from returned slice")
+
+	if !Panics(func() { LogSpan(nil, 1, 5) }) {
+		t.Errorf("Span accepts nil argument")
+	}
+	if !Panics(func() { LogSpan(make([]float64, 1), 1, 5) }) {
+		t.Errorf("Span accepts argument of len = 1")
+	}
+}
+
+func TestLogSumExp(t *testing.T) {
+	s := []float64{1, 2, 3, 4, 5}
+	val := LogSumExp(s)
+	// http://www.wolframalpha.com/input/?i=log%28exp%281%29+%2B+exp%282%29+%2B+exp%283%29+%2B+exp%284%29+%2B+exp%285%29%29
+	truth := 5.4519143959375933331957225109748087179338972737576824
+	if math.Abs(val-truth) > EqTolerance {
+		t.Errorf("Wrong logsumexp for many values")
+	}
+	s = []float64{1, 2}
+	// http://www.wolframalpha.com/input/?i=log%28exp%281%29+%2B+exp%282%29%29
+	truth = 2.3132616875182228340489954949678556419152800856703483
+	val = LogSumExp(s)
+	if math.Abs(val-truth) > EqTolerance {
+		t.Errorf("Wrong logsumexp for two values. %v expected, %v found", truth, val)
+	}
+	// This case would normally underflow
+	s = []float64{-1001, -1002, -1003, -1004, -1005}
+	// http://www.wolframalpha.com/input/?i=log%28exp%28-1001%29%2Bexp%28-1002%29%2Bexp%28-1003%29%2Bexp%28-1004%29%2Bexp%28-1005%29%29
+	truth = -1000.54808560406240666680427748902519128206610272624
+	val = LogSumExp(s)
+	if math.Abs(val-truth) > EqTolerance {
+		t.Errorf("Doesn't match for underflow case. %v expected, %v found", truth, val)
+	}
+	// positive infinite case
+	s = []float64{1, 2, 3, 4, 5, math.Inf(1)}
+	val = LogSumExp(s)
+	truth = math.Inf(1)
+	if val != truth {
+		t.Errorf("Doesn't match for pos Infinity case. %v expected, %v found", truth, val)
+	}
+	// negative infinite case
+	s = []float64{1, 2, 3, 4, 5, math.Inf(-1)}
+	val = LogSumExp(s)
+	truth = 5.4519143959375933331957225109748087179338972737576824 // same as first case
+	if math.Abs(val-truth) > EqTolerance {
+		t.Errorf("Wrong logsumexp for values with negative infinity")
+	}
+
+}
+
+func TestMaxAndIdx(t *testing.T) {
+	s := []float64{3, 4, 1, 7, 5}
+	ind := MaxIdx(s)
+	val := Max(s)
+	if val != 7 {
+		t.Errorf("Wrong value returned")
+	}
+	if ind != 3 {
+		t.Errorf("Wrong index returned")
+	}
+}
+
+func TestMinAndIdx(t *testing.T) {
+	s := []float64{3, 4, 1, 7, 5}
+	ind := MinIdx(s)
+	val := Min(s)
+	if val != 1 {
+		t.Errorf("Wrong value returned")
+	}
+	if ind != 2 {
+		t.Errorf("Wrong index returned")
+	}
+}
+
+func TestMul(t *testing.T) {
+	s1 := []float64{1, 2, 3}
+	s2 := []float64{1, 2, 3}
+	ans := []float64{1, 4, 9}
+	Mul(s1, s2)
+	if !EqualApprox(s1, ans, EqTolerance) {
+		t.Errorf("Mul doesn't give correct answer")
+	}
+	s1short := []float64{1}
+	if !Panics(func() { Mul(s1short, s2) }) {
+		t.Errorf("Did not panic with unequal lengths")
+	}
+	s2short := []float64{1}
+	if !Panics(func() { Mul(s1, s2short) }) {
+		t.Errorf("Did not panic with unequal lengths")
+	}
+}
+
+func TestMulTo(t *testing.T) {
+	s1 := []float64{1, 2, 3}
+	s1orig := []float64{1, 2, 3}
+	s2 := []float64{1, 2, 3}
+	s2orig := []float64{1, 2, 3}
+	dst1 := make([]float64, 3)
+	ans := []float64{1, 4, 9}
+	dst2 := MulTo(dst1, s1, s2)
+	if !EqualApprox(dst1, ans, EqTolerance) {
+		t.Errorf("MulTo doesn't give correct answer in mutated slice")
+	}
+	if !EqualApprox(dst2, ans, EqTolerance) {
+		t.Errorf("MulTo doesn't give correct answer in returned slice")
+	}
+	if !EqualApprox(s1, s1orig, EqTolerance) {
+		t.Errorf("S1 changes during multo")
+	}
+	if !EqualApprox(s2, s2orig, EqTolerance) {
+		t.Errorf("s2 changes during multo")
+	}
+	MulTo(dst1, s1, s2)
+	if !EqualApprox(dst1, ans, EqTolerance) {
+		t.Errorf("MulTo doesn't give correct answer reusing dst")
+	}
+	dstShort := []float64{1}
+	if !Panics(func() { MulTo(dstShort, s1, s2) }) {
+		t.Errorf("Did not panic with s1 wrong length")
+	}
+	s1short := []float64{1}
+	if !Panics(func() { MulTo(dst1, s1short, s2) }) {
+		t.Errorf("Did not panic with s1 wrong length")
+	}
+	s2short := []float64{1}
+	if !Panics(func() { MulTo(dst1, s1, s2short) }) {
+		t.Errorf("Did not panic with s2 wrong length")
+	}
+}
+
+func TestNearest(t *testing.T) {
+	s := []float64{6.2, 3, 5, 6.2, 8}
+	ind := Nearest(s, 2.0)
+	if ind != 1 {
+		t.Errorf("Wrong index returned when value is less than all of elements")
+	}
+	ind = Nearest(s, 9.0)
+	if ind != 4 {
+		t.Errorf("Wrong index returned when value is greater than all of elements")
+	}
+	ind = Nearest(s, 3.1)
+	if ind != 1 {
+		t.Errorf("Wrong index returned when value is greater than closest element")
+	}
+	ind = Nearest(s, 3.1)
+	if ind != 1 {
+		t.Errorf("Wrong index returned when value is greater than closest element")
+	}
+	ind = Nearest(s, 2.9)
+	if ind != 1 {
+		t.Errorf("Wrong index returned when value is less than closest element")
+	}
+	ind = Nearest(s, 3)
+	if ind != 1 {
+		t.Errorf("Wrong index returned when value is equal to element")
+	}
+	ind = Nearest(s, 6.2)
+	if ind != 0 {
+		t.Errorf("Wrong index returned when value is equal to several elements")
+	}
+	ind = Nearest(s, 4)
+	if ind != 1 {
+		t.Errorf("Wrong index returned when value is exactly between two closest elements")
+	}
+}
+
+func TestNearestWithinSpan(t *testing.T) {
+	if !Panics(func() { NearestWithinSpan(10, 8, 2, 4.5) }) {
+		t.Errorf("Did not panic when upper bound is lower than greater bound")
+	}
+	for i, test := range []struct {
+		length int
+		lower  float64
+		upper  float64
+		value  float64
+		idx    int
+	}{
+		{
+			length: 13,
+			lower:  7,
+			upper:  8.2,
+			value:  6,
+			idx:    -1,
+		},
+		{
+			length: 13,
+			lower:  7,
+			upper:  8.2,
+			value:  10,
+			idx:    -1,
+		},
+		{
+			length: 13,
+			lower:  7,
+			upper:  8.2,
+			value:  7.19,
+			idx:    2,
+		},
+		{
+			length: 13,
+			lower:  7,
+			upper:  8.2,
+			value:  7.21,
+			idx:    2,
+		},
+		{
+			length: 13,
+			lower:  7,
+			upper:  8.2,
+			value:  7.2,
+			idx:    2,
+		},
+		{
+			length: 13,
+			lower:  7,
+			upper:  8.2,
+			value:  7.151,
+			idx:    2,
+		},
+		{
+			length: 13,
+			lower:  7,
+			upper:  8.2,
+			value:  7.249,
+			idx:    2,
+		},
+	} {
+		if idx := NearestWithinSpan(test.length, test.lower, test.upper, test.value); test.idx != idx {
+			t.Errorf("Case %v mismatch: Want: %v, Got: %v", i, test.idx, idx)
+		}
+	}
+}
+
+func TestNorm(t *testing.T) {
+	s := []float64{-1, -3.4, 5, -6}
+	val := Norm(s, math.Inf(1))
+	truth := 6.0
+	if math.Abs(val-truth) > EqTolerance {
+		t.Errorf("Doesn't match for inf norm. %v expected, %v found", truth, val)
+	}
+	// http://www.wolframalpha.com/input/?i=%28%28-1%29%5E2+%2B++%28-3.4%29%5E2+%2B+5%5E2%2B++6%5E2%29%5E%281%2F2%29
+	val = Norm(s, 2)
+	truth = 8.5767126569566267590651614132751986658027271236078592
+	if math.Abs(val-truth) > EqTolerance {
+		t.Errorf("Doesn't match for inf norm. %v expected, %v found", truth, val)
+	}
+	// http://www.wolframalpha.com/input/?i=%28%28%7C-1%7C%29%5E3+%2B++%28%7C-3.4%7C%29%5E3+%2B+%7C5%7C%5E3%2B++%7C6%7C%5E3%29%5E%281%2F3%29
+	val = Norm(s, 3)
+	truth = 7.2514321388020228478109121239004816430071237369356233
+	if math.Abs(val-truth) > EqTolerance {
+		t.Errorf("Doesn't match for inf norm. %v expected, %v found", truth, val)
+	}
+
+	//http://www.wolframalpha.com/input/?i=%7C-1%7C+%2B+%7C-3.4%7C+%2B+%7C5%7C%2B++%7C6%7C
+	val = Norm(s, 1)
+	truth = 15.4
+	if math.Abs(val-truth) > EqTolerance {
+		t.Errorf("Doesn't match for inf norm. %v expected, %v found", truth, val)
+	}
+}
+
+func TestProd(t *testing.T) {
+	s := []float64{}
+	val := Prod(s)
+	if val != 1 {
+		t.Errorf("Val not returned as default when slice length is zero")
+	}
+	s = []float64{3, 4, 1, 7, 5}
+	val = Prod(s)
+	if val != 420 {
+		t.Errorf("Wrong prod returned. Expected %v returned %v", 420, val)
+	}
+}
+
+func TestReverse(t *testing.T) {
+	for _, s := range [][]float64{
+		{0},
+		{1, 0},
+		{2, 1, 0},
+		{3, 2, 1, 0},
+		{9, 8, 7, 6, 5, 4, 3, 2, 1, 0},
+	} {
+		Reverse(s)
+		for i, v := range s {
+			if v != float64(i) {
+				t.Errorf("unexpected values for element %d: got:%v want:%v", i, v, i)
+			}
+		}
+	}
+}
+
+func TestRound(t *testing.T) {
+	for _, test := range []struct {
+		x    float64
+		prec int
+		want float64
+	}{
+		{x: 0, prec: 1, want: 0},
+		{x: math.Inf(1), prec: 1, want: math.Inf(1)},
+		{x: math.NaN(), prec: 1, want: math.NaN()},
+		{x: func() float64 { var f float64; return -f }(), prec: 1, want: 0},
+		{x: math.MaxFloat64 / 2, prec: 1, want: math.MaxFloat64 / 2},
+		{x: 1 << 64, prec: 1, want: 1 << 64},
+		{x: 454.4445, prec: 3, want: 454.445},
+		{x: 454.44445, prec: 4, want: 454.4445},
+		{x: 0.42499, prec: 4, want: 0.425},
+		{x: 0.42599, prec: 4, want: 0.426},
+		{x: 0.424999999999993, prec: 2, want: 0.42},
+		{x: 0.425, prec: 2, want: 0.43},
+		{x: 0.425000000000001, prec: 2, want: 0.43},
+		{x: 123.4244999999999, prec: 3, want: 123.424},
+		{x: 123.4245, prec: 3, want: 123.425},
+		{x: 123.4245000000001, prec: 3, want: 123.425},
+
+		{x: 454.45, prec: 0, want: 454},
+		{x: 454.45, prec: 1, want: 454.5},
+		{x: 454.45, prec: 2, want: 454.45},
+		{x: 454.45, prec: 3, want: 454.45},
+		{x: 454.445, prec: 0, want: 454},
+		{x: 454.445, prec: 1, want: 454.4},
+		{x: 454.445, prec: 2, want: 454.45},
+		{x: 454.445, prec: 3, want: 454.445},
+		{x: 454.445, prec: 4, want: 454.445},
+		{x: 454.55, prec: 0, want: 455},
+		{x: 454.55, prec: 1, want: 454.6},
+		{x: 454.55, prec: 2, want: 454.55},
+		{x: 454.55, prec: 3, want: 454.55},
+		{x: 454.455, prec: 0, want: 454},
+		{x: 454.455, prec: 1, want: 454.5},
+		{x: 454.455, prec: 2, want: 454.46},
+		{x: 454.455, prec: 3, want: 454.455},
+		{x: 454.455, prec: 4, want: 454.455},
+
+		// Negative precision.
+		{x: 454.45, prec: -1, want: 450},
+		{x: 454.45, prec: -2, want: 500},
+		{x: 500, prec: -3, want: 1000},
+		{x: 500, prec: -4, want: 0},
+		{x: 1500, prec: -3, want: 2000},
+		{x: 1500, prec: -4, want: 0},
+	} {
+		for _, sign := range []float64{1, -1} {
+			got := Round(sign*test.x, test.prec)
+			want := sign * test.want
+			if want == 0 {
+				want = 0
+			}
+			if (got != want || math.Signbit(got) != math.Signbit(want)) && !(math.IsNaN(got) && math.IsNaN(want)) {
+				t.Errorf("unexpected result for Round(%g, %d): got: %g, want: %g", sign*test.x, test.prec, got, want)
+			}
+		}
+	}
+}
+
+func TestRoundEven(t *testing.T) {
+	for _, test := range []struct {
+		x    float64
+		prec int
+		want float64
+	}{
+		{x: 0, prec: 1, want: 0},
+		{x: math.Inf(1), prec: 1, want: math.Inf(1)},
+		{x: math.NaN(), prec: 1, want: math.NaN()},
+		{x: func() float64 { var f float64; return -f }(), prec: 1, want: 0},
+		{x: math.MaxFloat64 / 2, prec: 1, want: math.MaxFloat64 / 2},
+		{x: 1 << 64, prec: 1, want: 1 << 64},
+		{x: 454.4445, prec: 3, want: 454.444},
+		{x: 454.44445, prec: 4, want: 454.4444},
+		{x: 0.42499, prec: 4, want: 0.425},
+		{x: 0.42599, prec: 4, want: 0.426},
+		{x: 0.424999999999993, prec: 2, want: 0.42},
+		{x: 0.425, prec: 2, want: 0.42},
+		{x: 0.425000000000001, prec: 2, want: 0.43},
+		{x: 123.4244999999999, prec: 3, want: 123.424},
+		{x: 123.4245, prec: 3, want: 123.424},
+		{x: 123.4245000000001, prec: 3, want: 123.425},
+
+		{x: 454.45, prec: 0, want: 454},
+		{x: 454.45, prec: 1, want: 454.4},
+		{x: 454.45, prec: 2, want: 454.45},
+		{x: 454.45, prec: 3, want: 454.45},
+		{x: 454.445, prec: 0, want: 454},
+		{x: 454.445, prec: 1, want: 454.4},
+		{x: 454.445, prec: 2, want: 454.44},
+		{x: 454.445, prec: 3, want: 454.445},
+		{x: 454.445, prec: 4, want: 454.445},
+		{x: 454.55, prec: 0, want: 455},
+		{x: 454.55, prec: 1, want: 454.6},
+		{x: 454.55, prec: 2, want: 454.55},
+		{x: 454.55, prec: 3, want: 454.55},
+		{x: 454.455, prec: 0, want: 454},
+		{x: 454.455, prec: 1, want: 454.5},
+		{x: 454.455, prec: 2, want: 454.46},
+		{x: 454.455, prec: 3, want: 454.455},
+		{x: 454.455, prec: 4, want: 454.455},
+
+		// Negative precision.
+		{x: 454.45, prec: -1, want: 450},
+		{x: 454.45, prec: -2, want: 500},
+		{x: 500, prec: -3, want: 0},
+		{x: 500, prec: -4, want: 0},
+		{x: 1500, prec: -3, want: 2000},
+		{x: 1500, prec: -4, want: 0},
+	} {
+		for _, sign := range []float64{1, -1} {
+			got := RoundEven(sign*test.x, test.prec)
+			want := sign * test.want
+			if want == 0 {
+				want = 0
+			}
+			if (got != want || math.Signbit(got) != math.Signbit(want)) && !(math.IsNaN(got) && math.IsNaN(want)) {
+				t.Errorf("unexpected result for RoundEven(%g, %d): got: %g, want: %g", sign*test.x, test.prec, got, want)
+			}
+		}
+	}
+}
+
+func TestSame(t *testing.T) {
+	s1 := []float64{1, 2, 3, 4}
+	s2 := []float64{1, 2, 3, 4}
+	if !Same(s1, s2) {
+		t.Errorf("Equal slices returned as unequal")
+	}
+	s2 = []float64{1, 2, 3, 4 + 1e-14}
+	if Same(s1, s2) {
+		t.Errorf("Unequal slices returned as equal")
+	}
+	if Same(s1, []float64{}) {
+		t.Errorf("Unequal slice lengths returned as equal")
+	}
+	s1 = []float64{1, 2, math.NaN(), 4}
+	s2 = []float64{1, 2, math.NaN(), 4}
+	if !Same(s1, s2) {
+		t.Errorf("Slices with matching NaN values returned as unequal")
+	}
+	s1 = []float64{1, 2, math.NaN(), 4}
+	s2 = []float64{1, math.NaN(), 3, 4}
+	if !Same(s1, s2) {
+		t.Errorf("Slices with unmatching NaN values returned as equal")
+	}
+}
+
+func TestScale(t *testing.T) {
+	s := []float64{3, 4, 1, 7, 5}
+	c := 5.0
+	truth := []float64{15, 20, 5, 35, 25}
+	Scale(c, s)
+	AreSlicesEqual(t, truth, s, "Bad scaling")
+}
+
+func TestSpan(t *testing.T) {
+	receiver1 := make([]float64, 5)
+	truth := []float64{1, 2, 3, 4, 5}
+	receiver2 := Span(receiver1, 1, 5)
+	AreSlicesEqual(t, truth, receiver1, "Improper linspace from mutator")
+	AreSlicesEqual(t, truth, receiver2, "Improper linspace from returned slice")
+	receiver1 = make([]float64, 6)
+	truth = []float64{0, 0.2, 0.4, 0.6, 0.8, 1.0}
+	Span(receiver1, 0, 1)
+	AreSlicesEqual(t, truth, receiver1, "Improper linspace")
+	if !Panics(func() { Span(nil, 1, 5) }) {
+		t.Errorf("Span accepts nil argument")
+	}
+	if !Panics(func() { Span(make([]float64, 1), 1, 5) }) {
+		t.Errorf("Span accepts argument of len = 1")
+	}
+}
+
+func TestSub(t *testing.T) {
+	s := []float64{3, 4, 1, 7, 5}
+	v := []float64{1, 2, 3, 4, 5}
+	truth := []float64{2, 2, -2, 3, 0}
+	Sub(s, v)
+	AreSlicesEqual(t, truth, s, "Bad subtract")
+	// Test that it panics
+	if !Panics(func() { Sub(make([]float64, 2), make([]float64, 3)) }) {
+		t.Errorf("Did not panic with length mismatch")
+	}
+}
+
+func TestSubTo(t *testing.T) {
+	s := []float64{3, 4, 1, 7, 5}
+	v := []float64{1, 2, 3, 4, 5}
+	truth := []float64{2, 2, -2, 3, 0}
+	dst1 := make([]float64, len(s))
+	dst2 := SubTo(dst1, s, v)
+	AreSlicesEqual(t, truth, dst1, "Bad subtract from mutator")
+	AreSlicesEqual(t, truth, dst2, "Bad subtract from returned slice")
+	// Test that all mismatch combinations panic
+	if !Panics(func() { SubTo(make([]float64, 2), make([]float64, 3), make([]float64, 3)) }) {
+		t.Errorf("Did not panic with dst different length")
+	}
+	if !Panics(func() { SubTo(make([]float64, 3), make([]float64, 2), make([]float64, 3)) }) {
+		t.Errorf("Did not panic with subtractor different length")
+	}
+	if !Panics(func() { SubTo(make([]float64, 3), make([]float64, 3), make([]float64, 2)) }) {
+		t.Errorf("Did not panic with subtractee different length")
+	}
+}
+
+func TestSum(t *testing.T) {
+	s := []float64{}
+	val := Sum(s)
+	if val != 0 {
+		t.Errorf("Val not returned as default when slice length is zero")
+	}
+	s = []float64{3, 4, 1, 7, 5}
+	val = Sum(s)
+	if val != 20 {
+		t.Errorf("Wrong sum returned")
+	}
+}
+
+func TestWithin(t *testing.T) {
+	for i, test := range []struct {
+		s      []float64
+		v      float64
+		idx    int
+		panics bool
+	}{
+		{
+			s:   []float64{1, 2, 5, 9},
+			v:   1,
+			idx: 0,
+		},
+		{
+			s:   []float64{1, 2, 5, 9},
+			v:   9,
+			idx: -1,
+		},
+		{
+			s:   []float64{1, 2, 5, 9},
+			v:   1.5,
+			idx: 0,
+		},
+		{
+			s:   []float64{1, 2, 5, 9},
+			v:   2,
+			idx: 1,
+		},
+		{
+			s:   []float64{1, 2, 5, 9},
+			v:   2.5,
+			idx: 1,
+		},
+		{
+			s:   []float64{1, 2, 5, 9},
+			v:   -3,
+			idx: -1,
+		},
+		{
+			s:   []float64{1, 2, 5, 9},
+			v:   15,
+			idx: -1,
+		},
+		{
+			s:   []float64{1, 2, 5, 9},
+			v:   math.NaN(),
+			idx: -1,
+		},
+		{
+			s:      []float64{5, 2, 6},
+			panics: true,
+		},
+		{
+			panics: true,
+		},
+		{
+			s:      []float64{1},
+			panics: true,
+		},
+	} {
+		var idx int
+		panics := Panics(func() { idx = Within(test.s, test.v) })
+		if panics {
+			if !test.panics {
+				t.Errorf("Case %v: bad panic", i)
+			}
+			continue
+		}
+		if test.panics {
+			if !panics {
+				t.Errorf("Case %v: did not panic when it should", i)
+			}
+			continue
+		}
+		if idx != test.idx {
+			t.Errorf("Case %v: Idx mismatch. Want: %v, got: %v", i, test.idx, idx)
+		}
+	}
+
+}
+
+func randomSlice(l int) []float64 {
+	s := make([]float64, l)
+	for i := range s {
+		s[i] = rand.Float64()
+	}
+	return s
+}
+
+func benchmarkMin(b *testing.B, size int) {
+	s := randomSlice(size)
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		Min(s)
+	}
+}
+func BenchmarkMinSmall(b *testing.B) { benchmarkMin(b, Small) }
+func BenchmarkMinMed(b *testing.B)   { benchmarkMin(b, Medium) }
+func BenchmarkMinLarge(b *testing.B) { benchmarkMin(b, Large) }
+func BenchmarkMinHuge(b *testing.B)  { benchmarkMin(b, Huge) }
+
+func benchmarkAdd(b *testing.B, size int) {
+	s1 := randomSlice(size)
+	s2 := randomSlice(size)
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		Add(s1, s2)
+	}
+}
+func BenchmarkAddSmall(b *testing.B) { benchmarkAdd(b, Small) }
+func BenchmarkAddMed(b *testing.B)   { benchmarkAdd(b, Medium) }
+func BenchmarkAddLarge(b *testing.B) { benchmarkAdd(b, Large) }
+func BenchmarkAddHuge(b *testing.B)  { benchmarkAdd(b, Huge) }
+
+func benchmarkAddTo(b *testing.B, size int) {
+	s1 := randomSlice(size)
+	s2 := randomSlice(size)
+	dst := randomSlice(size)
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		AddTo(dst, s1, s2)
+	}
+}
+func BenchmarkAddToSmall(b *testing.B) { benchmarkAddTo(b, Small) }
+func BenchmarkAddToMed(b *testing.B)   { benchmarkAddTo(b, Medium) }
+func BenchmarkAddToLarge(b *testing.B) { benchmarkAddTo(b, Large) }
+func BenchmarkAddToHuge(b *testing.B)  { benchmarkAddTo(b, Huge) }
+
+func benchmarkCumProd(b *testing.B, size int) {
+	s := randomSlice(size)
+	dst := randomSlice(size)
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		CumProd(dst, s)
+	}
+}
+func BenchmarkCumProdSmall(b *testing.B) { benchmarkCumProd(b, Small) }
+func BenchmarkCumProdMed(b *testing.B)   { benchmarkCumProd(b, Medium) }
+func BenchmarkCumProdLarge(b *testing.B) { benchmarkCumProd(b, Large) }
+func BenchmarkCumProdHuge(b *testing.B)  { benchmarkCumProd(b, Huge) }
+
+func benchmarkCumSum(b *testing.B, size int) {
+	s := randomSlice(size)
+	dst := randomSlice(size)
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		CumSum(dst, s)
+	}
+}
+func BenchmarkCumSumSmall(b *testing.B) { benchmarkCumSum(b, Small) }
+func BenchmarkCumSumMed(b *testing.B)   { benchmarkCumSum(b, Medium) }
+func BenchmarkCumSumLarge(b *testing.B) { benchmarkCumSum(b, Large) }
+func BenchmarkCumSumHuge(b *testing.B)  { benchmarkCumSum(b, Huge) }
+
+func benchmarkDiv(b *testing.B, size int) {
+	s := randomSlice(size)
+	dst := randomSlice(size)
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		Div(dst, s)
+	}
+}
+func BenchmarkDivSmall(b *testing.B) { benchmarkDiv(b, Small) }
+func BenchmarkDivMed(b *testing.B)   { benchmarkDiv(b, Medium) }
+func BenchmarkDivLarge(b *testing.B) { benchmarkDiv(b, Large) }
+func BenchmarkDivHuge(b *testing.B)  { benchmarkDiv(b, Huge) }
+
+func benchmarkDivTo(b *testing.B, size int) {
+	s1 := randomSlice(size)
+	s2 := randomSlice(size)
+	dst := randomSlice(size)
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		DivTo(dst, s1, s2)
+	}
+}
+func BenchmarkDivToSmall(b *testing.B) { benchmarkDivTo(b, Small) }
+func BenchmarkDivToMed(b *testing.B)   { benchmarkDivTo(b, Medium) }
+func BenchmarkDivToLarge(b *testing.B) { benchmarkDivTo(b, Large) }
+func BenchmarkDivToHuge(b *testing.B)  { benchmarkDivTo(b, Huge) }
+
+func benchmarkSub(b *testing.B, size int) {
+	s1 := randomSlice(size)
+	s2 := randomSlice(size)
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		Sub(s1, s2)
+	}
+}
+func BenchmarkSubSmall(b *testing.B) { benchmarkSub(b, Small) }
+func BenchmarkSubMed(b *testing.B)   { benchmarkSub(b, Medium) }
+func BenchmarkSubLarge(b *testing.B) { benchmarkSub(b, Large) }
+func BenchmarkSubHuge(b *testing.B)  { benchmarkSub(b, Huge) }
+
+func benchmarkSubTo(b *testing.B, size int) {
+	s1 := randomSlice(size)
+	s2 := randomSlice(size)
+	dst := randomSlice(size)
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		SubTo(dst, s1, s2)
+	}
+}
+func BenchmarkSubToSmall(b *testing.B) { benchmarkSubTo(b, Small) }
+func BenchmarkSubToMed(b *testing.B)   { benchmarkSubTo(b, Medium) }
+func BenchmarkSubToLarge(b *testing.B) { benchmarkSubTo(b, Large) }
+func BenchmarkSubToHuge(b *testing.B)  { benchmarkSubTo(b, Huge) }
+
+func benchmarkLogSumExp(b *testing.B, size int) {
+	s := randomSlice(size)
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		LogSumExp(s)
+	}
+}
+func BenchmarkLogSumExpSmall(b *testing.B) { benchmarkLogSumExp(b, Small) }
+func BenchmarkLogSumExpMed(b *testing.B)   { benchmarkLogSumExp(b, Medium) }
+func BenchmarkLogSumExpLarge(b *testing.B) { benchmarkLogSumExp(b, Large) }
+func BenchmarkLogSumExpHuge(b *testing.B)  { benchmarkLogSumExp(b, Huge) }
+
+func benchmarkDot(b *testing.B, size int) {
+	s1 := randomSlice(size)
+	s2 := randomSlice(size)
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		Dot(s1, s2)
+	}
+}
+func BenchmarkDotSmall(b *testing.B) { benchmarkDot(b, Small) }
+func BenchmarkDotMed(b *testing.B)   { benchmarkDot(b, Medium) }
+func BenchmarkDotLarge(b *testing.B) { benchmarkDot(b, Large) }
+func BenchmarkDotHuge(b *testing.B)  { benchmarkDot(b, Huge) }
+
+func benchmarkAddScaledTo(b *testing.B, size int) {
+	dst := randomSlice(size)
+	y := randomSlice(size)
+	s := randomSlice(size)
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		AddScaledTo(dst, y, 2.3, s)
+	}
+}
+func BenchmarkAddScaledToSmall(b *testing.B)  { benchmarkAddScaledTo(b, Small) }
+func BenchmarkAddScaledToMedium(b *testing.B) { benchmarkAddScaledTo(b, Medium) }
+func BenchmarkAddScaledToLarge(b *testing.B)  { benchmarkAddScaledTo(b, Large) }
+func BenchmarkAddScaledToHuge(b *testing.B)   { benchmarkAddScaledTo(b, Huge) }
+
+func benchmarkScale(b *testing.B, size int) {
+	dst := randomSlice(size)
+	b.ResetTimer()
+	for i := 0; i < b.N; i += 2 {
+		Scale(2.0, dst)
+		Scale(0.5, dst)
+	}
+}
+func BenchmarkScaleSmall(b *testing.B)  { benchmarkScale(b, Small) }
+func BenchmarkScaleMedium(b *testing.B) { benchmarkScale(b, Medium) }
+func BenchmarkScaleLarge(b *testing.B)  { benchmarkScale(b, Large) }
+func BenchmarkScaleHuge(b *testing.B)   { benchmarkScale(b, Huge) }
diff --git a/vendor/gonum.org/v1/gonum/floats/parse_example_test.go b/vendor/gonum.org/v1/gonum/floats/parse_example_test.go
new file mode 100644
index 00000000..cb8c4e51
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/floats/parse_example_test.go
@@ -0,0 +1,43 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this code is governed by a BSD-style
+// license that can be found in the LICENSE file
+
+package floats_test
+
+import (
+	"bufio"
+	"fmt"
+	"log"
+	"strings"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/stat"
+)
+
+func ExampleParseWithNA() {
+	// Calculate the mean of a list of numbers
+	// ignoring missing values.
+	const data = `6
+missing
+4
+`
+
+	var vals, weights []float64
+	sc := bufio.NewScanner(strings.NewReader(data))
+	for sc.Scan() {
+		v, w, err := floats.ParseWithNA(sc.Text(), "missing")
+		if err != nil {
+			log.Fatal(err)
+		}
+		vals = append(vals, v)
+		weights = append(weights, w)
+	}
+	err := sc.Err()
+	if err != nil {
+		log.Fatal(err)
+	}
+	fmt.Println(stat.Mean(vals, weights))
+
+	// Output:
+	// 5
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/.gitignore b/vendor/gonum.org/v1/gonum/graph/.gitignore
new file mode 100644
index 00000000..86e0d240
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/.gitignore
@@ -0,0 +1 @@
+test.out
\ No newline at end of file
diff --git a/vendor/gonum.org/v1/gonum/graph/README.md b/vendor/gonum.org/v1/gonum/graph/README.md
new file mode 100644
index 00000000..f0a9505e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/README.md
@@ -0,0 +1,3 @@
+# Gonum graph [![GoDoc](https://godoc.org/gonum.org/v1/gonum/graph?status.svg)](https://godoc.org/gonum.org/v1/gonum/graph)
+
+This is a generalized graph package for the Go language.
diff --git a/vendor/gonum.org/v1/gonum/graph/community/bisect.go b/vendor/gonum.org/v1/gonum/graph/community/bisect.go
new file mode 100644
index 00000000..ddfdb0a9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/community/bisect.go
@@ -0,0 +1,248 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package community
+
+import (
+	"errors"
+	"fmt"
+	"math"
+	"math/rand"
+
+	"gonum.org/v1/gonum/graph"
+)
+
+// Interval is an interval of resolutions with a common score.
+type Interval struct {
+	// Low and High delimit the interval
+	// such that the interval is [low, high).
+	Low, High float64
+
+	// Score is the score of the interval.
+	Score float64
+
+	// Reduced is the best scoring
+	// community membership found for the
+	// interval.
+	Reduced
+}
+
+// Reduced is a graph reduction.
+type Reduced interface {
+	// Communities returns the community
+	// structure of the reduction.
+	Communities() [][]graph.Node
+}
+
+// Size is a score function that is the reciprocal of the number of communities.
+func Size(g ReducedGraph) float64 { return 1 / float64(len(g.Structure())) }
+
+// Weight is a score function that is the sum of community weights. The concrete
+// type of g must be a pointer to a ReducedUndirected or a ReducedDirected, otherwise
+// Weight will panic.
+func Weight(g ReducedGraph) float64 {
+	var w float64
+	switch g := g.(type) {
+	case *ReducedUndirected:
+		for _, n := range g.nodes {
+			w += n.weight
+		}
+	case *ReducedDirected:
+		for _, n := range g.nodes {
+			w += n.weight
+		}
+	default:
+		panic(fmt.Sprintf("community: invalid graph type: %T", g))
+	}
+	return w
+}
+
+// ModularScore returns a modularized scoring function for Profile based on the
+// graph g and the given score function. The effort parameter determines how
+// many attempts will be made to get an improved score for any given resolution.
+func ModularScore(g graph.Graph, score func(ReducedGraph) float64, effort int, src *rand.Rand) func(float64) (float64, Reduced) {
+	return func(resolution float64) (float64, Reduced) {
+		max := math.Inf(-1)
+		var best Reduced
+		for i := 0; i < effort; i++ {
+			r := Modularize(g, resolution, src)
+			s := score(r)
+			if s > max {
+				max = s
+				best = r
+			}
+		}
+		return max, best
+	}
+}
+
+// SizeMultiplex is a score function that is the reciprocal of the number of communities.
+func SizeMultiplex(g ReducedMultiplex) float64 { return 1 / float64(len(g.Structure())) }
+
+// WeightMultiplex is a score function that is the sum of community weights. The concrete
+// type of g must be pointer to a ReducedUndirectedMultiplex or a ReducedDirectedMultiplex,
+// otherwise WeightMultiplex will panic.
+func WeightMultiplex(g ReducedMultiplex) float64 {
+	var w float64
+	switch g := g.(type) {
+	case *ReducedUndirectedMultiplex:
+		for _, n := range g.nodes {
+			for _, lw := range n.weights {
+				w += lw
+			}
+		}
+	case *ReducedDirectedMultiplex:
+		for _, n := range g.nodes {
+			for _, lw := range n.weights {
+				w += lw
+			}
+		}
+	default:
+		panic(fmt.Sprintf("community: invalid graph type: %T", g))
+	}
+	return w
+}
+
+// ModularMultiplexScore returns a modularized scoring function for Profile based
+// on the graph g and the given score function. The effort parameter determines how
+// many attempts will be made to get an improved score for any given resolution.
+func ModularMultiplexScore(g Multiplex, weights []float64, all bool, score func(ReducedMultiplex) float64, effort int, src *rand.Rand) func(float64) (float64, Reduced) {
+	return func(resolution float64) (float64, Reduced) {
+		max := math.Inf(-1)
+		var best Reduced
+		for i := 0; i < effort; i++ {
+			r := ModularizeMultiplex(g, weights, []float64{resolution}, all, src)
+			s := score(r)
+			if s > max {
+				max = s
+				best = r
+			}
+		}
+		return max, best
+	}
+}
+
+// Profile returns an approximate profile of score values in the resolution domain [low,high)
+// at the given granularity. The score is calculated by bisecting calls to fn. If log is true,
+// log space bisection is used, otherwise bisection is linear. The function fn should be
+// monotonically decreasing in at least 1/grain evaluations. Profile will attempt to detect
+// non-monotonicity during the bisection.
+//
+// Since exact modularity optimization is known to be NP-hard and Profile calls modularization
+// routines repeatedly, it is unlikely to return the exact resolution profile.
+func Profile(fn func(float64) (float64, Reduced), log bool, grain, low, high float64) (profile []Interval, err error) {
+	if low >= high {
+		return nil, errors.New("community: zero or negative width domain")
+	}
+
+	defer func() {
+		r := recover()
+		e, ok := r.(nonDecreasing)
+		if ok {
+			err = e
+			return
+		}
+		if r != nil {
+			panic(r)
+		}
+	}()
+	left, comm := fn(low)
+	right, _ := fn(high)
+	for i := 1; i < int(1/grain); i++ {
+		rt, _ := fn(high)
+		right = math.Max(right, rt)
+	}
+	profile = bisect(fn, log, grain, low, left, high, right, comm)
+
+	// We may have missed some non-monotonicity,
+	// so merge low score discordant domains into
+	// their lower resolution neighbours.
+	return fixUp(profile), nil
+}
+
+type nonDecreasing int
+
+func (n nonDecreasing) Error() string {
+	return fmt.Sprintf("community: profile does not reliably monotonically decrease: tried %d times", n)
+}
+
+func bisect(fn func(float64) (float64, Reduced), log bool, grain, low, scoreLow, high, scoreHigh float64, comm Reduced) []Interval {
+	if low >= high {
+		panic("community: zero or negative width domain")
+	}
+	if math.IsNaN(scoreLow) || math.IsNaN(scoreHigh) {
+		return nil
+	}
+
+	// Heuristically determine a reasonable number
+	// of times to try to get a higher value.
+	maxIter := int(1 / grain)
+
+	lowComm := comm
+	for n := 0; scoreLow < scoreHigh; n++ {
+		if n > maxIter {
+			panic(nonDecreasing(n))
+		}
+		scoreLow, lowComm = fn(low)
+	}
+
+	if scoreLow == scoreHigh || tooSmall(low, high, grain, log) {
+		return []Interval{{Low: low, High: high, Score: scoreLow, Reduced: lowComm}}
+	}
+
+	var mid float64
+	if log {
+		mid = math.Sqrt(low * high)
+	} else {
+		mid = (low + high) / 2
+	}
+
+	scoreMid := math.Inf(-1)
+	var midComm Reduced
+	for n := 0; scoreMid < scoreHigh; n++ {
+		if n > maxIter {
+			panic(nonDecreasing(n))
+		}
+		scoreMid, midComm = fn(mid)
+	}
+
+	lower := bisect(fn, log, grain, low, scoreLow, mid, scoreMid, lowComm)
+	higher := bisect(fn, log, grain, mid, scoreMid, high, scoreHigh, midComm)
+	for n := 0; lower[len(lower)-1].Score < higher[0].Score; n++ {
+		if n > maxIter {
+			panic(nonDecreasing(n))
+		}
+		lower[len(lower)-1].Score, lower[len(lower)-1].Reduced = fn(low)
+	}
+
+	if lower[len(lower)-1].Score == higher[0].Score {
+		higher[0].Low = lower[len(lower)-1].Low
+		lower = lower[:len(lower)-1]
+		if len(lower) == 0 {
+			return higher
+		}
+	}
+	return append(lower, higher...)
+}
+
+// fixUp non-monotonically decreasing interval scores.
+func fixUp(profile []Interval) []Interval {
+	max := profile[len(profile)-1].Score
+	for i := len(profile) - 2; i >= 0; i-- {
+		if profile[i].Score > max {
+			max = profile[i].Score
+			continue
+		}
+		profile[i+1].Low = profile[i].Low
+		profile = append(profile[:i], profile[i+1:]...)
+	}
+	return profile
+}
+
+func tooSmall(low, high, grain float64, log bool) bool {
+	if log {
+		return math.Log(high/low) < grain
+	}
+	return high-low < grain
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/community/bisect_test.go b/vendor/gonum.org/v1/gonum/graph/community/bisect_test.go
new file mode 100644
index 00000000..5a225d7e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/community/bisect_test.go
@@ -0,0 +1,311 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package community
+
+import (
+	"fmt"
+	"log"
+	"sort"
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/ordered"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+func ExampleProfile_simple() {
+	// Create dumbell graph:
+	//
+	//  0       4
+	//  |\     /|
+	//  | 2 - 3 |
+	//  |/     \|
+	//  1       5
+	//
+	g := simple.NewUndirectedGraph()
+	for u, e := range smallDumbell {
+		for v := range e {
+			g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+		}
+	}
+
+	// Get the profile of internal node weight for resolutions
+	// between 0.1 and 10 using logarithmic bisection.
+	p, err := Profile(ModularScore(g, Weight, 10, nil), true, 1e-3, 0.1, 10)
+	if err != nil {
+		log.Fatal(err)
+	}
+
+	// Print out each step with communities ordered.
+	for _, d := range p {
+		comm := d.Communities()
+		for _, c := range comm {
+			sort.Sort(ordered.ByID(c))
+		}
+		sort.Sort(ordered.BySliceIDs(comm))
+		fmt.Printf("Low:%.2v High:%.2v Score:%v Communities:%v Q=%.3v\n",
+			d.Low, d.High, d.Score, comm, Q(g, comm, d.Low))
+	}
+
+	// Output:
+	// Low:0.1 High:0.29 Score:14 Communities:[[0 1 2 3 4 5]] Q=0.9
+	// Low:0.29 High:2.3 Score:12 Communities:[[0 1 2] [3 4 5]] Q=0.714
+	// Low:2.3 High:3.5 Score:4 Communities:[[0 1] [2] [3] [4 5]] Q=-0.31
+	// Low:3.5 High:10 Score:0 Communities:[[0] [1] [2] [3] [4] [5]] Q=-0.607
+}
+
+var friends, enemies *simple.WeightedUndirectedGraph
+
+func init() {
+	friends = simple.NewWeightedUndirectedGraph(0, 0)
+	for u, e := range middleEast.friends {
+		// Ensure unconnected nodes are included.
+		if !friends.Has(simple.Node(u)) {
+			friends.AddNode(simple.Node(u))
+		}
+		for v := range e {
+			friends.SetWeightedEdge(simple.WeightedEdge{F: simple.Node(u), T: simple.Node(v), W: 1})
+		}
+	}
+	enemies = simple.NewWeightedUndirectedGraph(0, 0)
+	for u, e := range middleEast.enemies {
+		// Ensure unconnected nodes are included.
+		if !enemies.Has(simple.Node(u)) {
+			enemies.AddNode(simple.Node(u))
+		}
+		for v := range e {
+			enemies.SetWeightedEdge(simple.WeightedEdge{F: simple.Node(u), T: simple.Node(v), W: -1})
+		}
+	}
+}
+
+func ExampleProfile_multiplex() {
+	// The undirected graphs, friends and enemies, are the political relationships
+	// in the Middle East as described in the Slate article:
+	// http://www.slate.com/blogs/the_world_/2014/07/17/the_middle_east_friendship_chart.html
+	g, err := NewUndirectedLayers(friends, enemies)
+	if err != nil {
+		log.Fatal(err)
+	}
+	weights := []float64{1, -1}
+
+	// Get the profile of internal node weight for resolutions
+	// between 0.1 and 10 using logarithmic bisection.
+	p, err := Profile(ModularMultiplexScore(g, weights, true, WeightMultiplex, 10, nil), true, 1e-3, 0.1, 10)
+	if err != nil {
+		log.Fatal(err)
+	}
+
+	// Print out each step with communities ordered.
+	for _, d := range p {
+		comm := d.Communities()
+		for _, c := range comm {
+			sort.Sort(ordered.ByID(c))
+		}
+		sort.Sort(ordered.BySliceIDs(comm))
+		fmt.Printf("Low:%.2v High:%.2v Score:%v Communities:%v Q=%.3v\n",
+			d.Low, d.High, d.Score, comm, QMultiplex(g, comm, weights, []float64{d.Low}))
+	}
+
+	// Output:
+	// Low:0.1 High:0.72 Score:26 Communities:[[0] [1 7 9 12] [2 8 11] [3 4 5 10] [6]] Q=[24.7 1.97]
+	// Low:0.72 High:1.1 Score:24 Communities:[[0 6] [1 7 9 12] [2 8 11] [3 4 5 10]] Q=[16.9 14.1]
+	// Low:1.1 High:1.1 Score:18 Communities:[[0 2 6 11] [1 7 9 12] [3 4 5 8 10]] Q=[9.16 25.1]
+	// Low:1.1 High:1.6 Score:10 Communities:[[0 3 4 5 6 10] [1 7 9 12] [2 8 11]] Q=[11.5 23.9]
+	// Low:1.6 High:1.6 Score:8 Communities:[[0 1 6 7 9 12] [2 8 11] [3 4 5 10]] Q=[5.56 39.8]
+	// Low:1.6 High:1.8 Score:2 Communities:[[0 2 3 4 5 6 10] [1 7 8 9 11 12]] Q=[-1.82 48.6]
+	// Low:1.8 High:2.3 Score:-6 Communities:[[0 2 3 4 5 6 8 10 11] [1 7 9 12]] Q=[-5 57.5]
+	// Low:2.3 High:2.4 Score:-10 Communities:[[0 1 2 6 7 8 9 11 12] [3 4 5 10]] Q=[-11.2 79]
+	// Low:2.4 High:4.3 Score:-52 Communities:[[0 1 2 3 4 5 6 7 8 9 10 11 12]] Q=[-46.1 117]
+	// Low:4.3 High:10 Score:-54 Communities:[[0 1 2 3 4 6 7 8 9 10 11 12] [5]] Q=[-82 254]
+}
+
+func TestProfileUndirected(t *testing.T) {
+	for _, test := range communityUndirectedQTests {
+		g := simple.NewUndirectedGraph()
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+
+		testProfileUndirected(t, test, g)
+	}
+}
+
+func TestProfileWeightedUndirected(t *testing.T) {
+	for _, test := range communityUndirectedQTests {
+		g := simple.NewWeightedUndirectedGraph(0, 0)
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetWeightedEdge(simple.WeightedEdge{F: simple.Node(u), T: simple.Node(v), W: 1})
+			}
+		}
+
+		testProfileUndirected(t, test, g)
+	}
+}
+
+func testProfileUndirected(t *testing.T, test communityUndirectedQTest, g graph.Undirected) {
+	fn := ModularScore(g, Weight, 10, nil)
+	p, err := Profile(fn, true, 1e-3, 0.1, 10)
+	if err != nil {
+		t.Errorf("%s: unexpected error: %v", test.name, err)
+	}
+
+	const tries = 1000
+	for i, d := range p {
+		var score float64
+		for i := 0; i < tries; i++ {
+			score, _ = fn(d.Low)
+			if score >= d.Score {
+				break
+			}
+		}
+		if score < d.Score {
+			t.Errorf("%s: failed to recover low end score: got: %v want: %v", test.name, score, d.Score)
+		}
+		if i != 0 && d.Score >= p[i-1].Score {
+			t.Errorf("%s: not monotonically decreasing: %v -> %v", test.name, p[i-1], d)
+		}
+	}
+}
+
+func TestProfileDirected(t *testing.T) {
+	for _, test := range communityDirectedQTests {
+		g := simple.NewDirectedGraph()
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+
+		testProfileDirected(t, test, g)
+	}
+}
+
+func TestProfileWeightedDirected(t *testing.T) {
+	for _, test := range communityDirectedQTests {
+		g := simple.NewWeightedDirectedGraph(0, 0)
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetWeightedEdge(simple.WeightedEdge{F: simple.Node(u), T: simple.Node(v), W: 1})
+			}
+		}
+
+		testProfileDirected(t, test, g)
+	}
+}
+
+func testProfileDirected(t *testing.T, test communityDirectedQTest, g graph.Directed) {
+	fn := ModularScore(g, Weight, 10, nil)
+	p, err := Profile(fn, true, 1e-3, 0.1, 10)
+	if err != nil {
+		t.Errorf("%s: unexpected error: %v", test.name, err)
+	}
+
+	const tries = 1000
+	for i, d := range p {
+		var score float64
+		for i := 0; i < tries; i++ {
+			score, _ = fn(d.Low)
+			if score >= d.Score {
+				break
+			}
+		}
+		if score < d.Score {
+			t.Errorf("%s: failed to recover low end score: got: %v want: %v", test.name, score, d.Score)
+		}
+		if i != 0 && d.Score >= p[i-1].Score {
+			t.Errorf("%s: not monotonically decreasing: %v -> %v", test.name, p[i-1], d)
+		}
+	}
+}
+
+func TestProfileUndirectedMultiplex(t *testing.T) {
+	for _, test := range communityUndirectedMultiplexQTests {
+		g, weights, err := undirectedMultiplexFrom(test.layers)
+		if err != nil {
+			t.Errorf("unexpected error creating multiplex: %v", err)
+			continue
+		}
+
+		const all = true
+
+		fn := ModularMultiplexScore(g, weights, all, WeightMultiplex, 10, nil)
+		p, err := Profile(fn, true, 1e-3, 0.1, 10)
+		if err != nil {
+			t.Errorf("%s: unexpected error: %v", test.name, err)
+		}
+
+		const tries = 1000
+		for i, d := range p {
+			var score float64
+			for i := 0; i < tries; i++ {
+				score, _ = fn(d.Low)
+				if score >= d.Score {
+					break
+				}
+			}
+			if score < d.Score {
+				t.Errorf("%s: failed to recover low end score: got: %v want: %v", test.name, score, d.Score)
+			}
+			if i != 0 && d.Score >= p[i-1].Score {
+				t.Errorf("%s: not monotonically decreasing: %v -> %v", test.name, p[i-1], d)
+			}
+		}
+	}
+}
+
+func TestProfileDirectedMultiplex(t *testing.T) {
+	for _, test := range communityDirectedMultiplexQTests {
+		g, weights, err := directedMultiplexFrom(test.layers)
+		if err != nil {
+			t.Errorf("unexpected error creating multiplex: %v", err)
+			continue
+		}
+
+		const all = true
+
+		fn := ModularMultiplexScore(g, weights, all, WeightMultiplex, 10, nil)
+		p, err := Profile(fn, true, 1e-3, 0.1, 10)
+		if err != nil {
+			t.Errorf("%s: unexpected error: %v", test.name, err)
+		}
+
+		const tries = 1000
+		for i, d := range p {
+			var score float64
+			for i := 0; i < tries; i++ {
+				score, _ = fn(d.Low)
+				if score >= d.Score {
+					break
+				}
+			}
+			if score < d.Score {
+				t.Errorf("%s: failed to recover low end score: got: %v want: %v", test.name, score, d.Score)
+			}
+			if i != 0 && d.Score >= p[i-1].Score {
+				t.Errorf("%s: not monotonically decreasing: %v -> %v", test.name, p[i-1], d)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/community/doc.go b/vendor/gonum.org/v1/gonum/graph/community/doc.go
new file mode 100644
index 00000000..2509606b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/community/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package community provides graph community detection functions.
+package community // import "gonum.org/v1/gonum/graph/community"
diff --git a/vendor/gonum.org/v1/gonum/graph/community/louvain.tex b/vendor/gonum.org/v1/gonum/graph/community/louvain.tex
new file mode 100644
index 00000000..046c02ba
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/community/louvain.tex
@@ -0,0 +1,466 @@
+% Copyright ©2015 The gonum Authors. All rights reserved.
+% Use of this source code is governed by a BSD-style
+% license that can be found in the LICENSE file.
+
+\documentclass{article}
+
+\usepackage{amsmath,amsfonts}
+\usepackage[margin=4cm]{geometry}
+
+\title{Louvain algorithm for undirected and directed graphs}
+\author{The {\tt gonum} Authors}
+
+\begin{document}
+
+\maketitle
+
+The algorithm attempts to find communities (highly connected sub-graphs),
+and it does this by minimising the modularity function
+\begin{equation}
+	Q(c) = \frac{1}{2m}\sum_i\sum_j\left[ A_{ij} - \gamma \frac{k_ik_j}{2m} \right] \delta_{ij}(c),
+\end{equation}
+where $c$ is a partition of nodes into subsets or communities,
+$A_{ij}$ is the edge weight between nodes $i$ and $j$, 
+$\gamma$ is a tuning parameter,
+\begin{equation}
+m = \frac{1}{2}\sum_i\sum_jA_{ij},
+\end{equation}
+\begin{equation}
+k_i = \sum_j{A_{ij}},
+\end{equation}
+and 
+\begin{equation}
+	\delta_{ij}(c) = \left \{ \begin{array}{ll}
+	1 & \text{if} \quad  c(i) = c(j) \\
+	0 & \text{otherwise} \end{array} \right ..
+\end{equation}
+Here $c(i)$ denotes the community to which node $i$ belongs 
+in the partitioning $c$.
+
+The algorithm finds a hierarchical community structure by iterating 
+between two phases:
+\begin{enumerate}
+	\item Find a set of communities that minimise $Q$.
+	\item Construct a new graph, whose nodes are the communities 
+	found in the preceding phase one step.
+\end{enumerate}
+Each iteration of these two phases is called a `pass'.
+In this way, the algorithm obtains a nested community structure, 
+where at each level $Q$ is minimised for the relevant graph.
+We consider this process in more detail, in particular looking 
+at phase one first in the first pass, when each node is a single
+node, and then how this generalises to later passes when each node 
+is a community.
+
+\section{Undirected Graphs}
+
+\subsection{Initial Pass}
+\label{sec:initialPass}
+
+The initial pass is simple as the initial pass uses the original graph, 
+and in all following passes graphs constructed in the previous pass's 
+phase two are used.
+Here we will consider this initial simple formulation for phase one, and
+in Section~\ref{sec:laterPasses} we consider how this generalises for 
+passes two and onwards. 
+Phase one works by initially allocating each node to a separate community,
+and then iterating through each node $a$ and checking if moving it into 
+a different community $\beta$ will reduce $Q$.
+If there are possible moves that will reduce $Q$, $a$ is moved into the 
+the community which will generate the largest reduction in $Q$. 
+This process is continued until there are no moves left to reduce $Q$ 
+further, meaning a local minimum for $Q$ has been achieved. 
+Then the algorithm moves to phase two (constructing a new graph where
+each node in the new graph is a community in the old graph). 
+
+Note that we assume the original graph to be simple and undirected.
+First, we introduce some notation that will be useful:
+Let $c(i)$ denote the community to which node $i$ belongs, 
+and let $\alpha$ be the community that the node $a$ mentioned above
+belongs to, i.e., $\alpha = c_a$.
+Then we define
+\newcommand{\Stot}[1]{\Sigma_{\text{tot}}^{#1}}
+\begin{equation}
+	\Stot{\alpha} = \sum_{i \in \alpha}\sum_{j}A_{ij} = \sum_{i \in \alpha}k_i,
+\end{equation}
+\newcommand{\kin}[2]{k_{#1}^{#2}}
+\begin{equation}
+	\kin{i}{\alpha} = \sum_{j \in \alpha}A_{ij},
+\end{equation}
+and
+\newcommand{\Sin}[1]{\Sigma_{\text{in}}^{#1}}
+\begin{equation}
+	\Sin{\alpha} = \sum_{i \in \alpha}\sum_{j \in \alpha}A_{ij} = \sum_{i \in \alpha}\kin{i}{\alpha}.
+\end{equation}
+
+We are interested in how $Q$ will change if we move a node $a$ from its 
+current community $\alpha$, to a new community $\beta$.
+This will have two effects, it will remove the terms from $Q$ 
+related to $a$ in $\alpha$, which we will call $Q^-$ and it will add terms 
+related to $a$ in $\beta$, which we will call $Q^+$. 
+The total change in $Q$ caused by the movement of $a$ from $\alpha$ to $\beta$ is 
+\begin{equation}
+	\Delta Q = Q^{+} - Q^{-},
+\end{equation}
+where
+\begin{align*}
+Q^- &= \frac{1}{2m}\left[ \left( A_{aa} - \gamma \frac{k_a^2}{2m} \right) 
++ 2\sum_{i \in \alpha, \, i \neq a} \left( A_{ia} - \gamma \frac{k_ik_a}{2m} \right) \right] \\
+	&= \frac{1}{2m}\left[ \left( A_{aa} - \gamma \frac{k_a^2}{2m} \right) 
++ 2 \left( \kin{a}{\alpha} -A_{aa}\right) - \gamma \frac{2k_a}{2m}\sum_{i \in \alpha, \, i \neq a} k_i \right] \\
+	&= \frac{1}{2m}\left[ \left( A_{aa} - \gamma \frac{k_a^2}{2m} \right) 
++ 2 \left( \kin{a}{\alpha} -A_{aa}\right) - \gamma \frac{2k_a}{2m}\left( \Stot{\alpha} - k_a \right)  \right], \\
+\end{align*}
+and
+\begin{align*}
+Q^+ &= \frac{1}{2m}\left[ \left( A_{aa} - \gamma \frac{k_a^2}{2m} \right) 
++ 2\sum_{i \in \beta} \left( A_{ia} - \gamma \frac{k_ik_a}{2m} \right) \right] \\
+		&= \frac{1}{2m}\left[ \left( A_{aa} - \gamma \frac{k_a^2}{2m} \right) 
++ 2\kin{a}{\beta} - \gamma \frac{2k_a}{2m}\sum_{i \in \beta} k_i \right] \\
+		&= \frac{1}{2m}\left[ \left( A_{aa} - \gamma \frac{k_a^2}{2m} \right) 
++ 2\kin{a}{\beta} - \gamma \frac{2k_a\Stot{\beta}}{2m} \right]. \\
+\end{align*}
+The first term in both these expressions ($Q^-$ and $Q^+$) is the same, and so cancels:
+\begin{equation}
+\Delta Q = \frac{1}{2m}\left[ \left( 2\kin{a}{\beta} - \gamma \frac{2k_a\Stot{\beta}}{2m} \right) 
+		- \left( 2 \left( \kin{a}{\alpha} -A_{aa}\right) - \gamma \frac{2k_a}{2m}\left( \Stot{\alpha} - k_a \right) \right) \right]. 
+\end{equation}
+ 
+\subsection{Later Passes}
+\label{sec:laterPasses}
+
+In phase two a `meta-graph' is constructed where nodes correspond to 
+the communities found in the preceding phase one step, and edge weight
+between two such communities (nodes, in the meta-graph)
+$\alpha$ and $\beta$ are defined to be
+\begin{equation}
+	A_{\alpha \beta}^* = \sum_{i \in \alpha}\sum_{j \in \beta}A_{ij}.
+	\label{eqn:Aij*}
+\end{equation} 
+Note that $i$ and $j$ refer to nodes in the original graph, not nodes 
+in the previous graph, and so holds any meta-graph, not just the first.
+Also note that this definition of $A^*_{\alpha \beta}$ allows for 
+$A^*_{\alpha \alpha}$ to be non-zero as
+\begin{equation}
+A_{\alpha \alpha}^* = \sum_{i \in \alpha}\sum_{j \in \alpha}A_{ij} = \Sin{\alpha}.
+\end{equation} 
+
+In this newly constructed graph, $\alpha$ and $\beta$ are nodes, but 
+also refer to communities (sets of nodes) in the original graph, and I 
+use these two interpretations interchangeably.
+This should be the only ambiguous bit of notation in this document, I hope.
+
+The results of Section~\ref{sec:initialPass} generalise to these meta-graphs,
+and the generalised results mirror those of Section~\ref{sec:initialPass} closely
+-- I distinguish the new results from those of Section~\ref{sec:initialPass} by a 
+superscript $*$.
+I use $i$ and $j$ to denote nodes of the original graph as in Section~\ref{sec:initialPass}, 
+and use $z$ and $w$ to denote nodes of the meta-graph (communities of the original).
+I use analogous notation to Section~\ref{sec:initialPass}, $c^*(z)$, to 
+denote the community to which node $z$ of the meta-graph belongs, 
+and let $\mathfrak{a}$ be the community that the node $\alpha$ belongs to 
+($c^*(\alpha) = \mathfrak{a}$), i.e.
+\begin{equation}
+	\mathfrak{a} = \{z | c^*(z) = c^*(\alpha) \}.
+\end{equation}
+
+Given this notation, we can observe that
+\begin{equation}
+m^* = \frac{1}{2}\sum_{z}\sum_{w}{A_{zw}^*} = \frac{1}{2}\sum_{z}\sum_{w}{\sum_{i \in z}\sum_{j \in w}A_{ij}} = \frac{1}{2}\sum_i\sum_jA_{ij} = m,
+\end{equation}
+\begin{equation}
+k_{z}^* = \sum_{w}{A_{zw}^*} =  \sum_{w}{\sum_{i \in z}\sum_{j \in w}A_{ij}} = \sum_{i \in z}\sum_{j}A_{ij} = \Stot{z},
+\end{equation}
+\begin{equation}
+	\Stot{\mathfrak{a} *} = \sum_{z \in \mathfrak{a}}\sum_{w}A_{zw}^* = \sum_{z \in \mathfrak{a}}k_z^* = \sum_{z \in \mathfrak{a}}\Stot{z},
+\end{equation}
+\begin{equation}
+	\kin{z}{\mathfrak{a} *} = \sum_{w \in \mathfrak{a}}{A_{zw}^*} = \sum_{w \in \mathfrak{a}}{\sum_{i \in z}\sum_{j \in w}A_{ij}},
+\end{equation}
+and
+\begin{equation}
+\Sin{\mathfrak{a} *} = \sum_{z \in \mathfrak{a}}\sum_{w \in \mathfrak{a}}A_{zw}^* = \sum_{z \in \mathfrak{a}}\kin{z}{\mathfrak{a} *} = \sum_{z \in \mathfrak{a}}\sum_{w \in \mathfrak{a}}{\sum_{i \in z}\sum_{j \in w}A_{ij}}.
+	%\label{eqn:Sin}
+\end{equation}
+
+If we let $\mathfrak{b}$ denote the community to which we are considering moving $\alpha$,
+then the expression for $\Delta Q$ from Section~\ref{sec:initialPass} trivially generalises to
+\begin{equation}
+\Delta Q = \frac{1}{2m}\left[ \left( 2 \kin{\alpha}{\mathfrak{b} *} - \gamma \frac{2k_{\alpha}^*\Stot{\mathfrak{b} *}}{2m} \right) 
+		- \left( 2\left( \kin{\alpha}{\mathfrak{a} *} - A_{\alpha \alpha}^* \right) - \gamma \frac{2k_{\alpha}^*}{2m} \left( \Stot{\mathfrak{a} *} - k_{\alpha}^* \right ) \right) \right] \\
+\end{equation}
+
+\section{Directed Graphs}
+\label{sec:directedGraphs}
+
+It is of interest to consider how this generalises to directed graphs.
+If we are to treat incoming and outgoing nodes equally, there are several
+thoughts on how to extend the algorithm to directed graphs, of which we 
+will explore three: 
+\begin{itemize}
+	\item Construct an undirected graph first, and then use the undirected case.
+	\item Generalise the expressions from the undirected case to the directed case, 
+	we will consider two different suggestions for such generalisations. 
+\end{itemize}
+We will show that one of the two `generalisation of expressions' approaches is 
+equivalent to constructing an undirected graph, and the other is not.
+
+\subsection{Construction of an undirected graph}
+A simple approach to generalising to directed graphs is to construct 
+an undirected graph with edge weights
+\begin{equation}
+A_{ij} = B_{ij} + B_{ji},
+\label{eqn:undirectedAB}
+\end{equation}
+and simply use the undirected algorithm.
+Another suggestion is to average the directed edges to make
+an undirected graph, i.e. to use a directed graph with edge weights
+\begin{equation}
+A_{ij} = \frac{B_{ij} + B_{ji}}{2}.
+\end{equation}
+This raises an important question: does scaling all edge weights across 
+the entire graph by a constant affect the results of the algorithm?
+Hopefully not, but worth checking.
+We can follow this through the results for the undirected graph by 
+substituting $A_{ij}^{(1)} = pA_{ij}$, $p \in \mathbb{R}$, and 
+distinguishing the new expressions by a superscript ${(1)}$. These
+new expressions are:
+\begin{equation}
+m^{(1)} = \frac{1}{2}\sum_i\sum_jpA_{ij}  = p\frac{1}{2}\sum_i\sum_j A_{ij} = pm ,
+\end{equation}
+\begin{equation}
+k_i^{(1)} = \sum_j{pA_{ij}} = p\sum_j{A_{ij}} = pk_i,
+\end{equation}
+and so
+\begin{align*}
+	Q^{(1)}(c) &= \frac{1}{2pm}\sum_i\sum_j\left[ pA_{ij} - \gamma \frac{pk_ipk_j}{2pm} \right] \delta_{ij}(c) \\
+	&= \frac{1}{2m}\sum_i\sum_j\left[ A_{ij} - \gamma \frac{k_ik_j}{2m} \right] \delta_{ij}(c) \\
+	&= Q(c)
+\end{align*}
+Note that as we have shown $Q^{(1)} = Q$ there is no need to go into the remainder of the terms 
+involved in the algorithm, as they all derive from $Q$.
+
+\subsection{First generalisation of expressions approach}
+
+One suggested extension to directed graphs is to modify the expressions 
+involved by adding the `from' case and the `to' case for each term. 
+If we let $B_{ij}$ be the edge weight between nodes $i$ and $j$ in 
+the directed graph, and distinguishing these extended expressions by 
+a superscript $(2)$, the extended expressions become:
+\begin{equation}
+m^{(2)} = \frac{1}{2}\left ( \sum_i\sum_jB_{ij} + \sum_i\sum_jB_{ji}\right)  = \frac{1}{2}\sum_i\sum_j \left( B_{ij} + B_{ji} \right) ,
+\end{equation}
+\begin{equation}
+k_i^{(2)} = \sum_jB_{ij} + \sum_jB_{ji} = \sum_j{\left( B_{ij} + B_{ji} \right)},
+\end{equation}
+and similarly
+\begin{equation}
+	Q^{(2)}(c) = \frac{1}{2m}\sum_i\sum_j\left[ \left( B_{ij} + B_{ji} \right) - \gamma \frac{k_i^{(2)}k_j^{(2)}}{2m} \right] \delta_{ij}(c).
+\end{equation}
+
+Note how this is equivalent to the construction of an undirected graph as 
+per Equation~(\ref{eqn:undirectedAB}). Similarly to above, 
+there is no need to go into the remainder of the terms 
+involved in the algorithm, as they all derive from $Q$.
+
+
+\subsection{Second generalisation of expressions approach}
+
+Another approach to generalising the expressions to the 
+directed case, that still treats incoming and outgoing edges 
+as equally important, is to propose an alternative modularity 
+expression:
+\newcommand{\dkin}[1]{k_{#1}^{\text{in}}}
+\newcommand{\dkout}[1]{k_{#1}^{\text{out}}}
+\begin{equation}
+Q^{(3)}(c) = \frac{1}{2m}\sum_i\sum_j\left[ 2B_{ij} - 2\gamma \frac{\dkin{i}\dkout{j}}{2m} \right] \delta_{ij}(c), \\
+\end{equation}
+where 
+\begin{equation}
+\dkout{i} = \sum_j{B_{ij}} 
+\quad \quad \text{and} \quad \quad
+\dkin{i} = \sum_j{B_{ji}},
+\end{equation}
+so $k_i^{(2)} = \dkin{i} + \dkout{i}$.
+Note I leave the factor of two in the expression for $Q^{(3)}$ so that it 
+remains as comparable to that for $Q^{(2)}$ as possible.
+There is no need for alternative $m$, as it will still be the same as above.
+$Q^{(3)}$ will differ from $Q^{(2)}$ in two ways.
+Firstly, as $k_i^{(2)} = \dkin{i} + \dkout{i}$, 
+\begin{align*}
+\sum_i\sum_j k_i^{(2)} k_j^{(2)} \delta_{ij}(c)  &= \sum_i\sum_j  (\dkin{i} + \dkout{i}) (\dkin{j} + \dkout{j}) \delta_{ij}(c) \\
+ &= \sum_i\sum_j \left[ (\dkin{i}\dkin{j} + \dkout{i}\dkout{j}) + (\dkin{i}\dkout{j} + \dkin{j}\dkout{i}) \right] \delta_{ij}(c). \\
+ &= \sum_i\sum_j \left[ (\dkin{i}\dkin{j} + \dkout{i}\dkout{j}) + 2\dkin{i}\dkout{j} \right] \delta_{ij}(c), \\
+\end{align*}
+and similarly,
+\begin{equation}
+\sum_i\sum_j  \left( B_{ij} + B_{ji} \right) \delta_{ij}(c) = 2\sum_i\sum_j B_{ij} \delta_{ij}(c).
+\end{equation}
+From these two expressions, we can see that 
+\begin{equation}
+Q^{(3)} - Q^{(2)} = \frac{1}{2m}\sum_i\sum_j \gamma \frac{\dkin{i}\dkin{j} + \dkout{i}\dkout{j}}{2m} \delta_{ij}(c).
+\end{equation}
+
+
+\section{Directed Graphs in more detail}
+\label{sec:directedGraphsDetail}
+
+In Section \ref{sec:directedGraphs} we essentially showed three 
+things:
+\begin{itemize}
+	\item How an undirected graph could be constructed from a directed
+	graph, thereby allowing the undirected algorithm to be used for 
+	directed graphs.
+	\item How scaling all edge weights by a non-zero constant would not 
+	affect the modularity function.
+	\item An alternative approach to extending the algorithm to 
+	directed graphs that is not equivalent to first reducing it 
+	to an undirected graph.
+\end{itemize}
+It is this third point that we will explore here.
+Analogously to Sections \ref{sec:initialPass} and \ref{sec:laterPasses} we will 
+break this up into the initial pass and the later passes.
+
+\subsection{Initial pass}
+\label{sec:initialPassDirected}
+
+Continuing with the notation of Section \ref{sec:initialPass}, in which 
+$c(i)$ denotes the community to which node $i$ belongs, 
+and $\alpha = c(a)$, we define
+\newcommand{\dinStot}[1]{\Sigma_{\text{tot}}^{\text{in}(#1)}}
+\newcommand{\doutStot}[1]{\Sigma_{\text{tot}}^{\text{out}(#1)}}
+\begin{equation}
+	\doutStot{\alpha} = \sum_{i \in \alpha}\sum_{j}B_{ij} = \sum_{i \in \alpha}\dkout{i}
+	\quad \quad \text{and} \quad \quad
+	\dinStot{\alpha} = \sum_{i \in \alpha}\sum_{j}B_{ji} = \sum_{i \in \alpha}\dkin{i},
+\end{equation}
+\newcommand{\dinkin}[2]{k_{#1}^{\text{in}(#2)}}
+\newcommand{\doutkin}[2]{k_{#1}^{\text{out}(#2)}}
+\begin{equation}
+	\doutkin{i}{\alpha} = \sum_{j \in \alpha}B_{ij}
+	\quad \quad \text{and} \quad \quad
+	\dinkin{i}{\alpha} = \sum_{j \in \alpha}B_{ji},
+\end{equation}
+and we will entertain one more ambiguous notation choice:
+%\newcommand{\Sin}[1]{\Sigma_{\text{in}}^{#1}}
+\begin{equation}
+	\Sin{\alpha} = \sum_{i \in \alpha}\sum_{j \in \alpha}B_{ij} = \sum_{i \in \alpha}\doutkin{i}{\alpha} = \sum_{i \in \alpha}\dinkin{i}{\alpha}.
+\end{equation}
+
+Analogously to Section \ref{sec:initialPass}, we are interested in how 
+$Q^{(3)}$ will change if we move a node $a$ from its 
+current community $\alpha$, to a new community $\beta$, 
+and analogously this will have two effects -- it will remove the terms 
+from $Q^{(3)}$ related to $a$ in $\alpha$, which we will call $Q^{-(3)}$ 
+and it will add terms related to $a$ in $\beta$, which we will call $Q^{+(3)}$. 
+The total change in $Q^{(3)}$ caused by the movement of $a$ from $\alpha$ to $\beta$ is 
+\begin{equation}
+	\Delta Q^{(3)} = Q^{+(3)} - Q^{-(3)},
+\end{equation}
+where
+\begin{align*}
+Q^{-(3)} &= \frac{1}{2m}\left[ \left( 2B_{aa} - 2\gamma \frac{\dkin{a}\dkout{a}}{2m} \right) 
++ \sum_{i \in \alpha, \, i \neq a} \left( 2B_{ia} + 2B_{ai} - 2\gamma \frac{\dkin{i}\dkout{a}}{2m} - 2\gamma \frac{\dkin{a}\dkout{i}}{2m} \right) \right] \\
+				 &= \frac{1}{2m}\left[ \left( 2B_{aa} - 2\gamma \frac{\dkin{a}\dkout{a}}{2m} \right) 
++ 2(\dinkin{a}{\alpha} - B_{aa}) + 2(\doutkin{a}{\alpha} - B_{aa}) \hdots \right . \\
+ & \quad \quad \quad \quad \quad \quad \left .
+- \frac{2\gamma\dkout{a}}{2m} (\dinStot{\alpha} - \dkin{a}) - \frac{2\gamma\dkin{a}}{2m} (\doutStot{\alpha} - \dkout{a}) \right] \\
+\end{align*}
+and
+\begin{align*}
+Q^{+(3)} &= \frac{1}{2m}\left[ \left( 2B_{aa} - 2\gamma \frac{\dkin{a}\dkout{a}}{2m} \right) 
++ \sum_{i \in \beta} \left( 2B_{ia} + 2B_{ai} - 2\gamma \frac{\dkin{i}\dkout{a}}{2m} - 2\gamma \frac{\dkin{a}\dkout{i}}{2m} \right) \right] \\
+				 &= \frac{1}{2m}\left[ \left( 2B_{aa} - 2\gamma \frac{\dkin{a}\dkout{a}}{2m} \right) 
++ 2\dinkin{a}{\beta} + 2\doutkin{a}{\beta} - \frac{2\gamma\dkout{a}}{2m} \dinStot{\beta}  - \frac{2\gamma\dkin{a}}{2m} \doutStot{\beta} \right] \\
+\end{align*}
+Similarly to Section \ref{sec:initialPass}, the first term in both these expressions is the same, and so cancels, leaving:
+\begin{align*}
+\Delta Q^{(3)} &= \frac{2}{2m}\left[ 
+\left( \dinkin{a}{\beta} + \doutkin{a}{\beta} - \frac{\gamma\dkout{a}}{2m} \dinStot{\beta}  - \frac{\gamma\dkin{a}}{2m} \doutStot{\beta} \right) \right. \\
+& \hspace{-1cm}
+- \left. \left( (\dinkin{a}{\alpha} - B_{aa}) + (\doutkin{a}{\alpha} - B_{aa}) - \frac{\gamma\dkout{a}}{2m} (\dinStot{\alpha} - \dkin{a}) - \frac{\gamma\dkin{a}}{2m} (\doutStot{\alpha} - \dkout{a})  \right) \right] \\
+ &= \frac{2}{2m}\left[ (\dinkin{a}{\beta}-\dinkin{a}{\alpha}) + (\doutkin{a}{\beta}-\doutkin{a}{\alpha}) + 2B_{aa} \right. \\
+& \hspace{-1cm} \left.
+- \frac{\gamma\dkout{a}}{2m} (\dinStot{\beta}-\dinStot{\alpha}) - \frac{\gamma\dkin{a}}{2m} (\doutStot{\beta} - \doutStot{\alpha}) - \frac{2\gamma\dkin{a}\dkout{a}}{2m} \right]
+\end{align*}
+
+
+
+\subsection{Later passes}
+\label{sec:laterPassesDirected}
+
+In phase two a `meta-graph' is constructed where nodes correspond to 
+the communities found in the preceding phase one step, and edge weight
+between two such communities (nodes, in the meta-graph)
+$\alpha$ and $\beta$ are defined to be
+\begin{equation}
+	B_{\alpha \beta}^* = \sum_{i \in \alpha}\sum_{j \in \beta}B_{ij}.
+	\label{eqn:Bij*}
+\end{equation} 
+Note that $i$ and $j$ refer to nodes in the original graph, not nodes 
+in the previous graph, and so holds any meta-graph, not just the first.
+Also note that this definition of $B^*_{\alpha \beta}$ allows for 
+$B^*_{\alpha \alpha}$ to be non-zero, in fact
+\begin{equation}
+B_{\alpha \alpha}^* = \sum_{i \in \alpha}\sum_{j \in \alpha}B_{ij} = \Sin{\alpha}.
+\end{equation} 
+
+In this newly constructed graph, $\alpha$ and $\beta$ are nodes, but 
+also refer to communities (sets of nodes) in the original graph, and I 
+use these two interpretations interchangeably, completely analogously to 
+Section \ref{sec:laterPasses}.
+
+The results of Section~\ref{sec:initialPassDirected} generalise to these meta-graphs,
+and the generalised results mirror those of Section~\ref{sec:initialPassDirected} closely
+-- I distinguish the new results from those of Section~\ref{sec:initialPassDirected} by a 
+superscript $*$.
+I use $i$ and $j$ to denote nodes of the original graph as in Sections~\ref{sec:initialPass}
+and \ref{sec:initialPassDirected}, 
+and use $z$ and $w$ to denote nodes of the meta-graph (communities of the original).
+I use analogous notation to Section~\ref{sec:initialPass}, $c^*(z)$, to 
+denote the community to which node $z$ of the meta-graph belongs, 
+and let $\mathfrak{a}$ be the community that the node $\alpha$ belongs to, 
+i.e., $\mathfrak{a} = c^*(\alpha) $.
+
+Given this notation, we get all the same results as in \ref{sec:laterPasses}, but 
+each split into two cases `out' and `in', separating by direction, essentially, so
+\newcommand{\dkinStar}[1]{k_{#1}^{\text{in} *}}
+\newcommand{\dkoutStar}[1]{k_{#1}^{\text{out} *}}
+\begin{equation}
+\dkoutStar{z} = \sum_w{B_{zw}^*} = \sum_w\sum_{i \in z}\sum_{j \in w}B_{ij} = \sum_{i \in z}\sum_jB_{ij} = \doutStot{z},
+\end{equation}
+\begin{equation}
+\dkinStar{z}  = \sum_w{B_{wz}^*} = \sum_w\sum_{i \in z}\sum_{j \in w}B_{ji} = \sum_{i \in z}\sum_jB_{ji} = \dinStot{z},
+\end{equation}
+\newcommand{\dinStotStar}[1]{\Sigma_{\text{tot}}^{\text{in}(#1) *}}
+\newcommand{\doutStotStar}[1]{\Sigma_{\text{tot}}^{\text{out}(#1) *}}
+\begin{equation}
+	\doutStotStar{\mathfrak{a}} = \sum_{z \in \mathfrak{a}}\sum_{w}B_{zw}^* = \sum_{z \in \mathfrak{a}}\dkoutStar{z} = \sum_{z \in \mathfrak{a}}\doutStot{z},
+\end{equation}
+\begin{equation}
+	\dinStotStar{\mathfrak{a}}  = \sum_{z \in \mathfrak{a}}\sum_{w}B_{wz}^* = \sum_{z \in \mathfrak{a}}\dkinStar{z}  = \sum_{z \in \mathfrak{a}}\dinStot{z},
+\end{equation}
+\newcommand{\dinkinStar}[2]{k_{#1}^{\text{in}(#2) *}}
+\newcommand{\doutkinStar}[2]{k_{#1}^{\text{out}(#2) *}}
+\begin{equation}
+	\doutkinStar{z}{\mathfrak{a}} = \sum_{w \in \mathfrak{a}}{B_{zw}^*} = \sum_{w \in \mathfrak{a}}{\sum_{i \in z}\sum_{j \in w}B_{ij}},
+\end{equation}
+\begin{equation}
+	\dinkinStar{z}{\mathfrak{a}}  = \sum_{w \in \mathfrak{a}}{B_{wz}^*} = \sum_{w \in \mathfrak{a}}{\sum_{i \in z}\sum_{j \in w}B_{ji}},
+\end{equation}
+and
+\begin{equation}
+\Sin{\mathfrak{a} *} = \sum_{z \in \mathfrak{a}}\sum_{w \in \mathfrak{a}}A_{zw}^* = \sum_{z \in \mathfrak{a}}\kin{z}{\mathfrak{a} *} = \sum_{z \in \mathfrak{a}}\sum_{w \in \mathfrak{a}}{\sum_{i \in z}\sum_{j \in w}A_{ij}}.
+	%\label{eqn:Sin}
+\end{equation}
+
+If we let $\mathfrak{b}$ denote the community to which we are considering moving $\alpha$,
+then the expression for $\Delta Q$ from Section~\ref{sec:initialPassDirected} simply generalises as
+\begin{align*}
+\Delta Q^{(3)} &= \frac{2}{2m}\left[ (\dinkinStar{\alpha}{\mathfrak{b}}-\dinkinStar{\alpha}{\mathfrak{a}}) + (\doutkinStar{\alpha}{\mathfrak{b}}-\doutkinStar{\alpha}{\mathfrak{a}}) + 2B_{\alpha\alpha}^* \right. \\
+& \hspace{-1cm} \left.
+- \frac{\gamma\dkoutStar{\alpha}}{2m} (\dinStotStar{\mathfrak{b}}-\dinStotStar{\mathfrak{a}}) - \frac{\gamma\dkinStar{\alpha}}{2m} (\doutStotStar{\mathfrak{b}} - \doutStotStar{\mathfrak{a}}) - \frac{2\gamma\dkinStar{\alpha}\dkoutStar{\alpha}}{2m} \right]
+\end{align*}
+
+
+\end{document}
diff --git a/vendor/gonum.org/v1/gonum/graph/community/louvain_common.go b/vendor/gonum.org/v1/gonum/graph/community/louvain_common.go
new file mode 100644
index 00000000..987776c0
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/community/louvain_common.go
@@ -0,0 +1,415 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package community
+
+import (
+	"fmt"
+	"math/rand"
+	"sort"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/set"
+)
+
+// Q returns the modularity Q score of the graph g subdivided into the
+// given communities at the given resolution. If communities is nil, the
+// unclustered modularity score is returned. The resolution parameter
+// is γ as defined in Reichardt and Bornholdt doi:10.1103/PhysRevE.74.016110.
+// Q will panic if g has any edge with negative edge weight.
+//
+// If g is undirected, Q is calculated according to
+//  Q = 1/2m \sum_{ij} [ A_{ij} - (\gamma k_i k_j)/2m ] \delta(c_i,c_j),
+// If g is directed, it is calculated according to
+//  Q = 1/m \sum_{ij} [ A_{ij} - (\gamma k_i^in k_j^out)/m ] \delta(c_i,c_j).
+//
+// graph.Undirect may be used as a shim to allow calculation of Q for
+// directed graphs with the undirected modularity function.
+func Q(g graph.Graph, communities [][]graph.Node, resolution float64) float64 {
+	switch g := g.(type) {
+	case graph.Undirected:
+		return qUndirected(g, communities, resolution)
+	case graph.Directed:
+		return qDirected(g, communities, resolution)
+	default:
+		panic(fmt.Sprintf("community: invalid graph type: %T", g))
+	}
+}
+
+// ReducedGraph is a modularised graph.
+type ReducedGraph interface {
+	graph.Graph
+
+	// Communities returns the community memberships
+	// of the nodes in the graph used to generate
+	// the reduced graph.
+	Communities() [][]graph.Node
+
+	// Structure returns the community structure of
+	// the current level of the module clustering.
+	// Each slice in the returned value recursively
+	// describes the membership of a community at
+	// the current level by indexing via the node
+	// ID into the structure of the non-nil
+	// ReducedGraph returned by Expanded, or when the
+	// ReducedGraph is nil, by containing nodes
+	// from the original input graph.
+	//
+	// The returned value should not be mutated.
+	Structure() [][]graph.Node
+
+	// Expanded returns the next lower level of the
+	// module clustering or nil if at the lowest level.
+	//
+	// The returned ReducedGraph will be the same
+	// concrete type as the receiver.
+	Expanded() ReducedGraph
+}
+
+// Modularize returns the hierarchical modularization of g at the given resolution
+// using the Louvain algorithm. If src is nil, rand.Intn is used as the random
+// generator. Modularize will panic if g has any edge with negative edge weight.
+//
+// If g is undirected it is modularised to minimise
+//  Q = 1/2m \sum_{ij} [ A_{ij} - (\gamma k_i k_j)/2m ] \delta(c_i,c_j),
+// If g is directed it is modularised to minimise
+//  Q = 1/m \sum_{ij} [ A_{ij} - (\gamma k_i^in k_j^out)/m ] \delta(c_i,c_j).
+//
+// The concrete type of the ReducedGraph will be a pointer to either a
+// ReducedUndirected or a ReducedDirected depending on the type of g.
+//
+// graph.Undirect may be used as a shim to allow modularization of
+// directed graphs with the undirected modularity function.
+func Modularize(g graph.Graph, resolution float64, src *rand.Rand) ReducedGraph {
+	switch g := g.(type) {
+	case graph.Undirected:
+		return louvainUndirected(g, resolution, src)
+	case graph.Directed:
+		return louvainDirected(g, resolution, src)
+	default:
+		panic(fmt.Sprintf("community: invalid graph type: %T", g))
+	}
+}
+
+// Multiplex is a multiplex graph.
+type Multiplex interface {
+	// Nodes returns the slice of nodes
+	// for the multiplex graph.
+	// All layers must refer to the same
+	// set of nodes.
+	Nodes() []graph.Node
+
+	// Depth returns the number of layers
+	// in the multiplex graph.
+	Depth() int
+}
+
+// QMultiplex returns the modularity Q score of the multiplex graph layers
+// subdivided into the given communities at the given resolutions and weights. Q is
+// returned as the vector of weighted Q scores for each layer of the multiplex graph.
+// If communities is nil, the unclustered modularity score is returned.
+// If weights is nil layers are equally weighted, otherwise the length of
+// weights must equal the number of layers. If resolutions is nil, a resolution
+// of 1.0 is used for all layers, otherwise either a single element slice may be used
+// to specify a global resolution, or the length of resolutions must equal the number
+// of layers. The resolution parameter is γ as defined in Reichardt and Bornholdt
+// doi:10.1103/PhysRevE.74.016110.
+// QMultiplex will panic if the graph has any layer weight-scaled edge with
+// negative edge weight.
+//
+// If g is undirected, Q is calculated according to
+//  Q_{layer} = w_{layer} \sum_{ij} [ A_{layer}*_{ij} - (\gamma_{layer} k_i k_j)/2m_{layer} ] \delta(c_i,c_j),
+// If g is directed, it is calculated according to
+//  Q_{layer} = w_{layer} \sum_{ij} [ A_{layer}*_{ij} - (\gamma_{layer} k_i^in k_j^out)/m_{layer} ] \delta(c_i,c_j).
+//
+// Note that Q values for multiplex graphs are not scaled by the total layer edge weight.
+//
+// graph.Undirect may be used as a shim to allow calculation of Q for
+// directed graphs.
+func QMultiplex(g Multiplex, communities [][]graph.Node, weights, resolutions []float64) []float64 {
+	if weights != nil && len(weights) != g.Depth() {
+		panic("community: weights vector length mismatch")
+	}
+	if resolutions != nil && len(resolutions) != 1 && len(resolutions) != g.Depth() {
+		panic("community: resolutions vector length mismatch")
+	}
+
+	switch g := g.(type) {
+	case UndirectedMultiplex:
+		return qUndirectedMultiplex(g, communities, weights, resolutions)
+	case DirectedMultiplex:
+		return qDirectedMultiplex(g, communities, weights, resolutions)
+	default:
+		panic(fmt.Sprintf("community: invalid graph type: %T", g))
+	}
+}
+
+// ReducedMultiplex is a modularised multiplex graph.
+type ReducedMultiplex interface {
+	Multiplex
+
+	// Communities returns the community memberships
+	// of the nodes in the graph used to generate
+	// the reduced graph.
+	Communities() [][]graph.Node
+
+	// Structure returns the community structure of
+	// the current level of the module clustering.
+	// Each slice in the returned value recursively
+	// describes the membership of a community at
+	// the current level by indexing via the node
+	// ID into the structure of the non-nil
+	// ReducedGraph returned by Expanded, or when the
+	// ReducedGraph is nil, by containing nodes
+	// from the original input graph.
+	//
+	// The returned value should not be mutated.
+	Structure() [][]graph.Node
+
+	// Expanded returns the next lower level of the
+	// module clustering or nil if at the lowest level.
+	//
+	// The returned ReducedGraph will be the same
+	// concrete type as the receiver.
+	Expanded() ReducedMultiplex
+}
+
+// ModularizeMultiplex returns the hierarchical modularization of g at the given resolution
+// using the Louvain algorithm. If all is true and g have negatively weighted layers, all
+// communities will be searched during the modularization. If src is nil, rand.Intn is
+// used as the random generator. ModularizeMultiplex will panic if g has any edge with
+// edge weight that does not sign-match the layer weight.
+//
+// If g is undirected it is modularised to minimise
+//  Q = \sum w_{layer} \sum_{ij} [ A_{layer}*_{ij} - (\gamma_{layer} k_i k_j)/2m ] \delta(c_i,c_j).
+// If g is directed it is modularised to minimise
+//  Q = \sum w_{layer} \sum_{ij} [ A_{layer}*_{ij} - (\gamma_{layer} k_i^in k_j^out)/m_{layer} ] \delta(c_i,c_j).
+//
+// The concrete type of the ReducedMultiplex will be a pointer to a
+// ReducedUndirectedMultiplex.
+//
+// graph.Undirect may be used as a shim to allow modularization of
+// directed graphs with the undirected modularity function.
+func ModularizeMultiplex(g Multiplex, weights, resolutions []float64, all bool, src *rand.Rand) ReducedMultiplex {
+	if weights != nil && len(weights) != g.Depth() {
+		panic("community: weights vector length mismatch")
+	}
+	if resolutions != nil && len(resolutions) != 1 && len(resolutions) != g.Depth() {
+		panic("community: resolutions vector length mismatch")
+	}
+
+	switch g := g.(type) {
+	case UndirectedMultiplex:
+		return louvainUndirectedMultiplex(g, weights, resolutions, all, src)
+	case DirectedMultiplex:
+		return louvainDirectedMultiplex(g, weights, resolutions, all, src)
+	default:
+		panic(fmt.Sprintf("community: invalid graph type: %T", g))
+	}
+}
+
+// undirectedEdges is the edge structure of a reduced undirected graph.
+type undirectedEdges struct {
+	// edges and weights is the set
+	// of edges between nodes.
+	// weights is keyed such that
+	// the first element of the key
+	// is less than the second.
+	edges   [][]int
+	weights map[[2]int]float64
+}
+
+// directedEdges is the edge structure of a reduced directed graph.
+type directedEdges struct {
+	// edgesFrom, edgesTo and weights
+	// is the set of edges between nodes.
+	edgesFrom [][]int
+	edgesTo   [][]int
+	weights   map[[2]int]float64
+}
+
+// isValidID returns whether id is a valid ID for a community,
+// multiplexCommunity or node. These are all graph.Node types
+// stored in []T with a mapping between their index and their ID
+// so IDs must be positive and fit within the int type.
+func isValidID(id int64) bool {
+	return id == int64(int(id)) && id >= 0
+}
+
+// community is a reduced graph node describing its membership.
+type community struct {
+	// community graphs are internal, in-memory
+	// with dense IDs, so id is always an int.
+	id int
+
+	nodes []graph.Node
+
+	weight float64
+}
+
+func (n community) ID() int64 { return int64(n.id) }
+
+// edge is a reduced graph edge.
+type edge struct {
+	from, to community
+	weight   float64
+}
+
+func (e edge) From() graph.Node { return e.from }
+func (e edge) To() graph.Node   { return e.to }
+func (e edge) Weight() float64  { return e.weight }
+
+// multiplexCommunity is a reduced multiplex graph node describing its membership.
+type multiplexCommunity struct {
+	// community graphs are internal, in-memory
+	// with dense IDs, so id is always an int.
+	id int
+
+	nodes []graph.Node
+
+	weights []float64
+}
+
+func (n multiplexCommunity) ID() int64 { return int64(n.id) }
+
+// multiplexEdge is a reduced graph edge for a multiplex graph.
+type multiplexEdge struct {
+	from, to multiplexCommunity
+	weight   float64
+}
+
+func (e multiplexEdge) From() graph.Node { return e.from }
+func (e multiplexEdge) To() graph.Node   { return e.to }
+func (e multiplexEdge) Weight() float64  { return e.weight }
+
+// commIdx is an index of a node in a community held by a localMover.
+type commIdx struct {
+	community int
+	node      int
+}
+
+// node is defined to avoid an import of .../graph/simple. node is
+// used in in-memory, dense ID graphs and so is always an int.
+type node int
+
+func (n node) ID() int64 { return int64(n) }
+
+// minTaker is a set iterator.
+type minTaker interface {
+	TakeMin(p *int) bool
+}
+
+// dense is a dense integer set iterator.
+type dense struct {
+	pos int
+	n   int
+}
+
+// TakeMin mimics intsets.Sparse TakeMin for dense sets. If the dense
+// iterator position is less than the iterator size, TakeMin sets *p
+// to the the iterator position and increments the position and returns
+// true.
+// Otherwise, it returns false and *p is undefined.
+func (d *dense) TakeMin(p *int) bool {
+	if d.pos >= d.n {
+		return false
+	}
+	*p = d.pos
+	d.pos++
+	return true
+}
+
+// slice is a sparse integer set iterator.
+type slice struct {
+	pos   int
+	elems []int
+}
+
+// newSlice returns a new slice of elements from s, sorted ascending.
+func newSlice(s set.Ints) *slice {
+	elems := make([]int, 0, len(s))
+	for i := range s {
+		elems = append(elems, i)
+	}
+	sort.Ints(elems)
+	return &slice{elems: elems}
+}
+
+// TakeMin mimics intsets.Sparse TakeMin for a sorted set. If the set
+// iterator position is less than the iterator size, TakeMin sets *p
+// to the the iterator position's element and increments the position
+// and returns true.
+// Otherwise, it returns false and *p is undefined.
+func (s *slice) TakeMin(p *int) bool {
+	if s.pos >= len(s.elems) {
+		return false
+	}
+	*p = s.elems[s.pos]
+	s.pos++
+	return true
+}
+
+const (
+	negativeWeight = "community: unexpected negative edge weight"
+	positiveWeight = "community: unexpected positive edge weight"
+)
+
+// positiveWeightFuncFor returns a constructed weight function for the
+// positively weighted g. Unweighted graphs have unit weight for existing
+// edges.
+func positiveWeightFuncFor(g graph.Graph) func(x, y graph.Node) float64 {
+	if wg, ok := g.(graph.Weighted); ok {
+		return func(x, y graph.Node) float64 {
+			w, ok := wg.Weight(x, y)
+			if !ok {
+				return 0
+			}
+			if w < 0 {
+				panic(negativeWeight)
+			}
+			return w
+		}
+	}
+	return func(x, y graph.Node) float64 {
+		e := g.Edge(x, y)
+		if e == nil {
+			return 0
+		}
+		return 1
+	}
+}
+
+// negativeWeightFuncFor returns a constructed weight function for the
+// negatively weighted g. Unweighted graphs have unit weight for existing
+// edges.
+func negativeWeightFuncFor(g graph.Graph) func(x, y graph.Node) float64 {
+	if wg, ok := g.(graph.Weighted); ok {
+		return func(x, y graph.Node) float64 {
+			w, ok := wg.Weight(x, y)
+			if !ok {
+				return 0
+			}
+			if w > 0 {
+				panic(positiveWeight)
+			}
+			return -w
+		}
+	}
+	return func(x, y graph.Node) float64 {
+		e := g.Edge(x, y)
+		if e == nil {
+			return 0
+		}
+		return 1
+	}
+}
+
+// depth returns max(1, len(weights)). It is used to ensure
+// that multiplex community weights are properly initialised.
+func depth(weights []float64) int {
+	if weights == nil {
+		return 1
+	}
+	return len(weights)
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/community/louvain_directed.go b/vendor/gonum.org/v1/gonum/graph/community/louvain_directed.go
new file mode 100644
index 00000000..3bd5a319
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/community/louvain_directed.go
@@ -0,0 +1,650 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package community
+
+import (
+	"math"
+	"math/rand"
+	"sort"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/ordered"
+	"gonum.org/v1/gonum/graph/internal/set"
+)
+
+// qDirected returns the modularity Q score of the graph g subdivided into the
+// given communities at the given resolution. If communities is nil, the
+// unclustered modularity score is returned. The resolution parameter
+// is γ as defined in Reichardt and Bornholdt doi:10.1103/PhysRevE.74.016110.
+// qDirected will panic if g has any edge with negative edge weight.
+//
+//  Q = 1/m \sum_{ij} [ A_{ij} - (\gamma k_i^in k_j^out)/m ] \delta(c_i,c_j)
+//
+func qDirected(g graph.Directed, communities [][]graph.Node, resolution float64) float64 {
+	nodes := g.Nodes()
+	weight := positiveWeightFuncFor(g)
+
+	// Calculate the total edge weight of the graph
+	// and the table of penetrating edge weight sums.
+	var m float64
+	k := make(map[int64]directedWeights, len(nodes))
+	for _, n := range nodes {
+		var wOut float64
+		u := n
+		for _, v := range g.From(u) {
+			wOut += weight(u, v)
+		}
+		var wIn float64
+		v := n
+		for _, u := range g.To(v) {
+			wIn += weight(u, v)
+		}
+		w := weight(n, n)
+		m += w + wOut // We only need to count edges once.
+		k[n.ID()] = directedWeights{out: w + wOut, in: w + wIn}
+	}
+
+	if communities == nil {
+		var q float64
+		for _, u := range nodes {
+			kU := k[u.ID()]
+			q += weight(u, u) - resolution*kU.out*kU.in/m
+		}
+		return q / m
+	}
+
+	var q float64
+	for _, c := range communities {
+		for _, u := range c {
+			kU := k[u.ID()]
+			for _, v := range c {
+				kV := k[v.ID()]
+				q += weight(u, v) - resolution*kU.out*kV.in/m
+			}
+		}
+	}
+	return q / m
+}
+
+// louvainDirected returns the hierarchical modularization of g at the given
+// resolution using the Louvain algorithm. If src is nil, rand.Intn is used
+// as the random generator. louvainDirected will panic if g has any edge with negative
+// edge weight.
+func louvainDirected(g graph.Directed, resolution float64, src *rand.Rand) ReducedGraph {
+	// See louvain.tex for a detailed description
+	// of the algorithm used here.
+
+	c := reduceDirected(g, nil)
+	rnd := rand.Intn
+	if src != nil {
+		rnd = src.Intn
+	}
+	for {
+		l := newDirectedLocalMover(c, c.communities, resolution)
+		if l == nil {
+			return c
+		}
+		if done := l.localMovingHeuristic(rnd); done {
+			return c
+		}
+		c = reduceDirected(c, l.communities)
+	}
+}
+
+// ReducedDirected is a directed graph of communities derived from a
+// parent graph by reduction.
+type ReducedDirected struct {
+	// nodes is the set of nodes held
+	// by the graph. In a ReducedDirected
+	// the node ID is the index into
+	// nodes.
+	nodes []community
+	directedEdges
+
+	// communities is the community
+	// structure of the graph.
+	communities [][]graph.Node
+
+	parent *ReducedDirected
+}
+
+var (
+	reducedDirected = (*ReducedDirected)(nil)
+
+	_ graph.WeightedDirected = reducedDirected
+	_ ReducedGraph           = reducedDirected
+)
+
+// Communities returns the community memberships of the nodes in the
+// graph used to generate the reduced graph.
+func (g *ReducedDirected) Communities() [][]graph.Node {
+	communities := make([][]graph.Node, len(g.communities))
+	if g.parent == nil {
+		for i, members := range g.communities {
+			comm := make([]graph.Node, len(members))
+			for j, n := range members {
+				nodes := g.nodes[n.ID()].nodes
+				if len(nodes) != 1 {
+					panic("community: unexpected number of nodes in base graph community")
+				}
+				comm[j] = nodes[0]
+			}
+			communities[i] = comm
+		}
+		return communities
+	}
+	sub := g.parent.Communities()
+	for i, members := range g.communities {
+		var comm []graph.Node
+		for _, n := range members {
+			comm = append(comm, sub[n.ID()]...)
+		}
+		communities[i] = comm
+	}
+	return communities
+}
+
+// Structure returns the community structure of the current level of
+// the module clustering. The first index of the returned value
+// corresponds to the index of the nodes in the next higher level if
+// it exists. The returned value should not be mutated.
+func (g *ReducedDirected) Structure() [][]graph.Node {
+	return g.communities
+}
+
+// Expanded returns the next lower level of the module clustering or nil
+// if at the lowest level.
+func (g *ReducedDirected) Expanded() ReducedGraph {
+	return g.parent
+}
+
+// reduceDirected returns a reduced graph constructed from g divided
+// into the given communities. The communities value is mutated
+// by the call to reduceDirected. If communities is nil and g is a
+// ReducedDirected, it is returned unaltered.
+func reduceDirected(g graph.Directed, communities [][]graph.Node) *ReducedDirected {
+	if communities == nil {
+		if r, ok := g.(*ReducedDirected); ok {
+			return r
+		}
+
+		nodes := g.Nodes()
+		// TODO(kortschak) This sort is necessary really only
+		// for testing. In practice we would not be using the
+		// community provided by the user for a Q calculation.
+		// Probably we should use a function to map the
+		// communities in the test sets to the remapped order.
+		sort.Sort(ordered.ByID(nodes))
+		communities = make([][]graph.Node, len(nodes))
+		for i := range nodes {
+			communities[i] = []graph.Node{node(i)}
+		}
+
+		weight := positiveWeightFuncFor(g)
+		r := ReducedDirected{
+			nodes: make([]community, len(nodes)),
+			directedEdges: directedEdges{
+				edgesFrom: make([][]int, len(nodes)),
+				edgesTo:   make([][]int, len(nodes)),
+				weights:   make(map[[2]int]float64),
+			},
+			communities: communities,
+		}
+		communityOf := make(map[int64]int, len(nodes))
+		for i, n := range nodes {
+			r.nodes[i] = community{id: i, nodes: []graph.Node{n}}
+			communityOf[n.ID()] = i
+		}
+		for _, n := range nodes {
+			id := communityOf[n.ID()]
+
+			var out []int
+			u := n
+			for _, v := range g.From(u) {
+				vid := communityOf[v.ID()]
+				if vid != id {
+					out = append(out, vid)
+				}
+				r.weights[[2]int{id, vid}] = weight(u, v)
+			}
+			r.edgesFrom[id] = out
+
+			var in []int
+			v := n
+			for _, u := range g.To(v) {
+				uid := communityOf[u.ID()]
+				if uid != id {
+					in = append(in, uid)
+				}
+				r.weights[[2]int{uid, id}] = weight(u, v)
+			}
+			r.edgesTo[id] = in
+		}
+		return &r
+	}
+
+	// Remove zero length communities destructively.
+	var commNodes int
+	for i := 0; i < len(communities); {
+		comm := communities[i]
+		if len(comm) == 0 {
+			communities[i] = communities[len(communities)-1]
+			communities[len(communities)-1] = nil
+			communities = communities[:len(communities)-1]
+		} else {
+			commNodes += len(comm)
+			i++
+		}
+	}
+
+	r := ReducedDirected{
+		nodes: make([]community, len(communities)),
+		directedEdges: directedEdges{
+			edgesFrom: make([][]int, len(communities)),
+			edgesTo:   make([][]int, len(communities)),
+			weights:   make(map[[2]int]float64),
+		},
+	}
+	r.communities = make([][]graph.Node, len(communities))
+	for i := range r.communities {
+		r.communities[i] = []graph.Node{node(i)}
+	}
+	if g, ok := g.(*ReducedDirected); ok {
+		// Make sure we retain the truncated
+		// community structure.
+		g.communities = communities
+		r.parent = g
+	}
+	weight := positiveWeightFuncFor(g)
+	communityOf := make(map[int64]int, commNodes)
+	for i, comm := range communities {
+		r.nodes[i] = community{id: i, nodes: comm}
+		for _, n := range comm {
+			communityOf[n.ID()] = i
+		}
+	}
+	for id, comm := range communities {
+		var out, in []int
+		for _, n := range comm {
+			u := n
+			for _, v := range comm {
+				r.nodes[id].weight += weight(u, v)
+			}
+
+			for _, v := range g.From(u) {
+				vid := communityOf[v.ID()]
+				found := false
+				for _, e := range out {
+					if e == vid {
+						found = true
+						break
+					}
+				}
+				if !found && vid != id {
+					out = append(out, vid)
+				}
+				// Add half weights because the other
+				// ends of edges are also counted.
+				r.weights[[2]int{id, vid}] += weight(u, v) / 2
+			}
+
+			v := n
+			for _, u := range g.To(v) {
+				uid := communityOf[u.ID()]
+				found := false
+				for _, e := range in {
+					if e == uid {
+						found = true
+						break
+					}
+				}
+				if !found && uid != id {
+					in = append(in, uid)
+				}
+				// Add half weights because the other
+				// ends of edges are also counted.
+				r.weights[[2]int{uid, id}] += weight(u, v) / 2
+			}
+		}
+		r.edgesFrom[id] = out
+		r.edgesTo[id] = in
+	}
+	return &r
+}
+
+// Has returns whether the node exists within the graph.
+func (g *ReducedDirected) Has(n graph.Node) bool {
+	id := n.ID()
+	return 0 <= id && id < int64(len(g.nodes))
+}
+
+// Nodes returns all the nodes in the graph.
+func (g *ReducedDirected) Nodes() []graph.Node {
+	nodes := make([]graph.Node, len(g.nodes))
+	for i := range g.nodes {
+		nodes[i] = node(i)
+	}
+	return nodes
+}
+
+// From returns all nodes in g that can be reached directly from u.
+func (g *ReducedDirected) From(u graph.Node) []graph.Node {
+	out := g.edgesFrom[u.ID()]
+	nodes := make([]graph.Node, len(out))
+	for i, vid := range out {
+		nodes[i] = g.nodes[vid]
+	}
+	return nodes
+}
+
+// To returns all nodes in g that can reach directly to v.
+func (g *ReducedDirected) To(v graph.Node) []graph.Node {
+	in := g.edgesTo[v.ID()]
+	nodes := make([]graph.Node, len(in))
+	for i, uid := range in {
+		nodes[i] = g.nodes[uid]
+	}
+	return nodes
+}
+
+// HasEdgeBetween returns whether an edge exists between nodes x and y.
+func (g *ReducedDirected) HasEdgeBetween(x, y graph.Node) bool {
+	xid := x.ID()
+	yid := y.ID()
+	if xid == yid || !isValidID(xid) || !isValidID(yid) {
+		return false
+	}
+	_, ok := g.weights[[2]int{int(xid), int(yid)}]
+	if ok {
+		return true
+	}
+	_, ok = g.weights[[2]int{int(yid), int(xid)}]
+	return ok
+}
+
+// HasEdgeFromTo returns whether an edge exists from node u to v.
+func (g *ReducedDirected) HasEdgeFromTo(u, v graph.Node) bool {
+	uid := u.ID()
+	vid := v.ID()
+	if uid == vid || !isValidID(uid) || !isValidID(vid) {
+		return false
+	}
+	_, ok := g.weights[[2]int{int(uid), int(vid)}]
+	return ok
+}
+
+// Edge returns the edge from u to v if such an edge exists and nil otherwise.
+// The node v must be directly reachable from u as defined by the From method.
+func (g *ReducedDirected) Edge(u, v graph.Node) graph.Edge {
+	return g.WeightedEdge(u, v)
+}
+
+// WeightedEdge returns the weighted edge from u to v if such an edge exists and nil otherwise.
+// The node v must be directly reachable from u as defined by the From method.
+func (g *ReducedDirected) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
+	uid := u.ID()
+	vid := v.ID()
+	if uid == vid || !isValidID(uid) || !isValidID(vid) {
+		return nil
+	}
+	w, ok := g.weights[[2]int{int(uid), int(vid)}]
+	if !ok {
+		return nil
+	}
+	return edge{from: g.nodes[uid], to: g.nodes[vid], weight: w}
+}
+
+// Weight returns the weight for the edge between x and y if Edge(x, y) returns a non-nil Edge.
+// If x and y are the same node the internal node weight is returned. If there is no joining
+// edge between the two nodes the weight value returned is zero. Weight returns true if an edge
+// exists between x and y or if x and y have the same ID, false otherwise.
+func (g *ReducedDirected) Weight(x, y graph.Node) (w float64, ok bool) {
+	xid := x.ID()
+	yid := y.ID()
+	if !isValidID(xid) || !isValidID(yid) {
+		return 0, false
+	}
+	if xid == yid {
+		return g.nodes[xid].weight, true
+	}
+	w, ok = g.weights[[2]int{int(xid), int(yid)}]
+	return w, ok
+}
+
+// directedLocalMover is a step in graph modularity optimization.
+type directedLocalMover struct {
+	g *ReducedDirected
+
+	// nodes is the set of working nodes.
+	nodes []graph.Node
+	// edgeWeightsOf is the weighted degree
+	// of each node indexed by ID.
+	edgeWeightsOf []directedWeights
+
+	// m is the total sum of edge
+	// weights in g.
+	m float64
+
+	// weight is the weight function
+	// provided by g or a function
+	// that returns the Weight value
+	// of the non-nil edge between x
+	// and y.
+	weight func(x, y graph.Node) float64
+
+	// communities is the current
+	// division of g.
+	communities [][]graph.Node
+	// memberships is a mapping between
+	// node ID and community membership.
+	memberships []int
+
+	// resolution is the Reichardt and
+	// Bornholdt γ parameter as defined
+	// in doi:10.1103/PhysRevE.74.016110.
+	resolution float64
+
+	// moved indicates that a call to
+	// move has been made since the last
+	// call to shuffle.
+	moved bool
+
+	// changed indicates that a move
+	// has been made since the creation
+	// of the local mover.
+	changed bool
+}
+
+type directedWeights struct {
+	out, in float64
+}
+
+// newDirectedLocalMover returns a new directedLocalMover initialized with
+// the graph g, a set of communities and a modularity resolution parameter.
+// The node IDs of g must be contiguous in [0,n) where n is the number of
+// nodes.
+// If g has a zero edge weight sum, nil is returned.
+func newDirectedLocalMover(g *ReducedDirected, communities [][]graph.Node, resolution float64) *directedLocalMover {
+	nodes := g.Nodes()
+	l := directedLocalMover{
+		g:             g,
+		nodes:         nodes,
+		edgeWeightsOf: make([]directedWeights, len(nodes)),
+		communities:   communities,
+		memberships:   make([]int, len(nodes)),
+		resolution:    resolution,
+		weight:        positiveWeightFuncFor(g),
+	}
+
+	// Calculate the total edge weight of the graph
+	// and degree weights for each node.
+	for _, n := range l.nodes {
+		u := n
+		var wOut float64
+		for _, v := range g.From(u) {
+			wOut += l.weight(u, v)
+		}
+
+		v := n
+		var wIn float64
+		for _, u := range g.To(v) {
+			wIn += l.weight(u, v)
+		}
+
+		w := l.weight(n, n)
+		l.edgeWeightsOf[n.ID()] = directedWeights{out: w + wOut, in: w + wIn}
+		l.m += w + wOut
+	}
+
+	// Assign membership mappings.
+	for i, c := range communities {
+		for _, n := range c {
+			l.memberships[n.ID()] = i
+		}
+	}
+
+	return &l
+}
+
+// localMovingHeuristic performs the Louvain local moving heuristic until
+// no further moves can be made. It returns a boolean indicating that the
+// directedLocalMover has not made any improvement to the community structure and
+// so the Louvain algorithm is done.
+func (l *directedLocalMover) localMovingHeuristic(rnd func(int) int) (done bool) {
+	for {
+		l.shuffle(rnd)
+		for _, n := range l.nodes {
+			dQ, dst, src := l.deltaQ(n)
+			if dQ <= 0 {
+				continue
+			}
+			l.move(dst, src)
+		}
+		if !l.moved {
+			return !l.changed
+		}
+	}
+}
+
+// shuffle performs a Fisher-Yates shuffle on the nodes held by the
+// directedLocalMover using the random source rnd which should return an
+// integer in the range [0,n).
+func (l *directedLocalMover) shuffle(rnd func(n int) int) {
+	l.moved = false
+	for i := range l.nodes[:len(l.nodes)-1] {
+		j := i + rnd(len(l.nodes)-i)
+		l.nodes[i], l.nodes[j] = l.nodes[j], l.nodes[i]
+	}
+}
+
+// move moves the node at src to the community at dst.
+func (l *directedLocalMover) move(dst int, src commIdx) {
+	l.moved = true
+	l.changed = true
+
+	srcComm := l.communities[src.community]
+	n := srcComm[src.node]
+
+	l.memberships[n.ID()] = dst
+
+	l.communities[dst] = append(l.communities[dst], n)
+	srcComm[src.node], srcComm[len(srcComm)-1] = srcComm[len(srcComm)-1], nil
+	l.communities[src.community] = srcComm[:len(srcComm)-1]
+}
+
+// deltaQ returns the highest gain in modularity attainable by moving
+// n from its current community to another connected community and
+// the index of the chosen destination. The index into the directedLocalMover's
+// communities field is returned in src if n is in communities.
+func (l *directedLocalMover) deltaQ(n graph.Node) (deltaQ float64, dst int, src commIdx) {
+	id := n.ID()
+
+	a_aa := l.weight(n, n)
+	k_a := l.edgeWeightsOf[id]
+	m := l.m
+	gamma := l.resolution
+
+	// Find communities connected to n.
+	connected := make(set.Ints)
+	// The following for loop is equivalent to:
+	//
+	//  for _, v := range l.g.From(n) {
+	//  	connected.Add(l.memberships[v.ID()])
+	//  }
+	//  for _, v := range l.g.To(n) {
+	//  	connected.Add(l.memberships[v.ID()])
+	//  }
+	//
+	// This is done to avoid two allocations.
+	for _, vid := range l.g.edgesFrom[id] {
+		connected.Add(l.memberships[vid])
+	}
+	for _, vid := range l.g.edgesTo[id] {
+		connected.Add(l.memberships[vid])
+	}
+	// Insert the node's own community.
+	connected.Add(l.memberships[id])
+
+	candidates := make([]int, 0, len(connected))
+	for i := range connected {
+		candidates = append(candidates, i)
+	}
+	sort.Ints(candidates)
+
+	// Calculate the highest modularity gain
+	// from moving into another community and
+	// keep the index of that community.
+	var dQremove float64
+	dQadd, dst, src := math.Inf(-1), -1, commIdx{-1, -1}
+	for _, i := range candidates {
+		c := l.communities[i]
+		var k_aC, sigma_totC directedWeights // C is a substitution for ^𝛼 or ^𝛽.
+		var removal bool
+		for j, u := range c {
+			uid := u.ID()
+			if uid == id {
+				if src.community != -1 {
+					panic("community: multiple sources")
+				}
+				src = commIdx{i, j}
+				removal = true
+			}
+
+			k_aC.in += l.weight(u, n)
+			k_aC.out += l.weight(n, u)
+			// sigma_totC could be kept for each community
+			// and updated for moves, changing the calculation
+			// of sigma_totC here from O(n_c) to O(1), but
+			// in practice the time savings do not appear
+			// to be compelling and do not make up for the
+			// increase in code complexity and space required.
+			w := l.edgeWeightsOf[uid]
+			sigma_totC.in += w.in
+			sigma_totC.out += w.out
+		}
+
+		// See louvain.tex for a derivation of these equations.
+		switch {
+		case removal:
+			// The community c was the current community,
+			// so calculate the change due to removal.
+			dQremove = (k_aC.in /*^𝛼*/ - a_aa) + (k_aC.out /*^𝛼*/ - a_aa) -
+				gamma*(k_a.in*(sigma_totC.out /*^𝛼*/ -k_a.out)+k_a.out*(sigma_totC.in /*^𝛼*/ -k_a.in))/m
+
+		default:
+			// Otherwise calculate the change due to an addition
+			// to c and retain if it is the current best.
+			dQ := k_aC.in /*^𝛽*/ + k_aC.out /*^𝛽*/ -
+				gamma*(k_a.in*sigma_totC.out /*^𝛽*/ +k_a.out*sigma_totC.in /*^𝛽*/)/m
+
+			if dQ > dQadd {
+				dQadd = dQ
+				dst = i
+			}
+		}
+	}
+
+	return (dQadd - dQremove) / m, dst, src
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/community/louvain_directed_multiplex.go b/vendor/gonum.org/v1/gonum/graph/community/louvain_directed_multiplex.go
new file mode 100644
index 00000000..967ba758
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/community/louvain_directed_multiplex.go
@@ -0,0 +1,888 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package community
+
+import (
+	"fmt"
+	"math"
+	"math/rand"
+	"sort"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/ordered"
+	"gonum.org/v1/gonum/graph/internal/set"
+)
+
+// DirectedMultiplex is a directed multiplex graph.
+type DirectedMultiplex interface {
+	Multiplex
+
+	// Layer returns the lth layer of the
+	// multiplex graph.
+	Layer(l int) graph.Directed
+}
+
+// qDirectedMultiplex returns the modularity Q score of the multiplex graph layers
+// subdivided into the given communities at the given resolutions and weights. Q is
+// returned as the vector of weighted Q scores for each layer of the multiplex graph.
+// If communities is nil, the unclustered modularity score is returned.
+// If weights is nil layers are equally weighted, otherwise the length of
+// weights must equal the number of layers. If resolutions is nil, a resolution
+// of 1.0 is used for all layers, otherwise either a single element slice may be used
+// to specify a global resolution, or the length of resolutions must equal the number
+// of layers. The resolution parameter is γ as defined in Reichardt and Bornholdt
+// doi:10.1103/PhysRevE.74.016110.
+// qUndirectedMultiplex will panic if the graph has any layer weight-scaled edge with
+// negative edge weight.
+//
+//  Q_{layer} = w_{layer} \sum_{ij} [ A_{layer}*_{ij} - (\gamma_{layer} k_i k_j)/2m ] \delta(c_i,c_j)
+//
+// Note that Q values for multiplex graphs are not scaled by the total layer edge weight.
+func qDirectedMultiplex(g DirectedMultiplex, communities [][]graph.Node, weights, resolutions []float64) []float64 {
+	q := make([]float64, g.Depth())
+	nodes := g.Nodes()
+	layerWeight := 1.0
+	layerResolution := 1.0
+	if len(resolutions) == 1 {
+		layerResolution = resolutions[0]
+	}
+	for l := 0; l < g.Depth(); l++ {
+		layer := g.Layer(l)
+
+		if weights != nil {
+			layerWeight = weights[l]
+		}
+		if layerWeight == 0 {
+			continue
+		}
+
+		if len(resolutions) > 1 {
+			layerResolution = resolutions[l]
+		}
+
+		var weight func(x, y graph.Node) float64
+		if layerWeight < 0 {
+			weight = negativeWeightFuncFor(layer)
+		} else {
+			weight = positiveWeightFuncFor(layer)
+		}
+
+		// Calculate the total edge weight of the layer
+		// and the table of penetrating edge weight sums.
+		var m float64
+		k := make(map[int64]directedWeights, len(nodes))
+		for _, n := range nodes {
+			var wOut float64
+			u := n
+			for _, v := range layer.From(u) {
+				wOut += weight(u, v)
+			}
+			var wIn float64
+			v := n
+			for _, u := range layer.To(v) {
+				wIn += weight(u, v)
+			}
+			w := weight(n, n)
+			m += w + wOut // We only need to count edges once.
+			k[n.ID()] = directedWeights{out: w + wOut, in: w + wIn}
+		}
+
+		if communities == nil {
+			var qLayer float64
+			for _, u := range nodes {
+				kU := k[u.ID()]
+				qLayer += weight(u, u) - layerResolution*kU.out*kU.in/m
+			}
+			q[l] = layerWeight * qLayer
+			continue
+		}
+
+		var qLayer float64
+		for _, c := range communities {
+			for _, u := range c {
+				kU := k[u.ID()]
+				for _, v := range c {
+					kV := k[v.ID()]
+					qLayer += weight(u, v) - layerResolution*kU.out*kV.in/m
+				}
+			}
+		}
+		q[l] = layerWeight * qLayer
+	}
+
+	return q
+}
+
+// DirectedLayers implements DirectedMultiplex.
+type DirectedLayers []graph.Directed
+
+// NewDirectedLayers returns a DirectedLayers using the provided layers
+// ensuring there is a match between IDs for each layer.
+func NewDirectedLayers(layers ...graph.Directed) (DirectedLayers, error) {
+	if len(layers) == 0 {
+		return nil, nil
+	}
+	base := make(set.Int64s)
+	for _, n := range layers[0].Nodes() {
+		base.Add(n.ID())
+	}
+	for i, l := range layers[1:] {
+		next := make(set.Int64s)
+		for _, n := range l.Nodes() {
+			next.Add(n.ID())
+		}
+		if !set.Int64sEqual(base, next) {
+			return nil, fmt.Errorf("community: layer ID mismatch between layers: %d", i+1)
+		}
+	}
+	return layers, nil
+}
+
+// Nodes returns the nodes of the receiver.
+func (g DirectedLayers) Nodes() []graph.Node {
+	if len(g) == 0 {
+		return nil
+	}
+	return g[0].Nodes()
+}
+
+// Depth returns the depth of the multiplex graph.
+func (g DirectedLayers) Depth() int { return len(g) }
+
+// Layer returns the lth layer of the multiplex graph.
+func (g DirectedLayers) Layer(l int) graph.Directed { return g[l] }
+
+// louvainDirectedMultiplex returns the hierarchical modularization of g at the given resolution
+// using the Louvain algorithm. If all is true and g has negatively weighted layers, all
+// communities will be searched during the modularization. If src is nil, rand.Intn is
+// used as the random generator. louvainDirectedMultiplex will panic if g has any edge with
+// edge weight that does not sign-match the layer weight.
+//
+// graph.Undirect may be used as a shim to allow modularization of directed graphs.
+func louvainDirectedMultiplex(g DirectedMultiplex, weights, resolutions []float64, all bool, src *rand.Rand) *ReducedDirectedMultiplex {
+	if weights != nil && len(weights) != g.Depth() {
+		panic("community: weights vector length mismatch")
+	}
+	if resolutions != nil && len(resolutions) != 1 && len(resolutions) != g.Depth() {
+		panic("community: resolutions vector length mismatch")
+	}
+
+	// See louvain.tex for a detailed description
+	// of the algorithm used here.
+
+	c := reduceDirectedMultiplex(g, nil, weights)
+	rnd := rand.Intn
+	if src != nil {
+		rnd = src.Intn
+	}
+	for {
+		l := newDirectedMultiplexLocalMover(c, c.communities, weights, resolutions, all)
+		if l == nil {
+			return c
+		}
+		if done := l.localMovingHeuristic(rnd); done {
+			return c
+		}
+		c = reduceDirectedMultiplex(c, l.communities, weights)
+	}
+}
+
+// ReducedDirectedMultiplex is a directed graph of communities derived from a
+// parent graph by reduction.
+type ReducedDirectedMultiplex struct {
+	// nodes is the set of nodes held
+	// by the graph. In a ReducedDirectedMultiplex
+	// the node ID is the index into
+	// nodes.
+	nodes  []multiplexCommunity
+	layers []directedEdges
+
+	// communities is the community
+	// structure of the graph.
+	communities [][]graph.Node
+
+	parent *ReducedDirectedMultiplex
+}
+
+var (
+	_ DirectedMultiplex      = (*ReducedDirectedMultiplex)(nil)
+	_ graph.WeightedDirected = (*directedLayerHandle)(nil)
+)
+
+// Nodes returns all the nodes in the graph.
+func (g *ReducedDirectedMultiplex) Nodes() []graph.Node {
+	nodes := make([]graph.Node, len(g.nodes))
+	for i := range g.nodes {
+		nodes[i] = node(i)
+	}
+	return nodes
+}
+
+// Depth returns the number of layers in the multiplex graph.
+func (g *ReducedDirectedMultiplex) Depth() int { return len(g.layers) }
+
+// Layer returns the lth layer of the multiplex graph.
+func (g *ReducedDirectedMultiplex) Layer(l int) graph.Directed {
+	return directedLayerHandle{multiplex: g, layer: l}
+}
+
+// Communities returns the community memberships of the nodes in the
+// graph used to generate the reduced graph.
+func (g *ReducedDirectedMultiplex) Communities() [][]graph.Node {
+	communities := make([][]graph.Node, len(g.communities))
+	if g.parent == nil {
+		for i, members := range g.communities {
+			comm := make([]graph.Node, len(members))
+			for j, n := range members {
+				nodes := g.nodes[n.ID()].nodes
+				if len(nodes) != 1 {
+					panic("community: unexpected number of nodes in base graph community")
+				}
+				comm[j] = nodes[0]
+			}
+			communities[i] = comm
+		}
+		return communities
+	}
+	sub := g.parent.Communities()
+	for i, members := range g.communities {
+		var comm []graph.Node
+		for _, n := range members {
+			comm = append(comm, sub[n.ID()]...)
+		}
+		communities[i] = comm
+	}
+	return communities
+}
+
+// Structure returns the community structure of the current level of
+// the module clustering. The first index of the returned value
+// corresponds to the index of the nodes in the next higher level if
+// it exists. The returned value should not be mutated.
+func (g *ReducedDirectedMultiplex) Structure() [][]graph.Node {
+	return g.communities
+}
+
+// Expanded returns the next lower level of the module clustering or nil
+// if at the lowest level.
+func (g *ReducedDirectedMultiplex) Expanded() ReducedMultiplex {
+	return g.parent
+}
+
+// reduceDirectedMultiplex returns a reduced graph constructed from g divided
+// into the given communities. The communities value is mutated
+// by the call to reduceDirectedMultiplex. If communities is nil and g is a
+// ReducedDirectedMultiplex, it is returned unaltered.
+func reduceDirectedMultiplex(g DirectedMultiplex, communities [][]graph.Node, weights []float64) *ReducedDirectedMultiplex {
+	if communities == nil {
+		if r, ok := g.(*ReducedDirectedMultiplex); ok {
+			return r
+		}
+
+		nodes := g.Nodes()
+		// TODO(kortschak) This sort is necessary really only
+		// for testing. In practice we would not be using the
+		// community provided by the user for a Q calculation.
+		// Probably we should use a function to map the
+		// communities in the test sets to the remapped order.
+		sort.Sort(ordered.ByID(nodes))
+		communities = make([][]graph.Node, len(nodes))
+		for i := range nodes {
+			communities[i] = []graph.Node{node(i)}
+		}
+
+		r := ReducedDirectedMultiplex{
+			nodes:       make([]multiplexCommunity, len(nodes)),
+			layers:      make([]directedEdges, g.Depth()),
+			communities: communities,
+		}
+		communityOf := make(map[int64]int, len(nodes))
+		for i, n := range nodes {
+			r.nodes[i] = multiplexCommunity{id: i, nodes: []graph.Node{n}, weights: make([]float64, depth(weights))}
+			communityOf[n.ID()] = i
+		}
+		for i := range r.layers {
+			r.layers[i] = directedEdges{
+				edgesFrom: make([][]int, len(nodes)),
+				edgesTo:   make([][]int, len(nodes)),
+				weights:   make(map[[2]int]float64),
+			}
+		}
+		w := 1.0
+		for l := 0; l < g.Depth(); l++ {
+			layer := g.Layer(l)
+			if weights != nil {
+				w = weights[l]
+			}
+			if w == 0 {
+				continue
+			}
+			var sign float64
+			var weight func(x, y graph.Node) float64
+			if w < 0 {
+				sign, weight = -1, negativeWeightFuncFor(layer)
+			} else {
+				sign, weight = 1, positiveWeightFuncFor(layer)
+			}
+			for _, n := range nodes {
+				id := communityOf[n.ID()]
+
+				var out []int
+				u := n
+				for _, v := range layer.From(u) {
+					vid := communityOf[v.ID()]
+					if vid != id {
+						out = append(out, vid)
+					}
+					r.layers[l].weights[[2]int{id, vid}] = sign * weight(u, v)
+				}
+				r.layers[l].edgesFrom[id] = out
+
+				var in []int
+				v := n
+				for _, u := range layer.To(v) {
+					uid := communityOf[u.ID()]
+					if uid != id {
+						in = append(in, uid)
+					}
+					r.layers[l].weights[[2]int{uid, id}] = sign * weight(u, v)
+				}
+				r.layers[l].edgesTo[id] = in
+			}
+		}
+		return &r
+	}
+
+	// Remove zero length communities destructively.
+	var commNodes int
+	for i := 0; i < len(communities); {
+		comm := communities[i]
+		if len(comm) == 0 {
+			communities[i] = communities[len(communities)-1]
+			communities[len(communities)-1] = nil
+			communities = communities[:len(communities)-1]
+		} else {
+			commNodes += len(comm)
+			i++
+		}
+	}
+
+	r := ReducedDirectedMultiplex{
+		nodes:  make([]multiplexCommunity, len(communities)),
+		layers: make([]directedEdges, g.Depth()),
+	}
+	communityOf := make(map[int64]int, commNodes)
+	for i, comm := range communities {
+		r.nodes[i] = multiplexCommunity{id: i, nodes: comm, weights: make([]float64, depth(weights))}
+		for _, n := range comm {
+			communityOf[n.ID()] = i
+		}
+	}
+	for i := range r.layers {
+		r.layers[i] = directedEdges{
+			edgesFrom: make([][]int, len(communities)),
+			edgesTo:   make([][]int, len(communities)),
+			weights:   make(map[[2]int]float64),
+		}
+	}
+	r.communities = make([][]graph.Node, len(communities))
+	for i := range r.communities {
+		r.communities[i] = []graph.Node{node(i)}
+	}
+	if g, ok := g.(*ReducedDirectedMultiplex); ok {
+		// Make sure we retain the truncated
+		// community structure.
+		g.communities = communities
+		r.parent = g
+	}
+	w := 1.0
+	for l := 0; l < g.Depth(); l++ {
+		layer := g.Layer(l)
+		if weights != nil {
+			w = weights[l]
+		}
+		if w == 0 {
+			continue
+		}
+		var sign float64
+		var weight func(x, y graph.Node) float64
+		if w < 0 {
+			sign, weight = -1, negativeWeightFuncFor(layer)
+		} else {
+			sign, weight = 1, positiveWeightFuncFor(layer)
+		}
+		for id, comm := range communities {
+			var out, in []int
+			for _, n := range comm {
+				u := n
+				for _, v := range comm {
+					r.nodes[id].weights[l] += sign * weight(u, v)
+				}
+
+				for _, v := range layer.From(u) {
+					vid := communityOf[v.ID()]
+					found := false
+					for _, e := range out {
+						if e == vid {
+							found = true
+							break
+						}
+					}
+					if !found && vid != id {
+						out = append(out, vid)
+					}
+					// Add half weights because the other
+					// ends of edges are also counted.
+					r.layers[l].weights[[2]int{id, vid}] += sign * weight(u, v) / 2
+				}
+
+				v := n
+				for _, u := range layer.To(v) {
+					uid := communityOf[u.ID()]
+					found := false
+					for _, e := range in {
+						if e == uid {
+							found = true
+							break
+						}
+					}
+					if !found && uid != id {
+						in = append(in, uid)
+					}
+					// Add half weights because the other
+					// ends of edges are also counted.
+					r.layers[l].weights[[2]int{uid, id}] += sign * weight(u, v) / 2
+				}
+
+			}
+			r.layers[l].edgesFrom[id] = out
+			r.layers[l].edgesTo[id] = in
+		}
+	}
+	return &r
+}
+
+// directedLayerHandle is a handle to a multiplex graph layer.
+type directedLayerHandle struct {
+	// multiplex is the complete
+	// multiplex graph.
+	multiplex *ReducedDirectedMultiplex
+
+	// layer is an index into the
+	// multiplex for the current
+	// layer.
+	layer int
+}
+
+// Has returns whether the node exists within the graph.
+func (g directedLayerHandle) Has(n graph.Node) bool {
+	id := n.ID()
+	return 0 <= id && id < int64(len(g.multiplex.nodes))
+}
+
+// Nodes returns all the nodes in the graph.
+func (g directedLayerHandle) Nodes() []graph.Node {
+	nodes := make([]graph.Node, len(g.multiplex.nodes))
+	for i := range g.multiplex.nodes {
+		nodes[i] = node(i)
+	}
+	return nodes
+}
+
+// From returns all nodes in g that can be reached directly from u.
+func (g directedLayerHandle) From(u graph.Node) []graph.Node {
+	out := g.multiplex.layers[g.layer].edgesFrom[u.ID()]
+	nodes := make([]graph.Node, len(out))
+	for i, vid := range out {
+		nodes[i] = g.multiplex.nodes[vid]
+	}
+	return nodes
+}
+
+// To returns all nodes in g that can reach directly to v.
+func (g directedLayerHandle) To(v graph.Node) []graph.Node {
+	in := g.multiplex.layers[g.layer].edgesTo[v.ID()]
+	nodes := make([]graph.Node, len(in))
+	for i, uid := range in {
+		nodes[i] = g.multiplex.nodes[uid]
+	}
+	return nodes
+}
+
+// HasEdgeBetween returns whether an edge exists between nodes x and y.
+func (g directedLayerHandle) HasEdgeBetween(x, y graph.Node) bool {
+	xid := x.ID()
+	yid := y.ID()
+	if xid == yid {
+		return false
+	}
+	if xid == yid || !isValidID(xid) || !isValidID(yid) {
+		return false
+	}
+	_, ok := g.multiplex.layers[g.layer].weights[[2]int{int(xid), int(yid)}]
+	if ok {
+		return true
+	}
+	_, ok = g.multiplex.layers[g.layer].weights[[2]int{int(yid), int(xid)}]
+	return ok
+}
+
+// HasEdgeFromTo returns whether an edge exists from node u to v.
+func (g directedLayerHandle) HasEdgeFromTo(u, v graph.Node) bool {
+	uid := u.ID()
+	vid := v.ID()
+	if uid == vid || !isValidID(uid) || !isValidID(vid) {
+		return false
+	}
+	_, ok := g.multiplex.layers[g.layer].weights[[2]int{int(uid), int(vid)}]
+	return ok
+}
+
+// Edge returns the edge from u to v if such an edge exists and nil otherwise.
+// The node v must be directly reachable from u as defined by the From method.
+func (g directedLayerHandle) Edge(u, v graph.Node) graph.Edge {
+	return g.WeightedEdge(u, v)
+}
+
+// WeightedEdge returns the weighted edge from u to v if such an edge exists and nil otherwise.
+// The node v must be directly reachable from u as defined by the From method.
+func (g directedLayerHandle) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
+	uid := u.ID()
+	vid := v.ID()
+	if uid == vid || !isValidID(uid) || !isValidID(vid) {
+		return nil
+	}
+	w, ok := g.multiplex.layers[g.layer].weights[[2]int{int(uid), int(vid)}]
+	if !ok {
+		return nil
+	}
+	return multiplexEdge{from: g.multiplex.nodes[u.ID()], to: g.multiplex.nodes[v.ID()], weight: w}
+}
+
+// Weight returns the weight for the edge between x and y if Edge(x, y) returns a non-nil Edge.
+// If x and y are the same node the internal node weight is returned. If there is no joining
+// edge between the two nodes the weight value returned is zero. Weight returns true if an edge
+// exists between x and y or if x and y have the same ID, false otherwise.
+func (g directedLayerHandle) Weight(x, y graph.Node) (w float64, ok bool) {
+	xid := x.ID()
+	yid := y.ID()
+	if !isValidID(xid) || !isValidID(yid) {
+		return 0, false
+	}
+	if xid == yid {
+		return g.multiplex.nodes[xid].weights[g.layer], true
+	}
+	w, ok = g.multiplex.layers[g.layer].weights[[2]int{int(xid), int(yid)}]
+	return w, ok
+}
+
+// directedMultiplexLocalMover is a step in graph modularity optimization.
+type directedMultiplexLocalMover struct {
+	g *ReducedDirectedMultiplex
+
+	// nodes is the set of working nodes.
+	nodes []graph.Node
+	// edgeWeightsOf is the weighted degree
+	// of each node indexed by ID.
+	edgeWeightsOf [][]directedWeights
+
+	// m is the total sum of
+	// edge weights in g.
+	m []float64
+
+	// weight is the weight function
+	// provided by g or a function
+	// that returns the Weight value
+	// of the non-nil edge between x
+	// and y.
+	weight []func(x, y graph.Node) float64
+
+	// communities is the current
+	// division of g.
+	communities [][]graph.Node
+	// memberships is a mapping between
+	// node ID and community membership.
+	memberships []int
+
+	// resolution is the Reichardt and
+	// Bornholdt γ parameter as defined
+	// in doi:10.1103/PhysRevE.74.016110.
+	resolutions []float64
+
+	// weights is the layer weights for
+	// the modularisation.
+	weights []float64
+
+	// searchAll specifies whether the local
+	// mover should consider non-connected
+	// communities during the local moving
+	// heuristic.
+	searchAll bool
+
+	// moved indicates that a call to
+	// move has been made since the last
+	// call to shuffle.
+	moved bool
+
+	// changed indicates that a move
+	// has been made since the creation
+	// of the local mover.
+	changed bool
+}
+
+// newDirectedMultiplexLocalMover returns a new directedMultiplexLocalMover initialized with
+// the graph g, a set of communities and a modularity resolution parameter. The
+// node IDs of g must be contiguous in [0,n) where n is the number of nodes.
+// If g has a zero edge weight sum, nil is returned.
+func newDirectedMultiplexLocalMover(g *ReducedDirectedMultiplex, communities [][]graph.Node, weights, resolutions []float64, all bool) *directedMultiplexLocalMover {
+	nodes := g.Nodes()
+	l := directedMultiplexLocalMover{
+		g:             g,
+		nodes:         nodes,
+		edgeWeightsOf: make([][]directedWeights, g.Depth()),
+		m:             make([]float64, g.Depth()),
+		communities:   communities,
+		memberships:   make([]int, len(nodes)),
+		resolutions:   resolutions,
+		weights:       weights,
+		weight:        make([]func(x, y graph.Node) float64, g.Depth()),
+	}
+
+	// Calculate the total edge weight of the graph
+	// and degree weights for each node.
+	var zero int
+	for i := 0; i < g.Depth(); i++ {
+		l.edgeWeightsOf[i] = make([]directedWeights, len(nodes))
+		var weight func(x, y graph.Node) float64
+
+		if weights != nil {
+			if weights[i] == 0 {
+				zero++
+				continue
+			}
+			if weights[i] < 0 {
+				weight = negativeWeightFuncFor(g.Layer(i))
+				l.searchAll = all
+			} else {
+				weight = positiveWeightFuncFor(g.Layer(i))
+			}
+		} else {
+			weight = positiveWeightFuncFor(g.Layer(i))
+		}
+
+		l.weight[i] = weight
+		layer := g.Layer(i)
+		for _, n := range l.nodes {
+			u := n
+			var wOut float64
+			for _, v := range layer.From(u) {
+				wOut += weight(u, v)
+			}
+
+			v := n
+			var wIn float64
+			for _, u := range layer.To(v) {
+				wIn += weight(u, v)
+			}
+
+			w := weight(n, n)
+			l.edgeWeightsOf[i][u.ID()] = directedWeights{out: w + wOut, in: w + wIn}
+			l.m[i] += w + wOut
+		}
+		if l.m[i] == 0 {
+			zero++
+		}
+	}
+	if zero == g.Depth() {
+		return nil
+	}
+
+	// Assign membership mappings.
+	for i, c := range communities {
+		for _, n := range c {
+			l.memberships[n.ID()] = i
+		}
+	}
+
+	return &l
+}
+
+// localMovingHeuristic performs the Louvain local moving heuristic until
+// no further moves can be made. It returns a boolean indicating that the
+// directedMultiplexLocalMover has not made any improvement to the community
+// structure and so the Louvain algorithm is done.
+func (l *directedMultiplexLocalMover) localMovingHeuristic(rnd func(int) int) (done bool) {
+	for {
+		l.shuffle(rnd)
+		for _, n := range l.nodes {
+			dQ, dst, src := l.deltaQ(n)
+			if dQ <= 0 {
+				continue
+			}
+			l.move(dst, src)
+		}
+		if !l.moved {
+			return !l.changed
+		}
+	}
+}
+
+// shuffle performs a Fisher-Yates shuffle on the nodes held by the
+// directedMultiplexLocalMover using the random source rnd which should return
+// an integer in the range [0,n).
+func (l *directedMultiplexLocalMover) shuffle(rnd func(n int) int) {
+	l.moved = false
+	for i := range l.nodes[:len(l.nodes)-1] {
+		j := i + rnd(len(l.nodes)-i)
+		l.nodes[i], l.nodes[j] = l.nodes[j], l.nodes[i]
+	}
+}
+
+// move moves the node at src to the community at dst.
+func (l *directedMultiplexLocalMover) move(dst int, src commIdx) {
+	l.moved = true
+	l.changed = true
+
+	srcComm := l.communities[src.community]
+	n := srcComm[src.node]
+
+	l.memberships[n.ID()] = dst
+
+	l.communities[dst] = append(l.communities[dst], n)
+	srcComm[src.node], srcComm[len(srcComm)-1] = srcComm[len(srcComm)-1], nil
+	l.communities[src.community] = srcComm[:len(srcComm)-1]
+}
+
+// deltaQ returns the highest gain in modularity attainable by moving
+// n from its current community to another connected community and
+// the index of the chosen destination. The index into the
+// directedMultiplexLocalMover's communities field is returned in src if n
+// is in communities.
+func (l *directedMultiplexLocalMover) deltaQ(n graph.Node) (deltaQ float64, dst int, src commIdx) {
+	id := n.ID()
+
+	var iterator minTaker
+	if l.searchAll {
+		iterator = &dense{n: len(l.communities)}
+	} else {
+		// Find communities connected to n.
+		connected := make(set.Ints)
+		// The following for loop is equivalent to:
+		//
+		//  for i := 0; i < l.g.Depth(); i++ {
+		//  	for _, v := range l.g.Layer(i).From(n) {
+		//  		connected.Add(l.memberships[v.ID()])
+		//  	}
+		//  	for _, v := range l.g.Layer(i).To(n) {
+		//  		connected.Add(l.memberships[v.ID()])
+		//  	}
+		//  }
+		//
+		// This is done to avoid an allocation for
+		// each layer.
+		for _, layer := range l.g.layers {
+			for _, vid := range layer.edgesFrom[id] {
+				connected.Add(l.memberships[vid])
+			}
+			for _, vid := range layer.edgesTo[id] {
+				connected.Add(l.memberships[vid])
+			}
+		}
+		// Insert the node's own community.
+		connected.Add(l.memberships[id])
+		iterator = newSlice(connected)
+	}
+
+	// Calculate the highest modularity gain
+	// from moving into another community and
+	// keep the index of that community.
+	var dQremove float64
+	dQadd, dst, src := math.Inf(-1), -1, commIdx{-1, -1}
+	var i int
+	for iterator.TakeMin(&i) {
+		c := l.communities[i]
+		var removal bool
+		var _dQadd float64
+		for layer := 0; layer < l.g.Depth(); layer++ {
+			m := l.m[layer]
+			if m == 0 {
+				// Do not consider layers with zero sum edge weight.
+				continue
+			}
+			w := 1.0
+			if l.weights != nil {
+				w = l.weights[layer]
+			}
+			if w == 0 {
+				// Do not consider layers with zero weighting.
+				continue
+			}
+
+			var k_aC, sigma_totC directedWeights // C is a substitution for ^𝛼 or ^𝛽.
+			removal = false
+			for j, u := range c {
+				uid := u.ID()
+				if uid == id {
+					// Only mark and check src community on the first layer.
+					if layer == 0 {
+						if src.community != -1 {
+							panic("community: multiple sources")
+						}
+						src = commIdx{i, j}
+					}
+					removal = true
+				}
+
+				k_aC.in += l.weight[layer](n, u)
+				k_aC.out += l.weight[layer](u, n)
+				// sigma_totC could be kept for each community
+				// and updated for moves, changing the calculation
+				// of sigma_totC here from O(n_c) to O(1), but
+				// in practice the time savings do not appear
+				// to be compelling and do not make up for the
+				// increase in code complexity and space required.
+				w := l.edgeWeightsOf[layer][uid]
+				sigma_totC.in += w.in
+				sigma_totC.out += w.out
+			}
+
+			a_aa := l.weight[layer](n, n)
+			k_a := l.edgeWeightsOf[layer][id]
+			gamma := 1.0
+			if l.resolutions != nil {
+				if len(l.resolutions) == 1 {
+					gamma = l.resolutions[0]
+				} else {
+					gamma = l.resolutions[layer]
+				}
+			}
+
+			// See louvain.tex for a derivation of these equations.
+			// The weighting term, w, is described in V Traag,
+			// "Algorithms and dynamical models for communities and
+			// reputation in social networks", chapter 5.
+			// http://www.traag.net/wp/wp-content/papercite-data/pdf/traag_algorithms_2013.pdf
+			switch {
+			case removal:
+				// The community c was the current community,
+				// so calculate the change due to removal.
+				dQremove += w * ((k_aC.in /*^𝛼*/ - a_aa) + (k_aC.out /*^𝛼*/ - a_aa) -
+					gamma*(k_a.in*(sigma_totC.out /*^𝛼*/ -k_a.out)+k_a.out*(sigma_totC.in /*^𝛼*/ -k_a.in))/m)
+
+			default:
+				// Otherwise calculate the change due to an addition
+				// to c.
+				_dQadd += w * (k_aC.in /*^𝛽*/ + k_aC.out /*^𝛽*/ -
+					gamma*(k_a.in*sigma_totC.out /*^𝛽*/ +k_a.out*sigma_totC.in /*^𝛽*/)/m)
+			}
+		}
+		if !removal && _dQadd > dQadd {
+			dQadd = _dQadd
+			dst = i
+		}
+	}
+
+	return dQadd - dQremove, dst, src
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/community/louvain_directed_multiplex_test.go b/vendor/gonum.org/v1/gonum/graph/community/louvain_directed_multiplex_test.go
new file mode 100644
index 00000000..896c6122
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/community/louvain_directed_multiplex_test.go
@@ -0,0 +1,722 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package community
+
+import (
+	"math"
+	"math/rand"
+	"reflect"
+	"sort"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/ordered"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+var communityDirectedMultiplexQTests = []struct {
+	name       string
+	layers     []layer
+	structures []structure
+
+	wantLevels []level
+}{
+	{
+		name:   "unconnected",
+		layers: []layer{{g: unconnected, weight: 1}},
+		structures: []structure{
+			{
+				resolution: 1,
+				memberships: []intset{
+					0: linksTo(0),
+					1: linksTo(1),
+					2: linksTo(2),
+					3: linksTo(3),
+					4: linksTo(4),
+					5: linksTo(5),
+				},
+				want: math.NaN(),
+			},
+		},
+		wantLevels: []level{
+			{
+				q: math.Inf(-1), // Here math.Inf(-1) is used as a place holder for NaN to allow use of reflect.DeepEqual.
+				communities: [][]graph.Node{
+					{simple.Node(0)},
+					{simple.Node(1)},
+					{simple.Node(2)},
+					{simple.Node(3)},
+					{simple.Node(4)},
+					{simple.Node(5)},
+				},
+			},
+		},
+	},
+	{
+		name:   "simple_directed",
+		layers: []layer{{g: simpleDirected, weight: 1}},
+		// community structure and modularity calculated by C++ implementation: louvain igraph.
+		// Note that louvain igraph returns Q as an unscaled value.
+		structures: []structure{
+			{
+				resolution: 1,
+				memberships: []intset{
+					0: linksTo(0, 1),
+					1: linksTo(2, 3, 4),
+				},
+				want: 0.5714285714285716,
+				tol:  1e-10,
+			},
+		},
+		wantLevels: []level{
+			{
+				communities: [][]graph.Node{
+					{simple.Node(0), simple.Node(1)},
+					{simple.Node(2), simple.Node(3), simple.Node(4)},
+				},
+				q: 0.5714285714285716,
+			},
+			{
+				communities: [][]graph.Node{
+					{simple.Node(0)},
+					{simple.Node(1)},
+					{simple.Node(2)},
+					{simple.Node(3)},
+					{simple.Node(4)},
+				},
+				q: -1.2857142857142856,
+			},
+		},
+	},
+	{
+		name: "simple_directed_twice",
+		layers: []layer{
+			{g: simpleDirected, weight: 0.5},
+			{g: simpleDirected, weight: 0.5},
+		},
+		// community structure and modularity calculated by C++ implementation: louvain igraph.
+		// Note that louvain igraph returns Q as an unscaled value.
+		structures: []structure{
+			{
+				resolution: 1,
+				memberships: []intset{
+					0: linksTo(0, 1),
+					1: linksTo(2, 3, 4),
+				},
+				want: 0.5714285714285716,
+				tol:  1e-10,
+			},
+		},
+		wantLevels: []level{
+			{
+				q: 0.5714285714285716,
+				communities: [][]graph.Node{
+					{simple.Node(0), simple.Node(1)},
+					{simple.Node(2), simple.Node(3), simple.Node(4)},
+				},
+			},
+			{
+				q: -1.2857142857142856,
+				communities: [][]graph.Node{
+					{simple.Node(0)},
+					{simple.Node(1)},
+					{simple.Node(2)},
+					{simple.Node(3)},
+					{simple.Node(4)},
+				},
+			},
+		},
+	},
+	{
+		name: "small_dumbell",
+		layers: []layer{
+			{g: smallDumbell, edgeWeight: 1, weight: 1},
+			{g: dumbellRepulsion, edgeWeight: -1, weight: -1},
+		},
+		structures: []structure{
+			{
+				resolution: 1,
+				memberships: []intset{
+					0: linksTo(0, 1, 2),
+					1: linksTo(3, 4, 5),
+				},
+				want: 2.5714285714285716, tol: 1e-10,
+			},
+			{
+				resolution: 1,
+				memberships: []intset{
+					0: linksTo(0, 1, 2, 3, 4, 5),
+				},
+				want: 0, tol: 1e-14,
+			},
+		},
+		wantLevels: []level{
+			{
+				q: 2.5714285714285716,
+				communities: [][]graph.Node{
+					{simple.Node(0), simple.Node(1), simple.Node(2)},
+					{simple.Node(3), simple.Node(4), simple.Node(5)},
+				},
+			},
+			{
+				q: -0.857142857142857,
+				communities: [][]graph.Node{
+					{simple.Node(0)},
+					{simple.Node(1)},
+					{simple.Node(2)},
+					{simple.Node(3)},
+					{simple.Node(4)},
+					{simple.Node(5)},
+				},
+			},
+		},
+	},
+	{
+		name:   "repulsion",
+		layers: []layer{{g: repulsion, edgeWeight: -1, weight: -1}},
+		structures: []structure{
+			{
+				resolution: 1,
+				memberships: []intset{
+					0: linksTo(0, 1, 2),
+					1: linksTo(3, 4, 5),
+				},
+				want: 9.0, tol: 1e-10,
+			},
+			{
+				resolution: 1,
+				memberships: []intset{
+					0: linksTo(0),
+					1: linksTo(1),
+					2: linksTo(2),
+					3: linksTo(3),
+					4: linksTo(4),
+					5: linksTo(5),
+				},
+				want: 3, tol: 1e-14,
+			},
+		},
+		wantLevels: []level{
+			{
+				q: 9.0,
+				communities: [][]graph.Node{
+					{simple.Node(0), simple.Node(1), simple.Node(2)},
+					{simple.Node(3), simple.Node(4), simple.Node(5)},
+				},
+			},
+			{
+				q: 3.0,
+				communities: [][]graph.Node{
+					{simple.Node(0)},
+					{simple.Node(1)},
+					{simple.Node(2)},
+					{simple.Node(3)},
+					{simple.Node(4)},
+					{simple.Node(5)},
+				},
+			},
+		},
+	},
+	{
+		name: "middle_east",
+		layers: []layer{
+			{g: middleEast.friends, edgeWeight: 1, weight: 1},
+			{g: middleEast.enemies, edgeWeight: -1, weight: -1},
+		},
+		structures: []structure{
+			{
+				resolution: 1,
+				memberships: []intset{
+					0: linksTo(0, 6),
+					1: linksTo(1, 7, 9, 12),
+					2: linksTo(2, 8, 11),
+					3: linksTo(3, 4, 5, 10),
+				},
+				want: 33.818057455540355, tol: 1e-9,
+			},
+			{
+				resolution: 1,
+				memberships: []intset{
+					0: linksTo(0, 2, 3, 4, 5, 10),
+					1: linksTo(1, 7, 9, 12),
+					2: linksTo(6),
+					3: linksTo(8, 11),
+				},
+				want: 30.92749658, tol: 1e-7,
+			},
+			{
+				resolution: 1,
+				memberships: []intset{
+					0: linksTo(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12),
+				},
+				want: 0, tol: 1e-14,
+			},
+		},
+		wantLevels: []level{
+			{
+				q: 33.818057455540355,
+				communities: [][]graph.Node{
+					{simple.Node(0), simple.Node(6)},
+					{simple.Node(1), simple.Node(7), simple.Node(9), simple.Node(12)},
+					{simple.Node(2), simple.Node(8), simple.Node(11)},
+					{simple.Node(3), simple.Node(4), simple.Node(5), simple.Node(10)},
+				},
+			},
+			{
+				q: 3.8071135430916545,
+				communities: [][]graph.Node{
+					{simple.Node(0)},
+					{simple.Node(1)},
+					{simple.Node(2)},
+					{simple.Node(3)},
+					{simple.Node(4)},
+					{simple.Node(5)},
+					{simple.Node(6)},
+					{simple.Node(7)},
+					{simple.Node(8)},
+					{simple.Node(9)},
+					{simple.Node(10)},
+					{simple.Node(11)},
+					{simple.Node(12)},
+				},
+			},
+		},
+	},
+}
+
+func TestCommunityQDirectedMultiplex(t *testing.T) {
+	for _, test := range communityDirectedMultiplexQTests {
+		g, weights, err := directedMultiplexFrom(test.layers)
+		if err != nil {
+			t.Errorf("unexpected error creating multiplex: %v", err)
+			continue
+		}
+
+		for _, structure := range test.structures {
+			communities := make([][]graph.Node, len(structure.memberships))
+			for i, c := range structure.memberships {
+				for n := range c {
+					communities[i] = append(communities[i], simple.Node(n))
+				}
+			}
+			q := QMultiplex(g, communities, weights, []float64{structure.resolution})
+			got := floats.Sum(q)
+			if !floats.EqualWithinAbsOrRel(got, structure.want, structure.tol, structure.tol) && !math.IsNaN(structure.want) {
+				for _, c := range communities {
+					sort.Sort(ordered.ByID(c))
+				}
+				t.Errorf("unexpected Q value for %q %v: got: %v %.3v want: %v",
+					test.name, communities, got, q, structure.want)
+			}
+		}
+	}
+}
+
+func TestCommunityDeltaQDirectedMultiplex(t *testing.T) {
+tests:
+	for _, test := range communityDirectedMultiplexQTests {
+		g, weights, err := directedMultiplexFrom(test.layers)
+		if err != nil {
+			t.Errorf("unexpected error creating multiplex: %v", err)
+			continue
+		}
+
+		rnd := rand.New(rand.NewSource(1)).Intn
+		for _, structure := range test.structures {
+			communityOf := make(map[int64]int)
+			communities := make([][]graph.Node, len(structure.memberships))
+			for i, c := range structure.memberships {
+				for n := range c {
+					n := int64(n)
+					communityOf[n] = i
+					communities[i] = append(communities[i], simple.Node(n))
+				}
+				sort.Sort(ordered.ByID(communities[i]))
+			}
+			resolution := []float64{structure.resolution}
+
+			before := QMultiplex(g, communities, weights, resolution)
+
+			// We test exhaustively.
+			const all = true
+
+			l := newDirectedMultiplexLocalMover(
+				reduceDirectedMultiplex(g, nil, weights),
+				communities, weights, resolution, all)
+			if l == nil {
+				if !math.IsNaN(floats.Sum(before)) {
+					t.Errorf("unexpected nil localMover with non-NaN Q graph: Q=%.4v", before)
+				}
+				continue tests
+			}
+
+			// This is done to avoid run-to-run
+			// variation due to map iteration order.
+			sort.Sort(ordered.ByID(l.nodes))
+
+			l.shuffle(rnd)
+
+			for _, target := range l.nodes {
+				got, gotDst, gotSrc := l.deltaQ(target)
+
+				want, wantDst := math.Inf(-1), -1
+				migrated := make([][]graph.Node, len(structure.memberships))
+				for i, c := range structure.memberships {
+					for n := range c {
+						n := int64(n)
+						if n == target.ID() {
+							continue
+						}
+						migrated[i] = append(migrated[i], simple.Node(n))
+					}
+					sort.Sort(ordered.ByID(migrated[i]))
+				}
+
+				for i, c := range structure.memberships {
+					if i == communityOf[target.ID()] {
+						continue
+					}
+					if !(all && hasNegative(weights)) {
+						connected := false
+					search:
+						for l := 0; l < g.Depth(); l++ {
+							if weights[l] < 0 {
+								connected = true
+								break search
+							}
+							layer := g.Layer(l)
+							for n := range c {
+								if layer.HasEdgeBetween(simple.Node(n), target) {
+									connected = true
+									break search
+								}
+							}
+						}
+						if !connected {
+							continue
+						}
+					}
+					migrated[i] = append(migrated[i], target)
+					after := QMultiplex(g, migrated, weights, resolution)
+					migrated[i] = migrated[i][:len(migrated[i])-1]
+					if delta := floats.Sum(after) - floats.Sum(before); delta > want {
+						want = delta
+						wantDst = i
+					}
+				}
+
+				if !floats.EqualWithinAbsOrRel(got, want, structure.tol, structure.tol) || gotDst != wantDst {
+					t.Errorf("unexpected result moving n=%d in c=%d of %s/%.4v: got: %.4v,%d want: %.4v,%d"+
+						"\n\t%v\n\t%v",
+						target.ID(), communityOf[target.ID()], test.name, structure.resolution, got, gotDst, want, wantDst,
+						communities, migrated)
+				}
+				if gotSrc.community != communityOf[target.ID()] {
+					t.Errorf("unexpected source community index: got: %d want: %d", gotSrc, communityOf[target.ID()])
+				} else if communities[gotSrc.community][gotSrc.node].ID() != target.ID() {
+					wantNodeIdx := -1
+					for i, n := range communities[gotSrc.community] {
+						if n.ID() == target.ID() {
+							wantNodeIdx = i
+							break
+						}
+					}
+					t.Errorf("unexpected source node index: got: %d want: %d", gotSrc.node, wantNodeIdx)
+				}
+			}
+		}
+	}
+}
+
+func TestReduceQConsistencyDirectedMultiplex(t *testing.T) {
+tests:
+	for _, test := range communityDirectedMultiplexQTests {
+		g, weights, err := directedMultiplexFrom(test.layers)
+		if err != nil {
+			t.Errorf("unexpected error creating multiplex: %v", err)
+			continue
+		}
+
+		for _, structure := range test.structures {
+			if math.IsNaN(structure.want) {
+				continue tests
+			}
+
+			communities := make([][]graph.Node, len(structure.memberships))
+			for i, c := range structure.memberships {
+				for n := range c {
+					communities[i] = append(communities[i], simple.Node(n))
+				}
+				sort.Sort(ordered.ByID(communities[i]))
+			}
+
+			gQ := QMultiplex(g, communities, weights, []float64{structure.resolution})
+			gQnull := QMultiplex(g, nil, weights, nil)
+
+			cg0 := reduceDirectedMultiplex(g, nil, weights)
+			cg0Qnull := QMultiplex(cg0, cg0.Structure(), weights, nil)
+			if !floats.EqualWithinAbsOrRel(floats.Sum(gQnull), floats.Sum(cg0Qnull), structure.tol, structure.tol) {
+				t.Errorf("disagreement between null Q from method: %v and function: %v", cg0Qnull, gQnull)
+			}
+			cg0Q := QMultiplex(cg0, communities, weights, []float64{structure.resolution})
+			if !floats.EqualWithinAbsOrRel(floats.Sum(gQ), floats.Sum(cg0Q), structure.tol, structure.tol) {
+				t.Errorf("unexpected Q result after initial reduction: got: %v want :%v", cg0Q, gQ)
+			}
+
+			cg1 := reduceDirectedMultiplex(cg0, communities, weights)
+			cg1Q := QMultiplex(cg1, cg1.Structure(), weights, []float64{structure.resolution})
+			if !floats.EqualWithinAbsOrRel(floats.Sum(gQ), floats.Sum(cg1Q), structure.tol, structure.tol) {
+				t.Errorf("unexpected Q result after second reduction: got: %v want :%v", cg1Q, gQ)
+			}
+		}
+	}
+}
+
+var localDirectedMultiplexMoveTests = []struct {
+	name       string
+	layers     []layer
+	structures []moveStructures
+}{
+	{
+		name:   "blondel",
+		layers: []layer{{g: blondel, weight: 1}, {g: blondel, weight: 0.5}},
+		structures: []moveStructures{
+			{
+				memberships: []intset{
+					0: linksTo(0, 1, 2, 4, 5),
+					1: linksTo(3, 6, 7),
+					2: linksTo(8, 9, 10, 12, 14, 15),
+					3: linksTo(11, 13),
+				},
+				targetNodes: []graph.Node{simple.Node(0)},
+				resolution:  1,
+				tol:         1e-14,
+			},
+			{
+				memberships: []intset{
+					0: linksTo(0, 1, 2, 4, 5),
+					1: linksTo(3, 6, 7),
+					2: linksTo(8, 9, 10, 12, 14, 15),
+					3: linksTo(11, 13),
+				},
+				targetNodes: []graph.Node{simple.Node(3)},
+				resolution:  1,
+				tol:         1e-14,
+			},
+			{
+				memberships: []intset{
+					0: linksTo(0, 1, 2, 4, 5),
+					1: linksTo(3, 6, 7),
+					2: linksTo(8, 9, 10, 12, 14, 15),
+					3: linksTo(11, 13),
+				},
+				// Case to demonstrate when A_aa != k_a^𝛼.
+				targetNodes: []graph.Node{simple.Node(3), simple.Node(2)},
+				resolution:  1,
+				tol:         1e-14,
+			},
+		},
+	},
+}
+
+func TestMoveLocalDirectedMultiplex(t *testing.T) {
+	for _, test := range localDirectedMultiplexMoveTests {
+		g, weights, err := directedMultiplexFrom(test.layers)
+		if err != nil {
+			t.Errorf("unexpected error creating multiplex: %v", err)
+			continue
+		}
+
+		for _, structure := range test.structures {
+			communities := make([][]graph.Node, len(structure.memberships))
+			for i, c := range structure.memberships {
+				for n := range c {
+					communities[i] = append(communities[i], simple.Node(n))
+				}
+				sort.Sort(ordered.ByID(communities[i]))
+			}
+
+			r := reduceDirectedMultiplex(reduceDirectedMultiplex(g, nil, weights), communities, weights)
+
+			l := newDirectedMultiplexLocalMover(r, r.communities, weights, []float64{structure.resolution}, true)
+			for _, n := range structure.targetNodes {
+				dQ, dst, src := l.deltaQ(n)
+				if dQ > 0 {
+					before := floats.Sum(QMultiplex(r, l.communities, weights, []float64{structure.resolution}))
+					l.move(dst, src)
+					after := floats.Sum(QMultiplex(r, l.communities, weights, []float64{structure.resolution}))
+					want := after - before
+					if !floats.EqualWithinAbsOrRel(dQ, want, structure.tol, structure.tol) {
+						t.Errorf("unexpected deltaQ: got: %v want: %v", dQ, want)
+					}
+				}
+			}
+		}
+	}
+}
+
+func TestLouvainDirectedMultiplex(t *testing.T) {
+	const louvainIterations = 20
+
+	for _, test := range communityDirectedMultiplexQTests {
+		g, weights, err := directedMultiplexFrom(test.layers)
+		if err != nil {
+			t.Errorf("unexpected error creating multiplex: %v", err)
+			continue
+		}
+
+		if test.structures[0].resolution != 1 {
+			panic("bad test: expect resolution=1")
+		}
+		want := make([][]graph.Node, len(test.structures[0].memberships))
+		for i, c := range test.structures[0].memberships {
+			for n := range c {
+				want[i] = append(want[i], simple.Node(n))
+			}
+			sort.Sort(ordered.ByID(want[i]))
+		}
+		sort.Sort(ordered.BySliceIDs(want))
+
+		var (
+			got   *ReducedDirectedMultiplex
+			bestQ = math.Inf(-1)
+		)
+		// Modularize is randomised so we do this to
+		// ensure the level tests are consistent.
+		src := rand.New(rand.NewSource(1))
+		for i := 0; i < louvainIterations; i++ {
+			r := ModularizeMultiplex(g, weights, nil, true, src).(*ReducedDirectedMultiplex)
+			if q := floats.Sum(QMultiplex(r, nil, weights, nil)); q > bestQ || math.IsNaN(q) {
+				bestQ = q
+				got = r
+
+				if math.IsNaN(q) {
+					// Don't try again for non-connected case.
+					break
+				}
+			}
+
+			var qs []float64
+			for p := r; p != nil; p = p.Expanded().(*ReducedDirectedMultiplex) {
+				qs = append(qs, floats.Sum(QMultiplex(p, nil, weights, nil)))
+			}
+
+			// Recovery of Q values is reversed.
+			if reverse(qs); !sort.Float64sAreSorted(qs) {
+				t.Errorf("Q values not monotonically increasing: %.5v", qs)
+			}
+		}
+
+		gotCommunities := got.Communities()
+		for _, c := range gotCommunities {
+			sort.Sort(ordered.ByID(c))
+		}
+		sort.Sort(ordered.BySliceIDs(gotCommunities))
+		if !reflect.DeepEqual(gotCommunities, want) {
+			t.Errorf("unexpected community membership for %s Q=%.4v:\n\tgot: %v\n\twant:%v",
+				test.name, bestQ, gotCommunities, want)
+			continue
+		}
+
+		var levels []level
+		for p := got; p != nil; p = p.Expanded().(*ReducedDirectedMultiplex) {
+			var communities [][]graph.Node
+			if p.parent != nil {
+				communities = p.parent.Communities()
+				for _, c := range communities {
+					sort.Sort(ordered.ByID(c))
+				}
+				sort.Sort(ordered.BySliceIDs(communities))
+			} else {
+				communities = reduceDirectedMultiplex(g, nil, weights).Communities()
+			}
+			q := floats.Sum(QMultiplex(p, nil, weights, nil))
+			if math.IsNaN(q) {
+				// Use an equalable flag value in place of NaN.
+				q = math.Inf(-1)
+			}
+			levels = append(levels, level{q: q, communities: communities})
+		}
+		if !reflect.DeepEqual(levels, test.wantLevels) {
+			t.Errorf("unexpected level structure:\n\tgot: %v\n\twant:%v", levels, test.wantLevels)
+		}
+	}
+}
+
+func TestNonContiguousDirectedMultiplex(t *testing.T) {
+	g := simple.NewDirectedGraph()
+	for _, e := range []simple.Edge{
+		{F: simple.Node(0), T: simple.Node(1)},
+		{F: simple.Node(4), T: simple.Node(5)},
+	} {
+		g.SetEdge(e)
+	}
+
+	func() {
+		defer func() {
+			r := recover()
+			if r != nil {
+				t.Error("unexpected panic with non-contiguous ID range")
+			}
+		}()
+		ModularizeMultiplex(DirectedLayers{g}, nil, nil, true, nil)
+	}()
+}
+
+func TestNonContiguousWeightedDirectedMultiplex(t *testing.T) {
+	g := simple.NewWeightedDirectedGraph(0, 0)
+	for _, e := range []simple.WeightedEdge{
+		{F: simple.Node(0), T: simple.Node(1), W: 1},
+		{F: simple.Node(4), T: simple.Node(5), W: 1},
+	} {
+		g.SetWeightedEdge(e)
+	}
+
+	func() {
+		defer func() {
+			r := recover()
+			if r != nil {
+				t.Error("unexpected panic with non-contiguous ID range")
+			}
+		}()
+		ModularizeMultiplex(DirectedLayers{g}, nil, nil, true, nil)
+	}()
+}
+
+func BenchmarkLouvainDirectedMultiplex(b *testing.B) {
+	src := rand.New(rand.NewSource(1))
+	for i := 0; i < b.N; i++ {
+		ModularizeMultiplex(DirectedLayers{dupGraphDirected}, nil, nil, true, src)
+	}
+}
+
+func directedMultiplexFrom(raw []layer) (DirectedLayers, []float64, error) {
+	var layers []graph.Directed
+	var weights []float64
+	for _, l := range raw {
+		g := simple.NewWeightedDirectedGraph(0, 0)
+		for u, e := range l.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				w := 1.0
+				if l.edgeWeight != 0 {
+					w = l.edgeWeight
+				}
+				g.SetWeightedEdge(simple.WeightedEdge{F: simple.Node(u), T: simple.Node(v), W: w})
+			}
+		}
+		layers = append(layers, g)
+		weights = append(weights, l.weight)
+	}
+	g, err := NewDirectedLayers(layers...)
+	if err != nil {
+		return nil, nil, err
+	}
+	return g, weights, nil
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/community/louvain_directed_test.go b/vendor/gonum.org/v1/gonum/graph/community/louvain_directed_test.go
new file mode 100644
index 00000000..5810ffb7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/community/louvain_directed_test.go
@@ -0,0 +1,719 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package community
+
+import (
+	"math"
+	"math/rand"
+	"reflect"
+	"sort"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/ordered"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+type communityDirectedQTest struct {
+	name       string
+	g          []intset
+	structures []structure
+
+	wantLevels []level
+}
+
+var communityDirectedQTests = []communityDirectedQTest{
+	{
+		name: "simple_directed",
+		g:    simpleDirected,
+		// community structure and modularity calculated by C++ implementation: louvain igraph.
+		// Note that louvain igraph returns Q as an unscaled value.
+		structures: []structure{
+			{
+				resolution: 1,
+				memberships: []intset{
+					0: linksTo(0, 1),
+					1: linksTo(2, 3, 4),
+				},
+				want: 0.5714285714285716 / 7,
+				tol:  1e-10,
+			},
+		},
+		wantLevels: []level{
+			{
+				communities: [][]graph.Node{
+					{simple.Node(0), simple.Node(1)},
+					{simple.Node(2), simple.Node(3), simple.Node(4)},
+				},
+				q: 0.5714285714285716 / 7,
+			},
+			{
+				communities: [][]graph.Node{
+					{simple.Node(0)},
+					{simple.Node(1)},
+					{simple.Node(2)},
+					{simple.Node(3)},
+					{simple.Node(4)},
+				},
+				q: -1.2857142857142856 / 7,
+			},
+		},
+	},
+	{
+		name: "zachary",
+		g:    zachary,
+		// community structure and modularity calculated by C++ implementation: louvain igraph.
+		// Note that louvain igraph returns Q as an unscaled value.
+		structures: []structure{
+			{
+				resolution: 1,
+				memberships: []intset{
+					0: linksTo(0, 1, 2, 3, 7, 11, 12, 13, 17, 19, 21),
+					1: linksTo(4, 5, 6, 10, 16),
+					2: linksTo(8, 9, 14, 15, 18, 20, 22, 26, 29, 30, 32, 33),
+					3: linksTo(23, 24, 25, 27, 28, 31),
+				},
+				want: 34.3417721519 / 79 /* 5->6 and 6->5 because of co-equal rank */, tol: 1e-4,
+			},
+		},
+		wantLevels: []level{
+			{
+				q: 0.43470597660631316,
+				communities: [][]graph.Node{
+					{simple.Node(0), simple.Node(1), simple.Node(2), simple.Node(3), simple.Node(7), simple.Node(11), simple.Node(12), simple.Node(13), simple.Node(17), simple.Node(19), simple.Node(21)},
+					{simple.Node(4), simple.Node(5), simple.Node(6), simple.Node(10), simple.Node(16)},
+					{simple.Node(8), simple.Node(9), simple.Node(14), simple.Node(15), simple.Node(18), simple.Node(20), simple.Node(22), simple.Node(26), simple.Node(29), simple.Node(30), simple.Node(32), simple.Node(33)},
+					{simple.Node(23), simple.Node(24), simple.Node(25), simple.Node(27), simple.Node(28), simple.Node(31)},
+				},
+			},
+			{
+				q: 0.3911232174331037,
+				communities: [][]graph.Node{
+					{simple.Node(0), simple.Node(1), simple.Node(2), simple.Node(3), simple.Node(7), simple.Node(11), simple.Node(12), simple.Node(13), simple.Node(17), simple.Node(19), simple.Node(21)},
+					{simple.Node(4), simple.Node(10)},
+					{simple.Node(5), simple.Node(6), simple.Node(16)},
+					{simple.Node(8), simple.Node(30)},
+					{simple.Node(9), simple.Node(14), simple.Node(15), simple.Node(18), simple.Node(20), simple.Node(22), simple.Node(32), simple.Node(33)},
+					{simple.Node(23), simple.Node(24), simple.Node(25), simple.Node(27), simple.Node(28), simple.Node(31)},
+					{simple.Node(26), simple.Node(29)},
+				},
+			},
+			{
+				q: -0.014580996635154624,
+				communities: [][]graph.Node{
+					{simple.Node(0)},
+					{simple.Node(1)},
+					{simple.Node(2)},
+					{simple.Node(3)},
+					{simple.Node(4)},
+					{simple.Node(5)},
+					{simple.Node(6)},
+					{simple.Node(7)},
+					{simple.Node(8)},
+					{simple.Node(9)},
+					{simple.Node(10)},
+					{simple.Node(11)},
+					{simple.Node(12)},
+					{simple.Node(13)},
+					{simple.Node(14)},
+					{simple.Node(15)},
+					{simple.Node(16)},
+					{simple.Node(17)},
+					{simple.Node(18)},
+					{simple.Node(19)},
+					{simple.Node(20)},
+					{simple.Node(21)},
+					{simple.Node(22)},
+					{simple.Node(23)},
+					{simple.Node(24)},
+					{simple.Node(25)},
+					{simple.Node(26)},
+					{simple.Node(27)},
+					{simple.Node(28)},
+					{simple.Node(29)},
+					{simple.Node(30)},
+					{simple.Node(31)},
+					{simple.Node(32)},
+					{simple.Node(33)},
+				},
+			},
+		},
+	},
+	{
+		name: "blondel",
+		g:    blondel,
+		// community structure and modularity calculated by C++ implementation: louvain igraph.
+		// Note that louvain igraph returns Q as an unscaled value.
+		structures: []structure{
+			{
+				resolution: 1,
+				memberships: []intset{
+					0: linksTo(0, 1, 2, 3, 4, 5, 6, 7),
+					1: linksTo(8, 9, 10, 11, 12, 13, 14, 15),
+				},
+				want: 11.1428571429 / 28, tol: 1e-4,
+			},
+		},
+		wantLevels: []level{
+			{
+				q: 0.3979591836734694,
+				communities: [][]graph.Node{
+					{simple.Node(0), simple.Node(1), simple.Node(2), simple.Node(3), simple.Node(4), simple.Node(5), simple.Node(6), simple.Node(7)},
+					{simple.Node(8), simple.Node(9), simple.Node(10), simple.Node(11), simple.Node(12), simple.Node(13), simple.Node(14), simple.Node(15)},
+				},
+			},
+			{
+				q: 0.32525510204081637,
+				communities: [][]graph.Node{
+					{simple.Node(0), simple.Node(3), simple.Node(5), simple.Node(7)},
+					{simple.Node(1), simple.Node(2), simple.Node(4), simple.Node(6)},
+					{simple.Node(8), simple.Node(10), simple.Node(11), simple.Node(13), simple.Node(15)},
+					{simple.Node(9), simple.Node(12), simple.Node(14)},
+				},
+			},
+			{
+				q: -0.022959183673469385,
+				communities: [][]graph.Node{
+					{simple.Node(0)},
+					{simple.Node(1)},
+					{simple.Node(2)},
+					{simple.Node(3)},
+					{simple.Node(4)},
+					{simple.Node(5)},
+					{simple.Node(6)},
+					{simple.Node(7)},
+					{simple.Node(8)},
+					{simple.Node(9)},
+					{simple.Node(10)},
+					{simple.Node(11)},
+					{simple.Node(12)},
+					{simple.Node(13)},
+					{simple.Node(14)},
+					{simple.Node(15)},
+				},
+			},
+		},
+	},
+}
+
+func TestCommunityQDirected(t *testing.T) {
+	for _, test := range communityDirectedQTests {
+		g := simple.NewDirectedGraph()
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+
+		testCommunityQDirected(t, test, g)
+	}
+}
+
+func TestCommunityQWeightedDirected(t *testing.T) {
+	for _, test := range communityDirectedQTests {
+		g := simple.NewWeightedDirectedGraph(0, 0)
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetWeightedEdge(simple.WeightedEdge{F: simple.Node(u), T: simple.Node(v), W: 1})
+			}
+		}
+
+		testCommunityQDirected(t, test, g)
+	}
+}
+
+func testCommunityQDirected(t *testing.T, test communityDirectedQTest, g graph.Directed) {
+	for _, structure := range test.structures {
+		communities := make([][]graph.Node, len(structure.memberships))
+		for i, c := range structure.memberships {
+			for n := range c {
+				communities[i] = append(communities[i], simple.Node(n))
+			}
+		}
+		got := Q(g, communities, structure.resolution)
+		if !floats.EqualWithinAbsOrRel(got, structure.want, structure.tol, structure.tol) && !math.IsNaN(structure.want) {
+			for _, c := range communities {
+				sort.Sort(ordered.ByID(c))
+			}
+			t.Errorf("unexpected Q value for %q %v: got: %v want: %v",
+				test.name, communities, got, structure.want)
+		}
+	}
+}
+
+func TestCommunityDeltaQDirected(t *testing.T) {
+	for _, test := range communityDirectedQTests {
+		g := simple.NewDirectedGraph()
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+
+		testCommunityDeltaQDirected(t, test, g)
+	}
+}
+
+func TestCommunityDeltaQWeightedDirected(t *testing.T) {
+	for _, test := range communityDirectedQTests {
+		g := simple.NewWeightedDirectedGraph(0, 0)
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetWeightedEdge(simple.WeightedEdge{F: simple.Node(u), T: simple.Node(v), W: 1})
+			}
+		}
+
+		testCommunityDeltaQDirected(t, test, g)
+	}
+}
+
+func testCommunityDeltaQDirected(t *testing.T, test communityDirectedQTest, g graph.Directed) {
+	rnd := rand.New(rand.NewSource(1)).Intn
+	for _, structure := range test.structures {
+		communityOf := make(map[int64]int)
+		communities := make([][]graph.Node, len(structure.memberships))
+		for i, c := range structure.memberships {
+			for n := range c {
+				n := int64(n)
+				communityOf[n] = i
+				communities[i] = append(communities[i], simple.Node(n))
+			}
+			sort.Sort(ordered.ByID(communities[i]))
+		}
+
+		before := Q(g, communities, structure.resolution)
+
+		l := newDirectedLocalMover(reduceDirected(g, nil), communities, structure.resolution)
+		if l == nil {
+			if !math.IsNaN(before) {
+				t.Errorf("unexpected nil localMover with non-NaN Q graph: Q=%.4v", before)
+			}
+			return
+		}
+
+		// This is done to avoid run-to-run
+		// variation due to map iteration order.
+		sort.Sort(ordered.ByID(l.nodes))
+
+		l.shuffle(rnd)
+
+		for _, target := range l.nodes {
+			got, gotDst, gotSrc := l.deltaQ(target)
+
+			want, wantDst := math.Inf(-1), -1
+			migrated := make([][]graph.Node, len(structure.memberships))
+			for i, c := range structure.memberships {
+				for n := range c {
+					n := int64(n)
+					if n == target.ID() {
+						continue
+					}
+					migrated[i] = append(migrated[i], simple.Node(n))
+				}
+				sort.Sort(ordered.ByID(migrated[i]))
+			}
+
+			for i, c := range structure.memberships {
+				if i == communityOf[target.ID()] {
+					continue
+				}
+				connected := false
+				for n := range c {
+					if g.HasEdgeBetween(simple.Node(n), target) {
+						connected = true
+						break
+					}
+				}
+				if !connected {
+					continue
+				}
+				migrated[i] = append(migrated[i], target)
+				after := Q(g, migrated, structure.resolution)
+				migrated[i] = migrated[i][:len(migrated[i])-1]
+				if after-before > want {
+					want = after - before
+					wantDst = i
+				}
+			}
+
+			if !floats.EqualWithinAbsOrRel(got, want, structure.tol, structure.tol) || gotDst != wantDst {
+				t.Errorf("unexpected result moving n=%d in c=%d of %s/%.4v: got: %.4v,%d want: %.4v,%d"+
+					"\n\t%v\n\t%v",
+					target.ID(), communityOf[target.ID()], test.name, structure.resolution, got, gotDst, want, wantDst,
+					communities, migrated)
+			}
+			if gotSrc.community != communityOf[target.ID()] {
+				t.Errorf("unexpected source community index: got: %d want: %d", gotSrc, communityOf[target.ID()])
+			} else if communities[gotSrc.community][gotSrc.node].ID() != target.ID() {
+				wantNodeIdx := -1
+				for i, n := range communities[gotSrc.community] {
+					if n.ID() == target.ID() {
+						wantNodeIdx = i
+						break
+					}
+				}
+				t.Errorf("unexpected source node index: got: %d want: %d", gotSrc.node, wantNodeIdx)
+			}
+		}
+	}
+}
+
+func TestReduceQConsistencyDirected(t *testing.T) {
+	for _, test := range communityDirectedQTests {
+		g := simple.NewDirectedGraph()
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+
+		testReduceQConsistencyDirected(t, test, g)
+	}
+}
+
+func TestReduceQConsistencyWeightedDirected(t *testing.T) {
+	for _, test := range communityDirectedQTests {
+		g := simple.NewWeightedDirectedGraph(0, 0)
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetWeightedEdge(simple.WeightedEdge{F: simple.Node(u), T: simple.Node(v), W: 1})
+			}
+		}
+
+		testReduceQConsistencyDirected(t, test, g)
+	}
+}
+
+func testReduceQConsistencyDirected(t *testing.T, test communityDirectedQTest, g graph.Directed) {
+	for _, structure := range test.structures {
+		if math.IsNaN(structure.want) {
+			return
+		}
+
+		communities := make([][]graph.Node, len(structure.memberships))
+		for i, c := range structure.memberships {
+			for n := range c {
+				communities[i] = append(communities[i], simple.Node(n))
+			}
+			sort.Sort(ordered.ByID(communities[i]))
+		}
+
+		gQ := Q(g, communities, structure.resolution)
+		gQnull := Q(g, nil, 1)
+
+		cg0 := reduceDirected(g, nil)
+		cg0Qnull := Q(cg0, cg0.Structure(), 1)
+		if !floats.EqualWithinAbsOrRel(gQnull, cg0Qnull, structure.tol, structure.tol) {
+			t.Errorf("disagreement between null Q from method: %v and function: %v", cg0Qnull, gQnull)
+		}
+		cg0Q := Q(cg0, communities, structure.resolution)
+		if !floats.EqualWithinAbsOrRel(gQ, cg0Q, structure.tol, structure.tol) {
+			t.Errorf("unexpected Q result after initial reduction: got: %v want :%v", cg0Q, gQ)
+		}
+
+		cg1 := reduceDirected(cg0, communities)
+		cg1Q := Q(cg1, cg1.Structure(), structure.resolution)
+		if !floats.EqualWithinAbsOrRel(gQ, cg1Q, structure.tol, structure.tol) {
+			t.Errorf("unexpected Q result after second reduction: got: %v want :%v", cg1Q, gQ)
+		}
+	}
+}
+
+type localDirectedMoveTest struct {
+	name       string
+	g          []intset
+	structures []moveStructures
+}
+
+var localDirectedMoveTests = []localDirectedMoveTest{
+	{
+		name: "blondel",
+		g:    blondel,
+		structures: []moveStructures{
+			{
+				memberships: []intset{
+					0: linksTo(0, 1, 2, 4, 5),
+					1: linksTo(3, 6, 7),
+					2: linksTo(8, 9, 10, 12, 14, 15),
+					3: linksTo(11, 13),
+				},
+				targetNodes: []graph.Node{simple.Node(0)},
+				resolution:  1,
+				tol:         1e-14,
+			},
+			{
+				memberships: []intset{
+					0: linksTo(0, 1, 2, 4, 5),
+					1: linksTo(3, 6, 7),
+					2: linksTo(8, 9, 10, 12, 14, 15),
+					3: linksTo(11, 13),
+				},
+				targetNodes: []graph.Node{simple.Node(3)},
+				resolution:  1,
+				tol:         1e-14,
+			},
+			{
+				memberships: []intset{
+					0: linksTo(0, 1, 2, 4, 5),
+					1: linksTo(3, 6, 7),
+					2: linksTo(8, 9, 10, 12, 14, 15),
+					3: linksTo(11, 13),
+				},
+				// Case to demonstrate when A_aa != k_a^𝛼.
+				targetNodes: []graph.Node{simple.Node(3), simple.Node(2)},
+				resolution:  1,
+				tol:         1e-14,
+			},
+		},
+	},
+}
+
+func TestMoveLocalDirected(t *testing.T) {
+	for _, test := range localDirectedMoveTests {
+		g := simple.NewDirectedGraph()
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+
+		testMoveLocalDirected(t, test, g)
+	}
+}
+
+func TestMoveLocalWeightedDirected(t *testing.T) {
+	for _, test := range localDirectedMoveTests {
+		g := simple.NewWeightedDirectedGraph(0, 0)
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetWeightedEdge(simple.WeightedEdge{F: simple.Node(u), T: simple.Node(v), W: 1})
+			}
+		}
+
+		testMoveLocalDirected(t, test, g)
+	}
+}
+
+func testMoveLocalDirected(t *testing.T, test localDirectedMoveTest, g graph.Directed) {
+	for _, structure := range test.structures {
+		communities := make([][]graph.Node, len(structure.memberships))
+		for i, c := range structure.memberships {
+			for n := range c {
+				communities[i] = append(communities[i], simple.Node(n))
+			}
+			sort.Sort(ordered.ByID(communities[i]))
+		}
+
+		r := reduceDirected(reduceDirected(g, nil), communities)
+
+		l := newDirectedLocalMover(r, r.communities, structure.resolution)
+		for _, n := range structure.targetNodes {
+			dQ, dst, src := l.deltaQ(n)
+			if dQ > 0 {
+				before := Q(r, l.communities, structure.resolution)
+				l.move(dst, src)
+				after := Q(r, l.communities, structure.resolution)
+				want := after - before
+				if !floats.EqualWithinAbsOrRel(dQ, want, structure.tol, structure.tol) {
+					t.Errorf("unexpected deltaQ: got: %v want: %v", dQ, want)
+				}
+			}
+		}
+	}
+}
+
+func TestModularizeDirected(t *testing.T) {
+	for _, test := range communityDirectedQTests {
+		g := simple.NewDirectedGraph()
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+
+		testModularizeDirected(t, test, g)
+	}
+}
+
+func TestModularizeWeightedDirected(t *testing.T) {
+	for _, test := range communityDirectedQTests {
+		g := simple.NewWeightedDirectedGraph(0, 0)
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetWeightedEdge(simple.WeightedEdge{F: simple.Node(u), T: simple.Node(v), W: 1})
+			}
+		}
+
+		testModularizeDirected(t, test, g)
+	}
+}
+
+func testModularizeDirected(t *testing.T, test communityDirectedQTest, g graph.Directed) {
+	const louvainIterations = 20
+
+	if test.structures[0].resolution != 1 {
+		panic("bad test: expect resolution=1")
+	}
+	want := make([][]graph.Node, len(test.structures[0].memberships))
+	for i, c := range test.structures[0].memberships {
+		for n := range c {
+			want[i] = append(want[i], simple.Node(n))
+		}
+		sort.Sort(ordered.ByID(want[i]))
+	}
+	sort.Sort(ordered.BySliceIDs(want))
+
+	var (
+		got   *ReducedDirected
+		bestQ = math.Inf(-1)
+	)
+	// Modularize is randomised so we do this to
+	// ensure the level tests are consistent.
+	src := rand.New(rand.NewSource(1))
+	for i := 0; i < louvainIterations; i++ {
+		r := Modularize(g, 1, src).(*ReducedDirected)
+		if q := Q(r, nil, 1); q > bestQ || math.IsNaN(q) {
+			bestQ = q
+			got = r
+
+			if math.IsNaN(q) {
+				// Don't try again for non-connected case.
+				break
+			}
+		}
+
+		var qs []float64
+		for p := r; p != nil; p = p.Expanded().(*ReducedDirected) {
+			qs = append(qs, Q(p, nil, 1))
+		}
+
+		// Recovery of Q values is reversed.
+		if reverse(qs); !sort.Float64sAreSorted(qs) {
+			t.Errorf("Q values not monotonically increasing: %.5v", qs)
+		}
+	}
+
+	gotCommunities := got.Communities()
+	for _, c := range gotCommunities {
+		sort.Sort(ordered.ByID(c))
+	}
+	sort.Sort(ordered.BySliceIDs(gotCommunities))
+	if !reflect.DeepEqual(gotCommunities, want) {
+		t.Errorf("unexpected community membership for %s Q=%.4v:\n\tgot: %v\n\twant:%v",
+			test.name, bestQ, gotCommunities, want)
+		return
+	}
+
+	var levels []level
+	for p := got; p != nil; p = p.Expanded().(*ReducedDirected) {
+		var communities [][]graph.Node
+		if p.parent != nil {
+			communities = p.parent.Communities()
+			for _, c := range communities {
+				sort.Sort(ordered.ByID(c))
+			}
+			sort.Sort(ordered.BySliceIDs(communities))
+		} else {
+			communities = reduceDirected(g, nil).Communities()
+		}
+		q := Q(p, nil, 1)
+		if math.IsNaN(q) {
+			// Use an equalable flag value in place of NaN.
+			q = math.Inf(-1)
+		}
+		levels = append(levels, level{q: q, communities: communities})
+	}
+	if !reflect.DeepEqual(levels, test.wantLevels) {
+		t.Errorf("unexpected level structure:\n\tgot: %v\n\twant:%v", levels, test.wantLevels)
+	}
+}
+
+func TestNonContiguousDirected(t *testing.T) {
+	g := simple.NewDirectedGraph()
+	for _, e := range []simple.Edge{
+		{F: simple.Node(0), T: simple.Node(1)},
+		{F: simple.Node(4), T: simple.Node(5)},
+	} {
+		g.SetEdge(e)
+	}
+
+	func() {
+		defer func() {
+			r := recover()
+			if r != nil {
+				t.Error("unexpected panic with non-contiguous ID range")
+			}
+		}()
+		Modularize(g, 1, nil)
+	}()
+}
+
+func TestNonContiguousWeightedDirected(t *testing.T) {
+	g := simple.NewWeightedDirectedGraph(0, 0)
+	for _, e := range []simple.WeightedEdge{
+		{F: simple.Node(0), T: simple.Node(1), W: 1},
+		{F: simple.Node(4), T: simple.Node(5), W: 1},
+	} {
+		g.SetWeightedEdge(e)
+	}
+
+	func() {
+		defer func() {
+			r := recover()
+			if r != nil {
+				t.Error("unexpected panic with non-contiguous ID range")
+			}
+		}()
+		Modularize(g, 1, nil)
+	}()
+}
+
+func BenchmarkLouvainDirected(b *testing.B) {
+	src := rand.New(rand.NewSource(1))
+	for i := 0; i < b.N; i++ {
+		Modularize(dupGraphDirected, 1, src)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/community/louvain_test.go b/vendor/gonum.org/v1/gonum/graph/community/louvain_test.go
new file mode 100644
index 00000000..32631404
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/community/louvain_test.go
@@ -0,0 +1,277 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package community
+
+import (
+	"fmt"
+	"math/rand"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/graphs/gen"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+// intset is an integer set.
+type intset map[int]struct{}
+
+func linksTo(i ...int) intset {
+	if len(i) == 0 {
+		return nil
+	}
+	s := make(intset)
+	for _, v := range i {
+		s[v] = struct{}{}
+	}
+	return s
+}
+
+type layer struct {
+	g          []intset
+	edgeWeight float64 // Zero edge weight is interpreted as 1.0.
+	weight     float64
+}
+
+var (
+	unconnected = []intset{ /* Nodes 0-4 are implicit .*/ 5: nil}
+
+	smallDumbell = []intset{
+		0: linksTo(1, 2),
+		1: linksTo(2),
+		2: linksTo(3),
+		3: linksTo(4, 5),
+		4: linksTo(5),
+		5: nil,
+	}
+	dumbellRepulsion = []intset{
+		0: linksTo(4),
+		1: linksTo(5),
+		2: nil,
+		3: nil,
+		4: nil,
+		5: nil,
+	}
+
+	repulsion = []intset{
+		0: linksTo(3, 4, 5),
+		1: linksTo(3, 4, 5),
+		2: linksTo(3, 4, 5),
+		3: linksTo(0, 1, 2),
+		4: linksTo(0, 1, 2),
+		5: linksTo(0, 1, 2),
+	}
+
+	simpleDirected = []intset{
+		0: linksTo(1),
+		1: linksTo(0, 4),
+		2: linksTo(1),
+		3: linksTo(0, 4),
+		4: linksTo(2),
+	}
+
+	// http://www.slate.com/blogs/the_world_/2014/07/17/the_middle_east_friendship_chart.html
+	middleEast = struct{ friends, complicated, enemies []intset }{
+		// green cells
+		friends: []intset{
+			0:  nil,
+			1:  linksTo(5, 7, 9, 12),
+			2:  linksTo(11),
+			3:  linksTo(4, 5, 10),
+			4:  linksTo(3, 5, 10),
+			5:  linksTo(1, 3, 4, 8, 10, 12),
+			6:  nil,
+			7:  linksTo(1, 12),
+			8:  linksTo(5, 9, 11),
+			9:  linksTo(1, 8, 12),
+			10: linksTo(3, 4, 5),
+			11: linksTo(2, 8),
+			12: linksTo(1, 5, 7, 9),
+		},
+
+		// yellow cells
+		complicated: []intset{
+			0:  linksTo(2, 4),
+			1:  linksTo(4, 8),
+			2:  linksTo(0, 3, 4, 5, 8, 9),
+			3:  linksTo(2, 8, 11),
+			4:  linksTo(0, 1, 2, 8),
+			5:  linksTo(2),
+			6:  nil,
+			7:  linksTo(9, 11),
+			8:  linksTo(1, 2, 3, 4, 10, 12),
+			9:  linksTo(2, 7, 11),
+			10: linksTo(8),
+			11: linksTo(3, 7, 9, 12),
+			12: linksTo(8, 11),
+		},
+
+		// red cells
+		enemies: []intset{
+			0:  linksTo(1, 3, 5, 6, 7, 8, 9, 10, 11, 12),
+			1:  linksTo(0, 2, 3, 6, 10, 11),
+			2:  linksTo(1, 6, 7, 10, 12),
+			3:  linksTo(0, 1, 6, 7, 9, 12),
+			4:  linksTo(6, 7, 9, 11, 12),
+			5:  linksTo(0, 6, 7, 9, 11),
+			6:  linksTo(0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12),
+			7:  linksTo(0, 2, 3, 4, 5, 6, 8, 10),
+			8:  linksTo(0, 6, 7),
+			9:  linksTo(0, 3, 4, 5, 6, 10),
+			10: linksTo(0, 1, 2, 6, 7, 9, 11, 12),
+			11: linksTo(0, 1, 4, 5, 6, 10),
+			12: linksTo(0, 2, 3, 4, 6, 10),
+		},
+	}
+
+	// W. W. Zachary, An information flow model for conflict and fission in small groups,
+	// Journal of Anthropological Research 33, 452-473 (1977).
+	//
+	// The edge list here is constructed such that all link descriptions
+	// head from a node with lower Page Rank to a node with higher Page
+	// Rank. This has no impact on undirected tests, but allows a sensible
+	// view for directed tests.
+	zachary = []intset{
+		0:  nil,                     // rank=0.097
+		1:  linksTo(0, 2),           // rank=0.05288
+		2:  linksTo(0, 32),          // rank=0.05708
+		3:  linksTo(0, 1, 2),        // rank=0.03586
+		4:  linksTo(0, 6, 10),       // rank=0.02198
+		5:  linksTo(0, 6),           // rank=0.02911
+		6:  linksTo(0, 5),           // rank=0.02911
+		7:  linksTo(0, 1, 2, 3),     // rank=0.02449
+		8:  linksTo(0, 2, 32, 33),   // rank=0.02977
+		9:  linksTo(2, 33),          // rank=0.01431
+		10: linksTo(0, 5),           // rank=0.02198
+		11: linksTo(0),              // rank=0.009565
+		12: linksTo(0, 3),           // rank=0.01464
+		13: linksTo(0, 1, 2, 3, 33), // rank=0.02954
+		14: linksTo(32, 33),         // rank=0.01454
+		15: linksTo(32, 33),         // rank=0.01454
+		16: linksTo(5, 6),           // rank=0.01678
+		17: linksTo(0, 1),           // rank=0.01456
+		18: linksTo(32, 33),         // rank=0.01454
+		19: linksTo(0, 1, 33),       // rank=0.0196
+		20: linksTo(32, 33),         // rank=0.01454
+		21: linksTo(0, 1),           // rank=0.01456
+		22: linksTo(32, 33),         // rank=0.01454
+		23: linksTo(32, 33),         // rank=0.03152
+		24: linksTo(27, 31),         // rank=0.02108
+		25: linksTo(23, 24, 31),     // rank=0.02101
+		26: linksTo(29, 33),         // rank=0.01504
+		27: linksTo(2, 23, 33),      // rank=0.02564
+		28: linksTo(2, 31, 33),      // rank=0.01957
+		29: linksTo(23, 32, 33),     // rank=0.02629
+		30: linksTo(1, 8, 32, 33),   // rank=0.02459
+		31: linksTo(0, 32, 33),      // rank=0.03716
+		32: linksTo(33),             // rank=0.07169
+		33: nil,                     // rank=0.1009
+	}
+
+	// doi:10.1088/1742-5468/2008/10/P10008 figure 1
+	//
+	// The edge list here is constructed such that all link descriptions
+	// head from a node with lower Page Rank to a node with higher Page
+	// Rank. This has no impact on undirected tests, but allows a sensible
+	// view for directed tests.
+	blondel = []intset{
+		0:  linksTo(2),           // rank=0.06858
+		1:  linksTo(2, 4, 7),     // rank=0.05264
+		2:  nil,                  // rank=0.08249
+		3:  linksTo(0, 7),        // rank=0.03884
+		4:  linksTo(0, 2, 10),    // rank=0.06754
+		5:  linksTo(0, 2, 7, 11), // rank=0.06738
+		6:  linksTo(2, 7, 11),    // rank=0.0528
+		7:  nil,                  // rank=0.07008
+		8:  linksTo(10),          // rank=0.09226
+		9:  linksTo(8),           // rank=0.05821
+		10: nil,                  // rank=0.1035
+		11: linksTo(8, 10),       // rank=0.08538
+		12: linksTo(9, 10),       // rank=0.04052
+		13: linksTo(10, 11),      // rank=0.03855
+		14: linksTo(8, 9, 10),    // rank=0.05621
+		15: linksTo(8),           // rank=0.02506
+	}
+)
+
+type structure struct {
+	resolution  float64
+	memberships []intset
+	want, tol   float64
+}
+
+type level struct {
+	q           float64
+	communities [][]graph.Node
+}
+
+type moveStructures struct {
+	memberships []intset
+	targetNodes []graph.Node
+
+	resolution float64
+	tol        float64
+}
+
+func reverse(f []float64) {
+	for i, j := 0, len(f)-1; i < j; i, j = i+1, j-1 {
+		f[i], f[j] = f[j], f[i]
+	}
+}
+
+func hasNegative(f []float64) bool {
+	for _, v := range f {
+		if v < 0 {
+			return true
+		}
+	}
+	return false
+}
+
+var (
+	dupGraph         = simple.NewUndirectedGraph()
+	dupGraphDirected = simple.NewDirectedGraph()
+)
+
+func init() {
+	err := gen.Duplication(dupGraph, 1000, 0.8, 0.1, 0.5, rand.New(rand.NewSource(1)))
+	if err != nil {
+		panic(err)
+	}
+
+	// Construct a directed graph from dupGraph
+	// such that every edge dupGraph is replaced
+	// with an edge that flows from the low node
+	// ID to the high node ID.
+	for _, e := range dupGraph.Edges() {
+		if e.To().ID() < e.From().ID() {
+			se := e.(simple.Edge)
+			se.F, se.T = se.T, se.F
+			e = se
+		}
+		dupGraphDirected.SetEdge(e)
+	}
+}
+
+// This init function checks the Middle East relationship data.
+func init() {
+	world := make([]intset, len(middleEast.friends))
+	for i := range world {
+		world[i] = make(intset)
+	}
+	for _, relationships := range [][]intset{middleEast.friends, middleEast.complicated, middleEast.enemies} {
+		for i, rel := range relationships {
+			for inter := range rel {
+				if _, ok := world[i][inter]; ok {
+					panic(fmt.Sprintf("unexpected relationship: %v--%v", i, inter))
+				}
+				world[i][inter] = struct{}{}
+			}
+		}
+	}
+	for i := range world {
+		if len(world[i]) != len(middleEast.friends)-1 {
+			panic(fmt.Sprintf("missing relationship in %v: %v", i, world[i]))
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/community/louvain_undirected.go b/vendor/gonum.org/v1/gonum/graph/community/louvain_undirected.go
new file mode 100644
index 00000000..450a438c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/community/louvain_undirected.go
@@ -0,0 +1,590 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package community
+
+import (
+	"math"
+	"math/rand"
+	"sort"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/ordered"
+	"gonum.org/v1/gonum/graph/internal/set"
+)
+
+// qUndirected returns the modularity Q score of the graph g subdivided into the
+// given communities at the given resolution. If communities is nil, the
+// unclustered modularity score is returned. The resolution parameter
+// is γ as defined in Reichardt and Bornholdt doi:10.1103/PhysRevE.74.016110.
+// qUndirected will panic if g has any edge with negative edge weight.
+//
+//  Q = 1/2m \sum_{ij} [ A_{ij} - (\gamma k_i k_j)/2m ] \delta(c_i,c_j)
+//
+// graph.Undirect may be used as a shim to allow calculation of Q for
+// directed graphs.
+func qUndirected(g graph.Undirected, communities [][]graph.Node, resolution float64) float64 {
+	nodes := g.Nodes()
+	weight := positiveWeightFuncFor(g)
+
+	// Calculate the total edge weight of the graph
+	// and the table of penetrating edge weight sums.
+	var m2 float64
+	k := make(map[int64]float64, len(nodes))
+	for _, u := range nodes {
+		w := weight(u, u)
+		for _, v := range g.From(u) {
+			w += weight(u, v)
+		}
+		m2 += w
+		k[u.ID()] = w
+	}
+
+	if communities == nil {
+		var q float64
+		for _, u := range nodes {
+			kU := k[u.ID()]
+			q += weight(u, u) - resolution*kU*kU/m2
+		}
+		return q / m2
+	}
+
+	// Iterate over the communities, calculating
+	// the non-self edge weights for the upper
+	// triangle and adjust the diagonal.
+	var q float64
+	for _, c := range communities {
+		for i, u := range c {
+			kU := k[u.ID()]
+			q += weight(u, u) - resolution*kU*kU/m2
+			for _, v := range c[i+1:] {
+				q += 2 * (weight(u, v) - resolution*kU*k[v.ID()]/m2)
+			}
+		}
+	}
+	return q / m2
+}
+
+// louvainUndirected returns the hierarchical modularization of g at the given
+// resolution using the Louvain algorithm. If src is nil, rand.Intn is used as
+// the random generator. louvainUndirected will panic if g has any edge with negative edge
+// weight.
+//
+// graph.Undirect may be used as a shim to allow modularization of directed graphs.
+func louvainUndirected(g graph.Undirected, resolution float64, src *rand.Rand) *ReducedUndirected {
+	// See louvain.tex for a detailed description
+	// of the algorithm used here.
+
+	c := reduceUndirected(g, nil)
+	rnd := rand.Intn
+	if src != nil {
+		rnd = src.Intn
+	}
+	for {
+		l := newUndirectedLocalMover(c, c.communities, resolution)
+		if l == nil {
+			return c
+		}
+		if done := l.localMovingHeuristic(rnd); done {
+			return c
+		}
+		c = reduceUndirected(c, l.communities)
+	}
+}
+
+// ReducedUndirected is an undirected graph of communities derived from a
+// parent graph by reduction.
+type ReducedUndirected struct {
+	// nodes is the set of nodes held
+	// by the graph. In a ReducedUndirected
+	// the node ID is the index into
+	// nodes.
+	nodes []community
+	undirectedEdges
+
+	// communities is the community
+	// structure of the graph.
+	communities [][]graph.Node
+
+	parent *ReducedUndirected
+}
+
+var (
+	reducedUndirected = (*ReducedUndirected)(nil)
+
+	_ graph.WeightedUndirected = reducedUndirected
+	_ ReducedGraph             = reducedUndirected
+)
+
+// Communities returns the community memberships of the nodes in the
+// graph used to generate the reduced graph.
+func (g *ReducedUndirected) Communities() [][]graph.Node {
+	communities := make([][]graph.Node, len(g.communities))
+	if g.parent == nil {
+		for i, members := range g.communities {
+			comm := make([]graph.Node, len(members))
+			for j, n := range members {
+				nodes := g.nodes[n.ID()].nodes
+				if len(nodes) != 1 {
+					panic("community: unexpected number of nodes in base graph community")
+				}
+				comm[j] = nodes[0]
+			}
+			communities[i] = comm
+		}
+		return communities
+	}
+	sub := g.parent.Communities()
+	for i, members := range g.communities {
+		var comm []graph.Node
+		for _, n := range members {
+			comm = append(comm, sub[n.ID()]...)
+		}
+		communities[i] = comm
+	}
+	return communities
+}
+
+// Structure returns the community structure of the current level of
+// the module clustering. The first index of the returned value
+// corresponds to the index of the nodes in the next higher level if
+// it exists. The returned value should not be mutated.
+func (g *ReducedUndirected) Structure() [][]graph.Node {
+	return g.communities
+}
+
+// Expanded returns the next lower level of the module clustering or nil
+// if at the lowest level.
+func (g *ReducedUndirected) Expanded() ReducedGraph {
+	return g.parent
+}
+
+// reduceUndirected returns a reduced graph constructed from g divided
+// into the given communities. The communities value is mutated
+// by the call to reduceUndirected. If communities is nil and g is a
+// ReducedUndirected, it is returned unaltered.
+func reduceUndirected(g graph.Undirected, communities [][]graph.Node) *ReducedUndirected {
+	if communities == nil {
+		if r, ok := g.(*ReducedUndirected); ok {
+			return r
+		}
+
+		nodes := g.Nodes()
+		// TODO(kortschak) This sort is necessary really only
+		// for testing. In practice we would not be using the
+		// community provided by the user for a Q calculation.
+		// Probably we should use a function to map the
+		// communities in the test sets to the remapped order.
+		sort.Sort(ordered.ByID(nodes))
+		communities = make([][]graph.Node, len(nodes))
+		for i := range nodes {
+			communities[i] = []graph.Node{node(i)}
+		}
+
+		weight := positiveWeightFuncFor(g)
+		r := ReducedUndirected{
+			nodes: make([]community, len(nodes)),
+			undirectedEdges: undirectedEdges{
+				edges:   make([][]int, len(nodes)),
+				weights: make(map[[2]int]float64),
+			},
+			communities: communities,
+		}
+		communityOf := make(map[int64]int, len(nodes))
+		for i, n := range nodes {
+			r.nodes[i] = community{id: i, nodes: []graph.Node{n}}
+			communityOf[n.ID()] = i
+		}
+		for _, u := range nodes {
+			var out []int
+			uid := communityOf[u.ID()]
+			for _, v := range g.From(u) {
+				vid := communityOf[v.ID()]
+				if vid != uid {
+					out = append(out, vid)
+				}
+				if uid < vid {
+					// Only store the weight once.
+					r.weights[[2]int{uid, vid}] = weight(u, v)
+				}
+			}
+			r.edges[uid] = out
+		}
+		return &r
+	}
+
+	// Remove zero length communities destructively.
+	var commNodes int
+	for i := 0; i < len(communities); {
+		comm := communities[i]
+		if len(comm) == 0 {
+			communities[i] = communities[len(communities)-1]
+			communities[len(communities)-1] = nil
+			communities = communities[:len(communities)-1]
+		} else {
+			commNodes += len(comm)
+			i++
+		}
+	}
+
+	r := ReducedUndirected{
+		nodes: make([]community, len(communities)),
+		undirectedEdges: undirectedEdges{
+			edges:   make([][]int, len(communities)),
+			weights: make(map[[2]int]float64),
+		},
+	}
+	r.communities = make([][]graph.Node, len(communities))
+	for i := range r.communities {
+		r.communities[i] = []graph.Node{node(i)}
+	}
+	if g, ok := g.(*ReducedUndirected); ok {
+		// Make sure we retain the truncated
+		// community structure.
+		g.communities = communities
+		r.parent = g
+	}
+	weight := positiveWeightFuncFor(g)
+	communityOf := make(map[int64]int, commNodes)
+	for i, comm := range communities {
+		r.nodes[i] = community{id: i, nodes: comm}
+		for _, n := range comm {
+			communityOf[n.ID()] = i
+		}
+	}
+	for uid, comm := range communities {
+		var out []int
+		for i, u := range comm {
+			r.nodes[uid].weight += weight(u, u)
+			for _, v := range comm[i+1:] {
+				r.nodes[uid].weight += 2 * weight(u, v)
+			}
+			for _, v := range g.From(u) {
+				vid := communityOf[v.ID()]
+				found := false
+				for _, e := range out {
+					if e == vid {
+						found = true
+						break
+					}
+				}
+				if !found && vid != uid {
+					out = append(out, vid)
+				}
+				if uid < vid {
+					// Only store the weight once.
+					r.weights[[2]int{uid, vid}] += weight(u, v)
+				}
+			}
+		}
+		r.edges[uid] = out
+	}
+	return &r
+}
+
+// Has returns whether the node exists within the graph.
+func (g *ReducedUndirected) Has(n graph.Node) bool {
+	id := n.ID()
+	return 0 <= id || id < int64(len(g.nodes))
+}
+
+// Nodes returns all the nodes in the graph.
+func (g *ReducedUndirected) Nodes() []graph.Node {
+	nodes := make([]graph.Node, len(g.nodes))
+	for i := range g.nodes {
+		nodes[i] = node(i)
+	}
+	return nodes
+}
+
+// From returns all nodes in g that can be reached directly from u.
+func (g *ReducedUndirected) From(u graph.Node) []graph.Node {
+	out := g.edges[u.ID()]
+	nodes := make([]graph.Node, len(out))
+	for i, vid := range out {
+		nodes[i] = g.nodes[vid]
+	}
+	return nodes
+}
+
+// HasEdgeBetween returns whether an edge exists between nodes x and y.
+func (g *ReducedUndirected) HasEdgeBetween(x, y graph.Node) bool {
+	xid := x.ID()
+	yid := y.ID()
+	if xid == yid || !isValidID(xid) || !isValidID(yid) {
+		return false
+	}
+	if xid > yid {
+		xid, yid = yid, xid
+	}
+	_, ok := g.weights[[2]int{int(xid), int(yid)}]
+	return ok
+}
+
+// Edge returns the edge from u to v if such an edge exists and nil otherwise.
+// The node v must be directly reachable from u as defined by the From method.
+func (g *ReducedUndirected) Edge(u, v graph.Node) graph.Edge {
+	return g.WeightedEdgeBetween(u, v)
+}
+
+// WeightedEdge returns the weighted edge from u to v if such an edge exists and nil otherwise.
+// The node v must be directly reachable from u as defined by the From method.
+func (g *ReducedUndirected) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
+	return g.WeightedEdgeBetween(u, v)
+}
+
+// EdgeBetween returns the edge between nodes x and y.
+func (g *ReducedUndirected) EdgeBetween(x, y graph.Node) graph.Edge {
+	return g.WeightedEdgeBetween(x, y)
+}
+
+// WeightedEdgeBetween returns the weighted edge between nodes x and y.
+func (g *ReducedUndirected) WeightedEdgeBetween(x, y graph.Node) graph.WeightedEdge {
+	xid := x.ID()
+	yid := y.ID()
+	if xid == yid || !isValidID(xid) || !isValidID(yid) {
+		return nil
+	}
+	if yid < xid {
+		xid, yid = yid, xid
+	}
+	w, ok := g.weights[[2]int{int(xid), int(yid)}]
+	if !ok {
+		return nil
+	}
+	return edge{from: g.nodes[x.ID()], to: g.nodes[y.ID()], weight: w}
+}
+
+// Weight returns the weight for the edge between x and y if Edge(x, y) returns a non-nil Edge.
+// If x and y are the same node the internal node weight is returned. If there is no joining
+// edge between the two nodes the weight value returned is zero. Weight returns true if an edge
+// exists between x and y or if x and y have the same ID, false otherwise.
+func (g *ReducedUndirected) Weight(x, y graph.Node) (w float64, ok bool) {
+	xid := x.ID()
+	yid := y.ID()
+	if !isValidID(xid) || !isValidID(yid) {
+		return 0, false
+	}
+	if xid == yid {
+		return g.nodes[xid].weight, true
+	}
+	if xid > yid {
+		xid, yid = yid, xid
+	}
+	w, ok = g.weights[[2]int{int(xid), int(yid)}]
+	return w, ok
+}
+
+// undirectedLocalMover is a step in graph modularity optimization.
+type undirectedLocalMover struct {
+	g *ReducedUndirected
+
+	// nodes is the set of working nodes.
+	nodes []graph.Node
+	// edgeWeightOf is the weighted degree
+	// of each node indexed by ID.
+	edgeWeightOf []float64
+
+	// m2 is the total sum of
+	// edge weights in g.
+	m2 float64
+
+	// weight is the weight function
+	// provided by g or a function
+	// that returns the Weight value
+	// of the non-nil edge between x
+	// and y.
+	weight func(x, y graph.Node) float64
+
+	// communities is the current
+	// division of g.
+	communities [][]graph.Node
+	// memberships is a mapping between
+	// node ID and community membership.
+	memberships []int
+
+	// resolution is the Reichardt and
+	// Bornholdt γ parameter as defined
+	// in doi:10.1103/PhysRevE.74.016110.
+	resolution float64
+
+	// moved indicates that a call to
+	// move has been made since the last
+	// call to shuffle.
+	moved bool
+
+	// changed indicates that a move
+	// has been made since the creation
+	// of the local mover.
+	changed bool
+}
+
+// newUndirectedLocalMover returns a new undirectedLocalMover initialized with
+// the graph g, a set of communities and a modularity resolution parameter. The
+// node IDs of g must be contiguous in [0,n) where n is the number of nodes.
+// If g has a zero edge weight sum, nil is returned.
+func newUndirectedLocalMover(g *ReducedUndirected, communities [][]graph.Node, resolution float64) *undirectedLocalMover {
+	nodes := g.Nodes()
+	l := undirectedLocalMover{
+		g:            g,
+		nodes:        nodes,
+		edgeWeightOf: make([]float64, len(nodes)),
+		communities:  communities,
+		memberships:  make([]int, len(nodes)),
+		resolution:   resolution,
+		weight:       positiveWeightFuncFor(g),
+	}
+
+	// Calculate the total edge weight of the graph
+	// and degree weights for each node.
+	for _, u := range l.nodes {
+		w := l.weight(u, u)
+		for _, v := range g.From(u) {
+			w += l.weight(u, v)
+		}
+		l.edgeWeightOf[u.ID()] = w
+		l.m2 += w
+	}
+	if l.m2 == 0 {
+		return nil
+	}
+
+	// Assign membership mappings.
+	for i, c := range communities {
+		for _, u := range c {
+			l.memberships[u.ID()] = i
+		}
+	}
+
+	return &l
+}
+
+// localMovingHeuristic performs the Louvain local moving heuristic until
+// no further moves can be made. It returns a boolean indicating that the
+// undirectedLocalMover has not made any improvement to the community
+// structure and so the Louvain algorithm is done.
+func (l *undirectedLocalMover) localMovingHeuristic(rnd func(int) int) (done bool) {
+	for {
+		l.shuffle(rnd)
+		for _, n := range l.nodes {
+			dQ, dst, src := l.deltaQ(n)
+			if dQ <= 0 {
+				continue
+			}
+			l.move(dst, src)
+		}
+		if !l.moved {
+			return !l.changed
+		}
+	}
+}
+
+// shuffle performs a Fisher-Yates shuffle on the nodes held by the
+// undirectedLocalMover using the random source rnd which should return
+// an integer in the range [0,n).
+func (l *undirectedLocalMover) shuffle(rnd func(n int) int) {
+	l.moved = false
+	for i := range l.nodes[:len(l.nodes)-1] {
+		j := i + rnd(len(l.nodes)-i)
+		l.nodes[i], l.nodes[j] = l.nodes[j], l.nodes[i]
+	}
+}
+
+// move moves the node at src to the community at dst.
+func (l *undirectedLocalMover) move(dst int, src commIdx) {
+	l.moved = true
+	l.changed = true
+
+	srcComm := l.communities[src.community]
+	n := srcComm[src.node]
+
+	l.memberships[n.ID()] = dst
+
+	l.communities[dst] = append(l.communities[dst], n)
+	srcComm[src.node], srcComm[len(srcComm)-1] = srcComm[len(srcComm)-1], nil
+	l.communities[src.community] = srcComm[:len(srcComm)-1]
+}
+
+// deltaQ returns the highest gain in modularity attainable by moving
+// n from its current community to another connected community and
+// the index of the chosen destination. The index into the
+// undirectedLocalMover's communities field is returned in src if n
+// is in communities.
+func (l *undirectedLocalMover) deltaQ(n graph.Node) (deltaQ float64, dst int, src commIdx) {
+	id := n.ID()
+	a_aa := l.weight(n, n)
+	k_a := l.edgeWeightOf[id]
+	m2 := l.m2
+	gamma := l.resolution
+
+	// Find communities connected to n.
+	connected := make(set.Ints)
+	// The following for loop is equivalent to:
+	//
+	//  for _, v := range l.g.From(n) {
+	//  	connected.Add(l.memberships[v.ID()])
+	//  }
+	//
+	// This is done to avoid an allocation.
+	for _, vid := range l.g.edges[id] {
+		connected.Add(l.memberships[vid])
+	}
+	// Insert the node's own community.
+	connected.Add(l.memberships[id])
+
+	candidates := make([]int, 0, len(connected))
+	for i := range connected {
+		candidates = append(candidates, i)
+	}
+	sort.Ints(candidates)
+
+	// Calculate the highest modularity gain
+	// from moving into another community and
+	// keep the index of that community.
+	var dQremove float64
+	dQadd, dst, src := math.Inf(-1), -1, commIdx{-1, -1}
+	for _, i := range candidates {
+		c := l.communities[i]
+		var k_aC, sigma_totC float64 // C is a substitution for ^𝛼 or ^𝛽.
+		var removal bool
+		for j, u := range c {
+			uid := u.ID()
+			if uid == id {
+				if src.community != -1 {
+					panic("community: multiple sources")
+				}
+				src = commIdx{i, j}
+				removal = true
+			}
+
+			k_aC += l.weight(n, u)
+			// sigma_totC could be kept for each community
+			// and updated for moves, changing the calculation
+			// of sigma_totC here from O(n_c) to O(1), but
+			// in practice the time savings do not appear
+			// to be compelling and do not make up for the
+			// increase in code complexity and space required.
+			sigma_totC += l.edgeWeightOf[uid]
+		}
+
+		// See louvain.tex for a derivation of these equations.
+		switch {
+		case removal:
+			// The community c was the current community,
+			// so calculate the change due to removal.
+			dQremove = k_aC /*^𝛼*/ - a_aa - gamma*k_a*(sigma_totC /*^𝛼*/ -k_a)/m2
+
+		default:
+			// Otherwise calculate the change due to an addition
+			// to c and retain if it is the current best.
+			dQ := k_aC /*^𝛽*/ - gamma*k_a*sigma_totC /*^𝛽*/ /m2
+			if dQ > dQadd {
+				dQadd = dQ
+				dst = i
+			}
+		}
+	}
+
+	return 2 * (dQadd - dQremove) / m2, dst, src
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/community/louvain_undirected_multiplex.go b/vendor/gonum.org/v1/gonum/graph/community/louvain_undirected_multiplex.go
new file mode 100644
index 00000000..23799522
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/community/louvain_undirected_multiplex.go
@@ -0,0 +1,826 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package community
+
+import (
+	"fmt"
+	"math"
+	"math/rand"
+	"sort"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/ordered"
+	"gonum.org/v1/gonum/graph/internal/set"
+)
+
+// UndirectedMultiplex is an undirected multiplex graph.
+type UndirectedMultiplex interface {
+	Multiplex
+
+	// Layer returns the lth layer of the
+	// multiplex graph.
+	Layer(l int) graph.Undirected
+}
+
+// qUndirectedMultiplex returns the modularity Q score of the multiplex graph layers
+// subdivided into the given communities at the given resolutions and weights. Q is
+// returned as the vector of weighted Q scores for each layer of the multiplex graph.
+// If communities is nil, the unclustered modularity score is returned.
+// If weights is nil layers are equally weighted, otherwise the length of
+// weights must equal the number of layers. If resolutions is nil, a resolution
+// of 1.0 is used for all layers, otherwise either a single element slice may be used
+// to specify a global resolution, or the length of resolutions must equal the number
+// of layers. The resolution parameter is γ as defined in Reichardt and Bornholdt
+// doi:10.1103/PhysRevE.74.016110.
+// qUndirectedMultiplex will panic if the graph has any layer weight-scaled edge with
+// negative edge weight.
+//
+//  Q_{layer} = w_{layer} \sum_{ij} [ A_{layer}*_{ij} - (\gamma_{layer} k_i k_j)/2m ] \delta(c_i,c_j)
+//
+// Note that Q values for multiplex graphs are not scaled by the total layer edge weight.
+//
+// graph.Undirect may be used as a shim to allow calculation of Q for
+// directed graphs.
+func qUndirectedMultiplex(g UndirectedMultiplex, communities [][]graph.Node, weights, resolutions []float64) []float64 {
+	q := make([]float64, g.Depth())
+	nodes := g.Nodes()
+	layerWeight := 1.0
+	layerResolution := 1.0
+	if len(resolutions) == 1 {
+		layerResolution = resolutions[0]
+	}
+	for l := 0; l < g.Depth(); l++ {
+		layer := g.Layer(l)
+
+		if weights != nil {
+			layerWeight = weights[l]
+		}
+		if layerWeight == 0 {
+			continue
+		}
+
+		if len(resolutions) > 1 {
+			layerResolution = resolutions[l]
+		}
+
+		var weight func(x, y graph.Node) float64
+		if layerWeight < 0 {
+			weight = negativeWeightFuncFor(layer)
+		} else {
+			weight = positiveWeightFuncFor(layer)
+		}
+
+		// Calculate the total edge weight of the layer
+		// and the table of penetrating edge weight sums.
+		var m2 float64
+		k := make(map[int64]float64, len(nodes))
+		for _, u := range nodes {
+			w := weight(u, u)
+			for _, v := range layer.From(u) {
+				w += weight(u, v)
+			}
+			m2 += w
+			k[u.ID()] = w
+		}
+
+		if communities == nil {
+			var qLayer float64
+			for _, u := range nodes {
+				kU := k[u.ID()]
+				qLayer += weight(u, u) - layerResolution*kU*kU/m2
+			}
+			q[l] = layerWeight * qLayer
+			continue
+		}
+
+		// Iterate over the communities, calculating
+		// the non-self edge weights for the upper
+		// triangle and adjust the diagonal.
+		var qLayer float64
+		for _, c := range communities {
+			for i, u := range c {
+				kU := k[u.ID()]
+				qLayer += weight(u, u) - layerResolution*kU*kU/m2
+				for _, v := range c[i+1:] {
+					qLayer += 2 * (weight(u, v) - layerResolution*kU*k[v.ID()]/m2)
+				}
+			}
+		}
+		q[l] = layerWeight * qLayer
+	}
+
+	return q
+}
+
+// UndirectedLayers implements UndirectedMultiplex.
+type UndirectedLayers []graph.Undirected
+
+// NewUndirectedLayers returns an UndirectedLayers using the provided layers
+// ensuring there is a match between IDs for each layer.
+func NewUndirectedLayers(layers ...graph.Undirected) (UndirectedLayers, error) {
+	if len(layers) == 0 {
+		return nil, nil
+	}
+	base := make(set.Int64s)
+	for _, n := range layers[0].Nodes() {
+		base.Add(n.ID())
+	}
+	for i, l := range layers[1:] {
+		next := make(set.Int64s)
+		for _, n := range l.Nodes() {
+			next.Add(n.ID())
+		}
+		if !set.Int64sEqual(next, base) {
+			return nil, fmt.Errorf("community: layer ID mismatch between layers: %d", i+1)
+		}
+	}
+	return layers, nil
+}
+
+// Nodes returns the nodes of the receiver.
+func (g UndirectedLayers) Nodes() []graph.Node {
+	if len(g) == 0 {
+		return nil
+	}
+	return g[0].Nodes()
+}
+
+// Depth returns the depth of the multiplex graph.
+func (g UndirectedLayers) Depth() int { return len(g) }
+
+// Layer returns the lth layer of the multiplex graph.
+func (g UndirectedLayers) Layer(l int) graph.Undirected { return g[l] }
+
+// louvainUndirectedMultiplex returns the hierarchical modularization of g at the given resolution
+// using the Louvain algorithm. If all is true and g has negatively weighted layers, all
+// communities will be searched during the modularization. If src is nil, rand.Intn is
+// used as the random generator. louvainUndirectedMultiplex will panic if g has any edge with
+// edge weight that does not sign-match the layer weight.
+//
+// graph.Undirect may be used as a shim to allow modularization of directed graphs.
+func louvainUndirectedMultiplex(g UndirectedMultiplex, weights, resolutions []float64, all bool, src *rand.Rand) *ReducedUndirectedMultiplex {
+	if weights != nil && len(weights) != g.Depth() {
+		panic("community: weights vector length mismatch")
+	}
+	if resolutions != nil && len(resolutions) != 1 && len(resolutions) != g.Depth() {
+		panic("community: resolutions vector length mismatch")
+	}
+
+	// See louvain.tex for a detailed description
+	// of the algorithm used here.
+
+	c := reduceUndirectedMultiplex(g, nil, weights)
+	rnd := rand.Intn
+	if src != nil {
+		rnd = src.Intn
+	}
+	for {
+		l := newUndirectedMultiplexLocalMover(c, c.communities, weights, resolutions, all)
+		if l == nil {
+			return c
+		}
+		if done := l.localMovingHeuristic(rnd); done {
+			return c
+		}
+		c = reduceUndirectedMultiplex(c, l.communities, weights)
+	}
+}
+
+// ReducedUndirectedMultiplex is an undirected graph of communities derived from a
+// parent graph by reduction.
+type ReducedUndirectedMultiplex struct {
+	// nodes is the set of nodes held
+	// by the graph. In a ReducedUndirectedMultiplex
+	// the node ID is the index into
+	// nodes.
+	nodes  []multiplexCommunity
+	layers []undirectedEdges
+
+	// communities is the community
+	// structure of the graph.
+	communities [][]graph.Node
+
+	parent *ReducedUndirectedMultiplex
+}
+
+var (
+	_ UndirectedMultiplex      = (*ReducedUndirectedMultiplex)(nil)
+	_ graph.WeightedUndirected = (*undirectedLayerHandle)(nil)
+)
+
+// Nodes returns all the nodes in the graph.
+func (g *ReducedUndirectedMultiplex) Nodes() []graph.Node {
+	nodes := make([]graph.Node, len(g.nodes))
+	for i := range g.nodes {
+		nodes[i] = node(i)
+	}
+	return nodes
+}
+
+// Depth returns the number of layers in the multiplex graph.
+func (g *ReducedUndirectedMultiplex) Depth() int { return len(g.layers) }
+
+// Layer returns the lth layer of the multiplex graph.
+func (g *ReducedUndirectedMultiplex) Layer(l int) graph.Undirected {
+	return undirectedLayerHandle{multiplex: g, layer: l}
+}
+
+// Communities returns the community memberships of the nodes in the
+// graph used to generate the reduced graph.
+func (g *ReducedUndirectedMultiplex) Communities() [][]graph.Node {
+	communities := make([][]graph.Node, len(g.communities))
+	if g.parent == nil {
+		for i, members := range g.communities {
+			comm := make([]graph.Node, len(members))
+			for j, n := range members {
+				nodes := g.nodes[n.ID()].nodes
+				if len(nodes) != 1 {
+					panic("community: unexpected number of nodes in base graph community")
+				}
+				comm[j] = nodes[0]
+			}
+			communities[i] = comm
+		}
+		return communities
+	}
+	sub := g.parent.Communities()
+	for i, members := range g.communities {
+		var comm []graph.Node
+		for _, n := range members {
+			comm = append(comm, sub[n.ID()]...)
+		}
+		communities[i] = comm
+	}
+	return communities
+}
+
+// Structure returns the community structure of the current level of
+// the module clustering. The first index of the returned value
+// corresponds to the index of the nodes in the next higher level if
+// it exists. The returned value should not be mutated.
+func (g *ReducedUndirectedMultiplex) Structure() [][]graph.Node {
+	return g.communities
+}
+
+// Expanded returns the next lower level of the module clustering or nil
+// if at the lowest level.
+func (g *ReducedUndirectedMultiplex) Expanded() ReducedMultiplex {
+	return g.parent
+}
+
+// reduceUndirectedMultiplex returns a reduced graph constructed from g divided
+// into the given communities. The communities value is mutated
+// by the call to reduceUndirectedMultiplex. If communities is nil and g is a
+// ReducedUndirectedMultiplex, it is returned unaltered.
+func reduceUndirectedMultiplex(g UndirectedMultiplex, communities [][]graph.Node, weights []float64) *ReducedUndirectedMultiplex {
+	if communities == nil {
+		if r, ok := g.(*ReducedUndirectedMultiplex); ok {
+			return r
+		}
+
+		nodes := g.Nodes()
+		// TODO(kortschak) This sort is necessary really only
+		// for testing. In practice we would not be using the
+		// community provided by the user for a Q calculation.
+		// Probably we should use a function to map the
+		// communities in the test sets to the remapped order.
+		sort.Sort(ordered.ByID(nodes))
+		communities = make([][]graph.Node, len(nodes))
+		for i := range nodes {
+			communities[i] = []graph.Node{node(i)}
+		}
+
+		r := ReducedUndirectedMultiplex{
+			nodes:       make([]multiplexCommunity, len(nodes)),
+			layers:      make([]undirectedEdges, g.Depth()),
+			communities: communities,
+		}
+		communityOf := make(map[int64]int, len(nodes))
+		for i, n := range nodes {
+			r.nodes[i] = multiplexCommunity{id: i, nodes: []graph.Node{n}, weights: make([]float64, depth(weights))}
+			communityOf[n.ID()] = i
+		}
+		for i := range r.layers {
+			r.layers[i] = undirectedEdges{
+				edges:   make([][]int, len(nodes)),
+				weights: make(map[[2]int]float64),
+			}
+		}
+		w := 1.0
+		for l := 0; l < g.Depth(); l++ {
+			layer := g.Layer(l)
+			if weights != nil {
+				w = weights[l]
+			}
+			if w == 0 {
+				continue
+			}
+			var sign float64
+			var weight func(x, y graph.Node) float64
+			if w < 0 {
+				sign, weight = -1, negativeWeightFuncFor(layer)
+			} else {
+				sign, weight = 1, positiveWeightFuncFor(layer)
+			}
+			for _, u := range nodes {
+				var out []int
+				uid := communityOf[u.ID()]
+				for _, v := range layer.From(u) {
+					vid := communityOf[v.ID()]
+					if vid != uid {
+						out = append(out, vid)
+					}
+					if uid < vid {
+						// Only store the weight once.
+						r.layers[l].weights[[2]int{uid, vid}] = sign * weight(u, v)
+					}
+				}
+				r.layers[l].edges[uid] = out
+			}
+		}
+		return &r
+	}
+
+	// Remove zero length communities destructively.
+	var commNodes int
+	for i := 0; i < len(communities); {
+		comm := communities[i]
+		if len(comm) == 0 {
+			communities[i] = communities[len(communities)-1]
+			communities[len(communities)-1] = nil
+			communities = communities[:len(communities)-1]
+		} else {
+			commNodes += len(comm)
+			i++
+		}
+	}
+
+	r := ReducedUndirectedMultiplex{
+		nodes:  make([]multiplexCommunity, len(communities)),
+		layers: make([]undirectedEdges, g.Depth()),
+	}
+	communityOf := make(map[int64]int, commNodes)
+	for i, comm := range communities {
+		r.nodes[i] = multiplexCommunity{id: i, nodes: comm, weights: make([]float64, depth(weights))}
+		for _, n := range comm {
+			communityOf[n.ID()] = i
+		}
+	}
+	for i := range r.layers {
+		r.layers[i] = undirectedEdges{
+			edges:   make([][]int, len(communities)),
+			weights: make(map[[2]int]float64),
+		}
+	}
+	r.communities = make([][]graph.Node, len(communities))
+	for i := range r.communities {
+		r.communities[i] = []graph.Node{node(i)}
+	}
+	if g, ok := g.(*ReducedUndirectedMultiplex); ok {
+		// Make sure we retain the truncated
+		// community structure.
+		g.communities = communities
+		r.parent = g
+	}
+	w := 1.0
+	for l := 0; l < g.Depth(); l++ {
+		layer := g.Layer(l)
+		if weights != nil {
+			w = weights[l]
+		}
+		if w == 0 {
+			continue
+		}
+		var sign float64
+		var weight func(x, y graph.Node) float64
+		if w < 0 {
+			sign, weight = -1, negativeWeightFuncFor(layer)
+		} else {
+			sign, weight = 1, positiveWeightFuncFor(layer)
+		}
+		for uid, comm := range communities {
+			var out []int
+			for i, u := range comm {
+				r.nodes[uid].weights[l] += sign * weight(u, u)
+				for _, v := range comm[i+1:] {
+					r.nodes[uid].weights[l] += 2 * sign * weight(u, v)
+				}
+				for _, v := range layer.From(u) {
+					vid := communityOf[v.ID()]
+					found := false
+					for _, e := range out {
+						if e == vid {
+							found = true
+							break
+						}
+					}
+					if !found && vid != uid {
+						out = append(out, vid)
+					}
+					if uid < vid {
+						// Only store the weight once.
+						r.layers[l].weights[[2]int{uid, vid}] += sign * weight(u, v)
+					}
+				}
+			}
+			r.layers[l].edges[uid] = out
+		}
+	}
+	return &r
+}
+
+// undirectedLayerHandle is a handle to a multiplex graph layer.
+type undirectedLayerHandle struct {
+	// multiplex is the complete
+	// multiplex graph.
+	multiplex *ReducedUndirectedMultiplex
+
+	// layer is an index into the
+	// multiplex for the current
+	// layer.
+	layer int
+}
+
+// Has returns whether the node exists within the graph.
+func (g undirectedLayerHandle) Has(n graph.Node) bool {
+	id := n.ID()
+	return 0 <= id && id < int64(len(g.multiplex.nodes))
+}
+
+// Nodes returns all the nodes in the graph.
+func (g undirectedLayerHandle) Nodes() []graph.Node {
+	nodes := make([]graph.Node, len(g.multiplex.nodes))
+	for i := range g.multiplex.nodes {
+		nodes[i] = node(i)
+	}
+	return nodes
+}
+
+// From returns all nodes in g that can be reached directly from u.
+func (g undirectedLayerHandle) From(u graph.Node) []graph.Node {
+	out := g.multiplex.layers[g.layer].edges[u.ID()]
+	nodes := make([]graph.Node, len(out))
+	for i, vid := range out {
+		nodes[i] = g.multiplex.nodes[vid]
+	}
+	return nodes
+}
+
+// HasEdgeBetween returns whether an edge exists between nodes x and y.
+func (g undirectedLayerHandle) HasEdgeBetween(x, y graph.Node) bool {
+	xid := x.ID()
+	yid := y.ID()
+	if xid == yid || !isValidID(xid) || !isValidID(yid) {
+		return false
+	}
+	if xid > yid {
+		xid, yid = yid, xid
+	}
+	_, ok := g.multiplex.layers[g.layer].weights[[2]int{int(xid), int(yid)}]
+	return ok
+}
+
+// Edge returns the edge from u to v if such an edge exists and nil otherwise.
+// The node v must be directly reachable from u as defined by the From method.
+func (g undirectedLayerHandle) Edge(u, v graph.Node) graph.Edge {
+	return g.WeightedEdgeBetween(u, v)
+}
+
+// WeightedEdge returns the weighted edge from u to v if such an edge exists and nil otherwise.
+// The node v must be directly reachable from u as defined by the From method.
+func (g undirectedLayerHandle) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
+	return g.WeightedEdgeBetween(u, v)
+}
+
+// EdgeBetween returns the edge between nodes x and y.
+func (g undirectedLayerHandle) EdgeBetween(x, y graph.Node) graph.Edge {
+	return g.WeightedEdgeBetween(x, y)
+}
+
+// WeightedEdgeBetween returns the weighted edge between nodes x and y.
+func (g undirectedLayerHandle) WeightedEdgeBetween(x, y graph.Node) graph.WeightedEdge {
+	xid := x.ID()
+	yid := y.ID()
+	if xid == yid || !isValidID(xid) || !isValidID(yid) {
+		return nil
+	}
+	if yid < xid {
+		xid, yid = yid, xid
+	}
+	w, ok := g.multiplex.layers[g.layer].weights[[2]int{int(xid), int(yid)}]
+	if !ok {
+		return nil
+	}
+	return multiplexEdge{from: g.multiplex.nodes[x.ID()], to: g.multiplex.nodes[y.ID()], weight: w}
+}
+
+// Weight returns the weight for the edge between x and y if Edge(x, y) returns a non-nil Edge.
+// If x and y are the same node the internal node weight is returned. If there is no joining
+// edge between the two nodes the weight value returned is zero. Weight returns true if an edge
+// exists between x and y or if x and y have the same ID, false otherwise.
+func (g undirectedLayerHandle) Weight(x, y graph.Node) (w float64, ok bool) {
+	xid := x.ID()
+	yid := y.ID()
+	if !isValidID(xid) || !isValidID(yid) {
+		return 0, false
+	}
+	if xid == yid {
+		return g.multiplex.nodes[xid].weights[g.layer], true
+	}
+	if xid > yid {
+		xid, yid = yid, xid
+	}
+	w, ok = g.multiplex.layers[g.layer].weights[[2]int{int(xid), int(yid)}]
+	return w, ok
+}
+
+// undirectedMultiplexLocalMover is a step in graph modularity optimization.
+type undirectedMultiplexLocalMover struct {
+	g *ReducedUndirectedMultiplex
+
+	// nodes is the set of working nodes.
+	nodes []graph.Node
+	// edgeWeightOf is the weighted degree
+	// of each node indexed by ID.
+	edgeWeightOf [][]float64
+
+	// m2 is the total sum of
+	// edge weights in g.
+	m2 []float64
+
+	// weight is the weight function
+	// provided by g or a function
+	// that returns the Weight value
+	// of the non-nil edge between x
+	// and y.
+	weight []func(x, y graph.Node) float64
+
+	// communities is the current
+	// division of g.
+	communities [][]graph.Node
+	// memberships is a mapping between
+	// node ID and community membership.
+	memberships []int
+
+	// resolution is the Reichardt and
+	// Bornholdt γ parameter as defined
+	// in doi:10.1103/PhysRevE.74.016110.
+	resolutions []float64
+
+	// weights is the layer weights for
+	// the modularisation.
+	weights []float64
+
+	// searchAll specifies whether the local
+	// mover should consider non-connected
+	// communities during the local moving
+	// heuristic.
+	searchAll bool
+
+	// moved indicates that a call to
+	// move has been made since the last
+	// call to shuffle.
+	moved bool
+
+	// changed indicates that a move
+	// has been made since the creation
+	// of the local mover.
+	changed bool
+}
+
+// newUndirectedMultiplexLocalMover returns a new undirectedMultiplexLocalMover initialized with
+// the graph g, a set of communities and a modularity resolution parameter. The
+// node IDs of g must be contiguous in [0,n) where n is the number of nodes.
+// If g has a zero edge weight sum, nil is returned.
+func newUndirectedMultiplexLocalMover(g *ReducedUndirectedMultiplex, communities [][]graph.Node, weights, resolutions []float64, all bool) *undirectedMultiplexLocalMover {
+	nodes := g.Nodes()
+	l := undirectedMultiplexLocalMover{
+		g:            g,
+		nodes:        nodes,
+		edgeWeightOf: make([][]float64, g.Depth()),
+		m2:           make([]float64, g.Depth()),
+		communities:  communities,
+		memberships:  make([]int, len(nodes)),
+		resolutions:  resolutions,
+		weights:      weights,
+		weight:       make([]func(x, y graph.Node) float64, g.Depth()),
+	}
+
+	// Calculate the total edge weight of the graph
+	// and degree weights for each node.
+	var zero int
+	for i := 0; i < g.Depth(); i++ {
+		l.edgeWeightOf[i] = make([]float64, len(nodes))
+		var weight func(x, y graph.Node) float64
+
+		if weights != nil {
+			if weights[i] == 0 {
+				zero++
+				continue
+			}
+			if weights[i] < 0 {
+				weight = negativeWeightFuncFor(g.Layer(i))
+				l.searchAll = all
+			} else {
+				weight = positiveWeightFuncFor(g.Layer(i))
+			}
+		} else {
+			weight = positiveWeightFuncFor(g.Layer(i))
+		}
+
+		l.weight[i] = weight
+		layer := g.Layer(i)
+		for _, u := range l.nodes {
+			w := weight(u, u)
+			for _, v := range layer.From(u) {
+				w += weight(u, v)
+			}
+			l.edgeWeightOf[i][u.ID()] = w
+			l.m2[i] += w
+		}
+		if l.m2[i] == 0 {
+			zero++
+		}
+	}
+	if zero == g.Depth() {
+		return nil
+	}
+
+	// Assign membership mappings.
+	for i, c := range communities {
+		for _, u := range c {
+			l.memberships[u.ID()] = i
+		}
+	}
+
+	return &l
+}
+
+// localMovingHeuristic performs the Louvain local moving heuristic until
+// no further moves can be made. It returns a boolean indicating that the
+// undirectedMultiplexLocalMover has not made any improvement to the community
+// structure and so the Louvain algorithm is done.
+func (l *undirectedMultiplexLocalMover) localMovingHeuristic(rnd func(int) int) (done bool) {
+	for {
+		l.shuffle(rnd)
+		for _, n := range l.nodes {
+			dQ, dst, src := l.deltaQ(n)
+			if dQ <= 0 {
+				continue
+			}
+			l.move(dst, src)
+		}
+		if !l.moved {
+			return !l.changed
+		}
+	}
+}
+
+// shuffle performs a Fisher-Yates shuffle on the nodes held by the
+// undirectedMultiplexLocalMover using the random source rnd which should return
+// an integer in the range [0,n).
+func (l *undirectedMultiplexLocalMover) shuffle(rnd func(n int) int) {
+	l.moved = false
+	for i := range l.nodes[:len(l.nodes)-1] {
+		j := i + rnd(len(l.nodes)-i)
+		l.nodes[i], l.nodes[j] = l.nodes[j], l.nodes[i]
+	}
+}
+
+// move moves the node at src to the community at dst.
+func (l *undirectedMultiplexLocalMover) move(dst int, src commIdx) {
+	l.moved = true
+	l.changed = true
+
+	srcComm := l.communities[src.community]
+	n := srcComm[src.node]
+
+	l.memberships[n.ID()] = dst
+
+	l.communities[dst] = append(l.communities[dst], n)
+	srcComm[src.node], srcComm[len(srcComm)-1] = srcComm[len(srcComm)-1], nil
+	l.communities[src.community] = srcComm[:len(srcComm)-1]
+}
+
+// deltaQ returns the highest gain in modularity attainable by moving
+// n from its current community to another connected community and
+// the index of the chosen destination. The index into the
+// undirectedMultiplexLocalMover's communities field is returned in src if n
+// is in communities.
+func (l *undirectedMultiplexLocalMover) deltaQ(n graph.Node) (deltaQ float64, dst int, src commIdx) {
+	id := n.ID()
+
+	var iterator minTaker
+	if l.searchAll {
+		iterator = &dense{n: len(l.communities)}
+	} else {
+		// Find communities connected to n.
+		connected := make(set.Ints)
+		// The following for loop is equivalent to:
+		//
+		//  for i := 0; i < l.g.Depth(); i++ {
+		//  	for _, v := range l.g.Layer(i).From(n) {
+		//  		connected.Add(l.memberships[v.ID()])
+		//  	}
+		//  }
+		//
+		// This is done to avoid an allocation for
+		// each layer.
+		for _, layer := range l.g.layers {
+			for _, vid := range layer.edges[id] {
+				connected.Add(l.memberships[vid])
+			}
+		}
+		// Insert the node's own community.
+		connected.Add(l.memberships[id])
+		iterator = newSlice(connected)
+	}
+
+	// Calculate the highest modularity gain
+	// from moving into another community and
+	// keep the index of that community.
+	var dQremove float64
+	dQadd, dst, src := math.Inf(-1), -1, commIdx{-1, -1}
+	var i int
+	for iterator.TakeMin(&i) {
+		c := l.communities[i]
+		var removal bool
+		var _dQadd float64
+		for layer := 0; layer < l.g.Depth(); layer++ {
+			m2 := l.m2[layer]
+			if m2 == 0 {
+				// Do not consider layers with zero sum edge weight.
+				continue
+			}
+			w := 1.0
+			if l.weights != nil {
+				w = l.weights[layer]
+			}
+			if w == 0 {
+				// Do not consider layers with zero weighting.
+				continue
+			}
+
+			var k_aC, sigma_totC float64 // C is a substitution for ^𝛼 or ^𝛽.
+			removal = false
+			for j, u := range c {
+				uid := u.ID()
+				if uid == id {
+					// Only mark and check src community on the first layer.
+					if layer == 0 {
+						if src.community != -1 {
+							panic("community: multiple sources")
+						}
+						src = commIdx{i, j}
+					}
+					removal = true
+				}
+
+				k_aC += l.weight[layer](n, u)
+				// sigma_totC could be kept for each community
+				// and updated for moves, changing the calculation
+				// of sigma_totC here from O(n_c) to O(1), but
+				// in practice the time savings do not appear
+				// to be compelling and do not make up for the
+				// increase in code complexity and space required.
+				sigma_totC += l.edgeWeightOf[layer][uid]
+			}
+
+			a_aa := l.weight[layer](n, n)
+			k_a := l.edgeWeightOf[layer][id]
+			gamma := 1.0
+			if l.resolutions != nil {
+				if len(l.resolutions) == 1 {
+					gamma = l.resolutions[0]
+				} else {
+					gamma = l.resolutions[layer]
+				}
+			}
+
+			// See louvain.tex for a derivation of these equations.
+			// The weighting term, w, is described in V Traag,
+			// "Algorithms and dynamical models for communities and
+			// reputation in social networks", chapter 5.
+			// http://www.traag.net/wp/wp-content/papercite-data/pdf/traag_algorithms_2013.pdf
+			switch {
+			case removal:
+				// The community c was the current community,
+				// so calculate the change due to removal.
+				dQremove += w * (k_aC /*^𝛼*/ - a_aa - gamma*k_a*(sigma_totC /*^𝛼*/ -k_a)/m2)
+
+			default:
+				// Otherwise calculate the change due to an addition
+				// to c.
+				_dQadd += w * (k_aC /*^𝛽*/ - gamma*k_a*sigma_totC /*^𝛽*/ /m2)
+			}
+		}
+		if !removal && _dQadd > dQadd {
+			dQadd = _dQadd
+			dst = i
+		}
+	}
+
+	return 2 * (dQadd - dQremove), dst, src
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/community/louvain_undirected_multiplex_test.go b/vendor/gonum.org/v1/gonum/graph/community/louvain_undirected_multiplex_test.go
new file mode 100644
index 00000000..6f593777
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/community/louvain_undirected_multiplex_test.go
@@ -0,0 +1,691 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package community
+
+import (
+	"math"
+	"math/rand"
+	"reflect"
+	"sort"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/ordered"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+var communityUndirectedMultiplexQTests = []struct {
+	name       string
+	layers     []layer
+	structures []structure
+
+	wantLevels []level
+}{
+	{
+		name:   "unconnected",
+		layers: []layer{{g: unconnected, weight: 1}},
+		structures: []structure{
+			{
+				resolution: 1,
+				memberships: []intset{
+					0: linksTo(0),
+					1: linksTo(1),
+					2: linksTo(2),
+					3: linksTo(3),
+					4: linksTo(4),
+					5: linksTo(5),
+				},
+				want: math.NaN(),
+			},
+		},
+		wantLevels: []level{
+			{
+				q: math.Inf(-1), // Here math.Inf(-1) is used as a place holder for NaN to allow use of reflect.DeepEqual.
+				communities: [][]graph.Node{
+					{simple.Node(0)},
+					{simple.Node(1)},
+					{simple.Node(2)},
+					{simple.Node(3)},
+					{simple.Node(4)},
+					{simple.Node(5)},
+				},
+			},
+		},
+	},
+	{
+		name: "small_dumbell",
+		layers: []layer{
+			{g: smallDumbell, edgeWeight: 1, weight: 1},
+			{g: dumbellRepulsion, edgeWeight: -1, weight: -1},
+		},
+		structures: []structure{
+			{
+				resolution: 1,
+				memberships: []intset{
+					0: linksTo(0, 1, 2),
+					1: linksTo(3, 4, 5),
+				},
+				want: 7.0, tol: 1e-10,
+			},
+			{
+				resolution: 1,
+				memberships: []intset{
+					0: linksTo(0, 1, 2, 3, 4, 5),
+				},
+				want: 0, tol: 1e-14,
+			},
+		},
+		wantLevels: []level{
+			{
+				q: 7.0,
+				communities: [][]graph.Node{
+					{simple.Node(0), simple.Node(1), simple.Node(2)},
+					{simple.Node(3), simple.Node(4), simple.Node(5)},
+				},
+			},
+			{
+				q: -1.4285714285714284,
+				communities: [][]graph.Node{
+					{simple.Node(0)},
+					{simple.Node(1)},
+					{simple.Node(2)},
+					{simple.Node(3)},
+					{simple.Node(4)},
+					{simple.Node(5)},
+				},
+			},
+		},
+	},
+	{
+		name: "small_dumbell_twice",
+		layers: []layer{
+			{g: smallDumbell, weight: 0.5},
+			{g: smallDumbell, weight: 0.5},
+		},
+		structures: []structure{
+			{
+				resolution: 1,
+				memberships: []intset{
+					0: linksTo(0, 1, 2),
+					1: linksTo(3, 4, 5),
+				},
+				want: 5, tol: 1e-10,
+			},
+			{
+				resolution: 1,
+				memberships: []intset{
+					0: linksTo(0, 1, 2, 3, 4, 5),
+				},
+				want: 0, tol: 1e-14,
+			},
+		},
+		wantLevels: []level{
+			{
+				q: 0.35714285714285715 * 14,
+				communities: [][]graph.Node{
+					{simple.Node(0), simple.Node(1), simple.Node(2)},
+					{simple.Node(3), simple.Node(4), simple.Node(5)},
+				},
+			},
+			{
+				q: -0.17346938775510204 * 14,
+				communities: [][]graph.Node{
+					{simple.Node(0)},
+					{simple.Node(1)},
+					{simple.Node(2)},
+					{simple.Node(3)},
+					{simple.Node(4)},
+					{simple.Node(5)},
+				},
+			},
+		},
+	},
+	{
+		name:   "repulsion",
+		layers: []layer{{g: repulsion, edgeWeight: -1, weight: -1}},
+		structures: []structure{
+			{
+				resolution: 1,
+				memberships: []intset{
+					0: linksTo(0, 1, 2),
+					1: linksTo(3, 4, 5),
+				},
+				want: 9.0, tol: 1e-10,
+			},
+			{
+				resolution: 1,
+				memberships: []intset{
+					0: linksTo(0),
+					1: linksTo(1),
+					2: linksTo(2),
+					3: linksTo(3),
+					4: linksTo(4),
+					5: linksTo(5),
+				},
+				want: 3, tol: 1e-14,
+			},
+		},
+		wantLevels: []level{
+			{
+				q: 9.0,
+				communities: [][]graph.Node{
+					{simple.Node(0), simple.Node(1), simple.Node(2)},
+					{simple.Node(3), simple.Node(4), simple.Node(5)},
+				},
+			},
+			{
+				q: 3.0,
+				communities: [][]graph.Node{
+					{simple.Node(0)},
+					{simple.Node(1)},
+					{simple.Node(2)},
+					{simple.Node(3)},
+					{simple.Node(4)},
+					{simple.Node(5)},
+				},
+			},
+		},
+	},
+	{
+		name: "middle_east",
+		layers: []layer{
+			{g: middleEast.friends, edgeWeight: 1, weight: 1},
+			{g: middleEast.enemies, edgeWeight: -1, weight: -1},
+		},
+		structures: []structure{
+			{
+				resolution: 1,
+				memberships: []intset{
+					0: linksTo(0, 6),
+					1: linksTo(1, 7, 9, 12),
+					2: linksTo(2, 8, 11),
+					3: linksTo(3, 4, 5, 10),
+				},
+				want: 33.8180574555, tol: 1e-9,
+			},
+			{
+				resolution: 1,
+				memberships: []intset{
+					0: linksTo(0, 2, 3, 4, 5, 10),
+					1: linksTo(1, 7, 9, 12),
+					2: linksTo(6),
+					3: linksTo(8, 11),
+				},
+				want: 30.92749658, tol: 1e-7,
+			},
+			{
+				resolution: 1,
+				memberships: []intset{
+					0: linksTo(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12),
+				},
+				want: 0, tol: 1e-14,
+			},
+		},
+		wantLevels: []level{
+			{
+				q: 33.818057455540355,
+				communities: [][]graph.Node{
+					{simple.Node(0), simple.Node(6)},
+					{simple.Node(1), simple.Node(7), simple.Node(9), simple.Node(12)},
+					{simple.Node(2), simple.Node(8), simple.Node(11)},
+					{simple.Node(3), simple.Node(4), simple.Node(5), simple.Node(10)},
+				},
+			},
+			{
+				q: 3.8071135430916545,
+				communities: [][]graph.Node{
+					{simple.Node(0)},
+					{simple.Node(1)},
+					{simple.Node(2)},
+					{simple.Node(3)},
+					{simple.Node(4)},
+					{simple.Node(5)},
+					{simple.Node(6)},
+					{simple.Node(7)},
+					{simple.Node(8)},
+					{simple.Node(9)},
+					{simple.Node(10)},
+					{simple.Node(11)},
+					{simple.Node(12)},
+				},
+			},
+		},
+	},
+}
+
+func TestCommunityQUndirectedMultiplex(t *testing.T) {
+	for _, test := range communityUndirectedMultiplexQTests {
+		g, weights, err := undirectedMultiplexFrom(test.layers)
+		if err != nil {
+			t.Errorf("unexpected error creating multiplex: %v", err)
+			continue
+		}
+
+		for _, structure := range test.structures {
+			communities := make([][]graph.Node, len(structure.memberships))
+			for i, c := range structure.memberships {
+				for n := range c {
+					communities[i] = append(communities[i], simple.Node(n))
+				}
+			}
+			q := QMultiplex(g, communities, weights, []float64{structure.resolution})
+			got := floats.Sum(q)
+			if !floats.EqualWithinAbsOrRel(got, structure.want, structure.tol, structure.tol) && !math.IsNaN(structure.want) {
+				for _, c := range communities {
+					sort.Sort(ordered.ByID(c))
+				}
+				t.Errorf("unexpected Q value for %q %v: got: %v %.3v want: %v",
+					test.name, communities, got, q, structure.want)
+			}
+		}
+	}
+}
+
+func TestCommunityDeltaQUndirectedMultiplex(t *testing.T) {
+tests:
+	for _, test := range communityUndirectedMultiplexQTests {
+		g, weights, err := undirectedMultiplexFrom(test.layers)
+		if err != nil {
+			t.Errorf("unexpected error creating multiplex: %v", err)
+			continue
+		}
+
+		rnd := rand.New(rand.NewSource(1)).Intn
+		for _, structure := range test.structures {
+			communityOf := make(map[int64]int)
+			communities := make([][]graph.Node, len(structure.memberships))
+			for i, c := range structure.memberships {
+				for n := range c {
+					n := int64(n)
+					communityOf[n] = i
+					communities[i] = append(communities[i], simple.Node(n))
+				}
+				sort.Sort(ordered.ByID(communities[i]))
+			}
+			resolution := []float64{structure.resolution}
+
+			before := QMultiplex(g, communities, weights, resolution)
+
+			// We test exhaustively.
+			const all = true
+
+			l := newUndirectedMultiplexLocalMover(
+				reduceUndirectedMultiplex(g, nil, weights),
+				communities, weights, resolution, all)
+			if l == nil {
+				if !math.IsNaN(floats.Sum(before)) {
+					t.Errorf("unexpected nil localMover with non-NaN Q graph: Q=%.4v", before)
+				}
+				continue tests
+			}
+
+			// This is done to avoid run-to-run
+			// variation due to map iteration order.
+			sort.Sort(ordered.ByID(l.nodes))
+
+			l.shuffle(rnd)
+
+			for _, target := range l.nodes {
+				got, gotDst, gotSrc := l.deltaQ(target)
+
+				want, wantDst := math.Inf(-1), -1
+				migrated := make([][]graph.Node, len(structure.memberships))
+				for i, c := range structure.memberships {
+					for n := range c {
+						n := int64(n)
+						if n == target.ID() {
+							continue
+						}
+						migrated[i] = append(migrated[i], simple.Node(n))
+					}
+					sort.Sort(ordered.ByID(migrated[i]))
+				}
+
+				for i, c := range structure.memberships {
+					if i == communityOf[target.ID()] {
+						continue
+					}
+					if !(all && hasNegative(weights)) {
+						connected := false
+					search:
+						for l := 0; l < g.Depth(); l++ {
+							if weights[l] < 0 {
+								connected = true
+								break search
+							}
+							layer := g.Layer(l)
+							for n := range c {
+								if layer.HasEdgeBetween(simple.Node(n), target) {
+									connected = true
+									break search
+								}
+							}
+						}
+						if !connected {
+							continue
+						}
+					}
+					migrated[i] = append(migrated[i], target)
+					after := QMultiplex(g, migrated, weights, resolution)
+					migrated[i] = migrated[i][:len(migrated[i])-1]
+					if delta := floats.Sum(after) - floats.Sum(before); delta > want {
+						want = delta
+						wantDst = i
+					}
+				}
+
+				if !floats.EqualWithinAbsOrRel(got, want, structure.tol, structure.tol) || gotDst != wantDst {
+					t.Errorf("unexpected result moving n=%d in c=%d of %s/%.4v: got: %.4v,%d want: %.4v,%d"+
+						"\n\t%v\n\t%v",
+						target.ID(), communityOf[target.ID()], test.name, structure.resolution, got, gotDst, want, wantDst,
+						communities, migrated)
+				}
+				if gotSrc.community != communityOf[target.ID()] {
+					t.Errorf("unexpected source community index: got: %d want: %d", gotSrc, communityOf[target.ID()])
+				} else if communities[gotSrc.community][gotSrc.node].ID() != target.ID() {
+					wantNodeIdx := -1
+					for i, n := range communities[gotSrc.community] {
+						if n.ID() == target.ID() {
+							wantNodeIdx = i
+							break
+						}
+					}
+					t.Errorf("unexpected source node index: got: %d want: %d", gotSrc.node, wantNodeIdx)
+				}
+			}
+		}
+	}
+}
+
+func TestReduceQConsistencyUndirectedMultiplex(t *testing.T) {
+tests:
+	for _, test := range communityUndirectedMultiplexQTests {
+		g, weights, err := undirectedMultiplexFrom(test.layers)
+		if err != nil {
+			t.Errorf("unexpected error creating multiplex: %v", err)
+			continue
+		}
+
+		for _, structure := range test.structures {
+			if math.IsNaN(structure.want) {
+				continue tests
+			}
+
+			communities := make([][]graph.Node, len(structure.memberships))
+			for i, c := range structure.memberships {
+				for n := range c {
+					communities[i] = append(communities[i], simple.Node(n))
+				}
+				sort.Sort(ordered.ByID(communities[i]))
+			}
+
+			gQ := QMultiplex(g, communities, weights, []float64{structure.resolution})
+			gQnull := QMultiplex(g, nil, weights, nil)
+
+			cg0 := reduceUndirectedMultiplex(g, nil, weights)
+			cg0Qnull := QMultiplex(cg0, cg0.Structure(), weights, nil)
+			if !floats.EqualWithinAbsOrRel(floats.Sum(gQnull), floats.Sum(cg0Qnull), structure.tol, structure.tol) {
+				t.Errorf("disagreement between null Q from method: %v and function: %v", cg0Qnull, gQnull)
+			}
+			cg0Q := QMultiplex(cg0, communities, weights, []float64{structure.resolution})
+			if !floats.EqualWithinAbsOrRel(floats.Sum(gQ), floats.Sum(cg0Q), structure.tol, structure.tol) {
+				t.Errorf("unexpected Q result after initial reduction: got: %v want :%v", cg0Q, gQ)
+			}
+
+			cg1 := reduceUndirectedMultiplex(cg0, communities, weights)
+			cg1Q := QMultiplex(cg1, cg1.Structure(), weights, []float64{structure.resolution})
+			if !floats.EqualWithinAbsOrRel(floats.Sum(gQ), floats.Sum(cg1Q), structure.tol, structure.tol) {
+				t.Errorf("unexpected Q result after second reduction: got: %v want :%v", cg1Q, gQ)
+			}
+		}
+	}
+}
+
+var localUndirectedMultiplexMoveTests = []struct {
+	name       string
+	layers     []layer
+	structures []moveStructures
+}{
+	{
+		name:   "blondel",
+		layers: []layer{{g: blondel, weight: 1}, {g: blondel, weight: 0.5}},
+		structures: []moveStructures{
+			{
+				memberships: []intset{
+					0: linksTo(0, 1, 2, 4, 5),
+					1: linksTo(3, 6, 7),
+					2: linksTo(8, 9, 10, 12, 14, 15),
+					3: linksTo(11, 13),
+				},
+				targetNodes: []graph.Node{simple.Node(0)},
+				resolution:  1,
+				tol:         1e-14,
+			},
+			{
+				memberships: []intset{
+					0: linksTo(0, 1, 2, 4, 5),
+					1: linksTo(3, 6, 7),
+					2: linksTo(8, 9, 10, 12, 14, 15),
+					3: linksTo(11, 13),
+				},
+				targetNodes: []graph.Node{simple.Node(3)},
+				resolution:  1,
+				tol:         1e-14,
+			},
+			{
+				memberships: []intset{
+					0: linksTo(0, 1, 2, 4, 5),
+					1: linksTo(3, 6, 7),
+					2: linksTo(8, 9, 10, 12, 14, 15),
+					3: linksTo(11, 13),
+				},
+				// Case to demonstrate when A_aa != k_a^𝛼.
+				targetNodes: []graph.Node{simple.Node(3), simple.Node(2)},
+				resolution:  1,
+				tol:         1e-14,
+			},
+		},
+	},
+}
+
+func TestMoveLocalUndirectedMultiplex(t *testing.T) {
+	for _, test := range localUndirectedMultiplexMoveTests {
+		g, weights, err := undirectedMultiplexFrom(test.layers)
+		if err != nil {
+			t.Errorf("unexpected error creating multiplex: %v", err)
+			continue
+		}
+
+		for _, structure := range test.structures {
+			communities := make([][]graph.Node, len(structure.memberships))
+			for i, c := range structure.memberships {
+				for n := range c {
+					communities[i] = append(communities[i], simple.Node(n))
+				}
+				sort.Sort(ordered.ByID(communities[i]))
+			}
+
+			r := reduceUndirectedMultiplex(reduceUndirectedMultiplex(g, nil, weights), communities, weights)
+
+			l := newUndirectedMultiplexLocalMover(r, r.communities, weights, []float64{structure.resolution}, true)
+			for _, n := range structure.targetNodes {
+				dQ, dst, src := l.deltaQ(n)
+				if dQ > 0 {
+					before := floats.Sum(QMultiplex(r, l.communities, weights, []float64{structure.resolution}))
+					l.move(dst, src)
+					after := floats.Sum(QMultiplex(r, l.communities, weights, []float64{structure.resolution}))
+					want := after - before
+					if !floats.EqualWithinAbsOrRel(dQ, want, structure.tol, structure.tol) {
+						t.Errorf("unexpected deltaQ: got: %v want: %v", dQ, want)
+					}
+				}
+			}
+		}
+	}
+}
+
+func TestLouvainMultiplex(t *testing.T) {
+	const louvainIterations = 20
+
+	for _, test := range communityUndirectedMultiplexQTests {
+		g, weights, err := undirectedMultiplexFrom(test.layers)
+		if err != nil {
+			t.Errorf("unexpected error creating multiplex: %v", err)
+			continue
+		}
+
+		if test.structures[0].resolution != 1 {
+			panic("bad test: expect resolution=1")
+		}
+		want := make([][]graph.Node, len(test.structures[0].memberships))
+		for i, c := range test.structures[0].memberships {
+			for n := range c {
+				want[i] = append(want[i], simple.Node(n))
+			}
+			sort.Sort(ordered.ByID(want[i]))
+		}
+		sort.Sort(ordered.BySliceIDs(want))
+
+		var (
+			got   *ReducedUndirectedMultiplex
+			bestQ = math.Inf(-1)
+		)
+		// Modularize is randomised so we do this to
+		// ensure the level tests are consistent.
+		src := rand.New(rand.NewSource(1))
+		for i := 0; i < louvainIterations; i++ {
+			r := ModularizeMultiplex(g, weights, nil, true, src).(*ReducedUndirectedMultiplex)
+			if q := floats.Sum(QMultiplex(r, nil, weights, nil)); q > bestQ || math.IsNaN(q) {
+				bestQ = q
+				got = r
+
+				if math.IsNaN(q) {
+					// Don't try again for non-connected case.
+					break
+				}
+			}
+
+			var qs []float64
+			for p := r; p != nil; p = p.Expanded().(*ReducedUndirectedMultiplex) {
+				qs = append(qs, floats.Sum(QMultiplex(p, nil, weights, nil)))
+			}
+
+			// Recovery of Q values is reversed.
+			if reverse(qs); !sort.Float64sAreSorted(qs) {
+				t.Errorf("Q values not monotonically increasing: %.5v", qs)
+			}
+		}
+
+		gotCommunities := got.Communities()
+		for _, c := range gotCommunities {
+			sort.Sort(ordered.ByID(c))
+		}
+		sort.Sort(ordered.BySliceIDs(gotCommunities))
+		if !reflect.DeepEqual(gotCommunities, want) {
+			t.Errorf("unexpected community membership for %s Q=%.4v:\n\tgot: %v\n\twant:%v",
+				test.name, bestQ, gotCommunities, want)
+			continue
+		}
+
+		var levels []level
+		for p := got; p != nil; p = p.Expanded().(*ReducedUndirectedMultiplex) {
+			var communities [][]graph.Node
+			if p.parent != nil {
+				communities = p.parent.Communities()
+				for _, c := range communities {
+					sort.Sort(ordered.ByID(c))
+				}
+				sort.Sort(ordered.BySliceIDs(communities))
+			} else {
+				communities = reduceUndirectedMultiplex(g, nil, weights).Communities()
+			}
+			q := floats.Sum(QMultiplex(p, nil, weights, nil))
+			if math.IsNaN(q) {
+				// Use an equalable flag value in place of NaN.
+				q = math.Inf(-1)
+			}
+			levels = append(levels, level{q: q, communities: communities})
+		}
+		if !reflect.DeepEqual(levels, test.wantLevels) {
+			t.Errorf("unexpected level structure:\n\tgot: %v\n\twant:%v", levels, test.wantLevels)
+		}
+	}
+}
+
+func TestNonContiguousUndirectedMultiplex(t *testing.T) {
+	g := simple.NewUndirectedGraph()
+	for _, e := range []simple.Edge{
+		{F: simple.Node(0), T: simple.Node(1)},
+		{F: simple.Node(4), T: simple.Node(5)},
+	} {
+		g.SetEdge(e)
+	}
+
+	func() {
+		defer func() {
+			r := recover()
+			if r != nil {
+				t.Error("unexpected panic with non-contiguous ID range")
+			}
+		}()
+		ModularizeMultiplex(UndirectedLayers{g}, nil, nil, true, nil)
+	}()
+}
+
+func TestNonContiguousWeightedUndirectedMultiplex(t *testing.T) {
+	g := simple.NewWeightedUndirectedGraph(0, 0)
+	for _, e := range []simple.WeightedEdge{
+		{F: simple.Node(0), T: simple.Node(1), W: 1},
+		{F: simple.Node(4), T: simple.Node(5), W: 1},
+	} {
+		g.SetWeightedEdge(e)
+	}
+
+	func() {
+		defer func() {
+			r := recover()
+			if r != nil {
+				t.Error("unexpected panic with non-contiguous ID range")
+			}
+		}()
+		ModularizeMultiplex(UndirectedLayers{g}, nil, nil, true, nil)
+	}()
+}
+
+func BenchmarkLouvainMultiplex(b *testing.B) {
+	src := rand.New(rand.NewSource(1))
+	for i := 0; i < b.N; i++ {
+		ModularizeMultiplex(UndirectedLayers{dupGraph}, nil, nil, true, src)
+	}
+}
+
+func undirectedMultiplexFrom(raw []layer) (UndirectedLayers, []float64, error) {
+	var layers []graph.Undirected
+	var weights []float64
+	for _, l := range raw {
+		g := simple.NewWeightedUndirectedGraph(0, 0)
+		for u, e := range l.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				w := 1.0
+				if l.edgeWeight != 0 {
+					w = l.edgeWeight
+				}
+				g.SetWeightedEdge(simple.WeightedEdge{F: simple.Node(u), T: simple.Node(v), W: w})
+			}
+		}
+		layers = append(layers, g)
+		weights = append(weights, l.weight)
+	}
+	g, err := NewUndirectedLayers(layers...)
+	if err != nil {
+		return nil, nil, err
+	}
+	return g, weights, nil
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/community/louvain_undirected_test.go b/vendor/gonum.org/v1/gonum/graph/community/louvain_undirected_test.go
new file mode 100644
index 00000000..b9a87722
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/community/louvain_undirected_test.go
@@ -0,0 +1,778 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package community
+
+import (
+	"math"
+	"math/rand"
+	"reflect"
+	"sort"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/ordered"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+type communityUndirectedQTest struct {
+	name       string
+	g          []intset
+	structures []structure
+
+	wantLevels []level
+}
+
+var communityUndirectedQTests = []communityUndirectedQTest{
+	// The java reference implementation is available from http://www.ludowaltman.nl/slm/.
+	{
+		name: "unconnected",
+		g:    unconnected,
+		structures: []structure{
+			{
+				resolution: 1,
+				memberships: []intset{
+					0: linksTo(0),
+					1: linksTo(1),
+					2: linksTo(2),
+					3: linksTo(3),
+					4: linksTo(4),
+					5: linksTo(5),
+				},
+				want: math.NaN(),
+			},
+		},
+		wantLevels: []level{
+			{
+				q: math.Inf(-1), // Here math.Inf(-1) is used as a place holder for NaN to allow use of reflect.DeepEqual.
+				communities: [][]graph.Node{
+					{simple.Node(0)},
+					{simple.Node(1)},
+					{simple.Node(2)},
+					{simple.Node(3)},
+					{simple.Node(4)},
+					{simple.Node(5)},
+				},
+			},
+		},
+	},
+	{
+		name: "small_dumbell",
+		g:    smallDumbell,
+		structures: []structure{
+			{
+				resolution: 1,
+				// community structure and modularity calculated by java reference implementation.
+				memberships: []intset{
+					0: linksTo(0, 1, 2),
+					1: linksTo(3, 4, 5),
+				},
+				want: 0.357, tol: 1e-3,
+			},
+			{
+				resolution: 1,
+				memberships: []intset{
+					0: linksTo(0, 1, 2, 3, 4, 5),
+				},
+				// theoretical expectation.
+				want: 0, tol: 1e-14,
+			},
+		},
+		wantLevels: []level{
+			{
+				q: 0.35714285714285715,
+				communities: [][]graph.Node{
+					{simple.Node(0), simple.Node(1), simple.Node(2)},
+					{simple.Node(3), simple.Node(4), simple.Node(5)},
+				},
+			},
+			{
+				q: -0.17346938775510204,
+				communities: [][]graph.Node{
+					{simple.Node(0)},
+					{simple.Node(1)},
+					{simple.Node(2)},
+					{simple.Node(3)},
+					{simple.Node(4)},
+					{simple.Node(5)},
+				},
+			},
+		},
+	},
+	{
+		name: "zachary",
+		g:    zachary,
+		structures: []structure{
+			{
+				resolution: 1,
+				// community structure and modularity from doi: 10.1140/epjb/e2013-40829-0
+				memberships: []intset{
+					0: linksTo(0, 1, 2, 3, 7, 11, 12, 13, 17, 19, 21),
+					1: linksTo(4, 5, 6, 10, 16),
+					2: linksTo(8, 9, 14, 15, 18, 20, 22, 26, 29, 30, 32, 33),
+					3: linksTo(23, 24, 25, 27, 28, 31),
+				},
+				// Noted to be the optimal modularisation in the paper above.
+				want: 0.4198, tol: 1e-4,
+			},
+			{
+				resolution: 0.5,
+				// community structure and modularity calculated by java reference implementation.
+				memberships: []intset{
+					0: linksTo(0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 16, 17, 19, 21),
+					1: linksTo(8, 14, 15, 18, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33),
+				},
+				want: 0.6218, tol: 1e-3,
+			},
+			{
+				resolution: 2,
+				// community structure and modularity calculated by java reference implementation.
+				memberships: []intset{
+					0: linksTo(14, 18, 20, 22, 32, 33, 15),
+					1: linksTo(0, 1, 11, 17, 19, 21),
+					2: linksTo(2, 3, 7, 9, 12, 13),
+					3: linksTo(4, 5, 6, 10, 16),
+					4: linksTo(24, 25, 28, 31),
+					5: linksTo(23, 26, 27, 29),
+					6: linksTo(8, 30),
+				},
+				want: 0.1645, tol: 1e-3,
+			},
+		},
+		wantLevels: []level{
+			{
+				q: 0.4197896120973044,
+				communities: [][]graph.Node{
+					{simple.Node(0), simple.Node(1), simple.Node(2), simple.Node(3), simple.Node(7), simple.Node(11), simple.Node(12), simple.Node(13), simple.Node(17), simple.Node(19), simple.Node(21)},
+					{simple.Node(4), simple.Node(5), simple.Node(6), simple.Node(10), simple.Node(16)},
+					{simple.Node(8), simple.Node(9), simple.Node(14), simple.Node(15), simple.Node(18), simple.Node(20), simple.Node(22), simple.Node(26), simple.Node(29), simple.Node(30), simple.Node(32), simple.Node(33)},
+					{simple.Node(23), simple.Node(24), simple.Node(25), simple.Node(27), simple.Node(28), simple.Node(31)},
+				},
+			},
+			{
+				q: 0.39907955292570674,
+				communities: [][]graph.Node{
+					{simple.Node(0), simple.Node(1), simple.Node(2), simple.Node(3), simple.Node(7), simple.Node(11), simple.Node(12), simple.Node(13), simple.Node(17), simple.Node(19), simple.Node(21)},
+					{simple.Node(4), simple.Node(10)},
+					{simple.Node(5), simple.Node(6), simple.Node(16)},
+					{simple.Node(8), simple.Node(9), simple.Node(14), simple.Node(15), simple.Node(18), simple.Node(20), simple.Node(22), simple.Node(26), simple.Node(29), simple.Node(30), simple.Node(32), simple.Node(33)},
+					{simple.Node(23), simple.Node(24), simple.Node(25), simple.Node(27), simple.Node(28), simple.Node(31)},
+				},
+			},
+			{
+				q: -0.04980276134122286,
+				communities: [][]graph.Node{
+					{simple.Node(0)},
+					{simple.Node(1)},
+					{simple.Node(2)},
+					{simple.Node(3)},
+					{simple.Node(4)},
+					{simple.Node(5)},
+					{simple.Node(6)},
+					{simple.Node(7)},
+					{simple.Node(8)},
+					{simple.Node(9)},
+					{simple.Node(10)},
+					{simple.Node(11)},
+					{simple.Node(12)},
+					{simple.Node(13)},
+					{simple.Node(14)},
+					{simple.Node(15)},
+					{simple.Node(16)},
+					{simple.Node(17)},
+					{simple.Node(18)},
+					{simple.Node(19)},
+					{simple.Node(20)},
+					{simple.Node(21)},
+					{simple.Node(22)},
+					{simple.Node(23)},
+					{simple.Node(24)},
+					{simple.Node(25)},
+					{simple.Node(26)},
+					{simple.Node(27)},
+					{simple.Node(28)},
+					{simple.Node(29)},
+					{simple.Node(30)},
+					{simple.Node(31)},
+					{simple.Node(32)},
+					{simple.Node(33)},
+				},
+			},
+		},
+	},
+	{
+		name: "blondel",
+		g:    blondel,
+		structures: []structure{
+			{
+				resolution: 1,
+				// community structure and modularity calculated by java reference implementation.
+				memberships: []intset{
+					0: linksTo(0, 1, 2, 3, 4, 5, 6, 7),
+					1: linksTo(8, 9, 10, 11, 12, 13, 14, 15),
+				},
+				want: 0.3922, tol: 1e-4,
+			},
+		},
+		wantLevels: []level{
+			{
+				q: 0.39221938775510207,
+				communities: [][]graph.Node{
+					{simple.Node(0), simple.Node(1), simple.Node(2), simple.Node(3), simple.Node(4), simple.Node(5), simple.Node(6), simple.Node(7)},
+					{simple.Node(8), simple.Node(9), simple.Node(10), simple.Node(11), simple.Node(12), simple.Node(13), simple.Node(14), simple.Node(15)},
+				},
+			},
+			{
+				q: 0.34630102040816324,
+				communities: [][]graph.Node{
+					{simple.Node(0), simple.Node(1), simple.Node(2), simple.Node(4), simple.Node(5)},
+					{simple.Node(3), simple.Node(6), simple.Node(7)},
+					{simple.Node(8), simple.Node(9), simple.Node(10), simple.Node(12), simple.Node(14), simple.Node(15)},
+					{simple.Node(11), simple.Node(13)},
+				},
+			},
+			{
+				q: -0.07142857142857144,
+				communities: [][]graph.Node{
+					{simple.Node(0)},
+					{simple.Node(1)},
+					{simple.Node(2)},
+					{simple.Node(3)},
+					{simple.Node(4)},
+					{simple.Node(5)},
+					{simple.Node(6)},
+					{simple.Node(7)},
+					{simple.Node(8)},
+					{simple.Node(9)},
+					{simple.Node(10)},
+					{simple.Node(11)},
+					{simple.Node(12)},
+					{simple.Node(13)},
+					{simple.Node(14)},
+					{simple.Node(15)},
+				},
+			},
+		},
+	},
+}
+
+func TestCommunityQUndirected(t *testing.T) {
+	for _, test := range communityUndirectedQTests {
+		g := simple.NewUndirectedGraph()
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+
+		testCommunityQUndirected(t, test, g)
+	}
+}
+
+func TestCommunityQWeightedUndirected(t *testing.T) {
+	for _, test := range communityUndirectedQTests {
+		g := simple.NewWeightedUndirectedGraph(0, 0)
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetWeightedEdge(simple.WeightedEdge{F: simple.Node(u), T: simple.Node(v), W: 1})
+			}
+		}
+
+		testCommunityQUndirected(t, test, g)
+	}
+}
+
+func testCommunityQUndirected(t *testing.T, test communityUndirectedQTest, g graph.Undirected) {
+	for _, structure := range test.structures {
+		communities := make([][]graph.Node, len(structure.memberships))
+		for i, c := range structure.memberships {
+			for n := range c {
+				communities[i] = append(communities[i], simple.Node(n))
+			}
+		}
+		got := Q(g, communities, structure.resolution)
+		if !floats.EqualWithinAbsOrRel(got, structure.want, structure.tol, structure.tol) && !math.IsNaN(structure.want) {
+			for _, c := range communities {
+				sort.Sort(ordered.ByID(c))
+			}
+			t.Errorf("unexpected Q value for %q %v: got: %v want: %v",
+				test.name, communities, got, structure.want)
+		}
+	}
+}
+
+func TestCommunityDeltaQUndirected(t *testing.T) {
+	for _, test := range communityUndirectedQTests {
+		g := simple.NewUndirectedGraph()
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+
+		testCommunityDeltaQUndirected(t, test, g)
+	}
+}
+
+func TestCommunityDeltaQWeightedUndirected(t *testing.T) {
+	for _, test := range communityUndirectedQTests {
+		g := simple.NewWeightedUndirectedGraph(0, 0)
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetWeightedEdge(simple.WeightedEdge{F: simple.Node(u), T: simple.Node(v), W: 1})
+			}
+		}
+
+		testCommunityDeltaQUndirected(t, test, g)
+	}
+}
+
+func testCommunityDeltaQUndirected(t *testing.T, test communityUndirectedQTest, g graph.Undirected) {
+	rnd := rand.New(rand.NewSource(1)).Intn
+	for _, structure := range test.structures {
+		communityOf := make(map[int64]int)
+		communities := make([][]graph.Node, len(structure.memberships))
+		for i, c := range structure.memberships {
+			for n := range c {
+				n := int64(n)
+				communityOf[n] = i
+				communities[i] = append(communities[i], simple.Node(n))
+			}
+			sort.Sort(ordered.ByID(communities[i]))
+		}
+
+		before := Q(g, communities, structure.resolution)
+
+		l := newUndirectedLocalMover(reduceUndirected(g, nil), communities, structure.resolution)
+		if l == nil {
+			if !math.IsNaN(before) {
+				t.Errorf("unexpected nil localMover with non-NaN Q graph: Q=%.4v", before)
+			}
+			return
+		}
+
+		// This is done to avoid run-to-run
+		// variation due to map iteration order.
+		sort.Sort(ordered.ByID(l.nodes))
+
+		l.shuffle(rnd)
+
+		for _, target := range l.nodes {
+			got, gotDst, gotSrc := l.deltaQ(target)
+
+			want, wantDst := math.Inf(-1), -1
+			migrated := make([][]graph.Node, len(structure.memberships))
+			for i, c := range structure.memberships {
+				for n := range c {
+					n := int64(n)
+					if n == target.ID() {
+						continue
+					}
+					migrated[i] = append(migrated[i], simple.Node(n))
+				}
+				sort.Sort(ordered.ByID(migrated[i]))
+			}
+
+			for i, c := range structure.memberships {
+				if i == communityOf[target.ID()] {
+					continue
+				}
+				connected := false
+				for n := range c {
+					if g.HasEdgeBetween(simple.Node(n), target) {
+						connected = true
+						break
+					}
+				}
+				if !connected {
+					continue
+				}
+				migrated[i] = append(migrated[i], target)
+				after := Q(g, migrated, structure.resolution)
+				migrated[i] = migrated[i][:len(migrated[i])-1]
+				if after-before > want {
+					want = after - before
+					wantDst = i
+				}
+			}
+
+			if !floats.EqualWithinAbsOrRel(got, want, structure.tol, structure.tol) || gotDst != wantDst {
+				t.Errorf("unexpected result moving n=%d in c=%d of %s/%.4v: got: %.4v,%d want: %.4v,%d"+
+					"\n\t%v\n\t%v",
+					target.ID(), communityOf[target.ID()], test.name, structure.resolution, got, gotDst, want, wantDst,
+					communities, migrated)
+			}
+			if gotSrc.community != communityOf[target.ID()] {
+				t.Errorf("unexpected source community index: got: %d want: %d", gotSrc, communityOf[target.ID()])
+			} else if communities[gotSrc.community][gotSrc.node].ID() != target.ID() {
+				wantNodeIdx := -1
+				for i, n := range communities[gotSrc.community] {
+					if n.ID() == target.ID() {
+						wantNodeIdx = i
+						break
+					}
+				}
+				t.Errorf("unexpected source node index: got: %d want: %d", gotSrc.node, wantNodeIdx)
+			}
+		}
+	}
+}
+
+func TestReduceQConsistencyUndirected(t *testing.T) {
+	for _, test := range communityUndirectedQTests {
+		g := simple.NewUndirectedGraph()
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+
+		testReduceQConsistencyUndirected(t, test, g)
+	}
+}
+
+func TestReduceQConsistencyWeightedUndirected(t *testing.T) {
+	for _, test := range communityUndirectedQTests {
+		g := simple.NewWeightedUndirectedGraph(0, 0)
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetWeightedEdge(simple.WeightedEdge{F: simple.Node(u), T: simple.Node(v), W: 1})
+			}
+		}
+
+		testReduceQConsistencyUndirected(t, test, g)
+	}
+}
+
+func testReduceQConsistencyUndirected(t *testing.T, test communityUndirectedQTest, g graph.Undirected) {
+	for _, structure := range test.structures {
+		if math.IsNaN(structure.want) {
+			return
+		}
+
+		communities := make([][]graph.Node, len(structure.memberships))
+		for i, c := range structure.memberships {
+			for n := range c {
+				communities[i] = append(communities[i], simple.Node(n))
+			}
+			sort.Sort(ordered.ByID(communities[i]))
+		}
+
+		gQ := Q(g, communities, structure.resolution)
+		gQnull := Q(g, nil, 1)
+
+		cg0 := reduceUndirected(g, nil)
+		cg0Qnull := Q(cg0, cg0.Structure(), 1)
+		if !floats.EqualWithinAbsOrRel(gQnull, cg0Qnull, structure.tol, structure.tol) {
+			t.Errorf("disagreement between null Q from method: %v and function: %v", cg0Qnull, gQnull)
+		}
+		cg0Q := Q(cg0, communities, structure.resolution)
+		if !floats.EqualWithinAbsOrRel(gQ, cg0Q, structure.tol, structure.tol) {
+			t.Errorf("unexpected Q result after initial reduction: got: %v want :%v", cg0Q, gQ)
+		}
+
+		cg1 := reduceUndirected(cg0, communities)
+		cg1Q := Q(cg1, cg1.Structure(), structure.resolution)
+		if !floats.EqualWithinAbsOrRel(gQ, cg1Q, structure.tol, structure.tol) {
+			t.Errorf("unexpected Q result after second reduction: got: %v want :%v", cg1Q, gQ)
+		}
+	}
+}
+
+type localUndirectedMoveTest struct {
+	name       string
+	g          []intset
+	structures []moveStructures
+}
+
+var localUndirectedMoveTests = []localUndirectedMoveTest{
+	{
+		name: "blondel",
+		g:    blondel,
+		structures: []moveStructures{
+			{
+				memberships: []intset{
+					0: linksTo(0, 1, 2, 4, 5),
+					1: linksTo(3, 6, 7),
+					2: linksTo(8, 9, 10, 12, 14, 15),
+					3: linksTo(11, 13),
+				},
+				targetNodes: []graph.Node{simple.Node(0)},
+				resolution:  1,
+				tol:         1e-14,
+			},
+			{
+				memberships: []intset{
+					0: linksTo(0, 1, 2, 4, 5),
+					1: linksTo(3, 6, 7),
+					2: linksTo(8, 9, 10, 12, 14, 15),
+					3: linksTo(11, 13),
+				},
+				targetNodes: []graph.Node{simple.Node(3)},
+				resolution:  1,
+				tol:         1e-14,
+			},
+			{
+				memberships: []intset{
+					0: linksTo(0, 1, 2, 4, 5),
+					1: linksTo(3, 6, 7),
+					2: linksTo(8, 9, 10, 12, 14, 15),
+					3: linksTo(11, 13),
+				},
+				// Case to demonstrate when A_aa != k_a^𝛼.
+				targetNodes: []graph.Node{simple.Node(3), simple.Node(2)},
+				resolution:  1,
+				tol:         1e-14,
+			},
+		},
+	},
+}
+
+func TestMoveLocalUndirected(t *testing.T) {
+	for _, test := range localUndirectedMoveTests {
+		g := simple.NewUndirectedGraph()
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+
+		testMoveLocalUndirected(t, test, g)
+	}
+}
+
+func TestMoveLocalWeightedUndirected(t *testing.T) {
+	for _, test := range localUndirectedMoveTests {
+		g := simple.NewWeightedUndirectedGraph(0, 0)
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetWeightedEdge(simple.WeightedEdge{F: simple.Node(u), T: simple.Node(v), W: 1})
+			}
+		}
+
+		testMoveLocalUndirected(t, test, g)
+	}
+}
+
+func testMoveLocalUndirected(t *testing.T, test localUndirectedMoveTest, g graph.Undirected) {
+	for _, structure := range test.structures {
+		communities := make([][]graph.Node, len(structure.memberships))
+		for i, c := range structure.memberships {
+			for n := range c {
+				communities[i] = append(communities[i], simple.Node(n))
+			}
+			sort.Sort(ordered.ByID(communities[i]))
+		}
+
+		r := reduceUndirected(reduceUndirected(g, nil), communities)
+
+		l := newUndirectedLocalMover(r, r.communities, structure.resolution)
+		for _, n := range structure.targetNodes {
+			dQ, dst, src := l.deltaQ(n)
+			if dQ > 0 {
+				before := Q(r, l.communities, structure.resolution)
+				l.move(dst, src)
+				after := Q(r, l.communities, structure.resolution)
+				want := after - before
+				if !floats.EqualWithinAbsOrRel(dQ, want, structure.tol, structure.tol) {
+					t.Errorf("unexpected deltaQ: got: %v want: %v", dQ, want)
+				}
+			}
+		}
+	}
+}
+
+func TestModularizeUndirected(t *testing.T) {
+	for _, test := range communityUndirectedQTests {
+		g := simple.NewUndirectedGraph()
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+
+		testModularizeUndirected(t, test, g)
+	}
+}
+
+func TestModularizeWeightedUndirected(t *testing.T) {
+	for _, test := range communityUndirectedQTests {
+		g := simple.NewWeightedUndirectedGraph(0, 0)
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetWeightedEdge(simple.WeightedEdge{F: simple.Node(u), T: simple.Node(v), W: 1})
+			}
+		}
+
+		testModularizeUndirected(t, test, g)
+	}
+}
+
+func testModularizeUndirected(t *testing.T, test communityUndirectedQTest, g graph.Undirected) {
+	const louvainIterations = 20
+
+	if test.structures[0].resolution != 1 {
+		panic("bad test: expect resolution=1")
+	}
+	want := make([][]graph.Node, len(test.structures[0].memberships))
+	for i, c := range test.structures[0].memberships {
+		for n := range c {
+			want[i] = append(want[i], simple.Node(n))
+		}
+		sort.Sort(ordered.ByID(want[i]))
+	}
+	sort.Sort(ordered.BySliceIDs(want))
+
+	var (
+		got   *ReducedUndirected
+		bestQ = math.Inf(-1)
+	)
+	// Modularize is randomised so we do this to
+	// ensure the level tests are consistent.
+	src := rand.New(rand.NewSource(1))
+	for i := 0; i < louvainIterations; i++ {
+		r := Modularize(g, 1, src).(*ReducedUndirected)
+		if q := Q(r, nil, 1); q > bestQ || math.IsNaN(q) {
+			bestQ = q
+			got = r
+
+			if math.IsNaN(q) {
+				// Don't try again for non-connected case.
+				break
+			}
+		}
+
+		var qs []float64
+		for p := r; p != nil; p = p.Expanded().(*ReducedUndirected) {
+			qs = append(qs, Q(p, nil, 1))
+		}
+
+		// Recovery of Q values is reversed.
+		if reverse(qs); !sort.Float64sAreSorted(qs) {
+			t.Errorf("Q values not monotonically increasing: %.5v", qs)
+		}
+	}
+
+	gotCommunities := got.Communities()
+	for _, c := range gotCommunities {
+		sort.Sort(ordered.ByID(c))
+	}
+	sort.Sort(ordered.BySliceIDs(gotCommunities))
+	if !reflect.DeepEqual(gotCommunities, want) {
+		t.Errorf("unexpected community membership for %s Q=%.4v:\n\tgot: %v\n\twant:%v",
+			test.name, bestQ, gotCommunities, want)
+		return
+	}
+
+	var levels []level
+	for p := got; p != nil; p = p.Expanded().(*ReducedUndirected) {
+		var communities [][]graph.Node
+		if p.parent != nil {
+			communities = p.parent.Communities()
+			for _, c := range communities {
+				sort.Sort(ordered.ByID(c))
+			}
+			sort.Sort(ordered.BySliceIDs(communities))
+		} else {
+			communities = reduceUndirected(g, nil).Communities()
+		}
+		q := Q(p, nil, 1)
+		if math.IsNaN(q) {
+			// Use an equalable flag value in place of NaN.
+			q = math.Inf(-1)
+		}
+		levels = append(levels, level{q: q, communities: communities})
+	}
+	if !reflect.DeepEqual(levels, test.wantLevels) {
+		t.Errorf("unexpected level structure:\n\tgot: %v\n\twant:%v", levels, test.wantLevels)
+	}
+}
+
+func TestNonContiguousUndirected(t *testing.T) {
+	g := simple.NewUndirectedGraph()
+	for _, e := range []simple.Edge{
+		{F: simple.Node(0), T: simple.Node(1)},
+		{F: simple.Node(4), T: simple.Node(5)},
+	} {
+		g.SetEdge(e)
+	}
+
+	func() {
+		defer func() {
+			r := recover()
+			if r != nil {
+				t.Error("unexpected panic with non-contiguous ID range")
+			}
+		}()
+		Modularize(g, 1, nil)
+	}()
+}
+
+func TestNonContiguousWeightedUndirected(t *testing.T) {
+	g := simple.NewWeightedUndirectedGraph(0, 0)
+	for _, e := range []simple.WeightedEdge{
+		{F: simple.Node(0), T: simple.Node(1), W: 1},
+		{F: simple.Node(4), T: simple.Node(5), W: 1},
+	} {
+		g.SetWeightedEdge(e)
+	}
+
+	func() {
+		defer func() {
+			r := recover()
+			if r != nil {
+				t.Error("unexpected panic with non-contiguous ID range")
+			}
+		}()
+		Modularize(g, 1, nil)
+	}()
+}
+
+func BenchmarkLouvain(b *testing.B) {
+	src := rand.New(rand.NewSource(1))
+	for i := 0; i < b.N; i++ {
+		Modularize(dupGraph, 1, src)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/community/printgraphs.go b/vendor/gonum.org/v1/gonum/graph/community/printgraphs.go
new file mode 100644
index 00000000..9d8eb1b7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/community/printgraphs.go
@@ -0,0 +1,142 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build ignore
+
+// printgraphs allows us to generate a consistent directed view of
+// a set of edges that follows a reasonably real-world-meaningful
+// graph. The interpretation of the links in the resulting directed
+// graphs are either "suggests" in the context of a Page Ranking or
+// possibly "looks up to" in the Zachary graph.
+package main
+
+import (
+	"fmt"
+	"sort"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/ordered"
+	"gonum.org/v1/gonum/graph/network"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+// set is an integer set.
+type set map[int]struct{}
+
+func linksTo(i ...int) set {
+	if len(i) == 0 {
+		return nil
+	}
+	s := make(set)
+	for _, v := range i {
+		s[v] = struct{}{}
+	}
+	return s
+}
+
+var (
+	zachary = []set{
+		0:  linksTo(1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 17, 19, 21, 31),
+		1:  linksTo(2, 3, 7, 13, 17, 19, 21, 30),
+		2:  linksTo(3, 7, 8, 9, 13, 27, 28, 32),
+		3:  linksTo(7, 12, 13),
+		4:  linksTo(6, 10),
+		5:  linksTo(6, 10, 16),
+		6:  linksTo(16),
+		8:  linksTo(30, 32, 33),
+		9:  linksTo(33),
+		13: linksTo(33),
+		14: linksTo(32, 33),
+		15: linksTo(32, 33),
+		18: linksTo(32, 33),
+		19: linksTo(33),
+		20: linksTo(32, 33),
+		22: linksTo(32, 33),
+		23: linksTo(25, 27, 29, 32, 33),
+		24: linksTo(25, 27, 31),
+		25: linksTo(31),
+		26: linksTo(29, 33),
+		27: linksTo(33),
+		28: linksTo(31, 33),
+		29: linksTo(32, 33),
+		30: linksTo(32, 33),
+		31: linksTo(32, 33),
+		32: linksTo(33),
+		33: nil,
+	}
+
+	blondel = []set{
+		0:  linksTo(2, 3, 4, 5),
+		1:  linksTo(2, 4, 7),
+		2:  linksTo(4, 5, 6),
+		3:  linksTo(7),
+		4:  linksTo(10),
+		5:  linksTo(7, 11),
+		6:  linksTo(7, 11),
+		8:  linksTo(9, 10, 11, 14, 15),
+		9:  linksTo(12, 14),
+		10: linksTo(11, 12, 13, 14),
+		11: linksTo(13),
+		15: nil,
+	}
+)
+
+func main() {
+	for _, raw := range []struct {
+		name string
+		set  []set
+	}{
+		{"zachary", zachary},
+		{"blondel", blondel},
+	} {
+		g := simple.NewUndirectedGraph(0, 0)
+		for u, e := range raw.set {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
+			}
+		}
+
+		nodes := g.Nodes()
+		sort.Sort(ordered.ByID(nodes))
+
+		fmt.Printf("%s = []set{\n", raw.name)
+		rank := network.PageRank(asDirected{g}, 0.85, 1e-8)
+		for _, u := range nodes {
+			to := g.From(nodes[u.ID()])
+			sort.Sort(ordered.ByID(to))
+			var links []int
+			for _, v := range to {
+				if rank[u.ID()] <= rank[v.ID()] {
+					links = append(links, v.ID())
+				}
+			}
+
+			if links == nil {
+				fmt.Printf("\t%d: nil, // rank=%.4v\n", u.ID(), rank[u.ID()])
+				continue
+			}
+
+			fmt.Printf("\t%d: linksTo(", u.ID())
+			for i, v := range links {
+				if i != 0 {
+					fmt.Print(", ")
+				}
+				fmt.Print(v)
+			}
+			fmt.Printf("), // rank=%.4v\n", rank[u.ID()])
+		}
+		fmt.Println("}")
+	}
+}
+
+type asDirected struct{ *simple.UndirectedGraph }
+
+func (g asDirected) HasEdgeFromTo(u, v graph.Node) bool {
+	return g.UndirectedGraph.HasEdgeBetween(u, v)
+}
+func (g asDirected) To(v graph.Node) []graph.Node { return g.From(v) }
diff --git a/vendor/gonum.org/v1/gonum/graph/doc.go b/vendor/gonum.org/v1/gonum/graph/doc.go
new file mode 100644
index 00000000..74477274
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/doc.go
@@ -0,0 +1,38 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+/*
+Package graph implements functions and interfaces to deal with formal discrete graphs. It aims to
+be first and foremost flexible, with speed as a strong second priority.
+
+In this package, graphs are taken to be directed, and undirected graphs are considered to be a
+special case of directed graphs that happen to have reciprocal edges. Graphs are, by default,
+unweighted, but functions that require weighted edges have several methods of dealing with this.
+In order of precedence:
+
+1. These functions have an argument called Cost (and in some cases, HeuristicCost). If this is
+present, it will always be used to determine the cost between two nodes.
+
+2. These functions will check if your graph implements the Coster (and/or HeuristicCoster)
+interface. If this is present, and the Cost (or HeuristicCost) argument is nil, these functions
+will be used.
+
+3. Finally, if no user data is supplied, it will use the functions UniformCost (always returns 1)
+and/or NulLHeuristic (always returns 0).
+
+For information on the specification for Cost functions, please see the Coster interface.
+
+Finally, although the functions take in a Graph -- they will always use the correct behavior.
+If your graph implements DirectedGraph, it will use Successors and To where applicable,
+if undirected, it will use From instead. If it implements neither, it will scan the edge list
+for successors and predecessors where applicable. (This is slow, you should always implement either
+Directed or Undirected)
+
+This package will never modify a graph that is not Mutable (and the interface does not allow it to
+do so). However, return values are free to be modified, so never pass a reference to your own edge
+list or node list.  It also guarantees that any nodes passed back to the user will be the same
+nodes returned to it -- that is, it will never take a Node's ID and then wrap the ID in a new
+struct and return that. You'll always get back your original data.
+*/
+package graph // import "gonum.org/v1/gonum/graph"
diff --git a/vendor/gonum.org/v1/gonum/graph/encoding/doc.go b/vendor/gonum.org/v1/gonum/graph/encoding/doc.go
new file mode 100644
index 00000000..1f51390f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/encoding/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package encoding provides a common graph encoding API.
+package encoding // import "gonum.org/v1/gonum/graph/encoding"
diff --git a/vendor/gonum.org/v1/gonum/graph/encoding/dot/decode.go b/vendor/gonum.org/v1/gonum/graph/encoding/dot/decode.go
new file mode 100644
index 00000000..ccc2868d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/encoding/dot/decode.go
@@ -0,0 +1,278 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package dot
+
+import (
+	"fmt"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/encoding"
+	"gonum.org/v1/gonum/graph/formats/dot"
+	"gonum.org/v1/gonum/graph/formats/dot/ast"
+	"gonum.org/v1/gonum/graph/internal/set"
+)
+
+// AttributeSetters is implemented by graph values that can set global
+// DOT attributes.
+type AttributeSetters interface {
+	// DOTAttributeSetters returns the global attribute setters.
+	DOTAttributeSetters() (graph, node, edge encoding.AttributeSetter)
+}
+
+// DOTIDSetter is implemented by types that can set a DOT ID.
+type DOTIDSetter interface {
+	SetDOTID(id string)
+}
+
+// Unmarshal parses the Graphviz DOT-encoded data and stores the result in dst.
+func Unmarshal(data []byte, dst encoding.Builder) error {
+	file, err := dot.ParseBytes(data)
+	if err != nil {
+		return err
+	}
+	if len(file.Graphs) != 1 {
+		return fmt.Errorf("invalid number of graphs; expected 1, got %d", len(file.Graphs))
+	}
+	return copyGraph(dst, file.Graphs[0])
+}
+
+// copyGraph copies the nodes and edges from the Graphviz AST source graph to
+// the destination graph. Edge direction is maintained if present.
+func copyGraph(dst encoding.Builder, src *ast.Graph) (err error) {
+	defer func() {
+		switch e := recover().(type) {
+		case nil:
+		case error:
+			err = e
+		default:
+			panic(e)
+		}
+	}()
+	gen := &generator{
+		directed: src.Directed,
+		ids:      make(map[string]graph.Node),
+	}
+	if a, ok := dst.(AttributeSetters); ok {
+		gen.graphAttr, gen.nodeAttr, gen.edgeAttr = a.DOTAttributeSetters()
+	}
+	for _, stmt := range src.Stmts {
+		gen.addStmt(dst, stmt)
+	}
+	return err
+}
+
+// A generator keeps track of the information required for generating a gonum
+// graph from a dot AST graph.
+type generator struct {
+	// Directed graph.
+	directed bool
+	// Map from dot AST node ID to gonum node.
+	ids map[string]graph.Node
+	// Nodes processed within the context of a subgraph, that is to be used as a
+	// vertex of an edge.
+	subNodes []graph.Node
+	// Stack of start indices into the subgraph node slice. The top element
+	// corresponds to the start index of the active (or inner-most) subgraph.
+	subStart []int
+	// graphAttr, nodeAttr and edgeAttr are global graph attributes.
+	graphAttr, nodeAttr, edgeAttr encoding.AttributeSetter
+}
+
+// node returns the gonum node corresponding to the given dot AST node ID,
+// generating a new such node if none exist.
+func (gen *generator) node(dst encoding.Builder, id string) graph.Node {
+	if n, ok := gen.ids[id]; ok {
+		return n
+	}
+	n := dst.NewNode()
+	dst.AddNode(n)
+	if n, ok := n.(DOTIDSetter); ok {
+		n.SetDOTID(id)
+	}
+	gen.ids[id] = n
+	// Check if within the context of a subgraph, that is to be used as a vertex
+	// of an edge.
+	if gen.isInSubgraph() {
+		// Append node processed within the context of a subgraph, that is to be
+		// used as a vertex of an edge
+		gen.appendSubgraphNode(n)
+	}
+	return n
+}
+
+// addStmt adds the given statement to the graph.
+func (gen *generator) addStmt(dst encoding.Builder, stmt ast.Stmt) {
+	switch stmt := stmt.(type) {
+	case *ast.NodeStmt:
+		n, ok := gen.node(dst, stmt.Node.ID).(encoding.AttributeSetter)
+		if !ok {
+			return
+		}
+		for _, attr := range stmt.Attrs {
+			a := encoding.Attribute{
+				Key:   attr.Key,
+				Value: attr.Val,
+			}
+			if err := n.SetAttribute(a); err != nil {
+				panic(fmt.Errorf("unable to unmarshal node DOT attribute (%s=%s)", a.Key, a.Value))
+			}
+		}
+	case *ast.EdgeStmt:
+		gen.addEdgeStmt(dst, stmt)
+	case *ast.AttrStmt:
+		var n encoding.AttributeSetter
+		var dst string
+		switch stmt.Kind {
+		case ast.GraphKind:
+			if gen.graphAttr == nil {
+				return
+			}
+			n = gen.graphAttr
+			dst = "graph"
+		case ast.NodeKind:
+			if gen.nodeAttr == nil {
+				return
+			}
+			n = gen.nodeAttr
+			dst = "node"
+		case ast.EdgeKind:
+			if gen.edgeAttr == nil {
+				return
+			}
+			n = gen.edgeAttr
+			dst = "edge"
+		default:
+			panic("unreachable")
+		}
+		for _, attr := range stmt.Attrs {
+			a := encoding.Attribute{
+				Key:   attr.Key,
+				Value: attr.Val,
+			}
+			if err := n.SetAttribute(a); err != nil {
+				panic(fmt.Errorf("unable to unmarshal global %s DOT attribute (%s=%s)", dst, a.Key, a.Value))
+			}
+		}
+	case *ast.Attr:
+		// ignore.
+	case *ast.Subgraph:
+		for _, stmt := range stmt.Stmts {
+			gen.addStmt(dst, stmt)
+		}
+	default:
+		panic(fmt.Sprintf("unknown statement type %T", stmt))
+	}
+}
+
+// addEdgeStmt adds the given edge statement to the graph.
+func (gen *generator) addEdgeStmt(dst encoding.Builder, stmt *ast.EdgeStmt) {
+	fs := gen.addVertex(dst, stmt.From)
+	ts := gen.addEdge(dst, stmt.To)
+	for _, f := range fs {
+		for _, t := range ts {
+			edge := dst.NewEdge(f, t)
+			dst.SetEdge(edge)
+			e, ok := edge.(encoding.AttributeSetter)
+			if !ok {
+				continue
+			}
+			for _, attr := range stmt.Attrs {
+				a := encoding.Attribute{
+					Key:   attr.Key,
+					Value: attr.Val,
+				}
+				if err := e.SetAttribute(a); err != nil {
+					panic(fmt.Errorf("unable to unmarshal edge DOT attribute (%s=%s)", a.Key, a.Value))
+				}
+			}
+		}
+	}
+}
+
+// addVertex adds the given vertex to the graph, and returns its set of nodes.
+func (gen *generator) addVertex(dst encoding.Builder, v ast.Vertex) []graph.Node {
+	switch v := v.(type) {
+	case *ast.Node:
+		n := gen.node(dst, v.ID)
+		return []graph.Node{n}
+	case *ast.Subgraph:
+		gen.pushSubgraph()
+		for _, stmt := range v.Stmts {
+			gen.addStmt(dst, stmt)
+		}
+		return gen.popSubgraph()
+	default:
+		panic(fmt.Sprintf("unknown vertex type %T", v))
+	}
+}
+
+// addEdge adds the given edge to the graph, and returns its set of nodes.
+func (gen *generator) addEdge(dst encoding.Builder, to *ast.Edge) []graph.Node {
+	if !gen.directed && to.Directed {
+		panic(fmt.Errorf("directed edge to %v in undirected graph", to.Vertex))
+	}
+	fs := gen.addVertex(dst, to.Vertex)
+	if to.To != nil {
+		ts := gen.addEdge(dst, to.To)
+		for _, f := range fs {
+			for _, t := range ts {
+				edge := dst.NewEdge(f, t)
+				dst.SetEdge(edge)
+			}
+		}
+	}
+	return fs
+}
+
+// pushSubgraph pushes the node start index of the active subgraph onto the
+// stack.
+func (gen *generator) pushSubgraph() {
+	gen.subStart = append(gen.subStart, len(gen.subNodes))
+}
+
+// popSubgraph pops the node start index of the active subgraph from the stack,
+// and returns the nodes processed since.
+func (gen *generator) popSubgraph() []graph.Node {
+	// Get nodes processed since the subgraph became active.
+	start := gen.subStart[len(gen.subStart)-1]
+	// TODO: Figure out a better way to store subgraph nodes, so that duplicates
+	// may not occur.
+	nodes := unique(gen.subNodes[start:])
+	// Remove subgraph from stack.
+	gen.subStart = gen.subStart[:len(gen.subStart)-1]
+	if len(gen.subStart) == 0 {
+		// Remove subgraph nodes when the bottom-most subgraph has been processed.
+		gen.subNodes = gen.subNodes[:0]
+	}
+	return nodes
+}
+
+// unique returns the set of unique nodes contained within ns.
+func unique(ns []graph.Node) []graph.Node {
+	var nodes []graph.Node
+	seen := make(set.Int64s)
+	for _, n := range ns {
+		id := n.ID()
+		if seen.Has(id) {
+			// skip duplicate node
+			continue
+		}
+		seen.Add(id)
+		nodes = append(nodes, n)
+	}
+	return nodes
+}
+
+// isInSubgraph reports whether the active context is within a subgraph, that is
+// to be used as a vertex of an edge.
+func (gen *generator) isInSubgraph() bool {
+	return len(gen.subStart) > 0
+}
+
+// appendSubgraphNode appends the given node to the slice of nodes processed
+// within the context of a subgraph.
+func (gen *generator) appendSubgraphNode(n graph.Node) {
+	gen.subNodes = append(gen.subNodes, n)
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/encoding/dot/decode_test.go b/vendor/gonum.org/v1/gonum/graph/encoding/dot/decode_test.go
new file mode 100644
index 00000000..d05b0507
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/encoding/dot/decode_test.go
@@ -0,0 +1,247 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package dot
+
+import (
+	"fmt"
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/encoding"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+func TestRoundTrip(t *testing.T) {
+	golden := []struct {
+		want     string
+		directed bool
+	}{
+		{
+			want:     directed,
+			directed: true,
+		},
+		{
+			want:     undirected,
+			directed: false,
+		},
+	}
+	for i, g := range golden {
+		var dst encoding.Builder
+		if g.directed {
+			dst = newDotDirectedGraph()
+		} else {
+			dst = newDotUndirectedGraph()
+		}
+		data := []byte(g.want)
+		if err := Unmarshal(data, dst); err != nil {
+			t.Errorf("i=%d: unable to unmarshal DOT graph; %v", i, err)
+			continue
+		}
+		buf, err := Marshal(dst, "", "", "\t", false)
+		if err != nil {
+			t.Errorf("i=%d: unable to marshal graph; %v", i, dst)
+			continue
+		}
+		got := string(buf)
+		if got != g.want {
+			t.Errorf("i=%d: graph content mismatch; want:\n%s\n\ngot:\n%s", i, g.want, got)
+			continue
+		}
+	}
+}
+
+const directed = `digraph {
+	graph [
+		outputorder=edgesfirst
+	];
+	node [
+		shape=circle
+		style=filled
+	];
+	edge [
+		penwidth=5
+		color=gray
+	];
+
+	// Node definitions.
+	A [label="foo 2"];
+	B [label="bar 2"];
+
+	// Edge definitions.
+	A -> B [label="baz 2"];
+}`
+
+const undirected = `graph {
+	graph [
+		outputorder=edgesfirst
+	];
+	node [
+		shape=circle
+		style=filled
+	];
+	edge [
+		penwidth=5
+		color=gray
+	];
+
+	// Node definitions.
+	A [label="foo 2"];
+	B [label="bar 2"];
+
+	// Edge definitions.
+	A -- B [label="baz 2"];
+}`
+
+// Below follows a minimal implementation of a graph capable of validating the
+// round-trip encoding and decoding of DOT graphs with nodes and edges
+// containing DOT attributes.
+
+// dotDirectedGraph extends simple.DirectedGraph to add NewNode and NewEdge
+// methods for creating user-defined nodes and edges.
+//
+// dotDirectedGraph implements the dot.Builder interface.
+type dotDirectedGraph struct {
+	*simple.DirectedGraph
+	graph, node, edge attributes
+}
+
+// newDotDirectedGraph returns a new directed capable of creating user-defined
+// nodes and edges.
+func newDotDirectedGraph() *dotDirectedGraph {
+	return &dotDirectedGraph{DirectedGraph: simple.NewDirectedGraph()}
+}
+
+// NewNode returns a new node with a unique node ID for the graph.
+func (g *dotDirectedGraph) NewNode() graph.Node {
+	return &dotNode{Node: g.DirectedGraph.NewNode()}
+}
+
+// NewEdge returns a new Edge from the source to the destination node.
+func (g *dotDirectedGraph) NewEdge(from, to graph.Node) graph.Edge {
+	return &dotEdge{Edge: g.DirectedGraph.NewEdge(from, to)}
+}
+
+// DOTAttributers implements the dot.Attributers interface.
+func (g *dotDirectedGraph) DOTAttributers() (graph, node, edge encoding.Attributer) {
+	return g.graph, g.node, g.edge
+}
+
+// DOTAttributeSetters implements the dot.AttributeSetters interface.
+func (g *dotDirectedGraph) DOTAttributeSetters() (graph, node, edge encoding.AttributeSetter) {
+	return &g.graph, &g.node, &g.edge
+}
+
+// dotUndirectedGraph extends simple.UndirectedGraph to add NewNode and NewEdge
+// methods for creating user-defined nodes and edges.
+//
+// dotUndirectedGraph implements the dot.Builder interface.
+type dotUndirectedGraph struct {
+	*simple.UndirectedGraph
+	graph, node, edge attributes
+}
+
+// newDotUndirectedGraph returns a new undirected capable of creating user-
+// defined nodes and edges.
+func newDotUndirectedGraph() *dotUndirectedGraph {
+	return &dotUndirectedGraph{UndirectedGraph: simple.NewUndirectedGraph()}
+}
+
+// NewNode adds a new node with a unique node ID to the graph.
+func (g *dotUndirectedGraph) NewNode() graph.Node {
+	return &dotNode{Node: g.UndirectedGraph.NewNode()}
+}
+
+// NewEdge returns a new Edge from the source to the destination node.
+func (g *dotUndirectedGraph) NewEdge(from, to graph.Node) graph.Edge {
+	return &dotEdge{Edge: g.UndirectedGraph.NewEdge(from, to)}
+}
+
+// DOTAttributers implements the dot.Attributers interface.
+func (g *dotUndirectedGraph) DOTAttributers() (graph, node, edge encoding.Attributer) {
+	return g.graph, g.node, g.edge
+}
+
+// DOTUnmarshalerAttrs implements the dot.UnmarshalerAttrs interface.
+func (g *dotUndirectedGraph) DOTAttributeSetters() (graph, node, edge encoding.AttributeSetter) {
+	return &g.graph, &g.node, &g.edge
+}
+
+// dotNode extends simple.Node with a label field to test round-trip encoding
+// and decoding of node DOT label attributes.
+type dotNode struct {
+	graph.Node
+	dotID string
+	// Node label.
+	Label string
+}
+
+// DOTID returns the node's DOT ID.
+func (n *dotNode) DOTID() string {
+	return n.dotID
+}
+
+// SetDOTID sets a DOT ID.
+func (n *dotNode) SetDOTID(id string) {
+	n.dotID = id
+}
+
+// SetAttribute sets a DOT attribute.
+func (n *dotNode) SetAttribute(attr encoding.Attribute) error {
+	if attr.Key != "label" {
+		return fmt.Errorf("unable to unmarshal node DOT attribute with key %q", attr.Key)
+	}
+	n.Label = attr.Value
+	return nil
+}
+
+// Attributes returns the DOT attributes of the node.
+func (n *dotNode) Attributes() []encoding.Attribute {
+	if len(n.Label) == 0 {
+		return nil
+	}
+	return []encoding.Attribute{{
+		Key:   "label",
+		Value: n.Label,
+	}}
+}
+
+// dotEdge extends simple.Edge with a label field to test round-trip encoding and
+// decoding of edge DOT label attributes.
+type dotEdge struct {
+	graph.Edge
+	// Edge label.
+	Label string
+}
+
+// SetAttribute sets a DOT attribute.
+func (e *dotEdge) SetAttribute(attr encoding.Attribute) error {
+	if attr.Key != "label" {
+		return fmt.Errorf("unable to unmarshal node DOT attribute with key %q", attr.Key)
+	}
+	e.Label = attr.Value
+	return nil
+}
+
+// Attributes returns the DOT attributes of the edge.
+func (e *dotEdge) Attributes() []encoding.Attribute {
+	if len(e.Label) == 0 {
+		return nil
+	}
+	return []encoding.Attribute{{
+		Key:   "label",
+		Value: e.Label,
+	}}
+}
+
+// attributes is a helper for global attributes.
+type attributes []encoding.Attribute
+
+func (a attributes) Attributes() []encoding.Attribute {
+	return []encoding.Attribute(a)
+}
+func (a *attributes) SetAttribute(attr encoding.Attribute) error {
+	*a = append(*a, attr)
+	return nil
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/encoding/dot/doc.go b/vendor/gonum.org/v1/gonum/graph/encoding/dot/doc.go
new file mode 100644
index 00000000..6a4a6675
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/encoding/dot/doc.go
@@ -0,0 +1,14 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package dot implements GraphViz DOT marshaling and unmarshaling of graphs.
+//
+// See the GraphViz DOT Guide and the DOT grammar for more information
+// on using specific aspects of the DOT language:
+//
+// DOT Guide: http://www.graphviz.org/Documentation/dotguide.pdf
+//
+// DOT grammar: http://www.graphviz.org/doc/info/lang.html
+//
+package dot // import "gonum.org/v1/gonum/graph/encoding/dot"
diff --git a/vendor/gonum.org/v1/gonum/graph/encoding/dot/dot.go b/vendor/gonum.org/v1/gonum/graph/encoding/dot/dot.go
new file mode 100644
index 00000000..2272d7ae
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/encoding/dot/dot.go
@@ -0,0 +1,5 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package dot
diff --git a/vendor/gonum.org/v1/gonum/graph/encoding/dot/encode.go b/vendor/gonum.org/v1/gonum/graph/encoding/dot/encode.go
new file mode 100644
index 00000000..a7a15493
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/encoding/dot/encode.go
@@ -0,0 +1,359 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package dot
+
+import (
+	"bytes"
+	"errors"
+	"fmt"
+	"sort"
+	"strings"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/encoding"
+	"gonum.org/v1/gonum/graph/internal/ordered"
+)
+
+// Node is a DOT graph node.
+type Node interface {
+	// DOTID returns a DOT node ID.
+	//
+	// An ID is one of the following:
+	//
+	//  - a string of alphabetic ([a-zA-Z\x80-\xff]) characters, underscores ('_').
+	//    digits ([0-9]), not beginning with a digit.
+	//  - a numeral [-]?(.[0-9]+ | [0-9]+(.[0-9]*)?).
+	//  - a double-quoted string ("...") possibly containing escaped quotes (\").
+	//  - an HTML string (<...>).
+	DOTID() string
+}
+
+// Attributers are graph.Graph values that specify top-level DOT
+// attributes.
+type Attributers interface {
+	DOTAttributers() (graph, node, edge encoding.Attributer)
+}
+
+// Porter defines the behavior of graph.Edge values that can specify
+// connection ports for their end points. The returned port corresponds
+// to the the DOT node port to be used by the edge, compass corresponds
+// to DOT compass point to which the edge will be aimed.
+type Porter interface {
+	FromPort() (port, compass string)
+	ToPort() (port, compass string)
+}
+
+// Structurer represents a graph.Graph that can define subgraphs.
+type Structurer interface {
+	Structure() []Graph
+}
+
+// Graph wraps named graph.Graph values.
+type Graph interface {
+	graph.Graph
+	DOTID() string
+}
+
+// Subgrapher wraps graph.Node values that represent subgraphs.
+type Subgrapher interface {
+	Subgraph() graph.Graph
+}
+
+// Marshal returns the DOT encoding for the graph g, applying the prefix
+// and indent to the encoding. Name is used to specify the graph name. If
+// name is empty and g implements Graph, the returned string from DOTID
+// will be used. If strict is true the output bytes will be prefixed with
+// the DOT "strict" keyword.
+//
+// Graph serialization will work for a graph.Graph without modification,
+// however, advanced GraphViz DOT features provided by Marshal depend on
+// implementation of the Node, Attributer, Porter, Attributers, Structurer,
+// Subgrapher and Graph interfaces.
+func Marshal(g graph.Graph, name, prefix, indent string, strict bool) ([]byte, error) {
+	var p printer
+	p.indent = indent
+	p.prefix = prefix
+	p.visited = make(map[edge]bool)
+	if strict {
+		p.buf.WriteString("strict ")
+	}
+	err := p.print(g, name, false, false)
+	if err != nil {
+		return nil, err
+	}
+	return p.buf.Bytes(), nil
+}
+
+type printer struct {
+	buf bytes.Buffer
+
+	prefix string
+	indent string
+	depth  int
+
+	visited map[edge]bool
+
+	err error
+}
+
+type edge struct {
+	inGraph  string
+	from, to int64
+}
+
+func (p *printer) print(g graph.Graph, name string, needsIndent, isSubgraph bool) error {
+	nodes := g.Nodes()
+	sort.Sort(ordered.ByID(nodes))
+
+	p.buf.WriteString(p.prefix)
+	if needsIndent {
+		for i := 0; i < p.depth; i++ {
+			p.buf.WriteString(p.indent)
+		}
+	}
+	_, isDirected := g.(graph.Directed)
+	if isSubgraph {
+		p.buf.WriteString("sub")
+	} else if isDirected {
+		p.buf.WriteString("di")
+	}
+	p.buf.WriteString("graph")
+
+	if name == "" {
+		if g, ok := g.(Graph); ok {
+			name = g.DOTID()
+		}
+	}
+	if name != "" {
+		p.buf.WriteByte(' ')
+		p.buf.WriteString(name)
+	}
+
+	p.openBlock(" {")
+	if a, ok := g.(Attributers); ok {
+		p.writeAttributeComplex(a)
+	}
+	if s, ok := g.(Structurer); ok {
+		for _, g := range s.Structure() {
+			_, subIsDirected := g.(graph.Directed)
+			if subIsDirected != isDirected {
+				return errors.New("dot: mismatched graph type")
+			}
+			p.buf.WriteByte('\n')
+			p.print(g, g.DOTID(), true, true)
+		}
+	}
+
+	havePrintedNodeHeader := false
+	for _, n := range nodes {
+		if s, ok := n.(Subgrapher); ok {
+			// If the node is not linked to any other node
+			// the graph needs to be written now.
+			if len(g.From(n)) == 0 {
+				g := s.Subgraph()
+				_, subIsDirected := g.(graph.Directed)
+				if subIsDirected != isDirected {
+					return errors.New("dot: mismatched graph type")
+				}
+				if !havePrintedNodeHeader {
+					p.newline()
+					p.buf.WriteString("// Node definitions.")
+					havePrintedNodeHeader = true
+				}
+				p.newline()
+				p.print(g, graphID(g, n), false, true)
+			}
+			continue
+		}
+		if !havePrintedNodeHeader {
+			p.newline()
+			p.buf.WriteString("// Node definitions.")
+			havePrintedNodeHeader = true
+		}
+		p.newline()
+		p.writeNode(n)
+		if a, ok := n.(encoding.Attributer); ok {
+			p.writeAttributeList(a)
+		}
+		p.buf.WriteByte(';')
+	}
+
+	havePrintedEdgeHeader := false
+	for _, n := range nodes {
+		to := g.From(n)
+		sort.Sort(ordered.ByID(to))
+		for _, t := range to {
+			if isDirected {
+				if p.visited[edge{inGraph: name, from: n.ID(), to: t.ID()}] {
+					continue
+				}
+				p.visited[edge{inGraph: name, from: n.ID(), to: t.ID()}] = true
+			} else {
+				if p.visited[edge{inGraph: name, from: n.ID(), to: t.ID()}] {
+					continue
+				}
+				p.visited[edge{inGraph: name, from: n.ID(), to: t.ID()}] = true
+				p.visited[edge{inGraph: name, from: t.ID(), to: n.ID()}] = true
+			}
+
+			if !havePrintedEdgeHeader {
+				p.buf.WriteByte('\n')
+				p.buf.WriteString(strings.TrimRight(p.prefix, " \t\n")) // Trim whitespace suffix.
+				p.newline()
+				p.buf.WriteString("// Edge definitions.")
+				havePrintedEdgeHeader = true
+			}
+			p.newline()
+
+			if s, ok := n.(Subgrapher); ok {
+				g := s.Subgraph()
+				_, subIsDirected := g.(graph.Directed)
+				if subIsDirected != isDirected {
+					return errors.New("dot: mismatched graph type")
+				}
+				p.print(g, graphID(g, n), false, true)
+			} else {
+				p.writeNode(n)
+			}
+			e, edgeIsPorter := g.Edge(n, t).(Porter)
+			if edgeIsPorter {
+				p.writePorts(e.FromPort())
+			}
+
+			if isDirected {
+				p.buf.WriteString(" -> ")
+			} else {
+				p.buf.WriteString(" -- ")
+			}
+
+			if s, ok := t.(Subgrapher); ok {
+				g := s.Subgraph()
+				_, subIsDirected := g.(graph.Directed)
+				if subIsDirected != isDirected {
+					return errors.New("dot: mismatched graph type")
+				}
+				p.print(g, graphID(g, t), false, true)
+			} else {
+				p.writeNode(t)
+			}
+			if edgeIsPorter {
+				p.writePorts(e.ToPort())
+			}
+
+			if a, ok := g.Edge(n, t).(encoding.Attributer); ok {
+				p.writeAttributeList(a)
+			}
+
+			p.buf.WriteByte(';')
+		}
+	}
+	p.closeBlock("}")
+
+	return nil
+}
+
+func (p *printer) writeNode(n graph.Node) {
+	p.buf.WriteString(nodeID(n))
+}
+
+func (p *printer) writePorts(port, cp string) {
+	if port != "" {
+		p.buf.WriteByte(':')
+		p.buf.WriteString(port)
+	}
+	if cp != "" {
+		p.buf.WriteByte(':')
+		p.buf.WriteString(cp)
+	}
+}
+
+func nodeID(n graph.Node) string {
+	switch n := n.(type) {
+	case Node:
+		return n.DOTID()
+	default:
+		return fmt.Sprint(n.ID())
+	}
+}
+
+func graphID(g graph.Graph, n graph.Node) string {
+	switch g := g.(type) {
+	case Node:
+		return g.DOTID()
+	default:
+		return nodeID(n)
+	}
+}
+
+func (p *printer) writeAttributeList(a encoding.Attributer) {
+	attributes := a.Attributes()
+	switch len(attributes) {
+	case 0:
+	case 1:
+		p.buf.WriteString(" [")
+		p.buf.WriteString(attributes[0].Key)
+		p.buf.WriteByte('=')
+		p.buf.WriteString(attributes[0].Value)
+		p.buf.WriteString("]")
+	default:
+		p.openBlock(" [")
+		for _, att := range attributes {
+			p.newline()
+			p.buf.WriteString(att.Key)
+			p.buf.WriteByte('=')
+			p.buf.WriteString(att.Value)
+		}
+		p.closeBlock("]")
+	}
+}
+
+var attType = []string{"graph", "node", "edge"}
+
+func (p *printer) writeAttributeComplex(ca Attributers) {
+	g, n, e := ca.DOTAttributers()
+	haveWrittenBlock := false
+	for i, a := range []encoding.Attributer{g, n, e} {
+		attributes := a.Attributes()
+		if len(attributes) == 0 {
+			continue
+		}
+		if haveWrittenBlock {
+			p.buf.WriteByte(';')
+		}
+		p.newline()
+		p.buf.WriteString(attType[i])
+		p.openBlock(" [")
+		for _, att := range attributes {
+			p.newline()
+			p.buf.WriteString(att.Key)
+			p.buf.WriteByte('=')
+			p.buf.WriteString(att.Value)
+		}
+		p.closeBlock("]")
+		haveWrittenBlock = true
+	}
+	if haveWrittenBlock {
+		p.buf.WriteString(";\n")
+	}
+}
+
+func (p *printer) newline() {
+	p.buf.WriteByte('\n')
+	p.buf.WriteString(p.prefix)
+	for i := 0; i < p.depth; i++ {
+		p.buf.WriteString(p.indent)
+	}
+}
+
+func (p *printer) openBlock(b string) {
+	p.buf.WriteString(b)
+	p.depth++
+}
+
+func (p *printer) closeBlock(b string) {
+	p.depth--
+	p.newline()
+	p.buf.WriteString(b)
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/encoding/dot/encode_test.go b/vendor/gonum.org/v1/gonum/graph/encoding/dot/encode_test.go
new file mode 100644
index 00000000..d4dba18c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/encoding/dot/encode_test.go
@@ -0,0 +1,1436 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package dot
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/encoding"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+// intset is an integer set.
+type intset map[int64]struct{}
+
+func linksTo(i ...int64) intset {
+	if len(i) == 0 {
+		return nil
+	}
+	s := make(intset)
+	for _, v := range i {
+		s[v] = struct{}{}
+	}
+	return s
+}
+
+var (
+	// Example graph from http://en.wikipedia.org/wiki/File:PageRanks-Example.svg 16:17, 8 July 2009
+	// Node identities are rewritten here to use integers from 0 to match with the DOT output.
+	pageRankGraph = []intset{
+		0:  nil,
+		1:  linksTo(2),
+		2:  linksTo(1),
+		3:  linksTo(0, 1),
+		4:  linksTo(3, 1, 5),
+		5:  linksTo(1, 4),
+		6:  linksTo(1, 4),
+		7:  linksTo(1, 4),
+		8:  linksTo(1, 4),
+		9:  linksTo(4),
+		10: linksTo(4),
+	}
+
+	// Example graph from http://en.wikipedia.org/w/index.php?title=PageRank&oldid=659286279#Power_Method
+	powerMethodGraph = []intset{
+		0: linksTo(1, 2),
+		1: linksTo(3),
+		2: linksTo(3, 4),
+		3: linksTo(4),
+		4: linksTo(0),
+	}
+)
+
+func directedGraphFrom(g []intset) graph.Directed {
+	dg := simple.NewDirectedGraph()
+	for u, e := range g {
+		for v := range e {
+			dg.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+		}
+	}
+	return dg
+}
+
+func undirectedGraphFrom(g []intset) graph.Graph {
+	dg := simple.NewUndirectedGraph()
+	for u, e := range g {
+		for v := range e {
+			dg.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+		}
+	}
+	return dg
+}
+
+const alpha = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
+
+type namedNode struct {
+	id   int64
+	name string
+}
+
+func (n namedNode) ID() int64     { return n.id }
+func (n namedNode) DOTID() string { return n.name }
+
+func directedNamedIDGraphFrom(g []intset) graph.Directed {
+	dg := simple.NewDirectedGraph()
+	for u, e := range g {
+		u := int64(u)
+		nu := namedNode{id: u, name: alpha[u : u+1]}
+		for v := range e {
+			nv := namedNode{id: v, name: alpha[v : v+1]}
+			dg.SetEdge(simple.Edge{F: nu, T: nv})
+		}
+	}
+	return dg
+}
+
+func undirectedNamedIDGraphFrom(g []intset) graph.Graph {
+	dg := simple.NewUndirectedGraph()
+	for u, e := range g {
+		u := int64(u)
+		nu := namedNode{id: u, name: alpha[u : u+1]}
+		for v := range e {
+			nv := namedNode{id: v, name: alpha[v : v+1]}
+			dg.SetEdge(simple.Edge{F: nu, T: nv})
+		}
+	}
+	return dg
+}
+
+type attrNode struct {
+	id   int64
+	name string
+	attr []encoding.Attribute
+}
+
+func (n attrNode) ID() int64                        { return n.id }
+func (n attrNode) Attributes() []encoding.Attribute { return n.attr }
+
+func directedNodeAttrGraphFrom(g []intset, attr [][]encoding.Attribute) graph.Directed {
+	dg := simple.NewDirectedGraph()
+	for u, e := range g {
+		u := int64(u)
+		var at []encoding.Attribute
+		if u < int64(len(attr)) {
+			at = attr[u]
+		}
+		nu := attrNode{id: u, attr: at}
+		for v := range e {
+			if v < int64(len(attr)) {
+				at = attr[v]
+			}
+			nv := attrNode{id: v, attr: at}
+			dg.SetEdge(simple.Edge{F: nu, T: nv})
+		}
+	}
+	return dg
+}
+
+func undirectedNodeAttrGraphFrom(g []intset, attr [][]encoding.Attribute) graph.Graph {
+	dg := simple.NewUndirectedGraph()
+	for u, e := range g {
+		u := int64(u)
+		var at []encoding.Attribute
+		if u < int64(len(attr)) {
+			at = attr[u]
+		}
+		nu := attrNode{id: u, attr: at}
+		for v := range e {
+			if v < int64(len(attr)) {
+				at = attr[v]
+			}
+			nv := attrNode{id: v, attr: at}
+			dg.SetEdge(simple.Edge{F: nu, T: nv})
+		}
+	}
+	return dg
+}
+
+type namedAttrNode struct {
+	id   int64
+	name string
+	attr []encoding.Attribute
+}
+
+func (n namedAttrNode) ID() int64                        { return n.id }
+func (n namedAttrNode) DOTID() string                    { return n.name }
+func (n namedAttrNode) Attributes() []encoding.Attribute { return n.attr }
+
+func directedNamedIDNodeAttrGraphFrom(g []intset, attr [][]encoding.Attribute) graph.Directed {
+	dg := simple.NewDirectedGraph()
+	for u, e := range g {
+		u := int64(u)
+		var at []encoding.Attribute
+		if u < int64(len(attr)) {
+			at = attr[u]
+		}
+		nu := namedAttrNode{id: u, name: alpha[u : u+1], attr: at}
+		for v := range e {
+			if v < int64(len(attr)) {
+				at = attr[v]
+			}
+			nv := namedAttrNode{id: v, name: alpha[v : v+1], attr: at}
+			dg.SetEdge(simple.Edge{F: nu, T: nv})
+		}
+	}
+	return dg
+}
+
+func undirectedNamedIDNodeAttrGraphFrom(g []intset, attr [][]encoding.Attribute) graph.Graph {
+	dg := simple.NewUndirectedGraph()
+	for u, e := range g {
+		u := int64(u)
+		var at []encoding.Attribute
+		if u < int64(len(attr)) {
+			at = attr[u]
+		}
+		nu := namedAttrNode{id: u, name: alpha[u : u+1], attr: at}
+		for v := range e {
+			if v < int64(len(attr)) {
+				at = attr[v]
+			}
+			nv := namedAttrNode{id: v, name: alpha[v : v+1], attr: at}
+			dg.SetEdge(simple.Edge{F: nu, T: nv})
+		}
+	}
+	return dg
+}
+
+type attrEdge struct {
+	from, to graph.Node
+
+	attr []encoding.Attribute
+}
+
+func (e attrEdge) From() graph.Node                 { return e.from }
+func (e attrEdge) To() graph.Node                   { return e.to }
+func (e attrEdge) Weight() float64                  { return 0 }
+func (e attrEdge) Attributes() []encoding.Attribute { return e.attr }
+
+func directedEdgeAttrGraphFrom(g []intset, attr map[edge][]encoding.Attribute) graph.Directed {
+	dg := simple.NewDirectedGraph()
+	for u, e := range g {
+		u := int64(u)
+		for v := range e {
+			dg.SetEdge(attrEdge{from: simple.Node(u), to: simple.Node(v), attr: attr[edge{from: u, to: v}]})
+		}
+	}
+	return dg
+}
+
+func undirectedEdgeAttrGraphFrom(g []intset, attr map[edge][]encoding.Attribute) graph.Graph {
+	dg := simple.NewUndirectedGraph()
+	for u, e := range g {
+		u := int64(u)
+		for v := range e {
+			dg.SetEdge(attrEdge{from: simple.Node(u), to: simple.Node(v), attr: attr[edge{from: u, to: v}]})
+		}
+	}
+	return dg
+}
+
+type portedEdge struct {
+	from, to graph.Node
+
+	directed bool
+
+	fromPort    string
+	fromCompass string
+	toPort      string
+	toCompass   string
+}
+
+func (e portedEdge) From() graph.Node { return e.from }
+func (e portedEdge) To() graph.Node   { return e.to }
+func (e portedEdge) Weight() float64  { return 0 }
+
+// TODO(kortschak): Figure out a better way to handle the fact that
+// headedness is an undefined concept in undirected graphs. We sort
+// nodes by ID, so lower ID nodes are always from nodes in undirected
+// graphs. We can probably do this in the printer, but I am leaving
+// this here as a WARNING.
+// Maybe the approach should be to document that for undirected graphs
+// the low ID node should be returned by the FromPort and the high ID
+// by the ToPort calls.
+func (e portedEdge) FromPort() (port, compass string) {
+	return e.fromPort, e.fromCompass
+}
+func (e portedEdge) ToPort() (port, compass string) {
+	return e.toPort, e.toCompass
+}
+
+func directedPortedAttrGraphFrom(g []intset, attr [][]encoding.Attribute, ports map[edge]portedEdge) graph.Directed {
+	dg := simple.NewDirectedGraph()
+	for u, e := range g {
+		u := int64(u)
+		var at []encoding.Attribute
+		if u < int64(len(attr)) {
+			at = attr[u]
+		}
+		nu := attrNode{id: u, attr: at}
+		for v := range e {
+			if v < int64(len(attr)) {
+				at = attr[v]
+			}
+			pe := ports[edge{from: u, to: v}]
+			pe.from = nu
+			pe.to = attrNode{id: v, attr: at}
+			dg.SetEdge(pe)
+		}
+	}
+	return dg
+}
+
+func undirectedPortedAttrGraphFrom(g []intset, attr [][]encoding.Attribute, ports map[edge]portedEdge) graph.Graph {
+	dg := simple.NewUndirectedGraph()
+	for u, e := range g {
+		u := int64(u)
+		var at []encoding.Attribute
+		if u < int64(len(attr)) {
+			at = attr[u]
+		}
+		nu := attrNode{id: u, attr: at}
+		for v := range e {
+			if v < int64(len(attr)) {
+				at = attr[v]
+			}
+			pe := ports[edge{from: u, to: v}]
+			pe.from = nu
+			pe.to = attrNode{id: v, attr: at}
+			dg.SetEdge(pe)
+		}
+	}
+	return dg
+}
+
+type graphAttributer struct {
+	graph.Graph
+	graph attributer
+	node  attributer
+	edge  attributer
+}
+
+type attributer []encoding.Attribute
+
+func (a attributer) Attributes() []encoding.Attribute { return a }
+
+func (g graphAttributer) DOTAttributers() (graph, node, edge encoding.Attributer) {
+	return g.graph, g.node, g.edge
+}
+
+type structuredGraph struct {
+	*simple.UndirectedGraph
+	sub []Graph
+}
+
+func undirectedStructuredGraphFrom(c []edge, g ...[]intset) graph.Graph {
+	s := &structuredGraph{UndirectedGraph: simple.NewUndirectedGraph()}
+	var base int64
+	for i, sg := range g {
+		sub := simple.NewUndirectedGraph()
+		for u, e := range sg {
+			u := int64(u)
+			for v := range e {
+				ce := simple.Edge{F: simple.Node(u + base), T: simple.Node(v + base)}
+				sub.SetEdge(ce)
+			}
+		}
+		s.sub = append(s.sub, namedGraph{id: int64(i), Graph: sub})
+		base += int64(len(sg))
+	}
+	for _, e := range c {
+		s.SetEdge(simple.Edge{F: simple.Node(e.from), T: simple.Node(e.to)})
+	}
+	return s
+}
+
+func (g structuredGraph) Structure() []Graph {
+	return g.sub
+}
+
+type namedGraph struct {
+	id int64
+	graph.Graph
+}
+
+func (g namedGraph) DOTID() string { return alpha[g.id : g.id+1] }
+
+type subGraph struct {
+	id int64
+	graph.Graph
+}
+
+func (g subGraph) ID() int64 { return g.id }
+func (g subGraph) Subgraph() graph.Graph {
+	return namedGraph(g)
+}
+
+func undirectedSubGraphFrom(g []intset, s map[int64][]intset) graph.Graph {
+	var base int64
+	subs := make(map[int64]subGraph)
+	for i, sg := range s {
+		sub := simple.NewUndirectedGraph()
+		for u, e := range sg {
+			u := int64(u)
+			for v := range e {
+				ce := simple.Edge{F: simple.Node(u + base), T: simple.Node(v + base)}
+				sub.SetEdge(ce)
+			}
+		}
+		subs[i] = subGraph{id: int64(i), Graph: sub}
+		base += int64(len(sg))
+	}
+
+	dg := simple.NewUndirectedGraph()
+	for u, e := range g {
+		u := int64(u)
+		var nu graph.Node
+		if sg, ok := subs[u]; ok {
+			sg.id += base
+			nu = sg
+		} else {
+			nu = simple.Node(u + base)
+		}
+		for v := range e {
+			var nv graph.Node
+			if sg, ok := subs[v]; ok {
+				sg.id += base
+				nv = sg
+			} else {
+				nv = simple.Node(v + base)
+			}
+			dg.SetEdge(simple.Edge{F: nu, T: nv})
+		}
+	}
+	return dg
+}
+
+var encodeTests = []struct {
+	name   string
+	g      graph.Graph
+	strict bool
+
+	prefix string
+
+	want string
+}{
+	// Basic graph.Graph handling.
+	{
+		name: "PageRank",
+		g:    directedGraphFrom(pageRankGraph),
+
+		want: `digraph PageRank {
+	// Node definitions.
+	0;
+	1;
+	2;
+	3;
+	4;
+	5;
+	6;
+	7;
+	8;
+	9;
+	10;
+
+	// Edge definitions.
+	1 -> 2;
+	2 -> 1;
+	3 -> 0;
+	3 -> 1;
+	4 -> 1;
+	4 -> 3;
+	4 -> 5;
+	5 -> 1;
+	5 -> 4;
+	6 -> 1;
+	6 -> 4;
+	7 -> 1;
+	7 -> 4;
+	8 -> 1;
+	8 -> 4;
+	9 -> 4;
+	10 -> 4;
+}`,
+	},
+	{
+		g: undirectedGraphFrom(pageRankGraph),
+
+		want: `graph {
+	// Node definitions.
+	0;
+	1;
+	2;
+	3;
+	4;
+	5;
+	6;
+	7;
+	8;
+	9;
+	10;
+
+	// Edge definitions.
+	0 -- 3;
+	1 -- 2;
+	1 -- 3;
+	1 -- 4;
+	1 -- 5;
+	1 -- 6;
+	1 -- 7;
+	1 -- 8;
+	3 -- 4;
+	4 -- 5;
+	4 -- 6;
+	4 -- 7;
+	4 -- 8;
+	4 -- 9;
+	4 -- 10;
+}`,
+	},
+	{
+		g: directedGraphFrom(powerMethodGraph),
+
+		want: `digraph {
+	// Node definitions.
+	0;
+	1;
+	2;
+	3;
+	4;
+
+	// Edge definitions.
+	0 -> 1;
+	0 -> 2;
+	1 -> 3;
+	2 -> 3;
+	2 -> 4;
+	3 -> 4;
+	4 -> 0;
+}`,
+	},
+	{
+		g: undirectedGraphFrom(powerMethodGraph),
+
+		want: `graph {
+	// Node definitions.
+	0;
+	1;
+	2;
+	3;
+	4;
+
+	// Edge definitions.
+	0 -- 1;
+	0 -- 2;
+	0 -- 4;
+	1 -- 3;
+	2 -- 3;
+	2 -- 4;
+	3 -- 4;
+}`,
+	},
+	{
+		g:      undirectedGraphFrom(powerMethodGraph),
+		prefix: "# ",
+
+		want: `# graph {
+# 	// Node definitions.
+# 	0;
+# 	1;
+# 	2;
+# 	3;
+# 	4;
+#
+# 	// Edge definitions.
+# 	0 -- 1;
+# 	0 -- 2;
+# 	0 -- 4;
+# 	1 -- 3;
+# 	2 -- 3;
+# 	2 -- 4;
+# 	3 -- 4;
+# }`,
+	},
+
+	// Names named nodes.
+	{
+		name: "PageRank",
+		g:    directedNamedIDGraphFrom(pageRankGraph),
+
+		want: `digraph PageRank {
+	// Node definitions.
+	A;
+	B;
+	C;
+	D;
+	E;
+	F;
+	G;
+	H;
+	I;
+	J;
+	K;
+
+	// Edge definitions.
+	B -> C;
+	C -> B;
+	D -> A;
+	D -> B;
+	E -> B;
+	E -> D;
+	E -> F;
+	F -> B;
+	F -> E;
+	G -> B;
+	G -> E;
+	H -> B;
+	H -> E;
+	I -> B;
+	I -> E;
+	J -> E;
+	K -> E;
+}`,
+	},
+	{
+		g: undirectedNamedIDGraphFrom(pageRankGraph),
+
+		want: `graph {
+	// Node definitions.
+	A;
+	B;
+	C;
+	D;
+	E;
+	F;
+	G;
+	H;
+	I;
+	J;
+	K;
+
+	// Edge definitions.
+	A -- D;
+	B -- C;
+	B -- D;
+	B -- E;
+	B -- F;
+	B -- G;
+	B -- H;
+	B -- I;
+	D -- E;
+	E -- F;
+	E -- G;
+	E -- H;
+	E -- I;
+	E -- J;
+	E -- K;
+}`,
+	},
+	{
+		g: directedNamedIDGraphFrom(powerMethodGraph),
+
+		want: `digraph {
+	// Node definitions.
+	A;
+	B;
+	C;
+	D;
+	E;
+
+	// Edge definitions.
+	A -> B;
+	A -> C;
+	B -> D;
+	C -> D;
+	C -> E;
+	D -> E;
+	E -> A;
+}`,
+	},
+	{
+		g: undirectedNamedIDGraphFrom(powerMethodGraph),
+
+		want: `graph {
+	// Node definitions.
+	A;
+	B;
+	C;
+	D;
+	E;
+
+	// Edge definitions.
+	A -- B;
+	A -- C;
+	A -- E;
+	B -- D;
+	C -- D;
+	C -- E;
+	D -- E;
+}`,
+	},
+	{
+		g:      undirectedNamedIDGraphFrom(powerMethodGraph),
+		prefix: "# ",
+
+		want: `# graph {
+# 	// Node definitions.
+# 	A;
+# 	B;
+# 	C;
+# 	D;
+# 	E;
+#
+# 	// Edge definitions.
+# 	A -- B;
+# 	A -- C;
+# 	A -- E;
+# 	B -- D;
+# 	C -- D;
+# 	C -- E;
+# 	D -- E;
+# }`,
+	},
+
+	// Handling nodes with attributes.
+	{
+		g: directedNodeAttrGraphFrom(powerMethodGraph, nil),
+
+		want: `digraph {
+	// Node definitions.
+	0;
+	1;
+	2;
+	3;
+	4;
+
+	// Edge definitions.
+	0 -> 1;
+	0 -> 2;
+	1 -> 3;
+	2 -> 3;
+	2 -> 4;
+	3 -> 4;
+	4 -> 0;
+}`,
+	},
+	{
+		g: undirectedNodeAttrGraphFrom(powerMethodGraph, nil),
+
+		want: `graph {
+	// Node definitions.
+	0;
+	1;
+	2;
+	3;
+	4;
+
+	// Edge definitions.
+	0 -- 1;
+	0 -- 2;
+	0 -- 4;
+	1 -- 3;
+	2 -- 3;
+	2 -- 4;
+	3 -- 4;
+}`,
+	},
+	{
+		g: directedNodeAttrGraphFrom(powerMethodGraph, [][]encoding.Attribute{
+			2: {{"fontsize", "16"}, {"shape", "ellipse"}},
+			4: {},
+		}),
+
+		want: `digraph {
+	// Node definitions.
+	0;
+	1;
+	2 [
+		fontsize=16
+		shape=ellipse
+	];
+	3;
+	4;
+
+	// Edge definitions.
+	0 -> 1;
+	0 -> 2;
+	1 -> 3;
+	2 -> 3;
+	2 -> 4;
+	3 -> 4;
+	4 -> 0;
+}`,
+	},
+	{
+		g: undirectedNodeAttrGraphFrom(powerMethodGraph, [][]encoding.Attribute{
+			2: {{"fontsize", "16"}, {"shape", "ellipse"}},
+			4: {},
+		}),
+
+		want: `graph {
+	// Node definitions.
+	0;
+	1;
+	2 [
+		fontsize=16
+		shape=ellipse
+	];
+	3;
+	4;
+
+	// Edge definitions.
+	0 -- 1;
+	0 -- 2;
+	0 -- 4;
+	1 -- 3;
+	2 -- 3;
+	2 -- 4;
+	3 -- 4;
+}`,
+	},
+	{
+		g: directedNamedIDNodeAttrGraphFrom(powerMethodGraph, [][]encoding.Attribute{
+			2: {{"fontsize", "16"}, {"shape", "ellipse"}},
+			4: {},
+		}),
+
+		want: `digraph {
+	// Node definitions.
+	A;
+	B;
+	C [
+		fontsize=16
+		shape=ellipse
+	];
+	D;
+	E;
+
+	// Edge definitions.
+	A -> B;
+	A -> C;
+	B -> D;
+	C -> D;
+	C -> E;
+	D -> E;
+	E -> A;
+}`,
+	},
+	{
+		g: undirectedNamedIDNodeAttrGraphFrom(powerMethodGraph, [][]encoding.Attribute{
+			0: nil,
+			1: nil,
+			2: {{"fontsize", "16"}, {"shape", "ellipse"}},
+			3: nil,
+			4: {},
+		}),
+
+		want: `graph {
+	// Node definitions.
+	A;
+	B;
+	C [
+		fontsize=16
+		shape=ellipse
+	];
+	D;
+	E;
+
+	// Edge definitions.
+	A -- B;
+	A -- C;
+	A -- E;
+	B -- D;
+	C -- D;
+	C -- E;
+	D -- E;
+}`,
+	},
+
+	// Handling edge with attributes.
+	{
+		g: directedEdgeAttrGraphFrom(powerMethodGraph, nil),
+
+		want: `digraph {
+	// Node definitions.
+	0;
+	1;
+	2;
+	3;
+	4;
+
+	// Edge definitions.
+	0 -> 1;
+	0 -> 2;
+	1 -> 3;
+	2 -> 3;
+	2 -> 4;
+	3 -> 4;
+	4 -> 0;
+}`,
+	},
+	{
+		g: undirectedEdgeAttrGraphFrom(powerMethodGraph, nil),
+
+		want: `graph {
+	// Node definitions.
+	0;
+	1;
+	2;
+	3;
+	4;
+
+	// Edge definitions.
+	0 -- 1;
+	0 -- 2;
+	0 -- 4;
+	1 -- 3;
+	2 -- 3;
+	2 -- 4;
+	3 -- 4;
+}`,
+	},
+	{
+		g: directedEdgeAttrGraphFrom(powerMethodGraph, map[edge][]encoding.Attribute{
+			{from: 0, to: 2}: {{"label", `"???"`}, {"style", "dashed"}},
+			{from: 2, to: 4}: {},
+			{from: 3, to: 4}: {{"color", "red"}},
+		}),
+
+		want: `digraph {
+	// Node definitions.
+	0;
+	1;
+	2;
+	3;
+	4;
+
+	// Edge definitions.
+	0 -> 1;
+	0 -> 2 [
+		label="???"
+		style=dashed
+	];
+	1 -> 3;
+	2 -> 3;
+	2 -> 4;
+	3 -> 4 [color=red];
+	4 -> 0;
+}`,
+	},
+	{
+		g: undirectedEdgeAttrGraphFrom(powerMethodGraph, map[edge][]encoding.Attribute{
+			{from: 0, to: 2}: {{"label", `"???"`}, {"style", "dashed"}},
+			{from: 2, to: 4}: {},
+			{from: 3, to: 4}: {{"color", "red"}},
+		}),
+
+		want: `graph {
+	// Node definitions.
+	0;
+	1;
+	2;
+	3;
+	4;
+
+	// Edge definitions.
+	0 -- 1;
+	0 -- 2 [
+		label="???"
+		style=dashed
+	];
+	0 -- 4;
+	1 -- 3;
+	2 -- 3;
+	2 -- 4;
+	3 -- 4 [color=red];
+}`,
+	},
+
+	// Handling nodes with ports.
+	{
+		g: directedPortedAttrGraphFrom(powerMethodGraph, nil, nil),
+
+		want: `digraph {
+	// Node definitions.
+	0;
+	1;
+	2;
+	3;
+	4;
+
+	// Edge definitions.
+	0 -> 1;
+	0 -> 2;
+	1 -> 3;
+	2 -> 3;
+	2 -> 4;
+	3 -> 4;
+	4 -> 0;
+}`,
+	},
+	{
+		g: undirectedPortedAttrGraphFrom(powerMethodGraph, nil, nil),
+
+		want: `graph {
+	// Node definitions.
+	0;
+	1;
+	2;
+	3;
+	4;
+
+	// Edge definitions.
+	0 -- 1;
+	0 -- 2;
+	0 -- 4;
+	1 -- 3;
+	2 -- 3;
+	2 -- 4;
+	3 -- 4;
+}`,
+	},
+	{
+		g: directedPortedAttrGraphFrom(powerMethodGraph,
+			[][]encoding.Attribute{
+				2: {{"shape", "record"}, {"label", `"<Two>English|<Zwei>German"`}},
+				4: {{"shape", "record"}, {"label", `"<Four>English|<Vier>German"`}},
+			},
+			map[edge]portedEdge{
+				{from: 0, to: 1}: {fromCompass: "s"},
+				{from: 0, to: 2}: {fromCompass: "s", toPort: "Zwei", toCompass: "e"},
+				{from: 2, to: 3}: {fromPort: "Zwei", fromCompass: "e"},
+				{from: 2, to: 4}: {fromPort: "Two", fromCompass: "w", toPort: "Four", toCompass: "w"},
+				{from: 3, to: 4}: {toPort: "Four", toCompass: "w"},
+				{from: 4, to: 0}: {fromPort: "Four", fromCompass: "_", toCompass: "s"},
+			},
+		),
+
+		want: `digraph {
+	// Node definitions.
+	0;
+	1;
+	2 [
+		shape=record
+		label="<Two>English|<Zwei>German"
+	];
+	3;
+	4 [
+		shape=record
+		label="<Four>English|<Vier>German"
+	];
+
+	// Edge definitions.
+	0:s -> 1;
+	0:s -> 2:Zwei:e;
+	1 -> 3;
+	2:Zwei:e -> 3;
+	2:Two:w -> 4:Four:w;
+	3 -> 4:Four:w;
+	4:Four:_ -> 0:s;
+}`,
+	},
+	{
+		g: undirectedPortedAttrGraphFrom(powerMethodGraph,
+			[][]encoding.Attribute{
+				2: {{"shape", "record"}, {"label", `"<Two>English|<Zwei>German"`}},
+				4: {{"shape", "record"}, {"label", `"<Four>English|<Vier>German"`}},
+			},
+			map[edge]portedEdge{
+				{from: 0, to: 1}: {fromCompass: "s"},
+				{from: 0, to: 2}: {fromCompass: "s", toPort: "Zwei", toCompass: "e"},
+				{from: 2, to: 3}: {fromPort: "Zwei", fromCompass: "e"},
+				{from: 2, to: 4}: {fromPort: "Two", fromCompass: "w", toPort: "Four", toCompass: "w"},
+				{from: 3, to: 4}: {toPort: "Four", toCompass: "w"},
+
+				// This definition is reversed (see comment above at portedEdge
+				// definition) so that 4 gets the from port. This is a result
+				// of the fact that we sort nodes by ID, so the lower node
+				// will be always be printed first when the graph is undirected,
+				// thus becoming the from port, but we define the edges here
+				// from a directed adjacency list.
+				{from: 4, to: 0}: {fromCompass: "s", toPort: "Four", toCompass: "_"},
+			},
+		),
+
+		want: `graph {
+	// Node definitions.
+	0;
+	1;
+	2 [
+		shape=record
+		label="<Two>English|<Zwei>German"
+	];
+	3;
+	4 [
+		shape=record
+		label="<Four>English|<Vier>German"
+	];
+
+	// Edge definitions.
+	0:s -- 1;
+	0:s -- 2:Zwei:e;
+	0:s -- 4:Four:_;
+	1 -- 3;
+	2:Zwei:e -- 3;
+	2:Two:w -- 4:Four:w;
+	3 -- 4:Four:w;
+}`,
+	},
+
+	// Handling graph attributes.
+	{
+		g: graphAttributer{Graph: undirectedEdgeAttrGraphFrom(powerMethodGraph, map[edge][]encoding.Attribute{
+			{from: 0, to: 2}: {{"label", `"???"`}, {"style", "dashed"}},
+			{from: 2, to: 4}: {},
+			{from: 3, to: 4}: {{"color", "red"}},
+		})},
+
+		want: `graph {
+	// Node definitions.
+	0;
+	1;
+	2;
+	3;
+	4;
+
+	// Edge definitions.
+	0 -- 1;
+	0 -- 2 [
+		label="???"
+		style=dashed
+	];
+	0 -- 4;
+	1 -- 3;
+	2 -- 3;
+	2 -- 4;
+	3 -- 4 [color=red];
+}`,
+	},
+	{
+		g: graphAttributer{Graph: undirectedEdgeAttrGraphFrom(powerMethodGraph, map[edge][]encoding.Attribute{
+			{from: 0, to: 2}: {{"label", `"???"`}, {"style", "dashed"}},
+			{from: 2, to: 4}: {},
+			{from: 3, to: 4}: {{"color", "red"}},
+		}),
+			graph: []encoding.Attribute{{"rankdir", `"LR"`}},
+			node:  []encoding.Attribute{{"fontsize", "16"}, {"shape", "ellipse"}},
+		},
+
+		want: `graph {
+	graph [
+		rankdir="LR"
+	];
+	node [
+		fontsize=16
+		shape=ellipse
+	];
+
+	// Node definitions.
+	0;
+	1;
+	2;
+	3;
+	4;
+
+	// Edge definitions.
+	0 -- 1;
+	0 -- 2 [
+		label="???"
+		style=dashed
+	];
+	0 -- 4;
+	1 -- 3;
+	2 -- 3;
+	2 -- 4;
+	3 -- 4 [color=red];
+}`,
+	},
+
+	// Handling structured graphs.
+	{
+		g: undirectedStructuredGraphFrom(nil, powerMethodGraph, pageRankGraph),
+
+		want: `graph {
+	subgraph A {
+		// Node definitions.
+		0;
+		1;
+		2;
+		3;
+		4;
+
+		// Edge definitions.
+		0 -- 1;
+		0 -- 2;
+		0 -- 4;
+		1 -- 3;
+		2 -- 3;
+		2 -- 4;
+		3 -- 4;
+	}
+	subgraph B {
+		// Node definitions.
+		5;
+		6;
+		7;
+		8;
+		9;
+		10;
+		11;
+		12;
+		13;
+		14;
+		15;
+
+		// Edge definitions.
+		5 -- 8;
+		6 -- 7;
+		6 -- 8;
+		6 -- 9;
+		6 -- 10;
+		6 -- 11;
+		6 -- 12;
+		6 -- 13;
+		8 -- 9;
+		9 -- 10;
+		9 -- 11;
+		9 -- 12;
+		9 -- 13;
+		9 -- 14;
+		9 -- 15;
+	}
+}`,
+	},
+	{
+		g: undirectedStructuredGraphFrom([]edge{{from: 0, to: 9}}, powerMethodGraph, pageRankGraph),
+
+		want: `graph {
+	subgraph A {
+		// Node definitions.
+		0;
+		1;
+		2;
+		3;
+		4;
+
+		// Edge definitions.
+		0 -- 1;
+		0 -- 2;
+		0 -- 4;
+		1 -- 3;
+		2 -- 3;
+		2 -- 4;
+		3 -- 4;
+	}
+	subgraph B {
+		// Node definitions.
+		5;
+		6;
+		7;
+		8;
+		9;
+		10;
+		11;
+		12;
+		13;
+		14;
+		15;
+
+		// Edge definitions.
+		5 -- 8;
+		6 -- 7;
+		6 -- 8;
+		6 -- 9;
+		6 -- 10;
+		6 -- 11;
+		6 -- 12;
+		6 -- 13;
+		8 -- 9;
+		9 -- 10;
+		9 -- 11;
+		9 -- 12;
+		9 -- 13;
+		9 -- 14;
+		9 -- 15;
+	}
+	// Node definitions.
+	0;
+	9;
+
+	// Edge definitions.
+	0 -- 9;
+}`,
+	},
+
+	// Handling subgraphs.
+	{
+		g: undirectedSubGraphFrom(pageRankGraph, map[int64][]intset{2: powerMethodGraph}),
+
+		want: `graph {
+	// Node definitions.
+	5;
+	6;
+	8;
+	9;
+	10;
+	11;
+	12;
+	13;
+	14;
+	15;
+
+	// Edge definitions.
+	5 -- 8;
+	6 -- subgraph H {
+		// Node definitions.
+		0;
+		1;
+		2;
+		3;
+		4;
+
+		// Edge definitions.
+		0 -- 1;
+		0 -- 2;
+		0 -- 4;
+		1 -- 3;
+		2 -- 3;
+		2 -- 4;
+		3 -- 4;
+	};
+	6 -- 8;
+	6 -- 9;
+	6 -- 10;
+	6 -- 11;
+	6 -- 12;
+	6 -- 13;
+	8 -- 9;
+	9 -- 10;
+	9 -- 11;
+	9 -- 12;
+	9 -- 13;
+	9 -- 14;
+	9 -- 15;
+}`,
+	},
+	{
+		name:   "H",
+		g:      undirectedSubGraphFrom(pageRankGraph, map[int64][]intset{1: powerMethodGraph}),
+		strict: true,
+
+		want: `strict graph H {
+	// Node definitions.
+	5;
+	7;
+	8;
+	9;
+	10;
+	11;
+	12;
+	13;
+	14;
+	15;
+
+	// Edge definitions.
+	5 -- 8;
+	subgraph G {
+		// Node definitions.
+		0;
+		1;
+		2;
+		3;
+		4;
+
+		// Edge definitions.
+		0 -- 1;
+		0 -- 2;
+		0 -- 4;
+		1 -- 3;
+		2 -- 3;
+		2 -- 4;
+		3 -- 4;
+	} -- 7;
+	subgraph G {
+		// Node definitions.
+		0;
+		1;
+		2;
+		3;
+		4;
+	} -- 8;
+	subgraph G {
+		// Node definitions.
+		0;
+		1;
+		2;
+		3;
+		4;
+	} -- 9;
+	subgraph G {
+		// Node definitions.
+		0;
+		1;
+		2;
+		3;
+		4;
+	} -- 10;
+	subgraph G {
+		// Node definitions.
+		0;
+		1;
+		2;
+		3;
+		4;
+	} -- 11;
+	subgraph G {
+		// Node definitions.
+		0;
+		1;
+		2;
+		3;
+		4;
+	} -- 12;
+	subgraph G {
+		// Node definitions.
+		0;
+		1;
+		2;
+		3;
+		4;
+	} -- 13;
+	8 -- 9;
+	9 -- 10;
+	9 -- 11;
+	9 -- 12;
+	9 -- 13;
+	9 -- 14;
+	9 -- 15;
+}`,
+	},
+}
+
+func TestEncode(t *testing.T) {
+	for i, test := range encodeTests {
+		got, err := Marshal(test.g, test.name, test.prefix, "\t", test.strict)
+		if err != nil {
+			t.Errorf("unexpected error: %v", err)
+			continue
+		}
+		if string(got) != test.want {
+			t.Errorf("unexpected DOT result for test %d:\ngot: %s\nwant:%s", i, got, test.want)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/encoding/encoding.go b/vendor/gonum.org/v1/gonum/graph/encoding/encoding.go
new file mode 100644
index 00000000..0f99ac73
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/encoding/encoding.go
@@ -0,0 +1,30 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package encoding
+
+import "gonum.org/v1/gonum/graph"
+
+// Builder is a graph that can have user-defined nodes and edges added.
+type Builder interface {
+	graph.Graph
+	graph.Builder
+}
+
+// AttributeSetter is implemented by types that can set an encoded graph
+// attribute.
+type AttributeSetter interface {
+	SetAttribute(Attribute) error
+}
+
+// Attributer defines graph.Node or graph.Edge values that can
+// specify graph attributes.
+type Attributer interface {
+	Attributes() []Attribute
+}
+
+// Attribute is an encoded key value attribute pair use in graph encoding.
+type Attribute struct {
+	Key, Value string
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/encoding/graphql/decode.go b/vendor/gonum.org/v1/gonum/graph/encoding/graphql/decode.go
new file mode 100644
index 00000000..8ad758c1
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/encoding/graphql/decode.go
@@ -0,0 +1,157 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package graphql
+
+import (
+	"bytes"
+	"encoding/json"
+	"errors"
+	"fmt"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/encoding"
+)
+
+// Unmarshal parses the the JSON-encoded data and stores the result in dst.
+// Node IDs are obtained from the JSON fields identified by the uid parameter.
+// UIDs obtained from the JSON encoding must map to unique node ID values
+// consistently across the JSON-encoded spanning tree.
+func Unmarshal(data []byte, uid string, dst encoding.Builder) error {
+	if uid == "" {
+		return errors.New("graphql: invalid UID field name")
+	}
+	var src json.RawMessage
+	err := json.Unmarshal(data, &src)
+	if err != nil {
+		return err
+	}
+	gen := generator{dst: dst, uidName: uid, nodes: make(map[string]graph.Node)}
+	return gen.walk(src, nil, "")
+}
+
+// StringIDSetter is a graph node that can set its ID based on the given uid string.
+type StringIDSetter interface {
+	SetIDFromString(uid string) error
+}
+
+// LabelSetter is a graph edge that can set its label.
+type LabelSetter interface {
+	SetLabel(string)
+}
+
+type generator struct {
+	dst encoding.Builder
+
+	// uidName is the name of the UID field in the source JSON.
+	uidName string
+	// nodes maps from GraphQL UID string to graph.Node.
+	nodes map[string]graph.Node
+}
+
+func (g *generator) walk(src json.RawMessage, node graph.Node, attr string) error {
+	switch src[0] {
+	case '{':
+		var val map[string]json.RawMessage
+		err := json.Unmarshal(src, &val)
+		if err != nil {
+			return err
+		}
+		if next, ok := val[g.uidName]; !ok {
+			if node != nil {
+				var buf bytes.Buffer
+				err := json.Compact(&buf, src)
+				if err != nil {
+					panic(err)
+				}
+				return fmt.Errorf("graphql: no UID for node: `%s`", &buf)
+			}
+		} else {
+			var v interface{}
+			err = json.Unmarshal(next, &v)
+			if err != nil {
+				return err
+			}
+			value := fmt.Sprint(v)
+			child, ok := g.nodes[value]
+			if !ok {
+				child = g.dst.NewNode()
+				s, ok := child.(StringIDSetter)
+				if !ok {
+					return errors.New("graphql: cannot set UID")
+				}
+				err = s.SetIDFromString(value)
+				if err != nil {
+					return err
+				}
+				g.nodes[value] = child
+				g.dst.AddNode(child)
+			}
+			if node != nil {
+				e := g.dst.NewEdge(node, child)
+				if s, ok := e.(LabelSetter); ok {
+					s.SetLabel(attr)
+				}
+				g.dst.SetEdge(e)
+			}
+			node = child
+		}
+		for attr, src := range val {
+			if attr == g.uidName {
+				continue
+			}
+			err = g.walk(src, node, attr)
+			if err != nil {
+				return err
+			}
+		}
+
+	case '[':
+		var val []json.RawMessage
+		err := json.Unmarshal(src, &val)
+		if err != nil {
+			return err
+		}
+		for _, src := range val {
+			err = g.walk(src, node, attr)
+			if err != nil {
+				return err
+			}
+		}
+
+	default:
+		var v interface{}
+		err := json.Unmarshal(src, &v)
+		if err != nil {
+			return err
+		}
+		if attr == g.uidName {
+			value := fmt.Sprint(v)
+			if s, ok := node.(StringIDSetter); ok {
+				if _, ok := g.nodes[value]; !ok {
+					err = s.SetIDFromString(value)
+					if err != nil {
+						return err
+					}
+					g.nodes[value] = node
+				}
+			} else {
+				return errors.New("graphql: cannot set ID")
+			}
+		} else if s, ok := node.(encoding.AttributeSetter); ok {
+			var value string
+			if _, ok := v.(float64); ok {
+				value = string(src)
+			} else {
+				value = fmt.Sprint(v)
+			}
+			err = s.SetAttribute(encoding.Attribute{Key: attr, Value: value})
+			if err != nil {
+				return err
+			}
+		}
+	}
+
+	return nil
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/encoding/graphql/decode_test.go b/vendor/gonum.org/v1/gonum/graph/encoding/graphql/decode_test.go
new file mode 100644
index 00000000..4bcc7925
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/encoding/graphql/decode_test.go
@@ -0,0 +1,221 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package graphql
+
+import (
+	"errors"
+	"fmt"
+	"sort"
+	"strconv"
+	"strings"
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/encoding"
+	"gonum.org/v1/gonum/graph/encoding/dot"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+var decodeTests = []struct {
+	name    string
+	json    string
+	roots   map[uint64]bool
+	wantDOT string
+	wantErr error
+}{
+	{
+		name: "starwars",
+		json: starwars,
+		roots: map[uint64]bool{
+			0xa3cff1a4c3ef3bb6: true,
+			0xb39aa14d66aedad5: true,
+		},
+		wantDOT: `digraph {
+  // Node definitions.
+  0x8a10d5a2611fd03f [name="Richard Marquand"];
+  0xa3cff1a4c3ef3bb6 [
+    name="Star Wars: Episode V - The Empire Strikes Back"
+    release_date=1980-05-21T00:00:00Z
+    revenue=534000000
+    running_time=124
+  ];
+  0xb39aa14d66aedad5 [
+    name="Star Wars: Episode VI - Return of the Jedi"
+    release_date=1983-05-25T00:00:00Z
+    revenue=572000000
+    running_time=131
+  ];
+  0x0312de17a7ee89f9 [name="Luke Skywalker"];
+  0x3da8d1dcab1bb381 [name="Han Solo"];
+  0x4a7d0b5fe91e78a4 [name="Irvin Kernshner"];
+  0x718337b9dcbaa7d9 [name="Princess Leia"];
+
+  // Edge definitions.
+  0xa3cff1a4c3ef3bb6 -> 0x0312de17a7ee89f9 [label=starring];
+  0xa3cff1a4c3ef3bb6 -> 0x3da8d1dcab1bb381 [label=starring];
+  0xa3cff1a4c3ef3bb6 -> 0x4a7d0b5fe91e78a4 [label=director];
+  0xa3cff1a4c3ef3bb6 -> 0x718337b9dcbaa7d9 [label=starring];
+  0xb39aa14d66aedad5 -> 0x8a10d5a2611fd03f [label=director];
+  0xb39aa14d66aedad5 -> 0x0312de17a7ee89f9 [label=starring];
+  0xb39aa14d66aedad5 -> 0x3da8d1dcab1bb381 [label=starring];
+  0xb39aa14d66aedad5 -> 0x718337b9dcbaa7d9 [label=starring];
+}`,
+	},
+	{
+		name: "tutorial",
+		json: dgraphTutorial,
+		roots: map[uint64]bool{
+			0xfd90205a458151f:  true,
+			0x52a80955d40ec819: true,
+		},
+		wantDOT: `digraph {
+  // Node definitions.
+  0x892a6da7ee1fbdec [
+    age=55
+    name=Sarah
+  ];
+  0x99b74c1b5ab100ec [
+    age=35
+    name=Artyom
+  ];
+  0xb9e12a67e34d6acc [
+    age=19
+    name=Catalina
+  ];
+  0xbf104824c777525d [name=Perro];
+  0xf590a923ea1fccaa [name=Goldie];
+  0xf92d7dbe272d680b [name="Hyung Sin"];
+  0x0fd90205a458151f [
+    age=39
+    name=Michael
+  ];
+  0x37734fcf0a6fcc69 [name="Rammy the sheep"];
+  0x52a80955d40ec819 [
+    age=35
+    name=Amit
+  ];
+  0x5e9ad1cd9466228c [
+    age=24
+    name="Sang Hyun"
+  ];
+
+  // Edge definitions.
+  0xb9e12a67e34d6acc -> 0xbf104824c777525d [label=owns_pet];
+  0xb9e12a67e34d6acc -> 0x5e9ad1cd9466228c [label=friend];
+  0xf92d7dbe272d680b -> 0x5e9ad1cd9466228c [label=friend];
+  0x0fd90205a458151f -> 0x892a6da7ee1fbdec [label=friend];
+  0x0fd90205a458151f -> 0x99b74c1b5ab100ec [label=friend];
+  0x0fd90205a458151f -> 0xb9e12a67e34d6acc [label=friend];
+  0x0fd90205a458151f -> 0x37734fcf0a6fcc69 [label=owns_pet];
+  0x0fd90205a458151f -> 0x52a80955d40ec819 [label=friend];
+  0x0fd90205a458151f -> 0x5e9ad1cd9466228c [label=friend];
+  0x52a80955d40ec819 -> 0x99b74c1b5ab100ec [label=friend];
+  0x52a80955d40ec819 -> 0x0fd90205a458151f [label=friend];
+  0x52a80955d40ec819 -> 0x5e9ad1cd9466228c [label=friend];
+  0x5e9ad1cd9466228c -> 0xb9e12a67e34d6acc [label=friend];
+  0x5e9ad1cd9466228c -> 0xf590a923ea1fccaa [label=owns_pet];
+  0x5e9ad1cd9466228c -> 0xf92d7dbe272d680b [label=friend];
+  0x5e9ad1cd9466228c -> 0x52a80955d40ec819 [label=friend];
+}`,
+	},
+	{
+		name:    "tutorial missing IDs",
+		json:    dgraphTutorialMissingIDs,
+		wantErr: errors.New("graphql: no UID for node"), // Incomplete error string.
+	},
+}
+
+func TestDecode(t *testing.T) {
+	for _, test := range decodeTests {
+		dst := newDirectedGraph()
+		err := Unmarshal([]byte(test.json), "_uid_", dst)
+		if test.wantErr == nil && err != nil {
+			t.Errorf("failed to unmarshal GraphQL JSON graph for %q: %v", test.name, err)
+		} else if test.wantErr != nil {
+			if err == nil {
+				t.Errorf("expected error for %q: got:%v want:%v", test.name, err, test.wantErr)
+			}
+			continue
+		}
+		b, err := dot.Marshal(dst, "", "", "  ", false)
+		if err != nil {
+			t.Fatalf("failed to DOT marshal graph %q: %v", test.name, err)
+		}
+		gotDOT := string(b)
+		if gotDOT != test.wantDOT {
+			t.Errorf("unexpected DOT encoding for %q:\ngot:\n%s\nwant:\n%s", test.name, gotDOT, test.wantDOT)
+		}
+	}
+}
+
+type directedGraph struct {
+	*simple.DirectedGraph
+}
+
+func newDirectedGraph() *directedGraph {
+	return &directedGraph{DirectedGraph: simple.NewDirectedGraph()}
+}
+
+func (g *directedGraph) NewNode() graph.Node {
+	return &node{attributes: make(attributes)}
+}
+
+func (g *directedGraph) NewEdge(from, to graph.Node) graph.Edge {
+	return &edge{Edge: g.DirectedGraph.NewEdge(from, to)}
+}
+
+type node struct {
+	id uint64
+	attributes
+}
+
+func (n *node) ID() int64     { return int64(n.id) }
+func (n *node) DOTID() string { return fmt.Sprintf("0x%016x", uint64(n.id)) }
+
+func (n *node) SetIDFromString(uid string) error {
+	if !strings.HasPrefix(uid, "0x") {
+		return fmt.Errorf("uid is not hex value: %q", uid)
+	}
+	var err error
+	n.id, err = strconv.ParseUint(uid[2:], 16, 64)
+	return err
+}
+
+type edge struct {
+	graph.Edge
+	label string
+}
+
+func (e *edge) SetLabel(l string) {
+	e.label = l
+}
+
+func (e *edge) Attributes() []encoding.Attribute {
+	return []encoding.Attribute{{"label", e.label}}
+}
+
+type attributes map[string]encoding.Attribute
+
+func (a attributes) SetAttribute(attr encoding.Attribute) error {
+	a[attr.Key] = attr
+	return nil
+}
+
+func (a attributes) Attributes() []encoding.Attribute {
+	keys := make([]string, 0, len(a))
+	for k := range a {
+		keys = append(keys, k)
+	}
+	sort.Strings(keys)
+	attr := make([]encoding.Attribute, 0, len(keys))
+	for _, k := range keys {
+		v := a[k]
+		if strings.Contains(v.Value, " ") {
+			v.Value = `"` + v.Value + `"`
+		}
+		attr = append(attr, v)
+	}
+	return attr
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/encoding/graphql/doc.go b/vendor/gonum.org/v1/gonum/graph/encoding/graphql/doc.go
new file mode 100644
index 00000000..dd405034
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/encoding/graphql/doc.go
@@ -0,0 +1,7 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package graphql implements JSON marshaling and unmarshaling of graph as
+// used by GraphQL
+package graphql // import "gonum.org/v1/gonum/graph/encoding/graphql"
diff --git a/vendor/gonum.org/v1/gonum/graph/encoding/graphql/graphql.go b/vendor/gonum.org/v1/gonum/graph/encoding/graphql/graphql.go
new file mode 100644
index 00000000..7598cb1a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/encoding/graphql/graphql.go
@@ -0,0 +1,5 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package graphql
diff --git a/vendor/gonum.org/v1/gonum/graph/encoding/graphql/graphs_test.go b/vendor/gonum.org/v1/gonum/graph/encoding/graphql/graphs_test.go
new file mode 100644
index 00000000..0e90348f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/encoding/graphql/graphs_test.go
@@ -0,0 +1,1013 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package graphql
+
+const (
+	starwars = `{
+  "movie": [
+    {
+      "_uid_": "0xa3cff1a4c3ef3bb6",
+      "director": [
+        {
+          "_uid_": "0x4a7d0b5fe91e78a4",
+          "name": "Irvin Kernshner"
+        }
+      ],
+      "name": "Star Wars: Episode V - The Empire Strikes Back",
+      "release_date": "1980-05-21T00:00:00Z",
+      "revenue": 534000000,
+      "running_time": 124,
+      "starring": [
+        {
+          "_uid_": "0x312de17a7ee89f9",
+          "name": "Luke Skywalker"
+        },
+        {
+          "_uid_": "0x3da8d1dcab1bb381",
+          "name": "Han Solo"
+        },
+        {
+          "_uid_": "0x718337b9dcbaa7d9",
+          "name": "Princess Leia"
+        }
+      ]
+    },
+    {
+      "_uid_": "0xb39aa14d66aedad5",
+      "director": [
+        {
+          "_uid_": "0x8a10d5a2611fd03f",
+          "name": "Richard Marquand"
+        }
+      ],
+      "name": "Star Wars: Episode VI - Return of the Jedi",
+      "release_date": "1983-05-25T00:00:00Z",
+      "revenue": 572000000,
+      "running_time": 131,
+      "starring": [
+        {
+          "_uid_": "0x312de17a7ee89f9",
+          "name": "Luke Skywalker"
+        },
+        {
+          "_uid_": "0x3da8d1dcab1bb381",
+          "name": "Han Solo"
+        },
+        {
+          "_uid_": "0x718337b9dcbaa7d9",
+          "name": "Princess Leia"
+        }
+      ]
+    }
+  ]
+}
+`
+
+	dgraphTutorialMissingIDs = `{
+    "everyone": [
+        {
+            "_uid_": "0xfd90205a458151f",
+            "friend": [
+                {
+                    "_uid_": "0x52a80955d40ec819",
+                    "friend": [
+                        {
+                            "_uid_": "0xfd90205a458151f",
+                            "age": 39,
+                            "friend": [
+                                {
+                                    "age": 35,
+                                    "name": "Amit"
+                                },
+                                {
+                                    "age": 24,
+                                    "name": "Sang Hyun"
+                                },
+                                {
+                                    "age": 55,
+                                    "name": "Sarah"
+                                },
+                                {
+                                    "age": 35,
+                                    "name": "Artyom"
+                                },
+                                {
+                                    "age": 19,
+                                    "name": "Catalina"
+                                }
+                            ],
+                            "name": "Michael",
+                            "owns_pet": [
+                                {
+                                    "name": "Rammy the sheep"
+                                }
+                            ]
+                        },
+                        {
+                            "_uid_": "0x5e9ad1cd9466228c",
+                            "age": 24,
+                            "friend": [
+                                {
+                                    "age": 35,
+                                    "name": "Amit"
+                                },
+                                {
+                                    "age": 19,
+                                    "name": "Catalina"
+                                },
+                                {
+                                    "name": "Hyung Sin"
+                                }
+                            ],
+                            "name": "Sang Hyun",
+                            "owns_pet": [
+                                {
+                                    "name": "Goldie"
+                                }
+                            ]
+                        },
+                        {
+                            "_uid_": "0x99b74c1b5ab100ec",
+                            "age": 35,
+                            "name": "Artyom"
+                        }
+                    ],
+                    "name": "Amit"
+                },
+                {
+                    "_uid_": "0x5e9ad1cd9466228c",
+                    "friend": [
+                        {
+                            "_uid_": "0x52a80955d40ec819",
+                            "age": 35,
+                            "friend": [
+                                {
+                                    "age": 39,
+                                    "name": "Michael"
+                                },
+                                {
+                                    "age": 24,
+                                    "name": "Sang Hyun"
+                                },
+                                {
+                                    "age": 35,
+                                    "name": "Artyom"
+                                }
+                            ],
+                            "name": "Amit"
+                        },
+                        {
+                            "_uid_": "0xb9e12a67e34d6acc",
+                            "age": 19,
+                            "friend": [
+                                {
+                                    "age": 24,
+                                    "name": "Sang Hyun"
+                                }
+                            ],
+                            "name": "Catalina",
+                            "owns_pet": [
+                                {
+                                    "name": "Perro"
+                                }
+                            ]
+                        },
+                        {
+                            "_uid_": "0xf92d7dbe272d680b",
+                            "friend": [
+                                {
+                                    "age": 24,
+                                    "name": "Sang Hyun"
+                                }
+                            ],
+                            "name": "Hyung Sin"
+                        }
+                    ],
+                    "name": "Sang Hyun"
+                },
+                {
+                    "_uid_": "0x892a6da7ee1fbdec",
+                    "name": "Sarah"
+                },
+                {
+                    "_uid_": "0x99b74c1b5ab100ec",
+                    "name": "Artyom"
+                },
+                {
+                    "_uid_": "0xb9e12a67e34d6acc",
+                    "friend": [
+                        {
+                            "_uid_": "0x5e9ad1cd9466228c",
+                            "age": 24,
+                            "friend": [
+                                {
+                                    "age": 35,
+                                    "name": "Amit"
+                                },
+                                {
+                                    "age": 19,
+                                    "name": "Catalina"
+                                },
+                                {
+                                    "name": "Hyung Sin"
+                                }
+                            ],
+                            "name": "Sang Hyun",
+                            "owns_pet": [
+                                {
+                                    "name": "Goldie"
+                                }
+                            ]
+                        }
+                    ],
+                    "name": "Catalina"
+                }
+            ],
+            "name": "Michael"
+        },
+        {
+            "_uid_": "0x52a80955d40ec819",
+            "friend": [
+                {
+                    "_uid_": "0xfd90205a458151f",
+                    "friend": [
+                        {
+                            "_uid_": "0x52a80955d40ec819",
+                            "age": 35,
+                            "friend": [
+                                {
+                                    "age": 39,
+                                    "name": "Michael"
+                                },
+                                {
+                                    "age": 24,
+                                    "name": "Sang Hyun"
+                                },
+                                {
+                                    "age": 35,
+                                    "name": "Artyom"
+                                }
+                            ],
+                            "name": "Amit"
+                        },
+                        {
+                            "_uid_": "0x5e9ad1cd9466228c",
+                            "age": 24,
+                            "friend": [
+                                {
+                                    "age": 35,
+                                    "name": "Amit"
+                                },
+                                {
+                                    "age": 19,
+                                    "name": "Catalina"
+                                },
+                                {
+                                    "name": "Hyung Sin"
+                                }
+                            ],
+                            "name": "Sang Hyun",
+                            "owns_pet": [
+                                {
+                                    "name": "Goldie"
+                                }
+                            ]
+                        },
+                        {
+                            "_uid_": "0x892a6da7ee1fbdec",
+                            "age": 55,
+                            "name": "Sarah"
+                        },
+                        {
+                            "_uid_": "0x99b74c1b5ab100ec",
+                            "age": 35,
+                            "name": "Artyom"
+                        },
+                        {
+                            "_uid_": "0xb9e12a67e34d6acc",
+                            "age": 19,
+                            "friend": [
+                                {
+                                    "age": 24,
+                                    "name": "Sang Hyun"
+                                }
+                            ],
+                            "name": "Catalina",
+                            "owns_pet": [
+                                {
+                                    "name": "Perro"
+                                }
+                            ]
+                        }
+                    ],
+                    "name": "Michael"
+                },
+                {
+                    "_uid_": "0x5e9ad1cd9466228c",
+                    "friend": [
+                        {
+                            "_uid_": "0x52a80955d40ec819",
+                            "age": 35,
+                            "friend": [
+                                {
+                                    "age": 39,
+                                    "name": "Michael"
+                                },
+                                {
+                                    "age": 24,
+                                    "name": "Sang Hyun"
+                                },
+                                {
+                                    "age": 35,
+                                    "name": "Artyom"
+                                }
+                            ],
+                            "name": "Amit"
+                        },
+                        {
+                            "_uid_": "0xb9e12a67e34d6acc",
+                            "age": 19,
+                            "friend": [
+                                {
+                                    "age": 24,
+                                    "name": "Sang Hyun"
+                                }
+                            ],
+                            "name": "Catalina",
+                            "owns_pet": [
+                                {
+                                    "name": "Perro"
+                                }
+                            ]
+                        },
+                        {
+                            "_uid_": "0xf92d7dbe272d680b",
+                            "friend": [
+                                {
+                                    "age": 24,
+                                    "name": "Sang Hyun"
+                                }
+                            ],
+                            "name": "Hyung Sin"
+                        }
+                    ],
+                    "name": "Sang Hyun"
+                },
+                {
+                    "_uid_": "0x99b74c1b5ab100ec",
+                    "name": "Artyom"
+                }
+            ],
+            "name": "Amit"
+        }
+    ]
+}
+`
+
+	dgraphTutorial = `{
+  "everyone": [
+    {
+      "_uid_": "0xfd90205a458151f",
+      "friend": [
+        {
+          "_uid_": "0x52a80955d40ec819",
+          "friend": [
+            {
+              "_uid_": "0xfd90205a458151f",
+              "age": 39,
+              "friend": [
+                {
+                  "_uid_": "0x52a80955d40ec819",
+                  "age": 35,
+                  "friend": [
+                    {
+                      "_uid_": "0xfd90205a458151f"
+                    },
+                    {
+                      "_uid_": "0x5e9ad1cd9466228c"
+                    },
+                    {
+                      "_uid_": "0x99b74c1b5ab100ec"
+                    }
+                  ],
+                  "name": "Amit"
+                },
+                {
+                  "_uid_": "0x5e9ad1cd9466228c",
+                  "age": 24,
+                  "friend": [
+                    {
+                      "_uid_": "0x52a80955d40ec819"
+                    },
+                    {
+                      "_uid_": "0xb9e12a67e34d6acc"
+                    },
+                    {
+                      "_uid_": "0xf92d7dbe272d680b"
+                    }
+                  ],
+                  "name": "Sang Hyun",
+                  "owns_pet": [
+                    {
+                      "_uid_": "0xf590a923ea1fccaa"
+                    }
+                  ]
+                },
+                {
+                  "_uid_": "0x892a6da7ee1fbdec",
+                  "age": 55,
+                  "name": "Sarah"
+                },
+                {
+                  "_uid_": "0x99b74c1b5ab100ec",
+                  "age": 35,
+                  "name": "Artyom"
+                },
+                {
+                  "_uid_": "0xb9e12a67e34d6acc",
+                  "age": 19,
+                  "friend": [
+                    {
+                      "_uid_": "0x5e9ad1cd9466228c"
+                    }
+                  ],
+                  "name": "Catalina",
+                  "owns_pet": [
+                    {
+                      "_uid_": "0xbf104824c777525d"
+                    }
+                  ]
+                }
+              ],
+              "name": "Michael",
+              "owns_pet": [
+                {
+                  "_uid_": "0x37734fcf0a6fcc69",
+                  "name": "Rammy the sheep"
+                }
+              ]
+            },
+            {
+              "_uid_": "0x5e9ad1cd9466228c",
+              "age": 24,
+              "friend": [
+                {
+                  "_uid_": "0x52a80955d40ec819",
+                  "age": 35,
+                  "friend": [
+                    {
+                      "_uid_": "0xfd90205a458151f"
+                    },
+                    {
+                      "_uid_": "0x5e9ad1cd9466228c"
+                    },
+                    {
+                      "_uid_": "0x99b74c1b5ab100ec"
+                    }
+                  ],
+                  "name": "Amit"
+                },
+                {
+                  "_uid_": "0xb9e12a67e34d6acc",
+                  "age": 19,
+                  "friend": [
+                    {
+                      "_uid_": "0x5e9ad1cd9466228c"
+                    }
+                  ],
+                  "name": "Catalina",
+                  "owns_pet": [
+                    {
+                      "_uid_": "0xbf104824c777525d"
+                    }
+                  ]
+                },
+                {
+                  "_uid_": "0xf92d7dbe272d680b",
+                  "friend": [
+                    {
+                      "_uid_": "0x5e9ad1cd9466228c"
+                    }
+                  ],
+                  "name": "Hyung Sin"
+                }
+              ],
+              "name": "Sang Hyun",
+              "owns_pet": [
+                {
+                  "_uid_": "0xf590a923ea1fccaa",
+                  "name": "Goldie"
+                }
+              ]
+            },
+            {
+              "_uid_": "0x99b74c1b5ab100ec",
+              "age": 35,
+              "name": "Artyom"
+            }
+          ],
+          "name": "Amit"
+        },
+        {
+          "_uid_": "0x5e9ad1cd9466228c",
+          "friend": [
+            {
+              "_uid_": "0x52a80955d40ec819",
+              "age": 35,
+              "friend": [
+                {
+                  "_uid_": "0xfd90205a458151f",
+                  "age": 39,
+                  "friend": [
+                    {
+                      "_uid_": "0x52a80955d40ec819"
+                    },
+                    {
+                      "_uid_": "0x5e9ad1cd9466228c"
+                    },
+                    {
+                      "_uid_": "0x892a6da7ee1fbdec"
+                    },
+                    {
+                      "_uid_": "0x99b74c1b5ab100ec"
+                    },
+                    {
+                      "_uid_": "0xb9e12a67e34d6acc"
+                    }
+                  ],
+                  "name": "Michael",
+                  "owns_pet": [
+                    {
+                      "_uid_": "0x37734fcf0a6fcc69"
+                    }
+                  ]
+                },
+                {
+                  "_uid_": "0x5e9ad1cd9466228c",
+                  "age": 24,
+                  "friend": [
+                    {
+                      "_uid_": "0x52a80955d40ec819"
+                    },
+                    {
+                      "_uid_": "0xb9e12a67e34d6acc"
+                    },
+                    {
+                      "_uid_": "0xf92d7dbe272d680b"
+                    }
+                  ],
+                  "name": "Sang Hyun",
+                  "owns_pet": [
+                    {
+                      "_uid_": "0xf590a923ea1fccaa"
+                    }
+                  ]
+                },
+                {
+                  "_uid_": "0x99b74c1b5ab100ec",
+                  "age": 35,
+                  "name": "Artyom"
+                }
+              ],
+              "name": "Amit"
+            },
+            {
+              "_uid_": "0xb9e12a67e34d6acc",
+              "age": 19,
+              "friend": [
+                {
+                  "_uid_": "0x5e9ad1cd9466228c",
+                  "age": 24,
+                  "friend": [
+                    {
+                      "_uid_": "0x52a80955d40ec819"
+                    },
+                    {
+                      "_uid_": "0xb9e12a67e34d6acc"
+                    },
+                    {
+                      "_uid_": "0xf92d7dbe272d680b"
+                    }
+                  ],
+                  "name": "Sang Hyun",
+                  "owns_pet": [
+                    {
+                      "_uid_": "0xf590a923ea1fccaa"
+                    }
+                  ]
+                }
+              ],
+              "name": "Catalina",
+              "owns_pet": [
+                {
+                  "_uid_": "0xbf104824c777525d",
+                  "name": "Perro"
+                }
+              ]
+            },
+            {
+              "_uid_": "0xf92d7dbe272d680b",
+              "friend": [
+                {
+                  "_uid_": "0x5e9ad1cd9466228c",
+                  "age": 24,
+                  "friend": [
+                    {
+                      "_uid_": "0x52a80955d40ec819"
+                    },
+                    {
+                      "_uid_": "0xb9e12a67e34d6acc"
+                    },
+                    {
+                      "_uid_": "0xf92d7dbe272d680b"
+                    }
+                  ],
+                  "name": "Sang Hyun",
+                  "owns_pet": [
+                    {
+                      "_uid_": "0xf590a923ea1fccaa"
+                    }
+                  ]
+                }
+              ],
+              "name": "Hyung Sin"
+            }
+          ],
+          "name": "Sang Hyun"
+        },
+        {
+          "_uid_": "0x892a6da7ee1fbdec",
+          "name": "Sarah"
+        },
+        {
+          "_uid_": "0x99b74c1b5ab100ec",
+          "name": "Artyom"
+        },
+        {
+          "_uid_": "0xb9e12a67e34d6acc",
+          "friend": [
+            {
+              "_uid_": "0x5e9ad1cd9466228c",
+              "age": 24,
+              "friend": [
+                {
+                  "_uid_": "0x52a80955d40ec819",
+                  "age": 35,
+                  "friend": [
+                    {
+                      "_uid_": "0xfd90205a458151f"
+                    },
+                    {
+                      "_uid_": "0x5e9ad1cd9466228c"
+                    },
+                    {
+                      "_uid_": "0x99b74c1b5ab100ec"
+                    }
+                  ],
+                  "name": "Amit"
+                },
+                {
+                  "_uid_": "0xb9e12a67e34d6acc",
+                  "age": 19,
+                  "friend": [
+                    {
+                      "_uid_": "0x5e9ad1cd9466228c"
+                    }
+                  ],
+                  "name": "Catalina",
+                  "owns_pet": [
+                    {
+                      "_uid_": "0xbf104824c777525d"
+                    }
+                  ]
+                },
+                {
+                  "_uid_": "0xf92d7dbe272d680b",
+                  "friend": [
+                    {
+                      "_uid_": "0x5e9ad1cd9466228c"
+                    }
+                  ],
+                  "name": "Hyung Sin"
+                }
+              ],
+              "name": "Sang Hyun",
+              "owns_pet": [
+                {
+                  "_uid_": "0xf590a923ea1fccaa",
+                  "name": "Goldie"
+                }
+              ]
+            }
+          ],
+          "name": "Catalina"
+        }
+      ],
+      "name": "Michael"
+    },
+    {
+      "_uid_": "0x52a80955d40ec819",
+      "friend": [
+        {
+          "_uid_": "0xfd90205a458151f",
+          "friend": [
+            {
+              "_uid_": "0x52a80955d40ec819",
+              "age": 35,
+              "friend": [
+                {
+                  "_uid_": "0xfd90205a458151f",
+                  "age": 39,
+                  "friend": [
+                    {
+                      "_uid_": "0x52a80955d40ec819"
+                    },
+                    {
+                      "_uid_": "0x5e9ad1cd9466228c"
+                    },
+                    {
+                      "_uid_": "0x892a6da7ee1fbdec"
+                    },
+                    {
+                      "_uid_": "0x99b74c1b5ab100ec"
+                    },
+                    {
+                      "_uid_": "0xb9e12a67e34d6acc"
+                    }
+                  ],
+                  "name": "Michael",
+                  "owns_pet": [
+                    {
+                      "_uid_": "0x37734fcf0a6fcc69"
+                    }
+                  ]
+                },
+                {
+                  "_uid_": "0x5e9ad1cd9466228c",
+                  "age": 24,
+                  "friend": [
+                    {
+                      "_uid_": "0x52a80955d40ec819"
+                    },
+                    {
+                      "_uid_": "0xb9e12a67e34d6acc"
+                    },
+                    {
+                      "_uid_": "0xf92d7dbe272d680b"
+                    }
+                  ],
+                  "name": "Sang Hyun",
+                  "owns_pet": [
+                    {
+                      "_uid_": "0xf590a923ea1fccaa"
+                    }
+                  ]
+                },
+                {
+                  "_uid_": "0x99b74c1b5ab100ec",
+                  "age": 35,
+                  "name": "Artyom"
+                }
+              ],
+              "name": "Amit"
+            },
+            {
+              "_uid_": "0x5e9ad1cd9466228c",
+              "age": 24,
+              "friend": [
+                {
+                  "_uid_": "0x52a80955d40ec819",
+                  "age": 35,
+                  "friend": [
+                    {
+                      "_uid_": "0xfd90205a458151f"
+                    },
+                    {
+                      "_uid_": "0x5e9ad1cd9466228c"
+                    },
+                    {
+                      "_uid_": "0x99b74c1b5ab100ec"
+                    }
+                  ],
+                  "name": "Amit"
+                },
+                {
+                  "_uid_": "0xb9e12a67e34d6acc",
+                  "age": 19,
+                  "friend": [
+                    {
+                      "_uid_": "0x5e9ad1cd9466228c"
+                    }
+                  ],
+                  "name": "Catalina",
+                  "owns_pet": [
+                    {
+                      "_uid_": "0xbf104824c777525d"
+                    }
+                  ]
+                },
+                {
+                  "_uid_": "0xf92d7dbe272d680b",
+                  "friend": [
+                    {
+                      "_uid_": "0x5e9ad1cd9466228c"
+                    }
+                  ],
+                  "name": "Hyung Sin"
+                }
+              ],
+              "name": "Sang Hyun",
+              "owns_pet": [
+                {
+                  "_uid_": "0xf590a923ea1fccaa",
+                  "name": "Goldie"
+                }
+              ]
+            },
+            {
+              "_uid_": "0x892a6da7ee1fbdec",
+              "age": 55,
+              "name": "Sarah"
+            },
+            {
+              "_uid_": "0x99b74c1b5ab100ec",
+              "age": 35,
+              "name": "Artyom"
+            },
+            {
+              "_uid_": "0xb9e12a67e34d6acc",
+              "age": 19,
+              "friend": [
+                {
+                  "_uid_": "0x5e9ad1cd9466228c",
+                  "age": 24,
+                  "friend": [
+                    {
+                      "_uid_": "0x52a80955d40ec819"
+                    },
+                    {
+                      "_uid_": "0xb9e12a67e34d6acc"
+                    },
+                    {
+                      "_uid_": "0xf92d7dbe272d680b"
+                    }
+                  ],
+                  "name": "Sang Hyun",
+                  "owns_pet": [
+                    {
+                      "_uid_": "0xf590a923ea1fccaa"
+                    }
+                  ]
+                }
+              ],
+              "name": "Catalina",
+              "owns_pet": [
+                {
+                  "_uid_": "0xbf104824c777525d",
+                  "name": "Perro"
+                }
+              ]
+            }
+          ],
+          "name": "Michael"
+        },
+        {
+          "_uid_": "0x5e9ad1cd9466228c",
+          "friend": [
+            {
+              "_uid_": "0x52a80955d40ec819",
+              "age": 35,
+              "friend": [
+                {
+                  "_uid_": "0xfd90205a458151f",
+                  "age": 39,
+                  "friend": [
+                    {
+                      "_uid_": "0x52a80955d40ec819"
+                    },
+                    {
+                      "_uid_": "0x5e9ad1cd9466228c"
+                    },
+                    {
+                      "_uid_": "0x892a6da7ee1fbdec"
+                    },
+                    {
+                      "_uid_": "0x99b74c1b5ab100ec"
+                    },
+                    {
+                      "_uid_": "0xb9e12a67e34d6acc"
+                    }
+                  ],
+                  "name": "Michael",
+                  "owns_pet": [
+                    {
+                      "_uid_": "0x37734fcf0a6fcc69"
+                    }
+                  ]
+                },
+                {
+                  "_uid_": "0x5e9ad1cd9466228c",
+                  "age": 24,
+                  "friend": [
+                    {
+                      "_uid_": "0x52a80955d40ec819"
+                    },
+                    {
+                      "_uid_": "0xb9e12a67e34d6acc"
+                    },
+                    {
+                      "_uid_": "0xf92d7dbe272d680b"
+                    }
+                  ],
+                  "name": "Sang Hyun",
+                  "owns_pet": [
+                    {
+                      "_uid_": "0xf590a923ea1fccaa"
+                    }
+                  ]
+                },
+                {
+                  "_uid_": "0x99b74c1b5ab100ec",
+                  "age": 35,
+                  "name": "Artyom"
+                }
+              ],
+              "name": "Amit"
+            },
+            {
+              "_uid_": "0xb9e12a67e34d6acc",
+              "age": 19,
+              "friend": [
+                {
+                  "_uid_": "0x5e9ad1cd9466228c",
+                  "age": 24,
+                  "friend": [
+                    {
+                      "_uid_": "0x52a80955d40ec819"
+                    },
+                    {
+                      "_uid_": "0xb9e12a67e34d6acc"
+                    },
+                    {
+                      "_uid_": "0xf92d7dbe272d680b"
+                    }
+                  ],
+                  "name": "Sang Hyun",
+                  "owns_pet": [
+                    {
+                      "_uid_": "0xf590a923ea1fccaa"
+                    }
+                  ]
+                }
+              ],
+              "name": "Catalina",
+              "owns_pet": [
+                {
+                  "_uid_": "0xbf104824c777525d",
+                  "name": "Perro"
+                }
+              ]
+            },
+            {
+              "_uid_": "0xf92d7dbe272d680b",
+              "friend": [
+                {
+                  "_uid_": "0x5e9ad1cd9466228c",
+                  "age": 24,
+                  "friend": [
+                    {
+                      "_uid_": "0x52a80955d40ec819"
+                    },
+                    {
+                      "_uid_": "0xb9e12a67e34d6acc"
+                    },
+                    {
+                      "_uid_": "0xf92d7dbe272d680b"
+                    }
+                  ],
+                  "name": "Sang Hyun",
+                  "owns_pet": [
+                    {
+                      "_uid_": "0xf590a923ea1fccaa"
+                    }
+                  ]
+                }
+              ],
+              "name": "Hyung Sin"
+            }
+          ],
+          "name": "Sang Hyun"
+        },
+        {
+          "_uid_": "0x99b74c1b5ab100ec",
+          "name": "Artyom"
+        }
+      ],
+      "name": "Amit"
+    }
+  ]
+}
+`
+)
diff --git a/vendor/gonum.org/v1/gonum/graph/ex/fdpclust/gn.go b/vendor/gonum.org/v1/gonum/graph/ex/fdpclust/gn.go
new file mode 100644
index 00000000..bcb1aad1
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/ex/fdpclust/gn.go
@@ -0,0 +1,278 @@
+package main
+
+import (
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+type GraphNode struct {
+	id        int64
+	neighbors []graph.Node
+	roots     []*GraphNode
+}
+
+func (g *GraphNode) Has(n graph.Node) bool {
+	if n.ID() == g.id {
+		return true
+	}
+
+	visited := map[int64]struct{}{g.id: {}}
+	for _, root := range g.roots {
+		if root.ID() == n.ID() {
+			return true
+		}
+
+		if root.has(n, visited) {
+			return true
+		}
+	}
+
+	for _, neigh := range g.neighbors {
+		if neigh.ID() == n.ID() {
+			return true
+		}
+
+		if gn, ok := neigh.(*GraphNode); ok {
+			if gn.has(n, visited) {
+				return true
+			}
+		}
+	}
+
+	return false
+}
+
+func (g *GraphNode) has(n graph.Node, visited map[int64]struct{}) bool {
+	for _, root := range g.roots {
+		if _, ok := visited[root.ID()]; ok {
+			continue
+		}
+
+		visited[root.ID()] = struct{}{}
+		if root.ID() == n.ID() {
+			return true
+		}
+
+		if root.has(n, visited) {
+			return true
+		}
+
+	}
+
+	for _, neigh := range g.neighbors {
+		if _, ok := visited[neigh.ID()]; ok {
+			continue
+		}
+
+		visited[neigh.ID()] = struct{}{}
+		if neigh.ID() == n.ID() {
+			return true
+		}
+
+		if gn, ok := neigh.(*GraphNode); ok {
+			if gn.has(n, visited) {
+				return true
+			}
+		}
+
+	}
+
+	return false
+}
+
+func (g *GraphNode) Nodes() []graph.Node {
+	toReturn := []graph.Node{g}
+	visited := map[int64]struct{}{g.id: {}}
+
+	for _, root := range g.roots {
+		toReturn = append(toReturn, root)
+		visited[root.ID()] = struct{}{}
+
+		toReturn = root.nodes(toReturn, visited)
+	}
+
+	for _, neigh := range g.neighbors {
+		toReturn = append(toReturn, neigh)
+		visited[neigh.ID()] = struct{}{}
+
+		if gn, ok := neigh.(*GraphNode); ok {
+			toReturn = gn.nodes(toReturn, visited)
+		}
+	}
+
+	return toReturn
+}
+
+func (g *GraphNode) nodes(list []graph.Node, visited map[int64]struct{}) []graph.Node {
+	for _, root := range g.roots {
+		if _, ok := visited[root.ID()]; ok {
+			continue
+		}
+		visited[root.ID()] = struct{}{}
+		list = append(list, graph.Node(root))
+
+		list = root.nodes(list, visited)
+	}
+
+	for _, neigh := range g.neighbors {
+		if _, ok := visited[neigh.ID()]; ok {
+			continue
+		}
+
+		list = append(list, neigh)
+		if gn, ok := neigh.(*GraphNode); ok {
+			list = gn.nodes(list, visited)
+		}
+	}
+
+	return list
+}
+
+func (g *GraphNode) From(n graph.Node) []graph.Node {
+	if n.ID() == g.ID() {
+		return g.neighbors
+	}
+
+	visited := map[int64]struct{}{g.id: {}}
+	for _, root := range g.roots {
+		visited[root.ID()] = struct{}{}
+
+		if result := root.findNeighbors(n, visited); result != nil {
+			return result
+		}
+	}
+
+	for _, neigh := range g.neighbors {
+		visited[neigh.ID()] = struct{}{}
+
+		if gn, ok := neigh.(*GraphNode); ok {
+			if result := gn.findNeighbors(n, visited); result != nil {
+				return result
+			}
+		}
+	}
+
+	return nil
+}
+
+func (g *GraphNode) findNeighbors(n graph.Node, visited map[int64]struct{}) []graph.Node {
+	if n.ID() == g.ID() {
+		return g.neighbors
+	}
+
+	for _, root := range g.roots {
+		if _, ok := visited[root.ID()]; ok {
+			continue
+		}
+		visited[root.ID()] = struct{}{}
+
+		if result := root.findNeighbors(n, visited); result != nil {
+			return result
+		}
+	}
+
+	for _, neigh := range g.neighbors {
+		if _, ok := visited[neigh.ID()]; ok {
+			continue
+		}
+		visited[neigh.ID()] = struct{}{}
+
+		if gn, ok := neigh.(*GraphNode); ok {
+			if result := gn.findNeighbors(n, visited); result != nil {
+				return result
+			}
+		}
+	}
+
+	return nil
+}
+
+func (g *GraphNode) HasEdgeBetween(u, v graph.Node) bool {
+	return g.EdgeBetween(u, v) != nil
+}
+
+func (g *GraphNode) Edge(u, v graph.Node) graph.Edge {
+	return g.EdgeBetween(u, v)
+}
+
+func (g *GraphNode) EdgeBetween(u, v graph.Node) graph.Edge {
+	if u.ID() == g.id || v.ID() == g.id {
+		for _, neigh := range g.neighbors {
+			if neigh.ID() == u.ID() || neigh.ID() == v.ID() {
+				return simple.Edge{F: g, T: neigh}
+			}
+		}
+		return nil
+	}
+
+	visited := map[int64]struct{}{g.id: {}}
+	for _, root := range g.roots {
+		visited[root.ID()] = struct{}{}
+		if result := root.edgeBetween(u, v, visited); result != nil {
+			return result
+		}
+	}
+
+	for _, neigh := range g.neighbors {
+		visited[neigh.ID()] = struct{}{}
+		if gn, ok := neigh.(*GraphNode); ok {
+			if result := gn.edgeBetween(u, v, visited); result != nil {
+				return result
+			}
+		}
+	}
+
+	return nil
+}
+
+func (g *GraphNode) edgeBetween(u, v graph.Node, visited map[int64]struct{}) graph.Edge {
+	if u.ID() == g.id || v.ID() == g.id {
+		for _, neigh := range g.neighbors {
+			if neigh.ID() == u.ID() || neigh.ID() == v.ID() {
+				return simple.Edge{F: g, T: neigh}
+			}
+		}
+		return nil
+	}
+
+	for _, root := range g.roots {
+		if _, ok := visited[root.ID()]; ok {
+			continue
+		}
+		visited[root.ID()] = struct{}{}
+		if result := root.edgeBetween(u, v, visited); result != nil {
+			return result
+		}
+	}
+
+	for _, neigh := range g.neighbors {
+		if _, ok := visited[neigh.ID()]; ok {
+			continue
+		}
+
+		visited[neigh.ID()] = struct{}{}
+		if gn, ok := neigh.(*GraphNode); ok {
+			if result := gn.edgeBetween(u, v, visited); result != nil {
+				return result
+			}
+		}
+	}
+
+	return nil
+}
+
+func (g *GraphNode) ID() int64 {
+	return g.id
+}
+
+func (g *GraphNode) AddNeighbor(n *GraphNode) {
+	g.neighbors = append(g.neighbors, graph.Node(n))
+}
+
+func (g *GraphNode) AddRoot(n *GraphNode) {
+	g.roots = append(g.roots, n)
+}
+
+func NewGraphNode(id int64) *GraphNode {
+	return &GraphNode{id: id}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/ex/fdpclust/main.go b/vendor/gonum.org/v1/gonum/graph/ex/fdpclust/main.go
new file mode 100644
index 00000000..eb14226a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/ex/fdpclust/main.go
@@ -0,0 +1,75 @@
+package main
+
+import (
+	"fmt"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/topo"
+)
+
+func main() {
+	// graph G {
+	G := NewGraphNode(0)
+	// e
+	e := NewGraphNode(1)
+
+	// subgraph clusterA {
+	clusterA := NewGraphNode(2)
+
+	// a -- b
+	a := NewGraphNode(3)
+	b := NewGraphNode(4)
+	a.AddNeighbor(b)
+	b.AddNeighbor(a)
+	clusterA.AddRoot(a)
+	clusterA.AddRoot(b)
+
+	// subgraph clusterC {
+	clusterC := NewGraphNode(5)
+	// C -- D
+	C := NewGraphNode(6)
+	D := NewGraphNode(7)
+	C.AddNeighbor(D)
+	D.AddNeighbor(C)
+
+	clusterC.AddRoot(C)
+	clusterC.AddRoot(D)
+	// }
+	clusterA.AddRoot(clusterC)
+	// }
+
+	// subgraph clusterB {
+	clusterB := NewGraphNode(8)
+
+	// d -- f
+	d := NewGraphNode(9)
+	f := NewGraphNode(10)
+	d.AddNeighbor(f)
+	f.AddNeighbor(d)
+	clusterB.AddRoot(d)
+	clusterB.AddRoot(f)
+	// }
+
+	// d -- D
+	d.AddNeighbor(D)
+	D.AddNeighbor(d)
+
+	// e -- clusterB
+	e.AddNeighbor(clusterB)
+	clusterB.AddNeighbor(e)
+
+	// clusterC -- clusterB
+	clusterC.AddNeighbor(clusterB)
+	clusterB.AddNeighbor(clusterC)
+
+	G.AddRoot(e)
+	G.AddRoot(clusterA)
+	G.AddRoot(clusterB)
+	// }
+
+	if !topo.IsPathIn(G, []graph.Node{C, D, d, f}) {
+		fmt.Println("Not working!")
+	} else {
+		fmt.Println("Working!")
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/README.md b/vendor/gonum.org/v1/gonum/graph/formats/dot/README.md
new file mode 100644
index 00000000..a26ca902
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/README.md
@@ -0,0 +1,9 @@
+# formats/dot
+
+## License
+
+The source code and any original content of the formats/dot directory is released under [Public Domain Dedication](https://creativecommons.org/publicdomain/zero/1.0/).
+
+The source code is also licensed under the gonum license, and users are free to choose the license which suits their needs.
+
+Please see gonum.org/v1/gonum for general license information, contributors, authors, etc on the Gonum suite of packages.
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/ast/ast.go b/vendor/gonum.org/v1/gonum/graph/formats/dot/ast/ast.go
new file mode 100644
index 00000000..8bb961ce
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/ast/ast.go
@@ -0,0 +1,406 @@
+// This file is dual licensed under CC0 and The gonum license.
+//
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Copyright ©2017 Robin Eklind.
+// This file is made available under a Creative Commons CC0 1.0
+// Universal Public Domain Dedication.
+
+package ast
+
+import (
+	"bytes"
+	"fmt"
+)
+
+// === [ File ] ================================================================
+
+// A File represents a DOT file.
+//
+// Examples.
+//
+//    digraph G {
+//       A -> B
+//    }
+//    graph H {
+//       C - D
+//    }
+type File struct {
+	// Graphs.
+	Graphs []*Graph
+}
+
+// String returns the string representation of the file.
+func (f *File) String() string {
+	buf := new(bytes.Buffer)
+	for i, graph := range f.Graphs {
+		if i != 0 {
+			buf.WriteString("\n")
+		}
+		buf.WriteString(graph.String())
+	}
+	return buf.String()
+}
+
+// === [ Graphs ] ==============================================================
+
+// A Graph represents a directed or an undirected graph.
+//
+// Examples.
+//
+//    digraph G {
+//       A -> {B C}
+//       B -> C
+//    }
+type Graph struct {
+	// Strict graph; multi-edges forbidden.
+	Strict bool
+	// Directed graph.
+	Directed bool
+	// Graph ID; or empty if anonymous.
+	ID string
+	// Graph statements.
+	Stmts []Stmt
+}
+
+// String returns the string representation of the graph.
+func (g *Graph) String() string {
+	buf := new(bytes.Buffer)
+	if g.Strict {
+		buf.WriteString("strict ")
+	}
+	if g.Directed {
+		buf.WriteString("digraph ")
+	} else {
+		buf.WriteString("graph ")
+	}
+	if len(g.ID) > 0 {
+		fmt.Fprintf(buf, "%s ", g.ID)
+	}
+	buf.WriteString("{\n")
+	for _, stmt := range g.Stmts {
+		fmt.Fprintf(buf, "\t%s\n", stmt)
+	}
+	buf.WriteString("}")
+	return buf.String()
+}
+
+// === [ Statements ] ==========================================================
+
+// A Stmt represents a statement, and has one of the following underlying types.
+//
+//    *NodeStmt
+//    *EdgeStmt
+//    *AttrStmt
+//    *Attr
+//    *Subgraph
+type Stmt interface {
+	fmt.Stringer
+	// isStmt ensures that only statements can be assigned to the Stmt interface.
+	isStmt()
+}
+
+// --- [ Node statement ] ------------------------------------------------------
+
+// A NodeStmt represents a node statement.
+//
+// Examples.
+//
+//    A [color=blue]
+type NodeStmt struct {
+	// Node.
+	Node *Node
+	// Node attributes.
+	Attrs []*Attr
+}
+
+// String returns the string representation of the node statement.
+func (e *NodeStmt) String() string {
+	buf := new(bytes.Buffer)
+	buf.WriteString(e.Node.String())
+	if len(e.Attrs) > 0 {
+		buf.WriteString(" [")
+		for i, attr := range e.Attrs {
+			if i != 0 {
+				buf.WriteString(" ")
+			}
+			buf.WriteString(attr.String())
+		}
+		buf.WriteString("]")
+	}
+	return buf.String()
+}
+
+// --- [ Edge statement ] ------------------------------------------------------
+
+// An EdgeStmt represents an edge statement.
+//
+// Examples.
+//
+//    A -> B
+//    A -> {B C}
+//    A -> B -> C
+type EdgeStmt struct {
+	// Source vertex.
+	From Vertex
+	// Outgoing edge.
+	To *Edge
+	// Edge attributes.
+	Attrs []*Attr
+}
+
+// String returns the string representation of the edge statement.
+func (e *EdgeStmt) String() string {
+	buf := new(bytes.Buffer)
+	fmt.Fprintf(buf, "%s %s", e.From, e.To)
+	if len(e.Attrs) > 0 {
+		buf.WriteString(" [")
+		for i, attr := range e.Attrs {
+			if i != 0 {
+				buf.WriteString(" ")
+			}
+			buf.WriteString(attr.String())
+		}
+		buf.WriteString("]")
+	}
+	return buf.String()
+}
+
+// An Edge represents an edge between two vertices.
+type Edge struct {
+	// Directed edge.
+	Directed bool
+	// Destination vertex.
+	Vertex Vertex
+	// Outgoing edge; or nil if none.
+	To *Edge
+}
+
+// String returns the string representation of the edge.
+func (e *Edge) String() string {
+	op := "--"
+	if e.Directed {
+		op = "->"
+	}
+	if e.To != nil {
+		return fmt.Sprintf("%s %s %s", op, e.Vertex, e.To)
+	}
+	return fmt.Sprintf("%s %s", op, e.Vertex)
+}
+
+// --- [ Attribute statement ] -------------------------------------------------
+
+// An AttrStmt represents an attribute statement.
+//
+// Examples.
+//
+//    graph [rankdir=LR]
+//    node [color=blue fillcolor=red]
+//    edge [minlen=1]
+type AttrStmt struct {
+	// Graph component kind to which the attributes are assigned.
+	Kind Kind
+	// Attributes.
+	Attrs []*Attr
+}
+
+// String returns the string representation of the attribute statement.
+func (a *AttrStmt) String() string {
+	buf := new(bytes.Buffer)
+	fmt.Fprintf(buf, "%s [", a.Kind)
+	for i, attr := range a.Attrs {
+		if i != 0 {
+			buf.WriteString(" ")
+		}
+		buf.WriteString(attr.String())
+	}
+	buf.WriteString("]")
+	return buf.String()
+}
+
+// Kind specifies the set of graph components to which attribute statements may
+// be assigned.
+type Kind uint
+
+// Graph component kinds.
+const (
+	GraphKind Kind = iota // graph
+	NodeKind              // node
+	EdgeKind              // edge
+)
+
+// String returns the string representation of the graph component kind.
+func (k Kind) String() string {
+	switch k {
+	case GraphKind:
+		return "graph"
+	case NodeKind:
+		return "node"
+	case EdgeKind:
+		return "edge"
+	}
+	panic(fmt.Sprintf("invalid graph component kind (%d)", k))
+}
+
+// --- [ Attribute ] -----------------------------------------------------------
+
+// An Attr represents an attribute.
+//
+// Examples.
+//
+//    rank=same
+type Attr struct {
+	// Attribute key.
+	Key string
+	// Attribute value.
+	Val string
+}
+
+// String returns the string representation of the attribute.
+func (a *Attr) String() string {
+	return fmt.Sprintf("%s=%s", a.Key, a.Val)
+}
+
+// --- [ Subgraph ] ------------------------------------------------------------
+
+// A Subgraph represents a subgraph vertex.
+//
+// Examples.
+//
+//    subgraph S {A B C}
+type Subgraph struct {
+	// Subgraph ID; or empty if none.
+	ID string
+	// Subgraph statements.
+	Stmts []Stmt
+}
+
+// String returns the string representation of the subgraph.
+func (s *Subgraph) String() string {
+	buf := new(bytes.Buffer)
+	if len(s.ID) > 0 {
+		fmt.Fprintf(buf, "subgraph %s ", s.ID)
+	}
+	buf.WriteString("{")
+	for i, stmt := range s.Stmts {
+		if i != 0 {
+			buf.WriteString(" ")
+		}
+		buf.WriteString(stmt.String())
+	}
+	buf.WriteString("}")
+	return buf.String()
+}
+
+// isStmt ensures that only statements can be assigned to the Stmt interface.
+func (*NodeStmt) isStmt() {}
+func (*EdgeStmt) isStmt() {}
+func (*AttrStmt) isStmt() {}
+func (*Attr) isStmt()     {}
+func (*Subgraph) isStmt() {}
+
+// === [ Vertices ] ============================================================
+
+// A Vertex represents a vertex, and has one of the following underlying types.
+//
+//    *Node
+//    *Subgraph
+type Vertex interface {
+	fmt.Stringer
+	// isVertex ensures that only vertices can be assigned to the Vertex
+	// interface.
+	isVertex()
+}
+
+// --- [ Node identifier ] -----------------------------------------------------
+
+// A Node represents a node vertex.
+//
+// Examples.
+//
+//    A
+//    A:nw
+type Node struct {
+	// Node ID.
+	ID string
+	// Node port; or nil if none.
+	Port *Port
+}
+
+// String returns the string representation of the node.
+func (n *Node) String() string {
+	if n.Port != nil {
+		return fmt.Sprintf("%s%s", n.ID, n.Port)
+	}
+	return n.ID
+}
+
+// A Port specifies where on a node an edge should be aimed.
+type Port struct {
+	// Port ID; or empty if none.
+	ID string
+	// Compass point.
+	CompassPoint CompassPoint
+}
+
+// String returns the string representation of the port.
+func (p *Port) String() string {
+	buf := new(bytes.Buffer)
+	if len(p.ID) > 0 {
+		fmt.Fprintf(buf, ":%s", p.ID)
+	}
+	if p.CompassPoint != CompassPointDefault {
+		fmt.Fprintf(buf, ":%s", p.CompassPoint)
+	}
+	return buf.String()
+}
+
+// CompassPoint specifies the set of compass points.
+type CompassPoint uint
+
+// Compass points.
+const (
+	CompassPointDefault   CompassPoint = iota // _
+	CompassPointNorth                         // n
+	CompassPointNorthEast                     // ne
+	CompassPointEast                          // e
+	CompassPointSouthEast                     // se
+	CompassPointSouth                         // s
+	CompassPointSouthWest                     // sw
+	CompassPointWest                          // w
+	CompassPointNorthWest                     // nw
+	CompassPointCenter                        // c
+)
+
+// String returns the string representation of the compass point.
+func (c CompassPoint) String() string {
+	switch c {
+	case CompassPointDefault:
+		return "_"
+	case CompassPointNorth:
+		return "n"
+	case CompassPointNorthEast:
+		return "ne"
+	case CompassPointEast:
+		return "e"
+	case CompassPointSouthEast:
+		return "se"
+	case CompassPointSouth:
+		return "s"
+	case CompassPointSouthWest:
+		return "sw"
+	case CompassPointWest:
+		return "w"
+	case CompassPointNorthWest:
+		return "nw"
+	case CompassPointCenter:
+		return "c"
+	}
+	panic(fmt.Sprintf("invalid compass point (%d)", uint(c)))
+}
+
+// isVertex ensures that only vertices can be assigned to the Vertex interface.
+func (*Node) isVertex()     {}
+func (*Subgraph) isVertex() {}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/ast/ast_test.go b/vendor/gonum.org/v1/gonum/graph/formats/dot/ast/ast_test.go
new file mode 100644
index 00000000..2417dce5
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/ast/ast_test.go
@@ -0,0 +1,101 @@
+// This file is dual licensed under CC0 and The gonum license.
+//
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Copyright ©2017 Robin Eklind.
+// This file is made available under a Creative Commons CC0 1.0
+// Universal Public Domain Dedication.
+
+package ast_test
+
+import (
+	"bytes"
+	"io/ioutil"
+	"testing"
+
+	"gonum.org/v1/gonum/graph/formats/dot"
+	"gonum.org/v1/gonum/graph/formats/dot/ast"
+)
+
+func TestParseFile(t *testing.T) {
+	golden := []struct {
+		in  string
+		out string
+	}{
+		{in: "../internal/testdata/empty.dot"},
+		{in: "../internal/testdata/graph.dot"},
+		{in: "../internal/testdata/digraph.dot"},
+		{in: "../internal/testdata/strict.dot"},
+		{in: "../internal/testdata/multi.dot"},
+		{in: "../internal/testdata/named_graph.dot"},
+		{in: "../internal/testdata/node_stmt.dot"},
+		{in: "../internal/testdata/edge_stmt.dot"},
+		{in: "../internal/testdata/attr_stmt.dot"},
+		{in: "../internal/testdata/attr.dot"},
+		{
+			in:  "../internal/testdata/subgraph.dot",
+			out: "../internal/testdata/subgraph.golden",
+		},
+		{
+			in:  "../internal/testdata/semi.dot",
+			out: "../internal/testdata/semi.golden",
+		},
+		{
+			in:  "../internal/testdata/empty_attr.dot",
+			out: "../internal/testdata/empty_attr.golden",
+		},
+		{
+			in:  "../internal/testdata/attr_lists.dot",
+			out: "../internal/testdata/attr_lists.golden",
+		},
+		{
+			in:  "../internal/testdata/attr_sep.dot",
+			out: "../internal/testdata/attr_sep.golden",
+		},
+		{in: "../internal/testdata/subgraph_vertex.dot"},
+		{
+			in:  "../internal/testdata/port.dot",
+			out: "../internal/testdata/port.golden",
+		},
+	}
+	for _, g := range golden {
+		file, err := dot.ParseFile(g.in)
+		if err != nil {
+			t.Errorf("%q: unable to parse file; %v", g.in, err)
+			continue
+		}
+		// If no output path is specified, the input is already golden.
+		out := g.in
+		if len(g.out) > 0 {
+			out = g.out
+		}
+		buf, err := ioutil.ReadFile(out)
+		if err != nil {
+			t.Errorf("%q: unable to read file; %v", g.in, err)
+			continue
+		}
+		got := file.String()
+		// Remove trailing newline.
+		want := string(bytes.TrimSpace(buf))
+		if got != want {
+			t.Errorf("%q: graph mismatch; expected %q, got %q", g.in, want, got)
+		}
+	}
+}
+
+// Verify that all statements implement the Stmt interface.
+var (
+	_ ast.Stmt = (*ast.NodeStmt)(nil)
+	_ ast.Stmt = (*ast.EdgeStmt)(nil)
+	_ ast.Stmt = (*ast.AttrStmt)(nil)
+	_ ast.Stmt = (*ast.Attr)(nil)
+	_ ast.Stmt = (*ast.Subgraph)(nil)
+)
+
+// Verify that all vertices implement the Vertex interface.
+var (
+	_ ast.Vertex = (*ast.Node)(nil)
+	_ ast.Vertex = (*ast.Subgraph)(nil)
+)
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/ast/doc.go b/vendor/gonum.org/v1/gonum/graph/formats/dot/ast/doc.go
new file mode 100644
index 00000000..2d96617c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/ast/doc.go
@@ -0,0 +1,7 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package ast declares the types used to represent abstract syntax trees of
+// Graphviz DOT graphs.
+package ast // import "gonum.org/v1/gonum/graph/formats/dot/ast"
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/doc.go b/vendor/gonum.org/v1/gonum/graph/formats/dot/doc.go
new file mode 100644
index 00000000..4337ff08
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package dot implements a parser for Graphviz DOT files.
+package dot // import "gonum.org/v1/gonum/graph/formats/dot"
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/dot.go b/vendor/gonum.org/v1/gonum/graph/formats/dot/dot.go
new file mode 100644
index 00000000..edc44f68
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/dot.go
@@ -0,0 +1,64 @@
+// This file is dual licensed under CC0 and The gonum license.
+//
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Copyright ©2017 Robin Eklind.
+// This file is made available under a Creative Commons CC0 1.0
+// Universal Public Domain Dedication.
+
+//go:generate ./makeinternal.bash
+
+package dot
+
+import (
+	"fmt"
+	"io"
+	"io/ioutil"
+
+	"gonum.org/v1/gonum/graph/formats/dot/ast"
+	"gonum.org/v1/gonum/graph/formats/dot/internal/lexer"
+	"gonum.org/v1/gonum/graph/formats/dot/internal/parser"
+)
+
+// ParseFile parses the given Graphviz DOT file into an AST.
+func ParseFile(path string) (*ast.File, error) {
+	buf, err := ioutil.ReadFile(path)
+	if err != nil {
+		return nil, err
+	}
+	return ParseBytes(buf)
+}
+
+// Parse parses the given Graphviz DOT file into an AST, reading from r.
+func Parse(r io.Reader) (*ast.File, error) {
+	buf, err := ioutil.ReadAll(r)
+	if err != nil {
+		return nil, err
+	}
+	return ParseBytes(buf)
+}
+
+// ParseBytes parses the given Graphviz DOT file into an AST, reading from b.
+func ParseBytes(b []byte) (*ast.File, error) {
+	l := lexer.NewLexer(b)
+	p := parser.NewParser()
+	file, err := p.Parse(l)
+	if err != nil {
+		return nil, err
+	}
+	f, ok := file.(*ast.File)
+	if !ok {
+		return nil, fmt.Errorf("invalid file type; expected *ast.File, got %T", file)
+	}
+	if err := check(f); err != nil {
+		return nil, err
+	}
+	return f, nil
+}
+
+// ParseString parses the given Graphviz DOT file into an AST, reading from s.
+func ParseString(s string) (*ast.File, error) {
+	return ParseBytes([]byte(s))
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/Makefile b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/Makefile
new file mode 100644
index 00000000..ba04504a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/Makefile
@@ -0,0 +1,33 @@
+gen: dot.bnf
+	gocc $<
+	./paste_copyright.bash
+
+debug_lexer: dot.bnf
+	gocc -debug_lexer -v -a $<
+	./paste_copyright.bash
+
+debug_parser: dot.bnf
+	gocc -debug_parser -v -a $<
+	./paste_copyright.bash
+
+clean:
+	rm -f errors/errors.go
+	rm -f lexer/acttab.go
+	rm -f lexer/lexer.go
+	rm -f lexer/transitiontable.go
+	rm -f parser/action.go
+	rm -f parser/actiontable.go
+	rm -f parser/gototable.go
+	rm -f parser/parser.go
+	rm -f parser/productionstable.go
+	rm -f token/token.go
+	rm -f util/litconv.go
+	rm -f util/rune.go
+	-rmdir --ignore-fail-on-non-empty errors
+	-rmdir --ignore-fail-on-non-empty lexer
+	-rmdir --ignore-fail-on-non-empty parser
+	-rmdir --ignore-fail-on-non-empty token
+	-rmdir --ignore-fail-on-non-empty util
+	rm -f terminals.txt LR1_conflicts.txt LR1_sets.txt first.txt lexer_sets.txt
+
+.PHONY: gen debug_lexer debug_parser clean
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/astx/astx.go b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/astx/astx.go
new file mode 100644
index 00000000..1b3bff55
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/astx/astx.go
@@ -0,0 +1,326 @@
+// This file is dual licensed under CC0 and The gonum license.
+//
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Copyright ©2017 Robin Eklind.
+// This file is made available under a Creative Commons CC0 1.0
+// Universal Public Domain Dedication.
+
+package astx
+
+import (
+	"fmt"
+	"strings"
+
+	"gonum.org/v1/gonum/graph/formats/dot/ast"
+	"gonum.org/v1/gonum/graph/formats/dot/internal/token"
+)
+
+// === [ File ] ================================================================
+
+// NewFile returns a new file based on the given graph.
+func NewFile(graph interface{}) (*ast.File, error) {
+	g, ok := graph.(*ast.Graph)
+	if !ok {
+		return nil, fmt.Errorf("invalid graph type; expected *ast.Graph, got %T", graph)
+	}
+	return &ast.File{Graphs: []*ast.Graph{g}}, nil
+}
+
+// AppendGraph appends graph to the given file.
+func AppendGraph(file, graph interface{}) (*ast.File, error) {
+	f, ok := file.(*ast.File)
+	if !ok {
+		return nil, fmt.Errorf("invalid file type; expected *ast.File, got %T", file)
+	}
+	g, ok := graph.(*ast.Graph)
+	if !ok {
+		return nil, fmt.Errorf("invalid graph type; expected *ast.Graph, got %T", graph)
+	}
+	f.Graphs = append(f.Graphs, g)
+	return f, nil
+}
+
+// === [ Graphs ] ==============================================================
+
+// NewGraph returns a new graph based on the given graph strictness, direction,
+// optional ID and optional statements.
+func NewGraph(strict, directed, optID, optStmts interface{}) (*ast.Graph, error) {
+	s, ok := strict.(bool)
+	if !ok {
+		return nil, fmt.Errorf("invalid strictness type; expected bool, got %T", strict)
+	}
+	d, ok := directed.(bool)
+	if !ok {
+		return nil, fmt.Errorf("invalid direction type; expected bool, got %T", directed)
+	}
+	id, ok := optID.(string)
+	if optID != nil && !ok {
+		return nil, fmt.Errorf("invalid ID type; expected string or nil, got %T", optID)
+	}
+	stmts, ok := optStmts.([]ast.Stmt)
+	if optStmts != nil && !ok {
+		return nil, fmt.Errorf("invalid statements type; expected []ast.Stmt or nil, got %T", optStmts)
+	}
+	return &ast.Graph{Strict: s, Directed: d, ID: id, Stmts: stmts}, nil
+}
+
+// === [ Statements ] ==========================================================
+
+// NewStmtList returns a new statement list based on the given statement.
+func NewStmtList(stmt interface{}) ([]ast.Stmt, error) {
+	s, ok := stmt.(ast.Stmt)
+	if !ok {
+		return nil, fmt.Errorf("invalid statement type; expected ast.Stmt, got %T", stmt)
+	}
+	return []ast.Stmt{s}, nil
+}
+
+// AppendStmt appends stmt to the given statement list.
+func AppendStmt(list, stmt interface{}) ([]ast.Stmt, error) {
+	l, ok := list.([]ast.Stmt)
+	if !ok {
+		return nil, fmt.Errorf("invalid statement list type; expected []ast.Stmt, got %T", list)
+	}
+	s, ok := stmt.(ast.Stmt)
+	if !ok {
+		return nil, fmt.Errorf("invalid statement type; expected ast.Stmt, got %T", stmt)
+	}
+	return append(l, s), nil
+}
+
+// --- [ Node statement ] ------------------------------------------------------
+
+// NewNodeStmt returns a new node statement based on the given node and optional
+// attributes.
+func NewNodeStmt(node, optAttrs interface{}) (*ast.NodeStmt, error) {
+	n, ok := node.(*ast.Node)
+	if !ok {
+		return nil, fmt.Errorf("invalid node type; expected *ast.Node, got %T", node)
+	}
+	attrs, ok := optAttrs.([]*ast.Attr)
+	if optAttrs != nil && !ok {
+		return nil, fmt.Errorf("invalid attributes type; expected []*ast.Attr or nil, got %T", optAttrs)
+	}
+	return &ast.NodeStmt{Node: n, Attrs: attrs}, nil
+}
+
+// --- [ Edge statement ] ------------------------------------------------------
+
+// NewEdgeStmt returns a new edge statement based on the given source vertex,
+// outgoing edge and optional attributes.
+func NewEdgeStmt(from, to, optAttrs interface{}) (*ast.EdgeStmt, error) {
+	f, ok := from.(ast.Vertex)
+	if !ok {
+		return nil, fmt.Errorf("invalid source vertex type; expected ast.Vertex, got %T", from)
+	}
+	t, ok := to.(*ast.Edge)
+	if !ok {
+		return nil, fmt.Errorf("invalid outgoing edge type; expected *ast.Edge, got %T", to)
+	}
+	attrs, ok := optAttrs.([]*ast.Attr)
+	if optAttrs != nil && !ok {
+		return nil, fmt.Errorf("invalid attributes type; expected []*ast.Attr or nil, got %T", optAttrs)
+	}
+	return &ast.EdgeStmt{From: f, To: t, Attrs: attrs}, nil
+}
+
+// NewEdge returns a new edge based on the given edge direction, destination
+// vertex and optional outgoing edge.
+func NewEdge(directed, vertex, optTo interface{}) (*ast.Edge, error) {
+	d, ok := directed.(bool)
+	if !ok {
+		return nil, fmt.Errorf("invalid direction type; expected bool, got %T", directed)
+	}
+	v, ok := vertex.(ast.Vertex)
+	if !ok {
+		return nil, fmt.Errorf("invalid destination vertex type; expected ast.Vertex, got %T", vertex)
+	}
+	to, ok := optTo.(*ast.Edge)
+	if optTo != nil && !ok {
+		return nil, fmt.Errorf("invalid outgoing edge type; expected *ast.Edge or nil, got %T", optTo)
+	}
+	return &ast.Edge{Directed: d, Vertex: v, To: to}, nil
+}
+
+// --- [ Attribute statement ] -------------------------------------------------
+
+// NewAttrStmt returns a new attribute statement based on the given graph
+// component kind and attributes.
+func NewAttrStmt(kind, optAttrs interface{}) (*ast.AttrStmt, error) {
+	k, ok := kind.(ast.Kind)
+	if !ok {
+		return nil, fmt.Errorf("invalid graph component kind type; expected ast.Kind, got %T", kind)
+	}
+	attrs, ok := optAttrs.([]*ast.Attr)
+	if optAttrs != nil && !ok {
+		return nil, fmt.Errorf("invalid attributes type; expected []*ast.Attr or nil, got %T", optAttrs)
+	}
+	return &ast.AttrStmt{Kind: k, Attrs: attrs}, nil
+}
+
+// NewAttrList returns a new attribute list based on the given attribute.
+func NewAttrList(attr interface{}) ([]*ast.Attr, error) {
+	a, ok := attr.(*ast.Attr)
+	if !ok {
+		return nil, fmt.Errorf("invalid attribute type; expected *ast.Attr, got %T", attr)
+	}
+	return []*ast.Attr{a}, nil
+}
+
+// AppendAttr appends attr to the given attribute list.
+func AppendAttr(list, attr interface{}) ([]*ast.Attr, error) {
+	l, ok := list.([]*ast.Attr)
+	if !ok {
+		return nil, fmt.Errorf("invalid attribute list type; expected []*ast.Attr, got %T", list)
+	}
+	a, ok := attr.(*ast.Attr)
+	if !ok {
+		return nil, fmt.Errorf("invalid attribute type; expected *ast.Attr, got %T", attr)
+	}
+	return append(l, a), nil
+}
+
+// AppendAttrList appends the optional attrs to the given optional attribute
+// list.
+func AppendAttrList(optList, optAttrs interface{}) ([]*ast.Attr, error) {
+	list, ok := optList.([]*ast.Attr)
+	if optList != nil && !ok {
+		return nil, fmt.Errorf("invalid attribute list type; expected []*ast.Attr or nil, got %T", optList)
+	}
+	attrs, ok := optAttrs.([]*ast.Attr)
+	if optAttrs != nil && !ok {
+		return nil, fmt.Errorf("invalid attributes type; expected []*ast.Attr or nil, got %T", optAttrs)
+	}
+	return append(list, attrs...), nil
+}
+
+// --- [ Attribute ] -----------------------------------------------------------
+
+// NewAttr returns a new attribute based on the given key-value pair.
+func NewAttr(key, val interface{}) (*ast.Attr, error) {
+	k, ok := key.(string)
+	if !ok {
+		return nil, fmt.Errorf("invalid key type; expected string, got %T", key)
+	}
+	v, ok := val.(string)
+	if !ok {
+		return nil, fmt.Errorf("invalid value type; expected string, got %T", val)
+	}
+	return &ast.Attr{Key: k, Val: v}, nil
+}
+
+// --- [ Subgraph ] ------------------------------------------------------------
+
+// NewSubgraph returns a new subgraph based on the given optional subgraph ID
+// and optional statements.
+func NewSubgraph(optID, optStmts interface{}) (*ast.Subgraph, error) {
+	id, ok := optID.(string)
+	if optID != nil && !ok {
+		return nil, fmt.Errorf("invalid ID type; expected string or nil, got %T", optID)
+	}
+	stmts, ok := optStmts.([]ast.Stmt)
+	if optStmts != nil && !ok {
+		return nil, fmt.Errorf("invalid statements type; expected []ast.Stmt or nil, got %T", optStmts)
+	}
+	return &ast.Subgraph{ID: id, Stmts: stmts}, nil
+}
+
+// === [ Vertices ] ============================================================
+
+// --- [ Node identifier ] -----------------------------------------------------
+
+// NewNode returns a new node based on the given node id and optional port.
+func NewNode(id, optPort interface{}) (*ast.Node, error) {
+	i, ok := id.(string)
+	if !ok {
+		return nil, fmt.Errorf("invalid ID type; expected string, got %T", id)
+	}
+	port, ok := optPort.(*ast.Port)
+	if optPort != nil && !ok {
+		return nil, fmt.Errorf("invalid port type; expected *ast.Port or nil, got %T", optPort)
+	}
+	return &ast.Node{ID: i, Port: port}, nil
+}
+
+// NewPort returns a new port based on the given id and optional compass point.
+func NewPort(id, optCompassPoint interface{}) (*ast.Port, error) {
+	// Note, if optCompassPoint is nil, id may be either an identifier or a
+	// compass point.
+	//
+	// The following strings are valid compass points:
+	//
+	//    "n", "ne", "e", "se", "s", "sw", "w", "nw", "c" and "_"
+	i, ok := id.(string)
+	if !ok {
+		return nil, fmt.Errorf("invalid ID type; expected string, got %T", id)
+	}
+
+	// Early return if optional compass point is absent and ID is a valid compass
+	// point.
+	if optCompassPoint == nil {
+		if compassPoint, ok := getCompassPoint(i); ok {
+			return &ast.Port{CompassPoint: compassPoint}, nil
+		}
+	}
+
+	c, ok := optCompassPoint.(string)
+	if optCompassPoint != nil && !ok {
+		return nil, fmt.Errorf("invalid compass point type; expected string or nil, got %T", optCompassPoint)
+	}
+	compassPoint, _ := getCompassPoint(c)
+	return &ast.Port{ID: i, CompassPoint: compassPoint}, nil
+}
+
+// getCompassPoint returns the corresponding compass point to the given string,
+// and a boolean value indicating if such a compass point exists.
+func getCompassPoint(s string) (ast.CompassPoint, bool) {
+	switch s {
+	case "_":
+		return ast.CompassPointDefault, true
+	case "n":
+		return ast.CompassPointNorth, true
+	case "ne":
+		return ast.CompassPointNorthEast, true
+	case "e":
+		return ast.CompassPointEast, true
+	case "se":
+		return ast.CompassPointSouthEast, true
+	case "s":
+		return ast.CompassPointSouth, true
+	case "sw":
+		return ast.CompassPointSouthWest, true
+	case "w":
+		return ast.CompassPointWest, true
+	case "nw":
+		return ast.CompassPointNorthWest, true
+	case "c":
+		return ast.CompassPointCenter, true
+	}
+	return ast.CompassPointDefault, false
+}
+
+// === [ Identifiers ] =========================================================
+
+// NewID returns a new identifier based on the given ID token.
+func NewID(id interface{}) (string, error) {
+	i, ok := id.(*token.Token)
+	if !ok {
+		return "", fmt.Errorf("invalid identifier type; expected *token.Token, got %T", id)
+	}
+	s := string(i.Lit)
+
+	// As another aid for readability, dot allows double-quoted strings to span
+	// multiple physical lines using the standard C convention of a backslash
+	// immediately preceding a newline character.
+	if strings.HasPrefix(s, `"`) && strings.HasSuffix(s, `"`) {
+		// Strip "\\\n" sequences.
+		s = strings.Replace(s, "\\\n", "", -1)
+	}
+
+	// TODO: Add support for concatenated using a '+' operator.
+
+	return s, nil
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/astx/astx_test.go b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/astx/astx_test.go
new file mode 100644
index 00000000..4ec55000
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/astx/astx_test.go
@@ -0,0 +1,90 @@
+// This file is dual licensed under CC0 and The gonum license.
+//
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Copyright ©2017 Robin Eklind.
+// This file is made available under a Creative Commons CC0 1.0
+// Universal Public Domain Dedication.
+
+package astx_test
+
+import (
+	"bytes"
+	"io/ioutil"
+	"testing"
+
+	"gonum.org/v1/gonum/graph/formats/dot"
+)
+
+func TestParseFile(t *testing.T) {
+	golden := []struct {
+		in  string
+		out string
+	}{
+		{in: "../testdata/empty.dot"},
+		{in: "../testdata/graph.dot"},
+		{in: "../testdata/digraph.dot"},
+		{in: "../testdata/strict.dot"},
+		{in: "../testdata/multi.dot"},
+		{in: "../testdata/named_graph.dot"},
+		{in: "../testdata/node_stmt.dot"},
+		{in: "../testdata/edge_stmt.dot"},
+		{in: "../testdata/attr_stmt.dot"},
+		{in: "../testdata/attr.dot"},
+		{
+			in:  "../testdata/subgraph.dot",
+			out: "../testdata/subgraph.golden",
+		},
+		{
+			in:  "../testdata/semi.dot",
+			out: "../testdata/semi.golden",
+		},
+		{
+			in:  "../testdata/empty_attr.dot",
+			out: "../testdata/empty_attr.golden",
+		},
+		{
+			in:  "../testdata/attr_lists.dot",
+			out: "../testdata/attr_lists.golden",
+		},
+		{
+			in:  "../testdata/attr_sep.dot",
+			out: "../testdata/attr_sep.golden",
+		},
+		{in: "../testdata/subgraph_vertex.dot"},
+		{
+			in:  "../testdata/port.dot",
+			out: "../testdata/port.golden",
+		},
+		{in: "../testdata/quoted_id.dot"},
+		{
+			in:  "../testdata/backslash_newline_id.dot",
+			out: "../testdata/backslash_newline_id.golden",
+		},
+	}
+	for _, g := range golden {
+		file, err := dot.ParseFile(g.in)
+		if err != nil {
+			t.Errorf("%q: unable to parse file; %v", g.in, err)
+			continue
+		}
+		// If no output path is specified, the input is already golden.
+		out := g.in
+		if len(g.out) > 0 {
+			out = g.out
+		}
+		buf, err := ioutil.ReadFile(out)
+		if err != nil {
+			t.Errorf("%q: unable to read file; %v", g.in, err)
+			continue
+		}
+		got := file.String()
+		// Remove trailing newline.
+		want := string(bytes.TrimSpace(buf))
+		if got != want {
+			t.Errorf("%q: graph mismatch; expected `%s`, got `%s`", g.in, want, got)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/astx/doc.go b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/astx/doc.go
new file mode 100644
index 00000000..65fd9011
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/astx/doc.go
@@ -0,0 +1,7 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package astx implements utility functions for generating abstract syntax
+// trees of Graphviz DOT graphs.
+package astx // import "gonum.org/v1/gonum/graph/formats/dot/internal/astx"
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/dot.bnf b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/dot.bnf
new file mode 100644
index 00000000..b2eafb3a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/dot.bnf
@@ -0,0 +1,358 @@
+// The DOT Language
+//
+// http://www.graphviz.org/doc/info/lang.html
+
+// ### [ Tokens ] ##############################################################
+
+// The keywords node, edge, graph, digraph, subgraph, and strict are case-
+// independent.
+
+node
+	: 'n' 'o' 'd' 'e'
+	| 'N' 'o' 'd' 'e'
+	| 'N' 'O' 'D' 'E'
+;
+
+edge
+	: 'e' 'd' 'g' 'e'
+	| 'E' 'd' 'g' 'e'
+	| 'E' 'D' 'G' 'E'
+;
+
+// TODO: Rename graphx to graph once gocc#20 is fixed [1].
+//
+// [1]: https://github.com/goccmack/gocc/issues/20
+
+graphx
+	: 'g' 'r' 'a' 'p' 'h'
+	| 'G' 'r' 'a' 'p' 'h'
+	| 'G' 'R' 'A' 'P' 'H'
+;
+
+digraph
+	: 'd' 'i' 'g' 'r' 'a' 'p' 'h'
+	| 'D' 'i' 'g' 'r' 'a' 'p' 'h'
+	| 'd' 'i' 'G' 'r' 'a' 'p' 'h'
+	| 'D' 'i' 'G' 'r' 'a' 'p' 'h'
+	| 'D' 'I' 'G' 'R' 'A' 'P' 'H'
+;
+
+subgraph
+	: 's' 'u' 'b' 'g' 'r' 'a' 'p' 'h'
+	| 'S' 'u' 'b' 'g' 'r' 'a' 'p' 'h'
+	| 's' 'u' 'b' 'G' 'r' 'a' 'p' 'h'
+	| 'S' 'u' 'b' 'G' 'r' 'a' 'p' 'h'
+	| 'S' 'U' 'B' 'G' 'R' 'A' 'P' 'H'
+;
+
+strict
+	: 's' 't' 'r' 'i' 'c' 't'
+	| 'S' 't' 'r' 'i' 'c' 't'
+	| 'S' 'T' 'R' 'I' 'C' 'T'
+;
+
+// An arbitrary ASCII character except null (0x00), double quote (0x22) and
+// backslash (0x5C).
+_ascii_char
+	// skip null (0x00)
+	: '\x01' - '\x21'
+	// skip double quote (0x22)
+	| '\x23' - '\x5B'
+	// skip backslash (0x5C)
+	| '\x5D' - '\x7F'
+;
+
+_ascii_letter
+	: 'a' - 'z'
+	| 'A' - 'Z'
+;
+
+_ascii_digit : '0' - '9' ;
+
+_unicode_char
+	: _ascii_char
+	| _unicode_byte
+;
+
+_unicode_byte
+	: '\u0080' - '\uFFFC'
+	// skip invalid code point (\uFFFD)
+	| '\uFFFE' - '\U0010FFFF'
+;
+
+_letter        : _ascii_letter | _unicode_byte | '_' ;
+_decimal_digit : _ascii_digit ;
+_decimals      : _decimal_digit { _decimal_digit } ;
+
+// An ID is one of the following:
+//
+//    1) Any string of alphabetic ([a-zA-Z\200-\377]) characters, underscores
+//       ('_') or digits ([0-9]), not beginning with a digit;
+//
+//    2) a numeral [-]?(.[0-9]+ | [0-9]+(.[0-9]*)? );
+//
+//    3) any double-quoted string ("...") possibly containing escaped quotes
+//       (\");
+//
+//    4) an HTML string (<...>).
+
+id
+	: _letter { _letter | _decimal_digit }
+	| _int_lit
+	| _string_lit
+	| _html_lit
+;
+
+_int_lit
+	: [ '-' ] '.' _decimals
+	| [ '-' ] _decimals [ '.' { _decimal_digit } ]
+;
+
+// In quoted strings in DOT, the only escaped character is double-quote (").
+// That is, in quoted strings, the dyad \" is converted to "; all other
+// characters are left unchanged. In particular, \\ remains \\.
+
+// As another aid for readability, dot allows double-quoted strings to span
+// multiple physical lines using the standard C convention of a backslash
+// immediately preceding a newline character.
+
+// In addition, double-quoted strings can be concatenated using a '+' operator.
+
+_escaped_char : '\\' ( _unicode_char | '"' | '\\' ) ;
+_char         : _unicode_char | _escaped_char ;
+_string_lit   : '"' { _char } '"' ;
+
+// An arbitrary HTML character except null (0x00), left angle bracket (0x3C) and
+// right angle bracket (0x3E).
+_html_char
+	// skip null (0x00)
+	: '\x01' - '\x3B'
+	// skip left angle bracket (0x3C)
+	| '\x3D'
+	// skip right angle bracket (0x3E)
+	| '\x3F' - '\xFF'
+;
+
+_html_chars : { _html_char } ;
+_html_tag   : '<' _html_chars '>' ;
+_html_lit   : '<' { _html_chars | _html_tag } '>' ;
+
+// The language supports C++-style comments: /* */ and //. In addition, a line
+// beginning with a '#' character is considered a line output from a C
+// preprocessor (e.g., # 34 to indicate line 34 ) and discarded.
+
+_line_comment
+	: '/' '/' { . } '\n'
+	| '#' { . } '\n'
+;
+
+_block_comment : '/' '*' { . | '*' } '*' '/' ;
+!comment       : _line_comment | _block_comment ;
+
+!whitespace : ' ' | '\t' | '\r' | '\n' ;
+
+// ### [ Syntax ] ##############################################################
+
+<< import (
+	"gonum.org/v1/gonum/graph/formats/dot/ast"
+	"gonum.org/v1/gonum/graph/formats/dot/internal/astx"
+) >>
+
+// === [ Files ] ===============================================================
+
+File
+	: Graph                                       << astx.NewFile($0) >>
+	| File Graph                                  << astx.AppendGraph($0, $1) >>
+;
+
+// === [ Graphs ] ==============================================================
+
+// Graph : [ "strict" ] ( "graph" | "digraph" ) [ ID ] "{" [ StmtList ] "}"
+
+Graph
+	: OptStrict DirectedGraph OptID
+	  "{" OptStmtList "}"                         << astx.NewGraph($0, $1, $2, $4) >>
+;
+
+OptStrict
+	: empty                                       << false, nil >>
+	| strict                                      << true, nil >>
+;
+
+DirectedGraph
+	: graphx                                      << false, nil >>
+	| digraph                                     << true, nil >>
+;
+
+// === [ Statements ] ==========================================================
+
+// StmtList
+//    : Stmt [ ";" ]
+//    | StmtList Stmt [ ";" ]
+
+StmtList
+	: Stmt OptSemi                                << astx.NewStmtList($0) >>
+	| StmtList Stmt OptSemi                       << astx.AppendStmt($0, $1) >>
+;
+
+OptStmtList
+	: empty
+	| StmtList
+;
+
+Stmt
+	: NodeStmt
+	| EdgeStmt
+	| AttrStmt
+	| Attr
+	| Subgraph
+;
+
+OptSemi
+	: empty
+	| ";"
+;
+
+// --- [ Node statement ] ------------------------------------------------------
+
+// NodeStmt : Node [ AttrList ]
+
+NodeStmt
+	: Node OptAttrList                            << astx.NewNodeStmt($0, $1) >>
+;
+
+// --- [ Edge statement ] ------------------------------------------------------
+
+// EdgeStmt : ( Node | Subgraph ) Edge [ AttrList ]
+
+EdgeStmt
+	: Vertex Edge OptAttrList                     << astx.NewEdgeStmt($0, $1, $2) >>
+;
+
+// Edge : ( "--" | "-->" ) ( Node | Subgraph ) [ Edge ]
+
+Edge
+	: DirectedEdge Vertex OptEdge                 << astx.NewEdge($0, $1, $2) >>
+;
+
+DirectedEdge
+	: "--"                                        << false, nil >>
+	| "->"                                        << true, nil >>
+;
+
+OptEdge
+	: empty
+	| Edge
+;
+
+// --- [ Attribute statement ] -------------------------------------------------
+
+// AttrStmt : ( "graph" | "node" | "edge" ) AttrList
+
+AttrStmt
+	: Component AttrList                          << astx.NewAttrStmt($0, $1) >>
+;
+
+Component
+	: graphx                                      << ast.GraphKind, nil >>
+	| node                                        << ast.NodeKind, nil >>
+	| edge                                        << ast.EdgeKind, nil >>
+;
+
+// AttrList : "[" [ AList ] "]" [ AttrList ]
+
+AttrList
+	: "[" OptAList "]"                            << $1, nil >>
+	| AttrList "[" OptAList "]"                   << astx.AppendAttrList($0, $2) >>
+;
+
+OptAttrList
+	: empty
+	| AttrList
+;
+
+// AList
+//    : Attr [ ( ";" | "," ) ]
+//    | AList Attr [ ( ";" | "," ) ]
+
+AList
+	: Attr OptSep                                 << astx.NewAttrList($0) >>
+	| AList Attr OptSep                           << astx.AppendAttr($0, $1) >>
+;
+
+OptAList
+	: empty
+	| AList
+;
+
+OptSep
+	: empty
+	| ";"
+	| ","
+;
+
+// --- [ Attribute ] -----------------------------------------------------------
+
+Attr
+	: ID "=" ID                                   << astx.NewAttr($0, $2) >>
+;
+
+// --- [ Subgraph ] ------------------------------------------------------------
+
+// Subgraph : [ "subgraph" [ ID ] ] "{" [ StmtList ] "}"
+
+Subgraph
+	: OptSubgraphID "{" OptStmtList "}"           << astx.NewSubgraph($0, $2) >>
+;
+
+OptSubgraphID
+	: empty
+	| subgraph OptID                              << $1, nil >>
+;
+
+// === [ Vertices ] ============================================================
+
+Vertex
+	: Node
+	| Subgraph
+;
+
+// --- [ Node identifier ] -----------------------------------------------------
+
+// Node : ID [ Port ]
+
+Node
+	: ID OptPort                                  << astx.NewNode($0, $1) >>
+;
+
+// Port
+//    : ":" ID [ ":" CompassPoint ]
+//    | ":" CompassPoint
+//
+// CompassPoint
+//    : "n" | "ne" | "e" | "se" | "s" | "sw" | "w" | "nw" | "c" | "_"
+
+// Note also that the allowed compass point values are not keywords, so these
+// strings can be used elsewhere as ordinary identifiers and, conversely, the
+// parser will actually accept any identifier.
+
+Port
+	: ":" ID                                      << astx.NewPort($1, nil) >>
+	| ":" ID ":" ID                               << astx.NewPort($1, $3) >>
+;
+
+OptPort
+	: empty
+	| Port
+;
+
+// === [ Identifiers ] =========================================================
+
+ID
+	: id                                          << astx.NewID($0) >>
+;
+
+OptID
+	: empty                                       << "", nil >>
+	| ID
+;
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/errors/errors.go b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/errors/errors.go
new file mode 100644
index 00000000..44f8825e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/errors/errors.go
@@ -0,0 +1,66 @@
+// Code generated by gocc; DO NOT EDIT.
+
+// This file is dual licensed under CC0 and The gonum license.
+//
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Copyright ©2017 Robin Eklind.
+// This file is made available under a Creative Commons CC0 1.0
+// Universal Public Domain Dedication.
+
+package errors
+
+import (
+	"bytes"
+	"fmt"
+
+	"gonum.org/v1/gonum/graph/formats/dot/internal/token"
+)
+
+type ErrorSymbol interface {
+}
+
+type Error struct {
+	Err            error
+	ErrorToken     *token.Token
+	ErrorSymbols   []ErrorSymbol
+	ExpectedTokens []string
+	StackTop       int
+}
+
+func (e *Error) String() string {
+	w := new(bytes.Buffer)
+	fmt.Fprintf(w, "Error")
+	if e.Err != nil {
+		fmt.Fprintf(w, " %s\n", e.Err)
+	} else {
+		fmt.Fprintf(w, "\n")
+	}
+	fmt.Fprintf(w, "Token: type=%d, lit=%s\n", e.ErrorToken.Type, e.ErrorToken.Lit)
+	fmt.Fprintf(w, "Pos: offset=%d, line=%d, column=%d\n", e.ErrorToken.Pos.Offset, e.ErrorToken.Pos.Line, e.ErrorToken.Pos.Column)
+	fmt.Fprintf(w, "Expected one of: ")
+	for _, sym := range e.ExpectedTokens {
+		fmt.Fprintf(w, "%s ", sym)
+	}
+	fmt.Fprintf(w, "ErrorSymbol:\n")
+	for _, sym := range e.ErrorSymbols {
+		fmt.Fprintf(w, "%v\n", sym)
+	}
+	return w.String()
+}
+
+func (e *Error) Error() string {
+	w := new(bytes.Buffer)
+	fmt.Fprintf(w, "Error in S%d: %s, %s", e.StackTop, token.TokMap.TokenString(e.ErrorToken), e.ErrorToken.Pos.String())
+	if e.Err != nil {
+		fmt.Fprintf(w, e.Err.Error())
+	} else {
+		fmt.Fprintf(w, ", expected one of: ")
+		for _, expected := range e.ExpectedTokens {
+			fmt.Fprintf(w, "%s ", expected)
+		}
+	}
+	return w.String()
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/lexer/acttab.go b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/lexer/acttab.go
new file mode 100644
index 00000000..34c9d4dd
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/lexer/acttab.go
@@ -0,0 +1,597 @@
+// Code generated by gocc; DO NOT EDIT.
+
+// This file is dual licensed under CC0 and The gonum license.
+//
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Copyright ©2017 Robin Eklind.
+// This file is made available under a Creative Commons CC0 1.0
+// Universal Public Domain Dedication.
+
+package lexer
+
+import (
+	"fmt"
+
+	"gonum.org/v1/gonum/graph/formats/dot/internal/token"
+)
+
+type ActionTable [NumStates]ActionRow
+
+type ActionRow struct {
+	Accept token.Type
+	Ignore string
+}
+
+func (a ActionRow) String() string {
+	return fmt.Sprintf("Accept=%d, Ignore=%s", a.Accept, a.Ignore)
+}
+
+var ActTab = ActionTable{
+	ActionRow{ // S0
+		Accept: 0,
+		Ignore: "",
+	},
+	ActionRow{ // S1
+		Accept: -1,
+		Ignore: "!whitespace",
+	},
+	ActionRow{ // S2
+		Accept: 0,
+		Ignore: "",
+	},
+	ActionRow{ // S3
+		Accept: 0,
+		Ignore: "",
+	},
+	ActionRow{ // S4
+		Accept: 15,
+		Ignore: "",
+	},
+	ActionRow{ // S5
+		Accept: 0,
+		Ignore: "",
+	},
+	ActionRow{ // S6
+		Accept: 0,
+		Ignore: "",
+	},
+	ActionRow{ // S7
+		Accept: 0,
+		Ignore: "",
+	},
+	ActionRow{ // S8
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S9
+		Accept: 18,
+		Ignore: "",
+	},
+	ActionRow{ // S10
+		Accept: 8,
+		Ignore: "",
+	},
+	ActionRow{ // S11
+		Accept: 0,
+		Ignore: "",
+	},
+	ActionRow{ // S12
+		Accept: 16,
+		Ignore: "",
+	},
+	ActionRow{ // S13
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S14
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S15
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S16
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S17
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S18
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S19
+		Accept: 13,
+		Ignore: "",
+	},
+	ActionRow{ // S20
+		Accept: 14,
+		Ignore: "",
+	},
+	ActionRow{ // S21
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S22
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S23
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S24
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S25
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S26
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S27
+		Accept: 2,
+		Ignore: "",
+	},
+	ActionRow{ // S28
+		Accept: 3,
+		Ignore: "",
+	},
+	ActionRow{ // S29
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S30
+		Accept: 0,
+		Ignore: "",
+	},
+	ActionRow{ // S31
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S32
+		Accept: 0,
+		Ignore: "",
+	},
+	ActionRow{ // S33
+		Accept: 0,
+		Ignore: "",
+	},
+	ActionRow{ // S34
+		Accept: -1,
+		Ignore: "!comment",
+	},
+	ActionRow{ // S35
+		Accept: 9,
+		Ignore: "",
+	},
+	ActionRow{ // S36
+		Accept: 10,
+		Ignore: "",
+	},
+	ActionRow{ // S37
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S38
+		Accept: 0,
+		Ignore: "",
+	},
+	ActionRow{ // S39
+		Accept: 0,
+		Ignore: "",
+	},
+	ActionRow{ // S40
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S41
+		Accept: 0,
+		Ignore: "",
+	},
+	ActionRow{ // S42
+		Accept: 0,
+		Ignore: "",
+	},
+	ActionRow{ // S43
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S44
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S45
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S46
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S47
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S48
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S49
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S50
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S51
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S52
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S53
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S54
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S55
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S56
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S57
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S58
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S59
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S60
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S61
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S62
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S63
+		Accept: 0,
+		Ignore: "",
+	},
+	ActionRow{ // S64
+		Accept: 0,
+		Ignore: "",
+	},
+	ActionRow{ // S65
+		Accept: 0,
+		Ignore: "",
+	},
+	ActionRow{ // S66
+		Accept: 0,
+		Ignore: "",
+	},
+	ActionRow{ // S67
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S68
+		Accept: 0,
+		Ignore: "",
+	},
+	ActionRow{ // S69
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S70
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S71
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S72
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S73
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S74
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S75
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S76
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S77
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S78
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S79
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S80
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S81
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S82
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S83
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S84
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S85
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S86
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S87
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S88
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S89
+		Accept: -1,
+		Ignore: "!comment",
+	},
+	ActionRow{ // S90
+		Accept: 0,
+		Ignore: "",
+	},
+	ActionRow{ // S91
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S92
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S93
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S94
+		Accept: 12,
+		Ignore: "",
+	},
+	ActionRow{ // S95
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S96
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S97
+		Accept: 11,
+		Ignore: "",
+	},
+	ActionRow{ // S98
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S99
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S100
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S101
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S102
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S103
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S104
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S105
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S106
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S107
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S108
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S109
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S110
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S111
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S112
+		Accept: 6,
+		Ignore: "",
+	},
+	ActionRow{ // S113
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S114
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S115
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S116
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S117
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S118
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S119
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S120
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S121
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S122
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S123
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S124
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S125
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S126
+		Accept: 5,
+		Ignore: "",
+	},
+	ActionRow{ // S127
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S128
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S129
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S130
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S131
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S132
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S133
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S134
+		Accept: 7,
+		Ignore: "",
+	},
+	ActionRow{ // S135
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S136
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S137
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S138
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S139
+		Accept: 19,
+		Ignore: "",
+	},
+	ActionRow{ // S140
+		Accept: 17,
+		Ignore: "",
+	},
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/lexer/lexer.go b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/lexer/lexer.go
new file mode 100644
index 00000000..caa9c461
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/lexer/lexer.go
@@ -0,0 +1,310 @@
+// Code generated by gocc; DO NOT EDIT.
+
+// This file is dual licensed under CC0 and The gonum license.
+//
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Copyright ©2017 Robin Eklind.
+// This file is made available under a Creative Commons CC0 1.0
+// Universal Public Domain Dedication.
+
+package lexer
+
+import (
+	"io/ioutil"
+	"unicode/utf8"
+
+	"gonum.org/v1/gonum/graph/formats/dot/internal/token"
+)
+
+const (
+	NoState    = -1
+	NumStates  = 141
+	NumSymbols = 184
+)
+
+type Lexer struct {
+	src    []byte
+	pos    int
+	line   int
+	column int
+}
+
+func NewLexer(src []byte) *Lexer {
+	lexer := &Lexer{
+		src:    src,
+		pos:    0,
+		line:   1,
+		column: 1,
+	}
+	return lexer
+}
+
+func NewLexerFile(fpath string) (*Lexer, error) {
+	src, err := ioutil.ReadFile(fpath)
+	if err != nil {
+		return nil, err
+	}
+	return NewLexer(src), nil
+}
+
+func (l *Lexer) Scan() (tok *token.Token) {
+	tok = new(token.Token)
+	if l.pos >= len(l.src) {
+		tok.Type = token.EOF
+		tok.Pos.Offset, tok.Pos.Line, tok.Pos.Column = l.pos, l.line, l.column
+		return
+	}
+	start, startLine, startColumn, end := l.pos, l.line, l.column, 0
+	tok.Type = token.INVALID
+	state, rune1, size := 0, rune(-1), 0
+	for state != -1 {
+		if l.pos >= len(l.src) {
+			rune1 = -1
+		} else {
+			rune1, size = utf8.DecodeRune(l.src[l.pos:])
+			l.pos += size
+		}
+
+		nextState := -1
+		if rune1 != -1 {
+			nextState = TransTab[state](rune1)
+		}
+		state = nextState
+
+		if state != -1 {
+
+			switch rune1 {
+			case '\n':
+				l.line++
+				l.column = 1
+			case '\r':
+				l.column = 1
+			case '\t':
+				l.column += 4
+			default:
+				l.column++
+			}
+
+			switch {
+			case ActTab[state].Accept != -1:
+				tok.Type = ActTab[state].Accept
+				end = l.pos
+			case ActTab[state].Ignore != "":
+				start, startLine, startColumn = l.pos, l.line, l.column
+				state = 0
+				if start >= len(l.src) {
+					tok.Type = token.EOF
+				}
+
+			}
+		} else {
+			if tok.Type == token.INVALID {
+				end = l.pos
+			}
+		}
+	}
+	if end > start {
+		l.pos = end
+		tok.Lit = l.src[start:end]
+	} else {
+		tok.Lit = []byte{}
+	}
+	tok.Pos.Offset, tok.Pos.Line, tok.Pos.Column = start, startLine, startColumn
+
+	return
+}
+
+func (l *Lexer) Reset() {
+	l.pos = 0
+}
+
+/*
+Lexer symbols:
+0: 'n'
+1: 'o'
+2: 'd'
+3: 'e'
+4: 'N'
+5: 'o'
+6: 'd'
+7: 'e'
+8: 'N'
+9: 'O'
+10: 'D'
+11: 'E'
+12: 'e'
+13: 'd'
+14: 'g'
+15: 'e'
+16: 'E'
+17: 'd'
+18: 'g'
+19: 'e'
+20: 'E'
+21: 'D'
+22: 'G'
+23: 'E'
+24: 'g'
+25: 'r'
+26: 'a'
+27: 'p'
+28: 'h'
+29: 'G'
+30: 'r'
+31: 'a'
+32: 'p'
+33: 'h'
+34: 'G'
+35: 'R'
+36: 'A'
+37: 'P'
+38: 'H'
+39: 'd'
+40: 'i'
+41: 'g'
+42: 'r'
+43: 'a'
+44: 'p'
+45: 'h'
+46: 'D'
+47: 'i'
+48: 'g'
+49: 'r'
+50: 'a'
+51: 'p'
+52: 'h'
+53: 'd'
+54: 'i'
+55: 'G'
+56: 'r'
+57: 'a'
+58: 'p'
+59: 'h'
+60: 'D'
+61: 'i'
+62: 'G'
+63: 'r'
+64: 'a'
+65: 'p'
+66: 'h'
+67: 'D'
+68: 'I'
+69: 'G'
+70: 'R'
+71: 'A'
+72: 'P'
+73: 'H'
+74: 's'
+75: 'u'
+76: 'b'
+77: 'g'
+78: 'r'
+79: 'a'
+80: 'p'
+81: 'h'
+82: 'S'
+83: 'u'
+84: 'b'
+85: 'g'
+86: 'r'
+87: 'a'
+88: 'p'
+89: 'h'
+90: 's'
+91: 'u'
+92: 'b'
+93: 'G'
+94: 'r'
+95: 'a'
+96: 'p'
+97: 'h'
+98: 'S'
+99: 'u'
+100: 'b'
+101: 'G'
+102: 'r'
+103: 'a'
+104: 'p'
+105: 'h'
+106: 'S'
+107: 'U'
+108: 'B'
+109: 'G'
+110: 'R'
+111: 'A'
+112: 'P'
+113: 'H'
+114: 's'
+115: 't'
+116: 'r'
+117: 'i'
+118: 'c'
+119: 't'
+120: 'S'
+121: 't'
+122: 'r'
+123: 'i'
+124: 'c'
+125: 't'
+126: 'S'
+127: 'T'
+128: 'R'
+129: 'I'
+130: 'C'
+131: 'T'
+132: '{'
+133: '}'
+134: ';'
+135: '-'
+136: '-'
+137: '-'
+138: '>'
+139: '['
+140: ']'
+141: ','
+142: '='
+143: ':'
+144: '_'
+145: '-'
+146: '.'
+147: '-'
+148: '.'
+149: '\'
+150: '"'
+151: '\'
+152: '"'
+153: '"'
+154: '='
+155: '<'
+156: '>'
+157: '<'
+158: '>'
+159: '/'
+160: '/'
+161: '\n'
+162: '#'
+163: '\n'
+164: '/'
+165: '*'
+166: '*'
+167: '*'
+168: '/'
+169: ' '
+170: '\t'
+171: '\r'
+172: '\n'
+173: \u0001-'!'
+174: '#'-'['
+175: ']'-\u007f
+176: 'a'-'z'
+177: 'A'-'Z'
+178: '0'-'9'
+179: \u0080-\ufffc
+180: \ufffe-\U0010ffff
+181: \u0001-';'
+182: '?'-\u00ff
+183: .
+*/
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/lexer/lexer_test.go b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/lexer/lexer_test.go
new file mode 100644
index 00000000..f90964fc
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/lexer/lexer_test.go
@@ -0,0 +1,54 @@
+// This file is dual licensed under CC0 and The gonum license.
+//
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Copyright ©2017 Robin Eklind.
+// This file is made available under a Creative Commons CC0 1.0
+// Universal Public Domain Dedication.
+
+package lexer_test
+
+import (
+	"bytes"
+	"io/ioutil"
+	"testing"
+
+	"gonum.org/v1/gonum/graph/formats/dot"
+)
+
+func TestParseFile(t *testing.T) {
+	golden := []struct {
+		in  string
+		out string
+	}{
+		{
+			in:  "testdata/tokens.dot",
+			out: "testdata/tokens.golden",
+		},
+	}
+	for _, g := range golden {
+		file, err := dot.ParseFile(g.in)
+		if err != nil {
+			t.Errorf("%q: unable to parse file; %v", g.in, err)
+			continue
+		}
+		// If no output path is specified, the input is already golden.
+		out := g.in
+		if len(g.out) > 0 {
+			out = g.out
+		}
+		buf, err := ioutil.ReadFile(out)
+		if err != nil {
+			t.Errorf("%q: unable to read file; %v", g.in, err)
+			continue
+		}
+		got := file.String()
+		// Remove trailing newline.
+		want := string(bytes.TrimSpace(buf))
+		if got != want {
+			t.Errorf("%q: graph mismatch; expected %q, got %q", g.in, want, got)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/lexer/testdata/tokens.dot b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/lexer/testdata/tokens.dot
new file mode 100644
index 00000000..3a161951
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/lexer/testdata/tokens.dot
@@ -0,0 +1,39 @@
+# C preprocessing directives act as comments.
+/* block comment */
+// keywords are case-insensitive.
+graph {
+	node []
+	Node []
+	NODE []
+	edge []
+	Edge []
+	EDGE []
+	subgraph {}
+	subGraph {}
+	Subgraph {}
+	SubGraph {}
+	SUBGRAPH S {}
+	A; B [style=filled, fillcolor=red]
+	C:nw -- D:se
+	"foo"
+	.10
+	-20
+	3.14
+	F [label=<<div>foo</div>>]
+	_foo
+	a10
+}
+Graph {
+}
+GRAPH {
+}
+digraph {
+}
+Digraph {
+}
+diGraph {
+}
+DiGraph {
+}
+DIGRAPH {
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/lexer/testdata/tokens.golden b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/lexer/testdata/tokens.golden
new file mode 100644
index 00000000..f64bdefc
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/lexer/testdata/tokens.golden
@@ -0,0 +1,37 @@
+graph {
+	node []
+	node []
+	node []
+	edge []
+	edge []
+	edge []
+	{}
+	{}
+	{}
+	{}
+	subgraph S {}
+	A
+	B [style=filled fillcolor=red]
+	C:nw -- D:se
+	"foo"
+	.10
+	-20
+	3.14
+	F [label=<<div>foo</div>>]
+	_foo
+	a10
+}
+graph {
+}
+graph {
+}
+digraph {
+}
+digraph {
+}
+digraph {
+}
+digraph {
+}
+digraph {
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/lexer/transitiontable.go b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/lexer/transitiontable.go
new file mode 100644
index 00000000..8f8f8393
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/lexer/transitiontable.go
@@ -0,0 +1,2741 @@
+// Code generated by gocc; DO NOT EDIT.
+
+// This file is dual licensed under CC0 and The gonum license.
+//
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Copyright ©2017 Robin Eklind.
+// This file is made available under a Creative Commons CC0 1.0
+// Universal Public Domain Dedication.
+
+package lexer
+
+/*
+Let s be the current state
+Let r be the current input rune
+transitionTable[s](r) returns the next state.
+*/
+type TransitionTable [NumStates]func(rune) int
+
+var TransTab = TransitionTable{
+	// S0
+	func(r rune) int {
+		switch {
+		case r == 9: // ['\t','\t']
+			return 1
+		case r == 10: // ['\n','\n']
+			return 1
+		case r == 13: // ['\r','\r']
+			return 1
+		case r == 32: // [' ',' ']
+			return 1
+		case r == 34: // ['"','"']
+			return 2
+		case r == 35: // ['#','#']
+			return 3
+		case r == 44: // [',',',']
+			return 4
+		case r == 45: // ['-','-']
+			return 5
+		case r == 46: // ['.','.']
+			return 6
+		case r == 47: // ['/','/']
+			return 7
+		case 48 <= r && r <= 57: // ['0','9']
+			return 8
+		case r == 58: // [':',':']
+			return 9
+		case r == 59: // [';',';']
+			return 10
+		case r == 60: // ['<','<']
+			return 11
+		case r == 61: // ['=','=']
+			return 12
+		case 65 <= r && r <= 67: // ['A','C']
+			return 13
+		case r == 68: // ['D','D']
+			return 14
+		case r == 69: // ['E','E']
+			return 15
+		case r == 70: // ['F','F']
+			return 13
+		case r == 71: // ['G','G']
+			return 16
+		case 72 <= r && r <= 77: // ['H','M']
+			return 13
+		case r == 78: // ['N','N']
+			return 17
+		case 79 <= r && r <= 82: // ['O','R']
+			return 13
+		case r == 83: // ['S','S']
+			return 18
+		case 84 <= r && r <= 90: // ['T','Z']
+			return 13
+		case r == 91: // ['[','[']
+			return 19
+		case r == 93: // [']',']']
+			return 20
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 99: // ['a','c']
+			return 13
+		case r == 100: // ['d','d']
+			return 22
+		case r == 101: // ['e','e']
+			return 23
+		case r == 102: // ['f','f']
+			return 13
+		case r == 103: // ['g','g']
+			return 24
+		case 104 <= r && r <= 109: // ['h','m']
+			return 13
+		case r == 110: // ['n','n']
+			return 25
+		case 111 <= r && r <= 114: // ['o','r']
+			return 13
+		case r == 115: // ['s','s']
+			return 26
+		case 116 <= r && r <= 122: // ['t','z']
+			return 13
+		case r == 123: // ['{','{']
+			return 27
+		case r == 125: // ['}','}']
+			return 28
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S1
+	func(r rune) int {
+		switch {
+		}
+		return NoState
+	},
+	// S2
+	func(r rune) int {
+		switch {
+		case 1 <= r && r <= 33: // [\u0001,'!']
+			return 30
+		case r == 34: // ['"','"']
+			return 31
+		case 35 <= r && r <= 91: // ['#','[']
+			return 30
+		case r == 92: // ['\','\']
+			return 32
+		case 93 <= r && r <= 127: // [']',\u007f]
+			return 30
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 33
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 33
+		}
+		return NoState
+	},
+	// S3
+	func(r rune) int {
+		switch {
+		case r == 10: // ['\n','\n']
+			return 34
+		default:
+			return 3
+		}
+	},
+	// S4
+	func(r rune) int {
+		switch {
+		}
+		return NoState
+	},
+	// S5
+	func(r rune) int {
+		switch {
+		case r == 45: // ['-','-']
+			return 35
+		case r == 46: // ['.','.']
+			return 6
+		case 48 <= r && r <= 57: // ['0','9']
+			return 8
+		case r == 62: // ['>','>']
+			return 36
+		}
+		return NoState
+	},
+	// S6
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 37
+		}
+		return NoState
+	},
+	// S7
+	func(r rune) int {
+		switch {
+		case r == 42: // ['*','*']
+			return 38
+		case r == 47: // ['/','/']
+			return 39
+		}
+		return NoState
+	},
+	// S8
+	func(r rune) int {
+		switch {
+		case r == 46: // ['.','.']
+			return 40
+		case 48 <= r && r <= 57: // ['0','9']
+			return 8
+		}
+		return NoState
+	},
+	// S9
+	func(r rune) int {
+		switch {
+		}
+		return NoState
+	},
+	// S10
+	func(r rune) int {
+		switch {
+		}
+		return NoState
+	},
+	// S11
+	func(r rune) int {
+		switch {
+		case 1 <= r && r <= 59: // [\u0001,';']
+			return 41
+		case r == 60: // ['<','<']
+			return 42
+		case r == 61: // ['=','=']
+			return 41
+		case r == 62: // ['>','>']
+			return 43
+		case 63 <= r && r <= 255: // ['?',\u00ff]
+			return 41
+		}
+		return NoState
+	},
+	// S12
+	func(r rune) int {
+		switch {
+		}
+		return NoState
+	},
+	// S13
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S14
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 72: // ['A','H']
+			return 13
+		case r == 73: // ['I','I']
+			return 45
+		case 74 <= r && r <= 90: // ['J','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 104: // ['a','h']
+			return 13
+		case r == 105: // ['i','i']
+			return 46
+		case 106 <= r && r <= 122: // ['j','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S15
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 67: // ['A','C']
+			return 13
+		case r == 68: // ['D','D']
+			return 47
+		case 69 <= r && r <= 90: // ['E','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 99: // ['a','c']
+			return 13
+		case r == 100: // ['d','d']
+			return 48
+		case 101 <= r && r <= 122: // ['e','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S16
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 81: // ['A','Q']
+			return 13
+		case r == 82: // ['R','R']
+			return 49
+		case 83 <= r && r <= 90: // ['S','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 113: // ['a','q']
+			return 13
+		case r == 114: // ['r','r']
+			return 50
+		case 115 <= r && r <= 122: // ['s','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S17
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 78: // ['A','N']
+			return 13
+		case r == 79: // ['O','O']
+			return 51
+		case 80 <= r && r <= 90: // ['P','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 110: // ['a','n']
+			return 13
+		case r == 111: // ['o','o']
+			return 52
+		case 112 <= r && r <= 122: // ['p','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S18
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 83: // ['A','S']
+			return 13
+		case r == 84: // ['T','T']
+			return 53
+		case r == 85: // ['U','U']
+			return 54
+		case 86 <= r && r <= 90: // ['V','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 115: // ['a','s']
+			return 13
+		case r == 116: // ['t','t']
+			return 55
+		case r == 117: // ['u','u']
+			return 56
+		case 118 <= r && r <= 122: // ['v','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S19
+	func(r rune) int {
+		switch {
+		}
+		return NoState
+	},
+	// S20
+	func(r rune) int {
+		switch {
+		}
+		return NoState
+	},
+	// S21
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S22
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 104: // ['a','h']
+			return 13
+		case r == 105: // ['i','i']
+			return 57
+		case 106 <= r && r <= 122: // ['j','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S23
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 99: // ['a','c']
+			return 13
+		case r == 100: // ['d','d']
+			return 58
+		case 101 <= r && r <= 122: // ['e','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S24
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 113: // ['a','q']
+			return 13
+		case r == 114: // ['r','r']
+			return 59
+		case 115 <= r && r <= 122: // ['s','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S25
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 110: // ['a','n']
+			return 13
+		case r == 111: // ['o','o']
+			return 60
+		case 112 <= r && r <= 122: // ['p','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S26
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 115: // ['a','s']
+			return 13
+		case r == 116: // ['t','t']
+			return 61
+		case r == 117: // ['u','u']
+			return 62
+		case 118 <= r && r <= 122: // ['v','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S27
+	func(r rune) int {
+		switch {
+		}
+		return NoState
+	},
+	// S28
+	func(r rune) int {
+		switch {
+		}
+		return NoState
+	},
+	// S29
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S30
+	func(r rune) int {
+		switch {
+		case 1 <= r && r <= 33: // [\u0001,'!']
+			return 30
+		case r == 34: // ['"','"']
+			return 31
+		case 35 <= r && r <= 91: // ['#','[']
+			return 30
+		case r == 92: // ['\','\']
+			return 32
+		case 93 <= r && r <= 127: // [']',\u007f]
+			return 30
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 33
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 33
+		}
+		return NoState
+	},
+	// S31
+	func(r rune) int {
+		switch {
+		}
+		return NoState
+	},
+	// S32
+	func(r rune) int {
+		switch {
+		case 1 <= r && r <= 33: // [\u0001,'!']
+			return 63
+		case r == 34: // ['"','"']
+			return 64
+		case 35 <= r && r <= 91: // ['#','[']
+			return 63
+		case r == 92: // ['\','\']
+			return 64
+		case 93 <= r && r <= 127: // [']',\u007f]
+			return 63
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 65
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 65
+		}
+		return NoState
+	},
+	// S33
+	func(r rune) int {
+		switch {
+		case 1 <= r && r <= 33: // [\u0001,'!']
+			return 30
+		case r == 34: // ['"','"']
+			return 31
+		case 35 <= r && r <= 91: // ['#','[']
+			return 30
+		case r == 92: // ['\','\']
+			return 32
+		case 93 <= r && r <= 127: // [']',\u007f]
+			return 30
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 33
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 33
+		}
+		return NoState
+	},
+	// S34
+	func(r rune) int {
+		switch {
+		}
+		return NoState
+	},
+	// S35
+	func(r rune) int {
+		switch {
+		}
+		return NoState
+	},
+	// S36
+	func(r rune) int {
+		switch {
+		}
+		return NoState
+	},
+	// S37
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 37
+		}
+		return NoState
+	},
+	// S38
+	func(r rune) int {
+		switch {
+		case r == 42: // ['*','*']
+			return 66
+		default:
+			return 38
+		}
+	},
+	// S39
+	func(r rune) int {
+		switch {
+		case r == 10: // ['\n','\n']
+			return 34
+		default:
+			return 39
+		}
+	},
+	// S40
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 67
+		}
+		return NoState
+	},
+	// S41
+	func(r rune) int {
+		switch {
+		case 1 <= r && r <= 59: // [\u0001,';']
+			return 41
+		case r == 60: // ['<','<']
+			return 42
+		case r == 61: // ['=','=']
+			return 41
+		case r == 62: // ['>','>']
+			return 43
+		case 63 <= r && r <= 255: // ['?',\u00ff]
+			return 41
+		}
+		return NoState
+	},
+	// S42
+	func(r rune) int {
+		switch {
+		case 1 <= r && r <= 59: // [\u0001,';']
+			return 68
+		case r == 61: // ['=','=']
+			return 68
+		case 63 <= r && r <= 255: // ['?',\u00ff]
+			return 68
+		}
+		return NoState
+	},
+	// S43
+	func(r rune) int {
+		switch {
+		}
+		return NoState
+	},
+	// S44
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S45
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 70: // ['A','F']
+			return 13
+		case r == 71: // ['G','G']
+			return 69
+		case 72 <= r && r <= 90: // ['H','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S46
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 70: // ['A','F']
+			return 13
+		case r == 71: // ['G','G']
+			return 70
+		case 72 <= r && r <= 90: // ['H','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 102: // ['a','f']
+			return 13
+		case r == 103: // ['g','g']
+			return 71
+		case 104 <= r && r <= 122: // ['h','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S47
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 70: // ['A','F']
+			return 13
+		case r == 71: // ['G','G']
+			return 72
+		case 72 <= r && r <= 90: // ['H','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S48
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 102: // ['a','f']
+			return 13
+		case r == 103: // ['g','g']
+			return 73
+		case 104 <= r && r <= 122: // ['h','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S49
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case r == 65: // ['A','A']
+			return 74
+		case 66 <= r && r <= 90: // ['B','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S50
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case r == 97: // ['a','a']
+			return 75
+		case 98 <= r && r <= 122: // ['b','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S51
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 67: // ['A','C']
+			return 13
+		case r == 68: // ['D','D']
+			return 76
+		case 69 <= r && r <= 90: // ['E','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S52
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 99: // ['a','c']
+			return 13
+		case r == 100: // ['d','d']
+			return 77
+		case 101 <= r && r <= 122: // ['e','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S53
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 81: // ['A','Q']
+			return 13
+		case r == 82: // ['R','R']
+			return 78
+		case 83 <= r && r <= 90: // ['S','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S54
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case r == 65: // ['A','A']
+			return 13
+		case r == 66: // ['B','B']
+			return 79
+		case 67 <= r && r <= 90: // ['C','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S55
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 113: // ['a','q']
+			return 13
+		case r == 114: // ['r','r']
+			return 80
+		case 115 <= r && r <= 122: // ['s','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S56
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case r == 97: // ['a','a']
+			return 13
+		case r == 98: // ['b','b']
+			return 81
+		case 99 <= r && r <= 122: // ['c','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S57
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 70: // ['A','F']
+			return 13
+		case r == 71: // ['G','G']
+			return 82
+		case 72 <= r && r <= 90: // ['H','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 102: // ['a','f']
+			return 13
+		case r == 103: // ['g','g']
+			return 83
+		case 104 <= r && r <= 122: // ['h','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S58
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 102: // ['a','f']
+			return 13
+		case r == 103: // ['g','g']
+			return 84
+		case 104 <= r && r <= 122: // ['h','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S59
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case r == 97: // ['a','a']
+			return 85
+		case 98 <= r && r <= 122: // ['b','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S60
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 99: // ['a','c']
+			return 13
+		case r == 100: // ['d','d']
+			return 86
+		case 101 <= r && r <= 122: // ['e','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S61
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 113: // ['a','q']
+			return 13
+		case r == 114: // ['r','r']
+			return 87
+		case 115 <= r && r <= 122: // ['s','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S62
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case r == 97: // ['a','a']
+			return 13
+		case r == 98: // ['b','b']
+			return 88
+		case 99 <= r && r <= 122: // ['c','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S63
+	func(r rune) int {
+		switch {
+		case 1 <= r && r <= 33: // [\u0001,'!']
+			return 30
+		case r == 34: // ['"','"']
+			return 31
+		case 35 <= r && r <= 91: // ['#','[']
+			return 30
+		case r == 92: // ['\','\']
+			return 32
+		case 93 <= r && r <= 127: // [']',\u007f]
+			return 30
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 33
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 33
+		}
+		return NoState
+	},
+	// S64
+	func(r rune) int {
+		switch {
+		case 1 <= r && r <= 33: // [\u0001,'!']
+			return 30
+		case r == 34: // ['"','"']
+			return 31
+		case 35 <= r && r <= 91: // ['#','[']
+			return 30
+		case r == 92: // ['\','\']
+			return 32
+		case 93 <= r && r <= 127: // [']',\u007f]
+			return 30
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 33
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 33
+		}
+		return NoState
+	},
+	// S65
+	func(r rune) int {
+		switch {
+		case 1 <= r && r <= 33: // [\u0001,'!']
+			return 30
+		case r == 34: // ['"','"']
+			return 31
+		case 35 <= r && r <= 91: // ['#','[']
+			return 30
+		case r == 92: // ['\','\']
+			return 32
+		case 93 <= r && r <= 127: // [']',\u007f]
+			return 30
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 33
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 33
+		}
+		return NoState
+	},
+	// S66
+	func(r rune) int {
+		switch {
+		case r == 42: // ['*','*']
+			return 66
+		case r == 47: // ['/','/']
+			return 89
+		default:
+			return 38
+		}
+	},
+	// S67
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 67
+		}
+		return NoState
+	},
+	// S68
+	func(r rune) int {
+		switch {
+		case 1 <= r && r <= 59: // [\u0001,';']
+			return 68
+		case r == 61: // ['=','=']
+			return 68
+		case r == 62: // ['>','>']
+			return 90
+		case 63 <= r && r <= 255: // ['?',\u00ff]
+			return 68
+		}
+		return NoState
+	},
+	// S69
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 81: // ['A','Q']
+			return 13
+		case r == 82: // ['R','R']
+			return 91
+		case 83 <= r && r <= 90: // ['S','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S70
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 113: // ['a','q']
+			return 13
+		case r == 114: // ['r','r']
+			return 92
+		case 115 <= r && r <= 122: // ['s','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S71
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 113: // ['a','q']
+			return 13
+		case r == 114: // ['r','r']
+			return 93
+		case 115 <= r && r <= 122: // ['s','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S72
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 68: // ['A','D']
+			return 13
+		case r == 69: // ['E','E']
+			return 94
+		case 70 <= r && r <= 90: // ['F','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S73
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 100: // ['a','d']
+			return 13
+		case r == 101: // ['e','e']
+			return 94
+		case 102 <= r && r <= 122: // ['f','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S74
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 79: // ['A','O']
+			return 13
+		case r == 80: // ['P','P']
+			return 95
+		case 81 <= r && r <= 90: // ['Q','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S75
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 111: // ['a','o']
+			return 13
+		case r == 112: // ['p','p']
+			return 96
+		case 113 <= r && r <= 122: // ['q','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S76
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 68: // ['A','D']
+			return 13
+		case r == 69: // ['E','E']
+			return 97
+		case 70 <= r && r <= 90: // ['F','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S77
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 100: // ['a','d']
+			return 13
+		case r == 101: // ['e','e']
+			return 97
+		case 102 <= r && r <= 122: // ['f','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S78
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 72: // ['A','H']
+			return 13
+		case r == 73: // ['I','I']
+			return 98
+		case 74 <= r && r <= 90: // ['J','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S79
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 70: // ['A','F']
+			return 13
+		case r == 71: // ['G','G']
+			return 99
+		case 72 <= r && r <= 90: // ['H','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S80
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 104: // ['a','h']
+			return 13
+		case r == 105: // ['i','i']
+			return 100
+		case 106 <= r && r <= 122: // ['j','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S81
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 70: // ['A','F']
+			return 13
+		case r == 71: // ['G','G']
+			return 101
+		case 72 <= r && r <= 90: // ['H','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 102: // ['a','f']
+			return 13
+		case r == 103: // ['g','g']
+			return 102
+		case 104 <= r && r <= 122: // ['h','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S82
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 113: // ['a','q']
+			return 13
+		case r == 114: // ['r','r']
+			return 103
+		case 115 <= r && r <= 122: // ['s','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S83
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 113: // ['a','q']
+			return 13
+		case r == 114: // ['r','r']
+			return 104
+		case 115 <= r && r <= 122: // ['s','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S84
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 100: // ['a','d']
+			return 13
+		case r == 101: // ['e','e']
+			return 94
+		case 102 <= r && r <= 122: // ['f','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S85
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 111: // ['a','o']
+			return 13
+		case r == 112: // ['p','p']
+			return 105
+		case 113 <= r && r <= 122: // ['q','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S86
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 100: // ['a','d']
+			return 13
+		case r == 101: // ['e','e']
+			return 97
+		case 102 <= r && r <= 122: // ['f','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S87
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 104: // ['a','h']
+			return 13
+		case r == 105: // ['i','i']
+			return 106
+		case 106 <= r && r <= 122: // ['j','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S88
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 70: // ['A','F']
+			return 13
+		case r == 71: // ['G','G']
+			return 107
+		case 72 <= r && r <= 90: // ['H','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 102: // ['a','f']
+			return 13
+		case r == 103: // ['g','g']
+			return 108
+		case 104 <= r && r <= 122: // ['h','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S89
+	func(r rune) int {
+		switch {
+		}
+		return NoState
+	},
+	// S90
+	func(r rune) int {
+		switch {
+		case 1 <= r && r <= 59: // [\u0001,';']
+			return 41
+		case r == 60: // ['<','<']
+			return 42
+		case r == 61: // ['=','=']
+			return 41
+		case r == 62: // ['>','>']
+			return 43
+		case 63 <= r && r <= 255: // ['?',\u00ff]
+			return 41
+		}
+		return NoState
+	},
+	// S91
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case r == 65: // ['A','A']
+			return 109
+		case 66 <= r && r <= 90: // ['B','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S92
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case r == 97: // ['a','a']
+			return 110
+		case 98 <= r && r <= 122: // ['b','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S93
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case r == 97: // ['a','a']
+			return 111
+		case 98 <= r && r <= 122: // ['b','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S94
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S95
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 71: // ['A','G']
+			return 13
+		case r == 72: // ['H','H']
+			return 112
+		case 73 <= r && r <= 90: // ['I','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S96
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 103: // ['a','g']
+			return 13
+		case r == 104: // ['h','h']
+			return 112
+		case 105 <= r && r <= 122: // ['i','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S97
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S98
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 66: // ['A','B']
+			return 13
+		case r == 67: // ['C','C']
+			return 113
+		case 68 <= r && r <= 90: // ['D','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S99
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 81: // ['A','Q']
+			return 13
+		case r == 82: // ['R','R']
+			return 114
+		case 83 <= r && r <= 90: // ['S','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S100
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 98: // ['a','b']
+			return 13
+		case r == 99: // ['c','c']
+			return 115
+		case 100 <= r && r <= 122: // ['d','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S101
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 113: // ['a','q']
+			return 13
+		case r == 114: // ['r','r']
+			return 116
+		case 115 <= r && r <= 122: // ['s','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S102
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 113: // ['a','q']
+			return 13
+		case r == 114: // ['r','r']
+			return 117
+		case 115 <= r && r <= 122: // ['s','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S103
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case r == 97: // ['a','a']
+			return 118
+		case 98 <= r && r <= 122: // ['b','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S104
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case r == 97: // ['a','a']
+			return 119
+		case 98 <= r && r <= 122: // ['b','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S105
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 103: // ['a','g']
+			return 13
+		case r == 104: // ['h','h']
+			return 112
+		case 105 <= r && r <= 122: // ['i','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S106
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 98: // ['a','b']
+			return 13
+		case r == 99: // ['c','c']
+			return 120
+		case 100 <= r && r <= 122: // ['d','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S107
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 113: // ['a','q']
+			return 13
+		case r == 114: // ['r','r']
+			return 121
+		case 115 <= r && r <= 122: // ['s','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S108
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 113: // ['a','q']
+			return 13
+		case r == 114: // ['r','r']
+			return 122
+		case 115 <= r && r <= 122: // ['s','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S109
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 79: // ['A','O']
+			return 13
+		case r == 80: // ['P','P']
+			return 123
+		case 81 <= r && r <= 90: // ['Q','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S110
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 111: // ['a','o']
+			return 13
+		case r == 112: // ['p','p']
+			return 124
+		case 113 <= r && r <= 122: // ['q','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S111
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 111: // ['a','o']
+			return 13
+		case r == 112: // ['p','p']
+			return 125
+		case 113 <= r && r <= 122: // ['q','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S112
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S113
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 83: // ['A','S']
+			return 13
+		case r == 84: // ['T','T']
+			return 126
+		case 85 <= r && r <= 90: // ['U','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S114
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case r == 65: // ['A','A']
+			return 127
+		case 66 <= r && r <= 90: // ['B','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S115
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 115: // ['a','s']
+			return 13
+		case r == 116: // ['t','t']
+			return 126
+		case 117 <= r && r <= 122: // ['u','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S116
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case r == 97: // ['a','a']
+			return 128
+		case 98 <= r && r <= 122: // ['b','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S117
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case r == 97: // ['a','a']
+			return 129
+		case 98 <= r && r <= 122: // ['b','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S118
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 111: // ['a','o']
+			return 13
+		case r == 112: // ['p','p']
+			return 130
+		case 113 <= r && r <= 122: // ['q','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S119
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 111: // ['a','o']
+			return 13
+		case r == 112: // ['p','p']
+			return 131
+		case 113 <= r && r <= 122: // ['q','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S120
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 115: // ['a','s']
+			return 13
+		case r == 116: // ['t','t']
+			return 126
+		case 117 <= r && r <= 122: // ['u','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S121
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case r == 97: // ['a','a']
+			return 132
+		case 98 <= r && r <= 122: // ['b','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S122
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case r == 97: // ['a','a']
+			return 133
+		case 98 <= r && r <= 122: // ['b','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S123
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 71: // ['A','G']
+			return 13
+		case r == 72: // ['H','H']
+			return 134
+		case 73 <= r && r <= 90: // ['I','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S124
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 103: // ['a','g']
+			return 13
+		case r == 104: // ['h','h']
+			return 134
+		case 105 <= r && r <= 122: // ['i','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S125
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 103: // ['a','g']
+			return 13
+		case r == 104: // ['h','h']
+			return 134
+		case 105 <= r && r <= 122: // ['i','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S126
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S127
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 79: // ['A','O']
+			return 13
+		case r == 80: // ['P','P']
+			return 135
+		case 81 <= r && r <= 90: // ['Q','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S128
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 111: // ['a','o']
+			return 13
+		case r == 112: // ['p','p']
+			return 136
+		case 113 <= r && r <= 122: // ['q','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S129
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 111: // ['a','o']
+			return 13
+		case r == 112: // ['p','p']
+			return 137
+		case 113 <= r && r <= 122: // ['q','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S130
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 103: // ['a','g']
+			return 13
+		case r == 104: // ['h','h']
+			return 134
+		case 105 <= r && r <= 122: // ['i','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S131
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 103: // ['a','g']
+			return 13
+		case r == 104: // ['h','h']
+			return 134
+		case 105 <= r && r <= 122: // ['i','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S132
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 111: // ['a','o']
+			return 13
+		case r == 112: // ['p','p']
+			return 138
+		case 113 <= r && r <= 122: // ['q','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S133
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 111: // ['a','o']
+			return 13
+		case r == 112: // ['p','p']
+			return 139
+		case 113 <= r && r <= 122: // ['q','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S134
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S135
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 71: // ['A','G']
+			return 13
+		case r == 72: // ['H','H']
+			return 140
+		case 73 <= r && r <= 90: // ['I','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S136
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 103: // ['a','g']
+			return 13
+		case r == 104: // ['h','h']
+			return 140
+		case 105 <= r && r <= 122: // ['i','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S137
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 103: // ['a','g']
+			return 13
+		case r == 104: // ['h','h']
+			return 140
+		case 105 <= r && r <= 122: // ['i','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S138
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 103: // ['a','g']
+			return 13
+		case r == 104: // ['h','h']
+			return 140
+		case 105 <= r && r <= 122: // ['i','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S139
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 103: // ['a','g']
+			return 13
+		case r == 104: // ['h','h']
+			return 140
+		case 105 <= r && r <= 122: // ['i','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+	// S140
+	func(r rune) int {
+		switch {
+		case 48 <= r && r <= 57: // ['0','9']
+			return 44
+		case 65 <= r && r <= 90: // ['A','Z']
+			return 13
+		case r == 95: // ['_','_']
+			return 21
+		case 97 <= r && r <= 122: // ['a','z']
+			return 13
+		case 128 <= r && r <= 65532: // [\u0080,\ufffc]
+			return 29
+		case 65534 <= r && r <= 1114111: // [\ufffe,\U0010ffff]
+			return 29
+		}
+		return NoState
+	},
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/parser/action.go b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/parser/action.go
new file mode 100644
index 00000000..10d7eccb
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/parser/action.go
@@ -0,0 +1,61 @@
+// Code generated by gocc; DO NOT EDIT.
+
+// This file is dual licensed under CC0 and The gonum license.
+//
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Copyright ©2017 Robin Eklind.
+// This file is made available under a Creative Commons CC0 1.0
+// Universal Public Domain Dedication.
+
+package parser
+
+import (
+	"fmt"
+)
+
+type action interface {
+	act()
+	String() string
+}
+
+type (
+	accept bool
+	shift  int // value is next state index
+	reduce int // value is production index
+)
+
+func (this accept) act() {}
+func (this shift) act()  {}
+func (this reduce) act() {}
+
+func (this accept) Equal(that action) bool {
+	if _, ok := that.(accept); ok {
+		return true
+	}
+	return false
+}
+
+func (this reduce) Equal(that action) bool {
+	that1, ok := that.(reduce)
+	if !ok {
+		return false
+	}
+	return this == that1
+}
+
+func (this shift) Equal(that action) bool {
+	that1, ok := that.(shift)
+	if !ok {
+		return false
+	}
+	return this == that1
+}
+
+func (this accept) String() string { return "accept(0)" }
+func (this shift) String() string  { return fmt.Sprintf("shift:%d", this) }
+func (this reduce) String() string {
+	return fmt.Sprintf("reduce:%d(%s)", this, productionsTable[this].String)
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/parser/actiontable.go b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/parser/actiontable.go
new file mode 100644
index 00000000..9596d120
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/parser/actiontable.go
@@ -0,0 +1,2199 @@
+// Code generated by gocc; DO NOT EDIT.
+
+// This file is dual licensed under CC0 and The gonum license.
+//
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Copyright ©2017 Robin Eklind.
+// This file is made available under a Creative Commons CC0 1.0
+// Universal Public Domain Dedication.
+
+package parser
+
+type (
+	actionTable [numStates]actionRow
+	actionRow   struct {
+		canRecover bool
+		actions    [numSymbols]action
+	}
+)
+
+var actionTab = actionTable{
+	actionRow{ // S0
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,       /* INVALID */
+			nil,       /* $ */
+			nil,       /* { */
+			nil,       /* } */
+			nil,       /* empty */
+			shift(4),  /* strict */
+			reduce(4), /* graphx, reduce: OptStrict */
+			reduce(4), /* digraph, reduce: OptStrict */
+			nil,       /* ; */
+			nil,       /* -- */
+			nil,       /* -> */
+			nil,       /* node */
+			nil,       /* edge */
+			nil,       /* [ */
+			nil,       /* ] */
+			nil,       /* , */
+			nil,       /* = */
+			nil,       /* subgraph */
+			nil,       /* : */
+			nil,       /* id */
+		},
+	},
+	actionRow{ // S1
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,          /* INVALID */
+			accept(true), /* $ */
+			nil,          /* { */
+			nil,          /* } */
+			nil,          /* empty */
+			shift(4),     /* strict */
+			reduce(4),    /* graphx, reduce: OptStrict */
+			reduce(4),    /* digraph, reduce: OptStrict */
+			nil,          /* ; */
+			nil,          /* -- */
+			nil,          /* -> */
+			nil,          /* node */
+			nil,          /* edge */
+			nil,          /* [ */
+			nil,          /* ] */
+			nil,          /* , */
+			nil,          /* = */
+			nil,          /* subgraph */
+			nil,          /* : */
+			nil,          /* id */
+		},
+	},
+	actionRow{ // S2
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,       /* INVALID */
+			reduce(1), /* $, reduce: File */
+			nil,       /* { */
+			nil,       /* } */
+			nil,       /* empty */
+			reduce(1), /* strict, reduce: File */
+			reduce(1), /* graphx, reduce: File */
+			reduce(1), /* digraph, reduce: File */
+			nil,       /* ; */
+			nil,       /* -- */
+			nil,       /* -> */
+			nil,       /* node */
+			nil,       /* edge */
+			nil,       /* [ */
+			nil,       /* ] */
+			nil,       /* , */
+			nil,       /* = */
+			nil,       /* subgraph */
+			nil,       /* : */
+			nil,       /* id */
+		},
+	},
+	actionRow{ // S3
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,      /* INVALID */
+			nil,      /* $ */
+			nil,      /* { */
+			nil,      /* } */
+			nil,      /* empty */
+			nil,      /* strict */
+			shift(7), /* graphx */
+			shift(8), /* digraph */
+			nil,      /* ; */
+			nil,      /* -- */
+			nil,      /* -> */
+			nil,      /* node */
+			nil,      /* edge */
+			nil,      /* [ */
+			nil,      /* ] */
+			nil,      /* , */
+			nil,      /* = */
+			nil,      /* subgraph */
+			nil,      /* : */
+			nil,      /* id */
+		},
+	},
+	actionRow{ // S4
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,       /* INVALID */
+			nil,       /* $ */
+			nil,       /* { */
+			nil,       /* } */
+			nil,       /* empty */
+			nil,       /* strict */
+			reduce(5), /* graphx, reduce: OptStrict */
+			reduce(5), /* digraph, reduce: OptStrict */
+			nil,       /* ; */
+			nil,       /* -- */
+			nil,       /* -> */
+			nil,       /* node */
+			nil,       /* edge */
+			nil,       /* [ */
+			nil,       /* ] */
+			nil,       /* , */
+			nil,       /* = */
+			nil,       /* subgraph */
+			nil,       /* : */
+			nil,       /* id */
+		},
+	},
+	actionRow{ // S5
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,       /* INVALID */
+			reduce(2), /* $, reduce: File */
+			nil,       /* { */
+			nil,       /* } */
+			nil,       /* empty */
+			reduce(2), /* strict, reduce: File */
+			reduce(2), /* graphx, reduce: File */
+			reduce(2), /* digraph, reduce: File */
+			nil,       /* ; */
+			nil,       /* -- */
+			nil,       /* -> */
+			nil,       /* node */
+			nil,       /* edge */
+			nil,       /* [ */
+			nil,       /* ] */
+			nil,       /* , */
+			nil,       /* = */
+			nil,       /* subgraph */
+			nil,       /* : */
+			nil,       /* id */
+		},
+	},
+	actionRow{ // S6
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(53), /* {, reduce: OptID */
+			nil,        /* } */
+			nil,        /* empty */
+			nil,        /* strict */
+			nil,        /* graphx */
+			nil,        /* digraph */
+			nil,        /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			nil,        /* node */
+			nil,        /* edge */
+			nil,        /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			nil,        /* subgraph */
+			nil,        /* : */
+			shift(11),  /* id */
+		},
+	},
+	actionRow{ // S7
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,       /* INVALID */
+			nil,       /* $ */
+			reduce(6), /* {, reduce: DirectedGraph */
+			nil,       /* } */
+			nil,       /* empty */
+			nil,       /* strict */
+			nil,       /* graphx */
+			nil,       /* digraph */
+			nil,       /* ; */
+			nil,       /* -- */
+			nil,       /* -> */
+			nil,       /* node */
+			nil,       /* edge */
+			nil,       /* [ */
+			nil,       /* ] */
+			nil,       /* , */
+			nil,       /* = */
+			nil,       /* subgraph */
+			nil,       /* : */
+			reduce(6), /* id, reduce: DirectedGraph */
+		},
+	},
+	actionRow{ // S8
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,       /* INVALID */
+			nil,       /* $ */
+			reduce(7), /* {, reduce: DirectedGraph */
+			nil,       /* } */
+			nil,       /* empty */
+			nil,       /* strict */
+			nil,       /* graphx */
+			nil,       /* digraph */
+			nil,       /* ; */
+			nil,       /* -- */
+			nil,       /* -> */
+			nil,       /* node */
+			nil,       /* edge */
+			nil,       /* [ */
+			nil,       /* ] */
+			nil,       /* , */
+			nil,       /* = */
+			nil,       /* subgraph */
+			nil,       /* : */
+			reduce(7), /* id, reduce: DirectedGraph */
+		},
+	},
+	actionRow{ // S9
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,       /* INVALID */
+			nil,       /* $ */
+			shift(12), /* { */
+			nil,       /* } */
+			nil,       /* empty */
+			nil,       /* strict */
+			nil,       /* graphx */
+			nil,       /* digraph */
+			nil,       /* ; */
+			nil,       /* -- */
+			nil,       /* -> */
+			nil,       /* node */
+			nil,       /* edge */
+			nil,       /* [ */
+			nil,       /* ] */
+			nil,       /* , */
+			nil,       /* = */
+			nil,       /* subgraph */
+			nil,       /* : */
+			nil,       /* id */
+		},
+	},
+	actionRow{ // S10
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(54), /* {, reduce: OptID */
+			nil,        /* } */
+			nil,        /* empty */
+			nil,        /* strict */
+			nil,        /* graphx */
+			nil,        /* digraph */
+			nil,        /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			nil,        /* node */
+			nil,        /* edge */
+			nil,        /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			nil,        /* subgraph */
+			nil,        /* : */
+			nil,        /* id */
+		},
+	},
+	actionRow{ // S11
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(52), /* {, reduce: ID */
+			nil,        /* } */
+			nil,        /* empty */
+			nil,        /* strict */
+			nil,        /* graphx */
+			nil,        /* digraph */
+			nil,        /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			nil,        /* node */
+			nil,        /* edge */
+			nil,        /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			nil,        /* subgraph */
+			nil,        /* : */
+			nil,        /* id */
+		},
+	},
+	actionRow{ // S12
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(43), /* {, reduce: OptSubgraphID */
+			reduce(10), /* }, reduce: OptStmtList */
+			nil,        /* empty */
+			nil,        /* strict */
+			shift(14),  /* graphx */
+			nil,        /* digraph */
+			nil,        /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			shift(25),  /* node */
+			shift(26),  /* edge */
+			nil,        /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			shift(29),  /* subgraph */
+			nil,        /* : */
+			shift(30),  /* id */
+		},
+	},
+	actionRow{ // S13
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,       /* INVALID */
+			nil,       /* $ */
+			nil,       /* { */
+			shift(31), /* } */
+			nil,       /* empty */
+			nil,       /* strict */
+			nil,       /* graphx */
+			nil,       /* digraph */
+			nil,       /* ; */
+			nil,       /* -- */
+			nil,       /* -> */
+			nil,       /* node */
+			nil,       /* edge */
+			nil,       /* [ */
+			nil,       /* ] */
+			nil,       /* , */
+			nil,       /* = */
+			nil,       /* subgraph */
+			nil,       /* : */
+			nil,       /* id */
+		},
+	},
+	actionRow{ // S14
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			nil,        /* { */
+			nil,        /* } */
+			nil,        /* empty */
+			nil,        /* strict */
+			nil,        /* graphx */
+			nil,        /* digraph */
+			nil,        /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			nil,        /* node */
+			nil,        /* edge */
+			reduce(27), /* [, reduce: Component */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			nil,        /* subgraph */
+			nil,        /* : */
+			nil,        /* id */
+		},
+	},
+	actionRow{ // S15
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(43), /* {, reduce: OptSubgraphID */
+			reduce(11), /* }, reduce: OptStmtList */
+			nil,        /* empty */
+			nil,        /* strict */
+			shift(14),  /* graphx */
+			nil,        /* digraph */
+			nil,        /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			shift(25),  /* node */
+			shift(26),  /* edge */
+			nil,        /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			shift(29),  /* subgraph */
+			nil,        /* : */
+			shift(30),  /* id */
+		},
+	},
+	actionRow{ // S16
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(17), /* {, reduce: OptSemi */
+			reduce(17), /* }, reduce: OptSemi */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(17), /* graphx, reduce: OptSemi */
+			nil,        /* digraph */
+			shift(34),  /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			reduce(17), /* node, reduce: OptSemi */
+			reduce(17), /* edge, reduce: OptSemi */
+			nil,        /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(17), /* subgraph, reduce: OptSemi */
+			nil,        /* : */
+			reduce(17), /* id, reduce: OptSemi */
+		},
+	},
+	actionRow{ // S17
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(12), /* {, reduce: Stmt */
+			reduce(12), /* }, reduce: Stmt */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(12), /* graphx, reduce: Stmt */
+			nil,        /* digraph */
+			reduce(12), /* ;, reduce: Stmt */
+			nil,        /* -- */
+			nil,        /* -> */
+			reduce(12), /* node, reduce: Stmt */
+			reduce(12), /* edge, reduce: Stmt */
+			nil,        /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(12), /* subgraph, reduce: Stmt */
+			nil,        /* : */
+			reduce(12), /* id, reduce: Stmt */
+		},
+	},
+	actionRow{ // S18
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(13), /* {, reduce: Stmt */
+			reduce(13), /* }, reduce: Stmt */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(13), /* graphx, reduce: Stmt */
+			nil,        /* digraph */
+			reduce(13), /* ;, reduce: Stmt */
+			nil,        /* -- */
+			nil,        /* -> */
+			reduce(13), /* node, reduce: Stmt */
+			reduce(13), /* edge, reduce: Stmt */
+			nil,        /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(13), /* subgraph, reduce: Stmt */
+			nil,        /* : */
+			reduce(13), /* id, reduce: Stmt */
+		},
+	},
+	actionRow{ // S19
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(14), /* {, reduce: Stmt */
+			reduce(14), /* }, reduce: Stmt */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(14), /* graphx, reduce: Stmt */
+			nil,        /* digraph */
+			reduce(14), /* ;, reduce: Stmt */
+			nil,        /* -- */
+			nil,        /* -> */
+			reduce(14), /* node, reduce: Stmt */
+			reduce(14), /* edge, reduce: Stmt */
+			nil,        /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(14), /* subgraph, reduce: Stmt */
+			nil,        /* : */
+			reduce(14), /* id, reduce: Stmt */
+		},
+	},
+	actionRow{ // S20
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(15), /* {, reduce: Stmt */
+			reduce(15), /* }, reduce: Stmt */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(15), /* graphx, reduce: Stmt */
+			nil,        /* digraph */
+			reduce(15), /* ;, reduce: Stmt */
+			nil,        /* -- */
+			nil,        /* -> */
+			reduce(15), /* node, reduce: Stmt */
+			reduce(15), /* edge, reduce: Stmt */
+			nil,        /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(15), /* subgraph, reduce: Stmt */
+			nil,        /* : */
+			reduce(15), /* id, reduce: Stmt */
+		},
+	},
+	actionRow{ // S21
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(16), /* {, reduce: Stmt */
+			reduce(16), /* }, reduce: Stmt */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(16), /* graphx, reduce: Stmt */
+			nil,        /* digraph */
+			reduce(16), /* ;, reduce: Stmt */
+			reduce(46), /* --, reduce: Vertex */
+			reduce(46), /* ->, reduce: Vertex */
+			reduce(16), /* node, reduce: Stmt */
+			reduce(16), /* edge, reduce: Stmt */
+			nil,        /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(16), /* subgraph, reduce: Stmt */
+			nil,        /* : */
+			reduce(16), /* id, reduce: Stmt */
+		},
+	},
+	actionRow{ // S22
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(32), /* {, reduce: OptAttrList */
+			reduce(32), /* }, reduce: OptAttrList */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(32), /* graphx, reduce: OptAttrList */
+			nil,        /* digraph */
+			reduce(32), /* ;, reduce: OptAttrList */
+			reduce(45), /* --, reduce: Vertex */
+			reduce(45), /* ->, reduce: Vertex */
+			reduce(32), /* node, reduce: OptAttrList */
+			reduce(32), /* edge, reduce: OptAttrList */
+			shift(37),  /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(32), /* subgraph, reduce: OptAttrList */
+			nil,        /* : */
+			reduce(32), /* id, reduce: OptAttrList */
+		},
+	},
+	actionRow{ // S23
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,       /* INVALID */
+			nil,       /* $ */
+			nil,       /* { */
+			nil,       /* } */
+			nil,       /* empty */
+			nil,       /* strict */
+			nil,       /* graphx */
+			nil,       /* digraph */
+			nil,       /* ; */
+			shift(40), /* -- */
+			shift(41), /* -> */
+			nil,       /* node */
+			nil,       /* edge */
+			nil,       /* [ */
+			nil,       /* ] */
+			nil,       /* , */
+			nil,       /* = */
+			nil,       /* subgraph */
+			nil,       /* : */
+			nil,       /* id */
+		},
+	},
+	actionRow{ // S24
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,       /* INVALID */
+			nil,       /* $ */
+			nil,       /* { */
+			nil,       /* } */
+			nil,       /* empty */
+			nil,       /* strict */
+			nil,       /* graphx */
+			nil,       /* digraph */
+			nil,       /* ; */
+			nil,       /* -- */
+			nil,       /* -> */
+			nil,       /* node */
+			nil,       /* edge */
+			shift(37), /* [ */
+			nil,       /* ] */
+			nil,       /* , */
+			nil,       /* = */
+			nil,       /* subgraph */
+			nil,       /* : */
+			nil,       /* id */
+		},
+	},
+	actionRow{ // S25
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			nil,        /* { */
+			nil,        /* } */
+			nil,        /* empty */
+			nil,        /* strict */
+			nil,        /* graphx */
+			nil,        /* digraph */
+			nil,        /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			nil,        /* node */
+			nil,        /* edge */
+			reduce(28), /* [, reduce: Component */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			nil,        /* subgraph */
+			nil,        /* : */
+			nil,        /* id */
+		},
+	},
+	actionRow{ // S26
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			nil,        /* { */
+			nil,        /* } */
+			nil,        /* empty */
+			nil,        /* strict */
+			nil,        /* graphx */
+			nil,        /* digraph */
+			nil,        /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			nil,        /* node */
+			nil,        /* edge */
+			reduce(29), /* [, reduce: Component */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			nil,        /* subgraph */
+			nil,        /* : */
+			nil,        /* id */
+		},
+	},
+	actionRow{ // S27
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(50), /* {, reduce: OptPort */
+			reduce(50), /* }, reduce: OptPort */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(50), /* graphx, reduce: OptPort */
+			nil,        /* digraph */
+			reduce(50), /* ;, reduce: OptPort */
+			reduce(50), /* --, reduce: OptPort */
+			reduce(50), /* ->, reduce: OptPort */
+			reduce(50), /* node, reduce: OptPort */
+			reduce(50), /* edge, reduce: OptPort */
+			reduce(50), /* [, reduce: OptPort */
+			nil,        /* ] */
+			nil,        /* , */
+			shift(43),  /* = */
+			reduce(50), /* subgraph, reduce: OptPort */
+			shift(46),  /* : */
+			reduce(50), /* id, reduce: OptPort */
+		},
+	},
+	actionRow{ // S28
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,       /* INVALID */
+			nil,       /* $ */
+			shift(47), /* { */
+			nil,       /* } */
+			nil,       /* empty */
+			nil,       /* strict */
+			nil,       /* graphx */
+			nil,       /* digraph */
+			nil,       /* ; */
+			nil,       /* -- */
+			nil,       /* -> */
+			nil,       /* node */
+			nil,       /* edge */
+			nil,       /* [ */
+			nil,       /* ] */
+			nil,       /* , */
+			nil,       /* = */
+			nil,       /* subgraph */
+			nil,       /* : */
+			nil,       /* id */
+		},
+	},
+	actionRow{ // S29
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(53), /* {, reduce: OptID */
+			nil,        /* } */
+			nil,        /* empty */
+			nil,        /* strict */
+			nil,        /* graphx */
+			nil,        /* digraph */
+			nil,        /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			nil,        /* node */
+			nil,        /* edge */
+			nil,        /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			nil,        /* subgraph */
+			nil,        /* : */
+			shift(11),  /* id */
+		},
+	},
+	actionRow{ // S30
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(52), /* {, reduce: ID */
+			reduce(52), /* }, reduce: ID */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(52), /* graphx, reduce: ID */
+			nil,        /* digraph */
+			reduce(52), /* ;, reduce: ID */
+			reduce(52), /* --, reduce: ID */
+			reduce(52), /* ->, reduce: ID */
+			reduce(52), /* node, reduce: ID */
+			reduce(52), /* edge, reduce: ID */
+			reduce(52), /* [, reduce: ID */
+			nil,        /* ] */
+			nil,        /* , */
+			reduce(52), /* =, reduce: ID */
+			reduce(52), /* subgraph, reduce: ID */
+			reduce(52), /* :, reduce: ID */
+			reduce(52), /* id, reduce: ID */
+		},
+	},
+	actionRow{ // S31
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,       /* INVALID */
+			reduce(3), /* $, reduce: Graph */
+			nil,       /* { */
+			nil,       /* } */
+			nil,       /* empty */
+			reduce(3), /* strict, reduce: Graph */
+			reduce(3), /* graphx, reduce: Graph */
+			reduce(3), /* digraph, reduce: Graph */
+			nil,       /* ; */
+			nil,       /* -- */
+			nil,       /* -> */
+			nil,       /* node */
+			nil,       /* edge */
+			nil,       /* [ */
+			nil,       /* ] */
+			nil,       /* , */
+			nil,       /* = */
+			nil,       /* subgraph */
+			nil,       /* : */
+			nil,       /* id */
+		},
+	},
+	actionRow{ // S32
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(17), /* {, reduce: OptSemi */
+			reduce(17), /* }, reduce: OptSemi */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(17), /* graphx, reduce: OptSemi */
+			nil,        /* digraph */
+			shift(34),  /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			reduce(17), /* node, reduce: OptSemi */
+			reduce(17), /* edge, reduce: OptSemi */
+			nil,        /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(17), /* subgraph, reduce: OptSemi */
+			nil,        /* : */
+			reduce(17), /* id, reduce: OptSemi */
+		},
+	},
+	actionRow{ // S33
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,       /* INVALID */
+			nil,       /* $ */
+			reduce(8), /* {, reduce: StmtList */
+			reduce(8), /* }, reduce: StmtList */
+			nil,       /* empty */
+			nil,       /* strict */
+			reduce(8), /* graphx, reduce: StmtList */
+			nil,       /* digraph */
+			nil,       /* ; */
+			nil,       /* -- */
+			nil,       /* -> */
+			reduce(8), /* node, reduce: StmtList */
+			reduce(8), /* edge, reduce: StmtList */
+			nil,       /* [ */
+			nil,       /* ] */
+			nil,       /* , */
+			nil,       /* = */
+			reduce(8), /* subgraph, reduce: StmtList */
+			nil,       /* : */
+			reduce(8), /* id, reduce: StmtList */
+		},
+	},
+	actionRow{ // S34
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(18), /* {, reduce: OptSemi */
+			reduce(18), /* }, reduce: OptSemi */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(18), /* graphx, reduce: OptSemi */
+			nil,        /* digraph */
+			nil,        /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			reduce(18), /* node, reduce: OptSemi */
+			reduce(18), /* edge, reduce: OptSemi */
+			nil,        /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(18), /* subgraph, reduce: OptSemi */
+			nil,        /* : */
+			reduce(18), /* id, reduce: OptSemi */
+		},
+	},
+	actionRow{ // S35
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(19), /* {, reduce: NodeStmt */
+			reduce(19), /* }, reduce: NodeStmt */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(19), /* graphx, reduce: NodeStmt */
+			nil,        /* digraph */
+			reduce(19), /* ;, reduce: NodeStmt */
+			nil,        /* -- */
+			nil,        /* -> */
+			reduce(19), /* node, reduce: NodeStmt */
+			reduce(19), /* edge, reduce: NodeStmt */
+			nil,        /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(19), /* subgraph, reduce: NodeStmt */
+			nil,        /* : */
+			reduce(19), /* id, reduce: NodeStmt */
+		},
+	},
+	actionRow{ // S36
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(33), /* {, reduce: OptAttrList */
+			reduce(33), /* }, reduce: OptAttrList */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(33), /* graphx, reduce: OptAttrList */
+			nil,        /* digraph */
+			reduce(33), /* ;, reduce: OptAttrList */
+			nil,        /* -- */
+			nil,        /* -> */
+			reduce(33), /* node, reduce: OptAttrList */
+			reduce(33), /* edge, reduce: OptAttrList */
+			shift(50),  /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(33), /* subgraph, reduce: OptAttrList */
+			nil,        /* : */
+			reduce(33), /* id, reduce: OptAttrList */
+		},
+	},
+	actionRow{ // S37
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			nil,        /* { */
+			nil,        /* } */
+			nil,        /* empty */
+			nil,        /* strict */
+			nil,        /* graphx */
+			nil,        /* digraph */
+			nil,        /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			nil,        /* node */
+			nil,        /* edge */
+			nil,        /* [ */
+			reduce(36), /* ], reduce: OptAList */
+			nil,        /* , */
+			nil,        /* = */
+			nil,        /* subgraph */
+			nil,        /* : */
+			shift(55),  /* id */
+		},
+	},
+	actionRow{ // S38
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(32), /* {, reduce: OptAttrList */
+			reduce(32), /* }, reduce: OptAttrList */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(32), /* graphx, reduce: OptAttrList */
+			nil,        /* digraph */
+			reduce(32), /* ;, reduce: OptAttrList */
+			nil,        /* -- */
+			nil,        /* -> */
+			reduce(32), /* node, reduce: OptAttrList */
+			reduce(32), /* edge, reduce: OptAttrList */
+			shift(37),  /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(32), /* subgraph, reduce: OptAttrList */
+			nil,        /* : */
+			reduce(32), /* id, reduce: OptAttrList */
+		},
+	},
+	actionRow{ // S39
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(43), /* {, reduce: OptSubgraphID */
+			nil,        /* } */
+			nil,        /* empty */
+			nil,        /* strict */
+			nil,        /* graphx */
+			nil,        /* digraph */
+			nil,        /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			nil,        /* node */
+			nil,        /* edge */
+			nil,        /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			shift(29),  /* subgraph */
+			nil,        /* : */
+			shift(62),  /* id */
+		},
+	},
+	actionRow{ // S40
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(22), /* {, reduce: DirectedEdge */
+			nil,        /* } */
+			nil,        /* empty */
+			nil,        /* strict */
+			nil,        /* graphx */
+			nil,        /* digraph */
+			nil,        /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			nil,        /* node */
+			nil,        /* edge */
+			nil,        /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(22), /* subgraph, reduce: DirectedEdge */
+			nil,        /* : */
+			reduce(22), /* id, reduce: DirectedEdge */
+		},
+	},
+	actionRow{ // S41
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(23), /* {, reduce: DirectedEdge */
+			nil,        /* } */
+			nil,        /* empty */
+			nil,        /* strict */
+			nil,        /* graphx */
+			nil,        /* digraph */
+			nil,        /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			nil,        /* node */
+			nil,        /* edge */
+			nil,        /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(23), /* subgraph, reduce: DirectedEdge */
+			nil,        /* : */
+			reduce(23), /* id, reduce: DirectedEdge */
+		},
+	},
+	actionRow{ // S42
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(26), /* {, reduce: AttrStmt */
+			reduce(26), /* }, reduce: AttrStmt */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(26), /* graphx, reduce: AttrStmt */
+			nil,        /* digraph */
+			reduce(26), /* ;, reduce: AttrStmt */
+			nil,        /* -- */
+			nil,        /* -> */
+			reduce(26), /* node, reduce: AttrStmt */
+			reduce(26), /* edge, reduce: AttrStmt */
+			shift(50),  /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(26), /* subgraph, reduce: AttrStmt */
+			nil,        /* : */
+			reduce(26), /* id, reduce: AttrStmt */
+		},
+	},
+	actionRow{ // S43
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,       /* INVALID */
+			nil,       /* $ */
+			nil,       /* { */
+			nil,       /* } */
+			nil,       /* empty */
+			nil,       /* strict */
+			nil,       /* graphx */
+			nil,       /* digraph */
+			nil,       /* ; */
+			nil,       /* -- */
+			nil,       /* -> */
+			nil,       /* node */
+			nil,       /* edge */
+			nil,       /* [ */
+			nil,       /* ] */
+			nil,       /* , */
+			nil,       /* = */
+			nil,       /* subgraph */
+			nil,       /* : */
+			shift(64), /* id */
+		},
+	},
+	actionRow{ // S44
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(47), /* {, reduce: Node */
+			reduce(47), /* }, reduce: Node */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(47), /* graphx, reduce: Node */
+			nil,        /* digraph */
+			reduce(47), /* ;, reduce: Node */
+			reduce(47), /* --, reduce: Node */
+			reduce(47), /* ->, reduce: Node */
+			reduce(47), /* node, reduce: Node */
+			reduce(47), /* edge, reduce: Node */
+			reduce(47), /* [, reduce: Node */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(47), /* subgraph, reduce: Node */
+			nil,        /* : */
+			reduce(47), /* id, reduce: Node */
+		},
+	},
+	actionRow{ // S45
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(51), /* {, reduce: OptPort */
+			reduce(51), /* }, reduce: OptPort */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(51), /* graphx, reduce: OptPort */
+			nil,        /* digraph */
+			reduce(51), /* ;, reduce: OptPort */
+			reduce(51), /* --, reduce: OptPort */
+			reduce(51), /* ->, reduce: OptPort */
+			reduce(51), /* node, reduce: OptPort */
+			reduce(51), /* edge, reduce: OptPort */
+			reduce(51), /* [, reduce: OptPort */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(51), /* subgraph, reduce: OptPort */
+			nil,        /* : */
+			reduce(51), /* id, reduce: OptPort */
+		},
+	},
+	actionRow{ // S46
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,       /* INVALID */
+			nil,       /* $ */
+			nil,       /* { */
+			nil,       /* } */
+			nil,       /* empty */
+			nil,       /* strict */
+			nil,       /* graphx */
+			nil,       /* digraph */
+			nil,       /* ; */
+			nil,       /* -- */
+			nil,       /* -> */
+			nil,       /* node */
+			nil,       /* edge */
+			nil,       /* [ */
+			nil,       /* ] */
+			nil,       /* , */
+			nil,       /* = */
+			nil,       /* subgraph */
+			nil,       /* : */
+			shift(62), /* id */
+		},
+	},
+	actionRow{ // S47
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(43), /* {, reduce: OptSubgraphID */
+			reduce(10), /* }, reduce: OptStmtList */
+			nil,        /* empty */
+			nil,        /* strict */
+			shift(14),  /* graphx */
+			nil,        /* digraph */
+			nil,        /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			shift(25),  /* node */
+			shift(26),  /* edge */
+			nil,        /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			shift(29),  /* subgraph */
+			nil,        /* : */
+			shift(30),  /* id */
+		},
+	},
+	actionRow{ // S48
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(44), /* {, reduce: OptSubgraphID */
+			nil,        /* } */
+			nil,        /* empty */
+			nil,        /* strict */
+			nil,        /* graphx */
+			nil,        /* digraph */
+			nil,        /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			nil,        /* node */
+			nil,        /* edge */
+			nil,        /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			nil,        /* subgraph */
+			nil,        /* : */
+			nil,        /* id */
+		},
+	},
+	actionRow{ // S49
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,       /* INVALID */
+			nil,       /* $ */
+			reduce(9), /* {, reduce: StmtList */
+			reduce(9), /* }, reduce: StmtList */
+			nil,       /* empty */
+			nil,       /* strict */
+			reduce(9), /* graphx, reduce: StmtList */
+			nil,       /* digraph */
+			nil,       /* ; */
+			nil,       /* -- */
+			nil,       /* -> */
+			reduce(9), /* node, reduce: StmtList */
+			reduce(9), /* edge, reduce: StmtList */
+			nil,       /* [ */
+			nil,       /* ] */
+			nil,       /* , */
+			nil,       /* = */
+			reduce(9), /* subgraph, reduce: StmtList */
+			nil,       /* : */
+			reduce(9), /* id, reduce: StmtList */
+		},
+	},
+	actionRow{ // S50
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			nil,        /* { */
+			nil,        /* } */
+			nil,        /* empty */
+			nil,        /* strict */
+			nil,        /* graphx */
+			nil,        /* digraph */
+			nil,        /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			nil,        /* node */
+			nil,        /* edge */
+			nil,        /* [ */
+			reduce(36), /* ], reduce: OptAList */
+			nil,        /* , */
+			nil,        /* = */
+			nil,        /* subgraph */
+			nil,        /* : */
+			shift(55),  /* id */
+		},
+	},
+	actionRow{ // S51
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			nil,        /* { */
+			nil,        /* } */
+			nil,        /* empty */
+			nil,        /* strict */
+			nil,        /* graphx */
+			nil,        /* digraph */
+			shift(68),  /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			nil,        /* node */
+			nil,        /* edge */
+			nil,        /* [ */
+			reduce(38), /* ], reduce: OptSep */
+			shift(70),  /* , */
+			nil,        /* = */
+			nil,        /* subgraph */
+			nil,        /* : */
+			reduce(38), /* id, reduce: OptSep */
+		},
+	},
+	actionRow{ // S52
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,       /* INVALID */
+			nil,       /* $ */
+			nil,       /* { */
+			nil,       /* } */
+			nil,       /* empty */
+			nil,       /* strict */
+			nil,       /* graphx */
+			nil,       /* digraph */
+			nil,       /* ; */
+			nil,       /* -- */
+			nil,       /* -> */
+			nil,       /* node */
+			nil,       /* edge */
+			nil,       /* [ */
+			shift(71), /* ] */
+			nil,       /* , */
+			nil,       /* = */
+			nil,       /* subgraph */
+			nil,       /* : */
+			nil,       /* id */
+		},
+	},
+	actionRow{ // S53
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			nil,        /* { */
+			nil,        /* } */
+			nil,        /* empty */
+			nil,        /* strict */
+			nil,        /* graphx */
+			nil,        /* digraph */
+			nil,        /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			nil,        /* node */
+			nil,        /* edge */
+			nil,        /* [ */
+			reduce(37), /* ], reduce: OptAList */
+			nil,        /* , */
+			nil,        /* = */
+			nil,        /* subgraph */
+			nil,        /* : */
+			shift(55),  /* id */
+		},
+	},
+	actionRow{ // S54
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,       /* INVALID */
+			nil,       /* $ */
+			nil,       /* { */
+			nil,       /* } */
+			nil,       /* empty */
+			nil,       /* strict */
+			nil,       /* graphx */
+			nil,       /* digraph */
+			nil,       /* ; */
+			nil,       /* -- */
+			nil,       /* -> */
+			nil,       /* node */
+			nil,       /* edge */
+			nil,       /* [ */
+			nil,       /* ] */
+			nil,       /* , */
+			shift(73), /* = */
+			nil,       /* subgraph */
+			nil,       /* : */
+			nil,       /* id */
+		},
+	},
+	actionRow{ // S55
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			nil,        /* { */
+			nil,        /* } */
+			nil,        /* empty */
+			nil,        /* strict */
+			nil,        /* graphx */
+			nil,        /* digraph */
+			nil,        /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			nil,        /* node */
+			nil,        /* edge */
+			nil,        /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			reduce(52), /* =, reduce: ID */
+			nil,        /* subgraph */
+			nil,        /* : */
+			nil,        /* id */
+		},
+	},
+	actionRow{ // S56
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(20), /* {, reduce: EdgeStmt */
+			reduce(20), /* }, reduce: EdgeStmt */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(20), /* graphx, reduce: EdgeStmt */
+			nil,        /* digraph */
+			reduce(20), /* ;, reduce: EdgeStmt */
+			nil,        /* -- */
+			nil,        /* -> */
+			reduce(20), /* node, reduce: EdgeStmt */
+			reduce(20), /* edge, reduce: EdgeStmt */
+			nil,        /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(20), /* subgraph, reduce: EdgeStmt */
+			nil,        /* : */
+			reduce(20), /* id, reduce: EdgeStmt */
+		},
+	},
+	actionRow{ // S57
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(46), /* {, reduce: Vertex */
+			reduce(46), /* }, reduce: Vertex */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(46), /* graphx, reduce: Vertex */
+			nil,        /* digraph */
+			reduce(46), /* ;, reduce: Vertex */
+			reduce(46), /* --, reduce: Vertex */
+			reduce(46), /* ->, reduce: Vertex */
+			reduce(46), /* node, reduce: Vertex */
+			reduce(46), /* edge, reduce: Vertex */
+			reduce(46), /* [, reduce: Vertex */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(46), /* subgraph, reduce: Vertex */
+			nil,        /* : */
+			reduce(46), /* id, reduce: Vertex */
+		},
+	},
+	actionRow{ // S58
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(45), /* {, reduce: Vertex */
+			reduce(45), /* }, reduce: Vertex */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(45), /* graphx, reduce: Vertex */
+			nil,        /* digraph */
+			reduce(45), /* ;, reduce: Vertex */
+			reduce(45), /* --, reduce: Vertex */
+			reduce(45), /* ->, reduce: Vertex */
+			reduce(45), /* node, reduce: Vertex */
+			reduce(45), /* edge, reduce: Vertex */
+			reduce(45), /* [, reduce: Vertex */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(45), /* subgraph, reduce: Vertex */
+			nil,        /* : */
+			reduce(45), /* id, reduce: Vertex */
+		},
+	},
+	actionRow{ // S59
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(24), /* {, reduce: OptEdge */
+			reduce(24), /* }, reduce: OptEdge */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(24), /* graphx, reduce: OptEdge */
+			nil,        /* digraph */
+			reduce(24), /* ;, reduce: OptEdge */
+			shift(40),  /* -- */
+			shift(41),  /* -> */
+			reduce(24), /* node, reduce: OptEdge */
+			reduce(24), /* edge, reduce: OptEdge */
+			reduce(24), /* [, reduce: OptEdge */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(24), /* subgraph, reduce: OptEdge */
+			nil,        /* : */
+			reduce(24), /* id, reduce: OptEdge */
+		},
+	},
+	actionRow{ // S60
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(50), /* {, reduce: OptPort */
+			reduce(50), /* }, reduce: OptPort */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(50), /* graphx, reduce: OptPort */
+			nil,        /* digraph */
+			reduce(50), /* ;, reduce: OptPort */
+			reduce(50), /* --, reduce: OptPort */
+			reduce(50), /* ->, reduce: OptPort */
+			reduce(50), /* node, reduce: OptPort */
+			reduce(50), /* edge, reduce: OptPort */
+			reduce(50), /* [, reduce: OptPort */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(50), /* subgraph, reduce: OptPort */
+			shift(46),  /* : */
+			reduce(50), /* id, reduce: OptPort */
+		},
+	},
+	actionRow{ // S61
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,       /* INVALID */
+			nil,       /* $ */
+			shift(76), /* { */
+			nil,       /* } */
+			nil,       /* empty */
+			nil,       /* strict */
+			nil,       /* graphx */
+			nil,       /* digraph */
+			nil,       /* ; */
+			nil,       /* -- */
+			nil,       /* -> */
+			nil,       /* node */
+			nil,       /* edge */
+			nil,       /* [ */
+			nil,       /* ] */
+			nil,       /* , */
+			nil,       /* = */
+			nil,       /* subgraph */
+			nil,       /* : */
+			nil,       /* id */
+		},
+	},
+	actionRow{ // S62
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(52), /* {, reduce: ID */
+			reduce(52), /* }, reduce: ID */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(52), /* graphx, reduce: ID */
+			nil,        /* digraph */
+			reduce(52), /* ;, reduce: ID */
+			reduce(52), /* --, reduce: ID */
+			reduce(52), /* ->, reduce: ID */
+			reduce(52), /* node, reduce: ID */
+			reduce(52), /* edge, reduce: ID */
+			reduce(52), /* [, reduce: ID */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(52), /* subgraph, reduce: ID */
+			reduce(52), /* :, reduce: ID */
+			reduce(52), /* id, reduce: ID */
+		},
+	},
+	actionRow{ // S63
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(41), /* {, reduce: Attr */
+			reduce(41), /* }, reduce: Attr */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(41), /* graphx, reduce: Attr */
+			nil,        /* digraph */
+			reduce(41), /* ;, reduce: Attr */
+			nil,        /* -- */
+			nil,        /* -> */
+			reduce(41), /* node, reduce: Attr */
+			reduce(41), /* edge, reduce: Attr */
+			nil,        /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(41), /* subgraph, reduce: Attr */
+			nil,        /* : */
+			reduce(41), /* id, reduce: Attr */
+		},
+	},
+	actionRow{ // S64
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(52), /* {, reduce: ID */
+			reduce(52), /* }, reduce: ID */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(52), /* graphx, reduce: ID */
+			nil,        /* digraph */
+			reduce(52), /* ;, reduce: ID */
+			nil,        /* -- */
+			nil,        /* -> */
+			reduce(52), /* node, reduce: ID */
+			reduce(52), /* edge, reduce: ID */
+			nil,        /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(52), /* subgraph, reduce: ID */
+			nil,        /* : */
+			reduce(52), /* id, reduce: ID */
+		},
+	},
+	actionRow{ // S65
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(48), /* {, reduce: Port */
+			reduce(48), /* }, reduce: Port */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(48), /* graphx, reduce: Port */
+			nil,        /* digraph */
+			reduce(48), /* ;, reduce: Port */
+			reduce(48), /* --, reduce: Port */
+			reduce(48), /* ->, reduce: Port */
+			reduce(48), /* node, reduce: Port */
+			reduce(48), /* edge, reduce: Port */
+			reduce(48), /* [, reduce: Port */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(48), /* subgraph, reduce: Port */
+			shift(77),  /* : */
+			reduce(48), /* id, reduce: Port */
+		},
+	},
+	actionRow{ // S66
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,       /* INVALID */
+			nil,       /* $ */
+			nil,       /* { */
+			shift(78), /* } */
+			nil,       /* empty */
+			nil,       /* strict */
+			nil,       /* graphx */
+			nil,       /* digraph */
+			nil,       /* ; */
+			nil,       /* -- */
+			nil,       /* -> */
+			nil,       /* node */
+			nil,       /* edge */
+			nil,       /* [ */
+			nil,       /* ] */
+			nil,       /* , */
+			nil,       /* = */
+			nil,       /* subgraph */
+			nil,       /* : */
+			nil,       /* id */
+		},
+	},
+	actionRow{ // S67
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,       /* INVALID */
+			nil,       /* $ */
+			nil,       /* { */
+			nil,       /* } */
+			nil,       /* empty */
+			nil,       /* strict */
+			nil,       /* graphx */
+			nil,       /* digraph */
+			nil,       /* ; */
+			nil,       /* -- */
+			nil,       /* -> */
+			nil,       /* node */
+			nil,       /* edge */
+			nil,       /* [ */
+			shift(79), /* ] */
+			nil,       /* , */
+			nil,       /* = */
+			nil,       /* subgraph */
+			nil,       /* : */
+			nil,       /* id */
+		},
+	},
+	actionRow{ // S68
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			nil,        /* { */
+			nil,        /* } */
+			nil,        /* empty */
+			nil,        /* strict */
+			nil,        /* graphx */
+			nil,        /* digraph */
+			nil,        /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			nil,        /* node */
+			nil,        /* edge */
+			nil,        /* [ */
+			reduce(39), /* ], reduce: OptSep */
+			nil,        /* , */
+			nil,        /* = */
+			nil,        /* subgraph */
+			nil,        /* : */
+			reduce(39), /* id, reduce: OptSep */
+		},
+	},
+	actionRow{ // S69
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			nil,        /* { */
+			nil,        /* } */
+			nil,        /* empty */
+			nil,        /* strict */
+			nil,        /* graphx */
+			nil,        /* digraph */
+			nil,        /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			nil,        /* node */
+			nil,        /* edge */
+			nil,        /* [ */
+			reduce(34), /* ], reduce: AList */
+			nil,        /* , */
+			nil,        /* = */
+			nil,        /* subgraph */
+			nil,        /* : */
+			reduce(34), /* id, reduce: AList */
+		},
+	},
+	actionRow{ // S70
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			nil,        /* { */
+			nil,        /* } */
+			nil,        /* empty */
+			nil,        /* strict */
+			nil,        /* graphx */
+			nil,        /* digraph */
+			nil,        /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			nil,        /* node */
+			nil,        /* edge */
+			nil,        /* [ */
+			reduce(40), /* ], reduce: OptSep */
+			nil,        /* , */
+			nil,        /* = */
+			nil,        /* subgraph */
+			nil,        /* : */
+			reduce(40), /* id, reduce: OptSep */
+		},
+	},
+	actionRow{ // S71
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(30), /* {, reduce: AttrList */
+			reduce(30), /* }, reduce: AttrList */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(30), /* graphx, reduce: AttrList */
+			nil,        /* digraph */
+			reduce(30), /* ;, reduce: AttrList */
+			nil,        /* -- */
+			nil,        /* -> */
+			reduce(30), /* node, reduce: AttrList */
+			reduce(30), /* edge, reduce: AttrList */
+			reduce(30), /* [, reduce: AttrList */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(30), /* subgraph, reduce: AttrList */
+			nil,        /* : */
+			reduce(30), /* id, reduce: AttrList */
+		},
+	},
+	actionRow{ // S72
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			nil,        /* { */
+			nil,        /* } */
+			nil,        /* empty */
+			nil,        /* strict */
+			nil,        /* graphx */
+			nil,        /* digraph */
+			shift(68),  /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			nil,        /* node */
+			nil,        /* edge */
+			nil,        /* [ */
+			reduce(38), /* ], reduce: OptSep */
+			shift(70),  /* , */
+			nil,        /* = */
+			nil,        /* subgraph */
+			nil,        /* : */
+			reduce(38), /* id, reduce: OptSep */
+		},
+	},
+	actionRow{ // S73
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,       /* INVALID */
+			nil,       /* $ */
+			nil,       /* { */
+			nil,       /* } */
+			nil,       /* empty */
+			nil,       /* strict */
+			nil,       /* graphx */
+			nil,       /* digraph */
+			nil,       /* ; */
+			nil,       /* -- */
+			nil,       /* -> */
+			nil,       /* node */
+			nil,       /* edge */
+			nil,       /* [ */
+			nil,       /* ] */
+			nil,       /* , */
+			nil,       /* = */
+			nil,       /* subgraph */
+			nil,       /* : */
+			shift(82), /* id */
+		},
+	},
+	actionRow{ // S74
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(25), /* {, reduce: OptEdge */
+			reduce(25), /* }, reduce: OptEdge */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(25), /* graphx, reduce: OptEdge */
+			nil,        /* digraph */
+			reduce(25), /* ;, reduce: OptEdge */
+			nil,        /* -- */
+			nil,        /* -> */
+			reduce(25), /* node, reduce: OptEdge */
+			reduce(25), /* edge, reduce: OptEdge */
+			reduce(25), /* [, reduce: OptEdge */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(25), /* subgraph, reduce: OptEdge */
+			nil,        /* : */
+			reduce(25), /* id, reduce: OptEdge */
+		},
+	},
+	actionRow{ // S75
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(21), /* {, reduce: Edge */
+			reduce(21), /* }, reduce: Edge */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(21), /* graphx, reduce: Edge */
+			nil,        /* digraph */
+			reduce(21), /* ;, reduce: Edge */
+			nil,        /* -- */
+			nil,        /* -> */
+			reduce(21), /* node, reduce: Edge */
+			reduce(21), /* edge, reduce: Edge */
+			reduce(21), /* [, reduce: Edge */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(21), /* subgraph, reduce: Edge */
+			nil,        /* : */
+			reduce(21), /* id, reduce: Edge */
+		},
+	},
+	actionRow{ // S76
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(43), /* {, reduce: OptSubgraphID */
+			reduce(10), /* }, reduce: OptStmtList */
+			nil,        /* empty */
+			nil,        /* strict */
+			shift(14),  /* graphx */
+			nil,        /* digraph */
+			nil,        /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			shift(25),  /* node */
+			shift(26),  /* edge */
+			nil,        /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			shift(29),  /* subgraph */
+			nil,        /* : */
+			shift(30),  /* id */
+		},
+	},
+	actionRow{ // S77
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,       /* INVALID */
+			nil,       /* $ */
+			nil,       /* { */
+			nil,       /* } */
+			nil,       /* empty */
+			nil,       /* strict */
+			nil,       /* graphx */
+			nil,       /* digraph */
+			nil,       /* ; */
+			nil,       /* -- */
+			nil,       /* -> */
+			nil,       /* node */
+			nil,       /* edge */
+			nil,       /* [ */
+			nil,       /* ] */
+			nil,       /* , */
+			nil,       /* = */
+			nil,       /* subgraph */
+			nil,       /* : */
+			shift(85), /* id */
+		},
+	},
+	actionRow{ // S78
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(42), /* {, reduce: Subgraph */
+			reduce(42), /* }, reduce: Subgraph */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(42), /* graphx, reduce: Subgraph */
+			nil,        /* digraph */
+			reduce(42), /* ;, reduce: Subgraph */
+			reduce(42), /* --, reduce: Subgraph */
+			reduce(42), /* ->, reduce: Subgraph */
+			reduce(42), /* node, reduce: Subgraph */
+			reduce(42), /* edge, reduce: Subgraph */
+			nil,        /* [ */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(42), /* subgraph, reduce: Subgraph */
+			nil,        /* : */
+			reduce(42), /* id, reduce: Subgraph */
+		},
+	},
+	actionRow{ // S79
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(31), /* {, reduce: AttrList */
+			reduce(31), /* }, reduce: AttrList */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(31), /* graphx, reduce: AttrList */
+			nil,        /* digraph */
+			reduce(31), /* ;, reduce: AttrList */
+			nil,        /* -- */
+			nil,        /* -> */
+			reduce(31), /* node, reduce: AttrList */
+			reduce(31), /* edge, reduce: AttrList */
+			reduce(31), /* [, reduce: AttrList */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(31), /* subgraph, reduce: AttrList */
+			nil,        /* : */
+			reduce(31), /* id, reduce: AttrList */
+		},
+	},
+	actionRow{ // S80
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			nil,        /* { */
+			nil,        /* } */
+			nil,        /* empty */
+			nil,        /* strict */
+			nil,        /* graphx */
+			nil,        /* digraph */
+			nil,        /* ; */
+			nil,        /* -- */
+			nil,        /* -> */
+			nil,        /* node */
+			nil,        /* edge */
+			nil,        /* [ */
+			reduce(35), /* ], reduce: AList */
+			nil,        /* , */
+			nil,        /* = */
+			nil,        /* subgraph */
+			nil,        /* : */
+			reduce(35), /* id, reduce: AList */
+		},
+	},
+	actionRow{ // S81
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			nil,        /* { */
+			nil,        /* } */
+			nil,        /* empty */
+			nil,        /* strict */
+			nil,        /* graphx */
+			nil,        /* digraph */
+			reduce(41), /* ;, reduce: Attr */
+			nil,        /* -- */
+			nil,        /* -> */
+			nil,        /* node */
+			nil,        /* edge */
+			nil,        /* [ */
+			reduce(41), /* ], reduce: Attr */
+			reduce(41), /* ,, reduce: Attr */
+			nil,        /* = */
+			nil,        /* subgraph */
+			nil,        /* : */
+			reduce(41), /* id, reduce: Attr */
+		},
+	},
+	actionRow{ // S82
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			nil,        /* { */
+			nil,        /* } */
+			nil,        /* empty */
+			nil,        /* strict */
+			nil,        /* graphx */
+			nil,        /* digraph */
+			reduce(52), /* ;, reduce: ID */
+			nil,        /* -- */
+			nil,        /* -> */
+			nil,        /* node */
+			nil,        /* edge */
+			nil,        /* [ */
+			reduce(52), /* ], reduce: ID */
+			reduce(52), /* ,, reduce: ID */
+			nil,        /* = */
+			nil,        /* subgraph */
+			nil,        /* : */
+			reduce(52), /* id, reduce: ID */
+		},
+	},
+	actionRow{ // S83
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,       /* INVALID */
+			nil,       /* $ */
+			nil,       /* { */
+			shift(86), /* } */
+			nil,       /* empty */
+			nil,       /* strict */
+			nil,       /* graphx */
+			nil,       /* digraph */
+			nil,       /* ; */
+			nil,       /* -- */
+			nil,       /* -> */
+			nil,       /* node */
+			nil,       /* edge */
+			nil,       /* [ */
+			nil,       /* ] */
+			nil,       /* , */
+			nil,       /* = */
+			nil,       /* subgraph */
+			nil,       /* : */
+			nil,       /* id */
+		},
+	},
+	actionRow{ // S84
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(49), /* {, reduce: Port */
+			reduce(49), /* }, reduce: Port */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(49), /* graphx, reduce: Port */
+			nil,        /* digraph */
+			reduce(49), /* ;, reduce: Port */
+			reduce(49), /* --, reduce: Port */
+			reduce(49), /* ->, reduce: Port */
+			reduce(49), /* node, reduce: Port */
+			reduce(49), /* edge, reduce: Port */
+			reduce(49), /* [, reduce: Port */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(49), /* subgraph, reduce: Port */
+			nil,        /* : */
+			reduce(49), /* id, reduce: Port */
+		},
+	},
+	actionRow{ // S85
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(52), /* {, reduce: ID */
+			reduce(52), /* }, reduce: ID */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(52), /* graphx, reduce: ID */
+			nil,        /* digraph */
+			reduce(52), /* ;, reduce: ID */
+			reduce(52), /* --, reduce: ID */
+			reduce(52), /* ->, reduce: ID */
+			reduce(52), /* node, reduce: ID */
+			reduce(52), /* edge, reduce: ID */
+			reduce(52), /* [, reduce: ID */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(52), /* subgraph, reduce: ID */
+			nil,        /* : */
+			reduce(52), /* id, reduce: ID */
+		},
+	},
+	actionRow{ // S86
+		canRecover: false,
+		actions: [numSymbols]action{
+			nil,        /* INVALID */
+			nil,        /* $ */
+			reduce(42), /* {, reduce: Subgraph */
+			reduce(42), /* }, reduce: Subgraph */
+			nil,        /* empty */
+			nil,        /* strict */
+			reduce(42), /* graphx, reduce: Subgraph */
+			nil,        /* digraph */
+			reduce(42), /* ;, reduce: Subgraph */
+			reduce(42), /* --, reduce: Subgraph */
+			reduce(42), /* ->, reduce: Subgraph */
+			reduce(42), /* node, reduce: Subgraph */
+			reduce(42), /* edge, reduce: Subgraph */
+			reduce(42), /* [, reduce: Subgraph */
+			nil,        /* ] */
+			nil,        /* , */
+			nil,        /* = */
+			reduce(42), /* subgraph, reduce: Subgraph */
+			nil,        /* : */
+			reduce(42), /* id, reduce: Subgraph */
+		},
+	},
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/parser/gototable.go b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/parser/gototable.go
new file mode 100644
index 00000000..9c55e43d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/parser/gototable.go
@@ -0,0 +1,2807 @@
+// Code generated by gocc; DO NOT EDIT.
+
+// This file is dual licensed under CC0 and The gonum license.
+//
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Copyright ©2017 Robin Eklind.
+// This file is made available under a Creative Commons CC0 1.0
+// Universal Public Domain Dedication.
+
+package parser
+
+const numNTSymbols = 30
+
+type (
+	gotoTable [numStates]gotoRow
+	gotoRow   [numNTSymbols]int
+)
+
+var gotoTab = gotoTable{
+	gotoRow{ // S0
+		-1, // S'
+		1,  // File
+		2,  // Graph
+		3,  // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S1
+		-1, // S'
+		-1, // File
+		5,  // Graph
+		3,  // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S2
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S3
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		6,  // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S4
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S5
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S6
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		10, // ID
+		9,  // OptID
+	},
+	gotoRow{ // S7
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S8
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S9
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S10
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S11
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S12
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		15, // StmtList
+		13, // OptStmtList
+		16, // Stmt
+		-1, // OptSemi
+		17, // NodeStmt
+		18, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		19, // AttrStmt
+		24, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		20, // Attr
+		21, // Subgraph
+		28, // OptSubgraphID
+		23, // Vertex
+		22, // Node
+		-1, // Port
+		-1, // OptPort
+		27, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S13
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S14
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S15
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		32, // Stmt
+		-1, // OptSemi
+		17, // NodeStmt
+		18, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		19, // AttrStmt
+		24, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		20, // Attr
+		21, // Subgraph
+		28, // OptSubgraphID
+		23, // Vertex
+		22, // Node
+		-1, // Port
+		-1, // OptPort
+		27, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S16
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		33, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S17
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S18
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S19
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S20
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S21
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S22
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		36, // AttrList
+		35, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S23
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		38, // Edge
+		39, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S24
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		42, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S25
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S26
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S27
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		45, // Port
+		44, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S28
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S29
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		10, // ID
+		48, // OptID
+	},
+	gotoRow{ // S30
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S31
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S32
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		49, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S33
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S34
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S35
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S36
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S37
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		53, // AList
+		52, // OptAList
+		-1, // OptSep
+		51, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		54, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S38
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		36, // AttrList
+		56, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S39
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		57, // Subgraph
+		61, // OptSubgraphID
+		59, // Vertex
+		58, // Node
+		-1, // Port
+		-1, // OptPort
+		60, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S40
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S41
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S42
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S43
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		63, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S44
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S45
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S46
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		65, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S47
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		15, // StmtList
+		66, // OptStmtList
+		16, // Stmt
+		-1, // OptSemi
+		17, // NodeStmt
+		18, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		19, // AttrStmt
+		24, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		20, // Attr
+		21, // Subgraph
+		28, // OptSubgraphID
+		23, // Vertex
+		22, // Node
+		-1, // Port
+		-1, // OptPort
+		27, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S48
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S49
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S50
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		53, // AList
+		67, // OptAList
+		-1, // OptSep
+		51, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		54, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S51
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		69, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S52
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S53
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		72, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		54, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S54
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S55
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S56
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S57
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S58
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S59
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		74, // Edge
+		39, // DirectedEdge
+		75, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S60
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		45, // Port
+		44, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S61
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S62
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S63
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S64
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S65
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S66
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S67
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S68
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S69
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S70
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S71
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S72
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		80, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S73
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		81, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S74
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S75
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S76
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		15, // StmtList
+		83, // OptStmtList
+		16, // Stmt
+		-1, // OptSemi
+		17, // NodeStmt
+		18, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		19, // AttrStmt
+		24, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		20, // Attr
+		21, // Subgraph
+		28, // OptSubgraphID
+		23, // Vertex
+		22, // Node
+		-1, // Port
+		-1, // OptPort
+		27, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S77
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		84, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S78
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S79
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S80
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S81
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S82
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S83
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S84
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S85
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+	gotoRow{ // S86
+		-1, // S'
+		-1, // File
+		-1, // Graph
+		-1, // OptStrict
+		-1, // DirectedGraph
+		-1, // StmtList
+		-1, // OptStmtList
+		-1, // Stmt
+		-1, // OptSemi
+		-1, // NodeStmt
+		-1, // EdgeStmt
+		-1, // Edge
+		-1, // DirectedEdge
+		-1, // OptEdge
+		-1, // AttrStmt
+		-1, // Component
+		-1, // AttrList
+		-1, // OptAttrList
+		-1, // AList
+		-1, // OptAList
+		-1, // OptSep
+		-1, // Attr
+		-1, // Subgraph
+		-1, // OptSubgraphID
+		-1, // Vertex
+		-1, // Node
+		-1, // Port
+		-1, // OptPort
+		-1, // ID
+		-1, // OptID
+	},
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/parser/parser.go b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/parser/parser.go
new file mode 100644
index 00000000..18e146e0
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/parser/parser.go
@@ -0,0 +1,221 @@
+// Code generated by gocc; DO NOT EDIT.
+
+// This file is dual licensed under CC0 and The gonum license.
+//
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Copyright ©2017 Robin Eklind.
+// This file is made available under a Creative Commons CC0 1.0
+// Universal Public Domain Dedication.
+
+package parser
+
+import (
+	"bytes"
+	"fmt"
+
+	parseError "gonum.org/v1/gonum/graph/formats/dot/internal/errors"
+	"gonum.org/v1/gonum/graph/formats/dot/internal/token"
+)
+
+const (
+	numProductions = 55
+	numStates      = 87
+	numSymbols     = 50
+)
+
+// Stack
+
+type stack struct {
+	state  []int
+	attrib []Attrib
+}
+
+const iNITIAL_STACK_SIZE = 100
+
+func newStack() *stack {
+	return &stack{
+		state:  make([]int, 0, iNITIAL_STACK_SIZE),
+		attrib: make([]Attrib, 0, iNITIAL_STACK_SIZE),
+	}
+}
+
+func (s *stack) reset() {
+	s.state = s.state[:0]
+	s.attrib = s.attrib[:0]
+}
+
+func (s *stack) push(state int, a Attrib) {
+	s.state = append(s.state, state)
+	s.attrib = append(s.attrib, a)
+}
+
+func (s *stack) top() int {
+	return s.state[len(s.state)-1]
+}
+
+func (s *stack) peek(pos int) int {
+	return s.state[pos]
+}
+
+func (s *stack) topIndex() int {
+	return len(s.state) - 1
+}
+
+func (s *stack) popN(items int) []Attrib {
+	lo, hi := len(s.state)-items, len(s.state)
+
+	attrib := s.attrib[lo:hi]
+
+	s.state = s.state[:lo]
+	s.attrib = s.attrib[:lo]
+
+	return attrib
+}
+
+func (s *stack) String() string {
+	w := new(bytes.Buffer)
+	fmt.Fprintf(w, "stack:\n")
+	for i, st := range s.state {
+		fmt.Fprintf(w, "\t%d:%d , ", i, st)
+		if s.attrib[i] == nil {
+			fmt.Fprintf(w, "nil")
+		} else {
+			fmt.Fprintf(w, "%v", s.attrib[i])
+		}
+		fmt.Fprintf(w, "\n")
+	}
+	return w.String()
+}
+
+// Parser
+
+type Parser struct {
+	stack     *stack
+	nextToken *token.Token
+	pos       int
+}
+
+type Scanner interface {
+	Scan() (tok *token.Token)
+}
+
+func NewParser() *Parser {
+	p := &Parser{stack: newStack()}
+	p.Reset()
+	return p
+}
+
+func (p *Parser) Reset() {
+	p.stack.reset()
+	p.stack.push(0, nil)
+}
+
+func (p *Parser) Error(err error, scanner Scanner) (recovered bool, errorAttrib *parseError.Error) {
+	errorAttrib = &parseError.Error{
+		Err:            err,
+		ErrorToken:     p.nextToken,
+		ErrorSymbols:   p.popNonRecoveryStates(),
+		ExpectedTokens: make([]string, 0, 8),
+	}
+	for t, action := range actionTab[p.stack.top()].actions {
+		if action != nil {
+			errorAttrib.ExpectedTokens = append(errorAttrib.ExpectedTokens, token.TokMap.Id(token.Type(t)))
+		}
+	}
+
+	if action := actionTab[p.stack.top()].actions[token.TokMap.Type("error")]; action != nil {
+		p.stack.push(int(action.(shift)), errorAttrib) // action can only be shift
+	} else {
+		return
+	}
+
+	if action := actionTab[p.stack.top()].actions[p.nextToken.Type]; action != nil {
+		recovered = true
+	}
+	for !recovered && p.nextToken.Type != token.EOF {
+		p.nextToken = scanner.Scan()
+		if action := actionTab[p.stack.top()].actions[p.nextToken.Type]; action != nil {
+			recovered = true
+		}
+	}
+
+	return
+}
+
+func (p *Parser) popNonRecoveryStates() (removedAttribs []parseError.ErrorSymbol) {
+	if rs, ok := p.firstRecoveryState(); ok {
+		errorSymbols := p.stack.popN(int(p.stack.topIndex() - rs))
+		removedAttribs = make([]parseError.ErrorSymbol, len(errorSymbols))
+		for i, e := range errorSymbols {
+			removedAttribs[i] = e
+		}
+	} else {
+		removedAttribs = []parseError.ErrorSymbol{}
+	}
+	return
+}
+
+// recoveryState points to the highest state on the stack, which can recover
+func (p *Parser) firstRecoveryState() (recoveryState int, canRecover bool) {
+	recoveryState, canRecover = p.stack.topIndex(), actionTab[p.stack.top()].canRecover
+	for recoveryState > 0 && !canRecover {
+		recoveryState--
+		canRecover = actionTab[p.stack.peek(recoveryState)].canRecover
+	}
+	return
+}
+
+func (p *Parser) newError(err error) error {
+	e := &parseError.Error{
+		Err:        err,
+		StackTop:   p.stack.top(),
+		ErrorToken: p.nextToken,
+	}
+	actRow := actionTab[p.stack.top()]
+	for i, t := range actRow.actions {
+		if t != nil {
+			e.ExpectedTokens = append(e.ExpectedTokens, token.TokMap.Id(token.Type(i)))
+		}
+	}
+	return e
+}
+
+func (p *Parser) Parse(scanner Scanner) (res interface{}, err error) {
+	p.Reset()
+	p.nextToken = scanner.Scan()
+	for acc := false; !acc; {
+		action := actionTab[p.stack.top()].actions[p.nextToken.Type]
+		if action == nil {
+			if recovered, errAttrib := p.Error(nil, scanner); !recovered {
+				p.nextToken = errAttrib.ErrorToken
+				return nil, p.newError(nil)
+			}
+			if action = actionTab[p.stack.top()].actions[p.nextToken.Type]; action == nil {
+				panic("Error recovery led to invalid action")
+			}
+		}
+
+		switch act := action.(type) {
+		case accept:
+			res = p.stack.popN(1)[0]
+			acc = true
+		case shift:
+			p.stack.push(int(act), p.nextToken)
+			p.nextToken = scanner.Scan()
+		case reduce:
+			prod := productionsTable[int(act)]
+			attrib, err := prod.ReduceFunc(p.stack.popN(prod.NumSymbols))
+			if err != nil {
+				return nil, p.newError(err)
+			} else {
+				p.stack.push(gotoTab[p.stack.top()][prod.NTType], attrib)
+			}
+		default:
+			panic("unknown action: " + action.String())
+		}
+	}
+	return res, nil
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/parser/parser_test.go b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/parser/parser_test.go
new file mode 100644
index 00000000..c48cd6f6
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/parser/parser_test.go
@@ -0,0 +1,114 @@
+// This file is dual licensed under CC0 and The gonum license.
+//
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Copyright ©2017 Robin Eklind.
+// This file is made available under a Creative Commons CC0 1.0
+// Universal Public Domain Dedication.
+
+package parser_test
+
+import (
+	"bytes"
+	"io/ioutil"
+	"testing"
+
+	"gonum.org/v1/gonum/graph/formats/dot"
+)
+
+func TestParseFile(t *testing.T) {
+	golden := []struct {
+		in  string
+		out string
+	}{
+		{in: "../testdata/empty.dot"},
+		{in: "../testdata/graph.dot"},
+		{in: "../testdata/digraph.dot"},
+		{in: "../testdata/strict.dot"},
+		{in: "../testdata/multi.dot"},
+		{in: "../testdata/named_graph.dot"},
+		{in: "../testdata/node_stmt.dot"},
+		{in: "../testdata/edge_stmt.dot"},
+		{in: "../testdata/attr_stmt.dot"},
+		{in: "../testdata/attr.dot"},
+		{
+			in:  "../testdata/subgraph.dot",
+			out: "../testdata/subgraph.golden",
+		},
+		{
+			in:  "../testdata/semi.dot",
+			out: "../testdata/semi.golden",
+		},
+		{
+			in:  "../testdata/empty_attr.dot",
+			out: "../testdata/empty_attr.golden",
+		},
+		{
+			in:  "../testdata/attr_lists.dot",
+			out: "../testdata/attr_lists.golden",
+		},
+		{
+			in:  "../testdata/attr_sep.dot",
+			out: "../testdata/attr_sep.golden",
+		},
+		{in: "../testdata/subgraph_vertex.dot"},
+		{
+			in:  "../testdata/port.dot",
+			out: "../testdata/port.golden",
+		},
+		{in: "../testdata/quoted_id.dot"},
+		{
+			in:  "../testdata/backslash_newline_id.dot",
+			out: "../testdata/backslash_newline_id.golden",
+		},
+	}
+	for _, g := range golden {
+		file, err := dot.ParseFile(g.in)
+		if err != nil {
+			t.Errorf("%q: unable to parse file; %v", g.in, err)
+			continue
+		}
+		// If no output path is specified, the input is already golden.
+		out := g.in
+		if len(g.out) > 0 {
+			out = g.out
+		}
+		buf, err := ioutil.ReadFile(out)
+		if err != nil {
+			t.Errorf("%q: unable to read file; %v", g.in, err)
+			continue
+		}
+		got := file.String()
+		// Remove trailing newline.
+		want := string(bytes.TrimSpace(buf))
+		if got != want {
+			t.Errorf("%q: graph mismatch; expected `%s`, got `%s`", g.in, want, got)
+		}
+	}
+}
+
+func TestParseError(t *testing.T) {
+	golden := []struct {
+		path string
+		want string
+	}{
+		{
+			path: "../testdata/error.dot",
+			want: `Error in S30: INVALID(0,~), Pos(offset=13, line=2, column=7), expected one of: { } graphx ; -- -> node edge [ = subgraph : id `,
+		},
+	}
+	for _, g := range golden {
+		_, err := dot.ParseFile(g.path)
+		if err == nil {
+			t.Errorf("%q: expected error, got nil", g.path)
+			continue
+		}
+		got := err.Error()
+		if got != g.want {
+			t.Errorf("%q: error mismatch; expected `%v`, got `%v`", g.path, g.want, got)
+			continue
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/parser/productionstable.go b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/parser/productionstable.go
new file mode 100644
index 00000000..96c56350
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/parser/productionstable.go
@@ -0,0 +1,586 @@
+// Code generated by gocc; DO NOT EDIT.
+
+// This file is dual licensed under CC0 and The gonum license.
+//
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Copyright ©2017 Robin Eklind.
+// This file is made available under a Creative Commons CC0 1.0
+// Universal Public Domain Dedication.
+
+package parser
+
+import (
+	"gonum.org/v1/gonum/graph/formats/dot/ast"
+	"gonum.org/v1/gonum/graph/formats/dot/internal/astx"
+)
+
+type (
+	//TODO: change type and variable names to be consistent with other tables
+	ProdTab      [numProductions]ProdTabEntry
+	ProdTabEntry struct {
+		String     string
+		Id         string
+		NTType     int
+		Index      int
+		NumSymbols int
+		ReduceFunc func([]Attrib) (Attrib, error)
+	}
+	Attrib interface {
+	}
+)
+
+var productionsTable = ProdTab{
+	ProdTabEntry{
+		String: `S' : File	<<  >>`,
+		Id:         "S'",
+		NTType:     0,
+		Index:      0,
+		NumSymbols: 1,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return X[0], nil
+		},
+	},
+	ProdTabEntry{
+		String: `File : Graph	<< astx.NewFile(X[0]) >>`,
+		Id:         "File",
+		NTType:     1,
+		Index:      1,
+		NumSymbols: 1,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return astx.NewFile(X[0])
+		},
+	},
+	ProdTabEntry{
+		String: `File : File Graph	<< astx.AppendGraph(X[0], X[1]) >>`,
+		Id:         "File",
+		NTType:     1,
+		Index:      2,
+		NumSymbols: 2,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return astx.AppendGraph(X[0], X[1])
+		},
+	},
+	ProdTabEntry{
+		String: `Graph : OptStrict DirectedGraph OptID "{" OptStmtList "}"	<< astx.NewGraph(X[0], X[1], X[2], X[4]) >>`,
+		Id:         "Graph",
+		NTType:     2,
+		Index:      3,
+		NumSymbols: 6,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return astx.NewGraph(X[0], X[1], X[2], X[4])
+		},
+	},
+	ProdTabEntry{
+		String: `OptStrict : empty	<< false, nil >>`,
+		Id:         "OptStrict",
+		NTType:     3,
+		Index:      4,
+		NumSymbols: 0,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return false, nil
+		},
+	},
+	ProdTabEntry{
+		String: `OptStrict : strict	<< true, nil >>`,
+		Id:         "OptStrict",
+		NTType:     3,
+		Index:      5,
+		NumSymbols: 1,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return true, nil
+		},
+	},
+	ProdTabEntry{
+		String: `DirectedGraph : graphx	<< false, nil >>`,
+		Id:         "DirectedGraph",
+		NTType:     4,
+		Index:      6,
+		NumSymbols: 1,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return false, nil
+		},
+	},
+	ProdTabEntry{
+		String: `DirectedGraph : digraph	<< true, nil >>`,
+		Id:         "DirectedGraph",
+		NTType:     4,
+		Index:      7,
+		NumSymbols: 1,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return true, nil
+		},
+	},
+	ProdTabEntry{
+		String: `StmtList : Stmt OptSemi	<< astx.NewStmtList(X[0]) >>`,
+		Id:         "StmtList",
+		NTType:     5,
+		Index:      8,
+		NumSymbols: 2,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return astx.NewStmtList(X[0])
+		},
+	},
+	ProdTabEntry{
+		String: `StmtList : StmtList Stmt OptSemi	<< astx.AppendStmt(X[0], X[1]) >>`,
+		Id:         "StmtList",
+		NTType:     5,
+		Index:      9,
+		NumSymbols: 3,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return astx.AppendStmt(X[0], X[1])
+		},
+	},
+	ProdTabEntry{
+		String: `OptStmtList : empty	<<  >>`,
+		Id:         "OptStmtList",
+		NTType:     6,
+		Index:      10,
+		NumSymbols: 0,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return nil, nil
+		},
+	},
+	ProdTabEntry{
+		String: `OptStmtList : StmtList	<<  >>`,
+		Id:         "OptStmtList",
+		NTType:     6,
+		Index:      11,
+		NumSymbols: 1,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return X[0], nil
+		},
+	},
+	ProdTabEntry{
+		String: `Stmt : NodeStmt	<<  >>`,
+		Id:         "Stmt",
+		NTType:     7,
+		Index:      12,
+		NumSymbols: 1,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return X[0], nil
+		},
+	},
+	ProdTabEntry{
+		String: `Stmt : EdgeStmt	<<  >>`,
+		Id:         "Stmt",
+		NTType:     7,
+		Index:      13,
+		NumSymbols: 1,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return X[0], nil
+		},
+	},
+	ProdTabEntry{
+		String: `Stmt : AttrStmt	<<  >>`,
+		Id:         "Stmt",
+		NTType:     7,
+		Index:      14,
+		NumSymbols: 1,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return X[0], nil
+		},
+	},
+	ProdTabEntry{
+		String: `Stmt : Attr	<<  >>`,
+		Id:         "Stmt",
+		NTType:     7,
+		Index:      15,
+		NumSymbols: 1,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return X[0], nil
+		},
+	},
+	ProdTabEntry{
+		String: `Stmt : Subgraph	<<  >>`,
+		Id:         "Stmt",
+		NTType:     7,
+		Index:      16,
+		NumSymbols: 1,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return X[0], nil
+		},
+	},
+	ProdTabEntry{
+		String: `OptSemi : empty	<<  >>`,
+		Id:         "OptSemi",
+		NTType:     8,
+		Index:      17,
+		NumSymbols: 0,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return nil, nil
+		},
+	},
+	ProdTabEntry{
+		String: `OptSemi : ";"	<<  >>`,
+		Id:         "OptSemi",
+		NTType:     8,
+		Index:      18,
+		NumSymbols: 1,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return X[0], nil
+		},
+	},
+	ProdTabEntry{
+		String: `NodeStmt : Node OptAttrList	<< astx.NewNodeStmt(X[0], X[1]) >>`,
+		Id:         "NodeStmt",
+		NTType:     9,
+		Index:      19,
+		NumSymbols: 2,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return astx.NewNodeStmt(X[0], X[1])
+		},
+	},
+	ProdTabEntry{
+		String: `EdgeStmt : Vertex Edge OptAttrList	<< astx.NewEdgeStmt(X[0], X[1], X[2]) >>`,
+		Id:         "EdgeStmt",
+		NTType:     10,
+		Index:      20,
+		NumSymbols: 3,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return astx.NewEdgeStmt(X[0], X[1], X[2])
+		},
+	},
+	ProdTabEntry{
+		String: `Edge : DirectedEdge Vertex OptEdge	<< astx.NewEdge(X[0], X[1], X[2]) >>`,
+		Id:         "Edge",
+		NTType:     11,
+		Index:      21,
+		NumSymbols: 3,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return astx.NewEdge(X[0], X[1], X[2])
+		},
+	},
+	ProdTabEntry{
+		String: `DirectedEdge : "--"	<< false, nil >>`,
+		Id:         "DirectedEdge",
+		NTType:     12,
+		Index:      22,
+		NumSymbols: 1,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return false, nil
+		},
+	},
+	ProdTabEntry{
+		String: `DirectedEdge : "->"	<< true, nil >>`,
+		Id:         "DirectedEdge",
+		NTType:     12,
+		Index:      23,
+		NumSymbols: 1,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return true, nil
+		},
+	},
+	ProdTabEntry{
+		String: `OptEdge : empty	<<  >>`,
+		Id:         "OptEdge",
+		NTType:     13,
+		Index:      24,
+		NumSymbols: 0,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return nil, nil
+		},
+	},
+	ProdTabEntry{
+		String: `OptEdge : Edge	<<  >>`,
+		Id:         "OptEdge",
+		NTType:     13,
+		Index:      25,
+		NumSymbols: 1,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return X[0], nil
+		},
+	},
+	ProdTabEntry{
+		String: `AttrStmt : Component AttrList	<< astx.NewAttrStmt(X[0], X[1]) >>`,
+		Id:         "AttrStmt",
+		NTType:     14,
+		Index:      26,
+		NumSymbols: 2,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return astx.NewAttrStmt(X[0], X[1])
+		},
+	},
+	ProdTabEntry{
+		String: `Component : graphx	<< ast.GraphKind, nil >>`,
+		Id:         "Component",
+		NTType:     15,
+		Index:      27,
+		NumSymbols: 1,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return ast.GraphKind, nil
+		},
+	},
+	ProdTabEntry{
+		String: `Component : node	<< ast.NodeKind, nil >>`,
+		Id:         "Component",
+		NTType:     15,
+		Index:      28,
+		NumSymbols: 1,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return ast.NodeKind, nil
+		},
+	},
+	ProdTabEntry{
+		String: `Component : edge	<< ast.EdgeKind, nil >>`,
+		Id:         "Component",
+		NTType:     15,
+		Index:      29,
+		NumSymbols: 1,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return ast.EdgeKind, nil
+		},
+	},
+	ProdTabEntry{
+		String: `AttrList : "[" OptAList "]"	<< X[1], nil >>`,
+		Id:         "AttrList",
+		NTType:     16,
+		Index:      30,
+		NumSymbols: 3,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return X[1], nil
+		},
+	},
+	ProdTabEntry{
+		String: `AttrList : AttrList "[" OptAList "]"	<< astx.AppendAttrList(X[0], X[2]) >>`,
+		Id:         "AttrList",
+		NTType:     16,
+		Index:      31,
+		NumSymbols: 4,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return astx.AppendAttrList(X[0], X[2])
+		},
+	},
+	ProdTabEntry{
+		String: `OptAttrList : empty	<<  >>`,
+		Id:         "OptAttrList",
+		NTType:     17,
+		Index:      32,
+		NumSymbols: 0,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return nil, nil
+		},
+	},
+	ProdTabEntry{
+		String: `OptAttrList : AttrList	<<  >>`,
+		Id:         "OptAttrList",
+		NTType:     17,
+		Index:      33,
+		NumSymbols: 1,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return X[0], nil
+		},
+	},
+	ProdTabEntry{
+		String: `AList : Attr OptSep	<< astx.NewAttrList(X[0]) >>`,
+		Id:         "AList",
+		NTType:     18,
+		Index:      34,
+		NumSymbols: 2,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return astx.NewAttrList(X[0])
+		},
+	},
+	ProdTabEntry{
+		String: `AList : AList Attr OptSep	<< astx.AppendAttr(X[0], X[1]) >>`,
+		Id:         "AList",
+		NTType:     18,
+		Index:      35,
+		NumSymbols: 3,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return astx.AppendAttr(X[0], X[1])
+		},
+	},
+	ProdTabEntry{
+		String: `OptAList : empty	<<  >>`,
+		Id:         "OptAList",
+		NTType:     19,
+		Index:      36,
+		NumSymbols: 0,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return nil, nil
+		},
+	},
+	ProdTabEntry{
+		String: `OptAList : AList	<<  >>`,
+		Id:         "OptAList",
+		NTType:     19,
+		Index:      37,
+		NumSymbols: 1,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return X[0], nil
+		},
+	},
+	ProdTabEntry{
+		String: `OptSep : empty	<<  >>`,
+		Id:         "OptSep",
+		NTType:     20,
+		Index:      38,
+		NumSymbols: 0,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return nil, nil
+		},
+	},
+	ProdTabEntry{
+		String: `OptSep : ";"	<<  >>`,
+		Id:         "OptSep",
+		NTType:     20,
+		Index:      39,
+		NumSymbols: 1,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return X[0], nil
+		},
+	},
+	ProdTabEntry{
+		String: `OptSep : ","	<<  >>`,
+		Id:         "OptSep",
+		NTType:     20,
+		Index:      40,
+		NumSymbols: 1,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return X[0], nil
+		},
+	},
+	ProdTabEntry{
+		String: `Attr : ID "=" ID	<< astx.NewAttr(X[0], X[2]) >>`,
+		Id:         "Attr",
+		NTType:     21,
+		Index:      41,
+		NumSymbols: 3,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return astx.NewAttr(X[0], X[2])
+		},
+	},
+	ProdTabEntry{
+		String: `Subgraph : OptSubgraphID "{" OptStmtList "}"	<< astx.NewSubgraph(X[0], X[2]) >>`,
+		Id:         "Subgraph",
+		NTType:     22,
+		Index:      42,
+		NumSymbols: 4,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return astx.NewSubgraph(X[0], X[2])
+		},
+	},
+	ProdTabEntry{
+		String: `OptSubgraphID : empty	<<  >>`,
+		Id:         "OptSubgraphID",
+		NTType:     23,
+		Index:      43,
+		NumSymbols: 0,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return nil, nil
+		},
+	},
+	ProdTabEntry{
+		String: `OptSubgraphID : subgraph OptID	<< X[1], nil >>`,
+		Id:         "OptSubgraphID",
+		NTType:     23,
+		Index:      44,
+		NumSymbols: 2,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return X[1], nil
+		},
+	},
+	ProdTabEntry{
+		String: `Vertex : Node	<<  >>`,
+		Id:         "Vertex",
+		NTType:     24,
+		Index:      45,
+		NumSymbols: 1,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return X[0], nil
+		},
+	},
+	ProdTabEntry{
+		String: `Vertex : Subgraph	<<  >>`,
+		Id:         "Vertex",
+		NTType:     24,
+		Index:      46,
+		NumSymbols: 1,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return X[0], nil
+		},
+	},
+	ProdTabEntry{
+		String: `Node : ID OptPort	<< astx.NewNode(X[0], X[1]) >>`,
+		Id:         "Node",
+		NTType:     25,
+		Index:      47,
+		NumSymbols: 2,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return astx.NewNode(X[0], X[1])
+		},
+	},
+	ProdTabEntry{
+		String: `Port : ":" ID	<< astx.NewPort(X[1], nil) >>`,
+		Id:         "Port",
+		NTType:     26,
+		Index:      48,
+		NumSymbols: 2,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return astx.NewPort(X[1], nil)
+		},
+	},
+	ProdTabEntry{
+		String: `Port : ":" ID ":" ID	<< astx.NewPort(X[1], X[3]) >>`,
+		Id:         "Port",
+		NTType:     26,
+		Index:      49,
+		NumSymbols: 4,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return astx.NewPort(X[1], X[3])
+		},
+	},
+	ProdTabEntry{
+		String: `OptPort : empty	<<  >>`,
+		Id:         "OptPort",
+		NTType:     27,
+		Index:      50,
+		NumSymbols: 0,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return nil, nil
+		},
+	},
+	ProdTabEntry{
+		String: `OptPort : Port	<<  >>`,
+		Id:         "OptPort",
+		NTType:     27,
+		Index:      51,
+		NumSymbols: 1,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return X[0], nil
+		},
+	},
+	ProdTabEntry{
+		String: `ID : id	<< astx.NewID(X[0]) >>`,
+		Id:         "ID",
+		NTType:     28,
+		Index:      52,
+		NumSymbols: 1,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return astx.NewID(X[0])
+		},
+	},
+	ProdTabEntry{
+		String: `OptID : empty	<< "", nil >>`,
+		Id:         "OptID",
+		NTType:     29,
+		Index:      53,
+		NumSymbols: 0,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return "", nil
+		},
+	},
+	ProdTabEntry{
+		String: `OptID : ID	<<  >>`,
+		Id:         "OptID",
+		NTType:     29,
+		Index:      54,
+		NumSymbols: 1,
+		ReduceFunc: func(X []Attrib) (Attrib, error) {
+			return X[0], nil
+		},
+	},
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/paste_copyright.bash b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/paste_copyright.bash
new file mode 100755
index 00000000..569bd925
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/paste_copyright.bash
@@ -0,0 +1,17 @@
+#!/usr/bin/env bash
+
+find . -type f -name '*.go' \
+| xargs sed -i -e "s|// Code generated by gocc; DO NOT EDIT.|\
+// Code generated by gocc; DO NOT EDIT.\n\
+\n\
+// This file is dual licensed under CC0 and The gonum license.\n\
+//\n\
+// Copyright ©2017 The gonum Authors. All rights reserved.\n\
+// Use of this source code is governed by a BSD-style\n\
+// license that can be found in the LICENSE file.\n\
+//\n\
+// Copyright ©2017 Robin Eklind.\n\
+// This file is made available under a Creative Commons CC0 1.0\n\
+// Universal Public Domain Dedication.\
+|"
+
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/attr.dot b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/attr.dot
new file mode 100644
index 00000000..dabe9734
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/attr.dot
@@ -0,0 +1,4 @@
+digraph {
+	bgcolor=transparent
+	A
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/attr_lists.dot b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/attr_lists.dot
new file mode 100644
index 00000000..b71411cd
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/attr_lists.dot
@@ -0,0 +1,3 @@
+digraph {
+	A [style=filled] [fillcolor=red]
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/attr_lists.golden b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/attr_lists.golden
new file mode 100644
index 00000000..14316d93
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/attr_lists.golden
@@ -0,0 +1,3 @@
+digraph {
+	A [style=filled fillcolor=red]
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/attr_sep.dot b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/attr_sep.dot
new file mode 100644
index 00000000..ef47a120
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/attr_sep.dot
@@ -0,0 +1,3 @@
+digraph {
+	A [style=filled, fillcolor=red; color=blue]
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/attr_sep.golden b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/attr_sep.golden
new file mode 100644
index 00000000..95bfd972
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/attr_sep.golden
@@ -0,0 +1,3 @@
+digraph {
+	A [style=filled fillcolor=red color=blue]
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/attr_stmt.dot b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/attr_stmt.dot
new file mode 100644
index 00000000..e87d70a4
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/attr_stmt.dot
@@ -0,0 +1,6 @@
+digraph {
+	graph [bgcolor=transparent]
+	node [style=filled fillcolor=white]
+	edge [minlen=2]
+	A -> B
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/backslash_newline_id.dot b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/backslash_newline_id.dot
new file mode 100644
index 00000000..81051384
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/backslash_newline_id.dot
@@ -0,0 +1,4 @@
+digraph {
+	A [name="hello \
+world"]
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/backslash_newline_id.golden b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/backslash_newline_id.golden
new file mode 100644
index 00000000..449c3a3e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/backslash_newline_id.golden
@@ -0,0 +1,3 @@
+digraph {
+	A [name="hello world"]
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/digraph.dot b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/digraph.dot
new file mode 100644
index 00000000..1063ebfa
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/digraph.dot
@@ -0,0 +1,3 @@
+digraph {
+	A -> B
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/edge_stmt.dot b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/edge_stmt.dot
new file mode 100644
index 00000000..019d23d7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/edge_stmt.dot
@@ -0,0 +1,4 @@
+digraph {
+	A -> B -> C
+	D -> E [color=red minlen=2]
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/empty.dot b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/empty.dot
new file mode 100644
index 00000000..418b7bca
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/empty.dot
@@ -0,0 +1,2 @@
+graph {
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/empty_attr.dot b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/empty_attr.dot
new file mode 100644
index 00000000..b92d60e5
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/empty_attr.dot
@@ -0,0 +1,3 @@
+digraph {
+	A []
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/empty_attr.golden b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/empty_attr.golden
new file mode 100644
index 00000000..369e4495
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/empty_attr.golden
@@ -0,0 +1,3 @@
+digraph {
+	A
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/error.dot b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/error.dot
new file mode 100644
index 00000000..ad77f61f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/error.dot
@@ -0,0 +1,3 @@
+digraph {
+	A ~ B
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/graph.dot b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/graph.dot
new file mode 100644
index 00000000..0524c144
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/graph.dot
@@ -0,0 +1,3 @@
+graph {
+	A -- B
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/multi.dot b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/multi.dot
new file mode 100644
index 00000000..21945188
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/multi.dot
@@ -0,0 +1,6 @@
+digraph {
+	A -> B
+}
+digraph {
+	C -> D
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/named_graph.dot b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/named_graph.dot
new file mode 100644
index 00000000..3fc680da
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/named_graph.dot
@@ -0,0 +1,3 @@
+graph G {
+	A
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/node_stmt.dot b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/node_stmt.dot
new file mode 100644
index 00000000..369e4495
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/node_stmt.dot
@@ -0,0 +1,3 @@
+digraph {
+	A
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/port.dot b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/port.dot
new file mode 100644
index 00000000..1d4bf415
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/port.dot
@@ -0,0 +1,11 @@
+digraph {
+	A:ne -> B:sw
+	C:foo -> D:bar:se
+	E:_ -> F
+	G:n
+	H:e
+	I:s
+	J:w
+	K:nw
+	L:c
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/port.golden b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/port.golden
new file mode 100644
index 00000000..18ca1f30
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/port.golden
@@ -0,0 +1,11 @@
+digraph {
+	A:ne -> B:sw
+	C:foo -> D:bar:se
+	E -> F
+	G:n
+	H:e
+	I:s
+	J:w
+	K:nw
+	L:c
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/quoted_id.dot b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/quoted_id.dot
new file mode 100644
index 00000000..0c3b5652
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/quoted_id.dot
@@ -0,0 +1,3 @@
+digraph {
+	"A" -> "B" ["color"="red"]
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/semi.dot b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/semi.dot
new file mode 100644
index 00000000..c8bcbf34
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/semi.dot
@@ -0,0 +1,3 @@
+digraph {
+	A -> B; C
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/semi.golden b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/semi.golden
new file mode 100644
index 00000000..61bca268
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/semi.golden
@@ -0,0 +1,4 @@
+digraph {
+	A -> B
+	C
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/strict.dot b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/strict.dot
new file mode 100644
index 00000000..bf222ad9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/strict.dot
@@ -0,0 +1,4 @@
+strict digraph {
+	A -> B
+	A -> B
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/subgraph.dot b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/subgraph.dot
new file mode 100644
index 00000000..a03667dd
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/subgraph.dot
@@ -0,0 +1,5 @@
+digraph {
+	{A}
+	subgraph {B}
+	subgraph S {C}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/subgraph.golden b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/subgraph.golden
new file mode 100644
index 00000000..0cd6fe72
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/subgraph.golden
@@ -0,0 +1,5 @@
+digraph {
+	{A}
+	{B}
+	subgraph S {C}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/subgraph_vertex.dot b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/subgraph_vertex.dot
new file mode 100644
index 00000000..b414ad84
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/testdata/subgraph_vertex.dot
@@ -0,0 +1,3 @@
+digraph {
+	{A B} -> C
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/token/token.go b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/token/token.go
new file mode 100644
index 00000000..1492df0d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/token/token.go
@@ -0,0 +1,116 @@
+// Code generated by gocc; DO NOT EDIT.
+
+// This file is dual licensed under CC0 and The gonum license.
+//
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Copyright ©2017 Robin Eklind.
+// This file is made available under a Creative Commons CC0 1.0
+// Universal Public Domain Dedication.
+
+package token
+
+import (
+	"fmt"
+)
+
+type Token struct {
+	Type
+	Lit []byte
+	Pos
+}
+
+type Type int
+
+const (
+	INVALID Type = iota
+	EOF
+)
+
+type Pos struct {
+	Offset int
+	Line   int
+	Column int
+}
+
+func (p Pos) String() string {
+	return fmt.Sprintf("Pos(offset=%d, line=%d, column=%d)", p.Offset, p.Line, p.Column)
+}
+
+type TokenMap struct {
+	typeMap []string
+	idMap   map[string]Type
+}
+
+func (m TokenMap) Id(tok Type) string {
+	if int(tok) < len(m.typeMap) {
+		return m.typeMap[tok]
+	}
+	return "unknown"
+}
+
+func (m TokenMap) Type(tok string) Type {
+	if typ, exist := m.idMap[tok]; exist {
+		return typ
+	}
+	return INVALID
+}
+
+func (m TokenMap) TokenString(tok *Token) string {
+	//TODO: refactor to print pos & token string properly
+	return fmt.Sprintf("%s(%d,%s)", m.Id(tok.Type), tok.Type, tok.Lit)
+}
+
+func (m TokenMap) StringType(typ Type) string {
+	return fmt.Sprintf("%s(%d)", m.Id(typ), typ)
+}
+
+var TokMap = TokenMap{
+	typeMap: []string{
+		"INVALID",
+		"$",
+		"{",
+		"}",
+		"empty",
+		"strict",
+		"graphx",
+		"digraph",
+		";",
+		"--",
+		"->",
+		"node",
+		"edge",
+		"[",
+		"]",
+		",",
+		"=",
+		"subgraph",
+		":",
+		"id",
+	},
+
+	idMap: map[string]Type{
+		"INVALID":  0,
+		"$":        1,
+		"{":        2,
+		"}":        3,
+		"empty":    4,
+		"strict":   5,
+		"graphx":   6,
+		"digraph":  7,
+		";":        8,
+		"--":       9,
+		"->":       10,
+		"node":     11,
+		"edge":     12,
+		"[":        13,
+		"]":        14,
+		",":        15,
+		"=":        16,
+		"subgraph": 17,
+		":":        18,
+		"id":       19,
+	},
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/util/litconv.go b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/util/litconv.go
new file mode 100644
index 00000000..ed6e348b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/util/litconv.go
@@ -0,0 +1,118 @@
+// Code generated by gocc; DO NOT EDIT.
+
+// This file is dual licensed under CC0 and The gonum license.
+//
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Copyright ©2017 Robin Eklind.
+// This file is made available under a Creative Commons CC0 1.0
+// Universal Public Domain Dedication.
+
+package util
+
+import (
+	"fmt"
+	"strconv"
+	"unicode"
+	"unicode/utf8"
+)
+
+/* Interface */
+
+/*
+Convert the literal value of a scanned token to rune
+*/
+func RuneValue(lit []byte) rune {
+	if lit[1] == '\\' {
+		return escapeCharVal(lit)
+	}
+	r, size := utf8.DecodeRune(lit[1:])
+	if size != len(lit)-2 {
+		panic(fmt.Sprintf("Error decoding rune. Lit: %s, rune: %d, size%d\n", lit, r, size))
+	}
+	return r
+}
+
+/*
+Convert the literal value of a scanned token to int64
+*/
+func IntValue(lit []byte) (int64, error) {
+	return strconv.ParseInt(string(lit), 10, 64)
+}
+
+/*
+Convert the literal value of a scanned token to uint64
+*/
+func UintValue(lit []byte) (uint64, error) {
+	return strconv.ParseUint(string(lit), 10, 64)
+}
+
+/* Util */
+
+func escapeCharVal(lit []byte) rune {
+	var i, base, max uint32
+	offset := 2
+	switch lit[offset] {
+	case 'a':
+		return '\a'
+	case 'b':
+		return '\b'
+	case 'f':
+		return '\f'
+	case 'n':
+		return '\n'
+	case 'r':
+		return '\r'
+	case 't':
+		return '\t'
+	case 'v':
+		return '\v'
+	case '\\':
+		return '\\'
+	case '\'':
+		return '\''
+	case '0', '1', '2', '3', '4', '5', '6', '7':
+		i, base, max = 3, 8, 255
+	case 'x':
+		i, base, max = 2, 16, 255
+		offset++
+	case 'u':
+		i, base, max = 4, 16, unicode.MaxRune
+		offset++
+	case 'U':
+		i, base, max = 8, 16, unicode.MaxRune
+		offset++
+	default:
+		panic(fmt.Sprintf("Error decoding character literal: %s\n", lit))
+	}
+
+	var x uint32
+	for ; i > 0 && offset < len(lit)-1; i-- {
+		ch, size := utf8.DecodeRune(lit[offset:])
+		offset += size
+		d := uint32(digitVal(ch))
+		if d >= base {
+			panic(fmt.Sprintf("charVal(%s): illegal character (%c) in escape sequence. size=%d, offset=%d", lit, ch, size, offset))
+		}
+		x = x*base + d
+	}
+	if x > max || 0xD800 <= x && x < 0xE000 {
+		panic(fmt.Sprintf("Error decoding escape char value. Lit:%s, offset:%d, escape sequence is invalid Unicode code point\n", lit, offset))
+	}
+
+	return rune(x)
+}
+
+func digitVal(ch rune) int {
+	switch {
+	case '0' <= ch && ch <= '9':
+		return int(ch) - '0'
+	case 'a' <= ch && ch <= 'f':
+		return int(ch) - 'a' + 10
+	case 'A' <= ch && ch <= 'F':
+		return int(ch) - 'A' + 10
+	}
+	return 16 // larger than any legal digit val
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/util/rune.go b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/util/rune.go
new file mode 100644
index 00000000..583b1e06
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/internal/util/rune.go
@@ -0,0 +1,49 @@
+// Code generated by gocc; DO NOT EDIT.
+
+// This file is dual licensed under CC0 and The gonum license.
+//
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Copyright ©2017 Robin Eklind.
+// This file is made available under a Creative Commons CC0 1.0
+// Universal Public Domain Dedication.
+
+package util
+
+import (
+	"fmt"
+)
+
+func RuneToString(r rune) string {
+	if r >= 0x20 && r < 0x7f {
+		return fmt.Sprintf("'%c'", r)
+	}
+	switch r {
+	case 0x07:
+		return "'\\a'"
+	case 0x08:
+		return "'\\b'"
+	case 0x0C:
+		return "'\\f'"
+	case 0x0A:
+		return "'\\n'"
+	case 0x0D:
+		return "'\\r'"
+	case 0x09:
+		return "'\\t'"
+	case 0x0b:
+		return "'\\v'"
+	case 0x5c:
+		return "'\\\\\\'"
+	case 0x27:
+		return "'\\''"
+	case 0x22:
+		return "'\\\"'"
+	}
+	if r < 0x10000 {
+		return fmt.Sprintf("\\u%04x", r)
+	}
+	return fmt.Sprintf("\\U%08x", r)
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/makeinternal.bash b/vendor/gonum.org/v1/gonum/graph/formats/dot/makeinternal.bash
new file mode 100755
index 00000000..df377163
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/makeinternal.bash
@@ -0,0 +1,4 @@
+#!/usr/bin/env bash
+
+cd internal
+make clean && make
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/sem.go b/vendor/gonum.org/v1/gonum/graph/formats/dot/sem.go
new file mode 100644
index 00000000..eb55b031
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/sem.go
@@ -0,0 +1,160 @@
+// This file is dual licensed under CC0 and The gonum license.
+//
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Copyright ©2017 Robin Eklind.
+// This file is made available under a Creative Commons CC0 1.0
+// Universal Public Domain Dedication.
+
+package dot
+
+import (
+	"fmt"
+
+	"gonum.org/v1/gonum/graph/formats/dot/ast"
+)
+
+// check validates the semantics of the given DOT file.
+func check(file *ast.File) error {
+	for _, graph := range file.Graphs {
+		// TODO: Check graph.ID for duplicates?
+		if err := checkGraph(graph); err != nil {
+			return err
+		}
+	}
+	return nil
+}
+
+// check validates the semantics of the given graph.
+func checkGraph(graph *ast.Graph) error {
+	for _, stmt := range graph.Stmts {
+		if err := checkStmt(graph, stmt); err != nil {
+			return err
+		}
+	}
+	return nil
+}
+
+// check validates the semantics of the given statement.
+func checkStmt(graph *ast.Graph, stmt ast.Stmt) error {
+	switch stmt := stmt.(type) {
+	case *ast.NodeStmt:
+		return checkNodeStmt(graph, stmt)
+	case *ast.EdgeStmt:
+		return checkEdgeStmt(graph, stmt)
+	case *ast.AttrStmt:
+		return checkAttrStmt(graph, stmt)
+	case *ast.Attr:
+		// TODO: Verify that the attribute is indeed of graph component kind.
+		return checkAttr(graph, ast.GraphKind, stmt)
+	case *ast.Subgraph:
+		return checkSubgraph(graph, stmt)
+	default:
+		panic(fmt.Sprintf("support for statement of type %T not yet implemented", stmt))
+	}
+}
+
+// checkNodeStmt validates the semantics of the given node statement.
+func checkNodeStmt(graph *ast.Graph, stmt *ast.NodeStmt) error {
+	if err := checkNode(graph, stmt.Node); err != nil {
+		return err
+	}
+	for _, attr := range stmt.Attrs {
+		// TODO: Verify that the attribute is indeed of node component kind.
+		if err := checkAttr(graph, ast.NodeKind, attr); err != nil {
+			return err
+		}
+	}
+	return nil
+}
+
+// checkEdgeStmt validates the semantics of the given edge statement.
+func checkEdgeStmt(graph *ast.Graph, stmt *ast.EdgeStmt) error {
+	// TODO: if graph.Strict, check for multi-edges.
+	if err := checkVertex(graph, stmt.From); err != nil {
+		return err
+	}
+	for _, attr := range stmt.Attrs {
+		// TODO: Verify that the attribute is indeed of edge component kind.
+		if err := checkAttr(graph, ast.EdgeKind, attr); err != nil {
+			return err
+		}
+	}
+	return checkEdge(graph, stmt.From, stmt.To)
+}
+
+// checkEdge validates the semantics of the given edge.
+func checkEdge(graph *ast.Graph, from ast.Vertex, to *ast.Edge) error {
+	if !graph.Directed && to.Directed {
+		return fmt.Errorf("undirected graph %q contains directed edge from %q to %q", graph.ID, from, to.Vertex)
+	}
+	if err := checkVertex(graph, to.Vertex); err != nil {
+		return err
+	}
+	if to.To != nil {
+		return checkEdge(graph, to.Vertex, to.To)
+	}
+	return nil
+}
+
+// checkAttrStmt validates the semantics of the given attribute statement.
+func checkAttrStmt(graph *ast.Graph, stmt *ast.AttrStmt) error {
+	for _, attr := range stmt.Attrs {
+		if err := checkAttr(graph, stmt.Kind, attr); err != nil {
+			return err
+		}
+	}
+	return nil
+}
+
+// checkAttr validates the semantics of the given attribute for the given
+// component kind.
+func checkAttr(graph *ast.Graph, kind ast.Kind, attr *ast.Attr) error {
+	switch kind {
+	case ast.GraphKind:
+		// TODO: Validate key-value pairs for graphs.
+		return nil
+	case ast.NodeKind:
+		// TODO: Validate key-value pairs for nodes.
+		return nil
+	case ast.EdgeKind:
+		// TODO: Validate key-value pairs for edges.
+		return nil
+	default:
+		panic(fmt.Sprintf("support for component kind %v not yet supported", kind))
+	}
+}
+
+// checkSubgraph validates the semantics of the given subgraph.
+func checkSubgraph(graph *ast.Graph, subgraph *ast.Subgraph) error {
+	// TODO: Check subgraph.ID for duplicates?
+	for _, stmt := range subgraph.Stmts {
+		// TODO: Refine handling of subgraph statements?
+		//    checkSubgraphStmt(graph, subgraph, stmt)
+		if err := checkStmt(graph, stmt); err != nil {
+			return err
+		}
+	}
+	return nil
+}
+
+// checkVertex validates the semantics of the given vertex.
+func checkVertex(graph *ast.Graph, vertex ast.Vertex) error {
+	switch vertex := vertex.(type) {
+	case *ast.Node:
+		return checkNode(graph, vertex)
+	case *ast.Subgraph:
+		return checkSubgraph(graph, vertex)
+	default:
+		panic(fmt.Sprintf("support for vertex of type %T not yet supported", vertex))
+	}
+}
+
+// checNode validates the semantics of the given node.
+func checkNode(graph *ast.Graph, node *ast.Node) error {
+	// TODO: Check node.ID for duplicates?
+	// TODO: Validate node.Port.
+	return nil
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/testdata/.gitignore b/vendor/gonum.org/v1/gonum/graph/formats/dot/testdata/.gitignore
new file mode 100644
index 00000000..90453be2
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/testdata/.gitignore
@@ -0,0 +1,5 @@
+*.dot
+*.png
+graphviz
+input
+output
diff --git a/vendor/gonum.org/v1/gonum/graph/formats/dot/testdata/Makefile b/vendor/gonum.org/v1/gonum/graph/formats/dot/testdata/Makefile
new file mode 100644
index 00000000..c3bfcb9b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/formats/dot/testdata/Makefile
@@ -0,0 +1,106 @@
+# Dependencies:
+#
+# * imgcmp
+#    go get github.com/mewkiz/cmd/imgcmp
+# * dotfmt
+#    go get github.com/graphism/dot/cmd/dotfmt
+# * dot
+#    sudo pacman -S graphviz
+# * recode
+#    sudo pacman -S recode
+
+DOT=$(wildcard *.dot)
+
+# Skip DOT files for which the generated PNG images mismatch.
+#
+# ref: https://github.com/graphism/dot/issues/2
+#
+#    pixel colors differ at x=550, y=1885
+DOT:=$(filter-out b51.dot, $(DOT))
+#    pixel colors differ at x=5395, y=1920
+DOT:=$(filter-out b106.dot, $(DOT))
+
+# Skip segfaulting files.
+#
+#    Segmentation fault (core dumped)
+DOT:=$(filter-out b15.dot, $(DOT))
+#    Segmentation fault (core dumped)
+DOT:=$(filter-out b81.dot, $(DOT))
+#    *** stack smashing detected ***: dot terminated
+DOT:=$(filter-out sides.dot, $(DOT))
+#    *** stack smashing detected ***: dot terminated
+DOT:=$(filter-out tee.dot, $(DOT))
+
+# Skip DOT files above 100 kB.
+DOT:=$(filter-out 4elt.dot, $(DOT))
+DOT:=$(filter-out b29.dot, $(DOT))
+DOT:=$(filter-out b81.dot, $(DOT))
+DOT:=$(filter-out b100.dot, $(DOT))
+DOT:=$(filter-out b102.dot, $(DOT))
+DOT:=$(filter-out b103.dot, $(DOT))
+DOT:=$(filter-out b104.dot, $(DOT))
+DOT:=$(filter-out root.dot, $(DOT))
+DOT:=$(filter-out root_circo.dot, $(DOT))
+DOT:=$(filter-out root_twopi.dot, $(DOT))
+
+# Skip invalid DOT file.
+#
+#    Error: No or improper image file="eqn.png"
+#    in label of node struct1
+DOT:=$(filter-out html4.dot, $(DOT))
+
+# Skip multi-graph DOT file which outputs to standard output.
+DOT:=$(filter-out multi.dot, $(DOT))
+
+# *.dot -> *.png
+PNG=$(DOT:.dot=.png)
+
+INPUT_PNG=$(addprefix input/,$(PNG))
+OUTPUT_PNG=$(addprefix output/,$(PNG))
+
+all:
+
+test: input $(INPUT_PNG) output $(OUTPUT_PNG)
+	@echo "PASS"
+
+input:
+	mkdir -p $@
+	dot -V
+
+input/%.png: %.dot
+	dot -Tpng -o $@ $<
+
+output:
+	mkdir -p $@
+
+output/%.png: %.dot
+	dotfmt -o "output/$<" $<
+	dot -Tpng -o $@ "output/$<"
+	imgcmp "input/$(notdir $@)" $@
+
+fetch: graphviz
+	# Copy *.gv and *.dot files.
+	find graphviz -type f -name '*.gv' -not -wholename "graphviz/rtest/share/b545.gv" -not -name "base.gv" | xargs -I '{}' cp "{}" .
+	find graphviz -type f -name '*.dot' | xargs -I '{}' cp "{}" .
+
+	# Rename *.gv to *.dot.
+	#rename .gv .dot *.gv
+	ls *.gv | xargs -I '{}' basename "{}" .gv | xargs -I '{}' mv "{}.gv" "{}.dot"
+
+	# Remove execute permissions.
+	chmod 0644 *.dot
+
+	# Convert Latin1 encoded files to UTF-8.
+	grep -l "charset=latin1" *.dot | xargs -I '{}' recode ISO-8859-1..UTF8 "{}"
+	recode ISO-8859-1..UTF8 Latin1.dot
+
+	# Clean up.
+	rm -rf graphviz
+
+graphviz:
+	git clone https://github.com/ellson/graphviz.git
+
+clean:
+	rm -rf *.dot input output
+
+.PHONY: all test fetch clean
diff --git a/vendor/gonum.org/v1/gonum/graph/graph.go b/vendor/gonum.org/v1/gonum/graph/graph.go
new file mode 100644
index 00000000..0ca587d8
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/graph.go
@@ -0,0 +1,247 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package graph
+
+// Node is a graph node. It returns a graph-unique integer ID.
+type Node interface {
+	ID() int64
+}
+
+// Edge is a graph edge. In directed graphs, the direction of the
+// edge is given from -> to, otherwise the edge is semantically
+// unordered.
+type Edge interface {
+	From() Node
+	To() Node
+}
+
+// WeightedEdge is a weighted graph edge. In directed graphs, the direction
+// of the edge is given from -> to, otherwise the edge is semantically
+// unordered.
+type WeightedEdge interface {
+	Edge
+	Weight() float64
+}
+
+// Graph is a generalized graph.
+type Graph interface {
+	// Has returns whether the node exists within the graph.
+	Has(Node) bool
+
+	// Nodes returns all the nodes in the graph.
+	Nodes() []Node
+
+	// From returns all nodes that can be reached directly
+	// from the given node.
+	From(Node) []Node
+
+	// HasEdgeBetween returns whether an edge exists between
+	// nodes x and y without considering direction.
+	HasEdgeBetween(x, y Node) bool
+
+	// Edge returns the edge from u to v if such an edge
+	// exists and nil otherwise. The node v must be directly
+	// reachable from u as defined by the From method.
+	Edge(u, v Node) Edge
+}
+
+// Weighted is a weighted graph.
+type Weighted interface {
+	Graph
+
+	// WeightedEdge returns the weighted edge from u to v if
+	// such an edge exists and nil otherwise. The node v must
+	// be directly reachable from u as defined by the
+	// From method.
+	WeightedEdge(u, v Node) WeightedEdge
+
+	// Weight returns the weight for the edge between
+	// x and y if Edge(x, y) returns a non-nil Edge.
+	// If x and y are the same node or there is no
+	// joining edge between the two nodes the weight
+	// value returned is implementation dependent.
+	// Weight returns true if an edge exists between
+	// x and y or if x and y have the same ID, false
+	// otherwise.
+	Weight(x, y Node) (w float64, ok bool)
+}
+
+// Undirected is an undirected graph.
+type Undirected interface {
+	Graph
+
+	// EdgeBetween returns the edge between nodes x and y.
+	EdgeBetween(x, y Node) Edge
+}
+
+// WeightedUndirected is a weighted undirected graph.
+type WeightedUndirected interface {
+	Weighted
+
+	// WeightedEdgeBetween returns the edge between nodes
+	// x and y.
+	WeightedEdgeBetween(x, y Node) WeightedEdge
+}
+
+// Directed is a directed graph.
+type Directed interface {
+	Graph
+
+	// HasEdgeFromTo returns whether an edge exists
+	// in the graph from u to v.
+	HasEdgeFromTo(u, v Node) bool
+
+	// To returns all nodes that can reach directly
+	// to the given node.
+	To(Node) []Node
+}
+
+// WeightedDirected is a weighted directed graph.
+type WeightedDirected interface {
+	Weighted
+
+	// HasEdgeFromTo returns whether an edge exists
+	// in the graph from u to v.
+	HasEdgeFromTo(u, v Node) bool
+
+	// To returns all nodes that can reach directly
+	// to the given node.
+	To(Node) []Node
+}
+
+// NodeAdder is an interface for adding arbitrary nodes to a graph.
+type NodeAdder interface {
+	// NewNode returns a new Node with a unique
+	// arbitrary ID.
+	NewNode() Node
+
+	// Adds a node to the graph. AddNode panics if
+	// the added node ID matches an existing node ID.
+	AddNode(Node)
+}
+
+// NodeRemover is an interface for removing nodes from a graph.
+type NodeRemover interface {
+	// RemoveNode removes a node from the graph, as
+	// well as any edges attached to it. If the node
+	// is not in the graph it is a no-op.
+	RemoveNode(Node)
+}
+
+// EdgeAdder is an interface for adding edges to a graph.
+type EdgeAdder interface {
+	// NewEdge returns a new Edge from the source to the destination node.
+	NewEdge(from, to Node) Edge
+
+	// SetEdge adds an edge from one node to another.
+	// If the graph supports node addition the nodes
+	// will be added if they do not exist, otherwise
+	// SetEdge will panic.
+	// The behavior of an EdgeAdder when the IDs
+	// returned by e.From and e.To are equal is
+	// implementation-dependent.
+	SetEdge(e Edge)
+}
+
+// WeightedEdgeAdder is an interface for adding edges to a graph.
+type WeightedEdgeAdder interface {
+	// NewWeightedEdge returns a new WeightedEdge from
+	// the source to the destination node.
+	NewWeightedEdge(from, to Node, weight float64) WeightedEdge
+
+	// SetWeightedEdge adds an edge from one node to
+	// another. If the graph supports node addition
+	// the nodes will be added if they do not exist,
+	// otherwise SetWeightedEdge will panic.
+	// The behavior of a WeightedEdgeAdder when the IDs
+	// returned by e.From and e.To are equal is
+	// implementation-dependent.
+	SetWeightedEdge(e WeightedEdge)
+}
+
+// EdgeRemover is an interface for removing nodes from a graph.
+type EdgeRemover interface {
+	// RemoveEdge removes the given edge, leaving the
+	// terminal nodes. If the edge does not exist it
+	// is a no-op.
+	RemoveEdge(Edge)
+}
+
+// Builder is a graph that can have nodes and edges added.
+type Builder interface {
+	NodeAdder
+	EdgeAdder
+}
+
+// WeightedBuilder is a graph that can have nodes and weighted edges added.
+type WeightedBuilder interface {
+	NodeAdder
+	WeightedEdgeAdder
+}
+
+// UndirectedBuilder is an undirected graph builder.
+type UndirectedBuilder interface {
+	Undirected
+	Builder
+}
+
+// UndirectedWeightedBuilder is an undirected weighted graph builder.
+type UndirectedWeightedBuilder interface {
+	Undirected
+	WeightedBuilder
+}
+
+// DirectedBuilder is a directed graph builder.
+type DirectedBuilder interface {
+	Directed
+	Builder
+}
+
+// DirectedWeightedBuilder is a directed weighted graph builder.
+type DirectedWeightedBuilder interface {
+	Directed
+	WeightedBuilder
+}
+
+// Copy copies nodes and edges as undirected edges from the source to the destination
+// without first clearing the destination. Copy will panic if a node ID in the source
+// graph matches a node ID in the destination.
+//
+// If the source is undirected and the destination is directed both directions will
+// be present in the destination after the copy is complete.
+func Copy(dst Builder, src Graph) {
+	nodes := src.Nodes()
+	for _, n := range nodes {
+		dst.AddNode(n)
+	}
+	for _, u := range nodes {
+		for _, v := range src.From(u) {
+			dst.SetEdge(src.Edge(u, v))
+		}
+	}
+}
+
+// CopyWeighted copies nodes and edges as undirected edges from the source to the destination
+// without first clearing the destination. Copy will panic if a node ID in the source
+// graph matches a node ID in the destination.
+//
+// If the source is undirected and the destination is directed both directions will
+// be present in the destination after the copy is complete.
+//
+// If the source is a directed graph, the destination is undirected, and a fundamental
+// cycle exists with two nodes where the edge weights differ, the resulting destination
+// graph's edge weight between those nodes is undefined. If there is a defined function
+// to resolve such conflicts, an UndirectWeighted may be used to do this.
+func CopyWeighted(dst WeightedBuilder, src Weighted) {
+	nodes := src.Nodes()
+	for _, n := range nodes {
+		dst.AddNode(n)
+	}
+	for _, u := range nodes {
+		for _, v := range src.From(u) {
+			dst.SetWeightedEdge(src.WeightedEdge(u, v))
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/graphs/gen/batagelj_brandes.go b/vendor/gonum.org/v1/gonum/graph/graphs/gen/batagelj_brandes.go
new file mode 100644
index 00000000..4c578927
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/graphs/gen/batagelj_brandes.go
@@ -0,0 +1,357 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// The functions in this file are random graph generators from the paper
+// by Batagelj and Brandes http://algo.uni-konstanz.de/publications/bb-eglrn-05.pdf
+
+package gen
+
+import (
+	"fmt"
+	"math"
+	"math/rand"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+// Gnp constructs a Gilbert’s model graph in the destination, dst, of order n. Edges
+// between nodes are formed with the probability, p. If src is not nil it is used
+// as the random source, otherwise rand.Float64 is used. The graph is constructed
+// in O(n+m) time where m is the number of edges added.
+func Gnp(dst GraphBuilder, n int, p float64, src *rand.Rand) error {
+	if p == 0 {
+		return nil
+	}
+	if p < 0 || p > 1 {
+		return fmt.Errorf("gen: bad probability: p=%v", p)
+	}
+	var r func() float64
+	if src == nil {
+		r = rand.Float64
+	} else {
+		r = src.Float64
+	}
+
+	for i := 0; i < n; i++ {
+		if !dst.Has(simple.Node(i)) {
+			dst.AddNode(simple.Node(i))
+		}
+	}
+
+	lp := math.Log(1 - p)
+
+	// Add forward edges for all graphs.
+	for v, w := 1, -1; v < n; {
+		w += 1 + int(math.Log(1-r())/lp)
+		for w >= v && v < n {
+			w -= v
+			v++
+		}
+		if v < n {
+			dst.SetEdge(simple.Edge{F: simple.Node(w), T: simple.Node(v)})
+		}
+	}
+
+	// Add backward edges for directed graphs.
+	if _, ok := dst.(graph.Directed); !ok {
+		return nil
+	}
+	for v, w := 1, -1; v < n; {
+		w += 1 + int(math.Log(1-r())/lp)
+		for w >= v && v < n {
+			w -= v
+			v++
+		}
+		if v < n {
+			dst.SetEdge(simple.Edge{F: simple.Node(v), T: simple.Node(w)})
+		}
+	}
+
+	return nil
+}
+
+// edgeNodesFor returns the pair of nodes for the ith edge in a simple
+// undirected graph. The pair is returned such that w.ID < v.ID.
+func edgeNodesFor(i int) (v, w simple.Node) {
+	// This is an algebraic simplification of the expressions described
+	// on p3 of http://algo.uni-konstanz.de/publications/bb-eglrn-05.pdf
+	v = simple.Node(0.5 + math.Sqrt(float64(1+8*i))/2)
+	w = simple.Node(i) - v*(v-1)/2
+	return v, w
+}
+
+// Gnm constructs a Erdős-Rényi model graph in the destination, dst, of
+// order n and size m. If src is not nil it is used as the random source,
+// otherwise rand.Intn is used. The graph is constructed in O(m) expected
+// time for m ≤ (n choose 2)/2.
+func Gnm(dst GraphBuilder, n, m int, src *rand.Rand) error {
+	if m == 0 {
+		return nil
+	}
+
+	hasEdge := dst.HasEdgeBetween
+	d, isDirected := dst.(graph.Directed)
+	if isDirected {
+		m /= 2
+		hasEdge = d.HasEdgeFromTo
+	}
+
+	nChoose2 := (n - 1) * n / 2
+	if m < 0 || m > nChoose2 {
+		return fmt.Errorf("gen: bad size: m=%d", m)
+	}
+
+	var rnd func(int) int
+	if src == nil {
+		rnd = rand.Intn
+	} else {
+		rnd = src.Intn
+	}
+
+	for i := 0; i < n; i++ {
+		if !dst.Has(simple.Node(i)) {
+			dst.AddNode(simple.Node(i))
+		}
+	}
+
+	// Add forward edges for all graphs.
+	for i := 0; i < m; i++ {
+		for {
+			v, w := edgeNodesFor(rnd(nChoose2))
+			e := simple.Edge{F: w, T: v}
+			if !hasEdge(e.F, e.T) {
+				dst.SetEdge(e)
+				break
+			}
+		}
+	}
+
+	// Add backward edges for directed graphs.
+	if !isDirected {
+		return nil
+	}
+	for i := 0; i < m; i++ {
+		for {
+			v, w := edgeNodesFor(rnd(nChoose2))
+			e := simple.Edge{F: v, T: w}
+			if !hasEdge(e.F, e.T) {
+				dst.SetEdge(e)
+				break
+			}
+		}
+	}
+
+	return nil
+}
+
+// SmallWorldsBB constructs a small worlds graph of order n in the destination, dst.
+// Node degree is specified by d and edge replacement by the probability, p.
+// If src is not nil it is used as the random source, otherwise rand.Float64 is used.
+// The graph is constructed in O(nd) time.
+//
+// The algorithm used is described in http://algo.uni-konstanz.de/publications/bb-eglrn-05.pdf
+func SmallWorldsBB(dst GraphBuilder, n, d int, p float64, src *rand.Rand) error {
+	if d < 1 || d > (n-1)/2 {
+		return fmt.Errorf("gen: bad degree: d=%d", d)
+	}
+	if p == 0 {
+		return nil
+	}
+	if p < 0 || p >= 1 {
+		return fmt.Errorf("gen: bad replacement: p=%v", p)
+	}
+	var (
+		rnd  func() float64
+		rndN func(int) int
+	)
+	if src == nil {
+		rnd = rand.Float64
+		rndN = rand.Intn
+	} else {
+		rnd = src.Float64
+		rndN = src.Intn
+	}
+
+	hasEdge := dst.HasEdgeBetween
+	dg, isDirected := dst.(graph.Directed)
+	if isDirected {
+		hasEdge = dg.HasEdgeFromTo
+	}
+
+	for i := 0; i < n; i++ {
+		if !dst.Has(simple.Node(i)) {
+			dst.AddNode(simple.Node(i))
+		}
+	}
+
+	nChoose2 := (n - 1) * n / 2
+
+	lp := math.Log(1 - p)
+
+	// Add forward edges for all graphs.
+	k := int(math.Log(1-rnd()) / lp)
+	m := 0
+	replace := make(map[int]int)
+	for v := 0; v < n; v++ {
+		for i := 1; i <= d; i++ {
+			if k > 0 {
+				j := v*(v-1)/2 + (v+i)%n
+				var ej simple.Edge
+				ej.T, ej.F = edgeNodesFor(j)
+				if !hasEdge(ej.From(), ej.To()) {
+					dst.SetEdge(ej)
+				}
+				k--
+				m++
+				var em simple.Edge
+				em.T, em.F = edgeNodesFor(m)
+				if !hasEdge(em.From(), em.To()) {
+					replace[j] = m
+				} else {
+					replace[j] = replace[m]
+				}
+			} else {
+				k = int(math.Log(1-rnd()) / lp)
+			}
+		}
+	}
+	for i := m + 1; i <= n*d && i < nChoose2; i++ {
+		r := rndN(nChoose2-i) + i
+		var er simple.Edge
+		er.T, er.F = edgeNodesFor(r)
+		if !hasEdge(er.From(), er.To()) {
+			dst.SetEdge(er)
+		} else {
+			er.T, er.F = edgeNodesFor(replace[r])
+			if !hasEdge(er.From(), er.To()) {
+				dst.SetEdge(er)
+			}
+		}
+		var ei simple.Edge
+		ei.T, ei.F = edgeNodesFor(i)
+		if !hasEdge(ei.From(), ei.To()) {
+			replace[r] = i
+		} else {
+			replace[r] = replace[i]
+		}
+	}
+
+	// Add backward edges for directed graphs.
+	if !isDirected {
+		return nil
+	}
+	k = int(math.Log(1-rnd()) / lp)
+	m = 0
+	replace = make(map[int]int)
+	for v := 0; v < n; v++ {
+		for i := 1; i <= d; i++ {
+			if k > 0 {
+				j := v*(v-1)/2 + (v+i)%n
+				var ej simple.Edge
+				ej.F, ej.T = edgeNodesFor(j)
+				if !hasEdge(ej.From(), ej.To()) {
+					dst.SetEdge(ej)
+				}
+				k--
+				m++
+				if !hasEdge(edgeNodesFor(m)) {
+					replace[j] = m
+				} else {
+					replace[j] = replace[m]
+				}
+			} else {
+				k = int(math.Log(1-rnd()) / lp)
+			}
+		}
+	}
+	for i := m + 1; i <= n*d && i < nChoose2; i++ {
+		r := rndN(nChoose2-i) + i
+		var er simple.Edge
+		er.F, er.T = edgeNodesFor(r)
+		if !hasEdge(er.From(), er.To()) {
+			dst.SetEdge(er)
+		} else {
+			er.F, er.T = edgeNodesFor(replace[r])
+			if !hasEdge(er.From(), er.To()) {
+				dst.SetEdge(er)
+			}
+		}
+		if !hasEdge(edgeNodesFor(i)) {
+			replace[r] = i
+		} else {
+			replace[r] = replace[i]
+		}
+	}
+
+	return nil
+}
+
+/*
+// Multigraph generators.
+
+type EdgeAdder interface {
+	AddEdge(graph.Edge)
+}
+
+func PreferentialAttachment(dst EdgeAdder, n, d int, src *rand.Rand) {
+	if d < 1 {
+		panic("gen: bad d")
+	}
+	var rnd func(int) int
+	if src == nil {
+		rnd = rand.Intn
+	} else {
+		rnd = src.Intn
+	}
+
+	m := make([]simple.Node, 2*n*d)
+	for v := 0; v < n; v++ {
+		for i := 0; i < d; i++ {
+			m[2*(v*d+i)] = simple.Node(v)
+			m[2*(v*d+i)+1] = simple.Node(m[rnd(2*v*d+i+1)])
+		}
+	}
+	for i := 0; i < n*d; i++ {
+		dst.AddEdge(simple.Edge{F: m[2*i], T: m[2*i+1], W: 1})
+	}
+}
+
+func BipartitePreferentialAttachment(dst EdgeAdder, n, d int, src *rand.Rand) {
+	if d < 1 {
+		panic("gen: bad d")
+	}
+	var rnd func(int) int
+	if src == nil {
+		rnd = rand.Intn
+	} else {
+		rnd = src.Intn
+	}
+
+	m1 := make([]simple.Node, 2*n*d)
+	m2 := make([]simple.Node, 2*n*d)
+	for v := 0; v < n; v++ {
+		for i := 0; i < d; i++ {
+			m1[2*(v*d+i)] = simple.Node(v)
+			m2[2*(v*d+i)] = simple.Node(n + v)
+
+			if r := rnd(2*v*d + i + 1); r&0x1 == 0 {
+				m1[2*(v*d+i)+1] = m2[r]
+			} else {
+				m1[2*(v*d+i)+1] = m1[r]
+			}
+
+			if r := rnd(2*v*d + i + 1); r&0x1 == 0 {
+				m2[2*(v*d+i)+1] = m1[r]
+			} else {
+				m2[2*(v*d+i)+1] = m2[r]
+			}
+		}
+	}
+	for i := 0; i < n*d; i++ {
+		dst.AddEdge(simple.Edge{F: m1[2*i], T: m1[2*i+1], W: 1})
+		dst.AddEdge(simple.Edge{F: m2[2*i], T: m2[2*i+1], W: 1})
+	}
+}
+*/
diff --git a/vendor/gonum.org/v1/gonum/graph/graphs/gen/batagelj_brandes_test.go b/vendor/gonum.org/v1/gonum/graph/graphs/gen/batagelj_brandes_test.go
new file mode 100644
index 00000000..544e2e96
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/graphs/gen/batagelj_brandes_test.go
@@ -0,0 +1,174 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gen
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+type gnUndirected struct {
+	graph.UndirectedBuilder
+	addBackwards    bool
+	addSelfLoop     bool
+	addMultipleEdge bool
+}
+
+func (g *gnUndirected) SetEdge(e graph.Edge) {
+	switch {
+	case e.From().ID() == e.To().ID():
+		g.addSelfLoop = true
+		return
+	case e.From().ID() > e.To().ID():
+		g.addBackwards = true
+	case g.UndirectedBuilder.HasEdgeBetween(e.From(), e.To()):
+		g.addMultipleEdge = true
+	}
+
+	g.UndirectedBuilder.SetEdge(e)
+}
+
+type gnDirected struct {
+	graph.DirectedBuilder
+	addSelfLoop     bool
+	addMultipleEdge bool
+}
+
+func (g *gnDirected) SetEdge(e graph.Edge) {
+	switch {
+	case e.From().ID() == e.To().ID():
+		g.addSelfLoop = true
+		return
+	case g.DirectedBuilder.HasEdgeFromTo(e.From(), e.To()):
+		g.addMultipleEdge = true
+	}
+
+	g.DirectedBuilder.SetEdge(e)
+}
+
+func TestGnpUndirected(t *testing.T) {
+	for n := 2; n <= 20; n++ {
+		for p := 0.; p <= 1; p += 0.1 {
+			g := &gnUndirected{UndirectedBuilder: simple.NewUndirectedGraph()}
+			err := Gnp(g, n, p, nil)
+			if err != nil {
+				t.Fatalf("unexpected error: n=%d, p=%v: %v", n, p, err)
+			}
+			if g.addBackwards {
+				t.Errorf("edge added with From.ID > To.ID: n=%d, p=%v", n, p)
+			}
+			if g.addSelfLoop {
+				t.Errorf("unexpected self edge: n=%d, p=%v", n, p)
+			}
+			if g.addMultipleEdge {
+				t.Errorf("unexpected multiple edge: n=%d, p=%v", n, p)
+			}
+		}
+	}
+}
+
+func TestGnpDirected(t *testing.T) {
+	for n := 2; n <= 20; n++ {
+		for p := 0.; p <= 1; p += 0.1 {
+			g := &gnDirected{DirectedBuilder: simple.NewDirectedGraph()}
+			err := Gnp(g, n, p, nil)
+			if err != nil {
+				t.Fatalf("unexpected error: n=%d, p=%v: %v", n, p, err)
+			}
+			if g.addSelfLoop {
+				t.Errorf("unexpected self edge: n=%d, p=%v", n, p)
+			}
+			if g.addMultipleEdge {
+				t.Errorf("unexpected multiple edge: n=%d, p=%v", n, p)
+			}
+		}
+	}
+}
+
+func TestGnmUndirected(t *testing.T) {
+	for n := 2; n <= 20; n++ {
+		nChoose2 := (n - 1) * n / 2
+		for m := 0; m <= nChoose2; m++ {
+			g := &gnUndirected{UndirectedBuilder: simple.NewUndirectedGraph()}
+			err := Gnm(g, n, m, nil)
+			if err != nil {
+				t.Fatalf("unexpected error: n=%d, m=%d: %v", n, m, err)
+			}
+			if g.addBackwards {
+				t.Errorf("edge added with From.ID > To.ID: n=%d, m=%d", n, m)
+			}
+			if g.addSelfLoop {
+				t.Errorf("unexpected self edge: n=%d, m=%d", n, m)
+			}
+			if g.addMultipleEdge {
+				t.Errorf("unexpected multiple edge: n=%d, m=%d", n, m)
+			}
+		}
+	}
+}
+
+func TestGnmDirected(t *testing.T) {
+	for n := 2; n <= 20; n++ {
+		nChoose2 := (n - 1) * n / 2
+		for m := 0; m <= nChoose2*2; m++ {
+			g := &gnDirected{DirectedBuilder: simple.NewDirectedGraph()}
+			err := Gnm(g, n, m, nil)
+			if err != nil {
+				t.Fatalf("unexpected error: n=%d, m=%d: %v", n, m, err)
+			}
+			if g.addSelfLoop {
+				t.Errorf("unexpected self edge: n=%d, m=%d", n, m)
+			}
+			if g.addMultipleEdge {
+				t.Errorf("unexpected multiple edge: n=%d, m=%d", n, m)
+			}
+		}
+	}
+}
+
+func TestSmallWorldsBBUndirected(t *testing.T) {
+	for n := 2; n <= 20; n++ {
+		for d := 1; d <= (n-1)/2; d++ {
+			for p := 0.; p < 1; p += 0.1 {
+				g := &gnUndirected{UndirectedBuilder: simple.NewUndirectedGraph()}
+				err := SmallWorldsBB(g, n, d, p, nil)
+				if err != nil {
+					t.Fatalf("unexpected error: n=%d, d=%d, p=%v: %v", n, d, p, err)
+				}
+				if g.addBackwards {
+					t.Errorf("edge added with From.ID > To.ID: n=%d, d=%d, p=%v", n, d, p)
+				}
+				if g.addSelfLoop {
+					t.Errorf("unexpected self edge: n=%d, d=%d, p=%v", n, d, p)
+				}
+				if g.addMultipleEdge {
+					t.Errorf("unexpected multiple edge: n=%d, d=%d, p=%v", n, d, p)
+				}
+			}
+		}
+	}
+}
+
+func TestSmallWorldsBBDirected(t *testing.T) {
+	for n := 2; n <= 20; n++ {
+		for d := 1; d <= (n-1)/2; d++ {
+			for p := 0.; p < 1; p += 0.1 {
+				g := &gnDirected{DirectedBuilder: simple.NewDirectedGraph()}
+				err := SmallWorldsBB(g, n, d, p, nil)
+				if err != nil {
+					t.Fatalf("unexpected error: n=%d, d=%d, p=%v: %v", n, d, p, err)
+				}
+				if g.addSelfLoop {
+					t.Errorf("unexpected self edge: n=%d, d=%d, p=%v", n, d, p)
+				}
+				if g.addMultipleEdge {
+					t.Errorf("unexpected multiple edge: n=%d, d=%d, p=%v", n, d, p)
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/graphs/gen/doc.go b/vendor/gonum.org/v1/gonum/graph/graphs/gen/doc.go
new file mode 100644
index 00000000..f5ebfcb5
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/graphs/gen/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package gen provides random graph generation functions.
+package gen // import "gonum.org/v1/gonum/graph/graphs/gen"
diff --git a/vendor/gonum.org/v1/gonum/graph/graphs/gen/duplication.go b/vendor/gonum.org/v1/gonum/graph/graphs/gen/duplication.go
new file mode 100644
index 00000000..8ffa578d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/graphs/gen/duplication.go
@@ -0,0 +1,125 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gen
+
+import (
+	"fmt"
+	"math"
+	"math/rand"
+	"sort"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/ordered"
+)
+
+// UndirectedMutator is an undirected graph builder that can remove edges.
+type UndirectedMutator interface {
+	graph.UndirectedBuilder
+	graph.EdgeRemover
+}
+
+// Duplication constructs a graph in the destination, dst, of order n. New nodes
+// are created by duplicating an existing node and all its edges. Each new edge is
+// deleted with probability delta. Additional edges are added between the new node
+// and existing nodes with probability alpha/|V|. An exception to this addition
+// rule is made for the parent node when sigma is not NaN; in this case an edge is
+// created with probability sigma. With the exception of the sigma parameter, this
+// corresponds to the completely correlated case in doi:10.1016/S0022-5193(03)00028-6.
+// If src is not nil it is used as the random source, otherwise rand.Float64 is used.
+func Duplication(dst UndirectedMutator, n int, delta, alpha, sigma float64, src *rand.Rand) error {
+	// As described in doi:10.1016/S0022-5193(03)00028-6 but
+	// also clarified in doi:10.1186/gb-2007-8-4-r51.
+
+	if delta < 0 || delta > 1 {
+		return fmt.Errorf("gen: bad delta: delta=%v", delta)
+	}
+	if alpha <= 0 || alpha > 1 {
+		return fmt.Errorf("gen: bad alpha: alpha=%v", alpha)
+	}
+	if sigma < 0 || sigma > 1 {
+		return fmt.Errorf("gen: bad sigma: sigma=%v", sigma)
+	}
+
+	var (
+		rnd  func() float64
+		rndN func(int) int
+	)
+	if src == nil {
+		rnd = rand.Float64
+		rndN = rand.Intn
+	} else {
+		rnd = src.Float64
+		rndN = src.Intn
+	}
+
+	nodes := dst.Nodes()
+	sort.Sort(ordered.ByID(nodes))
+	if len(nodes) == 0 {
+		n--
+		u := dst.NewNode()
+		dst.AddNode(u)
+		nodes = append(nodes, u)
+	}
+	for i := 0; i < n; i++ {
+		u := nodes[rndN(len(nodes))]
+		d := dst.NewNode()
+
+		// Add the duplicate node.
+		dst.AddNode(d)
+
+		// Loop until we have connectivity
+		// into the rest of the graph.
+		for {
+			// Add edges to parent's neighbours.
+			to := dst.From(u)
+			sort.Sort(ordered.ByID(to))
+			for _, v := range to {
+				if rnd() < delta || dst.HasEdgeBetween(v, d) {
+					continue
+				}
+				if v.ID() < d.ID() {
+					dst.SetEdge(dst.NewEdge(v, d))
+				} else {
+					dst.SetEdge(dst.NewEdge(d, v))
+				}
+			}
+
+			// Add edges to old nodes.
+			scaledAlpha := alpha / float64(len(nodes))
+			for _, v := range nodes {
+				switch v.ID() {
+				case u.ID():
+					if !math.IsNaN(sigma) {
+						if i == 0 || rnd() < sigma {
+							if v.ID() < d.ID() {
+								dst.SetEdge(dst.NewEdge(v, d))
+							} else {
+								dst.SetEdge(dst.NewEdge(d, v))
+							}
+						}
+						continue
+					}
+					fallthrough
+				default:
+					if rnd() < scaledAlpha && !dst.HasEdgeBetween(v, d) {
+						if v.ID() < d.ID() {
+							dst.SetEdge(dst.NewEdge(v, d))
+						} else {
+							dst.SetEdge(dst.NewEdge(d, v))
+						}
+					}
+				}
+			}
+
+			if len(dst.From(d)) != 0 {
+				break
+			}
+		}
+
+		nodes = append(nodes, d)
+	}
+
+	return nil
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/graphs/gen/duplication_test.go b/vendor/gonum.org/v1/gonum/graph/graphs/gen/duplication_test.go
new file mode 100644
index 00000000..b58eb899
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/graphs/gen/duplication_test.go
@@ -0,0 +1,58 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gen
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+type duplication struct {
+	UndirectedMutator
+	addBackwards    bool
+	addSelfLoop     bool
+	addMultipleEdge bool
+}
+
+func (g *duplication) SetEdge(e graph.Edge) {
+	switch {
+	case e.From().ID() == e.To().ID():
+		g.addSelfLoop = true
+		return
+	case e.From().ID() > e.To().ID():
+		g.addBackwards = true
+	case g.UndirectedMutator.HasEdgeBetween(e.From(), e.To()):
+		g.addMultipleEdge = true
+	}
+
+	g.UndirectedMutator.SetEdge(e)
+}
+
+func TestDuplication(t *testing.T) {
+	for n := 2; n <= 50; n++ {
+		for alpha := 0.1; alpha <= 1; alpha += 0.1 {
+			for delta := 0.; delta <= 1; delta += 0.2 {
+				for sigma := 0.; sigma <= 1; sigma += 0.2 {
+					g := &duplication{UndirectedMutator: simple.NewUndirectedGraph()}
+					err := Duplication(g, n, delta, alpha, sigma, nil)
+					if err != nil {
+						t.Fatalf("unexpected error: n=%d, alpha=%v, delta=%v sigma=%v: %v", n, alpha, delta, sigma, err)
+					}
+					if g.addBackwards {
+						t.Errorf("edge added with From.ID > To.ID: n=%d, alpha=%v, delta=%v sigma=%v", n, alpha, delta, sigma)
+					}
+					if g.addSelfLoop {
+						t.Errorf("unexpected self edge: n=%d, alpha=%v, delta=%v sigma=%v", n, alpha, delta, sigma)
+					}
+					if g.addMultipleEdge {
+						t.Errorf("unexpected multiple edge: n=%d, alpha=%v, delta=%v sigma=%v", n, alpha, delta, sigma)
+					}
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/graphs/gen/gen.go b/vendor/gonum.org/v1/gonum/graph/graphs/gen/gen.go
new file mode 100644
index 00000000..85c484e6
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/graphs/gen/gen.go
@@ -0,0 +1,21 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gen
+
+import "gonum.org/v1/gonum/graph"
+
+// GraphBuilder is a graph that can have nodes and edges added.
+type GraphBuilder interface {
+	Has(graph.Node) bool
+	HasEdgeBetween(x, y graph.Node) bool
+	graph.Builder
+}
+
+func abs(a int) int {
+	if a < 0 {
+		return -a
+	}
+	return a
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/graphs/gen/holme_kim.go b/vendor/gonum.org/v1/gonum/graph/graphs/gen/holme_kim.go
new file mode 100644
index 00000000..457fb1be
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/graphs/gen/holme_kim.go
@@ -0,0 +1,160 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gen
+
+import (
+	"errors"
+	"fmt"
+	"math/rand"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/simple"
+	"gonum.org/v1/gonum/stat/sampleuv"
+)
+
+// TunableClusteringScaleFree constructs a graph in the destination, dst, of order n.
+// The graph is constructed successively starting from an m order graph with one node
+// having degree m-1. At each iteration of graph addition, one node is added with m
+// additional edges joining existing nodes with probability proportional to the nodes'
+// degrees. The edges are formed as a triad with probability, p.
+// If src is not nil it is used as the random source, otherwise rand.Float64 and
+// rand.Intn are used.
+//
+// The algorithm is essentially as described in http://arxiv.org/abs/cond-mat/0110452.
+func TunableClusteringScaleFree(dst graph.UndirectedBuilder, n, m int, p float64, src *rand.Rand) error {
+	if p < 0 || p > 1 {
+		return fmt.Errorf("gen: bad probability: p=%v", p)
+	}
+	if n <= m {
+		return fmt.Errorf("gen: n <= m: n=%v m=%d", n, m)
+	}
+
+	var (
+		rnd  func() float64
+		rndN func(int) int
+	)
+	if src == nil {
+		rnd = rand.Float64
+		rndN = rand.Intn
+	} else {
+		rnd = src.Float64
+		rndN = src.Intn
+	}
+
+	// Initial condition.
+	wt := make([]float64, n)
+	for u := 0; u < m; u++ {
+		if !dst.Has(simple.Node(u)) {
+			dst.AddNode(simple.Node(u))
+		}
+		// We need to give equal probability for
+		// adding the first generation of edges.
+		wt[u] = 1
+	}
+	ws := sampleuv.NewWeighted(wt, src)
+	for i := range wt {
+		// These weights will organically grow
+		// after the first growth iteration.
+		wt[i] = 0
+	}
+
+	// Growth.
+	for v := m; v < n; v++ {
+		var u int
+	pa:
+		for i := 0; i < m; i++ {
+			// Triad formation.
+			if i != 0 && rnd() < p {
+				for _, w := range permute(dst.From(simple.Node(u)), rndN) {
+					wid := w.ID()
+					if wid == int64(v) || dst.HasEdgeBetween(w, simple.Node(v)) {
+						continue
+					}
+					dst.SetEdge(simple.Edge{F: w, T: simple.Node(v)})
+					wt[wid]++
+					wt[v]++
+					continue pa
+				}
+			}
+
+			// Preferential attachment.
+			for {
+				var ok bool
+				u, ok = ws.Take()
+				if !ok {
+					return errors.New("gen: depleted distribution")
+				}
+				if u == v || dst.HasEdgeBetween(simple.Node(u), simple.Node(v)) {
+					continue
+				}
+				dst.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+				wt[u]++
+				wt[v]++
+				break
+			}
+		}
+
+		ws.ReweightAll(wt)
+	}
+
+	return nil
+}
+
+func permute(n []graph.Node, rnd func(int) int) []graph.Node {
+	for i := range n[:len(n)-1] {
+		j := rnd(len(n)-i) + i
+		n[i], n[j] = n[j], n[i]
+	}
+	return n
+}
+
+// PreferentialAttachment constructs a graph in the destination, dst, of order n.
+// The graph is constructed successively starting from an m order graph with one
+// node having degree m-1. At each iteration of graph addition, one node is added
+// with m additional edges joining existing nodes with probability proportional
+// to the nodes' degrees. If src is not nil it is used as the random source,
+// otherwise rand.Float64 is used.
+//
+// The algorithm is essentially as described in http://arxiv.org/abs/cond-mat/0110452
+// after 10.1126/science.286.5439.509.
+func PreferentialAttachment(dst graph.UndirectedBuilder, n, m int, src *rand.Rand) error {
+	if n <= m {
+		return fmt.Errorf("gen: n <= m: n=%v m=%d", n, m)
+	}
+
+	// Initial condition.
+	wt := make([]float64, n)
+	for u := 0; u < m; u++ {
+		if !dst.Has(simple.Node(u)) {
+			dst.AddNode(simple.Node(u))
+		}
+		// We need to give equal probability for
+		// adding the first generation of edges.
+		wt[u] = 1
+	}
+	ws := sampleuv.NewWeighted(wt, src)
+	for i := range wt {
+		// These weights will organically grow
+		// after the first growth iteration.
+		wt[i] = 0
+	}
+
+	// Growth.
+	for v := m; v < n; v++ {
+		for i := 0; i < m; i++ {
+			// Preferential attachment.
+			u, ok := ws.Take()
+			if !ok {
+				return errors.New("gen: depleted distribution")
+			}
+			dst.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			wt[u]++
+			wt[v]++
+		}
+		ws.ReweightAll(wt)
+	}
+
+	return nil
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/graphs/gen/holme_kim_test.go b/vendor/gonum.org/v1/gonum/graph/graphs/gen/holme_kim_test.go
new file mode 100644
index 00000000..82eb62a8
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/graphs/gen/holme_kim_test.go
@@ -0,0 +1,55 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gen
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+func TestTunableClusteringScaleFree(t *testing.T) {
+	for n := 2; n <= 20; n++ {
+		for m := 0; m < n; m++ {
+			for p := 0.; p <= 1; p += 0.1 {
+				g := &gnUndirected{UndirectedBuilder: simple.NewUndirectedGraph()}
+				err := TunableClusteringScaleFree(g, n, m, p, nil)
+				if err != nil {
+					t.Fatalf("unexpected error: n=%d, m=%d, p=%v: %v", n, m, p, err)
+				}
+				if g.addBackwards {
+					t.Errorf("edge added with From.ID > To.ID: n=%d, m=%d, p=%v", n, m, p)
+				}
+				if g.addSelfLoop {
+					t.Errorf("unexpected self edge: n=%d, m=%d, p=%v", n, m, p)
+				}
+				if g.addMultipleEdge {
+					t.Errorf("unexpected multiple edge: n=%d, m=%d, p=%v", n, m, p)
+				}
+			}
+		}
+	}
+}
+
+func TestPreferentialAttachment(t *testing.T) {
+	for n := 2; n <= 20; n++ {
+		for m := 0; m < n; m++ {
+			g := &gnUndirected{UndirectedBuilder: simple.NewUndirectedGraph()}
+			err := PreferentialAttachment(g, n, m, nil)
+			if err != nil {
+				t.Fatalf("unexpected error: n=%d, m=%d: %v", n, m, err)
+			}
+			if g.addBackwards {
+				t.Errorf("edge added with From.ID > To.ID: n=%d, m=%d", n, m)
+			}
+			if g.addSelfLoop {
+				t.Errorf("unexpected self edge: n=%d, m=%d", n, m)
+			}
+			if g.addMultipleEdge {
+				t.Errorf("unexpected multiple edge: n=%d, m=%d", n, m)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/graphs/gen/small_world.go b/vendor/gonum.org/v1/gonum/graph/graphs/gen/small_world.go
new file mode 100644
index 00000000..3ff40e87
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/graphs/gen/small_world.go
@@ -0,0 +1,204 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gen
+
+import (
+	"errors"
+	"fmt"
+	"math"
+	"math/rand"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/simple"
+	"gonum.org/v1/gonum/stat/sampleuv"
+)
+
+// NavigableSmallWorld constructs an N-dimensional grid with guaranteed local connectivity
+// and random long-range connectivity in the destination, dst. The dims parameters specifies
+// the length of each of the N dimensions, p defines the Manhattan distance between local
+// nodes, and q defines the number of out-going long-range connections from each node. Long-
+// range connections are made with a probability proportional to |d(u,v)|^-r where d is the
+// Manhattan distance between non-local nodes.
+//
+// The algorithm is essentially as described on p4 of http://www.cs.cornell.edu/home/kleinber/swn.pdf.
+func NavigableSmallWorld(dst GraphBuilder, dims []int, p, q int, r float64, src *rand.Rand) (err error) {
+	if p < 1 {
+		return fmt.Errorf("gen: bad local distance: p=%v", p)
+	}
+	if q < 0 {
+		return fmt.Errorf("gen: bad distant link count: q=%v", q)
+	}
+	if r < 0 {
+		return fmt.Errorf("gen: bad decay constant: r=%v", r)
+	}
+
+	n := 1
+	for _, d := range dims {
+		n *= d
+	}
+	for i := 0; i < n; i++ {
+		if !dst.Has(simple.Node(i)) {
+			dst.AddNode(simple.Node(i))
+		}
+	}
+
+	hasEdge := dst.HasEdgeBetween
+	d, isDirected := dst.(graph.Directed)
+	if isDirected {
+		hasEdge = d.HasEdgeFromTo
+	}
+
+	locality := make([]int, len(dims))
+	for i := range locality {
+		locality[i] = p*2 + 1
+	}
+	iterateOver(dims, func(u []int) {
+		uid := idFrom(u, dims)
+		iterateOver(locality, func(delta []int) {
+			d := manhattanDelta(u, delta, dims, -p)
+			if d == 0 || d > p {
+				return
+			}
+			vid := idFromDelta(u, delta, dims, -p)
+			e := simple.Edge{F: simple.Node(uid), T: simple.Node(vid)}
+			if uid > vid {
+				e.F, e.T = e.T, e.F
+			}
+			if !hasEdge(e.From(), e.To()) {
+				dst.SetEdge(e)
+			}
+			if !isDirected {
+				return
+			}
+			e.F, e.T = e.T, e.F
+			if !hasEdge(e.From(), e.To()) {
+				dst.SetEdge(e)
+			}
+		})
+	})
+
+	defer func() {
+		r := recover()
+		if r != nil {
+			if r != "depleted distribution" {
+				panic(r)
+			}
+			err = errors.New("depleted distribution")
+		}
+	}()
+	w := make([]float64, n)
+	ws := sampleuv.NewWeighted(w, src)
+	iterateOver(dims, func(u []int) {
+		uid := idFrom(u, dims)
+		iterateOver(dims, func(v []int) {
+			d := manhattanBetween(u, v)
+			if d <= p {
+				return
+			}
+			w[idFrom(v, dims)] = math.Pow(float64(d), -r)
+		})
+		ws.ReweightAll(w)
+		for i := 0; i < q; i++ {
+			vid, ok := ws.Take()
+			if !ok {
+				panic("depleted distribution")
+			}
+			e := simple.Edge{F: simple.Node(uid), T: simple.Node(vid)}
+			if !isDirected && uid > vid {
+				e.F, e.T = e.T, e.F
+			}
+			if !hasEdge(e.From(), e.To()) {
+				dst.SetEdge(e)
+			}
+		}
+		for i := range w {
+			w[i] = 0
+		}
+	})
+
+	return nil
+}
+
+// iterateOver performs an iteration over all dimensions of dims, calling fn
+// for each state. The elements of state must not be mutated by fn.
+func iterateOver(dims []int, fn func(state []int)) {
+	iterator(0, dims, make([]int, len(dims)), fn)
+}
+
+func iterator(d int, dims, state []int, fn func(state []int)) {
+	if d >= len(dims) {
+		fn(state)
+		return
+	}
+	for i := 0; i < dims[d]; i++ {
+		state[d] = i
+		iterator(d+1, dims, state, fn)
+	}
+}
+
+// manhattanBetween returns the Manhattan distance between a and b.
+func manhattanBetween(a, b []int) int {
+	if len(a) != len(b) {
+		panic("gen: unexpected dimension")
+	}
+	var d int
+	for i, v := range a {
+		d += abs(v - b[i])
+	}
+	return d
+}
+
+// manhattanDelta returns the Manhattan norm of delta+translate. If a
+// translated by delta+translate is out of the range given by dims,
+// zero is returned.
+func manhattanDelta(a, delta, dims []int, translate int) int {
+	if len(a) != len(dims) {
+		panic("gen: unexpected dimension")
+	}
+	if len(delta) != len(dims) {
+		panic("gen: unexpected dimension")
+	}
+	var d int
+	for i, v := range delta {
+		v += translate
+		t := a[i] + v
+		if t < 0 || t >= dims[i] {
+			return 0
+		}
+		d += abs(v)
+	}
+	return d
+}
+
+// idFrom returns a node id for the slice n over the given dimensions.
+func idFrom(n, dims []int) int {
+	s := 1
+	var id int
+	for d, m := range dims {
+		p := n[d]
+		if p < 0 || p >= m {
+			panic("gen: element out of range")
+		}
+		id += p * s
+		s *= m
+	}
+	return id
+}
+
+// idFromDelta returns a node id for the slice base plus the delta over the given
+// dimensions and applying the translation.
+func idFromDelta(base, delta, dims []int, translate int) int {
+	s := 1
+	var id int
+	for d, m := range dims {
+		n := base[d] + delta[d] + translate
+		if n < 0 || n >= m {
+			panic("gen: element out of range")
+		}
+		id += n * s
+		s *= m
+	}
+	return id
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/graphs/gen/small_world_test.go b/vendor/gonum.org/v1/gonum/graph/graphs/gen/small_world_test.go
new file mode 100644
index 00000000..ef667146
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/graphs/gen/small_world_test.go
@@ -0,0 +1,72 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gen
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+var smallWorldDimensionParameters = [][]int{
+	{50},
+	{10, 10},
+	{6, 5, 4},
+}
+
+func TestNavigableSmallWorldUndirected(t *testing.T) {
+	for p := 1; p < 5; p++ {
+		for q := 0; q < 10; q++ {
+			for r := 0.5; r < 10; r++ {
+				for _, dims := range smallWorldDimensionParameters {
+					g := &gnUndirected{UndirectedBuilder: simple.NewUndirectedGraph()}
+					err := NavigableSmallWorld(g, dims, p, q, r, nil)
+					n := 1
+					for _, d := range dims {
+						n *= d
+					}
+					if err != nil {
+						t.Fatalf("unexpected error: dims=%v n=%d, p=%d, q=%d, r=%v: %v", dims, n, p, q, r, err)
+					}
+					if g.addBackwards {
+						t.Errorf("edge added with From.ID > To.ID: dims=%v n=%d, p=%d, q=%d, r=%v", dims, n, p, q, r)
+					}
+					if g.addSelfLoop {
+						t.Errorf("unexpected self edge: dims=%v n=%d, p=%d, q=%d, r=%v", dims, n, p, q, r)
+					}
+					if g.addMultipleEdge {
+						t.Errorf("unexpected multiple edge: dims=%v n=%d, p=%d, q=%d, r=%v", dims, n, p, q, r)
+					}
+				}
+			}
+		}
+	}
+}
+
+func TestNavigableSmallWorldDirected(t *testing.T) {
+	for p := 1; p < 5; p++ {
+		for q := 0; q < 10; q++ {
+			for r := 0.5; r < 10; r++ {
+				for _, dims := range smallWorldDimensionParameters {
+					g := &gnDirected{DirectedBuilder: simple.NewDirectedGraph()}
+					err := NavigableSmallWorld(g, dims, p, q, r, nil)
+					n := 1
+					for _, d := range dims {
+						n *= d
+					}
+					if err != nil {
+						t.Fatalf("unexpected error: dims=%v n=%d, p=%d, q=%d, r=%v: %v", dims, n, p, q, r, err)
+					}
+					if g.addSelfLoop {
+						t.Errorf("unexpected self edge: dims=%v n=%d, p=%d, q=%d, r=%v", dims, n, p, q, r)
+					}
+					if g.addMultipleEdge {
+						t.Errorf("unexpected multiple edge: dims=%v n=%d, p=%d, q=%d, r=%v", dims, n, p, q, r)
+					}
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/internal/linear/doc.go b/vendor/gonum.org/v1/gonum/graph/internal/linear/doc.go
new file mode 100644
index 00000000..8828a561
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/internal/linear/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package linear provides common linear data structures.
+package linear // import "gonum.org/v1/gonum/graph/internal/linear"
diff --git a/vendor/gonum.org/v1/gonum/graph/internal/linear/linear.go b/vendor/gonum.org/v1/gonum/graph/internal/linear/linear.go
new file mode 100644
index 00000000..610b45eb
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/internal/linear/linear.go
@@ -0,0 +1,73 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package linear
+
+import (
+	"gonum.org/v1/gonum/graph"
+)
+
+// NodeStack implements a LIFO stack of graph.Node.
+type NodeStack []graph.Node
+
+// Len returns the number of graph.Nodes on the stack.
+func (s *NodeStack) Len() int { return len(*s) }
+
+// Pop returns the last graph.Node on the stack and removes it
+// from the stack.
+func (s *NodeStack) Pop() graph.Node {
+	v := *s
+	v, n := v[:len(v)-1], v[len(v)-1]
+	*s = v
+	return n
+}
+
+// Push adds the node n to the stack at the last position.
+func (s *NodeStack) Push(n graph.Node) { *s = append(*s, n) }
+
+// NodeQueue implements a FIFO queue.
+type NodeQueue struct {
+	head int
+	data []graph.Node
+}
+
+// Len returns the number of graph.Nodes in the queue.
+func (q *NodeQueue) Len() int { return len(q.data) - q.head }
+
+// Enqueue adds the node n to the back of the queue.
+func (q *NodeQueue) Enqueue(n graph.Node) {
+	if len(q.data) == cap(q.data) && q.head > 0 {
+		l := q.Len()
+		copy(q.data, q.data[q.head:])
+		q.head = 0
+		q.data = append(q.data[:l], n)
+	} else {
+		q.data = append(q.data, n)
+	}
+}
+
+// Dequeue returns the graph.Node at the front of the queue and
+// removes it from the queue.
+func (q *NodeQueue) Dequeue() graph.Node {
+	if q.Len() == 0 {
+		panic("queue: empty queue")
+	}
+
+	var n graph.Node
+	n, q.data[q.head] = q.data[q.head], nil
+	q.head++
+
+	if q.Len() == 0 {
+		q.head = 0
+		q.data = q.data[:0]
+	}
+
+	return n
+}
+
+// Reset clears the queue for reuse.
+func (q *NodeQueue) Reset() {
+	q.head = 0
+	q.data = q.data[:0]
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/internal/ordered/doc.go b/vendor/gonum.org/v1/gonum/graph/internal/ordered/doc.go
new file mode 100644
index 00000000..8220c8fd
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/internal/ordered/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package ordered provides common sort ordering types.
+package ordered // import "gonum.org/v1/gonum/graph/internal/ordered"
diff --git a/vendor/gonum.org/v1/gonum/graph/internal/ordered/sort.go b/vendor/gonum.org/v1/gonum/graph/internal/ordered/sort.go
new file mode 100644
index 00000000..4342daf1
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/internal/ordered/sort.go
@@ -0,0 +1,69 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package ordered
+
+import "gonum.org/v1/gonum/graph"
+
+// ByID implements the sort.Interface sorting a slice of graph.Node
+// by ID.
+type ByID []graph.Node
+
+func (n ByID) Len() int           { return len(n) }
+func (n ByID) Less(i, j int) bool { return n[i].ID() < n[j].ID() }
+func (n ByID) Swap(i, j int)      { n[i], n[j] = n[j], n[i] }
+
+// BySliceValues implements the sort.Interface sorting a slice of
+// []int64 lexically by the values of the []int64.
+type BySliceValues [][]int64
+
+func (c BySliceValues) Len() int { return len(c) }
+func (c BySliceValues) Less(i, j int) bool {
+	a, b := c[i], c[j]
+	l := len(a)
+	if len(b) < l {
+		l = len(b)
+	}
+	for k, v := range a[:l] {
+		if v < b[k] {
+			return true
+		}
+		if v > b[k] {
+			return false
+		}
+	}
+	return len(a) < len(b)
+}
+func (c BySliceValues) Swap(i, j int) { c[i], c[j] = c[j], c[i] }
+
+// BySliceIDs implements the sort.Interface sorting a slice of
+// []graph.Node lexically by the IDs of the []graph.Node.
+type BySliceIDs [][]graph.Node
+
+func (c BySliceIDs) Len() int { return len(c) }
+func (c BySliceIDs) Less(i, j int) bool {
+	a, b := c[i], c[j]
+	l := len(a)
+	if len(b) < l {
+		l = len(b)
+	}
+	for k, v := range a[:l] {
+		if v.ID() < b[k].ID() {
+			return true
+		}
+		if v.ID() > b[k].ID() {
+			return false
+		}
+	}
+	return len(a) < len(b)
+}
+func (c BySliceIDs) Swap(i, j int) { c[i], c[j] = c[j], c[i] }
+
+// Int64s implements the sort.Interface sorting a slice of
+// int64.
+type Int64s []int64
+
+func (s Int64s) Len() int           { return len(s) }
+func (s Int64s) Less(i, j int) bool { return s[i] < s[j] }
+func (s Int64s) Swap(i, j int)      { s[i], s[j] = s[j], s[i] }
diff --git a/vendor/gonum.org/v1/gonum/graph/internal/set/doc.go b/vendor/gonum.org/v1/gonum/graph/internal/set/doc.go
new file mode 100644
index 00000000..383615ef
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/internal/set/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package set provides integer and graph.Node sets.
+package set // import "gonum.org/v1/gonum/graph/internal/set"
diff --git a/vendor/gonum.org/v1/gonum/graph/internal/set/same.go b/vendor/gonum.org/v1/gonum/graph/internal/set/same.go
new file mode 100644
index 00000000..c776dc32
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/internal/set/same.go
@@ -0,0 +1,36 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !appengine
+
+package set
+
+import "unsafe"
+
+// same determines whether two sets are backed by the same store. In the
+// current implementation using hash maps it makes use of the fact that
+// hash maps are passed as a pointer to a runtime Hmap struct. A map is
+// not seen by the runtime as a pointer though, so we use unsafe to get
+// the maps' pointer values to compare.
+func same(a, b Nodes) bool {
+	return *(*uintptr)(unsafe.Pointer(&a)) == *(*uintptr)(unsafe.Pointer(&b))
+}
+
+// intsSame determines whether two sets are backed by the same store. In the
+// current implementation using hash maps it makes use of the fact that
+// hash maps are passed as a pointer to a runtime Hmap struct. A map is
+// not seen by the runtime as a pointer though, so we use unsafe to get
+// the maps' pointer values to compare.
+func intsSame(a, b Ints) bool {
+	return *(*uintptr)(unsafe.Pointer(&a)) == *(*uintptr)(unsafe.Pointer(&b))
+}
+
+// int64sSame determines whether two sets are backed by the same store. In the
+// current implementation using hash maps it makes use of the fact that
+// hash maps are passed as a pointer to a runtime Hmap struct. A map is
+// not seen by the runtime as a pointer though, so we use unsafe to get
+// the maps' pointer values to compare.
+func int64sSame(a, b Int64s) bool {
+	return *(*uintptr)(unsafe.Pointer(&a)) == *(*uintptr)(unsafe.Pointer(&b))
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/internal/set/same_appengine.go b/vendor/gonum.org/v1/gonum/graph/internal/set/same_appengine.go
new file mode 100644
index 00000000..082ed265
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/internal/set/same_appengine.go
@@ -0,0 +1,36 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build appengine
+
+package set
+
+import "reflect"
+
+// same determines whether two sets are backed by the same store. In the
+// current implementation using hash maps it makes use of the fact that
+// hash maps are passed as a pointer to a runtime Hmap struct. A map is
+// not seen by the runtime as a pointer though, so we use reflect to get
+// the maps' pointer values to compare.
+func same(a, b Nodes) bool {
+	return reflect.ValueOf(a).Pointer() == reflect.ValueOf(b).Pointer()
+}
+
+// intsSame determines whether two sets are backed by the same store. In the
+// current implementation using hash maps it makes use of the fact that
+// hash maps are passed as a pointer to a runtime Hmap struct. A map is
+// not seen by the runtime as a pointer though, so we use reflect to get
+// the maps' pointer values to compare.
+func intsSame(a, b Ints) bool {
+	return reflect.ValueOf(a).Pointer() == reflect.ValueOf(b).Pointer()
+}
+
+// int64sSame determines whether two sets are backed by the same store. In the
+// current implementation using hash maps it makes use of the fact that
+// hash maps are passed as a pointer to a runtime Hmap struct. A map is
+// not seen by the runtime as a pointer though, so we use reflect to get
+// the maps' pointer values to compare.
+func int64sSame(a, b Int64s) bool {
+	return reflect.ValueOf(a).Pointer() == reflect.ValueOf(b).Pointer()
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/internal/set/set.go b/vendor/gonum.org/v1/gonum/graph/internal/set/set.go
new file mode 100644
index 00000000..339e9f63
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/internal/set/set.go
@@ -0,0 +1,256 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package set
+
+import "gonum.org/v1/gonum/graph"
+
+// Ints is a set of int identifiers.
+type Ints map[int]struct{}
+
+// The simple accessor methods for Ints are provided to allow ease of
+// implementation change should the need arise.
+
+// Add inserts an element into the set.
+func (s Ints) Add(e int) {
+	s[e] = struct{}{}
+}
+
+// Has reports the existence of the element in the set.
+func (s Ints) Has(e int) bool {
+	_, ok := s[e]
+	return ok
+}
+
+// Remove deletes the specified element from the set.
+func (s Ints) Remove(e int) {
+	delete(s, e)
+}
+
+// Count reports the number of elements stored in the set.
+func (s Ints) Count() int {
+	return len(s)
+}
+
+// IntsEqual reports set equality between the parameters. Sets are equal if
+// and only if they have the same elements.
+func IntsEqual(a, b Ints) bool {
+	if intsSame(a, b) {
+		return true
+	}
+
+	if len(a) != len(b) {
+		return false
+	}
+
+	for e := range a {
+		if _, ok := b[e]; !ok {
+			return false
+		}
+	}
+
+	return true
+}
+
+// Int64s is a set of int64 identifiers.
+type Int64s map[int64]struct{}
+
+// The simple accessor methods for Ints are provided to allow ease of
+// implementation change should the need arise.
+
+// Add inserts an element into the set.
+func (s Int64s) Add(e int64) {
+	s[e] = struct{}{}
+}
+
+// Has reports the existence of the element in the set.
+func (s Int64s) Has(e int64) bool {
+	_, ok := s[e]
+	return ok
+}
+
+// Remove deletes the specified element from the set.
+func (s Int64s) Remove(e int64) {
+	delete(s, e)
+}
+
+// Count reports the number of elements stored in the set.
+func (s Int64s) Count() int {
+	return len(s)
+}
+
+// Int64sEqual reports set equality between the parameters. Sets are equal if
+// and only if they have the same elements.
+func Int64sEqual(a, b Int64s) bool {
+	if int64sSame(a, b) {
+		return true
+	}
+
+	if len(a) != len(b) {
+		return false
+	}
+
+	for e := range a {
+		if _, ok := b[e]; !ok {
+			return false
+		}
+	}
+
+	return true
+}
+
+// Nodes is a set of nodes keyed in their integer identifiers.
+type Nodes map[int64]graph.Node
+
+// The simple accessor methods for Nodes are provided to allow ease of
+// implementation change should the need arise.
+
+// Add inserts an element into the set.
+func (s Nodes) Add(n graph.Node) {
+	s[n.ID()] = n
+}
+
+// Remove deletes the specified element from the set.
+func (s Nodes) Remove(e graph.Node) {
+	delete(s, e.ID())
+}
+
+// Has reports the existence of the element in the set.
+func (s Nodes) Has(n graph.Node) bool {
+	_, ok := s[n.ID()]
+	return ok
+}
+
+// clear clears the set, possibly using the same backing store.
+func (s *Nodes) clear() {
+	if len(*s) != 0 {
+		*s = make(Nodes)
+	}
+}
+
+// Copy performs a perfect copy from src to dst (meaning the sets will
+// be equal).
+func (dst Nodes) Copy(src Nodes) Nodes {
+	if same(src, dst) {
+		return dst
+	}
+
+	if len(dst) > 0 {
+		dst = make(Nodes, len(src))
+	}
+
+	for e, n := range src {
+		dst[e] = n
+	}
+
+	return dst
+}
+
+// Equal reports set equality between the parameters. Sets are equal if
+// and only if they have the same elements.
+func Equal(a, b Nodes) bool {
+	if same(a, b) {
+		return true
+	}
+
+	if len(a) != len(b) {
+		return false
+	}
+
+	for e := range a {
+		if _, ok := b[e]; !ok {
+			return false
+		}
+	}
+
+	return true
+}
+
+// Union takes the union of a and b, and stores it in dst.
+//
+// The union of two sets, a and b, is the set containing all the
+// elements of each, for instance:
+//
+//     {a,b,c} UNION {d,e,f} = {a,b,c,d,e,f}
+//
+// Since sets may not have repetition, unions of two sets that overlap
+// do not contain repeat elements, that is:
+//
+//     {a,b,c} UNION {b,c,d} = {a,b,c,d}
+//
+func (dst Nodes) Union(a, b Nodes) Nodes {
+	if same(a, b) {
+		return dst.Copy(a)
+	}
+
+	if !same(a, dst) && !same(b, dst) {
+		dst.clear()
+	}
+
+	if !same(dst, a) {
+		for e, n := range a {
+			dst[e] = n
+		}
+	}
+
+	if !same(dst, b) {
+		for e, n := range b {
+			dst[e] = n
+		}
+	}
+
+	return dst
+}
+
+// Intersect takes the intersection of a and b, and stores it in dst.
+//
+// The intersection of two sets, a and b, is the set containing all
+// the elements shared between the two sets, for instance:
+//
+//     {a,b,c} INTERSECT {b,c,d} = {b,c}
+//
+// The intersection between a set and itself is itself, and thus
+// effectively a copy operation:
+//
+//     {a,b,c} INTERSECT {a,b,c} = {a,b,c}
+//
+// The intersection between two sets that share no elements is the empty
+// set:
+//
+//     {a,b,c} INTERSECT {d,e,f} = {}
+//
+func (dst Nodes) Intersect(a, b Nodes) Nodes {
+	var swap Nodes
+
+	if same(a, b) {
+		return dst.Copy(a)
+	}
+	if same(a, dst) {
+		swap = b
+	} else if same(b, dst) {
+		swap = a
+	} else {
+		dst.clear()
+
+		if len(a) > len(b) {
+			a, b = b, a
+		}
+
+		for e, n := range a {
+			if _, ok := b[e]; ok {
+				dst[e] = n
+			}
+		}
+
+		return dst
+	}
+
+	for e := range dst {
+		if _, ok := swap[e]; !ok {
+			delete(dst, e)
+		}
+	}
+
+	return dst
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/internal/set/set_test.go b/vendor/gonum.org/v1/gonum/graph/internal/set/set_test.go
new file mode 100644
index 00000000..f665b398
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/internal/set/set_test.go
@@ -0,0 +1,413 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package set
+
+import "testing"
+
+type node int64
+
+func (n node) ID() int64 { return int64(n) }
+
+// count reports the number of elements stored in the node set.
+func (s Nodes) count() int {
+	return len(s)
+}
+
+// TestSame tests the assumption that pointer equality via unsafe conversion
+// of a map[int]struct{} to uintptr is a valid test for perfect identity between
+// set values. If any of the tests in TestSame fail, the package is broken and same
+// must be reimplemented to conform to the runtime map implementation. The relevant
+// code to look at (at least for gc) is in runtime/hashmap.{h,goc}.
+func TestSame(t *testing.T) {
+	var (
+		a = make(Nodes)
+		b = make(Nodes)
+		c = a
+	)
+
+	if same(a, b) {
+		t.Error("Independently created sets test as same")
+	}
+	if !same(a, c) {
+		t.Error("Set copy and original test as not same.")
+	}
+	a.Add(node(1))
+	if !same(a, c) {
+		t.Error("Set copy and original test as not same after addition.")
+	}
+	if !same(nil, nil) {
+		t.Error("nil sets test as not same.")
+	}
+	if same(b, nil) {
+		t.Error("nil and empty sets test as same.")
+	}
+}
+
+func TestAdd(t *testing.T) {
+	s := make(Nodes)
+	if s == nil {
+		t.Fatal("Set cannot be created successfully")
+	}
+
+	if s.count() != 0 {
+		t.Error("Set somehow contains new elements upon creation")
+	}
+
+	s.Add(node(1))
+	s.Add(node(3))
+	s.Add(node(5))
+
+	if s.count() != 3 {
+		t.Error("Incorrect number of set elements after adding")
+	}
+
+	if !s.Has(node(1)) || !s.Has(node(3)) || !s.Has(node(5)) {
+		t.Error("Set doesn't contain element that was added")
+	}
+
+	s.Add(node(1))
+
+	if s.count() > 3 {
+		t.Error("Set double-adds element (element not unique)")
+	} else if s.count() < 3 {
+		t.Error("Set double-add lowered len")
+	}
+
+	if !s.Has(node(1)) {
+		t.Error("Set doesn't contain double-added element")
+	}
+
+	if !s.Has(node(3)) || !s.Has(node(5)) {
+		t.Error("Set removes element on double-add")
+	}
+
+	for e, n := range s {
+		if e != n.ID() {
+			t.Errorf("Element ID did not match key: %d != %d", e, n.ID())
+		}
+	}
+}
+
+func TestRemove(t *testing.T) {
+	s := make(Nodes)
+
+	s.Add(node(1))
+	s.Add(node(3))
+	s.Add(node(5))
+
+	s.Remove(node(1))
+
+	if s.count() != 2 {
+		t.Error("Incorrect number of set elements after removing an element")
+	}
+
+	if s.Has(node(1)) {
+		t.Error("Element present after removal")
+	}
+
+	if !s.Has(node(3)) || !s.Has(node(5)) {
+		t.Error("Set remove removed wrong element")
+	}
+
+	s.Remove(node(1))
+
+	if s.count() != 2 || s.Has(node(1)) {
+		t.Error("Double set remove does something strange")
+	}
+
+	s.Add(node(1))
+
+	if s.count() != 3 || !s.Has(node(1)) {
+		t.Error("Cannot add element after removal")
+	}
+}
+
+func TestClear(t *testing.T) {
+	s := make(Nodes)
+
+	s.Add(node(8))
+	s.Add(node(9))
+	s.Add(node(10))
+
+	s.clear()
+
+	if s.count() != 0 {
+		t.Error("clear did not properly reset set to size 0")
+	}
+}
+
+func TestSelfEqual(t *testing.T) {
+	s := make(Nodes)
+
+	if !Equal(s, s) {
+		t.Error("Set is not equal to itself")
+	}
+
+	s.Add(node(1))
+
+	if !Equal(s, s) {
+		t.Error("Set ceases self equality after adding element")
+	}
+}
+
+func TestEqual(t *testing.T) {
+	a := make(Nodes)
+	b := make(Nodes)
+
+	if !Equal(a, b) {
+		t.Error("Two different empty sets not equal")
+	}
+
+	a.Add(node(1))
+	if Equal(a, b) {
+		t.Error("Two different sets with different elements not equal")
+	}
+
+	b.Add(node(1))
+	if !Equal(a, b) {
+		t.Error("Two sets with same element not equal")
+	}
+}
+
+func TestCopy(t *testing.T) {
+	a := make(Nodes)
+	b := make(Nodes)
+
+	a.Add(node(1))
+	a.Add(node(2))
+	a.Add(node(3))
+
+	b.Copy(a)
+
+	if !Equal(a, b) {
+		t.Fatalf("Two sets not equal after copy")
+	}
+
+	b.Remove(node(1))
+
+	if Equal(a, b) {
+		t.Errorf("Mutating one set mutated another after copy")
+	}
+}
+
+func TestSelfCopy(t *testing.T) {
+	a := make(Nodes)
+
+	a.Add(node(1))
+	a.Add(node(2))
+
+	a.Copy(a)
+
+	if a.count() != 2 {
+		t.Error("Something strange happened when copying into self")
+	}
+}
+
+func TestUnionSame(t *testing.T) {
+	a := make(Nodes)
+	b := make(Nodes)
+	c := make(Nodes)
+
+	a.Add(node(1))
+	a.Add(node(2))
+
+	b.Add(node(1))
+	b.Add(node(2))
+
+	c.Union(a, b)
+
+	if c.count() != 2 {
+		t.Error("Union of same sets yields set with wrong len")
+	}
+
+	if !c.Has(node(1)) || !c.Has(node(2)) {
+		t.Error("Union of same sets yields wrong elements")
+	}
+
+	for i, s := range []Nodes{a, b, c} {
+		for e, n := range s {
+			if e != n.ID() {
+				t.Errorf("Element ID did not match key in s%d: %d != %d", i+1, e, n.ID())
+			}
+		}
+	}
+}
+
+func TestUnionDiff(t *testing.T) {
+	a := make(Nodes)
+	b := make(Nodes)
+	c := make(Nodes)
+
+	a.Add(node(1))
+	a.Add(node(2))
+
+	b.Add(node(3))
+
+	c.Union(a, b)
+
+	if c.count() != 3 {
+		t.Error("Union of different sets yields set with wrong len")
+	}
+
+	if !c.Has(node(1)) || !c.Has(node(2)) || !c.Has(node(3)) {
+		t.Error("Union of different sets yields set with wrong elements")
+	}
+
+	if a.Has(node(3)) || !a.Has(node(2)) || !a.Has(node(1)) || a.count() != 2 {
+		t.Error("Union of sets mutates non-destination set (argument 1)")
+	}
+
+	if !b.Has(node(3)) || b.Has(node(1)) || b.Has(node(2)) || b.count() != 1 {
+		t.Error("Union of sets mutates non-destination set (argument 2)")
+	}
+
+	for i, s := range []Nodes{a, b, c} {
+		for e, n := range s {
+			if e != n.ID() {
+				t.Errorf("Element ID did not match key in s%d: %d != %d", i+1, e, n.ID())
+			}
+		}
+	}
+}
+
+func TestUnionOverlapping(t *testing.T) {
+	a := make(Nodes)
+	b := make(Nodes)
+	c := make(Nodes)
+
+	a.Add(node(1))
+	a.Add(node(2))
+
+	b.Add(node(2))
+	b.Add(node(3))
+
+	c.Union(a, b)
+
+	if c.count() != 3 {
+		t.Error("Union of overlapping sets yields set with wrong len")
+	}
+
+	if !c.Has(node(1)) || !c.Has(node(2)) || !c.Has(node(3)) {
+		t.Error("Union of overlapping sets yields set with wrong elements")
+	}
+
+	if a.Has(node(3)) || !a.Has(node(2)) || !a.Has(node(1)) || a.count() != 2 {
+		t.Error("Union of sets mutates non-destination set (argument 1)")
+	}
+
+	if !b.Has(node(3)) || b.Has(node(1)) || !b.Has(node(2)) || b.count() != 2 {
+		t.Error("Union of sets mutates non-destination set (argument 2)")
+	}
+
+	for i, s := range []Nodes{a, b, c} {
+		for e, n := range s {
+			if e != n.ID() {
+				t.Errorf("Element ID did not match key in s%d: %d != %d", i+1, e, n.ID())
+			}
+		}
+	}
+}
+
+func TestIntersectSame(t *testing.T) {
+	a := make(Nodes)
+	b := make(Nodes)
+	c := make(Nodes)
+
+	a.Add(node(2))
+	a.Add(node(3))
+
+	b.Add(node(2))
+	b.Add(node(3))
+
+	c.Intersect(a, b)
+
+	if card := c.count(); card != 2 {
+		t.Errorf("Intersection of identical sets yields set of wrong len %d", card)
+	}
+
+	if !c.Has(node(2)) || !c.Has(node(3)) {
+		t.Error("Intersection of identical sets yields set of wrong elements")
+	}
+
+	for i, s := range []Nodes{a, b, c} {
+		for e, n := range s {
+			if e != n.ID() {
+				t.Errorf("Element ID did not match key in s%d: %d != %d", i+1, e, n.ID())
+			}
+		}
+	}
+}
+
+func TestIntersectDiff(t *testing.T) {
+	a := make(Nodes)
+	b := make(Nodes)
+	c := make(Nodes)
+
+	a.Add(node(2))
+	a.Add(node(3))
+
+	b.Add(node(1))
+	b.Add(node(4))
+
+	c.Intersect(a, b)
+
+	if card := c.count(); card != 0 {
+		t.Errorf("Intersection of different yields non-empty set %d", card)
+	}
+
+	if !a.Has(node(2)) || !a.Has(node(3)) || a.Has(node(1)) || a.Has(node(4)) || a.count() != 2 {
+		t.Error("Intersection of sets mutates non-destination set (argument 1)")
+	}
+
+	if b.Has(node(2)) || b.Has(node(3)) || !b.Has(node(1)) || !b.Has(node(4)) || b.count() != 2 {
+		t.Error("Intersection of sets mutates non-destination set (argument 1)")
+	}
+
+	for i, s := range []Nodes{a, b, c} {
+		for e, n := range s {
+			if e != n.ID() {
+				t.Errorf("Element ID did not match key in s%d: %d != %d", i+1, e, n.ID())
+			}
+		}
+	}
+}
+
+func TestIntersectOverlapping(t *testing.T) {
+	a := make(Nodes)
+	b := make(Nodes)
+	c := make(Nodes)
+
+	a.Add(node(2))
+	a.Add(node(3))
+
+	b.Add(node(3))
+	b.Add(node(4))
+
+	c.Intersect(a, b)
+
+	if card := c.count(); card != 1 {
+		t.Errorf("Intersection of overlapping sets yields set of incorrect len %d", card)
+	}
+
+	if !c.Has(node(3)) {
+		t.Errorf("Intersection of overlapping sets yields set with wrong element")
+	}
+
+	if !a.Has(node(2)) || !a.Has(node(3)) || a.Has(node(4)) || a.count() != 2 {
+		t.Error("Intersection of sets mutates non-destination set (argument 1)")
+	}
+
+	if b.Has(node(2)) || !b.Has(node(3)) || !b.Has(node(4)) || b.count() != 2 {
+		t.Error("Intersection of sets mutates non-destination set (argument 1)")
+	}
+
+	for i, s := range []Nodes{a, b, c} {
+		for e, n := range s {
+			if e != n.ID() {
+				t.Errorf("Element ID did not match key in s%d: %d != %d", i+1, e, n.ID())
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/network/betweenness.go b/vendor/gonum.org/v1/gonum/graph/network/betweenness.go
new file mode 100644
index 00000000..547f44f7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/network/betweenness.go
@@ -0,0 +1,250 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package network
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/linear"
+	"gonum.org/v1/gonum/graph/path"
+)
+
+// Betweenness returns the non-zero betweenness centrality for nodes in the unweighted graph g.
+//
+//  C_B(v) = \sum_{s ≠ v ≠ t ∈ V} (\sigma_{st}(v) / \sigma_{st})
+//
+// where \sigma_{st} and \sigma_{st}(v) are the number of shortest paths from s to t,
+// and the subset of those paths containing v respectively.
+func Betweenness(g graph.Graph) map[int64]float64 {
+	// Brandes' algorithm for finding betweenness centrality for nodes in
+	// and unweighted graph:
+	//
+	// http://www.inf.uni-konstanz.de/algo/publications/b-fabc-01.pdf
+
+	// TODO(kortschak): Consider using the parallel algorithm when
+	// GOMAXPROCS != 1.
+	//
+	// http://htor.inf.ethz.ch/publications/img/edmonds-hoefler-lumsdaine-bc.pdf
+
+	// Also note special case for sparse networks:
+	// http://wwwold.iit.cnr.it/staff/marco.pellegrini/papiri/asonam-final.pdf
+
+	cb := make(map[int64]float64)
+	brandes(g, func(s graph.Node, stack linear.NodeStack, p map[int64][]graph.Node, delta, sigma map[int64]float64) {
+		for stack.Len() != 0 {
+			w := stack.Pop()
+			for _, v := range p[w.ID()] {
+				delta[v.ID()] += sigma[v.ID()] / sigma[w.ID()] * (1 + delta[w.ID()])
+			}
+			if w.ID() != s.ID() {
+				if d := delta[w.ID()]; d != 0 {
+					cb[w.ID()] += d
+				}
+			}
+		}
+	})
+	return cb
+}
+
+// EdgeBetweenness returns the non-zero betweenness centrality for edges in the
+// unweighted graph g. For an edge e the centrality C_B is computed as
+//
+//  C_B(e) = \sum_{s ≠ t ∈ V} (\sigma_{st}(e) / \sigma_{st}),
+//
+// where \sigma_{st} and \sigma_{st}(e) are the number of shortest paths from s
+// to t, and the subset of those paths containing e, respectively.
+//
+// If g is undirected, edges are retained such that u.ID < v.ID where u and v are
+// the nodes of e.
+func EdgeBetweenness(g graph.Graph) map[[2]int64]float64 {
+	// Modified from Brandes' original algorithm as described in Algorithm 7
+	// with the exception that node betweenness is not calculated:
+	//
+	// http://algo.uni-konstanz.de/publications/b-vspbc-08.pdf
+
+	_, isUndirected := g.(graph.Undirected)
+	cb := make(map[[2]int64]float64)
+	brandes(g, func(s graph.Node, stack linear.NodeStack, p map[int64][]graph.Node, delta, sigma map[int64]float64) {
+		for stack.Len() != 0 {
+			w := stack.Pop()
+			for _, v := range p[w.ID()] {
+				c := sigma[v.ID()] / sigma[w.ID()] * (1 + delta[w.ID()])
+				vid := v.ID()
+				wid := w.ID()
+				if isUndirected && wid < vid {
+					vid, wid = wid, vid
+				}
+				cb[[2]int64{vid, wid}] += c
+				delta[v.ID()] += c
+			}
+		}
+	})
+	return cb
+}
+
+// brandes is the common code for Betweenness and EdgeBetweenness. It corresponds
+// to algorithm 1 in http://algo.uni-konstanz.de/publications/b-vspbc-08.pdf with
+// the accumulation loop provided by the accumulate closure.
+func brandes(g graph.Graph, accumulate func(s graph.Node, stack linear.NodeStack, p map[int64][]graph.Node, delta, sigma map[int64]float64)) {
+	var (
+		nodes = g.Nodes()
+		stack linear.NodeStack
+		p     = make(map[int64][]graph.Node, len(nodes))
+		sigma = make(map[int64]float64, len(nodes))
+		d     = make(map[int64]int, len(nodes))
+		delta = make(map[int64]float64, len(nodes))
+		queue linear.NodeQueue
+	)
+	for _, s := range nodes {
+		stack = stack[:0]
+
+		for _, w := range nodes {
+			p[w.ID()] = p[w.ID()][:0]
+		}
+
+		for _, t := range nodes {
+			sigma[t.ID()] = 0
+			d[t.ID()] = -1
+		}
+		sigma[s.ID()] = 1
+		d[s.ID()] = 0
+
+		queue.Enqueue(s)
+		for queue.Len() != 0 {
+			v := queue.Dequeue()
+			stack.Push(v)
+			for _, w := range g.From(v) {
+				// w found for the first time?
+				if d[w.ID()] < 0 {
+					queue.Enqueue(w)
+					d[w.ID()] = d[v.ID()] + 1
+				}
+				// shortest path to w via v?
+				if d[w.ID()] == d[v.ID()]+1 {
+					sigma[w.ID()] += sigma[v.ID()]
+					p[w.ID()] = append(p[w.ID()], v)
+				}
+			}
+		}
+
+		for _, v := range nodes {
+			delta[v.ID()] = 0
+		}
+
+		// S returns vertices in order of non-increasing distance from s
+		accumulate(s, stack, p, delta, sigma)
+	}
+}
+
+// BetweennessWeighted returns the non-zero betweenness centrality for nodes in the weighted
+// graph g used to construct the given shortest paths.
+//
+//  C_B(v) = \sum_{s ≠ v ≠ t ∈ V} (\sigma_{st}(v) / \sigma_{st})
+//
+// where \sigma_{st} and \sigma_{st}(v) are the number of shortest paths from s to t,
+// and the subset of those paths containing v respectively.
+func BetweennessWeighted(g graph.Weighted, p path.AllShortest) map[int64]float64 {
+	cb := make(map[int64]float64)
+
+	nodes := g.Nodes()
+	for i, s := range nodes {
+		for j, t := range nodes {
+			if i == j {
+				continue
+			}
+			d := p.Weight(s, t)
+			if math.IsInf(d, 0) {
+				continue
+			}
+
+			// If we have a unique path, don't do the
+			// extra work needed to get all paths.
+			path, _, unique := p.Between(s, t)
+			if unique {
+				for _, v := range path[1 : len(path)-1] {
+					// For undirected graphs we double count
+					// passage though nodes. This is consistent
+					// with Brandes' algorithm's behaviour.
+					cb[v.ID()]++
+				}
+				continue
+			}
+
+			// Otherwise iterate over all paths.
+			paths, _ := p.AllBetween(s, t)
+			stFrac := 1 / float64(len(paths))
+			for _, path := range paths {
+				for _, v := range path[1 : len(path)-1] {
+					cb[v.ID()] += stFrac
+				}
+			}
+		}
+	}
+
+	return cb
+}
+
+// EdgeBetweennessWeighted returns the non-zero betweenness centrality for edges in
+// the weighted graph g. For an edge e the centrality C_B is computed as
+//
+//  C_B(e) = \sum_{s ≠ t ∈ V} (\sigma_{st}(e) / \sigma_{st}),
+//
+// where \sigma_{st} and \sigma_{st}(e) are the number of shortest paths from s
+// to t, and the subset of those paths containing e, respectively.
+//
+// If g is undirected, edges are retained such that u.ID < v.ID where u and v are
+// the nodes of e.
+func EdgeBetweennessWeighted(g graph.Weighted, p path.AllShortest) map[[2]int64]float64 {
+	cb := make(map[[2]int64]float64)
+
+	_, isUndirected := g.(graph.Undirected)
+	nodes := g.Nodes()
+	for i, s := range nodes {
+		for j, t := range nodes {
+			if i == j {
+				continue
+			}
+			d := p.Weight(s, t)
+			if math.IsInf(d, 0) {
+				continue
+			}
+
+			// If we have a unique path, don't do the
+			// extra work needed to get all paths.
+			path, _, unique := p.Between(s, t)
+			if unique {
+				for k, v := range path[1:] {
+					// For undirected graphs we double count
+					// passage though edges. This is consistent
+					// with Brandes' algorithm's behaviour.
+					uid := path[k].ID()
+					vid := v.ID()
+					if isUndirected && vid < uid {
+						uid, vid = vid, uid
+					}
+					cb[[2]int64{uid, vid}]++
+				}
+				continue
+			}
+
+			// Otherwise iterate over all paths.
+			paths, _ := p.AllBetween(s, t)
+			stFrac := 1 / float64(len(paths))
+			for _, path := range paths {
+				for k, v := range path[1:] {
+					uid := path[k].ID()
+					vid := v.ID()
+					if isUndirected && vid < uid {
+						uid, vid = vid, uid
+					}
+					cb[[2]int64{uid, vid}] += stFrac
+				}
+			}
+		}
+	}
+
+	return cb
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/network/betweenness_test.go b/vendor/gonum.org/v1/gonum/graph/network/betweenness_test.go
new file mode 100644
index 00000000..04fcd056
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/network/betweenness_test.go
@@ -0,0 +1,338 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package network
+
+import (
+	"fmt"
+	"math"
+	"sort"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/graph/path"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+var betweennessTests = []struct {
+	g []set
+
+	wantTol   float64
+	want      map[int64]float64
+	wantEdges map[[2]int64]float64
+}{
+	{
+		// Example graph from http://en.wikipedia.org/wiki/File:PageRanks-Example.svg 16:17, 8 July 2009
+		g: []set{
+			A: nil,
+			B: linksTo(C),
+			C: linksTo(B),
+			D: linksTo(A, B),
+			E: linksTo(D, B, F),
+			F: linksTo(B, E),
+			G: linksTo(B, E),
+			H: linksTo(B, E),
+			I: linksTo(B, E),
+			J: linksTo(E),
+			K: linksTo(E),
+		},
+
+		wantTol: 1e-1,
+		want: map[int64]float64{
+			B: 32,
+			D: 18,
+			E: 48,
+		},
+		wantEdges: map[[2]int64]float64{
+			{A, D}: 20,
+			{B, C}: 20,
+			{B, D}: 16,
+			{B, E}: 12,
+			{B, F}: 9,
+			{B, G}: 9,
+			{B, H}: 9,
+			{B, I}: 9,
+			{D, E}: 20,
+			{E, F}: 11,
+			{E, G}: 11,
+			{E, H}: 11,
+			{E, I}: 11,
+			{E, J}: 20,
+			{E, K}: 20,
+		},
+	},
+	{
+		// Example graph from http://en.wikipedia.org/w/index.php?title=PageRank&oldid=659286279#Power_Method
+		g: []set{
+			A: linksTo(B, C),
+			B: linksTo(D),
+			C: linksTo(D, E),
+			D: linksTo(E),
+			E: linksTo(A),
+		},
+
+		wantTol: 1e-3,
+		want: map[int64]float64{
+			A: 2,
+			B: 0.6667,
+			C: 0.6667,
+			D: 2,
+			E: 0.6667,
+		},
+		wantEdges: map[[2]int64]float64{
+			{A, B}: 2 + 2/3. + 4/2.,
+			{A, C}: 2 + 2/3. + 2/2.,
+			{A, E}: 2 + 2/3. + 2/2.,
+			{B, D}: 2 + 2/3. + 4/2.,
+			{C, D}: 2 + 2/3. + 2/2.,
+			{C, E}: 2,
+			{D, E}: 2 + 2/3. + 2/2.,
+		},
+	},
+	{
+		g: []set{
+			A: linksTo(B),
+			B: linksTo(C),
+			C: nil,
+		},
+
+		wantTol: 1e-3,
+		want: map[int64]float64{
+			B: 2,
+		},
+		wantEdges: map[[2]int64]float64{
+			{A, B}: 4,
+			{B, C}: 4,
+		},
+	},
+	{
+		g: []set{
+			A: linksTo(B),
+			B: linksTo(C),
+			C: linksTo(D),
+			D: linksTo(E),
+			E: nil,
+		},
+
+		wantTol: 1e-3,
+		want: map[int64]float64{
+			B: 6,
+			C: 8,
+			D: 6,
+		},
+		wantEdges: map[[2]int64]float64{
+			{A, B}: 8,
+			{B, C}: 12,
+			{C, D}: 12,
+			{D, E}: 8,
+		},
+	},
+	{
+		g: []set{
+			A: linksTo(C),
+			B: linksTo(C),
+			C: nil,
+			D: linksTo(C),
+			E: linksTo(C),
+		},
+
+		wantTol: 1e-3,
+		want: map[int64]float64{
+			C: 12,
+		},
+		wantEdges: map[[2]int64]float64{
+			{A, C}: 8,
+			{B, C}: 8,
+			{C, D}: 8,
+			{C, E}: 8,
+		},
+	},
+	{
+		g: []set{
+			A: linksTo(B, C, D, E),
+			B: linksTo(C, D, E),
+			C: linksTo(D, E),
+			D: linksTo(E),
+			E: nil,
+		},
+
+		wantTol: 1e-3,
+		want:    map[int64]float64{},
+		wantEdges: map[[2]int64]float64{
+			{A, B}: 2,
+			{A, C}: 2,
+			{A, D}: 2,
+			{A, E}: 2,
+			{B, C}: 2,
+			{B, D}: 2,
+			{B, E}: 2,
+			{C, D}: 2,
+			{C, E}: 2,
+			{D, E}: 2,
+		},
+	},
+}
+
+func TestBetweenness(t *testing.T) {
+	for i, test := range betweennessTests {
+		g := simple.NewUndirectedGraph()
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+		got := Betweenness(g)
+		prec := 1 - int(math.Log10(test.wantTol))
+		for n := range test.g {
+			wantN, gotOK := got[int64(n)]
+			gotN, wantOK := test.want[int64(n)]
+			if gotOK != wantOK {
+				t.Errorf("unexpected betweenness result for test %d, node %c", i, n+'A')
+			}
+			if !floats.EqualWithinAbsOrRel(gotN, wantN, test.wantTol, test.wantTol) {
+				t.Errorf("unexpected betweenness result for test %d:\ngot: %v\nwant:%v",
+					i, orderedFloats(got, prec), orderedFloats(test.want, prec))
+				break
+			}
+		}
+	}
+}
+
+func TestEdgeBetweenness(t *testing.T) {
+	for i, test := range betweennessTests {
+		g := simple.NewUndirectedGraph()
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+		got := EdgeBetweenness(g)
+		prec := 1 - int(math.Log10(test.wantTol))
+	outer:
+		for u := range test.g {
+			for v := range test.g {
+				wantQ, gotOK := got[[2]int64{int64(u), int64(v)}]
+				gotQ, wantOK := test.wantEdges[[2]int64{int64(u), int64(v)}]
+				if gotOK != wantOK {
+					t.Errorf("unexpected betweenness result for test %d, edge (%c,%c)", i, u+'A', v+'A')
+				}
+				if !floats.EqualWithinAbsOrRel(gotQ, wantQ, test.wantTol, test.wantTol) {
+					t.Errorf("unexpected betweenness result for test %d:\ngot: %v\nwant:%v",
+						i, orderedPairFloats(got, prec), orderedPairFloats(test.wantEdges, prec))
+					break outer
+				}
+			}
+		}
+	}
+}
+
+func TestBetweennessWeighted(t *testing.T) {
+	for i, test := range betweennessTests {
+		g := simple.NewWeightedUndirectedGraph(0, math.Inf(1))
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetWeightedEdge(simple.WeightedEdge{F: simple.Node(u), T: simple.Node(v), W: 1})
+			}
+		}
+
+		p, ok := path.FloydWarshall(g)
+		if !ok {
+			t.Errorf("unexpected negative cycle in test %d", i)
+			continue
+		}
+
+		got := BetweennessWeighted(g, p)
+		prec := 1 - int(math.Log10(test.wantTol))
+		for n := range test.g {
+			gotN, gotOK := got[int64(n)]
+			wantN, wantOK := test.want[int64(n)]
+			if gotOK != wantOK {
+				t.Errorf("unexpected betweenness existence for test %d, node %c", i, n+'A')
+			}
+			if !floats.EqualWithinAbsOrRel(gotN, wantN, test.wantTol, test.wantTol) {
+				t.Errorf("unexpected betweenness result for test %d:\ngot: %v\nwant:%v",
+					i, orderedFloats(got, prec), orderedFloats(test.want, prec))
+				break
+			}
+		}
+	}
+}
+
+func TestEdgeBetweennessWeighted(t *testing.T) {
+	for i, test := range betweennessTests {
+		g := simple.NewWeightedUndirectedGraph(0, math.Inf(1))
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetWeightedEdge(simple.WeightedEdge{F: simple.Node(u), T: simple.Node(v), W: 1})
+			}
+		}
+
+		p, ok := path.FloydWarshall(g)
+		if !ok {
+			t.Errorf("unexpected negative cycle in test %d", i)
+			continue
+		}
+
+		got := EdgeBetweennessWeighted(g, p)
+		prec := 1 - int(math.Log10(test.wantTol))
+	outer:
+		for u := range test.g {
+			for v := range test.g {
+				wantQ, gotOK := got[[2]int64{int64(u), int64(v)}]
+				gotQ, wantOK := test.wantEdges[[2]int64{int64(u), int64(v)}]
+				if gotOK != wantOK {
+					t.Errorf("unexpected betweenness result for test %d, edge (%c,%c)", i, u+'A', v+'A')
+				}
+				if !floats.EqualWithinAbsOrRel(gotQ, wantQ, test.wantTol, test.wantTol) {
+					t.Errorf("unexpected betweenness result for test %d:\ngot: %v\nwant:%v",
+						i, orderedPairFloats(got, prec), orderedPairFloats(test.wantEdges, prec))
+					break outer
+				}
+			}
+		}
+	}
+}
+
+func orderedPairFloats(w map[[2]int64]float64, prec int) []pairKeyFloatVal {
+	o := make(orderedPairFloatsMap, 0, len(w))
+	for k, v := range w {
+		o = append(o, pairKeyFloatVal{prec: prec, key: k, val: v})
+	}
+	sort.Sort(o)
+	return o
+}
+
+type pairKeyFloatVal struct {
+	prec int
+	key  [2]int64
+	val  float64
+}
+
+func (kv pairKeyFloatVal) String() string {
+	return fmt.Sprintf("(%c,%c):%.*f", kv.key[0]+'A', kv.key[1]+'A', kv.prec, kv.val)
+}
+
+type orderedPairFloatsMap []pairKeyFloatVal
+
+func (o orderedPairFloatsMap) Len() int { return len(o) }
+func (o orderedPairFloatsMap) Less(i, j int) bool {
+	return o[i].key[0] < o[j].key[0] || (o[i].key[0] == o[j].key[0] && o[i].key[1] < o[j].key[1])
+}
+func (o orderedPairFloatsMap) Swap(i, j int) { o[i], o[j] = o[j], o[i] }
diff --git a/vendor/gonum.org/v1/gonum/graph/network/distance.go b/vendor/gonum.org/v1/gonum/graph/network/distance.go
new file mode 100644
index 00000000..7e5ef6a3
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/network/distance.go
@@ -0,0 +1,124 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package network
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/path"
+)
+
+// Closeness returns the closeness centrality for nodes in the graph g used to
+// construct the given shortest paths.
+//
+//  C(v) = 1 / \sum_u d(u,v)
+//
+// For directed graphs the incoming paths are used. Infinite distances are
+// not considered.
+func Closeness(g graph.Graph, p path.AllShortest) map[int64]float64 {
+	nodes := g.Nodes()
+	c := make(map[int64]float64, len(nodes))
+	for _, u := range nodes {
+		var sum float64
+		for _, v := range nodes {
+			// The ordering here is not relevant for
+			// undirected graphs, but we make sure we
+			// are counting incoming paths.
+			d := p.Weight(v, u)
+			if math.IsInf(d, 0) {
+				continue
+			}
+			sum += d
+		}
+		c[u.ID()] = 1 / sum
+	}
+	return c
+}
+
+// Farness returns the farness for nodes in the graph g used to construct
+// the given shortest paths.
+//
+//  F(v) = \sum_u d(u,v)
+//
+// For directed graphs the incoming paths are used. Infinite distances are
+// not considered.
+func Farness(g graph.Graph, p path.AllShortest) map[int64]float64 {
+	nodes := g.Nodes()
+	f := make(map[int64]float64, len(nodes))
+	for _, u := range nodes {
+		var sum float64
+		for _, v := range nodes {
+			// The ordering here is not relevant for
+			// undirected graphs, but we make sure we
+			// are counting incoming paths.
+			d := p.Weight(v, u)
+			if math.IsInf(d, 0) {
+				continue
+			}
+			sum += d
+		}
+		f[u.ID()] = sum
+	}
+	return f
+}
+
+// Harmonic returns the harmonic centrality for nodes in the graph g used to
+// construct the given shortest paths.
+//
+//  H(v)= \sum_{u ≠ v} 1 / d(u,v)
+//
+// For directed graphs the incoming paths are used. Infinite distances are
+// not considered.
+func Harmonic(g graph.Graph, p path.AllShortest) map[int64]float64 {
+	nodes := g.Nodes()
+	h := make(map[int64]float64, len(nodes))
+	for i, u := range nodes {
+		var sum float64
+		for j, v := range nodes {
+			// The ordering here is not relevant for
+			// undirected graphs, but we make sure we
+			// are counting incoming paths.
+			d := p.Weight(v, u)
+			if math.IsInf(d, 0) {
+				continue
+			}
+			if i != j {
+				sum += 1 / d
+			}
+		}
+		h[u.ID()] = sum
+	}
+	return h
+}
+
+// Residual returns the Dangalchev's residual closeness for nodes in the graph
+// g used to construct the given shortest paths.
+//
+//  C(v)= \sum_{u ≠ v} 1 / 2^d(u,v)
+//
+// For directed graphs the incoming paths are used. Infinite distances are
+// not considered.
+func Residual(g graph.Graph, p path.AllShortest) map[int64]float64 {
+	nodes := g.Nodes()
+	r := make(map[int64]float64, len(nodes))
+	for i, u := range nodes {
+		var sum float64
+		for j, v := range nodes {
+			// The ordering here is not relevant for
+			// undirected graphs, but we make sure we
+			// are counting incoming paths.
+			d := p.Weight(v, u)
+			if math.IsInf(d, 0) {
+				continue
+			}
+			if i != j {
+				sum += math.Exp2(-d)
+			}
+		}
+		r[u.ID()] = sum
+	}
+	return r
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/network/distance_test.go b/vendor/gonum.org/v1/gonum/graph/network/distance_test.go
new file mode 100644
index 00000000..4015883b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/network/distance_test.go
@@ -0,0 +1,394 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package network
+
+import (
+	"math"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/graph/path"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+var undirectedCentralityTests = []struct {
+	g []set
+
+	farness  map[int64]float64
+	harmonic map[int64]float64
+	residual map[int64]float64
+}{
+	{
+		g: []set{
+			A: linksTo(B),
+			B: linksTo(C),
+			C: nil,
+		},
+
+		farness: map[int64]float64{
+			A: 1 + 2,
+			B: 1 + 1,
+			C: 2 + 1,
+		},
+		harmonic: map[int64]float64{
+			A: 1 + 1.0/2.0,
+			B: 1 + 1,
+			C: 1.0/2.0 + 1,
+		},
+		residual: map[int64]float64{
+			A: 1/math.Exp2(1) + 1/math.Exp2(2),
+			B: 1/math.Exp2(1) + 1/math.Exp2(1),
+			C: 1/math.Exp2(2) + 1/math.Exp2(1),
+		},
+	},
+	{
+		g: []set{
+			A: linksTo(B),
+			B: linksTo(C),
+			C: linksTo(D),
+			D: linksTo(E),
+			E: nil,
+		},
+
+		farness: map[int64]float64{
+			A: 1 + 2 + 3 + 4,
+			B: 1 + 1 + 2 + 3,
+			C: 2 + 1 + 1 + 2,
+			D: 3 + 2 + 1 + 1,
+			E: 4 + 3 + 2 + 1,
+		},
+		harmonic: map[int64]float64{
+			A: 1 + 1.0/2.0 + 1.0/3.0 + 1.0/4.0,
+			B: 1 + 1 + 1.0/2.0 + 1.0/3.0,
+			C: 1.0/2.0 + 1 + 1 + 1.0/2.0,
+			D: 1.0/3.0 + 1.0/2.0 + 1 + 1,
+			E: 1.0/4.0 + 1.0/3.0 + 1.0/2.0 + 1,
+		},
+		residual: map[int64]float64{
+			A: 1/math.Exp2(1) + 1/math.Exp2(2) + 1/math.Exp2(3) + 1/math.Exp2(4),
+			B: 1/math.Exp2(1) + 1/math.Exp2(1) + 1/math.Exp2(2) + 1/math.Exp2(3),
+			C: 1/math.Exp2(2) + 1/math.Exp2(1) + 1/math.Exp2(1) + 1/math.Exp2(2),
+			D: 1/math.Exp2(3) + 1/math.Exp2(2) + 1/math.Exp2(1) + 1/math.Exp2(1),
+			E: 1/math.Exp2(4) + 1/math.Exp2(3) + 1/math.Exp2(2) + 1/math.Exp2(1),
+		},
+	},
+	{
+		g: []set{
+			A: linksTo(C),
+			B: linksTo(C),
+			C: nil,
+			D: linksTo(C),
+			E: linksTo(C),
+		},
+
+		farness: map[int64]float64{
+			A: 2 + 2 + 1 + 2,
+			B: 2 + 1 + 2 + 2,
+			C: 1 + 1 + 1 + 1,
+			D: 2 + 1 + 2 + 2,
+			E: 2 + 2 + 1 + 2,
+		},
+		harmonic: map[int64]float64{
+			A: 1.0/2.0 + 1.0/2.0 + 1 + 1.0/2.0,
+			B: 1.0/2.0 + 1 + 1.0/2.0 + 1.0/2.0,
+			C: 1 + 1 + 1 + 1,
+			D: 1.0/2.0 + 1 + 1.0/2.0 + 1.0/2.0,
+			E: 1.0/2.0 + 1.0/2.0 + 1 + 1.0/2.0,
+		},
+		residual: map[int64]float64{
+			A: 1/math.Exp2(2) + 1/math.Exp2(2) + 1/math.Exp2(1) + 1/math.Exp2(2),
+			B: 1/math.Exp2(2) + 1/math.Exp2(1) + 1/math.Exp2(2) + 1/math.Exp2(2),
+			C: 1/math.Exp2(1) + 1/math.Exp2(1) + 1/math.Exp2(1) + 1/math.Exp2(1),
+			D: 1/math.Exp2(2) + 1/math.Exp2(1) + 1/math.Exp2(2) + 1/math.Exp2(2),
+			E: 1/math.Exp2(2) + 1/math.Exp2(2) + 1/math.Exp2(1) + 1/math.Exp2(2),
+		},
+	},
+	{
+		g: []set{
+			A: linksTo(B, C, D, E),
+			B: linksTo(C, D, E),
+			C: linksTo(D, E),
+			D: linksTo(E),
+			E: nil,
+		},
+
+		farness: map[int64]float64{
+			A: 1 + 1 + 1 + 1,
+			B: 1 + 1 + 1 + 1,
+			C: 1 + 1 + 1 + 1,
+			D: 1 + 1 + 1 + 1,
+			E: 1 + 1 + 1 + 1,
+		},
+		harmonic: map[int64]float64{
+			A: 1 + 1 + 1 + 1,
+			B: 1 + 1 + 1 + 1,
+			C: 1 + 1 + 1 + 1,
+			D: 1 + 1 + 1 + 1,
+			E: 1 + 1 + 1 + 1,
+		},
+		residual: map[int64]float64{
+			A: 1/math.Exp2(1) + 1/math.Exp2(1) + 1/math.Exp2(1) + 1/math.Exp2(1),
+			B: 1/math.Exp2(1) + 1/math.Exp2(1) + 1/math.Exp2(1) + 1/math.Exp2(1),
+			C: 1/math.Exp2(1) + 1/math.Exp2(1) + 1/math.Exp2(1) + 1/math.Exp2(1),
+			D: 1/math.Exp2(1) + 1/math.Exp2(1) + 1/math.Exp2(1) + 1/math.Exp2(1),
+			E: 1/math.Exp2(1) + 1/math.Exp2(1) + 1/math.Exp2(1) + 1/math.Exp2(1),
+		},
+	},
+}
+
+func TestDistanceCentralityUndirected(t *testing.T) {
+	const tol = 1e-12
+	prec := 1 - int(math.Log10(tol))
+
+	for i, test := range undirectedCentralityTests {
+		g := simple.NewWeightedUndirectedGraph(0, math.Inf(1))
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetWeightedEdge(simple.WeightedEdge{F: simple.Node(u), T: simple.Node(v), W: 1})
+			}
+		}
+		p, ok := path.FloydWarshall(g)
+		if !ok {
+			t.Errorf("unexpected negative cycle in test %d", i)
+			continue
+		}
+
+		var got map[int64]float64
+
+		got = Closeness(g, p)
+		for n := range test.g {
+			if !floats.EqualWithinAbsOrRel(got[int64(n)], 1/test.farness[int64(n)], tol, tol) {
+				want := make(map[int64]float64)
+				for n, v := range test.farness {
+					want[n] = 1 / v
+				}
+				t.Errorf("unexpected closeness centrality for test %d:\ngot: %v\nwant:%v",
+					i, orderedFloats(got, prec), orderedFloats(want, prec))
+				break
+			}
+		}
+
+		got = Farness(g, p)
+		for n := range test.g {
+			if !floats.EqualWithinAbsOrRel(got[int64(n)], test.farness[int64(n)], tol, tol) {
+				t.Errorf("unexpected farness for test %d:\ngot: %v\nwant:%v",
+					i, orderedFloats(got, prec), orderedFloats(test.farness, prec))
+				break
+			}
+		}
+
+		got = Harmonic(g, p)
+		for n := range test.g {
+			if !floats.EqualWithinAbsOrRel(got[int64(n)], test.harmonic[int64(n)], tol, tol) {
+				t.Errorf("unexpected harmonic centrality for test %d:\ngot: %v\nwant:%v",
+					i, orderedFloats(got, prec), orderedFloats(test.harmonic, prec))
+				break
+			}
+		}
+
+		got = Residual(g, p)
+		for n := range test.g {
+			if !floats.EqualWithinAbsOrRel(got[int64(n)], test.residual[int64(n)], tol, tol) {
+				t.Errorf("unexpected residual closeness for test %d:\ngot: %v\nwant:%v",
+					i, orderedFloats(got, prec), orderedFloats(test.residual, prec))
+				break
+			}
+		}
+	}
+}
+
+var directedCentralityTests = []struct {
+	g []set
+
+	farness  map[int64]float64
+	harmonic map[int64]float64
+	residual map[int64]float64
+}{
+	{
+		g: []set{
+			A: linksTo(B),
+			B: linksTo(C),
+			C: nil,
+		},
+
+		farness: map[int64]float64{
+			A: 0,
+			B: 1,
+			C: 2 + 1,
+		},
+		harmonic: map[int64]float64{
+			A: 0,
+			B: 1,
+			C: 1.0/2.0 + 1,
+		},
+		residual: map[int64]float64{
+			A: 0,
+			B: 1 / math.Exp2(1),
+			C: 1/math.Exp2(2) + 1/math.Exp2(1),
+		},
+	},
+	{
+		g: []set{
+			A: linksTo(B),
+			B: linksTo(C),
+			C: linksTo(D),
+			D: linksTo(E),
+			E: nil,
+		},
+
+		farness: map[int64]float64{
+			A: 0,
+			B: 1,
+			C: 2 + 1,
+			D: 3 + 2 + 1,
+			E: 4 + 3 + 2 + 1,
+		},
+		harmonic: map[int64]float64{
+			A: 0,
+			B: 1,
+			C: 1.0/2.0 + 1,
+			D: 1.0/3.0 + 1.0/2.0 + 1,
+			E: 1.0/4.0 + 1.0/3.0 + 1.0/2.0 + 1,
+		},
+		residual: map[int64]float64{
+			A: 0,
+			B: 1 / math.Exp2(1),
+			C: 1/math.Exp2(2) + 1/math.Exp2(1),
+			D: 1/math.Exp2(3) + 1/math.Exp2(2) + 1/math.Exp2(1),
+			E: 1/math.Exp2(4) + 1/math.Exp2(3) + 1/math.Exp2(2) + 1/math.Exp2(1),
+		},
+	},
+	{
+		g: []set{
+			A: linksTo(C),
+			B: linksTo(C),
+			C: nil,
+			D: linksTo(C),
+			E: linksTo(C),
+		},
+
+		farness: map[int64]float64{
+			A: 0,
+			B: 0,
+			C: 1 + 1 + 1 + 1,
+			D: 0,
+			E: 0,
+		},
+		harmonic: map[int64]float64{
+			A: 0,
+			B: 0,
+			C: 1 + 1 + 1 + 1,
+			D: 0,
+			E: 0,
+		},
+		residual: map[int64]float64{
+			A: 0,
+			B: 0,
+			C: 1/math.Exp2(1) + 1/math.Exp2(1) + 1/math.Exp2(1) + 1/math.Exp2(1),
+			D: 0,
+			E: 0,
+		},
+	},
+	{
+		g: []set{
+			A: linksTo(B, C, D, E),
+			B: linksTo(C, D, E),
+			C: linksTo(D, E),
+			D: linksTo(E),
+			E: nil,
+		},
+
+		farness: map[int64]float64{
+			A: 0,
+			B: 1,
+			C: 1 + 1,
+			D: 1 + 1 + 1,
+			E: 1 + 1 + 1 + 1,
+		},
+		harmonic: map[int64]float64{
+			A: 0,
+			B: 1,
+			C: 1 + 1,
+			D: 1 + 1 + 1,
+			E: 1 + 1 + 1 + 1,
+		},
+		residual: map[int64]float64{
+			A: 0,
+			B: 1 / math.Exp2(1),
+			C: 1/math.Exp2(1) + 1/math.Exp2(1),
+			D: 1/math.Exp2(1) + 1/math.Exp2(1) + 1/math.Exp2(1),
+			E: 1/math.Exp2(1) + 1/math.Exp2(1) + 1/math.Exp2(1) + 1/math.Exp2(1),
+		},
+	},
+}
+
+func TestDistanceCentralityDirected(t *testing.T) {
+	const tol = 1e-12
+	prec := 1 - int(math.Log10(tol))
+
+	for i, test := range directedCentralityTests {
+		g := simple.NewWeightedDirectedGraph(0, math.Inf(1))
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetWeightedEdge(simple.WeightedEdge{F: simple.Node(u), T: simple.Node(v), W: 1})
+			}
+		}
+		p, ok := path.FloydWarshall(g)
+		if !ok {
+			t.Errorf("unexpected negative cycle in test %d", i)
+			continue
+		}
+
+		var got map[int64]float64
+
+		got = Closeness(g, p)
+		for n := range test.g {
+			if !floats.EqualWithinAbsOrRel(got[int64(n)], 1/test.farness[int64(n)], tol, tol) {
+				want := make(map[int64]float64)
+				for n, v := range test.farness {
+					want[int64(n)] = 1 / v
+				}
+				t.Errorf("unexpected closeness centrality for test %d:\ngot: %v\nwant:%v",
+					i, orderedFloats(got, prec), orderedFloats(want, prec))
+				break
+			}
+		}
+
+		got = Farness(g, p)
+		for n := range test.g {
+			if !floats.EqualWithinAbsOrRel(got[int64(n)], test.farness[int64(n)], tol, tol) {
+				t.Errorf("unexpected farness for test %d:\ngot: %v\nwant:%v",
+					i, orderedFloats(got, prec), orderedFloats(test.farness, prec))
+				break
+			}
+		}
+
+		got = Harmonic(g, p)
+		for n := range test.g {
+			if !floats.EqualWithinAbsOrRel(got[int64(n)], test.harmonic[int64(n)], tol, tol) {
+				t.Errorf("unexpected harmonic centrality for test %d:\ngot: %v\nwant:%v",
+					i, orderedFloats(got, prec), orderedFloats(test.harmonic, prec))
+				break
+			}
+		}
+
+		got = Residual(g, p)
+		for n := range test.g {
+			if !floats.EqualWithinAbsOrRel(got[int64(n)], test.residual[int64(n)], tol, tol) {
+				t.Errorf("unexpected residual closeness for test %d:\ngot: %v\nwant:%v",
+					i, orderedFloats(got, prec), orderedFloats(test.residual, prec))
+				break
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/network/doc.go b/vendor/gonum.org/v1/gonum/graph/network/doc.go
new file mode 100644
index 00000000..c456f2da
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/network/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package network provides network analysis functions.
+package network // import "gonum.org/v1/gonum/graph/network"
diff --git a/vendor/gonum.org/v1/gonum/graph/network/hits.go b/vendor/gonum.org/v1/gonum/graph/network/hits.go
new file mode 100644
index 00000000..53ef944c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/network/hits.go
@@ -0,0 +1,101 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package network
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/graph"
+)
+
+// HubAuthority is a Hyperlink-Induced Topic Search hub-authority score pair.
+type HubAuthority struct {
+	Hub       float64
+	Authority float64
+}
+
+// HITS returns the Hyperlink-Induced Topic Search hub-authority scores for
+// nodes of the directed graph g. HITS terminates when the 2-norm of the
+// vector difference between iterations is below tol. The returned map is
+// keyed on the graph node IDs.
+func HITS(g graph.Directed, tol float64) map[int64]HubAuthority {
+	nodes := g.Nodes()
+
+	// Make a topological copy of g with dense node IDs.
+	indexOf := make(map[int64]int, len(nodes))
+	for i, n := range nodes {
+		indexOf[n.ID()] = i
+	}
+	nodesLinkingTo := make([][]int, len(nodes))
+	nodesLinkedFrom := make([][]int, len(nodes))
+	for i, n := range nodes {
+		for _, u := range g.To(n) {
+			nodesLinkingTo[i] = append(nodesLinkingTo[i], indexOf[u.ID()])
+		}
+		for _, v := range g.From(n) {
+			nodesLinkedFrom[i] = append(nodesLinkedFrom[i], indexOf[v.ID()])
+		}
+	}
+	indexOf = nil
+
+	w := make([]float64, 4*len(nodes))
+	auth := w[:len(nodes)]
+	hub := w[len(nodes) : 2*len(nodes)]
+	for i := range nodes {
+		auth[i] = 1
+		hub[i] = 1
+	}
+	deltaAuth := w[2*len(nodes) : 3*len(nodes)]
+	deltaHub := w[3*len(nodes):]
+
+	var norm float64
+	for {
+		norm = 0
+		for v := range nodes {
+			var a float64
+			for _, u := range nodesLinkingTo[v] {
+				a += hub[u]
+			}
+			deltaAuth[v] = auth[v]
+			auth[v] = a
+			norm += a * a
+		}
+		norm = math.Sqrt(norm)
+
+		for i := range auth {
+			auth[i] /= norm
+			deltaAuth[i] -= auth[i]
+		}
+
+		norm = 0
+		for u := range nodes {
+			var h float64
+			for _, v := range nodesLinkedFrom[u] {
+				h += auth[v]
+			}
+			deltaHub[u] = hub[u]
+			hub[u] = h
+			norm += h * h
+		}
+		norm = math.Sqrt(norm)
+
+		for i := range hub {
+			hub[i] /= norm
+			deltaHub[i] -= hub[i]
+		}
+
+		if floats.Norm(deltaAuth, 2) < tol && floats.Norm(deltaHub, 2) < tol {
+			break
+		}
+	}
+
+	hubAuth := make(map[int64]HubAuthority, len(nodes))
+	for i, n := range nodes {
+		hubAuth[n.ID()] = HubAuthority{Hub: hub[i], Authority: auth[i]}
+	}
+
+	return hubAuth
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/network/hits_test.go b/vendor/gonum.org/v1/gonum/graph/network/hits_test.go
new file mode 100644
index 00000000..b711f36e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/network/hits_test.go
@@ -0,0 +1,98 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package network
+
+import (
+	"fmt"
+	"math"
+	"sort"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+var hitsTests = []struct {
+	g   []set
+	tol float64
+
+	wantTol float64
+	want    map[int64]HubAuthority
+}{
+	{
+		// Example graph from http://www.cis.hut.fi/Opinnot/T-61.6020/2008/pagerank_hits.pdf page 8.
+		g: []set{
+			A: linksTo(B, C, D),
+			B: linksTo(C, D),
+			C: linksTo(B),
+			D: nil,
+		},
+		tol: 1e-4,
+
+		wantTol: 1e-4,
+		want: map[int64]HubAuthority{
+			A: {Hub: 0.7887, Authority: 0},
+			B: {Hub: 0.5774, Authority: 0.4597},
+			C: {Hub: 0.2113, Authority: 0.6280},
+			D: {Hub: 0, Authority: 0.6280},
+		},
+	},
+}
+
+func TestHITS(t *testing.T) {
+	for i, test := range hitsTests {
+		g := simple.NewDirectedGraph()
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+		got := HITS(g, test.tol)
+		prec := 1 - int(math.Log10(test.wantTol))
+		for n := range test.g {
+			if !floats.EqualWithinAbsOrRel(got[int64(n)].Hub, test.want[int64(n)].Hub, test.wantTol, test.wantTol) {
+				t.Errorf("unexpected HITS result for test %d:\ngot: %v\nwant:%v",
+					i, orderedHubAuth(got, prec), orderedHubAuth(test.want, prec))
+				break
+			}
+			if !floats.EqualWithinAbsOrRel(got[int64(n)].Authority, test.want[int64(n)].Authority, test.wantTol, test.wantTol) {
+				t.Errorf("unexpected HITS result for test %d:\ngot: %v\nwant:%v",
+					i, orderedHubAuth(got, prec), orderedHubAuth(test.want, prec))
+				break
+			}
+		}
+	}
+}
+
+func orderedHubAuth(w map[int64]HubAuthority, prec int) []keyHubAuthVal {
+	o := make(orderedHubAuthMap, 0, len(w))
+	for k, v := range w {
+		o = append(o, keyHubAuthVal{prec: prec, key: k, val: v})
+	}
+	sort.Sort(o)
+	return o
+}
+
+type keyHubAuthVal struct {
+	prec int
+	key  int64
+	val  HubAuthority
+}
+
+func (kv keyHubAuthVal) String() string {
+	return fmt.Sprintf("%d:{H:%.*f, A:%.*f}",
+		kv.key, kv.prec, kv.val.Hub, kv.prec, kv.val.Authority,
+	)
+}
+
+type orderedHubAuthMap []keyHubAuthVal
+
+func (o orderedHubAuthMap) Len() int           { return len(o) }
+func (o orderedHubAuthMap) Less(i, j int) bool { return o[i].key < o[j].key }
+func (o orderedHubAuthMap) Swap(i, j int)      { o[i], o[j] = o[j], o[i] }
diff --git a/vendor/gonum.org/v1/gonum/graph/network/network.go b/vendor/gonum.org/v1/gonum/graph/network/network.go
new file mode 100644
index 00000000..2faabdea
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/network/network.go
@@ -0,0 +1,13 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// TODO(kortschak): Implement:
+// * edge-weighted PageRank and HITS
+// * PersonalizedPageRank:
+//    http://infolab.stanford.edu/~backrub/google.html 2.1.2 Intuitive Justification
+//    http://ilpubs.stanford.edu:8090/596/1/2003-35.pdf
+//    http://www.vldb.org/pvldb/vol7/p1023-maehara.pdf
+// * other centrality measures
+
+package network
diff --git a/vendor/gonum.org/v1/gonum/graph/network/network_test.go b/vendor/gonum.org/v1/gonum/graph/network/network_test.go
new file mode 100644
index 00000000..b999c218
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/network/network_test.go
@@ -0,0 +1,33 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package network
+
+const (
+	A = iota
+	B
+	C
+	D
+	E
+	F
+	G
+	H
+	I
+	J
+	K
+)
+
+// set is an integer set.
+type set map[int64]struct{}
+
+func linksTo(i ...int64) set {
+	if len(i) == 0 {
+		return nil
+	}
+	s := make(set)
+	for _, v := range i {
+		s[v] = struct{}{}
+	}
+	return s
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/network/page.go b/vendor/gonum.org/v1/gonum/graph/network/page.go
new file mode 100644
index 00000000..fb2c58e3
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/network/page.go
@@ -0,0 +1,228 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package network
+
+import (
+	"math"
+	"math/rand"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/mat"
+)
+
+// PageRank returns the PageRank weights for nodes of the directed graph g
+// using the given damping factor and terminating when the 2-norm of the
+// vector difference between iterations is below tol. The returned map is
+// keyed on the graph node IDs.
+func PageRank(g graph.Directed, damp, tol float64) map[int64]float64 {
+	// PageRank is implemented according to "How Google Finds Your Needle
+	// in the Web's Haystack".
+	//
+	// G.I^k = alpha.S.I^k + (1-alpha).1/n.1.I^k
+	//
+	// http://www.ams.org/samplings/feature-column/fcarc-pagerank
+
+	nodes := g.Nodes()
+	indexOf := make(map[int64]int, len(nodes))
+	for i, n := range nodes {
+		indexOf[n.ID()] = i
+	}
+
+	m := mat.NewDense(len(nodes), len(nodes), nil)
+	dangling := damp / float64(len(nodes))
+	for j, u := range nodes {
+		to := g.From(u)
+		f := damp / float64(len(to))
+		for _, v := range to {
+			m.Set(indexOf[v.ID()], j, f)
+		}
+		if len(to) == 0 {
+			for i := range nodes {
+				m.Set(i, j, dangling)
+			}
+		}
+	}
+	matrix := m.RawMatrix().Data
+	dt := (1 - damp) / float64(len(nodes))
+	for i := range matrix {
+		matrix[i] += dt
+	}
+
+	last := make([]float64, len(nodes))
+	for i := range last {
+		last[i] = 1
+	}
+	lastV := mat.NewVecDense(len(nodes), last)
+
+	vec := make([]float64, len(nodes))
+	var sum float64
+	for i := range vec {
+		r := rand.NormFloat64()
+		sum += r
+		vec[i] = r
+	}
+	f := 1 / sum
+	for i := range vec {
+		vec[i] *= f
+	}
+	v := mat.NewVecDense(len(nodes), vec)
+
+	for {
+		lastV, v = v, lastV
+		v.MulVec(m, lastV)
+		if normDiff(vec, last) < tol {
+			break
+		}
+	}
+
+	ranks := make(map[int64]float64, len(nodes))
+	for i, r := range v.RawVector().Data {
+		ranks[nodes[i].ID()] = r
+	}
+
+	return ranks
+}
+
+// PageRankSparse returns the PageRank weights for nodes of the sparse directed
+// graph g using the given damping factor and terminating when the 2-norm of the
+// vector difference between iterations is below tol. The returned map is
+// keyed on the graph node IDs.
+func PageRankSparse(g graph.Directed, damp, tol float64) map[int64]float64 {
+	// PageRankSparse is implemented according to "How Google Finds Your Needle
+	// in the Web's Haystack".
+	//
+	// G.I^k = alpha.H.I^k + alpha.A.I^k + (1-alpha).1/n.1.I^k
+	//
+	// http://www.ams.org/samplings/feature-column/fcarc-pagerank
+
+	nodes := g.Nodes()
+	indexOf := make(map[int64]int, len(nodes))
+	for i, n := range nodes {
+		indexOf[n.ID()] = i
+	}
+
+	m := make(rowCompressedMatrix, len(nodes))
+	var dangling compressedRow
+	df := damp / float64(len(nodes))
+	for j, u := range nodes {
+		to := g.From(u)
+		f := damp / float64(len(to))
+		for _, v := range to {
+			m.addTo(indexOf[v.ID()], j, f)
+		}
+		if len(to) == 0 {
+			dangling.addTo(j, df)
+		}
+	}
+
+	last := make([]float64, len(nodes))
+	for i := range last {
+		last[i] = 1
+	}
+	lastV := mat.NewVecDense(len(nodes), last)
+
+	vec := make([]float64, len(nodes))
+	var sum float64
+	for i := range vec {
+		r := rand.NormFloat64()
+		sum += r
+		vec[i] = r
+	}
+	f := 1 / sum
+	for i := range vec {
+		vec[i] *= f
+	}
+	v := mat.NewVecDense(len(nodes), vec)
+
+	dt := (1 - damp) / float64(len(nodes))
+	for {
+		lastV, v = v, lastV
+
+		m.mulVecUnitary(v, lastV)          // First term of the G matrix equation;
+		with := dangling.dotUnitary(lastV) // Second term;
+		away := onesDotUnitary(dt, lastV)  // Last term.
+
+		floats.AddConst(with+away, v.RawVector().Data)
+		if normDiff(vec, last) < tol {
+			break
+		}
+	}
+
+	ranks := make(map[int64]float64, len(nodes))
+	for i, r := range v.RawVector().Data {
+		ranks[nodes[i].ID()] = r
+	}
+
+	return ranks
+}
+
+// rowCompressedMatrix implements row-compressed
+// matrix/vector multiplication.
+type rowCompressedMatrix []compressedRow
+
+// addTo adds the value v to the matrix element at (i,j). Repeated
+// calls to addTo with the same column index will result in
+// non-unique element representation.
+func (m rowCompressedMatrix) addTo(i, j int, v float64) { m[i].addTo(j, v) }
+
+// mulVecUnitary multiplies the receiver by the src vector, storing
+// the result in dst. It assumes src and dst are the same length as m
+// and that both have unitary vector increments.
+func (m rowCompressedMatrix) mulVecUnitary(dst, src *mat.VecDense) {
+	dMat := dst.RawVector().Data
+	for i, r := range m {
+		dMat[i] = r.dotUnitary(src)
+	}
+}
+
+// compressedRow implements a simplified scatter-based Ddot.
+type compressedRow []sparseElement
+
+// addTo adds the value v to the vector element at j. Repeated
+// calls to addTo with the same vector index will result in
+// non-unique element representation.
+func (r *compressedRow) addTo(j int, v float64) {
+	*r = append(*r, sparseElement{index: j, value: v})
+}
+
+// dotUnitary performs a simplified scatter-based Ddot operations on
+// v and the receiver. v must have have a unitary vector increment.
+func (r compressedRow) dotUnitary(v *mat.VecDense) float64 {
+	var sum float64
+	vec := v.RawVector().Data
+	for _, e := range r {
+		sum += vec[e.index] * e.value
+	}
+	return sum
+}
+
+// sparseElement is a sparse vector or matrix element.
+type sparseElement struct {
+	index int
+	value float64
+}
+
+// onesDotUnitary performs the equivalent of a Ddot of v with
+// a ones vector of equal length. v must have have a unitary
+// vector increment.
+func onesDotUnitary(alpha float64, v *mat.VecDense) float64 {
+	var sum float64
+	for _, f := range v.RawVector().Data {
+		sum += alpha * f
+	}
+	return sum
+}
+
+// normDiff returns the 2-norm of the difference between x and y.
+// This is a cut down version of gonum/floats.Distance.
+func normDiff(x, y []float64) float64 {
+	var sum float64
+	for i, v := range x {
+		d := v - y[i]
+		sum += d * d
+	}
+	return math.Sqrt(sum)
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/network/page_test.go b/vendor/gonum.org/v1/gonum/graph/network/page_test.go
new file mode 100644
index 00000000..0a85dcf2
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/network/page_test.go
@@ -0,0 +1,151 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package network
+
+import (
+	"fmt"
+	"math"
+	"sort"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+var pageRankTests = []struct {
+	g    []set
+	damp float64
+	tol  float64
+
+	wantTol float64
+	want    map[int64]float64
+}{
+	{
+		// Example graph from http://en.wikipedia.org/wiki/File:PageRanks-Example.svg 16:17, 8 July 2009
+		g: []set{
+			A: nil,
+			B: linksTo(C),
+			C: linksTo(B),
+			D: linksTo(A, B),
+			E: linksTo(D, B, F),
+			F: linksTo(B, E),
+			G: linksTo(B, E),
+			H: linksTo(B, E),
+			I: linksTo(B, E),
+			J: linksTo(E),
+			K: linksTo(E),
+		},
+		damp: 0.85,
+		tol:  1e-8,
+
+		wantTol: 1e-8,
+		want: map[int64]float64{
+			A: 0.03278149,
+			B: 0.38440095,
+			C: 0.34291029,
+			D: 0.03908709,
+			E: 0.08088569,
+			F: 0.03908709,
+			G: 0.01616948,
+			H: 0.01616948,
+			I: 0.01616948,
+			J: 0.01616948,
+			K: 0.01616948,
+		},
+	},
+	{
+		// Example graph from http://en.wikipedia.org/w/index.php?title=PageRank&oldid=659286279#Power_Method
+		// Expected result calculated with the given MATLAB code.
+		g: []set{
+			A: linksTo(B, C),
+			B: linksTo(D),
+			C: linksTo(D, E),
+			D: linksTo(E),
+			E: linksTo(A),
+		},
+		damp: 0.80,
+		tol:  1e-3,
+
+		wantTol: 1e-3,
+		want: map[int64]float64{
+			A: 0.250,
+			B: 0.140,
+			C: 0.140,
+			D: 0.208,
+			E: 0.262,
+		},
+	},
+}
+
+func TestPageRank(t *testing.T) {
+	for i, test := range pageRankTests {
+		g := simple.NewDirectedGraph()
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+		got := PageRank(g, test.damp, test.tol)
+		prec := 1 - int(math.Log10(test.wantTol))
+		for n := range test.g {
+			if !floats.EqualWithinAbsOrRel(got[int64(n)], test.want[int64(n)], test.wantTol, test.wantTol) {
+				t.Errorf("unexpected PageRank result for test %d:\ngot: %v\nwant:%v",
+					i, orderedFloats(got, prec), orderedFloats(test.want, prec))
+				break
+			}
+		}
+	}
+}
+
+func TestPageRankSparse(t *testing.T) {
+	for i, test := range pageRankTests {
+		g := simple.NewDirectedGraph()
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+		got := PageRankSparse(g, test.damp, test.tol)
+		prec := 1 - int(math.Log10(test.wantTol))
+		for n := range test.g {
+			if !floats.EqualWithinAbsOrRel(got[int64(n)], test.want[int64(n)], test.wantTol, test.wantTol) {
+				t.Errorf("unexpected PageRank result for test %d:\ngot: %v\nwant:%v",
+					i, orderedFloats(got, prec), orderedFloats(test.want, prec))
+				break
+			}
+		}
+	}
+}
+
+func orderedFloats(w map[int64]float64, prec int) []keyFloatVal {
+	o := make(orderedFloatsMap, 0, len(w))
+	for k, v := range w {
+		o = append(o, keyFloatVal{prec: prec, key: k, val: v})
+	}
+	sort.Sort(o)
+	return o
+}
+
+type keyFloatVal struct {
+	prec int
+	key  int64
+	val  float64
+}
+
+func (kv keyFloatVal) String() string { return fmt.Sprintf("%c:%.*f", kv.key+'A', kv.prec, kv.val) }
+
+type orderedFloatsMap []keyFloatVal
+
+func (o orderedFloatsMap) Len() int           { return len(o) }
+func (o orderedFloatsMap) Less(i, j int) bool { return o[i].key < o[j].key }
+func (o orderedFloatsMap) Swap(i, j int)      { o[i], o[j] = o[j], o[i] }
diff --git a/vendor/gonum.org/v1/gonum/graph/path/a_star.go b/vendor/gonum.org/v1/gonum/graph/path/a_star.go
new file mode 100644
index 00000000..0d24c084
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/a_star.go
@@ -0,0 +1,151 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package path
+
+import (
+	"container/heap"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/set"
+)
+
+// AStar finds the A*-shortest path from s to t in g using the heuristic h. The path and
+// its cost are returned in a Shortest along with paths and costs to all nodes explored
+// during the search. The number of expanded nodes is also returned. This value may help
+// with heuristic tuning.
+//
+// The path will be the shortest path if the heuristic is admissible. A heuristic is
+// admissible if for any node, n, in the graph, the heuristic estimate of the cost of
+// the path from n to t is less than or equal to the true cost of that path.
+//
+// If h is nil, AStar will use the g.HeuristicCost method if g implements HeuristicCoster,
+// falling back to NullHeuristic otherwise. If the graph does not implement graph.Weighter,
+// UniformCost is used. AStar will panic if g has an A*-reachable negative edge weight.
+func AStar(s, t graph.Node, g graph.Graph, h Heuristic) (path Shortest, expanded int) {
+	if !g.Has(s) || !g.Has(t) {
+		return Shortest{from: s}, 0
+	}
+	var weight Weighting
+	if wg, ok := g.(graph.Weighted); ok {
+		weight = wg.Weight
+	} else {
+		weight = UniformCost(g)
+	}
+	if h == nil {
+		if g, ok := g.(HeuristicCoster); ok {
+			h = g.HeuristicCost
+		} else {
+			h = NullHeuristic
+		}
+	}
+
+	path = newShortestFrom(s, g.Nodes())
+	tid := t.ID()
+
+	visited := make(set.Int64s)
+	open := &aStarQueue{indexOf: make(map[int64]int)}
+	heap.Push(open, aStarNode{node: s, gscore: 0, fscore: h(s, t)})
+
+	for open.Len() != 0 {
+		u := heap.Pop(open).(aStarNode)
+		uid := u.node.ID()
+		i := path.indexOf[uid]
+		expanded++
+
+		if uid == tid {
+			break
+		}
+
+		visited.Add(uid)
+		for _, v := range g.From(u.node) {
+			vid := v.ID()
+			if visited.Has(vid) {
+				continue
+			}
+			j := path.indexOf[vid]
+
+			w, ok := weight(u.node, v)
+			if !ok {
+				panic("A*: unexpected invalid weight")
+			}
+			if w < 0 {
+				panic("A*: negative edge weight")
+			}
+			g := u.gscore + w
+			if n, ok := open.node(vid); !ok {
+				path.set(j, g, i)
+				heap.Push(open, aStarNode{node: v, gscore: g, fscore: g + h(v, t)})
+			} else if g < n.gscore {
+				path.set(j, g, i)
+				open.update(vid, g, g+h(v, t))
+			}
+		}
+	}
+
+	return path, expanded
+}
+
+// NullHeuristic is an admissible, consistent heuristic that will not speed up computation.
+func NullHeuristic(_, _ graph.Node) float64 {
+	return 0
+}
+
+// aStarNode adds A* accounting to a graph.Node.
+type aStarNode struct {
+	node   graph.Node
+	gscore float64
+	fscore float64
+}
+
+// aStarQueue is an A* priority queue.
+type aStarQueue struct {
+	indexOf map[int64]int
+	nodes   []aStarNode
+}
+
+func (q *aStarQueue) Less(i, j int) bool {
+	return q.nodes[i].fscore < q.nodes[j].fscore
+}
+
+func (q *aStarQueue) Swap(i, j int) {
+	q.indexOf[q.nodes[i].node.ID()] = j
+	q.indexOf[q.nodes[j].node.ID()] = i
+	q.nodes[i], q.nodes[j] = q.nodes[j], q.nodes[i]
+}
+
+func (q *aStarQueue) Len() int {
+	return len(q.nodes)
+}
+
+func (q *aStarQueue) Push(x interface{}) {
+	n := x.(aStarNode)
+	q.indexOf[n.node.ID()] = len(q.nodes)
+	q.nodes = append(q.nodes, n)
+}
+
+func (q *aStarQueue) Pop() interface{} {
+	n := q.nodes[len(q.nodes)-1]
+	q.nodes = q.nodes[:len(q.nodes)-1]
+	delete(q.indexOf, n.node.ID())
+	return n
+}
+
+func (q *aStarQueue) update(id int64, g, f float64) {
+	i, ok := q.indexOf[id]
+	if !ok {
+		return
+	}
+	q.nodes[i].gscore = g
+	q.nodes[i].fscore = f
+	heap.Fix(q, i)
+}
+
+func (q *aStarQueue) node(id int64) (aStarNode, bool) {
+	loc, ok := q.indexOf[id]
+	if ok {
+		return q.nodes[loc], true
+	}
+	return aStarNode{}, false
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/path/a_star_test.go b/vendor/gonum.org/v1/gonum/graph/path/a_star_test.go
new file mode 100644
index 00000000..dd63d4b9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/a_star_test.go
@@ -0,0 +1,310 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package path
+
+import (
+	"math"
+	"reflect"
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/path/internal"
+	"gonum.org/v1/gonum/graph/path/internal/testgraphs"
+	"gonum.org/v1/gonum/graph/simple"
+	"gonum.org/v1/gonum/graph/topo"
+)
+
+var aStarTests = []struct {
+	name string
+	g    graph.Graph
+
+	s, t      int64
+	heuristic Heuristic
+	wantPath  []int64
+}{
+	{
+		name: "simple path",
+		g: func() graph.Graph {
+			return internal.NewGridFrom(
+				"*..*",
+				"**.*",
+				"**.*",
+				"**.*",
+			)
+		}(),
+
+		s: 1, t: 14,
+		wantPath: []int64{1, 2, 6, 10, 14},
+	},
+	{
+		name: "small open graph",
+		g:    internal.NewGrid(3, 3, true),
+
+		s: 0, t: 8,
+	},
+	{
+		name: "large open graph",
+		g:    internal.NewGrid(1000, 1000, true),
+
+		s: 0, t: 999*1000 + 999,
+	},
+	{
+		name: "no path",
+		g: func() graph.Graph {
+			tg := internal.NewGrid(5, 5, true)
+
+			// Create a complete "wall" across the middle row.
+			tg.Set(2, 0, false)
+			tg.Set(2, 1, false)
+			tg.Set(2, 2, false)
+			tg.Set(2, 3, false)
+			tg.Set(2, 4, false)
+
+			return tg
+		}(),
+
+		s: 2, t: 22,
+	},
+	{
+		name: "partially obstructed",
+		g: func() graph.Graph {
+			tg := internal.NewGrid(10, 10, true)
+
+			// Create a partial "wall" across the middle
+			// row with a gap at the left-hand end.
+			tg.Set(4, 1, false)
+			tg.Set(4, 2, false)
+			tg.Set(4, 3, false)
+			tg.Set(4, 4, false)
+			tg.Set(4, 5, false)
+			tg.Set(4, 6, false)
+			tg.Set(4, 7, false)
+			tg.Set(4, 8, false)
+			tg.Set(4, 9, false)
+
+			return tg
+		}(),
+
+		s: 5, t: 9*10 + 9,
+	},
+	{
+		name: "partially obstructed with heuristic",
+		g: func() graph.Graph {
+			tg := internal.NewGrid(10, 10, true)
+
+			// Create a partial "wall" across the middle
+			// row with a gap at the left-hand end.
+			tg.Set(4, 1, false)
+			tg.Set(4, 2, false)
+			tg.Set(4, 3, false)
+			tg.Set(4, 4, false)
+			tg.Set(4, 5, false)
+			tg.Set(4, 6, false)
+			tg.Set(4, 7, false)
+			tg.Set(4, 8, false)
+			tg.Set(4, 9, false)
+
+			return tg
+		}(),
+
+		s: 5, t: 9*10 + 9,
+		// Manhattan Heuristic
+		heuristic: func(u, v graph.Node) float64 {
+			uid := u.ID()
+			cu := (uid % 10)
+			ru := (uid - cu) / 10
+
+			vid := v.ID()
+			cv := (vid % 10)
+			rv := (vid - cv) / 10
+
+			return math.Abs(float64(ru-rv)) + math.Abs(float64(cu-cv))
+		},
+	},
+}
+
+func TestAStar(t *testing.T) {
+	for _, test := range aStarTests {
+		pt, _ := AStar(simple.Node(test.s), simple.Node(test.t), test.g, test.heuristic)
+
+		p, cost := pt.To(simple.Node(test.t))
+
+		if !topo.IsPathIn(test.g, p) {
+			t.Errorf("got path that is not path in input graph for %q", test.name)
+		}
+
+		bfp, ok := BellmanFordFrom(simple.Node(test.s), test.g)
+		if !ok {
+			t.Fatalf("unexpected negative cycle in %q", test.name)
+		}
+		if want := bfp.WeightTo(simple.Node(test.t)); cost != want {
+			t.Errorf("unexpected cost for %q: got:%v want:%v", test.name, cost, want)
+		}
+
+		var got = make([]int64, 0, len(p))
+		for _, n := range p {
+			got = append(got, n.ID())
+		}
+		if test.wantPath != nil && !reflect.DeepEqual(got, test.wantPath) {
+			t.Errorf("unexpected result for %q:\ngot: %v\nwant:%v", test.name, got, test.wantPath)
+		}
+	}
+}
+
+func TestExhaustiveAStar(t *testing.T) {
+	g := simple.NewWeightedUndirectedGraph(0, math.Inf(1))
+	nodes := []locatedNode{
+		{id: 1, x: 0, y: 6},
+		{id: 2, x: 1, y: 0},
+		{id: 3, x: 8, y: 7},
+		{id: 4, x: 16, y: 0},
+		{id: 5, x: 17, y: 6},
+		{id: 6, x: 9, y: 8},
+	}
+	for _, n := range nodes {
+		g.AddNode(n)
+	}
+
+	edges := []weightedEdge{
+		{from: g.Node(1), to: g.Node(2), cost: 7},
+		{from: g.Node(1), to: g.Node(3), cost: 9},
+		{from: g.Node(1), to: g.Node(6), cost: 14},
+		{from: g.Node(2), to: g.Node(3), cost: 10},
+		{from: g.Node(2), to: g.Node(4), cost: 15},
+		{from: g.Node(3), to: g.Node(4), cost: 11},
+		{from: g.Node(3), to: g.Node(6), cost: 2},
+		{from: g.Node(4), to: g.Node(5), cost: 7},
+		{from: g.Node(5), to: g.Node(6), cost: 9},
+	}
+	for _, e := range edges {
+		g.SetWeightedEdge(e)
+	}
+
+	heuristic := func(u, v graph.Node) float64 {
+		lu := u.(locatedNode)
+		lv := v.(locatedNode)
+		return math.Hypot(lu.x-lv.x, lu.y-lv.y)
+	}
+
+	if ok, edge, goal := isMonotonic(g, heuristic); !ok {
+		t.Fatalf("non-monotonic heuristic at edge:%v for goal:%v", edge, goal)
+	}
+
+	ps := DijkstraAllPaths(g)
+	for _, start := range g.Nodes() {
+		for _, goal := range g.Nodes() {
+			pt, _ := AStar(start, goal, g, heuristic)
+			gotPath, gotWeight := pt.To(goal)
+			wantPath, wantWeight, _ := ps.Between(start, goal)
+			if gotWeight != wantWeight {
+				t.Errorf("unexpected path weight from %v to %v result: got:%f want:%f",
+					start, goal, gotWeight, wantWeight)
+			}
+			if !reflect.DeepEqual(gotPath, wantPath) {
+				t.Errorf("unexpected path from %v to %v result:\ngot: %v\nwant:%v",
+					start, goal, gotPath, wantPath)
+			}
+		}
+	}
+}
+
+type locatedNode struct {
+	id   int64
+	x, y float64
+}
+
+func (n locatedNode) ID() int64 { return n.id }
+
+type weightedEdge struct {
+	from, to graph.Node
+	cost     float64
+}
+
+func (e weightedEdge) From() graph.Node { return e.from }
+func (e weightedEdge) To() graph.Node   { return e.to }
+func (e weightedEdge) Weight() float64  { return e.cost }
+
+func isMonotonic(g UndirectedWeightLister, h Heuristic) (ok bool, at graph.Edge, goal graph.Node) {
+	for _, goal := range g.Nodes() {
+		for _, edge := range g.WeightedEdges() {
+			from := edge.From()
+			to := edge.To()
+			w, ok := g.Weight(from, to)
+			if !ok {
+				panic("A*: unexpected invalid weight")
+			}
+			if h(from, goal) > w+h(to, goal) {
+				return false, edge, goal
+			}
+		}
+	}
+	return true, nil, nil
+}
+
+func TestAStarNullHeuristic(t *testing.T) {
+	for _, test := range testgraphs.ShortestPathTests {
+		g := test.Graph()
+		for _, e := range test.Edges {
+			g.SetWeightedEdge(e)
+		}
+
+		var (
+			pt Shortest
+
+			panicked bool
+		)
+		func() {
+			defer func() {
+				panicked = recover() != nil
+			}()
+			pt, _ = AStar(test.Query.From(), test.Query.To(), g.(graph.Graph), nil)
+		}()
+		if panicked || test.HasNegativeWeight {
+			if !test.HasNegativeWeight {
+				t.Errorf("%q: unexpected panic", test.Name)
+			}
+			if !panicked {
+				t.Errorf("%q: expected panic for negative edge weight", test.Name)
+			}
+			continue
+		}
+
+		if pt.From().ID() != test.Query.From().ID() {
+			t.Fatalf("%q: unexpected from node ID: got:%d want:%d", test.Name, pt.From().ID(), test.Query.From().ID())
+		}
+
+		p, weight := pt.To(test.Query.To())
+		if weight != test.Weight {
+			t.Errorf("%q: unexpected weight from Between: got:%f want:%f",
+				test.Name, weight, test.Weight)
+		}
+		if weight := pt.WeightTo(test.Query.To()); weight != test.Weight {
+			t.Errorf("%q: unexpected weight from Weight: got:%f want:%f",
+				test.Name, weight, test.Weight)
+		}
+
+		var got []int64
+		for _, n := range p {
+			got = append(got, n.ID())
+		}
+		ok := len(got) == 0 && len(test.WantPaths) == 0
+		for _, sp := range test.WantPaths {
+			if reflect.DeepEqual(got, sp) {
+				ok = true
+				break
+			}
+		}
+		if !ok {
+			t.Errorf("%q: unexpected shortest path:\ngot: %v\nwant from:%v",
+				test.Name, p, test.WantPaths)
+		}
+
+		np, weight := pt.To(test.NoPathFor.To())
+		if pt.From().ID() == test.NoPathFor.From().ID() && (np != nil || !math.IsInf(weight, 1)) {
+			t.Errorf("%q: unexpected path:\ngot: path=%v weight=%f\nwant:path=<nil> weight=+Inf",
+				test.Name, np, weight)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/path/bellman_ford_moore.go b/vendor/gonum.org/v1/gonum/graph/path/bellman_ford_moore.go
new file mode 100644
index 00000000..e7370b7c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/bellman_ford_moore.go
@@ -0,0 +1,67 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package path
+
+import "gonum.org/v1/gonum/graph"
+
+// BellmanFordFrom returns a shortest-path tree for a shortest path from u to all nodes in
+// the graph g, or false indicating that a negative cycle exists in the graph. If the graph
+// does not implement graph.Weighter, UniformCost is used.
+//
+// The time complexity of BellmanFordFrom is O(|V|.|E|).
+func BellmanFordFrom(u graph.Node, g graph.Graph) (path Shortest, ok bool) {
+	if !g.Has(u) {
+		return Shortest{from: u}, true
+	}
+	var weight Weighting
+	if wg, ok := g.(graph.Weighted); ok {
+		weight = wg.Weight
+	} else {
+		weight = UniformCost(g)
+	}
+
+	nodes := g.Nodes()
+
+	path = newShortestFrom(u, nodes)
+	path.dist[path.indexOf[u.ID()]] = 0
+
+	// TODO(kortschak): Consider adding further optimisations
+	// from http://arxiv.org/abs/1111.5414.
+	for i := 1; i < len(nodes); i++ {
+		changed := false
+		for j, u := range nodes {
+			for _, v := range g.From(u) {
+				k := path.indexOf[v.ID()]
+				w, ok := weight(u, v)
+				if !ok {
+					panic("bellman-ford: unexpected invalid weight")
+				}
+				joint := path.dist[j] + w
+				if joint < path.dist[k] {
+					path.set(k, joint, j)
+					changed = true
+				}
+			}
+		}
+		if !changed {
+			break
+		}
+	}
+
+	for j, u := range nodes {
+		for _, v := range g.From(u) {
+			k := path.indexOf[v.ID()]
+			w, ok := weight(u, v)
+			if !ok {
+				panic("bellman-ford: unexpected invalid weight")
+			}
+			if path.dist[j]+w < path.dist[k] {
+				return path, false
+			}
+		}
+	}
+
+	return path, true
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/path/bellman_ford_moore_test.go b/vendor/gonum.org/v1/gonum/graph/path/bellman_ford_moore_test.go
new file mode 100644
index 00000000..b753368f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/bellman_ford_moore_test.go
@@ -0,0 +1,70 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package path
+
+import (
+	"math"
+	"reflect"
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/path/internal/testgraphs"
+)
+
+func TestBellmanFordFrom(t *testing.T) {
+	for _, test := range testgraphs.ShortestPathTests {
+		g := test.Graph()
+		for _, e := range test.Edges {
+			g.SetWeightedEdge(e)
+		}
+
+		pt, ok := BellmanFordFrom(test.Query.From(), g.(graph.Graph))
+		if test.HasNegativeCycle {
+			if ok {
+				t.Errorf("%q: expected negative cycle", test.Name)
+			}
+			continue
+		}
+		if !ok {
+			t.Fatalf("%q: unexpected negative cycle", test.Name)
+		}
+
+		if pt.From().ID() != test.Query.From().ID() {
+			t.Fatalf("%q: unexpected from node ID: got:%d want:%d", test.Name, pt.From().ID(), test.Query.From().ID())
+		}
+
+		p, weight := pt.To(test.Query.To())
+		if weight != test.Weight {
+			t.Errorf("%q: unexpected weight from Between: got:%f want:%f",
+				test.Name, weight, test.Weight)
+		}
+		if weight := pt.WeightTo(test.Query.To()); weight != test.Weight {
+			t.Errorf("%q: unexpected weight from Weight: got:%f want:%f",
+				test.Name, weight, test.Weight)
+		}
+
+		var got []int64
+		for _, n := range p {
+			got = append(got, n.ID())
+		}
+		ok = len(got) == 0 && len(test.WantPaths) == 0
+		for _, sp := range test.WantPaths {
+			if reflect.DeepEqual(got, sp) {
+				ok = true
+				break
+			}
+		}
+		if !ok {
+			t.Errorf("%q: unexpected shortest path:\ngot: %v\nwant from:%v",
+				test.Name, p, test.WantPaths)
+		}
+
+		np, weight := pt.To(test.NoPathFor.To())
+		if pt.From().ID() == test.NoPathFor.From().ID() && (np != nil || !math.IsInf(weight, 1)) {
+			t.Errorf("%q: unexpected path:\ngot: path=%v weight=%f\nwant:path=<nil> weight=+Inf",
+				test.Name, np, weight)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/path/bench_test.go b/vendor/gonum.org/v1/gonum/graph/path/bench_test.go
new file mode 100644
index 00000000..e08525f0
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/bench_test.go
@@ -0,0 +1,141 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package path
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/graphs/gen"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+var (
+	gnpUndirected_10_tenth   = gnpUndirected(10, 0.1)
+	gnpUndirected_100_tenth  = gnpUndirected(100, 0.1)
+	gnpUndirected_1000_tenth = gnpUndirected(1000, 0.1)
+	gnpUndirected_10_half    = gnpUndirected(10, 0.5)
+	gnpUndirected_100_half   = gnpUndirected(100, 0.5)
+	gnpUndirected_1000_half  = gnpUndirected(1000, 0.5)
+)
+
+func gnpUndirected(n int, p float64) graph.Undirected {
+	g := simple.NewUndirectedGraph()
+	gen.Gnp(g, n, p, nil)
+	return g
+}
+
+func benchmarkAStarNilHeuristic(b *testing.B, g graph.Undirected) {
+	var expanded int
+	for i := 0; i < b.N; i++ {
+		_, expanded = AStar(simple.Node(0), simple.Node(1), g, nil)
+	}
+	if expanded == 0 {
+		b.Fatal("unexpected number of expanded nodes")
+	}
+}
+
+func BenchmarkAStarGnp_10_tenth(b *testing.B) {
+	benchmarkAStarNilHeuristic(b, gnpUndirected_10_tenth)
+}
+func BenchmarkAStarGnp_100_tenth(b *testing.B) {
+	benchmarkAStarNilHeuristic(b, gnpUndirected_100_tenth)
+}
+func BenchmarkAStarGnp_1000_tenth(b *testing.B) {
+	benchmarkAStarNilHeuristic(b, gnpUndirected_1000_tenth)
+}
+func BenchmarkAStarGnp_10_half(b *testing.B) {
+	benchmarkAStarNilHeuristic(b, gnpUndirected_10_half)
+}
+func BenchmarkAStarGnp_100_half(b *testing.B) {
+	benchmarkAStarNilHeuristic(b, gnpUndirected_100_half)
+}
+func BenchmarkAStarGnp_1000_half(b *testing.B) {
+	benchmarkAStarNilHeuristic(b, gnpUndirected_1000_half)
+}
+
+var (
+	nswUndirected_10_2_2_2   = navigableSmallWorldUndirected(10, 2, 2, 2)
+	nswUndirected_10_2_5_2   = navigableSmallWorldUndirected(10, 2, 5, 2)
+	nswUndirected_100_5_10_2 = navigableSmallWorldUndirected(100, 5, 10, 2)
+	nswUndirected_100_5_20_2 = navigableSmallWorldUndirected(100, 5, 20, 2)
+)
+
+func navigableSmallWorldUndirected(n, p, q int, r float64) graph.Undirected {
+	g := simple.NewUndirectedGraph()
+	gen.NavigableSmallWorld(g, []int{n, n}, p, q, r, nil)
+	return g
+}
+
+func coordinatesForID(n graph.Node, c, r int) [2]int {
+	id := n.ID()
+	if id >= int64(c*r) {
+		panic("out of range")
+	}
+	return [2]int{int(id) / r, int(id) % r}
+}
+
+// manhattanBetween returns the Manhattan distance between a and b.
+func manhattanBetween(a, b [2]int) float64 {
+	var d int
+	for i, v := range a {
+		d += abs(v - b[i])
+	}
+	return float64(d)
+}
+
+func abs(a int) int {
+	if a < 0 {
+		return -a
+	}
+	return a
+}
+
+func benchmarkAStarHeuristic(b *testing.B, g graph.Undirected, h Heuristic) {
+	var expanded int
+	for i := 0; i < b.N; i++ {
+		_, expanded = AStar(simple.Node(0), simple.Node(1), g, h)
+	}
+	if expanded == 0 {
+		b.Fatal("unexpected number of expanded nodes")
+	}
+}
+
+func BenchmarkAStarUndirectedmallWorld_10_2_2_2(b *testing.B) {
+	benchmarkAStarHeuristic(b, nswUndirected_10_2_2_2, nil)
+}
+func BenchmarkAStarUndirectedmallWorld_10_2_2_2_Heur(b *testing.B) {
+	h := func(x, y graph.Node) float64 {
+		return manhattanBetween(coordinatesForID(x, 10, 10), coordinatesForID(y, 10, 10))
+	}
+	benchmarkAStarHeuristic(b, nswUndirected_10_2_2_2, h)
+}
+func BenchmarkAStarUndirectedmallWorld_10_2_5_2(b *testing.B) {
+	benchmarkAStarHeuristic(b, nswUndirected_10_2_5_2, nil)
+}
+func BenchmarkAStarUndirectedmallWorld_10_2_5_2_Heur(b *testing.B) {
+	h := func(x, y graph.Node) float64 {
+		return manhattanBetween(coordinatesForID(x, 10, 10), coordinatesForID(y, 10, 10))
+	}
+	benchmarkAStarHeuristic(b, nswUndirected_10_2_5_2, h)
+}
+func BenchmarkAStarUndirectedmallWorld_100_5_10_2(b *testing.B) {
+	benchmarkAStarHeuristic(b, nswUndirected_100_5_10_2, nil)
+}
+func BenchmarkAStarUndirectedmallWorld_100_5_10_2_Heur(b *testing.B) {
+	h := func(x, y graph.Node) float64 {
+		return manhattanBetween(coordinatesForID(x, 100, 100), coordinatesForID(y, 100, 100))
+	}
+	benchmarkAStarHeuristic(b, nswUndirected_100_5_10_2, h)
+}
+func BenchmarkAStarUndirectedmallWorld_100_5_20_2(b *testing.B) {
+	benchmarkAStarHeuristic(b, nswUndirected_100_5_20_2, nil)
+}
+func BenchmarkAStarUndirectedmallWorld_100_5_20_2_Heur(b *testing.B) {
+	h := func(x, y graph.Node) float64 {
+		return manhattanBetween(coordinatesForID(x, 100, 100), coordinatesForID(y, 100, 100))
+	}
+	benchmarkAStarHeuristic(b, nswUndirected_100_5_20_2, h)
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/path/control_flow.go b/vendor/gonum.org/v1/gonum/graph/path/control_flow.go
new file mode 100644
index 00000000..5633e391
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/control_flow.go
@@ -0,0 +1,118 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package path
+
+import (
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/set"
+)
+
+// Dominators returns all dominators for all nodes in g. It does not
+// prune for strict post-dominators, immediate dominators etc.
+//
+// A dominates B if and only if the only path through B travels through A.
+func Dominators(start graph.Node, g graph.Graph) map[int64]set.Nodes {
+	allNodes := make(set.Nodes)
+	nlist := g.Nodes()
+	dominators := make(map[int64]set.Nodes, len(nlist))
+	for _, node := range nlist {
+		allNodes.Add(node)
+	}
+
+	var to func(graph.Node) []graph.Node
+	switch g := g.(type) {
+	case graph.Directed:
+		to = g.To
+	default:
+		to = g.From
+	}
+
+	for _, node := range nlist {
+		dominators[node.ID()] = make(set.Nodes)
+		if node.ID() == start.ID() {
+			dominators[node.ID()].Add(start)
+		} else {
+			dominators[node.ID()].Copy(allNodes)
+		}
+	}
+
+	for somethingChanged := true; somethingChanged; {
+		somethingChanged = false
+		for _, node := range nlist {
+			if node.ID() == start.ID() {
+				continue
+			}
+			preds := to(node)
+			if len(preds) == 0 {
+				continue
+			}
+			tmp := make(set.Nodes).Copy(dominators[preds[0].ID()])
+			for _, pred := range preds[1:] {
+				tmp.Intersect(tmp, dominators[pred.ID()])
+			}
+
+			dom := make(set.Nodes)
+			dom.Add(node)
+
+			dom.Union(dom, tmp)
+			if !set.Equal(dom, dominators[node.ID()]) {
+				dominators[node.ID()] = dom
+				somethingChanged = true
+			}
+		}
+	}
+
+	return dominators
+}
+
+// PostDominators returns all post-dominators for all nodes in g. It does not
+// prune for strict post-dominators, immediate post-dominators etc.
+//
+// A post-dominates B if and only if all paths from B travel through A.
+func PostDominators(end graph.Node, g graph.Graph) map[int64]set.Nodes {
+	allNodes := make(set.Nodes)
+	nlist := g.Nodes()
+	dominators := make(map[int64]set.Nodes, len(nlist))
+	for _, node := range nlist {
+		allNodes.Add(node)
+	}
+
+	for _, node := range nlist {
+		dominators[node.ID()] = make(set.Nodes)
+		if node.ID() == end.ID() {
+			dominators[node.ID()].Add(end)
+		} else {
+			dominators[node.ID()].Copy(allNodes)
+		}
+	}
+
+	for somethingChanged := true; somethingChanged; {
+		somethingChanged = false
+		for _, node := range nlist {
+			if node.ID() == end.ID() {
+				continue
+			}
+			succs := g.From(node)
+			if len(succs) == 0 {
+				continue
+			}
+			tmp := make(set.Nodes).Copy(dominators[succs[0].ID()])
+			for _, succ := range succs[1:] {
+				tmp.Intersect(tmp, dominators[succ.ID()])
+			}
+
+			dom := make(set.Nodes)
+			dom.Add(node)
+
+			dom.Union(dom, tmp)
+			if !set.Equal(dom, dominators[node.ID()]) {
+				dominators[node.ID()] = dom
+				somethingChanged = true
+			}
+		}
+	}
+
+	return dominators
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/path/dijkstra.go b/vendor/gonum.org/v1/gonum/graph/path/dijkstra.go
new file mode 100644
index 00000000..4c14d2b4
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/dijkstra.go
@@ -0,0 +1,147 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package path
+
+import (
+	"container/heap"
+
+	"gonum.org/v1/gonum/graph"
+)
+
+// DijkstraFrom returns a shortest-path tree for a shortest path from u to all nodes in
+// the graph g. If the graph does not implement graph.Weighter, UniformCost is used.
+// DijkstraFrom will panic if g has a u-reachable negative edge weight.
+//
+// The time complexity of DijkstrFrom is O(|E|.log|V|).
+func DijkstraFrom(u graph.Node, g graph.Graph) Shortest {
+	if !g.Has(u) {
+		return Shortest{from: u}
+	}
+	var weight Weighting
+	if wg, ok := g.(graph.Weighted); ok {
+		weight = wg.Weight
+	} else {
+		weight = UniformCost(g)
+	}
+
+	nodes := g.Nodes()
+	path := newShortestFrom(u, nodes)
+
+	// Dijkstra's algorithm here is implemented essentially as
+	// described in Function B.2 in figure 6 of UTCS Technical
+	// Report TR-07-54.
+	//
+	// This implementation deviates from the report as follows:
+	// - the value of path.dist for the start vertex u is initialized to 0;
+	// - outdated elements from the priority queue (i.e. with respect to the dist value)
+	//   are skipped.
+	//
+	// http://www.cs.utexas.edu/ftp/techreports/tr07-54.pdf
+	Q := priorityQueue{{node: u, dist: 0}}
+	for Q.Len() != 0 {
+		mid := heap.Pop(&Q).(distanceNode)
+		k := path.indexOf[mid.node.ID()]
+		if mid.dist > path.dist[k] {
+			continue
+		}
+		for _, v := range g.From(mid.node) {
+			j := path.indexOf[v.ID()]
+			w, ok := weight(mid.node, v)
+			if !ok {
+				panic("dijkstra: unexpected invalid weight")
+			}
+			if w < 0 {
+				panic("dijkstra: negative edge weight")
+			}
+			joint := path.dist[k] + w
+			if joint < path.dist[j] {
+				heap.Push(&Q, distanceNode{node: v, dist: joint})
+				path.set(j, joint, k)
+			}
+		}
+	}
+
+	return path
+}
+
+// DijkstraAllPaths returns a shortest-path tree for shortest paths in the graph g.
+// If the graph does not implement graph.Weighter, UniformCost is used.
+// DijkstraAllPaths will panic if g has a negative edge weight.
+//
+// The time complexity of DijkstrAllPaths is O(|V|.|E|+|V|^2.log|V|).
+func DijkstraAllPaths(g graph.Graph) (paths AllShortest) {
+	paths = newAllShortest(g.Nodes(), false)
+	dijkstraAllPaths(g, paths)
+	return paths
+}
+
+// dijkstraAllPaths is the all-paths implementation of Dijkstra. It is shared
+// between DijkstraAllPaths and JohnsonAllPaths to avoid repeated allocation
+// of the nodes slice and the indexOf map. It returns nothing, but stores the
+// result of the work in the paths parameter which is a reference type.
+func dijkstraAllPaths(g graph.Graph, paths AllShortest) {
+	var weight Weighting
+	if wg, ok := g.(graph.Weighted); ok {
+		weight = wg.Weight
+	} else {
+		weight = UniformCost(g)
+	}
+
+	var Q priorityQueue
+	for i, u := range paths.nodes {
+		// Dijkstra's algorithm here is implemented essentially as
+		// described in Function B.2 in figure 6 of UTCS Technical
+		// Report TR-07-54 with the addition of handling multiple
+		// co-equal paths.
+		//
+		// http://www.cs.utexas.edu/ftp/techreports/tr07-54.pdf
+
+		// Q must be empty at this point.
+		heap.Push(&Q, distanceNode{node: u, dist: 0})
+		for Q.Len() != 0 {
+			mid := heap.Pop(&Q).(distanceNode)
+			k := paths.indexOf[mid.node.ID()]
+			if mid.dist < paths.dist.At(i, k) {
+				paths.dist.Set(i, k, mid.dist)
+			}
+			for _, v := range g.From(mid.node) {
+				j := paths.indexOf[v.ID()]
+				w, ok := weight(mid.node, v)
+				if !ok {
+					panic("dijkstra: unexpected invalid weight")
+				}
+				if w < 0 {
+					panic("dijkstra: negative edge weight")
+				}
+				joint := paths.dist.At(i, k) + w
+				if joint < paths.dist.At(i, j) {
+					heap.Push(&Q, distanceNode{node: v, dist: joint})
+					paths.set(i, j, joint, k)
+				} else if joint == paths.dist.At(i, j) {
+					paths.add(i, j, k)
+				}
+			}
+		}
+	}
+}
+
+type distanceNode struct {
+	node graph.Node
+	dist float64
+}
+
+// priorityQueue implements a no-dec priority queue.
+type priorityQueue []distanceNode
+
+func (q priorityQueue) Len() int            { return len(q) }
+func (q priorityQueue) Less(i, j int) bool  { return q[i].dist < q[j].dist }
+func (q priorityQueue) Swap(i, j int)       { q[i], q[j] = q[j], q[i] }
+func (q *priorityQueue) Push(n interface{}) { *q = append(*q, n.(distanceNode)) }
+func (q *priorityQueue) Pop() interface{} {
+	t := *q
+	var n interface{}
+	n, *q = t[len(t)-1], t[:len(t)-1]
+	return n
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/path/dijkstra_test.go b/vendor/gonum.org/v1/gonum/graph/path/dijkstra_test.go
new file mode 100644
index 00000000..ccb74644
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/dijkstra_test.go
@@ -0,0 +1,178 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package path
+
+import (
+	"math"
+	"reflect"
+	"sort"
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/ordered"
+	"gonum.org/v1/gonum/graph/path/internal/testgraphs"
+)
+
+func TestDijkstraFrom(t *testing.T) {
+	for _, test := range testgraphs.ShortestPathTests {
+		g := test.Graph()
+		for _, e := range test.Edges {
+			g.SetWeightedEdge(e)
+		}
+
+		var (
+			pt Shortest
+
+			panicked bool
+		)
+		func() {
+			defer func() {
+				panicked = recover() != nil
+			}()
+			pt = DijkstraFrom(test.Query.From(), g.(graph.Graph))
+		}()
+		if panicked || test.HasNegativeWeight {
+			if !test.HasNegativeWeight {
+				t.Errorf("%q: unexpected panic", test.Name)
+			}
+			if !panicked {
+				t.Errorf("%q: expected panic for negative edge weight", test.Name)
+			}
+			continue
+		}
+
+		if pt.From().ID() != test.Query.From().ID() {
+			t.Fatalf("%q: unexpected from node ID: got:%d want:%d", test.Name, pt.From().ID(), test.Query.From().ID())
+		}
+
+		p, weight := pt.To(test.Query.To())
+		if weight != test.Weight {
+			t.Errorf("%q: unexpected weight from Between: got:%f want:%f",
+				test.Name, weight, test.Weight)
+		}
+		if weight := pt.WeightTo(test.Query.To()); weight != test.Weight {
+			t.Errorf("%q: unexpected weight from Weight: got:%f want:%f",
+				test.Name, weight, test.Weight)
+		}
+
+		var got []int64
+		for _, n := range p {
+			got = append(got, n.ID())
+		}
+		ok := len(got) == 0 && len(test.WantPaths) == 0
+		for _, sp := range test.WantPaths {
+			if reflect.DeepEqual(got, sp) {
+				ok = true
+				break
+			}
+		}
+		if !ok {
+			t.Errorf("%q: unexpected shortest path:\ngot: %v\nwant from:%v",
+				test.Name, p, test.WantPaths)
+		}
+
+		np, weight := pt.To(test.NoPathFor.To())
+		if pt.From().ID() == test.NoPathFor.From().ID() && (np != nil || !math.IsInf(weight, 1)) {
+			t.Errorf("%q: unexpected path:\ngot: path=%v weight=%f\nwant:path=<nil> weight=+Inf",
+				test.Name, np, weight)
+		}
+	}
+}
+
+func TestDijkstraAllPaths(t *testing.T) {
+	for _, test := range testgraphs.ShortestPathTests {
+		g := test.Graph()
+		for _, e := range test.Edges {
+			g.SetWeightedEdge(e)
+		}
+
+		var (
+			pt AllShortest
+
+			panicked bool
+		)
+		func() {
+			defer func() {
+				panicked = recover() != nil
+			}()
+			pt = DijkstraAllPaths(g.(graph.Graph))
+		}()
+		if panicked || test.HasNegativeWeight {
+			if !test.HasNegativeWeight {
+				t.Errorf("%q: unexpected panic", test.Name)
+			}
+			if !panicked {
+				t.Errorf("%q: expected panic for negative edge weight", test.Name)
+			}
+			continue
+		}
+
+		// Check all random paths returned are OK.
+		for i := 0; i < 10; i++ {
+			p, weight, unique := pt.Between(test.Query.From(), test.Query.To())
+			if weight != test.Weight {
+				t.Errorf("%q: unexpected weight from Between: got:%f want:%f",
+					test.Name, weight, test.Weight)
+			}
+			if weight := pt.Weight(test.Query.From(), test.Query.To()); weight != test.Weight {
+				t.Errorf("%q: unexpected weight from Weight: got:%f want:%f",
+					test.Name, weight, test.Weight)
+			}
+			if unique != test.HasUniquePath {
+				t.Errorf("%q: unexpected number of paths: got: unique=%t want: unique=%t",
+					test.Name, unique, test.HasUniquePath)
+			}
+
+			var got []int64
+			for _, n := range p {
+				got = append(got, n.ID())
+			}
+			ok := len(got) == 0 && len(test.WantPaths) == 0
+			for _, sp := range test.WantPaths {
+				if reflect.DeepEqual(got, sp) {
+					ok = true
+					break
+				}
+			}
+			if !ok {
+				t.Errorf("%q: unexpected shortest path:\ngot: %v\nwant from:%v",
+					test.Name, p, test.WantPaths)
+			}
+		}
+
+		np, weight, unique := pt.Between(test.NoPathFor.From(), test.NoPathFor.To())
+		if np != nil || !math.IsInf(weight, 1) || unique {
+			t.Errorf("%q: unexpected path:\ngot: path=%v weight=%f unique=%t\nwant:path=<nil> weight=+Inf unique=false",
+				test.Name, np, weight, unique)
+		}
+
+		paths, weight := pt.AllBetween(test.Query.From(), test.Query.To())
+		if weight != test.Weight {
+			t.Errorf("%q: unexpected weight from Between: got:%f want:%f",
+				test.Name, weight, test.Weight)
+		}
+
+		var got [][]int64
+		if len(paths) != 0 {
+			got = make([][]int64, len(paths))
+		}
+		for i, p := range paths {
+			for _, v := range p {
+				got[i] = append(got[i], v.ID())
+			}
+		}
+		sort.Sort(ordered.BySliceValues(got))
+		if !reflect.DeepEqual(got, test.WantPaths) {
+			t.Errorf("testing %q: unexpected shortest paths:\ngot: %v\nwant:%v",
+				test.Name, got, test.WantPaths)
+		}
+
+		nps, weight := pt.AllBetween(test.NoPathFor.From(), test.NoPathFor.To())
+		if nps != nil || !math.IsInf(weight, 1) {
+			t.Errorf("%q: unexpected path:\ngot: paths=%v weight=%f\nwant:path=<nil> weight=+Inf",
+				test.Name, nps, weight)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/path/disjoint.go b/vendor/gonum.org/v1/gonum/graph/path/disjoint.go
new file mode 100644
index 00000000..4f530f69
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/disjoint.go
@@ -0,0 +1,87 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package path
+
+// A disjoint set is a collection of non-overlapping sets. That is, for any two sets in the
+// disjoint set, their intersection is the empty set.
+//
+// A disjoint set has three principle operations: Make Set, Find, and Union.
+//
+// Make set creates a new set for an element (presuming it does not already exist in any set in
+// the disjoint set), Find finds the set containing that element (if any), and Union merges two
+// sets in the disjoint set. In general, algorithms operating on disjoint sets are "union-find"
+// algorithms, where two sets are found with Find, and then joined with Union.
+//
+// A concrete example of a union-find algorithm can be found as discrete.Kruskal -- which unions
+// two sets when an edge is created between two vertices, and refuses to make an edge between two
+// vertices if they're part of the same set.
+type disjointSet struct {
+	master map[int64]*disjointSetNode
+}
+
+type disjointSetNode struct {
+	parent *disjointSetNode
+	rank   int
+}
+
+func newDisjointSet() *disjointSet {
+	return &disjointSet{master: make(map[int64]*disjointSetNode)}
+}
+
+// If the element isn't already somewhere in there, adds it to the master set and its own tiny set.
+func (ds *disjointSet) makeSet(e int64) {
+	if _, ok := ds.master[e]; ok {
+		return
+	}
+	dsNode := &disjointSetNode{rank: 0}
+	dsNode.parent = dsNode
+	ds.master[e] = dsNode
+}
+
+// Returns the set the element belongs to, or nil if none.
+func (ds *disjointSet) find(e int64) *disjointSetNode {
+	dsNode, ok := ds.master[e]
+	if !ok {
+		return nil
+	}
+
+	return find(dsNode)
+}
+
+func find(dsNode *disjointSetNode) *disjointSetNode {
+	if dsNode.parent != dsNode {
+		dsNode.parent = find(dsNode.parent)
+	}
+
+	return dsNode.parent
+}
+
+// Unions two subsets within the disjointSet.
+//
+// If x or y are not in this disjoint set, the behavior is undefined. If either pointer is nil,
+// this function will panic.
+func (ds *disjointSet) union(x, y *disjointSetNode) {
+	if x == nil || y == nil {
+		panic("Disjoint Set union on nil sets")
+	}
+	xRoot := find(x)
+	yRoot := find(y)
+	if xRoot == nil || yRoot == nil {
+		return
+	}
+
+	if xRoot == yRoot {
+		return
+	}
+
+	if xRoot.rank < yRoot.rank {
+		xRoot.parent = yRoot
+	} else if yRoot.rank < xRoot.rank {
+		yRoot.parent = xRoot
+	} else {
+		yRoot.parent = xRoot
+		xRoot.rank++
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/path/disjoint_test.go b/vendor/gonum.org/v1/gonum/graph/path/disjoint_test.go
new file mode 100644
index 00000000..2639592a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/disjoint_test.go
@@ -0,0 +1,63 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package path
+
+import (
+	"testing"
+)
+
+func TestDisjointSetMakeSet(t *testing.T) {
+	ds := newDisjointSet()
+	if ds.master == nil {
+		t.Fatal("Internal disjoint set map erroneously nil")
+	} else if len(ds.master) != 0 {
+		t.Error("Disjoint set master map of wrong size")
+	}
+
+	ds.makeSet(3)
+	if len(ds.master) != 1 {
+		t.Error("Disjoint set master map of wrong size")
+	}
+
+	if node, ok := ds.master[3]; !ok {
+		t.Error("Make set did not successfully add element")
+	} else {
+		if node == nil {
+			t.Fatal("Disjoint set node from makeSet is nil")
+		}
+
+		if node.rank != 0 {
+			t.Error("Node rank set incorrectly")
+		}
+
+		if node.parent != node {
+			t.Error("Node parent set incorrectly")
+		}
+	}
+}
+
+func TestDisjointSetFind(t *testing.T) {
+	ds := newDisjointSet()
+
+	ds.makeSet(3)
+	ds.makeSet(5)
+
+	if ds.find(3) == ds.find(5) {
+		t.Error("Disjoint sets incorrectly found to be the same")
+	}
+}
+
+func TestUnion(t *testing.T) {
+	ds := newDisjointSet()
+
+	ds.makeSet(3)
+	ds.makeSet(5)
+
+	ds.union(ds.find(3), ds.find(5))
+
+	if ds.find(3) != ds.find(5) {
+		t.Error("Sets found to be disjoint after union")
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/path/doc.go b/vendor/gonum.org/v1/gonum/graph/path/doc.go
new file mode 100644
index 00000000..f9e7b1dd
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package path provides graph path finding functions.
+package path // import "gonum.org/v1/gonum/graph/path"
diff --git a/vendor/gonum.org/v1/gonum/graph/path/dynamic/doc.go b/vendor/gonum.org/v1/gonum/graph/path/dynamic/doc.go
new file mode 100644
index 00000000..a0e9458f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/dynamic/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package dynamic provides incremental heuristic graph path finding functions.
+package dynamic // import "gonum.org/v1/gonum/graph/path/dynamic"
diff --git a/vendor/gonum.org/v1/gonum/graph/path/dynamic/dstarlite.go b/vendor/gonum.org/v1/gonum/graph/path/dynamic/dstarlite.go
new file mode 100644
index 00000000..e8794dc8
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/dynamic/dstarlite.go
@@ -0,0 +1,491 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package dynamic
+
+import (
+	"container/heap"
+	"fmt"
+	"math"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/path"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+// DStarLite implements the D* Lite dynamic re-planning path search algorithm.
+//
+//  doi:10.1109/tro.2004.838026 and ISBN:0-262-51129-0 pp476-483
+//
+type DStarLite struct {
+	s, t *dStarLiteNode
+	last *dStarLiteNode
+
+	model       WorldModel
+	queue       dStarLiteQueue
+	keyModifier float64
+
+	weight    path.Weighting
+	heuristic path.Heuristic
+}
+
+// WorldModel is a mutable weighted directed graph that returns nodes identified
+// by id number.
+type WorldModel interface {
+	graph.WeightedBuilder
+	graph.WeightedDirected
+	Node(id int64) graph.Node
+}
+
+// NewDStarLite returns a new DStarLite planner for the path from s to t in g using the
+// heuristic h. The world model, m, is used to store shortest path information during path
+// planning. The world model must be an empty graph when NewDStarLite is called.
+//
+// If h is nil, the DStarLite will use the g.HeuristicCost method if g implements
+// path.HeuristicCoster, falling back to path.NullHeuristic otherwise. If the graph does not
+// implement graph.Weighter, path.UniformCost is used. NewDStarLite will panic if g has
+// a negative edge weight.
+func NewDStarLite(s, t graph.Node, g graph.Graph, h path.Heuristic, m WorldModel) *DStarLite {
+	/*
+	   procedure Initialize()
+	   {02”} U = ∅;
+	   {03”} k_m = 0;
+	   {04”} for all s ∈ S rhs(s) = g(s) = ∞;
+	   {05”} rhs(s_goal) = 0;
+	   {06”} U.Insert(s_goal, [h(s_start, s_goal); 0]);
+	*/
+
+	d := &DStarLite{
+		s: newDStarLiteNode(s),
+		t: newDStarLiteNode(t), // badKey is overwritten below.
+
+		model: m,
+
+		heuristic: h,
+	}
+	d.t.rhs = 0
+
+	/*
+		procedure Main()
+		{29”} s_last = s_start;
+		{30”} Initialize();
+	*/
+	d.last = d.s
+
+	if wg, ok := g.(graph.Weighted); ok {
+		d.weight = wg.Weight
+	} else {
+		d.weight = path.UniformCost(g)
+	}
+	if d.heuristic == nil {
+		if g, ok := g.(path.HeuristicCoster); ok {
+			d.heuristic = g.HeuristicCost
+		} else {
+			d.heuristic = path.NullHeuristic
+		}
+	}
+
+	d.queue.insert(d.t, key{d.heuristic(s, t), 0})
+
+	for _, n := range g.Nodes() {
+		switch n.ID() {
+		case d.s.ID():
+			d.model.AddNode(d.s)
+		case d.t.ID():
+			d.model.AddNode(d.t)
+		default:
+			d.model.AddNode(newDStarLiteNode(n))
+		}
+	}
+	for _, u := range d.model.Nodes() {
+		for _, v := range g.From(u) {
+			w := edgeWeight(d.weight, u, v)
+			if w < 0 {
+				panic("D* Lite: negative edge weight")
+			}
+			d.model.SetWeightedEdge(simple.WeightedEdge{F: u, T: d.model.Node(v.ID()), W: w})
+		}
+	}
+
+	/*
+		procedure Main()
+		{31”} ComputeShortestPath();
+	*/
+	d.findShortestPath()
+
+	return d
+}
+
+// edgeWeight is a helper function that returns the weight of the edge between
+// two connected nodes, u and v, using the provided weight function. It panics
+// if there is no edge between u and v.
+func edgeWeight(weight path.Weighting, u, v graph.Node) float64 {
+	w, ok := weight(u, v)
+	if !ok {
+		panic("D* Lite: unexpected invalid weight")
+	}
+	return w
+}
+
+// keyFor is the CalculateKey procedure in the D* Lite papers.
+func (d *DStarLite) keyFor(s *dStarLiteNode) key {
+	/*
+	   procedure CalculateKey(s)
+	   {01”} return [min(g(s), rhs(s)) + h(s_start, s) + k_m; min(g(s), rhs(s))];
+	*/
+	k := key{1: math.Min(s.g, s.rhs)}
+	k[0] = k[1] + d.heuristic(d.s.Node, s.Node) + d.keyModifier
+	return k
+}
+
+// update is the UpdateVertex procedure in the D* Lite papers.
+func (d *DStarLite) update(u *dStarLiteNode) {
+	/*
+	   procedure UpdateVertex(u)
+	   {07”} if (g(u) != rhs(u) AND u ∈ U) U.Update(u,CalculateKey(u));
+	   {08”} else if (g(u) != rhs(u) AND u /∈ U) U.Insert(u,CalculateKey(u));
+	   {09”} else if (g(u) = rhs(u) AND u ∈ U) U.Remove(u);
+	*/
+	inQueue := u.inQueue()
+	switch {
+	case inQueue && u.g != u.rhs:
+		d.queue.update(u, d.keyFor(u))
+	case !inQueue && u.g != u.rhs:
+		d.queue.insert(u, d.keyFor(u))
+	case inQueue && u.g == u.rhs:
+		d.queue.remove(u)
+	}
+}
+
+// findShortestPath is the ComputeShortestPath procedure in the D* Lite papers.
+func (d *DStarLite) findShortestPath() {
+	/*
+	   procedure ComputeShortestPath()
+	   {10”} while (U.TopKey() < CalculateKey(s_start) OR rhs(s_start) > g(s_start))
+	   {11”} u = U.Top();
+	   {12”} k_old = U.TopKey();
+	   {13”} k_new = CalculateKey(u);
+	   {14”} if(k_old < k_new)
+	   {15”}   U.Update(u, k_new);
+	   {16”} else if (g(u) > rhs(u))
+	   {17”}   g(u) = rhs(u);
+	   {18”}   U.Remove(u);
+	   {19”}   for all s ∈ Pred(u)
+	   {20”}     if (s != s_goal) rhs(s) = min(rhs(s), c(s, u) + g(u));
+	   {21”}     UpdateVertex(s);
+	   {22”} else
+	   {23”}   g_old = g(u);
+	   {24”}   g(u) = ∞;
+	   {25”}   for all s ∈ Pred(u) ∪ {u}
+	   {26”}     if (rhs(s) = c(s, u) + g_old)
+	   {27”}       if (s != s_goal) rhs(s) = min s'∈Succ(s)(c(s, s') + g(s'));
+	   {28”}     UpdateVertex(s);
+	*/
+	for d.queue.Len() != 0 { // We use d.queue.Len since d.queue does not return an infinite key when empty.
+		u := d.queue.top()
+		if !u.key.less(d.keyFor(d.s)) && d.s.rhs <= d.s.g {
+			break
+		}
+		switch kNew := d.keyFor(u); {
+		case u.key.less(kNew):
+			d.queue.update(u, kNew)
+		case u.g > u.rhs:
+			u.g = u.rhs
+			d.queue.remove(u)
+			for _, _s := range d.model.To(u) {
+				s := _s.(*dStarLiteNode)
+				if s.ID() != d.t.ID() {
+					s.rhs = math.Min(s.rhs, edgeWeight(d.model.Weight, s, u)+u.g)
+				}
+				d.update(s)
+			}
+		default:
+			gOld := u.g
+			u.g = math.Inf(1)
+			for _, _s := range append(d.model.To(u), u) {
+				s := _s.(*dStarLiteNode)
+				if s.rhs == edgeWeight(d.model.Weight, s, u)+gOld {
+					if s.ID() != d.t.ID() {
+						s.rhs = math.Inf(1)
+						for _, t := range d.model.From(s) {
+							s.rhs = math.Min(s.rhs, edgeWeight(d.model.Weight, s, t)+t.(*dStarLiteNode).g)
+						}
+					}
+				}
+				d.update(s)
+			}
+		}
+	}
+}
+
+// Step performs one movement step along the best path towards the goal.
+// It returns false if no further progression toward the goal can be
+// achieved, either because the goal has been reached or because there
+// is no path.
+func (d *DStarLite) Step() bool {
+	/*
+	   procedure Main()
+	   {32”} while (s_start != s_goal)
+	   {33”} // if (rhs(s_start) = ∞) then there is no known path
+	   {34”}   s_start = argmin s'∈Succ(s_start)(c(s_start, s') + g(s'));
+	*/
+	if d.s.ID() == d.t.ID() {
+		return false
+	}
+	if math.IsInf(d.s.rhs, 1) {
+		return false
+	}
+
+	// We use rhs comparison to break ties
+	// between coequally weighted nodes.
+	rhs := math.Inf(1)
+	min := math.Inf(1)
+
+	var next *dStarLiteNode
+	for _, _s := range d.model.From(d.s) {
+		s := _s.(*dStarLiteNode)
+		w := edgeWeight(d.model.Weight, d.s, s) + s.g
+		if w < min || (w == min && s.rhs < rhs) {
+			next = s
+			min = w
+			rhs = s.rhs
+		}
+	}
+	d.s = next
+
+	/*
+	   procedure Main()
+	   {35”}   Move to s_start;
+	*/
+	return true
+}
+
+// MoveTo moves to n in the world graph.
+func (d *DStarLite) MoveTo(n graph.Node) {
+	d.last = d.s
+	d.s = d.model.Node(n.ID()).(*dStarLiteNode)
+	d.keyModifier += d.heuristic(d.last, d.s)
+}
+
+// UpdateWorld updates or adds edges in the world graph. UpdateWorld will
+// panic if changes include a negative edge weight.
+func (d *DStarLite) UpdateWorld(changes []graph.Edge) {
+	/*
+	   procedure Main()
+	   {36”}   Scan graph for changed edge costs;
+	   {37”}   if any edge costs changed
+	   {38”}     k_m = k_m + h(s_last, s_start);
+	   {39”}     s_last = s_start;
+	   {40”}     for all directed edges (u, v) with changed edge costs
+	   {41”}       c_old = c(u, v);
+	   {42”}       Update the edge cost c(u, v);
+	   {43”}       if (c_old > c(u, v))
+	   {44”}         if (u != s_goal) rhs(u) = min(rhs(u), c(u, v) + g(v));
+	   {45”}       else if (rhs(u) = c_old + g(v))
+	   {46”}         if (u != s_goal) rhs(u) = min s'∈Succ(u)(c(u, s') + g(s'));
+	   {47”}       UpdateVertex(u);
+	   {48”}     ComputeShortestPath()
+	*/
+	if len(changes) == 0 {
+		return
+	}
+	d.keyModifier += d.heuristic(d.last, d.s)
+	d.last = d.s
+	for _, e := range changes {
+		from := e.From()
+		to := e.To()
+		c, _ := d.weight(from, to)
+		if c < 0 {
+			panic("D* Lite: negative edge weight")
+		}
+		cOld, _ := d.model.Weight(from, to)
+		u := d.worldNodeFor(from)
+		v := d.worldNodeFor(to)
+		d.model.SetWeightedEdge(simple.WeightedEdge{F: u, T: v, W: c})
+		if cOld > c {
+			if u.ID() != d.t.ID() {
+				u.rhs = math.Min(u.rhs, c+v.g)
+			}
+		} else if u.rhs == cOld+v.g {
+			if u.ID() != d.t.ID() {
+				u.rhs = math.Inf(1)
+				for _, t := range d.model.From(u) {
+					u.rhs = math.Min(u.rhs, edgeWeight(d.model.Weight, u, t)+t.(*dStarLiteNode).g)
+				}
+			}
+		}
+		d.update(u)
+	}
+	d.findShortestPath()
+}
+
+func (d *DStarLite) worldNodeFor(n graph.Node) *dStarLiteNode {
+	switch w := d.model.Node(n.ID()).(type) {
+	case *dStarLiteNode:
+		return w
+	case graph.Node:
+		panic(fmt.Sprintf("D* Lite: illegal world model node type: %T", w))
+	default:
+		return newDStarLiteNode(n)
+	}
+}
+
+// Here returns the current location.
+func (d *DStarLite) Here() graph.Node {
+	return d.s.Node
+}
+
+// Path returns the path from the current location to the goal and the
+// weight of the path.
+func (d *DStarLite) Path() (p []graph.Node, weight float64) {
+	u := d.s
+	p = []graph.Node{u.Node}
+	for u.ID() != d.t.ID() {
+		if math.IsInf(u.rhs, 1) {
+			return nil, math.Inf(1)
+		}
+
+		// We use stored rhs comparison to break
+		// ties between calculated rhs-coequal nodes.
+		rhsMin := math.Inf(1)
+		min := math.Inf(1)
+		var (
+			next *dStarLiteNode
+			cost float64
+		)
+		for _, _v := range d.model.From(u) {
+			v := _v.(*dStarLiteNode)
+			w := edgeWeight(d.model.Weight, u, v)
+			if rhs := w + v.g; rhs < min || (rhs == min && v.rhs < rhsMin) {
+				next = v
+				min = rhs
+				rhsMin = v.rhs
+				cost = w
+			}
+		}
+		if next == nil {
+			return nil, math.NaN()
+		}
+		u = next
+		weight += cost
+		p = append(p, u.Node)
+	}
+	return p, weight
+}
+
+/*
+The pseudocode uses the following functions to manage the priority
+queue:
+
+      * U.Top() returns a vertex with the smallest priority of all
+        vertices in priority queue U.
+      * U.TopKey() returns the smallest priority of all vertices in
+        priority queue U. (If is empty, then U.TopKey() returns [∞;∞].)
+      * U.Pop() deletes the vertex with the smallest priority in
+        priority queue U and returns the vertex.
+      * U.Insert(s, k) inserts vertex s into priority queue with
+        priority k.
+      * U.Update(s, k) changes the priority of vertex s in priority
+        queue U to k. (It does nothing if the current priority of vertex
+        s already equals k.)
+      * Finally, U.Remove(s) removes vertex s from priority queue U.
+*/
+
+// key is a D* Lite priority queue key.
+type key [2]float64
+
+var badKey = key{math.NaN(), math.NaN()}
+
+// less returns whether k is less than other. From ISBN:0-262-51129-0 pp476-483:
+//
+//  k ≤ k' iff k₁ < k'₁ OR (k₁ == k'₁ AND k₂ ≤ k'₂)
+//
+func (k key) less(other key) bool {
+	if k != k || other != other {
+		panic("D* Lite: poisoned key")
+	}
+	return k[0] < other[0] || (k[0] == other[0] && k[1] < other[1])
+}
+
+// dStarLiteNode adds D* Lite accounting to a graph.Node.
+type dStarLiteNode struct {
+	graph.Node
+	key key
+	idx int
+	rhs float64
+	g   float64
+}
+
+// newDStarLiteNode returns a dStarLite node that is in a legal state
+// for existence outside the DStarLite priority queue.
+func newDStarLiteNode(n graph.Node) *dStarLiteNode {
+	return &dStarLiteNode{
+		Node: n,
+		rhs:  math.Inf(1),
+		g:    math.Inf(1),
+		key:  badKey,
+		idx:  -1,
+	}
+}
+
+// inQueue returns whether the node is in the queue.
+func (q *dStarLiteNode) inQueue() bool {
+	return q.idx >= 0
+}
+
+// dStarLiteQueue is a D* Lite priority queue.
+type dStarLiteQueue []*dStarLiteNode
+
+func (q dStarLiteQueue) Less(i, j int) bool {
+	return q[i].key.less(q[j].key)
+}
+
+func (q dStarLiteQueue) Swap(i, j int) {
+	q[i], q[j] = q[j], q[i]
+	q[i].idx = i
+	q[j].idx = j
+}
+
+func (q dStarLiteQueue) Len() int {
+	return len(q)
+}
+
+func (q *dStarLiteQueue) Push(x interface{}) {
+	n := x.(*dStarLiteNode)
+	n.idx = len(*q)
+	*q = append(*q, n)
+}
+
+func (q *dStarLiteQueue) Pop() interface{} {
+	n := (*q)[len(*q)-1]
+	n.idx = -1
+	*q = (*q)[:len(*q)-1]
+	return n
+}
+
+// top returns the top node in the queue. Note that instead of
+// returning a key [∞;∞] when q is empty, the caller checks for
+// an empty queue by calling q.Len.
+func (q dStarLiteQueue) top() *dStarLiteNode {
+	return q[0]
+}
+
+// insert puts the node u into the queue with the key k.
+func (q *dStarLiteQueue) insert(u *dStarLiteNode, k key) {
+	u.key = k
+	heap.Push(q, u)
+}
+
+// update updates the node in the queue identified by id with the key k.
+func (q *dStarLiteQueue) update(n *dStarLiteNode, k key) {
+	n.key = k
+	heap.Fix(q, n.idx)
+}
+
+// remove removes the node identified by id from the queue.
+func (q *dStarLiteQueue) remove(n *dStarLiteNode) {
+	heap.Remove(q, n.idx)
+	n.key = badKey
+	n.idx = -1
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/path/dynamic/dstarlite_test.go b/vendor/gonum.org/v1/gonum/graph/path/dynamic/dstarlite_test.go
new file mode 100644
index 00000000..9c53a5da
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/dynamic/dstarlite_test.go
@@ -0,0 +1,680 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package dynamic
+
+import (
+	"bytes"
+	"flag"
+	"fmt"
+	"math"
+	"reflect"
+	"strings"
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/path"
+	"gonum.org/v1/gonum/graph/path/internal"
+	"gonum.org/v1/gonum/graph/path/internal/testgraphs"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+var (
+	debug   = flag.Bool("debug", false, "write path progress for failing dynamic case tests")
+	vdebug  = flag.Bool("vdebug", false, "write path progress for all dynamic case tests (requires test.v)")
+	maxWide = flag.Int("maxwidth", 5, "maximum width grid to dump for debugging")
+)
+
+func TestDStarLiteNullHeuristic(t *testing.T) {
+	for _, test := range testgraphs.ShortestPathTests {
+		// Skip zero-weight cycles.
+		if strings.HasPrefix(test.Name, "zero-weight") {
+			continue
+		}
+
+		g := test.Graph()
+		for _, e := range test.Edges {
+			g.SetWeightedEdge(e)
+		}
+
+		var (
+			d *DStarLite
+
+			panicked bool
+		)
+		func() {
+			defer func() {
+				panicked = recover() != nil
+			}()
+			d = NewDStarLite(test.Query.From(), test.Query.To(), g.(graph.Graph), path.NullHeuristic, simple.NewWeightedDirectedGraph(0, math.Inf(1)))
+		}()
+		if panicked || test.HasNegativeWeight {
+			if !test.HasNegativeWeight {
+				t.Errorf("%q: unexpected panic", test.Name)
+			}
+			if !panicked {
+				t.Errorf("%q: expected panic for negative edge weight", test.Name)
+			}
+			continue
+		}
+
+		p, weight := d.Path()
+
+		if !math.IsInf(weight, 1) && p[0].ID() != test.Query.From().ID() {
+			t.Fatalf("%q: unexpected from node ID: got:%d want:%d", test.Name, p[0].ID(), test.Query.From().ID())
+		}
+		if weight != test.Weight {
+			t.Errorf("%q: unexpected weight from Between: got:%f want:%f",
+				test.Name, weight, test.Weight)
+		}
+
+		var got []int64
+		for _, n := range p {
+			got = append(got, n.ID())
+		}
+		ok := len(got) == 0 && len(test.WantPaths) == 0
+		for _, sp := range test.WantPaths {
+			if reflect.DeepEqual(got, sp) {
+				ok = true
+				break
+			}
+		}
+		if !ok {
+			t.Errorf("%q: unexpected shortest path:\ngot: %v\nwant from:%v",
+				test.Name, p, test.WantPaths)
+		}
+	}
+}
+
+var dynamicDStarLiteTests = []struct {
+	g          *internal.Grid
+	radius     float64
+	all        bool
+	diag, unit bool
+	remember   []bool
+	modify     func(*internal.LimitedVisionGrid)
+
+	heuristic func(dx, dy float64) float64
+
+	s, t graph.Node
+
+	want        []graph.Node
+	weight      float64
+	wantedPaths map[int64][]graph.Node
+}{
+	{
+		// This is the example shown in figures 6 and 7 of doi:10.1109/tro.2004.838026.
+		g: internal.NewGridFrom(
+			"...",
+			".*.",
+			".*.",
+			".*.",
+			"...",
+		),
+		radius:   1.5,
+		all:      true,
+		diag:     true,
+		unit:     true,
+		remember: []bool{false, true},
+
+		heuristic: func(dx, dy float64) float64 {
+			return math.Max(math.Abs(dx), math.Abs(dy))
+		},
+
+		s: simple.Node(3),
+		t: simple.Node(14),
+
+		want: []graph.Node{
+			simple.Node(3),
+			simple.Node(6),
+			simple.Node(9),
+			simple.Node(13),
+			simple.Node(14),
+		},
+		weight: 4,
+	},
+	{
+		// This is a small example that has the property that the first corner
+		// may be taken incorrectly at 90° or correctly at 45° because the
+		// calculated rhs values of 12 and 17 are tied when moving from node
+		// 16, and the grid is small enough to examine by a dump.
+		g: internal.NewGridFrom(
+			".....",
+			"...*.",
+			"**.*.",
+			"...*.",
+		),
+		radius:   1.5,
+		all:      true,
+		diag:     true,
+		remember: []bool{false, true},
+
+		heuristic: func(dx, dy float64) float64 {
+			return math.Max(math.Abs(dx), math.Abs(dy))
+		},
+
+		s: simple.Node(15),
+		t: simple.Node(14),
+
+		want: []graph.Node{
+			simple.Node(15),
+			simple.Node(16),
+			simple.Node(12),
+			simple.Node(7),
+			simple.Node(3),
+			simple.Node(9),
+			simple.Node(14),
+		},
+		weight: 7.242640687119285,
+		wantedPaths: map[int64][]graph.Node{
+			12: {simple.Node(12), simple.Node(7), simple.Node(3), simple.Node(9), simple.Node(14)},
+		},
+	},
+	{
+		// This is the example shown in figure 2 of doi:10.1109/tro.2004.838026
+		// with the exception that diagonal edge weights are calculated with the hypot
+		// function instead of a step count and only allowing information to be known
+		// from exploration.
+		g: internal.NewGridFrom(
+			"..................",
+			"..................",
+			"..................",
+			"..................",
+			"..................",
+			"..................",
+			"....*.*...........",
+			"*****.***.........",
+			"......*...........",
+			"......***.........",
+			"......*...........",
+			"......*...........",
+			"......*...........",
+			"*****.*...........",
+			"......*...........",
+		),
+		radius:   1.5,
+		all:      true,
+		diag:     true,
+		remember: []bool{false, true},
+
+		heuristic: func(dx, dy float64) float64 {
+			return math.Max(math.Abs(dx), math.Abs(dy))
+		},
+
+		s: simple.Node(253),
+		t: simple.Node(122),
+
+		want: []graph.Node{
+			simple.Node(253),
+			simple.Node(254),
+			simple.Node(255),
+			simple.Node(256),
+			simple.Node(239),
+			simple.Node(221),
+			simple.Node(203),
+			simple.Node(185),
+			simple.Node(167),
+			simple.Node(149),
+			simple.Node(131),
+			simple.Node(113),
+			simple.Node(96),
+
+			// The following section depends
+			// on map iteration order.
+			nil,
+			nil,
+			nil,
+			nil,
+			nil,
+			nil,
+			nil,
+
+			simple.Node(122),
+		},
+		weight: 21.242640687119287,
+	},
+	{
+		// This is the example shown in figure 2 of doi:10.1109/tro.2004.838026
+		// with the exception that diagonal edge weights are calculated with the hypot
+		// function instead of a step count, not closing the exit and only allowing
+		// information to be known from exploration.
+		g: internal.NewGridFrom(
+			"..................",
+			"..................",
+			"..................",
+			"..................",
+			"..................",
+			"..................",
+			"....*.*...........",
+			"*****.***.........",
+			"..................", // Keep open.
+			"......***.........",
+			"......*...........",
+			"......*...........",
+			"......*...........",
+			"*****.*...........",
+			"......*...........",
+		),
+		radius:   1.5,
+		all:      true,
+		diag:     true,
+		remember: []bool{false, true},
+
+		heuristic: func(dx, dy float64) float64 {
+			return math.Max(math.Abs(dx), math.Abs(dy))
+		},
+
+		s: simple.Node(253),
+		t: simple.Node(122),
+
+		want: []graph.Node{
+			simple.Node(253),
+			simple.Node(254),
+			simple.Node(255),
+			simple.Node(256),
+			simple.Node(239),
+			simple.Node(221),
+			simple.Node(203),
+			simple.Node(185),
+			simple.Node(167),
+			simple.Node(150),
+			simple.Node(151),
+			simple.Node(152),
+
+			// The following section depends
+			// on map iteration order.
+			nil,
+			nil,
+			nil,
+			nil,
+			nil,
+
+			simple.Node(122),
+		},
+		weight: 18.656854249492383,
+	},
+	{
+		// This is the example shown in figure 2 of doi:10.1109/tro.2004.838026
+		// with the exception that diagonal edge weights are calculated with the hypot
+		// function instead of a step count, the exit is closed at a distance and
+		// information is allowed to be known from exploration.
+		g: internal.NewGridFrom(
+			"..................",
+			"..................",
+			"..................",
+			"..................",
+			"..................",
+			"..................",
+			"....*.*...........",
+			"*****.***.........",
+			"........*.........",
+			"......***.........",
+			"......*...........",
+			"......*...........",
+			"......*...........",
+			"*****.*...........",
+			"......*...........",
+		),
+		radius:   1.5,
+		all:      true,
+		diag:     true,
+		remember: []bool{false, true},
+
+		heuristic: func(dx, dy float64) float64 {
+			return math.Max(math.Abs(dx), math.Abs(dy))
+		},
+
+		s: simple.Node(253),
+		t: simple.Node(122),
+
+		want: []graph.Node{
+			simple.Node(253),
+			simple.Node(254),
+			simple.Node(255),
+			simple.Node(256),
+			simple.Node(239),
+			simple.Node(221),
+			simple.Node(203),
+			simple.Node(185),
+			simple.Node(167),
+			simple.Node(150),
+			simple.Node(151),
+			simple.Node(150),
+			simple.Node(131),
+			simple.Node(113),
+			simple.Node(96),
+
+			// The following section depends
+			// on map iteration order.
+			nil,
+			nil,
+			nil,
+			nil,
+			nil,
+			nil,
+			nil,
+
+			simple.Node(122),
+		},
+		weight: 24.07106781186548,
+	},
+	{
+		// This is the example shown in figure 2 of doi:10.1109/tro.2004.838026
+		// with the exception that diagonal edge weights are calculated with the hypot
+		// function instead of a step count.
+		g: internal.NewGridFrom(
+			"..................",
+			"..................",
+			"..................",
+			"..................",
+			"..................",
+			"..................",
+			"....*.*...........",
+			"*****.***.........",
+			"......*...........", // Forget this wall.
+			"......***.........",
+			"......*...........",
+			"......*...........",
+			"......*...........",
+			"*****.*...........",
+			"......*...........",
+		),
+		radius:   1.5,
+		all:      true,
+		diag:     true,
+		remember: []bool{true},
+
+		modify: func(l *internal.LimitedVisionGrid) {
+			all := l.Grid.AllVisible
+			l.Grid.AllVisible = false
+			for _, n := range l.Nodes() {
+				l.Known[n.ID()] = !l.Grid.Has(n)
+			}
+			l.Grid.AllVisible = all
+
+			const (
+				wallRow = 8
+				wallCol = 6
+			)
+			l.Known[l.NodeAt(wallRow, wallCol).ID()] = false
+
+			// Check we have a correctly modified representation.
+			for _, u := range l.Nodes() {
+				for _, v := range l.Nodes() {
+					if l.HasEdgeBetween(u, v) != l.Grid.HasEdgeBetween(u, v) {
+						ur, uc := l.RowCol(u.ID())
+						vr, vc := l.RowCol(v.ID())
+						if (ur == wallRow && uc == wallCol) || (vr == wallRow && vc == wallCol) {
+							if !l.HasEdgeBetween(u, v) {
+								panic(fmt.Sprintf("expected to believe edge between %v (%d,%d) and %v (%d,%d) is passable",
+									u, v, ur, uc, vr, vc))
+							}
+							continue
+						}
+						panic(fmt.Sprintf("disagreement about edge between %v (%d,%d) and %v (%d,%d): got:%t want:%t",
+							u, v, ur, uc, vr, vc, l.HasEdgeBetween(u, v), l.Grid.HasEdgeBetween(u, v)))
+					}
+				}
+			}
+		},
+
+		heuristic: func(dx, dy float64) float64 {
+			return math.Max(math.Abs(dx), math.Abs(dy))
+		},
+
+		s: simple.Node(253),
+		t: simple.Node(122),
+
+		want: []graph.Node{
+			simple.Node(253),
+			simple.Node(254),
+			simple.Node(255),
+			simple.Node(256),
+			simple.Node(239),
+			simple.Node(221),
+			simple.Node(203),
+			simple.Node(185),
+			simple.Node(167),
+			simple.Node(149),
+			simple.Node(131),
+			simple.Node(113),
+			simple.Node(96),
+
+			// The following section depends
+			// on map iteration order.
+			nil,
+			nil,
+			nil,
+			nil,
+			nil,
+			nil,
+			nil,
+
+			simple.Node(122),
+		},
+		weight: 21.242640687119287,
+	},
+	{
+		g: internal.NewGridFrom(
+			"*..*",
+			"**.*",
+			"**.*",
+			"**.*",
+		),
+		radius:   1,
+		all:      true,
+		diag:     false,
+		remember: []bool{false, true},
+
+		heuristic: func(dx, dy float64) float64 {
+			return math.Hypot(dx, dy)
+		},
+
+		s: simple.Node(1),
+		t: simple.Node(14),
+
+		want: []graph.Node{
+			simple.Node(1),
+			simple.Node(2),
+			simple.Node(6),
+			simple.Node(10),
+			simple.Node(14),
+		},
+		weight: 4,
+	},
+	{
+		g: internal.NewGridFrom(
+			"*..*",
+			"**.*",
+			"**.*",
+			"**.*",
+		),
+		radius:   1.5,
+		all:      true,
+		diag:     true,
+		remember: []bool{false, true},
+
+		heuristic: func(dx, dy float64) float64 {
+			return math.Hypot(dx, dy)
+		},
+
+		s: simple.Node(1),
+		t: simple.Node(14),
+
+		want: []graph.Node{
+			simple.Node(1),
+			simple.Node(6),
+			simple.Node(10),
+			simple.Node(14),
+		},
+		weight: math.Sqrt2 + 2,
+	},
+	{
+		g: internal.NewGridFrom(
+			"...",
+			".*.",
+			".*.",
+			".*.",
+			".*.",
+		),
+		radius:   1,
+		all:      true,
+		diag:     false,
+		remember: []bool{false, true},
+
+		heuristic: func(dx, dy float64) float64 {
+			return math.Hypot(dx, dy)
+		},
+
+		s: simple.Node(6),
+		t: simple.Node(14),
+
+		want: []graph.Node{
+			simple.Node(6),
+			simple.Node(9),
+			simple.Node(12),
+			simple.Node(9),
+			simple.Node(6),
+			simple.Node(3),
+			simple.Node(0),
+			simple.Node(1),
+			simple.Node(2),
+			simple.Node(5),
+			simple.Node(8),
+			simple.Node(11),
+			simple.Node(14),
+		},
+		weight: 12,
+	},
+}
+
+func TestDStarLiteDynamic(t *testing.T) {
+	for i, test := range dynamicDStarLiteTests {
+		for _, remember := range test.remember {
+			l := &internal.LimitedVisionGrid{
+				Grid:         test.g,
+				VisionRadius: test.radius,
+				Location:     test.s,
+			}
+			if remember {
+				l.Known = make(map[int64]bool)
+			}
+
+			l.Grid.AllVisible = test.all
+
+			l.Grid.AllowDiagonal = test.diag
+			l.Grid.UnitEdgeWeight = test.unit
+
+			if test.modify != nil {
+				test.modify(l)
+			}
+
+			got := []graph.Node{test.s}
+			l.MoveTo(test.s)
+
+			heuristic := func(a, b graph.Node) float64 {
+				ax, ay := l.XY(a)
+				bx, by := l.XY(b)
+				return test.heuristic(ax-bx, ay-by)
+			}
+
+			world := simple.NewWeightedDirectedGraph(0, math.Inf(1))
+			d := NewDStarLite(test.s, test.t, l, heuristic, world)
+			var (
+				dp  *dumper
+				buf bytes.Buffer
+			)
+			_, c := l.Grid.Dims()
+			if c <= *maxWide && (*debug || *vdebug) {
+				dp = &dumper{
+					w: &buf,
+
+					dStarLite: d,
+					grid:      l,
+				}
+			}
+
+			dp.dump(true)
+			dp.printEdges("Initial world knowledge: %s\n\n", simpleWeightedEdgesOf(l, world.Edges()))
+			for d.Step() {
+				changes, _ := l.MoveTo(d.Here())
+				got = append(got, l.Location)
+				d.UpdateWorld(changes)
+				dp.dump(true)
+				if wantedPath, ok := test.wantedPaths[l.Location.ID()]; ok {
+					gotPath, _ := d.Path()
+					if !samePath(gotPath, wantedPath) {
+						t.Errorf("unexpected intermediate path estimation for test %d %s memory:\ngot: %v\nwant:%v",
+							i, memory(remember), gotPath, wantedPath)
+					}
+				}
+				dp.printEdges("Edges changing after last step:\n%s\n\n", simpleWeightedEdgesOf(l, changes))
+			}
+
+			if weight := weightOf(got, l.Grid); !samePath(got, test.want) || weight != test.weight {
+				t.Errorf("unexpected path for test %d %s memory got weight:%v want weight:%v:\ngot: %v\nwant:%v",
+					i, memory(remember), weight, test.weight, got, test.want)
+				b, err := l.Render(got)
+				t.Errorf("path taken (err:%v):\n%s", err, b)
+				if c <= *maxWide && (*debug || *vdebug) {
+					t.Error(buf.String())
+				}
+			} else if c <= *maxWide && *vdebug {
+				t.Logf("Test %d:\n%s", i, buf.String())
+			}
+		}
+	}
+}
+
+type memory bool
+
+func (m memory) String() string {
+	if m {
+		return "with"
+	}
+	return "without"
+}
+
+// samePath compares two paths for equality ignoring nodes that are nil.
+func samePath(a, b []graph.Node) bool {
+	if len(a) != len(b) {
+		return false
+	}
+	for i, e := range a {
+		if e == nil || b[i] == nil {
+			continue
+		}
+		if e.ID() != b[i].ID() {
+			return false
+		}
+	}
+	return true
+}
+
+// weightOf return the weight of the path in g.
+func weightOf(path []graph.Node, g graph.Weighted) float64 {
+	var w float64
+	if len(path) > 1 {
+		for p, n := range path[1:] {
+			ew, ok := g.Weight(path[p], n)
+			if !ok {
+				return math.Inf(1)
+			}
+			w += ew
+		}
+	}
+	return w
+}
+
+// simpleWeightedEdgesOf returns the weighted edges in g corresponding to the given edges.
+func simpleWeightedEdgesOf(g graph.Weighted, edges []graph.Edge) []simple.WeightedEdge {
+	w := make([]simple.WeightedEdge, len(edges))
+	for i, e := range edges {
+		w[i].F = e.From()
+		w[i].T = e.To()
+		ew, _ := g.Weight(e.From(), e.To())
+		w[i].W = ew
+	}
+	return w
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/path/dynamic/dumper_test.go b/vendor/gonum.org/v1/gonum/graph/path/dynamic/dumper_test.go
new file mode 100644
index 00000000..f76a3649
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/dynamic/dumper_test.go
@@ -0,0 +1,153 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package dynamic
+
+import (
+	"bytes"
+	"fmt"
+	"io"
+	"sort"
+	"text/tabwriter"
+
+	"gonum.org/v1/gonum/graph/path/internal"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+// dumper implements a grid D* Lite statistics dump.
+type dumper struct {
+	step int
+
+	dStarLite *DStarLite
+	grid      *internal.LimitedVisionGrid
+
+	w io.Writer
+}
+
+// dump writes a single step of a D* Lite path search to the dumper's io.Writer.
+func (d *dumper) dump(withpath bool) {
+	if d == nil {
+		return
+	}
+	var pathStep map[int64]int
+	if withpath {
+		pathStep = make(map[int64]int)
+		path, _ := d.dStarLite.Path()
+		for i, n := range path {
+			pathStep[n.ID()] = i
+		}
+	}
+	fmt.Fprintf(d.w, "Step:%d kₘ=%v\n", d.step, d.dStarLite.keyModifier)
+	d.step++
+	w := tabwriter.NewWriter(d.w, 0, 0, 0, ' ', tabwriter.Debug)
+	rows, cols := d.grid.Grid.Dims()
+	for r := 0; r < rows; r++ {
+		if r == 0 {
+			for c := 0; c < cols; c++ {
+				if c != 0 {
+					fmt.Fprint(w, "\t")
+				}
+				fmt.Fprint(w, "-------------------")
+			}
+			fmt.Fprintln(w)
+		}
+		for ln := 0; ln < 6; ln++ {
+			for c := 0; c < cols; c++ {
+				if c != 0 {
+					fmt.Fprint(w, "\t")
+				}
+				n := d.dStarLite.model.Node(d.grid.NodeAt(r, c).ID()).(*dStarLiteNode)
+				switch ln {
+				case 0:
+					if n.ID() == d.grid.Location.ID() {
+						if d.grid.Grid.HasOpen(n) {
+							fmt.Fprintf(w, "id:%2d  >@<", n.ID())
+						} else {
+							// Mark location as illegal.
+							fmt.Fprintf(w, "id:%2d  >!<", n.ID())
+						}
+					} else if n.ID() == d.dStarLite.t.ID() {
+						fmt.Fprintf(w, "id:%2d   G", n.ID())
+						// Mark goal cell as illegal.
+						if !d.grid.Grid.HasOpen(n) {
+							fmt.Fprint(w, "!")
+						}
+					} else if pathStep[n.ID()] > 0 {
+						fmt.Fprintf(w, "id:%2d  %2d", n.ID(), pathStep[n.ID()])
+						// Mark path cells with an obstruction.
+						if !d.grid.Grid.HasOpen(n) {
+							fmt.Fprint(w, "!")
+						}
+					} else {
+						fmt.Fprintf(w, "id:%2d", n.ID())
+						// Mark cells with an obstruction.
+						if !d.grid.Grid.HasOpen(n) {
+							fmt.Fprint(w, "   *")
+						}
+					}
+				case 1:
+					fmt.Fprintf(w, "h:  %.4v", d.dStarLite.heuristic(n, d.dStarLite.Here()))
+				case 2:
+					fmt.Fprintf(w, "g:  %.4v", n.g)
+				case 3:
+					fmt.Fprintf(w, "rhs:%.4v", n.rhs)
+				case 4:
+					if n.g != n.rhs {
+						fmt.Fprintf(w, "key:%.3f", n.key)
+					}
+					if n.key == n.key {
+						// Mark keys for nodes in the priority queue.
+						// We use NaN inequality for this check since all
+						// keys not in the queue must have their key set
+						// to badKey.
+						//
+						// This should always mark cells where key is
+						// printed.
+						fmt.Fprint(w, "*")
+					}
+					if n.g > n.rhs {
+						fmt.Fprint(w, "^")
+					}
+					if n.g < n.rhs {
+						fmt.Fprint(w, "v")
+					}
+				default:
+					fmt.Fprint(w, "-------------------")
+				}
+			}
+			fmt.Fprintln(w)
+		}
+	}
+	w.Flush()
+	fmt.Fprintln(d.w)
+}
+
+// printEdges pretty prints the given edges to the dumper's io.Writer using the provided
+// format string. The edges are first formated to a string, so the format string must use
+// the %s verb to indicate where the edges are to be printed.
+func (d *dumper) printEdges(format string, edges []simple.WeightedEdge) {
+	if d == nil {
+		return
+	}
+	var buf bytes.Buffer
+	sort.Sort(lexically(edges))
+	for i, e := range edges {
+		if i != 0 {
+			fmt.Fprint(&buf, ", ")
+		}
+		fmt.Fprintf(&buf, "%d->%d:%.4v", e.From().ID(), e.To().ID(), e.Weight())
+	}
+	if len(edges) == 0 {
+		fmt.Fprint(&buf, "none")
+	}
+	fmt.Fprintf(d.w, format, buf.Bytes())
+}
+
+type lexically []simple.WeightedEdge
+
+func (l lexically) Len() int { return len(l) }
+func (l lexically) Less(i, j int) bool {
+	return l[i].From().ID() < l[j].From().ID() || (l[i].From().ID() == l[j].From().ID() && l[i].To().ID() < l[j].To().ID())
+}
+func (l lexically) Swap(i, j int) { l[i], l[j] = l[j], l[i] }
diff --git a/vendor/gonum.org/v1/gonum/graph/path/floydwarshall.go b/vendor/gonum.org/v1/gonum/graph/path/floydwarshall.go
new file mode 100644
index 00000000..310fec6d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/floydwarshall.go
@@ -0,0 +1,59 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package path
+
+import "gonum.org/v1/gonum/graph"
+
+// FloydWarshall returns a shortest-path tree for the graph g or false indicating
+// that a negative cycle exists in the graph. If the graph does not implement
+// graph.Weighter, UniformCost is used.
+//
+// The time complexity of FloydWarshall is O(|V|^3).
+func FloydWarshall(g graph.Graph) (paths AllShortest, ok bool) {
+	var weight Weighting
+	if wg, ok := g.(graph.Weighted); ok {
+		weight = wg.Weight
+	} else {
+		weight = UniformCost(g)
+	}
+
+	nodes := g.Nodes()
+	paths = newAllShortest(nodes, true)
+	for i, u := range nodes {
+		paths.dist.Set(i, i, 0)
+		for _, v := range g.From(u) {
+			j := paths.indexOf[v.ID()]
+			w, ok := weight(u, v)
+			if !ok {
+				panic("floyd-warshall: unexpected invalid weight")
+			}
+			paths.set(i, j, w, j)
+		}
+	}
+
+	for k := range nodes {
+		for i := range nodes {
+			for j := range nodes {
+				ij := paths.dist.At(i, j)
+				joint := paths.dist.At(i, k) + paths.dist.At(k, j)
+				if ij > joint {
+					paths.set(i, j, joint, paths.at(i, k)...)
+				} else if ij-joint == 0 {
+					paths.add(i, j, paths.at(i, k)...)
+				}
+			}
+		}
+	}
+
+	ok = true
+	for i := range nodes {
+		if paths.dist.At(i, i) < 0 {
+			ok = false
+			break
+		}
+	}
+
+	return paths, ok
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/path/floydwarshall_test.go b/vendor/gonum.org/v1/gonum/graph/path/floydwarshall_test.go
new file mode 100644
index 00000000..d23c0341
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/floydwarshall_test.go
@@ -0,0 +1,102 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package path
+
+import (
+	"math"
+	"reflect"
+	"sort"
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/ordered"
+	"gonum.org/v1/gonum/graph/path/internal/testgraphs"
+)
+
+func TestFloydWarshall(t *testing.T) {
+	for _, test := range testgraphs.ShortestPathTests {
+		g := test.Graph()
+		for _, e := range test.Edges {
+			g.SetWeightedEdge(e)
+		}
+
+		pt, ok := FloydWarshall(g.(graph.Graph))
+		if test.HasNegativeCycle {
+			if ok {
+				t.Errorf("%q: expected negative cycle", test.Name)
+			}
+			continue
+		}
+		if !ok {
+			t.Fatalf("%q: unexpected negative cycle", test.Name)
+		}
+
+		// Check all random paths returned are OK.
+		for i := 0; i < 10; i++ {
+			p, weight, unique := pt.Between(test.Query.From(), test.Query.To())
+			if weight != test.Weight {
+				t.Errorf("%q: unexpected weight from Between: got:%f want:%f",
+					test.Name, weight, test.Weight)
+			}
+			if weight := pt.Weight(test.Query.From(), test.Query.To()); weight != test.Weight {
+				t.Errorf("%q: unexpected weight from Weight: got:%f want:%f",
+					test.Name, weight, test.Weight)
+			}
+			if unique != test.HasUniquePath {
+				t.Errorf("%q: unexpected number of paths: got: unique=%t want: unique=%t",
+					test.Name, unique, test.HasUniquePath)
+			}
+
+			var got []int64
+			for _, n := range p {
+				got = append(got, n.ID())
+			}
+			ok := len(got) == 0 && len(test.WantPaths) == 0
+			for _, sp := range test.WantPaths {
+				if reflect.DeepEqual(got, sp) {
+					ok = true
+					break
+				}
+			}
+			if !ok {
+				t.Errorf("%q: unexpected shortest path:\ngot: %v\nwant from:%v",
+					test.Name, p, test.WantPaths)
+			}
+		}
+
+		np, weight, unique := pt.Between(test.NoPathFor.From(), test.NoPathFor.To())
+		if np != nil || !math.IsInf(weight, 1) || unique {
+			t.Errorf("%q: unexpected path:\ngot: path=%v weight=%f unique=%t\nwant:path=<nil> weight=+Inf unique=false",
+				test.Name, np, weight, unique)
+		}
+
+		paths, weight := pt.AllBetween(test.Query.From(), test.Query.To())
+		if weight != test.Weight {
+			t.Errorf("%q: unexpected weight from Between: got:%f want:%f",
+				test.Name, weight, test.Weight)
+		}
+
+		var got [][]int64
+		if len(paths) != 0 {
+			got = make([][]int64, len(paths))
+		}
+		for i, p := range paths {
+			for _, v := range p {
+				got[i] = append(got[i], v.ID())
+			}
+		}
+		sort.Sort(ordered.BySliceValues(got))
+		if !reflect.DeepEqual(got, test.WantPaths) {
+			t.Errorf("testing %q: unexpected shortest paths:\ngot: %v\nwant:%v",
+				test.Name, got, test.WantPaths)
+		}
+
+		nps, weight := pt.AllBetween(test.NoPathFor.From(), test.NoPathFor.To())
+		if nps != nil || !math.IsInf(weight, 1) {
+			t.Errorf("%q: unexpected path:\ngot: paths=%v weight=%f\nwant:path=<nil> weight=+Inf",
+				test.Name, nps, weight)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/path/internal/grid.go b/vendor/gonum.org/v1/gonum/graph/path/internal/grid.go
new file mode 100644
index 00000000..4afe8fb6
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/internal/grid.go
@@ -0,0 +1,296 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package internal
+
+import (
+	"errors"
+	"fmt"
+	"math"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+const (
+	Closed  = '*' // Closed is the closed grid node representation.
+	Open    = '.' // Open is the open grid node repesentation.
+	Unknown = '?' // Unknown is the unknown grid node repesentation.
+)
+
+// Grid is a 2D grid planar undirected graph.
+type Grid struct {
+	// AllowDiagonal specifies whether
+	// diagonally adjacent nodes can
+	// be connected by an edge.
+	AllowDiagonal bool
+	// UnitEdgeWeight specifies whether
+	// finite edge weights are returned as
+	// the unit length. Otherwise edge
+	// weights are the Euclidean distance
+	// between connected nodes.
+	UnitEdgeWeight bool
+
+	// AllVisible specifies whether
+	// non-open nodes are visible
+	// in calls to Nodes and HasNode.
+	AllVisible bool
+
+	open []bool
+	r, c int
+}
+
+// NewGrid returns an r by c grid with all positions
+// set to the specified open state.
+func NewGrid(r, c int, open bool) *Grid {
+	states := make([]bool, r*c)
+	if open {
+		for i := range states {
+			states[i] = true
+		}
+	}
+	return &Grid{
+		open: states,
+		r:    r,
+		c:    c,
+	}
+}
+
+// NewGridFrom returns a grid specified by the rows strings. All rows must
+// be the same length and must only contain the Open or Closed characters,
+// NewGridFrom will panic otherwise.
+func NewGridFrom(rows ...string) *Grid {
+	if len(rows) == 0 {
+		return nil
+	}
+	for i, r := range rows[:len(rows)-1] {
+		if len(r) != len(rows[i+1]) {
+			panic("grid: unequal row lengths")
+		}
+	}
+	states := make([]bool, 0, len(rows)*len(rows[0]))
+	for _, r := range rows {
+		for _, b := range r {
+			switch b {
+			case Closed:
+				states = append(states, false)
+			case Open:
+				states = append(states, true)
+			default:
+				panic(fmt.Sprintf("grid: invalid state: %q", r))
+			}
+		}
+	}
+	return &Grid{
+		open: states,
+		r:    len(rows),
+		c:    len(rows[0]),
+	}
+}
+
+// Nodes returns all the open nodes in the grid if AllVisible is
+// false, otherwise all nodes are returned.
+func (g *Grid) Nodes() []graph.Node {
+	var nodes []graph.Node
+	for id, ok := range g.open {
+		if ok || g.AllVisible {
+			nodes = append(nodes, simple.Node(id))
+		}
+	}
+	return nodes
+}
+
+// Has returns whether n is a node in the grid. The state of
+// the AllVisible field determines whether a non-open node is
+// present.
+func (g *Grid) Has(n graph.Node) bool {
+	return g.has(n.ID())
+}
+
+func (g *Grid) has(id int64) bool {
+	return 0 <= id && id < int64(len(g.open)) && (g.AllVisible || g.open[id])
+}
+
+// HasOpen returns whether n is an open node in the grid.
+func (g *Grid) HasOpen(n graph.Node) bool {
+	id := n.ID()
+	return 0 <= id && id < int64(len(g.open)) && g.open[id]
+}
+
+// Set sets the node at position (r, c) to the specified open state.
+func (g *Grid) Set(r, c int, open bool) {
+	if r < 0 || r >= g.r {
+		panic("grid: illegal row index")
+	}
+	if c < 0 || c >= g.c {
+		panic("grid: illegal column index")
+	}
+	g.open[r*g.c+c] = open
+}
+
+// Dims returns the dimensions of the grid.
+func (g *Grid) Dims() (r, c int) {
+	return g.r, g.c
+}
+
+// RowCol returns the row and column of the id. RowCol will panic if the
+// node id is outside the range of the grid.
+func (g *Grid) RowCol(id int64) (r, c int) {
+	if id < 0 || int64(len(g.open)) <= id {
+		panic("grid: illegal node id")
+	}
+	return int(id) / g.c, int(id) % g.c
+}
+
+// XY returns the cartesian coordinates of n. If n is not a node
+// in the grid, (NaN, NaN) is returned.
+func (g *Grid) XY(n graph.Node) (x, y float64) {
+	if !g.Has(n) {
+		return math.NaN(), math.NaN()
+	}
+	r, c := g.RowCol(n.ID())
+	return float64(c), float64(r)
+}
+
+// NodeAt returns the node at (r, c). The returned node may be open or closed.
+func (g *Grid) NodeAt(r, c int) graph.Node {
+	if r < 0 || r >= g.r || c < 0 || c >= g.c {
+		return nil
+	}
+	return simple.Node(r*g.c + c)
+}
+
+// From returns all the nodes reachable from u. Reachabilty requires that both
+// ends of an edge must be open.
+func (g *Grid) From(u graph.Node) []graph.Node {
+	if !g.HasOpen(u) {
+		return nil
+	}
+	nr, nc := g.RowCol(u.ID())
+	var to []graph.Node
+	for r := nr - 1; r <= nr+1; r++ {
+		for c := nc - 1; c <= nc+1; c++ {
+			if v := g.NodeAt(r, c); v != nil && g.HasEdgeBetween(u, v) {
+				to = append(to, v)
+			}
+		}
+	}
+	return to
+}
+
+// HasEdgeBetween returns whether there is an edge between u and v.
+func (g *Grid) HasEdgeBetween(u, v graph.Node) bool {
+	if !g.HasOpen(u) || !g.HasOpen(v) || u.ID() == v.ID() {
+		return false
+	}
+	ur, uc := g.RowCol(u.ID())
+	vr, vc := g.RowCol(v.ID())
+	if abs(ur-vr) > 1 || abs(uc-vc) > 1 {
+		return false
+	}
+	return g.AllowDiagonal || ur == vr || uc == vc
+}
+
+func abs(i int) int {
+	if i < 0 {
+		return -i
+	}
+	return i
+}
+
+// Edge returns the edge between u and v.
+func (g *Grid) Edge(u, v graph.Node) graph.Edge {
+	return g.WeightedEdgeBetween(u, v)
+}
+
+// WeightedEdge returns the weighted edge between u and v.
+func (g *Grid) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
+	return g.WeightedEdgeBetween(u, v)
+}
+
+// EdgeBetween returns the edge between u and v.
+func (g *Grid) EdgeBetween(u, v graph.Node) graph.Edge {
+	return g.WeightedEdgeBetween(u, v)
+}
+
+// WeightedEdgeBetween returns the weighted edge between u and v.
+func (g *Grid) WeightedEdgeBetween(u, v graph.Node) graph.WeightedEdge {
+	if g.HasEdgeBetween(u, v) {
+		if !g.AllowDiagonal || g.UnitEdgeWeight {
+			return simple.WeightedEdge{F: u, T: v, W: 1}
+		}
+		ux, uy := g.XY(u)
+		vx, vy := g.XY(v)
+		return simple.WeightedEdge{F: u, T: v, W: math.Hypot(ux-vx, uy-vy)}
+	}
+	return nil
+}
+
+// Weight returns the weight of the given edge.
+func (g *Grid) Weight(x, y graph.Node) (w float64, ok bool) {
+	if x.ID() == y.ID() {
+		return 0, true
+	}
+	if !g.HasEdgeBetween(x, y) {
+		return math.Inf(1), false
+	}
+	if e := g.EdgeBetween(x, y); e != nil {
+		if !g.AllowDiagonal || g.UnitEdgeWeight {
+			return 1, true
+		}
+		ux, uy := g.XY(e.From())
+		vx, vy := g.XY(e.To())
+		return math.Hypot(ux-vx, uy-vy), true
+	}
+	return math.Inf(1), true
+}
+
+// String returns a string representation of the grid.
+func (g *Grid) String() string {
+	b, _ := g.Render(nil)
+	return string(b)
+}
+
+// Render returns a text representation of the graph
+// with the given path included. If the path is not a path
+// in the grid Render returns a non-nil error and the
+// path up to that point.
+func (g *Grid) Render(path []graph.Node) ([]byte, error) {
+	b := make([]byte, g.r*(g.c+1)-1)
+	for r := 0; r < g.r; r++ {
+		for c := 0; c < g.c; c++ {
+			if g.open[r*g.c+c] {
+				b[r*(g.c+1)+c] = Open
+			} else {
+				b[r*(g.c+1)+c] = Closed
+			}
+		}
+		if r < g.r-1 {
+			b[r*(g.c+1)+g.c] = '\n'
+		}
+	}
+
+	// We don't use topo.IsPathIn at the outset because we
+	// want to draw as much as possible before failing.
+	for i, n := range path {
+		if !g.Has(n) || (i != 0 && !g.HasEdgeBetween(path[i-1], n)) {
+			id := n.ID()
+			if 0 <= id && id < int64(len(g.open)) {
+				r, c := g.RowCol(n.ID())
+				b[r*(g.c+1)+c] = '!'
+			}
+			return b, errors.New("grid: not a path in graph")
+		}
+		r, c := g.RowCol(n.ID())
+		switch i {
+		case len(path) - 1:
+			b[r*(g.c+1)+c] = 'G'
+		case 0:
+			b[r*(g.c+1)+c] = 'S'
+		default:
+			b[r*(g.c+1)+c] = 'o'
+		}
+	}
+	return b, nil
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/path/internal/grid_test.go b/vendor/gonum.org/v1/gonum/graph/path/internal/grid_test.go
new file mode 100644
index 00000000..66ff4d8f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/internal/grid_test.go
@@ -0,0 +1,258 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package internal
+
+import (
+	"bytes"
+	"errors"
+	"reflect"
+	"strings"
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+var _ graph.Graph = (*Grid)(nil)
+
+func join(g ...string) string { return strings.Join(g, "\n") }
+
+type node int64
+
+func (n node) ID() int64 { return int64(n) }
+
+func TestGrid(t *testing.T) {
+	g := NewGrid(4, 4, false)
+
+	got := g.String()
+	want := join(
+		"****",
+		"****",
+		"****",
+		"****",
+	)
+	if got != want {
+		t.Fatalf("unexpected grid rendering:\ngot: %q\nwant:%q", got, want)
+	}
+
+	var ops = []struct {
+		r, c  int
+		state bool
+		want  string
+	}{
+		{
+			r: 0, c: 1,
+			state: true,
+			want: join(
+				"*.**",
+				"****",
+				"****",
+				"****",
+			),
+		},
+		{
+			r: 0, c: 1,
+			state: false,
+			want: join(
+				"****",
+				"****",
+				"****",
+				"****",
+			),
+		},
+		{
+			r: 0, c: 1,
+			state: true,
+			want: join(
+				"*.**",
+				"****",
+				"****",
+				"****",
+			),
+		},
+		{
+			r: 0, c: 2,
+			state: true,
+			want: join(
+				"*..*",
+				"****",
+				"****",
+				"****",
+			),
+		},
+		{
+			r: 1, c: 2,
+			state: true,
+			want: join(
+				"*..*",
+				"**.*",
+				"****",
+				"****",
+			),
+		},
+		{
+			r: 2, c: 2,
+			state: true,
+			want: join(
+				"*..*",
+				"**.*",
+				"**.*",
+				"****",
+			),
+		},
+		{
+			r: 3, c: 2,
+			state: true,
+			want: join(
+				"*..*",
+				"**.*",
+				"**.*",
+				"**.*",
+			),
+		},
+	}
+	for _, test := range ops {
+		g.Set(test.r, test.c, test.state)
+		got := g.String()
+		if got != test.want {
+			t.Fatalf("unexpected grid rendering after set (%d, %d) open state to %t:\ngot: %q\nwant:%q",
+				test.r, test.c, test.state, got, test.want)
+		}
+	}
+
+	// Match the last state from the loop against the
+	// explicit description of the grid.
+	got = NewGridFrom(
+		"*..*",
+		"**.*",
+		"**.*",
+		"**.*",
+	).String()
+	want = g.String()
+	if got != want {
+		t.Fatalf("unexpected grid rendering from NewGridFrom:\ngot: %q\nwant:%q", got, want)
+	}
+
+	var paths = []struct {
+		path     []graph.Node
+		diagonal bool
+		want     string
+	}{
+		{
+			path:     nil,
+			diagonal: false,
+			want: join(
+				"*..*",
+				"**.*",
+				"**.*",
+				"**.*",
+			),
+		},
+		{
+			path:     []graph.Node{node(1), node(2), node(6), node(10), node(14)},
+			diagonal: false,
+			want: join(
+				"*So*",
+				"**o*",
+				"**o*",
+				"**G*",
+			),
+		},
+		{
+			path:     []graph.Node{node(1), node(6), node(10), node(14)},
+			diagonal: false,
+			want: join(
+				"*S.*",
+				"**!*",
+				"**.*",
+				"**.*",
+			),
+		},
+		{
+			path:     []graph.Node{node(1), node(6), node(10), node(14)},
+			diagonal: true,
+			want: join(
+				"*S.*",
+				"**o*",
+				"**o*",
+				"**G*",
+			),
+		},
+		{
+			path:     []graph.Node{node(1), node(5), node(9)},
+			diagonal: false,
+			want: join(
+				"*S.*",
+				"*!.*",
+				"**.*",
+				"**.*",
+			),
+		},
+	}
+	for _, test := range paths {
+		g.AllowDiagonal = test.diagonal
+		got, err := g.Render(test.path)
+		errored := err != nil
+		if bytes.Contains(got, []byte{'!'}) != errored {
+			t.Fatalf("unexpected error return: got:%v want:%v", err, errors.New("grid: not a path in graph"))
+		}
+		if string(got) != test.want {
+			t.Fatalf("unexpected grid path rendering for %v:\ngot: %q\nwant:%q", test.path, got, want)
+		}
+	}
+
+	var coords = []struct {
+		r, c int
+		id   int64
+	}{
+		{r: 0, c: 0, id: 0},
+		{r: 0, c: 3, id: 3},
+		{r: 3, c: 0, id: 12},
+		{r: 3, c: 3, id: 15},
+	}
+	for _, test := range coords {
+		if id := g.NodeAt(test.r, test.c).ID(); id != test.id {
+			t.Fatalf("unexpected ID for node at (%d, %d):\ngot: %d\nwant:%d", test.r, test.c, id, test.id)
+		}
+		if r, c := g.RowCol(test.id); r != test.r || c != test.c {
+			t.Fatalf("unexpected row/col for node %d:\ngot: (%d, %d)\nwant:(%d, %d)", test.id, r, c, test.r, test.c)
+		}
+	}
+
+	var reach = []struct {
+		from     graph.Node
+		diagonal bool
+		to       []graph.Node
+	}{
+		{
+			from:     node(0),
+			diagonal: false,
+			to:       nil,
+		},
+		{
+			from:     node(2),
+			diagonal: false,
+			to:       []graph.Node{simple.Node(1), simple.Node(6)},
+		},
+		{
+			from:     node(1),
+			diagonal: false,
+			to:       []graph.Node{simple.Node(2)},
+		},
+		{
+			from:     node(1),
+			diagonal: true,
+			to:       []graph.Node{simple.Node(2), simple.Node(6)},
+		},
+	}
+	for _, test := range reach {
+		g.AllowDiagonal = test.diagonal
+		got := g.From(test.from)
+		if !reflect.DeepEqual(got, test.to) {
+			t.Fatalf("unexpected nodes from %d with allow diagonal=%t:\ngot: %v\nwant:%v",
+				test.from, test.diagonal, got, test.to)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/path/internal/limited.go b/vendor/gonum.org/v1/gonum/graph/path/internal/limited.go
new file mode 100644
index 00000000..3a2d768d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/internal/limited.go
@@ -0,0 +1,316 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package internal
+
+import (
+	"errors"
+	"math"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+// LimitedVisionGrid is a 2D grid planar undirected graph where the capacity
+// to determine the presence of edges is dependent on the current and past
+// positions on the grid. In the absence of information, the grid is
+// optimistic.
+type LimitedVisionGrid struct {
+	Grid *Grid
+
+	// Location is the current
+	// location on the grid.
+	Location graph.Node
+
+	// VisionRadius specifies how far
+	// away edges can be detected.
+	VisionRadius float64
+
+	// Known holds a store of known
+	// nodes, if not nil.
+	Known map[int64]bool
+}
+
+// MoveTo moves to the node n on the grid and returns a slice of newly seen and
+// already known edges. MoveTo panics if n is nil.
+func (l *LimitedVisionGrid) MoveTo(n graph.Node) (new, old []graph.Edge) {
+	l.Location = n
+	row, column := l.RowCol(n.ID())
+	x := float64(column)
+	y := float64(row)
+	seen := make(map[[2]int64]bool)
+	bound := int(l.VisionRadius + 0.5)
+	for r := row - bound; r <= row+bound; r++ {
+		for c := column - bound; c <= column+bound; c++ {
+			u := l.NodeAt(r, c)
+			if u == nil {
+				continue
+			}
+			ux, uy := l.XY(u)
+			if math.Hypot(x-ux, y-uy) > l.VisionRadius {
+				continue
+			}
+			for _, v := range l.allPossibleFrom(u) {
+				if seen[[2]int64{u.ID(), v.ID()}] {
+					continue
+				}
+				seen[[2]int64{u.ID(), v.ID()}] = true
+
+				vx, vy := l.XY(v)
+				if !l.Known[v.ID()] && math.Hypot(x-vx, y-vy) > l.VisionRadius {
+					continue
+				}
+
+				e := simple.Edge{F: u, T: v}
+				if !l.Known[u.ID()] || !l.Known[v.ID()] {
+					new = append(new, e)
+				} else {
+					old = append(old, e)
+				}
+			}
+		}
+	}
+
+	if l.Known != nil {
+		for r := row - bound; r <= row+bound; r++ {
+			for c := column - bound; c <= column+bound; c++ {
+				u := l.NodeAt(r, c)
+				if u == nil {
+					continue
+				}
+				ux, uy := l.XY(u)
+				if math.Hypot(x-ux, y-uy) > l.VisionRadius {
+					continue
+				}
+				for _, v := range l.allPossibleFrom(u) {
+					vx, vy := l.XY(v)
+					if math.Hypot(x-vx, y-vy) > l.VisionRadius {
+						continue
+					}
+					l.Known[v.ID()] = true
+				}
+				l.Known[u.ID()] = true
+			}
+		}
+
+	}
+
+	return new, old
+}
+
+// allPossibleFrom returns all the nodes possibly reachable from u.
+func (l *LimitedVisionGrid) allPossibleFrom(u graph.Node) []graph.Node {
+	if !l.Has(u) {
+		return nil
+	}
+	nr, nc := l.RowCol(u.ID())
+	var to []graph.Node
+	for r := nr - 1; r <= nr+1; r++ {
+		for c := nc - 1; c <= nc+1; c++ {
+			v := l.NodeAt(r, c)
+			if v == nil || u.ID() == v.ID() {
+				continue
+			}
+			ur, uc := l.RowCol(u.ID())
+			vr, vc := l.RowCol(v.ID())
+			if abs(ur-vr) > 1 || abs(uc-vc) > 1 {
+				continue
+			}
+			if !l.Grid.AllowDiagonal && ur != vr && uc != vc {
+				continue
+			}
+			to = append(to, v)
+		}
+	}
+	return to
+}
+
+// RowCol returns the row and column of the id. RowCol will panic if the
+// node id is outside the range of the grid.
+func (l *LimitedVisionGrid) RowCol(id int64) (r, c int) {
+	return l.Grid.RowCol(id)
+}
+
+// XY returns the cartesian coordinates of n. If n is not a node
+// in the grid, (NaN, NaN) is returned.
+func (l *LimitedVisionGrid) XY(n graph.Node) (x, y float64) {
+	if !l.Has(n) {
+		return math.NaN(), math.NaN()
+	}
+	r, c := l.RowCol(n.ID())
+	return float64(c), float64(r)
+}
+
+// Nodes returns all the nodes in the grid.
+func (l *LimitedVisionGrid) Nodes() []graph.Node {
+	nodes := make([]graph.Node, 0, len(l.Grid.open))
+	for id := range l.Grid.open {
+		nodes = append(nodes, simple.Node(id))
+	}
+	return nodes
+}
+
+// NodeAt returns the node at (r, c). The returned node may be open or closed.
+func (l *LimitedVisionGrid) NodeAt(r, c int) graph.Node {
+	return l.Grid.NodeAt(r, c)
+}
+
+// Has returns whether n is a node in the grid.
+func (l *LimitedVisionGrid) Has(n graph.Node) bool {
+	return l.has(n.ID())
+}
+
+func (l *LimitedVisionGrid) has(id int64) bool {
+	return 0 <= id && id < int64(len(l.Grid.open))
+}
+
+// From returns nodes that are optimistically reachable from u.
+func (l *LimitedVisionGrid) From(u graph.Node) []graph.Node {
+	if !l.Has(u) {
+		return nil
+	}
+
+	nr, nc := l.RowCol(u.ID())
+	var to []graph.Node
+	for r := nr - 1; r <= nr+1; r++ {
+		for c := nc - 1; c <= nc+1; c++ {
+			if v := l.NodeAt(r, c); v != nil && l.HasEdgeBetween(u, v) {
+				to = append(to, v)
+			}
+		}
+	}
+	return to
+}
+
+// HasEdgeBetween optimistically returns whether an edge is exists between u and v.
+func (l *LimitedVisionGrid) HasEdgeBetween(u, v graph.Node) bool {
+	if u.ID() == v.ID() {
+		return false
+	}
+	ur, uc := l.RowCol(u.ID())
+	vr, vc := l.RowCol(v.ID())
+	if abs(ur-vr) > 1 || abs(uc-vc) > 1 {
+		return false
+	}
+	if !l.Grid.AllowDiagonal && ur != vr && uc != vc {
+		return false
+	}
+
+	x, y := l.XY(l.Location)
+	ux, uy := l.XY(u)
+	vx, vy := l.XY(v)
+	uKnown := l.Known[u.ID()] || math.Hypot(x-ux, y-uy) <= l.VisionRadius
+	vKnown := l.Known[v.ID()] || math.Hypot(x-vx, y-vy) <= l.VisionRadius
+
+	switch {
+	case uKnown && vKnown:
+		return l.Grid.HasEdgeBetween(u, v)
+	case uKnown:
+		return l.Grid.HasOpen(u)
+	case vKnown:
+		return l.Grid.HasOpen(v)
+	default:
+		return true
+	}
+}
+
+// Edge optimistically returns the edge from u to v.
+func (l *LimitedVisionGrid) Edge(u, v graph.Node) graph.Edge {
+	return l.WeightedEdgeBetween(u, v)
+}
+
+// Edge optimistically returns the weighted edge from u to v.
+func (l *LimitedVisionGrid) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
+	return l.WeightedEdgeBetween(u, v)
+}
+
+// WeightedEdgeBetween optimistically returns the edge between u and v.
+func (l *LimitedVisionGrid) EdgeBetween(u, v graph.Node) graph.Edge {
+	return l.WeightedEdgeBetween(u, v)
+}
+
+// WeightedEdgeBetween optimistically returns the weighted edge between u and v.
+func (l *LimitedVisionGrid) WeightedEdgeBetween(u, v graph.Node) graph.WeightedEdge {
+	if l.HasEdgeBetween(u, v) {
+		if !l.Grid.AllowDiagonal || l.Grid.UnitEdgeWeight {
+			return simple.WeightedEdge{F: u, T: v, W: 1}
+		}
+		ux, uy := l.XY(u)
+		vx, vy := l.XY(v)
+		return simple.WeightedEdge{F: u, T: v, W: math.Hypot(ux-vx, uy-vy)}
+	}
+	return nil
+}
+
+// Weight returns the weight of the given edge.
+func (l *LimitedVisionGrid) Weight(x, y graph.Node) (w float64, ok bool) {
+	if x.ID() == y.ID() {
+		return 0, true
+	}
+	if !l.HasEdgeBetween(x, y) {
+		return math.Inf(1), false
+	}
+	if e := l.EdgeBetween(x, y); e != nil {
+		if !l.Grid.AllowDiagonal || l.Grid.UnitEdgeWeight {
+			return 1, true
+		}
+		ux, uy := l.XY(e.From())
+		vx, vy := l.XY(e.To())
+		return math.Hypot(ux-vx, uy-vy), true
+
+	}
+	return math.Inf(1), true
+}
+
+// String returns a string representation of the grid.
+func (l *LimitedVisionGrid) String() string {
+	b, _ := l.Render(nil)
+	return string(b)
+}
+
+// Render returns a text representation of the graph
+// with the given path included. If the path is not a path
+// in the grid Render returns a non-nil error and the
+// path up to that point.
+func (l *LimitedVisionGrid) Render(path []graph.Node) ([]byte, error) {
+	rows, cols := l.Grid.Dims()
+	b := make([]byte, rows*(cols+1)-1)
+	for r := 0; r < rows; r++ {
+		for c := 0; c < cols; c++ {
+			if !l.Known[int64(r*cols+c)] {
+				b[r*(cols+1)+c] = Unknown
+			} else if l.Grid.open[r*cols+c] {
+				b[r*(cols+1)+c] = Open
+			} else {
+				b[r*(cols+1)+c] = Closed
+			}
+		}
+		if r < rows-1 {
+			b[r*(cols+1)+cols] = '\n'
+		}
+	}
+
+	// We don't use topo.IsPathIn at the outset because we
+	// want to draw as much as possible before failing.
+	for i, n := range path {
+		if !l.Has(n) || (i != 0 && !l.HasEdgeBetween(path[i-1], n)) {
+			id := n.ID()
+			if 0 <= id && id < int64(len(l.Grid.open)) {
+				r, c := l.RowCol(n.ID())
+				b[r*(cols+1)+c] = '!'
+			}
+			return b, errors.New("grid: not a path in graph")
+		}
+		r, c := l.RowCol(n.ID())
+		switch i {
+		case len(path) - 1:
+			b[r*(cols+1)+c] = 'G'
+		case 0:
+			b[r*(cols+1)+c] = 'S'
+		default:
+			b[r*(cols+1)+c] = 'o'
+		}
+	}
+	return b, nil
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/path/internal/limited_test.go b/vendor/gonum.org/v1/gonum/graph/path/internal/limited_test.go
new file mode 100644
index 00000000..018dd778
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/internal/limited_test.go
@@ -0,0 +1,1242 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package internal
+
+import (
+	"math"
+	"reflect"
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+type changes struct {
+	n graph.Node
+
+	new, old []simple.WeightedEdge
+}
+
+var limitedVisionTests = []struct {
+	g        *Grid
+	radius   float64
+	diag     bool
+	remember bool
+
+	path []graph.Node
+
+	want []changes
+}{
+	{
+		g: NewGridFrom(
+			"*..*",
+			"**.*",
+			"**.*",
+			"**.*",
+		),
+		radius:   1,
+		diag:     false,
+		remember: false,
+		path:     []graph.Node{node(1), node(2), node(6), node(10), node(14)},
+
+		want: []changes{
+			{
+				n: node(1),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(0), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(0), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(2), W: 1},
+					{F: simple.Node(1), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(1), W: 1},
+					{F: simple.Node(5), T: simple.Node(1), W: math.Inf(1)},
+				},
+				old: nil,
+			},
+			{
+				n: node(2),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(1), T: simple.Node(2), W: 1},
+					{F: simple.Node(2), T: simple.Node(1), W: 1},
+					{F: simple.Node(2), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(6), W: 1},
+					{F: simple.Node(3), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(2), W: 1},
+				},
+				old: nil,
+			},
+			{
+				n: node(6),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(2), T: simple.Node(6), W: 1},
+					{F: simple.Node(5), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(2), W: 1},
+					{F: simple.Node(6), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(10), W: 1},
+					{F: simple.Node(7), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(6), W: 1},
+				},
+				old: nil,
+			},
+			{
+				n: node(10),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(6), T: simple.Node(10), W: 1},
+					{F: simple.Node(9), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(6), W: 1},
+					{F: simple.Node(10), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(14), W: 1},
+					{F: simple.Node(11), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(10), W: 1},
+				},
+				old: nil,
+			},
+			{
+				n: node(14),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(10), T: simple.Node(14), W: 1},
+					{F: simple.Node(13), T: simple.Node(14), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(10), W: 1},
+					{F: simple.Node(14), T: simple.Node(13), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(15), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(14), W: math.Inf(1)},
+				},
+				old: nil,
+			},
+		},
+	},
+	{
+		g: NewGridFrom(
+			"*..*",
+			"**.*",
+			"**.*",
+			"**.*",
+		),
+		radius:   1.5,
+		diag:     false,
+		remember: false,
+		path:     []graph.Node{node(1), node(2), node(6), node(10), node(14)},
+
+		want: []changes{
+			{
+				n: node(1),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(0), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(0), T: simple.Node(4), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(0), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(2), W: 1},
+					{F: simple.Node(1), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(1), W: 1},
+					{F: simple.Node(2), T: simple.Node(6), W: 1},
+					{F: simple.Node(4), T: simple.Node(0), W: math.Inf(1)},
+					{F: simple.Node(4), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(4), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(2), W: 1},
+					{F: simple.Node(6), T: simple.Node(5), W: math.Inf(1)},
+				},
+				old: nil,
+			},
+			{
+				n: node(2),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(1), T: simple.Node(2), W: 1},
+					{F: simple.Node(1), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(1), W: 1},
+					{F: simple.Node(2), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(6), W: 1},
+					{F: simple.Node(3), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(3), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(2), W: 1},
+					{F: simple.Node(6), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(6), W: math.Inf(1)},
+				},
+				old: nil,
+			},
+			{
+				n: node(6),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(1), T: simple.Node(2), W: 1},
+					{F: simple.Node(1), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(1), W: 1},
+					{F: simple.Node(2), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(6), W: 1},
+					{F: simple.Node(3), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(3), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(2), W: 1},
+					{F: simple.Node(6), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(10), W: 1},
+					{F: simple.Node(7), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(6), W: 1},
+					{F: simple.Node(10), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(10), W: math.Inf(1)},
+				},
+				old: nil,
+			},
+			{
+				n: node(10),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(5), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(10), W: 1},
+					{F: simple.Node(7), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(13), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(6), W: 1},
+					{F: simple.Node(10), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(14), W: 1},
+					{F: simple.Node(11), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(15), W: math.Inf(1)},
+					{F: simple.Node(13), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(13), T: simple.Node(14), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(10), W: 1},
+					{F: simple.Node(14), T: simple.Node(13), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(15), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(14), W: math.Inf(1)},
+				},
+				old: nil,
+			},
+			{
+				n: node(14),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(9), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(13), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(14), W: 1},
+					{F: simple.Node(11), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(15), W: math.Inf(1)},
+					{F: simple.Node(13), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(13), T: simple.Node(14), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(10), W: 1},
+					{F: simple.Node(14), T: simple.Node(13), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(15), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(14), W: math.Inf(1)},
+				},
+				old: nil,
+			},
+		},
+	},
+	{
+		g: NewGridFrom(
+			"*..*",
+			"**.*",
+			"**.*",
+			"**.*",
+		),
+		radius:   1,
+		diag:     false,
+		remember: true,
+		path:     []graph.Node{node(1), node(2), node(6), node(10), node(14)},
+
+		want: []changes{
+			{
+				n: node(1),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(0), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(0), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(2), W: 1},
+					{F: simple.Node(1), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(1), W: 1},
+					{F: simple.Node(5), T: simple.Node(1), W: math.Inf(1)},
+				},
+				old: nil,
+			},
+			{
+				n: node(2),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(2), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(6), W: 1},
+					{F: simple.Node(3), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(2), W: 1},
+					{F: simple.Node(6), T: simple.Node(5), W: math.Inf(1)},
+				},
+				old: []simple.WeightedEdge{
+					{F: simple.Node(1), T: simple.Node(0), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(2), W: 1},
+					{F: simple.Node(1), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(1), W: 1},
+				},
+			},
+			{
+				n: node(6),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(6), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(10), W: 1},
+					{F: simple.Node(7), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(6), W: 1},
+				},
+				old: []simple.WeightedEdge{
+					{F: simple.Node(2), T: simple.Node(1), W: 1},
+					{F: simple.Node(2), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(6), W: 1},
+					{F: simple.Node(5), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(2), W: 1},
+					{F: simple.Node(6), T: simple.Node(5), W: math.Inf(1)},
+				},
+			},
+			{
+				n: node(10),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(9), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(14), W: 1},
+					{F: simple.Node(11), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(10), W: 1},
+				},
+				old: []simple.WeightedEdge{
+					{F: simple.Node(6), T: simple.Node(2), W: 1},
+					{F: simple.Node(6), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(10), W: 1},
+					{F: simple.Node(10), T: simple.Node(6), W: 1},
+				},
+			},
+			{
+				n: node(14),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(13), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(13), T: simple.Node(14), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(13), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(15), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(14), W: math.Inf(1)},
+				},
+				old: []simple.WeightedEdge{
+					{F: simple.Node(10), T: simple.Node(6), W: 1},
+					{F: simple.Node(10), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(14), W: 1},
+					{F: simple.Node(14), T: simple.Node(10), W: 1},
+				},
+			},
+		},
+	},
+	{
+		g: NewGridFrom(
+			"*..*",
+			"**.*",
+			"**.*",
+			"**.*",
+		),
+		radius:   1.5,
+		diag:     false,
+		remember: true,
+		path:     []graph.Node{node(1), node(2), node(6), node(10), node(14)},
+
+		want: []changes{
+			{
+				n: node(1),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(0), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(0), T: simple.Node(4), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(0), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(2), W: 1},
+					{F: simple.Node(1), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(1), W: 1},
+					{F: simple.Node(2), T: simple.Node(6), W: 1},
+					{F: simple.Node(4), T: simple.Node(0), W: math.Inf(1)},
+					{F: simple.Node(4), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(4), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(2), W: 1},
+					{F: simple.Node(6), T: simple.Node(5), W: math.Inf(1)},
+				},
+				old: nil,
+			},
+			{
+				n: node(2),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(2), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(3), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(3), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(6), W: math.Inf(1)},
+				},
+				old: []simple.WeightedEdge{
+					{F: simple.Node(1), T: simple.Node(0), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(2), W: 1},
+					{F: simple.Node(1), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(1), W: 1},
+					{F: simple.Node(2), T: simple.Node(6), W: 1},
+					{F: simple.Node(5), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(4), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(2), W: 1},
+					{F: simple.Node(6), T: simple.Node(5), W: math.Inf(1)},
+				},
+			},
+			{
+				n: node(6),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(5), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(10), W: 1},
+					{F: simple.Node(7), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(6), W: 1},
+					{F: simple.Node(10), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(10), W: math.Inf(1)},
+				},
+				old: []simple.WeightedEdge{
+					{F: simple.Node(1), T: simple.Node(0), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(2), W: 1},
+					{F: simple.Node(1), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(1), W: 1},
+					{F: simple.Node(2), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(6), W: 1},
+					{F: simple.Node(3), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(3), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(4), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(2), W: 1},
+					{F: simple.Node(6), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(6), W: math.Inf(1)},
+				},
+			},
+			{
+				n: node(10),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(9), T: simple.Node(13), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(14), W: 1},
+					{F: simple.Node(11), T: simple.Node(15), W: math.Inf(1)},
+					{F: simple.Node(13), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(13), T: simple.Node(14), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(10), W: 1},
+					{F: simple.Node(14), T: simple.Node(13), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(15), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(14), W: math.Inf(1)},
+				},
+				old: []simple.WeightedEdge{
+					{F: simple.Node(5), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(4), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(2), W: 1},
+					{F: simple.Node(6), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(10), W: 1},
+					{F: simple.Node(7), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(6), W: 1},
+					{F: simple.Node(10), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(10), W: math.Inf(1)},
+				},
+			},
+			{
+				n:   node(14),
+				new: nil,
+				old: []simple.WeightedEdge{
+					{F: simple.Node(9), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(13), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(6), W: 1},
+					{F: simple.Node(10), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(14), W: 1},
+					{F: simple.Node(11), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(15), W: math.Inf(1)},
+					{F: simple.Node(13), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(13), T: simple.Node(14), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(10), W: 1},
+					{F: simple.Node(14), T: simple.Node(13), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(15), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(14), W: math.Inf(1)},
+				},
+			},
+		},
+	},
+	{
+		g: NewGridFrom(
+			"*..*",
+			"**.*",
+			"**.*",
+			"**.*",
+		),
+		radius:   1,
+		diag:     true,
+		remember: false,
+		path:     []graph.Node{node(1), node(2), node(6), node(10), node(14)},
+
+		want: []changes{
+			{
+				n: node(1),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(0), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(0), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(0), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(2), W: 1},
+					{F: simple.Node(1), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(1), W: 1},
+					{F: simple.Node(2), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(0), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(2), W: math.Inf(1)},
+				},
+				old: nil,
+			},
+			{
+				n: node(2),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(1), T: simple.Node(2), W: 1},
+					{F: simple.Node(1), T: simple.Node(6), W: math.Sqrt2},
+					{F: simple.Node(2), T: simple.Node(1), W: 1},
+					{F: simple.Node(2), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(6), W: 1},
+					{F: simple.Node(3), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(3), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(1), W: math.Sqrt2},
+					{F: simple.Node(6), T: simple.Node(2), W: 1},
+					{F: simple.Node(6), T: simple.Node(3), W: math.Inf(1)},
+				},
+				old: nil,
+			},
+			{
+				n: node(6),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(2), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(6), W: 1},
+					{F: simple.Node(2), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(2), W: 1},
+					{F: simple.Node(6), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(10), W: 1},
+					{F: simple.Node(7), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(6), W: 1},
+					{F: simple.Node(10), T: simple.Node(7), W: math.Inf(1)},
+				},
+				old: nil,
+			},
+			{
+				n: node(10),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(6), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(10), W: 1},
+					{F: simple.Node(6), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(14), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(6), W: 1},
+					{F: simple.Node(10), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(14), W: 1},
+					{F: simple.Node(11), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(14), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(10), W: 1},
+					{F: simple.Node(14), T: simple.Node(11), W: math.Inf(1)},
+				},
+				old: nil,
+			},
+			{
+				n: node(14),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(10), T: simple.Node(13), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(14), W: 1},
+					{F: simple.Node(10), T: simple.Node(15), W: math.Inf(1)},
+					{F: simple.Node(13), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(13), T: simple.Node(14), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(10), W: 1},
+					{F: simple.Node(14), T: simple.Node(13), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(15), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(14), W: math.Inf(1)},
+				},
+				old: nil,
+			},
+		},
+	},
+	{
+		g: NewGridFrom(
+			"*..*",
+			"**.*",
+			"**.*",
+			"**.*",
+		),
+		radius:   1.5,
+		diag:     true,
+		remember: false,
+		path:     []graph.Node{node(1), node(2), node(6), node(10), node(14)},
+
+		want: []changes{
+			{
+				n: node(1),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(0), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(0), T: simple.Node(4), W: math.Inf(1)},
+					{F: simple.Node(0), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(0), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(2), W: 1},
+					{F: simple.Node(1), T: simple.Node(4), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(6), W: math.Sqrt2},
+					{F: simple.Node(2), T: simple.Node(1), W: 1},
+					{F: simple.Node(2), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(6), W: 1},
+					{F: simple.Node(4), T: simple.Node(0), W: math.Inf(1)},
+					{F: simple.Node(4), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(4), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(0), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(4), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(1), W: math.Sqrt2},
+					{F: simple.Node(6), T: simple.Node(2), W: 1},
+					{F: simple.Node(6), T: simple.Node(5), W: math.Inf(1)},
+				},
+				old: nil,
+			},
+			{
+				n: node(2),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(1), T: simple.Node(2), W: 1},
+					{F: simple.Node(1), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(6), W: math.Sqrt2},
+					{F: simple.Node(2), T: simple.Node(1), W: 1},
+					{F: simple.Node(2), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(6), W: 1},
+					{F: simple.Node(2), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(3), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(3), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(3), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(1), W: math.Sqrt2},
+					{F: simple.Node(6), T: simple.Node(2), W: 1},
+					{F: simple.Node(6), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(6), W: math.Inf(1)},
+				},
+				old: nil,
+			},
+			{
+				n: node(6),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(1), T: simple.Node(2), W: 1},
+					{F: simple.Node(1), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(6), W: math.Sqrt2},
+					{F: simple.Node(2), T: simple.Node(1), W: 1},
+					{F: simple.Node(2), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(6), W: 1},
+					{F: simple.Node(2), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(3), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(3), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(3), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(1), W: math.Sqrt2},
+					{F: simple.Node(6), T: simple.Node(2), W: 1},
+					{F: simple.Node(6), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(10), W: 1},
+					{F: simple.Node(6), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(6), W: 1},
+					{F: simple.Node(10), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(10), W: math.Inf(1)},
+				},
+				old: nil,
+			},
+			{
+				n: node(10),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(5), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(9), W: math.Inf(1)},
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+					{F: simple.Node(7), T: simple.Node(11), W: math.Inf(1)},
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+					{F: simple.Node(9), T: simple.Node(13), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(14), W: math.Inf(1)},
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+					{F: simple.Node(10), T: simple.Node(6), W: 1},
+					{F: simple.Node(10), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(13), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(14), W: 1},
+					{F: simple.Node(10), T: simple.Node(15), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(14), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(15), W: math.Inf(1)},
+					{F: simple.Node(13), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(13), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(13), T: simple.Node(14), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(10), W: 1},
+					{F: simple.Node(14), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(13), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(15), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(14), W: math.Inf(1)},
+				},
+				old: nil,
+			},
+			{
+				n: node(14),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(9), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(13), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(14), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(13), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(14), W: 1},
+					{F: simple.Node(10), T: simple.Node(15), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(14), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(15), W: math.Inf(1)},
+					{F: simple.Node(13), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(13), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(13), T: simple.Node(14), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(10), W: 1},
+					{F: simple.Node(14), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(13), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(15), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(14), W: math.Inf(1)},
+				},
+				old: nil,
+			},
+		},
+	},
+	{
+		g: NewGridFrom(
+			"*..*",
+			"**.*",
+			"**.*",
+			"**.*",
+		),
+		radius:   1,
+		diag:     true,
+		remember: true,
+		path:     []graph.Node{node(1), node(2), node(6), node(10), node(14)},
+
+		want: []changes{
+			{
+				n: node(1),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(0), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(0), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(0), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(2), W: 1},
+					{F: simple.Node(1), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(1), W: 1},
+					{F: simple.Node(2), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(0), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(2), W: math.Inf(1)},
+				},
+				old: nil,
+			},
+			{
+				n: node(2),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(1), T: simple.Node(6), W: math.Sqrt2},
+					{F: simple.Node(2), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(6), W: 1},
+					{F: simple.Node(3), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(3), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(1), W: math.Sqrt2},
+					{F: simple.Node(6), T: simple.Node(2), W: 1},
+					{F: simple.Node(6), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(5), W: math.Inf(1)},
+				},
+				old: []simple.WeightedEdge{
+					{F: simple.Node(1), T: simple.Node(0), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(2), W: 1},
+					{F: simple.Node(1), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(1), W: 1},
+					{F: simple.Node(2), T: simple.Node(5), W: math.Inf(1)},
+				},
+			},
+			{
+				n: node(6),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(2), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(10), W: 1},
+					{F: simple.Node(7), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(6), W: 1},
+					{F: simple.Node(10), T: simple.Node(7), W: math.Inf(1)},
+				},
+				old: []simple.WeightedEdge{
+					{F: simple.Node(2), T: simple.Node(1), W: 1},
+					{F: simple.Node(2), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(6), W: 1},
+					{F: simple.Node(5), T: simple.Node(0), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(1), W: math.Sqrt2},
+					{F: simple.Node(6), T: simple.Node(2), W: 1},
+					{F: simple.Node(6), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(5), W: math.Inf(1)},
+				},
+			},
+			{
+				n: node(10),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(6), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(14), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(14), W: 1},
+					{F: simple.Node(11), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(14), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(10), W: 1},
+					{F: simple.Node(14), T: simple.Node(11), W: math.Inf(1)},
+				},
+				old: []simple.WeightedEdge{
+					{F: simple.Node(6), T: simple.Node(1), W: math.Sqrt2},
+					{F: simple.Node(6), T: simple.Node(2), W: 1},
+					{F: simple.Node(6), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(10), W: 1},
+					{F: simple.Node(10), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(6), W: 1},
+					{F: simple.Node(10), T: simple.Node(7), W: math.Inf(1)},
+				},
+			},
+			{
+				n: node(14),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(10), T: simple.Node(13), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(15), W: math.Inf(1)},
+					{F: simple.Node(13), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(13), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(13), T: simple.Node(14), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(13), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(15), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(14), W: math.Inf(1)},
+				},
+				old: []simple.WeightedEdge{
+					{F: simple.Node(10), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(6), W: 1},
+					{F: simple.Node(10), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(14), W: 1},
+					{F: simple.Node(14), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(10), W: 1},
+					{F: simple.Node(14), T: simple.Node(11), W: math.Inf(1)},
+				},
+			},
+		},
+	},
+	{
+		g: NewGridFrom(
+			"*..*",
+			"**.*",
+			"**.*",
+			"**.*",
+		),
+		radius:   1.5,
+		diag:     true,
+		remember: true,
+		path:     []graph.Node{node(1), node(2), node(6), node(10), node(14)},
+
+		want: []changes{
+			{
+				n: node(1),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(0), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(0), T: simple.Node(4), W: math.Inf(1)},
+					{F: simple.Node(0), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(0), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(2), W: 1},
+					{F: simple.Node(1), T: simple.Node(4), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(6), W: math.Sqrt2},
+					{F: simple.Node(2), T: simple.Node(1), W: 1},
+					{F: simple.Node(2), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(6), W: 1},
+					{F: simple.Node(4), T: simple.Node(0), W: math.Inf(1)},
+					{F: simple.Node(4), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(4), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(0), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(4), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(1), W: math.Sqrt2},
+					{F: simple.Node(6), T: simple.Node(2), W: 1},
+					{F: simple.Node(6), T: simple.Node(5), W: math.Inf(1)},
+				},
+				old: nil,
+			},
+			{
+				n: node(2),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(2), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(3), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(3), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(3), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(6), W: math.Inf(1)},
+				},
+				old: []simple.WeightedEdge{
+					{F: simple.Node(1), T: simple.Node(0), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(2), W: 1},
+					{F: simple.Node(1), T: simple.Node(4), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(6), W: math.Sqrt2},
+					{F: simple.Node(2), T: simple.Node(1), W: 1},
+					{F: simple.Node(2), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(6), W: 1},
+					{F: simple.Node(5), T: simple.Node(0), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(4), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(1), W: math.Sqrt2},
+					{F: simple.Node(6), T: simple.Node(2), W: 1},
+					{F: simple.Node(6), T: simple.Node(5), W: math.Inf(1)},
+				},
+			},
+			{
+				n: node(6),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(5), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(10), W: 1},
+					{F: simple.Node(6), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(4), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(6), W: 1},
+					{F: simple.Node(10), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(10), W: math.Inf(1)},
+				},
+				old: []simple.WeightedEdge{
+					{F: simple.Node(1), T: simple.Node(0), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(2), W: 1},
+					{F: simple.Node(1), T: simple.Node(4), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(1), T: simple.Node(6), W: math.Sqrt2},
+					{F: simple.Node(2), T: simple.Node(1), W: 1},
+					{F: simple.Node(2), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(2), T: simple.Node(6), W: 1},
+					{F: simple.Node(2), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(3), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(3), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(3), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(0), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(4), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(1), W: math.Sqrt2},
+					{F: simple.Node(6), T: simple.Node(2), W: 1},
+					{F: simple.Node(6), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(6), W: math.Inf(1)},
+				},
+			},
+			{
+				n: node(10),
+				new: []simple.WeightedEdge{
+					{F: simple.Node(9), T: simple.Node(13), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(14), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(13), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(14), W: 1},
+					{F: simple.Node(10), T: simple.Node(15), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(14), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(15), W: math.Inf(1)},
+					{F: simple.Node(13), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(13), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(13), T: simple.Node(14), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(10), W: 1},
+					{F: simple.Node(14), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(13), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(15), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(14), W: math.Inf(1)},
+				},
+				old: []simple.WeightedEdge{
+					{F: simple.Node(5), T: simple.Node(0), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(1), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(4), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(5), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(1), W: math.Sqrt2},
+					{F: simple.Node(6), T: simple.Node(2), W: 1},
+					{F: simple.Node(6), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(6), T: simple.Node(10), W: 1},
+					{F: simple.Node(6), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(2), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(3), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(7), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(4), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(6), W: 1},
+					{F: simple.Node(10), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(10), W: math.Inf(1)},
+				},
+			},
+			{
+				n:   node(14),
+				new: nil,
+				old: []simple.WeightedEdge{
+					{F: simple.Node(9), T: simple.Node(4), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(13), W: math.Inf(1)},
+					{F: simple.Node(9), T: simple.Node(14), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(5), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(6), W: 1},
+					{F: simple.Node(10), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(13), W: math.Inf(1)},
+					{F: simple.Node(10), T: simple.Node(14), W: 1},
+					{F: simple.Node(10), T: simple.Node(15), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(6), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(7), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(14), W: math.Inf(1)},
+					{F: simple.Node(11), T: simple.Node(15), W: math.Inf(1)},
+					{F: simple.Node(13), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(13), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(13), T: simple.Node(14), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(9), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(10), W: 1},
+					{F: simple.Node(14), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(13), W: math.Inf(1)},
+					{F: simple.Node(14), T: simple.Node(15), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(10), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(11), W: math.Inf(1)},
+					{F: simple.Node(15), T: simple.Node(14), W: math.Inf(1)},
+				},
+			},
+		},
+	},
+}
+
+func TestLimitedVisionGrid(t *testing.T) {
+	for i, test := range limitedVisionTests {
+		l := &LimitedVisionGrid{
+			Grid:         test.g,
+			VisionRadius: test.radius,
+			Location:     test.path[0],
+		}
+		if test.remember {
+			l.Known = make(map[int64]bool)
+		}
+		l.Grid.AllowDiagonal = test.diag
+
+		x, y := l.XY(test.path[0])
+		for _, u := range l.Nodes() {
+			ux, uy := l.XY(u)
+			uNear := math.Hypot(x-ux, y-uy) <= test.radius
+			for _, v := range l.Nodes() {
+				vx, vy := l.XY(v)
+				vNear := math.Hypot(x-vx, y-vy) <= test.radius
+				if u.ID() == v.ID() && l.HasEdgeBetween(u, v) {
+					t.Errorf("unexpected self edge: %v -- %v", u, v)
+				}
+				if !uNear && !vNear && !l.HasEdgeBetween(u, v) && couldConnectIn(l, u, v) {
+					t.Errorf("unexpected pessimism: no hope in distant edge between %v and %v for test %d",
+						u, v, i)
+				}
+				if (uNear && vNear) && l.HasEdgeBetween(u, v) != l.Grid.HasEdgeBetween(u, v) {
+					t.Errorf("unrealistic optimism: disagreement about edge between %v and %v for test %d: got:%t want:%t",
+						u, v, i, l.HasEdgeBetween(u, v), l.Grid.HasEdgeBetween(u, v))
+				}
+			}
+		}
+
+		var got []changes
+		for _, n := range test.path {
+			new, old := l.MoveTo(n)
+			got = append(got, changes{n: n, new: asConcreteEdges(new, l), old: asConcreteEdges(old, l)})
+		}
+		if !reflect.DeepEqual(got, test.want) {
+			t.Errorf("unexpected walk for test %d:\ngot: %+v\nwant:%+v", i, got, test.want)
+		}
+	}
+}
+
+func asConcreteEdges(changes []graph.Edge, in graph.Weighted) []simple.WeightedEdge {
+	if changes == nil {
+		return nil
+	}
+	we := make([]simple.WeightedEdge, len(changes))
+	for i, e := range changes {
+		we[i].F = e.From()
+		we[i].T = e.To()
+		w, ok := in.Weight(e.From(), e.To())
+		if !ok && !math.IsInf(w, 1) {
+			panic("unexpected invalid finite weight")
+		}
+		we[i].W = w
+	}
+	return we
+}
+
+func couldConnectIn(l *LimitedVisionGrid, u, v graph.Node) bool {
+	if u.ID() == v.ID() {
+		return false
+	}
+
+	ur, uc := l.RowCol(u.ID())
+	vr, vc := l.RowCol(v.ID())
+	if abs(ur-vr) > 1 || abs(uc-vc) > 1 {
+		return false
+	}
+	if (ur != vr || uc != vc) && !l.Grid.AllowDiagonal {
+		return false
+	}
+
+	if !l.Known[u.ID()] && !l.Known[v.ID()] {
+		return true
+	}
+	if l.Known[u.ID()] && !l.Grid.HasOpen(u) {
+		return false
+	}
+	if l.Known[v.ID()] && !l.Grid.HasOpen(v) {
+		return false
+	}
+
+	return true
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/path/internal/testgraphs/shortest.go b/vendor/gonum.org/v1/gonum/graph/path/internal/testgraphs/shortest.go
new file mode 100644
index 00000000..3a9c6bc8
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/internal/testgraphs/shortest.go
@@ -0,0 +1,654 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testgraphs
+
+import (
+	"fmt"
+	"math"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+func init() {
+	for _, test := range ShortestPathTests {
+		if len(test.WantPaths) != 1 && test.HasUniquePath {
+			panic(fmt.Sprintf("%q: bad shortest path test: non-unique paths marked unique", test.Name))
+		}
+	}
+}
+
+// ShortestPathTests are graphs used to test the static shortest path routines in path: BellmanFord,
+// DijkstraAllPaths, DijkstraFrom, FloydWarshall and Johnson, and the static degenerate case for the
+// dynamic shortest path routine in path/dynamic: DStarLite.
+var ShortestPathTests = []struct {
+	Name              string
+	Graph             func() graph.WeightedEdgeAdder
+	Edges             []simple.WeightedEdge
+	HasNegativeWeight bool
+	HasNegativeCycle  bool
+
+	Query         simple.Edge
+	Weight        float64
+	WantPaths     [][]int64
+	HasUniquePath bool
+
+	NoPathFor simple.Edge
+}{
+	// Positive weighted graphs.
+	{
+		Name:  "empty directed",
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
+
+		Query:  simple.Edge{F: simple.Node(0), T: simple.Node(1)},
+		Weight: math.Inf(1),
+
+		NoPathFor: simple.Edge{F: simple.Node(0), T: simple.Node(1)},
+	},
+	{
+		Name:  "empty undirected",
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
+
+		Query:  simple.Edge{F: simple.Node(0), T: simple.Node(1)},
+		Weight: math.Inf(1),
+
+		NoPathFor: simple.Edge{F: simple.Node(0), T: simple.Node(1)},
+	},
+	{
+		Name:  "one edge directed",
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
+		Edges: []simple.WeightedEdge{
+			{F: simple.Node(0), T: simple.Node(1), W: 1},
+		},
+
+		Query:  simple.Edge{F: simple.Node(0), T: simple.Node(1)},
+		Weight: 1,
+		WantPaths: [][]int64{
+			{0, 1},
+		},
+		HasUniquePath: true,
+
+		NoPathFor: simple.Edge{F: simple.Node(2), T: simple.Node(3)},
+	},
+	{
+		Name:  "one edge self directed",
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
+		Edges: []simple.WeightedEdge{
+			{F: simple.Node(0), T: simple.Node(1), W: 1},
+		},
+
+		Query:  simple.Edge{F: simple.Node(0), T: simple.Node(0)},
+		Weight: 0,
+		WantPaths: [][]int64{
+			{0},
+		},
+		HasUniquePath: true,
+
+		NoPathFor: simple.Edge{F: simple.Node(2), T: simple.Node(3)},
+	},
+	{
+		Name:  "one edge undirected",
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
+		Edges: []simple.WeightedEdge{
+			{F: simple.Node(0), T: simple.Node(1), W: 1},
+		},
+
+		Query:  simple.Edge{F: simple.Node(0), T: simple.Node(1)},
+		Weight: 1,
+		WantPaths: [][]int64{
+			{0, 1},
+		},
+		HasUniquePath: true,
+
+		NoPathFor: simple.Edge{F: simple.Node(2), T: simple.Node(3)},
+	},
+	{
+		Name:  "two paths directed",
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
+		Edges: []simple.WeightedEdge{
+			{F: simple.Node(0), T: simple.Node(2), W: 2},
+			{F: simple.Node(0), T: simple.Node(1), W: 1},
+			{F: simple.Node(1), T: simple.Node(2), W: 1},
+		},
+
+		Query:  simple.Edge{F: simple.Node(0), T: simple.Node(2)},
+		Weight: 2,
+		WantPaths: [][]int64{
+			{0, 1, 2},
+			{0, 2},
+		},
+		HasUniquePath: false,
+
+		NoPathFor: simple.Edge{F: simple.Node(2), T: simple.Node(1)},
+	},
+	{
+		Name:  "two paths undirected",
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
+		Edges: []simple.WeightedEdge{
+			{F: simple.Node(0), T: simple.Node(2), W: 2},
+			{F: simple.Node(0), T: simple.Node(1), W: 1},
+			{F: simple.Node(1), T: simple.Node(2), W: 1},
+		},
+
+		Query:  simple.Edge{F: simple.Node(0), T: simple.Node(2)},
+		Weight: 2,
+		WantPaths: [][]int64{
+			{0, 1, 2},
+			{0, 2},
+		},
+		HasUniquePath: false,
+
+		NoPathFor: simple.Edge{F: simple.Node(2), T: simple.Node(4)},
+	},
+	{
+		Name:  "confounding paths directed",
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
+		Edges: []simple.WeightedEdge{
+			// Add a path from 0->5 of weight 4
+			{F: simple.Node(0), T: simple.Node(1), W: 1},
+			{F: simple.Node(1), T: simple.Node(2), W: 1},
+			{F: simple.Node(2), T: simple.Node(3), W: 1},
+			{F: simple.Node(3), T: simple.Node(5), W: 1},
+
+			// Add direct edge to goal of weight 4
+			{F: simple.Node(0), T: simple.Node(5), W: 4},
+
+			// Add edge to a node that's still optimal
+			{F: simple.Node(0), T: simple.Node(2), W: 2},
+
+			// Add edge to 3 that's overpriced
+			{F: simple.Node(0), T: simple.Node(3), W: 4},
+
+			// Add very cheap edge to 4 which is a dead end
+			{F: simple.Node(0), T: simple.Node(4), W: 0.25},
+		},
+
+		Query:  simple.Edge{F: simple.Node(0), T: simple.Node(5)},
+		Weight: 4,
+		WantPaths: [][]int64{
+			{0, 1, 2, 3, 5},
+			{0, 2, 3, 5},
+			{0, 5},
+		},
+		HasUniquePath: false,
+
+		NoPathFor: simple.Edge{F: simple.Node(4), T: simple.Node(5)},
+	},
+	{
+		Name:  "confounding paths undirected",
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
+		Edges: []simple.WeightedEdge{
+			// Add a path from 0->5 of weight 4
+			{F: simple.Node(0), T: simple.Node(1), W: 1},
+			{F: simple.Node(1), T: simple.Node(2), W: 1},
+			{F: simple.Node(2), T: simple.Node(3), W: 1},
+			{F: simple.Node(3), T: simple.Node(5), W: 1},
+
+			// Add direct edge to goal of weight 4
+			{F: simple.Node(0), T: simple.Node(5), W: 4},
+
+			// Add edge to a node that's still optimal
+			{F: simple.Node(0), T: simple.Node(2), W: 2},
+
+			// Add edge to 3 that's overpriced
+			{F: simple.Node(0), T: simple.Node(3), W: 4},
+
+			// Add very cheap edge to 4 which is a dead end
+			{F: simple.Node(0), T: simple.Node(4), W: 0.25},
+		},
+
+		Query:  simple.Edge{F: simple.Node(0), T: simple.Node(5)},
+		Weight: 4,
+		WantPaths: [][]int64{
+			{0, 1, 2, 3, 5},
+			{0, 2, 3, 5},
+			{0, 5},
+		},
+		HasUniquePath: false,
+
+		NoPathFor: simple.Edge{F: simple.Node(5), T: simple.Node(6)},
+	},
+	{
+		Name:  "confounding paths directed 2-step",
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
+		Edges: []simple.WeightedEdge{
+			// Add a path from 0->5 of weight 4
+			{F: simple.Node(0), T: simple.Node(1), W: 1},
+			{F: simple.Node(1), T: simple.Node(2), W: 1},
+			{F: simple.Node(2), T: simple.Node(3), W: 1},
+			{F: simple.Node(3), T: simple.Node(5), W: 1},
+
+			// Add two step path to goal of weight 4
+			{F: simple.Node(0), T: simple.Node(6), W: 2},
+			{F: simple.Node(6), T: simple.Node(5), W: 2},
+
+			// Add edge to a node that's still optimal
+			{F: simple.Node(0), T: simple.Node(2), W: 2},
+
+			// Add edge to 3 that's overpriced
+			{F: simple.Node(0), T: simple.Node(3), W: 4},
+
+			// Add very cheap edge to 4 which is a dead end
+			{F: simple.Node(0), T: simple.Node(4), W: 0.25},
+		},
+
+		Query:  simple.Edge{F: simple.Node(0), T: simple.Node(5)},
+		Weight: 4,
+		WantPaths: [][]int64{
+			{0, 1, 2, 3, 5},
+			{0, 2, 3, 5},
+			{0, 6, 5},
+		},
+		HasUniquePath: false,
+
+		NoPathFor: simple.Edge{F: simple.Node(4), T: simple.Node(5)},
+	},
+	{
+		Name:  "confounding paths undirected 2-step",
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
+		Edges: []simple.WeightedEdge{
+			// Add a path from 0->5 of weight 4
+			{F: simple.Node(0), T: simple.Node(1), W: 1},
+			{F: simple.Node(1), T: simple.Node(2), W: 1},
+			{F: simple.Node(2), T: simple.Node(3), W: 1},
+			{F: simple.Node(3), T: simple.Node(5), W: 1},
+
+			// Add two step path to goal of weight 4
+			{F: simple.Node(0), T: simple.Node(6), W: 2},
+			{F: simple.Node(6), T: simple.Node(5), W: 2},
+
+			// Add edge to a node that's still optimal
+			{F: simple.Node(0), T: simple.Node(2), W: 2},
+
+			// Add edge to 3 that's overpriced
+			{F: simple.Node(0), T: simple.Node(3), W: 4},
+
+			// Add very cheap edge to 4 which is a dead end
+			{F: simple.Node(0), T: simple.Node(4), W: 0.25},
+		},
+
+		Query:  simple.Edge{F: simple.Node(0), T: simple.Node(5)},
+		Weight: 4,
+		WantPaths: [][]int64{
+			{0, 1, 2, 3, 5},
+			{0, 2, 3, 5},
+			{0, 6, 5},
+		},
+		HasUniquePath: false,
+
+		NoPathFor: simple.Edge{F: simple.Node(5), T: simple.Node(7)},
+	},
+	{
+		Name:  "zero-weight cycle directed",
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
+		Edges: []simple.WeightedEdge{
+			// Add a path from 0->4 of weight 4
+			{F: simple.Node(0), T: simple.Node(1), W: 1},
+			{F: simple.Node(1), T: simple.Node(2), W: 1},
+			{F: simple.Node(2), T: simple.Node(3), W: 1},
+			{F: simple.Node(3), T: simple.Node(4), W: 1},
+
+			// Add a zero-weight cycle.
+			{F: simple.Node(1), T: simple.Node(5), W: 0},
+			{F: simple.Node(5), T: simple.Node(1), W: 0},
+		},
+
+		Query:  simple.Edge{F: simple.Node(0), T: simple.Node(4)},
+		Weight: 4,
+		WantPaths: [][]int64{
+			{0, 1, 2, 3, 4},
+		},
+		HasUniquePath: false,
+
+		NoPathFor: simple.Edge{F: simple.Node(4), T: simple.Node(5)},
+	},
+	{
+		Name:  "zero-weight cycle^2 directed",
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
+		Edges: []simple.WeightedEdge{
+			// Add a path from 0->4 of weight 4
+			{F: simple.Node(0), T: simple.Node(1), W: 1},
+			{F: simple.Node(1), T: simple.Node(2), W: 1},
+			{F: simple.Node(2), T: simple.Node(3), W: 1},
+			{F: simple.Node(3), T: simple.Node(4), W: 1},
+
+			// Add a zero-weight cycle.
+			{F: simple.Node(1), T: simple.Node(5), W: 0},
+			{F: simple.Node(5), T: simple.Node(1), W: 0},
+			// With its own zero-weight cycle.
+			{F: simple.Node(5), T: simple.Node(6), W: 0},
+			{F: simple.Node(6), T: simple.Node(5), W: 0},
+		},
+
+		Query:  simple.Edge{F: simple.Node(0), T: simple.Node(4)},
+		Weight: 4,
+		WantPaths: [][]int64{
+			{0, 1, 2, 3, 4},
+		},
+		HasUniquePath: false,
+
+		NoPathFor: simple.Edge{F: simple.Node(4), T: simple.Node(5)},
+	},
+	{
+		Name:  "zero-weight cycle^2 confounding directed",
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
+		Edges: []simple.WeightedEdge{
+			// Add a path from 0->4 of weight 4
+			{F: simple.Node(0), T: simple.Node(1), W: 1},
+			{F: simple.Node(1), T: simple.Node(2), W: 1},
+			{F: simple.Node(2), T: simple.Node(3), W: 1},
+			{F: simple.Node(3), T: simple.Node(4), W: 1},
+
+			// Add a zero-weight cycle.
+			{F: simple.Node(1), T: simple.Node(5), W: 0},
+			{F: simple.Node(5), T: simple.Node(1), W: 0},
+			// With its own zero-weight cycle.
+			{F: simple.Node(5), T: simple.Node(6), W: 0},
+			{F: simple.Node(6), T: simple.Node(5), W: 0},
+			// But leading to the target.
+			{F: simple.Node(5), T: simple.Node(4), W: 3},
+		},
+
+		Query:  simple.Edge{F: simple.Node(0), T: simple.Node(4)},
+		Weight: 4,
+		WantPaths: [][]int64{
+			{0, 1, 2, 3, 4},
+			{0, 1, 5, 4},
+		},
+		HasUniquePath: false,
+
+		NoPathFor: simple.Edge{F: simple.Node(4), T: simple.Node(5)},
+	},
+	{
+		Name:  "zero-weight cycle^3 directed",
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
+		Edges: []simple.WeightedEdge{
+			// Add a path from 0->4 of weight 4
+			{F: simple.Node(0), T: simple.Node(1), W: 1},
+			{F: simple.Node(1), T: simple.Node(2), W: 1},
+			{F: simple.Node(2), T: simple.Node(3), W: 1},
+			{F: simple.Node(3), T: simple.Node(4), W: 1},
+
+			// Add a zero-weight cycle.
+			{F: simple.Node(1), T: simple.Node(5), W: 0},
+			{F: simple.Node(5), T: simple.Node(1), W: 0},
+			// With its own zero-weight cycle.
+			{F: simple.Node(5), T: simple.Node(6), W: 0},
+			{F: simple.Node(6), T: simple.Node(5), W: 0},
+			// With its own zero-weight cycle.
+			{F: simple.Node(6), T: simple.Node(7), W: 0},
+			{F: simple.Node(7), T: simple.Node(6), W: 0},
+		},
+
+		Query:  simple.Edge{F: simple.Node(0), T: simple.Node(4)},
+		Weight: 4,
+		WantPaths: [][]int64{
+			{0, 1, 2, 3, 4},
+		},
+		HasUniquePath: false,
+
+		NoPathFor: simple.Edge{F: simple.Node(4), T: simple.Node(5)},
+	},
+	{
+		Name:  "zero-weight 3·cycle^2 confounding directed",
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
+		Edges: []simple.WeightedEdge{
+			// Add a path from 0->4 of weight 4
+			{F: simple.Node(0), T: simple.Node(1), W: 1},
+			{F: simple.Node(1), T: simple.Node(2), W: 1},
+			{F: simple.Node(2), T: simple.Node(3), W: 1},
+			{F: simple.Node(3), T: simple.Node(4), W: 1},
+
+			// Add a zero-weight cycle.
+			{F: simple.Node(1), T: simple.Node(5), W: 0},
+			{F: simple.Node(5), T: simple.Node(1), W: 0},
+			// With 3 of its own zero-weight cycles.
+			{F: simple.Node(5), T: simple.Node(6), W: 0},
+			{F: simple.Node(6), T: simple.Node(5), W: 0},
+			{F: simple.Node(5), T: simple.Node(7), W: 0},
+			{F: simple.Node(7), T: simple.Node(5), W: 0},
+			// Each leading to the target.
+			{F: simple.Node(5), T: simple.Node(4), W: 3},
+			{F: simple.Node(6), T: simple.Node(4), W: 3},
+			{F: simple.Node(7), T: simple.Node(4), W: 3},
+		},
+
+		Query:  simple.Edge{F: simple.Node(0), T: simple.Node(4)},
+		Weight: 4,
+		WantPaths: [][]int64{
+			{0, 1, 2, 3, 4},
+			{0, 1, 5, 4},
+			{0, 1, 5, 6, 4},
+			{0, 1, 5, 7, 4},
+		},
+		HasUniquePath: false,
+
+		NoPathFor: simple.Edge{F: simple.Node(4), T: simple.Node(5)},
+	},
+	{
+		Name:  "zero-weight reversed 3·cycle^2 confounding directed",
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
+		Edges: []simple.WeightedEdge{
+			// Add a path from 0->4 of weight 4
+			{F: simple.Node(0), T: simple.Node(1), W: 1},
+			{F: simple.Node(1), T: simple.Node(2), W: 1},
+			{F: simple.Node(2), T: simple.Node(3), W: 1},
+			{F: simple.Node(3), T: simple.Node(4), W: 1},
+
+			// Add a zero-weight cycle.
+			{F: simple.Node(3), T: simple.Node(5), W: 0},
+			{F: simple.Node(5), T: simple.Node(3), W: 0},
+			// With 3 of its own zero-weight cycles.
+			{F: simple.Node(5), T: simple.Node(6), W: 0},
+			{F: simple.Node(6), T: simple.Node(5), W: 0},
+			{F: simple.Node(5), T: simple.Node(7), W: 0},
+			{F: simple.Node(7), T: simple.Node(5), W: 0},
+			// Each leading from the source.
+			{F: simple.Node(0), T: simple.Node(5), W: 3},
+			{F: simple.Node(0), T: simple.Node(6), W: 3},
+			{F: simple.Node(0), T: simple.Node(7), W: 3},
+		},
+
+		Query:  simple.Edge{F: simple.Node(0), T: simple.Node(4)},
+		Weight: 4,
+		WantPaths: [][]int64{
+			{0, 1, 2, 3, 4},
+			{0, 5, 3, 4},
+			{0, 6, 5, 3, 4},
+			{0, 7, 5, 3, 4},
+		},
+		HasUniquePath: false,
+
+		NoPathFor: simple.Edge{F: simple.Node(4), T: simple.Node(5)},
+	},
+	{
+		Name:  "zero-weight |V|·cycle^(n/|V|) directed",
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
+		Edges: func() []simple.WeightedEdge {
+			e := []simple.WeightedEdge{
+				// Add a path from 0->4 of weight 4
+				{F: simple.Node(0), T: simple.Node(1), W: 1},
+				{F: simple.Node(1), T: simple.Node(2), W: 1},
+				{F: simple.Node(2), T: simple.Node(3), W: 1},
+				{F: simple.Node(3), T: simple.Node(4), W: 1},
+			}
+			next := len(e) + 1
+
+			// Add n zero-weight cycles.
+			const n = 100
+			for i := 0; i < n; i++ {
+				e = append(e,
+					simple.WeightedEdge{F: simple.Node(next + i), T: simple.Node(i), W: 0},
+					simple.WeightedEdge{F: simple.Node(i), T: simple.Node(next + i), W: 0},
+				)
+			}
+			return e
+		}(),
+
+		Query:  simple.Edge{F: simple.Node(0), T: simple.Node(4)},
+		Weight: 4,
+		WantPaths: [][]int64{
+			{0, 1, 2, 3, 4},
+		},
+		HasUniquePath: false,
+
+		NoPathFor: simple.Edge{F: simple.Node(4), T: simple.Node(5)},
+	},
+	{
+		Name:  "zero-weight n·cycle directed",
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
+		Edges: func() []simple.WeightedEdge {
+			e := []simple.WeightedEdge{
+				// Add a path from 0->4 of weight 4
+				{F: simple.Node(0), T: simple.Node(1), W: 1},
+				{F: simple.Node(1), T: simple.Node(2), W: 1},
+				{F: simple.Node(2), T: simple.Node(3), W: 1},
+				{F: simple.Node(3), T: simple.Node(4), W: 1},
+			}
+			next := len(e) + 1
+
+			// Add n zero-weight cycles.
+			const n = 100
+			for i := 0; i < n; i++ {
+				e = append(e,
+					simple.WeightedEdge{F: simple.Node(next + i), T: simple.Node(1), W: 0},
+					simple.WeightedEdge{F: simple.Node(1), T: simple.Node(next + i), W: 0},
+				)
+			}
+			return e
+		}(),
+
+		Query:  simple.Edge{F: simple.Node(0), T: simple.Node(4)},
+		Weight: 4,
+		WantPaths: [][]int64{
+			{0, 1, 2, 3, 4},
+		},
+		HasUniquePath: false,
+
+		NoPathFor: simple.Edge{F: simple.Node(4), T: simple.Node(5)},
+	},
+	{
+		Name:  "zero-weight bi-directional tree with single exit directed",
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
+		Edges: func() []simple.WeightedEdge {
+			e := []simple.WeightedEdge{
+				// Add a path from 0->4 of weight 4
+				{F: simple.Node(0), T: simple.Node(1), W: 1},
+				{F: simple.Node(1), T: simple.Node(2), W: 1},
+				{F: simple.Node(2), T: simple.Node(3), W: 1},
+				{F: simple.Node(3), T: simple.Node(4), W: 1},
+			}
+
+			// Make a bi-directional tree rooted at node 2 with
+			// a single exit to node 4 and co-equal cost from
+			// 2 to 4.
+			const (
+				depth     = 4
+				branching = 4
+			)
+
+			next := len(e) + 1
+			src := 2
+			var i, last int
+			for l := 0; l < depth; l++ {
+				for i = 0; i < branching; i++ {
+					last = next + i
+					e = append(e, simple.WeightedEdge{F: simple.Node(src), T: simple.Node(last), W: 0})
+					e = append(e, simple.WeightedEdge{F: simple.Node(last), T: simple.Node(src), W: 0})
+				}
+				src = next + 1
+				next += branching
+			}
+			e = append(e, simple.WeightedEdge{F: simple.Node(last), T: simple.Node(4), W: 2})
+			return e
+		}(),
+
+		Query:  simple.Edge{F: simple.Node(0), T: simple.Node(4)},
+		Weight: 4,
+		WantPaths: [][]int64{
+			{0, 1, 2, 3, 4},
+			{0, 1, 2, 6, 10, 14, 20, 4},
+		},
+		HasUniquePath: false,
+
+		NoPathFor: simple.Edge{F: simple.Node(4), T: simple.Node(5)},
+	},
+
+	// Negative weighted graphs.
+	{
+		Name:  "one edge directed negative",
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
+		Edges: []simple.WeightedEdge{
+			{F: simple.Node(0), T: simple.Node(1), W: -1},
+		},
+		HasNegativeWeight: true,
+
+		Query:  simple.Edge{F: simple.Node(0), T: simple.Node(1)},
+		Weight: -1,
+		WantPaths: [][]int64{
+			{0, 1},
+		},
+		HasUniquePath: true,
+
+		NoPathFor: simple.Edge{F: simple.Node(2), T: simple.Node(3)},
+	},
+	{
+		Name:  "one edge undirected negative",
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
+		Edges: []simple.WeightedEdge{
+			{F: simple.Node(0), T: simple.Node(1), W: -1},
+		},
+		HasNegativeWeight: true,
+		HasNegativeCycle:  true,
+
+		Query: simple.Edge{F: simple.Node(0), T: simple.Node(1)},
+	},
+	{
+		Name:  "wp graph negative", // http://en.wikipedia.org/w/index.php?title=Johnson%27s_algorithm&oldid=564595231
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
+		Edges: []simple.WeightedEdge{
+			{F: simple.Node('w'), T: simple.Node('z'), W: 2},
+			{F: simple.Node('x'), T: simple.Node('w'), W: 6},
+			{F: simple.Node('x'), T: simple.Node('y'), W: 3},
+			{F: simple.Node('y'), T: simple.Node('w'), W: 4},
+			{F: simple.Node('y'), T: simple.Node('z'), W: 5},
+			{F: simple.Node('z'), T: simple.Node('x'), W: -7},
+			{F: simple.Node('z'), T: simple.Node('y'), W: -3},
+		},
+		HasNegativeWeight: true,
+
+		Query:  simple.Edge{F: simple.Node('z'), T: simple.Node('y')},
+		Weight: -4,
+		WantPaths: [][]int64{
+			{'z', 'x', 'y'},
+		},
+		HasUniquePath: true,
+
+		NoPathFor: simple.Edge{F: simple.Node(2), T: simple.Node(3)},
+	},
+	{
+		Name:  "roughgarden negative",
+		Graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedDirectedGraph(0, math.Inf(1)) },
+		Edges: []simple.WeightedEdge{
+			{F: simple.Node('a'), T: simple.Node('b'), W: -2},
+			{F: simple.Node('b'), T: simple.Node('c'), W: -1},
+			{F: simple.Node('c'), T: simple.Node('a'), W: 4},
+			{F: simple.Node('c'), T: simple.Node('x'), W: 2},
+			{F: simple.Node('c'), T: simple.Node('y'), W: -3},
+			{F: simple.Node('z'), T: simple.Node('x'), W: 1},
+			{F: simple.Node('z'), T: simple.Node('y'), W: -4},
+		},
+		HasNegativeWeight: true,
+
+		Query:  simple.Edge{F: simple.Node('a'), T: simple.Node('y')},
+		Weight: -6,
+		WantPaths: [][]int64{
+			{'a', 'b', 'c', 'y'},
+		},
+		HasUniquePath: true,
+
+		NoPathFor: simple.Edge{F: simple.Node(2), T: simple.Node(3)},
+	},
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/path/johnson_apsp.go b/vendor/gonum.org/v1/gonum/graph/path/johnson_apsp.go
new file mode 100644
index 00000000..444564f1
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/johnson_apsp.go
@@ -0,0 +1,142 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package path
+
+import (
+	"math"
+	"math/rand"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+// JohnsonAllPaths returns a shortest-path tree for shortest paths in the graph g.
+// If the graph does not implement graph.Weighter, UniformCost is used.
+//
+// The time complexity of JohnsonAllPaths is O(|V|.|E|+|V|^2.log|V|).
+func JohnsonAllPaths(g graph.Graph) (paths AllShortest, ok bool) {
+	jg := johnsonWeightAdjuster{
+		g:      g,
+		from:   g.From,
+		edgeTo: g.Edge,
+	}
+	if wg, ok := g.(graph.Weighted); ok {
+		jg.weight = wg.Weight
+	} else {
+		jg.weight = UniformCost(g)
+	}
+
+	paths = newAllShortest(g.Nodes(), false)
+
+	sign := int64(-1)
+	for {
+		// Choose a random node ID until we find
+		// one that is not in g.
+		jg.q = sign * rand.Int63()
+		if _, exists := paths.indexOf[jg.q]; !exists {
+			break
+		}
+		sign *= -1
+	}
+
+	jg.bellmanFord = true
+	jg.adjustBy, ok = BellmanFordFrom(johnsonGraphNode(jg.q), jg)
+	if !ok {
+		return paths, false
+	}
+
+	jg.bellmanFord = false
+	dijkstraAllPaths(jg, paths)
+
+	for i, u := range paths.nodes {
+		hu := jg.adjustBy.WeightTo(u)
+		for j, v := range paths.nodes {
+			if i == j {
+				continue
+			}
+			hv := jg.adjustBy.WeightTo(v)
+			paths.dist.Set(i, j, paths.dist.At(i, j)-hu+hv)
+		}
+	}
+
+	return paths, ok
+}
+
+type johnsonWeightAdjuster struct {
+	q int64
+	g graph.Graph
+
+	from   func(graph.Node) []graph.Node
+	edgeTo func(graph.Node, graph.Node) graph.Edge
+	weight Weighting
+
+	bellmanFord bool
+	adjustBy    Shortest
+}
+
+var (
+	// johnsonWeightAdjuster has the behaviour
+	// of a directed graph, but we don't need
+	// to be explicit with the type since it
+	// is not exported.
+	_ graph.Graph    = johnsonWeightAdjuster{}
+	_ graph.Weighted = johnsonWeightAdjuster{}
+)
+
+func (g johnsonWeightAdjuster) Has(n graph.Node) bool {
+	if g.bellmanFord && n.ID() == g.q {
+		return true
+	}
+	return g.g.Has(n)
+
+}
+
+func (g johnsonWeightAdjuster) Nodes() []graph.Node {
+	if g.bellmanFord {
+		return append(g.g.Nodes(), johnsonGraphNode(g.q))
+	}
+	return g.g.Nodes()
+}
+
+func (g johnsonWeightAdjuster) From(n graph.Node) []graph.Node {
+	if g.bellmanFord && n.ID() == g.q {
+		return g.g.Nodes()
+	}
+	return g.from(n)
+}
+
+func (g johnsonWeightAdjuster) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
+	panic("path: unintended use of johnsonWeightAdjuster")
+}
+
+func (g johnsonWeightAdjuster) Edge(u, v graph.Node) graph.Edge {
+	if g.bellmanFord && u.ID() == g.q && g.g.Has(v) {
+		return simple.Edge{F: johnsonGraphNode(g.q), T: v}
+	}
+	return g.edgeTo(u, v)
+}
+
+func (g johnsonWeightAdjuster) Weight(x, y graph.Node) (w float64, ok bool) {
+	if g.bellmanFord {
+		switch g.q {
+		case x.ID():
+			return 0, true
+		case y.ID():
+			return math.Inf(1), false
+		default:
+			return g.weight(x, y)
+		}
+	}
+	w, ok = g.weight(x, y)
+	return w + g.adjustBy.WeightTo(x) - g.adjustBy.WeightTo(y), ok
+}
+
+func (johnsonWeightAdjuster) HasEdgeBetween(_, _ graph.Node) bool {
+	panic("path: unintended use of johnsonWeightAdjuster")
+}
+
+type johnsonGraphNode int64
+
+func (n johnsonGraphNode) ID() int64 { return int64(n) }
diff --git a/vendor/gonum.org/v1/gonum/graph/path/johnson_apsp_test.go b/vendor/gonum.org/v1/gonum/graph/path/johnson_apsp_test.go
new file mode 100644
index 00000000..1635ce92
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/johnson_apsp_test.go
@@ -0,0 +1,102 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package path
+
+import (
+	"math"
+	"reflect"
+	"sort"
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/ordered"
+	"gonum.org/v1/gonum/graph/path/internal/testgraphs"
+)
+
+func TestJohnsonAllPaths(t *testing.T) {
+	for _, test := range testgraphs.ShortestPathTests {
+		g := test.Graph()
+		for _, e := range test.Edges {
+			g.SetWeightedEdge(e)
+		}
+
+		pt, ok := JohnsonAllPaths(g.(graph.Graph))
+		if test.HasNegativeCycle {
+			if ok {
+				t.Errorf("%q: expected negative cycle", test.Name)
+			}
+			continue
+		}
+		if !ok {
+			t.Fatalf("%q: unexpected negative cycle", test.Name)
+		}
+
+		// Check all random paths returned are OK.
+		for i := 0; i < 10; i++ {
+			p, weight, unique := pt.Between(test.Query.From(), test.Query.To())
+			if weight != test.Weight {
+				t.Errorf("%q: unexpected weight from Between: got:%f want:%f",
+					test.Name, weight, test.Weight)
+			}
+			if weight := pt.Weight(test.Query.From(), test.Query.To()); weight != test.Weight {
+				t.Errorf("%q: unexpected weight from Weight: got:%f want:%f",
+					test.Name, weight, test.Weight)
+			}
+			if unique != test.HasUniquePath {
+				t.Errorf("%q: unexpected number of paths: got: unique=%t want: unique=%t",
+					test.Name, unique, test.HasUniquePath)
+			}
+
+			var got []int64
+			for _, n := range p {
+				got = append(got, n.ID())
+			}
+			ok := len(got) == 0 && len(test.WantPaths) == 0
+			for _, sp := range test.WantPaths {
+				if reflect.DeepEqual(got, sp) {
+					ok = true
+					break
+				}
+			}
+			if !ok {
+				t.Errorf("%q: unexpected shortest path:\ngot: %v\nwant from:%v",
+					test.Name, p, test.WantPaths)
+			}
+		}
+
+		np, weight, unique := pt.Between(test.NoPathFor.From(), test.NoPathFor.To())
+		if np != nil || !math.IsInf(weight, 1) || unique {
+			t.Errorf("%q: unexpected path:\ngot: path=%v weight=%f unique=%t\nwant:path=<nil> weight=+Inf unique=false",
+				test.Name, np, weight, unique)
+		}
+
+		paths, weight := pt.AllBetween(test.Query.From(), test.Query.To())
+		if weight != test.Weight {
+			t.Errorf("%q: unexpected weight from Between: got:%f want:%f",
+				test.Name, weight, test.Weight)
+		}
+
+		var got [][]int64
+		if len(paths) != 0 {
+			got = make([][]int64, len(paths))
+		}
+		for i, p := range paths {
+			for _, v := range p {
+				got[i] = append(got[i], v.ID())
+			}
+		}
+		sort.Sort(ordered.BySliceValues(got))
+		if !reflect.DeepEqual(got, test.WantPaths) {
+			t.Errorf("testing %q: unexpected shortest paths:\ngot: %v\nwant:%v",
+				test.Name, got, test.WantPaths)
+		}
+
+		nps, weight := pt.AllBetween(test.NoPathFor.From(), test.NoPathFor.To())
+		if nps != nil || !math.IsInf(weight, 1) {
+			t.Errorf("%q: unexpected path:\ngot: paths=%v weight=%f\nwant:path=<nil> weight=+Inf",
+				test.Name, nps, weight)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/path/shortest.go b/vendor/gonum.org/v1/gonum/graph/path/shortest.go
new file mode 100644
index 00000000..a21a7d4f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/shortest.go
@@ -0,0 +1,319 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package path
+
+import (
+	"math"
+	"math/rand"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/mat"
+)
+
+// Shortest is a shortest-path tree created by the BellmanFordFrom or DijkstraFrom
+// single-source shortest path functions.
+type Shortest struct {
+	// from holds the source node given to
+	// DijkstraFrom.
+	from graph.Node
+
+	// nodes hold the nodes of the analysed
+	// graph.
+	nodes []graph.Node
+	// indexOf contains a mapping between
+	// the id-dense representation of the
+	// graph and the potentially id-sparse
+	// nodes held in nodes.
+	indexOf map[int64]int
+
+	// dist and next represent the shortest
+	// paths between nodes.
+	//
+	// Indices into dist and next are
+	// mapped through indexOf.
+	//
+	// dist contains the distances
+	// from the from node for each
+	// node in the graph.
+	dist []float64
+	// next contains the shortest-path
+	// tree of the graph. The index is a
+	// linear mapping of to-dense-id.
+	next []int
+}
+
+func newShortestFrom(u graph.Node, nodes []graph.Node) Shortest {
+	indexOf := make(map[int64]int, len(nodes))
+	uid := u.ID()
+	for i, n := range nodes {
+		indexOf[n.ID()] = i
+		if n.ID() == uid {
+			u = n
+		}
+	}
+
+	p := Shortest{
+		from: u,
+
+		nodes:   nodes,
+		indexOf: indexOf,
+
+		dist: make([]float64, len(nodes)),
+		next: make([]int, len(nodes)),
+	}
+	for i := range nodes {
+		p.dist[i] = math.Inf(1)
+		p.next[i] = -1
+	}
+	p.dist[indexOf[uid]] = 0
+
+	return p
+}
+
+func (p Shortest) set(to int, weight float64, mid int) {
+	p.dist[to] = weight
+	p.next[to] = mid
+}
+
+// From returns the starting node of the paths held by the Shortest.
+func (p Shortest) From() graph.Node { return p.from }
+
+// WeightTo returns the weight of the minimum path to v.
+func (p Shortest) WeightTo(v graph.Node) float64 {
+	to, toOK := p.indexOf[v.ID()]
+	if !toOK {
+		return math.Inf(1)
+	}
+	return p.dist[to]
+}
+
+// To returns a shortest path to v and the weight of the path.
+func (p Shortest) To(v graph.Node) (path []graph.Node, weight float64) {
+	to, toOK := p.indexOf[v.ID()]
+	if !toOK || math.IsInf(p.dist[to], 1) {
+		return nil, math.Inf(1)
+	}
+	from := p.indexOf[p.from.ID()]
+	path = []graph.Node{p.nodes[to]}
+	for to != from {
+		path = append(path, p.nodes[p.next[to]])
+		to = p.next[to]
+	}
+	reverse(path)
+	return path, p.dist[p.indexOf[v.ID()]]
+}
+
+// AllShortest is a shortest-path tree created by the DijkstraAllPaths, FloydWarshall
+// or JohnsonAllPaths all-pairs shortest paths functions.
+type AllShortest struct {
+	// nodes hold the nodes of the analysed
+	// graph.
+	nodes []graph.Node
+	// indexOf contains a mapping between
+	// the id-dense representation of the
+	// graph and the potentially id-sparse
+	// nodes held in nodes.
+	indexOf map[int64]int
+
+	// dist, next and forward represent
+	// the shortest paths between nodes.
+	//
+	// Indices into dist and next are
+	// mapped through indexOf.
+	//
+	// dist contains the pairwise
+	// distances between nodes.
+	dist *mat.Dense
+	// next contains the shortest-path
+	// tree of the graph. The first index
+	// is a linear mapping of from-dense-id
+	// and to-dense-id, to-major with a
+	// stride equal to len(nodes); the
+	// slice indexed to is the list of
+	// intermediates leading from the 'from'
+	// node to the 'to' node represented
+	// by dense id.
+	// The interpretation of next is
+	// dependent on the state of forward.
+	next [][]int
+	// forward indicates the direction of
+	// path reconstruction. Forward
+	// reconstruction is used for Floyd-
+	// Warshall and reverse is used for
+	// Dijkstra.
+	forward bool
+}
+
+func newAllShortest(nodes []graph.Node, forward bool) AllShortest {
+	indexOf := make(map[int64]int, len(nodes))
+	for i, n := range nodes {
+		indexOf[n.ID()] = i
+	}
+	dist := make([]float64, len(nodes)*len(nodes))
+	for i := range dist {
+		dist[i] = math.Inf(1)
+	}
+	return AllShortest{
+		nodes:   nodes,
+		indexOf: indexOf,
+
+		dist:    mat.NewDense(len(nodes), len(nodes), dist),
+		next:    make([][]int, len(nodes)*len(nodes)),
+		forward: forward,
+	}
+}
+
+func (p AllShortest) at(from, to int) (mid []int) {
+	return p.next[from+to*len(p.nodes)]
+}
+
+func (p AllShortest) set(from, to int, weight float64, mid ...int) {
+	p.dist.Set(from, to, weight)
+	p.next[from+to*len(p.nodes)] = append(p.next[from+to*len(p.nodes)][:0], mid...)
+}
+
+func (p AllShortest) add(from, to int, mid ...int) {
+loop: // These are likely to be rare, so just loop over collisions.
+	for _, k := range mid {
+		for _, v := range p.next[from+to*len(p.nodes)] {
+			if k == v {
+				continue loop
+			}
+		}
+		p.next[from+to*len(p.nodes)] = append(p.next[from+to*len(p.nodes)], k)
+	}
+}
+
+// Weight returns the weight of the minimum path between u and v.
+func (p AllShortest) Weight(u, v graph.Node) float64 {
+	from, fromOK := p.indexOf[u.ID()]
+	to, toOK := p.indexOf[v.ID()]
+	if !fromOK || !toOK {
+		return math.Inf(1)
+	}
+	return p.dist.At(from, to)
+}
+
+// Between returns a shortest path from u to v and the weight of the path. If more than
+// one shortest path exists between u and v, a randomly chosen path will be returned and
+// unique is returned false. If a cycle with zero weight exists in the path, it will not
+// be included, but unique will be returned false.
+func (p AllShortest) Between(u, v graph.Node) (path []graph.Node, weight float64, unique bool) {
+	from, fromOK := p.indexOf[u.ID()]
+	to, toOK := p.indexOf[v.ID()]
+	if !fromOK || !toOK || len(p.at(from, to)) == 0 {
+		if u.ID() == v.ID() {
+			return []graph.Node{p.nodes[from]}, 0, true
+		}
+		return nil, math.Inf(1), false
+	}
+
+	seen := make([]int, len(p.nodes))
+	for i := range seen {
+		seen[i] = -1
+	}
+	var n graph.Node
+	if p.forward {
+		n = p.nodes[from]
+		seen[from] = 0
+	} else {
+		n = p.nodes[to]
+		seen[to] = 0
+	}
+
+	path = []graph.Node{n}
+	weight = p.dist.At(from, to)
+	unique = true
+
+	var next int
+	for from != to {
+		c := p.at(from, to)
+		if len(c) != 1 {
+			unique = false
+			next = c[rand.Intn(len(c))]
+		} else {
+			next = c[0]
+		}
+		if seen[next] >= 0 {
+			path = path[:seen[next]]
+		}
+		seen[next] = len(path)
+		path = append(path, p.nodes[next])
+		if p.forward {
+			from = next
+		} else {
+			to = next
+		}
+	}
+	if !p.forward {
+		reverse(path)
+	}
+
+	return path, weight, unique
+}
+
+// AllBetween returns all shortest paths from u to v and the weight of the paths. Paths
+// containing zero-weight cycles are not returned.
+func (p AllShortest) AllBetween(u, v graph.Node) (paths [][]graph.Node, weight float64) {
+	from, fromOK := p.indexOf[u.ID()]
+	to, toOK := p.indexOf[v.ID()]
+	if !fromOK || !toOK || len(p.at(from, to)) == 0 {
+		if u.ID() == v.ID() {
+			return [][]graph.Node{{p.nodes[from]}}, 0
+		}
+		return nil, math.Inf(1)
+	}
+
+	var n graph.Node
+	if p.forward {
+		n = u
+	} else {
+		n = v
+	}
+	seen := make([]bool, len(p.nodes))
+	paths = p.allBetween(from, to, seen, []graph.Node{n}, nil)
+
+	return paths, p.dist.At(from, to)
+}
+
+func (p AllShortest) allBetween(from, to int, seen []bool, path []graph.Node, paths [][]graph.Node) [][]graph.Node {
+	if p.forward {
+		seen[from] = true
+	} else {
+		seen[to] = true
+	}
+	if from == to {
+		if path == nil {
+			return paths
+		}
+		if !p.forward {
+			reverse(path)
+		}
+		return append(paths, path)
+	}
+	first := true
+	for _, n := range p.at(from, to) {
+		if seen[n] {
+			continue
+		}
+		if first {
+			path = append([]graph.Node(nil), path...)
+			first = false
+		}
+		if p.forward {
+			from = n
+		} else {
+			to = n
+		}
+		paths = p.allBetween(from, to, append([]bool(nil), seen...), append(path, p.nodes[n]), paths)
+	}
+	return paths
+}
+
+func reverse(p []graph.Node) {
+	for i, j := 0, len(p)-1; i < j; i, j = i+1, j-1 {
+		p[i], p[j] = p[j], p[i]
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/path/spanning_tree.go b/vendor/gonum.org/v1/gonum/graph/path/spanning_tree.go
new file mode 100644
index 00000000..a21a3e83
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/spanning_tree.go
@@ -0,0 +1,187 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package path
+
+import (
+	"container/heap"
+	"math"
+	"sort"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+// WeightedBuilder is a type that can add nodes and weighted edges.
+type WeightedBuilder interface {
+	AddNode(graph.Node)
+	SetWeightedEdge(graph.WeightedEdge)
+}
+
+// Prim generates a minimum spanning tree of g by greedy tree extension, placing
+// the result in the destination, dst. If the edge weights of g are distinct
+// it will be the unique minimum spanning tree of g. The destination is not cleared
+// first. The weight of the minimum spanning tree is returned. If g is not connected,
+// a minimum spanning forest will be constructed in dst and the sum of minimum
+// spanning tree weights will be returned.
+//
+// Nodes and Edges from g are used to construct dst, so if the Node and Edge
+// types used in g are pointer or reference-like, then the values will be shared
+// between the graphs.
+//
+// If dst has nodes that exist in g, Prim will panic.
+func Prim(dst WeightedBuilder, g graph.WeightedUndirected) float64 {
+	nodes := g.Nodes()
+	if len(nodes) == 0 {
+		return 0
+	}
+
+	q := &primQueue{
+		indexOf: make(map[int64]int, len(nodes)-1),
+		nodes:   make([]simple.WeightedEdge, 0, len(nodes)-1),
+	}
+	dst.AddNode(nodes[0])
+	for _, u := range nodes[1:] {
+		dst.AddNode(u)
+		heap.Push(q, simple.WeightedEdge{F: u, W: math.Inf(1)})
+	}
+
+	u := nodes[0]
+	for _, v := range g.From(u) {
+		w, ok := g.Weight(u, v)
+		if !ok {
+			panic("prim: unexpected invalid weight")
+		}
+		q.update(v, u, w)
+	}
+
+	var w float64
+	for q.Len() > 0 {
+		e := heap.Pop(q).(simple.WeightedEdge)
+		if e.To() != nil && g.HasEdgeBetween(e.From(), e.To()) {
+			dst.SetWeightedEdge(g.WeightedEdge(e.From(), e.To()))
+			w += e.Weight()
+		}
+
+		u = e.From()
+		for _, n := range g.From(u) {
+			if key, ok := q.key(n); ok {
+				w, ok := g.Weight(u, n)
+				if !ok {
+					panic("prim: unexpected invalid weight")
+				}
+				if w < key {
+					q.update(n, u, w)
+				}
+			}
+		}
+	}
+	return w
+}
+
+// primQueue is a Prim's priority queue. The priority queue is a
+// queue of edge From nodes keyed on the minimum edge weight to
+// a node in the set of nodes already connected to the minimum
+// spanning forest.
+type primQueue struct {
+	indexOf map[int64]int
+	nodes   []simple.WeightedEdge
+}
+
+func (q *primQueue) Less(i, j int) bool {
+	return q.nodes[i].Weight() < q.nodes[j].Weight()
+}
+
+func (q *primQueue) Swap(i, j int) {
+	q.indexOf[q.nodes[i].From().ID()] = j
+	q.indexOf[q.nodes[j].From().ID()] = i
+	q.nodes[i], q.nodes[j] = q.nodes[j], q.nodes[i]
+}
+
+func (q *primQueue) Len() int {
+	return len(q.nodes)
+}
+
+func (q *primQueue) Push(x interface{}) {
+	n := x.(simple.WeightedEdge)
+	q.indexOf[n.From().ID()] = len(q.nodes)
+	q.nodes = append(q.nodes, n)
+}
+
+func (q *primQueue) Pop() interface{} {
+	n := q.nodes[len(q.nodes)-1]
+	q.nodes = q.nodes[:len(q.nodes)-1]
+	delete(q.indexOf, n.From().ID())
+	return n
+}
+
+// key returns the key for the node u and whether the node is
+// in the queue. If the node is not in the queue, key is returned
+// as +Inf.
+func (q *primQueue) key(u graph.Node) (key float64, ok bool) {
+	i, ok := q.indexOf[u.ID()]
+	if !ok {
+		return math.Inf(1), false
+	}
+	return q.nodes[i].Weight(), ok
+}
+
+// update updates u's position in the queue with the new closest
+// MST-connected neighbour, v, and the key weight between u and v.
+func (q *primQueue) update(u, v graph.Node, key float64) {
+	id := u.ID()
+	i, ok := q.indexOf[id]
+	if !ok {
+		return
+	}
+	q.nodes[i].T = v
+	q.nodes[i].W = key
+	heap.Fix(q, i)
+}
+
+// UndirectedWeightLister is an undirected graph that returns edge weights and
+// the set of edges in the graph.
+type UndirectedWeightLister interface {
+	graph.WeightedUndirected
+	WeightedEdges() []graph.WeightedEdge
+}
+
+// Kruskal generates a minimum spanning tree of g by greedy tree coalescence, placing
+// the result in the destination, dst. If the edge weights of g are distinct
+// it will be the unique minimum spanning tree of g. The destination is not cleared
+// first. The weight of the minimum spanning tree is returned. If g is not connected,
+// a minimum spanning forest will be constructed in dst and the sum of minimum
+// spanning tree weights will be returned.
+//
+// Nodes and Edges from g are used to construct dst, so if the Node and Edge
+// types used in g are pointer or reference-like, then the values will be shared
+// between the graphs.
+//
+// If dst has nodes that exist in g, Kruskal will panic.
+func Kruskal(dst WeightedBuilder, g UndirectedWeightLister) float64 {
+	edges := g.WeightedEdges()
+	sort.Sort(byWeight(edges))
+
+	ds := newDisjointSet()
+	for _, node := range g.Nodes() {
+		dst.AddNode(node)
+		ds.makeSet(node.ID())
+	}
+
+	var w float64
+	for _, e := range edges {
+		if s1, s2 := ds.find(e.From().ID()), ds.find(e.To().ID()); s1 != s2 {
+			ds.union(s1, s2)
+			dst.SetWeightedEdge(g.WeightedEdge(e.From(), e.To()))
+			w += e.Weight()
+		}
+	}
+	return w
+}
+
+type byWeight []graph.WeightedEdge
+
+func (e byWeight) Len() int           { return len(e) }
+func (e byWeight) Less(i, j int) bool { return e[i].Weight() < e[j].Weight() }
+func (e byWeight) Swap(i, j int)      { e[i], e[j] = e[j], e[i] }
diff --git a/vendor/gonum.org/v1/gonum/graph/path/spanning_tree_test.go b/vendor/gonum.org/v1/gonum/graph/path/spanning_tree_test.go
new file mode 100644
index 00000000..e6515335
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/spanning_tree_test.go
@@ -0,0 +1,294 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package path
+
+import (
+	"fmt"
+	"math"
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+func init() {
+	for _, test := range spanningTreeTests {
+		var w float64
+		for _, e := range test.treeEdges {
+			w += e.W
+		}
+		if w != test.want {
+			panic(fmt.Sprintf("bad test: %s weight mismatch: %v != %v", test.name, w, test.want))
+		}
+	}
+}
+
+type spanningGraph interface {
+	graph.WeightedBuilder
+	graph.WeightedUndirected
+	WeightedEdges() []graph.WeightedEdge
+}
+
+var spanningTreeTests = []struct {
+	name      string
+	graph     func() spanningGraph
+	edges     []simple.WeightedEdge
+	want      float64
+	treeEdges []simple.WeightedEdge
+}{
+	{
+		name:  "Empty",
+		graph: func() spanningGraph { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
+		want:  0,
+	},
+	{
+		// https://upload.wikimedia.org/wikipedia/commons/f/f7/Prim%27s_algorithm.svg
+		// Modified to make edge weights unique; A--B is increased to 2.5 otherwise
+		// to prevent the alternative solution being found.
+		name:  "Prim WP figure 1",
+		graph: func() spanningGraph { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
+		edges: []simple.WeightedEdge{
+			{F: simple.Node('A'), T: simple.Node('B'), W: 2.5},
+			{F: simple.Node('A'), T: simple.Node('D'), W: 1},
+			{F: simple.Node('B'), T: simple.Node('D'), W: 2},
+			{F: simple.Node('C'), T: simple.Node('D'), W: 3},
+		},
+
+		want: 6,
+		treeEdges: []simple.WeightedEdge{
+			{F: simple.Node('A'), T: simple.Node('D'), W: 1},
+			{F: simple.Node('B'), T: simple.Node('D'), W: 2},
+			{F: simple.Node('C'), T: simple.Node('D'), W: 3},
+		},
+	},
+	{
+		// https://upload.wikimedia.org/wikipedia/commons/5/5c/MST_kruskal_en.gif
+		name:  "Kruskal WP figure 1",
+		graph: func() spanningGraph { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
+		edges: []simple.WeightedEdge{
+			{F: simple.Node('a'), T: simple.Node('b'), W: 3},
+			{F: simple.Node('a'), T: simple.Node('e'), W: 1},
+			{F: simple.Node('b'), T: simple.Node('c'), W: 5},
+			{F: simple.Node('b'), T: simple.Node('e'), W: 4},
+			{F: simple.Node('c'), T: simple.Node('d'), W: 2},
+			{F: simple.Node('c'), T: simple.Node('e'), W: 6},
+			{F: simple.Node('d'), T: simple.Node('e'), W: 7},
+		},
+
+		want: 11,
+		treeEdges: []simple.WeightedEdge{
+			{F: simple.Node('a'), T: simple.Node('b'), W: 3},
+			{F: simple.Node('a'), T: simple.Node('e'), W: 1},
+			{F: simple.Node('b'), T: simple.Node('c'), W: 5},
+			{F: simple.Node('c'), T: simple.Node('d'), W: 2},
+		},
+	},
+	{
+		// https://upload.wikimedia.org/wikipedia/commons/8/87/Kruskal_Algorithm_6.svg
+		name:  "Kruskal WP example",
+		graph: func() spanningGraph { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
+		edges: []simple.WeightedEdge{
+			{F: simple.Node('A'), T: simple.Node('B'), W: 7},
+			{F: simple.Node('A'), T: simple.Node('D'), W: 5},
+			{F: simple.Node('B'), T: simple.Node('C'), W: 8},
+			{F: simple.Node('B'), T: simple.Node('D'), W: 9},
+			{F: simple.Node('B'), T: simple.Node('E'), W: 7},
+			{F: simple.Node('C'), T: simple.Node('E'), W: 5},
+			{F: simple.Node('D'), T: simple.Node('E'), W: 15},
+			{F: simple.Node('D'), T: simple.Node('F'), W: 6},
+			{F: simple.Node('E'), T: simple.Node('F'), W: 8},
+			{F: simple.Node('E'), T: simple.Node('G'), W: 9},
+			{F: simple.Node('F'), T: simple.Node('G'), W: 11},
+		},
+
+		want: 39,
+		treeEdges: []simple.WeightedEdge{
+			{F: simple.Node('A'), T: simple.Node('B'), W: 7},
+			{F: simple.Node('A'), T: simple.Node('D'), W: 5},
+			{F: simple.Node('B'), T: simple.Node('E'), W: 7},
+			{F: simple.Node('C'), T: simple.Node('E'), W: 5},
+			{F: simple.Node('D'), T: simple.Node('F'), W: 6},
+			{F: simple.Node('E'), T: simple.Node('G'), W: 9},
+		},
+	},
+	{
+		// https://upload.wikimedia.org/wikipedia/commons/2/2e/Boruvka%27s_algorithm_%28Sollin%27s_algorithm%29_Anim.gif
+		name:  "Borůvka WP example",
+		graph: func() spanningGraph { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
+		edges: []simple.WeightedEdge{
+			{F: simple.Node('A'), T: simple.Node('B'), W: 13},
+			{F: simple.Node('A'), T: simple.Node('C'), W: 6},
+			{F: simple.Node('B'), T: simple.Node('C'), W: 7},
+			{F: simple.Node('B'), T: simple.Node('D'), W: 1},
+			{F: simple.Node('C'), T: simple.Node('D'), W: 14},
+			{F: simple.Node('C'), T: simple.Node('E'), W: 8},
+			{F: simple.Node('C'), T: simple.Node('H'), W: 20},
+			{F: simple.Node('D'), T: simple.Node('E'), W: 9},
+			{F: simple.Node('D'), T: simple.Node('F'), W: 3},
+			{F: simple.Node('E'), T: simple.Node('F'), W: 2},
+			{F: simple.Node('E'), T: simple.Node('J'), W: 18},
+			{F: simple.Node('G'), T: simple.Node('H'), W: 15},
+			{F: simple.Node('G'), T: simple.Node('I'), W: 5},
+			{F: simple.Node('G'), T: simple.Node('J'), W: 19},
+			{F: simple.Node('G'), T: simple.Node('K'), W: 10},
+			{F: simple.Node('H'), T: simple.Node('J'), W: 17},
+			{F: simple.Node('I'), T: simple.Node('K'), W: 11},
+			{F: simple.Node('J'), T: simple.Node('K'), W: 16},
+			{F: simple.Node('J'), T: simple.Node('L'), W: 4},
+			{F: simple.Node('K'), T: simple.Node('L'), W: 12},
+		},
+
+		want: 83,
+		treeEdges: []simple.WeightedEdge{
+			{F: simple.Node('A'), T: simple.Node('C'), W: 6},
+			{F: simple.Node('B'), T: simple.Node('C'), W: 7},
+			{F: simple.Node('B'), T: simple.Node('D'), W: 1},
+			{F: simple.Node('D'), T: simple.Node('F'), W: 3},
+			{F: simple.Node('E'), T: simple.Node('F'), W: 2},
+			{F: simple.Node('E'), T: simple.Node('J'), W: 18},
+			{F: simple.Node('G'), T: simple.Node('H'), W: 15},
+			{F: simple.Node('G'), T: simple.Node('I'), W: 5},
+			{F: simple.Node('G'), T: simple.Node('K'), W: 10},
+			{F: simple.Node('J'), T: simple.Node('L'), W: 4},
+			{F: simple.Node('K'), T: simple.Node('L'), W: 12},
+		},
+	},
+	{
+		// https://upload.wikimedia.org/wikipedia/commons/d/d2/Minimum_spanning_tree.svg
+		// Nodes labelled row major.
+		name:  "Minimum Spanning Tree WP figure 1",
+		graph: func() spanningGraph { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
+		edges: []simple.WeightedEdge{
+			{F: simple.Node(1), T: simple.Node(2), W: 4},
+			{F: simple.Node(1), T: simple.Node(3), W: 1},
+			{F: simple.Node(1), T: simple.Node(4), W: 4},
+			{F: simple.Node(2), T: simple.Node(3), W: 5},
+			{F: simple.Node(2), T: simple.Node(5), W: 9},
+			{F: simple.Node(2), T: simple.Node(6), W: 9},
+			{F: simple.Node(2), T: simple.Node(8), W: 7},
+			{F: simple.Node(3), T: simple.Node(4), W: 3},
+			{F: simple.Node(3), T: simple.Node(8), W: 9},
+			{F: simple.Node(4), T: simple.Node(8), W: 10},
+			{F: simple.Node(4), T: simple.Node(10), W: 18},
+			{F: simple.Node(5), T: simple.Node(6), W: 2},
+			{F: simple.Node(5), T: simple.Node(7), W: 4},
+			{F: simple.Node(5), T: simple.Node(9), W: 6},
+			{F: simple.Node(6), T: simple.Node(7), W: 2},
+			{F: simple.Node(6), T: simple.Node(8), W: 8},
+			{F: simple.Node(7), T: simple.Node(8), W: 9},
+			{F: simple.Node(7), T: simple.Node(9), W: 3},
+			{F: simple.Node(7), T: simple.Node(10), W: 9},
+			{F: simple.Node(8), T: simple.Node(10), W: 8},
+			{F: simple.Node(9), T: simple.Node(10), W: 9},
+		},
+
+		want: 38,
+		treeEdges: []simple.WeightedEdge{
+			{F: simple.Node(1), T: simple.Node(2), W: 4},
+			{F: simple.Node(1), T: simple.Node(3), W: 1},
+			{F: simple.Node(2), T: simple.Node(8), W: 7},
+			{F: simple.Node(3), T: simple.Node(4), W: 3},
+			{F: simple.Node(5), T: simple.Node(6), W: 2},
+			{F: simple.Node(6), T: simple.Node(7), W: 2},
+			{F: simple.Node(6), T: simple.Node(8), W: 8},
+			{F: simple.Node(7), T: simple.Node(9), W: 3},
+			{F: simple.Node(8), T: simple.Node(10), W: 8},
+		},
+	},
+
+	{
+		// https://upload.wikimedia.org/wikipedia/commons/2/2e/Boruvka%27s_algorithm_%28Sollin%27s_algorithm%29_Anim.gif
+		// but with C--H and E--J cut.
+		name:  "Borůvka WP example cut",
+		graph: func() spanningGraph { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
+		edges: []simple.WeightedEdge{
+			{F: simple.Node('A'), T: simple.Node('B'), W: 13},
+			{F: simple.Node('A'), T: simple.Node('C'), W: 6},
+			{F: simple.Node('B'), T: simple.Node('C'), W: 7},
+			{F: simple.Node('B'), T: simple.Node('D'), W: 1},
+			{F: simple.Node('C'), T: simple.Node('D'), W: 14},
+			{F: simple.Node('C'), T: simple.Node('E'), W: 8},
+			{F: simple.Node('D'), T: simple.Node('E'), W: 9},
+			{F: simple.Node('D'), T: simple.Node('F'), W: 3},
+			{F: simple.Node('E'), T: simple.Node('F'), W: 2},
+			{F: simple.Node('G'), T: simple.Node('H'), W: 15},
+			{F: simple.Node('G'), T: simple.Node('I'), W: 5},
+			{F: simple.Node('G'), T: simple.Node('J'), W: 19},
+			{F: simple.Node('G'), T: simple.Node('K'), W: 10},
+			{F: simple.Node('H'), T: simple.Node('J'), W: 17},
+			{F: simple.Node('I'), T: simple.Node('K'), W: 11},
+			{F: simple.Node('J'), T: simple.Node('K'), W: 16},
+			{F: simple.Node('J'), T: simple.Node('L'), W: 4},
+			{F: simple.Node('K'), T: simple.Node('L'), W: 12},
+		},
+
+		want: 65,
+		treeEdges: []simple.WeightedEdge{
+			{F: simple.Node('A'), T: simple.Node('C'), W: 6},
+			{F: simple.Node('B'), T: simple.Node('C'), W: 7},
+			{F: simple.Node('B'), T: simple.Node('D'), W: 1},
+			{F: simple.Node('D'), T: simple.Node('F'), W: 3},
+			{F: simple.Node('E'), T: simple.Node('F'), W: 2},
+			{F: simple.Node('G'), T: simple.Node('H'), W: 15},
+			{F: simple.Node('G'), T: simple.Node('I'), W: 5},
+			{F: simple.Node('G'), T: simple.Node('K'), W: 10},
+			{F: simple.Node('J'), T: simple.Node('L'), W: 4},
+			{F: simple.Node('K'), T: simple.Node('L'), W: 12},
+		},
+	},
+}
+
+func testMinumumSpanning(mst func(dst WeightedBuilder, g spanningGraph) float64, t *testing.T) {
+	for _, test := range spanningTreeTests {
+		g := test.graph()
+		for _, e := range test.edges {
+			g.SetWeightedEdge(e)
+		}
+
+		dst := simple.NewWeightedUndirectedGraph(0, math.Inf(1))
+		w := mst(dst, g)
+		if w != test.want {
+			t.Errorf("unexpected minimum spanning tree weight for %q: got: %f want: %f",
+				test.name, w, test.want)
+		}
+		var got float64
+		for _, e := range dst.WeightedEdges() {
+			got += e.Weight()
+		}
+		if got != test.want {
+			t.Errorf("unexpected minimum spanning tree edge weight sum for %q: got: %f want: %f",
+				test.name, got, test.want)
+		}
+
+		gotEdges := dst.Edges()
+		if len(gotEdges) != len(test.treeEdges) {
+			t.Errorf("unexpected number of spanning tree edges for %q: got: %d want: %d",
+				test.name, len(gotEdges), len(test.treeEdges))
+		}
+		for _, e := range test.treeEdges {
+			w, ok := dst.Weight(e.From(), e.To())
+			if !ok {
+				t.Errorf("spanning tree edge not found in graph for %q: %+v",
+					test.name, e)
+			}
+			if w != e.Weight() {
+				t.Errorf("unexpected spanning tree edge weight for %q: got: %f want: %f",
+					test.name, w, e.Weight())
+			}
+		}
+	}
+}
+
+func TestKruskal(t *testing.T) {
+	testMinumumSpanning(func(dst WeightedBuilder, g spanningGraph) float64 {
+		return Kruskal(dst, g)
+	}, t)
+}
+
+func TestPrim(t *testing.T) {
+	testMinumumSpanning(func(dst WeightedBuilder, g spanningGraph) float64 {
+		return Prim(dst, g)
+	}, t)
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/path/weight.go b/vendor/gonum.org/v1/gonum/graph/path/weight.go
new file mode 100644
index 00000000..91b9d321
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/path/weight.go
@@ -0,0 +1,40 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package path
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/graph"
+)
+
+// Weighting is a mapping between a pair of nodes and a weight. It follows the
+// semantics of the Weighter interface.
+type Weighting func(x, y graph.Node) (w float64, ok bool)
+
+// UniformCost returns a Weighting that returns an edge cost of 1 for existing
+// edges, zero for node identity and Inf for otherwise absent edges.
+func UniformCost(g graph.Graph) Weighting {
+	return func(x, y graph.Node) (w float64, ok bool) {
+		xid := x.ID()
+		yid := y.ID()
+		if xid == yid {
+			return 0, true
+		}
+		if e := g.Edge(x, y); e != nil {
+			return 1, true
+		}
+		return math.Inf(1), false
+	}
+}
+
+// Heuristic returns an estimate of the cost of travelling between two nodes.
+type Heuristic func(x, y graph.Node) float64
+
+// HeuristicCoster wraps the HeuristicCost method. A graph implementing the
+// interface provides a heuristic between any two given nodes.
+type HeuristicCoster interface {
+	HeuristicCost(x, y graph.Node) float64
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/simple/dense_directed_matrix.go b/vendor/gonum.org/v1/gonum/graph/simple/dense_directed_matrix.go
new file mode 100644
index 00000000..b6db362d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/simple/dense_directed_matrix.go
@@ -0,0 +1,300 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package simple
+
+import (
+	"sort"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/ordered"
+	"gonum.org/v1/gonum/mat"
+)
+
+// DirectedMatrix represents a directed graph using an adjacency
+// matrix such that all IDs are in a contiguous block from 0 to n-1.
+// Edges are stored implicitly as an edge weight, so edges stored in
+// the graph are not recoverable.
+type DirectedMatrix struct {
+	mat   *mat.Dense
+	nodes []graph.Node
+
+	self   float64
+	absent float64
+}
+
+// NewDirectedMatrix creates a directed dense graph with n nodes.
+// All edges are initialized with the weight given by init. The self parameter
+// specifies the cost of self connection, and absent specifies the weight
+// returned for absent edges.
+func NewDirectedMatrix(n int, init, self, absent float64) *DirectedMatrix {
+	matrix := make([]float64, n*n)
+	if init != 0 {
+		for i := range matrix {
+			matrix[i] = init
+		}
+	}
+	for i := 0; i < len(matrix); i += n + 1 {
+		matrix[i] = self
+	}
+	return &DirectedMatrix{
+		mat:    mat.NewDense(n, n, matrix),
+		self:   self,
+		absent: absent,
+	}
+}
+
+// NewDirectedMatrixFrom creates a directed dense graph with the given nodes.
+// The IDs of the nodes must be contiguous from 0 to len(nodes)-1, but may
+// be in any order. If IDs are not contiguous NewDirectedMatrixFrom will panic.
+// All edges are initialized with the weight given by init. The self parameter
+// specifies the cost of self connection, and absent specifies the weight
+// returned for absent edges.
+func NewDirectedMatrixFrom(nodes []graph.Node, init, self, absent float64) *DirectedMatrix {
+	sort.Sort(ordered.ByID(nodes))
+	for i, n := range nodes {
+		if int64(i) != n.ID() {
+			panic("simple: non-contiguous node IDs")
+		}
+	}
+	g := NewDirectedMatrix(len(nodes), init, self, absent)
+	g.nodes = nodes
+	return g
+}
+
+// Node returns the node in the graph with the given ID.
+func (g *DirectedMatrix) Node(id int64) graph.Node {
+	if !g.has(id) {
+		return nil
+	}
+	if g.nodes == nil {
+		return Node(id)
+	}
+	return g.nodes[id]
+}
+
+// Has returns whether the node exists within the graph.
+func (g *DirectedMatrix) Has(n graph.Node) bool {
+	return g.has(n.ID())
+}
+
+func (g *DirectedMatrix) has(id int64) bool {
+	r, _ := g.mat.Dims()
+	return 0 <= id && id < int64(r)
+}
+
+// Nodes returns all the nodes in the graph.
+func (g *DirectedMatrix) Nodes() []graph.Node {
+	if g.nodes != nil {
+		nodes := make([]graph.Node, len(g.nodes))
+		copy(nodes, g.nodes)
+		return nodes
+	}
+	r, _ := g.mat.Dims()
+	nodes := make([]graph.Node, r)
+	for i := 0; i < r; i++ {
+		nodes[i] = Node(i)
+	}
+	return nodes
+}
+
+// Edges returns all the edges in the graph.
+func (g *DirectedMatrix) Edges() []graph.Edge {
+	var edges []graph.Edge
+	r, _ := g.mat.Dims()
+	for i := 0; i < r; i++ {
+		for j := 0; j < r; j++ {
+			if i == j {
+				continue
+			}
+			if w := g.mat.At(i, j); !isSame(w, g.absent) {
+				edges = append(edges, WeightedEdge{F: g.Node(int64(i)), T: g.Node(int64(j)), W: w})
+			}
+		}
+	}
+	return edges
+}
+
+// From returns all nodes in g that can be reached directly from n.
+func (g *DirectedMatrix) From(n graph.Node) []graph.Node {
+	id := n.ID()
+	if !g.has(id) {
+		return nil
+	}
+	var neighbors []graph.Node
+	_, c := g.mat.Dims()
+	for j := 0; j < c; j++ {
+		if int64(j) == id {
+			continue
+		}
+		// id is not greater than maximum int by this point.
+		if !isSame(g.mat.At(int(id), j), g.absent) {
+			neighbors = append(neighbors, g.Node(int64(j)))
+		}
+	}
+	return neighbors
+}
+
+// To returns all nodes in g that can reach directly to n.
+func (g *DirectedMatrix) To(n graph.Node) []graph.Node {
+	id := n.ID()
+	if !g.has(id) {
+		return nil
+	}
+	var neighbors []graph.Node
+	r, _ := g.mat.Dims()
+	for i := 0; i < r; i++ {
+		if int64(i) == id {
+			continue
+		}
+		// id is not greater than maximum int by this point.
+		if !isSame(g.mat.At(i, int(id)), g.absent) {
+			neighbors = append(neighbors, g.Node(int64(i)))
+		}
+	}
+	return neighbors
+}
+
+// HasEdgeBetween returns whether an edge exists between nodes x and y without
+// considering direction.
+func (g *DirectedMatrix) HasEdgeBetween(x, y graph.Node) bool {
+	xid := x.ID()
+	if !g.has(xid) {
+		return false
+	}
+	yid := y.ID()
+	if !g.has(yid) {
+		return false
+	}
+	// xid and yid are not greater than maximum int by this point.
+	return xid != yid && (!isSame(g.mat.At(int(xid), int(yid)), g.absent) || !isSame(g.mat.At(int(yid), int(xid)), g.absent))
+}
+
+// Edge returns the edge from u to v if such an edge exists and nil otherwise.
+// The node v must be directly reachable from u as defined by the From method.
+func (g *DirectedMatrix) Edge(u, v graph.Node) graph.Edge {
+	return g.WeightedEdge(u, v)
+}
+
+// WeightedEdge returns the weighted edge from u to v if such an edge exists and nil otherwise.
+// The node v must be directly reachable from u as defined by the From method.
+func (g *DirectedMatrix) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
+	if g.HasEdgeFromTo(u, v) {
+		// x.ID() and y.ID() are not greater than maximum int by this point.
+		return WeightedEdge{F: g.Node(u.ID()), T: g.Node(v.ID()), W: g.mat.At(int(u.ID()), int(v.ID()))}
+	}
+	return nil
+}
+
+// HasEdgeFromTo returns whether an edge exists in the graph from u to v.
+func (g *DirectedMatrix) HasEdgeFromTo(u, v graph.Node) bool {
+	uid := u.ID()
+	if !g.has(uid) {
+		return false
+	}
+	vid := v.ID()
+	if !g.has(vid) {
+		return false
+	}
+	// uid and vid are not greater than maximum int by this point.
+	return uid != vid && !isSame(g.mat.At(int(uid), int(vid)), g.absent)
+}
+
+// Weight returns the weight for the edge between x and y if Edge(x, y) returns a non-nil Edge.
+// If x and y are the same node or there is no joining edge between the two nodes the weight
+// value returned is either the graph's absent or self value. Weight returns true if an edge
+// exists between x and y or if x and y have the same ID, false otherwise.
+func (g *DirectedMatrix) Weight(x, y graph.Node) (w float64, ok bool) {
+	xid := x.ID()
+	yid := y.ID()
+	if xid == yid {
+		return g.self, true
+	}
+	if g.has(xid) && g.has(yid) {
+		// xid and yid are not greater than maximum int by this point.
+		return g.mat.At(int(xid), int(yid)), true
+	}
+	return g.absent, false
+}
+
+// SetEdge sets e, an edge from one node to another with unit weight. If the ends of the edge
+// are not in g or the edge is a self loop, SetEdge panics.
+func (g *DirectedMatrix) SetEdge(e graph.Edge) {
+	g.setWeightedEdge(e, 1)
+}
+
+// SetWeightedEdge sets e, an edge from one node to another. If the ends of the edge are not in g
+// or the edge is a self loop, SetWeightedEdge panics.
+func (g *DirectedMatrix) SetWeightedEdge(e graph.WeightedEdge) {
+	g.setWeightedEdge(e, e.Weight())
+}
+
+func (g *DirectedMatrix) setWeightedEdge(e graph.Edge, weight float64) {
+	fid := e.From().ID()
+	tid := e.To().ID()
+	if fid == tid {
+		panic("simple: set illegal edge")
+	}
+	if int64(int(fid)) != fid {
+		panic("simple: unavailable from node ID for dense graph")
+	}
+	if int64(int(tid)) != tid {
+		panic("simple: unavailable to node ID for dense graph")
+	}
+	// fid and tid are not greater than maximum int by this point.
+	g.mat.Set(int(fid), int(tid), weight)
+}
+
+// RemoveEdge removes e from the graph, leaving the terminal nodes. If the edge does not exist
+// it is a no-op.
+func (g *DirectedMatrix) RemoveEdge(e graph.Edge) {
+	fid := e.From().ID()
+	if !g.has(fid) {
+		return
+	}
+	tid := e.To().ID()
+	if !g.has(tid) {
+		return
+	}
+	// fid and tid are not greater than maximum int by this point.
+	g.mat.Set(int(fid), int(tid), g.absent)
+}
+
+// Degree returns the in+out degree of n in g.
+func (g *DirectedMatrix) Degree(n graph.Node) int {
+	id := n.ID()
+	if !g.has(id) {
+		return 0
+	}
+	var deg int
+	r, c := g.mat.Dims()
+	for i := 0; i < r; i++ {
+		if int64(i) == id {
+			continue
+		}
+		// id is not greater than maximum int by this point.
+		if !isSame(g.mat.At(int(id), i), g.absent) {
+			deg++
+		}
+	}
+	for i := 0; i < c; i++ {
+		if int64(i) == id {
+			continue
+		}
+		// id is not greater than maximum int by this point.
+		if !isSame(g.mat.At(i, int(id)), g.absent) {
+			deg++
+		}
+	}
+	return deg
+}
+
+// Matrix returns the mat.Matrix representation of the graph. The orientation
+// of the matrix is such that the matrix entry at G_{ij} is the weight of the edge
+// from node i to node j.
+func (g *DirectedMatrix) Matrix() mat.Matrix {
+	// Prevent alteration of dimensions of the returned matrix.
+	m := *g.mat
+	return &m
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/simple/dense_undirected_matrix.go b/vendor/gonum.org/v1/gonum/graph/simple/dense_undirected_matrix.go
new file mode 100644
index 00000000..da4cb4f3
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/simple/dense_undirected_matrix.go
@@ -0,0 +1,261 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package simple
+
+import (
+	"sort"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/ordered"
+	"gonum.org/v1/gonum/mat"
+)
+
+// UndirectedMatrix represents an undirected graph using an adjacency
+// matrix such that all IDs are in a contiguous block from 0 to n-1.
+// Edges are stored implicitly as an edge weight, so edges stored in
+// the graph are not recoverable.
+type UndirectedMatrix struct {
+	mat   *mat.SymDense
+	nodes []graph.Node
+
+	self   float64
+	absent float64
+}
+
+// NewUndirectedMatrix creates an undirected dense graph with n nodes.
+// All edges are initialized with the weight given by init. The self parameter
+// specifies the cost of self connection, and absent specifies the weight
+// returned for absent edges.
+func NewUndirectedMatrix(n int, init, self, absent float64) *UndirectedMatrix {
+	matrix := make([]float64, n*n)
+	if init != 0 {
+		for i := range matrix {
+			matrix[i] = init
+		}
+	}
+	for i := 0; i < len(matrix); i += n + 1 {
+		matrix[i] = self
+	}
+	return &UndirectedMatrix{
+		mat:    mat.NewSymDense(n, matrix),
+		self:   self,
+		absent: absent,
+	}
+}
+
+// NewUndirectedMatrixFrom creates an undirected dense graph with the given nodes.
+// The IDs of the nodes must be contiguous from 0 to len(nodes)-1, but may
+// be in any order. If IDs are not contiguous NewUndirectedMatrixFrom will panic.
+// All edges are initialized with the weight given by init. The self parameter
+// specifies the cost of self connection, and absent specifies the weight
+// returned for absent edges.
+func NewUndirectedMatrixFrom(nodes []graph.Node, init, self, absent float64) *UndirectedMatrix {
+	sort.Sort(ordered.ByID(nodes))
+	for i, n := range nodes {
+		if int64(i) != n.ID() {
+			panic("simple: non-contiguous node IDs")
+		}
+	}
+	g := NewUndirectedMatrix(len(nodes), init, self, absent)
+	g.nodes = nodes
+	return g
+}
+
+// Node returns the node in the graph with the given ID.
+func (g *UndirectedMatrix) Node(id int64) graph.Node {
+	if !g.has(id) {
+		return nil
+	}
+	if g.nodes == nil {
+		return Node(id)
+	}
+	return g.nodes[id]
+}
+
+// Has returns whether the node exists within the graph.
+func (g *UndirectedMatrix) Has(n graph.Node) bool {
+	return g.has(n.ID())
+}
+
+func (g *UndirectedMatrix) has(id int64) bool {
+	r := g.mat.Symmetric()
+	return 0 <= id && id < int64(r)
+}
+
+// Nodes returns all the nodes in the graph.
+func (g *UndirectedMatrix) Nodes() []graph.Node {
+	if g.nodes != nil {
+		nodes := make([]graph.Node, len(g.nodes))
+		copy(nodes, g.nodes)
+		return nodes
+	}
+	r := g.mat.Symmetric()
+	nodes := make([]graph.Node, r)
+	for i := 0; i < r; i++ {
+		nodes[i] = Node(i)
+	}
+	return nodes
+}
+
+// Edges returns all the edges in the graph.
+func (g *UndirectedMatrix) Edges() []graph.Edge {
+	var edges []graph.Edge
+	r, _ := g.mat.Dims()
+	for i := 0; i < r; i++ {
+		for j := i + 1; j < r; j++ {
+			if w := g.mat.At(i, j); !isSame(w, g.absent) {
+				edges = append(edges, WeightedEdge{F: g.Node(int64(i)), T: g.Node(int64(j)), W: w})
+			}
+		}
+	}
+	return edges
+}
+
+// From returns all nodes in g that can be reached directly from n.
+func (g *UndirectedMatrix) From(n graph.Node) []graph.Node {
+	id := n.ID()
+	if !g.has(id) {
+		return nil
+	}
+	var neighbors []graph.Node
+	r := g.mat.Symmetric()
+	for i := 0; i < r; i++ {
+		if int64(i) == id {
+			continue
+		}
+		// id is not greater than maximum int by this point.
+		if !isSame(g.mat.At(int(id), i), g.absent) {
+			neighbors = append(neighbors, g.Node(int64(i)))
+		}
+	}
+	return neighbors
+}
+
+// HasEdgeBetween returns whether an edge exists between nodes x and y.
+func (g *UndirectedMatrix) HasEdgeBetween(u, v graph.Node) bool {
+	uid := u.ID()
+	if !g.has(uid) {
+		return false
+	}
+	vid := v.ID()
+	if !g.has(vid) {
+		return false
+	}
+	// uid and vid are not greater than maximum int by this point.
+	return uid != vid && !isSame(g.mat.At(int(uid), int(vid)), g.absent)
+}
+
+// Edge returns the edge from u to v if such an edge exists and nil otherwise.
+// The node v must be directly reachable from u as defined by the From method.
+func (g *UndirectedMatrix) Edge(u, v graph.Node) graph.Edge {
+	return g.WeightedEdgeBetween(u, v)
+}
+
+// WeightedEdge returns the weighted edge from u to v if such an edge exists and nil otherwise.
+// The node v must be directly reachable from u as defined by the From method.
+func (g *UndirectedMatrix) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
+	return g.WeightedEdgeBetween(u, v)
+}
+
+// EdgeBetween returns the edge between nodes x and y.
+func (g *UndirectedMatrix) EdgeBetween(u, v graph.Node) graph.Edge {
+	return g.WeightedEdgeBetween(u, v)
+}
+
+// WeightedEdgeBetween returns the weighted edge between nodes x and y.
+func (g *UndirectedMatrix) WeightedEdgeBetween(u, v graph.Node) graph.WeightedEdge {
+	if g.HasEdgeBetween(u, v) {
+		// u.ID() and v.ID() are not greater than maximum int by this point.
+		return WeightedEdge{F: g.Node(u.ID()), T: g.Node(v.ID()), W: g.mat.At(int(u.ID()), int(v.ID()))}
+	}
+	return nil
+}
+
+// Weight returns the weight for the edge between x and y if Edge(x, y) returns a non-nil Edge.
+// If x and y are the same node or there is no joining edge between the two nodes the weight
+// value returned is either the graph's absent or self value. Weight returns true if an edge
+// exists between x and y or if x and y have the same ID, false otherwise.
+func (g *UndirectedMatrix) Weight(x, y graph.Node) (w float64, ok bool) {
+	xid := x.ID()
+	yid := y.ID()
+	if xid == yid {
+		return g.self, true
+	}
+	if g.has(xid) && g.has(yid) {
+		// xid and yid are not greater than maximum int by this point.
+		return g.mat.At(int(xid), int(yid)), true
+	}
+	return g.absent, false
+}
+
+// SetEdge sets e, an edge from one node to another with unit weight. If the ends of the edge are
+// not in g or the edge is a self loop, SetEdge panics.
+func (g *UndirectedMatrix) SetEdge(e graph.Edge) {
+	g.setWeightedEdge(e, 1)
+}
+
+// SetWeightedEdge sets e, an edge from one node to another. If the ends of the edge are not in g
+// or the edge is a self loop, SetWeightedEdge panics.
+func (g *UndirectedMatrix) SetWeightedEdge(e graph.WeightedEdge) {
+	g.setWeightedEdge(e, e.Weight())
+}
+
+func (g *UndirectedMatrix) setWeightedEdge(e graph.Edge, weight float64) {
+	fid := e.From().ID()
+	tid := e.To().ID()
+	if fid == tid {
+		panic("simple: set illegal edge")
+	}
+	if int64(int(fid)) != fid {
+		panic("simple: unavailable from node ID for dense graph")
+	}
+	if int64(int(tid)) != tid {
+		panic("simple: unavailable to node ID for dense graph")
+	}
+	// fid and tid are not greater than maximum int by this point.
+	g.mat.SetSym(int(fid), int(tid), weight)
+}
+
+// RemoveEdge removes e from the graph, leaving the terminal nodes. If the edge does not exist
+// it is a no-op.
+func (g *UndirectedMatrix) RemoveEdge(e graph.Edge) {
+	fid := e.From().ID()
+	if !g.has(fid) {
+		return
+	}
+	tid := e.To().ID()
+	if !g.has(tid) {
+		return
+	}
+	// fid and tid are not greater than maximum int by this point.
+	g.mat.SetSym(int(fid), int(tid), g.absent)
+}
+
+// Degree returns the degree of n in g.
+func (g *UndirectedMatrix) Degree(n graph.Node) int {
+	id := n.ID()
+	if !g.has(id) {
+		return 0
+	}
+	var deg int
+	r := g.mat.Symmetric()
+	for i := 0; i < r; i++ {
+		if int64(i) == id {
+			continue
+		}
+		// id is not greater than maximum int by this point.
+		if !isSame(g.mat.At(int(id), i), g.absent) {
+			deg++
+		}
+	}
+	return deg
+}
+
+// Matrix returns the mat.Matrix representation of the graph.
+func (g *UndirectedMatrix) Matrix() mat.Matrix {
+	// Prevent alteration of dimensions of the returned matrix.
+	m := *g.mat
+	return &m
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/simple/densegraph_test.go b/vendor/gonum.org/v1/gonum/graph/simple/densegraph_test.go
new file mode 100644
index 00000000..5a68c219
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/simple/densegraph_test.go
@@ -0,0 +1,149 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package simple
+
+import (
+	"math"
+	"sort"
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/ordered"
+)
+
+var (
+	directedMatrix = (*DirectedMatrix)(nil)
+
+	_ graph.Graph            = directedMatrix
+	_ graph.Directed         = directedMatrix
+	_ graph.WeightedDirected = directedMatrix
+
+	undirectedMatrix = (*UndirectedMatrix)(nil)
+
+	_ graph.Graph              = undirectedMatrix
+	_ graph.Undirected         = undirectedMatrix
+	_ graph.WeightedUndirected = undirectedMatrix
+)
+
+func TestBasicDenseImpassable(t *testing.T) {
+	dg := NewUndirectedMatrix(5, math.Inf(1), 0, math.Inf(1))
+	if dg == nil {
+		t.Fatal("Directed graph could not be made")
+	}
+
+	for i := 0; i < 5; i++ {
+		if !dg.Has(Node(i)) {
+			t.Errorf("Node that should exist doesn't: %d", i)
+		}
+
+		if degree := dg.Degree(Node(i)); degree != 0 {
+			t.Errorf("Node in impassable graph has a neighbor. Node: %d Degree: %d", i, degree)
+		}
+	}
+
+	for i := 5; i < 10; i++ {
+		if dg.Has(Node(i)) {
+			t.Errorf("Node exists that shouldn't: %d", i)
+		}
+	}
+}
+
+func TestBasicDensePassable(t *testing.T) {
+	dg := NewUndirectedMatrix(5, 1, 0, math.Inf(1))
+	if dg == nil {
+		t.Fatal("Directed graph could not be made")
+	}
+
+	for i := 0; i < 5; i++ {
+		if !dg.Has(Node(i)) {
+			t.Errorf("Node that should exist doesn't: %d", i)
+		}
+
+		if degree := dg.Degree(Node(i)); degree != 4 {
+			t.Errorf("Node in passable graph missing neighbors. Node: %d Degree: %d", i, degree)
+		}
+	}
+
+	for i := 5; i < 10; i++ {
+		if dg.Has(Node(i)) {
+			t.Errorf("Node exists that shouldn't: %d", i)
+		}
+	}
+}
+
+func TestDirectedDenseAddRemove(t *testing.T) {
+	dg := NewDirectedMatrix(10, math.Inf(1), 0, math.Inf(1))
+	dg.SetWeightedEdge(WeightedEdge{F: Node(0), T: Node(2), W: 1})
+
+	if neighbors := dg.From(Node(0)); len(neighbors) != 1 || neighbors[0].ID() != 2 ||
+		dg.Edge(Node(0), Node(2)) == nil {
+		t.Errorf("Adding edge didn't create successor")
+	}
+
+	dg.RemoveEdge(Edge{F: Node(0), T: Node(2)})
+
+	if neighbors := dg.From(Node(0)); len(neighbors) != 0 || dg.Edge(Node(0), Node(2)) != nil {
+		t.Errorf("Removing edge didn't properly remove successor")
+	}
+
+	if neighbors := dg.To(Node(2)); len(neighbors) != 0 || dg.Edge(Node(0), Node(2)) != nil {
+		t.Errorf("Removing directed edge wrongly kept predecessor")
+	}
+
+	dg.SetWeightedEdge(WeightedEdge{F: Node(0), T: Node(2), W: 2})
+	// I figure we've torture tested From/To at this point
+	// so we'll just use the bool functions now
+	if dg.Edge(Node(0), Node(2)) == nil {
+		t.Fatal("Adding directed edge didn't change successor back")
+	}
+	c1, _ := dg.Weight(Node(2), Node(0))
+	c2, _ := dg.Weight(Node(0), Node(2))
+	if c1 == c2 {
+		t.Error("Adding directed edge affected cost in undirected manner")
+	}
+}
+
+func TestUndirectedDenseAddRemove(t *testing.T) {
+	dg := NewUndirectedMatrix(10, math.Inf(1), 0, math.Inf(1))
+	dg.SetEdge(Edge{F: Node(0), T: Node(2)})
+
+	if neighbors := dg.From(Node(0)); len(neighbors) != 1 || neighbors[0].ID() != 2 ||
+		dg.EdgeBetween(Node(0), Node(2)) == nil {
+		t.Errorf("Couldn't add neighbor")
+	}
+
+	if neighbors := dg.From(Node(2)); len(neighbors) != 1 || neighbors[0].ID() != 0 ||
+		dg.EdgeBetween(Node(2), Node(0)) == nil {
+		t.Errorf("Adding an undirected neighbor didn't add it reciprocally")
+	}
+}
+
+func TestDenseLists(t *testing.T) {
+	dg := NewDirectedMatrix(15, 1, 0, math.Inf(1))
+	nodes := dg.Nodes()
+
+	if len(nodes) != 15 {
+		t.Fatalf("Wrong number of nodes")
+	}
+
+	sort.Sort(ordered.ByID(nodes))
+
+	for i, node := range dg.Nodes() {
+		if int64(i) != node.ID() {
+			t.Errorf("Node list doesn't return properly id'd nodes")
+		}
+	}
+
+	edges := dg.Edges()
+	if len(edges) != 15*14 {
+		t.Errorf("Improper number of edges for passable dense graph")
+	}
+
+	dg.RemoveEdge(Edge{F: Node(12), T: Node(11)})
+	edges = dg.Edges()
+	if len(edges) != (15*14)-1 {
+		t.Errorf("Removing edge didn't affect edge listing properly")
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/simple/directed.go b/vendor/gonum.org/v1/gonum/graph/simple/directed.go
new file mode 100644
index 00000000..0796cb13
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/simple/directed.go
@@ -0,0 +1,245 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package simple
+
+import (
+	"fmt"
+
+	"gonum.org/v1/gonum/graph"
+)
+
+// DirectedGraph implements a generalized directed graph.
+type DirectedGraph struct {
+	nodes map[int64]graph.Node
+	from  map[int64]map[int64]graph.Edge
+	to    map[int64]map[int64]graph.Edge
+
+	nodeIDs idSet
+}
+
+// NewDirectedGraph returns a DirectedGraph with the specified self and absent
+// edge weight values.
+func NewDirectedGraph() *DirectedGraph {
+	return &DirectedGraph{
+		nodes: make(map[int64]graph.Node),
+		from:  make(map[int64]map[int64]graph.Edge),
+		to:    make(map[int64]map[int64]graph.Edge),
+
+		nodeIDs: newIDSet(),
+	}
+}
+
+// NewNode returns a new unique Node to be added to g. The Node's ID does
+// not become valid in g until the Node is added to g.
+func (g *DirectedGraph) NewNode() graph.Node {
+	if len(g.nodes) == 0 {
+		return Node(0)
+	}
+	if int64(len(g.nodes)) == maxInt {
+		panic("simple: cannot allocate node: no slot")
+	}
+	return Node(g.nodeIDs.newID())
+}
+
+// AddNode adds n to the graph. It panics if the added node ID matches an existing node ID.
+func (g *DirectedGraph) AddNode(n graph.Node) {
+	if _, exists := g.nodes[n.ID()]; exists {
+		panic(fmt.Sprintf("simple: node ID collision: %d", n.ID()))
+	}
+	g.nodes[n.ID()] = n
+	g.from[n.ID()] = make(map[int64]graph.Edge)
+	g.to[n.ID()] = make(map[int64]graph.Edge)
+	g.nodeIDs.use(n.ID())
+}
+
+// RemoveNode removes n from the graph, as well as any edges attached to it. If the node
+// is not in the graph it is a no-op.
+func (g *DirectedGraph) RemoveNode(n graph.Node) {
+	if _, ok := g.nodes[n.ID()]; !ok {
+		return
+	}
+	delete(g.nodes, n.ID())
+
+	for from := range g.from[n.ID()] {
+		delete(g.to[from], n.ID())
+	}
+	delete(g.from, n.ID())
+
+	for to := range g.to[n.ID()] {
+		delete(g.from[to], n.ID())
+	}
+	delete(g.to, n.ID())
+
+	g.nodeIDs.release(n.ID())
+}
+
+// NewEdge returns a new Edge from the source to the destination node.
+func (g *DirectedGraph) NewEdge(from, to graph.Node) graph.Edge {
+	return &Edge{F: from, T: to}
+}
+
+// SetEdge adds e, an edge from one node to another. If the nodes do not exist, they are added.
+// It will panic if the IDs of the e.From and e.To are equal.
+func (g *DirectedGraph) SetEdge(e graph.Edge) {
+	var (
+		from = e.From()
+		fid  = from.ID()
+		to   = e.To()
+		tid  = to.ID()
+	)
+
+	if fid == tid {
+		panic("simple: adding self edge")
+	}
+
+	if !g.Has(from) {
+		g.AddNode(from)
+	}
+	if !g.Has(to) {
+		g.AddNode(to)
+	}
+
+	g.from[fid][tid] = e
+	g.to[tid][fid] = e
+}
+
+// RemoveEdge removes e from the graph, leaving the terminal nodes. If the edge does not exist
+// it is a no-op.
+func (g *DirectedGraph) RemoveEdge(e graph.Edge) {
+	from, to := e.From(), e.To()
+	if _, ok := g.nodes[from.ID()]; !ok {
+		return
+	}
+	if _, ok := g.nodes[to.ID()]; !ok {
+		return
+	}
+
+	delete(g.from[from.ID()], to.ID())
+	delete(g.to[to.ID()], from.ID())
+}
+
+// Node returns the node in the graph with the given ID.
+func (g *DirectedGraph) Node(id int64) graph.Node {
+	return g.nodes[id]
+}
+
+// Has returns whether the node exists within the graph.
+func (g *DirectedGraph) Has(n graph.Node) bool {
+	_, ok := g.nodes[n.ID()]
+
+	return ok
+}
+
+// Nodes returns all the nodes in the graph.
+func (g *DirectedGraph) Nodes() []graph.Node {
+	nodes := make([]graph.Node, len(g.from))
+	i := 0
+	for _, n := range g.nodes {
+		nodes[i] = n
+		i++
+	}
+
+	return nodes
+}
+
+// Edges returns all the edges in the graph.
+func (g *DirectedGraph) Edges() []graph.Edge {
+	var edges []graph.Edge
+	for _, u := range g.nodes {
+		for _, e := range g.from[u.ID()] {
+			edges = append(edges, e)
+		}
+	}
+	return edges
+}
+
+// From returns all nodes in g that can be reached directly from n.
+func (g *DirectedGraph) From(n graph.Node) []graph.Node {
+	if _, ok := g.from[n.ID()]; !ok {
+		return nil
+	}
+
+	from := make([]graph.Node, len(g.from[n.ID()]))
+	i := 0
+	for id := range g.from[n.ID()] {
+		from[i] = g.nodes[id]
+		i++
+	}
+
+	return from
+}
+
+// To returns all nodes in g that can reach directly to n.
+func (g *DirectedGraph) To(n graph.Node) []graph.Node {
+	if _, ok := g.from[n.ID()]; !ok {
+		return nil
+	}
+
+	to := make([]graph.Node, len(g.to[n.ID()]))
+	i := 0
+	for id := range g.to[n.ID()] {
+		to[i] = g.nodes[id]
+		i++
+	}
+
+	return to
+}
+
+// HasEdgeBetween returns whether an edge exists between nodes x and y without
+// considering direction.
+func (g *DirectedGraph) HasEdgeBetween(x, y graph.Node) bool {
+	xid := x.ID()
+	yid := y.ID()
+	if _, ok := g.nodes[xid]; !ok {
+		return false
+	}
+	if _, ok := g.nodes[yid]; !ok {
+		return false
+	}
+	if _, ok := g.from[xid][yid]; ok {
+		return true
+	}
+	_, ok := g.from[yid][xid]
+	return ok
+}
+
+// Edge returns the edge from u to v if such an edge exists and nil otherwise.
+// The node v must be directly reachable from u as defined by the From method.
+func (g *DirectedGraph) Edge(u, v graph.Node) graph.Edge {
+	if _, ok := g.nodes[u.ID()]; !ok {
+		return nil
+	}
+	if _, ok := g.nodes[v.ID()]; !ok {
+		return nil
+	}
+	edge, ok := g.from[u.ID()][v.ID()]
+	if !ok {
+		return nil
+	}
+	return edge
+}
+
+// HasEdgeFromTo returns whether an edge exists in the graph from u to v.
+func (g *DirectedGraph) HasEdgeFromTo(u, v graph.Node) bool {
+	if _, ok := g.nodes[u.ID()]; !ok {
+		return false
+	}
+	if _, ok := g.nodes[v.ID()]; !ok {
+		return false
+	}
+	if _, ok := g.from[u.ID()][v.ID()]; !ok {
+		return false
+	}
+	return true
+}
+
+// Degree returns the in+out degree of n in g.
+func (g *DirectedGraph) Degree(n graph.Node) int {
+	if _, ok := g.nodes[n.ID()]; !ok {
+		return 0
+	}
+
+	return len(g.from[n.ID()]) + len(g.to[n.ID()])
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/simple/directed_test.go b/vendor/gonum.org/v1/gonum/graph/simple/directed_test.go
new file mode 100644
index 00000000..b66845bd
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/simple/directed_test.go
@@ -0,0 +1,65 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package simple
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+)
+
+var (
+	directedGraph = (*DirectedGraph)(nil)
+
+	_ graph.Graph    = directedGraph
+	_ graph.Directed = directedGraph
+)
+
+// Tests Issue #27
+func TestEdgeOvercounting(t *testing.T) {
+	g := generateDummyGraph()
+
+	if neigh := g.From(Node(Node(2))); len(neigh) != 2 {
+		t.Errorf("Node 2 has incorrect number of neighbors got neighbors %v (count %d), expected 2 neighbors {0,1}", neigh, len(neigh))
+	}
+}
+
+func generateDummyGraph() *DirectedGraph {
+	nodes := [4]struct{ srcID, targetID int }{
+		{2, 1},
+		{1, 0},
+		{2, 0},
+		{0, 2},
+	}
+
+	g := NewDirectedGraph()
+
+	for _, n := range nodes {
+		g.SetEdge(Edge{F: Node(n.srcID), T: Node(n.targetID)})
+	}
+
+	return g
+}
+
+// Test for issue #123 https://github.com/gonum/graph/issues/123
+func TestIssue123DirectedGraph(t *testing.T) {
+	defer func() {
+		if r := recover(); r != nil {
+			t.Errorf("unexpected panic: %v", r)
+		}
+	}()
+	g := NewDirectedGraph()
+
+	n0 := g.NewNode()
+	g.AddNode(n0)
+
+	n1 := g.NewNode()
+	g.AddNode(n1)
+
+	g.RemoveNode(n0)
+
+	n2 := g.NewNode()
+	g.AddNode(n2)
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/simple/doc.go b/vendor/gonum.org/v1/gonum/graph/simple/doc.go
new file mode 100644
index 00000000..1b688a95
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/simple/doc.go
@@ -0,0 +1,7 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package simple provides a suite of simple graph implementations satisfying
+// the gonum/graph interfaces.
+package simple // import "gonum.org/v1/gonum/graph/simple"
diff --git a/vendor/gonum.org/v1/gonum/graph/simple/simple.go b/vendor/gonum.org/v1/gonum/graph/simple/simple.go
new file mode 100644
index 00000000..13c1618a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/simple/simple.go
@@ -0,0 +1,99 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package simple
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/set"
+)
+
+// Node is a simple graph node.
+type Node int64
+
+// ID returns the ID number of the node.
+func (n Node) ID() int64 {
+	return int64(n)
+}
+
+// Edge is a simple graph edge.
+type Edge struct {
+	F, T graph.Node
+}
+
+// From returns the from-node of the edge.
+func (e Edge) From() graph.Node { return e.F }
+
+// To returns the to-node of the edge.
+func (e Edge) To() graph.Node { return e.T }
+
+// WeightedEdge is a simple weighted graph edge.
+type WeightedEdge struct {
+	F, T graph.Node
+	W    float64
+}
+
+// From returns the from-node of the edge.
+func (e WeightedEdge) From() graph.Node { return e.F }
+
+// To returns the to-node of the edge.
+func (e WeightedEdge) To() graph.Node { return e.T }
+
+// Weight returns the weight of the edge.
+func (e WeightedEdge) Weight() float64 { return e.W }
+
+// isSame returns whether two float64 values are the same where NaN values
+// are equalable.
+func isSame(a, b float64) bool {
+	return a == b || (math.IsNaN(a) && math.IsNaN(b))
+}
+
+// maxInt is the maximum value of int64.
+const maxInt = int64(^uint64(0) >> 1)
+
+// idSet implements available ID storage.
+type idSet struct {
+	maxID      int64
+	used, free set.Int64s
+}
+
+// newIDSet returns a new idSet. The returned value should not be passed
+// except by pointer.
+func newIDSet() idSet {
+	return idSet{maxID: -1, used: make(set.Int64s), free: make(set.Int64s)}
+}
+
+// newID returns a new unique ID. The ID returned is not considered used
+// until passed in a call to use.
+func (s *idSet) newID() int64 {
+	for id := range s.free {
+		return id
+	}
+	if s.maxID != maxInt {
+		return s.maxID + 1
+	}
+	for id := int64(0); id <= s.maxID+1; id++ {
+		if !s.used.Has(id) {
+			return id
+		}
+	}
+	panic("unreachable")
+}
+
+// use adds the id to the used IDs in the idSet.
+func (s *idSet) use(id int64) {
+	s.used.Add(id)
+	s.free.Remove(id)
+	if id > s.maxID {
+		s.maxID = id
+	}
+}
+
+// free frees the id for reuse.
+func (s *idSet) release(id int64) {
+	s.free.Add(id)
+	s.used.Remove(id)
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/simple/undirected.go b/vendor/gonum.org/v1/gonum/graph/simple/undirected.go
new file mode 100644
index 00000000..7254e4a0
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/simple/undirected.go
@@ -0,0 +1,205 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package simple
+
+import (
+	"fmt"
+
+	"gonum.org/v1/gonum/graph"
+)
+
+// UndirectedGraph implements a generalized undirected graph.
+type UndirectedGraph struct {
+	nodes map[int64]graph.Node
+	edges map[int64]map[int64]graph.Edge
+
+	nodeIDs idSet
+}
+
+// NewUndirectedGraph returns an UndirectedGraph with the specified self and absent
+// edge weight values.
+func NewUndirectedGraph() *UndirectedGraph {
+	return &UndirectedGraph{
+		nodes: make(map[int64]graph.Node),
+		edges: make(map[int64]map[int64]graph.Edge),
+
+		nodeIDs: newIDSet(),
+	}
+}
+
+// NewNode returns a new unique Node to be added to g. The Node's ID does
+// not become valid in g until the Node is added to g.
+func (g *UndirectedGraph) NewNode() graph.Node {
+	if len(g.nodes) == 0 {
+		return Node(0)
+	}
+	if int64(len(g.nodes)) == maxInt {
+		panic("simple: cannot allocate node: no slot")
+	}
+	return Node(g.nodeIDs.newID())
+}
+
+// AddNode adds n to the graph. It panics if the added node ID matches an existing node ID.
+func (g *UndirectedGraph) AddNode(n graph.Node) {
+	if _, exists := g.nodes[n.ID()]; exists {
+		panic(fmt.Sprintf("simple: node ID collision: %d", n.ID()))
+	}
+	g.nodes[n.ID()] = n
+	g.edges[n.ID()] = make(map[int64]graph.Edge)
+	g.nodeIDs.use(n.ID())
+}
+
+// RemoveNode removes n from the graph, as well as any edges attached to it. If the node
+// is not in the graph it is a no-op.
+func (g *UndirectedGraph) RemoveNode(n graph.Node) {
+	if _, ok := g.nodes[n.ID()]; !ok {
+		return
+	}
+	delete(g.nodes, n.ID())
+
+	for from := range g.edges[n.ID()] {
+		delete(g.edges[from], n.ID())
+	}
+	delete(g.edges, n.ID())
+
+	g.nodeIDs.release(n.ID())
+}
+
+// NewEdge returns a new Edge from the source to the destination node.
+func (g *UndirectedGraph) NewEdge(from, to graph.Node) graph.Edge {
+	return &Edge{F: from, T: to}
+}
+
+// SetEdge adds e, an edge from one node to another. If the nodes do not exist, they are added.
+// It will panic if the IDs of the e.From and e.To are equal.
+func (g *UndirectedGraph) SetEdge(e graph.Edge) {
+	var (
+		from = e.From()
+		fid  = from.ID()
+		to   = e.To()
+		tid  = to.ID()
+	)
+
+	if fid == tid {
+		panic("simple: adding self edge")
+	}
+
+	if !g.Has(from) {
+		g.AddNode(from)
+	}
+	if !g.Has(to) {
+		g.AddNode(to)
+	}
+
+	g.edges[fid][tid] = e
+	g.edges[tid][fid] = e
+}
+
+// RemoveEdge removes e from the graph, leaving the terminal nodes. If the edge does not exist
+// it is a no-op.
+func (g *UndirectedGraph) RemoveEdge(e graph.Edge) {
+	from, to := e.From(), e.To()
+	if _, ok := g.nodes[from.ID()]; !ok {
+		return
+	}
+	if _, ok := g.nodes[to.ID()]; !ok {
+		return
+	}
+
+	delete(g.edges[from.ID()], to.ID())
+	delete(g.edges[to.ID()], from.ID())
+}
+
+// Node returns the node in the graph with the given ID.
+func (g *UndirectedGraph) Node(id int64) graph.Node {
+	return g.nodes[id]
+}
+
+// Has returns whether the node exists within the graph.
+func (g *UndirectedGraph) Has(n graph.Node) bool {
+	_, ok := g.nodes[n.ID()]
+	return ok
+}
+
+// Nodes returns all the nodes in the graph.
+func (g *UndirectedGraph) Nodes() []graph.Node {
+	nodes := make([]graph.Node, len(g.nodes))
+	i := 0
+	for _, n := range g.nodes {
+		nodes[i] = n
+		i++
+	}
+
+	return nodes
+}
+
+// Edges returns all the edges in the graph.
+func (g *UndirectedGraph) Edges() []graph.Edge {
+	var edges []graph.Edge
+
+	seen := make(map[[2]int64]struct{})
+	for _, u := range g.edges {
+		for _, e := range u {
+			uid := e.From().ID()
+			vid := e.To().ID()
+			if _, ok := seen[[2]int64{uid, vid}]; ok {
+				continue
+			}
+			seen[[2]int64{uid, vid}] = struct{}{}
+			seen[[2]int64{vid, uid}] = struct{}{}
+			edges = append(edges, e)
+		}
+	}
+
+	return edges
+}
+
+// From returns all nodes in g that can be reached directly from n.
+func (g *UndirectedGraph) From(n graph.Node) []graph.Node {
+	if !g.Has(n) {
+		return nil
+	}
+
+	nodes := make([]graph.Node, len(g.edges[n.ID()]))
+	i := 0
+	for from := range g.edges[n.ID()] {
+		nodes[i] = g.nodes[from]
+		i++
+	}
+
+	return nodes
+}
+
+// HasEdgeBetween returns whether an edge exists between nodes x and y.
+func (g *UndirectedGraph) HasEdgeBetween(x, y graph.Node) bool {
+	_, ok := g.edges[x.ID()][y.ID()]
+	return ok
+}
+
+// Edge returns the edge from u to v if such an edge exists and nil otherwise.
+// The node v must be directly reachable from u as defined by the From method.
+func (g *UndirectedGraph) Edge(u, v graph.Node) graph.Edge {
+	return g.EdgeBetween(u, v)
+}
+
+// EdgeBetween returns the edge between nodes x and y.
+func (g *UndirectedGraph) EdgeBetween(x, y graph.Node) graph.Edge {
+	// We don't need to check if neigh exists because
+	// it's implicit in the edges access.
+	if !g.Has(x) {
+		return nil
+	}
+
+	return g.edges[x.ID()][y.ID()]
+}
+
+// Degree returns the degree of n in g.
+func (g *UndirectedGraph) Degree(n graph.Node) int {
+	if _, ok := g.nodes[n.ID()]; !ok {
+		return 0
+	}
+
+	return len(g.edges[n.ID()])
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/simple/undirected_test.go b/vendor/gonum.org/v1/gonum/graph/simple/undirected_test.go
new file mode 100644
index 00000000..f5c0dafc
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/simple/undirected_test.go
@@ -0,0 +1,67 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package simple
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+)
+
+var (
+	undirectedGraph = (*UndirectedGraph)(nil)
+
+	_ graph.Graph      = undirectedGraph
+	_ graph.Undirected = undirectedGraph
+)
+
+func TestAssertMutableNotDirected(t *testing.T) {
+	var g graph.UndirectedBuilder = NewUndirectedGraph()
+	if _, ok := g.(graph.Directed); ok {
+		t.Fatal("Graph is directed, but a MutableGraph cannot safely be directed!")
+	}
+}
+
+func TestMaxID(t *testing.T) {
+	g := NewUndirectedGraph()
+	nodes := make(map[graph.Node]struct{})
+	for i := Node(0); i < 3; i++ {
+		g.AddNode(i)
+		nodes[i] = struct{}{}
+	}
+	g.RemoveNode(Node(0))
+	delete(nodes, Node(0))
+	g.RemoveNode(Node(2))
+	delete(nodes, Node(2))
+	n := g.NewNode()
+	g.AddNode(n)
+	if !g.Has(n) {
+		t.Error("added node does not exist in graph")
+	}
+	if _, exists := nodes[n]; exists {
+		t.Errorf("Created already existing node id: %v", n.ID())
+	}
+}
+
+// Test for issue #123 https://github.com/gonum/graph/issues/123
+func TestIssue123UndirectedGraph(t *testing.T) {
+	defer func() {
+		if r := recover(); r != nil {
+			t.Errorf("unexpected panic: %v", r)
+		}
+	}()
+	g := NewUndirectedGraph()
+
+	n0 := g.NewNode()
+	g.AddNode(n0)
+
+	n1 := g.NewNode()
+	g.AddNode(n1)
+
+	g.RemoveNode(n0)
+
+	n2 := g.NewNode()
+	g.AddNode(n2)
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/simple/weighted_directed.go b/vendor/gonum.org/v1/gonum/graph/simple/weighted_directed.go
new file mode 100644
index 00000000..fbe3ae80
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/simple/weighted_directed.go
@@ -0,0 +1,285 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package simple
+
+import (
+	"fmt"
+
+	"gonum.org/v1/gonum/graph"
+)
+
+// WeightedDirectedGraph implements a generalized weighted directed graph.
+type WeightedDirectedGraph struct {
+	nodes map[int64]graph.Node
+	from  map[int64]map[int64]graph.WeightedEdge
+	to    map[int64]map[int64]graph.WeightedEdge
+
+	self, absent float64
+
+	nodeIDs idSet
+}
+
+// NewWeightedDirectedGraph returns a WeightedDirectedGraph with the specified self and absent
+// edge weight values.
+func NewWeightedDirectedGraph(self, absent float64) *WeightedDirectedGraph {
+	return &WeightedDirectedGraph{
+		nodes: make(map[int64]graph.Node),
+		from:  make(map[int64]map[int64]graph.WeightedEdge),
+		to:    make(map[int64]map[int64]graph.WeightedEdge),
+
+		self:   self,
+		absent: absent,
+
+		nodeIDs: newIDSet(),
+	}
+}
+
+// NewNode returns a new unique Node to be added to g. The Node's ID does
+// not become valid in g until the Node is added to g.
+func (g *WeightedDirectedGraph) NewNode() graph.Node {
+	if len(g.nodes) == 0 {
+		return Node(0)
+	}
+	if int64(len(g.nodes)) == maxInt {
+		panic("simple: cannot allocate node: no slot")
+	}
+	return Node(g.nodeIDs.newID())
+}
+
+// AddNode adds n to the graph. It panics if the added node ID matches an existing node ID.
+func (g *WeightedDirectedGraph) AddNode(n graph.Node) {
+	if _, exists := g.nodes[n.ID()]; exists {
+		panic(fmt.Sprintf("simple: node ID collision: %d", n.ID()))
+	}
+	g.nodes[n.ID()] = n
+	g.from[n.ID()] = make(map[int64]graph.WeightedEdge)
+	g.to[n.ID()] = make(map[int64]graph.WeightedEdge)
+	g.nodeIDs.use(n.ID())
+}
+
+// RemoveNode removes n from the graph, as well as any edges attached to it. If the node
+// is not in the graph it is a no-op.
+func (g *WeightedDirectedGraph) RemoveNode(n graph.Node) {
+	if _, ok := g.nodes[n.ID()]; !ok {
+		return
+	}
+	delete(g.nodes, n.ID())
+
+	for from := range g.from[n.ID()] {
+		delete(g.to[from], n.ID())
+	}
+	delete(g.from, n.ID())
+
+	for to := range g.to[n.ID()] {
+		delete(g.from[to], n.ID())
+	}
+	delete(g.to, n.ID())
+
+	g.nodeIDs.release(n.ID())
+}
+
+// NewWeightedEdge returns a new weighted edge from the source to the destination node.
+func (g *WeightedDirectedGraph) NewWeightedEdge(from, to graph.Node, weight float64) graph.WeightedEdge {
+	return &WeightedEdge{F: from, T: to, W: weight}
+}
+
+// SetWeightedEdge adds a weighted edge from one node to another. If the nodes do not exist, they are added.
+// It will panic if the IDs of the e.From and e.To are equal.
+func (g *WeightedDirectedGraph) SetWeightedEdge(e graph.WeightedEdge) {
+	var (
+		from = e.From()
+		fid  = from.ID()
+		to   = e.To()
+		tid  = to.ID()
+	)
+
+	if fid == tid {
+		panic("simple: adding self edge")
+	}
+
+	if !g.Has(from) {
+		g.AddNode(from)
+	}
+	if !g.Has(to) {
+		g.AddNode(to)
+	}
+
+	g.from[fid][tid] = e
+	g.to[tid][fid] = e
+}
+
+// RemoveEdge removes e from the graph, leaving the terminal nodes. If the edge does not exist
+// it is a no-op.
+func (g *WeightedDirectedGraph) RemoveEdge(e graph.Edge) {
+	from, to := e.From(), e.To()
+	if _, ok := g.nodes[from.ID()]; !ok {
+		return
+	}
+	if _, ok := g.nodes[to.ID()]; !ok {
+		return
+	}
+
+	delete(g.from[from.ID()], to.ID())
+	delete(g.to[to.ID()], from.ID())
+}
+
+// Node returns the node in the graph with the given ID.
+func (g *WeightedDirectedGraph) Node(id int64) graph.Node {
+	return g.nodes[id]
+}
+
+// Has returns whether the node exists within the graph.
+func (g *WeightedDirectedGraph) Has(n graph.Node) bool {
+	_, ok := g.nodes[n.ID()]
+
+	return ok
+}
+
+// Nodes returns all the nodes in the graph.
+func (g *WeightedDirectedGraph) Nodes() []graph.Node {
+	nodes := make([]graph.Node, len(g.from))
+	i := 0
+	for _, n := range g.nodes {
+		nodes[i] = n
+		i++
+	}
+
+	return nodes
+}
+
+// Edges returns all the edges in the graph.
+func (g *WeightedDirectedGraph) Edges() []graph.Edge {
+	var edges []graph.Edge
+	for _, u := range g.nodes {
+		for _, e := range g.from[u.ID()] {
+			edges = append(edges, e)
+		}
+	}
+	return edges
+}
+
+// WeightedEdges returns all the weighted edges in the graph.
+func (g *WeightedDirectedGraph) WeightedEdges() []graph.WeightedEdge {
+	var edges []graph.WeightedEdge
+	for _, u := range g.nodes {
+		for _, e := range g.from[u.ID()] {
+			edges = append(edges, e)
+		}
+	}
+	return edges
+}
+
+// From returns all nodes in g that can be reached directly from n.
+func (g *WeightedDirectedGraph) From(n graph.Node) []graph.Node {
+	if _, ok := g.from[n.ID()]; !ok {
+		return nil
+	}
+
+	from := make([]graph.Node, len(g.from[n.ID()]))
+	i := 0
+	for id := range g.from[n.ID()] {
+		from[i] = g.nodes[id]
+		i++
+	}
+
+	return from
+}
+
+// To returns all nodes in g that can reach directly to n.
+func (g *WeightedDirectedGraph) To(n graph.Node) []graph.Node {
+	if _, ok := g.from[n.ID()]; !ok {
+		return nil
+	}
+
+	to := make([]graph.Node, len(g.to[n.ID()]))
+	i := 0
+	for id := range g.to[n.ID()] {
+		to[i] = g.nodes[id]
+		i++
+	}
+
+	return to
+}
+
+// HasEdgeBetween returns whether an edge exists between nodes x and y without
+// considering direction.
+func (g *WeightedDirectedGraph) HasEdgeBetween(x, y graph.Node) bool {
+	xid := x.ID()
+	yid := y.ID()
+	if _, ok := g.nodes[xid]; !ok {
+		return false
+	}
+	if _, ok := g.nodes[yid]; !ok {
+		return false
+	}
+	if _, ok := g.from[xid][yid]; ok {
+		return true
+	}
+	_, ok := g.from[yid][xid]
+	return ok
+}
+
+// Edge returns the edge from u to v if such an edge exists and nil otherwise.
+// The node v must be directly reachable from u as defined by the From method.
+func (g *WeightedDirectedGraph) Edge(u, v graph.Node) graph.Edge {
+	return g.WeightedEdge(u, v)
+}
+
+// WeightedEdge returns the weighted edge from u to v if such an edge exists and nil otherwise.
+// The node v must be directly reachable from u as defined by the From method.
+func (g *WeightedDirectedGraph) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
+	if _, ok := g.nodes[u.ID()]; !ok {
+		return nil
+	}
+	if _, ok := g.nodes[v.ID()]; !ok {
+		return nil
+	}
+	edge, ok := g.from[u.ID()][v.ID()]
+	if !ok {
+		return nil
+	}
+	return edge
+}
+
+// HasEdgeFromTo returns whether an edge exists in the graph from u to v.
+func (g *WeightedDirectedGraph) HasEdgeFromTo(u, v graph.Node) bool {
+	if _, ok := g.nodes[u.ID()]; !ok {
+		return false
+	}
+	if _, ok := g.nodes[v.ID()]; !ok {
+		return false
+	}
+	if _, ok := g.from[u.ID()][v.ID()]; !ok {
+		return false
+	}
+	return true
+}
+
+// Weight returns the weight for the edge between x and y if Edge(x, y) returns a non-nil Edge.
+// If x and y are the same node or there is no joining edge between the two nodes the weight
+// value returned is either the graph's absent or self value. Weight returns true if an edge
+// exists between x and y or if x and y have the same ID, false otherwise.
+func (g *WeightedDirectedGraph) Weight(x, y graph.Node) (w float64, ok bool) {
+	xid := x.ID()
+	yid := y.ID()
+	if xid == yid {
+		return g.self, true
+	}
+	if to, ok := g.from[xid]; ok {
+		if e, ok := to[yid]; ok {
+			return e.Weight(), true
+		}
+	}
+	return g.absent, false
+}
+
+// Degree returns the in+out degree of n in g.
+func (g *WeightedDirectedGraph) Degree(n graph.Node) int {
+	if _, ok := g.nodes[n.ID()]; !ok {
+		return 0
+	}
+
+	return len(g.from[n.ID()]) + len(g.to[n.ID()])
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/simple/weighted_directed_test.go b/vendor/gonum.org/v1/gonum/graph/simple/weighted_directed_test.go
new file mode 100644
index 00000000..714b067d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/simple/weighted_directed_test.go
@@ -0,0 +1,67 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package simple
+
+import (
+	"math"
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+)
+
+var (
+	weightedDirectedGraph = (*WeightedDirectedGraph)(nil)
+
+	_ graph.Graph            = weightedDirectedGraph
+	_ graph.Directed         = weightedDirectedGraph
+	_ graph.WeightedDirected = weightedDirectedGraph
+)
+
+// Tests Issue #27
+func TestWeightedEdgeOvercounting(t *testing.T) {
+	g := generateDummyGraph()
+
+	if neigh := g.From(Node(Node(2))); len(neigh) != 2 {
+		t.Errorf("Node 2 has incorrect number of neighbors got neighbors %v (count %d), expected 2 neighbors {0,1}", neigh, len(neigh))
+	}
+}
+
+func generateDummyWeightedGraph() *WeightedDirectedGraph {
+	nodes := [4]struct{ srcID, targetID int }{
+		{2, 1},
+		{1, 0},
+		{2, 0},
+		{0, 2},
+	}
+
+	g := NewWeightedDirectedGraph(0, math.Inf(1))
+
+	for _, n := range nodes {
+		g.SetWeightedEdge(WeightedEdge{F: Node(n.srcID), T: Node(n.targetID), W: 1})
+	}
+
+	return g
+}
+
+// Test for issue #123 https://github.com/gonum/graph/issues/123
+func TestIssue123WeightedDirectedGraph(t *testing.T) {
+	defer func() {
+		if r := recover(); r != nil {
+			t.Errorf("unexpected panic: %v", r)
+		}
+	}()
+	g := NewWeightedDirectedGraph(0, math.Inf(1))
+
+	n0 := g.NewNode()
+	g.AddNode(n0)
+
+	n1 := g.NewNode()
+	g.AddNode(n1)
+
+	g.RemoveNode(n0)
+
+	n2 := g.NewNode()
+	g.AddNode(n2)
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/simple/weighted_undirected.go b/vendor/gonum.org/v1/gonum/graph/simple/weighted_undirected.go
new file mode 100644
index 00000000..9ec4cd61
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/simple/weighted_undirected.go
@@ -0,0 +1,260 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package simple
+
+import (
+	"fmt"
+
+	"gonum.org/v1/gonum/graph"
+)
+
+// WeightedUndirectedGraph implements a generalized weighted undirected graph.
+type WeightedUndirectedGraph struct {
+	nodes map[int64]graph.Node
+	edges map[int64]map[int64]graph.WeightedEdge
+
+	self, absent float64
+
+	nodeIDs idSet
+}
+
+// NewWeightedUndirectedGraph returns an WeightedUndirectedGraph with the specified self and absent
+// edge weight values.
+func NewWeightedUndirectedGraph(self, absent float64) *WeightedUndirectedGraph {
+	return &WeightedUndirectedGraph{
+		nodes: make(map[int64]graph.Node),
+		edges: make(map[int64]map[int64]graph.WeightedEdge),
+
+		self:   self,
+		absent: absent,
+
+		nodeIDs: newIDSet(),
+	}
+}
+
+// NewNode returns a new unique Node to be added to g. The Node's ID does
+// not become valid in g until the Node is added to g.
+func (g *WeightedUndirectedGraph) NewNode() graph.Node {
+	if len(g.nodes) == 0 {
+		return Node(0)
+	}
+	if int64(len(g.nodes)) == maxInt {
+		panic("simple: cannot allocate node: no slot")
+	}
+	return Node(g.nodeIDs.newID())
+}
+
+// AddNode adds n to the graph. It panics if the added node ID matches an existing node ID.
+func (g *WeightedUndirectedGraph) AddNode(n graph.Node) {
+	if _, exists := g.nodes[n.ID()]; exists {
+		panic(fmt.Sprintf("simple: node ID collision: %d", n.ID()))
+	}
+	g.nodes[n.ID()] = n
+	g.edges[n.ID()] = make(map[int64]graph.WeightedEdge)
+	g.nodeIDs.use(n.ID())
+}
+
+// RemoveNode removes n from the graph, as well as any edges attached to it. If the node
+// is not in the graph it is a no-op.
+func (g *WeightedUndirectedGraph) RemoveNode(n graph.Node) {
+	if _, ok := g.nodes[n.ID()]; !ok {
+		return
+	}
+	delete(g.nodes, n.ID())
+
+	for from := range g.edges[n.ID()] {
+		delete(g.edges[from], n.ID())
+	}
+	delete(g.edges, n.ID())
+
+	g.nodeIDs.release(n.ID())
+}
+
+// NewWeightedEdge returns a new weighted edge from the source to the destination node.
+func (g *WeightedUndirectedGraph) NewWeightedEdge(from, to graph.Node, weight float64) graph.WeightedEdge {
+	return &WeightedEdge{F: from, T: to, W: weight}
+}
+
+// SetWeightedEdge adds a weighted edge from one node to another. If the nodes do not exist, they are added.
+// It will panic if the IDs of the e.From and e.To are equal.
+func (g *WeightedUndirectedGraph) SetWeightedEdge(e graph.WeightedEdge) {
+	var (
+		from = e.From()
+		fid  = from.ID()
+		to   = e.To()
+		tid  = to.ID()
+	)
+
+	if fid == tid {
+		panic("simple: adding self edge")
+	}
+
+	if !g.Has(from) {
+		g.AddNode(from)
+	}
+	if !g.Has(to) {
+		g.AddNode(to)
+	}
+
+	g.edges[fid][tid] = e
+	g.edges[tid][fid] = e
+}
+
+// RemoveEdge removes e from the graph, leaving the terminal nodes. If the edge does not exist
+// it is a no-op.
+func (g *WeightedUndirectedGraph) RemoveEdge(e graph.Edge) {
+	from, to := e.From(), e.To()
+	if _, ok := g.nodes[from.ID()]; !ok {
+		return
+	}
+	if _, ok := g.nodes[to.ID()]; !ok {
+		return
+	}
+
+	delete(g.edges[from.ID()], to.ID())
+	delete(g.edges[to.ID()], from.ID())
+}
+
+// Node returns the node in the graph with the given ID.
+func (g *WeightedUndirectedGraph) Node(id int64) graph.Node {
+	return g.nodes[id]
+}
+
+// Has returns whether the node exists within the graph.
+func (g *WeightedUndirectedGraph) Has(n graph.Node) bool {
+	_, ok := g.nodes[n.ID()]
+	return ok
+}
+
+// Nodes returns all the nodes in the graph.
+func (g *WeightedUndirectedGraph) Nodes() []graph.Node {
+	nodes := make([]graph.Node, len(g.nodes))
+	i := 0
+	for _, n := range g.nodes {
+		nodes[i] = n
+		i++
+	}
+
+	return nodes
+}
+
+// Edges returns all the edges in the graph.
+func (g *WeightedUndirectedGraph) Edges() []graph.Edge {
+	var edges []graph.Edge
+
+	seen := make(map[[2]int64]struct{})
+	for _, u := range g.edges {
+		for _, e := range u {
+			uid := e.From().ID()
+			vid := e.To().ID()
+			if _, ok := seen[[2]int64{uid, vid}]; ok {
+				continue
+			}
+			seen[[2]int64{uid, vid}] = struct{}{}
+			seen[[2]int64{vid, uid}] = struct{}{}
+			edges = append(edges, e)
+		}
+	}
+
+	return edges
+}
+
+// WeightedEdges returns all the weighted edges in the graph.
+func (g *WeightedUndirectedGraph) WeightedEdges() []graph.WeightedEdge {
+	var edges []graph.WeightedEdge
+
+	seen := make(map[[2]int64]struct{})
+	for _, u := range g.edges {
+		for _, e := range u {
+			uid := e.From().ID()
+			vid := e.To().ID()
+			if _, ok := seen[[2]int64{uid, vid}]; ok {
+				continue
+			}
+			seen[[2]int64{uid, vid}] = struct{}{}
+			seen[[2]int64{vid, uid}] = struct{}{}
+			edges = append(edges, e)
+		}
+	}
+
+	return edges
+}
+
+// From returns all nodes in g that can be reached directly from n.
+func (g *WeightedUndirectedGraph) From(n graph.Node) []graph.Node {
+	if !g.Has(n) {
+		return nil
+	}
+
+	nodes := make([]graph.Node, len(g.edges[n.ID()]))
+	i := 0
+	for from := range g.edges[n.ID()] {
+		nodes[i] = g.nodes[from]
+		i++
+	}
+
+	return nodes
+}
+
+// HasEdgeBetween returns whether an edge exists between nodes x and y.
+func (g *WeightedUndirectedGraph) HasEdgeBetween(x, y graph.Node) bool {
+	_, ok := g.edges[x.ID()][y.ID()]
+	return ok
+}
+
+// Edge returns the edge from u to v if such an edge exists and nil otherwise.
+// The node v must be directly reachable from u as defined by the From method.
+func (g *WeightedUndirectedGraph) Edge(u, v graph.Node) graph.Edge {
+	return g.WeightedEdgeBetween(u, v)
+}
+
+// WeightedEdge returns the weighted edge from u to v if such an edge exists and nil otherwise.
+// The node v must be directly reachable from u as defined by the From method.
+func (g *WeightedUndirectedGraph) WeightedEdge(u, v graph.Node) graph.WeightedEdge {
+	return g.WeightedEdgeBetween(u, v)
+}
+
+// EdgeBetween returns the edge between nodes x and y.
+func (g *WeightedUndirectedGraph) EdgeBetween(x, y graph.Node) graph.Edge {
+	return g.WeightedEdgeBetween(x, y)
+}
+
+// WeightedEdgeBetween returns the weighted edge between nodes x and y.
+func (g *WeightedUndirectedGraph) WeightedEdgeBetween(x, y graph.Node) graph.WeightedEdge {
+	// We don't need to check if neigh exists because
+	// it's implicit in the edges access.
+	if !g.Has(x) {
+		return nil
+	}
+
+	return g.edges[x.ID()][y.ID()]
+}
+
+// Weight returns the weight for the edge between x and y if Edge(x, y) returns a non-nil Edge.
+// If x and y are the same node or there is no joining edge between the two nodes the weight
+// value returned is either the graph's absent or self value. Weight returns true if an edge
+// exists between x and y or if x and y have the same ID, false otherwise.
+func (g *WeightedUndirectedGraph) Weight(x, y graph.Node) (w float64, ok bool) {
+	xid := x.ID()
+	yid := y.ID()
+	if xid == yid {
+		return g.self, true
+	}
+	if n, ok := g.edges[xid]; ok {
+		if e, ok := n[yid]; ok {
+			return e.Weight(), true
+		}
+	}
+	return g.absent, false
+}
+
+// Degree returns the degree of n in g.
+func (g *WeightedUndirectedGraph) Degree(n graph.Node) int {
+	if _, ok := g.nodes[n.ID()]; !ok {
+		return 0
+	}
+
+	return len(g.edges[n.ID()])
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/simple/weighted_undirected_test.go b/vendor/gonum.org/v1/gonum/graph/simple/weighted_undirected_test.go
new file mode 100644
index 00000000..a3796ee3
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/simple/weighted_undirected_test.go
@@ -0,0 +1,69 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package simple
+
+import (
+	"math"
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+)
+
+var (
+	weightedUndirectedGraph = (*WeightedUndirectedGraph)(nil)
+
+	_ graph.Graph              = weightedUndirectedGraph
+	_ graph.Undirected         = weightedUndirectedGraph
+	_ graph.WeightedUndirected = weightedUndirectedGraph
+)
+
+func TestAssertWeightedMutableNotDirected(t *testing.T) {
+	var g graph.UndirectedWeightedBuilder = NewWeightedUndirectedGraph(0, math.Inf(1))
+	if _, ok := g.(graph.Directed); ok {
+		t.Fatal("Graph is directed, but a MutableGraph cannot safely be directed!")
+	}
+}
+
+func TestWeightedMaxID(t *testing.T) {
+	g := NewWeightedUndirectedGraph(0, math.Inf(1))
+	nodes := make(map[graph.Node]struct{})
+	for i := Node(0); i < 3; i++ {
+		g.AddNode(i)
+		nodes[i] = struct{}{}
+	}
+	g.RemoveNode(Node(0))
+	delete(nodes, Node(0))
+	g.RemoveNode(Node(2))
+	delete(nodes, Node(2))
+	n := g.NewNode()
+	g.AddNode(n)
+	if !g.Has(n) {
+		t.Error("added node does not exist in graph")
+	}
+	if _, exists := nodes[n]; exists {
+		t.Errorf("Created already existing node id: %v", n.ID())
+	}
+}
+
+// Test for issue #123 https://github.com/gonum/graph/issues/123
+func TestIssue123WeightedUndirectedGraph(t *testing.T) {
+	defer func() {
+		if r := recover(); r != nil {
+			t.Errorf("unexpected panic: %v", r)
+		}
+	}()
+	g := NewWeightedUndirectedGraph(0, math.Inf(1))
+
+	n0 := g.NewNode()
+	g.AddNode(n0)
+
+	n1 := g.NewNode()
+	g.AddNode(n1)
+
+	g.RemoveNode(n0)
+
+	n2 := g.NewNode()
+	g.AddNode(n2)
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/topo/bench_test.go b/vendor/gonum.org/v1/gonum/graph/topo/bench_test.go
new file mode 100644
index 00000000..7b2bdc3e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/topo/bench_test.go
@@ -0,0 +1,57 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package topo
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/graphs/gen"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+var (
+	gnpDirected_10_tenth   = gnpDirected(10, 0.1)
+	gnpDirected_100_tenth  = gnpDirected(100, 0.1)
+	gnpDirected_1000_tenth = gnpDirected(1000, 0.1)
+	gnpDirected_10_half    = gnpDirected(10, 0.5)
+	gnpDirected_100_half   = gnpDirected(100, 0.5)
+	gnpDirected_1000_half  = gnpDirected(1000, 0.5)
+)
+
+func gnpDirected(n int, p float64) graph.Directed {
+	g := simple.NewDirectedGraph()
+	gen.Gnp(g, n, p, nil)
+	return g
+}
+
+func benchmarkTarjanSCC(b *testing.B, g graph.Directed) {
+	var sccs [][]graph.Node
+	for i := 0; i < b.N; i++ {
+		sccs = TarjanSCC(g)
+	}
+	if len(sccs) == 0 {
+		b.Fatal("unexpected number zero-sized SCC set")
+	}
+}
+
+func BenchmarkTarjanSCCGnp_10_tenth(b *testing.B) {
+	benchmarkTarjanSCC(b, gnpDirected_10_tenth)
+}
+func BenchmarkTarjanSCCGnp_100_tenth(b *testing.B) {
+	benchmarkTarjanSCC(b, gnpDirected_100_tenth)
+}
+func BenchmarkTarjanSCCGnp_1000_tenth(b *testing.B) {
+	benchmarkTarjanSCC(b, gnpDirected_1000_tenth)
+}
+func BenchmarkTarjanSCCGnp_10_half(b *testing.B) {
+	benchmarkTarjanSCC(b, gnpDirected_10_half)
+}
+func BenchmarkTarjanSCCGnp_100_half(b *testing.B) {
+	benchmarkTarjanSCC(b, gnpDirected_100_half)
+}
+func BenchmarkTarjanSCCGnp_1000_half(b *testing.B) {
+	benchmarkTarjanSCC(b, gnpDirected_1000_half)
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/topo/bron_kerbosch.go b/vendor/gonum.org/v1/gonum/graph/topo/bron_kerbosch.go
new file mode 100644
index 00000000..9c478056
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/topo/bron_kerbosch.go
@@ -0,0 +1,225 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package topo
+
+import (
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/set"
+)
+
+// VertexOrdering returns the vertex ordering and the k-cores of
+// the undirected graph g.
+func VertexOrdering(g graph.Undirected) (order []graph.Node, cores [][]graph.Node) {
+	nodes := g.Nodes()
+
+	// The algorithm used here is essentially as described at
+	// http://en.wikipedia.org/w/index.php?title=Degeneracy_%28graph_theory%29&oldid=640308710
+
+	// Initialize an output list L.
+	var l []graph.Node
+
+	// Compute a number d_v for each vertex v in G,
+	// the number of neighbors of v that are not already in L.
+	// Initially, these numbers are just the degrees of the vertices.
+	dv := make(map[int64]int, len(nodes))
+	var (
+		maxDegree  int
+		neighbours = make(map[int64][]graph.Node)
+	)
+	for _, n := range nodes {
+		adj := g.From(n)
+		neighbours[n.ID()] = adj
+		dv[n.ID()] = len(adj)
+		if len(adj) > maxDegree {
+			maxDegree = len(adj)
+		}
+	}
+
+	// Initialize an array D such that D[i] contains a list of the
+	// vertices v that are not already in L for which d_v = i.
+	d := make([][]graph.Node, maxDegree+1)
+	for _, n := range nodes {
+		deg := dv[n.ID()]
+		d[deg] = append(d[deg], n)
+	}
+
+	// Initialize k to 0.
+	k := 0
+	// Repeat n times:
+	s := []int{0}
+	for range nodes {
+		// Scan the array cells D[0], D[1], ... until
+		// finding an i for which D[i] is nonempty.
+		var (
+			i  int
+			di []graph.Node
+		)
+		for i, di = range d {
+			if len(di) != 0 {
+				break
+			}
+		}
+
+		// Set k to max(k,i).
+		if i > k {
+			k = i
+			s = append(s, make([]int, k-len(s)+1)...)
+		}
+
+		// Select a vertex v from D[i]. Add v to the
+		// beginning of L and remove it from D[i].
+		var v graph.Node
+		v, d[i] = di[len(di)-1], di[:len(di)-1]
+		l = append(l, v)
+		s[k]++
+		delete(dv, v.ID())
+
+		// For each neighbor w of v not already in L,
+		// subtract one from d_w and move w to the
+		// cell of D corresponding to the new value of d_w.
+		for _, w := range neighbours[v.ID()] {
+			dw, ok := dv[w.ID()]
+			if !ok {
+				continue
+			}
+			for i, n := range d[dw] {
+				if n.ID() == w.ID() {
+					d[dw][i], d[dw] = d[dw][len(d[dw])-1], d[dw][:len(d[dw])-1]
+					dw--
+					d[dw] = append(d[dw], w)
+					break
+				}
+			}
+			dv[w.ID()] = dw
+		}
+	}
+
+	for i, j := 0, len(l)-1; i < j; i, j = i+1, j-1 {
+		l[i], l[j] = l[j], l[i]
+	}
+	cores = make([][]graph.Node, len(s))
+	offset := len(l)
+	for i, n := range s {
+		cores[i] = l[offset-n : offset]
+		offset -= n
+	}
+	return l, cores
+}
+
+// BronKerbosch returns the set of maximal cliques of the undirected graph g.
+func BronKerbosch(g graph.Undirected) [][]graph.Node {
+	nodes := g.Nodes()
+
+	// The algorithm used here is essentially BronKerbosch3 as described at
+	// http://en.wikipedia.org/w/index.php?title=Bron%E2%80%93Kerbosch_algorithm&oldid=656805858
+
+	p := make(set.Nodes, len(nodes))
+	for _, n := range nodes {
+		p.Add(n)
+	}
+	x := make(set.Nodes)
+	var bk bronKerbosch
+	order, _ := VertexOrdering(g)
+	for _, v := range order {
+		neighbours := g.From(v)
+		nv := make(set.Nodes, len(neighbours))
+		for _, n := range neighbours {
+			nv.Add(n)
+		}
+		bk.maximalCliquePivot(g, []graph.Node{v}, make(set.Nodes).Intersect(p, nv), make(set.Nodes).Intersect(x, nv))
+		p.Remove(v)
+		x.Add(v)
+	}
+	return bk
+}
+
+type bronKerbosch [][]graph.Node
+
+func (bk *bronKerbosch) maximalCliquePivot(g graph.Undirected, r []graph.Node, p, x set.Nodes) {
+	if len(p) == 0 && len(x) == 0 {
+		*bk = append(*bk, r)
+		return
+	}
+
+	neighbours := bk.choosePivotFrom(g, p, x)
+	nu := make(set.Nodes, len(neighbours))
+	for _, n := range neighbours {
+		nu.Add(n)
+	}
+	for _, v := range p {
+		if nu.Has(v) {
+			continue
+		}
+		neighbours := g.From(v)
+		nv := make(set.Nodes, len(neighbours))
+		for _, n := range neighbours {
+			nv.Add(n)
+		}
+
+		var found bool
+		for _, n := range r {
+			if n.ID() == v.ID() {
+				found = true
+				break
+			}
+		}
+		var sr []graph.Node
+		if !found {
+			sr = append(r[:len(r):len(r)], v)
+		}
+
+		bk.maximalCliquePivot(g, sr, make(set.Nodes).Intersect(p, nv), make(set.Nodes).Intersect(x, nv))
+		p.Remove(v)
+		x.Add(v)
+	}
+}
+
+func (*bronKerbosch) choosePivotFrom(g graph.Undirected, p, x set.Nodes) (neighbors []graph.Node) {
+	// TODO(kortschak): Investigate the impact of pivot choice that maximises
+	// |p ⋂ neighbours(u)| as a function of input size. Until then, leave as
+	// compile time option.
+	if !tomitaTanakaTakahashi {
+		for _, n := range p {
+			return g.From(n)
+		}
+		for _, n := range x {
+			return g.From(n)
+		}
+		panic("bronKerbosch: empty set")
+	}
+
+	var (
+		max   = -1
+		pivot graph.Node
+	)
+	maxNeighbors := func(s set.Nodes) {
+	outer:
+		for _, u := range s {
+			nb := g.From(u)
+			c := len(nb)
+			if c <= max {
+				continue
+			}
+			for n := range nb {
+				if _, ok := p[int64(n)]; ok {
+					continue
+				}
+				c--
+				if c <= max {
+					continue outer
+				}
+			}
+			max = c
+			pivot = u
+			neighbors = nb
+		}
+	}
+	maxNeighbors(p)
+	maxNeighbors(x)
+	if pivot == nil {
+		panic("bronKerbosch: empty set")
+	}
+	return neighbors
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/topo/bron_kerbosch_test.go b/vendor/gonum.org/v1/gonum/graph/topo/bron_kerbosch_test.go
new file mode 100644
index 00000000..8fdb67c0
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/topo/bron_kerbosch_test.go
@@ -0,0 +1,163 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package topo
+
+import (
+	"reflect"
+	"sort"
+	"testing"
+
+	"gonum.org/v1/gonum/graph/internal/ordered"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+var vOrderTests = []struct {
+	g        []intset
+	wantCore [][]int64
+	wantK    int
+}{
+	{
+		g: []intset{
+			0: linksTo(1, 2, 4, 6),
+			1: linksTo(2, 4, 6),
+			2: linksTo(3, 6),
+			3: linksTo(4, 5),
+			4: linksTo(6),
+			5: nil,
+			6: nil,
+		},
+		wantCore: [][]int64{
+			{},
+			{5},
+			{3},
+			{0, 1, 2, 4, 6},
+		},
+		wantK: 3,
+	},
+	{
+		g: batageljZaversnikGraph,
+		wantCore: [][]int64{
+			{0},
+			{5, 9, 10, 16},
+			{1, 2, 3, 4, 11, 12, 13, 15},
+			{6, 7, 8, 14, 17, 18, 19, 20},
+		},
+		wantK: 3,
+	},
+}
+
+func TestVertexOrdering(t *testing.T) {
+	for i, test := range vOrderTests {
+		g := simple.NewUndirectedGraph()
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+		order, core := VertexOrdering(g)
+		if len(core)-1 != test.wantK {
+			t.Errorf("unexpected value of k for test %d: got: %d want: %d", i, len(core)-1, test.wantK)
+		}
+		var offset int
+		for k, want := range test.wantCore {
+			sort.Sort(ordered.Int64s(want))
+			got := make([]int64, len(want))
+			for j, n := range order[len(order)-len(want)-offset : len(order)-offset] {
+				got[j] = n.ID()
+			}
+			sort.Sort(ordered.Int64s(got))
+			if !reflect.DeepEqual(got, want) {
+				t.Errorf("unexpected %d-core for test %d:\ngot: %v\nwant:%v", k, i, got, test.wantCore)
+			}
+
+			for j, n := range core[k] {
+				got[j] = n.ID()
+			}
+			sort.Sort(ordered.Int64s(got))
+			if !reflect.DeepEqual(got, want) {
+				t.Errorf("unexpected %d-core for test %d:\ngot: %v\nwant:%v", k, i, got, test.wantCore)
+			}
+			offset += len(want)
+		}
+	}
+}
+
+var bronKerboschTests = []struct {
+	g    []intset
+	want [][]int64
+}{
+	{
+		// This is the example given in the Bron-Kerbosch article on wikipedia (renumbered).
+		// http://en.wikipedia.org/w/index.php?title=Bron%E2%80%93Kerbosch_algorithm&oldid=656805858
+		g: []intset{
+			0: linksTo(1, 4),
+			1: linksTo(2, 4),
+			2: linksTo(3),
+			3: linksTo(4, 5),
+			4: nil,
+			5: nil,
+		},
+		want: [][]int64{
+			{0, 1, 4},
+			{1, 2},
+			{2, 3},
+			{3, 4},
+			{3, 5},
+		},
+	},
+	{
+		g: batageljZaversnikGraph,
+		want: [][]int64{
+			{0},
+			{1, 2},
+			{1, 3},
+			{2, 4},
+			{3, 4},
+			{4, 5},
+			{6, 7, 8, 14},
+			{7, 11, 12},
+			{9, 11},
+			{10, 11},
+			{12, 18},
+			{13, 14, 15},
+			{14, 15, 17},
+			{15, 16},
+			{17, 18, 19, 20},
+		},
+	},
+}
+
+func TestBronKerbosch(t *testing.T) {
+	for i, test := range bronKerboschTests {
+		g := simple.NewUndirectedGraph()
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+		cliques := BronKerbosch(g)
+		got := make([][]int64, len(cliques))
+		for j, c := range cliques {
+			ids := make([]int64, len(c))
+			for k, n := range c {
+				ids[k] = n.ID()
+			}
+			sort.Sort(ordered.Int64s(ids))
+			got[j] = ids
+		}
+		sort.Sort(ordered.BySliceValues(got))
+		if !reflect.DeepEqual(got, test.want) {
+			t.Errorf("unexpected cliques for test %d:\ngot: %v\nwant:%v", i, got, test.want)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/topo/common_test.go b/vendor/gonum.org/v1/gonum/graph/topo/common_test.go
new file mode 100644
index 00000000..6b09e78b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/topo/common_test.go
@@ -0,0 +1,47 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package topo
+
+// batageljZaversnikGraph is the example graph from
+// figure 1 of http://arxiv.org/abs/cs/0310049v1
+var batageljZaversnikGraph = []intset{
+	0: nil,
+
+	1: linksTo(2, 3),
+	2: linksTo(4),
+	3: linksTo(4),
+	4: linksTo(5),
+	5: nil,
+
+	6:  linksTo(7, 8, 14),
+	7:  linksTo(8, 11, 12, 14),
+	8:  linksTo(14),
+	9:  linksTo(11),
+	10: linksTo(11),
+	11: linksTo(12),
+	12: linksTo(18),
+	13: linksTo(14, 15),
+	14: linksTo(15, 17),
+	15: linksTo(16, 17),
+	16: nil,
+	17: linksTo(18, 19, 20),
+	18: linksTo(19, 20),
+	19: linksTo(20),
+	20: nil,
+}
+
+// intset is an integer set.
+type intset map[int64]struct{}
+
+func linksTo(i ...int64) intset {
+	if len(i) == 0 {
+		return nil
+	}
+	s := make(intset)
+	for _, v := range i {
+		s[v] = struct{}{}
+	}
+	return s
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/topo/doc.go b/vendor/gonum.org/v1/gonum/graph/topo/doc.go
new file mode 100644
index 00000000..ba1bf552
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/topo/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package topo provides graph topology analysis functions.
+package topo // import "gonum.org/v1/gonum/graph/topo"
diff --git a/vendor/gonum.org/v1/gonum/graph/topo/johnson_cycles.go b/vendor/gonum.org/v1/gonum/graph/topo/johnson_cycles.go
new file mode 100644
index 00000000..de84cf9c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/topo/johnson_cycles.go
@@ -0,0 +1,280 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package topo
+
+import (
+	"sort"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/ordered"
+	"gonum.org/v1/gonum/graph/internal/set"
+)
+
+// johnson implements Johnson's "Finding all the elementary
+// circuits of a directed graph" algorithm. SIAM J. Comput. 4(1):1975.
+//
+// Comments in the johnson methods are kept in sync with the comments
+// and labels from the paper.
+type johnson struct {
+	adjacent johnsonGraph // SCC adjacency list.
+	b        []set.Ints   // Johnson's "B-list".
+	blocked  []bool
+	s        int
+
+	stack []graph.Node
+
+	result [][]graph.Node
+}
+
+// DirectedCyclesIn returns the set of elementary cycles in the graph g.
+func DirectedCyclesIn(g graph.Directed) [][]graph.Node {
+	jg := johnsonGraphFrom(g)
+	j := johnson{
+		adjacent: jg,
+		b:        make([]set.Ints, len(jg.orig)),
+		blocked:  make([]bool, len(jg.orig)),
+	}
+
+	// len(j.nodes) is the order of g.
+	for j.s < len(j.adjacent.orig)-1 {
+		// We use the previous SCC adjacency to reduce the work needed.
+		sccs := TarjanSCC(j.adjacent.subgraph(j.s))
+		// A_k = adjacency structure of strong component K with least
+		//       vertex in subgraph of G induced by {s, s+1, ... ,n}.
+		j.adjacent = j.adjacent.sccSubGraph(sccs, 2) // Only allow SCCs with >= 2 vertices.
+		if j.adjacent.order() == 0 {
+			break
+		}
+
+		// s = least vertex in V_k
+		if s := j.adjacent.leastVertexIndex(); s < j.s {
+			j.s = s
+		}
+		for i, v := range j.adjacent.orig {
+			if !j.adjacent.nodes.Has(v.ID()) {
+				continue
+			}
+			if len(j.adjacent.succ[v.ID()]) > 0 {
+				j.blocked[i] = false
+				j.b[i] = make(set.Ints)
+			}
+		}
+		//L3:
+		_ = j.circuit(j.s)
+		j.s++
+	}
+
+	return j.result
+}
+
+// circuit is the CIRCUIT sub-procedure in the paper.
+func (j *johnson) circuit(v int) bool {
+	f := false
+	n := j.adjacent.orig[v]
+	j.stack = append(j.stack, n)
+	j.blocked[v] = true
+
+	//L1:
+	for w := range j.adjacent.succ[n.ID()] {
+		w := j.adjacent.indexOf(w)
+		if w == j.s {
+			// Output circuit composed of stack followed by s.
+			r := make([]graph.Node, len(j.stack)+1)
+			copy(r, j.stack)
+			r[len(r)-1] = j.adjacent.orig[j.s]
+			j.result = append(j.result, r)
+			f = true
+		} else if !j.blocked[w] {
+			if j.circuit(w) {
+				f = true
+			}
+		}
+	}
+
+	//L2:
+	if f {
+		j.unblock(v)
+	} else {
+		for w := range j.adjacent.succ[n.ID()] {
+			j.b[j.adjacent.indexOf(w)].Add(v)
+		}
+	}
+	j.stack = j.stack[:len(j.stack)-1]
+
+	return f
+}
+
+// unblock is the UNBLOCK sub-procedure in the paper.
+func (j *johnson) unblock(u int) {
+	j.blocked[u] = false
+	for w := range j.b[u] {
+		j.b[u].Remove(w)
+		if j.blocked[w] {
+			j.unblock(w)
+		}
+	}
+}
+
+// johnsonGraph is an edge list representation of a graph with helpers
+// necessary for Johnson's algorithm
+type johnsonGraph struct {
+	// Keep the original graph nodes and a
+	// look-up to into the non-sparse
+	// collection of potentially sparse IDs.
+	orig  []graph.Node
+	index map[int64]int
+
+	nodes set.Int64s
+	succ  map[int64]set.Int64s
+}
+
+// johnsonGraphFrom returns a deep copy of the graph g.
+func johnsonGraphFrom(g graph.Directed) johnsonGraph {
+	nodes := g.Nodes()
+	sort.Sort(ordered.ByID(nodes))
+	c := johnsonGraph{
+		orig:  nodes,
+		index: make(map[int64]int, len(nodes)),
+
+		nodes: make(set.Int64s, len(nodes)),
+		succ:  make(map[int64]set.Int64s),
+	}
+	for i, u := range nodes {
+		c.index[u.ID()] = i
+		for _, v := range g.From(u) {
+			if c.succ[u.ID()] == nil {
+				c.succ[u.ID()] = make(set.Int64s)
+				c.nodes.Add(u.ID())
+			}
+			c.nodes.Add(v.ID())
+			c.succ[u.ID()].Add(v.ID())
+		}
+	}
+	return c
+}
+
+// order returns the order of the graph.
+func (g johnsonGraph) order() int { return g.nodes.Count() }
+
+// indexOf returns the index of the retained node for the given node ID.
+func (g johnsonGraph) indexOf(id int64) int {
+	return g.index[id]
+}
+
+// leastVertexIndex returns the index into orig of the least vertex.
+func (g johnsonGraph) leastVertexIndex() int {
+	for _, v := range g.orig {
+		if g.nodes.Has(v.ID()) {
+			return g.indexOf(v.ID())
+		}
+	}
+	panic("johnsonCycles: empty set")
+}
+
+// subgraph returns a subgraph of g induced by {s, s+1, ... , n}. The
+// subgraph is destructively generated in g.
+func (g johnsonGraph) subgraph(s int) johnsonGraph {
+	sn := g.orig[s].ID()
+	for u, e := range g.succ {
+		if u < sn {
+			g.nodes.Remove(u)
+			delete(g.succ, u)
+			continue
+		}
+		for v := range e {
+			if v < sn {
+				g.succ[u].Remove(v)
+			}
+		}
+	}
+	return g
+}
+
+// sccSubGraph returns the graph of the tarjan's strongly connected
+// components with each SCC containing at least min vertices.
+// sccSubGraph returns nil if there is no SCC with at least min
+// members.
+func (g johnsonGraph) sccSubGraph(sccs [][]graph.Node, min int) johnsonGraph {
+	if len(g.nodes) == 0 {
+		g.nodes = nil
+		g.succ = nil
+		return g
+	}
+	sub := johnsonGraph{
+		orig:  g.orig,
+		index: g.index,
+		nodes: make(set.Int64s),
+		succ:  make(map[int64]set.Int64s),
+	}
+
+	var n int
+	for _, scc := range sccs {
+		if len(scc) < min {
+			continue
+		}
+		n++
+		for _, u := range scc {
+			for _, v := range scc {
+				if _, ok := g.succ[u.ID()][v.ID()]; ok {
+					if sub.succ[u.ID()] == nil {
+						sub.succ[u.ID()] = make(set.Int64s)
+						sub.nodes.Add(u.ID())
+					}
+					sub.nodes.Add(v.ID())
+					sub.succ[u.ID()].Add(v.ID())
+				}
+			}
+		}
+	}
+	if n == 0 {
+		g.nodes = nil
+		g.succ = nil
+		return g
+	}
+
+	return sub
+}
+
+// Nodes is required to satisfy Tarjan.
+func (g johnsonGraph) Nodes() []graph.Node {
+	n := make([]graph.Node, 0, len(g.nodes))
+	for id := range g.nodes {
+		n = append(n, johnsonGraphNode(id))
+	}
+	return n
+}
+
+// Successors is required to satisfy Tarjan.
+func (g johnsonGraph) From(n graph.Node) []graph.Node {
+	adj := g.succ[n.ID()]
+	if len(adj) == 0 {
+		return nil
+	}
+	succ := make([]graph.Node, 0, len(adj))
+	for n := range adj {
+		succ = append(succ, johnsonGraphNode(n))
+	}
+	return succ
+}
+
+func (johnsonGraph) Has(graph.Node) bool {
+	panic("topo: unintended use of johnsonGraph")
+}
+func (johnsonGraph) HasEdgeBetween(_, _ graph.Node) bool {
+	panic("topo: unintended use of johnsonGraph")
+}
+func (johnsonGraph) Edge(_, _ graph.Node) graph.Edge {
+	panic("topo: unintended use of johnsonGraph")
+}
+func (johnsonGraph) HasEdgeFromTo(_, _ graph.Node) bool {
+	panic("topo: unintended use of johnsonGraph")
+}
+func (johnsonGraph) To(graph.Node) []graph.Node {
+	panic("topo: unintended use of johnsonGraph")
+}
+
+type johnsonGraphNode int64
+
+func (n johnsonGraphNode) ID() int64 { return int64(n) }
diff --git a/vendor/gonum.org/v1/gonum/graph/topo/johnson_cycles_test.go b/vendor/gonum.org/v1/gonum/graph/topo/johnson_cycles_test.go
new file mode 100644
index 00000000..bf53120d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/topo/johnson_cycles_test.go
@@ -0,0 +1,117 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package topo
+
+import (
+	"reflect"
+	"sort"
+	"testing"
+
+	"gonum.org/v1/gonum/graph/internal/ordered"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+var cyclesInTests = []struct {
+	g    []intset
+	want [][]int64
+}{
+	{
+		g: []intset{
+			0: linksTo(1),
+			1: linksTo(2, 7),
+			2: linksTo(3, 6),
+			3: linksTo(4),
+			4: linksTo(2, 5),
+			6: linksTo(3, 5),
+			7: linksTo(0, 6),
+		},
+		want: [][]int64{
+			{0, 1, 7, 0},
+			{2, 3, 4, 2},
+			{2, 6, 3, 4, 2},
+		},
+	},
+	{
+		g: []intset{
+			0: linksTo(1, 2, 3),
+			1: linksTo(2),
+			2: linksTo(3),
+			3: linksTo(1),
+		},
+		want: [][]int64{
+			{1, 2, 3, 1},
+		},
+	},
+	{
+		g: []intset{
+			0: linksTo(1),
+			1: linksTo(0, 2),
+			2: linksTo(1),
+		},
+		want: [][]int64{
+			{0, 1, 0},
+			{1, 2, 1},
+		},
+	},
+	{
+		g: []intset{
+			0: linksTo(1),
+			1: linksTo(2, 3),
+			2: linksTo(4, 5),
+			3: linksTo(4, 5),
+			4: linksTo(6),
+			5: nil,
+			6: nil,
+		},
+		want: nil,
+	},
+	{
+		g: []intset{
+			0: linksTo(1),
+			1: linksTo(2, 3, 4),
+			2: linksTo(0, 3),
+			3: linksTo(4),
+			4: linksTo(3),
+		},
+		want: [][]int64{
+			{0, 1, 2, 0},
+			{3, 4, 3},
+		},
+	},
+}
+
+func TestDirectedCyclesIn(t *testing.T) {
+	for i, test := range cyclesInTests {
+		g := simple.NewDirectedGraph()
+		g.AddNode(simple.Node(-10)) // Make sure we test graphs with sparse IDs.
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+		cycles := DirectedCyclesIn(g)
+		var got [][]int64
+		if cycles != nil {
+			got = make([][]int64, len(cycles))
+		}
+		// johnson.circuit does range iteration over maps,
+		// so sort to ensure consistent ordering.
+		for j, c := range cycles {
+			ids := make([]int64, len(c))
+			for k, n := range c {
+				ids[k] = n.ID()
+			}
+			got[j] = ids
+		}
+		sort.Sort(ordered.BySliceValues(got))
+		if !reflect.DeepEqual(got, test.want) {
+			t.Errorf("unexpected johnson result for %d:\n\tgot:%#v\n\twant:%#v", i, got, test.want)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/topo/non_tomita_choice.go b/vendor/gonum.org/v1/gonum/graph/topo/non_tomita_choice.go
new file mode 100644
index 00000000..de09ebd8
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/topo/non_tomita_choice.go
@@ -0,0 +1,9 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !tomita
+
+package topo
+
+const tomitaTanakaTakahashi = false
diff --git a/vendor/gonum.org/v1/gonum/graph/topo/paton_cycles.go b/vendor/gonum.org/v1/gonum/graph/topo/paton_cycles.go
new file mode 100644
index 00000000..d012ecaa
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/topo/paton_cycles.go
@@ -0,0 +1,81 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package topo
+
+import (
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/linear"
+	"gonum.org/v1/gonum/graph/internal/set"
+)
+
+// UndirectedCyclesIn returns a set of cycles that forms a cycle basis in the graph g.
+// Any cycle in g can be constructed as a symmetric difference of its elements.
+func UndirectedCyclesIn(g graph.Undirected) [][]graph.Node {
+	// From "An algorithm for finding a fundamental set of cycles of a graph"
+	// https://doi.org/10.1145/363219.363232
+
+	var cycles [][]graph.Node
+	done := make(set.Int64s)
+	var tree linear.NodeStack
+	for _, n := range g.Nodes() {
+		id := n.ID()
+		if done.Has(id) {
+			continue
+		}
+		done.Add(id)
+
+		tree = tree[:0]
+		tree.Push(n)
+		from := sets{id: set.Int64s{}}
+		to := map[int64]graph.Node{id: n}
+
+		for tree.Len() != 0 {
+			u := tree.Pop()
+			uid := u.ID()
+			adj := from[uid]
+			for _, v := range g.From(u) {
+				vid := v.ID()
+				switch {
+				case uid == vid:
+					cycles = append(cycles, []graph.Node{u})
+				case !from.has(vid):
+					done.Add(vid)
+					to[vid] = u
+					tree.Push(v)
+					from.add(uid, vid)
+				case !adj.Has(vid):
+					c := []graph.Node{v, u}
+					adj := from[vid]
+					p := to[uid]
+					for !adj.Has(p.ID()) {
+						c = append(c, p)
+						p = to[p.ID()]
+					}
+					c = append(c, p, c[0])
+					cycles = append(cycles, c)
+					adj.Add(uid)
+				}
+			}
+		}
+	}
+
+	return cycles
+}
+
+type sets map[int64]set.Int64s
+
+func (s sets) add(uid, vid int64) {
+	e, ok := s[vid]
+	if !ok {
+		e = make(set.Int64s)
+		s[vid] = e
+	}
+	e.Add(uid)
+}
+
+func (s sets) has(uid int64) bool {
+	_, ok := s[uid]
+	return ok
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/topo/paton_cycles_test.go b/vendor/gonum.org/v1/gonum/graph/topo/paton_cycles_test.go
new file mode 100644
index 00000000..c36590be
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/topo/paton_cycles_test.go
@@ -0,0 +1,143 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package topo
+
+import (
+	"reflect"
+	"sort"
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/ordered"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+var undirectedCyclesInTests = []struct {
+	g    []intset
+	want [][][]int64
+}{
+	{
+		g: []intset{
+			0:  linksTo(1, 2),
+			1:  linksTo(2, 4, 5, 9),
+			2:  linksTo(4, 7, 9),
+			3:  linksTo(5),
+			4:  linksTo(8),
+			5:  linksTo(7, 8),
+			6:  nil,
+			7:  nil,
+			8:  nil,
+			9:  nil,
+			10: linksTo(11, 12),
+			11: linksTo(12),
+			12: nil,
+		},
+		want: [][][]int64{
+			{
+				{0, 1, 2, 0},
+				{1, 2, 7, 5, 1},
+				{1, 2, 9, 1},
+				{1, 4, 8, 5, 1},
+				{2, 4, 8, 5, 7, 2},
+				{10, 11, 12, 10},
+			},
+			{
+				{0, 1, 2, 0},
+				{1, 2, 4, 1},
+				{1, 2, 7, 5, 1},
+				{1, 2, 9, 1},
+				{1, 4, 8, 5, 1},
+				{10, 11, 12, 10},
+			},
+			{
+				{0, 1, 2, 0},
+				{1, 2, 4, 1},
+				{1, 2, 9, 1},
+				{1, 4, 8, 5, 1},
+				{2, 4, 8, 5, 7, 2},
+				{10, 11, 12, 10},
+			},
+			{
+				{0, 1, 2, 0},
+				{1, 2, 4, 1},
+				{1, 2, 7, 5, 1},
+				{1, 2, 9, 1},
+				{2, 4, 8, 5, 7, 2},
+				{10, 11, 12, 10},
+			},
+		},
+	},
+}
+
+func TestUndirectedCyclesIn(t *testing.T) {
+	for i, test := range undirectedCyclesInTests {
+		g := simple.NewUndirectedGraph()
+		g.AddNode(simple.Node(-10)) // Make sure we test graphs with sparse IDs.
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+		cycles := UndirectedCyclesIn(g)
+		var got [][]int64
+		if cycles != nil {
+			got = make([][]int64, len(cycles))
+		}
+		// Canonicalise the cycles.
+		for j, c := range cycles {
+			ids := make([]int64, len(c))
+			for k, n := range canonicalise(c[:len(c)-1]) {
+				ids[k] = n.ID()
+			}
+			ids[len(ids)-1] = ids[0]
+			got[j] = ids
+		}
+		sort.Sort(ordered.BySliceValues(got))
+		var matched bool
+		for _, want := range test.want {
+			if reflect.DeepEqual(got, want) {
+				matched = true
+				break
+			}
+		}
+		if !matched {
+			t.Errorf("unexpected paton result for %d:\n\tgot:%#v\n\twant from:%#v", i, got, test.want)
+		}
+	}
+}
+
+// canonicalise returns the cycle path c cyclicly permuted such that
+// the first element has the lowest ID and then conditionally
+// reversed so that the second element has the lowest possible
+// neighbouring ID.
+// c lists each node only onces - the final node must not be a
+// reiteration of the first node.
+func canonicalise(c []graph.Node) []graph.Node {
+	if len(c) < 2 {
+		return c
+	}
+	idx := 0
+	min := c[0].ID()
+	for i, n := range c[1:] {
+		if id := n.ID(); id < min {
+			idx = i + 1
+			min = id
+		}
+	}
+	if idx != 0 {
+		c = append(c[idx:], c[:idx]...)
+	}
+	if c[len(c)-1].ID() < c[1].ID() {
+		s := c[1:]
+		for i, j := 0, len(s)-1; i < j; i, j = i+1, j-1 {
+			s[i], s[j] = s[j], s[i]
+		}
+	}
+	return c
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/topo/tarjan.go b/vendor/gonum.org/v1/gonum/graph/topo/tarjan.go
new file mode 100644
index 00000000..cd5d6a86
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/topo/tarjan.go
@@ -0,0 +1,203 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package topo
+
+import (
+	"fmt"
+	"sort"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/ordered"
+	"gonum.org/v1/gonum/graph/internal/set"
+)
+
+// Unorderable is an error containing sets of unorderable graph.Nodes.
+type Unorderable [][]graph.Node
+
+// Error satisfies the error interface.
+func (e Unorderable) Error() string {
+	const maxNodes = 10
+	var n int
+	for _, c := range e {
+		n += len(c)
+	}
+	if n > maxNodes {
+		// Don't return errors that are too long.
+		return fmt.Sprintf("topo: no topological ordering: %d nodes in %d cyclic components", n, len(e))
+	}
+	return fmt.Sprintf("topo: no topological ordering: cyclic components: %v", [][]graph.Node(e))
+}
+
+func lexical(nodes []graph.Node) { sort.Sort(ordered.ByID(nodes)) }
+
+// Sort performs a topological sort of the directed graph g returning the 'from' to 'to'
+// sort order. If a topological ordering is not possible, an Unorderable error is returned
+// listing cyclic components in g with each cyclic component's members sorted by ID. When
+// an Unorderable error is returned, each cyclic component's topological position within
+// the sorted nodes is marked with a nil graph.Node.
+func Sort(g graph.Directed) (sorted []graph.Node, err error) {
+	sccs := TarjanSCC(g)
+	return sortedFrom(sccs, lexical)
+}
+
+// SortStabilized performs a topological sort of the directed graph g returning the 'from'
+// to 'to' sort order, or the order defined by the in place order sort function where there
+// is no unambiguous topological ordering. If a topological ordering is not possible, an
+// Unorderable error is returned listing cyclic components in g with each cyclic component's
+// members sorted by the provided order function. If order is nil, nodes are ordered lexically
+// by node ID. When an Unorderable error is returned, each cyclic component's topological
+// position within the sorted nodes is marked with a nil graph.Node.
+func SortStabilized(g graph.Directed, order func([]graph.Node)) (sorted []graph.Node, err error) {
+	if order == nil {
+		order = lexical
+	}
+	sccs := tarjanSCCstabilized(g, order)
+	return sortedFrom(sccs, order)
+}
+
+func sortedFrom(sccs [][]graph.Node, order func([]graph.Node)) ([]graph.Node, error) {
+	sorted := make([]graph.Node, 0, len(sccs))
+	var sc Unorderable
+	for _, s := range sccs {
+		if len(s) != 1 {
+			order(s)
+			sc = append(sc, s)
+			sorted = append(sorted, nil)
+			continue
+		}
+		sorted = append(sorted, s[0])
+	}
+	var err error
+	if sc != nil {
+		for i, j := 0, len(sc)-1; i < j; i, j = i+1, j-1 {
+			sc[i], sc[j] = sc[j], sc[i]
+		}
+		err = sc
+	}
+	reverse(sorted)
+	return sorted, err
+}
+
+func reverse(p []graph.Node) {
+	for i, j := 0, len(p)-1; i < j; i, j = i+1, j-1 {
+		p[i], p[j] = p[j], p[i]
+	}
+}
+
+// TarjanSCC returns the strongly connected components of the graph g using Tarjan's algorithm.
+//
+// A strongly connected component of a graph is a set of vertices where it's possible to reach any
+// vertex in the set from any other (meaning there's a cycle between them.)
+//
+// Generally speaking, a directed graph where the number of strongly connected components is equal
+// to the number of nodes is acyclic, unless you count reflexive edges as a cycle (which requires
+// only a little extra testing.)
+//
+func TarjanSCC(g graph.Directed) [][]graph.Node {
+	return tarjanSCCstabilized(g, nil)
+}
+
+func tarjanSCCstabilized(g graph.Directed, order func([]graph.Node)) [][]graph.Node {
+	nodes := g.Nodes()
+	var succ func(graph.Node) []graph.Node
+	if order == nil {
+		succ = g.From
+	} else {
+		order(nodes)
+		reverse(nodes)
+
+		succ = func(n graph.Node) []graph.Node {
+			to := g.From(n)
+			order(to)
+			reverse(to)
+			return to
+		}
+	}
+
+	t := tarjan{
+		succ: succ,
+
+		indexTable: make(map[int64]int, len(nodes)),
+		lowLink:    make(map[int64]int, len(nodes)),
+		onStack:    make(set.Int64s),
+	}
+	for _, v := range nodes {
+		if t.indexTable[v.ID()] == 0 {
+			t.strongconnect(v)
+		}
+	}
+	return t.sccs
+}
+
+// tarjan implements Tarjan's strongly connected component finding
+// algorithm. The implementation is from the pseudocode at
+//
+// http://en.wikipedia.org/wiki/Tarjan%27s_strongly_connected_components_algorithm?oldid=642744644
+//
+type tarjan struct {
+	succ func(graph.Node) []graph.Node
+
+	index      int
+	indexTable map[int64]int
+	lowLink    map[int64]int
+	onStack    set.Int64s
+
+	stack []graph.Node
+
+	sccs [][]graph.Node
+}
+
+// strongconnect is the strongconnect function described in the
+// wikipedia article.
+func (t *tarjan) strongconnect(v graph.Node) {
+	vID := v.ID()
+
+	// Set the depth index for v to the smallest unused index.
+	t.index++
+	t.indexTable[vID] = t.index
+	t.lowLink[vID] = t.index
+	t.stack = append(t.stack, v)
+	t.onStack.Add(vID)
+
+	// Consider successors of v.
+	for _, w := range t.succ(v) {
+		wID := w.ID()
+		if t.indexTable[wID] == 0 {
+			// Successor w has not yet been visited; recur on it.
+			t.strongconnect(w)
+			t.lowLink[vID] = min(t.lowLink[vID], t.lowLink[wID])
+		} else if t.onStack.Has(wID) {
+			// Successor w is in stack s and hence in the current SCC.
+			t.lowLink[vID] = min(t.lowLink[vID], t.indexTable[wID])
+		}
+	}
+
+	// If v is a root node, pop the stack and generate an SCC.
+	if t.lowLink[vID] == t.indexTable[vID] {
+		// Start a new strongly connected component.
+		var (
+			scc []graph.Node
+			w   graph.Node
+		)
+		for {
+			w, t.stack = t.stack[len(t.stack)-1], t.stack[:len(t.stack)-1]
+			t.onStack.Remove(w.ID())
+			// Add w to current strongly connected component.
+			scc = append(scc, w)
+			if w.ID() == vID {
+				break
+			}
+		}
+		// Output the current strongly connected component.
+		t.sccs = append(t.sccs, scc)
+	}
+}
+
+func min(a, b int) int {
+	if a < b {
+		return a
+	}
+	return b
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/topo/tarjan_test.go b/vendor/gonum.org/v1/gonum/graph/topo/tarjan_test.go
new file mode 100644
index 00000000..8751c507
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/topo/tarjan_test.go
@@ -0,0 +1,308 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package topo
+
+import (
+	"reflect"
+	"sort"
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/ordered"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+type interval struct{ start, end int }
+
+var tarjanTests = []struct {
+	g []intset
+
+	ambiguousOrder []interval
+	want           [][]int64
+
+	sortedLength      int
+	unorderableLength int
+	sortable          bool
+}{
+	{
+		g: []intset{
+			0: linksTo(1),
+			1: linksTo(2, 7),
+			2: linksTo(3, 6),
+			3: linksTo(4),
+			4: linksTo(2, 5),
+			6: linksTo(3, 5),
+			7: linksTo(0, 6),
+		},
+
+		want: [][]int64{
+			{5},
+			{2, 3, 4, 6},
+			{0, 1, 7},
+		},
+
+		sortedLength:      1,
+		unorderableLength: 2,
+		sortable:          false,
+	},
+	{
+		g: []intset{
+			0: linksTo(1, 2, 3),
+			1: linksTo(2),
+			2: linksTo(3),
+			3: linksTo(1),
+		},
+
+		want: [][]int64{
+			{1, 2, 3},
+			{0},
+		},
+
+		sortedLength:      1,
+		unorderableLength: 1,
+		sortable:          false,
+	},
+	{
+		g: []intset{
+			0: linksTo(1),
+			1: linksTo(0, 2),
+			2: linksTo(1),
+		},
+
+		want: [][]int64{
+			{0, 1, 2},
+		},
+
+		sortedLength:      0,
+		unorderableLength: 1,
+		sortable:          false,
+	},
+	{
+		g: []intset{
+			0: linksTo(1),
+			1: linksTo(2, 3),
+			2: linksTo(4, 5),
+			3: linksTo(4, 5),
+			4: linksTo(6),
+			5: nil,
+			6: nil,
+		},
+
+		// Node pairs (2, 3) and (4, 5) are not
+		// relatively orderable within each pair.
+		ambiguousOrder: []interval{
+			{0, 3}, // This includes node 6 since it only needs to be before 4 in topo sort.
+			{3, 5},
+		},
+		want: [][]int64{
+			{6}, {5}, {4}, {3}, {2}, {1}, {0},
+		},
+
+		sortedLength: 7,
+		sortable:     true,
+	},
+	{
+		g: []intset{
+			0: linksTo(1),
+			1: linksTo(2, 3, 4),
+			2: linksTo(0, 3),
+			3: linksTo(4),
+			4: linksTo(3),
+		},
+
+		// SCCs are not relatively ordable.
+		ambiguousOrder: []interval{
+			{0, 2},
+		},
+		want: [][]int64{
+			{0, 1, 2},
+			{3, 4},
+		},
+
+		sortedLength:      0,
+		unorderableLength: 2,
+		sortable:          false,
+	},
+}
+
+func TestSort(t *testing.T) {
+	for i, test := range tarjanTests {
+		g := simple.NewDirectedGraph()
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+		sorted, err := Sort(g)
+		var gotSortedLen int
+		for _, n := range sorted {
+			if n != nil {
+				gotSortedLen++
+			}
+		}
+		if gotSortedLen != test.sortedLength {
+			t.Errorf("unexpected number of sortable nodes for test %d: got:%d want:%d", i, gotSortedLen, test.sortedLength)
+		}
+		if err == nil != test.sortable {
+			t.Errorf("unexpected sortability for test %d: got error: %v want: nil-error=%t", i, err, test.sortable)
+		}
+		if err != nil && len(err.(Unorderable)) != test.unorderableLength {
+			t.Errorf("unexpected number of unorderable nodes for test %d: got:%d want:%d", i, len(err.(Unorderable)), test.unorderableLength)
+		}
+	}
+}
+
+func TestTarjanSCC(t *testing.T) {
+	for i, test := range tarjanTests {
+		g := simple.NewDirectedGraph()
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+		gotSCCs := TarjanSCC(g)
+		// tarjan.strongconnect does range iteration over maps,
+		// so sort SCC members to ensure consistent ordering.
+		gotIDs := make([][]int64, len(gotSCCs))
+		for i, scc := range gotSCCs {
+			gotIDs[i] = make([]int64, len(scc))
+			for j, id := range scc {
+				gotIDs[i][j] = id.ID()
+			}
+			sort.Sort(ordered.Int64s(gotIDs[i]))
+		}
+		for _, iv := range test.ambiguousOrder {
+			sort.Sort(ordered.BySliceValues(test.want[iv.start:iv.end]))
+			sort.Sort(ordered.BySliceValues(gotIDs[iv.start:iv.end]))
+		}
+		if !reflect.DeepEqual(gotIDs, test.want) {
+			t.Errorf("unexpected Tarjan scc result for %d:\n\tgot:%v\n\twant:%v", i, gotIDs, test.want)
+		}
+	}
+}
+
+var stabilizedSortTests = []struct {
+	g []intset
+
+	want []graph.Node
+	err  error
+}{
+	{
+		g: []intset{
+			0: linksTo(1),
+			1: linksTo(2, 7),
+			2: linksTo(3, 6),
+			3: linksTo(4),
+			4: linksTo(2, 5),
+			6: linksTo(3, 5),
+			7: linksTo(0, 6),
+		},
+
+		want: []graph.Node{nil, nil, simple.Node(5)},
+		err: Unorderable{
+			{simple.Node(0), simple.Node(1), simple.Node(7)},
+			{simple.Node(2), simple.Node(3), simple.Node(4), simple.Node(6)},
+		},
+	},
+	{
+		g: []intset{
+			0: linksTo(1, 2, 3),
+			1: linksTo(2),
+			2: linksTo(3),
+			3: linksTo(1),
+		},
+
+		want: []graph.Node{simple.Node(0), nil},
+		err: Unorderable{
+			{simple.Node(1), simple.Node(2), simple.Node(3)},
+		},
+	},
+	{
+		g: []intset{
+			0: linksTo(1),
+			1: linksTo(0, 2),
+			2: linksTo(1),
+		},
+
+		want: []graph.Node{nil},
+		err: Unorderable{
+			{simple.Node(0), simple.Node(1), simple.Node(2)},
+		},
+	},
+	{
+		g: []intset{
+			0: linksTo(1),
+			1: linksTo(2, 3),
+			2: linksTo(4, 5),
+			3: linksTo(4, 5),
+			4: linksTo(6),
+			5: nil,
+			6: nil,
+		},
+
+		want: []graph.Node{simple.Node(0), simple.Node(1), simple.Node(2), simple.Node(3), simple.Node(4), simple.Node(5), simple.Node(6)},
+		err:  nil,
+	},
+	{
+		g: []intset{
+			0: linksTo(1),
+			1: linksTo(2, 3, 4),
+			2: linksTo(0, 3),
+			3: linksTo(4),
+			4: linksTo(3),
+		},
+
+		want: []graph.Node{nil, nil},
+		err: Unorderable{
+			{simple.Node(0), simple.Node(1), simple.Node(2)},
+			{simple.Node(3), simple.Node(4)},
+		},
+	},
+	{
+		g: []intset{
+			0: linksTo(1, 2, 3, 4, 5, 6),
+			1: linksTo(7),
+			2: linksTo(7),
+			3: linksTo(7),
+			4: linksTo(7),
+			5: linksTo(7),
+			6: linksTo(7),
+			7: nil,
+		},
+
+		want: []graph.Node{simple.Node(0), simple.Node(1), simple.Node(2), simple.Node(3), simple.Node(4), simple.Node(5), simple.Node(6), simple.Node(7)},
+		err:  nil,
+	},
+}
+
+func TestSortStabilized(t *testing.T) {
+	for i, test := range stabilizedSortTests {
+		g := simple.NewDirectedGraph()
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+		got, err := SortStabilized(g, nil)
+		if !reflect.DeepEqual(got, test.want) {
+			t.Errorf("unexpected sort result for test %d: got:%d want:%d", i, got, test.want)
+		}
+		if !reflect.DeepEqual(err, test.err) {
+			t.Errorf("unexpected sort error for test %d: got:%v want:%v", i, err, test.want)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/topo/tomita_choice.go b/vendor/gonum.org/v1/gonum/graph/topo/tomita_choice.go
new file mode 100644
index 00000000..d4eca625
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/topo/tomita_choice.go
@@ -0,0 +1,9 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build tomita
+
+package topo
+
+const tomitaTanakaTakahashi = true
diff --git a/vendor/gonum.org/v1/gonum/graph/topo/topo.go b/vendor/gonum.org/v1/gonum/graph/topo/topo.go
new file mode 100644
index 00000000..fe55f428
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/topo/topo.go
@@ -0,0 +1,68 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package topo
+
+import (
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/traverse"
+)
+
+// IsPathIn returns whether path is a path in g.
+//
+// As special cases, IsPathIn returns true for a zero length path or for
+// a path of length 1 when the node in path exists in the graph.
+func IsPathIn(g graph.Graph, path []graph.Node) bool {
+	switch len(path) {
+	case 0:
+		return true
+	case 1:
+		return g.Has(path[0])
+	default:
+		var canReach func(u, v graph.Node) bool
+		switch g := g.(type) {
+		case graph.Directed:
+			canReach = g.HasEdgeFromTo
+		default:
+			canReach = g.HasEdgeBetween
+		}
+
+		for i, u := range path[:len(path)-1] {
+			if !canReach(u, path[i+1]) {
+				return false
+			}
+		}
+		return true
+	}
+}
+
+// PathExistsIn returns whether there is a path in g starting at from extending
+// to to.
+//
+// PathExistsIn exists as a helper function. If many tests for path existence
+// are being performed, other approaches will be more efficient.
+func PathExistsIn(g graph.Graph, from, to graph.Node) bool {
+	var t traverse.BreadthFirst
+	return t.Walk(g, from, func(n graph.Node, _ int) bool { return n.ID() == to.ID() }) != nil
+}
+
+// ConnectedComponents returns the connected components of the undirected graph g.
+func ConnectedComponents(g graph.Undirected) [][]graph.Node {
+	var (
+		w  traverse.DepthFirst
+		c  []graph.Node
+		cc [][]graph.Node
+	)
+	during := func(n graph.Node) {
+		c = append(c, n)
+	}
+	after := func() {
+		cc = append(cc, []graph.Node(nil))
+		cc[len(cc)-1] = append(cc[len(cc)-1], c...)
+		c = c[:0]
+	}
+	w.WalkAll(g, nil, after, during)
+
+	return cc
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/topo/topo_test.go b/vendor/gonum.org/v1/gonum/graph/topo/topo_test.go
new file mode 100644
index 00000000..bb75796d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/topo/topo_test.go
@@ -0,0 +1,175 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package topo
+
+import (
+	"reflect"
+	"sort"
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/ordered"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+func TestIsPath(t *testing.T) {
+	dg := simple.NewDirectedGraph()
+	if !IsPathIn(dg, nil) {
+		t.Error("IsPath returns false on nil path")
+	}
+	p := []graph.Node{simple.Node(0)}
+	if IsPathIn(dg, p) {
+		t.Error("IsPath returns true on nonexistant node")
+	}
+	dg.AddNode(p[0])
+	if !IsPathIn(dg, p) {
+		t.Error("IsPath returns false on single-length path with existing node")
+	}
+	p = append(p, simple.Node(1))
+	dg.AddNode(p[1])
+	if IsPathIn(dg, p) {
+		t.Error("IsPath returns true on bad path of length 2")
+	}
+	dg.SetEdge(simple.Edge{F: p[0], T: p[1]})
+	if !IsPathIn(dg, p) {
+		t.Error("IsPath returns false on correct path of length 2")
+	}
+	p[0], p[1] = p[1], p[0]
+	if IsPathIn(dg, p) {
+		t.Error("IsPath erroneously returns true for a reverse path")
+	}
+	p = []graph.Node{p[1], p[0], simple.Node(2)}
+	dg.SetEdge(simple.Edge{F: p[1], T: p[2]})
+	if !IsPathIn(dg, p) {
+		t.Error("IsPath does not find a correct path for path > 2 nodes")
+	}
+	ug := simple.NewUndirectedGraph()
+	ug.SetEdge(simple.Edge{F: p[1], T: p[0]})
+	ug.SetEdge(simple.Edge{F: p[1], T: p[2]})
+	if !IsPathIn(dg, p) {
+		t.Error("IsPath does not correctly account for undirected behavior")
+	}
+}
+
+var pathExistsInUndirectedTests = []struct {
+	g        []intset
+	from, to int
+	want     bool
+}{
+	{g: batageljZaversnikGraph, from: 0, to: 0, want: true},
+	{g: batageljZaversnikGraph, from: 0, to: 1, want: false},
+	{g: batageljZaversnikGraph, from: 1, to: 2, want: true},
+	{g: batageljZaversnikGraph, from: 2, to: 1, want: true},
+	{g: batageljZaversnikGraph, from: 2, to: 12, want: false},
+	{g: batageljZaversnikGraph, from: 20, to: 6, want: true},
+}
+
+func TestPathExistsInUndirected(t *testing.T) {
+	for i, test := range pathExistsInUndirectedTests {
+		g := simple.NewUndirectedGraph()
+
+		for u, e := range test.g {
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				if !g.Has(simple.Node(v)) {
+					g.AddNode(simple.Node(v))
+				}
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+
+		got := PathExistsIn(g, simple.Node(test.from), simple.Node(test.to))
+		if got != test.want {
+			t.Errorf("unexpected result for path existence in test %d: got:%t want %t", i, got, test.want)
+		}
+	}
+}
+
+var pathExistsInDirectedTests = []struct {
+	g        []intset
+	from, to int
+	want     bool
+}{
+	// The graph definition is such that from node IDs are
+	// less than to node IDs.
+	{g: batageljZaversnikGraph, from: 0, to: 0, want: true},
+	{g: batageljZaversnikGraph, from: 0, to: 1, want: false},
+	{g: batageljZaversnikGraph, from: 1, to: 2, want: true},
+	{g: batageljZaversnikGraph, from: 2, to: 1, want: false},
+	{g: batageljZaversnikGraph, from: 2, to: 12, want: false},
+	{g: batageljZaversnikGraph, from: 20, to: 6, want: false},
+	{g: batageljZaversnikGraph, from: 6, to: 20, want: true},
+}
+
+func TestPathExistsInDirected(t *testing.T) {
+	for i, test := range pathExistsInDirectedTests {
+		g := simple.NewDirectedGraph()
+
+		for u, e := range test.g {
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				if !g.Has(simple.Node(v)) {
+					g.AddNode(simple.Node(v))
+				}
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+
+		got := PathExistsIn(g, simple.Node(test.from), simple.Node(test.to))
+		if got != test.want {
+			t.Errorf("unexpected result for path existence in test %d: got:%t want %t", i, got, test.want)
+		}
+	}
+}
+
+var connectedComponentTests = []struct {
+	g    []intset
+	want [][]int64
+}{
+	{
+		g: batageljZaversnikGraph,
+		want: [][]int64{
+			{0},
+			{1, 2, 3, 4, 5},
+			{6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20},
+		},
+	},
+}
+
+func TestConnectedComponents(t *testing.T) {
+	for i, test := range connectedComponentTests {
+		g := simple.NewUndirectedGraph()
+
+		for u, e := range test.g {
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				if !g.Has(simple.Node(v)) {
+					g.AddNode(simple.Node(v))
+				}
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+		cc := ConnectedComponents(g)
+		got := make([][]int64, len(cc))
+		for j, c := range cc {
+			ids := make([]int64, len(c))
+			for k, n := range c {
+				ids[k] = n.ID()
+			}
+			sort.Sort(ordered.Int64s(ids))
+			got[j] = ids
+		}
+		sort.Sort(ordered.BySliceValues(got))
+		if !reflect.DeepEqual(got, test.want) {
+			t.Errorf("unexpected connected components for test %d %T:\ngot: %v\nwant:%v", i, g, got, test.want)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/traverse/doc.go b/vendor/gonum.org/v1/gonum/graph/traverse/doc.go
new file mode 100644
index 00000000..7bb3ca11
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/traverse/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package traverse provides basic graph traversal primitives.
+package traverse // import "gonum.org/v1/gonum/graph/traverse"
diff --git a/vendor/gonum.org/v1/gonum/graph/traverse/traverse.go b/vendor/gonum.org/v1/gonum/graph/traverse/traverse.go
new file mode 100644
index 00000000..329649e2
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/traverse/traverse.go
@@ -0,0 +1,180 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package traverse
+
+import (
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/internal/linear"
+	"gonum.org/v1/gonum/graph/internal/set"
+)
+
+// BreadthFirst implements stateful breadth-first graph traversal.
+type BreadthFirst struct {
+	EdgeFilter func(graph.Edge) bool
+	Visit      func(u, v graph.Node)
+	queue      linear.NodeQueue
+	visited    set.Int64s
+}
+
+// Walk performs a breadth-first traversal of the graph g starting from the given node,
+// depending on the the EdgeFilter field and the until parameter if they are non-nil. The
+// traversal follows edges for which EdgeFilter(edge) is true and returns the first node
+// for which until(node, depth) is true. During the traversal, if the Visit field is
+// non-nil, it is called with the nodes joined by each followed edge.
+func (b *BreadthFirst) Walk(g graph.Graph, from graph.Node, until func(n graph.Node, d int) bool) graph.Node {
+	if b.visited == nil {
+		b.visited = make(set.Int64s)
+	}
+	b.queue.Enqueue(from)
+	b.visited.Add(from.ID())
+
+	var (
+		depth     int
+		children  int
+		untilNext = 1
+	)
+	for b.queue.Len() > 0 {
+		t := b.queue.Dequeue()
+		if until != nil && until(t, depth) {
+			return t
+		}
+		for _, n := range g.From(t) {
+			if b.EdgeFilter != nil && !b.EdgeFilter(g.Edge(t, n)) {
+				continue
+			}
+			if b.visited.Has(n.ID()) {
+				continue
+			}
+			if b.Visit != nil {
+				b.Visit(t, n)
+			}
+			b.visited.Add(n.ID())
+			children++
+			b.queue.Enqueue(n)
+		}
+		if untilNext--; untilNext == 0 {
+			depth++
+			untilNext = children
+			children = 0
+		}
+	}
+
+	return nil
+}
+
+// WalkAll calls Walk for each unvisited node of the graph g using edges independent
+// of their direction. The functions before and after are called prior to commencing
+// and after completing each walk if they are non-nil respectively. The function
+// during is called on each node as it is traversed.
+func (b *BreadthFirst) WalkAll(g graph.Undirected, before, after func(), during func(graph.Node)) {
+	b.Reset()
+	for _, from := range g.Nodes() {
+		if b.Visited(from) {
+			continue
+		}
+		if before != nil {
+			before()
+		}
+		b.Walk(g, from, func(n graph.Node, _ int) bool {
+			if during != nil {
+				during(n)
+			}
+			return false
+		})
+		if after != nil {
+			after()
+		}
+	}
+}
+
+// Visited returned whether the node n was visited during a traverse.
+func (b *BreadthFirst) Visited(n graph.Node) bool {
+	return b.visited.Has(n.ID())
+}
+
+// Reset resets the state of the traverser for reuse.
+func (b *BreadthFirst) Reset() {
+	b.queue.Reset()
+	b.visited = nil
+}
+
+// DepthFirst implements stateful depth-first graph traversal.
+type DepthFirst struct {
+	EdgeFilter func(graph.Edge) bool
+	Visit      func(u, v graph.Node)
+	stack      linear.NodeStack
+	visited    set.Int64s
+}
+
+// Walk performs a depth-first traversal of the graph g starting from the given node,
+// depending on the the EdgeFilter field and the until parameter if they are non-nil. The
+// traversal follows edges for which EdgeFilter(edge) is true and returns the first node
+// for which until(node) is true. During the traversal, if the Visit field is non-nil, it
+// is called with the nodes joined by each followed edge.
+func (d *DepthFirst) Walk(g graph.Graph, from graph.Node, until func(graph.Node) bool) graph.Node {
+	if d.visited == nil {
+		d.visited = make(set.Int64s)
+	}
+	d.stack.Push(from)
+	d.visited.Add(from.ID())
+
+	for d.stack.Len() > 0 {
+		t := d.stack.Pop()
+		if until != nil && until(t) {
+			return t
+		}
+		for _, n := range g.From(t) {
+			if d.EdgeFilter != nil && !d.EdgeFilter(g.Edge(t, n)) {
+				continue
+			}
+			if d.visited.Has(n.ID()) {
+				continue
+			}
+			if d.Visit != nil {
+				d.Visit(t, n)
+			}
+			d.visited.Add(n.ID())
+			d.stack.Push(n)
+		}
+	}
+
+	return nil
+}
+
+// WalkAll calls Walk for each unvisited node of the graph g using edges independent
+// of their direction. The functions before and after are called prior to commencing
+// and after completing each walk if they are non-nil respectively. The function
+// during is called on each node as it is traversed.
+func (d *DepthFirst) WalkAll(g graph.Undirected, before, after func(), during func(graph.Node)) {
+	d.Reset()
+	for _, from := range g.Nodes() {
+		if d.Visited(from) {
+			continue
+		}
+		if before != nil {
+			before()
+		}
+		d.Walk(g, from, func(n graph.Node) bool {
+			if during != nil {
+				during(n)
+			}
+			return false
+		})
+		if after != nil {
+			after()
+		}
+	}
+}
+
+// Visited returned whether the node n was visited during a traverse.
+func (d *DepthFirst) Visited(n graph.Node) bool {
+	return d.visited.Has(n.ID())
+}
+
+// Reset resets the state of the traverser for reuse.
+func (d *DepthFirst) Reset() {
+	d.stack = d.stack[:0]
+	d.visited = nil
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/traverse/traverse_test.go b/vendor/gonum.org/v1/gonum/graph/traverse/traverse_test.go
new file mode 100644
index 00000000..ad817352
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/traverse/traverse_test.go
@@ -0,0 +1,433 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package traverse
+
+import (
+	"fmt"
+	"reflect"
+	"sort"
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/graphs/gen"
+	"gonum.org/v1/gonum/graph/internal/ordered"
+	"gonum.org/v1/gonum/graph/simple"
+)
+
+var (
+	// batageljZaversnikGraph is the example graph from
+	// figure 1 of http://arxiv.org/abs/cs/0310049v1
+	batageljZaversnikGraph = []intset{
+		0: nil,
+
+		1: linksTo(2, 3),
+		2: linksTo(4),
+		3: linksTo(4),
+		4: linksTo(5),
+		5: nil,
+
+		6:  linksTo(7, 8, 14),
+		7:  linksTo(8, 11, 12, 14),
+		8:  linksTo(14),
+		9:  linksTo(11),
+		10: linksTo(11),
+		11: linksTo(12),
+		12: linksTo(18),
+		13: linksTo(14, 15),
+		14: linksTo(15, 17),
+		15: linksTo(16, 17),
+		16: nil,
+		17: linksTo(18, 19, 20),
+		18: linksTo(19, 20),
+		19: linksTo(20),
+		20: nil,
+	}
+
+	// wpBronKerboschGraph is the example given in the Bron-Kerbosch article on wikipedia (renumbered).
+	// http://en.wikipedia.org/w/index.php?title=Bron%E2%80%93Kerbosch_algorithm&oldid=656805858
+	wpBronKerboschGraph = []intset{
+		0: linksTo(1, 4),
+		1: linksTo(2, 4),
+		2: linksTo(3),
+		3: linksTo(4, 5),
+		4: nil,
+		5: nil,
+	}
+)
+
+var breadthFirstTests = []struct {
+	g     []intset
+	from  graph.Node
+	edge  func(graph.Edge) bool
+	until func(graph.Node, int) bool
+	final map[graph.Node]bool
+	want  [][]int64
+}{
+	{
+		g:     wpBronKerboschGraph,
+		from:  simple.Node(1),
+		final: map[graph.Node]bool{nil: true},
+		want: [][]int64{
+			{1},
+			{0, 2, 4},
+			{3},
+			{5},
+		},
+	},
+	{
+		g: wpBronKerboschGraph,
+		edge: func(e graph.Edge) bool {
+			// Do not traverse an edge between 3 and 5.
+			return (e.From().ID() != 3 || e.To().ID() != 5) && (e.From().ID() != 5 || e.To().ID() != 3)
+		},
+		from:  simple.Node(1),
+		final: map[graph.Node]bool{nil: true},
+		want: [][]int64{
+			{1},
+			{0, 2, 4},
+			{3},
+		},
+	},
+	{
+		g:     wpBronKerboschGraph,
+		from:  simple.Node(1),
+		until: func(n graph.Node, _ int) bool { return n == simple.Node(3) },
+		final: map[graph.Node]bool{simple.Node(3): true},
+		want: [][]int64{
+			{1},
+			{0, 2, 4},
+		},
+	},
+	{
+		g:     batageljZaversnikGraph,
+		from:  simple.Node(13),
+		final: map[graph.Node]bool{nil: true},
+		want: [][]int64{
+			{13},
+			{14, 15},
+			{6, 7, 8, 16, 17},
+			{11, 12, 18, 19, 20},
+			{9, 10},
+		},
+	},
+	{
+		g:     batageljZaversnikGraph,
+		from:  simple.Node(13),
+		until: func(_ graph.Node, d int) bool { return d > 2 },
+		final: map[graph.Node]bool{
+			simple.Node(11): true,
+			simple.Node(12): true,
+			simple.Node(18): true,
+			simple.Node(19): true,
+			simple.Node(20): true,
+		},
+		want: [][]int64{
+			{13},
+			{14, 15},
+			{6, 7, 8, 16, 17},
+		},
+	},
+}
+
+func TestBreadthFirst(t *testing.T) {
+	for i, test := range breadthFirstTests {
+		g := simple.NewUndirectedGraph()
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+		w := BreadthFirst{
+			EdgeFilter: test.edge,
+		}
+		var got [][]int64
+		final := w.Walk(g, test.from, func(n graph.Node, d int) bool {
+			if test.until != nil && test.until(n, d) {
+				return true
+			}
+			if d >= len(got) {
+				got = append(got, []int64(nil))
+			}
+			got[d] = append(got[d], n.ID())
+			return false
+		})
+		if !test.final[final] {
+			t.Errorf("unexepected final node for test %d:\ngot:  %v\nwant: %v", i, final, test.final)
+		}
+		for _, l := range got {
+			sort.Sort(ordered.Int64s(l))
+		}
+		if !reflect.DeepEqual(got, test.want) {
+			t.Errorf("unexepected BFS level structure for test %d:\ngot:  %v\nwant: %v", i, got, test.want)
+		}
+	}
+}
+
+var depthFirstTests = []struct {
+	g     []intset
+	from  graph.Node
+	edge  func(graph.Edge) bool
+	until func(graph.Node) bool
+	final map[graph.Node]bool
+	want  []int64
+}{
+	{
+		g:     wpBronKerboschGraph,
+		from:  simple.Node(1),
+		final: map[graph.Node]bool{nil: true},
+		want:  []int64{0, 1, 2, 3, 4, 5},
+	},
+	{
+		g: wpBronKerboschGraph,
+		edge: func(e graph.Edge) bool {
+			// Do not traverse an edge between 3 and 5.
+			return (e.From().ID() != 3 || e.To().ID() != 5) && (e.From().ID() != 5 || e.To().ID() != 3)
+		},
+		from:  simple.Node(1),
+		final: map[graph.Node]bool{nil: true},
+		want:  []int64{0, 1, 2, 3, 4},
+	},
+	{
+		g:     wpBronKerboschGraph,
+		from:  simple.Node(1),
+		until: func(n graph.Node) bool { return n == simple.Node(3) },
+		final: map[graph.Node]bool{simple.Node(3): true},
+	},
+	{
+		g:     batageljZaversnikGraph,
+		from:  simple.Node(0),
+		final: map[graph.Node]bool{nil: true},
+		want:  []int64{0},
+	},
+	{
+		g:     batageljZaversnikGraph,
+		from:  simple.Node(3),
+		final: map[graph.Node]bool{nil: true},
+		want:  []int64{1, 2, 3, 4, 5},
+	},
+	{
+		g:     batageljZaversnikGraph,
+		from:  simple.Node(13),
+		final: map[graph.Node]bool{nil: true},
+		want:  []int64{6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20},
+	},
+}
+
+func TestDepthFirst(t *testing.T) {
+	for i, test := range depthFirstTests {
+		g := simple.NewUndirectedGraph()
+		for u, e := range test.g {
+			// Add nodes that are not defined by an edge.
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+		w := DepthFirst{
+			EdgeFilter: test.edge,
+		}
+		var got []int64
+		final := w.Walk(g, test.from, func(n graph.Node) bool {
+			if test.until != nil && test.until(n) {
+				return true
+			}
+			got = append(got, n.ID())
+			return false
+		})
+		if !test.final[final] {
+			t.Errorf("unexepected final node for test %d:\ngot:  %v\nwant: %v", i, final, test.final)
+		}
+		sort.Sort(ordered.Int64s(got))
+		if test.want != nil && !reflect.DeepEqual(got, test.want) {
+			t.Errorf("unexepected DFS traversed nodes for test %d:\ngot:  %v\nwant: %v", i, got, test.want)
+		}
+	}
+}
+
+var walkAllTests = []struct {
+	g    []intset
+	edge func(graph.Edge) bool
+	want [][]int64
+}{
+	{
+		g: batageljZaversnikGraph,
+		want: [][]int64{
+			{0},
+			{1, 2, 3, 4, 5},
+			{6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20},
+		},
+	},
+	{
+		g: batageljZaversnikGraph,
+		edge: func(e graph.Edge) bool {
+			// Do not traverse an edge between 3 and 5.
+			return (e.From().ID() != 4 || e.To().ID() != 5) && (e.From().ID() != 5 || e.To().ID() != 4)
+		},
+		want: [][]int64{
+			{0},
+			{1, 2, 3, 4},
+			{5},
+			{6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20},
+		},
+	},
+}
+
+func TestWalkAll(t *testing.T) {
+	for i, test := range walkAllTests {
+		g := simple.NewUndirectedGraph()
+
+		for u, e := range test.g {
+			if !g.Has(simple.Node(u)) {
+				g.AddNode(simple.Node(u))
+			}
+			for v := range e {
+				if !g.Has(simple.Node(v)) {
+					g.AddNode(simple.Node(v))
+				}
+				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
+			}
+		}
+		type walker interface {
+			WalkAll(g graph.Undirected, before, after func(), during func(graph.Node))
+		}
+		for _, w := range []walker{
+			&BreadthFirst{},
+			&DepthFirst{},
+		} {
+			var (
+				c  []graph.Node
+				cc [][]graph.Node
+			)
+			switch w := w.(type) {
+			case *BreadthFirst:
+				w.EdgeFilter = test.edge
+			case *DepthFirst:
+				w.EdgeFilter = test.edge
+			default:
+				panic(fmt.Sprintf("bad walker type: %T", w))
+			}
+			during := func(n graph.Node) {
+				c = append(c, n)
+			}
+			after := func() {
+				cc = append(cc, []graph.Node(nil))
+				cc[len(cc)-1] = append(cc[len(cc)-1], c...)
+				c = c[:0]
+			}
+			w.WalkAll(g, nil, after, during)
+
+			got := make([][]int64, len(cc))
+			for j, c := range cc {
+				ids := make([]int64, len(c))
+				for k, n := range c {
+					ids[k] = n.ID()
+				}
+				sort.Sort(ordered.Int64s(ids))
+				got[j] = ids
+			}
+			sort.Sort(ordered.BySliceValues(got))
+			if !reflect.DeepEqual(got, test.want) {
+				t.Errorf("unexpected connected components for test %d using %T:\ngot: %v\nwant:%v", i, w, got, test.want)
+			}
+		}
+	}
+}
+
+// intset is an integer set.
+type intset map[int]struct{}
+
+func linksTo(i ...int) intset {
+	if len(i) == 0 {
+		return nil
+	}
+	s := make(intset)
+	for _, v := range i {
+		s[v] = struct{}{}
+	}
+	return s
+}
+
+var (
+	gnpUndirected_10_tenth   = gnpUndirected(10, 0.1)
+	gnpUndirected_100_tenth  = gnpUndirected(100, 0.1)
+	gnpUndirected_1000_tenth = gnpUndirected(1000, 0.1)
+	gnpUndirected_10_half    = gnpUndirected(10, 0.5)
+	gnpUndirected_100_half   = gnpUndirected(100, 0.5)
+	gnpUndirected_1000_half  = gnpUndirected(1000, 0.5)
+)
+
+func gnpUndirected(n int, p float64) graph.Undirected {
+	g := simple.NewUndirectedGraph()
+	gen.Gnp(g, n, p, nil)
+	return g
+}
+
+func benchmarkWalkAllBreadthFirst(b *testing.B, g graph.Undirected) {
+	n := len(g.Nodes())
+	b.ResetTimer()
+	var bft BreadthFirst
+	for i := 0; i < b.N; i++ {
+		bft.WalkAll(g, nil, nil, nil)
+	}
+	if len(bft.visited) != n {
+		b.Fatalf("unexpected number of nodes visited: want: %d got %d", n, len(bft.visited))
+	}
+}
+
+func BenchmarkWalkAllBreadthFirstGnp_10_tenth(b *testing.B) {
+	benchmarkWalkAllBreadthFirst(b, gnpUndirected_10_tenth)
+}
+func BenchmarkWalkAllBreadthFirstGnp_100_tenth(b *testing.B) {
+	benchmarkWalkAllBreadthFirst(b, gnpUndirected_100_tenth)
+}
+func BenchmarkWalkAllBreadthFirstGnp_1000_tenth(b *testing.B) {
+	benchmarkWalkAllBreadthFirst(b, gnpUndirected_1000_tenth)
+}
+func BenchmarkWalkAllBreadthFirstGnp_10_half(b *testing.B) {
+	benchmarkWalkAllBreadthFirst(b, gnpUndirected_10_half)
+}
+func BenchmarkWalkAllBreadthFirstGnp_100_half(b *testing.B) {
+	benchmarkWalkAllBreadthFirst(b, gnpUndirected_100_half)
+}
+func BenchmarkWalkAllBreadthFirstGnp_1000_half(b *testing.B) {
+	benchmarkWalkAllBreadthFirst(b, gnpUndirected_1000_half)
+}
+
+func benchmarkWalkAllDepthFirst(b *testing.B, g graph.Undirected) {
+	n := len(g.Nodes())
+	b.ResetTimer()
+	var dft DepthFirst
+	for i := 0; i < b.N; i++ {
+		dft.WalkAll(g, nil, nil, nil)
+	}
+	if len(dft.visited) != n {
+		b.Fatalf("unexpected number of nodes visited: want: %d got %d", n, len(dft.visited))
+	}
+}
+
+func BenchmarkWalkAllDepthFirstGnp_10_tenth(b *testing.B) {
+	benchmarkWalkAllDepthFirst(b, gnpUndirected_10_tenth)
+}
+func BenchmarkWalkAllDepthFirstGnp_100_tenth(b *testing.B) {
+	benchmarkWalkAllDepthFirst(b, gnpUndirected_100_tenth)
+}
+func BenchmarkWalkAllDepthFirstGnp_1000_tenth(b *testing.B) {
+	benchmarkWalkAllDepthFirst(b, gnpUndirected_1000_tenth)
+}
+func BenchmarkWalkAllDepthFirstGnp_10_half(b *testing.B) {
+	benchmarkWalkAllDepthFirst(b, gnpUndirected_10_half)
+}
+func BenchmarkWalkAllDepthFirstGnp_100_half(b *testing.B) {
+	benchmarkWalkAllDepthFirst(b, gnpUndirected_100_half)
+}
+func BenchmarkWalkAllDepthFirstGnp_1000_half(b *testing.B) {
+	benchmarkWalkAllDepthFirst(b, gnpUndirected_1000_half)
+}
diff --git a/vendor/gonum.org/v1/gonum/graph/undirect.go b/vendor/gonum.org/v1/gonum/graph/undirect.go
new file mode 100644
index 00000000..e045dad4
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/undirect.go
@@ -0,0 +1,224 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package graph
+
+// Undirect converts a directed graph to an undirected graph.
+type Undirect struct {
+	G Directed
+}
+
+var _ Undirected = Undirect{}
+
+// Has returns whether the node exists within the graph.
+func (g Undirect) Has(n Node) bool { return g.G.Has(n) }
+
+// Nodes returns all the nodes in the graph.
+func (g Undirect) Nodes() []Node { return g.G.Nodes() }
+
+// From returns all nodes in g that can be reached directly from u.
+func (g Undirect) From(u Node) []Node {
+	var nodes []Node
+	seen := make(map[int64]struct{})
+	for _, n := range g.G.From(u) {
+		seen[n.ID()] = struct{}{}
+		nodes = append(nodes, n)
+	}
+	for _, n := range g.G.To(u) {
+		id := n.ID()
+		if _, ok := seen[id]; ok {
+			continue
+		}
+		seen[n.ID()] = struct{}{}
+		nodes = append(nodes, n)
+	}
+	return nodes
+}
+
+// HasEdgeBetween returns whether an edge exists between nodes x and y.
+func (g Undirect) HasEdgeBetween(x, y Node) bool { return g.G.HasEdgeBetween(x, y) }
+
+// Edge returns the edge from u to v if such an edge exists and nil otherwise.
+// The node v must be directly reachable from u as defined by the From method.
+// If an edge exists, the Edge returned is an EdgePair. The weight of
+// the edge is determined by applying the Merge func to the weights of the
+// edges between u and v.
+func (g Undirect) Edge(u, v Node) Edge { return g.EdgeBetween(u, v) }
+
+// EdgeBetween returns the edge between nodes x and y. If an edge exists, the
+// Edge returned is an EdgePair. The weight of the edge is determined by
+// applying the Merge func to the weights of edges between x and y.
+func (g Undirect) EdgeBetween(x, y Node) Edge {
+	fe := g.G.Edge(x, y)
+	re := g.G.Edge(y, x)
+	if fe == nil && re == nil {
+		return nil
+	}
+
+	return EdgePair{fe, re}
+}
+
+// UndirectWeighted converts a directed weighted graph to an undirected weighted graph,
+// resolving edge weight conflicts.
+type UndirectWeighted struct {
+	G WeightedDirected
+
+	// Absent is the value used to
+	// represent absent edge weights
+	// passed to Merge if the reverse
+	// edge is present.
+	Absent float64
+
+	// Merge defines how discordant edge
+	// weights in G are resolved. A merge
+	// is performed if at least one edge
+	// exists between the nodes being
+	// considered. The edges corresponding
+	// to the two weights are also passed,
+	// in the same order.
+	// The order of weight parameters
+	// passed to Merge is not defined, so
+	// the function should be commutative.
+	// If Merge is nil, the arithmetic
+	// mean is used to merge weights.
+	Merge func(x, y float64, xe, ye Edge) float64
+}
+
+var (
+	_ Undirected         = UndirectWeighted{}
+	_ WeightedUndirected = UndirectWeighted{}
+)
+
+// Has returns whether the node exists within the graph.
+func (g UndirectWeighted) Has(n Node) bool { return g.G.Has(n) }
+
+// Nodes returns all the nodes in the graph.
+func (g UndirectWeighted) Nodes() []Node { return g.G.Nodes() }
+
+// From returns all nodes in g that can be reached directly from u.
+func (g UndirectWeighted) From(u Node) []Node {
+	var nodes []Node
+	seen := make(map[int64]struct{})
+	for _, n := range g.G.From(u) {
+		seen[n.ID()] = struct{}{}
+		nodes = append(nodes, n)
+	}
+	for _, n := range g.G.To(u) {
+		id := n.ID()
+		if _, ok := seen[id]; ok {
+			continue
+		}
+		seen[n.ID()] = struct{}{}
+		nodes = append(nodes, n)
+	}
+	return nodes
+}
+
+// HasEdgeBetween returns whether an edge exists between nodes x and y.
+func (g UndirectWeighted) HasEdgeBetween(x, y Node) bool { return g.G.HasEdgeBetween(x, y) }
+
+// Edge returns the edge from u to v if such an edge exists and nil otherwise.
+// The node v must be directly reachable from u as defined by the From method.
+// If an edge exists, the Edge returned is an EdgePair. The weight of
+// the edge is determined by applying the Merge func to the weights of the
+// edges between u and v.
+func (g UndirectWeighted) Edge(u, v Node) Edge { return g.WeightedEdgeBetween(u, v) }
+
+// WeightedEdge returns the weighted edge from u to v if such an edge exists and nil otherwise.
+// The node v must be directly reachable from u as defined by the From method.
+// If an edge exists, the Edge returned is an EdgePair. The weight of
+// the edge is determined by applying the Merge func to the weights of the
+// edges between u and v.
+func (g UndirectWeighted) WeightedEdge(u, v Node) WeightedEdge { return g.WeightedEdgeBetween(u, v) }
+
+// EdgeBetween returns the edge between nodes x and y. If an edge exists, the
+// Edge returned is an EdgePair. The weight of the edge is determined by
+// applying the Merge func to the weights of edges between x and y.
+func (g UndirectWeighted) EdgeBetween(x, y Node) Edge {
+	return g.WeightedEdgeBetween(x, y)
+}
+
+// WeightedEdgeBetween returns the weighted edge between nodes x and y. If an edge exists, the
+// Edge returned is an EdgePair. The weight of the edge is determined by
+// applying the Merge func to the weights of edges between x and y.
+func (g UndirectWeighted) WeightedEdgeBetween(x, y Node) WeightedEdge {
+	fe := g.G.Edge(x, y)
+	re := g.G.Edge(y, x)
+	if fe == nil && re == nil {
+		return nil
+	}
+
+	f, ok := g.G.Weight(x, y)
+	if !ok {
+		f = g.Absent
+	}
+	r, ok := g.G.Weight(y, x)
+	if !ok {
+		r = g.Absent
+	}
+
+	var w float64
+	if g.Merge == nil {
+		w = (f + r) / 2
+	} else {
+		w = g.Merge(f, r, fe, re)
+	}
+	return WeightedEdgePair{EdgePair: [2]Edge{fe, re}, W: w}
+}
+
+// Weight returns the weight for the edge between x and y if Edge(x, y) returns a non-nil Edge.
+// If x and y are the same node the internal node weight is returned. If there is no joining
+// edge between the two nodes the weight value returned is zero. Weight returns true if an edge
+// exists between x and y or if x and y have the same ID, false otherwise.
+func (g UndirectWeighted) Weight(x, y Node) (w float64, ok bool) {
+	fe := g.G.Edge(x, y)
+	re := g.G.Edge(y, x)
+
+	f, fOk := g.G.Weight(x, y)
+	if !fOk {
+		f = g.Absent
+	}
+	r, rOK := g.G.Weight(y, x)
+	if !rOK {
+		r = g.Absent
+	}
+	ok = fOk || rOK
+
+	if g.Merge == nil {
+		return (f + r) / 2, ok
+	}
+	return g.Merge(f, r, fe, re), ok
+}
+
+// EdgePair is an opposed pair of directed edges.
+type EdgePair [2]Edge
+
+// From returns the from node of the first non-nil edge, or nil.
+func (e EdgePair) From() Node {
+	if e[0] != nil {
+		return e[0].From()
+	} else if e[1] != nil {
+		return e[1].From()
+	}
+	return nil
+}
+
+// To returns the to node of the first non-nil edge, or nil.
+func (e EdgePair) To() Node {
+	if e[0] != nil {
+		return e[0].To()
+	} else if e[1] != nil {
+		return e[1].To()
+	}
+	return nil
+}
+
+// WeightedEdgePair is an opposed pair of directed edges.
+type WeightedEdgePair struct {
+	EdgePair
+	W float64
+}
+
+// Weight returns the merged edge weights of the two edges.
+func (e WeightedEdgePair) Weight() float64 { return e.W }
diff --git a/vendor/gonum.org/v1/gonum/graph/undirect_test.go b/vendor/gonum.org/v1/gonum/graph/undirect_test.go
new file mode 100644
index 00000000..8b9b9883
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/graph/undirect_test.go
@@ -0,0 +1,175 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package graph_test
+
+import (
+	"math"
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/simple"
+	"gonum.org/v1/gonum/mat"
+)
+
+type weightedDirectedBuilder interface {
+	graph.WeightedBuilder
+	graph.WeightedDirected
+}
+
+var weightedDirectedGraphs = []struct {
+	skipUnweighted bool
+
+	g      func() weightedDirectedBuilder
+	edges  []simple.WeightedEdge
+	absent float64
+	merge  func(x, y float64, xe, ye graph.Edge) float64
+
+	want mat.Matrix
+}{
+	{
+		g: func() weightedDirectedBuilder { return simple.NewWeightedDirectedGraph(0, 0) },
+		edges: []simple.WeightedEdge{
+			{F: simple.Node(0), T: simple.Node(1), W: 2},
+			{F: simple.Node(1), T: simple.Node(0), W: 1},
+			{F: simple.Node(1), T: simple.Node(2), W: 1},
+		},
+		want: mat.NewSymDense(3, []float64{
+			0, (1. + 2.) / 2., 0,
+			(1. + 2.) / 2., 0, 1. / 2.,
+			0, 1. / 2., 0,
+		}),
+	},
+	{
+		g: func() weightedDirectedBuilder { return simple.NewWeightedDirectedGraph(0, 0) },
+		edges: []simple.WeightedEdge{
+			{F: simple.Node(0), T: simple.Node(1), W: 2},
+			{F: simple.Node(1), T: simple.Node(0), W: 1},
+			{F: simple.Node(1), T: simple.Node(2), W: 1},
+		},
+		absent: 1,
+		merge:  func(x, y float64, _, _ graph.Edge) float64 { return math.Sqrt(x * y) },
+		want: mat.NewSymDense(3, []float64{
+			0, math.Sqrt(1 * 2), 0,
+			math.Sqrt(1 * 2), 0, math.Sqrt(1 * 1),
+			0, math.Sqrt(1 * 1), 0,
+		}),
+	},
+	{
+		skipUnweighted: true, // The min merge function cannot be used in the unweighted case.
+
+		g: func() weightedDirectedBuilder { return simple.NewWeightedDirectedGraph(0, 0) },
+		edges: []simple.WeightedEdge{
+			{F: simple.Node(0), T: simple.Node(1), W: 2},
+			{F: simple.Node(1), T: simple.Node(0), W: 1},
+			{F: simple.Node(1), T: simple.Node(2), W: 1},
+		},
+		merge: func(x, y float64, _, _ graph.Edge) float64 { return math.Min(x, y) },
+		want: mat.NewSymDense(3, []float64{
+			0, math.Min(1, 2), 0,
+			math.Min(1, 2), 0, math.Min(1, 0),
+			0, math.Min(1, 0), 0,
+		}),
+	},
+	{
+		g: func() weightedDirectedBuilder { return simple.NewWeightedDirectedGraph(0, 0) },
+		edges: []simple.WeightedEdge{
+			{F: simple.Node(0), T: simple.Node(1), W: 2},
+			{F: simple.Node(1), T: simple.Node(0), W: 1},
+			{F: simple.Node(1), T: simple.Node(2), W: 1},
+		},
+		merge: func(x, y float64, xe, ye graph.Edge) float64 {
+			if xe == nil {
+				return y
+			}
+			if ye == nil {
+				return x
+			}
+			return math.Min(x, y)
+		},
+		want: mat.NewSymDense(3, []float64{
+			0, math.Min(1, 2), 0,
+			math.Min(1, 2), 0, 1,
+			0, 1, 0,
+		}),
+	},
+	{
+		g: func() weightedDirectedBuilder { return simple.NewWeightedDirectedGraph(0, 0) },
+		edges: []simple.WeightedEdge{
+			{F: simple.Node(0), T: simple.Node(1), W: 2},
+			{F: simple.Node(1), T: simple.Node(0), W: 1},
+			{F: simple.Node(1), T: simple.Node(2), W: 1},
+		},
+		merge: func(x, y float64, _, _ graph.Edge) float64 { return math.Max(x, y) },
+		want: mat.NewSymDense(3, []float64{
+			0, math.Max(1, 2), 0,
+			math.Max(1, 2), 0, math.Max(1, 0),
+			0, math.Max(1, 0), 0,
+		}),
+	},
+}
+
+func TestUndirect(t *testing.T) {
+	for i, test := range weightedDirectedGraphs {
+		if test.skipUnweighted {
+			continue
+		}
+		g := test.g()
+		for _, e := range test.edges {
+			g.SetWeightedEdge(e)
+		}
+
+		src := graph.Undirect{G: g}
+		dst := simple.NewUndirectedMatrixFrom(src.Nodes(), 0, 0, 0)
+		for _, u := range src.Nodes() {
+			for _, v := range src.From(u) {
+				dst.SetEdge(src.Edge(u, v))
+			}
+		}
+
+		want := unit{test.want}
+		if !mat.Equal(dst.Matrix(), want) {
+			t.Errorf("unexpected result for case %d:\ngot:\n%.4v\nwant:\n%.4v", i,
+				mat.Formatted(dst.Matrix()),
+				mat.Formatted(want),
+			)
+		}
+	}
+}
+
+func TestUndirectWeighted(t *testing.T) {
+	for i, test := range weightedDirectedGraphs {
+		g := test.g()
+		for _, e := range test.edges {
+			g.SetWeightedEdge(e)
+		}
+
+		src := graph.UndirectWeighted{G: g, Absent: test.absent, Merge: test.merge}
+		dst := simple.NewUndirectedMatrixFrom(src.Nodes(), 0, 0, 0)
+		for _, u := range src.Nodes() {
+			for _, v := range src.From(u) {
+				dst.SetWeightedEdge(src.WeightedEdge(u, v))
+			}
+		}
+
+		if !mat.Equal(dst.Matrix(), test.want) {
+			t.Errorf("unexpected result for case %d:\ngot:\n%.4v\nwant:\n%.4v", i,
+				mat.Formatted(dst.Matrix()),
+				mat.Formatted(test.want),
+			)
+		}
+	}
+}
+
+type unit struct {
+	mat.Matrix
+}
+
+func (m unit) At(i, j int) float64 {
+	v := m.Matrix.At(i, j)
+	if v == 0 {
+		return 0
+	}
+	return 1
+}
diff --git a/vendor/gonum.org/v1/gonum/integrate/README.md b/vendor/gonum.org/v1/gonum/integrate/README.md
new file mode 100644
index 00000000..1c929a8d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/integrate/README.md
@@ -0,0 +1,3 @@
+# Gonum integrate [![GoDoc](https://godoc.org/gonum.org/v1/gonum/integrate?status.svg)](https://godoc.org/gonum.org/v1/gonum/integrate)
+
+Package integrate provides numerical evaluation of definite integrals of single-variable functions for the Go programming language.
diff --git a/vendor/gonum.org/v1/gonum/integrate/doc.go b/vendor/gonum.org/v1/gonum/integrate/doc.go
new file mode 100644
index 00000000..81bddb3b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/integrate/doc.go
@@ -0,0 +1,7 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package integrate provides functions to compute an integral given a
+// specific list of evaluations.
+package integrate // import "gonum.org/v1/gonum/integrate"
diff --git a/vendor/gonum.org/v1/gonum/integrate/quad/doc.go b/vendor/gonum.org/v1/gonum/integrate/quad/doc.go
new file mode 100644
index 00000000..480edcc0
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/integrate/quad/doc.go
@@ -0,0 +1,7 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package quad provides numerical evaluation of definite integrals of single-variable functions.
+//
+package quad // import "gonum.org/v1/gonum/integrate/quad"
diff --git a/vendor/gonum.org/v1/gonum/integrate/quad/example_test.go b/vendor/gonum.org/v1/gonum/integrate/quad/example_test.go
new file mode 100644
index 00000000..32a4886a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/integrate/quad/example_test.go
@@ -0,0 +1,47 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package quad_test
+
+import (
+	"fmt"
+	"math"
+	"runtime"
+
+	"gonum.org/v1/gonum/integrate/quad"
+	"gonum.org/v1/gonum/stat/distuv"
+)
+
+func Example() {
+	fmt.Println("Evaluate the expected value of x^2 + 3 under a Weibull distribution")
+	f := func(x float64) float64 {
+		d := distuv.Weibull{Lambda: 1, K: 1.5}
+		return (x*x + 3) * d.Prob(x)
+	}
+	ev := quad.Fixed(f, 0, math.Inf(1), 10, nil, 0)
+	fmt.Printf("EV with 10 points = %0.6v\n", ev)
+
+	ev = quad.Fixed(f, 0, math.Inf(1), 30, nil, 0)
+	fmt.Printf("EV with 30 points = %0.6v\n", ev)
+
+	ev = quad.Fixed(f, 0, math.Inf(1), 100, nil, 0)
+	fmt.Printf("EV with 100 points = %0.6v\n", ev)
+
+	ev = quad.Fixed(f, 0, math.Inf(1), 10000, nil, 0)
+	fmt.Printf("EV with 10000 points = %0.6v\n\n", ev)
+
+	fmt.Println("Estimate using parallel evaluations of f.")
+	concurrent := runtime.GOMAXPROCS(0)
+	ev = quad.Fixed(f, 0, math.Inf(1), 100, nil, concurrent)
+	fmt.Printf("EV = %0.6v\n", ev)
+	// Output:
+	// Evaluate the expected value of x^2 + 3 under a Weibull distribution
+	// EV with 10 points = 4.20175
+	// EV with 30 points = 4.19066
+	// EV with 100 points = 4.19064
+	// EV with 10000 points = 4.19064
+	//
+	// Estimate using parallel evaluations of f.
+	// EV = 4.19064
+}
diff --git a/vendor/gonum.org/v1/gonum/integrate/quad/hermite.go b/vendor/gonum.org/v1/gonum/integrate/quad/hermite.go
new file mode 100644
index 00000000..d2755f0e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/integrate/quad/hermite.go
@@ -0,0 +1,314 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package quad
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mathext"
+)
+
+// Hermite generates sample locations and weights for performing quadrature with
+// with a squared-exponential weight
+//  int_-inf^inf e^(-x^2) f(x) dx .
+type Hermite struct{}
+
+func (h Hermite) FixedLocations(x, weight []float64, min, max float64) {
+	// TODO(btracey): Implement the case where x > 20, x < 200 so that we don't
+	// need to store all of that data.
+
+	// Algorithm adapted from Chebfun http://www.chebfun.org/.
+	//
+	// References:
+	// Algorithm:
+	// G. H. Golub and J. A. Welsch, "Calculation of Gauss quadrature rules",
+	// Math. Comp. 23:221-230, 1969.
+	// A. Glaser, X. Liu and V. Rokhlin, "A fast algorithm for the
+	// calculation of the roots of special functions", SIAM Journal
+	// on Scientific Computing", 29(4):1420-1438:, 2007.
+	// A. Townsend, T. Trogdon, and S.Olver, Fast computation of Gauss quadrature
+	// nodes and weights on the whole real line, IMA J. Numer. Anal., 36: 337–358,
+	// 2016. http://arxiv.org/abs/1410.5286
+
+	if len(x) != len(weight) {
+		panic("hermite: slice length mismatch")
+	}
+	if min >= max {
+		panic("hermite: min >= max")
+	}
+	if !math.IsInf(min, -1) || !math.IsInf(max, 1) {
+		panic("hermite: non-infinite bound")
+	}
+	h.locations(x, weight)
+}
+
+func (h Hermite) locations(x, weights []float64) {
+	n := len(x)
+	switch {
+	case 0 < n && n <= 200:
+		copy(x, xCacheHermite[n-1])
+		copy(weights, wCacheHermite[n-1])
+	case n > 200:
+		h.locationsAsy(x, weights)
+	}
+}
+
+// Algorithm adapted from Chebfun http://www.chebfun.org/. Specific code
+// https://github.com/chebfun/chebfun/blob/development/hermpts.m.
+
+// Original Copyright Notice:
+
+/*
+Copyright (c) 2015, The Chancellor, Masters and Scholars of the University
+of Oxford, and the Chebfun Developers. All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+    * Redistributions of source code must retain the above copyright
+      notice, this list of conditions and the following disclaimer.
+    * Redistributions in binary form must reproduce the above copyright
+      notice, this list of conditions and the following disclaimer in the
+      documentation and/or other materials provided with the distribution.
+    * Neither the name of the University of Oxford nor the names of its
+      contributors may be used to endorse or promote products derived from
+      this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
+ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
+ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*/
+
+// locationAsy returns the node locations and weights of a Hermite quadrature rule
+// with len(x) points.
+func (h Hermite) locationsAsy(x, w []float64) {
+	// A. Townsend, T. Trogdon, and S.Olver, Fast computation of Gauss quadrature
+	// nodes and weights the whole real line, IMA J. Numer. Anal.,
+	// 36: 337–358, 2016. http://arxiv.org/abs/1410.5286
+
+	// Find the positive locations and weights.
+	n := len(x)
+	l := n / 2
+	xa := x[l:]
+	wa := w[l:]
+	for i := range xa {
+		xa[i], wa[i] = h.locationsAsy0(i, n)
+	}
+	// Flip around zero -- copy the negative x locations with the corresponding
+	// weights.
+	if n%2 == 0 {
+		l--
+	}
+	for i, v := range xa {
+		x[l-i] = -v
+	}
+	for i, v := range wa {
+		w[l-i] = v
+	}
+	sumW := floats.Sum(w)
+	c := math.SqrtPi / sumW
+	floats.Scale(c, w)
+}
+
+// locationsAsy0 returns the location and weight for location i in an n-point
+// quadrature rule. The rule is symmetric, so i should be <= n/2 + n%2.
+func (h Hermite) locationsAsy0(i, n int) (x, w float64) {
+	const convTol = 1e-16
+	const convIter = 20
+	theta0 := h.hermiteInitialGuess(i, n)
+	t0 := theta0 / math.Sqrt(2*float64(n)+1)
+	theta0 = math.Acos(t0)
+	sqrt2np1 := math.Sqrt(2*float64(n) + 1)
+	var vali, dvali float64
+	for k := 0; k < convIter; k++ {
+		vali, dvali = h.hermpolyAsyAiry(i, n, theta0)
+		dt := -vali / (math.Sqrt2 * sqrt2np1 * dvali * math.Sin(theta0))
+		theta0 -= dt
+		if math.Abs(theta0) < convTol {
+			break
+		}
+	}
+	x = sqrt2np1 * math.Cos(theta0)
+	ders := x*vali + math.Sqrt2*dvali
+	w = math.Exp(-x*x) / (ders * ders)
+	return x, w
+}
+
+// hermpolyAsyAiry evaluates the Hermite polynomials using the Airy asymptotic
+// formula in theta-space.
+func (h Hermite) hermpolyAsyAiry(i, n int, t float64) (valVec, dvalVec float64) {
+	musq := 2*float64(n) + 1
+	cosT := math.Cos(t)
+	sinT := math.Sin(t)
+	sin2T := 2 * cosT * sinT
+	eta := 0.5*t - 0.25*sin2T
+	chi := -math.Pow(3*eta/2, 2.0/3)
+	phi := math.Pow(-chi/(sinT*sinT), 1.0/4)
+	cnst := 2 * math.SqrtPi * math.Pow(musq, 1.0/6) * phi
+	airy0 := real(mathext.AiryAi(complex(math.Pow(musq, 2.0/3)*chi, 0)))
+	airy1 := real(mathext.AiryAiDeriv(complex(math.Pow(musq, 2.0/3)*chi, 0)))
+
+	// Terms in 12.10.43:
+	const (
+		a1 = 15.0 / 144
+		b1 = -7.0 / 5 * a1
+		a2 = 5.0 * 7 * 9 * 11.0 / 2.0 / 144.0 / 144.0
+		b2 = -13.0 / 11 * a2
+		a3 = 7.0 * 9 * 11 * 13 * 15 * 17 / 6.0 / 144.0 / 144.0 / 144.0
+		b3 = -19.0 / 17 * a3
+	)
+
+	// Pre-compute terms.
+	cos2T := cosT * cosT
+	cos3T := cos2T * cosT
+	cos4T := cos3T * cosT
+	cos5T := cos4T * cosT
+	cos7T := cos5T * cos2T
+	cos9T := cos7T * cos2T
+
+	chi2 := chi * chi
+	chi3 := chi2 * chi
+	chi4 := chi3 * chi
+	chi5 := chi4 * chi
+
+	phi6 := math.Pow(phi, 6)
+	phi12 := phi6 * phi6
+	phi18 := phi12 * phi6
+
+	// u polynomials in 12.10.9.
+	u1 := (cos3T - 6*cosT) / 24.0
+	u2 := (-9*cos4T + 249*cos2T + 145) / 1152.0
+	u3 := (-4042*cos9T + 18189*cos7T - 28287*cos5T - 151995*cos3T - 259290*cosT) / 414720.0
+
+	val := airy0
+	B0 := -(phi6*u1 + a1) / chi2
+	val += B0 * airy1 / math.Pow(musq, 4.0/3)
+	A1 := (phi12*u2 + b1*phi6*u1 + b2) / chi3
+	val += A1 * airy0 / (musq * musq)
+	B1 := -(phi18*u3 + a1*phi12*u2 + a2*phi6*u1 + a3) / chi5
+	val += B1 * airy1 / math.Pow(musq, 4.0/3+2)
+	val *= cnst
+
+	// Derivative.
+	eta = 0.5*t - 0.25*sin2T
+	chi = -math.Pow(3*eta/2, 2.0/3)
+	phi = math.Pow(-chi/(sinT*sinT), 1.0/4)
+	cnst = math.Sqrt2 * math.SqrtPi * math.Pow(musq, 1.0/3) / phi
+
+	// v polynomials in 12.10.10.
+	v1 := (cos3T + 6*cosT) / 24
+	v2 := (15*cos4T - 327*cos2T - 143) / 1152
+	v3 := (259290*cosT + 238425*cos3T - 36387*cos5T + 18189*cos7T - 4042*cos9T) / 414720
+
+	C0 := -(phi6*v1 + b1) / chi
+	dval := C0 * airy0 / math.Pow(musq, 2.0/3)
+	dval += airy1
+	C1 := -(phi18*v3 + b1*phi12*v2 + b2*phi6*v1 + b3) / chi4
+	dval += C1 * airy0 / math.Pow(musq, 2.0/3+2)
+	D1 := (phi12*v2 + a1*phi6*v1 + a2) / chi3
+	dval += D1 * airy1 / (musq * musq)
+	dval *= cnst
+	return val, dval
+}
+
+// hermiteInitialGuess returns the initial guess for node i in an n-point Hermite
+// quadrature rule. The rule is symmetric, so i should be <= n/2 + n%2.
+func (h Hermite) hermiteInitialGuess(i, n int) float64 {
+	// There are two different formulas for the initial guesses of the hermite
+	// quadrature locations. The first uses the Gatteschi formula and is good
+	// near x = sqrt(n+0.5)
+	//  [1] L. Gatteschi, Asymptotics and bounds for the zeros of Laguerre
+	//  polynomials: a survey, J. Comput. Appl. Math., 144 (2002), pp. 7-27.
+	// The second is the Tricomi initial guesses, good near x = 0. This is
+	// equation 2.1 in [1] and is originally from
+	//  [2] F. G. Tricomi, Sugli zeri delle funzioni di cui si conosce una
+	//  rappresentazione asintotica, Ann. Mat. Pura Appl. 26 (1947), pp. 283-300.
+
+	// If the number of points is odd, there is a quadrature point at 1, which
+	// has an initial guess of 0.
+	if n%2 == 1 {
+		if i == 0 {
+			return 0
+		}
+		i--
+	}
+
+	m := n / 2
+	a := -0.5
+	if n%2 == 1 {
+		a = 0.5
+	}
+	nu := 4*float64(m) + 2*a + 2
+
+	// Find the split between Gatteschi guesses and Tricomi guesses.
+	p := 0.4985 + math.SmallestNonzeroFloat64
+	pidx := int(math.Floor(p * float64(n)))
+
+	// Use the Tricomi initial guesses in the first half where x is nearer to zero.
+	// Note: zeros of besselj(+/-.5,x) are integer and half-integer multiples of pi.
+	if i < pidx {
+		rhs := math.Pi * (4*float64(m) - 4*(float64(i)+1) + 3) / nu
+		tnk := math.Pi / 2
+		for k := 0; k < 7; k++ {
+			val := tnk - math.Sin(tnk) - rhs
+			dval := 1 - math.Cos(tnk)
+			dTnk := val / dval
+			tnk -= dTnk
+			if math.Abs(dTnk) < 1e-14 {
+				break
+			}
+		}
+		vc := math.Cos(tnk / 2)
+		t := vc * vc
+		return math.Sqrt(nu*t - (5.0/(4.0*(1-t)*(1-t))-1.0/(1-t)-1+3*a*a)/3/nu)
+	}
+
+	// Use Gatteschi guesses in the second half where x is nearer to sqrt(n+0.5)
+	i = i + 1 - m
+	var ar float64
+	if i < len(airyRtsExact) {
+		ar = airyRtsExact[i]
+	} else {
+		t := 3.0 / 8 * math.Pi * (4*(float64(i)+1) - 1)
+		ar = math.Pow(t, 2.0/3) * (1 +
+			5.0/48*math.Pow(t, -2) -
+			5.0/36*math.Pow(t, -4) +
+			77125.0/82944*math.Pow(t, -6) -
+			108056875.0/6967296*math.Pow(t, -8) +
+			162375596875.0/334430208*math.Pow(t, -10))
+	}
+	r := nu + math.Pow(2, 2.0/3)*ar*math.Pow(nu, 1.0/3) +
+		0.2*math.Pow(2, 4.0/3)*ar*ar*math.Pow(nu, -1.0/3) +
+		(11.0/35-a*a-12.0/175*ar*ar*ar)/nu +
+		(16.0/1575*ar+92.0/7875*math.Pow(ar, 4))*math.Pow(2, 2.0/3)*math.Pow(nu, -5.0/3) -
+		(15152.0/3031875*math.Pow(ar, 5)+1088.0/121275*ar*ar)*math.Pow(2, 1.0/3)*math.Pow(nu, -7.0/3)
+	if r < 0 {
+		ar = 0
+	} else {
+		ar = math.Sqrt(r)
+	}
+	return ar
+}
+
+// airyRtsExact are the first airy roots.
+var airyRtsExact = []float64{
+	-2.338107410459762,
+	-4.087949444130970,
+	-5.520559828095555,
+	-6.786708090071765,
+	-7.944133587120863,
+	-9.022650853340979,
+	-10.040174341558084,
+	-11.008524303733260,
+	-11.936015563236262,
+	-12.828776752865757,
+}
diff --git a/vendor/gonum.org/v1/gonum/integrate/quad/hermite_data.go b/vendor/gonum.org/v1/gonum/integrate/quad/hermite_data.go
new file mode 100644
index 00000000..c50c8dbb
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/integrate/quad/hermite_data.go
@@ -0,0 +1,413 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package quad
+
+// xCache computed from Chebfun.
+var xCacheHermite = [][]float64{
+	{0.0000000000000000e+00},
+	{-7.0710678118654757e-01, 7.0710678118654757e-01},
+	{-1.2247448713915887e+00, 0.0000000000000000e+00, 1.2247448713915887e+00},
+	{-1.6506801238857842e+00, -5.2464762327529035e-01, 5.2464762327529035e-01, 1.6506801238857842e+00},
+	{-2.0201828704560856e+00, -9.5857246461381873e-01, 0.0000000000000000e+00, 9.5857246461381873e-01, 2.0201828704560856e+00},
+	{-2.3506049736744914e+00, -1.3358490740136970e+00, -4.3607741192761657e-01, 4.3607741192761657e-01, 1.3358490740136970e+00, 2.3506049736744914e+00},
+	{-2.6519613568352316e+00, -1.6735516287674714e+00, -8.1628788285896481e-01, 0.0000000000000000e+00, 8.1628788285896481e-01, 1.6735516287674714e+00, 2.6519613568352316e+00},
+	{-2.9306374202572436e+00, -1.9816567566958443e+00, -1.1571937124467804e+00, -3.8118699020732216e-01, 3.8118699020732216e-01, 1.1571937124467804e+00, 1.9816567566958443e+00, 2.9306374202572436e+00},
+	{-3.1909932017815295e+00, -2.2665805845318427e+00, -1.4685532892166682e+00, -7.2355101875283767e-01, 0.0000000000000000e+00, 7.2355101875283767e-01, 1.4685532892166682e+00, 2.2665805845318427e+00, 3.1909932017815295e+00},
+	{-3.4361591188377378e+00, -2.5327316742327901e+00, -1.7566836492998816e+00, -1.0366108297895138e+00, -3.4290132722370481e-01, 3.4290132722370481e-01, 1.0366108297895138e+00, 1.7566836492998816e+00, 2.5327316742327901e+00, 3.4361591188377378e+00},
+	{-3.6684708465595812e+00, -2.7832900997816514e+00, -2.0259480158257550e+00, -1.3265570844949326e+00, -6.5680956688209979e-01, 0.0000000000000000e+00, 6.5680956688209979e-01, 1.3265570844949326e+00, 2.0259480158257550e+00, 2.7832900997816514e+00, 3.6684708465595812e+00},
+	{-3.8897248978697814e+00, -3.0206370251208896e+00, -2.2795070805010593e+00, -1.5976826351526043e+00, -9.4778839124016367e-01, -3.1424037625435908e-01, 3.1424037625435908e-01, 9.4778839124016367e-01, 1.5976826351526043e+00, 2.2795070805010593e+00, 3.0206370251208896e+00, 3.8897248978697814e+00},
+	{-4.1013375961786389e+00, -3.2466089783724090e+00, -2.5197356856782389e+00, -1.8531076516015121e+00, -1.2200550365907483e+00, -6.0576387917106034e-01, 0.0000000000000000e+00, 6.0576387917106034e-01, 1.2200550365907483e+00, 1.8531076516015121e+00, 2.5197356856782389e+00, 3.2466089783724090e+00, 4.1013375961786389e+00},
+	{-4.3044485704736335e+00, -3.4626569336022701e+00, -2.7484707249854017e+00, -2.0951832585077166e+00, -1.4766827311411406e+00, -8.7871378732939931e-01, -2.9174551067256199e-01, 2.9174551067256199e-01, 8.7871378732939931e-01, 1.4766827311411406e+00, 2.0951832585077166e+00, 2.7484707249854017e+00, 3.4626569336022701e+00, 4.3044485704736335e+00},
+	{-4.4999907073093910e+00, -3.6699503734044541e+00, -2.9671669279056028e+00, -2.3257324861738580e+00, -1.7199925751864888e+00, -1.1361155852109204e+00, -5.6506958325557588e-01, 0.0000000000000000e+00, 5.6506958325557588e-01, 1.1361155852109204e+00, 1.7199925751864888e+00, 2.3257324861738580e+00, 2.9671669279056028e+00, 3.6699503734044541e+00, 4.4999907073093910e+00},
+	{-4.6887389393058223e+00, -3.8694479048601238e+00, -3.1769991619799529e+00, -2.5462021578474796e+00, -1.9517879909162528e+00, -1.3802585391988815e+00, -8.2295144914465546e-01, -2.7348104613815244e-01, 2.7348104613815244e-01, 8.2295144914465546e-01, 1.3802585391988815e+00, 1.9517879909162528e+00, 2.5462021578474796e+00, 3.1769991619799529e+00, 3.8694479048601238e+00, 4.6887389393058223e+00},
+	{-4.8713451936744061e+00, -4.0619466758754772e+00, -3.3789320911414946e+00, -2.7577629157038897e+00, -2.1735028266666214e+00, -1.6129243142212311e+00, -1.0676487257434508e+00, -5.3163300134265479e-01, 0.0000000000000000e+00, 5.3163300134265479e-01, 1.0676487257434508e+00, 1.6129243142212311e+00, 2.1735028266666214e+00, 2.7577629157038897e+00, 3.3789320911414946e+00, 4.0619466758754772e+00, 4.8713451936744061e+00},
+	{-5.0483640088744668e+00, -4.2481178735681260e+00, -3.5737690684862655e+00, -2.9613775055316052e+00, -2.3862990891666858e+00, -1.8355316042616294e+00, -1.3009208583896172e+00, -7.7668291926741173e-01, -2.5826775051909689e-01, 2.5826775051909689e-01, 7.7668291926741173e-01, 1.3009208583896172e+00, 1.8355316042616294e+00, 2.3862990891666858e+00, 2.9613775055316052e+00, 3.5737690684862655e+00, 4.2481178735681260e+00, 5.0483640088744668e+00},
+	{-5.2202716905374844e+00, -4.4285328066037799e+00, -3.7621873519640201e+00, -3.1578488183476034e+00, -2.5911337897945423e+00, -2.0492317098506181e+00, -1.5241706193935327e+00, -1.0103683871343114e+00, -5.0352016342388828e-01, 0.0000000000000000e+00, 5.0352016342388828e-01, 1.0103683871343114e+00, 1.5241706193935327e+00, 2.0492317098506181e+00, 2.5911337897945423e+00, 3.1578488183476034e+00, 3.7621873519640201e+00, 4.4285328066037799e+00, 5.2202716905374844e+00},
+	{-5.3874808900112319e+00, -4.6036824495507451e+00, -3.9447640401156265e+00, -3.3478545673832172e+00, -2.7888060584281313e+00, -2.2549740020892761e+00, -1.7385377121165857e+00, -1.2340762153953231e+00, -7.3747372854539406e-01, -2.4534070830090132e-01, 2.4534070830090132e-01, 7.3747372854539406e-01, 1.2340762153953231e+00, 1.7385377121165857e+00, 2.2549740020892761e+00, 2.7888060584281313e+00, 3.3478545673832172e+00, 3.9447640401156265e+00, 4.6036824495507451e+00, 5.3874808900112319e+00},
+	{-5.5503518732646775e+00, -4.7739923434112193e+00, -4.1219955474918395e+00, -3.5319728771376777e+00, -2.9799912077045980e+00, -2.4535521245128376e+00, -1.9449629491862539e+00, -1.4489342506507319e+00, -9.6149963441836894e-01, -4.7945070707910747e-01, -0.0000000000000000e+00, 4.7945070707910747e-01, 9.6149963441836894e-01, 1.4489342506507319e+00, 1.9449629491862539e+00, 2.4535521245128376e+00, 2.9799912077045980e+00, 3.5319728771376777e+00, 4.1219955474918395e+00, 4.7739923434112193e+00, 5.5503518732646775e+00},
+	{-5.7092013532052626e+00, -4.9398341310601763e+00, -4.2943124805931614e+00, -3.7107015328778048e+00, -3.1652659092021374e+00, -2.6456374410581724e+00, -2.1442335927985341e+00, -1.6558743732864223e+00, -1.1767139584812445e+00, -7.0368609717000696e-01, -2.3417913993099065e-01, 2.3417913993099065e-01, 7.0368609717000696e-01, 1.1767139584812445e+00, 1.6558743732864223e+00, 2.1442335927985341e+00, 2.6456374410581724e+00, 3.1652659092021374e+00, 3.7107015328778048e+00, 4.2943124805931614e+00, 4.9398341310601763e+00, 5.7092013532052626e+00},
+	{-5.8643094989845714e+00, -5.1015346104766763e+00, -4.4620911737400064e+00, -3.8844727081061015e+00, -3.3451271599412244e+00, -2.8318037871261570e+00, -2.3370162114744559e+00, -1.8556770376713707e+00, -1.3840395856824952e+00, -9.1915146544256365e-01, -4.5853835006810478e-01, -0.0000000000000000e+00, 4.5853835006810478e-01, 9.1915146544256365e-01, 1.3840395856824952e+00, 1.8556770376713707e+00, 2.3370162114744559e+00, 2.8318037871261570e+00, 3.3451271599412244e+00, 3.8844727081061015e+00, 4.4620911737400064e+00, 5.1015346104766763e+00, 5.8643094989845714e+00},
+	{-6.0159255614257390e+00, -5.2593829276680442e+00, -4.6256627564237878e+00, -4.0536644024481490e+00, -3.5200068130345241e+00, -3.0125461375655647e+00, -2.5238810170114268e+00, -2.0490035736616985e+00, -1.5842500109616942e+00, -1.1267608176112451e+00, -6.7417110703721217e-01, -2.2441454747251557e-01, 2.2441454747251557e-01, 6.7417110703721217e-01, 1.1267608176112451e+00, 1.5842500109616942e+00, 2.0490035736616985e+00, 2.5238810170114268e+00, 3.0125461375655647e+00, 3.5200068130345241e+00, 4.0536644024481490e+00, 4.6256627564237878e+00, 5.2593829276680442e+00, 6.0159255614257390e+00},
+	{-6.1642724340524513e+00, -5.4136363552800333e+00, -4.7853203673522238e+00, -4.2186094443865612e+00, -3.6902828769983551e+00, -3.1882949244251044e+00, -2.7053202371730256e+00, -2.2364201302672808e+00, -1.7780011243371474e+00, -1.3272807020730839e+00, -8.8198275621382138e-01, -4.4014729864530827e-01, -0.0000000000000000e+00, 4.4014729864530827e-01, 8.8198275621382138e-01, 1.3272807020730839e+00, 1.7780011243371474e+00, 2.2364201302672808e+00, 2.7053202371730256e+00, 3.1882949244251044e+00, 3.6902828769983551e+00, 4.2186094443865612e+00, 4.7853203673522238e+00, 5.4136363552800333e+00, 6.1642724340524513e+00},
+	{-6.3095503856256920e+00, -5.5645249819501030e+00, -4.9413249572413793e+00, -4.3796026629833040e+00, -3.8562884199091489e+00, -3.3594271823508297e+00, -2.8817622195430865e+00, -2.4184157647737790e+00, -1.9658547856411364e+00, -1.5213615166519212e+00, -1.0827330110778832e+00, -6.4809521399344827e-01, -2.1577785624346338e-01, 2.1577785624346338e-01, 6.4809521399344827e-01, 1.0827330110778832e+00, 1.5213615166519212e+00, 1.9658547856411364e+00, 2.4184157647737790e+00, 2.8817622195430865e+00, 3.3594271823508297e+00, 3.8562884199091489e+00, 4.3796026629833040e+00, 4.9413249572413793e+00, 5.5645249819501030e+00, 6.3095503856256920e+00},
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+}
+
+// wCache computed from Chebfun.
+var wCacheHermite = [][]float64{
+	{1.7724538509055159e+00},
+	{8.8622692545275794e-01, 8.8622692545275794e-01},
+	{2.9540897515091952e-01, 1.1816359006036770e+00, 2.9540897515091952e-01},
+	{8.1312835447245130e-02, 8.0491409000551273e-01, 8.0491409000551273e-01, 8.1312835447245130e-02},
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+	{2.2290934963031539e-163, 6.1716304223418473e-155, 3.9305958509063355e-148, 3.2706601334834755e-142, 7.0049069648137550e-137, 5.5049260050287900e-132, 1.9684692530020812e-127, 3.6957545112422320e-123, 4.0320327117616306e-119, 2.7559362749699724e-115, 1.2503894738744883e-111, 3.9416969862084461e-108, 8.9577890237321700e-105, 1.5127860735379895e-101, 1.9472732376896783e-98, 1.9519789398323314e-95, 1.5520652579926001e-92, 9.9458309202670908e-90, 5.2083206235820379e-87, 2.2562215375682347e-84, 8.1731118972592471e-82, 2.4997514837476365e-79, 6.5111285362111366e-77, 1.4555888776738779e-74, 2.8125155025369667e-72, 4.7271089337772468e-70, 6.9513137370020262e-68, 8.9912466505154563e-66, 1.0279594830695334e-63, 1.0434894316959833e-61, 9.4440639857201346e-60, 7.6499247670821092e-58, 5.5658406725957325e-56, 3.6493796373809251e-54, 2.1630323514364711e-52, 1.1622901525905010e-50, 5.6773339224732908e-49, 2.5272570465088243e-47, 1.0276815273410889e-45, 3.8259457909463708e-44, 1.3067728287128299e-42, 4.1029828415971428e-41, 1.1864415902523173e-39, 3.1652198121078916e-38, 7.8035886293155777e-37, 1.7807430428966829e-35, 3.7667945725159055e-34, 7.3963969744653024e-33, 1.3499836949356773e-31, 2.2932424003565328e-30, 3.6300293183361797e-29, 5.3605436078106824e-28, 7.3930155412655720e-27, 9.5323773039462743e-26, 1.1502145928125925e-24, 1.3000662757028629e-23, 1.3776941782313042e-22, 1.3699807056265559e-21, 1.2794012136597428e-20, 1.1229742763811151e-19, 9.2710336687274256e-19, 7.2042972150393114e-18, 5.2729781171856177e-17, 3.6375048889083554e-16, 2.3664867578847666e-15, 1.4528301518132017e-14, 8.4213476872404286e-14, 4.6114644502136799e-13, 2.3867692880717110e-12, 1.1681801468249808e-11, 5.4092941845487156e-11, 2.3708105480750139e-10, 9.8392832670094020e-10, 3.8682673753498617e-09, 1.4411972185221586e-08, 5.0903013962041357e-08, 1.7050141340191249e-07, 5.4177677321026202e-07, 1.6336412605871983e-06, 4.6759044289293238e-06, 1.2707753951032874e-05, 3.2800534876023489e-05, 8.0428506528979537e-05, 1.8739476963256670e-04, 4.1497155710923123e-04, 8.7353709789879039e-04, 1.7483531042542699e-03, 3.3276551358222884e-03, 6.0239245919995622e-03, 1.0373317514267365e-02, 1.6994637482018023e-02, 2.6492061401939205e-02, 3.9298609227795579e-02, 5.5480282208033298e-02, 7.4548212057078664e-02, 9.5346453940664169e-02, 1.1608254348974273e-01, 1.3453811804025481e-01, 1.4844158241213595e-01, 1.5592224232989221e-01, 1.5592224232989221e-01, 1.4844158241213595e-01, 1.3453811804025481e-01, 1.1608254348974273e-01, 9.5346453940664169e-02, 7.4548212057078664e-02, 5.5480282208033298e-02, 3.9298609227795579e-02, 2.6492061401939205e-02, 1.6994637482018023e-02, 1.0373317514267365e-02, 6.0239245919995622e-03, 3.3276551358222884e-03, 1.7483531042542699e-03, 8.7353709789879039e-04, 4.1497155710923123e-04, 1.8739476963256670e-04, 8.0428506528979537e-05, 3.2800534876023489e-05, 1.2707753951032874e-05, 4.6759044289293238e-06, 1.6336412605871983e-06, 5.4177677321026202e-07, 1.7050141340191249e-07, 5.0903013962041357e-08, 1.4411972185221586e-08, 3.8682673753498617e-09, 9.8392832670094020e-10, 2.3708105480750139e-10, 5.4092941845487156e-11, 1.1681801468249808e-11, 2.3867692880717110e-12, 4.6114644502136799e-13, 8.4213476872404286e-14, 1.4528301518132017e-14, 2.3664867578847666e-15, 3.6375048889083554e-16, 5.2729781171856177e-17, 7.2042972150393114e-18, 9.2710336687274256e-19, 1.1229742763811151e-19, 1.2794012136597428e-20, 1.3699807056265559e-21, 1.3776941782313042e-22, 1.3000662757028629e-23, 1.1502145928125925e-24, 9.5323773039462743e-26, 7.3930155412655720e-27, 5.3605436078106824e-28, 3.6300293183361797e-29, 2.2932424003565328e-30, 1.3499836949356773e-31, 7.3963969744653024e-33, 3.7667945725159055e-34, 1.7807430428966829e-35, 7.8035886293155777e-37, 3.1652198121078916e-38, 1.1864415902523173e-39, 4.1029828415971428e-41, 1.3067728287128299e-42, 3.8259457909463708e-44, 1.0276815273410889e-45, 2.5272570465088243e-47, 5.6773339224732908e-49, 1.1622901525905010e-50, 2.1630323514364711e-52, 3.6493796373809251e-54, 5.5658406725957325e-56, 7.6499247670821092e-58, 9.4440639857201346e-60, 1.0434894316959833e-61, 1.0279594830695334e-63, 8.9912466505154563e-66, 6.9513137370020262e-68, 4.7271089337772468e-70, 2.8125155025369667e-72, 1.4555888776738779e-74, 6.5111285362111366e-77, 2.4997514837476365e-79, 8.1731118972592471e-82, 2.2562215375682347e-84, 5.2083206235820379e-87, 9.9458309202670908e-90, 1.5520652579926001e-92, 1.9519789398323314e-95, 1.9472732376896783e-98, 1.5127860735379895e-101, 8.9577890237321700e-105, 3.9416969862084461e-108, 1.2503894738744883e-111, 2.7559362749699724e-115, 4.0320327117616306e-119, 3.6957545112422320e-123, 1.9684692530020812e-127, 5.5049260050287900e-132, 7.0049069648137550e-137, 3.2706601334834755e-142, 3.9305958509063355e-148, 6.1716304223418473e-155, 2.2290934963031539e-163},
+}
diff --git a/vendor/gonum.org/v1/gonum/integrate/quad/hermite_test.go b/vendor/gonum.org/v1/gonum/integrate/quad/hermite_test.go
new file mode 100644
index 00000000..d74b82dc
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/integrate/quad/hermite_test.go
@@ -0,0 +1,251 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package quad
+
+import (
+	"fmt"
+	"math"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+func TestHermite(t *testing.T) {
+	for cas, test := range []struct {
+		n   int
+		f   func(float64) float64
+		ev  float64
+		tol float64
+	}{
+		{
+			n:   2,
+			f:   func(x float64) float64 { return 1 },
+			ev:  math.SqrtPi,
+			tol: 1e-14,
+		},
+		{
+			n:   4,
+			f:   func(x float64) float64 { return math.Exp(-2 * 0.5 * x) },
+			ev:  math.SqrtPi * math.Exp(0.25),
+			tol: 1e-4,
+		},
+		{
+			n:   9,
+			f:   func(x float64) float64 { return math.Exp(-2 * 0.5 * x) },
+			ev:  math.SqrtPi * math.Exp(0.25),
+			tol: 1e-12,
+		},
+		{
+			n:   10,
+			f:   func(x float64) float64 { return math.Exp(-2 * 0.5 * x) },
+			ev:  math.SqrtPi * math.Exp(0.25),
+			tol: 1e-12,
+		},
+		{
+			n:   15,
+			f:   func(x float64) float64 { return math.Exp(-2 * 2 * x) },
+			ev:  math.SqrtPi * math.Exp(4),
+			tol: 1e-4,
+		},
+		{
+			n:   22,
+			f:   func(x float64) float64 { return math.Exp(-2 * 2 * x) },
+			ev:  math.SqrtPi * math.Exp(4),
+			tol: 1e-12,
+		},
+		{
+			n:   21,
+			f:   func(x float64) float64 { return math.Exp(-2 * 2 * x) },
+			ev:  math.SqrtPi * math.Exp(4),
+			tol: 1e-12,
+		},
+	} {
+		ev := Fixed(test.f, math.Inf(-1), math.Inf(1), test.n, Hermite{}, 0)
+		if !floats.EqualWithinAbsOrRel(test.ev, ev, test.tol, test.tol) {
+			t.Errorf("Case %d: expected value mismatch.\nWant %v\ngot %v", cas, test.ev, ev)
+		}
+	}
+}
+
+func TestHermiteLocations(t *testing.T) {
+	// Test the hermite locations and weights against other precomputed table.
+	// Data from http://dlmf.nist.gov/3.5.
+	for _, test := range []struct {
+		n int
+		x []float64
+		w []float64
+	}{
+		// Evaluated from Chebfun.
+		{
+			n: 5,
+			x: []float64{-0.202018287045609e1, -0.958572464613819, 0, 0.958572464613819, 0.202018287045609e1},
+			w: []float64{0.199532420590459e-1, 0.393619323152241, 0.945308720482942, 0.393619323152241, 0.199532420590459e-1},
+		},
+		{
+			n: 10,
+			x: []float64{-0.343615911883773760e1, -0.253273167423278980e1, -0.175668364929988177e1, -0.103661082978951365e1, -0.342901327223704609, 0.342901327223704609, 0.103661082978951365e1, 0.175668364929988177e1, 0.253273167423278980e1, 0.343615911883773760e1},
+			w: []float64{0.764043285523262063e-5, 0.134364574678123269e-2, 0.338743944554810631e-1, 0.240138611082314686, 0.610862633735325799, 0.610862633735325799, 0.240138611082314686, 0.338743944554810631e-1, 0.134364574678123269e-2, 0.764043285523262063e-5},
+		},
+		{
+			n: 215,
+			x: []float64{-2.0083110126223993e+01, -1.9573161931385755e+01, -1.9153731166695263e+01, -1.8781558404513735e+01, -1.8440108632764016e+01, -1.8120857960601569e+01, -1.7818692349773503e+01, -1.7530242081974308e+01, -1.7253139752773148e+01, -1.6985642449377284e+01, -1.6726420346886542e+01, -1.6474429782282726e+01, -1.6228832750513551e+01, -1.5988943547145137e+01, -1.5754192102761674e+01, -1.5524098014731747e+01, -1.5298251677453143e+01, -1.5076300264808333e+01, -1.4857937115425768e+01, -1.4642893558208563e+01, -1.4430932522616979e+01, -1.4221843477251845e+01, -1.4015438372554696e+01, -1.3811548353270942e+01, -1.3610021068540190e+01, -1.3410718451340038e+01, -1.3213514870431910e+01, -1.3018295580800100e+01, -1.2824955415404188e+01, -1.2633397673617059e+01, -1.2443533171189967e+01, -1.2255279423804318e+01, -1.2068559941826503e+01, -1.1883303618198463e+01, -1.1699444194777641e+01, -1.1516919795109878e+01, -1.1335672513742256e+01, -1.1155648053883823e+01, -1.0976795406593546e+01, 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1.8182269564169717e+00, 1.9701861238629792e+00, 2.1222518845837395e+00, 2.2744328011717010e+00, 2.4267375193157439e+00, 2.5791747746208049e+00, 2.7317533996228827e+00, 2.8844823310168755e+00, 3.0373706171156218e+00, 3.1904274255596032e+00, 3.3436620512978501e+00, 3.4970839248619634e+00, 3.6507026209565665e+00, 3.8045278673909002e+00, 3.9585695543782120e+00, 4.1128377442311503e+00, 4.2673426814837114e+00, 4.4220948034722349e+00, 4.5771047514106780e+00, 4.7323833819978187e+00, 4.8879417795972326e+00, 5.0437912690340267e+00, 5.1999434290559226e+00, 5.3564101065103049e+00, 5.5132034312931157e+00, 5.6703358321303936e+00, 5.8278200532585673e+00, 5.9856691720754620e+00, 6.1438966178406549e+00, 6.3025161915109100e+00, 6.4615420868046280e+00, 6.6209889125982082e+00, 6.7808717167671544e+00, 6.9412060115960434e+00, 7.1020078008938672e+00, 7.2632936089653120e+00, 7.4250805116042331e+00, 7.5873861692931381e+00, 7.7502288628124383e+00, 7.9136275314855800e+00, 8.0776018143113824e+00, 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1.5988943547145137e+01, 1.6228832750513551e+01, 1.6474429782282726e+01, 1.6726420346886542e+01, 1.6985642449377284e+01, 1.7253139752773148e+01, 1.7530242081974308e+01, 1.7818692349773503e+01, 1.8120857960601569e+01, 1.8440108632764016e+01, 1.8781558404513735e+01, 1.9153731166695263e+01, 1.9573161931385755e+01, 2.0083110126223993e+01},
+			w: []float64{4.0474005560499094e-176, 1.8797130400856443e-167, 1.8432377040276421e-160, 2.2601442864626069e-154, 6.9363023753259492e-149, 7.6575370428605554e-144, 3.7894855074137878e-139, 9.7310398950542353e-135, 1.4382941114934084e-130, 1.3214094652141891e-126, 8.0053233705919762e-123, 3.3506484324551954e-119, 1.0061133084529732e-115, 2.2355880918528976e-112, 3.7723274691873339e-109, 4.9410774014014167e-106, 5.1189805080467357e-103, 4.2633269887655389e-100, 2.8951564896303124e-97, 1.6231768954981774e-94, 7.5966487579367170e-92, 2.9971587600601123e-89, 1.0056653752640396e-86, 2.8926565116618279e-84, 7.1838069610206879e-82, 1.5504440487214177e-79, 2.9253709118548054e-77, 4.8516529695481360e-75, 7.1080340648382430e-73, 9.2417798747589595e-71, 1.0709039437896534e-68, 1.1102986726619406e-66, 1.0337280935884043e-64, 8.6720569345151135e-63, 6.5759615285599325e-61, 4.5206307708839604e-59, 2.8251413443094276e-57, 1.6091856250751163e-55, 8.3743579179261028e-54, 3.9908716881614503e-52, 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+		},
+		{
+			n: 216,
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5.0074481042562811e-112, 2.7680773700442792e-115, 1.1608863141459933e-118, 3.5986937020445443e-122, 7.9930519467022852e-126, 1.2247428452374434e-129, 1.2353061004428027e-133, 7.7287684331971630e-138, 2.7763562197121041e-142, 5.1593581306426363e-147, 4.2810879764792902e-152, 1.2712817065467470e-157, 9.3801386072360495e-164, 8.5565157993831952e-171, 1.6118004761490936e-179},
+		},
+		{
+			n: 220,
+			x: []float64{-2.0325189139629405e+01, -1.9817257977795947e+01, -1.9399516717870224e+01, -1.9028866794578029e+01, -1.8688834225534919e+01, -1.8370926385157830e+01, -1.8070047892967271e+01, -1.7782841268044042e+01, -1.7506947669788651e+01, -1.7240630469775191e+01, -1.6982564625621777e+01, -1.6731710220470223e+01, -1.6487232253468321e+01, -1.6248447477010238e+01, -1.6014787864496149e+01, -1.5785774736307584e+01, -1.5560999958339213e+01, -1.5340111975060188e+01, -1.5122805233008011e+01, -1.4908812035694833e+01, -1.4697896176804390e+01, -1.4489847896889446e+01, -1.4284479840564213e+01, -1.4081623780688842e+01, -1.3881127938034011e+01, -1.3682854768615876e+01, -1.3486679122200039e+01, -1.3292486698232523e+01, -1.3100172742223814e+01, -1.2909640938118768e+01, -1.2720802461619986e+01, -1.2533575166624548e+01, -1.2347882882470566e+01, -1.2163654803990811e+01, -1.1980824959739557e+01, -1.1799331746419007e+01, -1.1619117519647554e+01, -1.1440128232906956e+01, -1.1262313117871999e+01, 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1.5122805233008011e+01, 1.5340111975060188e+01, 1.5560999958339213e+01, 1.5785774736307584e+01, 1.6014787864496149e+01, 1.6248447477010238e+01, 1.6487232253468321e+01, 1.6731710220470223e+01, 1.6982564625621777e+01, 1.7240630469775191e+01, 1.7506947669788651e+01, 1.7782841268044042e+01, 1.8070047892967271e+01, 1.8370926385157830e+01, 1.8688834225534919e+01, 1.9028866794578029e+01, 1.9399516717870224e+01, 1.9817257977795947e+01, 2.0325189139629405e+01},
+			w: []float64{2.2761605731502931e-180, 1.2490844229282551e-171, 1.4077080884426324e-164, 1.9558070725961945e-158, 6.7396164617778564e-153, 8.3007451278928549e-148, 4.5605427168506885e-143, 1.2952107195320918e-138, 2.1106922482765282e-134, 2.1325182525295938e-130, 1.4176541142180510e-126, 6.4990818384221324e-123, 2.1340663816447175e-119, 5.1782994410611593e-116, 9.5303885471678039e-113, 1.3600769560707746e-109, 1.5337501625076215e-106, 1.3892626373123839e-103, 1.0252931948997944e-100, 6.2430026550428978e-98, 3.1713496923820005e-95, 1.3573663268548106e-92, 4.9385791079870452e-90, 1.5396613562557895e-87, 4.1428768007295419e-85, 9.6845718261332366e-83, 1.9785969337019459e-80, 3.5522955000635345e-78, 5.6327088700629997e-76, 7.9248469784581938e-74, 9.9353884108905009e-72, 1.1143371044053519e-69, 1.1222249771693660e-67, 1.0182568638449594e-65, 8.3508496445242703e-64, 6.2085535684767686e-62, 4.1960840622737107e-60, 2.5847807937901128e-58, 1.4547608917709417e-56, 7.4980265458380947e-55, 3.5467498009174184e-53, 1.5428702374218767e-51, 6.1841637682672203e-50, 2.2881100073201874e-48, 7.8282784948541621e-47, 2.4806114249059706e-45, 7.2916745732054914e-44, 1.9911806078855746e-42, 5.0584298583405264e-41, 1.1970700137586669e-39, 2.6422337190194530e-38, 5.4462015155980312e-37, 1.0495069994748297e-35, 1.8928725655710039e-34, 3.1985659419085236e-33, 5.0689745622498271e-32, 7.5410079936029980e-31, 1.0540919389712685e-29, 1.3856239612378123e-28, 1.7143191474654609e-27, 1.9978524188114189e-26, 2.1947842513043781e-25, 2.2745432296820405e-24, 2.2252271383645215e-23, 2.0564749726923156e-22, 1.7964719327802204e-21, 1.4843379300503135e-20, 1.1606915413845120e-19, 8.5944540731309027e-19, 6.0293824390549243e-18, 4.0096487904356170e-17, 2.5289217277543671e-16, 1.5134484435681475e-15, 8.5980922774659504e-15, 4.6390554602844329e-14, 2.3781148094626393e-13, 1.1587426167580950e-12, 5.3685841373417416e-12, 2.3659835874748833e-11, 9.9219381603477156e-11, 3.9606009206879336e-10, 1.5053791970450186e-09, 5.4498580894419877e-09, 1.8797800781026250e-08, 6.1792198822459984e-08, 1.9363392840773747e-07, 5.7857719375034532e-07, 1.6488403637671232e-06, 4.4826356596959815e-06, 1.1628419918195159e-05, 2.8789242845201347e-05, 6.8037279449589797e-05, 1.5351500720814013e-04, 3.3076323494923371e-04, 6.8063888690970183e-04, 1.3378748383672085e-03, 2.5123201954271616e-03, 4.5076732111920138e-03, 7.7285957578851656e-03, 1.2663915587278220e-02, 1.9833481075447929e-02, 2.9691593353631068e-02, 4.2492045448586743e-02, 5.8137078835965875e-02, 7.6049788530935164e-02, 9.5118681388506904e-02, 1.1375654825578213e-01, 1.3009049092173738e-01, 1.4226074789149157e-01, 1.4876572633109977e-01, 1.4876572633109977e-01, 1.4226074789149157e-01, 1.3009049092173738e-01, 1.1375654825578213e-01, 9.5118681388506904e-02, 7.6049788530935164e-02, 5.8137078835965875e-02, 4.2492045448586743e-02, 2.9691593353631068e-02, 1.9833481075447929e-02, 1.2663915587278220e-02, 7.7285957578851656e-03, 4.5076732111920138e-03, 2.5123201954271616e-03, 1.3378748383672085e-03, 6.8063888690970183e-04, 3.3076323494923371e-04, 1.5351500720814013e-04, 6.8037279449589797e-05, 2.8789242845201347e-05, 1.1628419918195159e-05, 4.4826356596959815e-06, 1.6488403637671232e-06, 5.7857719375034532e-07, 1.9363392840773747e-07, 6.1792198822459984e-08, 1.8797800781026250e-08, 5.4498580894419877e-09, 1.5053791970450186e-09, 3.9606009206879336e-10, 9.9219381603477156e-11, 2.3659835874748833e-11, 5.3685841373417416e-12, 1.1587426167580950e-12, 2.3781148094626393e-13, 4.6390554602844329e-14, 8.5980922774659504e-15, 1.5134484435681475e-15, 2.5289217277543671e-16, 4.0096487904356170e-17, 6.0293824390549243e-18, 8.5944540731309027e-19, 1.1606915413845120e-19, 1.4843379300503135e-20, 1.7964719327802204e-21, 2.0564749726923156e-22, 2.2252271383645215e-23, 2.2745432296820405e-24, 2.1947842513043781e-25, 1.9978524188114189e-26, 1.7143191474654609e-27, 1.3856239612378123e-28, 1.0540919389712685e-29, 7.5410079936029980e-31, 5.0689745622498271e-32, 3.1985659419085236e-33, 1.8928725655710039e-34, 1.0495069994748297e-35, 5.4462015155980312e-37, 2.6422337190194530e-38, 1.1970700137586669e-39, 5.0584298583405264e-41, 1.9911806078855746e-42, 7.2916745732054914e-44, 2.4806114249059706e-45, 7.8282784948541621e-47, 2.2881100073201874e-48, 6.1841637682672203e-50, 1.5428702374218767e-51, 3.5467498009174184e-53, 7.4980265458380947e-55, 1.4547608917709417e-56, 2.5847807937901128e-58, 4.1960840622737107e-60, 6.2085535684767686e-62, 8.3508496445242703e-64, 1.0182568638449594e-65, 1.1222249771693660e-67, 1.1143371044053519e-69, 9.9353884108905009e-72, 7.9248469784581938e-74, 5.6327088700629997e-76, 3.5522955000635345e-78, 1.9785969337019459e-80, 9.6845718261332366e-83, 4.1428768007295419e-85, 1.5396613562557895e-87, 4.9385791079870452e-90, 1.3573663268548106e-92, 3.1713496923820005e-95, 6.2430026550428978e-98, 1.0252931948997944e-100, 1.3892626373123839e-103, 1.5337501625076215e-106, 1.3600769560707746e-109, 9.5303885471678039e-113, 5.1782994410611593e-116, 2.1340663816447175e-119, 6.4990818384221324e-123, 1.4176541142180510e-126, 2.1325182525295938e-130, 2.1106922482765282e-134, 1.2952107195320918e-138, 4.5605427168506885e-143, 8.3007451278928549e-148, 6.7396164617778564e-153, 1.9558070725961945e-158, 1.4077080884426324e-164, 1.2490844229282551e-171, 2.2761605731502931e-180},
+		},
+	} {
+		h := Hermite{}
+		x := make([]float64, test.n)
+		weight := make([]float64, test.n)
+		h.FixedLocations(x, weight, math.Inf(-1), math.Inf(1))
+		if !floats.EqualApprox(x, test.x, 1e-14) {
+			t.Errorf("n = %v, x mismatch", test.n)
+			fmt.Println(x)
+			fmt.Println()
+			fmt.Println(test.x)
+			//t.Errorf("x mismatch. \nWant %v\ngot %v", test.x, x)
+		}
+		if !floats.EqualApprox(weight, test.w, 1e-14) {
+			t.Errorf("n = %v, w mismatch", test.n)
+			//t.Errorf("w mismatch. Want %v, got %v", test.w, weight)
+		}
+	}
+}
+
+func TestHermiteInitialGuesses(t *testing.T) {
+	for _, test := range []struct {
+		n    int
+		want []float64
+	}{
+		// Evaluated from Chebfun.
+		{
+			n:    215,
+			want: []float64{0, 0.151326329763712, 0.302660700793398, 0.454011159911720, 0.605385765065948, 0.756792590918330, 0.908239734470234, 1.059735320731617, 1.211287508447394, 1.362904495892717, 1.514594526749157, 1.666365896074552, 1.818226956379164, 1.970186123821706, 2.122251884538916, 2.274432801123240, 2.426737519263548, 2.579174774564779, 2.731753399562905, 2.884482330952826, 3.037370617047366, 3.190427425487010, 3.343662051220745, 3.497083924780193, 3.650702620869949, 3.804527867299248, 3.958569554281313, 4.112837744128784, 4.267342681375636, 4.422094803358200, 4.577104751290402, 4.732383381871004, 4.887941779463563, 5.043791268893151, 5.199943428907478, 5.356410106353889, 5.513203431128299, 5.670335831956713, 5.827820053075521, 5.985669171882509, 6.143896617637219, 6.302516191296349, 6.461542086578262, 6.620988912359293, 6.780871716514890, 6.941206011329554, 7.102007800612191, 7.263293608667420, 7.425080511288993, 7.587386168959320, 7.750228862458692, 7.913627531110426, 8.077601813913194, 8.242172093840729, 8.407359545621334, 8.573186187346858, 8.739674936302684, 8.906849669458699, 9.074735289116129, 9.243357794268617, 9.412744358308792, 9.582923413795772, 9.753924745096450, 9.925779589826769, 10.098520750150884, 10.272182715150265, 10.446801795655594, 10.622416273146731, 10.799066564577450, 10.976795405279171, 11.155648052452676, 11.335672512180423, 11.516919793401330, 11.699444192903831, 11.883303616137852, 12.068559939553955, 12.255279421290370, 12.443533168399910, 12.633397670509774, 12.824955411930718, 13.018295576901773, 13.213514866037960, 13.410718446364541, 13.610021062878001, 13.811548346792373, 14.015438365098394, 14.221843468615116, 14.430932512542578, 14.642893546366283, 14.857937101386424, 15.076300248006383, 15.298251657131900, 15.524097989861344, 15.754192071913305, 15.988943508292977, 16.228832700713156, 16.474429717130270, 16.726420259572109, 16.985642328947012, 17.253139580754688, 17.530241825363181, 17.818691945179868, 18.120857274390474, 18.440107345774539, 18.781555607447057, 19.153723464992801, 19.573128956064245, 20.082675660407357},
+		},
+		{
+			n:    216,
+			want: []float64{7.5487718957947841e-02, 2.2646713089416223e-01, 3.7745846761172613e-01, 5.2846968803819716e-01, 6.7950876473020116e-01, 8.3058368936317251e-01, 9.8170247825952706e-01, 1.1328731779663146e+00, 1.2841038708939367e+00, 1.4354026810274640e+00, 1.5867777797225648e+00, 1.7382373915984026e+00, 1.8897898005400910e+00, 2.0414433558240375e+00, 2.1932064783796412e+00, 2.3450876672018457e+00, 2.4970955059292010e+00, 2.6492386696032790e+00, 2.8015259316256671e+00, 2.9539661709299665e+00, 3.1065683793869288e+00, 3.2593416694621893e+00, 3.4122952821469283e+00, 3.5654385951833136e+00, 3.7187811316079062e+00, 3.8723325686377130e+00, 4.0261027469252912e+00, 4.1801016802112088e+00, 4.3343395654041350e+00, 4.4888267931211692e+00, 4.6435739587232687e+00, 4.7985918738836766e+00, 4.9538915787298405e+00, 5.1094843546028494e+00, 5.2653817374818566e+00, 5.4215955321250595e+00, 5.5781378269829656e+00, 5.7350210099447425e+00, 5.8922577849835758e+00, 6.0498611897730488e+00, 6.2078446143528714e+00, 6.3662218209298418e+00, 6.5250069649076838e+00, 6.6842146172486627e+00, 6.8438597882796577e+00, 7.0039579530666876e+00, 7.1645250784943162e+00, 7.3255776522003675e+00, 7.4871327135320032e+00, 7.6492078867069049e+00, 7.8118214163831334e+00, 7.9749922058635363e+00, 8.1387398581859554e+00, 8.3030847203790454e+00, 8.4680479311960379e+00, 8.6336514726757141e+00, 8.7999182259219690e+00, 8.9668720315415094e+00, 9.1345377552342626e+00, 9.3029413590944845e+00, 9.4721099792532808e+00, 9.6420720105775217e+00, 9.8128571992374614e+00, 9.9844967440684584e+00, 1.0157023407784097e+01, 1.0330471639251822e+01, 1.0504877708222864e+01, 1.0680279854120787e+01, 1.0856718450743809e+01, 1.1034236189033734e+01, 1.1212878280418622e+01, 1.1392692683659751e+01, 1.1573730358642214e+01, 1.1756045551162156e+01, 1.1939696113507749e+01, 1.2124743866538131e+01, 1.2311255010076101e+01, 1.2499300589800702e+01, 1.2688957030525529e+01, 1.2880306747870632e+01, 1.3073438853003600e+01, 1.3268449968504161e+01, 1.3465445177719724e+01, 1.3664539135531767e+01, 1.3865857375666192e+01, 1.4069537859142688e+01, 1.4275732821001174e+01, 1.4484610989259913e+01, 1.4696360272885402e+01, 1.4911191046953165e+01, 1.5129340207007946e+01, 1.5351076226802732e+01, 1.5576705543358910e+01, 1.5806580725457744e+01, 1.6041111080581306e+01, 1.6280776662107755e+01, 1.6526147125048691e+01, 1.6777907674840002e+01, 1.7036895705202610e+01, 1.7304154114531990e+01, 1.7581011746684457e+01, 1.7869210214084568e+01, 1.8171115120332015e+01, 1.8490093525334313e+01, 1.8831255107137672e+01, 1.9203114954794152e+01, 1.9622178785373663e+01, 2.0131752068311702e+01},
+		},
+	} {
+		got := make([]float64, test.n/2+test.n%2)
+		for i := range got {
+			got[i] = Hermite{}.hermiteInitialGuess(i, test.n)
+		}
+		if !floats.EqualApprox(got, test.want, 1e-14) {
+			t.Errorf("n = %v, hermite initial guesses mismatch", test.n)
+		}
+	}
+}
+
+func TestHermiteLocationsAsy0(t *testing.T) {
+	for _, test := range []struct {
+		n int
+		x []float64
+		w []float64
+	}{
+		// Evaluated from Chebfun.
+		{
+			n: 215,
+			x: []float64{-7.9483151672010196e-15, 1.5132632976672361e-01, 3.0266070079942864e-01, 4.5401115992078167e-01, 6.0538576507805808e-01, 7.5679259093351370e-01, 9.0823973448851325e-01, 1.0597353207530273e+00, 1.2112875084719879e+00, 1.3629044959205205e+00, 1.5145945267802365e+00, 1.6663658961089640e+00, 1.8182269564169717e+00, 1.9701861238629792e+00, 2.1222518845837395e+00, 2.2744328011717010e+00, 2.4267375193157439e+00, 2.5791747746208049e+00, 2.7317533996228827e+00, 2.8844823310168755e+00, 3.0373706171156218e+00, 3.1904274255596032e+00, 3.3436620512978501e+00, 3.4970839248619634e+00, 3.6507026209565665e+00, 3.8045278673909002e+00, 3.9585695543782120e+00, 4.1128377442311503e+00, 4.2673426814837114e+00, 4.4220948034722349e+00, 4.5771047514106780e+00, 4.7323833819978187e+00, 4.8879417795972326e+00, 5.0437912690340267e+00, 5.1999434290559226e+00, 5.3564101065103049e+00, 5.5132034312931157e+00, 5.6703358321303936e+00, 5.8278200532585673e+00, 5.9856691720754620e+00, 6.1438966178406549e+00, 6.3025161915109100e+00, 6.4615420868046280e+00, 6.6209889125982082e+00, 6.7808717167671544e+00, 6.9412060115960434e+00, 7.1020078008938672e+00, 7.2632936089653120e+00, 7.4250805116042331e+00, 7.5873861692931381e+00, 7.7502288628124383e+00, 7.9136275314855800e+00, 8.0776018143113824e+00, 8.2421720942637187e+00, 8.4073595460710955e+00, 8.5731861878255415e+00, 8.7396749368126798e+00, 8.9068496700026394e+00, 9.0747352896969389e+00, 9.2433577948895387e+00, 9.4127443589734394e+00, 9.5829234145081710e+00, 9.7539247458611111e+00, 9.9257795906487338e+00, 1.0098520751035824e+01, 1.0272182716104577e+01, 1.0446801796686490e+01, 1.0622416274262394e+01, 1.0799066565787168e+01, 1.0976795406593546e+01, 1.1155648053883823e+01, 1.1335672513742256e+01, 1.1516919795109878e+01, 1.1699444194777641e+01, 1.1883303618198463e+01, 1.2068559941826503e+01, 1.2255279423804318e+01, 1.2443533171189967e+01, 1.2633397673617059e+01, 1.2824955415404188e+01, 1.3018295580800100e+01, 1.3213514870431910e+01, 1.3410718451340038e+01, 1.3610021068540190e+01, 1.3811548353270942e+01, 1.4015438372554696e+01, 1.4221843477251845e+01, 1.4430932522616979e+01, 1.4642893558208563e+01, 1.4857937115425768e+01, 1.5076300264808333e+01, 1.5298251677453143e+01, 1.5524098014731747e+01, 1.5754192102761674e+01, 1.5988943547145137e+01, 1.6228832750513551e+01, 1.6474429782282726e+01, 1.6726420346886542e+01, 1.6985642449377284e+01, 1.7253139752773148e+01, 1.7530242081974308e+01, 1.7818692349773503e+01, 1.8120857960601569e+01, 1.8440108632764016e+01, 1.8781558404513735e+01, 1.9153731166695263e+01, 1.9573161931385755e+01, 2.0083110126223993e+01},
+			w: []float64{5.8004562850365771e-04, 5.6692877486338696e-04, 5.2932867305102921e-04, 4.7211368597165944e-04, 4.0223648470876573e-04, 3.2735218319190782e-04, 2.5446548811048362e-04, 1.8892919855999243e-04, 1.3396711152850057e-04, 9.0718165504482523e-05, 5.8661199606591556e-05, 3.6218251240150691e-05, 2.1349054444552587e-05, 1.2013089019084848e-05, 6.4521031002773646e-06, 3.3071925113778075e-06, 1.6175791039359969e-06, 7.5483313427524376e-07, 3.3600239642860852e-07, 1.4264659961771696e-07, 5.7746366478382785e-08, 2.2286582090203475e-08, 8.1983021699506761e-09, 2.8738670556378732e-09, 9.5976924324201262e-10, 3.0529085215378481e-10, 9.2467927287192434e-11, 2.6660996519674056e-11, 7.3154481204350507e-12, 1.9096325566425540e-12, 4.7409073505752031e-13, 1.1189936218333804e-13, 2.5101111888653927e-14, 5.3492761412487281e-15, 1.0825895304391782e-15, 2.0798005039728529e-16, 3.7912539356931888e-17, 6.5547084049896133e-18, 1.0743122119399353e-18, 1.6684093877262400e-19, 2.4538539136228336e-20, 3.4161583900178126e-21, 4.4991409209589655e-22, 5.6023724685401444e-23, 6.5917775903350454e-24, 7.3239791710744789e-25, 7.6792588730186891e-26, 7.5931172671070367e-27, 7.0751732949679160e-28, 6.2078867832748634e-29, 5.1250608797215456e-30, 3.9778286806416675e-31, 2.9000923323091595e-32, 1.9842934651116758e-33, 1.2729744163019100e-34, 7.6493618655638258e-36, 4.3010461850159373e-37, 2.2604572504006732e-38, 1.1091714341886240e-39, 5.0753225126752125e-41, 2.1629552371814077e-42, 8.5739087326714758e-44, 3.1568681170134092e-45, 1.0780709245918455e-46, 3.4094518277810594e-48, 9.9692987408874913e-50, 2.6905726285477170e-51, 6.6902112757430557e-53, 1.5297458011420645e-54, 3.2099851519180199e-56, 6.1681886704578063e-58, 1.0829083084555836e-59, 1.7328083889009238e-61, 2.5206396804555329e-63, 3.3240965181095399e-65, 3.9623955222122382e-67, 4.2558991248868728e-69, 4.1048947183601511e-71, 3.5424776999043975e-73, 2.7245890408644923e-75, 1.8596929038788086e-77, 1.1213274238978696e-79, 5.9430256314002078e-82, 2.7536336403486887e-84, 1.1087876280230634e-86, 3.8548279808836764e-89, 1.1488445098745636e-91, 2.9118805234147757e-94, 6.2218187764965726e-97, 1.1097458975689325e-99, 1.6341809683598844e-102, 1.9621625424695376e-105, 1.8939702898325753e-108, 1.4459753551186440e-111, 8.5692594596311645e-115, 3.8565449589488849e-118, 1.2843410590864927e-121, 3.0685300780965873e-125, 5.0651104293759753e-129, 5.5131423653412833e-133, 3.7300165435945031e-137, 1.4525522232777015e-141, 2.9352196847507026e-146, 2.6587623615117695e-151, 8.6633861029598960e-157, 7.0653364942986233e-163, 7.2051505413036788e-170, 1.5514139491189097e-178},
+		},
+		{
+			n: 216,
+			x: []float64{7.5487718959414210e-02, 2.2646713089859094e-01, 3.7745846761911317e-01, 5.2846968804856509e-01, 6.7950876474356448e-01, 8.3058368937955573e-01, 9.8170247827895785e-01, 1.1328731779888348e+00, 1.2841038709195900e+00, 1.4354026810562848e+00, 1.5867777797546210e+00, 1.7382373916337388e+00, 1.8897898005787916e+00, 2.0414433558661624e+00, 2.1932064784252856e+00, 2.3450876672510903e+00, 2.4970955059821409e+00, 2.6492386696600243e+00, 2.8015259316863266e+00, 2.9539661709946619e+00, 3.1065683794558021e+00, 3.2593416695353823e+00, 3.4122952822245907e+00, 3.5654385952656149e+00, 3.7187811316950210e+00, 3.8723325687298416e+00, 4.0261027470226392e+00, 4.1801016803139959e+00, 4.3343395655126109e+00, 4.4888267932355790e+00, 4.6435739588438905e+00, 4.7985918740108131e+00, 4.9538915788638089e+00, 5.1094843547439881e+00, 5.2653817376305465e+00, 5.4215955322816969e+00, 5.5781378271479722e+00, 5.7350210101185848e+00, 5.8922577851667635e+00, 6.0498611899661094e+00, 6.2078446145563948e+00, 6.3662218211444577e+00, 6.5250069651340752e+00, 6.6842146174875827e+00, 6.8438597885318986e+00, 7.0039579533331269e+00, 7.1645250787759087e+00, 7.3255776524981444e+00, 7.4871327138470951e+00, 7.6492078870405447e+00, 7.8118214167366684e+00, 7.9749922062384426e+00, 8.1387398585838486e+00, 8.3030847208017082e+00, 8.4680479316454296e+00, 8.6336514731539875e+00, 8.7999182264315081e+00, 8.9668720320849413e+00, 9.1345377558145096e+00, 9.3029413597147883e+00, 9.4721099799172528e+00, 9.6420720112891818e+00, 9.8128572000013108e+00, 9.9844967448895385e+00, 1.0157023408668081e+01, 1.0330471640205081e+01, 1.0504877709252620e+01, 1.0680279855235202e+01, 1.0856718451952171e+01, 1.1034236190346626e+01, 1.1212878281848150e+01, 1.1392692685219812e+01, 1.1573730360348824e+01, 1.1756045553033841e+01, 1.1939696115566026e+01, 1.2124743868808109e+01, 1.2311255012587219e+01, 1.2499300592587632e+01, 1.2688957033629340e+01, 1.2880306751340244e+01, 1.3073438856897617e+01, 1.3268449972893279e+01, 1.3465445182689793e+01, 1.3664539141187824e+01, 1.3865857382137794e+01, 1.4069537866591046e+01, 1.4275732829628778e+01, 1.4484610999323769e+01, 1.4696360284715409e+01, 1.4911191060978103e+01, 1.5129340223792830e+01, 1.5351076247103551e+01, 1.5576705568204593e+01, 1.5806580756275796e+01, 1.6041111119395726e+01, 1.6280776711860355e+01, 1.6526147190139376e+01, 1.6777907762072694e+01, 1.7036895825521608e+01, 1.7304154286393636e+01, 1.7581012003064874e+01, 1.7869210618319627e+01, 1.8171115805943941e+01, 1.8490094811217439e+01, 1.8831257901839155e+01, 1.9203122650098184e+01, 1.9622211733828486e+01, 2.0131752068397390e+01},
+			w: []float64{5.7408951238509774e-04, 5.4853385977693967e-04, 5.0077995633045094e-04, 4.3681926493182888e-04, 3.6404534695321319e-04, 2.8986205027358900e-04, 2.2048980967270541e-04, 1.6022189177224014e-04, 1.1121464501100074e-04, 7.3735261435177744e-05, 4.6689968632275442e-05, 2.8233496634858870e-05, 1.6302404527221912e-05, 8.9873835313609794e-06, 4.7299184092204348e-06, 2.3760322139117827e-06, 1.1391060264678187e-06, 5.2109775739704647e-07, 2.2742736124678848e-07, 9.4679280581569520e-08, 3.7589897335857270e-08, 1.4229883676778969e-08, 5.1351173480468011e-09, 1.7661093963625318e-09, 5.7875785413194057e-10, 1.8066600901602130e-10, 5.3707955985666741e-11, 1.5200567246892033e-11, 4.0945877360252466e-12, 1.0494304449814065e-12, 2.5582770078364328e-13, 5.9298335011290506e-14, 1.3064177735039720e-14, 2.7346561920969734e-15, 5.4366757055637182e-16, 1.0261135273171614e-16, 1.8378155831501011e-17, 3.1221798154524404e-18, 5.0287455392773255e-19, 7.6752848097550855e-20, 1.1095334788910946e-20, 1.5183281292392555e-21, 1.9657499371912346e-22, 2.4064442018314010e-23, 2.7838422576260478e-24, 3.0413021389695441e-25, 3.1356913424697775e-26, 3.0490587561112177e-27, 2.7941107980138270e-28, 2.4112340295373517e-29, 1.9579916032501855e-30, 1.4948591683644822e-31, 1.0720958700672810e-32, 7.2163812209007653e-34, 4.5545782039839515e-35, 2.6927171840186886e-36, 1.4896964129251313e-37, 7.7036780004272946e-39, 3.7196117693798106e-40, 1.6748563396289038e-41, 7.0241404150854973e-43, 2.7401344340734534e-44, 9.9291319468776600e-46, 3.3371619908503302e-47, 1.0387276524925886e-48, 2.9893704843803614e-50, 7.9408570659652511e-52, 1.9434716944530867e-53, 4.3740144067322860e-55, 9.0342460240718143e-57, 1.7087495134365174e-58, 2.9528859528856670e-60, 4.6509376421165100e-62, 6.6593952486160953e-64, 8.6442830921042970e-66, 1.0142381095581560e-67, 1.0722439547251424e-69, 1.0179251007077803e-71, 8.6461259693742430e-74, 6.5448969088799971e-76, 4.3965762236216239e-78, 2.6089085327841006e-80, 1.3607099985773063e-82, 6.2039892663366641e-85, 2.4580575133840935e-87, 8.4080554628125066e-90, 2.4652597109139967e-92, 6.1467455174872763e-95, 1.2918545805718045e-97, 2.2661732049781124e-100, 3.2815976681148591e-103, 3.8741015126651295e-106, 3.6760977386321105e-109, 2.7584831111443303e-112, 1.6064052012003602e-115, 7.1024252453209961e-119, 2.3230796238780657e-122, 5.4494213912665180e-126, 8.8284366174946482e-130, 9.4271378060446301e-134, 6.2539251873936211e-138, 2.3865140957941506e-142, 4.7220323342515999e-147, 4.1840743138172546e-152, 1.3319161291512504e-157, 1.0592510752538756e-163, 1.0503755670967946e-170, 2.1869674690632971e-179},
+		},
+	} {
+		n := test.n
+		x := make([]float64, n/2+n%2)
+		w := make([]float64, n/2+n%2)
+		for i := range x {
+			x[i], w[i] = Hermite{}.locationsAsy0(i, n)
+		}
+		if !floats.EqualApprox(x, test.x, 1e-13) {
+			t.Errorf("n = %v, x mismatch", n)
+			fmt.Println(x[107])
+			fmt.Println(test.x[107])
+		}
+		if !floats.EqualApprox(w, test.w, 1e-13) {
+			t.Errorf("n = %v, w mismatch", n)
+		}
+	}
+}
+
+func TestHermiteAsyAiry(t *testing.T) {
+	for _, test := range []struct {
+		n     int
+		theta []float64
+		val   []float64
+		dval  []float64
+	}{
+		{
+			n:     215,
+			theta: []float64{1.5707963267948966e+00, 1.5635071294267224e+00, 1.5562171573546757e+00, 1.5489256352159648e+00, 1.5416317863284521e+00, 1.5343348320272066e+00, 1.5270339909965103e+00, 1.5197284785957685e+00, 1.5124175061777518e+00, 1.5051002803975593e+00, 1.4977760025106577e+00, 1.4904438676582881e+00, 1.4831030641384946e+00, 1.4757527726609410e+00, 1.4683921655836265e+00, 1.4610204061295120e+00, 1.4536366475809854e+00, 1.4462400324499760e+00, 1.4388296916214274e+00, 1.4314047434676882e+00, 1.4239642929312548e+00, 1.4165074305731233e+00, 1.4090332315838545e+00, 1.4015407547542300e+00, 1.3940290414022056e+00, 1.3864971142525955e+00, 1.3789439762656834e+00, 1.3713686094106747e+00, 1.3637699733795743e+00, 1.3561470042367485e+00, 1.3484986129990375e+00, 1.3408236841408716e+00, 1.3331210740183812e+00, 1.3253896092059803e+00, 1.3176280847383373e+00, 1.3098352622500289e+00, 1.3020098680044709e+00, 1.2941505908029671e+00, 1.2862560797638511e+00, 1.2783249419607658e+00, 1.2703557399080556e+00, 1.2623469888800907e+00, 1.2542971540500127e+00, 1.2462046474319508e+00, 1.2380678246090893e+00, 1.2298849812281600e+00, 1.2216543492388388e+00, 1.2133740928542220e+00, 1.2050423042059359e+00, 1.1966569986644591e+00, 1.1882161097919153e+00, 1.1797174838907749e+00, 1.1711588741076131e+00, 1.1625379340461441e+00, 1.1538522108381697e+00, 1.1450991376146524e+00, 1.1362760253118058e+00, 1.1273800537386238e+00, 1.1184082618225748e+00, 1.1093575369389341e+00, 1.1002246032162142e+00, 1.0910060086950395e+00, 1.0816981112001869e+00, 1.0722970627649082e+00, 1.0627987924225111e+00, 1.0531989871517369e+00, 1.0434930707289145e+00, 1.0336761802000907e+00, 1.0237431396389916e+00, 1.0136884308001370e+00, 1.0035061602085740e+00, 9.9319002214595331e-01, 9.8273325689369295e-01, 9.7212860347355579e-01, 9.6136824597870241e-01, 9.5044375240720391e-01, 9.3934600468605900e-01, 9.2806511829511895e-01, 9.1659034955139063e-01, 9.0490998817422319e-01, 8.9301123219309975e-01, 8.8088004154453947e-01, 8.6850096578161351e-01, 8.5585694011780433e-01, 8.4292904244735056e-01, 8.2969620188675874e-01, 8.1613484656631152e-01, 8.0221847457494289e-01, 7.8791712669745728e-01, 7.7319673223616503e-01, 7.5801828879746735e-01, 7.4233682191908168e-01, 7.2610004838413222e-01, 7.0924663405346811e-01, 6.9170388642137270e-01, 6.7338464244284535e-01, 6.5418298314185364e-01, 6.3396819041411068e-01, 6.1257598542667102e-01, 5.8979540387821172e-01, 5.6534835113739590e-01, 5.3885619819698471e-01, 5.0978185232293227e-01, 4.7732127920035572e-01, 4.4017830784988765e-01, 3.9602307074600884e-01, 3.3985069280702440e-01, 2.5624520569356829e-01},
+			val:   []float64{-2.7524590607067879e-13, -1.2484792737707130e-10, 2.5043777255407545e-10, -3.7621487726711831e-10, 5.0266571286479591e-10, -6.3022107051014496e-10, 7.5847898514904004e-10, -8.8850597267422281e-10, 1.0201287099545048e-09, -1.1532700149758681e-09, 1.2885402426941860e-09, -1.4262514564750722e-09, 1.5667774694950304e-09, -1.7098460348004283e-09, 1.8563663242006209e-09, -2.0060430373954962e-09, 2.1597272205910619e-09, -2.3174687646872261e-09, 2.4795270439737100e-09, -2.6462815453642877e-09, 2.8188431716836157e-09, -2.9962948915230151e-09, 3.1805879826447352e-09, -3.3709772507788239e-09, 3.5681573894354513e-09, -3.7732681484183285e-09, 3.9863813736176932e-09, -4.2080297462347532e-09, 4.4391671460302399e-09, -4.6802436355831232e-09, 4.9322546933533433e-09, -5.1957881449299223e-09, 5.4715433664057677e-09, -5.7608265327475837e-09, 6.0644153161437157e-09, -6.3835515563504339e-09, 6.7192819880764795e-09, -7.0729371214636086e-09, 7.4458702579674617e-09, -7.8396410076078555e-09, 8.2556088536449877e-09, -8.6960989460562939e-09, 9.1626310723815202e-09, -9.6575986146054327e-09, 1.0182896152806950e-08, -1.0741758184989815e-08, 1.1337214303287172e-08, -1.1971481080324528e-08, 1.2648762056240369e-08, -1.3372488830525768e-08, 1.4147041859097387e-08, -1.4977276046958432e-08, 1.5868475891599271e-08, -1.6825823997480545e-08, 1.7856900524878266e-08, -1.8967833880184117e-08, 2.0167708166421882e-08, -2.1465280681285451e-08, 2.2870631970634630e-08, -2.4395881051717265e-08, 2.6054060647767539e-08, -2.7859818527100110e-08, 2.9830454146699167e-08, -3.1984835487787522e-08, 3.4345470368342559e-08, -3.6937900081988413e-08, 3.9790883510012329e-08, -4.2938418365980210e-08, 4.6419377177480922e-08, -5.0279213559974237e-08, 5.4570799296449321e-08, -5.9356303125081130e-08, 6.4708755363671345e-08, -7.0714511032393380e-08, 7.7475892426711618e-08, -8.5115456468135130e-08, 9.3779863576446978e-08, -1.0364644483987255e-07, 1.1493006182865740e-07, -1.2789317815470753e-07, 1.4285900893044798e-07, -1.6022759919461249e-07, 1.8049814080062288e-07, -2.0429953256541455e-07, 2.3243044535889061e-07, -2.6591504027157263e-07, 3.0608147425737922e-07, -3.5467098673335754e-07, 4.1399606056878556e-07, -4.8716979156405424e-07, 5.7844824292016844e-07, -6.9374768843585542e-07, 8.4144962449118331e-07, -1.0336795693201387e-06, 1.2884020459910342e-06, -1.6329629222918408e-06, 2.1103031286712709e-06, -2.7903321871954755e-06, 3.7918023218017778e-06, -5.3269144947324421e-06, 7.7989206456257246e-06, -1.2034979469568085e-05, 1.9905658561076196e-05, -3.6224899321604820e-05, 7.5828952282754516e-05, -1.9870421394114517e-04, 7.9136577883937422e-04, -9.1266148556594703e-03},
+			dval:  []float64{-2.9359856130945122e+01, 2.9359466144908318e+01, -2.9358296010652477e+01, 2.9356345199427643e+01, -2.9353612829040124e+01, 2.9350097662433203e+01, -2.9345798105693621e+01, 2.9340712205476308e+01, -2.9334837645838910e+01, 2.9328171744474840e+01, -2.9320711448331572e+01, 2.9312453328598885e+01, -2.9303393575049100e+01, 2.9293527989709109e+01, -2.9282851979841201e+01, 2.9271360550207458e+01, -2.9259048294588819e+01, 2.9245909386527540e+01, -2.9231937569258221e+01, 2.9217126144788914e+01, -2.9201467962090302e+01, 2.9184955404346876e+01, -2.9167580375219231e+01, 2.9149334284062498e+01, -2.9130208030040425e+01, 2.9110191985068752e+01, -2.9089275975516287e+01, 2.9067449262584436e+01, -2.9044700521279459e+01, 2.9021017817883425e+01, -2.8996388585821325e+01, 2.8970799599811933e+01, -2.8944236948180023e+01, 2.8916686003195348e+01, -2.8888131389291605e+01, 2.8858556949003951e+01, -2.8827945706448649e+01, 2.8796279828150279e+01, -2.8763540581003511e+01, 2.8729708287134507e+01, -2.8694762275403512e+01, 2.8658680829263385e+01, -2.8621441130659093e+01, 2.8583019199620328e+01, -2.8543389829161509e+01, 2.8502526515061927e+01, -2.8460401380051497e+01, 2.8416985091874277e+01, -2.8372246774642264e+01, 2.8326153912823031e+01, -2.8278672247129006e+01, 2.8229765661486788e+01, -2.8179396060166667e+01, 2.8127523234037287e+01, -2.8074104714780372e+01, 2.8019095615750665e+01, -2.7962448457994284e+01, 2.7904112979739956e+01, -2.7844035927448619e+01, 2.7782160826241125e+01, -2.7718427727214667e+01, 2.7652772928798932e+01, -2.7585128668881747e+01, 2.7515422783940370e+01, -2.7443578330833645e+01, 2.7369513166223737e+01, -2.7293139477783004e+01, 2.7214363260373997e+01, -2.7133083729234610e+01, 2.7049192660814331e+01, -2.6962573650237655e+01, 2.6873101272350414e+01, -2.6780640130847800e+01, 2.6685043776981303e+01, -2.6586153475654008e+01, 2.6483796792158788e+01, -2.6377785967154090e+01, 2.6267916040395331e+01, -2.6153962674834343e+01, 2.6035679621411951e+01, -2.5912795750458177e+01, 2.5785011557068390e+01, -2.5651995023754676e+01, 2.5513376692151432e+01, -2.5368743753874771e+01, 2.5217632914945654e+01, -2.5059521712941240e+01, 2.4893817863127197e+01, -2.4719846067215368e+01, 2.4536831517922174e+01, -2.4343879046260469e+01, 2.4139946442705973e+01, -2.3923809867871942e+01, 2.3694018337866666e+01, -2.3448832829666316e+01, 2.3186143264519330e+01, -2.2903352884396824e+01, 2.2597213200674400e+01, -2.2263581543467414e+01, 2.1897052703993687e+01, -2.1490376258364485e+01, 2.1033488463000687e+01, -2.0511802124454178e+01, 1.9902938182242686e+01, -1.9169784832381577e+01, 1.8243381598901596e+01, -1.6969663168974311e+01, 1.4853826851969115e+01},
+		},
+		{
+			n:     215,
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+			theta: []float64{1.5671686105755023e+00, 1.5599127961684220e+00, 1.5526558355346407e+00, 1.5453969634495357e+00, 1.5381354130756992e+00, 1.5308704153127000e+00, 1.5236011981417006e+00, 1.5163269859634152e+00, 1.5090469989278730e+00, 1.5017604522544048e+00, 1.4944665555402459e+00, 1.4871645120560699e+00, 1.4798535180267400e+00, 1.4725327618954691e+00, 1.4652014235695219e+00, 1.4578586736455008e+00, 1.4505036726121565e+00, 1.4431355700285682e+00, 1.4357535036754083e+00, 1.4283565986768869e+00, 1.4209439665908115e+00, 1.4135147044640579e+00, 1.4060678938505511e+00, 1.3986025997886760e+00, 1.3911178697348172e+00, 1.3836127324494960e+00, 1.3760861968323106e+00, 1.3685372507016056e+00, 1.3609648595144777e+00, 1.3533679650223920e+00, 1.3457454838572851e+00, 1.3380963060426339e+00, 1.3304192934234869e+00, 1.3227132780089634e+00, 1.3149770602201478e+00, 1.3072094070356892e+00, 1.2994090500267301e+00, 1.2915746832720101e+00, 1.2837049611431546e+00, 1.2757984959492026e+00, 1.2678538554283829e+00, 1.2598695600739727e+00, 1.2518440802797628e+00, 1.2437758332892002e+00, 1.2356631799306261e+00, 1.2275044211192108e+00, 1.2192977941041021e+00, 1.2110414684370108e+00, 1.2027335416358120e+00, 1.1943720345138122e+00, 1.1859548861419755e+00, 1.1774799484076148e+00, 1.1689449801287550e+00, 1.1603476406784692e+00, 1.1516854830678944e+00, 1.1429559464302423e+00, 1.1341563478407819e+00, 1.1252838733993509e+00, 1.1163355684922343e+00, 1.1073083271390356e+00, 1.0981988803171721e+00, 1.0890037831415225e+00, 1.0797194007591668e+00, 1.0703418927985888e+00, 1.0608671961885900e+00, 1.0512910061337959e+00, 1.0416087550001036e+00, 1.0318155888237164e+00, 1.0219063411101317e+00, 1.0118755035330074e+00, 1.0017171930750695e+00, 9.9142511507162645e-01, 9.8099252151840288e-01, 9.7041216388519547e-01, 9.5967623952979786e-01, 9.4877633062585665e-01, 9.3770333429470865e-01, 9.2644738235305046e-01, 9.1499774873988793e-01, 9.0334274224692235e-01, 8.9146958161860457e-01, 8.7936424937397950e-01, 8.6701131978084423e-01, 8.5439375521282512e-01, 8.4149266354281749e-01, 8.2828700713198744e-01, 8.1475325116200825e-01, 8.0086493523862246e-01, 7.8659214693830359e-01, 7.7190086863415974e-01, 7.5675215854165734e-01, 7.4110111194290051e-01, 7.2489552655247935e-01, 7.0807416302356885e-01, 6.9056444104412407e-01, 6.7227933193754241e-01, 6.5311307983969791e-01, 6.3293516775593595e-01, 6.1158156935716357e-01, 5.8884164425859431e-01, 5.6443772421506910e-01, 5.3799175946275157e-01, 5.0896747562778555e-01, 4.7656205323872197e-01, 4.3948124005672007e-01, 3.9539840620540745e-01, 3.3931369540774287e-01, 2.5576413755369809e-01},
+			val:   []float64{-2.1420664007171084e-13, 5.3170379037842784e-14, -3.4734236933038639e-15, 2.3242110868118431e-13, 3.7943143720204046e-14, -5.7160511614569708e-14, 2.1177269961331864e-13, -3.4948583926844979e-14, 1.7369271883827313e-13, 3.5623756291990570e-13, 6.5520118362261941e-14, 1.1255590127344777e-13, 9.4867994932892441e-14, -6.1601712969494469e-14, 4.7023788875015558e-14, -1.4272998866826663e-13, -2.6605445153274162e-14, -2.5223571223200907e-13, -1.3724084095111965e-13, -7.0111736669803626e-14, 5.7347666545680944e-14, -5.0924962889888544e-14, -5.2683776576685045e-15, -2.1544335394504838e-13, 4.0230445264824984e-15, 6.9175538975130938e-15, -1.1339463388095042e-13, -3.9896959286779273e-14, -8.8360560296236634e-14, -1.0474371284611670e-13, 1.2687327963040444e-14, -1.7782734520430910e-13, 2.0086781777635686e-13, -7.5400883703521135e-14, 1.2278140016266356e-13, -1.1244970732922019e-13, 1.6072100253117342e-14, 5.2340169298568757e-15, 1.1013085876614924e-13, -9.6621831158318670e-15, -1.8366177977891496e-13, 1.0601073284832238e-14, -1.3784763212103856e-13, -1.5863525424166753e-13, -1.6638681463670250e-13, 8.6360908147481066e-14, -7.8672683965135368e-14, 6.8378486764803313e-14, 9.0534733729868808e-14, 6.6505185887739604e-15, 3.3141885340142080e-15, -2.0537396911778824e-13, 7.3393589371575821e-14, 9.8483281662822096e-14, -2.3812738806298458e-13, 6.5975425886450090e-15, 8.7013139463913052e-14, 7.5278742714453987e-14, -1.0708940266003440e-13, 2.0958580081069137e-13, -1.5480716019053119e-14, 4.8469624575186930e-15, -6.1362291991375536e-14, -3.5942923464396180e-14, -7.6176865685553763e-14, 1.0095757892256693e-13, -4.2683956504767779e-14, -4.8938621882647329e-14, 1.6489272569372713e-15, -1.1390338364880240e-13, 2.1513601964632049e-14, -1.0152923724696736e-14, -3.9597826958407387e-14, -8.5123156147931521e-14, -6.5276802085245163e-14, 6.3966825794140229e-14, -2.8207572680644779e-14, -5.9767990455898208e-15, -1.1189271498293956e-13, -4.5600777141900301e-14, 1.5226732724861721e-14, 3.9473540473700922e-14, -5.6017378761616795e-15, -2.4079255903843183e-14, -3.1139558336514997e-14, -5.6034014603771978e-14, 6.9309294575728887e-14, -3.7871955014469560e-14, 4.2988763678275364e-14, 1.0661412180664073e-14, 6.2069599395465107e-14, -4.8913422170368503e-14, 3.3884911719768557e-14, 2.8191908465098299e-15, 2.1228960171536080e-14, -5.6191478942893769e-14, -1.4786950368470112e-14, -2.1665036441200809e-14, 1.4936420829725019e-14, -1.1615745673091571e-13, 1.4661728300981146e-13, -3.6088669931521093e-13, 1.1825080499589470e-12, -4.7300739521811106e-12, 2.5459387908526307e-11, -2.2842779135337983e-10, 5.3230524570865730e-09, 1.8504694403187737e-14},
+			dval:  []float64{-2.9427800603424888e+01, 2.9427025985916128e+01, -2.9425476404186732e+01, 2.9423151164251305e+01, -2.9420049223750453e+01, 2.9416169190288219e+01, -2.9411509319206210e+01, 2.9406067510787015e+01, -2.9399841306877356e+01, 2.9392827886918813e+01, -2.9385024063373031e+01, 2.9376426276524445e+01, -2.9367030588643043e+01, 2.9356832677485624e+01, -2.9345827829112846e+01, 2.9334010929995465e+01, -2.9321376458381234e+01, 2.9307918474890485e+01, -2.9293630612304742e+01, 2.9278506064510257e+01, -2.9262537574553480e+01, 2.9245717421762187e+01, -2.9228037407881235e+01, 2.9209488842167364e+01, -2.9190062525382206e+01, 2.9169748732617215e+01, -2.9148537194877896e+01, 2.9126417079348521e+01, -2.9103376968250736e+01, 2.9079404836201938e+01, -2.9054488025970500e+01, 2.9028613222515034e+01, -2.9001766425185131e+01, 2.8973932917948375e+01, -2.8945097237496743e+01, 2.8915243139070423e+01, -2.8884353559822181e+01, 2.8852410579527444e+01, -2.8819395378426645e+01, 2.8785288191964142e+01, -2.8750068262165122e+01, 2.8713713785364636e+01, -2.8676201855972852e+01, 2.8637508405928578e+01, -2.8597608139454227e+01, 2.8556474462684314e+01, -2.8514079407692350e+01, 2.8470393550387161e+01, -2.8425385921689987e+01, 2.8379023911335462e+01, -2.8331273163562233e+01, 2.8282097463870926e+01, -2.8231458615927728e+01, 2.8179316307577018e+01, -2.8125627964795974e+01, 2.8070348592274335e+01, -2.8013430599129794e+01, 2.7954823608071287e+01, -2.7894474246092045e+01, 2.7832325914509109e+01, -2.7768318535855656e+01, 2.7702388274772812e+01, -2.7634467229625294e+01, 2.7564483091071331e+01, -2.7492358763234883e+01, 2.7418011942441158e+01, -2.7341354647661582e+01, 2.7262292695845463e+01, -2.7180725114157763e+01, 2.7096543479754128e+01, -2.7009631176051940e+01, 2.6919862552432292e+01, -2.6827101971847430e+01, 2.6731202727801641e+01, -2.6632005808479885e+01, 2.6529338481236724e+01, -2.6423012664989066e+01, 2.6312823050968632e+01, -2.6198544923370196e+01, 2.6079931620126928e+01, -2.5956711559610671e+01, 2.5828584740479652e+01, -2.5695218597789530e+01, 2.5556243066913513e+01, -2.5411244665072843e+01, 2.5259759344501834e+01, -2.5101263795907666e+01, 2.4935164777812918e+01, -2.4760785904536036e+01, 2.4577351124782325e+01, -2.4383963836127013e+01, 2.4179580164228856e+01, -2.3962974319142369e+01, 2.3732693009181720e+01, -2.3486994450695558e+01, 2.3223765221219963e+01, -2.2940404454626893e+01, 2.2633658531160954e+01, -2.2299378247087898e+01, 2.1932149880590437e+01, -2.1524711604350518e+01, 2.1066983868178077e+01, -2.0544356598759389e+01, 1.9934415684120079e+01, -1.9199991281861426e+01, 1.8272015261833435e+01, -1.6996182557157578e+01, 1.4876958810870862e+01},
+		},
+	} {
+		got := make([]float64, len(test.theta))
+		gotD := make([]float64, len(test.theta))
+		for i := range got {
+			got[i], gotD[i] = Hermite{}.hermpolyAsyAiry(i, test.n, test.theta[i])
+		}
+		if !floats.EqualApprox(test.val, got, 1e-12) {
+			t.Errorf("n = %v, hermpolyAsyAiry mismatch", test.n)
+		}
+		if !floats.EqualApprox(test.dval, gotD, 1e-12) {
+			t.Errorf("n = %v, hermpolyAsyAiry deriv mismatch", test.n)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/integrate/quad/internal/PrintGoSlice.m b/vendor/gonum.org/v1/gonum/integrate/quad/internal/PrintGoSlice.m
new file mode 100644
index 00000000..d3a51b28
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/integrate/quad/internal/PrintGoSlice.m
@@ -0,0 +1,11 @@
+% Copyright �2016 The gonum Authors. All rights reserved.
+% Use of this source code is governed by a BSD-style
+% license that can be found in the LICENSE file.
+
+function PrintGoSlice(a)
+      fprintf('[]float64{')
+      for i = 1:length(a)
+            fprintf('%1.16e, ',a(i))
+      end
+      fprintf('}\n')
+end
\ No newline at end of file
diff --git a/vendor/gonum.org/v1/gonum/integrate/quad/internal/genherm.m b/vendor/gonum.org/v1/gonum/integrate/quad/internal/genherm.m
new file mode 100644
index 00000000..f673f97d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/integrate/quad/internal/genherm.m
@@ -0,0 +1,32 @@
+% Copyright �2016 The gonum Authors. All rights reserved.
+% Use of this source code is governed by a BSD-style
+% license that can be found in the LICENSE file.
+
+clc
+clear all
+close all
+
+% Generate herm points
+min = 216;
+max = 216;
+fprintf('xCache = [][]float64{\n')
+for i = min:max
+    [x,w] = hermpts(i);
+    fprintf('{')
+    for j = 1:i-1
+       fprintf('%1.16e, ',x(j)) 
+    end
+    fprintf('%1.16e},\n',x(i)) 
+end
+fprintf('}\n')
+
+fprintf('wCache = [][]float64{\n')
+for i = min:max
+    [x,w] = hermpts(i);
+    fprintf('{')
+    for j = 1:i-1
+       fprintf('%1.16e, ',w(j)) 
+    end
+    fprintf('%1.16e},\n',w(i)) 
+end
+fprintf('}\n')
diff --git a/vendor/gonum.org/v1/gonum/integrate/quad/internal/hermpts.m b/vendor/gonum.org/v1/gonum/integrate/quad/internal/hermpts.m
new file mode 100644
index 00000000..9306ad60
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/integrate/quad/internal/hermpts.m
@@ -0,0 +1,609 @@
+% Copyright (c) 2015, The Chancellor, Masters and Scholars of the University 
+% of Oxford, and the Chebfun Developers.
+% Copyright (c) 2016 The gonum Authors
+% All rights reserved.
+%
+% Redistribution and use in source and binary forms, with or without
+% modification, are permitted provided that the following conditions are met:
+%     * Redistributions of source code must retain the above copyright
+%       notice, this list of conditions and the following disclaimer.
+%     * Redistributions in binary form must reproduce the above copyright
+%       notice, this list of conditions and the following disclaimer in the
+%       documentation and/or other materials provided with the distribution.
+%     * Neither the name of the University of Oxford nor the names of its 
+%       contributors may be used to endorse or promote products derived from 
+%       this software without specific prior written permission.
+%
+% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+% ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+% WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+% DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR 
+% ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+% (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+% LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
+% ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+% (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+% SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+
+function [x, w, v] = hermpts(n, varargin)
+%HERMPTS   Hermite points and Gauss-Hermite Quadrature Weights.
+%   HERMPTS(N) returns N Hermite points X in (-inf, inf). By default these are
+%   roots of the 'physicist'-type Hermite polynomials, which are orthogonal with
+%   respect to the weight exp(-x.^2).
+%
+%   HERMPTS(N, 'PROB') normalises instead by the probablist's definition (with
+%   weight exp(-x.^2/2)), which gives rise to monomials.
+%
+%   [X, W] = HERMPTS(N) returns also a row vector W of weights for Gauss-Hermite
+%   quadrature. [X,W,V] = HERMPTS(N) returns in addition a column vector V of
+%   the barycentric weights corresponding to X.
+%
+%   [X, W] = HERMPTS(N, METHOD) where METHOD is one of 'GW', 'REC', 'GLR', or 
+%   'ASY' allows the user to select which method is used. 'GW' will use the 
+%   traditional Golub-Welsch eigenvalue method [1], best when n<=20. 'REC' 
+%   uses Newton's method with polynomial evaluation via the 3-term 
+%   recurrence for Hermite polynomials. 'GLR' uses Glaser-Liu-Rokhlin 
+%   fast algorithm which is much faster for large N [2]. 'ASY' uses Newton's 
+%   method with polynomial evaluation via asymptotic formula. 'ASY' is the 
+%   fastest for N>=200, 'GLR' is the most accurate for nodes close to 0. 
+%   By default HERMPTS uses 'GW' when N <= 20, 'REC' for 21<=N<200, and
+%   'ASY' when N>=200. 
+%
+% References:
+%   [1] G. H. Golub and J. A. Welsch, "Calculation of Gauss quadrature
+%       rules", Math. Comp. 23:221-230, 1969,
+%   [2] A. Glaser, X. Liu and V. Rokhlin, "A fast algorithm for the
+%       calculation of the roots of special functions", SIAM Journal
+%       on Scientific Computing", 29(4):1420-1438:, 2007.
+%   [3] A. Townsend, T. Trogdon and S. Olver, Fast computation of Gauss
+%       nodes and weights on the whole real line, submitted, 2014. 
+%
+% See also CHEBPTS, LEGPTS, LAGPTS, and JACPTS.
+
+% Copyright 2015 by The University of Oxford and The Chebfun Developers. 
+% See http://www.chebfun.org/ for Chebfun information.
+%
+% 'GW' by Nick Trefethen, March 2009 - algorithm adapted from [1].
+% 'GLR' by Nick Hale, March 2010 - algorithm adapted from [2].
+
+% Defaults:
+method = 'default';
+type = 'phys';
+
+if ( n < 0 )
+    error('CHEBFUN:hermpts:n', 'First input should be a positive integer.');
+end
+
+% Return empty vector if n = 0.
+if ( n == 0 )
+    [x, w, v] = deal([]); 
+    return
+end
+
+% Check the inputs
+while ( ~isempty(varargin) )
+    s = varargin{1}; 
+    varargin(1) = [];
+    if ( strcmpi(s, 'GW') )
+        method = 'GW';
+    elseif ( strcmpi(s,'glr') )
+        method = 'GLR';  
+    elseif ( strcmpi(s,'rec') )
+        method = 'REC';
+    elseif ( strcmpi(s,'asy') )
+        method = 'ASY';
+    elseif ( strncmpi(s, 'phys', 3) )
+        type = 'phys';
+    elseif ( strncmpi(s, 'prob', 3) )
+        type = 'prob'; 
+    else
+        error('CHEBFUN:hermpts:input', 'Unrecognised input string; %s.', s);
+    end
+end
+
+% Three cases: 
+% 
+%  N <= 20:  Use GW
+%  21<=N<200: Use REC
+%  N>=200: Use ASY
+if ( n == 1 )
+    % n = 1 case is trivial
+    x = 0; 
+    w = sqrt(pi); 
+    v = 1;           
+    
+elseif ( (n < 21 && strcmpi(method,'default')) || strcmpi(method,'GW') )
+    % GW, see [1]
+    
+    beta = sqrt(.5*(1:n-1));              % 3-term recurrence coeffs
+    T = diag(beta, 1) + diag(beta, -1);   % Jacobi matrix
+    [V, D] = eig(T);                      % Eigenvalue decomposition
+    [x, indx] = sort(diag(D));            % Hermite points
+    w = sqrt(pi)*V(1, indx).^2;           % weights
+    v = abs(V(1, indx)).';                % Barycentric weights
+    v = v./max(v);                        % Normalize
+    v(2:2:n) = -v(2:2:n);
+    
+    % Enforce symmetry:
+    ii = 1:floor(n/2);  
+    x = x(ii);  
+    w = w(ii);
+    vmid = v(floor(n/2)+1); 
+    v = v(ii);
+    if ( mod(n, 2) )
+        x = [x ; 0 ; -x(end:-1:1)];   
+        w = [w, sqrt(pi) - sum(2*w), w(end:-1:1)];
+        v = [v ; vmid ; v(end:-1:1)];
+    else
+        x = [x ; -x(end:-1:1)];
+        w = [w, w(end:-1:1)];
+        v = [v ; -v(end:-1:1)];
+    end
+    
+elseif ( strcmpi(method,'GLR') )
+    % Fast, see [2]
+    
+    [x, ders] = alg0_Herm(n);             % Nodes and H_n'(x)
+    w = (2*exp(-x.^2)./ders.^2)';         % Quadrature weights
+    v = exp(-x.^2/2)./ders;               % Barycentric weights
+    v = v./max(abs(v));                   % Normalize
+    if ( ~mod(n, 2) )
+        ii = (n/2+1):n; 
+        v(ii) = -v(ii); 
+    end
+    
+elseif ( (n < 200 && strcmpi(method,'default')) || strcmpi(method,'REC') )
+    
+    [x, w, v] = hermpts_rec( n ); 
+    
+else
+    
+    [x, w, v] = hermpts_asy( n ); 
+    
+end
+
+% Normalise so that sum(w) = sqrt(pi)
+w = (sqrt(pi)/sum(w))*w;                  
+
+if ( strcmpi(type, 'prob') )
+    x = x*sqrt(2);
+    w = w*sqrt(2);
+end
+
+end
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% %%%%%%%%%%%%%%%%%%%%%%% Routines for GLR algorithm %%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% Driver for 'GLR'.
+function [roots, ders] = alg0_Herm(n) 
+% Compute coefficients of H_m(0), H_m'(0), m = 0,..,N.
+
+Hm2 = 0; 
+Hm1 = pi^(-1/4); 
+Hpm2 = 0; 
+Hpm1 = 0;
+for k = 0:n-1
+    H = -sqrt(k/(k+1))*Hm2;
+    Hp = sqrt(2/(k+1))*Hm1-sqrt(k/(k+1))*Hpm2;
+    Hm2 = Hm1; 
+    Hm1 = H; 
+    Hpm2 = Hpm1; 
+    Hpm1 = Hp;
+end
+
+% allocate storage
+roots = zeros(n, 1); 
+ders = zeros(n, 1);                      
+if ( mod(n,2) )
+    % zero is a root:
+    roots((n-1)/2) = 0; 
+    ders((n+1)/2) = Hp;         
+else
+    % find first root:
+    [roots(n/2+1), ders(n/2+1)] = alg2_Herm(H,n); 
+end        
+
+% compute roots and derivatives:
+[roots, ders] = alg1_Herm(roots, ders); 
+
+end
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% Main algorithm for 'GLR'
+function [roots, ders] = alg1_Herm(roots, ders) 
+
+n = length(roots);
+s = mod(n, 2);
+N = (n - s) / 2;
+
+% number of terms in Taylor expansion
+m = 30; 
+
+% initialise
+hh1 = ones(m + 1, 1); 
+u = zeros(1, m + 1); 
+up = zeros(1, m + 1);
+
+for j = (N + 1):(n - 1)
+    
+    % previous root
+    x = roots(j); 
+    
+    % initial approx
+    h = rk2_Herm(pi/2,-pi/2,x,n) - x;
+
+    % scaling
+    M = 1/h;
+    
+    % recurrence relation for Hermite polynomials
+    c1 = -(2*n+1-x^2)/M^2; 
+    c2 = 2*x./M^3; 
+    c3 = 1./M^4;
+    u(1) = 0; 
+    u(2) = ders(j)/M; 
+    u(3) = .5*c1*u(1);
+    u(4) = (c1*u(2) + c2*u(1))/6;
+    up(1) = u(2); 
+    up(2) = 2*u(3)*M; 
+    up(3) = 3*u(4)*M; 
+    up(m+1) = 0;
+    
+    for k = 2:m-2
+        u(k+3) = (c1*u(k+1) + c2*u(k) + c3*u(k-1))/((k+1)*(k+2));
+        up(k+2) = (k+2)*u(k+3)*M;
+    end
+  
+    % flip for more accuracy in inner product calculation
+    u = u(m+1:-1:1);       
+    up = up(m+1:-1:1);
+    
+    % Newton iteration
+    hh = hh1; 
+    hh(end) = M;    
+    step = inf;  
+    l = 0; 
+    z = zeros(m, 1);
+    while ( (abs(step) > eps) && (l < 10) )
+        l = l + 1;
+        step = (u*hh)/(up*hh);
+        h = h - step;
+        % powers of h (This is the fastest way!)
+        hh = [M ; cumprod(M*h + z)]; 
+        % flip for more accuracy in inner product calculation
+        hh = hh(end:-1:1); 
+    end
+    
+    % update
+    roots(j+1) = x + h;
+    ders(j+1) = up*hh;
+end
+
+% nodes are symmetric
+roots(1:N+s) = -roots(n:-1:N+1);
+ders(1:N+s) = ders(n:-1:N+1);
+
+end
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% find the first root (note H_n'(0) = 0)
+function [x1, d1] = alg2_Herm(Hn0, n) 
+
+% advance ODE via Runge-Kutta for initial approx
+x1 = rk2_Herm(0, -pi/2, 0, n);
+
+% number of terms in Taylor expansion
+m = 30; 
+
+% scaling
+M = 1/x1;
+% c = log10(n);
+% M = 1./x1.^(1-1.25/(c));
+
+% initialise
+u = zeros(1,m+1); 
+up = zeros(1,m+1);
+
+% recurrence relation for Legendre polynomials
+u(1) = Hn0; 
+u(3) = -.5*(2*n+1)*u(1)/M^2;
+up(1) = 0; 
+up(2) = 2*u(3)*M;
+for k = 2:2:m-2
+    u(k+3) = (-(2*n+1)*u(k+1)/M^2 + u(k-1)/M^4)/((k+1)*(k+2));
+    up(k+2) = (k+2)*u(k+3)*M;
+end
+
+% flip for more accuracy in inner product calculation
+u = u(m+1:-1:1);
+up = up(m+1:-1:1);
+
+z = zeros(m, 1);
+x1k = [M ; cumprod(M*x1 + z)];
+step = inf; 
+l = 0;
+% Newton iteration
+while ( (abs(step) > eps) && (l < 10) )
+    l = l + 1;
+    step = (u*x1k)/(up*x1k);
+    x1 = x1 - step;
+    % powers of h (This is the fastest way!)
+    x1k = [1 ; cumprod(M*x1 + z)]; 
+    x1k = x1k(end:-1:1);
+end
+
+% Update derivative
+d1 = up*x1k;
+
+end
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% Runge-Kutta for Hermite Equation
+function x = rk2_Herm(t, tn, x, n) 
+m = 10; 
+h = (tn-t)/m;
+for j = 1:m
+    k1 = -h/(sqrt(2*n+1-x^2) - .5*x*sin(2*t)/(2*n+1-x^2));
+    t = t + h;
+    k2 = -h/(sqrt(2*n+1-(x+k1)^2) - .5*x*sin(2*t)/(2*n+1-(x+k1)^2));
+    x = x + .5*(k1 + k2);
+end
+end
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% %%%%%%%%%%%%%%%%%%%%%%% Routines for ASY algorithm %%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+function [x, w, v] = hermpts_asy(n)
+% HERMPTS_ASY, fast algorithm for computing Gauss-Hermite nodes and weights 
+% using Newton's method with polynomial evaluation via asymptotic expansions.  
+% 
+%  x = Gauss-Hermite nodes, w = quad weights, v = bary weights.
+% 
+%  See [3]. 
+
+[x, w, v] = hermpts_asy0( n );   
+
+if mod(n,2) == 1                              % fold out
+    x = [-x(end:-1:1);x(2:end)];
+    w = [w(end:-1:1) w(2:end)]; w = (sqrt(pi)/sum(w))*w;
+    v = [v(end:-1:1);v(2:end)]; v = v./max(abs(v));
+else
+    x = [-x(end:-1:1);x];
+    w = [w(end:-1:1) w]; w = (sqrt(pi)/sum(w))*w;
+    v = [v(end:-1:1);-v]; v = v./max(abs(v));
+end
+
+% debug
+%tic, exact = hermpts(n); toc
+%semilogy(abs(exact-x))
+end
+
+function [x, w, v] = hermpts_asy0(n)
+% Compute Hermite nodes and weights using asymptotic formula
+
+x0 = HermiteInitialGuesses(n);   % get initial guesses
+t0 = x0./sqrt(2*n+1);
+theta0 = acos(t0);               % convert to theta-variable
+for k = 1:20
+    [val, dval] = hermpoly_asy_airy(n, theta0);
+    dt = -val./(sqrt(2)*sqrt(2*n+1)*dval.*sin(theta0));
+    theta0 = theta0 - dt;                        % Newton update
+    if norm(dt,inf) < sqrt(eps)/10, break; end
+end
+t0 = cos(theta0);
+x = sqrt(2*n+1)*t0;                          % back to x-variable
+
+ders = x.*val + sqrt(2)*dval;
+%ders = dval;
+w = (exp(-x.^2)./ders.^2)';            % quadrature weights
+
+v = exp(-x.^2/2)./ders;               % Barycentric weights
+end
+
+function [val, dval] = hermpoly_asy_airy(n, theta)
+% HERMPOLY_ASY evaluation hermite poly using Airy asymptotic formula in
+% theta-space.
+
+musq = 2*n+1;
+cosT = cos(theta); sinT = sin(theta);
+sin2T = 2*cosT.*sinT;
+eta = .5*theta - .25*sin2T;
+chi = -(3*eta/2).^(2/3);
+phi = (-chi./sinT.^2).^(1/4);
+const = 2*sqrt(pi)*musq^(1/6)*phi; 
+Airy0 = real(airy(musq.^(2/3)*chi));
+Airy1 = real(airy(1,musq.^(2/3)*chi));
+
+% Terms in (12.10.43):
+a0 = 1; b0 = 1;
+a1 = 15/144; b1 = -7/5*a1;
+a2 = 5*7*9*11/2/144^2; b2 = -13/11*a2;
+a3 = 7*9*11*13*15*17/6/144^3;
+b3 = -19/17*a3;
+
+% u polynomials in (12.10.9)
+u0 = 1; u1 = (cosT.^3-6*cosT)/24;
+u2 = (-9*cosT.^4 + 249*cosT.^2 + 145)/1152;
+u3 = (-4042*cosT.^9+18189*cosT.^7-28287*cosT.^5-151995*cosT.^3-259290*cosT)/414720;
+
+%first term
+A0 = 1;
+val = A0*Airy0;
+
+%second term
+B0 = -(a0*phi.^6.*u1+a1*u0)./chi.^2;
+val = val + B0.*Airy1./musq.^(4/3);
+
+%third term
+A1 = (b0*phi.^12.*u2 + b1*phi.^6.*u1 + b2*u0)./chi.^3;
+val = val + A1.*Airy0/musq.^2;
+
+%fourth term
+B1 = -(phi.^18.*u3 + a1*phi.^12.*u2 + a2*phi.^6.*u1 + a3*u0)./chi.^5;
+val = val + B1.*Airy1./musq.^(4/3+2);
+
+val = const.*val;
+
+%% Derivative
+
+eta = .5*theta - .25*sin2T;
+chi = -(3*eta/2).^(2/3);
+phi = (-chi./sinT.^2).^(1/4);
+const = sqrt(2*pi)*musq^(1/3)./phi;
+
+% v polynomials in (12.10.10)
+v0 = 1; v1 = (cosT.^3+6*cosT)/24;
+v2 = (15*cosT.^4-327*cosT.^2-143)/1152;
+v3 = (259290*cosT + 238425*cosT.^3 - 36387*cosT.^5 + 18189*cosT.^7 -...
+    4042*cosT.^9)/414720;
+
+%first term
+C0 = -(b0*phi.^6.*v1 + b1.*v0)./chi;
+dval = C0.*Airy0/musq.^(2/3);
+
+% %second term
+D0 =  a0*v0;
+dval = dval + D0*Airy1;
+
+% %third term
+C1 = -(phi.^18.*v3 + b1*phi.^12.*v2 + b2*phi.^6.*v1 + b3*v0)./chi.^4;
+dval = dval + C1.*Airy0/musq.^(2/3+2);
+
+%fourth term
+D1 = (a0*phi.^12.*v2 + a1*phi.^6.*v1 + a2*v0)./chi.^3;
+dval = dval + D1.*Airy1/musq.^2;
+
+dval = const.*dval;
+
+end
+
+function x_init = HermiteInitialGuesses(n)
+%HERMITEINTITIALGUESSES(N), Initial guesses for Hermite zeros.
+%
+% [1] L. Gatteschi, Asymptotics and bounds for the zeros of Laguerre
+% polynomials: a survey, J. Comput. Appl. Math., 144 (2002), pp. 7-27.
+%
+% [2] F. G. Tricomi, Sugli zeri delle funzioni di cui si conosce una
+% rappresentazione asintotica, Ann. Mat. Pura Appl. 26 (1947), pp. 283-300.
+
+% Gatteschi formula involving airy roots [1].
+% These initial guess are good near x = sqrt(n+1/2);
+if mod(n,2) == 1
+    m = (n-1)/2; bess = (1:m)'*pi; a = .5;
+else
+    m = n/2; bess = ((0:m-1)'+.5)*pi; a = -.5;
+end
+nu = 4*m + 2*a + 2;
+T = @(t) t.^(2/3).*(1+5/48*t.^(-2)-5/36*t.^(-4)+(77125/82944)*t.^(-6) -...
+    108056875/6967296*t.^(-8)+162375596875/334430208*t.^(-10));
+airyrts = -T(3/8*pi*(4*(1:m)'-1));
+
+airyrts_exact = [  -2.338107410459762           % Exact Airy roots.
+    -4.087949444130970
+    -5.520559828095555
+    -6.786708090071765
+    -7.944133587120863
+    -9.022650853340979
+    -10.040174341558084
+    -11.008524303733260
+    -11.936015563236262
+    -12.828776752865757];
+airyrts(1:10) = airyrts_exact;  % correct first 10.
+
+x_init = sqrt(nu + 2^(2/3)*airyrts*nu^(1/3) +...
+    1/5*2^(4/3)*airyrts.^2*nu^(-1/3) +...
+    (11/35-a^2-12/175*airyrts.^3)/nu +...
+    (16/1575*airyrts+92/7875*airyrts.^4)*2^(2/3)*nu^(-5/3) -...
+    (15152/3031875*airyrts.^5+1088/121275*airyrts.^2)*2^(1/3)*nu^(-7/3));
+x_init_airy = real(x_init(end:-1:1));
+
+% Tricomi initial guesses. Equation (2.1) in [1]. Originally in [2].
+% These initial guesses are good near x = 0 . Note: zeros of besselj(+/-.5,x)
+% are integer and half-integer multiples of pi.
+% x_init_bess =  bess/sqrt(nu).*sqrt((1+ (bess.^2+2*(a^2-1))/3/nu^2) );
+Tnk0 = pi/2*ones(m,1);
+nu = (4*m+2*a+2);
+rhs = (4*m-4*(1:m)'+3)./nu*pi;
+
+for k = 1:7
+    val = Tnk0 - sin(Tnk0) - rhs;
+    dval = 1 - cos(Tnk0);
+    dTnk0 = val./dval;
+    Tnk0 = Tnk0 - dTnk0;
+end
+
+tnk = cos(Tnk0/2).^2;
+x_init_sin = sqrt(nu*tnk - (5./(4*(1-tnk).^2) - 1./(1-tnk)-1+3*a^2)/3/nu);
+
+% Patch together
+p = 0.4985+eps;
+x_init = [x_init_sin(1:floor(p*n));x_init_airy(ceil(p*n):end)];
+
+
+if mod(n,2) == 1
+    x_init = [0;x_init];
+    x_init = x_init(1:m+1); 
+else
+    x_init = x_init(1:m); 
+end
+
+% debug:
+%y = hermpts(n);
+%semilogy(abs(y - x_init));
+%yhalf = -y(m:-1:1);
+%semilogy(abs(yhalf - x_init));
+end
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% %%%%%%%%%%%%%%%%%%%%%%% Routines for REC algorithm %%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+function [x, w, v] = hermpts_rec(n)
+% Compute Hermite nodes and weights using recurrence relation.
+
+x0 = HermiteInitialGuesses(n);
+x0 = x0.*sqrt(2);
+
+for kk = 1:10
+    [val, dval] = hermpoly_rec(n, x0);
+    dx = val./dval;
+    dx(isnan(dx)) = 0;
+    x0 = x0 - dx;
+    if norm(dx, inf)<sqrt(eps), break; end
+end
+x = x0/sqrt(2);
+w = (exp(-x.^2)./dval.^2)';            % quadrature weights
+v = exp(-x.^2/2)./dval;               % Barycentric weights
+
+if mod(n,2) == 1                              % fold out
+    x = [-x(end:-1:1);x(2:end)];
+    w = [w(end:-1:1) w(2:end)]; w = (sqrt(pi)/sum(w))*w;
+    v = [v(end:-1:1);v(2:end)]; v = v./max(abs(v));
+else
+    x = [-x(end:-1:1);x];
+    w = [w(end:-1:1) w]; w = (sqrt(pi)/sum(w))*w;
+    v = [v(end:-1:1);-v]; v = v./max(abs(v));
+end
+
+
+end
+
+function [val, dval] = hermpoly_rec(n, x0)
+% HERMPOLY_rec evaluation of scaled Hermite poly using recurrence
+
+% evaluate:
+Hold = exp(-x0.^2/4); H = x0.*exp(-x0.^2/4);
+for k = 1:n-1
+    Hnew = (x0.*H./sqrt(k+1) - Hold./sqrt(1+1/k));
+    Hold = H; H = Hnew;
+end
+% evaluate derivative:
+val = Hnew;
+dval = (-x0.*Hnew + n^(1/2)*Hold);
+end
\ No newline at end of file
diff --git a/vendor/gonum.org/v1/gonum/integrate/quad/legendre.go b/vendor/gonum.org/v1/gonum/integrate/quad/legendre.go
new file mode 100644
index 00000000..a6855307
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/integrate/quad/legendre.go
@@ -0,0 +1,385 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package quad
+
+import "math"
+
+// Legendre integrates an unweighted function over finite bounds
+//  int_min^max f(x) dx
+type Legendre struct{}
+
+func (l Legendre) FixedLocations(x, weight []float64, min, max float64) {
+	// References:
+	// Algorithm:
+	// Bogaert, Ignace. "Iteration-Free Computation of Gauss--Legendre
+	// Quadrature Nodes and Weights." SIAM Journal on Scientific Computing
+	// 36.3 (2014): A1008-A1026.
+	//
+	// Excellent review article:
+	// Townsend, Alex. "The race for high order Gauss–Legendre quadrature."
+	// http://math.mit.edu/~ajt/papers/QuadratureEssay.pdf
+	//
+	// Original C++ source code: http://sourceforge.net/projects/fastgausslegendrequadrature
+
+	if len(x) != len(weight) {
+		panic("legendre: slice length mismatch")
+	}
+	if min >= max {
+		panic("legendre: min >= max")
+	}
+	if math.IsInf(min, 0) || math.IsInf(max, 0) {
+		panic("legendre: infinite bound")
+	}
+	for i := range x {
+		x[i], weight[i] = l.boundedLocation(len(x), i, min, max)
+	}
+}
+
+func (l Legendre) FixedLocationSingle(n, k int, min, max float64) (x, weight float64) {
+	if min >= max {
+		panic("legendre: min >= max")
+	}
+	if math.IsInf(min, 0) || math.IsInf(max, 0) {
+		panic("legendre: infinite bound")
+	}
+	return l.boundedLocation(n, k, min, max)
+}
+
+func (l Legendre) boundedLocation(n, k int, min, max float64) (x, weight float64) {
+	x, weight = l.location(n, k)
+	return (x+1)/2*(max-min) + min, weight * (max - min) / 2
+}
+
+// Algorithm adapted from http://sourceforge.net/projects/fastgausslegendrequadrature.
+
+// Original Copyright Notice:
+//*******************************************
+//   Copyright (C) 2014 by Ignace Bogaert   *
+//*******************************************
+
+// This software package is based on the paper
+//    I. Bogaert, "Iteration-Free Computation of Gauss-Legendre Quadrature Nodes and Weights",
+//    to be published in the SIAM Journal of Scientific Computing.
+
+// The main features of this software are:
+// - Speed: due to the simple formulas and the O(1) complexity computation of individual Gauss-Legendre
+//   quadrature nodes and weights. This makes it compatible with parallel computing paradigms.
+// - Accuracy: the error on the nodes and weights is within a few ulps (see the paper for details).
+
+// Disclaimer:
+// THIS SOFTWARE IS PROVIDED "AS IS" AND ANY EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+// WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR
+// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+// BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+// HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
+// OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+// location finds the location and weight for location k given n total samples.
+func (l Legendre) location(n, k int) (x, weight float64) {
+	// Note: k is 1-indexed in the original algorithm. It has been translated to
+	// zero-indexed here.
+	if n < 101 {
+		theta, weight := l.tabulated(n, k)
+		return math.Cos(theta), weight
+	}
+	if 2*k+1 > n {
+		theta, weight := l.computed(n, n-k)
+		return math.Cos(math.Pi - theta), weight
+	}
+	theta, weight := l.computed(n, k+1)
+	return math.Cos(theta), weight
+}
+
+// Returns tabulated theta and weight values: valid for l <= 100
+func (l Legendre) tabulated(n, k int) (theta, weight float64) {
+	if n%2 == 1 {
+		n2 := (n - 1) / 2
+		if k == n2 {
+			return math.Pi / 2, 2.0 / (cl[n] * cl[n])
+		}
+		if k < n2 {
+			return oddThetaZeros[n2-1][n2-k-1], oddWeights[n2-1][n2-k-1]
+		}
+		return math.Pi - oddThetaZeros[n2-1][k-n2-1], oddWeights[n2-1][k-n2-1]
+	}
+	n2 := n / 2
+	if k < n2 {
+		return evenThetaZeros[n2-1][n2-k-1], evenWeights[n2-1][n2-k-1]
+	}
+	return math.Pi - evenThetaZeros[n2-1][k-n2], evenWeights[n2-1][k-n2]
+}
+
+func (l Legendre) computed(n, k int) (theta, weight float64) {
+	// First, get the bessel zero
+	w := 1.0 / (float64(n) + 0.5)
+	nu := besselJZero(k)
+	theta = w * nu
+	x := theta * theta
+
+	// Get the asymptotic BesselJ(1, nu) squared
+	b := besselJ1Squared(k)
+
+	// Get the Chebyshev interpolants for the nodes.
+	sf1t := (((((-1.29052996274280508473467968379e-12*x+2.40724685864330121825976175184e-10)*x-3.13148654635992041468855740012e-8)*x+0.275573168962061235623801563453e-5)*x-0.148809523713909147898955880165e-3)*x+0.416666666665193394525296923981e-2)*x - 0.416666666666662959639712457549e-1
+	sf2t := (((((+2.20639421781871003734786884322e-9*x-7.53036771373769326811030753538e-8)*x+0.161969259453836261731700382098e-5)*x-0.253300326008232025914059965302e-4)*x+0.282116886057560434805998583817e-3)*x-0.209022248387852902722635654229e-2)*x + 0.815972221772932265640401128517e-2
+	sf3t := (((((-2.97058225375526229899781956673e-8*x+5.55845330223796209655886325712e-7)*x-0.567797841356833081642185432056e-5)*x+0.418498100329504574443885193835e-4)*x-0.251395293283965914823026348764e-3)*x+0.128654198542845137196151147483e-2)*x - 0.416012165620204364833694266818e-2
+
+	// and the weights
+	wsf1t := ((((((((-2.20902861044616638398573427475e-14*x+2.30365726860377376873232578871e-12)*x-1.75257700735423807659851042318e-10)*x+1.03756066927916795821098009353e-8)*x-4.63968647553221331251529631098e-7)*x+0.149644593625028648361395938176e-4)*x-0.326278659594412170300449074873e-3)*x+0.436507936507598105249726413120e-2)*x-0.305555555555553028279487898503e-1)*x + 0.833333333333333302184063103900e-1
+	wsf2t := (((((((+3.63117412152654783455929483029e-12*x+7.67643545069893130779501844323e-11)*x-7.12912857233642220650643150625e-9)*x+2.11483880685947151466370130277e-7)*x-0.381817918680045468483009307090e-5)*x+0.465969530694968391417927388162e-4)*x-0.407297185611335764191683161117e-3)*x+0.268959435694729660779984493795e-2)*x - 0.111111111111214923138249347172e-1
+	wsf3t := (((((((+2.01826791256703301806643264922e-9*x-4.38647122520206649251063212545e-8)*x+5.08898347288671653137451093208e-7)*x-0.397933316519135275712977531366e-5)*x+0.200559326396458326778521795392e-4)*x-0.422888059282921161626339411388e-4)*x-0.105646050254076140548678457002e-3)*x-0.947969308958577323145923317955e-4)*x + 0.656966489926484797412985260842e-2
+
+	// Then refine with the paper expansions
+	nuSin := nu / math.Sin(theta)
+	bNuSin := b * nuSin
+	wInvSinc := w * w * nuSin
+	wIS2 := wInvSinc * wInvSinc
+
+	// Finally, compute the node and the weight
+	theta = w * (nu + theta*wInvSinc*(sf1t+wIS2*(sf2t+wIS2*sf3t)))
+	deno := bNuSin + bNuSin*wIS2*(wsf1t+wIS2*(wsf2t+wIS2*wsf3t))
+	weight = 2.0 * w / deno
+	return theta, weight
+}
+
+func besselJZero(k int) float64 {
+	if k < 20 {
+		return jz[k-1]
+	}
+	z := math.Pi * (float64(k) - 0.25)
+	r := 1.0 / z
+	r2 := r * r
+	z += r * (0.125 + r2*(-0.807291666666666666666666666667e-1+r2*(0.246028645833333333333333333333+r2*(-1.82443876720610119047619047619+r2*(25.3364147973439050099206349206+r2*(-567.644412135183381139802038240+r2*(18690.4765282320653831636345064+r2*(-8.49353580299148769921876983660e5+5.09225462402226769498681286758e7*r2))))))))
+	return z
+}
+
+func besselJ1Squared(k int) float64 {
+	if k < 21 {
+		return j1[k-1]
+	}
+	x := 1.0 / (float64(k) - 0.25)
+	x2 := x * x
+	return x * (0.202642367284675542887758926420 + x2*x2*(-0.303380429711290253026202643516e-3+x2*(0.198924364245969295201137972743e-3+x2*(-0.228969902772111653038747229723e-3+x2*(0.433710719130746277915572905025e-3+x2*(-0.123632349727175414724737657367e-2+x2*(0.496101423268883102872271417616e-2+x2*(-0.266837393702323757700998557826e-1+.185395398206345628711318848386*x2))))))))
+}
+
+// Tabulated values
+var jz = [20]float64{2.40482555769577276862163187933, 5.52007811028631064959660411281, 8.65372791291101221695419871266, 11.7915344390142816137430449119, 14.9309177084877859477625939974, 18.0710639679109225431478829756, 21.2116366298792589590783933505, 24.3524715307493027370579447632, 27.4934791320402547958772882346, 30.6346064684319751175495789269, 33.7758202135735686842385463467, 36.9170983536640439797694930633, 40.0584257646282392947993073740, 43.1997917131767303575240727287, 46.3411883716618140186857888791, 49.4826098973978171736027615332, 52.6240518411149960292512853804, 55.7655107550199793116834927735, 58.9069839260809421328344066346, 62.0484691902271698828525002646}
+var j1 = [21]float64{0.269514123941916926139021992911, 0.115780138582203695807812836182, 0.0736863511364082151406476811985, 0.0540375731981162820417749182758, 0.0426614290172430912655106063495, 0.0352421034909961013587473033648, 0.0300210701030546726750888157688, 0.0261473914953080885904584675399, 0.0231591218246913922652676382178, 0.0207838291222678576039808057297, 0.0188504506693176678161056800214, 0.0172461575696650082995240053542, 0.0158935181059235978027065594287, 0.0147376260964721895895742982592, 0.0137384651453871179182880484134, 0.0128661817376151328791406637228, 0.0120980515486267975471075438497, 0.0114164712244916085168627222986, 0.0108075927911802040115547286830, 0.0102603729262807628110423992790, 0.00976589713979105054059846736696}
+
+// Tabulated nodes and weights
+// The required theta values for the Legendre nodes for l <= 100
+var evenThetaZeros = [][]float64{
+	{0.9553166181245092781638573e0},
+	{0.1223899586470372591854100e1, 0.5332956802491269896325121e0},
+	{0.1329852612388110166006182e1, 0.8483666264874876548310910e0, 0.3696066519448289481138796e0},
+	{0.1386317078892131346282665e1, 0.1017455539490153431016397e1, 0.6490365804607796100719162e0, 0.2827570635937967783987981e0},
+	{0.1421366498439524924081833e1, 0.1122539327631709474018620e1, 0.8238386589997556048023640e0, 0.5255196555285001171749362e0, 0.2289442988470260178701589e0},
+	{0.1445233238471440081118261e1, 0.1194120375947706635968399e1, 0.9430552870605735796668951e0, 0.6921076988818410126677201e0, 0.4414870814893317611922530e0, 0.1923346793046672033050762e0},
+	{0.1462529992921481833498746e1, 0.1246003586776677662375070e1, 0.1029498592525136749641068e1, 0.8130407055389454598609888e0, 0.5966877608172733931509619e0, 0.3806189306666775272453522e0, 0.1658171411523664030454318e0},
+	{0.1475640280808194256470687e1, 0.1285331444322965257106517e1, 0.1095033401803444343034890e1, 0.9047575323895165085030778e0, 0.7145252532340252146626998e0, 0.5243866409035941583262629e0, 0.3344986386876292124968005e0, 0.1457246820036738335698855e0},
+	{0.1485919440392653014379727e1, 0.1316167494718022699851110e1, 0.1146421481056642228295923e1, 0.9766871104439832694094465e0, 0.8069738930788195349918620e0, 0.6373005058706191519531139e0, 0.4677113145328286263205134e0, 0.2983460782092324727528346e0, 0.1299747364196768405406564e0},
+	{0.1494194914310399553510039e1, 0.1340993178589955138305166e1, 0.1187794926634098887711586e1, 0.1034603297590104231043189e1, 0.8814230742890135843662021e0, 0.7282625848696072912405713e0, 0.5751385026314284688366450e0, 0.4220907301111166004529037e0, 0.2692452880289302424376614e0, 0.1172969277059561308491253e0},
+	{0.1501000399130816063282492e1, 0.1361409225664372117193308e1, 0.1221820208990359866348145e1, 0.1082235198111836788818162e1, 0.9426568273796608630446470e0, 0.8030892957063359443650460e0, 0.6635400754448062852164288e0, 0.5240242709487281141128643e0, 0.3845781703583910933413978e0, 0.2453165389983612942439953e0, 0.1068723357985259945018899e0},
+	{0.1506695545558101030878728e1, 0.1378494427506219143960887e1, 0.1250294703417272987066314e1, 0.1122097523267250692925104e1, 0.9939044422989454674968570e0, 0.8657177770401081355080608e0, 0.7375413075437535618804594e0, 0.6093818382449565759195927e0, 0.4812531951313686873528891e0, 0.3531886675690780704072227e0, 0.2252936226353075734690198e0, 0.9814932949793685067733311e-1},
+	{0.1511531546703289231944719e1, 0.1393002286179807923400254e1, 0.1274473959424494104852958e1, 0.1155947313793812040125722e1, 0.1037423319077439147088755e1, 0.9189033445598992550553862e0, 0.8003894803353296871788647e0, 0.6818851814129298518332401e0, 0.5633967073169293284500428e0, 0.4449368152119130526034289e0, 0.3265362611165358134766736e0, 0.2082924425598466358987549e0, 0.9074274842993199730441784e-1},
+	{0.1515689149557281132993364e1, 0.1405475003062348722192382e1, 0.1295261501292316172835393e1, 0.1185049147889021579229406e1, 0.1074838574917869281769567e1, 0.9646306371285440922680794e0, 0.8544265718392254369377945e0, 0.7442282945111358297916378e0, 0.6340389954584301734412433e0, 0.5238644768825679339859620e0, 0.4137165857369637683488098e0, 0.3036239070914333637971179e0, 0.1936769929947376175341314e0, 0.8437551461511597225722252e-1},
+	{0.1519301729274526620713294e1, 0.1416312682230741743401738e1, 0.1313324092045794720169874e1, 0.1210336308624476413072722e1, 0.1107349759228459143499061e1, 0.1004365001539081003659288e1, 0.9013828087667156388167226e0, 0.7984043170121235411718744e0, 0.6954313000299367256853883e0, 0.5924667257887385542924194e0, 0.4895160050896970092628705e0, 0.3865901987860504829542802e0, 0.2837160095793466884313556e0, 0.1809780449917272162574031e0, 0.7884320726554945051322849e-1},
+	{0.1522469852641529230282387e1, 0.1425817011963825344615095e1, 0.1329164502391080681347666e1, 0.1232512573416362994802398e1, 0.1135861522840293704616614e1, 0.1039211728068951568003361e1, 0.9425636940046777101926515e0, 0.8459181315837993237739032e0, 0.7492760951181414487254243e0, 0.6526392394594561548023681e0, 0.5560103418005302722406995e0, 0.4593944730762095704649700e0, 0.3628020075350028174968692e0, 0.2662579994723859636910796e0, 0.1698418454282150179319973e0, 0.7399171309970959768773072e-1},
+	{0.1525270780617194430047563e1, 0.1434219768045409606267345e1, 0.1343169000217435981125683e1, 0.1252118659062444379491066e1, 0.1161068957629157748792749e1, 0.1070020159291475075961444e1, 0.9789726059789103169325141e0, 0.8879267623988119819560021e0, 0.7968832893748414870413015e0, 0.7058431727509840105946884e0, 0.6148079652926100198490992e0, 0.5237802779694730663856110e0, 0.4327648832448234459097574e0, 0.3417715500266717765568488e0, 0.2508238767288223767569849e0, 0.1599966542668327644694431e0, 0.6970264809814094464033170e-1},
+	{0.1527764849261740485876940e1, 0.1441701954349064743573367e1, 0.1355639243522655042028688e1, 0.1269576852063768424508476e1, 0.1183514935851550608323947e1, 0.1097453683555812711123880e1, 0.1011393333949027021740881e1, 0.9253342019812867059380523e0, 0.8392767201322475821509486e0, 0.7532215073977623159515351e0, 0.6671694908788198522546767e0, 0.5811221342350705406265672e0, 0.4950819018993074588093747e0, 0.4090533017972007314666814e0, 0.3230455648729987995657071e0, 0.2370809940997936908335290e0, 0.1512302802537625099602687e0, 0.6588357082399222649528476e-1},
+	{0.1529999863223206659623262e1, 0.1448406982124841835685420e1, 0.1366814241651488684482888e1, 0.1285221744143731581870833e1, 0.1203629605904952775544878e1, 0.1122037965173751996510051e1, 0.1040446993107623345153211e1, 0.9588569097730895525404200e0, 0.8772680085516152329147030e0, 0.7956806951062012653043722e0, 0.7140955526031660805347356e0, 0.6325134568448222221560326e0, 0.5509357927460004487348532e0, 0.4693648943475422765864580e0, 0.3878050333015201414955289e0, 0.3062649591511896679168503e0, 0.2247658146033686460963295e0, 0.1433746167818849555570557e0, 0.6246124541276674097388211e-1},
+	{0.1532014188279762793560699e1, 0.1454449946977268522285131e1, 0.1376885814601482670609845e1, 0.1299321869764876494939757e1, 0.1221758200747475205847413e1, 0.1144194910846247537582396e1, 0.1066632125552939823863593e1, 0.9890700026972186303565530e0, 0.9115087474225932692070479e0, 0.8339486352158799520695092e0, 0.7563900488174808348719219e0, 0.6788335401193977027577509e0, 0.6012799395312684623216685e0, 0.5237305617022755897200291e0, 0.4461876237541810478131970e0, 0.3686551849119556335824055e0, 0.2911415613085158758589405e0, 0.2136668503694680525340165e0, 0.1362947587312224822844743e0, 0.5937690028966411906487257e-1},
+	{0.1533838971193864306068338e1, 0.1459924288056445029654271e1, 0.1386009690354996919044862e1, 0.1312095239305276612560739e1, 0.1238181002944535867235042e1, 0.1164267059803796726229370e1, 0.1090353503721897748980095e1, 0.1016440450472067349837507e1, 0.9425280472651469176638349e0, 0.8686164868955467866176243e0, 0.7947060295895204342519786e0, 0.7207970381018823842440224e0, 0.6468900366403721167107352e0, 0.5729858150363658839291287e0, 0.4990856247464946058899833e0, 0.4251915773724379089467945e0, 0.3513075400485981451355368e0, 0.2774414365914335857735201e0, 0.2036124177925793565507033e0, 0.1298811916061515892914930e0, 0.5658282534660210272754152e-1},
+	{0.1535499761264077326499892e1, 0.1464906652494521470377318e1, 0.1394313611500109323616335e1, 0.1323720686538524176057236e1, 0.1253127930763390908996314e1, 0.1182535404796980113294400e1, 0.1111943180033868679273393e1, 0.1041351343083674290731439e1, 0.9707600019805773720746280e0, 0.9001692951667510715040632e0, 0.8295794049297955988640329e0, 0.7589905782114329186155957e0, 0.6884031600807736268672129e0, 0.6178176499732537480601935e0, 0.5472348011493452159473826e0, 0.4766558078624760377875119e0, 0.4060826859477620301047824e0, 0.3355191279517093844978473e0, 0.2649727008485465487101933e0, 0.1944616940738156405895778e0, 0.1240440866043499301839465e0, 0.5403988657613871827831605e-1},
+	{0.1537017713608809830855653e1, 0.1469460505124226636602925e1, 0.1401903350962364703169699e1, 0.1334346289590505369693957e1, 0.1266789363044399933941254e1, 0.1199232618763735058848455e1, 0.1131676111906105521856066e1, 0.1064119908394702657537061e1, 0.9965640890815034701957497e0, 0.9290087556203499065939494e0, 0.8614540390091103102510609e0, 0.7939001124053586164046432e0, 0.7263472110048245091518914e0, 0.6587956640463586742461796e0, 0.5912459486086227271608064e0, 0.5236987847717837556177452e0, 0.4561553147193391989386660e0, 0.3886174669444433167860783e0, 0.3210887745896478259115420e0, 0.2535764786314617292100029e0, 0.1860980813776342452540915e0, 0.1187090676924131329841811e0, 0.5171568198966901682810573e-1},
+	{0.1538410494858190444190279e1, 0.1473638845472165977392911e1, 0.1408867240039222913928858e1, 0.1344095709533508756473909e1, 0.1279324287566779722061664e1, 0.1214553011719528935181709e1, 0.1149781925191718586091000e1, 0.1085011078936665906275419e1, 0.1020240534516704208782618e1, 0.9554703680422404498752066e0, 0.8907006757608306209160649e0, 0.8259315822134856671969566e0, 0.7611632524946588128425351e0, 0.6963959112887657683892237e0, 0.6316298735371143844913976e0, 0.5668655960010826255149266e0, 0.5021037684870694065589284e0, 0.4373454855522296089897130e0, 0.3725925956833896735786860e0, 0.3078484858841616878136371e0, 0.2431200981264999375962973e0, 0.1784242126043536701754986e0, 0.1138140258514833068653307e0, 0.4958315373802413441075340e-1},
+	{0.1539692973716708504412697e1, 0.1477486279394502338589519e1, 0.1415279620944410339318226e1, 0.1353073023537942666830874e1, 0.1290866514321280958405103e1, 0.1228660123395079609266898e1, 0.1166453885011658611362850e1, 0.1104247839096738022319035e1, 0.1042042033248543055386770e1, 0.9798365254403234947595400e0, 0.9176313877712591840677176e0, 0.8554267118081827231209625e0, 0.7932226163976800550406599e0, 0.7310192594231560707888939e0, 0.6688168560730805146438886e0, 0.6066157082814543103941755e0, 0.5444162542389049922529553e0, 0.4822191559963931133878621e0, 0.4200254643636986308379697e0, 0.3578369542536859435571624e0, 0.2956568781922605524959448e0, 0.2334919029083292837123583e0, 0.1713581437497397360313735e0, 0.1093066902335822942650053e0, 0.4761952998197036029817629e-1},
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+}
+
+var oddThetaZeros = [][]float64{
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+	{0.1539222930035210331902410e1, 0.1507649534071729882214386e1, 0.1476076139707032453353232e1, 0.1444502747756546556830706e1, 0.1412929359055252480197337e1, 0.1381355974464721552102928e1, 0.1349782594880622732927647e1, 0.1318209221240839295255046e1, 0.1286635854534357387243172e1, 0.1255062495811112994872428e1, 0.1223489146193015470717893e1, 0.1191915806886406014313715e1, 0.1160342479196260434661502e1, 0.1128769164542510055952304e1, 0.1097195864478936528824546e1, 0.1065622580715200621234508e1, 0.1034049315142698534418744e1, 0.1002476069865111021377467e1, 0.9709028472347329448081481e0, 0.9393296498959608456620406e0, 0.9077564808376970380335442e0, 0.8761833434569334264096395e0, 0.8446102416364528348063321e0, 0.8130371798404960344077378e0, 0.7814641632334840064334645e0, 0.7498911978285964532098456e0, 0.7183182906753955596314298e0, 0.6867454500990591398232408e0, 0.6551726860086246453663390e0, 0.6236000102986843027011345e0, 0.5920274373793840619034224e0, 0.5604549848852622707385612e0, 0.5288826746375584896948472e0, 0.4973105339724571989307663e0, 0.4657385976085971045914307e0, 0.4341669103277770901346174e0, 0.4025955309141879357899857e0, 0.3710245380997234377015025e0, 0.3394540398171456073906403e0, 0.3078841881262277508367562e0, 0.2763152043287541015913350e0, 0.2447474234189502677044064e0, 0.2131813777658572006989977e0, 0.1816179673056091210434906e0, 0.1500588419721174291665790e0, 0.1185073845935281602210493e0, 0.8697177361567243680812898e-1, 0.5547793843128156580348541e-1, 0.2416899936118312040170588e-1},
+}
+
+// The weights of these nodes
+var evenWeights = [][]float64{
+	{1.0},
+	{0.6521451548625461426269364e0, 0.3478548451374538573730642e0},
+	{0.4679139345726910473898704e0, 0.3607615730481386075698336e0, 0.1713244923791703450402969e0},
+	{0.3626837833783619829651504e0, 0.3137066458778872873379622e0, 0.2223810344533744705443556e0, 0.1012285362903762591525320e0},
+	{0.2955242247147528701738930e0, 0.2692667193099963550912268e0, 0.2190863625159820439955350e0, 0.1494513491505805931457764e0, 0.6667134430868813759356850e-1},
+	{0.2491470458134027850005624e0, 0.2334925365383548087608498e0, 0.2031674267230659217490644e0, 0.1600783285433462263346522e0, 0.1069393259953184309602552e0, 0.4717533638651182719461626e-1},
+	{0.2152638534631577901958766e0, 0.2051984637212956039659240e0, 0.1855383974779378137417164e0, 0.1572031671581935345696019e0, 0.1215185706879031846894145e0, 0.8015808715976020980563266e-1, 0.3511946033175186303183410e-1},
+	{0.1894506104550684962853967e0, 0.1826034150449235888667636e0, 0.1691565193950025381893119e0, 0.1495959888165767320815019e0, 0.1246289712555338720524763e0, 0.9515851168249278480992520e-1, 0.6225352393864789286284360e-1, 0.2715245941175409485178166e-1},
+	{0.1691423829631435918406565e0, 0.1642764837458327229860538e0, 0.1546846751262652449254180e0, 0.1406429146706506512047311e0, 0.1225552067114784601845192e0, 0.1009420441062871655628144e0, 0.7642573025488905652912984e-1, 0.4971454889496979645333512e-1, 0.2161601352648331031334248e-1},
+	{0.1527533871307258506980843e0, 0.1491729864726037467878288e0, 0.1420961093183820513292985e0, 0.1316886384491766268984948e0, 0.1181945319615184173123774e0, 0.1019301198172404350367504e0, 0.8327674157670474872475850e-1, 0.6267204833410906356950596e-1, 0.4060142980038694133103928e-1, 0.1761400713915211831186249e-1},
+	{0.1392518728556319933754102e0, 0.1365414983460151713525738e0, 0.1311735047870623707329649e0, 0.1232523768105124242855609e0, 0.1129322960805392183934005e0, 0.1004141444428809649320786e0, 0.8594160621706772741444398e-1, 0.6979646842452048809496104e-1, 0.5229333515268328594031142e-1, 0.3377490158481415479330258e-1, 0.1462799529827220068498987e-1},
+	{0.1279381953467521569740562e0, 0.1258374563468282961213754e0, 0.1216704729278033912044631e0, 0.1155056680537256013533445e0, 0.1074442701159656347825772e0, 0.9761865210411388826988072e-1, 0.8619016153195327591718514e-1, 0.7334648141108030573403386e-1, 0.5929858491543678074636724e-1, 0.4427743881741980616860272e-1, 0.2853138862893366318130802e-1, 0.1234122979998719954680507e-1},
+	{0.1183214152792622765163711e0, 0.1166604434852965820446624e0, 0.1133618165463196665494407e0, 0.1084718405285765906565795e0, 0.1020591610944254232384142e0, 0.9421380035591414846366474e-1, 0.8504589431348523921044770e-1, 0.7468414976565974588707538e-1, 0.6327404632957483553945402e-1, 0.5097582529714781199831990e-1, 0.3796238329436276395030342e-1, 0.2441785109263190878961718e-1, 0, .1055137261734300715565387e-1},
+	{0.1100470130164751962823763e0, 0.1087111922582941352535716e0, 0.1060557659228464179104165e0, 0.1021129675780607698142166e0, 0.9693065799792991585048880e-1, 0.9057174439303284094218612e-1, 0.8311341722890121839039666e-1, 0.7464621423456877902393178e-1, 0.6527292396699959579339794e-1, 0.5510734567571674543148330e-1, 0.4427293475900422783958756e-1, 0.3290142778230437997763004e-1, 0.2113211259277125975149896e-1, 0.9124282593094517738816778e-2},
+	{0.1028526528935588403412856e0, 0.1017623897484055045964290e0, 0.9959342058679526706278018e-1, 0.9636873717464425963946864e-1, 0.9212252223778612871763266e-1, 0.8689978720108297980238752e-1, 0.8075589522942021535469516e-1, 0.7375597473770520626824384e-1, 0.6597422988218049512812820e-1, 0.5749315621761906648172152e-1, 0.4840267283059405290293858e-1, 0.3879919256962704959680230e-1, 0.2878470788332336934971862e-1, 0.1846646831109095914230276e-1, 0.7968192496166605615469690e-2},
+	{0.9654008851472780056676488e-1, 0.9563872007927485941908208e-1, 0.9384439908080456563918026e-1, 0.9117387869576388471286854e-1, 0.8765209300440381114277140e-1, 0.8331192422694675522219922e-1, 0.7819389578707030647174106e-1, 0.7234579410884850622539954e-1, 0.6582222277636184683765034e-1, 0.5868409347853554714528360e-1, 0.5099805926237617619616316e-1, 0.4283589802222668065687810e-1, 0.3427386291302143310268716e-1, 0.2539206530926205945575196e-1, 0.1627439473090567060516896e-1, 0.7018610009470096600404748e-2},
+	{0.9095674033025987361533764e-1, 0.9020304437064072957394216e-1, 0.8870189783569386928707642e-1, 0.8646573974703574978424688e-1, 0.8351309969984565518702044e-1, 0.7986844433977184473881888e-1, 0.7556197466003193127083398e-1, 0.7062937581425572499903896e-1, 0.6511152155407641137854442e-1, 0.5905413582752449319396124e-1, 0.5250741457267810616824590e-1, 0.4552561152335327245382266e-1, 0.3816659379638751632176606e-1, 0.3049138063844613180944194e-1, 0.2256372198549497008409476e-1, 0.1445016274859503541520101e-1, 0.6229140555908684718603220e-2},
+	{0.8598327567039474749008516e-1, 0.8534668573933862749185052e-1, 0.8407821897966193493345756e-1, 0.8218726670433970951722338e-1, 0.7968782891207160190872470e-1, 0.7659841064587067452875784e-1, 0.7294188500565306135387342e-1, 0.6874532383573644261368974e-1, 0.6403979735501548955638454e-1, 0.5886014424532481730967550e-1, 0.5324471397775991909202590e-1, 0.4723508349026597841661708e-1, 0.4087575092364489547411412e-1, 0.3421381077030722992124474e-1, 0.2729862149856877909441690e-1, 0.2018151529773547153209770e-1, 0.1291594728406557440450307e-1, 0.5565719664245045361251818e-2},
+	{0.8152502928038578669921876e-1, 0.8098249377059710062326952e-1, 0.7990103324352782158602774e-1, 0.7828784465821094807537540e-1, 0.7615366354844639606599344e-1, 0.7351269258474345714520658e-1, 0.7038250706689895473928292e-1, 0.6678393797914041193504612e-1, 0.6274093339213305405296984e-1, 0.5828039914699720602230556e-1, 0.5343201991033231997375704e-1, 0.4822806186075868337435238e-1, 0.4270315850467443423587832e-1, 0.3689408159402473816493978e-1, 0.3083950054517505465873166e-1, 0.2457973973823237589520214e-1, 0.1815657770961323689887502e-1, 0.1161344471646867417766868e-1, 0.5002880749639345675901886e-2},
+	{0.7750594797842481126372404e-1, 0.7703981816424796558830758e-1, 0.7611036190062624237155810e-1, 0.7472316905796826420018930e-1, 0.7288658239580405906051074e-1, 0.7061164739128677969548346e-1, 0.6791204581523390382569024e-1, 0.6480401345660103807455446e-1, 0.6130624249292893916653822e-1, 0.5743976909939155136661768e-1, 0.5322784698393682435499678e-1, 0.4869580763507223206143380e-1, 0.4387090818567327199167442e-1, 0.3878216797447201763997196e-1, 0.3346019528254784739267780e-1, 0.2793700698002340109848970e-1, 0.2224584919416695726150432e-1, 0.1642105838190788871286396e-1, 0.1049828453115281361474434e-1, 0.4521277098533191258471490e-2},
+	{0.7386423423217287999638556e-1, 0.7346081345346752826402828e-1, 0.7265617524380410488790570e-1, 0.7145471426517098292181042e-1, 0.6986299249259415976615480e-1, 0.6788970337652194485536350e-1, 0.6554562436490897892700504e-1, 0.6284355804500257640931846e-1, 0.5979826222758665431283142e-1, 0.5642636935801838164642686e-1, 0.5274629569917407034394234e-1, 0.4877814079280324502744954e-1, 0.4454357777196587787431674e-1, 0.4006573518069226176059618e-1, 0.3536907109759211083266214e-1, 0.3047924069960346836290502e-1, 0.2542295952611304788674188e-1, 0.2022786956905264475705664e-1, 0.1492244369735749414467869e-1, 0.9536220301748502411822340e-2, 0.4105998604649084610599928e-2},
+	{0.7054915778935406881133824e-1, 0.7019768547355821258714200e-1, 0.6949649186157257803708402e-1, 0.6844907026936666098545864e-1, 0.6706063890629365239570506e-1, 0.6533811487918143498424096e-1, 0.6329007973320385495013890e-1, 0.6092673670156196803855800e-1, 0.5825985987759549533421064e-1, 0.5530273556372805254874660e-1, 0.5207009609170446188123162e-1, 0.4857804644835203752763920e-1, 0.4484398408197003144624282e-1, 0.4088651231034621890844686e-1, 0.3672534781380887364290888e-1, 0.3238122281206982088084682e-1, 0.2787578282128101008111450e-1, 0.2323148190201921062895910e-1, 0.1847148173681474917204335e-1, 0.1361958675557998552020491e-1, 0.8700481367524844122565470e-2, 0.3745404803112777515171456e-2},
+	{0.6751868584903645882021418e-1, 0.6721061360067817586237416e-1, 0.6659587476845488737576196e-1, 0.6567727426778120737875756e-1, 0.6445900346713906958827948e-1, 0.6294662106439450817895206e-1, 0.6114702772465048101535670e-1, 0.5906843459554631480755080e-1, 0.5672032584399123581687444e-1, 0.5411341538585675449163752e-1, 0.5125959800714302133536554e-1, 0.4817189510171220053046892e-1, 0.4486439527731812676709458e-1, 0.4135219010967872970421980e-1, 0.3765130535738607132766076e-1, 0.3377862799910689652060416e-1, 0.2975182955220275579905234e-1, 0.2558928639713001063470016e-1, 0.2130999875413650105447862e-1, 0.1693351400783623804623151e-1, 0.1247988377098868420673525e-1, 0.7969898229724622451610710e-2, 0.3430300868107048286016700e-2},
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+	{0.3255061449236316624196142e-1, 0.3251611871386883598720548e-1, 0.3244716371406426936401278e-1, 0.3234382256857592842877486e-1, 0.3220620479403025066866710e-1, 0.3203445623199266321813896e-1, 0.3182875889441100653475374e-1, 0.3158933077072716855802074e-1, 0.3131642559686135581278434e-1, 0.3101033258631383742324982e-1, 0.3067137612366914901422878e-1, 0.3029991542082759379408878e-1, 0.2989634413632838598438796e-1, 0.2946108995816790597043632e-1, 0.2899461415055523654267862e-1, 0.2849741106508538564559948e-1, 0.2797000761684833443981840e-1, 0.2741296272602924282342110e-1, 0.2682686672559176219805676e-1, 0.2621234073567241391345816e-1, 0.2557003600534936149879724e-1, 0.2490063322248361028838244e-1, 0.2420484179236469128226730e-1, 0.2348339908592621984223612e-1, 0.2273706965832937400134754e-1, 0.2196664443874434919475618e-1, 0.2117293989219129898767356e-1, 0.2035679715433332459524556e-1, 0.1951908114014502241008485e-1, 0.1866067962741146738515655e-1, 0.1778250231604526083761406e-1, 0.1688547986424517245047785e-1, 0.1597056290256229138061685e-1, 0.1503872102699493800587588e-1, 0.1409094177231486091586166e-1, 0.1312822956696157263706415e-1, 0.1215160467108831963518178e-1, 0.1116210209983849859121361e-1, 0.1016077053500841575758671e-1, 0.9148671230783386632584044e-2, 0.8126876925698759217383246e-2, 0.7096470791153865269143206e-2, 0.6058545504235961683315686e-2, 0.5014202742927517692471308e-2, 0.3964554338444686673733524e-2, 0.2910731817934946408411678e-2, 0.1853960788946921732331620e-2, 0.7967920655520124294367096e-3},
+	{0.3188987535287646727794502e-1, 0.3185743815812401071309920e-1, 0.3179259676252863019831786e-1, 0.3169541712034925160907410e-1, 0.3156599807910805290145092e-1, 0.3140447127904656151748860e-1, 0.3121100101922626441684056e-1, 0.3098578409040993463104290e-1, 0.3072904957489366992001356e-1, 0.3044105861349325839490764e-1, 0.3012210413992189884853100e-1, 0.2977251058282947626617570e-1, 0.2939263353580649216776328e-1, 0.2898285939568834204744914e-1, 0.2854360496952788570349054e-1, 0.2807531705063613875324586e-1, 0.2757847196412239390009986e-1, 0.2705357508239612827767608e-1, 0.2650116031112363935248738e-1, 0.2592178954616244891846836e-1, 0.2531605210202609734314644e-1, 0.2468456411246099618197954e-1, 0.2402796790374549880324124e-1, 0.2334693134134927471268304e-1, 0.2264214715061843311126274e-1, 0.2191433221217865041901888e-1, 0.2116422683277485691127980e-1, 0.2039259399229191457948346e-1, 0.1960021856772633077323700e-1, 0.1878790653490468656148738e-1, 0.1795648414877062812244296e-1, 0.1710679710308990026235402e-1, 0.1623970967045369565272614e-1, 0.1535610382349775576849818e-1, 0.1445687833830440197756895e-1, 0.1354294788102946514364726e-1, 0.1261524207892195285778215e-1, 0.1167470457713812428742924e-1, 0.1072229208322431712024324e-1, 0.9758973402174096835348026e-2, 0.8785728467392263202699392e-2, 0.7803547379100754890979542e-2, 0.6813429479165215998771186e-2, 0.5816382546439639112764538e-2, 0.4813422398586770918478190e-2, 0.3805574085352359565512666e-2, 0.2793881135722130870629084e-2, 0.1779477041014528741695358e-2, 0.7647669822743134580383448e-3},
+	{0.3125542345386335694764248e-1, 0.3122488425484935773237650e-1, 0.3116383569620990678381832e-1, 0.3107233742756651658781016e-1, 0.3095047885049098823406346e-1, 0.3079837903115259042771392e-1, 0.3061618658398044849645950e-1, 0.3040407952645482001650792e-1, 0.3016226510516914491906862e-1, 0.2989097959333283091683684e-1, 0.2959048805991264251175454e-1, 0.2926108411063827662011896e-1, 0.2890308960112520313487610e-1, 0.2851685432239509799093676e-1, 0.2810275565910117331764820e-1, 0.2766119822079238829420408e-1, 0.2719261344657688013649158e-1, 0.2669745918357096266038448e-1, 0.2617621923954567634230892e-1, 0.2562940291020811607564182e-1, 0.2505754448157958970376402e-1, 0.2446120270795705271997480e-1, 0.2384096026596820596256040e-1, 0.2319742318525412162248878e-1, 0.2253122025633627270179672e-1, 0.2184300241624738631395360e-1, 0.2113344211252764154267220e-1, 0.2040323264620943276683910e-1, 0.1965308749443530586538157e-1, 0.1888373961337490455294131e-1, 0.1809594072212811666439111e-1, 0.1729046056832358243934388e-1, 0.1646808617614521264310506e-1, 0.1562962107754600272393719e-1, 0.1477588452744130176887969e-1, 0.1390771070371877268795387e-1, 0.1302594789297154228555807e-1, 0.1213145766297949740774437e-1, 0.1122511402318597711722209e-1, 0.1030780257486896958578198e-1, 0.9380419653694457951417628e-2, 0.8443871469668971402620252e-2, 0.7499073255464711578829804e-2, 0.6546948450845322764152444e-2, 0.5588428003865515157213478e-2, 0.4624450063422119351093868e-2, 0.3655961201326375182342828e-2, 0.2683925371553482419437272e-2, 0.1709392653518105239533969e-2, 0.7346344905056717304142370e-3},
+}
+
+var oddWeights = [][]float64{
+	{0.5555555555555555555555555},
+	{0.4786286704993664680412916e0, 0.2369268850561890875142644e0},
+	{0.3818300505051189449503698e0, 0.2797053914892766679014680e0, 0.1294849661688696932706118e0},
+	{0.3123470770400028400686304e0, 0.2606106964029354623187428e0, 0.1806481606948574040584721e0, 0.8127438836157441197189206e-1},
+	{0.2628045445102466621806890e0, 0.2331937645919904799185238e0, 0.1862902109277342514260979e0, 0.1255803694649046246346947e0, 0.5566856711617366648275374e-1},
+	{0.2262831802628972384120902e0, 0.2078160475368885023125234e0, 0.1781459807619457382800468e0, 0.1388735102197872384636019e0, 0.9212149983772844791442126e-1, 0.4048400476531587952001996e-1},
+	{0.1984314853271115764561182e0, 0.1861610000155622110268006e0, 0.1662692058169939335532006e0, 0.1395706779261543144478051e0, 0.1071592204671719350118693e0, 0.7036604748810812470926662e-1, 0.3075324199611726835462762e-1},
+	{0.1765627053669926463252710e0, 0.1680041021564500445099705e0, 0.1540457610768102880814317e0, 0.1351363684685254732863199e0, 0.1118838471934039710947887e0, 0.8503614831717918088353538e-1, 0.5545952937398720112944102e-1, 0.2414830286854793196010920e-1},
+	{0.1589688433939543476499565e0, 0.1527660420658596667788553e0, 0.1426067021736066117757460e0, 0.1287539625393362276755159e0, 0.1115666455473339947160242e0, 0.9149002162244999946446222e-1, 0.6904454273764122658070790e-1, 0.4481422676569960033283728e-1, 0.1946178822972647703631351e-1},
+	{0.1445244039899700590638271e0, 0.1398873947910731547221335e0, 0.1322689386333374617810526e0, 0.1218314160537285341953671e0, 0.1087972991671483776634747e0, 0.9344442345603386155329010e-1, 0.7610011362837930201705132e-1, 0.5713442542685720828363528e-1, 0.3695378977085249379995034e-1, 0.1601722825777433332422273e-1},
+	{0.1324620394046966173716425e0, 0.1289057221880821499785954e0, 0.1230490843067295304675784e0, 0.1149966402224113649416434e0, 0.1048920914645414100740861e0, 0.9291576606003514747701876e-1, 0.7928141177671895492289248e-1, 0.6423242140852585212716980e-1, 0.4803767173108466857164124e-1, 0.3098800585697944431069484e-1, 0.1341185948714177208130864e-1},
+	{0.1222424429903100416889594e0, 0.1194557635357847722281782e0, 0.1148582591457116483393255e0, 0.1085196244742636531160939e0, 0.1005359490670506442022068e0, 0.9102826198296364981149704e-1, 0.8014070033500101801323524e-1, 0.6803833381235691720718712e-1, 0.5490469597583519192593686e-1, 0.4093915670130631265562402e-1, 0.2635498661503213726190216e-1, 0.1139379850102628794789998e-1},
+	{0.1134763461089651486203700e0, 0.1112524883568451926721632e0, 0.1075782857885331872121629e0, 0.1025016378177457986712478e0, 0.9608872737002850756565252e-1, 0.8842315854375695019432262e-1, 0.7960486777305777126307488e-1, 0.6974882376624559298432254e-1, 0.5898353685983359911030058e-1, 0.4744941252061506270409646e-1, 0.3529705375741971102257772e-1, 0.2268623159618062319603554e-1, 0.9798996051294360261149438e-2},
+	{0.1058761550973209414065914e0, 0.1040733100777293739133284e0, 0.1010912737599149661218204e0, 0.9696383409440860630190016e-1, 0.9173775713925876334796636e-1, 0.8547225736617252754534480e-1, 0.7823832713576378382814484e-1, 0.7011793325505127856958160e-1, 0.6120309065707913854210970e-1, 0.5159482690249792391259412e-1, 0.4140206251868283610482948e-1, 0.3074049220209362264440778e-1, 0.1973208505612270598385931e-1, 0.8516903878746409654261436e-2},
+	{0.9922501122667230787487546e-1, 0.9774333538632872509347402e-1, 0.9529024291231951280720412e-1, 0.9189011389364147821536290e-1, 0.8757674060847787612619794e-1, 0.8239299176158926390382334e-1, 0.7639038659877661642635764e-1, 0.6962858323541036616775632e-1, 0.6217478656102842691034334e-1, 0.5410308242491685371166596e-1, 0.4549370752720110290231576e-1, 0.3643227391238546402439264e-1, 0.2700901918497942180060860e-1, 0.1731862079031058246315918e-1, 0.7470831579248775858700554e-2},
+	{0.9335642606559611616099912e-1, 0.9212398664331684621324104e-1, 0.9008195866063857723974370e-1, 0.8724828761884433760728158e-1, 0.8364787606703870761392808e-1, 0.7931236479488673836390848e-1, 0.7427985484395414934247216e-1, 0.6859457281865671280595482e-1, 0.6230648253031748003162750e-1, 0.5547084663166356128494468e-1, 0.4814774281871169567014706e-1, 0.4040154133166959156340938e-1, 0.3230035863232895328156104e-1, 0.2391554810174948035053310e-1, 0.1532170151293467612794584e-1, 0.6606227847587378058647800e-2},
+	{0.8814053043027546297073886e-1, 0.8710444699718353424332214e-1, 0.8538665339209912522594402e-1, 0.8300059372885658837992644e-1, 0.7996494224232426293266204e-1, 0.7630345715544205353865872e-1, 0.7204479477256006466546180e-1, 0.6722228526908690396430546e-1, 0.6187367196608018888701398e-1, 0.5604081621237012857832772e-1, 0.4976937040135352980519956e-1, 0.4310842232617021878230592e-1, 0.3611011586346338053271748e-1, 0.2882926010889425404871630e-1, 0.2132297991148358088343844e-1, 0.1365082834836149226640441e-1, 0.5883433420443084975750336e-2},
+	{0.8347457362586278725225302e-1, 0.8259527223643725089123018e-1, 0.8113662450846503050987774e-1, 0.7910886183752938076721222e-1, 0.7652620757052923788588804e-1, 0.7340677724848817272462668e-1, 0.6977245155570034488508154e-1, 0.6564872287275124948402376e-1, 0.6106451652322598613098804e-1, 0.5605198799827491780853916e-1, 0.5064629765482460160387558e-1, 0.4488536466243716665741054e-1, 0.3880960250193454448896226e-1, 0.3246163984752148106723444e-1, 0.2588603699055893352275954e-1, 0.1912904448908396604350259e-1, 0.1223878010030755652630649e-1, 0.5273057279497939351724544e-2},
+	{0.7927622256836847101015574e-1, 0.7852361328737117672506330e-1, 0.7727455254468201672851160e-1, 0.7553693732283605770478448e-1, 0.7332175341426861738115402e-1, 0.7064300597060876077011486e-1, 0.6751763096623126536302120e-1, 0.6396538813868238898670650e-1, 0.6000873608859614957494160e-1, 0.5567269034091629990739094e-1, 0.5098466529212940521402098e-1, 0.4597430110891663188417682e-1, 0.4067327684793384393905618e-1, 0.3511511149813133076106530e-1, 0.2933495598390337859215654e-1, 0.2336938483217816459471240e-1, 0.1725622909372491904080491e-1, 0.1103478893916459424267603e-1, 0.4752944691635101370775866e-2},
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+	{0.3287800959763194823557646e-1, 0.3282463569369918669308888e-1, 0.3273574336068393226919658e-1, 0.3261142878598215425670652e-1, 0.3245182648620325926685946e-1, 0.3225710916161441434734840e-1, 0.3202748750926769529295728e-1, 0.3176320999501228029097900e-1, 0.3146456258463840201321734e-1, 0.3113186843444399825682258e-1, 0.3076548754155891475295788e-1, 0.3036581635440506677724356e-1, 0.2993328734371411225240016e-1, 0.2946836853456688237515152e-1, 0.2897156299996101153484194e-1, 0.2844340831645486261311894e-1, 0.2788447598247691424309350e-1, 0.2729537079993022266578380e-1, 0.2667673021976135431896846e-1, 0.2602922365220227153290076e-1, 0.2535355174243201293660006e-1, 0.2465044561244261997612948e-1, 0.2392066606993061007707546e-1, 0.2316500278507139174920030e-1, 0.2238427343606939184041926e-1, 0.2157932282441140120676856e-1, 0.2075102196078490181790884e-1, 0.1990026712265721124487174e-1, 0.1902797888454570639306994e-1, 0.1813510112204514410759734e-1, 0.1722259999071698441334003e-1, 0.1629146288099104326591566e-1, 0.1534269735028835663459242e-1, 0.1437733003365908208357459e-1, 0.1339640553436828544136536e-1, 0.1240098529611606104018197e-1, 0.1139214645908584403924275e-1, 0.1037098070311609684083942e-1, 0.9338593083876397086740596e-2, 0.8296100874530990238145090e-2, 0.7244632443933199672626606e-2, 0.6185326261033323769312750e-2, 0.5119330329927718280032034e-2, 0.4047803316371759906879922e-2, 0.2971924240818190718436604e-2, 0.1892968377922935762776147e-2, 0.8135642494541165010544716e-3},
+	{0.3220431459661350533475748e-1, 0.3215415737958550153577998e-1, 0.3207061987527279934927952e-1, 0.3195378880670864194528382e-1, 0.3180378546007149044495368e-1, 0.3162076555877401604294910e-1, 0.3140491910180172362457798e-1, 0.3115647016646904145775102e-1, 0.3087567667579765382432642e-1, 0.3056283013075858386135104e-1, 0.3021825530765601453452082e-1, 0.2984230992096702903457814e-1, 0.2943538425198732086424294e-1, 0.2899790074366843187205222e-1, 0.2853031356206718751823808e-1, 0.2803310812486267752680532e-1, 0.2750680059743034256009616e-1, 0.2695193735699644067363378e-1, 0.2636909442542934975707846e-1, 0.2575887687125678489535242e-1, 0.2512191818153004673565192e-1, 0.2445887960418784729059960e-1, 0.2377044946160306882104198e-1, 0.2305734243602599579639616e-1, 0.2232029882766713237862322e-1, 0.2156008378619171827843500e-1, 0.2077748651642656849799008e-1, 0.1997331945910804688818908e-1, 0.1914841744752812933525703e-1, 0.1830363684096414082229124e-1, 0.1743985463580780463940516e-1, 0.1655796755534245662902801e-1, 0.1565889111915692052020687e-1, 0.1474355869323695017635984e-1, 0.1381292052185304327114855e-1, 0.1286794274249338667571135e-1, 0.1190960638533075683273654e-1, 0.1093890635919594895396767e-1, 0.9956850427084044948237490e-2, 0.8964458176697999432566250e-2, 0.7962759997865495595598110e-2, 0.6952796096469405526464256e-2, 0.5935615630788222954183688e-2, 0.4912276262166028130833504e-2, 0.3883845329489294421733034e-2, 0.2851409243213055771419126e-2, 0.1816146398210039609502983e-2, 0.7805332219425612457264822e-3},
+	{0.3155766036791122885809208e-1, 0.3151046648162834771323796e-1, 0.3143186227722154616152128e-1, 0.3132192610907518012817474e-1, 0.3118076756395815837033438e-1, 0.3100852735178559535833486e-1, 0.3080537716535627949917920e-1, 0.3057151950920577999218210e-1, 0.3030718749774580397961262e-1, 0.3001264462289103447190280e-1, 0.2968818449140509844801766e-1, 0.2933413053222750347643324e-1, 0.2895083567407331040373860e-1, 0.2853868199362694972663692e-1, 0.2809808033468091126593440e-1, 0.2762946989859901232207604e-1, 0.2713331780651255092639320e-1, 0.2661011863368585130179228e-1, 0.2606039391651548254092866e-1, 0.2548469163265475465058230e-1, 0.2488358565478194644598738e-1, 0.2425767517855707823164026e-1, 0.2360758412533789404661778e-1, 0.2293396052025105528408320e-1, 0.2223747584623937158435550e-1, 0.2151882437473022381824646e-1, 0.2077872247359421120742490e-1, 0.2001790789308656620794778e-1, 0.1923713903048718479867380e-1, 0.1843719417417849927098560e-1, 0.1761887072792438050675710e-1, 0.1678298441613870708950299e-1, 0.1593036847096084971103802e-1, 0.1506187280199023331295260e-1, 0.1417836314957944606614279e-1, 0.1328072022265728347995425e-1, 0.1236983882217516210343368e-1, 0.1144662695149825376113323e-1, 0.1051200491552474540574917e-1, 0.9566904411326136356898158e-2, 0.8612267615478888991732218e-2, 0.7649046279335257935390770e-2, 0.6678200860575098165183170e-2, 0.5700699773395926875152328e-2, 0.4717519037520830079689318e-2, 0.3729643487243034749198276e-2, 0.2738075873626878091327392e-2, 0.1743906958219244938639563e-2, 0.7494736467374053633626714e-3},
+}
+
+// The factor in front of the direct product representation
+var cl = [...]float64{1.0, 1.0, -0.5000000000000000000000000e0, -0.1500000000000000000000000e1, 0.3750000000000000000000000e0, 0.1875000000000000000000000e1, -0.3125000000000000000000000e0, -0.2187500000000000000000000e1, 0.2734375000000000000000000e0, 0.2460937500000000000000000e1, -0.2460937500000000000000000e0, -0.2707031250000000000000000e1, 0.2255859375000000000000000e0, 0.2932617187500000000000000e1, -0.2094726562500000000000000e0, -0.3142089843750000000000000e1, 0.1963806152343750000000000e0, 0.3338470458984375000000000e1, -0.1854705810546875000000000e0, -0.3523941040039062500000000e1, 0.1761970520019531250000000e0, 0.3700138092041015625000000e1, -0.1681880950927734375000000e0, -0.3868326187133789062500000e1, 0.1611802577972412109375000e0, 0.4029506444931030273437500e1, -0.1549810171127319335937500e0, -0.4184487462043762207031250e1, 0.1494459807872772216796875e0, 0.4333933442831039428710938e1, -0.1444644480943679809570312e0, -0.4478397890925407409667969e1, 0.1399499340914189815521240e0, 0.4618347825016826391220093e1, -0.1358337595593184232711792e0, -0.4754181584576144814491272e1, 0.1320605995715595781803131e0, 0.4886242184147704392671585e1, -0.1285853206354659050703049e0, -0.5014827504783170297741890e1, 0.1253706876195792574435472e0, 0.5140198192402749555185437e1, -0.1223856712476845132187009e0, -0.5262583863650434068404138e1, 0.1196041787193280470091850e0, 0.5382188042369762115413323e1, -0.1170040878776035242481157e0, -0.5499192130247365639661439e1, 0.1145665027134867841596133e0, 0.5613758632960852423821052e1, -0.1122751726592170484764210e0, -0.5726033805620069472297473e1, 0.1101160347234628744672591e0, 0.5836149840343532346764732e1, -0.1080768488952505990141617e0, -0.5944226689238782945778894e1, 0.1061469051649782668889088e0, 0.6050373594403761212667803e1, -0.1043167861104096760804794e0, -0.6154690380514170888748282e1, 0.1025781730085695148124714e0, 0.6257268553522740403560753e1, -0.1009236863471409742509799e0, -0.6358192239869881377811733e1, 0.9934675374796689652830833e-1, 0.6457538993617848274340042e1, -0.9784149990330073142939457e-1, -0.6555380493521149005769436e1, 0.9640265431648748537896230e-1, 0.6651783147837636491148399e1, -0.9502547354053766415926284e-1, -0.6746808621378174155307661e1, 0.9370567529691908549038419e-1, 0.6840514296675093240798046e1, -0.9243938238750126001078440e-1, -0.6932953679062594500808830e1, 0.9122307472450782237906355e-1, 0.7024176753787102323187894e1, -0.9005354812547567081010120e-1, -0.7114230301912577993997995e1, 0.8892787877390722492497493e-1, 0.7203158180686485218922970e1, -0.8784339244739616120637768e-1, -0.7291001573133881380129347e1, 0.8679763777540334976344461e-1, 0.7377799210909284729892792e1, -0.8578836291754982244061386e-1, -0.7463587573826834552333406e1, 0.8481349515712311991287961e-1, 0.7548401068983957672246285e1, -0.8387112298871064080273650e-1, -0.7632272191972668313049022e1, 0.8295948034752900340270676e-1, 0.7715231672320197316451729e1, -0.8207693268425741826012477e-1, -0.7797308605004454734711853e1, 0.8122196463546307015324847e-1, 0.7878530569639917804865102e1, -0.8039316907795834494760308e-1, -0.7958923738717876149812705e1, 0.7958923738717876149812705e-1}
diff --git a/vendor/gonum.org/v1/gonum/integrate/quad/legendre_test.go b/vendor/gonum.org/v1/gonum/integrate/quad/legendre_test.go
new file mode 100644
index 00000000..7fb5bb09
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/integrate/quad/legendre_test.go
@@ -0,0 +1,84 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package quad
+
+import (
+	"math"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+func TestLegendre(t *testing.T) {
+	for i, test := range []struct {
+		f        func(float64) float64
+		min, max float64
+		n        []int
+		tol      []float64
+		ans      float64
+	}{
+		// Tolerances determined from intuition and a bit of post-hoc tweaking.
+		{
+			f:   func(x float64) float64 { return math.Exp(x) },
+			min: -3,
+			max: 5,
+			n:   []int{3, 4, 6, 7, 15, 16, 300, 301},
+			tol: []float64{5e-2, 5e-3, 5e-6, 1e-7, 1e-14, 1e-14, 1e-14, 1e-14},
+			ans: math.Exp(5) - math.Exp(-3),
+		},
+	} {
+		for j, n := range test.n {
+			ans := Fixed(test.f, test.min, test.max, n, Legendre{}, 0)
+			if !floats.EqualWithinAbsOrRel(ans, test.ans, test.tol[j], test.tol[j]) {
+				t.Errorf("Mismatch. Case = %d, n = %d. Want %v, got %v", i, n, test.ans, ans)
+			}
+			ans2 := Fixed(test.f, test.min, test.max, n, Legendre{}, 3)
+			if !floats.EqualWithinAbsOrRel(ans2, test.ans, test.tol[j], test.tol[j]) {
+				t.Errorf("Mismatch concurrent. Case = %d, n = %d. Want %v, got %v", i, n, test.ans, ans)
+			}
+		}
+	}
+}
+
+func TestLegendreSingle(t *testing.T) {
+	for c, test := range []struct {
+		n        int
+		min, max float64
+	}{
+		{
+			n:   100,
+			min: -1,
+			max: 1,
+		},
+		{
+			n:   50,
+			min: -3,
+			max: -1,
+		},
+		{
+			n:   1000,
+			min: 2,
+			max: 7,
+		},
+	} {
+		l := Legendre{}
+		n := test.n
+		xs := make([]float64, n)
+		weights := make([]float64, n)
+		l.FixedLocations(xs, weights, test.min, test.max)
+
+		xsSingle := make([]float64, n)
+		weightsSingle := make([]float64, n)
+		for i := range xsSingle {
+			xsSingle[i], weightsSingle[i] = l.FixedLocationSingle(n, i, test.min, test.max)
+		}
+		if !floats.Equal(xs, xsSingle) {
+			t.Errorf("Case %d: xs mismatch batch and single", c)
+		}
+		if !floats.Equal(weights, weightsSingle) {
+			t.Errorf("Case %d: weights mismatch batch and single", c)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/integrate/quad/quad.go b/vendor/gonum.org/v1/gonum/integrate/quad/quad.go
new file mode 100644
index 00000000..d222641c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/integrate/quad/quad.go
@@ -0,0 +1,157 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package quad
+
+import (
+	"math"
+	"sync"
+)
+
+// FixedLocationer computes a set of quadrature locations and weights and stores
+// them in-place into x and weight respectively. The number of points generated is equal to
+// the len(x). The weights and locations should be chosen such that
+//  int_min^max f(x) dx ≈ \sum_i w_i f(x_i)
+type FixedLocationer interface {
+	FixedLocations(x, weight []float64, min, max float64)
+}
+
+// FixedLocationSingle returns the location and weight for element k in a
+// fixed quadrature rule with n total samples and integral bounds from min to max.
+type FixedLocationSingler interface {
+	FixedLocationSingle(n, k int, min, max float64) (x, weight float64)
+}
+
+// Fixed approximates the integral of the function f from min to max using a fixed
+// n-point quadrature rule. During evaluation, f will be evaluated n times using
+// the weights and locations specified by rule. That is, Fixed estimates
+//  int_min^max f(x) dx ≈ \sum_i w_i f(x_i)
+// If rule is nil, an acceptable default is chosen, otherwise it is
+// assumed that the properties of the integral match the assumptions of rule.
+// For example, Legendre assumes that the integration bounds are finite. If
+// rule is also a FixedLocationSingler, the quadrature points are computed
+// individually rather than as a unit.
+//
+// If concurrent <= 0, f is evaluated serially, while if concurrent > 0, f
+// may be evaluated with at most concurrent simultaneous evaluations.
+//
+// min must be less than or equal to max, and n must be positive, otherwise
+// Fixed will panic.
+func Fixed(f func(float64) float64, min, max float64, n int, rule FixedLocationer, concurrent int) float64 {
+	// TODO(btracey): When there are Hermite polynomial quadrature, add an additional
+	// example to the documentation comment that talks about weight functions.
+	if n <= 0 {
+		panic("quad: non-positive number of locations")
+	}
+	if min > max {
+		panic("quad: min > max")
+	}
+	if min == max {
+		return 0
+	}
+	intfunc := f
+	// If rule is non-nil it is assumed that the function and the constraints
+	// of rule are aligned. If it is nil, wrap the function and do something
+	// reasonable.
+	// TODO(btracey): Replace wrapping with other quadrature rules when
+	// we have rules that support infinite-bound integrals.
+	if rule == nil {
+		// int_a^b f(x)dx = int_u^-1(a)^u^-1(b) f(u(t))u'(t)dt
+		switch {
+		case math.IsInf(max, 1) && math.IsInf(min, -1):
+			// u(t) = (t/(1-t^2))
+			min = -1
+			max = 1
+			intfunc = func(x float64) float64 {
+				v := 1 - x*x
+				return f(x/v) * (1 + x*x) / (v * v)
+			}
+		case math.IsInf(max, 1):
+			// u(t) = a + t / (1-t)
+			a := min
+			min = 0
+			max = 1
+			intfunc = func(x float64) float64 {
+				v := 1 - x
+				return f(a+x/v) / (v * v)
+			}
+		case math.IsInf(min, -1):
+			// u(t) = a - (1-t)/t
+			a := max
+			min = 0
+			max = 1
+			intfunc = func(x float64) float64 {
+				return f(a-(1-x)/x) / (x * x)
+			}
+		}
+		rule = Legendre{}
+	}
+	singler, isSingler := rule.(FixedLocationSingler)
+
+	var xs, weights []float64
+	if !isSingler {
+		xs = make([]float64, n)
+		weights = make([]float64, n)
+		rule.FixedLocations(xs, weights, min, max)
+	}
+
+	if concurrent > n {
+		concurrent = n
+	}
+
+	if concurrent <= 0 {
+		var integral float64
+		// Evaluate in serial.
+		if isSingler {
+			for k := 0; k < n; k++ {
+				x, weight := singler.FixedLocationSingle(n, k, min, max)
+				integral += weight * intfunc(x)
+			}
+			return integral
+		}
+		for i, x := range xs {
+			integral += weights[i] * intfunc(x)
+		}
+		return integral
+	}
+
+	// Evaluate concurrently
+	tasks := make(chan int)
+
+	// Launch distributor
+	go func() {
+		for i := 0; i < n; i++ {
+			tasks <- i
+		}
+		close(tasks)
+	}()
+
+	var mux sync.Mutex
+	var integral float64
+	var wg sync.WaitGroup
+	wg.Add(concurrent)
+	for i := 0; i < concurrent; i++ {
+		// Launch workers
+		go func() {
+			defer wg.Done()
+			var subIntegral float64
+			for k := range tasks {
+				var x, weight float64
+				if isSingler {
+					x, weight = singler.FixedLocationSingle(n, k, min, max)
+				} else {
+					x = xs[k]
+					weight = weights[k]
+				}
+				f := intfunc(x)
+				subIntegral += f * weight
+			}
+			mux.Lock()
+			integral += subIntegral
+			mux.Unlock()
+		}()
+	}
+	wg.Wait()
+	return integral
+}
diff --git a/vendor/gonum.org/v1/gonum/integrate/quad/quad_test.go b/vendor/gonum.org/v1/gonum/integrate/quad/quad_test.go
new file mode 100644
index 00000000..5e25ffdd
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/integrate/quad/quad_test.go
@@ -0,0 +1,126 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package quad
+
+import (
+	"math"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/stat/distuv"
+)
+
+func TestFixed(t *testing.T) {
+	for i, test := range []struct {
+		f        func(float64) float64
+		min, max float64
+		n        []int
+		tol      []float64
+		ans      float64
+	}{
+		// Tolerances determined from intuition and a bit of post-hoc tweaking.
+		{
+			f:   func(x float64) float64 { return math.Exp(x) },
+			min: -3,
+			max: 5,
+			n:   []int{3, 4, 6, 7, 15, 16, 300, 301},
+			tol: []float64{5e-2, 5e-3, 5e-6, 1e-7, 1e-14, 1e-14, 1e-14, 1e-14},
+			ans: math.Exp(5) - math.Exp(-3),
+		},
+		{
+			f:   distuv.UnitNormal.Prob,
+			min: math.Inf(-1),
+			max: math.Inf(1),
+			n:   []int{15, 16, 50, 51, 300, 301},
+			tol: []float64{5e-3, 1e-3, 1e-7, 1e-7, 1e-14, 1e-14},
+			ans: 1,
+		},
+		{
+			f:   func(x float64) float64 { return math.Exp(-x) },
+			min: 5,
+			max: math.Inf(1),
+			n:   []int{15, 16, 50, 51, 300, 301},
+			tol: []float64{5e-3, 1e-3, 1e-7, 1e-7, 1e-14, 1e-14},
+			ans: math.Exp(-5),
+		},
+		{
+			f:   func(x float64) float64 { return math.Exp(x) },
+			min: math.Inf(-1),
+			max: -5,
+			n:   []int{15, 16, 50, 51, 300, 301},
+			tol: []float64{5e-3, 1e-3, 1e-7, 1e-7, 1e-14, 1e-14},
+			ans: math.Exp(-5),
+		},
+		{
+			f:   func(x float64) float64 { return math.Exp(x) },
+			min: 3,
+			max: 3,
+			n:   []int{15, 16, 50, 51, 300, 301},
+			tol: []float64{0, 0, 0, 0, 0, 0},
+			ans: 0,
+		},
+	} {
+		for j, n := range test.n {
+			ans := Fixed(test.f, test.min, test.max, n, nil, 0)
+			if !floats.EqualWithinAbsOrRel(ans, test.ans, test.tol[j], test.tol[j]) {
+				t.Errorf("Case %d, n = %d: Mismatch. Want %v, got %v", i, n, test.ans, ans)
+			}
+			ans2 := Fixed(test.f, test.min, test.max, n, nil, 3)
+			if !floats.EqualWithinAbsOrRel(ans2, test.ans, test.tol[j], test.tol[j]) {
+				t.Errorf("Case %d, n = %d: Mismatch concurrent. Want %v, got %v", i, n, test.ans, ans)
+			}
+		}
+	}
+}
+
+// legendreNonSingle wraps Legendre but does not implement FixedLocationSingle.
+type legendreNonSingle struct {
+	Legendre Legendre
+}
+
+func (l legendreNonSingle) FixedLocations(x, weight []float64, min, max float64) {
+	l.Legendre.FixedLocations(x, weight, min, max)
+}
+
+func TestFixedNonSingle(t *testing.T) {
+	// TODO(btracey): Add tests with infinite bounds when we have native support
+	// for indefinite integrals.
+	for i, test := range []struct {
+		f        func(float64) float64
+		min, max float64
+		n        []int
+		tol      []float64
+		ans      float64
+	}{
+		// Tolerances determined from intuition and a bit of post-hoc tweaking.
+		{
+			f:   func(x float64) float64 { return math.Exp(x) },
+			min: -3,
+			max: 5,
+			n:   []int{3, 4, 6, 7, 15, 16, 300, 301},
+			tol: []float64{5e-2, 5e-3, 5e-6, 1e-7, 1e-14, 1e-14, 1e-14, 1e-14},
+			ans: math.Exp(5) - math.Exp(-3),
+		},
+		{
+			f:   func(x float64) float64 { return math.Exp(x) },
+			min: 3,
+			max: 3,
+			n:   []int{3, 4, 6, 7, 15, 16, 300, 301},
+			tol: []float64{0, 0, 0, 0, 0, 0, 0, 0},
+			ans: 0,
+		},
+	} {
+		for j, n := range test.n {
+			ans := Fixed(test.f, test.min, test.max, n, legendreNonSingle{}, 0)
+			if !floats.EqualWithinAbsOrRel(ans, test.ans, test.tol[j], test.tol[j]) {
+				t.Errorf("Case = %d, n = %d: Mismatch. Want %v, got %v", i, n, test.ans, ans)
+			}
+			ans2 := Fixed(test.f, test.min, test.max, n, legendreNonSingle{}, 3)
+			if !floats.EqualWithinAbsOrRel(ans2, test.ans, test.tol[j], test.tol[j]) {
+				t.Errorf("Case = %d, n = %d: Mismatch concurrent. Want %v, got %v", i, n, test.ans, ans)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/integrate/trapezoidal.go b/vendor/gonum.org/v1/gonum/integrate/trapezoidal.go
new file mode 100644
index 00000000..3f402ac3
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/integrate/trapezoidal.go
@@ -0,0 +1,40 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package integrate
+
+import "sort"
+
+// Trapezoidal estimates the integral of a function f
+//  \int_a^b f(x) dx
+// from a set of evaluations of the function using the trapezoidal rule.
+// The trapezoidal rule makes piecewise linear approximations to the function,
+// and estimates
+//  \int_x[i]^x[i+1] f(x) dx
+// as
+//  (x[i+1] - x[i]) * (f[i] + f[i+1])/2
+// where f[i] is the value of the function at x[i].
+// More details on the trapezoidal rule can be found at:
+// https://en.wikipedia.org/wiki/Trapezoidal_rule
+//
+// The (x,f) input data points must be sorted along x.
+// One can use github.com/gonum/stat.SortWeighted to do that.
+// The x and f slices must be of equal length and have length > 1.
+func Trapezoidal(x, f []float64) float64 {
+	switch {
+	case len(x) != len(f):
+		panic("integrate: slice length mismatch")
+	case len(x) < 2:
+		panic("integrate: input data too small")
+	case !sort.Float64sAreSorted(x):
+		panic("integrate: input must be sorted")
+	}
+
+	integral := 0.0
+	for i := 0; i < len(x)-1; i++ {
+		integral += 0.5 * (x[i+1] - x[i]) * (f[i+1] + f[i])
+	}
+
+	return integral
+}
diff --git a/vendor/gonum.org/v1/gonum/integrate/trapezoidal_test.go b/vendor/gonum.org/v1/gonum/integrate/trapezoidal_test.go
new file mode 100644
index 00000000..c52ee0e6
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/integrate/trapezoidal_test.go
@@ -0,0 +1,82 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package integrate
+
+import (
+	"math"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+func TestTrapezoidal(t *testing.T) {
+	const N = 1e6
+	x := floats.Span(make([]float64, N), 0, 1)
+	for i, test := range []struct {
+		x    []float64
+		f    func(x float64) float64
+		want float64
+	}{
+		{
+			x:    x,
+			f:    func(x float64) float64 { return x },
+			want: 0.5,
+		},
+		{
+			x:    floats.Span(make([]float64, N), -1, 1),
+			f:    func(x float64) float64 { return x },
+			want: 0,
+		},
+		{
+			x:    x,
+			f:    func(x float64) float64 { return x + 10 },
+			want: 10.5,
+		},
+		{
+			x:    x,
+			f:    func(x float64) float64 { return 3*x*x + 10 },
+			want: 11,
+		},
+		{
+			x:    x,
+			f:    func(x float64) float64 { return math.Exp(x) },
+			want: 1.7182818284591876,
+		},
+		{
+			x:    floats.Span(make([]float64, N), 0, math.Pi),
+			f:    func(x float64) float64 { return math.Cos(x) },
+			want: 0,
+		},
+		{
+			x:    floats.Span(make([]float64, N), 0, 2*math.Pi),
+			f:    func(x float64) float64 { return math.Cos(x) },
+			want: 0,
+		},
+		{
+			x:    floats.Span(make([]float64, N*10), 0, math.Pi),
+			f:    func(x float64) float64 { return math.Sin(x) },
+			want: 2,
+		},
+		{
+			x:    floats.Span(make([]float64, N*10), 0, 0.5*math.Pi),
+			f:    func(x float64) float64 { return math.Sin(x) },
+			want: 1,
+		},
+		{
+			x:    floats.Span(make([]float64, N), 0, 2*math.Pi),
+			f:    func(x float64) float64 { return math.Sin(x) },
+			want: 0,
+		},
+	} {
+		y := make([]float64, len(test.x))
+		for i, v := range test.x {
+			y[i] = test.f(v)
+		}
+		v := Trapezoidal(test.x, y)
+		if !floats.EqualWithinAbs(v, test.want, 1e-12) {
+			t.Errorf("test #%d: got=%v want=%v\n", i, v, test.want)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/README.md b/vendor/gonum.org/v1/gonum/internal/README.md
new file mode 100644
index 00000000..dd28a1f7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/README.md
@@ -0,0 +1,3 @@
+# Gonum internal [![GoDoc](https://godoc.org/gonum.org/v1/gonum/internal?status.svg)](https://godoc.org/gonum.org/v1/gonum/internal)
+
+This is the set of internal packages for the Gonum project.
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/bench_gen.sh b/vendor/gonum.org/v1/gonum/internal/asm/bench_gen.sh
new file mode 100755
index 00000000..e7115c07
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/bench_gen.sh
@@ -0,0 +1,30 @@
+#!/usr/bin/env bash
+
+# Copyright ©2016 The gonum Authors. All rights reserved.
+# Use of this source code is governed by a BSD-style
+# license that can be found in the LICENSE file.
+
+cat c64/bench_test.go \
+    | gofmt -r 'complex(float32(n), float32(n)) -> float32(n)' \
+    | gofmt -r 'complex64 -> float32' \
+    | gofmt -r '1 + 1i -> 1' \
+    | gofmt -r '2 + 2i -> 2' \
+    | sed 's/C64/F32/g' \
+    | sed 's/c64/f32/g' \
+    > f32/bench_test.go
+
+cat c64/bench_test.go \
+    | gofmt -r 'complex(float32(n), float32(n)) -> float64(n)' \
+    | gofmt -r 'complex64 -> float64' \
+    | gofmt -r '1 + 1i -> 1' \
+    | gofmt -r '2 + 2i -> 2' \
+    | sed 's/C64/F64/g' \
+    | sed 's/c64/f64/g' \
+    > f64/bench_test.go
+
+cat c64/bench_test.go \
+    | gofmt -r 'float32 -> float64' \
+    | gofmt -r 'complex64 -> complex128' \
+    | sed 's/C64/C128/g' \
+    | sed 's/c64/c128/g' \
+    > c128/bench_test.go
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c128/axpyinc_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/c128/axpyinc_amd64.s
new file mode 100644
index 00000000..c66a667b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c128/axpyinc_amd64.s
@@ -0,0 +1,134 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !noasm,!appengine
+
+#include "textflag.h"
+
+// MOVDDUP X2, X3
+#define MOVDDUP_X2_X3 BYTE $0xF2; BYTE $0x0F; BYTE $0x12; BYTE $0xDA
+// MOVDDUP X4, X5
+#define MOVDDUP_X4_X5 BYTE $0xF2; BYTE $0x0F; BYTE $0x12; BYTE $0xEC
+// MOVDDUP X6, X7
+#define MOVDDUP_X6_X7 BYTE $0xF2; BYTE $0x0F; BYTE $0x12; BYTE $0xFE
+// MOVDDUP X8, X9
+#define MOVDDUP_X8_X9 BYTE $0xF2; BYTE $0x45; BYTE $0x0F; BYTE $0x12; BYTE $0xC8
+
+// ADDSUBPD X2, X3
+#define ADDSUBPD_X2_X3 BYTE $0x66; BYTE $0x0F; BYTE $0xD0; BYTE $0xDA
+// ADDSUBPD X4, X5
+#define ADDSUBPD_X4_X5 BYTE $0x66; BYTE $0x0F; BYTE $0xD0; BYTE $0xEC
+// ADDSUBPD X6, X7
+#define ADDSUBPD_X6_X7 BYTE $0x66; BYTE $0x0F; BYTE $0xD0; BYTE $0xFE
+// ADDSUBPD X8, X9
+#define ADDSUBPD_X8_X9 BYTE $0x66; BYTE $0x45; BYTE $0x0F; BYTE $0xD0; BYTE $0xC8
+
+// func AxpyInc(alpha complex128, x, y []complex128, n, incX, incY, ix, iy uintptr)
+TEXT ·AxpyInc(SB), NOSPLIT, $0
+	MOVQ   x_base+16(FP), SI // SI = &x
+	MOVQ   y_base+40(FP), DI // DI = &y
+	MOVQ   n+64(FP), CX      // CX = n
+	CMPQ   CX, $0            // if n==0 { return }
+	JE     axpyi_end
+	MOVQ   ix+88(FP), R8     // R8 = ix  // Load the first index
+	SHLQ   $4, R8            // R8 *= sizeof(complex128)
+	MOVQ   iy+96(FP), R9     // R9 = iy
+	SHLQ   $4, R9            // R9 *= sizeof(complex128)
+	LEAQ   (SI)(R8*1), SI    // SI = &(x[ix])
+	LEAQ   (DI)(R9*1), DI    // DI = &(y[iy])
+	MOVQ   DI, DX            // DX = DI      // Separate Read/Write pointers
+	MOVQ   incX+72(FP), R8   // R8 = incX
+	SHLQ   $4, R8            // R8 *= sizeof(complex128)
+	MOVQ   incY+80(FP), R9   // R9 = iy
+	SHLQ   $4, R9            // R9 *= sizeof(complex128)
+	MOVUPS alpha+0(FP), X0   // X0 = { imag(a), real(a) }
+	MOVAPS X0, X1
+	SHUFPD $0x1, X1, X1      // X1 = { real(a), imag(a) }
+	MOVAPS X0, X10           // Copy X0 and X1 for pipelining
+	MOVAPS X1, X11
+	MOVQ   CX, BX
+	ANDQ   $3, CX            // CX = n % 4
+	SHRQ   $2, BX            // BX = floor( n / 4 )
+	JZ     axpyi_tail        // if BX == 0 { goto axpyi_tail }
+
+axpyi_loop: // do {
+	MOVUPS (SI), X2       // X_i = { imag(x[i]), real(x[i]) }
+	MOVUPS (SI)(R8*1), X4
+	LEAQ   (SI)(R8*2), SI // SI = &(SI[incX*2])
+	MOVUPS (SI), X6
+	MOVUPS (SI)(R8*1), X8
+
+	// X_(i+1) = { real(x[i], real(x[i]) }
+	MOVDDUP_X2_X3
+	MOVDDUP_X4_X5
+	MOVDDUP_X6_X7
+	MOVDDUP_X8_X9
+
+	// X_i = { imag(x[i]), imag(x[i]) }
+	SHUFPD $0x3, X2, X2
+	SHUFPD $0x3, X4, X4
+	SHUFPD $0x3, X6, X6
+	SHUFPD $0x3, X8, X8
+
+	// X_i     = { real(a) * imag(x[i]), imag(a) * imag(x[i])  }
+	// X_(i+1) = { imag(a) * real(x[i]), real(a) * real(x[i])  }
+	MULPD X1, X2
+	MULPD X0, X3
+	MULPD X11, X4
+	MULPD X10, X5
+	MULPD X1, X6
+	MULPD X0, X7
+	MULPD X11, X8
+	MULPD X10, X9
+
+	// X_(i+1) = {
+	//	imag(result[i]):  imag(a)*real(x[i]) + real(a)*imag(x[i]),
+	//	real(result[i]):  real(a)*real(x[i]) - imag(a)*imag(x[i])
+	//  }
+	ADDSUBPD_X2_X3
+	ADDSUBPD_X4_X5
+	ADDSUBPD_X6_X7
+	ADDSUBPD_X8_X9
+
+	// X_(i+1) = { imag(result[i]) + imag(y[i]), real(result[i]) + real(y[i]) }
+	ADDPD  (DX), X3
+	ADDPD  (DX)(R9*1), X5
+	LEAQ   (DX)(R9*2), DX // DX = &(DX[incY*2])
+	ADDPD  (DX), X7
+	ADDPD  (DX)(R9*1), X9
+	MOVUPS X3, (DI)       // dst[i] = X_(i+1)
+	MOVUPS X5, (DI)(R9*1)
+	LEAQ   (DI)(R9*2), DI
+	MOVUPS X7, (DI)
+	MOVUPS X9, (DI)(R9*1)
+	LEAQ   (SI)(R8*2), SI // SI = &(SI[incX*2])
+	LEAQ   (DX)(R9*2), DX // DX = &(DX[incY*2])
+	LEAQ   (DI)(R9*2), DI // DI = &(DI[incY*2])
+	DECQ   BX
+	JNZ    axpyi_loop     // } while --BX > 0
+	CMPQ   CX, $0         // if CX == 0 { return }
+	JE     axpyi_end
+
+axpyi_tail: // do {
+	MOVUPS (SI), X2     // X_i = { imag(x[i]), real(x[i]) }
+	MOVDDUP_X2_X3       // X_(i+1) = { real(x[i], real(x[i]) }
+	SHUFPD $0x3, X2, X2 // X_i = { imag(x[i]), imag(x[i]) }
+	MULPD  X1, X2       // X_i     = { real(a) * imag(x[i]), imag(a) * imag(x[i])  }
+	MULPD  X0, X3       // X_(i+1) = { imag(a) * real(x[i]), real(a) * real(x[i])  }
+
+	// X_(i+1) = {
+	//	imag(result[i]):  imag(a)*real(x[i]) + real(a)*imag(x[i]),
+	//	real(result[i]):  real(a)*real(x[i]) - imag(a)*imag(x[i])
+	//  }
+	ADDSUBPD_X2_X3
+
+	// X_(i+1) = { imag(result[i]) + imag(y[i]), real(result[i]) + real(y[i]) }
+	ADDPD  (DI), X3
+	MOVUPS X3, (DI)   // y[i] = X_i
+	ADDQ   R8, SI     // SI = &(SI[incX])
+	ADDQ   R9, DI     // DI = &(DI[incY])
+	LOOP   axpyi_tail // } while --CX > 0
+
+axpyi_end:
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c128/axpyincto_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/c128/axpyincto_amd64.s
new file mode 100644
index 00000000..edc0957c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c128/axpyincto_amd64.s
@@ -0,0 +1,141 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !noasm,!appengine
+
+#include "textflag.h"
+
+// MOVDDUP X2, X3
+#define MOVDDUP_X2_X3 BYTE $0xF2; BYTE $0x0F; BYTE $0x12; BYTE $0xDA
+// MOVDDUP X4, X5
+#define MOVDDUP_X4_X5 BYTE $0xF2; BYTE $0x0F; BYTE $0x12; BYTE $0xEC
+// MOVDDUP X6, X7
+#define MOVDDUP_X6_X7 BYTE $0xF2; BYTE $0x0F; BYTE $0x12; BYTE $0xFE
+// MOVDDUP X8, X9
+#define MOVDDUP_X8_X9 BYTE $0xF2; BYTE $0x45; BYTE $0x0F; BYTE $0x12; BYTE $0xC8
+
+// ADDSUBPD X2, X3
+#define ADDSUBPD_X2_X3 BYTE $0x66; BYTE $0x0F; BYTE $0xD0; BYTE $0xDA
+// ADDSUBPD X4, X5
+#define ADDSUBPD_X4_X5 BYTE $0x66; BYTE $0x0F; BYTE $0xD0; BYTE $0xEC
+// ADDSUBPD X6, X7
+#define ADDSUBPD_X6_X7 BYTE $0x66; BYTE $0x0F; BYTE $0xD0; BYTE $0xFE
+// ADDSUBPD X8, X9
+#define ADDSUBPD_X8_X9 BYTE $0x66; BYTE $0x45; BYTE $0x0F; BYTE $0xD0; BYTE $0xC8
+
+// func AxpyIncTo(dst []complex128, incDst, idst uintptr, alpha complex128, x, y []complex128, n, incX, incY, ix, iy uintptr)
+TEXT ·AxpyIncTo(SB), NOSPLIT, $0
+	MOVQ   dst_base+0(FP), DI // DI = &dst
+	MOVQ   x_base+56(FP), SI  // SI = &x
+	MOVQ   y_base+80(FP), DX  // DX = &y
+	MOVQ   n+104(FP), CX      // CX = n
+	CMPQ   CX, $0             // if n==0 { return }
+	JE     axpyi_end
+	MOVQ   ix+128(FP), R8     // R8 = ix  // Load the first index
+	SHLQ   $4, R8             // R8 *= sizeof(complex128)
+	MOVQ   iy+136(FP), R9     // R9 = iy
+	SHLQ   $4, R9             // R9 *= sizeof(complex128)
+	MOVQ   idst+32(FP), R10   // R10 = idst
+	SHLQ   $4, R10            // R10 *= sizeof(complex128)
+	LEAQ   (SI)(R8*1), SI     // SI = &(x[ix])
+	LEAQ   (DX)(R9*1), DX     // DX = &(y[iy])
+	LEAQ   (DI)(R10*1), DI    // DI = &(dst[idst])
+	MOVQ   incX+112(FP), R8   // R8 = incX
+	SHLQ   $4, R8             // R8 *= sizeof(complex128)
+	MOVQ   incY+120(FP), R9   // R9 = incY
+	SHLQ   $4, R9             // R9 *= sizeof(complex128)
+	MOVQ   incDst+24(FP), R10 // R10 = incDst
+	SHLQ   $4, R10            // R10 *= sizeof(complex128)
+	MOVUPS alpha+40(FP), X0   // X0 = { imag(a), real(a) }
+	MOVAPS X0, X1
+	SHUFPD $0x1, X1, X1       // X1 = { real(a), imag(a) }
+	MOVAPS X0, X10            // Copy X0 and X1 for pipelining
+	MOVAPS X1, X11
+	MOVQ   CX, BX
+	ANDQ   $3, CX             // CX = n % 4
+	SHRQ   $2, BX             // BX = floor( n / 4 )
+	JZ     axpyi_tail         // if BX == 0 { goto axpyi_tail }
+
+axpyi_loop: // do {
+	MOVUPS (SI), X2       // X_i = { imag(x[i]), real(x[i]) }
+	MOVUPS (SI)(R8*1), X4
+	LEAQ   (SI)(R8*2), SI // SI = &(SI[incX*2])
+
+	MOVUPS (SI), X6
+	MOVUPS (SI)(R8*1), X8
+
+	// X_(i+1) = { real(x[i], real(x[i]) }
+	MOVDDUP_X2_X3
+	MOVDDUP_X4_X5
+	MOVDDUP_X6_X7
+	MOVDDUP_X8_X9
+
+	// X_i = { imag(x[i]), imag(x[i]) }
+	SHUFPD $0x3, X2, X2
+	SHUFPD $0x3, X4, X4
+	SHUFPD $0x3, X6, X6
+	SHUFPD $0x3, X8, X8
+
+	// X_i     = { real(a) * imag(x[i]), imag(a) * imag(x[i])  }
+	// X_(i+1) = { imag(a) * real(x[i]), real(a) * real(x[i])  }
+	MULPD X1, X2
+	MULPD X0, X3
+	MULPD X11, X4
+	MULPD X10, X5
+	MULPD X1, X6
+	MULPD X0, X7
+	MULPD X11, X8
+	MULPD X10, X9
+
+	// X_(i+1) = {
+	//	imag(result[i]):  imag(a)*real(x[i]) + real(a)*imag(x[i]),
+	//	real(result[i]):  real(a)*real(x[i]) - imag(a)*imag(x[i])
+	//  }
+	ADDSUBPD_X2_X3
+	ADDSUBPD_X4_X5
+	ADDSUBPD_X6_X7
+	ADDSUBPD_X8_X9
+
+	// X_(i+1) = { imag(result[i]) + imag(y[i]), real(result[i]) + real(y[i]) }
+	ADDPD  (DX), X3
+	ADDPD  (DX)(R9*1), X5
+	LEAQ   (DX)(R9*2), DX  // DX = &(DX[incY*2])
+	ADDPD  (DX), X7
+	ADDPD  (DX)(R9*1), X9
+	MOVUPS X3, (DI)        // dst[i] = X_(i+1)
+	MOVUPS X5, (DI)(R10*1)
+	LEAQ   (DI)(R10*2), DI
+	MOVUPS X7, (DI)
+	MOVUPS X9, (DI)(R10*1)
+	LEAQ   (SI)(R8*2), SI  // SI = &(SI[incX*2])
+	LEAQ   (DX)(R9*2), DX  // DX = &(DX[incY*2])
+	LEAQ   (DI)(R10*2), DI // DI = &(DI[incDst*2])
+	DECQ   BX
+	JNZ    axpyi_loop      // } while --BX > 0
+	CMPQ   CX, $0          // if CX == 0 { return }
+	JE     axpyi_end
+
+axpyi_tail: // do {
+	MOVUPS (SI), X2     // X_i = { imag(x[i]), real(x[i]) }
+	MOVDDUP_X2_X3       // X_(i+1) = { real(x[i], real(x[i]) }
+	SHUFPD $0x3, X2, X2 // X_i = { imag(x[i]), imag(x[i]) }
+	MULPD  X1, X2       // X_i     = { real(a) * imag(x[i]), imag(a) * imag(x[i])  }
+	MULPD  X0, X3       // X_(i+1) = { imag(a) * real(x[i]), real(a) * real(x[i])  }
+
+	// X_(i+1) = {
+	//	imag(result[i]):  imag(a)*real(x[i]) + real(a)*imag(x[i]),
+	//	real(result[i]):  real(a)*real(x[i]) - imag(a)*imag(x[i])
+	//  }
+	ADDSUBPD_X2_X3
+
+	// X_(i+1) = { imag(result[i]) + imag(y[i]), real(result[i]) + real(y[i]) }
+	ADDPD  (DX), X3
+	MOVUPS X3, (DI)   // y[i] X_(i+1)
+	ADDQ   R8, SI     // SI += incX
+	ADDQ   R9, DX     // DX += incY
+	ADDQ   R10, DI    // DI += incDst
+	LOOP   axpyi_tail // } while --CX > 0
+
+axpyi_end:
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c128/axpyunitary_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/c128/axpyunitary_amd64.s
new file mode 100644
index 00000000..c9e119d3
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c128/axpyunitary_amd64.s
@@ -0,0 +1,122 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !noasm,!appengine
+
+#include "textflag.h"
+
+// MOVDDUP X2, X3
+#define MOVDDUP_X2_X3 BYTE $0xF2; BYTE $0x0F; BYTE $0x12; BYTE $0xDA
+// MOVDDUP X4, X5
+#define MOVDDUP_X4_X5 BYTE $0xF2; BYTE $0x0F; BYTE $0x12; BYTE $0xEC
+// MOVDDUP X6, X7
+#define MOVDDUP_X6_X7 BYTE $0xF2; BYTE $0x0F; BYTE $0x12; BYTE $0xFE
+// MOVDDUP X8, X9
+#define MOVDDUP_X8_X9 BYTE $0xF2; BYTE $0x45; BYTE $0x0F; BYTE $0x12; BYTE $0xC8
+
+// ADDSUBPD X2, X3
+#define ADDSUBPD_X2_X3 BYTE $0x66; BYTE $0x0F; BYTE $0xD0; BYTE $0xDA
+// ADDSUBPD X4, X5
+#define ADDSUBPD_X4_X5 BYTE $0x66; BYTE $0x0F; BYTE $0xD0; BYTE $0xEC
+// ADDSUBPD X6, X7
+#define ADDSUBPD_X6_X7 BYTE $0x66; BYTE $0x0F; BYTE $0xD0; BYTE $0xFE
+// ADDSUBPD X8, X9
+#define ADDSUBPD_X8_X9 BYTE $0x66; BYTE $0x45; BYTE $0x0F; BYTE $0xD0; BYTE $0xC8
+
+// func AxpyUnitary(alpha complex128, x, y []complex128)
+TEXT ·AxpyUnitary(SB), NOSPLIT, $0
+	MOVQ    x_base+16(FP), SI // SI = &x
+	MOVQ    y_base+40(FP), DI // DI = &y
+	MOVQ    x_len+24(FP), CX  // CX = min( len(x), len(y) )
+	CMPQ    y_len+48(FP), CX
+	CMOVQLE y_len+48(FP), CX
+	CMPQ    CX, $0            // if CX == 0 { return }
+	JE      caxy_end
+	PXOR    X0, X0            // Clear work registers and cache-align loop
+	PXOR    X1, X1
+	MOVUPS  alpha+0(FP), X0   // X0 = { imag(a), real(a) }
+	MOVAPS  X0, X1
+	SHUFPD  $0x1, X1, X1      // X1 = { real(a), imag(a) }
+	XORQ    AX, AX            // i = 0
+	MOVAPS  X0, X10           // Copy X0 and X1 for pipelining
+	MOVAPS  X1, X11
+	MOVQ    CX, BX
+	ANDQ    $3, CX            // CX = n % 4
+	SHRQ    $2, BX            // BX = floor( n / 4 )
+	JZ      caxy_tail         // if BX == 0 { goto caxy_tail }
+
+caxy_loop: // do {
+	MOVUPS (SI)(AX*8), X2   // X_i = { imag(x[i]), real(x[i]) }
+	MOVUPS 16(SI)(AX*8), X4
+	MOVUPS 32(SI)(AX*8), X6
+	MOVUPS 48(SI)(AX*8), X8
+
+	// X_(i+1) = { real(x[i], real(x[i]) }
+	MOVDDUP_X2_X3
+	MOVDDUP_X4_X5
+	MOVDDUP_X6_X7
+	MOVDDUP_X8_X9
+
+	// X_i = { imag(x[i]), imag(x[i]) }
+	SHUFPD $0x3, X2, X2
+	SHUFPD $0x3, X4, X4
+	SHUFPD $0x3, X6, X6
+	SHUFPD $0x3, X8, X8
+
+	// X_i     = { real(a) * imag(x[i]), imag(a) * imag(x[i])  }
+	// X_(i+1) = { imag(a) * real(x[i]), real(a) * real(x[i])  }
+	MULPD X1, X2
+	MULPD X0, X3
+	MULPD X11, X4
+	MULPD X10, X5
+	MULPD X1, X6
+	MULPD X0, X7
+	MULPD X11, X8
+	MULPD X10, X9
+
+	// X_(i+1) = {
+	//	imag(result[i]):  imag(a)*real(x[i]) + real(a)*imag(x[i]),
+	//	real(result[i]):  real(a)*real(x[i]) - imag(a)*imag(x[i])
+	//  }
+	ADDSUBPD_X2_X3
+	ADDSUBPD_X4_X5
+	ADDSUBPD_X6_X7
+	ADDSUBPD_X8_X9
+
+	// X_(i+1) = { imag(result[i]) + imag(y[i]), real(result[i]) + real(y[i]) }
+	ADDPD  (DI)(AX*8), X3
+	ADDPD  16(DI)(AX*8), X5
+	ADDPD  32(DI)(AX*8), X7
+	ADDPD  48(DI)(AX*8), X9
+	MOVUPS X3, (DI)(AX*8)   // y[i] = X_(i+1)
+	MOVUPS X5, 16(DI)(AX*8)
+	MOVUPS X7, 32(DI)(AX*8)
+	MOVUPS X9, 48(DI)(AX*8)
+	ADDQ   $8, AX           // i += 8
+	DECQ   BX
+	JNZ    caxy_loop        // } while --BX > 0
+	CMPQ   CX, $0           // if CX == 0 { return }
+	JE     caxy_end
+
+caxy_tail: // do {
+	MOVUPS (SI)(AX*8), X2 // X_i = { imag(x[i]), real(x[i]) }
+	MOVDDUP_X2_X3         // X_(i+1) = { real(x[i], real(x[i]) }
+	SHUFPD $0x3, X2, X2   // X_i = { imag(x[i]), imag(x[i]) }
+	MULPD  X1, X2         // X_i     = { real(a) * imag(x[i]), imag(a) * imag(x[i])  }
+	MULPD  X0, X3         // X_(i+1) = { imag(a) * real(x[i]), real(a) * real(x[i])  }
+
+	// X_(i+1) = {
+	//	imag(result[i]):  imag(a)*real(x[i]) + real(a)*imag(x[i]),
+	//	real(result[i]):  real(a)*real(x[i]) - imag(a)*imag(x[i])
+	//  }
+	ADDSUBPD_X2_X3
+
+	// X_(i+1) = { imag(result[i]) + imag(y[i]), real(result[i]) + real(y[i]) }
+	ADDPD  (DI)(AX*8), X3
+	MOVUPS X3, (DI)(AX*8) // y[i] = X_(i+1)
+	ADDQ   $2, AX         // i += 2
+	LOOP   caxy_tail      // }  while --CX > 0
+
+caxy_end:
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c128/axpyunitaryto_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/c128/axpyunitaryto_amd64.s
new file mode 100644
index 00000000..9dcfc67e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c128/axpyunitaryto_amd64.s
@@ -0,0 +1,123 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !noasm,!appengine
+
+#include "textflag.h"
+
+// MOVDDUP X2, X3
+#define MOVDDUP_X2_X3 BYTE $0xF2; BYTE $0x0F; BYTE $0x12; BYTE $0xDA
+// MOVDDUP X4, X5
+#define MOVDDUP_X4_X5 BYTE $0xF2; BYTE $0x0F; BYTE $0x12; BYTE $0xEC
+// MOVDDUP X6, X7
+#define MOVDDUP_X6_X7 BYTE $0xF2; BYTE $0x0F; BYTE $0x12; BYTE $0xFE
+// MOVDDUP X8, X9
+#define MOVDDUP_X8_X9 BYTE $0xF2; BYTE $0x45; BYTE $0x0F; BYTE $0x12; BYTE $0xC8
+
+// ADDSUBPD X2, X3
+#define ADDSUBPD_X2_X3 BYTE $0x66; BYTE $0x0F; BYTE $0xD0; BYTE $0xDA
+// ADDSUBPD X4, X5
+#define ADDSUBPD_X4_X5 BYTE $0x66; BYTE $0x0F; BYTE $0xD0; BYTE $0xEC
+// ADDSUBPD X6, X7
+#define ADDSUBPD_X6_X7 BYTE $0x66; BYTE $0x0F; BYTE $0xD0; BYTE $0xFE
+// ADDSUBPD X8, X9
+#define ADDSUBPD_X8_X9 BYTE $0x66; BYTE $0x45; BYTE $0x0F; BYTE $0xD0; BYTE $0xC8
+
+// func AxpyUnitaryTo(dst []complex128, alpha complex64, x, y []complex128)
+TEXT ·AxpyUnitaryTo(SB), NOSPLIT, $0
+	MOVQ    dst_base+0(FP), DI // DI = &dst
+	MOVQ    x_base+40(FP), SI  // SI = &x
+	MOVQ    y_base+64(FP), DX  // DX = &y
+	MOVQ    x_len+48(FP), CX   // CX = min( len(x), len(y), len(dst) )
+	CMPQ    y_len+72(FP), CX
+	CMOVQLE y_len+72(FP), CX
+	CMPQ    dst_len+8(FP), CX
+	CMOVQLE dst_len+8(FP), CX
+	CMPQ    CX, $0             // if CX == 0 { return }
+	JE      caxy_end
+	MOVUPS  alpha+24(FP), X0   // X0 = { imag(a), real(a) }
+	MOVAPS  X0, X1
+	SHUFPD  $0x1, X1, X1       // X1 = { real(a), imag(a) }
+	XORQ    AX, AX             // i = 0
+	MOVAPS  X0, X10            // Copy X0 and X1 for pipelining
+	MOVAPS  X1, X11
+	MOVQ    CX, BX
+	ANDQ    $3, CX             // CX = n % 4
+	SHRQ    $2, BX             // BX = floor( n / 4 )
+	JZ      caxy_tail          // if BX == 0 { goto caxy_tail }
+
+caxy_loop: // do {
+	MOVUPS (SI)(AX*8), X2   // X_i = { imag(x[i]), real(x[i]) }
+	MOVUPS 16(SI)(AX*8), X4
+	MOVUPS 32(SI)(AX*8), X6
+	MOVUPS 48(SI)(AX*8), X8
+
+	// X_(i+1) = { real(x[i], real(x[i]) }
+	MOVDDUP_X2_X3 // Load and duplicate imag elements (xi, xi)
+	MOVDDUP_X4_X5
+	MOVDDUP_X6_X7
+	MOVDDUP_X8_X9
+
+	// X_i = { imag(x[i]), imag(x[i]) }
+	SHUFPD $0x3, X2, X2 // duplicate real elements (xr, xr)
+	SHUFPD $0x3, X4, X4
+	SHUFPD $0x3, X6, X6
+	SHUFPD $0x3, X8, X8
+
+	// X_i     = { real(a) * imag(x[i]), imag(a) * imag(x[i])  }
+	// X_(i+1) = { imag(a) * real(x[i]), real(a) * real(x[i])  }
+	MULPD X1, X2
+	MULPD X0, X3
+	MULPD X11, X4
+	MULPD X10, X5
+	MULPD X1, X6
+	MULPD X0, X7
+	MULPD X11, X8
+	MULPD X10, X9
+
+	// X_(i+1) = {
+	//	imag(result[i]):  imag(a)*real(x[i]) + real(a)*imag(x[i]),
+	//	real(result[i]):  real(a)*real(x[i]) - imag(a)*imag(x[i])
+	//  }
+	ADDSUBPD_X2_X3
+	ADDSUBPD_X4_X5
+	ADDSUBPD_X6_X7
+	ADDSUBPD_X8_X9
+
+	// X_(i+1) = { imag(result[i]) + imag(y[i]), real(result[i]) + real(y[i]) }
+	ADDPD  (DX)(AX*8), X3
+	ADDPD  16(DX)(AX*8), X5
+	ADDPD  32(DX)(AX*8), X7
+	ADDPD  48(DX)(AX*8), X9
+	MOVUPS X3, (DI)(AX*8)   // y[i] = X_(i+1)
+	MOVUPS X5, 16(DI)(AX*8)
+	MOVUPS X7, 32(DI)(AX*8)
+	MOVUPS X9, 48(DI)(AX*8)
+	ADDQ   $8, AX           // i += 8
+	DECQ   BX
+	JNZ    caxy_loop        // } while --BX > 0
+	CMPQ   CX, $0           // if CX == 0 { return }
+	JE     caxy_end
+
+caxy_tail: // Same calculation, but read in values to avoid trampling memory
+	MOVUPS (SI)(AX*8), X2 // X_i = { imag(x[i]), real(x[i]) }
+	MOVDDUP_X2_X3         // X_(i+1) = { real(x[i], real(x[i]) }
+	SHUFPD $0x3, X2, X2   // X_i = { imag(x[i]), imag(x[i]) }
+	MULPD  X1, X2         // X_i     = { real(a) * imag(x[i]), imag(a) * imag(x[i])  }
+	MULPD  X0, X3         // X_(i+1) = { imag(a) * real(x[i]), real(a) * real(x[i])  }
+
+	// X_(i+1) = {
+	//	imag(result[i]):  imag(a)*real(x[i]) + real(a)*imag(x[i]),
+	//	real(result[i]):  real(a)*real(x[i]) - imag(a)*imag(x[i])
+	//  }
+	ADDSUBPD_X2_X3
+
+	// X_(i+1) = { imag(result[i]) + imag(y[i]), real(result[i]) + real(y[i]) }
+	ADDPD  (DX)(AX*8), X3
+	MOVUPS X3, (DI)(AX*8) // y[i] = X_(i+1)
+	ADDQ   $2, AX         // i += 2
+	LOOP   caxy_tail      // }  while --CX > 0
+
+caxy_end:
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c128/bench_test.go b/vendor/gonum.org/v1/gonum/internal/asm/c128/bench_test.go
new file mode 100644
index 00000000..61049beb
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c128/bench_test.go
@@ -0,0 +1,284 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package c128
+
+import "testing"
+
+var (
+	a = complex128(2 + 2i)
+	x = make([]complex128, 1000000)
+	y = make([]complex128, 1000000)
+	z = make([]complex128, 1000000)
+)
+
+func init() {
+	for n := range x {
+		x[n] = complex(float64(n), float64(n))
+		y[n] = complex(float64(n), float64(n))
+	}
+}
+
+func benchaxpyu(t *testing.B, n int, f func(a complex128, x, y []complex128)) {
+	x, y := x[:n], y[:n]
+	for i := 0; i < t.N; i++ {
+		f(a, x, y)
+	}
+}
+
+func naiveaxpyu(a complex128, x, y []complex128) {
+	for i, v := range x {
+		y[i] += a * v
+	}
+}
+
+func BenchmarkC128AxpyUnitary1(t *testing.B)     { benchaxpyu(t, 1, AxpyUnitary) }
+func BenchmarkC128AxpyUnitary2(t *testing.B)     { benchaxpyu(t, 2, AxpyUnitary) }
+func BenchmarkC128AxpyUnitary3(t *testing.B)     { benchaxpyu(t, 3, AxpyUnitary) }
+func BenchmarkC128AxpyUnitary4(t *testing.B)     { benchaxpyu(t, 4, AxpyUnitary) }
+func BenchmarkC128AxpyUnitary5(t *testing.B)     { benchaxpyu(t, 5, AxpyUnitary) }
+func BenchmarkC128AxpyUnitary10(t *testing.B)    { benchaxpyu(t, 10, AxpyUnitary) }
+func BenchmarkC128AxpyUnitary100(t *testing.B)   { benchaxpyu(t, 100, AxpyUnitary) }
+func BenchmarkC128AxpyUnitary1000(t *testing.B)  { benchaxpyu(t, 1000, AxpyUnitary) }
+func BenchmarkC128AxpyUnitary5000(t *testing.B)  { benchaxpyu(t, 5000, AxpyUnitary) }
+func BenchmarkC128AxpyUnitary10000(t *testing.B) { benchaxpyu(t, 10000, AxpyUnitary) }
+func BenchmarkC128AxpyUnitary50000(t *testing.B) { benchaxpyu(t, 50000, AxpyUnitary) }
+
+func BenchmarkLC128AxpyUnitary1(t *testing.B)     { benchaxpyu(t, 1, naiveaxpyu) }
+func BenchmarkLC128AxpyUnitary2(t *testing.B)     { benchaxpyu(t, 2, naiveaxpyu) }
+func BenchmarkLC128AxpyUnitary3(t *testing.B)     { benchaxpyu(t, 3, naiveaxpyu) }
+func BenchmarkLC128AxpyUnitary4(t *testing.B)     { benchaxpyu(t, 4, naiveaxpyu) }
+func BenchmarkLC128AxpyUnitary5(t *testing.B)     { benchaxpyu(t, 5, naiveaxpyu) }
+func BenchmarkLC128AxpyUnitary10(t *testing.B)    { benchaxpyu(t, 10, naiveaxpyu) }
+func BenchmarkLC128AxpyUnitary100(t *testing.B)   { benchaxpyu(t, 100, naiveaxpyu) }
+func BenchmarkLC128AxpyUnitary1000(t *testing.B)  { benchaxpyu(t, 1000, naiveaxpyu) }
+func BenchmarkLC128AxpyUnitary5000(t *testing.B)  { benchaxpyu(t, 5000, naiveaxpyu) }
+func BenchmarkLC128AxpyUnitary10000(t *testing.B) { benchaxpyu(t, 10000, naiveaxpyu) }
+func BenchmarkLC128AxpyUnitary50000(t *testing.B) { benchaxpyu(t, 50000, naiveaxpyu) }
+
+func benchaxpyut(t *testing.B, n int, f func(d []complex128, a complex128, x, y []complex128)) {
+	x, y, z := x[:n], y[:n], z[:n]
+	for i := 0; i < t.N; i++ {
+		f(z, a, x, y)
+	}
+}
+
+func naiveaxpyut(d []complex128, a complex128, x, y []complex128) {
+	for i, v := range x {
+		d[i] = y[i] + a*v
+	}
+}
+
+func BenchmarkC128AxpyUnitaryTo1(t *testing.B)     { benchaxpyut(t, 1, AxpyUnitaryTo) }
+func BenchmarkC128AxpyUnitaryTo2(t *testing.B)     { benchaxpyut(t, 2, AxpyUnitaryTo) }
+func BenchmarkC128AxpyUnitaryTo3(t *testing.B)     { benchaxpyut(t, 3, AxpyUnitaryTo) }
+func BenchmarkC128AxpyUnitaryTo4(t *testing.B)     { benchaxpyut(t, 4, AxpyUnitaryTo) }
+func BenchmarkC128AxpyUnitaryTo5(t *testing.B)     { benchaxpyut(t, 5, AxpyUnitaryTo) }
+func BenchmarkC128AxpyUnitaryTo10(t *testing.B)    { benchaxpyut(t, 10, AxpyUnitaryTo) }
+func BenchmarkC128AxpyUnitaryTo100(t *testing.B)   { benchaxpyut(t, 100, AxpyUnitaryTo) }
+func BenchmarkC128AxpyUnitaryTo1000(t *testing.B)  { benchaxpyut(t, 1000, AxpyUnitaryTo) }
+func BenchmarkC128AxpyUnitaryTo5000(t *testing.B)  { benchaxpyut(t, 5000, AxpyUnitaryTo) }
+func BenchmarkC128AxpyUnitaryTo10000(t *testing.B) { benchaxpyut(t, 10000, AxpyUnitaryTo) }
+func BenchmarkC128AxpyUnitaryTo50000(t *testing.B) { benchaxpyut(t, 50000, AxpyUnitaryTo) }
+
+func BenchmarkLC128AxpyUnitaryTo1(t *testing.B)     { benchaxpyut(t, 1, naiveaxpyut) }
+func BenchmarkLC128AxpyUnitaryTo2(t *testing.B)     { benchaxpyut(t, 2, naiveaxpyut) }
+func BenchmarkLC128AxpyUnitaryTo3(t *testing.B)     { benchaxpyut(t, 3, naiveaxpyut) }
+func BenchmarkLC128AxpyUnitaryTo4(t *testing.B)     { benchaxpyut(t, 4, naiveaxpyut) }
+func BenchmarkLC128AxpyUnitaryTo5(t *testing.B)     { benchaxpyut(t, 5, naiveaxpyut) }
+func BenchmarkLC128AxpyUnitaryTo10(t *testing.B)    { benchaxpyut(t, 10, naiveaxpyut) }
+func BenchmarkLC128AxpyUnitaryTo100(t *testing.B)   { benchaxpyut(t, 100, naiveaxpyut) }
+func BenchmarkLC128AxpyUnitaryTo1000(t *testing.B)  { benchaxpyut(t, 1000, naiveaxpyut) }
+func BenchmarkLC128AxpyUnitaryTo5000(t *testing.B)  { benchaxpyut(t, 5000, naiveaxpyut) }
+func BenchmarkLC128AxpyUnitaryTo10000(t *testing.B) { benchaxpyut(t, 10000, naiveaxpyut) }
+func BenchmarkLC128AxpyUnitaryTo50000(t *testing.B) { benchaxpyut(t, 50000, naiveaxpyut) }
+
+func benchaxpyinc(t *testing.B, ln, t_inc int, f func(alpha complex128, x, y []complex128, n, incX, incY, ix, iy uintptr)) {
+	n, inc := uintptr(ln), uintptr(t_inc)
+	var idx int
+	if t_inc < 0 {
+		idx = (-ln + 1) * t_inc
+	}
+	for i := 0; i < t.N; i++ {
+		f(1+1i, x, y, n, inc, inc, uintptr(idx), uintptr(idx))
+	}
+}
+
+func naiveaxpyinc(alpha complex128, x, y []complex128, n, incX, incY, ix, iy uintptr) {
+	for i := 0; i < int(n); i++ {
+		y[iy] += alpha * x[ix]
+		ix += incX
+		iy += incY
+	}
+}
+
+func BenchmarkC128AxpyIncN1Inc1(b *testing.B) { benchaxpyinc(b, 1, 1, AxpyInc) }
+
+func BenchmarkC128AxpyIncN2Inc1(b *testing.B)  { benchaxpyinc(b, 2, 1, AxpyInc) }
+func BenchmarkC128AxpyIncN2Inc2(b *testing.B)  { benchaxpyinc(b, 2, 2, AxpyInc) }
+func BenchmarkC128AxpyIncN2Inc4(b *testing.B)  { benchaxpyinc(b, 2, 4, AxpyInc) }
+func BenchmarkC128AxpyIncN2Inc10(b *testing.B) { benchaxpyinc(b, 2, 10, AxpyInc) }
+
+func BenchmarkC128AxpyIncN3Inc1(b *testing.B)  { benchaxpyinc(b, 3, 1, AxpyInc) }
+func BenchmarkC128AxpyIncN3Inc2(b *testing.B)  { benchaxpyinc(b, 3, 2, AxpyInc) }
+func BenchmarkC128AxpyIncN3Inc4(b *testing.B)  { benchaxpyinc(b, 3, 4, AxpyInc) }
+func BenchmarkC128AxpyIncN3Inc10(b *testing.B) { benchaxpyinc(b, 3, 10, AxpyInc) }
+
+func BenchmarkC128AxpyIncN4Inc1(b *testing.B)  { benchaxpyinc(b, 4, 1, AxpyInc) }
+func BenchmarkC128AxpyIncN4Inc2(b *testing.B)  { benchaxpyinc(b, 4, 2, AxpyInc) }
+func BenchmarkC128AxpyIncN4Inc4(b *testing.B)  { benchaxpyinc(b, 4, 4, AxpyInc) }
+func BenchmarkC128AxpyIncN4Inc10(b *testing.B) { benchaxpyinc(b, 4, 10, AxpyInc) }
+
+func BenchmarkC128AxpyIncN10Inc1(b *testing.B)  { benchaxpyinc(b, 10, 1, AxpyInc) }
+func BenchmarkC128AxpyIncN10Inc2(b *testing.B)  { benchaxpyinc(b, 10, 2, AxpyInc) }
+func BenchmarkC128AxpyIncN10Inc4(b *testing.B)  { benchaxpyinc(b, 10, 4, AxpyInc) }
+func BenchmarkC128AxpyIncN10Inc10(b *testing.B) { benchaxpyinc(b, 10, 10, AxpyInc) }
+
+func BenchmarkC128AxpyIncN1000Inc1(b *testing.B)  { benchaxpyinc(b, 1000, 1, AxpyInc) }
+func BenchmarkC128AxpyIncN1000Inc2(b *testing.B)  { benchaxpyinc(b, 1000, 2, AxpyInc) }
+func BenchmarkC128AxpyIncN1000Inc4(b *testing.B)  { benchaxpyinc(b, 1000, 4, AxpyInc) }
+func BenchmarkC128AxpyIncN1000Inc10(b *testing.B) { benchaxpyinc(b, 1000, 10, AxpyInc) }
+
+func BenchmarkC128AxpyIncN100000Inc1(b *testing.B)  { benchaxpyinc(b, 100000, 1, AxpyInc) }
+func BenchmarkC128AxpyIncN100000Inc2(b *testing.B)  { benchaxpyinc(b, 100000, 2, AxpyInc) }
+func BenchmarkC128AxpyIncN100000Inc4(b *testing.B)  { benchaxpyinc(b, 100000, 4, AxpyInc) }
+func BenchmarkC128AxpyIncN100000Inc10(b *testing.B) { benchaxpyinc(b, 100000, 10, AxpyInc) }
+
+func BenchmarkC128AxpyIncN100000IncM1(b *testing.B)  { benchaxpyinc(b, 100000, -1, AxpyInc) }
+func BenchmarkC128AxpyIncN100000IncM2(b *testing.B)  { benchaxpyinc(b, 100000, -2, AxpyInc) }
+func BenchmarkC128AxpyIncN100000IncM4(b *testing.B)  { benchaxpyinc(b, 100000, -4, AxpyInc) }
+func BenchmarkC128AxpyIncN100000IncM10(b *testing.B) { benchaxpyinc(b, 100000, -10, AxpyInc) }
+
+func BenchmarkLC128AxpyIncN1Inc1(b *testing.B) { benchaxpyinc(b, 1, 1, naiveaxpyinc) }
+
+func BenchmarkLC128AxpyIncN2Inc1(b *testing.B)  { benchaxpyinc(b, 2, 1, naiveaxpyinc) }
+func BenchmarkLC128AxpyIncN2Inc2(b *testing.B)  { benchaxpyinc(b, 2, 2, naiveaxpyinc) }
+func BenchmarkLC128AxpyIncN2Inc4(b *testing.B)  { benchaxpyinc(b, 2, 4, naiveaxpyinc) }
+func BenchmarkLC128AxpyIncN2Inc10(b *testing.B) { benchaxpyinc(b, 2, 10, naiveaxpyinc) }
+
+func BenchmarkLC128AxpyIncN3Inc1(b *testing.B)  { benchaxpyinc(b, 3, 1, naiveaxpyinc) }
+func BenchmarkLC128AxpyIncN3Inc2(b *testing.B)  { benchaxpyinc(b, 3, 2, naiveaxpyinc) }
+func BenchmarkLC128AxpyIncN3Inc4(b *testing.B)  { benchaxpyinc(b, 3, 4, naiveaxpyinc) }
+func BenchmarkLC128AxpyIncN3Inc10(b *testing.B) { benchaxpyinc(b, 3, 10, naiveaxpyinc) }
+
+func BenchmarkLC128AxpyIncN4Inc1(b *testing.B)  { benchaxpyinc(b, 4, 1, naiveaxpyinc) }
+func BenchmarkLC128AxpyIncN4Inc2(b *testing.B)  { benchaxpyinc(b, 4, 2, naiveaxpyinc) }
+func BenchmarkLC128AxpyIncN4Inc4(b *testing.B)  { benchaxpyinc(b, 4, 4, naiveaxpyinc) }
+func BenchmarkLC128AxpyIncN4Inc10(b *testing.B) { benchaxpyinc(b, 4, 10, naiveaxpyinc) }
+
+func BenchmarkLC128AxpyIncN10Inc1(b *testing.B)  { benchaxpyinc(b, 10, 1, naiveaxpyinc) }
+func BenchmarkLC128AxpyIncN10Inc2(b *testing.B)  { benchaxpyinc(b, 10, 2, naiveaxpyinc) }
+func BenchmarkLC128AxpyIncN10Inc4(b *testing.B)  { benchaxpyinc(b, 10, 4, naiveaxpyinc) }
+func BenchmarkLC128AxpyIncN10Inc10(b *testing.B) { benchaxpyinc(b, 10, 10, naiveaxpyinc) }
+
+func BenchmarkLC128AxpyIncN1000Inc1(b *testing.B)  { benchaxpyinc(b, 1000, 1, naiveaxpyinc) }
+func BenchmarkLC128AxpyIncN1000Inc2(b *testing.B)  { benchaxpyinc(b, 1000, 2, naiveaxpyinc) }
+func BenchmarkLC128AxpyIncN1000Inc4(b *testing.B)  { benchaxpyinc(b, 1000, 4, naiveaxpyinc) }
+func BenchmarkLC128AxpyIncN1000Inc10(b *testing.B) { benchaxpyinc(b, 1000, 10, naiveaxpyinc) }
+
+func BenchmarkLC128AxpyIncN100000Inc1(b *testing.B)  { benchaxpyinc(b, 100000, 1, naiveaxpyinc) }
+func BenchmarkLC128AxpyIncN100000Inc2(b *testing.B)  { benchaxpyinc(b, 100000, 2, naiveaxpyinc) }
+func BenchmarkLC128AxpyIncN100000Inc4(b *testing.B)  { benchaxpyinc(b, 100000, 4, naiveaxpyinc) }
+func BenchmarkLC128AxpyIncN100000Inc10(b *testing.B) { benchaxpyinc(b, 100000, 10, naiveaxpyinc) }
+
+func BenchmarkLC128AxpyIncN100000IncM1(b *testing.B)  { benchaxpyinc(b, 100000, -1, naiveaxpyinc) }
+func BenchmarkLC128AxpyIncN100000IncM2(b *testing.B)  { benchaxpyinc(b, 100000, -2, naiveaxpyinc) }
+func BenchmarkLC128AxpyIncN100000IncM4(b *testing.B)  { benchaxpyinc(b, 100000, -4, naiveaxpyinc) }
+func BenchmarkLC128AxpyIncN100000IncM10(b *testing.B) { benchaxpyinc(b, 100000, -10, naiveaxpyinc) }
+
+func benchaxpyincto(t *testing.B, ln, t_inc int, f func(dst []complex128, incDst, idst uintptr, alpha complex128, x, y []complex128, n, incX, incY, ix, iy uintptr)) {
+	n, inc := uintptr(ln), uintptr(t_inc)
+	var idx int
+	if t_inc < 0 {
+		idx = (-ln + 1) * t_inc
+	}
+	for i := 0; i < t.N; i++ {
+		f(z, inc, uintptr(idx), 1+1i, x, y, n, inc, inc, uintptr(idx), uintptr(idx))
+	}
+}
+
+func naiveaxpyincto(dst []complex128, incDst, idst uintptr, alpha complex128, x, y []complex128, n, incX, incY, ix, iy uintptr) {
+	for i := 0; i < int(n); i++ {
+		dst[idst] = alpha*x[ix] + y[iy]
+		ix += incX
+		iy += incY
+		idst += incDst
+	}
+}
+
+func BenchmarkC128AxpyIncToN1Inc1(b *testing.B) { benchaxpyincto(b, 1, 1, AxpyIncTo) }
+
+func BenchmarkC128AxpyIncToN2Inc1(b *testing.B)  { benchaxpyincto(b, 2, 1, AxpyIncTo) }
+func BenchmarkC128AxpyIncToN2Inc2(b *testing.B)  { benchaxpyincto(b, 2, 2, AxpyIncTo) }
+func BenchmarkC128AxpyIncToN2Inc4(b *testing.B)  { benchaxpyincto(b, 2, 4, AxpyIncTo) }
+func BenchmarkC128AxpyIncToN2Inc10(b *testing.B) { benchaxpyincto(b, 2, 10, AxpyIncTo) }
+
+func BenchmarkC128AxpyIncToN3Inc1(b *testing.B)  { benchaxpyincto(b, 3, 1, AxpyIncTo) }
+func BenchmarkC128AxpyIncToN3Inc2(b *testing.B)  { benchaxpyincto(b, 3, 2, AxpyIncTo) }
+func BenchmarkC128AxpyIncToN3Inc4(b *testing.B)  { benchaxpyincto(b, 3, 4, AxpyIncTo) }
+func BenchmarkC128AxpyIncToN3Inc10(b *testing.B) { benchaxpyincto(b, 3, 10, AxpyIncTo) }
+
+func BenchmarkC128AxpyIncToN4Inc1(b *testing.B)  { benchaxpyincto(b, 4, 1, AxpyIncTo) }
+func BenchmarkC128AxpyIncToN4Inc2(b *testing.B)  { benchaxpyincto(b, 4, 2, AxpyIncTo) }
+func BenchmarkC128AxpyIncToN4Inc4(b *testing.B)  { benchaxpyincto(b, 4, 4, AxpyIncTo) }
+func BenchmarkC128AxpyIncToN4Inc10(b *testing.B) { benchaxpyincto(b, 4, 10, AxpyIncTo) }
+
+func BenchmarkC128AxpyIncToN10Inc1(b *testing.B)  { benchaxpyincto(b, 10, 1, AxpyIncTo) }
+func BenchmarkC128AxpyIncToN10Inc2(b *testing.B)  { benchaxpyincto(b, 10, 2, AxpyIncTo) }
+func BenchmarkC128AxpyIncToN10Inc4(b *testing.B)  { benchaxpyincto(b, 10, 4, AxpyIncTo) }
+func BenchmarkC128AxpyIncToN10Inc10(b *testing.B) { benchaxpyincto(b, 10, 10, AxpyIncTo) }
+
+func BenchmarkC128AxpyIncToN1000Inc1(b *testing.B)  { benchaxpyincto(b, 1000, 1, AxpyIncTo) }
+func BenchmarkC128AxpyIncToN1000Inc2(b *testing.B)  { benchaxpyincto(b, 1000, 2, AxpyIncTo) }
+func BenchmarkC128AxpyIncToN1000Inc4(b *testing.B)  { benchaxpyincto(b, 1000, 4, AxpyIncTo) }
+func BenchmarkC128AxpyIncToN1000Inc10(b *testing.B) { benchaxpyincto(b, 1000, 10, AxpyIncTo) }
+
+func BenchmarkC128AxpyIncToN100000Inc1(b *testing.B)  { benchaxpyincto(b, 100000, 1, AxpyIncTo) }
+func BenchmarkC128AxpyIncToN100000Inc2(b *testing.B)  { benchaxpyincto(b, 100000, 2, AxpyIncTo) }
+func BenchmarkC128AxpyIncToN100000Inc4(b *testing.B)  { benchaxpyincto(b, 100000, 4, AxpyIncTo) }
+func BenchmarkC128AxpyIncToN100000Inc10(b *testing.B) { benchaxpyincto(b, 100000, 10, AxpyIncTo) }
+
+func BenchmarkC128AxpyIncToN100000IncM1(b *testing.B)  { benchaxpyincto(b, 100000, -1, AxpyIncTo) }
+func BenchmarkC128AxpyIncToN100000IncM2(b *testing.B)  { benchaxpyincto(b, 100000, -2, AxpyIncTo) }
+func BenchmarkC128AxpyIncToN100000IncM4(b *testing.B)  { benchaxpyincto(b, 100000, -4, AxpyIncTo) }
+func BenchmarkC128AxpyIncToN100000IncM10(b *testing.B) { benchaxpyincto(b, 100000, -10, AxpyIncTo) }
+
+func BenchmarkLC128AxpyIncToN1Inc1(b *testing.B) { benchaxpyincto(b, 1, 1, naiveaxpyincto) }
+
+func BenchmarkLC128AxpyIncToN2Inc1(b *testing.B)  { benchaxpyincto(b, 2, 1, naiveaxpyincto) }
+func BenchmarkLC128AxpyIncToN2Inc2(b *testing.B)  { benchaxpyincto(b, 2, 2, naiveaxpyincto) }
+func BenchmarkLC128AxpyIncToN2Inc4(b *testing.B)  { benchaxpyincto(b, 2, 4, naiveaxpyincto) }
+func BenchmarkLC128AxpyIncToN2Inc10(b *testing.B) { benchaxpyincto(b, 2, 10, naiveaxpyincto) }
+
+func BenchmarkLC128AxpyIncToN3Inc1(b *testing.B)  { benchaxpyincto(b, 3, 1, naiveaxpyincto) }
+func BenchmarkLC128AxpyIncToN3Inc2(b *testing.B)  { benchaxpyincto(b, 3, 2, naiveaxpyincto) }
+func BenchmarkLC128AxpyIncToN3Inc4(b *testing.B)  { benchaxpyincto(b, 3, 4, naiveaxpyincto) }
+func BenchmarkLC128AxpyIncToN3Inc10(b *testing.B) { benchaxpyincto(b, 3, 10, naiveaxpyincto) }
+
+func BenchmarkLC128AxpyIncToN4Inc1(b *testing.B)  { benchaxpyincto(b, 4, 1, naiveaxpyincto) }
+func BenchmarkLC128AxpyIncToN4Inc2(b *testing.B)  { benchaxpyincto(b, 4, 2, naiveaxpyincto) }
+func BenchmarkLC128AxpyIncToN4Inc4(b *testing.B)  { benchaxpyincto(b, 4, 4, naiveaxpyincto) }
+func BenchmarkLC128AxpyIncToN4Inc10(b *testing.B) { benchaxpyincto(b, 4, 10, naiveaxpyincto) }
+
+func BenchmarkLC128AxpyIncToN10Inc1(b *testing.B)  { benchaxpyincto(b, 10, 1, naiveaxpyincto) }
+func BenchmarkLC128AxpyIncToN10Inc2(b *testing.B)  { benchaxpyincto(b, 10, 2, naiveaxpyincto) }
+func BenchmarkLC128AxpyIncToN10Inc4(b *testing.B)  { benchaxpyincto(b, 10, 4, naiveaxpyincto) }
+func BenchmarkLC128AxpyIncToN10Inc10(b *testing.B) { benchaxpyincto(b, 10, 10, naiveaxpyincto) }
+
+func BenchmarkLC128AxpyIncToN1000Inc1(b *testing.B)  { benchaxpyincto(b, 1000, 1, naiveaxpyincto) }
+func BenchmarkLC128AxpyIncToN1000Inc2(b *testing.B)  { benchaxpyincto(b, 1000, 2, naiveaxpyincto) }
+func BenchmarkLC128AxpyIncToN1000Inc4(b *testing.B)  { benchaxpyincto(b, 1000, 4, naiveaxpyincto) }
+func BenchmarkLC128AxpyIncToN1000Inc10(b *testing.B) { benchaxpyincto(b, 1000, 10, naiveaxpyincto) }
+
+func BenchmarkLC128AxpyIncToN100000Inc1(b *testing.B)  { benchaxpyincto(b, 100000, 1, naiveaxpyincto) }
+func BenchmarkLC128AxpyIncToN100000Inc2(b *testing.B)  { benchaxpyincto(b, 100000, 2, naiveaxpyincto) }
+func BenchmarkLC128AxpyIncToN100000Inc4(b *testing.B)  { benchaxpyincto(b, 100000, 4, naiveaxpyincto) }
+func BenchmarkLC128AxpyIncToN100000Inc10(b *testing.B) { benchaxpyincto(b, 100000, 10, naiveaxpyincto) }
+
+func BenchmarkLC128AxpyIncToN100000IncM1(b *testing.B) { benchaxpyincto(b, 100000, -1, naiveaxpyincto) }
+func BenchmarkLC128AxpyIncToN100000IncM2(b *testing.B) { benchaxpyincto(b, 100000, -2, naiveaxpyincto) }
+func BenchmarkLC128AxpyIncToN100000IncM4(b *testing.B) { benchaxpyincto(b, 100000, -4, naiveaxpyincto) }
+func BenchmarkLC128AxpyIncToN100000IncM10(b *testing.B) {
+	benchaxpyincto(b, 100000, -10, naiveaxpyincto)
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c128/doc.go b/vendor/gonum.org/v1/gonum/internal/asm/c128/doc.go
new file mode 100644
index 00000000..3a77db39
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c128/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package c128 provides complex128 vector primitives.
+package c128 // import "gonum.org/v1/gonum/internal/asm/c128"
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c128/dotc.go b/vendor/gonum.org/v1/gonum/internal/asm/c128/dotc.go
new file mode 100644
index 00000000..a852f0d2
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c128/dotc.go
@@ -0,0 +1,35 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package c128
+
+import "math/cmplx"
+
+// DotcUnitary is
+//  for i, v := range x {
+//  	sum += y[i] * cmplx.Conj(v)
+//  }
+//  return sum
+func DotcUnitary(x, y []complex128) (sum complex128) {
+	for i, v := range x {
+		sum += y[i] * cmplx.Conj(v)
+	}
+	return sum
+}
+
+// DotcInc is
+//  for i := 0; i < int(n); i++ {
+//  	sum += y[iy] * cmplx.Conj(x[ix])
+//  	ix += incX
+//  	iy += incY
+//  }
+//  return sum
+func DotcInc(x, y []complex128, n, incX, incY, ix, iy uintptr) (sum complex128) {
+	for i := 0; i < int(n); i++ {
+		sum += y[iy] * cmplx.Conj(x[ix])
+		ix += incX
+		iy += incY
+	}
+	return sum
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c128/dotu.go b/vendor/gonum.org/v1/gonum/internal/asm/c128/dotu.go
new file mode 100644
index 00000000..d82dc467
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c128/dotu.go
@@ -0,0 +1,33 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package c128
+
+// DotuUnitary is
+//  for i, v := range x {
+//  	sum += y[i] * v
+//  }
+//  return sum
+func DotuUnitary(x, y []complex128) (sum complex128) {
+	for i, v := range x {
+		sum += y[i] * v
+	}
+	return sum
+}
+
+// DotuInc is
+//  for i := 0; i < int(n); i++ {
+//  	sum += y[iy] * x[ix]
+//  	ix += incX
+//  	iy += incY
+//  }
+//  return sum
+func DotuInc(x, y []complex128, n, incX, incY, ix, iy uintptr) (sum complex128) {
+	for i := 0; i < int(n); i++ {
+		sum += y[iy] * x[ix]
+		ix += incX
+		iy += incY
+	}
+	return sum
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c128/dscalinc_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/c128/dscalinc_amd64.s
new file mode 100644
index 00000000..778e2fab
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c128/dscalinc_amd64.s
@@ -0,0 +1,69 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !noasm,!appengine
+
+#include "textflag.h"
+
+#define SRC SI
+#define DST SI
+#define LEN CX
+#define TAIL BX
+#define INC R9
+#define INC3 R10
+#define ALPHA X0
+#define ALPHA_2 X1
+
+#define MOVDDUP_ALPHA    LONG $0x44120FF2; WORD $0x0824 // MOVDDUP 8(SP), X0
+
+// func DscalInc(alpha float64, x []complex128, n, inc uintptr)
+TEXT ·DscalInc(SB), NOSPLIT, $0
+	MOVQ x_base+8(FP), SRC // SRC = &x
+	MOVQ n+32(FP), LEN     // LEN = n
+	CMPQ LEN, $0           // if LEN == 0 { return }
+	JE   dscal_end
+
+	MOVDDUP_ALPHA             // ALPHA = alpha
+	MOVQ   inc+40(FP), INC    // INC = inc
+	SHLQ   $4, INC            // INC = INC * sizeof(complex128)
+	LEAQ   (INC)(INC*2), INC3 // INC3 = 3 * INC
+	MOVUPS ALPHA, ALPHA_2     // Copy ALPHA and ALPHA_2 for pipelining
+	MOVQ   LEN, TAIL          // TAIL = LEN
+	SHRQ   $2, LEN            // LEN = floor( n / 4 )
+	JZ     dscal_tail         // if LEN == 0 { goto dscal_tail }
+
+dscal_loop: // do {
+	MOVUPS (SRC), X2         // X_i = x[i]
+	MOVUPS (SRC)(INC*1), X3
+	MOVUPS (SRC)(INC*2), X4
+	MOVUPS (SRC)(INC3*1), X5
+
+	MULPD ALPHA, X2   // X_i *= ALPHA
+	MULPD ALPHA_2, X3
+	MULPD ALPHA, X4
+	MULPD ALPHA_2, X5
+
+	MOVUPS X2, (DST)         // x[i] = X_i
+	MOVUPS X3, (DST)(INC*1)
+	MOVUPS X4, (DST)(INC*2)
+	MOVUPS X5, (DST)(INC3*1)
+
+	LEAQ (SRC)(INC*4), SRC // SRC += INC*4
+	DECQ LEN
+	JNZ  dscal_loop        // } while --LEN > 0
+
+dscal_tail:
+	ANDQ $3, TAIL  // TAIL = TAIL % 4
+	JE   dscal_end // if TAIL == 0 { return }
+
+dscal_tail_loop: // do {
+	MOVUPS (SRC), X2       // X_i = x[i]
+	MULPD  ALPHA, X2       // X_i *= ALPHA
+	MOVUPS X2, (DST)       // x[i] = X_i
+	ADDQ   INC, SRC        // SRC += INC
+	DECQ   TAIL
+	JNZ    dscal_tail_loop // } while --TAIL > 0
+
+dscal_end:
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c128/dscalunitary_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/c128/dscalunitary_amd64.s
new file mode 100644
index 00000000..32ef1546
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c128/dscalunitary_amd64.s
@@ -0,0 +1,66 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !noasm,!appengine
+
+#include "textflag.h"
+
+#define SRC SI
+#define DST SI
+#define LEN CX
+#define IDX AX
+#define TAIL BX
+#define ALPHA X0
+#define ALPHA_2 X1
+
+#define MOVDDUP_ALPHA    LONG $0x44120FF2; WORD $0x0824 // MOVDDUP 8(SP), X0
+
+// func DscalUnitary(alpha float64, x []complex128)
+TEXT ·DscalUnitary(SB), NOSPLIT, $0
+	MOVQ x_base+8(FP), SRC // SRC = &x
+	MOVQ x_len+16(FP), LEN // LEN = len(x)
+	CMPQ LEN, $0           // if LEN == 0 { return }
+	JE   dscal_end
+
+	MOVDDUP_ALPHA         // ALPHA = alpha
+	XORQ   IDX, IDX       // IDX = 0
+	MOVUPS ALPHA, ALPHA_2 // Copy ALPHA to ALPHA_2 for pipelining
+	MOVQ   LEN, TAIL      // TAIL = LEN
+	SHRQ   $2, LEN        // LEN = floor( n / 4 )
+	JZ     dscal_tail     // if LEN == 0 { goto dscal_tail }
+
+dscal_loop: // do {
+	MOVUPS (SRC)(IDX*8), X2   // X_i = x[i]
+	MOVUPS 16(SRC)(IDX*8), X3
+	MOVUPS 32(SRC)(IDX*8), X4
+	MOVUPS 48(SRC)(IDX*8), X5
+
+	MULPD ALPHA, X2   // X_i *= ALPHA
+	MULPD ALPHA_2, X3
+	MULPD ALPHA, X4
+	MULPD ALPHA_2, X5
+
+	MOVUPS X2, (DST)(IDX*8)   // x[i] = X_i
+	MOVUPS X3, 16(DST)(IDX*8)
+	MOVUPS X4, 32(DST)(IDX*8)
+	MOVUPS X5, 48(DST)(IDX*8)
+
+	ADDQ $8, IDX    // IDX += 8
+	DECQ LEN
+	JNZ  dscal_loop // } while --LEN > 0
+
+dscal_tail:
+	ANDQ $3, TAIL  // TAIL = TAIL % 4
+	JZ   dscal_end // if TAIL == 0 { return }
+
+dscal_tail_loop: // do {
+	MOVUPS (SRC)(IDX*8), X2 // X_i = x[i]
+	MULPD  ALPHA, X2        // X_i *= ALPHA
+	MOVUPS X2, (DST)(IDX*8) // x[i] = X_i
+	ADDQ   $2, IDX          // IDX += 2
+	DECQ   TAIL
+	JNZ    dscal_tail_loop  // } while --TAIL > 0
+
+dscal_end:
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c128/scal.go b/vendor/gonum.org/v1/gonum/internal/asm/c128/scal.go
new file mode 100644
index 00000000..580b4d8d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c128/scal.go
@@ -0,0 +1,31 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package c128
+
+// ScalUnitaryTo is
+//  for i, v := range x {
+//  	dst[i] = alpha * v
+//  }
+func ScalUnitaryTo(dst []complex128, alpha complex128, x []complex128) {
+	for i, v := range x {
+		dst[i] = alpha * v
+	}
+}
+
+// ScalIncTo is
+//  var idst, ix uintptr
+//  for i := 0; i < int(n); i++ {
+//  	dst[idst] = alpha * x[ix]
+//  	ix += incX
+//  	idst += incDst
+//  }
+func ScalIncTo(dst []complex128, incDst uintptr, alpha complex128, x []complex128, n, incX uintptr) {
+	var idst, ix uintptr
+	for i := 0; i < int(n); i++ {
+		dst[idst] = alpha * x[ix]
+		ix += incX
+		idst += incDst
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c128/scalUnitary_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/c128/scalUnitary_amd64.s
new file mode 100644
index 00000000..22152a0e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c128/scalUnitary_amd64.s
@@ -0,0 +1,116 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !noasm,!appengine
+
+#include "textflag.h"
+
+#define SRC SI
+#define DST SI
+#define LEN CX
+#define IDX AX
+#define TAIL BX
+#define ALPHA X0
+#define ALPHA_C X1
+#define ALPHA2 X10
+#define ALPHA_C2 X11
+
+#define MOVDDUP_X2_X3    LONG $0xDA120FF2 // MOVDDUP X2, X3
+#define MOVDDUP_X4_X5    LONG $0xEC120FF2 // MOVDDUP X4, X5
+#define MOVDDUP_X6_X7    LONG $0xFE120FF2 // MOVDDUP X6, X7
+#define MOVDDUP_X8_X9    LONG $0x120F45F2; BYTE $0xC8 // MOVDDUP X8, X9
+
+#define ADDSUBPD_X2_X3    LONG $0xDAD00F66 // ADDSUBPD X2, X3
+#define ADDSUBPD_X4_X5    LONG $0xECD00F66 // ADDSUBPD X4, X5
+#define ADDSUBPD_X6_X7    LONG $0xFED00F66 // ADDSUBPD X6, X7
+#define ADDSUBPD_X8_X9    LONG $0xD00F4566; BYTE $0xC8 // ADDSUBPD X8, X9
+
+// func ScalUnitary(alpha complex128, x []complex128)
+TEXT ·ScalUnitary(SB), NOSPLIT, $0
+	MOVQ x_base+16(FP), SRC // SRC = &x
+	MOVQ x_len+24(FP), LEN  // LEN = len(x)
+	CMPQ LEN, $0            // if LEN == 0 { return }
+	JE   scal_end
+
+	MOVUPS alpha+0(FP), ALPHA     // ALPHA = { imag(alpha), real(alpha) }
+	MOVAPS ALPHA, ALPHA_C
+	SHUFPD $0x1, ALPHA_C, ALPHA_C // ALPHA_C = { real(alpha), imag(alpha) }
+
+	XORQ   IDX, IDX          // IDX = 0
+	MOVAPS ALPHA, ALPHA2     // Copy ALPHA and ALPHA_C for pipelining
+	MOVAPS ALPHA_C, ALPHA_C2
+	MOVQ   LEN, TAIL
+	SHRQ   $2, LEN           // LEN = floor( n / 4 )
+	JZ     scal_tail         // if BX == 0 { goto scal_tail }
+
+scal_loop: // do {
+	MOVUPS (SRC)(IDX*8), X2   // X_i = { imag(x[i]), real(x[i]) }
+	MOVUPS 16(SRC)(IDX*8), X4
+	MOVUPS 32(SRC)(IDX*8), X6
+	MOVUPS 48(SRC)(IDX*8), X8
+
+	// X_(i+1) = { real(x[i], real(x[i]) }
+	MOVDDUP_X2_X3
+	MOVDDUP_X4_X5
+	MOVDDUP_X6_X7
+	MOVDDUP_X8_X9
+
+	// X_i = { imag(x[i]), imag(x[i]) }
+	SHUFPD $0x3, X2, X2
+	SHUFPD $0x3, X4, X4
+	SHUFPD $0x3, X6, X6
+	SHUFPD $0x3, X8, X8
+
+	// X_i     = { real(ALPHA) * imag(x[i]), imag(ALPHA) * imag(x[i])  }
+	// X_(i+1) = { imag(ALPHA) * real(x[i]), real(ALPHA) * real(x[i])  }
+	MULPD ALPHA_C, X2
+	MULPD ALPHA, X3
+	MULPD ALPHA_C2, X4
+	MULPD ALPHA2, X5
+	MULPD ALPHA_C, X6
+	MULPD ALPHA, X7
+	MULPD ALPHA_C2, X8
+	MULPD ALPHA2, X9
+
+	// X_(i+1) = {
+	//	imag(result[i]):  imag(ALPHA)*real(x[i]) + real(ALPHA)*imag(x[i]),
+	//	real(result[i]):  real(ALPHA)*real(x[i]) - imag(ALPHA)*imag(x[i])
+	//  }
+	ADDSUBPD_X2_X3
+	ADDSUBPD_X4_X5
+	ADDSUBPD_X6_X7
+	ADDSUBPD_X8_X9
+
+	MOVUPS X3, (DST)(IDX*8)   // x[i] = X_(i+1)
+	MOVUPS X5, 16(DST)(IDX*8)
+	MOVUPS X7, 32(DST)(IDX*8)
+	MOVUPS X9, 48(DST)(IDX*8)
+	ADDQ   $8, IDX            // IDX += 8
+	DECQ   LEN
+	JNZ    scal_loop          // } while --LEN > 0
+
+scal_tail:
+	ANDQ $3, TAIL // TAIL = TAIL % 4
+	JZ   scal_end // if TAIL == 0 { return }
+
+scal_tail_loop: // do {
+	MOVUPS (SRC)(IDX*8), X2 // X_i = { imag(x[i]), real(x[i]) }
+	MOVDDUP_X2_X3           // X_(i+1) = { real(x[i], real(x[i]) }
+	SHUFPD $0x3, X2, X2     // X_i = { imag(x[i]), imag(x[i]) }
+	MULPD  ALPHA_C, X2      // X_i     = { real(ALPHA) * imag(x[i]), imag(ALPHA) * imag(x[i])  }
+	MULPD  ALPHA, X3        // X_(i+1) = { imag(ALPHA) * real(x[i]), real(ALPHA) * real(x[i])  }
+
+	// X_(i+1) = {
+	//	imag(result[i]):  imag(ALPHA)*real(x[i]) + real(ALPHA)*imag(x[i]),
+	//	real(result[i]):  real(ALPHA)*real(x[i]) - imag(ALPHA)*imag(x[i])
+	//  }
+	ADDSUBPD_X2_X3
+
+	MOVUPS X3, (DST)(IDX*8) // x[i] = X_(i+1)
+	ADDQ   $2, IDX          // IDX += 2
+	DECQ   TAIL
+	JNZ    scal_tail_loop   // }  while --LEN > 0
+
+scal_end:
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c128/scalinc_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/c128/scalinc_amd64.s
new file mode 100644
index 00000000..ec0f1528
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c128/scalinc_amd64.s
@@ -0,0 +1,121 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !noasm,!appengine
+
+#include "textflag.h"
+
+#define SRC SI
+#define DST SI
+#define LEN CX
+#define TAIL BX
+#define INC R9
+#define INC3 R10
+#define ALPHA X0
+#define ALPHA_C X1
+#define ALPHA2 X10
+#define ALPHA_C2 X11
+
+#define MOVDDUP_X2_X3    LONG $0xDA120FF2 // MOVDDUP X2, X3
+#define MOVDDUP_X4_X5    LONG $0xEC120FF2 // MOVDDUP X4, X5
+#define MOVDDUP_X6_X7    LONG $0xFE120FF2 // MOVDDUP X6, X7
+#define MOVDDUP_X8_X9    LONG $0x120F45F2; BYTE $0xC8 // MOVDDUP X8, X9
+
+#define ADDSUBPD_X2_X3    LONG $0xDAD00F66 // ADDSUBPD X2, X3
+#define ADDSUBPD_X4_X5    LONG $0xECD00F66 // ADDSUBPD X4, X5
+#define ADDSUBPD_X6_X7    LONG $0xFED00F66 // ADDSUBPD X6, X7
+#define ADDSUBPD_X8_X9    LONG $0xD00F4566; BYTE $0xC8 // ADDSUBPD X8, X9
+
+// func ScalInc(alpha complex128, x []complex128, n, inc uintptr)
+TEXT ·ScalInc(SB), NOSPLIT, $0
+	MOVQ x_base+16(FP), SRC // SRC = &x
+	MOVQ n+40(FP), LEN      // LEN = len(x)
+	CMPQ LEN, $0
+	JE   scal_end           // if LEN == 0 { return }
+
+	MOVQ inc+48(FP), INC    // INC = inc
+	SHLQ $4, INC            // INC = INC * sizeof(complex128)
+	LEAQ (INC)(INC*2), INC3 // INC3 = 3 * INC
+
+	MOVUPS alpha+0(FP), ALPHA     // ALPHA = { imag(alpha), real(alpha) }
+	MOVAPS ALPHA, ALPHA_C
+	SHUFPD $0x1, ALPHA_C, ALPHA_C // ALPHA_C = { real(alpha), imag(alpha) }
+
+	MOVAPS ALPHA, ALPHA2     // Copy ALPHA and ALPHA_C for pipelining
+	MOVAPS ALPHA_C, ALPHA_C2
+	MOVQ   LEN, TAIL
+	SHRQ   $2, LEN           // LEN = floor( n / 4 )
+	JZ     scal_tail         // if BX == 0 { goto scal_tail }
+
+scal_loop: // do {
+	MOVUPS (SRC), X2         // X_i = { imag(x[i]), real(x[i]) }
+	MOVUPS (SRC)(INC*1), X4
+	MOVUPS (SRC)(INC*2), X6
+	MOVUPS (SRC)(INC3*1), X8
+
+	// X_(i+1) = { real(x[i], real(x[i]) }
+	MOVDDUP_X2_X3
+	MOVDDUP_X4_X5
+	MOVDDUP_X6_X7
+	MOVDDUP_X8_X9
+
+	// X_i = { imag(x[i]), imag(x[i]) }
+	SHUFPD $0x3, X2, X2
+	SHUFPD $0x3, X4, X4
+	SHUFPD $0x3, X6, X6
+	SHUFPD $0x3, X8, X8
+
+	// X_i     = { real(ALPHA) * imag(x[i]), imag(ALPHA) * imag(x[i])  }
+	// X_(i+1) = { imag(ALPHA) * real(x[i]), real(ALPHA) * real(x[i])  }
+	MULPD ALPHA_C, X2
+	MULPD ALPHA, X3
+	MULPD ALPHA_C2, X4
+	MULPD ALPHA2, X5
+	MULPD ALPHA_C, X6
+	MULPD ALPHA, X7
+	MULPD ALPHA_C2, X8
+	MULPD ALPHA2, X9
+
+	// X_(i+1) = {
+	//	imag(result[i]):  imag(ALPHA)*real(x[i]) + real(ALPHA)*imag(x[i]),
+	//	real(result[i]):  real(ALPHA)*real(x[i]) - imag(ALPHA)*imag(x[i])
+	//  }
+	ADDSUBPD_X2_X3
+	ADDSUBPD_X4_X5
+	ADDSUBPD_X6_X7
+	ADDSUBPD_X8_X9
+
+	MOVUPS X3, (DST)         // x[i] = X_(i+1)
+	MOVUPS X5, (DST)(INC*1)
+	MOVUPS X7, (DST)(INC*2)
+	MOVUPS X9, (DST)(INC3*1)
+
+	LEAQ (SRC)(INC*4), SRC // SRC = &(SRC[inc*4])
+	DECQ LEN
+	JNZ  scal_loop         // } while --BX > 0
+
+scal_tail:
+	ANDQ $3, TAIL // TAIL = TAIL % 4
+	JE   scal_end // if TAIL == 0 { return }
+
+scal_tail_loop: // do {
+	MOVUPS (SRC), X2    // X_i = { imag(x[i]), real(x[i]) }
+	MOVDDUP_X2_X3       // X_(i+1) = { real(x[i], real(x[i]) }
+	SHUFPD $0x3, X2, X2 // X_i = { imag(x[i]), imag(x[i]) }
+	MULPD  ALPHA_C, X2  // X_i     = { real(ALPHA) * imag(x[i]), imag(ALPHA) * imag(x[i])  }
+	MULPD  ALPHA, X3    // X_(i+1) = { imag(ALPHA) * real(x[i]), real(ALPHA) * real(x[i])  }
+
+	// X_(i+1) = {
+	//	imag(result[i]):  imag(ALPHA)*real(x[i]) + real(ALPHA)*imag(x[i]),
+	//	real(result[i]):  real(ALPHA)*real(x[i]) - imag(ALPHA)*imag(x[i])
+	//  }
+	ADDSUBPD_X2_X3
+
+	MOVUPS X3, (DST)      // x[i] = X_i
+	ADDQ   INC, SRC       // SRC = &(SRC[incX])
+	DECQ   TAIL
+	JNZ    scal_tail_loop // } while --TAIL > 0
+
+scal_end:
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c128/stubs_amd64.go b/vendor/gonum.org/v1/gonum/internal/asm/c128/stubs_amd64.go
new file mode 100644
index 00000000..f3494a78
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c128/stubs_amd64.go
@@ -0,0 +1,64 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !noasm,!appengine
+
+package c128
+
+// AxpyUnitary is
+//  for i, v := range x {
+//  	y[i] += alpha * v
+//  }
+func AxpyUnitary(alpha complex128, x, y []complex128)
+
+// AxpyUnitaryTo is
+//  for i, v := range x {
+//  	dst[i] = alpha*v + y[i]
+//  }
+func AxpyUnitaryTo(dst []complex128, alpha complex128, x, y []complex128)
+
+// AxpyInc is
+//  for i := 0; i < int(n); i++ {
+//  	y[iy] += alpha * x[ix]
+//  	ix += incX
+//  	iy += incY
+//  }
+func AxpyInc(alpha complex128, x, y []complex128, n, incX, incY, ix, iy uintptr)
+
+// AxpyIncTo is
+//  for i := 0; i < int(n); i++ {
+//  	dst[idst] = alpha*x[ix] + y[iy]
+//  	ix += incX
+//  	iy += incY
+//  	idst += incDst
+//  }
+func AxpyIncTo(dst []complex128, incDst, idst uintptr, alpha complex128, x, y []complex128, n, incX, incY, ix, iy uintptr)
+
+// DscalUnitary is
+//  for i, v := range x {
+//  	x[i] = complex(real(v)*alpha, imag(v)*alpha)
+//  }
+func DscalUnitary(alpha float64, x []complex128)
+
+// DscalInc is
+//  var ix uintptr
+//  for i := 0; i < int(n); i++ {
+//  	x[ix] = complex(real(x[ix])*alpha, imag(x[ix])*alpha)
+//  	ix += inc
+//  }
+func DscalInc(alpha float64, x []complex128, n, inc uintptr)
+
+// ScalInc is
+//  var ix uintptr
+//  for i := 0; i < int(n); i++ {
+//  	x[ix] *= alpha
+//  	ix += incX
+//  }
+func ScalInc(alpha complex128, x []complex128, n, inc uintptr)
+
+// ScalUnitary is
+//  for i := range x {
+//  	x[i] *= alpha
+//  }
+func ScalUnitary(alpha complex128, x []complex128)
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c128/stubs_noasm.go b/vendor/gonum.org/v1/gonum/internal/asm/c128/stubs_noasm.go
new file mode 100644
index 00000000..008a1e6a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c128/stubs_noasm.go
@@ -0,0 +1,105 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !amd64 noasm appengine
+
+package c128
+
+// AxpyUnitary is
+//  for i, v := range x {
+//  	y[i] += alpha * v
+//  }
+func AxpyUnitary(alpha complex128, x, y []complex128) {
+	for i, v := range x {
+		y[i] += alpha * v
+	}
+}
+
+// AxpyUnitaryTo is
+//  for i, v := range x {
+//  	dst[i] = alpha*v + y[i]
+//  }
+func AxpyUnitaryTo(dst []complex128, alpha complex128, x, y []complex128) {
+	for i, v := range x {
+		dst[i] = alpha*v + y[i]
+	}
+}
+
+// AxpyInc is
+//  for i := 0; i < int(n); i++ {
+//  	y[iy] += alpha * x[ix]
+//  	ix += incX
+//  	iy += incY
+//  }
+func AxpyInc(alpha complex128, x, y []complex128, n, incX, incY, ix, iy uintptr) {
+	for i := 0; i < int(n); i++ {
+		y[iy] += alpha * x[ix]
+		ix += incX
+		iy += incY
+	}
+}
+
+// AxpyIncTo is
+//  for i := 0; i < int(n); i++ {
+//  	dst[idst] = alpha*x[ix] + y[iy]
+//  	ix += incX
+//  	iy += incY
+//  	idst += incDst
+//  }
+func AxpyIncTo(dst []complex128, incDst, idst uintptr, alpha complex128, x, y []complex128, n, incX, incY, ix, iy uintptr) {
+	for i := 0; i < int(n); i++ {
+		dst[idst] = alpha*x[ix] + y[iy]
+		ix += incX
+		iy += incY
+		idst += incDst
+	}
+}
+
+// DscalUnitary is
+//  for i, v := range x {
+//  	x[i] = complex(real(v)*alpha, imag(v)*alpha)
+//  }
+func DscalUnitary(alpha float64, x []complex128) {
+	for i, v := range x {
+		x[i] = complex(real(v)*alpha, imag(v)*alpha)
+	}
+}
+
+// DscalInc is
+//  var ix uintptr
+//  for i := 0; i < int(n); i++ {
+//  	x[ix] = complex(real(x[ix])*alpha, imag(x[ix])*alpha)
+//  	ix += inc
+//  }
+func DscalInc(alpha float64, x []complex128, n, inc uintptr) {
+	var ix uintptr
+	for i := 0; i < int(n); i++ {
+		x[ix] = complex(real(x[ix])*alpha, imag(x[ix])*alpha)
+		ix += inc
+	}
+}
+
+// ScalInc is
+//  var ix uintptr
+//  for i := 0; i < int(n); i++ {
+//  	x[ix] *= alpha
+//  	ix += incX
+//  }
+func ScalInc(alpha complex128, x []complex128, n, inc uintptr) {
+	var ix uintptr
+	for i := 0; i < int(n); i++ {
+		x[ix] *= alpha
+		ix += inc
+	}
+}
+
+// ScalUnitary is
+//  for i := range x {
+//  	x[i] *= alpha
+//  }
+func ScalUnitary(alpha complex128, x []complex128) {
+	for i := range x {
+		x[i] *= alpha
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c128/stubs_test.go b/vendor/gonum.org/v1/gonum/internal/asm/c128/stubs_test.go
new file mode 100644
index 00000000..6af21e11
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c128/stubs_test.go
@@ -0,0 +1,335 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package c128
+
+import (
+	"fmt"
+	"testing"
+)
+
+var tests = []struct {
+	incX, incY, incDst int
+	ix, iy, idst       uintptr
+	a                  complex128
+	dst, x, y          []complex128
+	ex                 []complex128
+}{
+	{incX: 2, incY: 2, incDst: 3, ix: 0, iy: 0, idst: 0,
+		a:   1 + 1i,
+		dst: []complex128{5},
+		x:   []complex128{1},
+		y:   []complex128{1i},
+		ex:  []complex128{1 + 2i}},
+	{incX: 2, incY: 2, incDst: 3, ix: 0, iy: 0, idst: 0,
+		a:   1 + 2i,
+		dst: []complex128{0, 0, 0},
+		x:   []complex128{0, 0, 0},
+		y:   []complex128{1, 1, 1},
+		ex:  []complex128{1, 1, 1}},
+	{incX: 2, incY: 2, incDst: 3, ix: 0, iy: 0, idst: 0,
+		a:   1 + 2i,
+		dst: []complex128{0, 0, 0},
+		x:   []complex128{0, 0},
+		y:   []complex128{1, 1, 1},
+		ex:  []complex128{1, 1}},
+	{incX: 2, incY: 2, incDst: 3, ix: 0, iy: 0, idst: 0,
+		a:   1 + 2i,
+		dst: []complex128{1i, 1i, 1i},
+		x:   []complex128{1i, 1i, 1i},
+		y:   []complex128{1, 2, 1},
+		ex:  []complex128{-1 + 1i, 1i, -1 + 1i}},
+	{incX: 2, incY: 2, incDst: 3, ix: 0, iy: 0, idst: 0,
+		a:   -1i,
+		dst: []complex128{1i, 1i, 1i},
+		x:   []complex128{1i, 1i, 1i},
+		y:   []complex128{1, 2, 1},
+		ex:  []complex128{2, 3, 2}},
+	{incX: 2, incY: 2, incDst: 3, ix: 0, iy: 0, idst: 0,
+		a:   -1i,
+		dst: []complex128{1i, 1i, 1i},
+		x:   []complex128{1i, 1i, 1i, 1i, 1i}[1:4],
+		y:   []complex128{1, 1, 2, 1, 1}[1:4],
+		ex:  []complex128{2, 3, 2}},
+	{incX: 2, incY: 4, incDst: 3, ix: 0, iy: 0, idst: 0,
+		a:   -2,
+		dst: []complex128{1i, 1i, 1i, 1i, 1i},
+		x:   []complex128{2 + 1i, 2 + 1i, 2 + 1i, 2 + 1i, 2 + 1i},
+		y:   []complex128{1, 1, 2, 1, 1},
+		ex:  []complex128{-3 - 2i, -3 - 2i, -2 - 2i, -3 - 2i, -3 - 2i}},
+	// Run big test twice, once aligned once unaligned.
+	{incX: 2, incY: 2, incDst: 3, ix: 0, iy: 0, idst: 0,
+		a:   1 - 1i,
+		dst: make([]complex128, 10),
+		x:   []complex128{1i, 1i, 1i, 1i, 1i, 1i, 1i, 1i, 1i, 1i},
+		y:   []complex128{1, 1, 2, 1, 1, 1, 1, 2, 1, 1},
+		ex:  []complex128{2 + 1i, 2 + 1i, 3 + 1i, 2 + 1i, 2 + 1i, 2 + 1i, 2 + 1i, 3 + 1i, 2 + 1i, 2 + 1i}},
+	{incX: 2, incY: 2, incDst: 3, ix: 0, iy: 0, idst: 0,
+		a:   1 - 1i,
+		dst: make([]complex128, 10),
+		x:   []complex128{1i, 1i, 1i, 1i, 1i, 1i, 1i, 1i, 1i, 1i},
+		y:   []complex128{1, 1, 2, 1, 1, 1, 1, 2, 1, 1},
+		ex:  []complex128{2 + 1i, 2 + 1i, 3 + 1i, 2 + 1i, 2 + 1i, 2 + 1i, 2 + 1i, 3 + 1i, 2 + 1i, 2 + 1i}},
+	{incX: -2, incY: -2, incDst: -3, ix: 18, iy: 18, idst: 27,
+		a:   1 - 1i,
+		dst: make([]complex128, 10),
+		x:   []complex128{1i, 1i, 1i, 1i, 1i, 1i, 1i, 1i, 1i, 1i},
+		y:   []complex128{1, 1, 2, 1, 1, 1, 1, 2, 1, 1},
+		ex:  []complex128{2 + 1i, 2 + 1i, 3 + 1i, 2 + 1i, 2 + 1i, 2 + 1i, 2 + 1i, 3 + 1i, 2 + 1i, 2 + 1i}},
+	{incX: -2, incY: 2, incDst: -3, ix: 18, iy: 0, idst: 27,
+		a:   1 - 1i,
+		dst: make([]complex128, 10),
+		x:   []complex128{1i, 1i, 1i, 1i, 1i, 1i, 1i, 1i, 1i, 1i},
+		y:   []complex128{1, 1, 2, 1, 1, 1, 1, 2, 1, 1},
+		ex:  []complex128{2 + 1i, 2 + 1i, 3 + 1i, 2 + 1i, 2 + 1i, 2 + 1i, 2 + 1i, 3 + 1i, 2 + 1i, 2 + 1i}},
+}
+
+func TestAxpyUnitary(t *testing.T) {
+	const xGdVal, yGdVal = 1, 1
+	for cas, test := range tests {
+		xgLn, ygLn := 4+cas%2, 4+cas%3
+		test.x, test.y = guardVector(test.x, xGdVal, xgLn), guardVector(test.y, yGdVal, ygLn)
+		x, y := test.x[xgLn:len(test.x)-xgLn], test.y[ygLn:len(test.y)-ygLn]
+		AxpyUnitary(test.a, x, y)
+		for i := range test.ex {
+			if y[i] != test.ex[i] {
+				t.Errorf("Test %d Unexpected result at %d Got: %v Expected: %v", cas, i, y[i], test.ex[i])
+			}
+		}
+		if !isValidGuard(test.x, xGdVal, xgLn) {
+			t.Errorf("Test %d Guard violated in x vector %v %v", cas, test.x[:xgLn], test.x[len(test.x)-xgLn:])
+		}
+		if !isValidGuard(test.y, yGdVal, ygLn) {
+			t.Errorf("Test %d Guard violated in y vector %v %v", cas, test.y[:ygLn], test.y[len(test.y)-ygLn:])
+		}
+	}
+}
+
+func TestAxpyUnitaryTo(t *testing.T) {
+	const xGdVal, yGdVal, dstGdVal = 1, 1, 0
+	for cas, test := range tests {
+		xgLn, ygLn := 4+cas%2, 4+cas%3
+		test.x, test.y = guardVector(test.x, xGdVal, xgLn), guardVector(test.y, yGdVal, ygLn)
+		test.dst = guardVector(test.dst, dstGdVal, xgLn)
+		x, y := test.x[xgLn:len(test.x)-xgLn], test.y[ygLn:len(test.y)-ygLn]
+		dst := test.dst[xgLn : len(test.dst)-xgLn]
+		AxpyUnitaryTo(dst, test.a, x, y)
+		for i := range test.ex {
+			if dst[i] != test.ex[i] {
+				t.Errorf("Test %d Unexpected result at %d Got: %v Expected: %v", cas, i, dst[i], test.ex[i])
+			}
+		}
+		if !isValidGuard(test.x, xGdVal, xgLn) {
+			t.Errorf("Test %d Guard violated in x vector %v %v", cas, test.x[:xgLn], test.x[len(test.x)-xgLn:])
+		}
+		if !isValidGuard(test.y, yGdVal, ygLn) {
+			t.Errorf("Test %d Guard violated in y vector %v %v", cas, test.y[:ygLn], test.y[len(test.y)-ygLn:])
+		}
+		if !isValidGuard(test.dst, dstGdVal, xgLn) {
+			t.Errorf("Test %d Guard violated in dst vector %v %v", cas, test.dst[:xgLn], test.dst[len(test.dst)-xgLn:])
+		}
+
+	}
+}
+
+func TestAxpyInc(t *testing.T) {
+	const xGdVal, yGdVal = 1, 1
+	for cas, test := range tests {
+		xgLn, ygLn := 4+cas%2, 4+cas%3
+		test.x, test.y = guardIncVector(test.x, xGdVal, test.incX, xgLn), guardIncVector(test.y, yGdVal, test.incY, ygLn)
+		x, y := test.x[xgLn:len(test.x)-xgLn], test.y[ygLn:len(test.y)-ygLn]
+		AxpyInc(test.a, x, y, uintptr(len(test.ex)), uintptr(test.incX), uintptr(test.incY), test.ix, test.iy)
+		for i := range test.ex {
+			if y[int(test.iy)+i*int(test.incY)] != test.ex[i] {
+				t.Errorf("Test %d Unexpected result at %d Got: %v Expected: %v", cas, i, y[i*int(test.incY)], test.ex[i])
+			}
+		}
+		checkValidIncGuard(t, test.x, xGdVal, test.incX, xgLn)
+		checkValidIncGuard(t, test.y, yGdVal, test.incY, ygLn)
+	}
+}
+
+func TestAxpyIncTo(t *testing.T) {
+	const xGdVal, yGdVal, dstGdVal = 1, 1, 0
+	for cas, test := range tests {
+		xgLn, ygLn := 4+cas%2, 4+cas%3
+		test.x, test.y = guardIncVector(test.x, xGdVal, test.incX, xgLn), guardIncVector(test.y, yGdVal, test.incY, ygLn)
+		test.dst = guardIncVector(test.dst, dstGdVal, test.incDst, xgLn)
+		x, y := test.x[xgLn:len(test.x)-xgLn], test.y[ygLn:len(test.y)-ygLn]
+		dst := test.dst[xgLn : len(test.dst)-xgLn]
+		AxpyIncTo(dst, uintptr(test.incDst), test.idst, test.a, x, y, uintptr(len(test.ex)), uintptr(test.incX), uintptr(test.incY), test.ix, test.iy)
+		for i := range test.ex {
+			if dst[int(test.idst)+i*int(test.incDst)] != test.ex[i] {
+				t.Errorf("Test %d Unexpected result at %d Got: %v Expected: %v", cas, i, dst[i*int(test.incDst)], test.ex[i])
+			}
+		}
+		checkValidIncGuard(t, test.x, xGdVal, test.incX, xgLn)
+		checkValidIncGuard(t, test.y, yGdVal, test.incY, ygLn)
+		checkValidIncGuard(t, test.dst, dstGdVal, test.incDst, xgLn)
+	}
+}
+
+var dscalTests = []struct {
+	alpha float64
+	x     []complex128
+	want  []complex128
+}{
+	{
+		alpha: 0,
+		x:     []complex128{},
+		want:  []complex128{},
+	},
+	{
+		alpha: 1,
+		x:     []complex128{1 + 2i},
+		want:  []complex128{1 + 2i},
+	},
+	{
+		alpha: 2,
+		x:     []complex128{1 + 2i},
+		want:  []complex128{2 + 4i},
+	},
+	{
+		alpha: 2,
+		x:     []complex128{1 + 2i, 3 + 5i, 6 + 11i, 12 - 23i},
+		want:  []complex128{2 + 4i, 6 + 10i, 12 + 22i, 24 - 46i},
+	},
+	{
+		alpha: 3,
+		x:     []complex128{1 + 2i, 5 + 4i, 3 + 6i, 8 + 12i, -3 - 2i, -5 + 5i},
+		want:  []complex128{3 + 6i, 15 + 12i, 9 + 18i, 24 + 36i, -9 - 6i, -15 + 15i},
+	},
+	{
+		alpha: 5,
+		x:     []complex128{1 + 2i, 5 + 4i, 3 + 6i, 8 + 12i, -3 - 2i, -5 + 5i, 1 + 2i, 5 + 4i, 3 + 6i, 8 + 12i, -3 - 2i, -5 + 5i},
+		want:  []complex128{5 + 10i, 25 + 20i, 15 + 30i, 40 + 60i, -15 - 10i, -25 + 25i, 5 + 10i, 25 + 20i, 15 + 30i, 40 + 60i, -15 - 10i, -25 + 25i},
+	},
+}
+
+func TestDscalUnitary(t *testing.T) {
+	const xGdVal = -0.5
+	for i, test := range dscalTests {
+		for _, align := range align1 {
+			prefix := fmt.Sprintf("Test %v (x:%v)", i, align)
+			xgLn := 4 + align
+			xg := guardVector(test.x, xGdVal, xgLn)
+			x := xg[xgLn : len(xg)-xgLn]
+
+			DscalUnitary(test.alpha, x)
+
+			for i := range test.want {
+				if !same(x[i], test.want[i]) {
+					t.Errorf(msgVal, prefix, i, x[i], test.want[i])
+				}
+			}
+			if !isValidGuard(xg, xGdVal, xgLn) {
+				t.Errorf(msgGuard, prefix, "x", xg[:xgLn], xg[len(xg)-xgLn:])
+			}
+		}
+	}
+}
+
+func TestDscalInc(t *testing.T) {
+	const xGdVal = -0.5
+	gdLn := 4
+	for i, test := range dscalTests {
+		n := len(test.x)
+		for _, incX := range []int{1, 2, 3, 4, 7, 10} {
+			prefix := fmt.Sprintf("Test %v (x:%v)", i, incX)
+			xg := guardIncVector(test.x, xGdVal, incX, gdLn)
+			x := xg[gdLn : len(xg)-gdLn]
+
+			DscalInc(test.alpha, x, uintptr(n), uintptr(incX))
+
+			for i := range test.want {
+				if !same(x[i*incX], test.want[i]) {
+					t.Errorf(msgVal, prefix, i, x[i*incX], test.want[i])
+				}
+			}
+			checkValidIncGuard(t, xg, xGdVal, incX, gdLn)
+		}
+	}
+}
+
+var scalTests = []struct {
+	alpha complex128
+	x     []complex128
+	want  []complex128
+}{
+	{
+		alpha: 0,
+		x:     []complex128{},
+		want:  []complex128{},
+	},
+	{
+		alpha: 1 + 1i,
+		x:     []complex128{1 + 2i},
+		want:  []complex128{-1 + 3i},
+	},
+	{
+		alpha: 2 + 3i,
+		x:     []complex128{1 + 2i},
+		want:  []complex128{-4 + 7i},
+	},
+	{
+		alpha: 2 - 4i,
+		x:     []complex128{1 + 2i},
+		want:  []complex128{10},
+	},
+	{
+		alpha: 2 + 8i,
+		x:     []complex128{1 + 2i, 5 + 4i, 3 + 6i, 8 + 12i, -3 - 2i, -5 + 5i},
+		want:  []complex128{-14 + 12i, -22 + 48i, -42 + 36i, -80 + 88i, 10 - 28i, -50 - 30i},
+	},
+	{
+		alpha: 5 - 10i,
+		x:     []complex128{1 + 2i, 5 + 4i, 3 + 6i, 8 + 12i, -3 - 2i, -5 + 5i, 1 + 2i, 5 + 4i, 3 + 6i, 8 + 12i, -3 - 2i, -5 + 5i},
+		want:  []complex128{25, 65 - 30i, 75, 160 - 20i, -35 + 20i, 25 + 75i, 25, 65 - 30i, 75, 160 - 20i, -35 + 20i, 25 + 75i},
+	},
+}
+
+func TestScalUnitary(t *testing.T) {
+	const xGdVal = -0.5
+	for i, test := range scalTests {
+		for _, align := range align1 {
+			prefix := fmt.Sprintf("Test %v (x:%v)", i, align)
+			xgLn := 4 + align
+			xg := guardVector(test.x, xGdVal, xgLn)
+			x := xg[xgLn : len(xg)-xgLn]
+
+			ScalUnitary(test.alpha, x)
+
+			for i := range test.want {
+				if !same(x[i], test.want[i]) {
+					t.Errorf(msgVal, prefix, i, x[i], test.want[i])
+				}
+			}
+			if !isValidGuard(xg, xGdVal, xgLn) {
+				t.Errorf(msgGuard, prefix, "x", xg[:xgLn], xg[len(xg)-xgLn:])
+			}
+		}
+	}
+}
+
+func TestScalInc(t *testing.T) {
+	const xGdVal = -0.5
+	gdLn := 4
+	for i, test := range scalTests {
+		n := len(test.x)
+		for _, inc := range []int{1, 2, 3, 4, 7, 10} {
+			prefix := fmt.Sprintf("Test %v (x:%v)", i, inc)
+			xg := guardIncVector(test.x, xGdVal, inc, gdLn)
+			x := xg[gdLn : len(xg)-gdLn]
+
+			ScalInc(test.alpha, x, uintptr(n), uintptr(inc))
+
+			for i := range test.want {
+				if !same(x[i*inc], test.want[i]) {
+					t.Errorf(msgVal, prefix, i, x[i*inc], test.want[i])
+				}
+			}
+			checkValidIncGuard(t, xg, xGdVal, inc, gdLn)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c128/util_test.go b/vendor/gonum.org/v1/gonum/internal/asm/c128/util_test.go
new file mode 100644
index 00000000..e07470d9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c128/util_test.go
@@ -0,0 +1,123 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package c128
+
+import (
+	"math"
+	"testing"
+)
+
+const (
+	msgVal   = "%v: unexpected value at %v Got: %v Expected: %v"
+	msgGuard = "%v: Guard violated in %s vector %v %v"
+)
+
+func same(x, y complex128) bool {
+	return (x == y ||
+		math.IsNaN(real(x)) && math.IsNaN(real(y)) && imag(x) == imag(y) ||
+		math.IsNaN(imag(y)) && math.IsNaN(imag(x)) && real(y) == real(x) ||
+		math.IsNaN(real(x)) && math.IsNaN(real(y)) && math.IsNaN(imag(y)) && math.IsNaN(imag(x)))
+}
+
+func guardVector(vec []complex128, guard_val complex128, guard_len int) (guarded []complex128) {
+	guarded = make([]complex128, len(vec)+guard_len*2)
+	copy(guarded[guard_len:], vec)
+	for i := 0; i < guard_len; i++ {
+		guarded[i] = guard_val
+		guarded[len(guarded)-1-i] = guard_val
+	}
+	return guarded
+}
+
+func isValidGuard(vec []complex128, guard_val complex128, guard_len int) bool {
+	for i := 0; i < guard_len; i++ {
+		if vec[i] != guard_val || vec[len(vec)-1-i] != guard_val {
+			return false
+		}
+	}
+	return true
+}
+
+func guardIncVector(vec []complex128, guard_val complex128, inc, guard_len int) (guarded []complex128) {
+	s_ln := len(vec) * inc
+	if inc < 0 {
+		s_ln = len(vec) * -inc
+	}
+	guarded = make([]complex128, s_ln+guard_len*2)
+	for i, cas := 0, 0; i < len(guarded); i++ {
+		switch {
+		case i < guard_len, i > guard_len+s_ln:
+			guarded[i] = guard_val
+		case (i-guard_len)%(inc) == 0 && cas < len(vec):
+			guarded[i] = vec[cas]
+			cas++
+		default:
+			guarded[i] = guard_val
+		}
+	}
+	return guarded
+}
+
+func checkValidIncGuard(t *testing.T, vec []complex128, guard_val complex128, inc, guard_len int) {
+	s_ln := len(vec) - 2*guard_len
+	if inc < 0 {
+		s_ln = len(vec) * -inc
+	}
+
+	for i := range vec {
+		switch {
+		case vec[i] == guard_val:
+			// Correct value
+		case i < guard_len:
+			t.Errorf("Front guard violated at %d %v", i, vec[:guard_len])
+		case i > guard_len+s_ln:
+			t.Errorf("Back guard violated at %d %v", i-guard_len-s_ln, vec[guard_len+s_ln:])
+		case (i-guard_len)%inc == 0 && (i-guard_len)/inc < len(vec):
+			// Ignore input values
+		default:
+			t.Errorf("Internal guard violated at %d %v", i-guard_len, vec[guard_len:guard_len+s_ln])
+		}
+	}
+}
+
+var ( // Offset sets for testing alignment handling in Unitary assembly functions.
+	align1 = []int{0, 1}
+	align2 = newIncSet(0, 1)
+	align3 = newIncToSet(0, 1)
+)
+
+type incSet struct {
+	x, y int
+}
+
+// genInc will generate all (x,y) combinations of the input increment set.
+func newIncSet(inc ...int) []incSet {
+	n := len(inc)
+	is := make([]incSet, n*n)
+	for x := range inc {
+		for y := range inc {
+			is[x*n+y] = incSet{inc[x], inc[y]}
+		}
+	}
+	return is
+}
+
+type incToSet struct {
+	dst, x, y int
+}
+
+// genIncTo will generate all (dst,x,y) combinations of the input increment set.
+func newIncToSet(inc ...int) []incToSet {
+	n := len(inc)
+	is := make([]incToSet, n*n*n)
+	for i, dst := range inc {
+		for x := range inc {
+			for y := range inc {
+				is[i*n*n+x*n+y] = incToSet{dst, inc[x], inc[y]}
+			}
+		}
+	}
+	return is
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c64/axpyinc_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/c64/axpyinc_amd64.s
new file mode 100644
index 00000000..82c28862
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c64/axpyinc_amd64.s
@@ -0,0 +1,151 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !noasm,!appengine
+
+#include "textflag.h"
+
+// MOVSHDUP X3, X2
+#define MOVSHDUP_X3_X2 BYTE $0xF3; BYTE $0x0F; BYTE $0x16; BYTE $0xD3
+// MOVSLDUP X3, X3
+#define MOVSLDUP_X3_X3 BYTE $0xF3; BYTE $0x0F; BYTE $0x12; BYTE $0xDB
+// ADDSUBPS X2, X3
+#define ADDSUBPS_X2_X3 BYTE $0xF2; BYTE $0x0F; BYTE $0xD0; BYTE $0xDA
+
+// MOVSHDUP X5, X4
+#define MOVSHDUP_X5_X4 BYTE $0xF3; BYTE $0x0F; BYTE $0x16; BYTE $0xE5
+// MOVSLDUP X5, X5
+#define MOVSLDUP_X5_X5 BYTE $0xF3; BYTE $0x0F; BYTE $0x12; BYTE $0xED
+// ADDSUBPS X4, X5
+#define ADDSUBPS_X4_X5 BYTE $0xF2; BYTE $0x0F; BYTE $0xD0; BYTE $0xEC
+
+// MOVSHDUP X7, X6
+#define MOVSHDUP_X7_X6 BYTE $0xF3; BYTE $0x0F; BYTE $0x16; BYTE $0xF7
+// MOVSLDUP X7, X7
+#define MOVSLDUP_X7_X7 BYTE $0xF3; BYTE $0x0F; BYTE $0x12; BYTE $0xFF
+// ADDSUBPS X6, X7
+#define ADDSUBPS_X6_X7 BYTE $0xF2; BYTE $0x0F; BYTE $0xD0; BYTE $0xFE
+
+// MOVSHDUP X9, X8
+#define MOVSHDUP_X9_X8 BYTE $0xF3; BYTE $0x45; BYTE $0x0F; BYTE $0x16; BYTE $0xC1
+// MOVSLDUP X9, X9
+#define MOVSLDUP_X9_X9 BYTE $0xF3; BYTE $0x45; BYTE $0x0F; BYTE $0x12; BYTE $0xC9
+// ADDSUBPS X8, X9
+#define ADDSUBPS_X8_X9 BYTE $0xF2; BYTE $0x45; BYTE $0x0F; BYTE $0xD0; BYTE $0xC8
+
+// func AxpyInc(alpha complex64, x, y []complex64, n, incX, incY, ix, iy uintptr)
+TEXT ·AxpyInc(SB), NOSPLIT, $0
+	MOVQ   x_base+8(FP), SI  // SI = &x
+	MOVQ   y_base+32(FP), DI // DI = &y
+	MOVQ   n+56(FP), CX      // CX = n
+	CMPQ   CX, $0            // if n==0 { return }
+	JE     axpyi_end
+	MOVQ   ix+80(FP), R8     // R8 = ix
+	MOVQ   iy+88(FP), R9     // R9 = iy
+	LEAQ   (SI)(R8*8), SI    // SI = &(x[ix])
+	LEAQ   (DI)(R9*8), DI    // DI = &(y[iy])
+	MOVQ   DI, DX            // DX = DI    // Read/Write pointers
+	MOVQ   incX+64(FP), R8   // R8 = incX
+	SHLQ   $3, R8            // R8 *= sizeof(complex64)
+	MOVQ   incY+72(FP), R9   // R9 = incY
+	SHLQ   $3, R9            // R9 *= sizeof(complex64)
+	MOVSD  alpha+0(FP), X0   // X0 = { 0, 0, imag(a), real(a) }
+	MOVAPS X0, X1
+	SHUFPS $0x11, X1, X1     // X1 = { 0, 0, real(a), imag(a) }
+	MOVAPS X0, X10           // Copy X0 and X1 for pipelining
+	MOVAPS X1, X11
+	MOVQ   CX, BX
+	ANDQ   $3, CX            // CX = n % 4
+	SHRQ   $2, BX            // BX = floor( n / 4 )
+	JZ     axpyi_tail        // if BX == 0 { goto axpyi_tail }
+
+axpyi_loop: // do {
+	MOVSD (SI), X3       // X_i = { imag(x[i+1]), real(x[i+1]) }
+	MOVSD (SI)(R8*1), X5
+	LEAQ  (SI)(R8*2), SI // SI = &(SI[incX*2])
+	MOVSD (SI), X7
+	MOVSD (SI)(R8*1), X9
+
+	// X_(i-1) = { imag(x[i]), imag(x[i]) }
+	MOVSHDUP_X3_X2
+	MOVSHDUP_X5_X4
+	MOVSHDUP_X7_X6
+	MOVSHDUP_X9_X8
+
+	// X_i = { real(x[i]), real(x[i]) }
+	MOVSLDUP_X3_X3
+	MOVSLDUP_X5_X5
+	MOVSLDUP_X7_X7
+	MOVSLDUP_X9_X9
+
+	// X_(i-1) = {  real(a) * imag(x[i]),   imag(a) * imag(x[i]) }
+	// X_i     = {  imag(a) * real(x[i]),   real(a) * real(x[i])  }
+	MULPS X1, X2
+	MULPS X0, X3
+	MULPS X11, X4
+	MULPS X10, X5
+	MULPS X1, X6
+	MULPS X0, X7
+	MULPS X11, X8
+	MULPS X10, X9
+
+	// X_i = {
+	//	imag(result[i]):   imag(a)*real(x[i]) + real(a)*imag(x[i]),
+	//	real(result[i]):   real(a)*real(x[i]) - imag(a)*imag(x[i]),
+	//  }
+	ADDSUBPS_X2_X3
+	ADDSUBPS_X4_X5
+	ADDSUBPS_X6_X7
+	ADDSUBPS_X8_X9
+
+	// X_i = { imag(result[i]) + imag(y[i]), real(result[i]) + real(y[i]) }
+	MOVSD (DX), X2
+	MOVSD (DX)(R9*1), X4
+	LEAQ  (DX)(R9*2), DX // DX = &(DX[incY*2])
+	MOVSD (DX), X6
+	MOVSD (DX)(R9*1), X8
+	ADDPS X2, X3
+	ADDPS X4, X5
+	ADDPS X6, X7
+	ADDPS X8, X9
+
+	MOVSD X3, (DI)       // y[i] = X_i
+	MOVSD X5, (DI)(R9*1)
+	LEAQ  (DI)(R9*2), DI // DI = &(DI[incDst])
+	MOVSD X7, (DI)
+	MOVSD X9, (DI)(R9*1)
+	LEAQ  (SI)(R8*2), SI // SI = &(SI[incX*2])
+	LEAQ  (DX)(R9*2), DX // DX = &(DX[incY*2])
+	LEAQ  (DI)(R9*2), DI // DI = &(DI[incDst])
+	DECQ  BX
+	JNZ   axpyi_loop     // }  while --BX > 0
+	CMPQ  CX, $0         // if CX == 0 { return }
+	JE    axpyi_end
+
+axpyi_tail: // do {
+	MOVSD (SI), X3 // X_i = { imag(x[i+1]), real(x[i+1]) }
+	MOVSHDUP_X3_X2 // X_(i-1) = { real(x[i]), real(x[i]) }
+	MOVSLDUP_X3_X3 // X_i = { imag(x[i]), imag(x[i]) }
+
+	// X_i     = { imag(a) * real(x[i]),  real(a) * real(x[i]) }
+	// X_(i-1) = { real(a) * imag(x[i]),  imag(a) * imag(x[i]) }
+	MULPS X1, X2
+	MULPS X0, X3
+
+	// X_i = {
+	//	imag(result[i]):   imag(a)*real(x[i]) + real(a)*imag(x[i]),
+	//	real(result[i]):   real(a)*real(x[i]) - imag(a)*imag(x[i]),
+	//  }
+	ADDSUBPS_X2_X3 // (ai*x1r+ar*x1i, ar*x1r-ai*x1i)
+
+	// X_i = { imag(result[i]) + imag(y[i]),  real(result[i]) + real(y[i])  }
+	MOVSD (DI), X4
+	ADDPS X4, X3
+	MOVSD X3, (DI)   // y[i] = X_i
+	ADDQ  R8, SI     // SI += incX
+	ADDQ  R9, DI     // DI += incY
+	LOOP  axpyi_tail // } while --CX > 0
+
+axpyi_end:
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c64/axpyincto_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/c64/axpyincto_amd64.s
new file mode 100644
index 00000000..9fdc3ef3
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c64/axpyincto_amd64.s
@@ -0,0 +1,156 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !noasm,!appengine
+
+#include "textflag.h"
+
+// MOVSHDUP X3, X2
+#define MOVSHDUP_X3_X2 BYTE $0xF3; BYTE $0x0F; BYTE $0x16; BYTE $0xD3
+// MOVSLDUP X3, X3
+#define MOVSLDUP_X3_X3 BYTE $0xF3; BYTE $0x0F; BYTE $0x12; BYTE $0xDB
+// ADDSUBPS X2, X3
+#define ADDSUBPS_X2_X3 BYTE $0xF2; BYTE $0x0F; BYTE $0xD0; BYTE $0xDA
+
+// MOVSHDUP X5, X4
+#define MOVSHDUP_X5_X4 BYTE $0xF3; BYTE $0x0F; BYTE $0x16; BYTE $0xE5
+// MOVSLDUP X5, X5
+#define MOVSLDUP_X5_X5 BYTE $0xF3; BYTE $0x0F; BYTE $0x12; BYTE $0xED
+// ADDSUBPS X4, X5
+#define ADDSUBPS_X4_X5 BYTE $0xF2; BYTE $0x0F; BYTE $0xD0; BYTE $0xEC
+
+// MOVSHDUP X7, X6
+#define MOVSHDUP_X7_X6 BYTE $0xF3; BYTE $0x0F; BYTE $0x16; BYTE $0xF7
+// MOVSLDUP X7, X7
+#define MOVSLDUP_X7_X7 BYTE $0xF3; BYTE $0x0F; BYTE $0x12; BYTE $0xFF
+// ADDSUBPS X6, X7
+#define ADDSUBPS_X6_X7 BYTE $0xF2; BYTE $0x0F; BYTE $0xD0; BYTE $0xFE
+
+// MOVSHDUP X9, X8
+#define MOVSHDUP_X9_X8 BYTE $0xF3; BYTE $0x45; BYTE $0x0F; BYTE $0x16; BYTE $0xC1
+// MOVSLDUP X9, X9
+#define MOVSLDUP_X9_X9 BYTE $0xF3; BYTE $0x45; BYTE $0x0F; BYTE $0x12; BYTE $0xC9
+// ADDSUBPS X8, X9
+#define ADDSUBPS_X8_X9 BYTE $0xF2; BYTE $0x45; BYTE $0x0F; BYTE $0xD0; BYTE $0xC8
+
+// func AxpyIncTo(dst []complex64, incDst, idst uintptr, alpha complex64, x, y []complex64, n, incX, incY, ix, iy uintptr)
+TEXT ·AxpyIncTo(SB), NOSPLIT, $0
+	MOVQ   dst_base+0(FP), DI // DI = &dst
+	MOVQ   x_base+48(FP), SI  // SI = &x
+	MOVQ   y_base+72(FP), DX  // DX = &y
+	MOVQ   n+96(FP), CX       // CX = n
+	CMPQ   CX, $0             // if n==0 { return }
+	JE     axpyi_end
+	MOVQ   ix+120(FP), R8     // Load the first index
+	MOVQ   iy+128(FP), R9
+	MOVQ   idst+32(FP), R10
+	LEAQ   (SI)(R8*8), SI     // SI = &(x[ix])
+	LEAQ   (DX)(R9*8), DX     // DX = &(y[iy])
+	LEAQ   (DI)(R10*8), DI    // DI = &(dst[idst])
+	MOVQ   incX+104(FP), R8   // Incrementors*8 for easy iteration (ADDQ)
+	SHLQ   $3, R8
+	MOVQ   incY+112(FP), R9
+	SHLQ   $3, R9
+	MOVQ   incDst+24(FP), R10
+	SHLQ   $3, R10
+	MOVSD  alpha+40(FP), X0   // X0 = { 0, 0, imag(a), real(a) }
+	MOVAPS X0, X1
+	SHUFPS $0x11, X1, X1      // X1 = { 0, 0, real(a), imag(a) }
+	MOVAPS X0, X10            // Copy X0 and X1 for pipelining
+	MOVAPS X1, X11
+	MOVQ   CX, BX
+	ANDQ   $3, CX             // CX = n % 4
+	SHRQ   $2, BX             // BX = floor( n / 4 )
+	JZ     axpyi_tail         // if BX == 0 { goto axpyi_tail }
+
+axpyi_loop: // do {
+	MOVSD (SI), X3       // X_i = { imag(x[i]), real(x[i]) }
+	MOVSD (SI)(R8*1), X5
+	LEAQ  (SI)(R8*2), SI // SI = &(SI[incX*2])
+	MOVSD (SI), X7
+	MOVSD (SI)(R8*1), X9
+
+	// X_(i-1) = { imag(x[i]), imag(x[i]) }
+	MOVSHDUP_X3_X2
+	MOVSHDUP_X5_X4
+	MOVSHDUP_X7_X6
+	MOVSHDUP_X9_X8
+
+	// X_i = { real(x[i]), real(x[i]) }
+	MOVSLDUP_X3_X3
+	MOVSLDUP_X5_X5
+	MOVSLDUP_X7_X7
+	MOVSLDUP_X9_X9
+
+	// X_(i-1) = {  real(a) * imag(x[i]),   imag(a) * imag(x[i]) }
+	// X_i     = {  imag(a) * real(x[i]),   real(a) * real(x[i])  }
+	MULPS X1, X2
+	MULPS X0, X3
+	MULPS X11, X4
+	MULPS X10, X5
+	MULPS X1, X6
+	MULPS X0, X7
+	MULPS X11, X8
+	MULPS X10, X9
+
+	// X_i = {
+	//	imag(result[i]):   imag(a)*real(x[i]) + real(a)*imag(x[i]),
+	//	real(result[i]):   real(a)*real(x[i]) - imag(a)*imag(x[i]),
+	//  }
+	ADDSUBPS_X2_X3
+	ADDSUBPS_X4_X5
+	ADDSUBPS_X6_X7
+	ADDSUBPS_X8_X9
+
+	// X_i = { imag(result[i]) + imag(y[i]), real(result[i]) + real(y[i]) }
+	MOVSD (DX), X2
+	MOVSD (DX)(R9*1), X4
+	LEAQ  (DX)(R9*2), DX // DX = &(DX[incY*2])
+	MOVSD (DX), X6
+	MOVSD (DX)(R9*1), X8
+	ADDPS X2, X3
+	ADDPS X4, X5
+	ADDPS X6, X7
+	ADDPS X8, X9
+
+	MOVSD X3, (DI)        // y[i] = X_i
+	MOVSD X5, (DI)(R10*1)
+	LEAQ  (DI)(R10*2), DI // DI = &(DI[incDst])
+	MOVSD X7, (DI)
+	MOVSD X9, (DI)(R10*1)
+	LEAQ  (SI)(R8*2), SI  // SI = &(SI[incX*2])
+	LEAQ  (DX)(R9*2), DX  // DX = &(DX[incY*2])
+	LEAQ  (DI)(R10*2), DI // DI = &(DI[incDst])
+	DECQ  BX
+	JNZ   axpyi_loop      // } while --BX > 0
+	CMPQ  CX, $0          // if CX == 0 { return }
+	JE    axpyi_end
+
+axpyi_tail:
+	MOVSD (SI), X3 // X_i     = { imag(x[i]), real(x[i]) }
+	MOVSHDUP_X3_X2 // X_(i-1) = { imag(x[i]), imag(x[i]) }
+	MOVSLDUP_X3_X3 // X_i     = { real(x[i]), real(x[i]) }
+
+	// X_i     = { imag(a) * real(x[i]),  real(a) * real(x[i]) }
+	// X_(i-1) = { real(a) * imag(x[i]),  imag(a) * imag(x[i]) }
+	MULPS X1, X2
+	MULPS X0, X3
+
+	// X_i = {
+	//	imag(result[i]):   imag(a)*real(x[i]) + real(a)*imag(x[i]),
+	//	real(result[i]):   real(a)*real(x[i]) - imag(a)*imag(x[i]),
+	//  }
+	ADDSUBPS_X2_X3
+
+	// X_i = { imag(result[i]) + imag(y[i]),  real(result[i]) + real(y[i])  }
+	MOVSD (DX), X4
+	ADDPS X4, X3
+	MOVSD X3, (DI)   // y[i] = X_i
+	ADDQ  R8, SI     // SI += incX
+	ADDQ  R9, DX     // DX += incY
+	ADDQ  R10, DI    // DI += incDst
+	LOOP  axpyi_tail // } while --CX > 0
+
+axpyi_end:
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c64/axpyunitary_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/c64/axpyunitary_amd64.s
new file mode 100644
index 00000000..807a1c42
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c64/axpyunitary_amd64.s
@@ -0,0 +1,160 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !noasm,!appengine
+
+#include "textflag.h"
+
+// MOVSHDUP X3, X2
+#define MOVSHDUP_X3_X2 BYTE $0xF3; BYTE $0x0F; BYTE $0x16; BYTE $0xD3
+// MOVSLDUP X3, X3
+#define MOVSLDUP_X3_X3 BYTE $0xF3; BYTE $0x0F; BYTE $0x12; BYTE $0xDB
+// ADDSUBPS X2, X3
+#define ADDSUBPS_X2_X3 BYTE $0xF2; BYTE $0x0F; BYTE $0xD0; BYTE $0xDA
+
+// MOVSHDUP X5, X4
+#define MOVSHDUP_X5_X4 BYTE $0xF3; BYTE $0x0F; BYTE $0x16; BYTE $0xE5
+// MOVSLDUP X5, X5
+#define MOVSLDUP_X5_X5 BYTE $0xF3; BYTE $0x0F; BYTE $0x12; BYTE $0xED
+// ADDSUBPS X4, X5
+#define ADDSUBPS_X4_X5 BYTE $0xF2; BYTE $0x0F; BYTE $0xD0; BYTE $0xEC
+
+// MOVSHDUP X7, X6
+#define MOVSHDUP_X7_X6 BYTE $0xF3; BYTE $0x0F; BYTE $0x16; BYTE $0xF7
+// MOVSLDUP X7, X7
+#define MOVSLDUP_X7_X7 BYTE $0xF3; BYTE $0x0F; BYTE $0x12; BYTE $0xFF
+// ADDSUBPS X6, X7
+#define ADDSUBPS_X6_X7 BYTE $0xF2; BYTE $0x0F; BYTE $0xD0; BYTE $0xFE
+
+// MOVSHDUP X9, X8
+#define MOVSHDUP_X9_X8 BYTE $0xF3; BYTE $0x45; BYTE $0x0F; BYTE $0x16; BYTE $0xC1
+// MOVSLDUP X9, X9
+#define MOVSLDUP_X9_X9 BYTE $0xF3; BYTE $0x45; BYTE $0x0F; BYTE $0x12; BYTE $0xC9
+// ADDSUBPS X8, X9
+#define ADDSUBPS_X8_X9 BYTE $0xF2; BYTE $0x45; BYTE $0x0F; BYTE $0xD0; BYTE $0xC8
+
+// func AxpyUnitary(alpha complex64, x, y []complex64)
+TEXT ·AxpyUnitary(SB), NOSPLIT, $0
+	MOVQ    x_base+8(FP), SI  // SI = &x
+	MOVQ    y_base+32(FP), DI // DI = &y
+	MOVQ    x_len+16(FP), CX  // CX = min( len(x), len(y) )
+	CMPQ    y_len+40(FP), CX
+	CMOVQLE y_len+40(FP), CX
+	CMPQ    CX, $0            // if CX == 0 { return }
+	JE      caxy_end
+	PXOR    X0, X0            // Clear work registers and cache-align loop
+	PXOR    X1, X1
+	MOVSD   alpha+0(FP), X0   // X0 = { 0, 0, imag(a), real(a) }
+	SHUFPD  $0, X0, X0        // X0  = { imag(a), real(a), imag(a), real(a) }
+	MOVAPS  X0, X1
+	SHUFPS  $0x11, X1, X1     // X1 = { real(a), imag(a), real(a), imag(a) }
+	XORQ    AX, AX            // i = 0
+	MOVQ    DI, BX            // Align on 16-byte boundary for ADDPS
+	ANDQ    $15, BX           // BX = &y & 15
+	JZ      caxy_no_trim      // if BX == 0 { goto caxy_no_trim }
+
+	// Trim first value in unaligned buffer
+	XORPS X2, X2         // Clear work registers and cache-align loop
+	XORPS X3, X3
+	XORPS X4, X4
+	MOVSD (SI)(AX*8), X3 // X3 = { imag(x[i]), real(x[i]) }
+	MOVSHDUP_X3_X2       // X2 = { imag(x[i]), imag(x[i]) }
+	MOVSLDUP_X3_X3       // X3 = { real(x[i]), real(x[i]) }
+	MULPS X1, X2         // X2 = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
+	MULPS X0, X3         // X3 = { imag(a) * real(x[i]), real(a) * real(x[i]) }
+
+	// X3 = { imag(a)*real(x[i]) + real(a)*imag(x[i]), real(a)*real(x[i]) - imag(a)*imag(x[i]) }
+	ADDSUBPS_X2_X3
+	MOVSD (DI)(AX*8), X4 // X3 += y[i]
+	ADDPS X4, X3
+	MOVSD X3, (DI)(AX*8) // y[i]  = X3
+	INCQ  AX             // i++
+	DECQ  CX             // --CX
+	JZ    caxy_end       // if CX == 0 { return }
+
+caxy_no_trim:
+	MOVAPS X0, X10   // Copy X0 and X1 for pipelineing
+	MOVAPS X1, X11
+	MOVQ   CX, BX
+	ANDQ   $7, CX    // CX = n % 8
+	SHRQ   $3, BX    // BX = floor( n / 8 )
+	JZ     caxy_tail // if BX == 0 { goto caxy_tail }
+
+caxy_loop: // do {
+	// X_i = { imag(x[i]), real(x[i]), imag(x[i+1]), real(x[i+1]) }
+	MOVUPS (SI)(AX*8), X3
+	MOVUPS 16(SI)(AX*8), X5
+	MOVUPS 32(SI)(AX*8), X7
+	MOVUPS 48(SI)(AX*8), X9
+
+	// X_(i-1) = { imag(x[i]), imag(x[i]), imag(x[i]+1), imag(x[i]+1) }
+	MOVSHDUP_X3_X2
+	MOVSHDUP_X5_X4
+	MOVSHDUP_X7_X6
+	MOVSHDUP_X9_X8
+
+	// X_i = { real(x[i]), real(x[i]), real(x[i+1]), real(x[i+1]) }
+	MOVSLDUP_X3_X3
+	MOVSLDUP_X5_X5
+	MOVSLDUP_X7_X7
+	MOVSLDUP_X9_X9
+
+	// X_i     = {  imag(a) * real(x[i]),   real(a) * real(x[i]),
+	// 		imag(a) * real(x[i+1]), real(a) * real(x[i+1])  }
+	// X_(i-1) = {  real(a) * imag(x[i]),   imag(a) * imag(x[i]),
+	//		real(a) * imag(x[i+1]), imag(a) * imag(x[i+1])  }
+	MULPS X1, X2
+	MULPS X0, X3
+	MULPS X11, X4
+	MULPS X10, X5
+	MULPS X1, X6
+	MULPS X0, X7
+	MULPS X11, X8
+	MULPS X10, X9
+
+	// X_i = {
+	//	imag(result[i]):   imag(a)*real(x[i]) + real(a)*imag(x[i]),
+	//	real(result[i]):   real(a)*real(x[i]) - imag(a)*imag(x[i]),
+	//	imag(result[i+1]): imag(a)*real(x[i+1]) + real(a)*imag(x[i+1]),
+	//	real(result[i+1]): real(a)*real(x[i+1]) - imag(a)*imag(x[i+1]),
+	//  }
+	ADDSUBPS_X2_X3
+	ADDSUBPS_X4_X5
+	ADDSUBPS_X6_X7
+	ADDSUBPS_X8_X9
+
+	// X_i = { imag(result[i])   + imag(y[i]),   real(result[i])   + real(y[i]),
+	//	   imag(result[i+1]) + imag(y[i+1]), real(result[i+1]) + real(y[i+1])  }
+	ADDPS  (DI)(AX*8), X3
+	ADDPS  16(DI)(AX*8), X5
+	ADDPS  32(DI)(AX*8), X7
+	ADDPS  48(DI)(AX*8), X9
+	MOVUPS X3, (DI)(AX*8)   // y[i:i+1] = X_i
+	MOVUPS X5, 16(DI)(AX*8)
+	MOVUPS X7, 32(DI)(AX*8)
+	MOVUPS X9, 48(DI)(AX*8)
+	ADDQ   $8, AX           // i += 8
+	DECQ   BX               // --BX
+	JNZ    caxy_loop        // }  while BX > 0
+	CMPQ   CX, $0           // if CX == 0  { return }
+	JE     caxy_end
+
+caxy_tail: // do {
+	MOVSD (SI)(AX*8), X3 // X3 = { imag(x[i]), real(x[i]) }
+	MOVSHDUP_X3_X2       // X2 = { imag(x[i]), imag(x[i]) }
+	MOVSLDUP_X3_X3       // X3 = { real(x[i]), real(x[i]) }
+	MULPS X1, X2         // X2 = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
+	MULPS X0, X3         // X3 = { imag(a) * real(x[i]), real(a) * real(x[i]) }
+
+	// X3 = { imag(a)*real(x[i]) + real(a)*imag(x[i]),
+	//	  real(a)*real(x[i]) - imag(a)*imag(x[i])   }
+	ADDSUBPS_X2_X3
+	MOVSD (DI)(AX*8), X4 // X3 += y[i]
+	ADDPS X4, X3
+	MOVSD X3, (DI)(AX*8) // y[i]  = X3
+	INCQ  AX             // ++i
+	LOOP  caxy_tail      // } while --CX > 0
+
+caxy_end:
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c64/axpyunitaryto_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/c64/axpyunitaryto_amd64.s
new file mode 100644
index 00000000..ed5a8c93
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c64/axpyunitaryto_amd64.s
@@ -0,0 +1,157 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !noasm,!appengine
+
+#include "textflag.h"
+
+// MOVSHDUP X3, X2
+#define MOVSHDUP_X3_X2 BYTE $0xF3; BYTE $0x0F; BYTE $0x16; BYTE $0xD3
+// MOVSLDUP X3, X3
+#define MOVSLDUP_X3_X3 BYTE $0xF3; BYTE $0x0F; BYTE $0x12; BYTE $0xDB
+// ADDSUBPS X2, X3
+#define ADDSUBPS_X2_X3 BYTE $0xF2; BYTE $0x0F; BYTE $0xD0; BYTE $0xDA
+
+// MOVSHDUP X5, X4
+#define MOVSHDUP_X5_X4 BYTE $0xF3; BYTE $0x0F; BYTE $0x16; BYTE $0xE5
+// MOVSLDUP X5, X5
+#define MOVSLDUP_X5_X5 BYTE $0xF3; BYTE $0x0F; BYTE $0x12; BYTE $0xED
+// ADDSUBPS X4, X5
+#define ADDSUBPS_X4_X5 BYTE $0xF2; BYTE $0x0F; BYTE $0xD0; BYTE $0xEC
+
+// MOVSHDUP X7, X6
+#define MOVSHDUP_X7_X6 BYTE $0xF3; BYTE $0x0F; BYTE $0x16; BYTE $0xF7
+// MOVSLDUP X7, X7
+#define MOVSLDUP_X7_X7 BYTE $0xF3; BYTE $0x0F; BYTE $0x12; BYTE $0xFF
+// ADDSUBPS X6, X7
+#define ADDSUBPS_X6_X7 BYTE $0xF2; BYTE $0x0F; BYTE $0xD0; BYTE $0xFE
+
+// MOVSHDUP X9, X8
+#define MOVSHDUP_X9_X8 BYTE $0xF3; BYTE $0x45; BYTE $0x0F; BYTE $0x16; BYTE $0xC1
+// MOVSLDUP X9, X9
+#define MOVSLDUP_X9_X9 BYTE $0xF3; BYTE $0x45; BYTE $0x0F; BYTE $0x12; BYTE $0xC9
+// ADDSUBPS X8, X9
+#define ADDSUBPS_X8_X9 BYTE $0xF2; BYTE $0x45; BYTE $0x0F; BYTE $0xD0; BYTE $0xC8
+
+// func AxpyUnitaryTo(dst []complex64, alpha complex64, x, y []complex64)
+TEXT ·AxpyUnitaryTo(SB), NOSPLIT, $0
+	MOVQ    dst_base+0(FP), DI // DI = &dst
+	MOVQ    x_base+32(FP), SI  // SI = &x
+	MOVQ    y_base+56(FP), DX  // DX = &y
+	MOVQ    x_len+40(FP), CX
+	CMPQ    y_len+64(FP), CX   // CX = min( len(x), len(y), len(dst) )
+	CMOVQLE y_len+64(FP), CX
+	CMPQ    dst_len+8(FP), CX
+	CMOVQLE dst_len+8(FP), CX
+	CMPQ    CX, $0             // if CX == 0 { return }
+	JE      caxy_end
+	MOVSD   alpha+24(FP), X0   // X0 = { 0, 0, imag(a), real(a) }
+	SHUFPD  $0, X0, X0         // X0  = { imag(a), real(a), imag(a), real(a) }
+	MOVAPS  X0, X1
+	SHUFPS  $0x11, X1, X1      // X1 = { real(a), imag(a), real(a), imag(a) }
+	XORQ    AX, AX             // i = 0
+	MOVQ    DX, BX             // Align on 16-byte boundary for ADDPS
+	ANDQ    $15, BX            // BX = &y & 15
+	JZ      caxy_no_trim       // if BX == 0 { goto caxy_no_trim }
+
+	MOVSD (SI)(AX*8), X3 // X3 = { imag(x[i]), real(x[i]) }
+	MOVSHDUP_X3_X2       // X2 = { imag(x[i]), imag(x[i]) }
+	MOVSLDUP_X3_X3       // X3 = { real(x[i]), real(x[i]) }
+	MULPS X1, X2         // X2 = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
+	MULPS X0, X3         // X3 = { imag(a) * real(x[i]), real(a) * real(x[i]) }
+
+	// X3 = { imag(a)*real(x[i]) + real(a)*imag(x[i]), real(a)*real(x[i]) - imag(a)*imag(x[i]) }
+	ADDSUBPS_X2_X3
+	MOVSD (DX)(AX*8), X4 // X3 += y[i]
+	ADDPS X4, X3
+	MOVSD X3, (DI)(AX*8) // dst[i]  = X3
+	INCQ  AX             // i++
+	DECQ  CX             // --CX
+	JZ    caxy_tail      // if BX == 0 { goto caxy_tail }
+
+caxy_no_trim:
+	MOVAPS X0, X10   // Copy X0 and X1 for pipelineing
+	MOVAPS X1, X11
+	MOVQ   CX, BX
+	ANDQ   $7, CX    // CX = n % 8
+	SHRQ   $3, BX    // BX = floor( n / 8 )
+	JZ     caxy_tail // if BX == 0 { goto caxy_tail }
+
+caxy_loop:
+	// X_i = { imag(x[i]), real(x[i]), imag(x[i+1]), real(x[i+1]) }
+	MOVUPS (SI)(AX*8), X3
+	MOVUPS 16(SI)(AX*8), X5
+	MOVUPS 32(SI)(AX*8), X7
+	MOVUPS 48(SI)(AX*8), X9
+
+	// X_(i-1) = { imag(x[i]), imag(x[i]), imag(x[i]+1), imag(x[i]+1) }
+	MOVSHDUP_X3_X2
+	MOVSHDUP_X5_X4
+	MOVSHDUP_X7_X6
+	MOVSHDUP_X9_X8
+
+	// X_i = { real(x[i]), real(x[i]), real(x[i+1]), real(x[i+1]) }
+	MOVSLDUP_X3_X3
+	MOVSLDUP_X5_X5
+	MOVSLDUP_X7_X7
+	MOVSLDUP_X9_X9
+
+	// X_i     = {  imag(a) * real(x[i]),   real(a) * real(x[i]),
+	// 		imag(a) * real(x[i+1]), real(a) * real(x[i+1])  }
+	// X_(i-1) = {  real(a) * imag(x[i]),   imag(a) * imag(x[i]),
+	//		real(a) * imag(x[i+1]), imag(a) * imag(x[i+1])  }
+	MULPS X1, X2
+	MULPS X0, X3
+	MULPS X11, X4
+	MULPS X10, X5
+	MULPS X1, X6
+	MULPS X0, X7
+	MULPS X11, X8
+	MULPS X10, X9
+
+	// X_i = {
+	//	imag(result[i]):   imag(a)*real(x[i]) + real(a)*imag(x[i]),
+	//	real(result[i]):   real(a)*real(x[i]) - imag(a)*imag(x[i]),
+	//	imag(result[i+1]): imag(a)*real(x[i+1]) + real(a)*imag(x[i+1]),
+	//	real(result[i+1]): real(a)*real(x[i+1]) - imag(a)*imag(x[i+1]),
+	//  }
+	ADDSUBPS_X2_X3
+	ADDSUBPS_X4_X5
+	ADDSUBPS_X6_X7
+	ADDSUBPS_X8_X9
+
+	// X_i = { imag(result[i])   + imag(y[i]),   real(result[i])   + real(y[i]),
+	//	   imag(result[i+1]) + imag(y[i+1]), real(result[i+1]) + real(y[i+1])  }
+	ADDPS  (DX)(AX*8), X3
+	ADDPS  16(DX)(AX*8), X5
+	ADDPS  32(DX)(AX*8), X7
+	ADDPS  48(DX)(AX*8), X9
+	MOVUPS X3, (DI)(AX*8)   // y[i:i+1] = X_i
+	MOVUPS X5, 16(DI)(AX*8)
+	MOVUPS X7, 32(DI)(AX*8)
+	MOVUPS X9, 48(DI)(AX*8)
+	ADDQ   $8, AX           // i += 8
+	DECQ   BX               // --BX
+	JNZ    caxy_loop        // }  while BX > 0
+	CMPQ   CX, $0           // if CX == 0  { return }
+	JE     caxy_end
+
+caxy_tail: // do {
+	MOVSD (SI)(AX*8), X3 // X3 = { imag(x[i]), real(x[i]) }
+	MOVSHDUP_X3_X2       // X2 = { imag(x[i]), imag(x[i]) }
+	MOVSLDUP_X3_X3       // X3 = { real(x[i]), real(x[i]) }
+	MULPS X1, X2         // X2 = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
+	MULPS X0, X3         // X3 = { imag(a) * real(x[i]), real(a) * real(x[i]) }
+
+	// X3 = { imag(a)*real(x[i]) + real(a)*imag(x[i]),
+	//	  real(a)*real(x[i]) - imag(a)*imag(x[i])  }
+	ADDSUBPS_X2_X3
+	MOVSD (DX)(AX*8), X4 // X3 += y[i]
+	ADDPS X4, X3
+	MOVSD X3, (DI)(AX*8) // y[i]  = X3
+	INCQ  AX             // ++i
+	LOOP  caxy_tail      // } while --CX > 0
+
+caxy_end:
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c64/bench_test.go b/vendor/gonum.org/v1/gonum/internal/asm/c64/bench_test.go
new file mode 100644
index 00000000..0b7b5b83
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c64/bench_test.go
@@ -0,0 +1,282 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package c64
+
+import "testing"
+
+var (
+	a = complex64(2 + 2i)
+	x = make([]complex64, 1000000)
+	y = make([]complex64, 1000000)
+	z = make([]complex64, 1000000)
+)
+
+func init() {
+	for n := range x {
+		x[n] = complex(float32(n), float32(n))
+		y[n] = complex(float32(n), float32(n))
+	}
+}
+
+func benchaxpyu(t *testing.B, n int, f func(a complex64, x, y []complex64)) {
+	x, y := x[:n], y[:n]
+	for i := 0; i < t.N; i++ {
+		f(a, x, y)
+	}
+}
+
+func naiveaxpyu(a complex64, x, y []complex64) {
+	for i, v := range x {
+		y[i] += a * v
+	}
+}
+
+func BenchmarkC64AxpyUnitary1(t *testing.B)     { benchaxpyu(t, 1, AxpyUnitary) }
+func BenchmarkC64AxpyUnitary2(t *testing.B)     { benchaxpyu(t, 2, AxpyUnitary) }
+func BenchmarkC64AxpyUnitary3(t *testing.B)     { benchaxpyu(t, 3, AxpyUnitary) }
+func BenchmarkC64AxpyUnitary4(t *testing.B)     { benchaxpyu(t, 4, AxpyUnitary) }
+func BenchmarkC64AxpyUnitary5(t *testing.B)     { benchaxpyu(t, 5, AxpyUnitary) }
+func BenchmarkC64AxpyUnitary10(t *testing.B)    { benchaxpyu(t, 10, AxpyUnitary) }
+func BenchmarkC64AxpyUnitary100(t *testing.B)   { benchaxpyu(t, 100, AxpyUnitary) }
+func BenchmarkC64AxpyUnitary1000(t *testing.B)  { benchaxpyu(t, 1000, AxpyUnitary) }
+func BenchmarkC64AxpyUnitary5000(t *testing.B)  { benchaxpyu(t, 5000, AxpyUnitary) }
+func BenchmarkC64AxpyUnitary10000(t *testing.B) { benchaxpyu(t, 10000, AxpyUnitary) }
+func BenchmarkC64AxpyUnitary50000(t *testing.B) { benchaxpyu(t, 50000, AxpyUnitary) }
+
+func BenchmarkLC64AxpyUnitary1(t *testing.B)     { benchaxpyu(t, 1, naiveaxpyu) }
+func BenchmarkLC64AxpyUnitary2(t *testing.B)     { benchaxpyu(t, 2, naiveaxpyu) }
+func BenchmarkLC64AxpyUnitary3(t *testing.B)     { benchaxpyu(t, 3, naiveaxpyu) }
+func BenchmarkLC64AxpyUnitary4(t *testing.B)     { benchaxpyu(t, 4, naiveaxpyu) }
+func BenchmarkLC64AxpyUnitary5(t *testing.B)     { benchaxpyu(t, 5, naiveaxpyu) }
+func BenchmarkLC64AxpyUnitary10(t *testing.B)    { benchaxpyu(t, 10, naiveaxpyu) }
+func BenchmarkLC64AxpyUnitary100(t *testing.B)   { benchaxpyu(t, 100, naiveaxpyu) }
+func BenchmarkLC64AxpyUnitary1000(t *testing.B)  { benchaxpyu(t, 1000, naiveaxpyu) }
+func BenchmarkLC64AxpyUnitary5000(t *testing.B)  { benchaxpyu(t, 5000, naiveaxpyu) }
+func BenchmarkLC64AxpyUnitary10000(t *testing.B) { benchaxpyu(t, 10000, naiveaxpyu) }
+func BenchmarkLC64AxpyUnitary50000(t *testing.B) { benchaxpyu(t, 50000, naiveaxpyu) }
+
+func benchaxpyut(t *testing.B, n int, f func(d []complex64, a complex64, x, y []complex64)) {
+	x, y, z := x[:n], y[:n], z[:n]
+	for i := 0; i < t.N; i++ {
+		f(z, a, x, y)
+	}
+}
+
+func naiveaxpyut(d []complex64, a complex64, x, y []complex64) {
+	for i, v := range x {
+		d[i] = y[i] + a*v
+	}
+}
+
+func BenchmarkC64AxpyUnitaryTo1(t *testing.B)     { benchaxpyut(t, 1, AxpyUnitaryTo) }
+func BenchmarkC64AxpyUnitaryTo2(t *testing.B)     { benchaxpyut(t, 2, AxpyUnitaryTo) }
+func BenchmarkC64AxpyUnitaryTo3(t *testing.B)     { benchaxpyut(t, 3, AxpyUnitaryTo) }
+func BenchmarkC64AxpyUnitaryTo4(t *testing.B)     { benchaxpyut(t, 4, AxpyUnitaryTo) }
+func BenchmarkC64AxpyUnitaryTo5(t *testing.B)     { benchaxpyut(t, 5, AxpyUnitaryTo) }
+func BenchmarkC64AxpyUnitaryTo10(t *testing.B)    { benchaxpyut(t, 10, AxpyUnitaryTo) }
+func BenchmarkC64AxpyUnitaryTo100(t *testing.B)   { benchaxpyut(t, 100, AxpyUnitaryTo) }
+func BenchmarkC64AxpyUnitaryTo1000(t *testing.B)  { benchaxpyut(t, 1000, AxpyUnitaryTo) }
+func BenchmarkC64AxpyUnitaryTo5000(t *testing.B)  { benchaxpyut(t, 5000, AxpyUnitaryTo) }
+func BenchmarkC64AxpyUnitaryTo10000(t *testing.B) { benchaxpyut(t, 10000, AxpyUnitaryTo) }
+func BenchmarkC64AxpyUnitaryTo50000(t *testing.B) { benchaxpyut(t, 50000, AxpyUnitaryTo) }
+
+func BenchmarkLC64AxpyUnitaryTo1(t *testing.B)     { benchaxpyut(t, 1, naiveaxpyut) }
+func BenchmarkLC64AxpyUnitaryTo2(t *testing.B)     { benchaxpyut(t, 2, naiveaxpyut) }
+func BenchmarkLC64AxpyUnitaryTo3(t *testing.B)     { benchaxpyut(t, 3, naiveaxpyut) }
+func BenchmarkLC64AxpyUnitaryTo4(t *testing.B)     { benchaxpyut(t, 4, naiveaxpyut) }
+func BenchmarkLC64AxpyUnitaryTo5(t *testing.B)     { benchaxpyut(t, 5, naiveaxpyut) }
+func BenchmarkLC64AxpyUnitaryTo10(t *testing.B)    { benchaxpyut(t, 10, naiveaxpyut) }
+func BenchmarkLC64AxpyUnitaryTo100(t *testing.B)   { benchaxpyut(t, 100, naiveaxpyut) }
+func BenchmarkLC64AxpyUnitaryTo1000(t *testing.B)  { benchaxpyut(t, 1000, naiveaxpyut) }
+func BenchmarkLC64AxpyUnitaryTo5000(t *testing.B)  { benchaxpyut(t, 5000, naiveaxpyut) }
+func BenchmarkLC64AxpyUnitaryTo10000(t *testing.B) { benchaxpyut(t, 10000, naiveaxpyut) }
+func BenchmarkLC64AxpyUnitaryTo50000(t *testing.B) { benchaxpyut(t, 50000, naiveaxpyut) }
+
+func benchaxpyinc(t *testing.B, ln, t_inc int, f func(alpha complex64, x, y []complex64, n, incX, incY, ix, iy uintptr)) {
+	n, inc := uintptr(ln), uintptr(t_inc)
+	var idx int
+	if t_inc < 0 {
+		idx = (-ln + 1) * t_inc
+	}
+	for i := 0; i < t.N; i++ {
+		f(1+1i, x, y, n, inc, inc, uintptr(idx), uintptr(idx))
+	}
+}
+
+func naiveaxpyinc(alpha complex64, x, y []complex64, n, incX, incY, ix, iy uintptr) {
+	for i := 0; i < int(n); i++ {
+		y[iy] += alpha * x[ix]
+		ix += incX
+		iy += incY
+	}
+}
+
+func BenchmarkC64AxpyIncN1Inc1(b *testing.B) { benchaxpyinc(b, 1, 1, AxpyInc) }
+
+func BenchmarkC64AxpyIncN2Inc1(b *testing.B)  { benchaxpyinc(b, 2, 1, AxpyInc) }
+func BenchmarkC64AxpyIncN2Inc2(b *testing.B)  { benchaxpyinc(b, 2, 2, AxpyInc) }
+func BenchmarkC64AxpyIncN2Inc4(b *testing.B)  { benchaxpyinc(b, 2, 4, AxpyInc) }
+func BenchmarkC64AxpyIncN2Inc10(b *testing.B) { benchaxpyinc(b, 2, 10, AxpyInc) }
+
+func BenchmarkC64AxpyIncN3Inc1(b *testing.B)  { benchaxpyinc(b, 3, 1, AxpyInc) }
+func BenchmarkC64AxpyIncN3Inc2(b *testing.B)  { benchaxpyinc(b, 3, 2, AxpyInc) }
+func BenchmarkC64AxpyIncN3Inc4(b *testing.B)  { benchaxpyinc(b, 3, 4, AxpyInc) }
+func BenchmarkC64AxpyIncN3Inc10(b *testing.B) { benchaxpyinc(b, 3, 10, AxpyInc) }
+
+func BenchmarkC64AxpyIncN4Inc1(b *testing.B)  { benchaxpyinc(b, 4, 1, AxpyInc) }
+func BenchmarkC64AxpyIncN4Inc2(b *testing.B)  { benchaxpyinc(b, 4, 2, AxpyInc) }
+func BenchmarkC64AxpyIncN4Inc4(b *testing.B)  { benchaxpyinc(b, 4, 4, AxpyInc) }
+func BenchmarkC64AxpyIncN4Inc10(b *testing.B) { benchaxpyinc(b, 4, 10, AxpyInc) }
+
+func BenchmarkC64AxpyIncN10Inc1(b *testing.B)  { benchaxpyinc(b, 10, 1, AxpyInc) }
+func BenchmarkC64AxpyIncN10Inc2(b *testing.B)  { benchaxpyinc(b, 10, 2, AxpyInc) }
+func BenchmarkC64AxpyIncN10Inc4(b *testing.B)  { benchaxpyinc(b, 10, 4, AxpyInc) }
+func BenchmarkC64AxpyIncN10Inc10(b *testing.B) { benchaxpyinc(b, 10, 10, AxpyInc) }
+
+func BenchmarkC64AxpyIncN1000Inc1(b *testing.B)  { benchaxpyinc(b, 1000, 1, AxpyInc) }
+func BenchmarkC64AxpyIncN1000Inc2(b *testing.B)  { benchaxpyinc(b, 1000, 2, AxpyInc) }
+func BenchmarkC64AxpyIncN1000Inc4(b *testing.B)  { benchaxpyinc(b, 1000, 4, AxpyInc) }
+func BenchmarkC64AxpyIncN1000Inc10(b *testing.B) { benchaxpyinc(b, 1000, 10, AxpyInc) }
+
+func BenchmarkC64AxpyIncN100000Inc1(b *testing.B)  { benchaxpyinc(b, 100000, 1, AxpyInc) }
+func BenchmarkC64AxpyIncN100000Inc2(b *testing.B)  { benchaxpyinc(b, 100000, 2, AxpyInc) }
+func BenchmarkC64AxpyIncN100000Inc4(b *testing.B)  { benchaxpyinc(b, 100000, 4, AxpyInc) }
+func BenchmarkC64AxpyIncN100000Inc10(b *testing.B) { benchaxpyinc(b, 100000, 10, AxpyInc) }
+
+func BenchmarkC64AxpyIncN100000IncM1(b *testing.B)  { benchaxpyinc(b, 100000, -1, AxpyInc) }
+func BenchmarkC64AxpyIncN100000IncM2(b *testing.B)  { benchaxpyinc(b, 100000, -2, AxpyInc) }
+func BenchmarkC64AxpyIncN100000IncM4(b *testing.B)  { benchaxpyinc(b, 100000, -4, AxpyInc) }
+func BenchmarkC64AxpyIncN100000IncM10(b *testing.B) { benchaxpyinc(b, 100000, -10, AxpyInc) }
+
+func BenchmarkLC64AxpyIncN1Inc1(b *testing.B) { benchaxpyinc(b, 1, 1, naiveaxpyinc) }
+
+func BenchmarkLC64AxpyIncN2Inc1(b *testing.B)  { benchaxpyinc(b, 2, 1, naiveaxpyinc) }
+func BenchmarkLC64AxpyIncN2Inc2(b *testing.B)  { benchaxpyinc(b, 2, 2, naiveaxpyinc) }
+func BenchmarkLC64AxpyIncN2Inc4(b *testing.B)  { benchaxpyinc(b, 2, 4, naiveaxpyinc) }
+func BenchmarkLC64AxpyIncN2Inc10(b *testing.B) { benchaxpyinc(b, 2, 10, naiveaxpyinc) }
+
+func BenchmarkLC64AxpyIncN3Inc1(b *testing.B)  { benchaxpyinc(b, 3, 1, naiveaxpyinc) }
+func BenchmarkLC64AxpyIncN3Inc2(b *testing.B)  { benchaxpyinc(b, 3, 2, naiveaxpyinc) }
+func BenchmarkLC64AxpyIncN3Inc4(b *testing.B)  { benchaxpyinc(b, 3, 4, naiveaxpyinc) }
+func BenchmarkLC64AxpyIncN3Inc10(b *testing.B) { benchaxpyinc(b, 3, 10, naiveaxpyinc) }
+
+func BenchmarkLC64AxpyIncN4Inc1(b *testing.B)  { benchaxpyinc(b, 4, 1, naiveaxpyinc) }
+func BenchmarkLC64AxpyIncN4Inc2(b *testing.B)  { benchaxpyinc(b, 4, 2, naiveaxpyinc) }
+func BenchmarkLC64AxpyIncN4Inc4(b *testing.B)  { benchaxpyinc(b, 4, 4, naiveaxpyinc) }
+func BenchmarkLC64AxpyIncN4Inc10(b *testing.B) { benchaxpyinc(b, 4, 10, naiveaxpyinc) }
+
+func BenchmarkLC64AxpyIncN10Inc1(b *testing.B)  { benchaxpyinc(b, 10, 1, naiveaxpyinc) }
+func BenchmarkLC64AxpyIncN10Inc2(b *testing.B)  { benchaxpyinc(b, 10, 2, naiveaxpyinc) }
+func BenchmarkLC64AxpyIncN10Inc4(b *testing.B)  { benchaxpyinc(b, 10, 4, naiveaxpyinc) }
+func BenchmarkLC64AxpyIncN10Inc10(b *testing.B) { benchaxpyinc(b, 10, 10, naiveaxpyinc) }
+
+func BenchmarkLC64AxpyIncN1000Inc1(b *testing.B)  { benchaxpyinc(b, 1000, 1, naiveaxpyinc) }
+func BenchmarkLC64AxpyIncN1000Inc2(b *testing.B)  { benchaxpyinc(b, 1000, 2, naiveaxpyinc) }
+func BenchmarkLC64AxpyIncN1000Inc4(b *testing.B)  { benchaxpyinc(b, 1000, 4, naiveaxpyinc) }
+func BenchmarkLC64AxpyIncN1000Inc10(b *testing.B) { benchaxpyinc(b, 1000, 10, naiveaxpyinc) }
+
+func BenchmarkLC64AxpyIncN100000Inc1(b *testing.B)  { benchaxpyinc(b, 100000, 1, naiveaxpyinc) }
+func BenchmarkLC64AxpyIncN100000Inc2(b *testing.B)  { benchaxpyinc(b, 100000, 2, naiveaxpyinc) }
+func BenchmarkLC64AxpyIncN100000Inc4(b *testing.B)  { benchaxpyinc(b, 100000, 4, naiveaxpyinc) }
+func BenchmarkLC64AxpyIncN100000Inc10(b *testing.B) { benchaxpyinc(b, 100000, 10, naiveaxpyinc) }
+
+func BenchmarkLC64AxpyIncN100000IncM1(b *testing.B)  { benchaxpyinc(b, 100000, -1, naiveaxpyinc) }
+func BenchmarkLC64AxpyIncN100000IncM2(b *testing.B)  { benchaxpyinc(b, 100000, -2, naiveaxpyinc) }
+func BenchmarkLC64AxpyIncN100000IncM4(b *testing.B)  { benchaxpyinc(b, 100000, -4, naiveaxpyinc) }
+func BenchmarkLC64AxpyIncN100000IncM10(b *testing.B) { benchaxpyinc(b, 100000, -10, naiveaxpyinc) }
+
+func benchaxpyincto(t *testing.B, ln, t_inc int, f func(dst []complex64, incDst, idst uintptr, alpha complex64, x, y []complex64, n, incX, incY, ix, iy uintptr)) {
+	n, inc := uintptr(ln), uintptr(t_inc)
+	var idx int
+	if t_inc < 0 {
+		idx = (-ln + 1) * t_inc
+	}
+	for i := 0; i < t.N; i++ {
+		f(z, inc, uintptr(idx), 1+1i, x, y, n, inc, inc, uintptr(idx), uintptr(idx))
+	}
+}
+
+func naiveaxpyincto(dst []complex64, incDst, idst uintptr, alpha complex64, x, y []complex64, n, incX, incY, ix, iy uintptr) {
+	for i := 0; i < int(n); i++ {
+		dst[idst] = alpha*x[ix] + y[iy]
+		ix += incX
+		iy += incY
+		idst += incDst
+	}
+}
+
+func BenchmarkC64AxpyIncToN1Inc1(b *testing.B) { benchaxpyincto(b, 1, 1, AxpyIncTo) }
+
+func BenchmarkC64AxpyIncToN2Inc1(b *testing.B)  { benchaxpyincto(b, 2, 1, AxpyIncTo) }
+func BenchmarkC64AxpyIncToN2Inc2(b *testing.B)  { benchaxpyincto(b, 2, 2, AxpyIncTo) }
+func BenchmarkC64AxpyIncToN2Inc4(b *testing.B)  { benchaxpyincto(b, 2, 4, AxpyIncTo) }
+func BenchmarkC64AxpyIncToN2Inc10(b *testing.B) { benchaxpyincto(b, 2, 10, AxpyIncTo) }
+
+func BenchmarkC64AxpyIncToN3Inc1(b *testing.B)  { benchaxpyincto(b, 3, 1, AxpyIncTo) }
+func BenchmarkC64AxpyIncToN3Inc2(b *testing.B)  { benchaxpyincto(b, 3, 2, AxpyIncTo) }
+func BenchmarkC64AxpyIncToN3Inc4(b *testing.B)  { benchaxpyincto(b, 3, 4, AxpyIncTo) }
+func BenchmarkC64AxpyIncToN3Inc10(b *testing.B) { benchaxpyincto(b, 3, 10, AxpyIncTo) }
+
+func BenchmarkC64AxpyIncToN4Inc1(b *testing.B)  { benchaxpyincto(b, 4, 1, AxpyIncTo) }
+func BenchmarkC64AxpyIncToN4Inc2(b *testing.B)  { benchaxpyincto(b, 4, 2, AxpyIncTo) }
+func BenchmarkC64AxpyIncToN4Inc4(b *testing.B)  { benchaxpyincto(b, 4, 4, AxpyIncTo) }
+func BenchmarkC64AxpyIncToN4Inc10(b *testing.B) { benchaxpyincto(b, 4, 10, AxpyIncTo) }
+
+func BenchmarkC64AxpyIncToN10Inc1(b *testing.B)  { benchaxpyincto(b, 10, 1, AxpyIncTo) }
+func BenchmarkC64AxpyIncToN10Inc2(b *testing.B)  { benchaxpyincto(b, 10, 2, AxpyIncTo) }
+func BenchmarkC64AxpyIncToN10Inc4(b *testing.B)  { benchaxpyincto(b, 10, 4, AxpyIncTo) }
+func BenchmarkC64AxpyIncToN10Inc10(b *testing.B) { benchaxpyincto(b, 10, 10, AxpyIncTo) }
+
+func BenchmarkC64AxpyIncToN1000Inc1(b *testing.B)  { benchaxpyincto(b, 1000, 1, AxpyIncTo) }
+func BenchmarkC64AxpyIncToN1000Inc2(b *testing.B)  { benchaxpyincto(b, 1000, 2, AxpyIncTo) }
+func BenchmarkC64AxpyIncToN1000Inc4(b *testing.B)  { benchaxpyincto(b, 1000, 4, AxpyIncTo) }
+func BenchmarkC64AxpyIncToN1000Inc10(b *testing.B) { benchaxpyincto(b, 1000, 10, AxpyIncTo) }
+
+func BenchmarkC64AxpyIncToN100000Inc1(b *testing.B)  { benchaxpyincto(b, 100000, 1, AxpyIncTo) }
+func BenchmarkC64AxpyIncToN100000Inc2(b *testing.B)  { benchaxpyincto(b, 100000, 2, AxpyIncTo) }
+func BenchmarkC64AxpyIncToN100000Inc4(b *testing.B)  { benchaxpyincto(b, 100000, 4, AxpyIncTo) }
+func BenchmarkC64AxpyIncToN100000Inc10(b *testing.B) { benchaxpyincto(b, 100000, 10, AxpyIncTo) }
+
+func BenchmarkC64AxpyIncToN100000IncM1(b *testing.B)  { benchaxpyincto(b, 100000, -1, AxpyIncTo) }
+func BenchmarkC64AxpyIncToN100000IncM2(b *testing.B)  { benchaxpyincto(b, 100000, -2, AxpyIncTo) }
+func BenchmarkC64AxpyIncToN100000IncM4(b *testing.B)  { benchaxpyincto(b, 100000, -4, AxpyIncTo) }
+func BenchmarkC64AxpyIncToN100000IncM10(b *testing.B) { benchaxpyincto(b, 100000, -10, AxpyIncTo) }
+
+func BenchmarkLC64AxpyIncToN1Inc1(b *testing.B) { benchaxpyincto(b, 1, 1, naiveaxpyincto) }
+
+func BenchmarkLC64AxpyIncToN2Inc1(b *testing.B)  { benchaxpyincto(b, 2, 1, naiveaxpyincto) }
+func BenchmarkLC64AxpyIncToN2Inc2(b *testing.B)  { benchaxpyincto(b, 2, 2, naiveaxpyincto) }
+func BenchmarkLC64AxpyIncToN2Inc4(b *testing.B)  { benchaxpyincto(b, 2, 4, naiveaxpyincto) }
+func BenchmarkLC64AxpyIncToN2Inc10(b *testing.B) { benchaxpyincto(b, 2, 10, naiveaxpyincto) }
+
+func BenchmarkLC64AxpyIncToN3Inc1(b *testing.B)  { benchaxpyincto(b, 3, 1, naiveaxpyincto) }
+func BenchmarkLC64AxpyIncToN3Inc2(b *testing.B)  { benchaxpyincto(b, 3, 2, naiveaxpyincto) }
+func BenchmarkLC64AxpyIncToN3Inc4(b *testing.B)  { benchaxpyincto(b, 3, 4, naiveaxpyincto) }
+func BenchmarkLC64AxpyIncToN3Inc10(b *testing.B) { benchaxpyincto(b, 3, 10, naiveaxpyincto) }
+
+func BenchmarkLC64AxpyIncToN4Inc1(b *testing.B)  { benchaxpyincto(b, 4, 1, naiveaxpyincto) }
+func BenchmarkLC64AxpyIncToN4Inc2(b *testing.B)  { benchaxpyincto(b, 4, 2, naiveaxpyincto) }
+func BenchmarkLC64AxpyIncToN4Inc4(b *testing.B)  { benchaxpyincto(b, 4, 4, naiveaxpyincto) }
+func BenchmarkLC64AxpyIncToN4Inc10(b *testing.B) { benchaxpyincto(b, 4, 10, naiveaxpyincto) }
+
+func BenchmarkLC64AxpyIncToN10Inc1(b *testing.B)  { benchaxpyincto(b, 10, 1, naiveaxpyincto) }
+func BenchmarkLC64AxpyIncToN10Inc2(b *testing.B)  { benchaxpyincto(b, 10, 2, naiveaxpyincto) }
+func BenchmarkLC64AxpyIncToN10Inc4(b *testing.B)  { benchaxpyincto(b, 10, 4, naiveaxpyincto) }
+func BenchmarkLC64AxpyIncToN10Inc10(b *testing.B) { benchaxpyincto(b, 10, 10, naiveaxpyincto) }
+
+func BenchmarkLC64AxpyIncToN1000Inc1(b *testing.B)  { benchaxpyincto(b, 1000, 1, naiveaxpyincto) }
+func BenchmarkLC64AxpyIncToN1000Inc2(b *testing.B)  { benchaxpyincto(b, 1000, 2, naiveaxpyincto) }
+func BenchmarkLC64AxpyIncToN1000Inc4(b *testing.B)  { benchaxpyincto(b, 1000, 4, naiveaxpyincto) }
+func BenchmarkLC64AxpyIncToN1000Inc10(b *testing.B) { benchaxpyincto(b, 1000, 10, naiveaxpyincto) }
+
+func BenchmarkLC64AxpyIncToN100000Inc1(b *testing.B)  { benchaxpyincto(b, 100000, 1, naiveaxpyincto) }
+func BenchmarkLC64AxpyIncToN100000Inc2(b *testing.B)  { benchaxpyincto(b, 100000, 2, naiveaxpyincto) }
+func BenchmarkLC64AxpyIncToN100000Inc4(b *testing.B)  { benchaxpyincto(b, 100000, 4, naiveaxpyincto) }
+func BenchmarkLC64AxpyIncToN100000Inc10(b *testing.B) { benchaxpyincto(b, 100000, 10, naiveaxpyincto) }
+
+func BenchmarkLC64AxpyIncToN100000IncM1(b *testing.B)  { benchaxpyincto(b, 100000, -1, naiveaxpyincto) }
+func BenchmarkLC64AxpyIncToN100000IncM2(b *testing.B)  { benchaxpyincto(b, 100000, -2, naiveaxpyincto) }
+func BenchmarkLC64AxpyIncToN100000IncM4(b *testing.B)  { benchaxpyincto(b, 100000, -4, naiveaxpyincto) }
+func BenchmarkLC64AxpyIncToN100000IncM10(b *testing.B) { benchaxpyincto(b, 100000, -10, naiveaxpyincto) }
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c64/conj.go b/vendor/gonum.org/v1/gonum/internal/asm/c64/conj.go
new file mode 100644
index 00000000..932be953
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c64/conj.go
@@ -0,0 +1,7 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package c64
+
+func conj(c complex64) complex64 { return complex(real(c), -imag(c)) }
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c64/doc.go b/vendor/gonum.org/v1/gonum/internal/asm/c64/doc.go
new file mode 100644
index 00000000..a0b8862b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c64/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package c64 provides complex64 vector primitives.
+package c64 // import "gonum.org/v1/gonum/internal/asm/c64"
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c64/dotc.go b/vendor/gonum.org/v1/gonum/internal/asm/c64/dotc.go
new file mode 100644
index 00000000..cd5b862b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c64/dotc.go
@@ -0,0 +1,33 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package c64
+
+// DotcUnitary is
+//  for i, v := range x {
+//  	sum += y[i] * conj(v)
+//  }
+//  return sum
+func DotcUnitary(x, y []complex64) (sum complex64) {
+	for i, v := range x {
+		sum += y[i] * conj(v)
+	}
+	return sum
+}
+
+// DotcInc is
+//  for i := 0; i < int(n); i++ {
+//  	sum += y[iy] * conj(x[ix])
+//  	ix += incX
+//  	iy += incY
+//  }
+//  return sum
+func DotcInc(x, y []complex64, n, incX, incY, ix, iy uintptr) (sum complex64) {
+	for i := 0; i < int(n); i++ {
+		sum += y[iy] * conj(x[ix])
+		ix += incX
+		iy += incY
+	}
+	return sum
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c64/dotu.go b/vendor/gonum.org/v1/gonum/internal/asm/c64/dotu.go
new file mode 100644
index 00000000..ff15d659
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c64/dotu.go
@@ -0,0 +1,33 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package c64
+
+// DotuUnitary is
+//  for i, v := range x {
+//  	sum += y[i] * v
+//  }
+//  return sum
+func DotuUnitary(x, y []complex64) (sum complex64) {
+	for i, v := range x {
+		sum += y[i] * v
+	}
+	return sum
+}
+
+// DotuInc is
+//  for i := 0; i < int(n); i++ {
+//  	sum += y[iy] * x[ix]
+//  	ix += incX
+//  	iy += incY
+//  }
+//  return sum
+func DotuInc(x, y []complex64, n, incX, incY, ix, iy uintptr) (sum complex64) {
+	for i := 0; i < int(n); i++ {
+		sum += y[iy] * x[ix]
+		ix += incX
+		iy += incY
+	}
+	return sum
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c64/scal.go b/vendor/gonum.org/v1/gonum/internal/asm/c64/scal.go
new file mode 100644
index 00000000..11212813
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c64/scal.go
@@ -0,0 +1,55 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package c64
+
+// ScalUnitary is
+//  for i := range x {
+//  	x[i] *= alpha
+//  }
+func ScalUnitary(alpha complex64, x []complex64) {
+	for i := range x {
+		x[i] *= alpha
+	}
+}
+
+// ScalUnitaryTo is
+//  for i, v := range x {
+//  	dst[i] = alpha * v
+//  }
+func ScalUnitaryTo(dst []complex64, alpha complex64, x []complex64) {
+	for i, v := range x {
+		dst[i] = alpha * v
+	}
+}
+
+// ScalInc is
+//  var ix uintptr
+//  for i := 0; i < int(n); i++ {
+//  	x[ix] *= alpha
+//  	ix += incX
+//  }
+func ScalInc(alpha complex64, x []complex64, n, incX uintptr) {
+	var ix uintptr
+	for i := 0; i < int(n); i++ {
+		x[ix] *= alpha
+		ix += incX
+	}
+}
+
+// ScalIncTo is
+//  var idst, ix uintptr
+//  for i := 0; i < int(n); i++ {
+//  	dst[idst] = alpha * x[ix]
+//  	ix += incX
+//  	idst += incDst
+//  }
+func ScalIncTo(dst []complex64, incDst uintptr, alpha complex64, x []complex64, n, incX uintptr) {
+	var idst, ix uintptr
+	for i := 0; i < int(n); i++ {
+		dst[idst] = alpha * x[ix]
+		ix += incX
+		idst += incDst
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c64/stubs_amd64.go b/vendor/gonum.org/v1/gonum/internal/asm/c64/stubs_amd64.go
new file mode 100644
index 00000000..bd6486c3
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c64/stubs_amd64.go
@@ -0,0 +1,36 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !noasm,!appengine
+
+package c64
+
+// AxpyUnitary is
+//  for i, v := range x {
+//  	y[i] += alpha * v
+//  }
+func AxpyUnitary(alpha complex64, x, y []complex64)
+
+// AxpyUnitaryTo is
+//  for i, v := range x {
+//  	dst[i] = alpha*v + y[i]
+//  }
+func AxpyUnitaryTo(dst []complex64, alpha complex64, x, y []complex64)
+
+// AxpyInc is
+//  for i := 0; i < int(n); i++ {
+//  	y[iy] += alpha * x[ix]
+//  	ix += incX
+//  	iy += incY
+//  }
+func AxpyInc(alpha complex64, x, y []complex64, n, incX, incY, ix, iy uintptr)
+
+// AxpyIncTo is
+//  for i := 0; i < int(n); i++ {
+//  	dst[idst] = alpha*x[ix] + y[iy]
+//  	ix += incX
+//  	iy += incY
+//  	idst += incDst
+//  }
+func AxpyIncTo(dst []complex64, incDst, idst uintptr, alpha complex64, x, y []complex64, n, incX, incY, ix, iy uintptr)
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c64/stubs_noasm.go b/vendor/gonum.org/v1/gonum/internal/asm/c64/stubs_noasm.go
new file mode 100644
index 00000000..78aebbd6
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c64/stubs_noasm.go
@@ -0,0 +1,57 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !amd64 noasm appengine
+
+package c64
+
+// AxpyUnitary is
+//  for i, v := range x {
+//  	y[i] += alpha * v
+//  }
+func AxpyUnitary(alpha complex64, x, y []complex64) {
+	for i, v := range x {
+		y[i] += alpha * v
+	}
+}
+
+// AxpyUnitaryTo is
+//  for i, v := range x {
+//  	dst[i] = alpha*v + y[i]
+//  }
+func AxpyUnitaryTo(dst []complex64, alpha complex64, x, y []complex64) {
+	for i, v := range x {
+		dst[i] = alpha*v + y[i]
+	}
+}
+
+// AxpyInc is
+//  for i := 0; i < int(n); i++ {
+//  	y[iy] += alpha * x[ix]
+//  	ix += incX
+//  	iy += incY
+//  }
+func AxpyInc(alpha complex64, x, y []complex64, n, incX, incY, ix, iy uintptr) {
+	for i := 0; i < int(n); i++ {
+		y[iy] += alpha * x[ix]
+		ix += incX
+		iy += incY
+	}
+}
+
+// AxpyIncTo is
+//  for i := 0; i < int(n); i++ {
+//  	dst[idst] = alpha*x[ix] + y[iy]
+//  	ix += incX
+//  	iy += incY
+//  	idst += incDst
+//  }
+func AxpyIncTo(dst []complex64, incDst, idst uintptr, alpha complex64, x, y []complex64, n, incX, incY, ix, iy uintptr) {
+	for i := 0; i < int(n); i++ {
+		dst[idst] = alpha*x[ix] + y[iy]
+		ix += incX
+		iy += incY
+		idst += incDst
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/c64/stubs_test.go b/vendor/gonum.org/v1/gonum/internal/asm/c64/stubs_test.go
new file mode 100644
index 00000000..8049a763
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/c64/stubs_test.go
@@ -0,0 +1,231 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package c64
+
+import "testing"
+
+var tests = []struct {
+	incX, incY, incDst int
+	ix, iy, idst       uintptr
+	a                  complex64
+	dst, x, y          []complex64
+	ex                 []complex64
+}{
+	{incX: 2, incY: 2, incDst: 3, ix: 0, iy: 0, idst: 0,
+		a:   1 + 1i,
+		dst: []complex64{5},
+		x:   []complex64{1},
+		y:   []complex64{1i},
+		ex:  []complex64{1 + 2i}},
+	{incX: 2, incY: 2, incDst: 3, ix: 0, iy: 0, idst: 0,
+		a:   1 + 2i,
+		dst: []complex64{0, 0, 0},
+		x:   []complex64{0, 0, 0},
+		y:   []complex64{1, 1, 1},
+		ex:  []complex64{1, 1, 1}},
+	{incX: 2, incY: 2, incDst: 3, ix: 0, iy: 0, idst: 0,
+		a:   1 + 2i,
+		dst: []complex64{0, 0, 0},
+		x:   []complex64{0, 0},
+		y:   []complex64{1, 1, 1},
+		ex:  []complex64{1, 1}},
+	{incX: 2, incY: 2, incDst: 3, ix: 0, iy: 0, idst: 0,
+		a:   1 + 2i,
+		dst: []complex64{1i, 1i, 1i},
+		x:   []complex64{1i, 1i, 1i},
+		y:   []complex64{1, 2, 1},
+		ex:  []complex64{-1 + 1i, 1i, -1 + 1i}},
+	{incX: 2, incY: 2, incDst: 3, ix: 0, iy: 0, idst: 0,
+		a:   -1i,
+		dst: []complex64{1i, 1i, 1i},
+		x:   []complex64{1i, 1i, 1i},
+		y:   []complex64{1, 2, 1},
+		ex:  []complex64{2, 3, 2}},
+	{incX: 2, incY: 2, incDst: 3, ix: 0, iy: 0, idst: 0,
+		a:   -1i,
+		dst: []complex64{1i, 1i, 1i},
+		x:   []complex64{1i, 1i, 1i, 1i, 1i}[1:4],
+		y:   []complex64{1, 1, 2, 1, 1}[1:4],
+		ex:  []complex64{2, 3, 2}},
+	{incX: 2, incY: 4, incDst: 3, ix: 0, iy: 0, idst: 0,
+		a:   -2,
+		dst: []complex64{1i, 1i, 1i, 1i, 1i},
+		x:   []complex64{2 + 1i, 2 + 1i, 2 + 1i, 2 + 1i, 2 + 1i},
+		y:   []complex64{1, 1, 2, 1, 1},
+		ex:  []complex64{-3 - 2i, -3 - 2i, -2 - 2i, -3 - 2i, -3 - 2i}},
+	// Run big test twice, once aligned once unaligned.
+	{incX: 2, incY: 2, incDst: 3, ix: 0, iy: 0, idst: 0,
+		a:   1 - 1i,
+		dst: make([]complex64, 10),
+		x:   []complex64{1i, 1i, 1i, 1i, 1i, 1i, 1i, 1i, 1i, 1i},
+		y:   []complex64{1, 1, 2, 1, 1, 1, 1, 2, 1, 1},
+		ex:  []complex64{2 + 1i, 2 + 1i, 3 + 1i, 2 + 1i, 2 + 1i, 2 + 1i, 2 + 1i, 3 + 1i, 2 + 1i, 2 + 1i}},
+	{incX: 2, incY: 2, incDst: 3, ix: 0, iy: 0, idst: 0,
+		a:   1 - 1i,
+		dst: make([]complex64, 10),
+		x:   []complex64{1i, 1i, 1i, 1i, 1i, 1i, 1i, 1i, 1i, 1i},
+		y:   []complex64{1, 1, 2, 1, 1, 1, 1, 2, 1, 1},
+		ex:  []complex64{2 + 1i, 2 + 1i, 3 + 1i, 2 + 1i, 2 + 1i, 2 + 1i, 2 + 1i, 3 + 1i, 2 + 1i, 2 + 1i}},
+	{incX: -2, incY: -2, incDst: -3, ix: 18, iy: 18, idst: 27,
+		a:   1 - 1i,
+		dst: make([]complex64, 10),
+		x:   []complex64{1i, 1i, 1i, 1i, 1i, 1i, 1i, 1i, 1i, 1i},
+		y:   []complex64{1, 1, 2, 1, 1, 1, 1, 2, 1, 1},
+		ex:  []complex64{2 + 1i, 2 + 1i, 3 + 1i, 2 + 1i, 2 + 1i, 2 + 1i, 2 + 1i, 3 + 1i, 2 + 1i, 2 + 1i}},
+	{incX: -2, incY: 2, incDst: -3, ix: 18, iy: 0, idst: 27,
+		a:   1 - 1i,
+		dst: make([]complex64, 10),
+		x:   []complex64{1i, 1i, 1i, 1i, 1i, 1i, 1i, 1i, 1i, 1i},
+		y:   []complex64{1, 1, 2, 1, 1, 1, 1, 2, 1, 1},
+		ex:  []complex64{2 + 1i, 2 + 1i, 3 + 1i, 2 + 1i, 2 + 1i, 2 + 1i, 2 + 1i, 3 + 1i, 2 + 1i, 2 + 1i}},
+}
+
+func guardVector(vec []complex64, guard_val complex64, guard_len int) (guarded []complex64) {
+	guarded = make([]complex64, len(vec)+guard_len*2)
+	copy(guarded[guard_len:], vec)
+	for i := 0; i < guard_len; i++ {
+		guarded[i] = guard_val
+		guarded[len(guarded)-1-i] = guard_val
+	}
+	return guarded
+}
+
+func isValidGuard(vec []complex64, guard_val complex64, guard_len int) bool {
+	for i := 0; i < guard_len; i++ {
+		if vec[i] != guard_val || vec[len(vec)-1-i] != guard_val {
+			return false
+		}
+	}
+	return true
+}
+
+func TestAxpyUnitary(t *testing.T) {
+	var x_gd, y_gd complex64 = 1, 1
+	for cas, test := range tests {
+		xg_ln, yg_ln := 4+cas%2, 4+cas%3
+		test.x, test.y = guardVector(test.x, x_gd, xg_ln), guardVector(test.y, y_gd, yg_ln)
+		x, y := test.x[xg_ln:len(test.x)-xg_ln], test.y[yg_ln:len(test.y)-yg_ln]
+		AxpyUnitary(test.a, x, y)
+		for i := range test.ex {
+			if y[i] != test.ex[i] {
+				t.Errorf("Test %d Unexpected result at %d Got: %v Expected: %v", cas, i, y[i], test.ex[i])
+			}
+		}
+		if !isValidGuard(test.x, x_gd, xg_ln) {
+			t.Errorf("Test %d Guard violated in x vector %v %v", cas, test.x[:xg_ln], test.x[len(test.x)-xg_ln:])
+		}
+		if !isValidGuard(test.y, y_gd, yg_ln) {
+			t.Errorf("Test %d Guard violated in y vector %v %v", cas, test.y[:yg_ln], test.y[len(test.y)-yg_ln:])
+		}
+	}
+}
+
+func TestAxpyUnitaryTo(t *testing.T) {
+	var x_gd, y_gd, dst_gd complex64 = 1, 1, 0
+	for cas, test := range tests {
+		xg_ln, yg_ln := 4+cas%2, 4+cas%3
+		test.x, test.y = guardVector(test.x, x_gd, xg_ln), guardVector(test.y, y_gd, yg_ln)
+		test.dst = guardVector(test.dst, dst_gd, xg_ln)
+		x, y := test.x[xg_ln:len(test.x)-xg_ln], test.y[yg_ln:len(test.y)-yg_ln]
+		dst := test.dst[xg_ln : len(test.dst)-xg_ln]
+		AxpyUnitaryTo(dst, test.a, x, y)
+		for i := range test.ex {
+			if dst[i] != test.ex[i] {
+				t.Errorf("Test %d Unexpected result at %d Got: %v Expected: %v", cas, i, dst[i], test.ex[i])
+			}
+		}
+		if !isValidGuard(test.x, x_gd, xg_ln) {
+			t.Errorf("Test %d Guard violated in x vector %v %v", cas, test.x[:xg_ln], test.x[len(test.x)-xg_ln:])
+		}
+		if !isValidGuard(test.y, y_gd, yg_ln) {
+			t.Errorf("Test %d Guard violated in y vector %v %v", cas, test.y[:yg_ln], test.y[len(test.y)-yg_ln:])
+		}
+		if !isValidGuard(test.dst, dst_gd, xg_ln) {
+			t.Errorf("Test %d Guard violated in dst vector %v %v", cas, test.dst[:xg_ln], test.dst[len(test.dst)-xg_ln:])
+		}
+
+	}
+}
+
+func guardIncVector(vec []complex64, guard_val complex64, incV uintptr, guard_len int) (guarded []complex64) {
+	inc := int(incV)
+	s_ln := len(vec) * inc
+	if inc < 0 {
+		s_ln = len(vec) * -inc
+	}
+	guarded = make([]complex64, s_ln+guard_len*2)
+	for i, cas := 0, 0; i < len(guarded); i++ {
+		switch {
+		case i < guard_len, i > guard_len+s_ln:
+			guarded[i] = guard_val
+		case (i-guard_len)%(inc) == 0 && cas < len(vec):
+			guarded[i] = vec[cas]
+			cas++
+		default:
+			guarded[i] = guard_val
+		}
+	}
+	return guarded
+}
+
+func checkValidIncGuard(t *testing.T, vec []complex64, guard_val complex64, incV uintptr, guard_len int) {
+	inc := int(incV)
+	s_ln := len(vec) - 2*guard_len
+	if inc < 0 {
+		s_ln = len(vec) * -inc
+	}
+
+	for i := range vec {
+		switch {
+		case vec[i] == guard_val:
+			// Correct value
+		case i < guard_len:
+			t.Errorf("Front guard violated at %d %v", i, vec[:guard_len])
+		case i > guard_len+s_ln:
+			t.Errorf("Back guard violated at %d %v", i-guard_len-s_ln, vec[guard_len+s_ln:])
+		case (i-guard_len)%inc == 0 && (i-guard_len)/inc < len(vec):
+			// Ignore input values
+		default:
+			t.Errorf("Internal guard violated at %d %v", i-guard_len, vec[guard_len:guard_len+s_ln])
+		}
+	}
+}
+
+func TestAxpyInc(t *testing.T) {
+	var x_gd, y_gd complex64 = 1, 1
+	for cas, test := range tests {
+		xg_ln, yg_ln := 4+cas%2, 4+cas%3
+		test.x, test.y = guardIncVector(test.x, x_gd, uintptr(test.incX), xg_ln), guardIncVector(test.y, y_gd, uintptr(test.incY), yg_ln)
+		x, y := test.x[xg_ln:len(test.x)-xg_ln], test.y[yg_ln:len(test.y)-yg_ln]
+		AxpyInc(test.a, x, y, uintptr(len(test.ex)), uintptr(test.incX), uintptr(test.incY), test.ix, test.iy)
+		for i := range test.ex {
+			if y[int(test.iy)+i*int(test.incY)] != test.ex[i] {
+				t.Errorf("Test %d Unexpected result at %d Got: %v Expected: %v", cas, i, y[i*int(test.incY)], test.ex[i])
+			}
+		}
+		checkValidIncGuard(t, test.x, x_gd, uintptr(test.incX), xg_ln)
+		checkValidIncGuard(t, test.y, y_gd, uintptr(test.incY), yg_ln)
+	}
+}
+
+func TestAxpyIncTo(t *testing.T) {
+	var x_gd, y_gd, dst_gd complex64 = 1, 1, 0
+	for cas, test := range tests {
+		xg_ln, yg_ln := 4+cas%2, 4+cas%3
+		test.x, test.y = guardIncVector(test.x, x_gd, uintptr(test.incX), xg_ln), guardIncVector(test.y, y_gd, uintptr(test.incY), yg_ln)
+		test.dst = guardIncVector(test.dst, dst_gd, uintptr(test.incDst), xg_ln)
+		x, y := test.x[xg_ln:len(test.x)-xg_ln], test.y[yg_ln:len(test.y)-yg_ln]
+		dst := test.dst[xg_ln : len(test.dst)-xg_ln]
+		AxpyIncTo(dst, uintptr(test.incDst), test.idst, test.a, x, y, uintptr(len(test.ex)), uintptr(test.incX), uintptr(test.incY), test.ix, test.iy)
+		for i := range test.ex {
+			if dst[int(test.idst)+i*int(test.incDst)] != test.ex[i] {
+				t.Errorf("Test %d Unexpected result at %d Got: %v Expected: %v", cas, i, dst[i*int(test.incDst)], test.ex[i])
+			}
+		}
+		checkValidIncGuard(t, test.x, x_gd, uintptr(test.incX), xg_ln)
+		checkValidIncGuard(t, test.y, y_gd, uintptr(test.incY), yg_ln)
+		checkValidIncGuard(t, test.dst, dst_gd, uintptr(test.incDst), xg_ln)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f32/axpyinc_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/f32/axpyinc_amd64.s
new file mode 100644
index 00000000..a6462f0e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f32/axpyinc_amd64.s
@@ -0,0 +1,73 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !noasm,!appengine
+
+#include "textflag.h"
+
+// func AxpyInc(alpha float32, x, y []float32, n, incX, incY, ix, iy uintptr)
+TEXT ·AxpyInc(SB), NOSPLIT, $0
+	MOVQ  n+56(FP), CX      // CX = n
+	CMPQ  CX, $0            // if n==0 { return }
+	JLE   axpyi_end
+	MOVQ  x_base+8(FP), SI  // SI = &x
+	MOVQ  y_base+32(FP), DI // DI = &y
+	MOVQ  ix+80(FP), R8     // R8 = ix
+	MOVQ  iy+88(FP), R9     // R9 = iy
+	LEAQ  (SI)(R8*4), SI    // SI = &(x[ix])
+	LEAQ  (DI)(R9*4), DI    // DI = &(y[iy])
+	MOVQ  DI, DX            // DX = DI   Read Pointer for y
+	MOVQ  incX+64(FP), R8   // R8 = incX
+	SHLQ  $2, R8            // R8 *= sizeof(float32)
+	MOVQ  incY+72(FP), R9   // R9 = incY
+	SHLQ  $2, R9            // R9 *= sizeof(float32)
+	MOVSS alpha+0(FP), X0   // X0 = alpha
+	MOVSS X0, X1            // X1 = X0  // for pipelining
+	MOVQ  CX, BX
+	ANDQ  $3, BX            // BX = n % 4
+	SHRQ  $2, CX            // CX = floor( n / 4 )
+	JZ    axpyi_tail_start  // if CX == 0 { goto axpyi_tail_start }
+
+axpyi_loop: // Loop unrolled 4x   do {
+	MOVSS (SI), X2       // X_i = x[i]
+	MOVSS (SI)(R8*1), X3
+	LEAQ  (SI)(R8*2), SI // SI = &(SI[incX*2])
+	MOVSS (SI), X4
+	MOVSS (SI)(R8*1), X5
+	MULSS X1, X2         // X_i *= a
+	MULSS X0, X3
+	MULSS X1, X4
+	MULSS X0, X5
+	ADDSS (DX), X2       // X_i += y[i]
+	ADDSS (DX)(R9*1), X3
+	LEAQ  (DX)(R9*2), DX // DX = &(DX[incY*2])
+	ADDSS (DX), X4
+	ADDSS (DX)(R9*1), X5
+	MOVSS X2, (DI)       // y[i] = X_i
+	MOVSS X3, (DI)(R9*1)
+	LEAQ  (DI)(R9*2), DI // DI = &(DI[incY*2])
+	MOVSS X4, (DI)
+	MOVSS X5, (DI)(R9*1)
+	LEAQ  (SI)(R8*2), SI // SI = &(SI[incX*2])  // Increment addresses
+	LEAQ  (DX)(R9*2), DX // DX = &(DX[incY*2])
+	LEAQ  (DI)(R9*2), DI // DI = &(DI[incY*2])
+	LOOP  axpyi_loop     // } while --CX > 0
+	CMPQ  BX, $0         // if BX == 0 { return }
+	JE    axpyi_end
+
+axpyi_tail_start: // Reset loop registers
+	MOVQ BX, CX // Loop counter: CX = BX
+
+axpyi_tail: // do {
+	MOVSS (SI), X2   // X2 = x[i]
+	MULSS X1, X2     // X2 *= a
+	ADDSS (DI), X2   // X2 += y[i]
+	MOVSS X2, (DI)   // y[i] = X2
+	ADDQ  R8, SI     // SI = &(SI[incX])
+	ADDQ  R9, DI     // DI = &(DI[incY])
+	LOOP  axpyi_tail // } while --CX > 0
+
+axpyi_end:
+	RET
+
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f32/axpyincto_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/f32/axpyincto_amd64.s
new file mode 100644
index 00000000..e1c39e90
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f32/axpyincto_amd64.s
@@ -0,0 +1,78 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !noasm,!appengine
+
+#include "textflag.h"
+
+// func AxpyIncTo(dst []float32, incDst, idst uintptr, alpha float32, x, y []float32, n, incX, incY, ix, iy uintptr)
+TEXT ·AxpyIncTo(SB), NOSPLIT, $0
+	MOVQ  n+96(FP), CX       // CX = n
+	CMPQ  CX, $0             // if n==0 { return }
+	JLE   axpyi_end
+	MOVQ  dst_base+0(FP), DI // DI = &dst
+	MOVQ  x_base+48(FP), SI  // SI = &x
+	MOVQ  y_base+72(FP), DX  // DX = &y
+	MOVQ  ix+120(FP), R8     // R8 = ix  // Load the first index
+	MOVQ  iy+128(FP), R9     // R9 = iy
+	MOVQ  idst+32(FP), R10   // R10 = idst
+	LEAQ  (SI)(R8*4), SI     // SI = &(x[ix])
+	LEAQ  (DX)(R9*4), DX     // DX = &(y[iy])
+	LEAQ  (DI)(R10*4), DI    // DI = &(dst[idst])
+	MOVQ  incX+104(FP), R8   // R8 = incX
+	SHLQ  $2, R8             // R8 *= sizeof(float32)
+	MOVQ  incY+112(FP), R9   // R9 = incY
+	SHLQ  $2, R9             // R9 *= sizeof(float32)
+	MOVQ  incDst+24(FP), R10 // R10 = incDst
+	SHLQ  $2, R10            // R10 *= sizeof(float32)
+	MOVSS alpha+40(FP), X0   // X0 = alpha
+	MOVSS X0, X1             // X1 = X0  // for pipelining
+	MOVQ  CX, BX
+	ANDQ  $3, BX             // BX = n % 4
+	SHRQ  $2, CX             // CX = floor( n / 4 )
+	JZ    axpyi_tail_start   // if CX == 0 { goto axpyi_tail_start }
+
+axpyi_loop: // Loop unrolled 4x   do {
+	MOVSS (SI), X2        // X_i = x[i]
+	MOVSS (SI)(R8*1), X3
+	LEAQ  (SI)(R8*2), SI  // SI = &(SI[incX*2])
+	MOVSS (SI), X4
+	MOVSS (SI)(R8*1), X5
+	MULSS X1, X2          // X_i *= a
+	MULSS X0, X3
+	MULSS X1, X4
+	MULSS X0, X5
+	ADDSS (DX), X2        // X_i += y[i]
+	ADDSS (DX)(R9*1), X3
+	LEAQ  (DX)(R9*2), DX  // DX = &(DX[incY*2])
+	ADDSS (DX), X4
+	ADDSS (DX)(R9*1), X5
+	MOVSS X2, (DI)        // dst[i] = X_i
+	MOVSS X3, (DI)(R10*1)
+	LEAQ  (DI)(R10*2), DI // DI = &(DI[incDst*2])
+	MOVSS X4, (DI)
+	MOVSS X5, (DI)(R10*1)
+	LEAQ  (SI)(R8*2), SI  // SI = &(SI[incX*2])  // Increment addresses
+	LEAQ  (DX)(R9*2), DX  // DX = &(DX[incY*2])
+	LEAQ  (DI)(R10*2), DI // DI = &(DI[incDst*2])
+	LOOP  axpyi_loop      // } while --CX > 0
+	CMPQ  BX, $0          // if BX == 0 { return }
+	JE    axpyi_end
+
+axpyi_tail_start: // Reset loop registers
+	MOVQ BX, CX // Loop counter: CX = BX
+
+axpyi_tail: // do {
+	MOVSS (SI), X2   // X2 = x[i]
+	MULSS X1, X2     // X2 *= a
+	ADDSS (DX), X2   // X2 += y[i]
+	MOVSS X2, (DI)   // dst[i] = X2
+	ADDQ  R8, SI     // SI = &(SI[incX])
+	ADDQ  R9, DX     // DX = &(DX[incY])
+	ADDQ  R10, DI    // DI = &(DI[incY])
+	LOOP  axpyi_tail // } while --CX > 0
+
+axpyi_end:
+	RET
+
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f32/axpyunitary_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/f32/axpyunitary_amd64.s
new file mode 100644
index 00000000..a5bfaac9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f32/axpyunitary_amd64.s
@@ -0,0 +1,97 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !noasm,!appengine
+
+#include "textflag.h"
+
+// func AxpyUnitary(alpha float32, x, y []float32)
+TEXT ·AxpyUnitary(SB), NOSPLIT, $0
+	MOVQ    x_base+8(FP), SI  // SI = &x
+	MOVQ    y_base+32(FP), DI // DI = &y
+	MOVQ    x_len+16(FP), BX  // BX = min( len(x), len(y) )
+	CMPQ    y_len+40(FP), BX
+	CMOVQLE y_len+40(FP), BX
+	CMPQ    BX, $0            // if BX == 0 { return }
+	JE      axpy_end
+	MOVSS   alpha+0(FP), X0
+	SHUFPS  $0, X0, X0        // X0 = { a, a, a, a }
+	XORQ    AX, AX            // i = 0
+	PXOR    X2, X2            // 2 NOP instructions (PXOR) to align
+	PXOR    X3, X3            // loop to cache line
+	MOVQ    DI, CX
+	ANDQ    $0xF, CX          // Align on 16-byte boundary for ADDPS
+	JZ      axpy_no_trim      // if CX == 0 { goto axpy_no_trim }
+
+	XORQ $0xF, CX // CX = 4 - floor( BX % 16 / 4 )
+	INCQ CX
+	SHRQ $2, CX
+
+axpy_align: // Trim first value(s) in unaligned buffer  do {
+	MOVSS (SI)(AX*4), X2 // X2 = x[i]
+	MULSS X0, X2         // X2 *= a
+	ADDSS (DI)(AX*4), X2 // X2 += y[i]
+	MOVSS X2, (DI)(AX*4) // y[i] = X2
+	INCQ  AX             // i++
+	DECQ  BX
+	JZ    axpy_end       // if --BX == 0 { return }
+	LOOP  axpy_align     // } while --CX > 0
+
+axpy_no_trim:
+	MOVUPS X0, X1           // Copy X0 to X1 for pipelining
+	MOVQ   BX, CX
+	ANDQ   $0xF, BX         // BX = len % 16
+	SHRQ   $4, CX           // CX = int( len / 16 )
+	JZ     axpy_tail4_start // if CX == 0 { return }
+
+axpy_loop: // Loop unrolled 16x   do {
+	MOVUPS (SI)(AX*4), X2   // X2 = x[i:i+4]
+	MOVUPS 16(SI)(AX*4), X3
+	MOVUPS 32(SI)(AX*4), X4
+	MOVUPS 48(SI)(AX*4), X5
+	MULPS  X0, X2           // X2 *= a
+	MULPS  X1, X3
+	MULPS  X0, X4
+	MULPS  X1, X5
+	ADDPS  (DI)(AX*4), X2   // X2 += y[i:i+4]
+	ADDPS  16(DI)(AX*4), X3
+	ADDPS  32(DI)(AX*4), X4
+	ADDPS  48(DI)(AX*4), X5
+	MOVUPS X2, (DI)(AX*4)   // dst[i:i+4] = X2
+	MOVUPS X3, 16(DI)(AX*4)
+	MOVUPS X4, 32(DI)(AX*4)
+	MOVUPS X5, 48(DI)(AX*4)
+	ADDQ   $16, AX          // i += 16
+	LOOP   axpy_loop        // while (--CX) > 0
+	CMPQ   BX, $0           // if BX == 0 { return }
+	JE     axpy_end
+
+axpy_tail4_start: // Reset loop counter for 4-wide tail loop
+	MOVQ BX, CX          // CX = floor( BX / 4 )
+	SHRQ $2, CX
+	JZ   axpy_tail_start // if CX == 0 { goto axpy_tail_start }
+
+axpy_tail4: // Loop unrolled 4x   do {
+	MOVUPS (SI)(AX*4), X2 // X2 = x[i]
+	MULPS  X0, X2         // X2 *= a
+	ADDPS  (DI)(AX*4), X2 // X2 += y[i]
+	MOVUPS X2, (DI)(AX*4) // y[i] = X2
+	ADDQ   $4, AX         // i += 4
+	LOOP   axpy_tail4     // } while --CX > 0
+
+axpy_tail_start: // Reset loop counter for 1-wide tail loop
+	MOVQ BX, CX   // CX = BX % 4
+	ANDQ $3, CX
+	JZ   axpy_end // if CX == 0 { return }
+
+axpy_tail:
+	MOVSS (SI)(AX*4), X1 // X1 = x[i]
+	MULSS X0, X1         // X1 *= a
+	ADDSS (DI)(AX*4), X1 // X1 += y[i]
+	MOVSS X1, (DI)(AX*4) // y[i] = X1
+	INCQ  AX             // i++
+	LOOP  axpy_tail      // } while --CX > 0
+
+axpy_end:
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f32/axpyunitaryto_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/f32/axpyunitaryto_amd64.s
new file mode 100644
index 00000000..9a8289f8
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f32/axpyunitaryto_amd64.s
@@ -0,0 +1,98 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !noasm,!appengine
+
+#include "textflag.h"
+
+// func AxpyUnitaryTo(dst []float32, alpha float32, x, y []float32)
+TEXT ·AxpyUnitaryTo(SB), NOSPLIT, $0
+	MOVQ    dst_base+0(FP), DI // DI = &dst
+	MOVQ    x_base+32(FP), SI  // SI = &x
+	MOVQ    y_base+56(FP), DX  // DX = &y
+	MOVQ    x_len+40(FP), BX   // BX = min( len(x), len(y), len(dst) )
+	CMPQ    y_len+64(FP), BX
+	CMOVQLE y_len+64(FP), BX
+	CMPQ    dst_len+8(FP), BX
+	CMOVQLE dst_len+8(FP), BX
+	CMPQ    BX, $0             // if BX == 0 { return }
+	JE      axpy_end
+	MOVSS   alpha+24(FP), X0
+	SHUFPS  $0, X0, X0         // X0 = { a, a, a, a, }
+	XORQ    AX, AX             // i = 0
+	MOVQ    DX, CX
+	ANDQ    $0xF, CX           // Align on 16-byte boundary for ADDPS
+	JZ      axpy_no_trim       // if CX == 0 { goto axpy_no_trim }
+
+	XORQ $0xF, CX // CX = 4 - floor ( B % 16 / 4 )
+	INCQ CX
+	SHRQ $2, CX
+
+axpy_align: // Trim first value(s) in unaligned buffer  do {
+	MOVSS (SI)(AX*4), X2 // X2 = x[i]
+	MULSS X0, X2         // X2 *= a
+	ADDSS (DX)(AX*4), X2 // X2 += y[i]
+	MOVSS X2, (DI)(AX*4) // y[i] = X2
+	INCQ  AX             // i++
+	DECQ  BX
+	JZ    axpy_end       // if --BX == 0 { return }
+	LOOP  axpy_align     // } while --CX > 0
+
+axpy_no_trim:
+	MOVUPS X0, X1           // Copy X0 to X1 for pipelining
+	MOVQ   BX, CX
+	ANDQ   $0xF, BX         // BX = len % 16
+	SHRQ   $4, CX           // CX = floor( len / 16 )
+	JZ     axpy_tail4_start // if CX == 0 { return }
+
+axpy_loop: // Loop unrolled 16x  do {
+	MOVUPS (SI)(AX*4), X2   // X2 = x[i:i+4]
+	MOVUPS 16(SI)(AX*4), X3
+	MOVUPS 32(SI)(AX*4), X4
+	MOVUPS 48(SI)(AX*4), X5
+	MULPS  X0, X2           // X2 *= a
+	MULPS  X1, X3
+	MULPS  X0, X4
+	MULPS  X1, X5
+	ADDPS  (DX)(AX*4), X2   // X2 += y[i:i+4]
+	ADDPS  16(DX)(AX*4), X3
+	ADDPS  32(DX)(AX*4), X4
+	ADDPS  48(DX)(AX*4), X5
+	MOVUPS X2, (DI)(AX*4)   // dst[i:i+4] = X2
+	MOVUPS X3, 16(DI)(AX*4)
+	MOVUPS X4, 32(DI)(AX*4)
+	MOVUPS X5, 48(DI)(AX*4)
+	ADDQ   $16, AX          // i += 16
+	LOOP   axpy_loop        // while (--CX) > 0
+	CMPQ   BX, $0           // if BX == 0 { return }
+	JE     axpy_end
+
+axpy_tail4_start: // Reset loop counter for 4-wide tail loop
+	MOVQ BX, CX          // CX = floor( BX / 4 )
+	SHRQ $2, CX
+	JZ   axpy_tail_start // if CX == 0 { goto axpy_tail_start }
+
+axpy_tail4: // Loop unrolled 4x  do {
+	MOVUPS (SI)(AX*4), X2 // X2 = x[i]
+	MULPS  X0, X2         // X2 *= a
+	ADDPS  (DX)(AX*4), X2 // X2 += y[i]
+	MOVUPS X2, (DI)(AX*4) // y[i] = X2
+	ADDQ   $4, AX         // i += 4
+	LOOP   axpy_tail4     // } while --CX > 0
+
+axpy_tail_start: // Reset loop counter for 1-wide tail loop
+	MOVQ BX, CX   // CX = BX % 4
+	ANDQ $3, CX
+	JZ   axpy_end // if CX == 0 { return }
+
+axpy_tail:
+	MOVSS (SI)(AX*4), X1 // X1 = x[i]
+	MULSS X0, X1         // X1 *= a
+	ADDSS (DX)(AX*4), X1 // X1 += y[i]
+	MOVSS X1, (DI)(AX*4) // y[i] = X1
+	INCQ  AX             // i++
+	LOOP  axpy_tail      // } while --CX > 0
+
+axpy_end:
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f32/bench_test.go b/vendor/gonum.org/v1/gonum/internal/asm/f32/bench_test.go
new file mode 100644
index 00000000..a1c415ce
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f32/bench_test.go
@@ -0,0 +1,282 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package f32
+
+import "testing"
+
+var (
+	a = float32(2)
+	x = make([]float32, 1000000)
+	y = make([]float32, 1000000)
+	z = make([]float32, 1000000)
+)
+
+func init() {
+	for n := range x {
+		x[n] = float32(n)
+		y[n] = float32(n)
+	}
+}
+
+func benchaxpyu(t *testing.B, n int, f func(a float32, x, y []float32)) {
+	x, y := x[:n], y[:n]
+	for i := 0; i < t.N; i++ {
+		f(a, x, y)
+	}
+}
+
+func naiveaxpyu(a float32, x, y []float32) {
+	for i, v := range x {
+		y[i] += a * v
+	}
+}
+
+func BenchmarkF32AxpyUnitary1(t *testing.B)     { benchaxpyu(t, 1, AxpyUnitary) }
+func BenchmarkF32AxpyUnitary2(t *testing.B)     { benchaxpyu(t, 2, AxpyUnitary) }
+func BenchmarkF32AxpyUnitary3(t *testing.B)     { benchaxpyu(t, 3, AxpyUnitary) }
+func BenchmarkF32AxpyUnitary4(t *testing.B)     { benchaxpyu(t, 4, AxpyUnitary) }
+func BenchmarkF32AxpyUnitary5(t *testing.B)     { benchaxpyu(t, 5, AxpyUnitary) }
+func BenchmarkF32AxpyUnitary10(t *testing.B)    { benchaxpyu(t, 10, AxpyUnitary) }
+func BenchmarkF32AxpyUnitary100(t *testing.B)   { benchaxpyu(t, 100, AxpyUnitary) }
+func BenchmarkF32AxpyUnitary1000(t *testing.B)  { benchaxpyu(t, 1000, AxpyUnitary) }
+func BenchmarkF32AxpyUnitary5000(t *testing.B)  { benchaxpyu(t, 5000, AxpyUnitary) }
+func BenchmarkF32AxpyUnitary10000(t *testing.B) { benchaxpyu(t, 10000, AxpyUnitary) }
+func BenchmarkF32AxpyUnitary50000(t *testing.B) { benchaxpyu(t, 50000, AxpyUnitary) }
+
+func BenchmarkLF32AxpyUnitary1(t *testing.B)     { benchaxpyu(t, 1, naiveaxpyu) }
+func BenchmarkLF32AxpyUnitary2(t *testing.B)     { benchaxpyu(t, 2, naiveaxpyu) }
+func BenchmarkLF32AxpyUnitary3(t *testing.B)     { benchaxpyu(t, 3, naiveaxpyu) }
+func BenchmarkLF32AxpyUnitary4(t *testing.B)     { benchaxpyu(t, 4, naiveaxpyu) }
+func BenchmarkLF32AxpyUnitary5(t *testing.B)     { benchaxpyu(t, 5, naiveaxpyu) }
+func BenchmarkLF32AxpyUnitary10(t *testing.B)    { benchaxpyu(t, 10, naiveaxpyu) }
+func BenchmarkLF32AxpyUnitary100(t *testing.B)   { benchaxpyu(t, 100, naiveaxpyu) }
+func BenchmarkLF32AxpyUnitary1000(t *testing.B)  { benchaxpyu(t, 1000, naiveaxpyu) }
+func BenchmarkLF32AxpyUnitary5000(t *testing.B)  { benchaxpyu(t, 5000, naiveaxpyu) }
+func BenchmarkLF32AxpyUnitary10000(t *testing.B) { benchaxpyu(t, 10000, naiveaxpyu) }
+func BenchmarkLF32AxpyUnitary50000(t *testing.B) { benchaxpyu(t, 50000, naiveaxpyu) }
+
+func benchaxpyut(t *testing.B, n int, f func(d []float32, a float32, x, y []float32)) {
+	x, y, z := x[:n], y[:n], z[:n]
+	for i := 0; i < t.N; i++ {
+		f(z, a, x, y)
+	}
+}
+
+func naiveaxpyut(d []float32, a float32, x, y []float32) {
+	for i, v := range x {
+		d[i] = y[i] + a*v
+	}
+}
+
+func BenchmarkF32AxpyUnitaryTo1(t *testing.B)     { benchaxpyut(t, 1, AxpyUnitaryTo) }
+func BenchmarkF32AxpyUnitaryTo2(t *testing.B)     { benchaxpyut(t, 2, AxpyUnitaryTo) }
+func BenchmarkF32AxpyUnitaryTo3(t *testing.B)     { benchaxpyut(t, 3, AxpyUnitaryTo) }
+func BenchmarkF32AxpyUnitaryTo4(t *testing.B)     { benchaxpyut(t, 4, AxpyUnitaryTo) }
+func BenchmarkF32AxpyUnitaryTo5(t *testing.B)     { benchaxpyut(t, 5, AxpyUnitaryTo) }
+func BenchmarkF32AxpyUnitaryTo10(t *testing.B)    { benchaxpyut(t, 10, AxpyUnitaryTo) }
+func BenchmarkF32AxpyUnitaryTo100(t *testing.B)   { benchaxpyut(t, 100, AxpyUnitaryTo) }
+func BenchmarkF32AxpyUnitaryTo1000(t *testing.B)  { benchaxpyut(t, 1000, AxpyUnitaryTo) }
+func BenchmarkF32AxpyUnitaryTo5000(t *testing.B)  { benchaxpyut(t, 5000, AxpyUnitaryTo) }
+func BenchmarkF32AxpyUnitaryTo10000(t *testing.B) { benchaxpyut(t, 10000, AxpyUnitaryTo) }
+func BenchmarkF32AxpyUnitaryTo50000(t *testing.B) { benchaxpyut(t, 50000, AxpyUnitaryTo) }
+
+func BenchmarkLF32AxpyUnitaryTo1(t *testing.B)     { benchaxpyut(t, 1, naiveaxpyut) }
+func BenchmarkLF32AxpyUnitaryTo2(t *testing.B)     { benchaxpyut(t, 2, naiveaxpyut) }
+func BenchmarkLF32AxpyUnitaryTo3(t *testing.B)     { benchaxpyut(t, 3, naiveaxpyut) }
+func BenchmarkLF32AxpyUnitaryTo4(t *testing.B)     { benchaxpyut(t, 4, naiveaxpyut) }
+func BenchmarkLF32AxpyUnitaryTo5(t *testing.B)     { benchaxpyut(t, 5, naiveaxpyut) }
+func BenchmarkLF32AxpyUnitaryTo10(t *testing.B)    { benchaxpyut(t, 10, naiveaxpyut) }
+func BenchmarkLF32AxpyUnitaryTo100(t *testing.B)   { benchaxpyut(t, 100, naiveaxpyut) }
+func BenchmarkLF32AxpyUnitaryTo1000(t *testing.B)  { benchaxpyut(t, 1000, naiveaxpyut) }
+func BenchmarkLF32AxpyUnitaryTo5000(t *testing.B)  { benchaxpyut(t, 5000, naiveaxpyut) }
+func BenchmarkLF32AxpyUnitaryTo10000(t *testing.B) { benchaxpyut(t, 10000, naiveaxpyut) }
+func BenchmarkLF32AxpyUnitaryTo50000(t *testing.B) { benchaxpyut(t, 50000, naiveaxpyut) }
+
+func benchaxpyinc(t *testing.B, ln, t_inc int, f func(alpha float32, x, y []float32, n, incX, incY, ix, iy uintptr)) {
+	n, inc := uintptr(ln), uintptr(t_inc)
+	var idx int
+	if t_inc < 0 {
+		idx = (-ln + 1) * t_inc
+	}
+	for i := 0; i < t.N; i++ {
+		f(1, x, y, n, inc, inc, uintptr(idx), uintptr(idx))
+	}
+}
+
+func naiveaxpyinc(alpha float32, x, y []float32, n, incX, incY, ix, iy uintptr) {
+	for i := 0; i < int(n); i++ {
+		y[iy] += alpha * x[ix]
+		ix += incX
+		iy += incY
+	}
+}
+
+func BenchmarkF32AxpyIncN1Inc1(b *testing.B) { benchaxpyinc(b, 1, 1, AxpyInc) }
+
+func BenchmarkF32AxpyIncN2Inc1(b *testing.B)  { benchaxpyinc(b, 2, 1, AxpyInc) }
+func BenchmarkF32AxpyIncN2Inc2(b *testing.B)  { benchaxpyinc(b, 2, 2, AxpyInc) }
+func BenchmarkF32AxpyIncN2Inc4(b *testing.B)  { benchaxpyinc(b, 2, 4, AxpyInc) }
+func BenchmarkF32AxpyIncN2Inc10(b *testing.B) { benchaxpyinc(b, 2, 10, AxpyInc) }
+
+func BenchmarkF32AxpyIncN3Inc1(b *testing.B)  { benchaxpyinc(b, 3, 1, AxpyInc) }
+func BenchmarkF32AxpyIncN3Inc2(b *testing.B)  { benchaxpyinc(b, 3, 2, AxpyInc) }
+func BenchmarkF32AxpyIncN3Inc4(b *testing.B)  { benchaxpyinc(b, 3, 4, AxpyInc) }
+func BenchmarkF32AxpyIncN3Inc10(b *testing.B) { benchaxpyinc(b, 3, 10, AxpyInc) }
+
+func BenchmarkF32AxpyIncN4Inc1(b *testing.B)  { benchaxpyinc(b, 4, 1, AxpyInc) }
+func BenchmarkF32AxpyIncN4Inc2(b *testing.B)  { benchaxpyinc(b, 4, 2, AxpyInc) }
+func BenchmarkF32AxpyIncN4Inc4(b *testing.B)  { benchaxpyinc(b, 4, 4, AxpyInc) }
+func BenchmarkF32AxpyIncN4Inc10(b *testing.B) { benchaxpyinc(b, 4, 10, AxpyInc) }
+
+func BenchmarkF32AxpyIncN10Inc1(b *testing.B)  { benchaxpyinc(b, 10, 1, AxpyInc) }
+func BenchmarkF32AxpyIncN10Inc2(b *testing.B)  { benchaxpyinc(b, 10, 2, AxpyInc) }
+func BenchmarkF32AxpyIncN10Inc4(b *testing.B)  { benchaxpyinc(b, 10, 4, AxpyInc) }
+func BenchmarkF32AxpyIncN10Inc10(b *testing.B) { benchaxpyinc(b, 10, 10, AxpyInc) }
+
+func BenchmarkF32AxpyIncN1000Inc1(b *testing.B)  { benchaxpyinc(b, 1000, 1, AxpyInc) }
+func BenchmarkF32AxpyIncN1000Inc2(b *testing.B)  { benchaxpyinc(b, 1000, 2, AxpyInc) }
+func BenchmarkF32AxpyIncN1000Inc4(b *testing.B)  { benchaxpyinc(b, 1000, 4, AxpyInc) }
+func BenchmarkF32AxpyIncN1000Inc10(b *testing.B) { benchaxpyinc(b, 1000, 10, AxpyInc) }
+
+func BenchmarkF32AxpyIncN100000Inc1(b *testing.B)  { benchaxpyinc(b, 100000, 1, AxpyInc) }
+func BenchmarkF32AxpyIncN100000Inc2(b *testing.B)  { benchaxpyinc(b, 100000, 2, AxpyInc) }
+func BenchmarkF32AxpyIncN100000Inc4(b *testing.B)  { benchaxpyinc(b, 100000, 4, AxpyInc) }
+func BenchmarkF32AxpyIncN100000Inc10(b *testing.B) { benchaxpyinc(b, 100000, 10, AxpyInc) }
+
+func BenchmarkF32AxpyIncN100000IncM1(b *testing.B)  { benchaxpyinc(b, 100000, -1, AxpyInc) }
+func BenchmarkF32AxpyIncN100000IncM2(b *testing.B)  { benchaxpyinc(b, 100000, -2, AxpyInc) }
+func BenchmarkF32AxpyIncN100000IncM4(b *testing.B)  { benchaxpyinc(b, 100000, -4, AxpyInc) }
+func BenchmarkF32AxpyIncN100000IncM10(b *testing.B) { benchaxpyinc(b, 100000, -10, AxpyInc) }
+
+func BenchmarkLF32AxpyIncN1Inc1(b *testing.B) { benchaxpyinc(b, 1, 1, naiveaxpyinc) }
+
+func BenchmarkLF32AxpyIncN2Inc1(b *testing.B)  { benchaxpyinc(b, 2, 1, naiveaxpyinc) }
+func BenchmarkLF32AxpyIncN2Inc2(b *testing.B)  { benchaxpyinc(b, 2, 2, naiveaxpyinc) }
+func BenchmarkLF32AxpyIncN2Inc4(b *testing.B)  { benchaxpyinc(b, 2, 4, naiveaxpyinc) }
+func BenchmarkLF32AxpyIncN2Inc10(b *testing.B) { benchaxpyinc(b, 2, 10, naiveaxpyinc) }
+
+func BenchmarkLF32AxpyIncN3Inc1(b *testing.B)  { benchaxpyinc(b, 3, 1, naiveaxpyinc) }
+func BenchmarkLF32AxpyIncN3Inc2(b *testing.B)  { benchaxpyinc(b, 3, 2, naiveaxpyinc) }
+func BenchmarkLF32AxpyIncN3Inc4(b *testing.B)  { benchaxpyinc(b, 3, 4, naiveaxpyinc) }
+func BenchmarkLF32AxpyIncN3Inc10(b *testing.B) { benchaxpyinc(b, 3, 10, naiveaxpyinc) }
+
+func BenchmarkLF32AxpyIncN4Inc1(b *testing.B)  { benchaxpyinc(b, 4, 1, naiveaxpyinc) }
+func BenchmarkLF32AxpyIncN4Inc2(b *testing.B)  { benchaxpyinc(b, 4, 2, naiveaxpyinc) }
+func BenchmarkLF32AxpyIncN4Inc4(b *testing.B)  { benchaxpyinc(b, 4, 4, naiveaxpyinc) }
+func BenchmarkLF32AxpyIncN4Inc10(b *testing.B) { benchaxpyinc(b, 4, 10, naiveaxpyinc) }
+
+func BenchmarkLF32AxpyIncN10Inc1(b *testing.B)  { benchaxpyinc(b, 10, 1, naiveaxpyinc) }
+func BenchmarkLF32AxpyIncN10Inc2(b *testing.B)  { benchaxpyinc(b, 10, 2, naiveaxpyinc) }
+func BenchmarkLF32AxpyIncN10Inc4(b *testing.B)  { benchaxpyinc(b, 10, 4, naiveaxpyinc) }
+func BenchmarkLF32AxpyIncN10Inc10(b *testing.B) { benchaxpyinc(b, 10, 10, naiveaxpyinc) }
+
+func BenchmarkLF32AxpyIncN1000Inc1(b *testing.B)  { benchaxpyinc(b, 1000, 1, naiveaxpyinc) }
+func BenchmarkLF32AxpyIncN1000Inc2(b *testing.B)  { benchaxpyinc(b, 1000, 2, naiveaxpyinc) }
+func BenchmarkLF32AxpyIncN1000Inc4(b *testing.B)  { benchaxpyinc(b, 1000, 4, naiveaxpyinc) }
+func BenchmarkLF32AxpyIncN1000Inc10(b *testing.B) { benchaxpyinc(b, 1000, 10, naiveaxpyinc) }
+
+func BenchmarkLF32AxpyIncN100000Inc1(b *testing.B)  { benchaxpyinc(b, 100000, 1, naiveaxpyinc) }
+func BenchmarkLF32AxpyIncN100000Inc2(b *testing.B)  { benchaxpyinc(b, 100000, 2, naiveaxpyinc) }
+func BenchmarkLF32AxpyIncN100000Inc4(b *testing.B)  { benchaxpyinc(b, 100000, 4, naiveaxpyinc) }
+func BenchmarkLF32AxpyIncN100000Inc10(b *testing.B) { benchaxpyinc(b, 100000, 10, naiveaxpyinc) }
+
+func BenchmarkLF32AxpyIncN100000IncM1(b *testing.B)  { benchaxpyinc(b, 100000, -1, naiveaxpyinc) }
+func BenchmarkLF32AxpyIncN100000IncM2(b *testing.B)  { benchaxpyinc(b, 100000, -2, naiveaxpyinc) }
+func BenchmarkLF32AxpyIncN100000IncM4(b *testing.B)  { benchaxpyinc(b, 100000, -4, naiveaxpyinc) }
+func BenchmarkLF32AxpyIncN100000IncM10(b *testing.B) { benchaxpyinc(b, 100000, -10, naiveaxpyinc) }
+
+func benchaxpyincto(t *testing.B, ln, t_inc int, f func(dst []float32, incDst, idst uintptr, alpha float32, x, y []float32, n, incX, incY, ix, iy uintptr)) {
+	n, inc := uintptr(ln), uintptr(t_inc)
+	var idx int
+	if t_inc < 0 {
+		idx = (-ln + 1) * t_inc
+	}
+	for i := 0; i < t.N; i++ {
+		f(z, inc, uintptr(idx), 1, x, y, n, inc, inc, uintptr(idx), uintptr(idx))
+	}
+}
+
+func naiveaxpyincto(dst []float32, incDst, idst uintptr, alpha float32, x, y []float32, n, incX, incY, ix, iy uintptr) {
+	for i := 0; i < int(n); i++ {
+		dst[idst] = alpha*x[ix] + y[iy]
+		ix += incX
+		iy += incY
+		idst += incDst
+	}
+}
+
+func BenchmarkF32AxpyIncToN1Inc1(b *testing.B) { benchaxpyincto(b, 1, 1, AxpyIncTo) }
+
+func BenchmarkF32AxpyIncToN2Inc1(b *testing.B)  { benchaxpyincto(b, 2, 1, AxpyIncTo) }
+func BenchmarkF32AxpyIncToN2Inc2(b *testing.B)  { benchaxpyincto(b, 2, 2, AxpyIncTo) }
+func BenchmarkF32AxpyIncToN2Inc4(b *testing.B)  { benchaxpyincto(b, 2, 4, AxpyIncTo) }
+func BenchmarkF32AxpyIncToN2Inc10(b *testing.B) { benchaxpyincto(b, 2, 10, AxpyIncTo) }
+
+func BenchmarkF32AxpyIncToN3Inc1(b *testing.B)  { benchaxpyincto(b, 3, 1, AxpyIncTo) }
+func BenchmarkF32AxpyIncToN3Inc2(b *testing.B)  { benchaxpyincto(b, 3, 2, AxpyIncTo) }
+func BenchmarkF32AxpyIncToN3Inc4(b *testing.B)  { benchaxpyincto(b, 3, 4, AxpyIncTo) }
+func BenchmarkF32AxpyIncToN3Inc10(b *testing.B) { benchaxpyincto(b, 3, 10, AxpyIncTo) }
+
+func BenchmarkF32AxpyIncToN4Inc1(b *testing.B)  { benchaxpyincto(b, 4, 1, AxpyIncTo) }
+func BenchmarkF32AxpyIncToN4Inc2(b *testing.B)  { benchaxpyincto(b, 4, 2, AxpyIncTo) }
+func BenchmarkF32AxpyIncToN4Inc4(b *testing.B)  { benchaxpyincto(b, 4, 4, AxpyIncTo) }
+func BenchmarkF32AxpyIncToN4Inc10(b *testing.B) { benchaxpyincto(b, 4, 10, AxpyIncTo) }
+
+func BenchmarkF32AxpyIncToN10Inc1(b *testing.B)  { benchaxpyincto(b, 10, 1, AxpyIncTo) }
+func BenchmarkF32AxpyIncToN10Inc2(b *testing.B)  { benchaxpyincto(b, 10, 2, AxpyIncTo) }
+func BenchmarkF32AxpyIncToN10Inc4(b *testing.B)  { benchaxpyincto(b, 10, 4, AxpyIncTo) }
+func BenchmarkF32AxpyIncToN10Inc10(b *testing.B) { benchaxpyincto(b, 10, 10, AxpyIncTo) }
+
+func BenchmarkF32AxpyIncToN1000Inc1(b *testing.B)  { benchaxpyincto(b, 1000, 1, AxpyIncTo) }
+func BenchmarkF32AxpyIncToN1000Inc2(b *testing.B)  { benchaxpyincto(b, 1000, 2, AxpyIncTo) }
+func BenchmarkF32AxpyIncToN1000Inc4(b *testing.B)  { benchaxpyincto(b, 1000, 4, AxpyIncTo) }
+func BenchmarkF32AxpyIncToN1000Inc10(b *testing.B) { benchaxpyincto(b, 1000, 10, AxpyIncTo) }
+
+func BenchmarkF32AxpyIncToN100000Inc1(b *testing.B)  { benchaxpyincto(b, 100000, 1, AxpyIncTo) }
+func BenchmarkF32AxpyIncToN100000Inc2(b *testing.B)  { benchaxpyincto(b, 100000, 2, AxpyIncTo) }
+func BenchmarkF32AxpyIncToN100000Inc4(b *testing.B)  { benchaxpyincto(b, 100000, 4, AxpyIncTo) }
+func BenchmarkF32AxpyIncToN100000Inc10(b *testing.B) { benchaxpyincto(b, 100000, 10, AxpyIncTo) }
+
+func BenchmarkF32AxpyIncToN100000IncM1(b *testing.B)  { benchaxpyincto(b, 100000, -1, AxpyIncTo) }
+func BenchmarkF32AxpyIncToN100000IncM2(b *testing.B)  { benchaxpyincto(b, 100000, -2, AxpyIncTo) }
+func BenchmarkF32AxpyIncToN100000IncM4(b *testing.B)  { benchaxpyincto(b, 100000, -4, AxpyIncTo) }
+func BenchmarkF32AxpyIncToN100000IncM10(b *testing.B) { benchaxpyincto(b, 100000, -10, AxpyIncTo) }
+
+func BenchmarkLF32AxpyIncToN1Inc1(b *testing.B) { benchaxpyincto(b, 1, 1, naiveaxpyincto) }
+
+func BenchmarkLF32AxpyIncToN2Inc1(b *testing.B)  { benchaxpyincto(b, 2, 1, naiveaxpyincto) }
+func BenchmarkLF32AxpyIncToN2Inc2(b *testing.B)  { benchaxpyincto(b, 2, 2, naiveaxpyincto) }
+func BenchmarkLF32AxpyIncToN2Inc4(b *testing.B)  { benchaxpyincto(b, 2, 4, naiveaxpyincto) }
+func BenchmarkLF32AxpyIncToN2Inc10(b *testing.B) { benchaxpyincto(b, 2, 10, naiveaxpyincto) }
+
+func BenchmarkLF32AxpyIncToN3Inc1(b *testing.B)  { benchaxpyincto(b, 3, 1, naiveaxpyincto) }
+func BenchmarkLF32AxpyIncToN3Inc2(b *testing.B)  { benchaxpyincto(b, 3, 2, naiveaxpyincto) }
+func BenchmarkLF32AxpyIncToN3Inc4(b *testing.B)  { benchaxpyincto(b, 3, 4, naiveaxpyincto) }
+func BenchmarkLF32AxpyIncToN3Inc10(b *testing.B) { benchaxpyincto(b, 3, 10, naiveaxpyincto) }
+
+func BenchmarkLF32AxpyIncToN4Inc1(b *testing.B)  { benchaxpyincto(b, 4, 1, naiveaxpyincto) }
+func BenchmarkLF32AxpyIncToN4Inc2(b *testing.B)  { benchaxpyincto(b, 4, 2, naiveaxpyincto) }
+func BenchmarkLF32AxpyIncToN4Inc4(b *testing.B)  { benchaxpyincto(b, 4, 4, naiveaxpyincto) }
+func BenchmarkLF32AxpyIncToN4Inc10(b *testing.B) { benchaxpyincto(b, 4, 10, naiveaxpyincto) }
+
+func BenchmarkLF32AxpyIncToN10Inc1(b *testing.B)  { benchaxpyincto(b, 10, 1, naiveaxpyincto) }
+func BenchmarkLF32AxpyIncToN10Inc2(b *testing.B)  { benchaxpyincto(b, 10, 2, naiveaxpyincto) }
+func BenchmarkLF32AxpyIncToN10Inc4(b *testing.B)  { benchaxpyincto(b, 10, 4, naiveaxpyincto) }
+func BenchmarkLF32AxpyIncToN10Inc10(b *testing.B) { benchaxpyincto(b, 10, 10, naiveaxpyincto) }
+
+func BenchmarkLF32AxpyIncToN1000Inc1(b *testing.B)  { benchaxpyincto(b, 1000, 1, naiveaxpyincto) }
+func BenchmarkLF32AxpyIncToN1000Inc2(b *testing.B)  { benchaxpyincto(b, 1000, 2, naiveaxpyincto) }
+func BenchmarkLF32AxpyIncToN1000Inc4(b *testing.B)  { benchaxpyincto(b, 1000, 4, naiveaxpyincto) }
+func BenchmarkLF32AxpyIncToN1000Inc10(b *testing.B) { benchaxpyincto(b, 1000, 10, naiveaxpyincto) }
+
+func BenchmarkLF32AxpyIncToN100000Inc1(b *testing.B)  { benchaxpyincto(b, 100000, 1, naiveaxpyincto) }
+func BenchmarkLF32AxpyIncToN100000Inc2(b *testing.B)  { benchaxpyincto(b, 100000, 2, naiveaxpyincto) }
+func BenchmarkLF32AxpyIncToN100000Inc4(b *testing.B)  { benchaxpyincto(b, 100000, 4, naiveaxpyincto) }
+func BenchmarkLF32AxpyIncToN100000Inc10(b *testing.B) { benchaxpyincto(b, 100000, 10, naiveaxpyincto) }
+
+func BenchmarkLF32AxpyIncToN100000IncM1(b *testing.B)  { benchaxpyincto(b, 100000, -1, naiveaxpyincto) }
+func BenchmarkLF32AxpyIncToN100000IncM2(b *testing.B)  { benchaxpyincto(b, 100000, -2, naiveaxpyincto) }
+func BenchmarkLF32AxpyIncToN100000IncM4(b *testing.B)  { benchaxpyincto(b, 100000, -4, naiveaxpyincto) }
+func BenchmarkLF32AxpyIncToN100000IncM10(b *testing.B) { benchaxpyincto(b, 100000, -10, naiveaxpyincto) }
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f32/ddot.go b/vendor/gonum.org/v1/gonum/internal/asm/f32/ddot.go
new file mode 100644
index 00000000..6920f659
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f32/ddot.go
@@ -0,0 +1,33 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package f32
+
+// DdotUnitary is
+//   for i, v := range x {
+//   	sum += float64(y[i]) * float64(v)
+//   }
+//   return
+func DdotUnitary(x, y []float32) (sum float64) {
+	for i, v := range x {
+		sum += float64(y[i]) * float64(v)
+	}
+	return
+}
+
+// DdotInc is
+//  for i := 0; i < int(n); i++ {
+//  	sum += float64(y[iy]) * float64(x[ix])
+//  	ix += incX
+//  	iy += incY
+//  }
+//  return
+func DdotInc(x, y []float32, n, incX, incY, ix, iy uintptr) (sum float64) {
+	for i := 0; i < int(n); i++ {
+		sum += float64(y[iy]) * float64(x[ix])
+		ix += incX
+		iy += incY
+	}
+	return
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f32/doc.go b/vendor/gonum.org/v1/gonum/internal/asm/f32/doc.go
new file mode 100644
index 00000000..89e9c224
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f32/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package f32 provides float32 vector primitives.
+package f32 // import "gonum.org/v1/gonum/internal/asm/f32"
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f32/dot.go b/vendor/gonum.org/v1/gonum/internal/asm/f32/dot.go
new file mode 100644
index 00000000..7a27d35e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f32/dot.go
@@ -0,0 +1,33 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package f32
+
+// DotUnitary is
+//  for i, v := range x {
+//  	sum += y[i] * v
+//  }
+//  return sum
+func DotUnitary(x, y []float32) (sum float32) {
+	for i, v := range x {
+		sum += y[i] * v
+	}
+	return sum
+}
+
+// DotInc is
+//  for i := 0; i < int(n); i++ {
+//  	sum += y[iy] * x[ix]
+//  	ix += incX
+//  	iy += incY
+//  }
+//  return sum
+func DotInc(x, y []float32, n, incX, incY, ix, iy uintptr) (sum float32) {
+	for i := 0; i < int(n); i++ {
+		sum += y[iy] * x[ix]
+		ix += incX
+		iy += incY
+	}
+	return sum
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f32/scal.go b/vendor/gonum.org/v1/gonum/internal/asm/f32/scal.go
new file mode 100644
index 00000000..c4f61e87
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f32/scal.go
@@ -0,0 +1,55 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package f32
+
+// ScalUnitary is
+//  for i := range x {
+//  	x[i] *= alpha
+//  }
+func ScalUnitary(alpha float32, x []float32) {
+	for i := range x {
+		x[i] *= alpha
+	}
+}
+
+// ScalUnitaryTo is
+//  for i, v := range x {
+//  	dst[i] = alpha * v
+//  }
+func ScalUnitaryTo(dst []float32, alpha float32, x []float32) {
+	for i, v := range x {
+		dst[i] = alpha * v
+	}
+}
+
+// ScalInc is
+//  var ix uintptr
+//  for i := 0; i < int(n); i++ {
+//  	x[ix] *= alpha
+//  	ix += incX
+//  }
+func ScalInc(alpha float32, x []float32, n, incX uintptr) {
+	var ix uintptr
+	for i := 0; i < int(n); i++ {
+		x[ix] *= alpha
+		ix += incX
+	}
+}
+
+// ScalIncTo is
+//  var idst, ix uintptr
+//  for i := 0; i < int(n); i++ {
+//  	dst[idst] = alpha * x[ix]
+//  	ix += incX
+//  	idst += incDst
+//  }
+func ScalIncTo(dst []float32, incDst uintptr, alpha float32, x []float32, n, incX uintptr) {
+	var idst, ix uintptr
+	for i := 0; i < int(n); i++ {
+		dst[idst] = alpha * x[ix]
+		ix += incX
+		idst += incDst
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f32/stubs_amd64.go b/vendor/gonum.org/v1/gonum/internal/asm/f32/stubs_amd64.go
new file mode 100644
index 00000000..00ad520a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f32/stubs_amd64.go
@@ -0,0 +1,36 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !noasm,!appengine
+
+package f32
+
+// AxpyUnitary is
+//  for i, v := range x {
+//  	y[i] += alpha * v
+//  }
+func AxpyUnitary(alpha float32, x, y []float32)
+
+// AxpyUnitaryTo is
+//  for i, v := range x {
+//  	dst[i] = alpha*v + y[i]
+//  }
+func AxpyUnitaryTo(dst []float32, alpha float32, x, y []float32)
+
+// AxpyInc is
+//  for i := 0; i < int(n); i++ {
+//  	y[iy] += alpha * x[ix]
+//  	ix += incX
+//  	iy += incY
+//  }
+func AxpyInc(alpha float32, x, y []float32, n, incX, incY, ix, iy uintptr)
+
+// AxpyIncTo is
+//  for i := 0; i < int(n); i++ {
+//  	dst[idst] = alpha*x[ix] + y[iy]
+//  	ix += incX
+//  	iy += incY
+//  	idst += incDst
+//  }
+func AxpyIncTo(dst []float32, incDst, idst uintptr, alpha float32, x, y []float32, n, incX, incY, ix, iy uintptr)
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f32/stubs_noasm.go b/vendor/gonum.org/v1/gonum/internal/asm/f32/stubs_noasm.go
new file mode 100644
index 00000000..a6272ea5
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f32/stubs_noasm.go
@@ -0,0 +1,57 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !amd64 noasm appengine
+
+package f32
+
+// AxpyUnitary is
+//  for i, v := range x {
+//  	y[i] += alpha * v
+//  }
+func AxpyUnitary(alpha float32, x, y []float32) {
+	for i, v := range x {
+		y[i] += alpha * v
+	}
+}
+
+// AxpyUnitaryTo is
+//  for i, v := range x {
+//  	dst[i] = alpha*v + y[i]
+//  }
+func AxpyUnitaryTo(dst []float32, alpha float32, x, y []float32) {
+	for i, v := range x {
+		dst[i] = alpha*v + y[i]
+	}
+}
+
+// AxpyInc is
+//  for i := 0; i < int(n); i++ {
+//  	y[iy] += alpha * x[ix]
+//  	ix += incX
+//  	iy += incY
+//  }
+func AxpyInc(alpha float32, x, y []float32, n, incX, incY, ix, iy uintptr) {
+	for i := 0; i < int(n); i++ {
+		y[iy] += alpha * x[ix]
+		ix += incX
+		iy += incY
+	}
+}
+
+// AxpyIncTo is
+//  for i := 0; i < int(n); i++ {
+//  	dst[idst] = alpha*x[ix] + y[iy]
+//  	ix += incX
+//  	iy += incY
+//  	idst += incDst
+//  }
+func AxpyIncTo(dst []float32, incDst, idst uintptr, alpha float32, x, y []float32, n, incX, incY, ix, iy uintptr) {
+	for i := 0; i < int(n); i++ {
+		dst[idst] = alpha*x[ix] + y[iy]
+		ix += incX
+		iy += incY
+		idst += incDst
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f32/stubs_test.go b/vendor/gonum.org/v1/gonum/internal/asm/f32/stubs_test.go
new file mode 100644
index 00000000..df7a1421
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f32/stubs_test.go
@@ -0,0 +1,217 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package f32
+
+import (
+	"math"
+	"testing"
+)
+
+var (
+	nan = float32(math.NaN())
+	inf = float32(math.Inf(1))
+)
+
+var tests = []struct {
+	incX, incY, incDst uintptr
+	ix, iy, idst       uintptr
+	a                  float32
+	dst, x, y          []float32
+	ex                 []float32
+}{
+	{incX: 2, incY: 2, incDst: 3, ix: 0, iy: 0, idst: 0,
+		a:   3,
+		dst: []float32{5},
+		x:   []float32{2},
+		y:   []float32{1},
+		ex:  []float32{7}},
+	{incX: 2, incY: 2, incDst: 3, ix: 0, iy: 0, idst: 0,
+		a:   5,
+		dst: []float32{0, 0, 0},
+		x:   []float32{0, 0, 0},
+		y:   []float32{1, 1, 1},
+		ex:  []float32{1, 1, 1}},
+	{incX: 2, incY: 2, incDst: 3, ix: 0, iy: 0, idst: 0,
+		a:   5,
+		dst: []float32{0, 0, 0},
+		x:   []float32{0, 0},
+		y:   []float32{1, 1, 1},
+		ex:  []float32{1, 1}},
+	{incX: 2, incY: 2, incDst: 3, ix: 0, iy: 0, idst: 0,
+		a:   -1,
+		dst: []float32{-1, -1, -1},
+		x:   []float32{1, 1, 1},
+		y:   []float32{1, 2, 1},
+		ex:  []float32{0, 1, 0}},
+	{incX: 2, incY: 2, incDst: 3, ix: 0, iy: 0, idst: 0,
+		a:   -1,
+		dst: []float32{1, 1, 1},
+		x:   []float32{1, 2, 1},
+		y:   []float32{-1, -2, -1},
+		ex:  []float32{-2, -4, -2}},
+	{incX: 2, incY: 2, incDst: 3, ix: 0, iy: 0, idst: 0,
+		a:   2.5,
+		dst: []float32{1, 1, 1, 1, 1},
+		x:   []float32{1, 2, 3, 2, 1},
+		y:   []float32{0, 0, 0, 0, 0},
+		ex:  []float32{2.5, 5, 7.5, 5, 2.5}},
+	{incX: 2, incY: 2, incDst: 3, ix: 0, iy: 0, idst: 0, // Run big test twice, once aligned once unaligned.
+		a:   16.5,
+		dst: make([]float32, 20),
+		x:   []float32{.5, .5, .5, .5, .5, .5, .5, .5, .5, .5, .5, .5, .5, .5, .5, .5, .5, .5, .5, .5},
+		y:   []float32{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
+		ex:  []float32{9.25, 10.25, 11.25, 12.25, 13.25, 14.25, 15.25, 16.25, 17.25, 18.25, 9.25, 10.25, 11.25, 12.25, 13.25, 14.25, 15.25, 16.25, 17.25, 18.25}},
+	{incX: 2, incY: 2, incDst: 3, ix: 0, iy: 0, idst: 0,
+		a:   16.5,
+		dst: make([]float32, 10),
+		x:   []float32{.5, .5, .5, .5, .5, .5, .5, .5, .5, .5},
+		y:   []float32{1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
+		ex:  []float32{9.25, 10.25, 11.25, 12.25, 13.25, 14.25, 15.25, 16.25, 17.25, 18.25}},
+}
+
+func guardVector(vec []float32, guard_val float32, guard_len int) (guarded []float32) {
+	guarded = make([]float32, len(vec)+guard_len*2)
+	copy(guarded[guard_len:], vec)
+	for i := 0; i < guard_len; i++ {
+		guarded[i] = guard_val
+		guarded[len(guarded)-1-i] = guard_val
+	}
+	return guarded
+}
+
+func isValidGuard(vec []float32, guard_val float32, guard_len int) bool {
+	for i := 0; i < guard_len; i++ {
+		if vec[i] != guard_val || vec[len(vec)-1-i] != guard_val {
+			return false
+		}
+	}
+	return true
+}
+
+func same(x, y float32) bool {
+	a, b := float64(x), float64(y)
+	return a == b || (math.IsNaN(a) && math.IsNaN(b))
+}
+
+func TestAxpyUnitary(t *testing.T) {
+	var x_gd, y_gd float32 = 1, 1
+	for cas, test := range tests {
+		xg_ln, yg_ln := 4+cas%2, 4+cas%3
+		test.x, test.y = guardVector(test.x, x_gd, xg_ln), guardVector(test.y, y_gd, yg_ln)
+		x, y := test.x[xg_ln:len(test.x)-xg_ln], test.y[yg_ln:len(test.y)-yg_ln]
+		AxpyUnitary(test.a, x, y)
+		for i := range test.ex {
+			if !same(y[i], test.ex[i]) {
+				t.Errorf("Test %d Unexpected result at %d Got: %v Expected: %v", cas, i, y[i], test.ex[i])
+			}
+		}
+		if !isValidGuard(test.x, x_gd, xg_ln) {
+			t.Errorf("Test %d Guard violated in x vector %v %v", cas, test.x[:xg_ln], test.x[len(test.x)-xg_ln:])
+		}
+		if !isValidGuard(test.y, y_gd, yg_ln) {
+			t.Errorf("Test %d Guard violated in y vector %v %v", cas, test.y[:yg_ln], test.y[len(test.y)-yg_ln:])
+		}
+	}
+}
+
+func TestAxpyUnitaryTo(t *testing.T) {
+	var x_gd, y_gd, dst_gd float32 = 1, 1, 0
+	for cas, test := range tests {
+		xg_ln, yg_ln := 4+cas%2, 4+cas%3
+		test.x, test.y = guardVector(test.x, x_gd, xg_ln), guardVector(test.y, y_gd, yg_ln)
+		test.dst = guardVector(test.dst, dst_gd, xg_ln)
+		x, y := test.x[xg_ln:len(test.x)-xg_ln], test.y[yg_ln:len(test.y)-yg_ln]
+		dst := test.dst[xg_ln : len(test.dst)-xg_ln]
+		AxpyUnitaryTo(dst, test.a, x, y)
+		for i := range test.ex {
+			if !same(test.ex[i], dst[i]) {
+				t.Errorf("Test %d Unexpected result at %d Got: %v Expected: %v", cas, i, dst[i], test.ex[i])
+			}
+		}
+		if !isValidGuard(test.x, x_gd, xg_ln) {
+			t.Errorf("Test %d Guard violated in x vector %v %v", cas, test.x[:xg_ln], test.x[len(test.x)-xg_ln:])
+		}
+		if !isValidGuard(test.y, y_gd, yg_ln) {
+			t.Errorf("Test %d Guard violated in y vector %v %v", cas, test.y[:yg_ln], test.y[len(test.y)-yg_ln:])
+		}
+		if !isValidGuard(test.dst, dst_gd, xg_ln) {
+			t.Errorf("Test %d Guard violated in dst vector %v %v", cas, test.dst[:xg_ln], test.dst[len(test.dst)-xg_ln:])
+		}
+	}
+}
+
+func guardIncVector(vec []float32, guard_val float32, incV uintptr, guard_len int) (guarded []float32) {
+	inc := int(incV)
+	s_ln := len(vec) * (inc)
+	guarded = make([]float32, s_ln+guard_len*2)
+	for i, j := 0, 0; i < len(guarded); i++ {
+		switch {
+		case i < guard_len, i > guard_len+s_ln:
+			guarded[i] = guard_val
+		case (i-guard_len)%(inc) == 0 && j < len(vec):
+			guarded[i] = vec[j]
+			j++
+		default:
+			guarded[i] = guard_val
+		}
+	}
+	return guarded
+}
+
+func checkValidIncGuard(t *testing.T, vec []float32, guard_val float32, incV uintptr, guard_len int) {
+	inc := int(incV)
+	s_ln := len(vec) - 2*guard_len
+	for i := range vec {
+		switch {
+		case same(vec[i], guard_val):
+			// Correct value
+		case i < guard_len:
+			t.Errorf("Front guard violated at %d %v", i, vec[:guard_len])
+		case i > guard_len+s_ln:
+			t.Errorf("Back guard violated at %d %v", i-guard_len-s_ln, vec[guard_len+s_ln:])
+		case (i-guard_len)%inc == 0 && (i-guard_len)/inc < len(vec):
+			// Ignore input values
+		default:
+			t.Errorf("Internal guard violated at %d %v", i-guard_len, vec[guard_len:guard_len+s_ln])
+		}
+	}
+}
+
+func TestAxpyInc(t *testing.T) {
+	var x_gd, y_gd float32 = 1, 1
+	for cas, test := range tests {
+		xg_ln, yg_ln := 4+cas%2, 4+cas%3
+		test.x, test.y = guardIncVector(test.x, x_gd, uintptr(test.incX), xg_ln), guardIncVector(test.y, y_gd, uintptr(test.incY), yg_ln)
+		x, y := test.x[xg_ln:len(test.x)-xg_ln], test.y[yg_ln:len(test.y)-yg_ln]
+		AxpyInc(test.a, x, y, uintptr(len(test.ex)), test.incX, test.incY, test.ix, test.iy)
+		for i := range test.ex {
+			if !same(y[i*int(test.incY)], test.ex[i]) {
+				t.Errorf("Test %d Unexpected result at %d Got: %v Expected: %v", cas, i, y[i*int(test.incY)], test.ex[i])
+			}
+		}
+		checkValidIncGuard(t, test.x, x_gd, uintptr(test.incX), xg_ln)
+		checkValidIncGuard(t, test.y, y_gd, uintptr(test.incY), yg_ln)
+	}
+}
+
+func TestAxpyIncTo(t *testing.T) {
+	var x_gd, y_gd, dst_gd float32 = 1, 1, 0
+	for cas, test := range tests {
+		xg_ln, yg_ln := 4+cas%2, 4+cas%3
+		test.x, test.y = guardIncVector(test.x, x_gd, uintptr(test.incX), xg_ln), guardIncVector(test.y, y_gd, uintptr(test.incY), yg_ln)
+		test.dst = guardIncVector(test.dst, dst_gd, uintptr(test.incDst), xg_ln)
+		x, y := test.x[xg_ln:len(test.x)-xg_ln], test.y[yg_ln:len(test.y)-yg_ln]
+		dst := test.dst[xg_ln : len(test.dst)-xg_ln]
+		AxpyIncTo(dst, test.incDst, test.idst, test.a, x, y, uintptr(len(test.ex)), test.incX, test.incY, test.ix, test.iy)
+		for i := range test.ex {
+			if !same(dst[i*int(test.incDst)], test.ex[i]) {
+				t.Errorf("Test %d Unexpected result at %d Got: %v Expected: %v", cas, i, dst[i*int(test.incDst)], test.ex[i])
+			}
+		}
+		checkValidIncGuard(t, test.x, x_gd, uintptr(test.incX), xg_ln)
+		checkValidIncGuard(t, test.y, y_gd, uintptr(test.incY), yg_ln)
+		checkValidIncGuard(t, test.dst, dst_gd, uintptr(test.incDst), xg_ln)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/abssum_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/f64/abssum_amd64.s
new file mode 100644
index 00000000..7e7e5d07
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/abssum_amd64.s
@@ -0,0 +1,82 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build !noasm,!appengine
+
+#include "textflag.h"
+
+// func L1Norm(x []float64) float64
+TEXT ·L1Norm(SB), NOSPLIT, $0
+	MOVQ x_base+0(FP), SI // SI = &x
+	MOVQ x_len+8(FP), CX  // CX = len(x)
+	XORQ AX, AX           // i = 0
+	PXOR X0, X0           // p_sum_i = 0
+	PXOR X1, X1
+	PXOR X2, X2
+	PXOR X3, X3
+	PXOR X4, X4
+	PXOR X5, X5
+	PXOR X6, X6
+	PXOR X7, X7
+	CMPQ CX, $0           // if CX == 0 { return 0 }
+	JE   absum_end
+	MOVQ CX, BX
+	ANDQ $7, BX           // BX = len(x) % 8
+	SHRQ $3, CX           // CX = floor( len(x) / 8 )
+	JZ   absum_tail_start // if CX == 0 { goto absum_tail_start }
+
+absum_loop: // do {
+	// p_sum += max( p_sum + x[i], p_sum - x[i] )
+	MOVUPS (SI)(AX*8), X8    // X_i = x[i:i+1]
+	MOVUPS 16(SI)(AX*8), X9
+	MOVUPS 32(SI)(AX*8), X10
+	MOVUPS 48(SI)(AX*8), X11
+	ADDPD  X8, X0            // p_sum_i += X_i  ( positive values )
+	ADDPD  X9, X2
+	ADDPD  X10, X4
+	ADDPD  X11, X6
+	SUBPD  X8, X1            // p_sum_(i+1) -= X_i  ( negative values )
+	SUBPD  X9, X3
+	SUBPD  X10, X5
+	SUBPD  X11, X7
+	MAXPD  X1, X0            // p_sum_i = max( p_sum_i, p_sum_(i+1) )
+	MAXPD  X3, X2
+	MAXPD  X5, X4
+	MAXPD  X7, X6
+	MOVAPS X0, X1            // p_sum_(i+1) = p_sum_i
+	MOVAPS X2, X3
+	MOVAPS X4, X5
+	MOVAPS X6, X7
+	ADDQ   $8, AX            // i += 8
+	LOOP   absum_loop        // } while --CX > 0
+
+	// p_sum_0 = \sum_{i=1}^{3}( p_sum_(i*2) )
+	ADDPD X3, X0
+	ADDPD X5, X7
+	ADDPD X7, X0
+
+	// p_sum_0[0] = p_sum_0[0] + p_sum_0[1]
+	MOVAPS X0, X1
+	SHUFPD $0x3, X0, X0 // lower( p_sum_0 ) = upper( p_sum_0 )
+	ADDSD  X1, X0
+	CMPQ   BX, $0
+	JE     absum_end    // if BX == 0 { goto absum_end }
+
+absum_tail_start: // Reset loop registers
+	MOVQ  BX, CX // Loop counter:  CX = BX
+	XORPS X8, X8 // X_8 = 0
+
+absum_tail: // do {
+	// p_sum += max( p_sum + x[i], p_sum - x[i] )
+	MOVSD (SI)(AX*8), X8 // X_8 = x[i]
+	MOVSD X0, X1         // p_sum_1 = p_sum_0
+	ADDSD X8, X0         // p_sum_0 += X_8
+	SUBSD X8, X1         // p_sum_1 -= X_8
+	MAXSD X1, X0         // p_sum_0 = max( p_sum_0, p_sum_1 )
+	INCQ  AX             // i++
+	LOOP  absum_tail     // } while --CX > 0
+
+absum_end: // return p_sum_0
+	MOVSD X0, sum+24(FP)
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/abssuminc_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/f64/abssuminc_amd64.s
new file mode 100644
index 00000000..f4db05bd
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/abssuminc_amd64.s
@@ -0,0 +1,90 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build !noasm,!appengine
+
+#include "textflag.h"
+
+// func L1NormInc(x []float64, n, incX int) (sum float64)
+TEXT ·L1NormInc(SB), NOSPLIT, $0
+	MOVQ  x_base+0(FP), SI // SI = &x
+	MOVQ  n+24(FP), CX     // CX = n
+	MOVQ  incX+32(FP), AX  // AX =  increment * sizeof( float64 )
+	SHLQ  $3, AX
+	MOVQ  AX, DX           // DX = AX * 3
+	IMULQ $3, DX
+	PXOR  X0, X0           // p_sum_i = 0
+	PXOR  X1, X1
+	PXOR  X2, X2
+	PXOR  X3, X3
+	PXOR  X4, X4
+	PXOR  X5, X5
+	PXOR  X6, X6
+	PXOR  X7, X7
+	CMPQ  CX, $0           // if CX == 0 { return 0 }
+	JE    absum_end
+	MOVQ  CX, BX
+	ANDQ  $7, BX           // BX = n % 8
+	SHRQ  $3, CX           // CX = floor( n / 8 )
+	JZ    absum_tail_start // if CX == 0 { goto absum_tail_start }
+
+absum_loop: // do {
+	// p_sum = max( p_sum + x[i], p_sum - x[i] )
+	MOVSD  (SI), X8        // X_i[0] = x[i]
+	MOVSD  (SI)(AX*1), X9
+	MOVSD  (SI)(AX*2), X10
+	MOVSD  (SI)(DX*1), X11
+	LEAQ   (SI)(AX*4), SI  // SI = SI + 4
+	MOVHPD (SI), X8        // X_i[1] = x[i+4]
+	MOVHPD (SI)(AX*1), X9
+	MOVHPD (SI)(AX*2), X10
+	MOVHPD (SI)(DX*1), X11
+	ADDPD  X8, X0          // p_sum_i += X_i  ( positive values )
+	ADDPD  X9, X2
+	ADDPD  X10, X4
+	ADDPD  X11, X6
+	SUBPD  X8, X1          // p_sum_(i+1) -= X_i  ( negative values )
+	SUBPD  X9, X3
+	SUBPD  X10, X5
+	SUBPD  X11, X7
+	MAXPD  X1, X0          // p_sum_i = max( p_sum_i, p_sum_(i+1) )
+	MAXPD  X3, X2
+	MAXPD  X5, X4
+	MAXPD  X7, X6
+	MOVAPS X0, X1          // p_sum_(i+1) = p_sum_i
+	MOVAPS X2, X3
+	MOVAPS X4, X5
+	MOVAPS X6, X7
+	LEAQ   (SI)(AX*4), SI  // SI = SI + 4
+	LOOP   absum_loop      // } while --CX > 0
+
+	// p_sum_0 = \sum_{i=1}^{3}( p_sum_(i*2) )
+	ADDPD X3, X0
+	ADDPD X5, X7
+	ADDPD X7, X0
+
+	// p_sum_0[0] = p_sum_0[0] + p_sum_0[1]
+	MOVAPS X0, X1
+	SHUFPD $0x3, X0, X0 // lower( p_sum_0 ) = upper( p_sum_0 )
+	ADDSD  X1, X0
+	CMPQ   BX, $0
+	JE     absum_end    // if BX == 0 { goto absum_end }
+
+absum_tail_start: // Reset loop registers
+	MOVQ  BX, CX // Loop counter:  CX = BX
+	XORPS X8, X8 // X_8 = 0
+
+absum_tail: // do {
+	// p_sum += max( p_sum + x[i], p_sum - x[i] )
+	MOVSD (SI), X8   // X_8 = x[i]
+	MOVSD X0, X1     // p_sum_1 = p_sum_0
+	ADDSD X8, X0     // p_sum_0 += X_8
+	SUBSD X8, X1     // p_sum_1 -= X_8
+	MAXSD X1, X0     // p_sum_0 = max( p_sum_0, p_sum_1 )
+	ADDQ  AX, SI     // i++
+	LOOP  absum_tail // } while --CX > 0
+
+absum_end: // return p_sum_0
+	MOVSD X0, sum+40(FP)
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/add_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/f64/add_amd64.s
new file mode 100644
index 00000000..27329699
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/add_amd64.s
@@ -0,0 +1,66 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build !noasm,!appengine
+
+#include "textflag.h"
+
+// func Add(dst, s []float64)
+TEXT ·Add(SB), NOSPLIT, $0
+	MOVQ    dst_base+0(FP), DI // DI = &dst
+	MOVQ    dst_len+8(FP), CX  // CX = len(dst)
+	MOVQ    s_base+24(FP), SI  // SI = &s
+	CMPQ    s_len+32(FP), CX   // CX = max( CX, len(s) )
+	CMOVQLE s_len+32(FP), CX
+	CMPQ    CX, $0             // if CX == 0 { return }
+	JE      add_end
+	XORQ    AX, AX
+	MOVQ    DI, BX
+	ANDQ    $0x0F, BX          // BX = &dst & 15
+	JZ      add_no_trim        // if BX == 0 { goto add_no_trim }
+
+	// Align on 16-bit boundary
+	MOVSD (SI)(AX*8), X0 // X0 = s[i]
+	ADDSD (DI)(AX*8), X0 // X0 += dst[i]
+	MOVSD X0, (DI)(AX*8) // dst[i] = X0
+	INCQ  AX             // i++
+	DECQ  CX             // --CX
+	JE    add_end        // if CX == 0 { return  }
+
+add_no_trim:
+	MOVQ CX, BX
+	ANDQ $7, BX         // BX = len(dst) % 8
+	SHRQ $3, CX         // CX = floor( len(dst) / 8 )
+	JZ   add_tail_start // if CX == 0 { goto add_tail_start }
+
+add_loop: // Loop unrolled 8x   do {
+	MOVUPS (SI)(AX*8), X0   // X_i = s[i:i+1]
+	MOVUPS 16(SI)(AX*8), X1
+	MOVUPS 32(SI)(AX*8), X2
+	MOVUPS 48(SI)(AX*8), X3
+	ADDPD  (DI)(AX*8), X0   // X_i += dst[i:i+1]
+	ADDPD  16(DI)(AX*8), X1
+	ADDPD  32(DI)(AX*8), X2
+	ADDPD  48(DI)(AX*8), X3
+	MOVUPS X0, (DI)(AX*8)   // dst[i:i+1] = X_i
+	MOVUPS X1, 16(DI)(AX*8)
+	MOVUPS X2, 32(DI)(AX*8)
+	MOVUPS X3, 48(DI)(AX*8)
+	ADDQ   $8, AX           // i += 8
+	LOOP   add_loop         // } while --CX > 0
+	CMPQ   BX, $0           // if BX == 0 { return }
+	JE     add_end
+
+add_tail_start: // Reset loop registers
+	MOVQ BX, CX // Loop counter: CX = BX
+
+add_tail: // do {
+	MOVSD (SI)(AX*8), X0 // X0 = s[i]
+	ADDSD (DI)(AX*8), X0 // X0 += dst[i]
+	MOVSD X0, (DI)(AX*8) // dst[i] = X0
+	INCQ  AX             // ++i
+	LOOP  add_tail       // } while --CX > 0
+
+add_end:
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/addconst_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/f64/addconst_amd64.s
new file mode 100644
index 00000000..88fed071
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/addconst_amd64.s
@@ -0,0 +1,53 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build !noasm,!appengine
+
+#include "textflag.h"
+
+// func Addconst(alpha float64, x []float64)
+TEXT ·AddConst(SB), NOSPLIT, $0
+	MOVQ   x_base+8(FP), SI // SI = &x
+	MOVQ   x_len+16(FP), CX // CX = len(x)
+	CMPQ   CX, $0           // if len(x) == 0 { return }
+	JE     ac_end
+	MOVSD  alpha+0(FP), X4  // X4 = { a, a }
+	SHUFPD $0, X4, X4
+	MOVUPS X4, X5           // X5 = X4
+	XORQ   AX, AX           // i = 0
+	MOVQ   CX, BX
+	ANDQ   $7, BX           // BX = len(x) % 8
+	SHRQ   $3, CX           // CX = floor( len(x) / 8 )
+	JZ     ac_tail_start    // if CX == 0 { goto ac_tail_start }
+
+ac_loop: // Loop unrolled 8x   do {
+	MOVUPS (SI)(AX*8), X0   // X_i = s[i:i+1]
+	MOVUPS 16(SI)(AX*8), X1
+	MOVUPS 32(SI)(AX*8), X2
+	MOVUPS 48(SI)(AX*8), X3
+	ADDPD  X4, X0           // X_i += a
+	ADDPD  X5, X1
+	ADDPD  X4, X2
+	ADDPD  X5, X3
+	MOVUPS X0, (SI)(AX*8)   // s[i:i+1] = X_i
+	MOVUPS X1, 16(SI)(AX*8)
+	MOVUPS X2, 32(SI)(AX*8)
+	MOVUPS X3, 48(SI)(AX*8)
+	ADDQ   $8, AX           // i += 8
+	LOOP   ac_loop          // } while --CX > 0
+	CMPQ   BX, $0           // if BX == 0 { return }
+	JE     ac_end
+
+ac_tail_start: // Reset loop counters
+	MOVQ BX, CX // Loop counter: CX = BX
+
+ac_tail: // do {
+	MOVSD (SI)(AX*8), X0 // X0 = s[i]
+	ADDSD X4, X0         // X0 += a
+	MOVSD X0, (SI)(AX*8) // s[i] = X0
+	INCQ  AX             // ++i
+	LOOP  ac_tail        // } while --CX > 0
+
+ac_end:
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/asm_test.go b/vendor/gonum.org/v1/gonum/internal/asm/f64/asm_test.go
new file mode 100644
index 00000000..cca86e84
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/asm_test.go
@@ -0,0 +1,204 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package f64
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+)
+
+var (
+	nan = math.NaN()
+	inf = math.Inf(1)
+)
+
+// newGuardedVector allocates a new slice and returns it as three subslices.
+// v is a strided vector that contains elements of data at indices i*inc and
+// NaN elsewhere. frontGuard and backGuard are filled with NaN values, and
+// their backing arrays are directly adjacent to v in memory. The three slices
+// can be used to detect invalid memory reads and writes.
+func newGuardedVector(data []float64, inc int) (v, frontGuard, backGuard []float64) {
+	if inc < 0 {
+		inc = -inc
+	}
+	guard := 2 * inc
+	size := (len(data)-1)*inc + 1
+	whole := make([]float64, size+2*guard)
+	v = whole[guard : len(whole)-guard]
+	for i := range whole {
+		whole[i] = math.NaN()
+	}
+	for i, d := range data {
+		v[i*inc] = d
+	}
+	return v, whole[:guard], whole[len(whole)-guard:]
+}
+
+// allNaN returns true if x contains only NaN values, and false otherwise.
+func allNaN(x []float64) bool {
+	for _, v := range x {
+		if !math.IsNaN(v) {
+			return false
+		}
+	}
+	return true
+}
+
+// equalStrided returns true if the strided vector x contains elements of the
+// dense vector ref at indices i*inc, false otherwise.
+func equalStrided(ref, x []float64, inc int) bool {
+	if inc < 0 {
+		inc = -inc
+	}
+	for i, v := range ref {
+		if !same(x[i*inc], v) {
+			return false
+		}
+	}
+	return true
+}
+
+// nonStridedWrite returns false if all elements of x at non-stride indices are
+// equal to NaN, true otherwise.
+func nonStridedWrite(x []float64, inc int) bool {
+	if inc < 0 {
+		inc = -inc
+	}
+	for i, v := range x {
+		if i%inc != 0 && !math.IsNaN(v) {
+			return true
+		}
+	}
+	return false
+}
+
+// guardVector copies the source vector (vec) into a new slice with guards.
+// Guards guarded[:gdLn] and guarded[len-gdLn:] will be filled with sigil value gdVal.
+func guardVector(vec []float64, gdVal float64, gdLn int) (guarded []float64) {
+	guarded = make([]float64, len(vec)+gdLn*2)
+	copy(guarded[gdLn:], vec)
+	for i := 0; i < gdLn; i++ {
+		guarded[i] = gdVal
+		guarded[len(guarded)-1-i] = gdVal
+	}
+	return guarded
+}
+
+// isValidGuard will test for violated guards, generated by guardVector.
+func isValidGuard(vec []float64, gdVal float64, gdLn int) bool {
+	for i := 0; i < gdLn; i++ {
+		if !same(vec[i], gdVal) || !same(vec[len(vec)-1-i], gdVal) {
+			return false
+		}
+	}
+	return true
+}
+
+// guardIncVector copies the source vector (vec) into a new incremented slice with guards.
+// End guards will be length gdLen.
+// Internal and end guards will be filled with sigil value gdVal.
+func guardIncVector(vec []float64, gdVal float64, inc, gdLen int) (guarded []float64) {
+	if inc < 0 {
+		inc = -inc
+	}
+	inrLen := len(vec) * inc
+	guarded = make([]float64, inrLen+gdLen*2)
+	for i := range guarded {
+		guarded[i] = gdVal
+	}
+	for i, v := range vec {
+		guarded[gdLen+i*inc] = v
+	}
+	return guarded
+}
+
+// checkValidIncGuard will test for violated guards, generated by guardIncVector
+func checkValidIncGuard(t *testing.T, vec []float64, gdVal float64, inc, gdLen int) {
+	srcLn := len(vec) - 2*gdLen
+	for i := range vec {
+		switch {
+		case same(vec[i], gdVal):
+			// Correct value
+		case (i-gdLen)%inc == 0 && (i-gdLen)/inc < len(vec):
+			// Ignore input values
+		case i < gdLen:
+			t.Errorf("Front guard violated at %d %v", i, vec[:gdLen])
+		case i > gdLen+srcLn:
+			t.Errorf("Back guard violated at %d %v", i-gdLen-srcLn, vec[gdLen+srcLn:])
+		default:
+			t.Errorf("Internal guard violated at %d %v", i-gdLen, vec[gdLen:gdLen+srcLn])
+		}
+	}
+}
+
+// same tests for nan-aware equality.
+func same(a, b float64) bool {
+	return a == b || (math.IsNaN(a) && math.IsNaN(b))
+}
+
+var ( // Offset sets for testing alignment handling in Unitary assembly functions.
+	align1 = []int{0, 1}
+	align2 = newIncSet(0, 1)
+	align3 = newIncToSet(0, 1)
+)
+
+type incSet struct {
+	x, y int
+}
+
+// genInc will generate all (x,y) combinations of the input increment set.
+func newIncSet(inc ...int) []incSet {
+	n := len(inc)
+	is := make([]incSet, n*n)
+	for x := range inc {
+		for y := range inc {
+			is[x*n+y] = incSet{inc[x], inc[y]}
+		}
+	}
+	return is
+}
+
+type incToSet struct {
+	dst, x, y int
+}
+
+// genIncTo will generate all (dst,x,y) combinations of the input increment set.
+func newIncToSet(inc ...int) []incToSet {
+	n := len(inc)
+	is := make([]incToSet, n*n*n)
+	for i, dst := range inc {
+		for x := range inc {
+			for y := range inc {
+				is[i*n*n+x*n+y] = incToSet{dst, inc[x], inc[y]}
+			}
+		}
+	}
+	return is
+}
+
+var benchSink []float64
+
+func randomSlice(n, inc int) []float64 {
+	if inc < 0 {
+		inc = -inc
+	}
+	x := make([]float64, (n-1)*inc+1)
+	for i := range x {
+		x[i] = rand.Float64()
+	}
+	return x
+}
+
+func randSlice(n, inc int, r *rand.Rand) []float64 {
+	if inc < 0 {
+		inc = -inc
+	}
+	x := make([]float64, (n-1)*inc+1)
+	for i := range x {
+		x[i] = r.Float64()
+	}
+	return x
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/axpy.go b/vendor/gonum.org/v1/gonum/internal/asm/f64/axpy.go
new file mode 100644
index 00000000..455a5d7e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/axpy.go
@@ -0,0 +1,57 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !amd64 noasm appengine
+
+package f64
+
+// AxpyUnitary is
+//  for i, v := range x {
+//  	y[i] += alpha * v
+//  }
+func AxpyUnitary(alpha float64, x, y []float64) {
+	for i, v := range x {
+		y[i] += alpha * v
+	}
+}
+
+// AxpyUnitaryTo is
+//  for i, v := range x {
+//  	dst[i] = alpha*v + y[i]
+//  }
+func AxpyUnitaryTo(dst []float64, alpha float64, x, y []float64) {
+	for i, v := range x {
+		dst[i] = alpha*v + y[i]
+	}
+}
+
+// AxpyInc is
+//  for i := 0; i < int(n); i++ {
+//  	y[iy] += alpha * x[ix]
+//  	ix += incX
+//  	iy += incY
+//  }
+func AxpyInc(alpha float64, x, y []float64, n, incX, incY, ix, iy uintptr) {
+	for i := 0; i < int(n); i++ {
+		y[iy] += alpha * x[ix]
+		ix += incX
+		iy += incY
+	}
+}
+
+// AxpyIncTo is
+//  for i := 0; i < int(n); i++ {
+//  	dst[idst] = alpha*x[ix] + y[iy]
+//  	ix += incX
+//  	iy += incY
+//  	idst += incDst
+//  }
+func AxpyIncTo(dst []float64, incDst, idst uintptr, alpha float64, x, y []float64, n, incX, incY, ix, iy uintptr) {
+	for i := 0; i < int(n); i++ {
+		dst[idst] = alpha*x[ix] + y[iy]
+		ix += incX
+		iy += incY
+		idst += incDst
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/axpy_test.go b/vendor/gonum.org/v1/gonum/internal/asm/f64/axpy_test.go
new file mode 100644
index 00000000..2f096aaf
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/axpy_test.go
@@ -0,0 +1,274 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package f64
+
+import (
+	"fmt"
+	"testing"
+)
+
+const (
+	msgVal   = "%v: unexpected value at %v Got: %v Expected: %v"
+	msgGuard = "%v: Guard violated in %s vector %v %v"
+)
+
+var axpyTests = []struct {
+	alpha   float64
+	x       []float64
+	y       []float64
+	want    []float64
+	wantRev []float64 // Result when x is traversed in reverse direction.
+}{
+	{
+		alpha:   0,
+		x:       []float64{},
+		y:       []float64{},
+		want:    []float64{},
+		wantRev: []float64{},
+	},
+	{
+		alpha:   0,
+		x:       []float64{2},
+		y:       []float64{-3},
+		want:    []float64{-3},
+		wantRev: []float64{-3},
+	},
+	{
+		alpha:   1,
+		x:       []float64{2},
+		y:       []float64{-3},
+		want:    []float64{-1},
+		wantRev: []float64{-1},
+	},
+	{
+		alpha:   3,
+		x:       []float64{2},
+		y:       []float64{-3},
+		want:    []float64{3},
+		wantRev: []float64{3},
+	},
+	{
+		alpha:   -3,
+		x:       []float64{2},
+		y:       []float64{-3},
+		want:    []float64{-9},
+		wantRev: []float64{-9},
+	},
+	{
+		alpha:   1,
+		x:       []float64{1, 5},
+		y:       []float64{2, -3},
+		want:    []float64{3, 2},
+		wantRev: []float64{7, -2},
+	},
+	{
+		alpha:   1,
+		x:       []float64{2, 3, 4},
+		y:       []float64{-3, -2, -1},
+		want:    []float64{-1, 1, 3},
+		wantRev: []float64{1, 1, 1},
+	},
+	{
+		alpha:   0,
+		x:       []float64{0, 0, 1, 1, 2, -3, -4},
+		y:       []float64{0, 1, 0, 3, -4, 5, -6},
+		want:    []float64{0, 1, 0, 3, -4, 5, -6},
+		wantRev: []float64{0, 1, 0, 3, -4, 5, -6},
+	},
+	{
+		alpha:   1,
+		x:       []float64{0, 0, 1, 1, 2, -3, -4},
+		y:       []float64{0, 1, 0, 3, -4, 5, -6},
+		want:    []float64{0, 1, 1, 4, -2, 2, -10},
+		wantRev: []float64{-4, -2, 2, 4, -3, 5, -6},
+	},
+	{
+		alpha:   3,
+		x:       []float64{0, 0, 1, 1, 2, -3, -4},
+		y:       []float64{0, 1, 0, 3, -4, 5, -6},
+		want:    []float64{0, 1, 3, 6, 2, -4, -18},
+		wantRev: []float64{-12, -8, 6, 6, -1, 5, -6},
+	},
+	{
+		alpha:   -3,
+		x:       []float64{0, 0, 1, 1, 2, -3, -4, 0, 0, 1, 1, 2, -3, -4},
+		y:       []float64{0, 1, 0, 3, -4, 5, -6, 0, 1, 0, 3, -4, 5, -6},
+		want:    []float64{0, 1, -3, 0, -10, 14, 6, 0, 1, -3, 0, -10, 14, 6},
+		wantRev: []float64{12, 10, -6, 0, -7, 5, -6, 12, 10, -6, 0, -7, 5, -6},
+	},
+	{
+		alpha:   -5,
+		x:       []float64{0, 0, 1, 1, 2, -3, -4, 5, 1, 2, -3, -4, 5},
+		y:       []float64{0, 1, 0, 3, -4, 5, -6, 7, 3, -4, 5, -6, 7},
+		want:    []float64{0, 1, -5, -2, -14, 20, 14, -18, -2, -14, 20, 14, -18},
+		wantRev: []float64{-25, 21, 15, -7, -9, -20, 14, 22, -7, -9, 0, -6, 7},
+	},
+}
+
+func TestAxpyUnitary(t *testing.T) {
+	const xGdVal, yGdVal = -1, 0.5
+	for i, test := range axpyTests {
+		for _, align := range align2 {
+			prefix := fmt.Sprintf("Test %v (x:%v y:%v)", i, align.x, align.y)
+			xgLn, ygLn := 4+align.x, 4+align.y
+			xg, yg := guardVector(test.x, xGdVal, xgLn), guardVector(test.y, yGdVal, ygLn)
+			x, y := xg[xgLn:len(xg)-xgLn], yg[ygLn:len(yg)-ygLn]
+			AxpyUnitary(test.alpha, x, y)
+			for i := range test.want {
+				if !same(y[i], test.want[i]) {
+					t.Errorf(msgVal, prefix, i, y[i], test.want[i])
+				}
+			}
+			if !isValidGuard(xg, xGdVal, xgLn) {
+				t.Errorf(msgGuard, prefix, "x", xg[:xgLn], xg[len(xg)-xgLn:])
+			}
+			if !isValidGuard(yg, yGdVal, ygLn) {
+				t.Errorf(msgGuard, prefix, "y", yg[:ygLn], yg[len(yg)-ygLn:])
+			}
+			if !equalStrided(test.x, x, 1) {
+				t.Errorf("%v: modified read-only x argument", prefix)
+			}
+		}
+	}
+}
+
+func TestAxpyUnitaryTo(t *testing.T) {
+	const dstGdVal, xGdVal, yGdVal = 1, -1, 0.5
+	for i, test := range axpyTests {
+		for _, align := range align3 {
+			prefix := fmt.Sprintf("Test %v (x:%v y:%v dst:%v)", i, align.x, align.y, align.dst)
+
+			dgLn, xgLn, ygLn := 4+align.dst, 4+align.x, 4+align.y
+			dstOrig := make([]float64, len(test.x))
+			xg, yg := guardVector(test.x, xGdVal, xgLn), guardVector(test.y, yGdVal, ygLn)
+			dstg := guardVector(dstOrig, dstGdVal, dgLn)
+			x, y := xg[xgLn:len(xg)-xgLn], yg[ygLn:len(yg)-ygLn]
+			dst := dstg[dgLn : len(dstg)-dgLn]
+
+			AxpyUnitaryTo(dst, test.alpha, x, y)
+			for i := range test.want {
+				if !same(dst[i], test.want[i]) {
+					t.Errorf(msgVal, prefix, i, dst[i], test.want[i])
+				}
+			}
+			if !isValidGuard(xg, xGdVal, xgLn) {
+				t.Errorf(msgGuard, prefix, "x", xg[:xgLn], xg[len(xg)-xgLn:])
+			}
+			if !isValidGuard(yg, yGdVal, ygLn) {
+				t.Errorf(msgGuard, prefix, "y", yg[:ygLn], yg[len(yg)-ygLn:])
+			}
+			if !isValidGuard(dstg, dstGdVal, dgLn) {
+				t.Errorf(msgGuard, prefix, "dst", dstg[:dgLn], dstg[len(dstg)-dgLn:])
+			}
+			if !equalStrided(test.x, x, 1) {
+				t.Errorf("%v: modified read-only x argument", prefix)
+			}
+			if !equalStrided(test.y, y, 1) {
+				t.Errorf("%v: modified read-only y argument", prefix)
+			}
+		}
+	}
+}
+
+func TestAxpyInc(t *testing.T) {
+	const xGdVal, yGdVal = -1, 0.5
+	gdLn := 4
+	for i, test := range axpyTests {
+		n := len(test.x)
+		for _, inc := range newIncSet(-7, -4, -3, -2, -1, 1, 2, 3, 4, 7) {
+			var ix, iy int
+			if inc.x < 0 {
+				ix = (-n + 1) * inc.x
+			}
+			if inc.y < 0 {
+				iy = (-n + 1) * inc.y
+			}
+			prefix := fmt.Sprintf("test %v, inc.x = %v, inc.y = %v", i, inc.x, inc.y)
+			xg := guardIncVector(test.x, xGdVal, inc.x, gdLn)
+			yg := guardIncVector(test.y, yGdVal, inc.y, gdLn)
+			x, y := xg[gdLn:len(xg)-gdLn], yg[gdLn:len(yg)-gdLn]
+
+			AxpyInc(test.alpha, x, y, uintptr(n),
+				uintptr(inc.x), uintptr(inc.y), uintptr(ix), uintptr(iy))
+
+			want := test.want
+			if inc.x*inc.y < 0 {
+				want = test.wantRev
+			}
+			if inc.y < 0 {
+				inc.y = -inc.y
+			}
+			for i := range want {
+				if !same(y[i*inc.y], want[i]) {
+					t.Errorf(msgVal, prefix, i, y[iy+i*inc.y], want[i])
+				}
+			}
+			if !equalStrided(test.x, x, inc.x) {
+				t.Errorf("%v: modified read-only x argument", prefix)
+			}
+			checkValidIncGuard(t, xg, xGdVal, inc.x, gdLn)
+			checkValidIncGuard(t, yg, yGdVal, inc.y, gdLn)
+		}
+	}
+}
+
+func TestAxpyIncTo(t *testing.T) {
+	const dstGdVal, xGdVal, yGdVal = 1, -1, 0.5
+	var want []float64
+	gdLn := 4
+	for i, test := range axpyTests {
+		n := len(test.x)
+		for _, inc := range newIncToSet(-7, -4, -3, -2, -1, 1, 2, 3, 4, 7) {
+			var ix, iy, idst uintptr
+			if inc.x < 0 {
+				ix = uintptr((-n + 1) * inc.x)
+			}
+			if inc.y < 0 {
+				iy = uintptr((-n + 1) * inc.y)
+			}
+			if inc.dst < 0 {
+				idst = uintptr((-n + 1) * inc.dst)
+			}
+
+			prefix := fmt.Sprintf("Test %v: (x: %v, y: %v, dst:%v)", i, inc.x, inc.y, inc.dst)
+			dstOrig := make([]float64, len(test.want))
+			xg := guardIncVector(test.x, xGdVal, inc.x, gdLn)
+			yg := guardIncVector(test.y, yGdVal, inc.y, gdLn)
+			dstg := guardIncVector(dstOrig, dstGdVal, inc.dst, gdLn)
+			x, y := xg[gdLn:len(xg)-gdLn], yg[gdLn:len(yg)-gdLn]
+			dst := dstg[gdLn : len(dstg)-gdLn]
+
+			AxpyIncTo(dst, uintptr(inc.dst), idst,
+				test.alpha, x, y, uintptr(n),
+				uintptr(inc.x), uintptr(inc.y), ix, iy)
+			want = test.want
+			if inc.x*inc.y < 0 {
+				want = test.wantRev
+			}
+			var iW, incW int = 0, 1
+			if inc.y*inc.dst < 0 {
+				iW, incW = len(want)-1, -1
+			}
+			if inc.dst < 0 {
+				inc.dst = -inc.dst
+			}
+			for i := range want {
+				if !same(dst[i*inc.dst], want[iW+i*incW]) {
+					t.Errorf(msgVal, prefix, i, dst[i*inc.dst], want[iW+i*incW])
+				}
+			}
+
+			checkValidIncGuard(t, xg, xGdVal, inc.x, gdLn)
+			checkValidIncGuard(t, yg, yGdVal, inc.y, gdLn)
+			checkValidIncGuard(t, dstg, dstGdVal, inc.dst, gdLn)
+			if !equalStrided(test.x, x, inc.x) {
+				t.Errorf("%v: modified read-only x argument", prefix)
+			}
+			if !equalStrided(test.y, y, inc.y) {
+				t.Errorf("%v: modified read-only y argument", prefix)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/axpyinc_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/f64/axpyinc_amd64.s
new file mode 100644
index 00000000..214f9704
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/axpyinc_amd64.s
@@ -0,0 +1,142 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Some of the loop unrolling code is copied from:
+// http://golang.org/src/math/big/arith_amd64.s
+// which is distributed under these terms:
+//
+// Copyright (c) 2012 The Go Authors. All rights reserved.
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+//    * Redistributions of source code must retain the above copyright
+// notice, this list of conditions and the following disclaimer.
+//    * Redistributions in binary form must reproduce the above
+// copyright notice, this list of conditions and the following disclaimer
+// in the documentation and/or other materials provided with the
+// distribution.
+//    * Neither the name of Google Inc. nor the names of its
+// contributors may be used to endorse or promote products derived from
+// this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+//+build !noasm,!appengine
+
+#include "textflag.h"
+
+#define X_PTR SI
+#define Y_PTR DI
+#define DST_PTR DI
+#define IDX AX
+#define LEN CX
+#define TAIL BX
+#define INC_X R8
+#define INCx3_X R11
+#define INC_Y R9
+#define INCx3_Y R12
+#define INC_DST R9
+#define INCx3_DST R12
+#define ALPHA X0
+#define ALPHA_2 X1
+
+// func AxpyInc(alpha float64, x, y []float64, n, incX, incY, ix, iy uintptr)
+TEXT ·AxpyInc(SB), NOSPLIT, $0
+	MOVQ x_base+8(FP), X_PTR  // X_PTR = &x
+	MOVQ y_base+32(FP), Y_PTR // Y_PTR = &y
+	MOVQ n+56(FP), LEN        // LEN = n
+	CMPQ LEN, $0              // if LEN == 0 { return }
+	JE   end
+
+	MOVQ ix+80(FP), INC_X
+	MOVQ iy+88(FP), INC_Y
+	LEAQ (X_PTR)(INC_X*8), X_PTR // X_PTR = &(x[ix])
+	LEAQ (Y_PTR)(INC_Y*8), Y_PTR // Y_PTR = &(y[iy])
+	MOVQ Y_PTR, DST_PTR          // DST_PTR = Y_PTR  // Write pointer
+
+	MOVQ incX+64(FP), INC_X // INC_X = incX * sizeof(float64)
+	SHLQ $3, INC_X
+	MOVQ incY+72(FP), INC_Y // INC_Y = incY * sizeof(float64)
+	SHLQ $3, INC_Y
+
+	MOVSD alpha+0(FP), ALPHA // ALPHA = alpha
+	MOVQ  LEN, TAIL
+	ANDQ  $3, TAIL           // TAIL = n % 4
+	SHRQ  $2, LEN            // LEN = floor( n / 4 )
+	JZ    tail_start         // if LEN == 0 { goto tail_start }
+
+	MOVAPS ALPHA, ALPHA_2            // ALPHA_2 = ALPHA  for pipelining
+	LEAQ   (INC_X)(INC_X*2), INCx3_X // INCx3_X = INC_X * 3
+	LEAQ   (INC_Y)(INC_Y*2), INCx3_Y // INCx3_Y = INC_Y * 3
+
+loop:  // do {  // y[i] += alpha * x[i] unrolled 4x.
+	MOVSD (X_PTR), X2            // X_i = x[i]
+	MOVSD (X_PTR)(INC_X*1), X3
+	MOVSD (X_PTR)(INC_X*2), X4
+	MOVSD (X_PTR)(INCx3_X*1), X5
+
+	MULSD ALPHA, X2   // X_i *= a
+	MULSD ALPHA_2, X3
+	MULSD ALPHA, X4
+	MULSD ALPHA_2, X5
+
+	ADDSD (Y_PTR), X2            // X_i += y[i]
+	ADDSD (Y_PTR)(INC_Y*1), X3
+	ADDSD (Y_PTR)(INC_Y*2), X4
+	ADDSD (Y_PTR)(INCx3_Y*1), X5
+
+	MOVSD X2, (DST_PTR)              // y[i] = X_i
+	MOVSD X3, (DST_PTR)(INC_DST*1)
+	MOVSD X4, (DST_PTR)(INC_DST*2)
+	MOVSD X5, (DST_PTR)(INCx3_DST*1)
+
+	LEAQ (X_PTR)(INC_X*4), X_PTR // X_PTR = &(X_PTR[incX*4])
+	LEAQ (Y_PTR)(INC_Y*4), Y_PTR // Y_PTR = &(Y_PTR[incY*4])
+	DECQ LEN
+	JNZ  loop                    // } while --LEN > 0
+	CMPQ TAIL, $0                // if TAIL == 0 { return }
+	JE   end
+
+tail_start: // Reset Loop registers
+	MOVQ TAIL, LEN // Loop counter: LEN = TAIL
+	SHRQ $1, LEN   // LEN = floor( LEN / 2 )
+	JZ   tail_one
+
+tail_two:
+	MOVSD (X_PTR), X2              // X_i = x[i]
+	MOVSD (X_PTR)(INC_X*1), X3
+	MULSD ALPHA, X2                // X_i *= a
+	MULSD ALPHA, X3
+	ADDSD (Y_PTR), X2              // X_i += y[i]
+	ADDSD (Y_PTR)(INC_Y*1), X3
+	MOVSD X2, (DST_PTR)            // y[i] = X_i
+	MOVSD X3, (DST_PTR)(INC_DST*1)
+
+	LEAQ (X_PTR)(INC_X*2), X_PTR // X_PTR = &(X_PTR[incX*2])
+	LEAQ (Y_PTR)(INC_Y*2), Y_PTR // Y_PTR = &(Y_PTR[incY*2])
+
+	ANDQ $1, TAIL
+	JZ   end      // if TAIL == 0 { goto end }
+
+tail_one:
+	// y[i] += alpha * x[i] for the last n % 4 iterations.
+	MOVSD (X_PTR), X2   // X2 = x[i]
+	MULSD ALPHA, X2     // X2 *= a
+	ADDSD (Y_PTR), X2   // X2 += y[i]
+	MOVSD X2, (DST_PTR) // y[i] = X2
+
+end:
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/axpyincto_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/f64/axpyincto_amd64.s
new file mode 100644
index 00000000..a873b1c9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/axpyincto_amd64.s
@@ -0,0 +1,148 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Some of the loop unrolling code is copied from:
+// http://golang.org/src/math/big/arith_amd64.s
+// which is distributed under these terms:
+//
+// Copyright (c) 2012 The Go Authors. All rights reserved.
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+//    * Redistributions of source code must retain the above copyright
+// notice, this list of conditions and the following disclaimer.
+//    * Redistributions in binary form must reproduce the above
+// copyright notice, this list of conditions and the following disclaimer
+// in the documentation and/or other materials provided with the
+// distribution.
+//    * Neither the name of Google Inc. nor the names of its
+// contributors may be used to endorse or promote products derived from
+// this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+//+build !noasm,!appengine
+
+#include "textflag.h"
+
+#define X_PTR SI
+#define Y_PTR DI
+#define DST_PTR DX
+#define IDX AX
+#define LEN CX
+#define TAIL BX
+#define INC_X R8
+#define INCx3_X R11
+#define INC_Y R9
+#define INCx3_Y R12
+#define INC_DST R10
+#define INCx3_DST R13
+#define ALPHA X0
+#define ALPHA_2 X1
+
+// func AxpyIncTo(dst []float64, incDst, idst uintptr, alpha float64, x, y []float64, n, incX, incY, ix, iy uintptr)
+TEXT ·AxpyIncTo(SB), NOSPLIT, $0
+	MOVQ dst_base+0(FP), DST_PTR // DST_PTR := &dst
+	MOVQ x_base+48(FP), X_PTR    // X_PTR := &x
+	MOVQ y_base+72(FP), Y_PTR    // Y_PTR := &y
+	MOVQ n+96(FP), LEN           // LEN := n
+	CMPQ LEN, $0                 // if LEN == 0 { return }
+	JE   end
+
+	MOVQ ix+120(FP), INC_X
+	LEAQ (X_PTR)(INC_X*8), X_PTR       // X_PTR = &(x[ix])
+	MOVQ iy+128(FP), INC_Y
+	LEAQ (Y_PTR)(INC_Y*8), Y_PTR       // Y_PTR = &(dst[idst])
+	MOVQ idst+32(FP), INC_DST
+	LEAQ (DST_PTR)(INC_DST*8), DST_PTR // DST_PTR = &(y[iy])
+
+	MOVQ  incX+104(FP), INC_X    // INC_X = incX * sizeof(float64)
+	SHLQ  $3, INC_X
+	MOVQ  incY+112(FP), INC_Y    // INC_Y = incY * sizeof(float64)
+	SHLQ  $3, INC_Y
+	MOVQ  incDst+24(FP), INC_DST // INC_DST = incDst * sizeof(float64)
+	SHLQ  $3, INC_DST
+	MOVSD alpha+40(FP), ALPHA
+
+	MOVQ LEN, TAIL
+	ANDQ $3, TAIL   // TAIL = n % 4
+	SHRQ $2, LEN    // LEN = floor( n / 4 )
+	JZ   tail_start // if LEN == 0 { goto tail_start }
+
+	MOVSD ALPHA, ALPHA_2                  // ALPHA_2 = ALPHA for pipelining
+	LEAQ  (INC_X)(INC_X*2), INCx3_X       // INCx3_X = INC_X * 3
+	LEAQ  (INC_Y)(INC_Y*2), INCx3_Y       // INCx3_Y = INC_Y * 3
+	LEAQ  (INC_DST)(INC_DST*2), INCx3_DST // INCx3_DST = INC_DST * 3
+
+loop:  // do {  // y[i] += alpha * x[i] unrolled 2x.
+	MOVSD (X_PTR), X2            // X_i = x[i]
+	MOVSD (X_PTR)(INC_X*1), X3
+	MOVSD (X_PTR)(INC_X*2), X4
+	MOVSD (X_PTR)(INCx3_X*1), X5
+
+	MULSD ALPHA, X2   // X_i *= a
+	MULSD ALPHA_2, X3
+	MULSD ALPHA, X4
+	MULSD ALPHA_2, X5
+
+	ADDSD (Y_PTR), X2            // X_i += y[i]
+	ADDSD (Y_PTR)(INC_Y*1), X3
+	ADDSD (Y_PTR)(INC_Y*2), X4
+	ADDSD (Y_PTR)(INCx3_Y*1), X5
+
+	MOVSD X2, (DST_PTR)              // y[i] = X_i
+	MOVSD X3, (DST_PTR)(INC_DST*1)
+	MOVSD X4, (DST_PTR)(INC_DST*2)
+	MOVSD X5, (DST_PTR)(INCx3_DST*1)
+
+	LEAQ (X_PTR)(INC_X*4), X_PTR       // X_PTR = &(X_PTR[incX*4])
+	LEAQ (Y_PTR)(INC_Y*4), Y_PTR       // Y_PTR = &(Y_PTR[incY*4])
+	LEAQ (DST_PTR)(INC_DST*4), DST_PTR // DST_PTR = &(DST_PTR[incDst*4]
+	DECQ LEN
+	JNZ  loop                          // } while --LEN > 0
+	CMPQ TAIL, $0                      // if TAIL == 0 { return }
+	JE   end
+
+tail_start: // Reset Loop registers
+	MOVQ TAIL, LEN // Loop counter: LEN = TAIL
+	SHRQ $1, LEN   // LEN = floor( LEN / 2 )
+	JZ   tail_one
+
+tail_two:
+	MOVSD (X_PTR), X2              // X_i = x[i]
+	MOVSD (X_PTR)(INC_X*1), X3
+	MULSD ALPHA, X2                // X_i *= a
+	MULSD ALPHA, X3
+	ADDSD (Y_PTR), X2              // X_i += y[i]
+	ADDSD (Y_PTR)(INC_Y*1), X3
+	MOVSD X2, (DST_PTR)            // y[i] = X_i
+	MOVSD X3, (DST_PTR)(INC_DST*1)
+
+	LEAQ (X_PTR)(INC_X*2), X_PTR       // X_PTR = &(X_PTR[incX*2])
+	LEAQ (Y_PTR)(INC_Y*2), Y_PTR       // Y_PTR = &(Y_PTR[incY*2])
+	LEAQ (DST_PTR)(INC_DST*2), DST_PTR // DST_PTR = &(DST_PTR[incY*2]
+
+	ANDQ $1, TAIL
+	JZ   end      // if TAIL == 0 { goto end }
+
+tail_one:
+	MOVSD (X_PTR), X2   // X2 = x[i]
+	MULSD ALPHA, X2     // X2 *= a
+	ADDSD (Y_PTR), X2   // X2 += y[i]
+	MOVSD X2, (DST_PTR) // y[i] = X2
+
+end:
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/axpyunitary_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/f64/axpyunitary_amd64.s
new file mode 100644
index 00000000..668f091e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/axpyunitary_amd64.s
@@ -0,0 +1,134 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Some of the loop unrolling code is copied from:
+// http://golang.org/src/math/big/arith_amd64.s
+// which is distributed under these terms:
+//
+// Copyright (c) 2012 The Go Authors. All rights reserved.
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+//    * Redistributions of source code must retain the above copyright
+// notice, this list of conditions and the following disclaimer.
+//    * Redistributions in binary form must reproduce the above
+// copyright notice, this list of conditions and the following disclaimer
+// in the documentation and/or other materials provided with the
+// distribution.
+//    * Neither the name of Google Inc. nor the names of its
+// contributors may be used to endorse or promote products derived from
+// this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+//+build !noasm,!appengine
+
+#include "textflag.h"
+
+#define X_PTR SI
+#define Y_PTR DI
+#define DST_PTR DI
+#define IDX AX
+#define LEN CX
+#define TAIL BX
+#define ALPHA X0
+#define ALPHA_2 X1
+
+// func AxpyUnitary(alpha float64, x, y []float64)
+TEXT ·AxpyUnitary(SB), NOSPLIT, $0
+	MOVQ    x_base+8(FP), X_PTR  // X_PTR := &x
+	MOVQ    y_base+32(FP), Y_PTR // Y_PTR := &y
+	MOVQ    x_len+16(FP), LEN    // LEN = min( len(x), len(y) )
+	CMPQ    y_len+40(FP), LEN
+	CMOVQLE y_len+40(FP), LEN
+	CMPQ    LEN, $0              // if LEN == 0 { return }
+	JE      end
+	XORQ    IDX, IDX
+	MOVSD   alpha+0(FP), ALPHA   // ALPHA := { alpha, alpha }
+	SHUFPD  $0, ALPHA, ALPHA
+	MOVUPS  ALPHA, ALPHA_2       // ALPHA_2 := ALPHA   for pipelining
+	MOVQ    Y_PTR, TAIL          // Check memory alignment
+	ANDQ    $15, TAIL            // TAIL = &y % 16
+	JZ      no_trim              // if TAIL == 0 { goto no_trim }
+
+	// Align on 16-byte boundary
+	MOVSD (X_PTR), X2   // X2 := x[0]
+	MULSD ALPHA, X2     // X2 *= a
+	ADDSD (Y_PTR), X2   // X2 += y[0]
+	MOVSD X2, (DST_PTR) // y[0] = X2
+	INCQ  IDX           // i++
+	DECQ  LEN           // LEN--
+	JZ    end           // if LEN == 0 { return }
+
+no_trim:
+	MOVQ LEN, TAIL
+	ANDQ $7, TAIL   // TAIL := n % 8
+	SHRQ $3, LEN    // LEN = floor( n / 8 )
+	JZ   tail_start // if LEN == 0 { goto tail2_start }
+
+loop:  // do {
+	// y[i] += alpha * x[i] unrolled 8x.
+	MOVUPS (X_PTR)(IDX*8), X2   // X_i = x[i]
+	MOVUPS 16(X_PTR)(IDX*8), X3
+	MOVUPS 32(X_PTR)(IDX*8), X4
+	MOVUPS 48(X_PTR)(IDX*8), X5
+
+	MULPD ALPHA, X2   // X_i *= a
+	MULPD ALPHA_2, X3
+	MULPD ALPHA, X4
+	MULPD ALPHA_2, X5
+
+	ADDPD (Y_PTR)(IDX*8), X2   // X_i += y[i]
+	ADDPD 16(Y_PTR)(IDX*8), X3
+	ADDPD 32(Y_PTR)(IDX*8), X4
+	ADDPD 48(Y_PTR)(IDX*8), X5
+
+	MOVUPS X2, (DST_PTR)(IDX*8)   // y[i] = X_i
+	MOVUPS X3, 16(DST_PTR)(IDX*8)
+	MOVUPS X4, 32(DST_PTR)(IDX*8)
+	MOVUPS X5, 48(DST_PTR)(IDX*8)
+
+	ADDQ $8, IDX  // i += 8
+	DECQ LEN
+	JNZ  loop     // } while --LEN > 0
+	CMPQ TAIL, $0 // if TAIL == 0 { return }
+	JE   end
+
+tail_start: // Reset loop registers
+	MOVQ TAIL, LEN // Loop counter: LEN = TAIL
+	SHRQ $1, LEN   // LEN = floor( TAIL / 2 )
+	JZ   tail_one  // if TAIL == 0 { goto tail }
+
+tail_two: // do {
+	MOVUPS (X_PTR)(IDX*8), X2   // X2 = x[i]
+	MULPD  ALPHA, X2            // X2 *= a
+	ADDPD  (Y_PTR)(IDX*8), X2   // X2 += y[i]
+	MOVUPS X2, (DST_PTR)(IDX*8) // y[i] = X2
+	ADDQ   $2, IDX              // i += 2
+	DECQ   LEN
+	JNZ    tail_two             // } while --LEN > 0
+
+	ANDQ $1, TAIL
+	JZ   end      // if TAIL == 0 { goto end }
+
+tail_one:
+	MOVSD (X_PTR)(IDX*8), X2   // X2 = x[i]
+	MULSD ALPHA, X2            // X2 *= a
+	ADDSD (Y_PTR)(IDX*8), X2   // X2 += y[i]
+	MOVSD X2, (DST_PTR)(IDX*8) // y[i] = X2
+
+end:
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/axpyunitaryto_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/f64/axpyunitaryto_amd64.s
new file mode 100644
index 00000000..03132e9d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/axpyunitaryto_amd64.s
@@ -0,0 +1,140 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Some of the loop unrolling code is copied from:
+// http://golang.org/src/math/big/arith_amd64.s
+// which is distributed under these terms:
+//
+// Copyright (c) 2012 The Go Authors. All rights reserved.
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+//    * Redistributions of source code must retain the above copyright
+// notice, this list of conditions and the following disclaimer.
+//    * Redistributions in binary form must reproduce the above
+// copyright notice, this list of conditions and the following disclaimer
+// in the documentation and/or other materials provided with the
+// distribution.
+//    * Neither the name of Google Inc. nor the names of its
+// contributors may be used to endorse or promote products derived from
+// this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+//+build !noasm,!appengine
+
+#include "textflag.h"
+
+#define X_PTR SI
+#define Y_PTR DX
+#define DST_PTR DI
+#define IDX AX
+#define LEN CX
+#define TAIL BX
+#define ALPHA X0
+#define ALPHA_2 X1
+
+// func AxpyUnitaryTo(dst []float64, alpha float64, x, y []float64)
+TEXT ·AxpyUnitaryTo(SB), NOSPLIT, $0
+	MOVQ    dst_base+0(FP), DST_PTR // DST_PTR := &dst
+	MOVQ    x_base+32(FP), X_PTR    // X_PTR := &x
+	MOVQ    y_base+56(FP), Y_PTR    // Y_PTR := &y
+	MOVQ    x_len+40(FP), LEN       // LEN = min( len(x), len(y), len(dst) )
+	CMPQ    y_len+64(FP), LEN
+	CMOVQLE y_len+64(FP), LEN
+	CMPQ    dst_len+8(FP), LEN
+	CMOVQLE dst_len+8(FP), LEN
+
+	CMPQ LEN, $0
+	JE   end     // if LEN == 0 { return }
+
+	XORQ   IDX, IDX            // IDX = 0
+	MOVSD  alpha+24(FP), ALPHA
+	SHUFPD $0, ALPHA, ALPHA    // ALPHA := { alpha, alpha }
+	MOVQ   Y_PTR, TAIL         // Check memory alignment
+	ANDQ   $15, TAIL           // TAIL = &y % 16
+	JZ     no_trim             // if TAIL == 0 { goto no_trim }
+
+	// Align on 16-byte boundary
+	MOVSD (X_PTR), X2   // X2 := x[0]
+	MULSD ALPHA, X2     // X2 *= a
+	ADDSD (Y_PTR), X2   // X2 += y[0]
+	MOVSD X2, (DST_PTR) // y[0] = X2
+	INCQ  IDX           // i++
+	DECQ  LEN           // LEN--
+	JZ    end           // if LEN == 0 { return }
+
+no_trim:
+	MOVQ LEN, TAIL
+	ANDQ $7, TAIL   // TAIL := n % 8
+	SHRQ $3, LEN    // LEN = floor( n / 8 )
+	JZ   tail_start // if LEN == 0 { goto tail_start }
+
+	MOVUPS ALPHA, ALPHA_2 // ALPHA_2 := ALPHA  for pipelining
+
+loop:  // do {
+	// y[i] += alpha * x[i] unrolled 8x.
+	MOVUPS (X_PTR)(IDX*8), X2   // X_i = x[i]
+	MOVUPS 16(X_PTR)(IDX*8), X3
+	MOVUPS 32(X_PTR)(IDX*8), X4
+	MOVUPS 48(X_PTR)(IDX*8), X5
+
+	MULPD ALPHA, X2   // X_i *= alpha
+	MULPD ALPHA_2, X3
+	MULPD ALPHA, X4
+	MULPD ALPHA_2, X5
+
+	ADDPD (Y_PTR)(IDX*8), X2   // X_i += y[i]
+	ADDPD 16(Y_PTR)(IDX*8), X3
+	ADDPD 32(Y_PTR)(IDX*8), X4
+	ADDPD 48(Y_PTR)(IDX*8), X5
+
+	MOVUPS X2, (DST_PTR)(IDX*8)   // y[i] = X_i
+	MOVUPS X3, 16(DST_PTR)(IDX*8)
+	MOVUPS X4, 32(DST_PTR)(IDX*8)
+	MOVUPS X5, 48(DST_PTR)(IDX*8)
+
+	ADDQ $8, IDX  // i += 8
+	DECQ LEN
+	JNZ  loop     // } while --LEN > 0
+	CMPQ TAIL, $0 // if TAIL == 0 { return }
+	JE   end
+
+tail_start: // Reset loop registers
+	MOVQ TAIL, LEN // Loop counter: LEN = TAIL
+	SHRQ $1, LEN   // LEN = floor( TAIL / 2 )
+	JZ   tail_one  // if LEN == 0 { goto tail }
+
+tail_two: // do {
+	MOVUPS (X_PTR)(IDX*8), X2   // X2 = x[i]
+	MULPD  ALPHA, X2            // X2 *= alpha
+	ADDPD  (Y_PTR)(IDX*8), X2   // X2 += y[i]
+	MOVUPS X2, (DST_PTR)(IDX*8) // y[i] = X2
+	ADDQ   $2, IDX              // i += 2
+	DECQ   LEN
+	JNZ    tail_two             // } while --LEN > 0
+
+	ANDQ $1, TAIL
+	JZ   end      // if TAIL == 0 { goto end }
+
+tail_one:
+	MOVSD (X_PTR)(IDX*8), X2   // X2 = x[i]
+	MULSD ALPHA, X2            // X2 *= a
+	ADDSD (Y_PTR)(IDX*8), X2   // X2 += y[i]
+	MOVSD X2, (DST_PTR)(IDX*8) // y[i] = X2
+
+end:
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/benchAxpy_test.go b/vendor/gonum.org/v1/gonum/internal/asm/f64/benchAxpy_test.go
new file mode 100644
index 00000000..7bd3dca7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/benchAxpy_test.go
@@ -0,0 +1,167 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build go1.7
+
+package f64
+
+import (
+	"fmt"
+	"testing"
+)
+
+const (
+	testLen = 1e5
+)
+
+var (
+	a = 2.0
+	x = make([]float64, testLen)
+	y = make([]float64, testLen)
+	z = make([]float64, testLen)
+)
+
+func init() {
+	for n := range x {
+		x[n] = float64(n)
+		y[n] = float64(n)
+	}
+}
+
+func BenchmarkAxpyUnitary(t *testing.B) {
+	naiveaxpyu := func(a float64, x, y []float64) {
+		for i, v := range x {
+			y[i] += a * v
+		}
+	}
+	tests := []struct {
+		name string
+		f    func(a float64, x, y []float64)
+	}{
+		{"AxpyUnitary", AxpyUnitary},
+		{"NaiveAxpyUnitary", naiveaxpyu},
+	}
+	for _, test := range tests {
+		for _, ln := range []uintptr{1, 3, 10, 30, 1e2, 3e2, 1e3, 3e3, 1e4, 3e4, 1e5} {
+			t.Run(fmt.Sprintf("%s-%d", test.name, ln), func(b *testing.B) {
+				b.SetBytes(int64(64 * ln))
+				x, y := x[:ln], y[:ln]
+				b.ResetTimer()
+				for i := 0; i < b.N; i++ {
+					test.f(a, x, y)
+				}
+			})
+		}
+	}
+}
+
+func BenchmarkAxpyUnitaryTo(t *testing.B) {
+	naiveaxpyut := func(d []float64, a float64, x, y []float64) {
+		for i, v := range x {
+			d[i] = y[i] + a*v
+		}
+	}
+	tests := []struct {
+		name string
+		f    func(z []float64, a float64, x, y []float64)
+	}{
+		{"AxpyUnitaryTo", AxpyUnitaryTo},
+		{"NaiveAxpyUnitaryTo", naiveaxpyut},
+	}
+	for _, test := range tests {
+		for _, ln := range []uintptr{1, 3, 10, 30, 1e2, 3e2, 1e3, 3e3, 1e4, 3e4, 1e5} {
+			t.Run(fmt.Sprintf("%s-%d", test.name, ln), func(b *testing.B) {
+				b.SetBytes(int64(64 * ln))
+				x, y, z := x[:ln], y[:ln], z[:ln]
+				b.ResetTimer()
+				for i := 0; i < b.N; i++ {
+					test.f(z, a, x, y)
+				}
+			})
+		}
+	}
+}
+
+var incsAxpy = []struct {
+	len uintptr
+	inc []int
+}{
+	{1, []int{1}},
+	{2, []int{1, 2, 4, 10}},
+	{3, []int{1, 2, 4, 10}},
+	{4, []int{1, 2, 4, 10}},
+	{5, []int{1, 2, 4, 10}},
+	{10, []int{1, 2, 4, 10}},
+	{500, []int{1, 2, 4, 10}},
+	{1e3, []int{1, 2, 4, 10}},
+	{1e4, []int{1, 2, 4, 10, -1, -2, -4, -10}},
+}
+
+func BenchmarkAxpyInc(t *testing.B) {
+	naiveaxpyinc := func(alpha float64, x, y []float64, n, incX, incY, ix, iy uintptr) {
+		for i := 0; i < int(n); i++ {
+			y[iy] += alpha * x[ix]
+			ix += incX
+			iy += incY
+		}
+	}
+	tests := []struct {
+		name string
+		f    func(alpha float64, x, y []float64, n, incX, incY, ix, iy uintptr)
+	}{
+		{"AxpyInc", AxpyInc},
+		{"NaiveAxpyInc", naiveaxpyinc},
+	}
+	for _, test := range tests {
+		for _, tt := range incsAxpy {
+			for _, inc := range tt.inc {
+				t.Run(fmt.Sprintf("%s-%d-inc(%d)", test.name, tt.len, inc), func(b *testing.B) {
+					b.SetBytes(int64(64 * tt.len))
+					var idx, tstInc uintptr = 0, uintptr(inc)
+					if inc < 0 {
+						idx = uintptr((-int(tt.len) + 1) * inc)
+					}
+					for i := 0; i < b.N; i++ {
+						test.f(a, x, y, uintptr(tt.len), tstInc, tstInc, idx, idx)
+					}
+				})
+			}
+		}
+	}
+}
+
+func BenchmarkAxpyIncTo(t *testing.B) {
+	naiveaxpyincto := func(dst []float64, incDst, idst uintptr, alpha float64, x, y []float64, n, incX, incY, ix, iy uintptr) {
+		for i := 0; i < int(n); i++ {
+			dst[idst] = alpha*x[ix] + y[iy]
+			ix += incX
+			iy += incY
+			idst += incDst
+		}
+	}
+	tests := []struct {
+		name string
+		f    func(dst []float64, incDst, idst uintptr, alpha float64, x, y []float64, n, incX, incY, ix, iy uintptr)
+	}{
+		{"AxpyIncTo", AxpyIncTo},
+		{"NaiveAxpyIncTo", naiveaxpyincto},
+	}
+	for _, test := range tests {
+		for _, tt := range incsAxpy {
+			for _, inc := range tt.inc {
+				t.Run(fmt.Sprintf("%s-%d-inc(%d)", test.name, tt.len, inc), func(b *testing.B) {
+					b.SetBytes(int64(64 * tt.len))
+					var idx, tstInc uintptr = 0, uintptr(inc)
+					if inc < 0 {
+						idx = uintptr((-int(tt.len) + 1) * inc)
+					}
+					for i := 0; i < b.N; i++ {
+						test.f(z, tstInc, idx, a, x, y, uintptr(tt.len),
+							tstInc, tstInc, idx, idx)
+					}
+				})
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/benchScal_test.go b/vendor/gonum.org/v1/gonum/internal/asm/f64/benchScal_test.go
new file mode 100644
index 00000000..b4fb19ad
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/benchScal_test.go
@@ -0,0 +1,87 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build go1.7
+
+package f64
+
+import (
+	"fmt"
+	"testing"
+)
+
+var uniScal = []int64{1, 3, 10, 30, 1e2, 3e2, 1e3, 3e3, 1e4, 3e4}
+
+func BenchmarkScalUnitary(t *testing.B) {
+	tstName := "ScalUnitary"
+	for _, ln := range uniScal {
+		t.Run(fmt.Sprintf("%s-%d", tstName, ln), func(b *testing.B) {
+			b.SetBytes(64 * ln)
+			x := x[:ln]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				ScalUnitary(a, x)
+			}
+		})
+	}
+}
+
+func BenchmarkScalUnitaryTo(t *testing.B) {
+	tstName := "ScalUnitaryTo"
+	for _, ln := range uniScal {
+		t.Run(fmt.Sprintf("%s-%d", tstName, ln), func(b *testing.B) {
+			b.SetBytes(int64(64 * ln))
+			x, y := x[:ln], y[:ln]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				ScalUnitaryTo(y, a, x)
+			}
+		})
+	}
+}
+
+var incScal = []struct {
+	len uintptr
+	inc []int
+}{
+	{1, []int{1}},
+	{3, []int{1, 2, 4, 10}},
+	{10, []int{1, 2, 4, 10}},
+	{30, []int{1, 2, 4, 10}},
+	{1e2, []int{1, 2, 4, 10}},
+	{3e2, []int{1, 2, 4, 10}},
+	{1e3, []int{1, 2, 4, 10}},
+	{3e3, []int{1, 2, 4, 10}},
+	{1e4, []int{1, 2, 4, 10}},
+}
+
+func BenchmarkScalInc(t *testing.B) {
+	tstName := "ScalInc"
+	for _, tt := range incScal {
+		for _, inc := range tt.inc {
+			t.Run(fmt.Sprintf("%s-%d-inc(%d)", tstName, tt.len, inc), func(b *testing.B) {
+				b.SetBytes(int64(64 * tt.len))
+				tstInc := uintptr(inc)
+				for i := 0; i < b.N; i++ {
+					ScalInc(a, x, uintptr(tt.len), tstInc)
+				}
+			})
+		}
+	}
+}
+
+func BenchmarkScalIncTo(t *testing.B) {
+	tstName := "ScalIncTo"
+	for _, tt := range incScal {
+		for _, inc := range tt.inc {
+			t.Run(fmt.Sprintf("%s-%d-inc(%d)", tstName, tt.len, inc), func(b *testing.B) {
+				b.SetBytes(int64(64 * tt.len))
+				tstInc := uintptr(inc)
+				for i := 0; i < b.N; i++ {
+					ScalIncTo(z, tstInc, a, x, uintptr(tt.len), tstInc)
+				}
+			})
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/bench_other_test.go b/vendor/gonum.org/v1/gonum/internal/asm/f64/bench_other_test.go
new file mode 100644
index 00000000..851252ba
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/bench_other_test.go
@@ -0,0 +1,443 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package f64
+
+import (
+	"math"
+	"testing"
+)
+
+func benchL1Norm(f func(x []float64) float64, sz int, t *testing.B) {
+	dst := y[:sz]
+	for i := 0; i < t.N; i++ {
+		f(dst)
+	}
+}
+
+var naiveL1Norm = func(x []float64) (sum float64) {
+	for _, v := range x {
+		sum += math.Abs(v)
+	}
+	return sum
+}
+
+func BenchmarkL1Norm1(t *testing.B)      { benchL1Norm(L1Norm, 1, t) }
+func BenchmarkL1Norm2(t *testing.B)      { benchL1Norm(L1Norm, 2, t) }
+func BenchmarkL1Norm3(t *testing.B)      { benchL1Norm(L1Norm, 3, t) }
+func BenchmarkL1Norm4(t *testing.B)      { benchL1Norm(L1Norm, 4, t) }
+func BenchmarkL1Norm5(t *testing.B)      { benchL1Norm(L1Norm, 5, t) }
+func BenchmarkL1Norm10(t *testing.B)     { benchL1Norm(L1Norm, 10, t) }
+func BenchmarkL1Norm100(t *testing.B)    { benchL1Norm(L1Norm, 100, t) }
+func BenchmarkL1Norm1000(t *testing.B)   { benchL1Norm(L1Norm, 1000, t) }
+func BenchmarkL1Norm10000(t *testing.B)  { benchL1Norm(L1Norm, 10000, t) }
+func BenchmarkL1Norm100000(t *testing.B) { benchL1Norm(L1Norm, 100000, t) }
+func BenchmarkL1Norm500000(t *testing.B) { benchL1Norm(L1Norm, 500000, t) }
+
+func BenchmarkLL1Norm1(t *testing.B)      { benchL1Norm(naiveL1Norm, 1, t) }
+func BenchmarkLL1Norm2(t *testing.B)      { benchL1Norm(naiveL1Norm, 2, t) }
+func BenchmarkLL1Norm3(t *testing.B)      { benchL1Norm(naiveL1Norm, 3, t) }
+func BenchmarkLL1Norm4(t *testing.B)      { benchL1Norm(naiveL1Norm, 4, t) }
+func BenchmarkLL1Norm5(t *testing.B)      { benchL1Norm(naiveL1Norm, 5, t) }
+func BenchmarkLL1Norm10(t *testing.B)     { benchL1Norm(naiveL1Norm, 10, t) }
+func BenchmarkLL1Norm100(t *testing.B)    { benchL1Norm(naiveL1Norm, 100, t) }
+func BenchmarkLL1Norm1000(t *testing.B)   { benchL1Norm(naiveL1Norm, 1000, t) }
+func BenchmarkLL1Norm10000(t *testing.B)  { benchL1Norm(naiveL1Norm, 10000, t) }
+func BenchmarkLL1Norm100000(t *testing.B) { benchL1Norm(naiveL1Norm, 100000, t) }
+func BenchmarkLL1Norm500000(t *testing.B) { benchL1Norm(naiveL1Norm, 500000, t) }
+
+func benchL1NormInc(t *testing.B, ln, inc int, f func(x []float64, n, incX int) float64) {
+	for i := 0; i < t.N; i++ {
+		f(x, ln, inc)
+	}
+}
+
+var naiveL1NormInc = func(x []float64, n, incX int) (sum float64) {
+	for i := 0; i < n*incX; i += incX {
+		sum += math.Abs(x[i])
+	}
+	return sum
+}
+
+func BenchmarkF64L1NormIncN1Inc1(b *testing.B) { benchL1NormInc(b, 1, 1, L1NormInc) }
+
+func BenchmarkF64L1NormIncN2Inc1(b *testing.B)  { benchL1NormInc(b, 2, 1, L1NormInc) }
+func BenchmarkF64L1NormIncN2Inc2(b *testing.B)  { benchL1NormInc(b, 2, 2, L1NormInc) }
+func BenchmarkF64L1NormIncN2Inc4(b *testing.B)  { benchL1NormInc(b, 2, 4, L1NormInc) }
+func BenchmarkF64L1NormIncN2Inc10(b *testing.B) { benchL1NormInc(b, 2, 10, L1NormInc) }
+
+func BenchmarkF64L1NormIncN3Inc1(b *testing.B)  { benchL1NormInc(b, 3, 1, L1NormInc) }
+func BenchmarkF64L1NormIncN3Inc2(b *testing.B)  { benchL1NormInc(b, 3, 2, L1NormInc) }
+func BenchmarkF64L1NormIncN3Inc4(b *testing.B)  { benchL1NormInc(b, 3, 4, L1NormInc) }
+func BenchmarkF64L1NormIncN3Inc10(b *testing.B) { benchL1NormInc(b, 3, 10, L1NormInc) }
+
+func BenchmarkF64L1NormIncN4Inc1(b *testing.B)  { benchL1NormInc(b, 4, 1, L1NormInc) }
+func BenchmarkF64L1NormIncN4Inc2(b *testing.B)  { benchL1NormInc(b, 4, 2, L1NormInc) }
+func BenchmarkF64L1NormIncN4Inc4(b *testing.B)  { benchL1NormInc(b, 4, 4, L1NormInc) }
+func BenchmarkF64L1NormIncN4Inc10(b *testing.B) { benchL1NormInc(b, 4, 10, L1NormInc) }
+
+func BenchmarkF64L1NormIncN10Inc1(b *testing.B)  { benchL1NormInc(b, 10, 1, L1NormInc) }
+func BenchmarkF64L1NormIncN10Inc2(b *testing.B)  { benchL1NormInc(b, 10, 2, L1NormInc) }
+func BenchmarkF64L1NormIncN10Inc4(b *testing.B)  { benchL1NormInc(b, 10, 4, L1NormInc) }
+func BenchmarkF64L1NormIncN10Inc10(b *testing.B) { benchL1NormInc(b, 10, 10, L1NormInc) }
+
+func BenchmarkF64L1NormIncN1000Inc1(b *testing.B)  { benchL1NormInc(b, 1000, 1, L1NormInc) }
+func BenchmarkF64L1NormIncN1000Inc2(b *testing.B)  { benchL1NormInc(b, 1000, 2, L1NormInc) }
+func BenchmarkF64L1NormIncN1000Inc4(b *testing.B)  { benchL1NormInc(b, 1000, 4, L1NormInc) }
+func BenchmarkF64L1NormIncN1000Inc10(b *testing.B) { benchL1NormInc(b, 1000, 10, L1NormInc) }
+
+func BenchmarkF64L1NormIncN100000Inc1(b *testing.B)  { benchL1NormInc(b, 100000, 1, L1NormInc) }
+func BenchmarkF64L1NormIncN100000Inc2(b *testing.B)  { benchL1NormInc(b, 100000, 2, L1NormInc) }
+func BenchmarkF64L1NormIncN100000Inc4(b *testing.B)  { benchL1NormInc(b, 100000, 4, L1NormInc) }
+func BenchmarkF64L1NormIncN100000Inc10(b *testing.B) { benchL1NormInc(b, 100000, 10, L1NormInc) }
+
+func BenchmarkLF64L1NormIncN1Inc1(b *testing.B) { benchL1NormInc(b, 1, 1, naiveL1NormInc) }
+
+func BenchmarkLF64L1NormIncN2Inc1(b *testing.B)  { benchL1NormInc(b, 2, 1, naiveL1NormInc) }
+func BenchmarkLF64L1NormIncN2Inc2(b *testing.B)  { benchL1NormInc(b, 2, 2, naiveL1NormInc) }
+func BenchmarkLF64L1NormIncN2Inc4(b *testing.B)  { benchL1NormInc(b, 2, 4, naiveL1NormInc) }
+func BenchmarkLF64L1NormIncN2Inc10(b *testing.B) { benchL1NormInc(b, 2, 10, naiveL1NormInc) }
+
+func BenchmarkLF64L1NormIncN3Inc1(b *testing.B)  { benchL1NormInc(b, 3, 1, naiveL1NormInc) }
+func BenchmarkLF64L1NormIncN3Inc2(b *testing.B)  { benchL1NormInc(b, 3, 2, naiveL1NormInc) }
+func BenchmarkLF64L1NormIncN3Inc4(b *testing.B)  { benchL1NormInc(b, 3, 4, naiveL1NormInc) }
+func BenchmarkLF64L1NormIncN3Inc10(b *testing.B) { benchL1NormInc(b, 3, 10, naiveL1NormInc) }
+
+func BenchmarkLF64L1NormIncN4Inc1(b *testing.B)  { benchL1NormInc(b, 4, 1, naiveL1NormInc) }
+func BenchmarkLF64L1NormIncN4Inc2(b *testing.B)  { benchL1NormInc(b, 4, 2, naiveL1NormInc) }
+func BenchmarkLF64L1NormIncN4Inc4(b *testing.B)  { benchL1NormInc(b, 4, 4, naiveL1NormInc) }
+func BenchmarkLF64L1NormIncN4Inc10(b *testing.B) { benchL1NormInc(b, 4, 10, naiveL1NormInc) }
+
+func BenchmarkLF64L1NormIncN10Inc1(b *testing.B)  { benchL1NormInc(b, 10, 1, naiveL1NormInc) }
+func BenchmarkLF64L1NormIncN10Inc2(b *testing.B)  { benchL1NormInc(b, 10, 2, naiveL1NormInc) }
+func BenchmarkLF64L1NormIncN10Inc4(b *testing.B)  { benchL1NormInc(b, 10, 4, naiveL1NormInc) }
+func BenchmarkLF64L1NormIncN10Inc10(b *testing.B) { benchL1NormInc(b, 10, 10, naiveL1NormInc) }
+
+func BenchmarkLF64L1NormIncN1000Inc1(b *testing.B)  { benchL1NormInc(b, 1000, 1, naiveL1NormInc) }
+func BenchmarkLF64L1NormIncN1000Inc2(b *testing.B)  { benchL1NormInc(b, 1000, 2, naiveL1NormInc) }
+func BenchmarkLF64L1NormIncN1000Inc4(b *testing.B)  { benchL1NormInc(b, 1000, 4, naiveL1NormInc) }
+func BenchmarkLF64L1NormIncN1000Inc10(b *testing.B) { benchL1NormInc(b, 1000, 10, naiveL1NormInc) }
+
+func BenchmarkLF64L1NormIncN100000Inc1(b *testing.B)  { benchL1NormInc(b, 100000, 1, naiveL1NormInc) }
+func BenchmarkLF64L1NormIncN100000Inc2(b *testing.B)  { benchL1NormInc(b, 100000, 2, naiveL1NormInc) }
+func BenchmarkLF64L1NormIncN100000Inc4(b *testing.B)  { benchL1NormInc(b, 100000, 4, naiveL1NormInc) }
+func BenchmarkLF64L1NormIncN100000Inc10(b *testing.B) { benchL1NormInc(b, 100000, 10, naiveL1NormInc) }
+
+func benchAdd(f func(dst, s []float64), sz int, t *testing.B) {
+	dst, s := y[:sz], x[:sz]
+	for i := 0; i < t.N; i++ {
+		f(dst, s)
+	}
+}
+
+var naiveAdd = func(dst, s []float64) {
+	for i, v := range s {
+		dst[i] += v
+	}
+}
+
+func BenchmarkAdd1(t *testing.B)      { benchAdd(Add, 1, t) }
+func BenchmarkAdd2(t *testing.B)      { benchAdd(Add, 2, t) }
+func BenchmarkAdd3(t *testing.B)      { benchAdd(Add, 3, t) }
+func BenchmarkAdd4(t *testing.B)      { benchAdd(Add, 4, t) }
+func BenchmarkAdd5(t *testing.B)      { benchAdd(Add, 5, t) }
+func BenchmarkAdd10(t *testing.B)     { benchAdd(Add, 10, t) }
+func BenchmarkAdd100(t *testing.B)    { benchAdd(Add, 100, t) }
+func BenchmarkAdd1000(t *testing.B)   { benchAdd(Add, 1000, t) }
+func BenchmarkAdd10000(t *testing.B)  { benchAdd(Add, 10000, t) }
+func BenchmarkAdd100000(t *testing.B) { benchAdd(Add, 100000, t) }
+func BenchmarkAdd500000(t *testing.B) { benchAdd(Add, 500000, t) }
+
+func BenchmarkLAdd1(t *testing.B)      { benchAdd(naiveAdd, 1, t) }
+func BenchmarkLAdd2(t *testing.B)      { benchAdd(naiveAdd, 2, t) }
+func BenchmarkLAdd3(t *testing.B)      { benchAdd(naiveAdd, 3, t) }
+func BenchmarkLAdd4(t *testing.B)      { benchAdd(naiveAdd, 4, t) }
+func BenchmarkLAdd5(t *testing.B)      { benchAdd(naiveAdd, 5, t) }
+func BenchmarkLAdd10(t *testing.B)     { benchAdd(naiveAdd, 10, t) }
+func BenchmarkLAdd100(t *testing.B)    { benchAdd(naiveAdd, 100, t) }
+func BenchmarkLAdd1000(t *testing.B)   { benchAdd(naiveAdd, 1000, t) }
+func BenchmarkLAdd10000(t *testing.B)  { benchAdd(naiveAdd, 10000, t) }
+func BenchmarkLAdd100000(t *testing.B) { benchAdd(naiveAdd, 100000, t) }
+func BenchmarkLAdd500000(t *testing.B) { benchAdd(naiveAdd, 500000, t) }
+
+func benchAddConst(f func(a float64, x []float64), sz int, t *testing.B) {
+	a, x := 1., x[:sz]
+	for i := 0; i < t.N; i++ {
+		f(a, x)
+	}
+}
+
+var naiveAddConst = func(a float64, x []float64) {
+	for i := range x {
+		x[i] += a
+	}
+}
+
+func BenchmarkAddConst1(t *testing.B)      { benchAddConst(AddConst, 1, t) }
+func BenchmarkAddConst2(t *testing.B)      { benchAddConst(AddConst, 2, t) }
+func BenchmarkAddConst3(t *testing.B)      { benchAddConst(AddConst, 3, t) }
+func BenchmarkAddConst4(t *testing.B)      { benchAddConst(AddConst, 4, t) }
+func BenchmarkAddConst5(t *testing.B)      { benchAddConst(AddConst, 5, t) }
+func BenchmarkAddConst10(t *testing.B)     { benchAddConst(AddConst, 10, t) }
+func BenchmarkAddConst100(t *testing.B)    { benchAddConst(AddConst, 100, t) }
+func BenchmarkAddConst1000(t *testing.B)   { benchAddConst(AddConst, 1000, t) }
+func BenchmarkAddConst10000(t *testing.B)  { benchAddConst(AddConst, 10000, t) }
+func BenchmarkAddConst100000(t *testing.B) { benchAddConst(AddConst, 100000, t) }
+func BenchmarkAddConst500000(t *testing.B) { benchAddConst(AddConst, 500000, t) }
+
+func BenchmarkLAddConst1(t *testing.B)      { benchAddConst(naiveAddConst, 1, t) }
+func BenchmarkLAddConst2(t *testing.B)      { benchAddConst(naiveAddConst, 2, t) }
+func BenchmarkLAddConst3(t *testing.B)      { benchAddConst(naiveAddConst, 3, t) }
+func BenchmarkLAddConst4(t *testing.B)      { benchAddConst(naiveAddConst, 4, t) }
+func BenchmarkLAddConst5(t *testing.B)      { benchAddConst(naiveAddConst, 5, t) }
+func BenchmarkLAddConst10(t *testing.B)     { benchAddConst(naiveAddConst, 10, t) }
+func BenchmarkLAddConst100(t *testing.B)    { benchAddConst(naiveAddConst, 100, t) }
+func BenchmarkLAddConst1000(t *testing.B)   { benchAddConst(naiveAddConst, 1000, t) }
+func BenchmarkLAddConst10000(t *testing.B)  { benchAddConst(naiveAddConst, 10000, t) }
+func BenchmarkLAddConst100000(t *testing.B) { benchAddConst(naiveAddConst, 100000, t) }
+func BenchmarkLAddConst500000(t *testing.B) { benchAddConst(naiveAddConst, 500000, t) }
+
+func benchCumSum(f func(a, b []float64) []float64, sz int, t *testing.B) {
+	a, b := x[:sz], y[:sz]
+	for i := 0; i < t.N; i++ {
+		f(a, b)
+	}
+}
+
+var naiveCumSum = func(dst, s []float64) []float64 {
+	if len(s) == 0 {
+		return dst
+	}
+	dst[0] = s[0]
+	for i, v := range s[1:] {
+		dst[i+1] = dst[i] + v
+	}
+	return dst
+}
+
+func BenchmarkCumSum1(t *testing.B)      { benchCumSum(CumSum, 1, t) }
+func BenchmarkCumSum2(t *testing.B)      { benchCumSum(CumSum, 2, t) }
+func BenchmarkCumSum3(t *testing.B)      { benchCumSum(CumSum, 3, t) }
+func BenchmarkCumSum4(t *testing.B)      { benchCumSum(CumSum, 4, t) }
+func BenchmarkCumSum5(t *testing.B)      { benchCumSum(CumSum, 5, t) }
+func BenchmarkCumSum10(t *testing.B)     { benchCumSum(CumSum, 10, t) }
+func BenchmarkCumSum100(t *testing.B)    { benchCumSum(CumSum, 100, t) }
+func BenchmarkCumSum1000(t *testing.B)   { benchCumSum(CumSum, 1000, t) }
+func BenchmarkCumSum10000(t *testing.B)  { benchCumSum(CumSum, 10000, t) }
+func BenchmarkCumSum100000(t *testing.B) { benchCumSum(CumSum, 100000, t) }
+func BenchmarkCumSum500000(t *testing.B) { benchCumSum(CumSum, 500000, t) }
+
+func BenchmarkLCumSum1(t *testing.B)      { benchCumSum(naiveCumSum, 1, t) }
+func BenchmarkLCumSum2(t *testing.B)      { benchCumSum(naiveCumSum, 2, t) }
+func BenchmarkLCumSum3(t *testing.B)      { benchCumSum(naiveCumSum, 3, t) }
+func BenchmarkLCumSum4(t *testing.B)      { benchCumSum(naiveCumSum, 4, t) }
+func BenchmarkLCumSum5(t *testing.B)      { benchCumSum(naiveCumSum, 5, t) }
+func BenchmarkLCumSum10(t *testing.B)     { benchCumSum(naiveCumSum, 10, t) }
+func BenchmarkLCumSum100(t *testing.B)    { benchCumSum(naiveCumSum, 100, t) }
+func BenchmarkLCumSum1000(t *testing.B)   { benchCumSum(naiveCumSum, 1000, t) }
+func BenchmarkLCumSum10000(t *testing.B)  { benchCumSum(naiveCumSum, 10000, t) }
+func BenchmarkLCumSum100000(t *testing.B) { benchCumSum(naiveCumSum, 100000, t) }
+func BenchmarkLCumSum500000(t *testing.B) { benchCumSum(naiveCumSum, 500000, t) }
+
+func benchCumProd(f func(a, b []float64) []float64, sz int, t *testing.B) {
+	a, b := x[:sz], y[:sz]
+	for i := 0; i < t.N; i++ {
+		f(a, b)
+	}
+}
+
+var naiveCumProd = func(dst, s []float64) []float64 {
+	if len(s) == 0 {
+		return dst
+	}
+	dst[0] = s[0]
+	for i, v := range s[1:] {
+		dst[i+1] = dst[i] + v
+	}
+	return dst
+}
+
+func BenchmarkCumProd1(t *testing.B)      { benchCumProd(CumProd, 1, t) }
+func BenchmarkCumProd2(t *testing.B)      { benchCumProd(CumProd, 2, t) }
+func BenchmarkCumProd3(t *testing.B)      { benchCumProd(CumProd, 3, t) }
+func BenchmarkCumProd4(t *testing.B)      { benchCumProd(CumProd, 4, t) }
+func BenchmarkCumProd5(t *testing.B)      { benchCumProd(CumProd, 5, t) }
+func BenchmarkCumProd10(t *testing.B)     { benchCumProd(CumProd, 10, t) }
+func BenchmarkCumProd100(t *testing.B)    { benchCumProd(CumProd, 100, t) }
+func BenchmarkCumProd1000(t *testing.B)   { benchCumProd(CumProd, 1000, t) }
+func BenchmarkCumProd10000(t *testing.B)  { benchCumProd(CumProd, 10000, t) }
+func BenchmarkCumProd100000(t *testing.B) { benchCumProd(CumProd, 100000, t) }
+func BenchmarkCumProd500000(t *testing.B) { benchCumProd(CumProd, 500000, t) }
+
+func BenchmarkLCumProd1(t *testing.B)      { benchCumProd(naiveCumProd, 1, t) }
+func BenchmarkLCumProd2(t *testing.B)      { benchCumProd(naiveCumProd, 2, t) }
+func BenchmarkLCumProd3(t *testing.B)      { benchCumProd(naiveCumProd, 3, t) }
+func BenchmarkLCumProd4(t *testing.B)      { benchCumProd(naiveCumProd, 4, t) }
+func BenchmarkLCumProd5(t *testing.B)      { benchCumProd(naiveCumProd, 5, t) }
+func BenchmarkLCumProd10(t *testing.B)     { benchCumProd(naiveCumProd, 10, t) }
+func BenchmarkLCumProd100(t *testing.B)    { benchCumProd(naiveCumProd, 100, t) }
+func BenchmarkLCumProd1000(t *testing.B)   { benchCumProd(naiveCumProd, 1000, t) }
+func BenchmarkLCumProd10000(t *testing.B)  { benchCumProd(naiveCumProd, 10000, t) }
+func BenchmarkLCumProd100000(t *testing.B) { benchCumProd(naiveCumProd, 100000, t) }
+func BenchmarkLCumProd500000(t *testing.B) { benchCumProd(naiveCumProd, 500000, t) }
+
+func benchDiv(f func(a, b []float64), sz int, t *testing.B) {
+	a, b := x[:sz], y[:sz]
+	for i := 0; i < t.N; i++ {
+		f(a, b)
+	}
+}
+
+var naiveDiv = func(a, b []float64) {
+	for i, v := range b {
+		a[i] /= v
+	}
+}
+
+func BenchmarkDiv1(t *testing.B)      { benchDiv(Div, 1, t) }
+func BenchmarkDiv2(t *testing.B)      { benchDiv(Div, 2, t) }
+func BenchmarkDiv3(t *testing.B)      { benchDiv(Div, 3, t) }
+func BenchmarkDiv4(t *testing.B)      { benchDiv(Div, 4, t) }
+func BenchmarkDiv5(t *testing.B)      { benchDiv(Div, 5, t) }
+func BenchmarkDiv10(t *testing.B)     { benchDiv(Div, 10, t) }
+func BenchmarkDiv100(t *testing.B)    { benchDiv(Div, 100, t) }
+func BenchmarkDiv1000(t *testing.B)   { benchDiv(Div, 1000, t) }
+func BenchmarkDiv10000(t *testing.B)  { benchDiv(Div, 10000, t) }
+func BenchmarkDiv100000(t *testing.B) { benchDiv(Div, 100000, t) }
+func BenchmarkDiv500000(t *testing.B) { benchDiv(Div, 500000, t) }
+
+func BenchmarkLDiv1(t *testing.B)      { benchDiv(naiveDiv, 1, t) }
+func BenchmarkLDiv2(t *testing.B)      { benchDiv(naiveDiv, 2, t) }
+func BenchmarkLDiv3(t *testing.B)      { benchDiv(naiveDiv, 3, t) }
+func BenchmarkLDiv4(t *testing.B)      { benchDiv(naiveDiv, 4, t) }
+func BenchmarkLDiv5(t *testing.B)      { benchDiv(naiveDiv, 5, t) }
+func BenchmarkLDiv10(t *testing.B)     { benchDiv(naiveDiv, 10, t) }
+func BenchmarkLDiv100(t *testing.B)    { benchDiv(naiveDiv, 100, t) }
+func BenchmarkLDiv1000(t *testing.B)   { benchDiv(naiveDiv, 1000, t) }
+func BenchmarkLDiv10000(t *testing.B)  { benchDiv(naiveDiv, 10000, t) }
+func BenchmarkLDiv100000(t *testing.B) { benchDiv(naiveDiv, 100000, t) }
+func BenchmarkLDiv500000(t *testing.B) { benchDiv(naiveDiv, 500000, t) }
+
+func benchDivTo(f func(dst, a, b []float64) []float64, sz int, t *testing.B) {
+	dst, a, b := z[:sz], x[:sz], y[:sz]
+	for i := 0; i < t.N; i++ {
+		f(dst, a, b)
+	}
+}
+
+var naiveDivTo = func(dst, s, t []float64) []float64 {
+	for i, v := range s {
+		dst[i] = v / t[i]
+	}
+	return dst
+}
+
+func BenchmarkDivTo1(t *testing.B)      { benchDivTo(DivTo, 1, t) }
+func BenchmarkDivTo2(t *testing.B)      { benchDivTo(DivTo, 2, t) }
+func BenchmarkDivTo3(t *testing.B)      { benchDivTo(DivTo, 3, t) }
+func BenchmarkDivTo4(t *testing.B)      { benchDivTo(DivTo, 4, t) }
+func BenchmarkDivTo5(t *testing.B)      { benchDivTo(DivTo, 5, t) }
+func BenchmarkDivTo10(t *testing.B)     { benchDivTo(DivTo, 10, t) }
+func BenchmarkDivTo100(t *testing.B)    { benchDivTo(DivTo, 100, t) }
+func BenchmarkDivTo1000(t *testing.B)   { benchDivTo(DivTo, 1000, t) }
+func BenchmarkDivTo10000(t *testing.B)  { benchDivTo(DivTo, 10000, t) }
+func BenchmarkDivTo100000(t *testing.B) { benchDivTo(DivTo, 100000, t) }
+func BenchmarkDivTo500000(t *testing.B) { benchDivTo(DivTo, 500000, t) }
+
+func BenchmarkLDivTo1(t *testing.B)      { benchDivTo(naiveDivTo, 1, t) }
+func BenchmarkLDivTo2(t *testing.B)      { benchDivTo(naiveDivTo, 2, t) }
+func BenchmarkLDivTo3(t *testing.B)      { benchDivTo(naiveDivTo, 3, t) }
+func BenchmarkLDivTo4(t *testing.B)      { benchDivTo(naiveDivTo, 4, t) }
+func BenchmarkLDivTo5(t *testing.B)      { benchDivTo(naiveDivTo, 5, t) }
+func BenchmarkLDivTo10(t *testing.B)     { benchDivTo(naiveDivTo, 10, t) }
+func BenchmarkLDivTo100(t *testing.B)    { benchDivTo(naiveDivTo, 100, t) }
+func BenchmarkLDivTo1000(t *testing.B)   { benchDivTo(naiveDivTo, 1000, t) }
+func BenchmarkLDivTo10000(t *testing.B)  { benchDivTo(naiveDivTo, 10000, t) }
+func BenchmarkLDivTo100000(t *testing.B) { benchDivTo(naiveDivTo, 100000, t) }
+func BenchmarkLDivTo500000(t *testing.B) { benchDivTo(naiveDivTo, 500000, t) }
+
+func benchL1Dist(f func(a, b []float64) float64, sz int, t *testing.B) {
+	a, b := x[:sz], y[:sz]
+	for i := 0; i < t.N; i++ {
+		f(a, b)
+	}
+}
+
+var naiveL1Dist = func(s, t []float64) float64 {
+	var norm float64
+	for i, v := range s {
+		norm += math.Abs(t[i] - v)
+	}
+	return norm
+}
+
+func BenchmarkL1Dist1(t *testing.B)      { benchL1Dist(L1Dist, 1, t) }
+func BenchmarkL1Dist2(t *testing.B)      { benchL1Dist(L1Dist, 2, t) }
+func BenchmarkL1Dist3(t *testing.B)      { benchL1Dist(L1Dist, 3, t) }
+func BenchmarkL1Dist4(t *testing.B)      { benchL1Dist(L1Dist, 4, t) }
+func BenchmarkL1Dist5(t *testing.B)      { benchL1Dist(L1Dist, 5, t) }
+func BenchmarkL1Dist10(t *testing.B)     { benchL1Dist(L1Dist, 10, t) }
+func BenchmarkL1Dist100(t *testing.B)    { benchL1Dist(L1Dist, 100, t) }
+func BenchmarkL1Dist1000(t *testing.B)   { benchL1Dist(L1Dist, 1000, t) }
+func BenchmarkL1Dist10000(t *testing.B)  { benchL1Dist(L1Dist, 10000, t) }
+func BenchmarkL1Dist100000(t *testing.B) { benchL1Dist(L1Dist, 100000, t) }
+func BenchmarkL1Dist500000(t *testing.B) { benchL1Dist(L1Dist, 500000, t) }
+
+func BenchmarkLL1Dist1(t *testing.B)      { benchL1Dist(naiveL1Dist, 1, t) }
+func BenchmarkLL1Dist2(t *testing.B)      { benchL1Dist(naiveL1Dist, 2, t) }
+func BenchmarkLL1Dist3(t *testing.B)      { benchL1Dist(naiveL1Dist, 3, t) }
+func BenchmarkLL1Dist4(t *testing.B)      { benchL1Dist(naiveL1Dist, 4, t) }
+func BenchmarkLL1Dist5(t *testing.B)      { benchL1Dist(naiveL1Dist, 5, t) }
+func BenchmarkLL1Dist10(t *testing.B)     { benchL1Dist(naiveL1Dist, 10, t) }
+func BenchmarkLL1Dist100(t *testing.B)    { benchL1Dist(naiveL1Dist, 100, t) }
+func BenchmarkLL1Dist1000(t *testing.B)   { benchL1Dist(naiveL1Dist, 1000, t) }
+func BenchmarkLL1Dist10000(t *testing.B)  { benchL1Dist(naiveL1Dist, 10000, t) }
+func BenchmarkLL1Dist100000(t *testing.B) { benchL1Dist(naiveL1Dist, 100000, t) }
+func BenchmarkLL1Dist500000(t *testing.B) { benchL1Dist(naiveL1Dist, 500000, t) }
+
+func benchLinfDist(f func(a, b []float64) float64, sz int, t *testing.B) {
+	a, b := x[:sz], y[:sz]
+	for i := 0; i < t.N; i++ {
+		f(a, b)
+	}
+}
+
+var naiveLinfDist = func(s, t []float64) float64 {
+	var norm float64
+	if len(s) == 0 {
+		return 0
+	}
+	norm = math.Abs(t[0] - s[0])
+	for i, v := range s[1:] {
+		absDiff := math.Abs(t[i+1] - v)
+		if absDiff > norm || math.IsNaN(norm) {
+			norm = absDiff
+		}
+	}
+	return norm
+}
+
+func BenchmarkLinfDist1(t *testing.B)      { benchLinfDist(LinfDist, 1, t) }
+func BenchmarkLinfDist2(t *testing.B)      { benchLinfDist(LinfDist, 2, t) }
+func BenchmarkLinfDist3(t *testing.B)      { benchLinfDist(LinfDist, 3, t) }
+func BenchmarkLinfDist4(t *testing.B)      { benchLinfDist(LinfDist, 4, t) }
+func BenchmarkLinfDist5(t *testing.B)      { benchLinfDist(LinfDist, 5, t) }
+func BenchmarkLinfDist10(t *testing.B)     { benchLinfDist(LinfDist, 10, t) }
+func BenchmarkLinfDist100(t *testing.B)    { benchLinfDist(LinfDist, 100, t) }
+func BenchmarkLinfDist1000(t *testing.B)   { benchLinfDist(LinfDist, 1000, t) }
+func BenchmarkLinfDist10000(t *testing.B)  { benchLinfDist(LinfDist, 10000, t) }
+func BenchmarkLinfDist100000(t *testing.B) { benchLinfDist(LinfDist, 100000, t) }
+func BenchmarkLinfDist500000(t *testing.B) { benchLinfDist(LinfDist, 500000, t) }
+
+func BenchmarkLLinfDist1(t *testing.B)      { benchLinfDist(naiveLinfDist, 1, t) }
+func BenchmarkLLinfDist2(t *testing.B)      { benchLinfDist(naiveLinfDist, 2, t) }
+func BenchmarkLLinfDist3(t *testing.B)      { benchLinfDist(naiveLinfDist, 3, t) }
+func BenchmarkLLinfDist4(t *testing.B)      { benchLinfDist(naiveLinfDist, 4, t) }
+func BenchmarkLLinfDist5(t *testing.B)      { benchLinfDist(naiveLinfDist, 5, t) }
+func BenchmarkLLinfDist10(t *testing.B)     { benchLinfDist(naiveLinfDist, 10, t) }
+func BenchmarkLLinfDist100(t *testing.B)    { benchLinfDist(naiveLinfDist, 100, t) }
+func BenchmarkLLinfDist1000(t *testing.B)   { benchLinfDist(naiveLinfDist, 1000, t) }
+func BenchmarkLLinfDist10000(t *testing.B)  { benchLinfDist(naiveLinfDist, 10000, t) }
+func BenchmarkLLinfDist100000(t *testing.B) { benchLinfDist(naiveLinfDist, 100000, t) }
+func BenchmarkLLinfDist500000(t *testing.B) { benchLinfDist(naiveLinfDist, 500000, t) }
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/bench_test.go b/vendor/gonum.org/v1/gonum/internal/asm/f64/bench_test.go
new file mode 100644
index 00000000..78d26d77
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/bench_test.go
@@ -0,0 +1,438 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build !go1.7
+
+package f64
+
+import (
+	"math/rand"
+	"testing"
+)
+
+var (
+	a = float64(2)
+	x = make([]float64, 1000000)
+	y = make([]float64, 1000000)
+	z = make([]float64, 1000000)
+)
+
+func init() {
+	for n := range x {
+		x[n] = float64(n)
+		y[n] = float64(n)
+	}
+}
+
+func benchaxpyu(t *testing.B, n int, f func(a float64, x, y []float64)) {
+	x, y := x[:n], y[:n]
+
+	for i := 0; i < t.N; i++ {
+		f(a, x, y)
+	}
+}
+
+func naiveaxpyu(a float64, x, y []float64) {
+	for i, v := range x {
+		y[i] += a * v
+	}
+}
+
+func BenchmarkF64AxpyUnitary1(t *testing.B)     { benchaxpyu(t, 1, AxpyUnitary) }
+func BenchmarkF64AxpyUnitary2(t *testing.B)     { benchaxpyu(t, 2, AxpyUnitary) }
+func BenchmarkF64AxpyUnitary3(t *testing.B)     { benchaxpyu(t, 3, AxpyUnitary) }
+func BenchmarkF64AxpyUnitary4(t *testing.B)     { benchaxpyu(t, 4, AxpyUnitary) }
+func BenchmarkF64AxpyUnitary5(t *testing.B)     { benchaxpyu(t, 5, AxpyUnitary) }
+func BenchmarkF64AxpyUnitary10(t *testing.B)    { benchaxpyu(t, 10, AxpyUnitary) }
+func BenchmarkF64AxpyUnitary100(t *testing.B)   { benchaxpyu(t, 100, AxpyUnitary) }
+func BenchmarkF64AxpyUnitary1000(t *testing.B)  { benchaxpyu(t, 1000, AxpyUnitary) }
+func BenchmarkF64AxpyUnitary5000(t *testing.B)  { benchaxpyu(t, 5000, AxpyUnitary) }
+func BenchmarkF64AxpyUnitary10000(t *testing.B) { benchaxpyu(t, 10000, AxpyUnitary) }
+func BenchmarkF64AxpyUnitary50000(t *testing.B) { benchaxpyu(t, 50000, AxpyUnitary) }
+
+func BenchmarkLF64AxpyUnitary1(t *testing.B)     { benchaxpyu(t, 1, naiveaxpyu) }
+func BenchmarkLF64AxpyUnitary2(t *testing.B)     { benchaxpyu(t, 2, naiveaxpyu) }
+func BenchmarkLF64AxpyUnitary3(t *testing.B)     { benchaxpyu(t, 3, naiveaxpyu) }
+func BenchmarkLF64AxpyUnitary4(t *testing.B)     { benchaxpyu(t, 4, naiveaxpyu) }
+func BenchmarkLF64AxpyUnitary5(t *testing.B)     { benchaxpyu(t, 5, naiveaxpyu) }
+func BenchmarkLF64AxpyUnitary10(t *testing.B)    { benchaxpyu(t, 10, naiveaxpyu) }
+func BenchmarkLF64AxpyUnitary100(t *testing.B)   { benchaxpyu(t, 100, naiveaxpyu) }
+func BenchmarkLF64AxpyUnitary1000(t *testing.B)  { benchaxpyu(t, 1000, naiveaxpyu) }
+func BenchmarkLF64AxpyUnitary5000(t *testing.B)  { benchaxpyu(t, 5000, naiveaxpyu) }
+func BenchmarkLF64AxpyUnitary10000(t *testing.B) { benchaxpyu(t, 10000, naiveaxpyu) }
+func BenchmarkLF64AxpyUnitary50000(t *testing.B) { benchaxpyu(t, 50000, naiveaxpyu) }
+
+func benchaxpyut(t *testing.B, n int, f func(d []float64, a float64, x, y []float64)) {
+	x, y, z := x[:n], y[:n], z[:n]
+
+	for i := 0; i < t.N; i++ {
+		f(z, a, x, y)
+	}
+}
+
+func naiveaxpyut(d []float64, a float64, x, y []float64) {
+	for i, v := range x {
+		d[i] = y[i] + a*v
+	}
+}
+
+func BenchmarkF64AxpyUnitaryTo1(t *testing.B)     { benchaxpyut(t, 1, AxpyUnitaryTo) }
+func BenchmarkF64AxpyUnitaryTo2(t *testing.B)     { benchaxpyut(t, 2, AxpyUnitaryTo) }
+func BenchmarkF64AxpyUnitaryTo3(t *testing.B)     { benchaxpyut(t, 3, AxpyUnitaryTo) }
+func BenchmarkF64AxpyUnitaryTo4(t *testing.B)     { benchaxpyut(t, 4, AxpyUnitaryTo) }
+func BenchmarkF64AxpyUnitaryTo5(t *testing.B)     { benchaxpyut(t, 5, AxpyUnitaryTo) }
+func BenchmarkF64AxpyUnitaryTo10(t *testing.B)    { benchaxpyut(t, 10, AxpyUnitaryTo) }
+func BenchmarkF64AxpyUnitaryTo100(t *testing.B)   { benchaxpyut(t, 100, AxpyUnitaryTo) }
+func BenchmarkF64AxpyUnitaryTo1000(t *testing.B)  { benchaxpyut(t, 1000, AxpyUnitaryTo) }
+func BenchmarkF64AxpyUnitaryTo5000(t *testing.B)  { benchaxpyut(t, 5000, AxpyUnitaryTo) }
+func BenchmarkF64AxpyUnitaryTo10000(t *testing.B) { benchaxpyut(t, 10000, AxpyUnitaryTo) }
+func BenchmarkF64AxpyUnitaryTo50000(t *testing.B) { benchaxpyut(t, 50000, AxpyUnitaryTo) }
+
+func BenchmarkLF64AxpyUnitaryTo1(t *testing.B)     { benchaxpyut(t, 1, naiveaxpyut) }
+func BenchmarkLF64AxpyUnitaryTo2(t *testing.B)     { benchaxpyut(t, 2, naiveaxpyut) }
+func BenchmarkLF64AxpyUnitaryTo3(t *testing.B)     { benchaxpyut(t, 3, naiveaxpyut) }
+func BenchmarkLF64AxpyUnitaryTo4(t *testing.B)     { benchaxpyut(t, 4, naiveaxpyut) }
+func BenchmarkLF64AxpyUnitaryTo5(t *testing.B)     { benchaxpyut(t, 5, naiveaxpyut) }
+func BenchmarkLF64AxpyUnitaryTo10(t *testing.B)    { benchaxpyut(t, 10, naiveaxpyut) }
+func BenchmarkLF64AxpyUnitaryTo100(t *testing.B)   { benchaxpyut(t, 100, naiveaxpyut) }
+func BenchmarkLF64AxpyUnitaryTo1000(t *testing.B)  { benchaxpyut(t, 1000, naiveaxpyut) }
+func BenchmarkLF64AxpyUnitaryTo5000(t *testing.B)  { benchaxpyut(t, 5000, naiveaxpyut) }
+func BenchmarkLF64AxpyUnitaryTo10000(t *testing.B) { benchaxpyut(t, 10000, naiveaxpyut) }
+func BenchmarkLF64AxpyUnitaryTo50000(t *testing.B) { benchaxpyut(t, 50000, naiveaxpyut) }
+
+func benchaxpyinc(t *testing.B, ln, t_inc int, f func(alpha float64, x, y []float64, n, incX, incY, ix, iy uintptr)) {
+	n, inc := uintptr(ln), uintptr(t_inc)
+	var idx int
+	if t_inc < 0 {
+		idx = (-ln + 1) * t_inc
+	}
+
+	for i := 0; i < t.N; i++ {
+		f(1, x, y, n, inc, inc, uintptr(idx), uintptr(idx))
+	}
+}
+
+func naiveaxpyinc(alpha float64, x, y []float64, n, incX, incY, ix, iy uintptr) {
+	for i := 0; i < int(n); i++ {
+		y[iy] += alpha * x[ix]
+		ix += incX
+		iy += incY
+	}
+}
+
+func BenchmarkF64AxpyIncN1Inc1(b *testing.B) { benchaxpyinc(b, 1, 1, AxpyInc) }
+
+func BenchmarkF64AxpyIncN2Inc1(b *testing.B)  { benchaxpyinc(b, 2, 1, AxpyInc) }
+func BenchmarkF64AxpyIncN2Inc2(b *testing.B)  { benchaxpyinc(b, 2, 2, AxpyInc) }
+func BenchmarkF64AxpyIncN2Inc4(b *testing.B)  { benchaxpyinc(b, 2, 4, AxpyInc) }
+func BenchmarkF64AxpyIncN2Inc10(b *testing.B) { benchaxpyinc(b, 2, 10, AxpyInc) }
+
+func BenchmarkF64AxpyIncN3Inc1(b *testing.B)  { benchaxpyinc(b, 3, 1, AxpyInc) }
+func BenchmarkF64AxpyIncN3Inc2(b *testing.B)  { benchaxpyinc(b, 3, 2, AxpyInc) }
+func BenchmarkF64AxpyIncN3Inc4(b *testing.B)  { benchaxpyinc(b, 3, 4, AxpyInc) }
+func BenchmarkF64AxpyIncN3Inc10(b *testing.B) { benchaxpyinc(b, 3, 10, AxpyInc) }
+
+func BenchmarkF64AxpyIncN4Inc1(b *testing.B)  { benchaxpyinc(b, 4, 1, AxpyInc) }
+func BenchmarkF64AxpyIncN4Inc2(b *testing.B)  { benchaxpyinc(b, 4, 2, AxpyInc) }
+func BenchmarkF64AxpyIncN4Inc4(b *testing.B)  { benchaxpyinc(b, 4, 4, AxpyInc) }
+func BenchmarkF64AxpyIncN4Inc10(b *testing.B) { benchaxpyinc(b, 4, 10, AxpyInc) }
+
+func BenchmarkF64AxpyIncN10Inc1(b *testing.B)  { benchaxpyinc(b, 10, 1, AxpyInc) }
+func BenchmarkF64AxpyIncN10Inc2(b *testing.B)  { benchaxpyinc(b, 10, 2, AxpyInc) }
+func BenchmarkF64AxpyIncN10Inc4(b *testing.B)  { benchaxpyinc(b, 10, 4, AxpyInc) }
+func BenchmarkF64AxpyIncN10Inc10(b *testing.B) { benchaxpyinc(b, 10, 10, AxpyInc) }
+
+func BenchmarkF64AxpyIncN1000Inc1(b *testing.B)  { benchaxpyinc(b, 1000, 1, AxpyInc) }
+func BenchmarkF64AxpyIncN1000Inc2(b *testing.B)  { benchaxpyinc(b, 1000, 2, AxpyInc) }
+func BenchmarkF64AxpyIncN1000Inc4(b *testing.B)  { benchaxpyinc(b, 1000, 4, AxpyInc) }
+func BenchmarkF64AxpyIncN1000Inc10(b *testing.B) { benchaxpyinc(b, 1000, 10, AxpyInc) }
+
+func BenchmarkF64AxpyIncN100000Inc1(b *testing.B)  { benchaxpyinc(b, 100000, 1, AxpyInc) }
+func BenchmarkF64AxpyIncN100000Inc2(b *testing.B)  { benchaxpyinc(b, 100000, 2, AxpyInc) }
+func BenchmarkF64AxpyIncN100000Inc4(b *testing.B)  { benchaxpyinc(b, 100000, 4, AxpyInc) }
+func BenchmarkF64AxpyIncN100000Inc10(b *testing.B) { benchaxpyinc(b, 100000, 10, AxpyInc) }
+
+func BenchmarkF64AxpyIncN100000IncM1(b *testing.B)  { benchaxpyinc(b, 100000, -1, AxpyInc) }
+func BenchmarkF64AxpyIncN100000IncM2(b *testing.B)  { benchaxpyinc(b, 100000, -2, AxpyInc) }
+func BenchmarkF64AxpyIncN100000IncM4(b *testing.B)  { benchaxpyinc(b, 100000, -4, AxpyInc) }
+func BenchmarkF64AxpyIncN100000IncM10(b *testing.B) { benchaxpyinc(b, 100000, -10, AxpyInc) }
+
+func BenchmarkLF64AxpyIncN1Inc1(b *testing.B) { benchaxpyinc(b, 1, 1, naiveaxpyinc) }
+
+func BenchmarkLF64AxpyIncN2Inc1(b *testing.B)  { benchaxpyinc(b, 2, 1, naiveaxpyinc) }
+func BenchmarkLF64AxpyIncN2Inc2(b *testing.B)  { benchaxpyinc(b, 2, 2, naiveaxpyinc) }
+func BenchmarkLF64AxpyIncN2Inc4(b *testing.B)  { benchaxpyinc(b, 2, 4, naiveaxpyinc) }
+func BenchmarkLF64AxpyIncN2Inc10(b *testing.B) { benchaxpyinc(b, 2, 10, naiveaxpyinc) }
+
+func BenchmarkLF64AxpyIncN3Inc1(b *testing.B)  { benchaxpyinc(b, 3, 1, naiveaxpyinc) }
+func BenchmarkLF64AxpyIncN3Inc2(b *testing.B)  { benchaxpyinc(b, 3, 2, naiveaxpyinc) }
+func BenchmarkLF64AxpyIncN3Inc4(b *testing.B)  { benchaxpyinc(b, 3, 4, naiveaxpyinc) }
+func BenchmarkLF64AxpyIncN3Inc10(b *testing.B) { benchaxpyinc(b, 3, 10, naiveaxpyinc) }
+
+func BenchmarkLF64AxpyIncN4Inc1(b *testing.B)  { benchaxpyinc(b, 4, 1, naiveaxpyinc) }
+func BenchmarkLF64AxpyIncN4Inc2(b *testing.B)  { benchaxpyinc(b, 4, 2, naiveaxpyinc) }
+func BenchmarkLF64AxpyIncN4Inc4(b *testing.B)  { benchaxpyinc(b, 4, 4, naiveaxpyinc) }
+func BenchmarkLF64AxpyIncN4Inc10(b *testing.B) { benchaxpyinc(b, 4, 10, naiveaxpyinc) }
+
+func BenchmarkLF64AxpyIncN10Inc1(b *testing.B)  { benchaxpyinc(b, 10, 1, naiveaxpyinc) }
+func BenchmarkLF64AxpyIncN10Inc2(b *testing.B)  { benchaxpyinc(b, 10, 2, naiveaxpyinc) }
+func BenchmarkLF64AxpyIncN10Inc4(b *testing.B)  { benchaxpyinc(b, 10, 4, naiveaxpyinc) }
+func BenchmarkLF64AxpyIncN10Inc10(b *testing.B) { benchaxpyinc(b, 10, 10, naiveaxpyinc) }
+
+func BenchmarkLF64AxpyIncN1000Inc1(b *testing.B)  { benchaxpyinc(b, 1000, 1, naiveaxpyinc) }
+func BenchmarkLF64AxpyIncN1000Inc2(b *testing.B)  { benchaxpyinc(b, 1000, 2, naiveaxpyinc) }
+func BenchmarkLF64AxpyIncN1000Inc4(b *testing.B)  { benchaxpyinc(b, 1000, 4, naiveaxpyinc) }
+func BenchmarkLF64AxpyIncN1000Inc10(b *testing.B) { benchaxpyinc(b, 1000, 10, naiveaxpyinc) }
+
+func BenchmarkLF64AxpyIncN100000Inc1(b *testing.B)  { benchaxpyinc(b, 100000, 1, naiveaxpyinc) }
+func BenchmarkLF64AxpyIncN100000Inc2(b *testing.B)  { benchaxpyinc(b, 100000, 2, naiveaxpyinc) }
+func BenchmarkLF64AxpyIncN100000Inc4(b *testing.B)  { benchaxpyinc(b, 100000, 4, naiveaxpyinc) }
+func BenchmarkLF64AxpyIncN100000Inc10(b *testing.B) { benchaxpyinc(b, 100000, 10, naiveaxpyinc) }
+
+func BenchmarkLF64AxpyIncN100000IncM1(b *testing.B)  { benchaxpyinc(b, 100000, -1, naiveaxpyinc) }
+func BenchmarkLF64AxpyIncN100000IncM2(b *testing.B)  { benchaxpyinc(b, 100000, -2, naiveaxpyinc) }
+func BenchmarkLF64AxpyIncN100000IncM4(b *testing.B)  { benchaxpyinc(b, 100000, -4, naiveaxpyinc) }
+func BenchmarkLF64AxpyIncN100000IncM10(b *testing.B) { benchaxpyinc(b, 100000, -10, naiveaxpyinc) }
+
+func benchaxpyincto(t *testing.B, ln, t_inc int, f func(dst []float64, incDst, idst uintptr, alpha float64, x, y []float64, n, incX, incY, ix, iy uintptr)) {
+	n, inc := uintptr(ln), uintptr(t_inc)
+	var idx int
+	if t_inc < 0 {
+		idx = (-ln + 1) * t_inc
+	}
+
+	for i := 0; i < t.N; i++ {
+		f(z, inc, uintptr(idx), 1, x, y, n, inc, inc, uintptr(idx), uintptr(idx))
+	}
+}
+
+func naiveaxpyincto(dst []float64, incDst, idst uintptr, alpha float64, x, y []float64, n, incX, incY, ix, iy uintptr) {
+	for i := 0; i < int(n); i++ {
+		dst[idst] = alpha*x[ix] + y[iy]
+		ix += incX
+		iy += incY
+		idst += incDst
+	}
+}
+
+func BenchmarkF64AxpyIncToN1Inc1(b *testing.B) { benchaxpyincto(b, 1, 1, AxpyIncTo) }
+
+func BenchmarkF64AxpyIncToN2Inc1(b *testing.B)  { benchaxpyincto(b, 2, 1, AxpyIncTo) }
+func BenchmarkF64AxpyIncToN2Inc2(b *testing.B)  { benchaxpyincto(b, 2, 2, AxpyIncTo) }
+func BenchmarkF64AxpyIncToN2Inc4(b *testing.B)  { benchaxpyincto(b, 2, 4, AxpyIncTo) }
+func BenchmarkF64AxpyIncToN2Inc10(b *testing.B) { benchaxpyincto(b, 2, 10, AxpyIncTo) }
+
+func BenchmarkF64AxpyIncToN3Inc1(b *testing.B)  { benchaxpyincto(b, 3, 1, AxpyIncTo) }
+func BenchmarkF64AxpyIncToN3Inc2(b *testing.B)  { benchaxpyincto(b, 3, 2, AxpyIncTo) }
+func BenchmarkF64AxpyIncToN3Inc4(b *testing.B)  { benchaxpyincto(b, 3, 4, AxpyIncTo) }
+func BenchmarkF64AxpyIncToN3Inc10(b *testing.B) { benchaxpyincto(b, 3, 10, AxpyIncTo) }
+
+func BenchmarkF64AxpyIncToN4Inc1(b *testing.B)  { benchaxpyincto(b, 4, 1, AxpyIncTo) }
+func BenchmarkF64AxpyIncToN4Inc2(b *testing.B)  { benchaxpyincto(b, 4, 2, AxpyIncTo) }
+func BenchmarkF64AxpyIncToN4Inc4(b *testing.B)  { benchaxpyincto(b, 4, 4, AxpyIncTo) }
+func BenchmarkF64AxpyIncToN4Inc10(b *testing.B) { benchaxpyincto(b, 4, 10, AxpyIncTo) }
+
+func BenchmarkF64AxpyIncToN10Inc1(b *testing.B)  { benchaxpyincto(b, 10, 1, AxpyIncTo) }
+func BenchmarkF64AxpyIncToN10Inc2(b *testing.B)  { benchaxpyincto(b, 10, 2, AxpyIncTo) }
+func BenchmarkF64AxpyIncToN10Inc4(b *testing.B)  { benchaxpyincto(b, 10, 4, AxpyIncTo) }
+func BenchmarkF64AxpyIncToN10Inc10(b *testing.B) { benchaxpyincto(b, 10, 10, AxpyIncTo) }
+
+func BenchmarkF64AxpyIncToN1000Inc1(b *testing.B)  { benchaxpyincto(b, 1000, 1, AxpyIncTo) }
+func BenchmarkF64AxpyIncToN1000Inc2(b *testing.B)  { benchaxpyincto(b, 1000, 2, AxpyIncTo) }
+func BenchmarkF64AxpyIncToN1000Inc4(b *testing.B)  { benchaxpyincto(b, 1000, 4, AxpyIncTo) }
+func BenchmarkF64AxpyIncToN1000Inc10(b *testing.B) { benchaxpyincto(b, 1000, 10, AxpyIncTo) }
+
+func BenchmarkF64AxpyIncToN100000Inc1(b *testing.B)  { benchaxpyincto(b, 100000, 1, AxpyIncTo) }
+func BenchmarkF64AxpyIncToN100000Inc2(b *testing.B)  { benchaxpyincto(b, 100000, 2, AxpyIncTo) }
+func BenchmarkF64AxpyIncToN100000Inc4(b *testing.B)  { benchaxpyincto(b, 100000, 4, AxpyIncTo) }
+func BenchmarkF64AxpyIncToN100000Inc10(b *testing.B) { benchaxpyincto(b, 100000, 10, AxpyIncTo) }
+
+func BenchmarkF64AxpyIncToN100000IncM1(b *testing.B)  { benchaxpyincto(b, 100000, -1, AxpyIncTo) }
+func BenchmarkF64AxpyIncToN100000IncM2(b *testing.B)  { benchaxpyincto(b, 100000, -2, AxpyIncTo) }
+func BenchmarkF64AxpyIncToN100000IncM4(b *testing.B)  { benchaxpyincto(b, 100000, -4, AxpyIncTo) }
+func BenchmarkF64AxpyIncToN100000IncM10(b *testing.B) { benchaxpyincto(b, 100000, -10, AxpyIncTo) }
+
+func BenchmarkLF64AxpyIncToN1Inc1(b *testing.B) { benchaxpyincto(b, 1, 1, naiveaxpyincto) }
+
+func BenchmarkLF64AxpyIncToN2Inc1(b *testing.B)  { benchaxpyincto(b, 2, 1, naiveaxpyincto) }
+func BenchmarkLF64AxpyIncToN2Inc2(b *testing.B)  { benchaxpyincto(b, 2, 2, naiveaxpyincto) }
+func BenchmarkLF64AxpyIncToN2Inc4(b *testing.B)  { benchaxpyincto(b, 2, 4, naiveaxpyincto) }
+func BenchmarkLF64AxpyIncToN2Inc10(b *testing.B) { benchaxpyincto(b, 2, 10, naiveaxpyincto) }
+
+func BenchmarkLF64AxpyIncToN3Inc1(b *testing.B)  { benchaxpyincto(b, 3, 1, naiveaxpyincto) }
+func BenchmarkLF64AxpyIncToN3Inc2(b *testing.B)  { benchaxpyincto(b, 3, 2, naiveaxpyincto) }
+func BenchmarkLF64AxpyIncToN3Inc4(b *testing.B)  { benchaxpyincto(b, 3, 4, naiveaxpyincto) }
+func BenchmarkLF64AxpyIncToN3Inc10(b *testing.B) { benchaxpyincto(b, 3, 10, naiveaxpyincto) }
+
+func BenchmarkLF64AxpyIncToN4Inc1(b *testing.B)  { benchaxpyincto(b, 4, 1, naiveaxpyincto) }
+func BenchmarkLF64AxpyIncToN4Inc2(b *testing.B)  { benchaxpyincto(b, 4, 2, naiveaxpyincto) }
+func BenchmarkLF64AxpyIncToN4Inc4(b *testing.B)  { benchaxpyincto(b, 4, 4, naiveaxpyincto) }
+func BenchmarkLF64AxpyIncToN4Inc10(b *testing.B) { benchaxpyincto(b, 4, 10, naiveaxpyincto) }
+
+func BenchmarkLF64AxpyIncToN10Inc1(b *testing.B)  { benchaxpyincto(b, 10, 1, naiveaxpyincto) }
+func BenchmarkLF64AxpyIncToN10Inc2(b *testing.B)  { benchaxpyincto(b, 10, 2, naiveaxpyincto) }
+func BenchmarkLF64AxpyIncToN10Inc4(b *testing.B)  { benchaxpyincto(b, 10, 4, naiveaxpyincto) }
+func BenchmarkLF64AxpyIncToN10Inc10(b *testing.B) { benchaxpyincto(b, 10, 10, naiveaxpyincto) }
+
+func BenchmarkLF64AxpyIncToN1000Inc1(b *testing.B)  { benchaxpyincto(b, 1000, 1, naiveaxpyincto) }
+func BenchmarkLF64AxpyIncToN1000Inc2(b *testing.B)  { benchaxpyincto(b, 1000, 2, naiveaxpyincto) }
+func BenchmarkLF64AxpyIncToN1000Inc4(b *testing.B)  { benchaxpyincto(b, 1000, 4, naiveaxpyincto) }
+func BenchmarkLF64AxpyIncToN1000Inc10(b *testing.B) { benchaxpyincto(b, 1000, 10, naiveaxpyincto) }
+
+func BenchmarkLF64AxpyIncToN100000Inc1(b *testing.B)  { benchaxpyincto(b, 100000, 1, naiveaxpyincto) }
+func BenchmarkLF64AxpyIncToN100000Inc2(b *testing.B)  { benchaxpyincto(b, 100000, 2, naiveaxpyincto) }
+func BenchmarkLF64AxpyIncToN100000Inc4(b *testing.B)  { benchaxpyincto(b, 100000, 4, naiveaxpyincto) }
+func BenchmarkLF64AxpyIncToN100000Inc10(b *testing.B) { benchaxpyincto(b, 100000, 10, naiveaxpyincto) }
+
+func BenchmarkLF64AxpyIncToN100000IncM1(b *testing.B)  { benchaxpyincto(b, 100000, -1, naiveaxpyincto) }
+func BenchmarkLF64AxpyIncToN100000IncM2(b *testing.B)  { benchaxpyincto(b, 100000, -2, naiveaxpyincto) }
+func BenchmarkLF64AxpyIncToN100000IncM4(b *testing.B)  { benchaxpyincto(b, 100000, -4, naiveaxpyincto) }
+func BenchmarkLF64AxpyIncToN100000IncM10(b *testing.B) { benchaxpyincto(b, 100000, -10, naiveaxpyincto) }
+
+// Scal* benchmarks
+func BenchmarkDscalUnitaryN1(b *testing.B)      { benchmarkDscalUnitary(b, 1) }
+func BenchmarkDscalUnitaryN2(b *testing.B)      { benchmarkDscalUnitary(b, 2) }
+func BenchmarkDscalUnitaryN3(b *testing.B)      { benchmarkDscalUnitary(b, 3) }
+func BenchmarkDscalUnitaryN4(b *testing.B)      { benchmarkDscalUnitary(b, 4) }
+func BenchmarkDscalUnitaryN10(b *testing.B)     { benchmarkDscalUnitary(b, 10) }
+func BenchmarkDscalUnitaryN100(b *testing.B)    { benchmarkDscalUnitary(b, 100) }
+func BenchmarkDscalUnitaryN1000(b *testing.B)   { benchmarkDscalUnitary(b, 1000) }
+func BenchmarkDscalUnitaryN10000(b *testing.B)  { benchmarkDscalUnitary(b, 10000) }
+func BenchmarkDscalUnitaryN100000(b *testing.B) { benchmarkDscalUnitary(b, 100000) }
+
+func benchmarkDscalUnitary(b *testing.B, n int) {
+	x := randomSlice(n, 1)
+	b.ResetTimer()
+	for i := 0; i < b.N; i += 2 {
+		ScalUnitary(2, x)
+		ScalUnitary(0.5, x)
+	}
+	benchSink = x
+}
+
+func BenchmarkDscalUnitaryToN1(b *testing.B)      { benchmarkDscalUnitaryTo(b, 1) }
+func BenchmarkDscalUnitaryToN2(b *testing.B)      { benchmarkDscalUnitaryTo(b, 2) }
+func BenchmarkDscalUnitaryToN3(b *testing.B)      { benchmarkDscalUnitaryTo(b, 3) }
+func BenchmarkDscalUnitaryToN4(b *testing.B)      { benchmarkDscalUnitaryTo(b, 4) }
+func BenchmarkDscalUnitaryToN10(b *testing.B)     { benchmarkDscalUnitaryTo(b, 10) }
+func BenchmarkDscalUnitaryToN100(b *testing.B)    { benchmarkDscalUnitaryTo(b, 100) }
+func BenchmarkDscalUnitaryToN1000(b *testing.B)   { benchmarkDscalUnitaryTo(b, 1000) }
+func BenchmarkDscalUnitaryToN10000(b *testing.B)  { benchmarkDscalUnitaryTo(b, 10000) }
+func BenchmarkDscalUnitaryToN100000(b *testing.B) { benchmarkDscalUnitaryTo(b, 100000) }
+
+func benchmarkDscalUnitaryTo(b *testing.B, n int) {
+	x := randomSlice(n, 1)
+	dst := randomSlice(n, 1)
+	a := rand.Float64()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		ScalUnitaryTo(dst, a, x)
+	}
+	benchSink = dst
+}
+
+func BenchmarkDscalUnitaryToXN1(b *testing.B)      { benchmarkDscalUnitaryToX(b, 1) }
+func BenchmarkDscalUnitaryToXN2(b *testing.B)      { benchmarkDscalUnitaryToX(b, 2) }
+func BenchmarkDscalUnitaryToXN3(b *testing.B)      { benchmarkDscalUnitaryToX(b, 3) }
+func BenchmarkDscalUnitaryToXN4(b *testing.B)      { benchmarkDscalUnitaryToX(b, 4) }
+func BenchmarkDscalUnitaryToXN10(b *testing.B)     { benchmarkDscalUnitaryToX(b, 10) }
+func BenchmarkDscalUnitaryToXN100(b *testing.B)    { benchmarkDscalUnitaryToX(b, 100) }
+func BenchmarkDscalUnitaryToXN1000(b *testing.B)   { benchmarkDscalUnitaryToX(b, 1000) }
+func BenchmarkDscalUnitaryToXN10000(b *testing.B)  { benchmarkDscalUnitaryToX(b, 10000) }
+func BenchmarkDscalUnitaryToXN100000(b *testing.B) { benchmarkDscalUnitaryToX(b, 100000) }
+
+func benchmarkDscalUnitaryToX(b *testing.B, n int) {
+	x := randomSlice(n, 1)
+	b.ResetTimer()
+	for i := 0; i < b.N; i += 2 {
+		ScalUnitaryTo(x, 2, x)
+		ScalUnitaryTo(x, 0.5, x)
+	}
+	benchSink = x
+}
+
+func BenchmarkDscalIncN1Inc1(b *testing.B) { benchmarkDscalInc(b, 1, 1) }
+
+func BenchmarkDscalIncN2Inc1(b *testing.B)  { benchmarkDscalInc(b, 2, 1) }
+func BenchmarkDscalIncN2Inc2(b *testing.B)  { benchmarkDscalInc(b, 2, 2) }
+func BenchmarkDscalIncN2Inc4(b *testing.B)  { benchmarkDscalInc(b, 2, 4) }
+func BenchmarkDscalIncN2Inc10(b *testing.B) { benchmarkDscalInc(b, 2, 10) }
+
+func BenchmarkDscalIncN3Inc1(b *testing.B)  { benchmarkDscalInc(b, 3, 1) }
+func BenchmarkDscalIncN3Inc2(b *testing.B)  { benchmarkDscalInc(b, 3, 2) }
+func BenchmarkDscalIncN3Inc4(b *testing.B)  { benchmarkDscalInc(b, 3, 4) }
+func BenchmarkDscalIncN3Inc10(b *testing.B) { benchmarkDscalInc(b, 3, 10) }
+
+func BenchmarkDscalIncN4Inc1(b *testing.B)  { benchmarkDscalInc(b, 4, 1) }
+func BenchmarkDscalIncN4Inc2(b *testing.B)  { benchmarkDscalInc(b, 4, 2) }
+func BenchmarkDscalIncN4Inc4(b *testing.B)  { benchmarkDscalInc(b, 4, 4) }
+func BenchmarkDscalIncN4Inc10(b *testing.B) { benchmarkDscalInc(b, 4, 10) }
+
+func BenchmarkDscalIncN10Inc1(b *testing.B)  { benchmarkDscalInc(b, 10, 1) }
+func BenchmarkDscalIncN10Inc2(b *testing.B)  { benchmarkDscalInc(b, 10, 2) }
+func BenchmarkDscalIncN10Inc4(b *testing.B)  { benchmarkDscalInc(b, 10, 4) }
+func BenchmarkDscalIncN10Inc10(b *testing.B) { benchmarkDscalInc(b, 10, 10) }
+
+func BenchmarkDscalIncN1000Inc1(b *testing.B)  { benchmarkDscalInc(b, 1000, 1) }
+func BenchmarkDscalIncN1000Inc2(b *testing.B)  { benchmarkDscalInc(b, 1000, 2) }
+func BenchmarkDscalIncN1000Inc4(b *testing.B)  { benchmarkDscalInc(b, 1000, 4) }
+func BenchmarkDscalIncN1000Inc10(b *testing.B) { benchmarkDscalInc(b, 1000, 10) }
+
+func BenchmarkDscalIncN100000Inc1(b *testing.B)  { benchmarkDscalInc(b, 100000, 1) }
+func BenchmarkDscalIncN100000Inc2(b *testing.B)  { benchmarkDscalInc(b, 100000, 2) }
+func BenchmarkDscalIncN100000Inc4(b *testing.B)  { benchmarkDscalInc(b, 100000, 4) }
+func BenchmarkDscalIncN100000Inc10(b *testing.B) { benchmarkDscalInc(b, 100000, 10) }
+
+func benchmarkDscalInc(b *testing.B, n, inc int) {
+	x := randomSlice(n, inc)
+	b.ResetTimer()
+	for i := 0; i < b.N; i += 2 {
+		ScalInc(2, x, uintptr(n), uintptr(inc))
+		ScalInc(0.5, x, uintptr(n), uintptr(inc))
+	}
+	benchSink = x
+}
+
+func BenchmarkDscalIncToN1Inc1(b *testing.B) { benchmarkDscalIncTo(b, 1, 1) }
+
+func BenchmarkDscalIncToN2Inc1(b *testing.B)  { benchmarkDscalIncTo(b, 2, 1) }
+func BenchmarkDscalIncToN2Inc2(b *testing.B)  { benchmarkDscalIncTo(b, 2, 2) }
+func BenchmarkDscalIncToN2Inc4(b *testing.B)  { benchmarkDscalIncTo(b, 2, 4) }
+func BenchmarkDscalIncToN2Inc10(b *testing.B) { benchmarkDscalIncTo(b, 2, 10) }
+
+func BenchmarkDscalIncToN3Inc1(b *testing.B)  { benchmarkDscalIncTo(b, 3, 1) }
+func BenchmarkDscalIncToN3Inc2(b *testing.B)  { benchmarkDscalIncTo(b, 3, 2) }
+func BenchmarkDscalIncToN3Inc4(b *testing.B)  { benchmarkDscalIncTo(b, 3, 4) }
+func BenchmarkDscalIncToN3Inc10(b *testing.B) { benchmarkDscalIncTo(b, 3, 10) }
+
+func BenchmarkDscalIncToN4Inc1(b *testing.B)  { benchmarkDscalIncTo(b, 4, 1) }
+func BenchmarkDscalIncToN4Inc2(b *testing.B)  { benchmarkDscalIncTo(b, 4, 2) }
+func BenchmarkDscalIncToN4Inc4(b *testing.B)  { benchmarkDscalIncTo(b, 4, 4) }
+func BenchmarkDscalIncToN4Inc10(b *testing.B) { benchmarkDscalIncTo(b, 4, 10) }
+
+func BenchmarkDscalIncToN10Inc1(b *testing.B)  { benchmarkDscalIncTo(b, 10, 1) }
+func BenchmarkDscalIncToN10Inc2(b *testing.B)  { benchmarkDscalIncTo(b, 10, 2) }
+func BenchmarkDscalIncToN10Inc4(b *testing.B)  { benchmarkDscalIncTo(b, 10, 4) }
+func BenchmarkDscalIncToN10Inc10(b *testing.B) { benchmarkDscalIncTo(b, 10, 10) }
+
+func BenchmarkDscalIncToN1000Inc1(b *testing.B)  { benchmarkDscalIncTo(b, 1000, 1) }
+func BenchmarkDscalIncToN1000Inc2(b *testing.B)  { benchmarkDscalIncTo(b, 1000, 2) }
+func BenchmarkDscalIncToN1000Inc4(b *testing.B)  { benchmarkDscalIncTo(b, 1000, 4) }
+func BenchmarkDscalIncToN1000Inc10(b *testing.B) { benchmarkDscalIncTo(b, 1000, 10) }
+
+func BenchmarkDscalIncToN100000Inc1(b *testing.B)  { benchmarkDscalIncTo(b, 100000, 1) }
+func BenchmarkDscalIncToN100000Inc2(b *testing.B)  { benchmarkDscalIncTo(b, 100000, 2) }
+func BenchmarkDscalIncToN100000Inc4(b *testing.B)  { benchmarkDscalIncTo(b, 100000, 4) }
+func BenchmarkDscalIncToN100000Inc10(b *testing.B) { benchmarkDscalIncTo(b, 100000, 10) }
+
+func benchmarkDscalIncTo(b *testing.B, n, inc int) {
+	x := randomSlice(n, inc)
+	dst := randomSlice(n, inc)
+	a := rand.Float64()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		ScalIncTo(dst, uintptr(inc), a, x, uintptr(n), uintptr(inc))
+	}
+	benchSink = dst
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/cumprod_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/f64/cumprod_amd64.s
new file mode 100644
index 00000000..3d438093
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/cumprod_amd64.s
@@ -0,0 +1,71 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build !noasm,!appengine
+
+#include "textflag.h"
+
+TEXT ·CumProd(SB), NOSPLIT, $0
+	MOVQ    dst_base+0(FP), DI // DI = &dst
+	MOVQ    dst_len+8(FP), CX  // CX = len(dst)
+	MOVQ    s_base+24(FP), SI  // SI = &s
+	CMPQ    s_len+32(FP), CX   // CX = max( CX, len(s) )
+	CMOVQLE s_len+32(FP), CX
+	MOVQ    CX, ret_len+56(FP) // len(ret) = CX
+	CMPQ    CX, $0             // if CX == 0 { return }
+	JE      cp_end
+	XORQ    AX, AX             // i = 0
+
+	MOVSD  (SI), X5   // p_prod = { s[0], s[0] }
+	SHUFPD $0, X5, X5
+	MOVSD  X5, (DI)   // dst[0] = s[0]
+	INCQ   AX         // ++i
+	DECQ   CX         // -- CX
+	JZ     cp_end     // if CX == 0 { return }
+
+	MOVQ CX, BX
+	ANDQ $3, BX        // BX = CX % 4
+	SHRQ $2, CX        // CX = floor( CX / 4 )
+	JZ   cp_tail_start // if CX == 0 { goto cp_tail_start }
+
+cp_loop: // Loop unrolled 4x   do {
+	MOVUPS (SI)(AX*8), X0   // X0 = s[i:i+1]
+	MOVUPS 16(SI)(AX*8), X2
+	MOVAPS X0, X1           // X1 = X0
+	MOVAPS X2, X3
+	SHUFPD $1, X1, X1       // { X1[0], X1[1] } = { X1[1], X1[0] }
+	SHUFPD $1, X3, X3
+	MULPD  X0, X1           // X1 *= X0
+	MULPD  X2, X3
+	SHUFPD $2, X1, X0       // { X0[0], X0[1] } = { X0[0], X1[1] }
+	SHUFPD $3, X1, X1       // { X1[0], X1[1] } = { X1[1], X1[1] }
+	SHUFPD $2, X3, X2
+	SHUFPD $3, X3, X3
+	MULPD  X5, X0           // X0 *= p_prod
+	MULPD  X1, X5           // p_prod *= X1
+	MULPD  X5, X2
+	MOVUPS X0, (DI)(AX*8)   // dst[i] = X0
+	MOVUPS X2, 16(DI)(AX*8)
+	MULPD  X3, X5
+	ADDQ   $4, AX           // i += 4
+	LOOP   cp_loop          // } while --CX > 0
+
+	// if BX == 0 { return }
+	CMPQ BX, $0
+	JE   cp_end
+
+cp_tail_start: // Reset loop registers
+	MOVQ BX, CX // Loop counter: CX = BX
+
+cp_tail: // do {
+	MULSD (SI)(AX*8), X5 // p_prod *= s[i]
+	MOVSD X5, (DI)(AX*8) // dst[i] = p_prod
+	INCQ  AX             // ++i
+	LOOP  cp_tail        // } while --CX > 0
+
+cp_end:
+	MOVQ DI, ret_base+48(FP) // &ret = &dst
+	MOVQ dst_cap+16(FP), SI  // cap(ret) = cap(dst)
+	MOVQ SI, ret_cap+64(FP)
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/cumsum_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/f64/cumsum_amd64.s
new file mode 100644
index 00000000..eecfbbe1
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/cumsum_amd64.s
@@ -0,0 +1,64 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build !noasm,!appengine
+
+#include "textflag.h"
+
+TEXT ·CumSum(SB), NOSPLIT, $0
+	MOVQ    dst_base+0(FP), DI // DI = &dst
+	MOVQ    dst_len+8(FP), CX  // CX = len(dst)
+	MOVQ    s_base+24(FP), SI  // SI = &s
+	CMPQ    s_len+32(FP), CX   // CX = max( CX, len(s) )
+	CMOVQLE s_len+32(FP), CX
+	MOVQ    CX, ret_len+56(FP) // len(ret) = CX
+	CMPQ    CX, $0             // if CX == 0 { return }
+	JE      cs_end
+	XORQ    AX, AX             // i = 0
+	PXOR    X5, X5             // p_sum = 0
+	MOVQ    CX, BX
+	ANDQ    $3, BX             // BX = CX % 4
+	SHRQ    $2, CX             // CX = floor( CX / 4 )
+	JZ      cs_tail_start      // if CX == 0 { goto cs_tail_start }
+
+cs_loop: // Loop unrolled 4x   do {
+	MOVUPS (SI)(AX*8), X0   // X0 = s[i:i+1]
+	MOVUPS 16(SI)(AX*8), X2
+	MOVAPS X0, X1           // X1 = X0
+	MOVAPS X2, X3
+	SHUFPD $1, X1, X1       // { X1[0], X1[1] } = { X1[1], X1[0] }
+	SHUFPD $1, X3, X3
+	ADDPD  X0, X1           // X1 += X0
+	ADDPD  X2, X3
+	SHUFPD $2, X1, X0       // { X0[0], X0[1] } = { X0[0], X1[1] }
+	SHUFPD $3, X1, X1       // { X1[0], X1[1] } = { X1[1], X1[1] }
+	SHUFPD $2, X3, X2
+	SHUFPD $3, X3, X3
+	ADDPD  X5, X0           // X0 += p_sum
+	ADDPD  X1, X5           // p_sum += X1
+	ADDPD  X5, X2
+	MOVUPS X0, (DI)(AX*8)   // dst[i] = X0
+	MOVUPS X2, 16(DI)(AX*8)
+	ADDPD  X3, X5
+	ADDQ   $4, AX           // i += 4
+	LOOP   cs_loop          // } while --CX > 0
+
+	// if BX == 0 { return }
+	CMPQ BX, $0
+	JE   cs_end
+
+cs_tail_start: // Reset loop registers
+	MOVQ BX, CX // Loop counter: CX = BX
+
+cs_tail: // do {
+	ADDSD (SI)(AX*8), X5 // p_sum *= s[i]
+	MOVSD X5, (DI)(AX*8) // dst[i] = p_sum
+	INCQ  AX             // ++i
+	LOOP  cs_tail        // } while --CX > 0
+
+cs_end:
+	MOVQ DI, ret_base+48(FP) // &ret = &dst
+	MOVQ dst_cap+16(FP), SI  // cap(ret) = cap(dst)
+	MOVQ SI, ret_cap+64(FP)
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/div_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/f64/div_amd64.s
new file mode 100644
index 00000000..da417708
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/div_amd64.s
@@ -0,0 +1,67 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build !noasm,!appengine
+
+#include "textflag.h"
+
+// func Div(dst, s []float64)
+TEXT ·Div(SB), NOSPLIT, $0
+	MOVQ    dst_base+0(FP), DI // DI = &dst
+	MOVQ    dst_len+8(FP), CX  // CX = len(dst)
+	MOVQ    s_base+24(FP), SI  // SI = &s
+	CMPQ    s_len+32(FP), CX   // CX = max( CX, len(s) )
+	CMOVQLE s_len+32(FP), CX
+	CMPQ    CX, $0             // if CX == 0 { return }
+	JE      div_end
+	XORQ    AX, AX             // i = 0
+	MOVQ    SI, BX
+	ANDQ    $15, BX            // BX = &s & 15
+	JZ      div_no_trim        // if BX == 0 { goto div_no_trim }
+
+	// Align on 16-bit boundary
+	MOVSD (DI)(AX*8), X0 // X0 = dst[i]
+	DIVSD (SI)(AX*8), X0 // X0 /= s[i]
+	MOVSD X0, (DI)(AX*8) // dst[i] = X0
+	INCQ  AX             // ++i
+	DECQ  CX             // --CX
+	JZ    div_end        // if CX == 0 { return }
+
+div_no_trim:
+	MOVQ CX, BX
+	ANDQ $7, BX         // BX = len(dst) % 8
+	SHRQ $3, CX         // CX = floor( len(dst) / 8 )
+	JZ   div_tail_start // if CX == 0 { goto div_tail_start }
+
+div_loop: // Loop unrolled 8x   do {
+	MOVUPS (DI)(AX*8), X0   // X0 = dst[i:i+1]
+	MOVUPS 16(DI)(AX*8), X1
+	MOVUPS 32(DI)(AX*8), X2
+	MOVUPS 48(DI)(AX*8), X3
+	DIVPD  (SI)(AX*8), X0   // X0 /= s[i:i+1]
+	DIVPD  16(SI)(AX*8), X1
+	DIVPD  32(SI)(AX*8), X2
+	DIVPD  48(SI)(AX*8), X3
+	MOVUPS X0, (DI)(AX*8)   // dst[i] = X0
+	MOVUPS X1, 16(DI)(AX*8)
+	MOVUPS X2, 32(DI)(AX*8)
+	MOVUPS X3, 48(DI)(AX*8)
+	ADDQ   $8, AX           // i += 8
+	LOOP   div_loop         // } while --CX > 0
+	CMPQ   BX, $0           // if BX == 0 { return }
+	JE     div_end
+
+div_tail_start: // Reset loop registers
+	MOVQ BX, CX // Loop counter: CX = BX
+
+div_tail: // do {
+	MOVSD (DI)(AX*8), X0 // X0 = dst[i]
+	DIVSD (SI)(AX*8), X0 // X0 /= s[i]
+	MOVSD X0, (DI)(AX*8) // dst[i] = X0
+	INCQ  AX             // ++i
+	LOOP  div_tail       // } while --CX > 0
+
+div_end:
+	RET
+
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/divto_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/f64/divto_amd64.s
new file mode 100644
index 00000000..6280aab4
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/divto_amd64.s
@@ -0,0 +1,73 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build !noasm,!appengine
+
+#include "textflag.h"
+
+// func DivTo(dst, x, y []float64)
+TEXT ·DivTo(SB), NOSPLIT, $0
+	MOVQ    dst_base+0(FP), DI // DI = &dst
+	MOVQ    dst_len+8(FP), CX  // CX = len(dst)
+	MOVQ    x_base+24(FP), SI  // SI = &x
+	MOVQ    y_base+48(FP), DX  // DX = &y
+	CMPQ    x_len+32(FP), CX   // CX = max( len(dst), len(x), len(y) )
+	CMOVQLE x_len+32(FP), CX
+	CMPQ    y_len+56(FP), CX
+	CMOVQLE y_len+56(FP), CX
+	MOVQ    CX, ret_len+80(FP) // len(ret) = CX
+	CMPQ    CX, $0             // if CX == 0 { return }
+	JE      div_end
+	XORQ    AX, AX             // i = 0
+	MOVQ    DX, BX
+	ANDQ    $15, BX            // BX = &y & OxF
+	JZ      div_no_trim        // if BX == 0 { goto div_no_trim }
+
+	// Align on 16-bit boundary
+	MOVSD (SI)(AX*8), X0 // X0 = s[i]
+	DIVSD (DX)(AX*8), X0 // X0 /= t[i]
+	MOVSD X0, (DI)(AX*8) // dst[i] = X0
+	INCQ  AX             // ++i
+	DECQ  CX             // --CX
+	JZ    div_end        // if CX == 0 { return }
+
+div_no_trim:
+	MOVQ CX, BX
+	ANDQ $7, BX         // BX = len(dst) % 8
+	SHRQ $3, CX         // CX = floor( len(dst) / 8 )
+	JZ   div_tail_start // if CX == 0 { goto div_tail_start }
+
+div_loop: // Loop unrolled 8x   do {
+	MOVUPS (SI)(AX*8), X0   // X0 = x[i:i+1]
+	MOVUPS 16(SI)(AX*8), X1
+	MOVUPS 32(SI)(AX*8), X2
+	MOVUPS 48(SI)(AX*8), X3
+	DIVPD  (DX)(AX*8), X0   // X0 /= y[i:i+1]
+	DIVPD  16(DX)(AX*8), X1
+	DIVPD  32(DX)(AX*8), X2
+	DIVPD  48(DX)(AX*8), X3
+	MOVUPS X0, (DI)(AX*8)   // dst[i:i+1] = X0
+	MOVUPS X1, 16(DI)(AX*8)
+	MOVUPS X2, 32(DI)(AX*8)
+	MOVUPS X3, 48(DI)(AX*8)
+	ADDQ   $8, AX           // i += 8
+	LOOP   div_loop         // } while --CX > 0
+	CMPQ   BX, $0           // if BX == 0 { return }
+	JE     div_end
+
+div_tail_start: // Reset loop registers
+	MOVQ BX, CX // Loop counter: CX = BX
+
+div_tail: // do {
+	MOVSD (SI)(AX*8), X0 // X0  = x[i]
+	DIVSD (DX)(AX*8), X0 // X0 /= y[i]
+	MOVSD X0, (DI)(AX*8)
+	INCQ  AX             // ++i
+	LOOP  div_tail       // } while --CX > 0
+
+div_end:
+	MOVQ DI, ret_base+72(FP) // &ret = &dst
+	MOVQ dst_cap+16(FP), DI  // cap(ret) = cap(dst)
+	MOVQ DI, ret_cap+88(FP)
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/doc.go b/vendor/gonum.org/v1/gonum/internal/asm/f64/doc.go
new file mode 100644
index 00000000..5b562b57
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package f64 provides float64 vector primitives.
+package f64 // import "gonum.org/v1/gonum/internal/asm/f64"
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/dot.go b/vendor/gonum.org/v1/gonum/internal/asm/f64/dot.go
new file mode 100644
index 00000000..7b86b5b4
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/dot.go
@@ -0,0 +1,35 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !amd64 noasm appengine
+
+package f64
+
+// DotUnitary is
+//  for i, v := range x {
+//  	sum += y[i] * v
+//  }
+//  return sum
+func DotUnitary(x, y []float64) (sum float64) {
+	for i, v := range x {
+		sum += y[i] * v
+	}
+	return sum
+}
+
+// DotInc is
+//  for i := 0; i < int(n); i++ {
+//  	sum += y[iy] * x[ix]
+//  	ix += incX
+//  	iy += incY
+//  }
+//  return sum
+func DotInc(x, y []float64, n, incX, incY, ix, iy uintptr) (sum float64) {
+	for i := 0; i < int(n); i++ {
+		sum += y[iy] * x[ix]
+		ix += incX
+		iy += incY
+	}
+	return sum
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/dot_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/f64/dot_amd64.s
new file mode 100644
index 00000000..02e654d5
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/dot_amd64.s
@@ -0,0 +1,145 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Some of the loop unrolling code is copied from:
+// http://golang.org/src/math/big/arith_amd64.s
+// which is distributed under these terms:
+//
+// Copyright (c) 2012 The Go Authors. All rights reserved.
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+//    * Redistributions of source code must retain the above copyright
+// notice, this list of conditions and the following disclaimer.
+//    * Redistributions in binary form must reproduce the above
+// copyright notice, this list of conditions and the following disclaimer
+// in the documentation and/or other materials provided with the
+// distribution.
+//    * Neither the name of Google Inc. nor the names of its
+// contributors may be used to endorse or promote products derived from
+// this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+//+build !noasm,!appengine
+
+#include "textflag.h"
+
+// func DdotUnitary(x, y []float64) (sum float64)
+// This function assumes len(y) >= len(x).
+TEXT ·DotUnitary(SB), NOSPLIT, $0
+	MOVQ x+0(FP), R8
+	MOVQ x_len+8(FP), DI // n = len(x)
+	MOVQ y+24(FP), R9
+
+	MOVSD $(0.0), X7 // sum = 0
+	MOVSD $(0.0), X8 // sum = 0
+
+	MOVQ $0, SI   // i = 0
+	SUBQ $4, DI   // n -= 4
+	JL   tail_uni // if n < 0 goto tail_uni
+
+loop_uni:
+	// sum += x[i] * y[i] unrolled 4x.
+	MOVUPD 0(R8)(SI*8), X0
+	MOVUPD 0(R9)(SI*8), X1
+	MOVUPD 16(R8)(SI*8), X2
+	MOVUPD 16(R9)(SI*8), X3
+	MULPD  X1, X0
+	MULPD  X3, X2
+	ADDPD  X0, X7
+	ADDPD  X2, X8
+
+	ADDQ $4, SI   // i += 4
+	SUBQ $4, DI   // n -= 4
+	JGE  loop_uni // if n >= 0 goto loop_uni
+
+tail_uni:
+	ADDQ $4, DI  // n += 4
+	JLE  end_uni // if n <= 0 goto end_uni
+
+onemore_uni:
+	// sum += x[i] * y[i] for the remaining 1-3 elements.
+	MOVSD 0(R8)(SI*8), X0
+	MOVSD 0(R9)(SI*8), X1
+	MULSD X1, X0
+	ADDSD X0, X7
+
+	ADDQ $1, SI      // i++
+	SUBQ $1, DI      // n--
+	JNZ  onemore_uni // if n != 0 goto onemore_uni
+
+end_uni:
+	// Add the four sums together.
+	ADDPD    X8, X7
+	MOVSD    X7, X0
+	UNPCKHPD X7, X7
+	ADDSD    X0, X7
+	MOVSD    X7, sum+48(FP) // Return final sum.
+	RET
+
+// func DdotInc(x, y []float64, n, incX, incY, ix, iy uintptr) (sum float64)
+TEXT ·DotInc(SB), NOSPLIT, $0
+	MOVQ x+0(FP), R8
+	MOVQ y+24(FP), R9
+	MOVQ n+48(FP), CX
+	MOVQ incX+56(FP), R11
+	MOVQ incY+64(FP), R12
+	MOVQ ix+72(FP), R13
+	MOVQ iy+80(FP), R14
+
+	MOVSD $(0.0), X7      // sum = 0
+	LEAQ  (R8)(R13*8), SI // p = &x[ix]
+	LEAQ  (R9)(R14*8), DI // q = &y[ix]
+	SHLQ  $3, R11         // incX *= sizeof(float64)
+	SHLQ  $3, R12         // indY *= sizeof(float64)
+
+	SUBQ $2, CX   // n -= 2
+	JL   tail_inc // if n < 0 goto tail_inc
+
+loop_inc:
+	// sum += *p * *q unrolled 2x.
+	MOVHPD (SI), X0
+	MOVHPD (DI), X1
+	ADDQ   R11, SI  // p += incX
+	ADDQ   R12, DI  // q += incY
+	MOVLPD (SI), X0
+	MOVLPD (DI), X1
+	ADDQ   R11, SI  // p += incX
+	ADDQ   R12, DI  // q += incY
+
+	MULPD X1, X0
+	ADDPD X0, X7
+
+	SUBQ $2, CX   // n -= 2
+	JGE  loop_inc // if n >= 0 goto loop_inc
+
+tail_inc:
+	ADDQ $2, CX  // n += 2
+	JLE  end_inc // if n <= 0 goto end_inc
+
+	// sum += *p * *q for the last iteration if n is odd.
+	MOVSD (SI), X0
+	MULSD (DI), X0
+	ADDSD X0, X7
+
+end_inc:
+	// Add the two sums together.
+	MOVSD    X7, X0
+	UNPCKHPD X7, X7
+	ADDSD    X0, X7
+	MOVSD    X7, sum+88(FP) // Return final sum.
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/dot_test.go b/vendor/gonum.org/v1/gonum/internal/asm/f64/dot_test.go
new file mode 100644
index 00000000..5ca88b8b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/dot_test.go
@@ -0,0 +1,280 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package f64
+
+import (
+	"fmt"
+	"math"
+	"math/rand"
+	"testing"
+)
+
+func TestDotUnitary(t *testing.T) {
+	for i, test := range []struct {
+		xData []float64
+		yData []float64
+
+		want float64
+	}{
+		{
+			xData: []float64{2},
+			yData: []float64{-3},
+			want:  -6,
+		},
+		{
+			xData: []float64{2, 3},
+			yData: []float64{-3, 4},
+			want:  6,
+		},
+		{
+			xData: []float64{2, 3, -4},
+			yData: []float64{-3, 4, 5},
+			want:  -14,
+		},
+		{
+			xData: []float64{2, 3, -4, -5},
+			yData: []float64{-3, 4, 5, -6},
+			want:  16,
+		},
+		{
+			xData: []float64{0, 2, 3, -4, -5},
+			yData: []float64{0, -3, 4, 5, -6},
+			want:  16,
+		},
+		{
+			xData: []float64{0, 0, 2, 3, -4, -5},
+			yData: []float64{0, 1, -3, 4, 5, -6},
+			want:  16,
+		},
+		{
+			xData: []float64{0, 0, 1, 1, 2, -3, -4},
+			yData: []float64{0, 1, 0, 3, -4, 5, -6},
+			want:  4,
+		},
+		{
+			xData: []float64{0, 0, 1, 1, 2, -3, -4, 5},
+			yData: []float64{0, 1, 0, 3, -4, 5, -6, 7},
+			want:  39,
+		},
+	} {
+		const msgGuard = "test %v: out-of-bounds write to %v argument\nfront guard: %v\nback guard: %v"
+
+		x, xFront, xBack := newGuardedVector(test.xData, 1)
+		y, yFront, yBack := newGuardedVector(test.yData, 1)
+		got := DotUnitary(x, y)
+
+		if !allNaN(xFront) || !allNaN(xBack) {
+			t.Errorf(msgGuard, i, "x", xFront, xBack)
+		}
+		if !allNaN(yFront) || !allNaN(yBack) {
+			t.Errorf(msgGuard, i, "y", yFront, yBack)
+		}
+		if !equalStrided(test.xData, x, 1) {
+			t.Errorf("test %v: modified read-only x argument", i)
+		}
+		if !equalStrided(test.yData, y, 1) {
+			t.Errorf("test %v: modified read-only y argument", i)
+		}
+		if math.IsNaN(got) {
+			t.Errorf("test %v: invalid memory read", i)
+			continue
+		}
+
+		if got != test.want {
+			t.Errorf("test %v: unexpected result. want %v, got %v", i, test.want, got)
+		}
+	}
+}
+
+func TestDotInc(t *testing.T) {
+	for i, test := range []struct {
+		xData []float64
+		yData []float64
+
+		want    float64
+		wantRev float64 // Result when one of the vectors is reversed.
+	}{
+		{
+			xData:   []float64{2},
+			yData:   []float64{-3},
+			want:    -6,
+			wantRev: -6,
+		},
+		{
+			xData:   []float64{2, 3},
+			yData:   []float64{-3, 4},
+			want:    6,
+			wantRev: -1,
+		},
+		{
+			xData:   []float64{2, 3, -4},
+			yData:   []float64{-3, 4, 5},
+			want:    -14,
+			wantRev: 34,
+		},
+		{
+			xData:   []float64{2, 3, -4, -5},
+			yData:   []float64{-3, 4, 5, -6},
+			want:    16,
+			wantRev: 2,
+		},
+		{
+			xData:   []float64{0, 2, 3, -4, -5},
+			yData:   []float64{0, -3, 4, 5, -6},
+			want:    16,
+			wantRev: 34,
+		},
+		{
+			xData:   []float64{0, 0, 2, 3, -4, -5},
+			yData:   []float64{0, 1, -3, 4, 5, -6},
+			want:    16,
+			wantRev: -5,
+		},
+		{
+			xData:   []float64{0, 0, 1, 1, 2, -3, -4},
+			yData:   []float64{0, 1, 0, 3, -4, 5, -6},
+			want:    4,
+			wantRev: -4,
+		},
+		{
+			xData:   []float64{0, 0, 1, 1, 2, -3, -4, 5},
+			yData:   []float64{0, 1, 0, 3, -4, 5, -6, 7},
+			want:    39,
+			wantRev: 3,
+		},
+	} {
+		const msgGuard = "%v: out-of-bounds write to %v argument\nfront guard: %v\nback guard: %v"
+
+		for _, incX := range []int{-7, -3, -2, -1, 1, 2, 3, 7} {
+			for _, incY := range []int{-7, -3, -2, -1, 1, 2, 3, 7} {
+				n := len(test.xData)
+				x, xFront, xBack := newGuardedVector(test.xData, incX)
+				y, yFront, yBack := newGuardedVector(test.yData, incY)
+
+				var ix, iy int
+				if incX < 0 {
+					ix = (-n + 1) * incX
+				}
+				if incY < 0 {
+					iy = (-n + 1) * incY
+				}
+				got := DotInc(x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
+
+				prefix := fmt.Sprintf("test %v, incX = %v, incY = %v", i, incX, incY)
+				if !allNaN(xFront) || !allNaN(xBack) {
+					t.Errorf(msgGuard, prefix, "x", xFront, xBack)
+				}
+				if !allNaN(yFront) || !allNaN(yBack) {
+					t.Errorf(msgGuard, prefix, "y", yFront, yBack)
+				}
+				if nonStridedWrite(x, incX) || !equalStrided(test.xData, x, incX) {
+					t.Errorf("%v: modified read-only x argument", prefix)
+				}
+				if nonStridedWrite(y, incY) || !equalStrided(test.yData, y, incY) {
+					t.Errorf("%v: modified read-only y argument", prefix)
+				}
+				if math.IsNaN(got) {
+					t.Errorf("%v: invalid memory read", prefix)
+					continue
+				}
+
+				want := test.want
+				if incX*incY < 0 {
+					want = test.wantRev
+				}
+				if got != want {
+					t.Errorf("%v: unexpected result. want %v, got %v", prefix, want, got)
+				}
+			}
+		}
+	}
+}
+
+func BenchmarkDotUnitaryN1(b *testing.B)      { dotUnitaryBenchmark(b, 1) }
+func BenchmarkDotUnitaryN2(b *testing.B)      { dotUnitaryBenchmark(b, 2) }
+func BenchmarkDotUnitaryN3(b *testing.B)      { dotUnitaryBenchmark(b, 3) }
+func BenchmarkDotUnitaryN4(b *testing.B)      { dotUnitaryBenchmark(b, 4) }
+func BenchmarkDotUnitaryN10(b *testing.B)     { dotUnitaryBenchmark(b, 10) }
+func BenchmarkDotUnitaryN100(b *testing.B)    { dotUnitaryBenchmark(b, 100) }
+func BenchmarkDotUnitaryN1000(b *testing.B)   { dotUnitaryBenchmark(b, 1000) }
+func BenchmarkDotUnitaryN10000(b *testing.B)  { dotUnitaryBenchmark(b, 10000) }
+func BenchmarkDotUnitaryN100000(b *testing.B) { dotUnitaryBenchmark(b, 100000) }
+
+var r float64
+
+func dotUnitaryBenchmark(b *testing.B, n int) {
+	x := make([]float64, n)
+	for i := range x {
+		x[i] = rand.Float64()
+	}
+	y := make([]float64, n)
+	for i := range y {
+		y[i] = rand.Float64()
+	}
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		r = DotUnitary(x, y)
+	}
+}
+
+func BenchmarkDotIncN1Inc1(b *testing.B) { dotIncBenchmark(b, 1, 1) }
+
+func BenchmarkDotIncN2Inc1(b *testing.B)  { dotIncBenchmark(b, 2, 1) }
+func BenchmarkDotIncN2Inc2(b *testing.B)  { dotIncBenchmark(b, 2, 2) }
+func BenchmarkDotIncN2Inc4(b *testing.B)  { dotIncBenchmark(b, 2, 4) }
+func BenchmarkDotIncN2Inc10(b *testing.B) { dotIncBenchmark(b, 2, 10) }
+
+func BenchmarkDotIncN3Inc1(b *testing.B)  { dotIncBenchmark(b, 3, 1) }
+func BenchmarkDotIncN3Inc2(b *testing.B)  { dotIncBenchmark(b, 3, 2) }
+func BenchmarkDotIncN3Inc4(b *testing.B)  { dotIncBenchmark(b, 3, 4) }
+func BenchmarkDotIncN3Inc10(b *testing.B) { dotIncBenchmark(b, 3, 10) }
+
+func BenchmarkDotIncN4Inc1(b *testing.B)  { dotIncBenchmark(b, 4, 1) }
+func BenchmarkDotIncN4Inc2(b *testing.B)  { dotIncBenchmark(b, 4, 2) }
+func BenchmarkDotIncN4Inc4(b *testing.B)  { dotIncBenchmark(b, 4, 4) }
+func BenchmarkDotIncN4Inc10(b *testing.B) { dotIncBenchmark(b, 4, 10) }
+
+func BenchmarkDotIncN10Inc1(b *testing.B)  { dotIncBenchmark(b, 10, 1) }
+func BenchmarkDotIncN10Inc2(b *testing.B)  { dotIncBenchmark(b, 10, 2) }
+func BenchmarkDotIncN10Inc4(b *testing.B)  { dotIncBenchmark(b, 10, 4) }
+func BenchmarkDotIncN10Inc10(b *testing.B) { dotIncBenchmark(b, 10, 10) }
+
+func BenchmarkDotIncN1000Inc1(b *testing.B)  { dotIncBenchmark(b, 1000, 1) }
+func BenchmarkDotIncN1000Inc2(b *testing.B)  { dotIncBenchmark(b, 1000, 2) }
+func BenchmarkDotIncN1000Inc4(b *testing.B)  { dotIncBenchmark(b, 1000, 4) }
+func BenchmarkDotIncN1000Inc10(b *testing.B) { dotIncBenchmark(b, 1000, 10) }
+
+func BenchmarkDotIncN100000Inc1(b *testing.B)  { dotIncBenchmark(b, 100000, 1) }
+func BenchmarkDotIncN100000Inc2(b *testing.B)  { dotIncBenchmark(b, 100000, 2) }
+func BenchmarkDotIncN100000Inc4(b *testing.B)  { dotIncBenchmark(b, 100000, 4) }
+func BenchmarkDotIncN100000Inc10(b *testing.B) { dotIncBenchmark(b, 100000, 10) }
+
+func BenchmarkDotIncN100000IncM1(b *testing.B)  { dotIncBenchmark(b, 100000, -1) }
+func BenchmarkDotIncN100000IncM2(b *testing.B)  { dotIncBenchmark(b, 100000, -2) }
+func BenchmarkDotIncN100000IncM4(b *testing.B)  { dotIncBenchmark(b, 100000, -4) }
+func BenchmarkDotIncN100000IncM10(b *testing.B) { dotIncBenchmark(b, 100000, -10) }
+
+func dotIncBenchmark(b *testing.B, n, inc int) {
+	absInc := inc
+	if inc < 0 {
+		absInc = -inc
+	}
+	x := make([]float64, (n-1)*absInc+1)
+	for i := range x {
+		x[i] = rand.Float64()
+	}
+	y := make([]float64, (n-1)*absInc+1)
+	for i := range y {
+		y[i] = rand.Float64()
+	}
+	var ini int
+	if inc < 0 {
+		ini = (-n + 1) * inc
+	}
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		r = DotInc(x, y, uintptr(n), uintptr(inc), uintptr(inc), uintptr(ini), uintptr(ini))
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/l1norm_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/f64/l1norm_amd64.s
new file mode 100644
index 00000000..2a8c5a38
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/l1norm_amd64.s
@@ -0,0 +1,58 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build !noasm,!appengine
+
+#include "textflag.h"
+
+// func L1Dist(s, t []float64) float64
+TEXT ·L1Dist(SB), NOSPLIT, $0
+	MOVQ    s_base+0(FP), DI  // DI = &s
+	MOVQ    t_base+24(FP), SI // SI = &t
+	MOVQ    s_len+8(FP), CX   // CX = len(s)
+	CMPQ    t_len+32(FP), CX  // CX = max( CX, len(t) )
+	CMOVQLE t_len+32(FP), CX
+	PXOR    X3, X3            // norm = 0
+	CMPQ    CX, $0            // if CX == 0 { return 0 }
+	JE      l1_end
+	XORQ    AX, AX            // i = 0
+	MOVQ    CX, BX
+	ANDQ    $1, BX            // BX = CX % 2
+	SHRQ    $1, CX            // CX = floor( CX / 2 )
+	JZ      l1_tail_start     // if CX == 0 { return 0 }
+
+l1_loop: // Loop unrolled 2x  do {
+	MOVUPS (SI)(AX*8), X0 // X0 = t[i:i+1]
+	MOVUPS (DI)(AX*8), X1 // X1 = s[i:i+1]
+	MOVAPS X0, X2
+	SUBPD  X1, X0
+	SUBPD  X2, X1
+	MAXPD  X1, X0         // X0 = max( X0 - X1, X1 - X0 )
+	ADDPD  X0, X3         // norm += X0
+	ADDQ   $2, AX         // i += 2
+	LOOP   l1_loop        // } while --CX > 0
+	CMPQ   BX, $0         // if BX == 0 { return }
+	JE     l1_end
+
+l1_tail_start: // Reset loop registers
+	MOVQ BX, CX // Loop counter: CX = BX
+	PXOR X0, X0 // reset X0, X1 to break dependencies
+	PXOR X1, X1
+
+l1_tail:
+	MOVSD  (SI)(AX*8), X0 // X0 = t[i]
+	MOVSD  (DI)(AX*8), X1 // x1 = s[i]
+	MOVAPD X0, X2
+	SUBSD  X1, X0
+	SUBSD  X2, X1
+	MAXSD  X1, X0         // X0 = max( X0 - X1, X1 - X0 )
+	ADDSD  X0, X3         // norm += X0
+
+l1_end:
+	MOVAPS X3, X2
+	SHUFPD $1, X2, X2
+	ADDSD  X3, X2         // X2 = X3[1] + X3[0]
+	MOVSD  X2, ret+48(FP) // return X2
+	RET
+
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/linfnorm_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/f64/linfnorm_amd64.s
new file mode 100644
index 00000000..fb6ef8d2
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/linfnorm_amd64.s
@@ -0,0 +1,57 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build !noasm,!appengine
+
+#include "textflag.h"
+
+// func LinfDist(s, t []float64) float64
+TEXT ·LinfDist(SB), NOSPLIT, $0
+	MOVQ    s_base+0(FP), DI  // DI = &s
+	MOVQ    t_base+24(FP), SI // SI = &t
+	MOVQ    s_len+8(FP), CX   // CX = len(s)
+	CMPQ    t_len+32(FP), CX  // CX = max( CX, len(t) )
+	CMOVQLE t_len+32(FP), CX
+	PXOR    X3, X3            // norm = 0
+	CMPQ    CX, $0            // if CX == 0 { return 0 }
+	JE      l1_end
+	XORQ    AX, AX            // i = 0
+	MOVQ    CX, BX
+	ANDQ    $1, BX            // BX = CX % 2
+	SHRQ    $1, CX            // CX = floor( CX / 2 )
+	JZ      l1_tail_start     // if CX == 0 { return 0 }
+
+l1_loop: // Loop unrolled 2x  do {
+	MOVUPS (SI)(AX*8), X0 // X0 = t[i:i+1]
+	MOVUPS (DI)(AX*8), X1 // X1 = s[i:i+1]
+	MOVAPS X0, X2
+	SUBPD  X1, X0
+	SUBPD  X2, X1
+	MAXPD  X1, X0         // X0 = max( X0 - X1, X1 - X0 )
+	MAXPD  X0, X3         // norm = max( norm, X0 )
+	ADDQ   $2, AX         // i += 2
+	LOOP   l1_loop        // } while --CX > 0
+	CMPQ   BX, $0         // if BX == 0 { return }
+	JE     l1_end
+
+l1_tail_start: // Reset loop registers
+	MOVQ BX, CX // Loop counter: CX = BX
+	PXOR X0, X0 // reset X0, X1 to break dependencies
+	PXOR X1, X1
+
+l1_tail:
+	MOVSD  (SI)(AX*8), X0 // X0 = t[i]
+	MOVSD  (DI)(AX*8), X1 // X1 = s[i]
+	MOVAPD X0, X2
+	SUBSD  X1, X0
+	SUBSD  X2, X1
+	MAXSD  X1, X0         // X0 = max( X0 - X1, X1 - X0 )
+	MAXSD  X0, X3         // norm = max( norm, X0 )
+
+l1_end:
+	MOVAPS X3, X2
+	SHUFPD $1, X2, X2
+	MAXSD  X3, X2         // X2 = max( X3[1], X3[0] )
+	MOVSD  X2, ret+48(FP) // return X2
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/scal.go b/vendor/gonum.org/v1/gonum/internal/asm/f64/scal.go
new file mode 100644
index 00000000..357e6c4a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/scal.go
@@ -0,0 +1,57 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !amd64 noasm appengine
+
+package f64
+
+// ScalUnitary is
+//  for i := range x {
+//  	x[i] *= alpha
+//  }
+func ScalUnitary(alpha float64, x []float64) {
+	for i := range x {
+		x[i] *= alpha
+	}
+}
+
+// ScalUnitaryTo is
+//  for i, v := range x {
+//  	dst[i] = alpha * v
+//  }
+func ScalUnitaryTo(dst []float64, alpha float64, x []float64) {
+	for i, v := range x {
+		dst[i] = alpha * v
+	}
+}
+
+// ScalInc is
+//  var ix uintptr
+//  for i := 0; i < int(n); i++ {
+//  	x[ix] *= alpha
+//  	ix += incX
+//  }
+func ScalInc(alpha float64, x []float64, n, incX uintptr) {
+	var ix uintptr
+	for i := 0; i < int(n); i++ {
+		x[ix] *= alpha
+		ix += incX
+	}
+}
+
+// ScalIncTo is
+//  var idst, ix uintptr
+//  for i := 0; i < int(n); i++ {
+//  	dst[idst] = alpha * x[ix]
+//  	ix += incX
+//  	idst += incDst
+//  }
+func ScalIncTo(dst []float64, incDst uintptr, alpha float64, x []float64, n, incX uintptr) {
+	var idst, ix uintptr
+	for i := 0; i < int(n); i++ {
+		dst[idst] = alpha * x[ix]
+		ix += incX
+		idst += incDst
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/scal_test.go b/vendor/gonum.org/v1/gonum/internal/asm/f64/scal_test.go
new file mode 100644
index 00000000..d88b7d10
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/scal_test.go
@@ -0,0 +1,179 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package f64
+
+import (
+	"fmt"
+	"math/rand"
+	"testing"
+)
+
+var scalTests = []struct {
+	alpha float64
+	x     []float64
+	want  []float64
+}{
+	{
+		alpha: 0,
+		x:     []float64{},
+		want:  []float64{},
+	},
+	{
+		alpha: 0,
+		x:     []float64{1},
+		want:  []float64{0},
+	},
+	{
+		alpha: 1,
+		x:     []float64{1},
+		want:  []float64{1},
+	},
+	{
+		alpha: 2,
+		x:     []float64{1, -2},
+		want:  []float64{2, -4},
+	},
+	{
+		alpha: 2,
+		x:     []float64{1, -2, 3},
+		want:  []float64{2, -4, 6},
+	},
+	{
+		alpha: 2,
+		x:     []float64{1, -2, 3, 4},
+		want:  []float64{2, -4, 6, 8},
+	},
+	{
+		alpha: 2,
+		x:     []float64{1, -2, 3, 4, -5},
+		want:  []float64{2, -4, 6, 8, -10},
+	},
+	{
+		alpha: 2,
+		x:     []float64{0, 1, -2, 3, 4, -5, 6, -7},
+		want:  []float64{0, 2, -4, 6, 8, -10, 12, -14},
+	},
+	{
+		alpha: 2,
+		x:     []float64{0, 1, -2, 3, 4, -5, 6, -7, 8},
+		want:  []float64{0, 2, -4, 6, 8, -10, 12, -14, 16},
+	},
+	{
+		alpha: 2,
+		x:     []float64{0, 1, -2, 3, 4, -5, 6, -7, 8, 9},
+		want:  []float64{0, 2, -4, 6, 8, -10, 12, -14, 16, 18},
+	},
+	{
+		alpha: 3,
+		x:     []float64{0, 1, -2, 3, 4, -5, 6, -7, 8, 9, 12},
+		want:  []float64{0, 3, -6, 9, 12, -15, 18, -21, 24, 27, 36},
+	},
+}
+
+func TestScalUnitary(t *testing.T) {
+	const xGdVal = -0.5
+	for i, test := range scalTests {
+		for _, align := range align1 {
+			prefix := fmt.Sprintf("Test %v (x:%v)", i, align)
+			xgLn := 4 + align
+			xg := guardVector(test.x, xGdVal, xgLn)
+			x := xg[xgLn : len(xg)-xgLn]
+
+			ScalUnitary(test.alpha, x)
+
+			for i := range test.want {
+				if !same(x[i], test.want[i]) {
+					t.Errorf(msgVal, prefix, i, x[i], test.want[i])
+				}
+			}
+			if !isValidGuard(xg, xGdVal, xgLn) {
+				t.Errorf(msgGuard, prefix, "x", xg[:xgLn], xg[len(xg)-xgLn:])
+			}
+		}
+	}
+}
+
+func TestScalUnitaryTo(t *testing.T) {
+	const xGdVal, dstGdVal = -1, 0.5
+	rng := rand.New(rand.NewSource(42))
+	for i, test := range scalTests {
+		n := len(test.x)
+		for _, align := range align2 {
+			prefix := fmt.Sprintf("Test %v (x:%v dst:%v)", i, align.x, align.y)
+			xgLn, dgLn := 4+align.x, 4+align.y
+			xg := guardVector(test.x, xGdVal, xgLn)
+			dg := guardVector(randSlice(n, 1, rng), dstGdVal, dgLn)
+			x, dst := xg[xgLn:len(xg)-xgLn], dg[dgLn:len(dg)-dgLn]
+
+			ScalUnitaryTo(dst, test.alpha, x)
+
+			for i := range test.want {
+				if !same(dst[i], test.want[i]) {
+					t.Errorf(msgVal, prefix, i, dst[i], test.want[i])
+				}
+			}
+			if !isValidGuard(xg, xGdVal, xgLn) {
+				t.Errorf(msgGuard, prefix, "x", xg[:xgLn], xg[len(xg)-xgLn:])
+			}
+			if !isValidGuard(dg, dstGdVal, dgLn) {
+				t.Errorf(msgGuard, prefix, "y", dg[:dgLn], dg[len(dg)-dgLn:])
+			}
+			if !equalStrided(test.x, x, 1) {
+				t.Errorf("%v: modified read-only x argument", prefix)
+			}
+		}
+	}
+}
+
+func TestScalInc(t *testing.T) {
+	const xGdVal = -0.5
+	gdLn := 4
+	for i, test := range scalTests {
+		n := len(test.x)
+		for _, incX := range []int{1, 2, 3, 4, 7, 10} {
+			prefix := fmt.Sprintf("Test %v (x:%v)", i, incX)
+			xg := guardIncVector(test.x, xGdVal, incX, gdLn)
+			x := xg[gdLn : len(xg)-gdLn]
+
+			ScalInc(test.alpha, x, uintptr(n), uintptr(incX))
+
+			for i := range test.want {
+				if !same(x[i*incX], test.want[i]) {
+					t.Errorf(msgVal, prefix, i, x[i*incX], test.want[i])
+				}
+			}
+			checkValidIncGuard(t, xg, xGdVal, incX, gdLn)
+		}
+	}
+}
+
+func TestScalIncTo(t *testing.T) {
+	const xGdVal, dstGdVal = -1, 0.5
+	gdLn := 4
+	rng := rand.New(rand.NewSource(42))
+	for i, test := range scalTests {
+		n := len(test.x)
+		for _, inc := range newIncSet(1, 2, 3, 4, 7, 10) {
+			prefix := fmt.Sprintf("test %v (x:%v dst:%v)", i, inc.x, inc.y)
+			xg := guardIncVector(test.x, xGdVal, inc.x, gdLn)
+			dg := guardIncVector(randSlice(n, 1, rng), dstGdVal, inc.y, gdLn)
+			x, dst := xg[gdLn:len(xg)-gdLn], dg[gdLn:len(dg)-gdLn]
+
+			ScalIncTo(dst, uintptr(inc.y), test.alpha, x, uintptr(n), uintptr(inc.x))
+
+			for i := range test.want {
+				if !same(dst[i*inc.y], test.want[i]) {
+					t.Errorf(msgVal, prefix, i, dst[i*inc.y], test.want[i])
+				}
+			}
+			checkValidIncGuard(t, xg, xGdVal, inc.x, gdLn)
+			checkValidIncGuard(t, dg, dstGdVal, inc.y, gdLn)
+			if !equalStrided(test.x, x, inc.x) {
+				t.Errorf("%v: modified read-only x argument", prefix)
+			}
+
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/scalinc_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/f64/scalinc_amd64.s
new file mode 100644
index 00000000..55a5758e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/scalinc_amd64.s
@@ -0,0 +1,113 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Some of the loop unrolling code is copied from:
+// http://golang.org/src/math/big/arith_amd64.s
+// which is distributed under these terms:
+//
+// Copyright (c) 2012 The Go Authors. All rights reserved.
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+//    * Redistributions of source code must retain the above copyright
+// notice, this list of conditions and the following disclaimer.
+//    * Redistributions in binary form must reproduce the above
+// copyright notice, this list of conditions and the following disclaimer
+// in the documentation and/or other materials provided with the
+// distribution.
+//    * Neither the name of Google Inc. nor the names of its
+// contributors may be used to endorse or promote products derived from
+// this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+//+build !noasm,!appengine
+
+#include "textflag.h"
+
+#define X_PTR SI
+#define LEN CX
+#define TAIL BX
+#define INC_X R8
+#define INCx3_X R9
+#define ALPHA X0
+#define ALPHA_2 X1
+
+// func ScalInc(alpha float64, x []float64, n, incX uintptr)
+TEXT ·ScalInc(SB), NOSPLIT, $0
+	MOVSD alpha+0(FP), ALPHA  // ALPHA = alpha
+	MOVQ  x_base+8(FP), X_PTR // X_PTR = &x
+	MOVQ  incX+40(FP), INC_X  // INC_X = incX
+	SHLQ  $3, INC_X           // INC_X *= sizeof(float64)
+	MOVQ  n+32(FP), LEN       // LEN = n
+	CMPQ  LEN, $0
+	JE    end                 // if LEN == 0 { return }
+
+	MOVQ LEN, TAIL
+	ANDQ $3, TAIL   // TAIL = LEN % 4
+	SHRQ $2, LEN    // LEN = floor( LEN / 4 )
+	JZ   tail_start // if LEN == 0 { goto tail_start }
+
+	MOVUPS ALPHA, ALPHA_2            // ALPHA_2 = ALPHA for pipelining
+	LEAQ   (INC_X)(INC_X*2), INCx3_X // INCx3_X = INC_X * 3
+
+loop:  // do { // x[i] *= alpha unrolled 4x.
+	MOVSD (X_PTR), X2            // X_i = x[i]
+	MOVSD (X_PTR)(INC_X*1), X3
+	MOVSD (X_PTR)(INC_X*2), X4
+	MOVSD (X_PTR)(INCx3_X*1), X5
+
+	MULSD ALPHA, X2   // X_i *= a
+	MULSD ALPHA_2, X3
+	MULSD ALPHA, X4
+	MULSD ALPHA_2, X5
+
+	MOVSD X2, (X_PTR)            // x[i] = X_i
+	MOVSD X3, (X_PTR)(INC_X*1)
+	MOVSD X4, (X_PTR)(INC_X*2)
+	MOVSD X5, (X_PTR)(INCx3_X*1)
+
+	LEAQ (X_PTR)(INC_X*4), X_PTR // X_PTR = &(X_PTR[incX*4])
+	DECQ LEN
+	JNZ  loop                    // } while --LEN > 0
+	CMPQ TAIL, $0
+	JE   end                     // if TAIL == 0 { return }
+
+tail_start: // Reset loop registers
+	MOVQ TAIL, LEN // Loop counter: LEN = TAIL
+	SHRQ $1, LEN   // LEN = floor( LEN / 2 )
+	JZ   tail_one
+
+tail_two: // do {
+	MOVSD (X_PTR), X2          // X_i = x[i]
+	MOVSD (X_PTR)(INC_X*1), X3
+	MULSD ALPHA, X2            // X_i *= a
+	MULSD ALPHA, X3
+	MOVSD X2, (X_PTR)          // x[i] = X_i
+	MOVSD X3, (X_PTR)(INC_X*1)
+
+	LEAQ (X_PTR)(INC_X*2), X_PTR // X_PTR = &(X_PTR[incX*2])
+
+	ANDQ $1, TAIL
+	JZ   end
+
+tail_one:
+	MOVSD (X_PTR), X2 // X_i = x[i]
+	MULSD ALPHA, X2   // X_i *= ALPHA
+	MOVSD X2, (X_PTR) // x[i] = X_i
+
+end:
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/scalincto_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/f64/scalincto_amd64.s
new file mode 100644
index 00000000..57c90a2a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/scalincto_amd64.s
@@ -0,0 +1,122 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Some of the loop unrolling code is copied from:
+// http://golang.org/src/math/big/arith_amd64.s
+// which is distributed under these terms:
+//
+// Copyright (c) 2012 The Go Authors. All rights reserved.
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+//    * Redistributions of source code must retain the above copyright
+// notice, this list of conditions and the following disclaimer.
+//    * Redistributions in binary form must reproduce the above
+// copyright notice, this list of conditions and the following disclaimer
+// in the documentation and/or other materials provided with the
+// distribution.
+//    * Neither the name of Google Inc. nor the names of its
+// contributors may be used to endorse or promote products derived from
+// this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+//+build !noasm,!appengine
+
+#include "textflag.h"
+
+#define X_PTR SI
+#define DST_PTR DI
+#define LEN CX
+#define TAIL BX
+#define INC_X R8
+#define INCx3_X R9
+#define INC_DST R10
+#define INCx3_DST R11
+#define ALPHA X0
+#define ALPHA_2 X1
+
+// func ScalIncTo(dst []float64, incDst uintptr, alpha float64, x []float64, n, incX uintptr)
+TEXT ·ScalIncTo(SB), NOSPLIT, $0
+	MOVQ  dst_base+0(FP), DST_PTR // DST_PTR = &dst
+	MOVQ  incDst+24(FP), INC_DST  // INC_DST = incDst
+	SHLQ  $3, INC_DST             // INC_DST *= sizeof(float64)
+	MOVSD alpha+32(FP), ALPHA     // ALPHA = alpha
+	MOVQ  x_base+40(FP), X_PTR    // X_PTR = &x
+	MOVQ  n+64(FP), LEN           // LEN = n
+	MOVQ  incX+72(FP), INC_X      // INC_X = incX
+	SHLQ  $3, INC_X               // INC_X *= sizeof(float64)
+	CMPQ  LEN, $0
+	JE    end                     // if LEN == 0 { return }
+
+	MOVQ LEN, TAIL
+	ANDQ $3, TAIL   // TAIL = LEN % 4
+	SHRQ $2, LEN    // LEN = floor( LEN / 4 )
+	JZ   tail_start // if LEN == 0 { goto tail_start }
+
+	MOVUPS ALPHA, ALPHA_2                  // ALPHA_2 = ALPHA for pipelining
+	LEAQ   (INC_X)(INC_X*2), INCx3_X       // INCx3_X = INC_X * 3
+	LEAQ   (INC_DST)(INC_DST*2), INCx3_DST // INCx3_DST = INC_DST * 3
+
+loop:  // do { // x[i] *= alpha unrolled 4x.
+	MOVSD (X_PTR), X2            // X_i = x[i]
+	MOVSD (X_PTR)(INC_X*1), X3
+	MOVSD (X_PTR)(INC_X*2), X4
+	MOVSD (X_PTR)(INCx3_X*1), X5
+
+	MULSD ALPHA, X2   // X_i *= a
+	MULSD ALPHA_2, X3
+	MULSD ALPHA, X4
+	MULSD ALPHA_2, X5
+
+	MOVSD X2, (DST_PTR)              // dst[i] = X_i
+	MOVSD X3, (DST_PTR)(INC_DST*1)
+	MOVSD X4, (DST_PTR)(INC_DST*2)
+	MOVSD X5, (DST_PTR)(INCx3_DST*1)
+
+	LEAQ (X_PTR)(INC_X*4), X_PTR       // X_PTR = &(X_PTR[incX*4])
+	LEAQ (DST_PTR)(INC_DST*4), DST_PTR // DST_PTR = &(DST_PTR[incDst*4])
+	DECQ LEN
+	JNZ  loop                          // } while --LEN > 0
+	CMPQ TAIL, $0
+	JE   end                           // if TAIL == 0 { return }
+
+tail_start: // Reset loop registers
+	MOVQ TAIL, LEN // Loop counter: LEN = TAIL
+	SHRQ $1, LEN   // LEN = floor( LEN / 2 )
+	JZ   tail_one
+
+tail_two:
+	MOVSD (X_PTR), X2              // X_i = x[i]
+	MOVSD (X_PTR)(INC_X*1), X3
+	MULSD ALPHA, X2                // X_i *= a
+	MULSD ALPHA, X3
+	MOVSD X2, (DST_PTR)            // dst[i] = X_i
+	MOVSD X3, (DST_PTR)(INC_DST*1)
+
+	LEAQ (X_PTR)(INC_X*2), X_PTR       // X_PTR = &(X_PTR[incX*2])
+	LEAQ (DST_PTR)(INC_DST*2), DST_PTR // DST_PTR = &(DST_PTR[incDst*2])
+
+	ANDQ $1, TAIL
+	JZ   end
+
+tail_one:
+	MOVSD (X_PTR), X2   // X_i = x[i]
+	MULSD ALPHA, X2     // X_i *= ALPHA
+	MOVSD X2, (DST_PTR) // x[i] = X_i
+
+end:
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/scalunitary_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/f64/scalunitary_amd64.s
new file mode 100644
index 00000000..da23af77
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/scalunitary_amd64.s
@@ -0,0 +1,112 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Some of the loop unrolling code is copied from:
+// http://golang.org/src/math/big/arith_amd64.s
+// which is distributed under these terms:
+//
+// Copyright (c) 2012 The Go Authors. All rights reserved.
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+//    * Redistributions of source code must retain the above copyright
+// notice, this list of conditions and the following disclaimer.
+//    * Redistributions in binary form must reproduce the above
+// copyright notice, this list of conditions and the following disclaimer
+// in the documentation and/or other materials provided with the
+// distribution.
+//    * Neither the name of Google Inc. nor the names of its
+// contributors may be used to endorse or promote products derived from
+// this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+//+build !noasm,!appengine
+
+#include "textflag.h"
+
+#define MOVDDUP_ALPHA    LONG $0x44120FF2; WORD $0x0824 // @ MOVDDUP XMM0, 8[RSP]
+
+#define X_PTR SI
+#define DST_PTR DI
+#define IDX AX
+#define LEN CX
+#define TAIL BX
+#define ALPHA X0
+#define ALPHA_2 X1
+
+// func ScalUnitary(alpha float64, x []float64)
+TEXT ·ScalUnitary(SB), NOSPLIT, $0
+	MOVDDUP_ALPHA            // ALPHA = { alpha, alpha }
+	MOVQ x_base+8(FP), X_PTR // X_PTR = &x
+	MOVQ x_len+16(FP), LEN   // LEN = len(x)
+	CMPQ LEN, $0
+	JE   end                 // if LEN == 0 { return }
+	XORQ IDX, IDX            // IDX = 0
+
+	MOVQ LEN, TAIL
+	ANDQ $7, TAIL   // TAIL = LEN % 8
+	SHRQ $3, LEN    // LEN = floor( LEN / 8 )
+	JZ   tail_start // if LEN == 0 { goto tail_start }
+
+	MOVUPS ALPHA, ALPHA_2
+
+loop:  // do {  // x[i] *= alpha unrolled 8x.
+	MOVUPS (X_PTR)(IDX*8), X2   // X_i = x[i]
+	MOVUPS 16(X_PTR)(IDX*8), X3
+	MOVUPS 32(X_PTR)(IDX*8), X4
+	MOVUPS 48(X_PTR)(IDX*8), X5
+
+	MULPD ALPHA, X2   // X_i *= ALPHA
+	MULPD ALPHA_2, X3
+	MULPD ALPHA, X4
+	MULPD ALPHA_2, X5
+
+	MOVUPS X2, (X_PTR)(IDX*8)   // x[i] = X_i
+	MOVUPS X3, 16(X_PTR)(IDX*8)
+	MOVUPS X4, 32(X_PTR)(IDX*8)
+	MOVUPS X5, 48(X_PTR)(IDX*8)
+
+	ADDQ $8, IDX  // i += 8
+	DECQ LEN
+	JNZ  loop     // while --LEN > 0
+	CMPQ TAIL, $0
+	JE   end      // if TAIL == 0 { return }
+
+tail_start: // Reset loop registers
+	MOVQ TAIL, LEN // Loop counter: LEN = TAIL
+	SHRQ $1, LEN   // LEN = floor( TAIL / 2 )
+	JZ   tail_one  // if n == 0 goto end
+
+tail_two: // do {
+	MOVUPS (X_PTR)(IDX*8), X2 // X_i = x[i]
+	MULPD  ALPHA, X2          // X_i *= ALPHA
+	MOVUPS X2, (X_PTR)(IDX*8) // x[i] = X_i
+	ADDQ   $2, IDX            // i += 2
+	DECQ   LEN
+	JNZ    tail_two           // while --LEN > 0
+
+	ANDQ $1, TAIL
+	JZ   end      // if TAIL == 0 { return }
+
+tail_one:
+	// x[i] *= alpha for the remaining element.
+	MOVSD (X_PTR)(IDX*8), X2
+	MULSD ALPHA, X2
+	MOVSD X2, (X_PTR)(IDX*8)
+
+end:
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/scalunitaryto_amd64.s b/vendor/gonum.org/v1/gonum/internal/asm/f64/scalunitaryto_amd64.s
new file mode 100644
index 00000000..3685d5b5
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/scalunitaryto_amd64.s
@@ -0,0 +1,113 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+//
+// Some of the loop unrolling code is copied from:
+// http://golang.org/src/math/big/arith_amd64.s
+// which is distributed under these terms:
+//
+// Copyright (c) 2012 The Go Authors. All rights reserved.
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+//    * Redistributions of source code must retain the above copyright
+// notice, this list of conditions and the following disclaimer.
+//    * Redistributions in binary form must reproduce the above
+// copyright notice, this list of conditions and the following disclaimer
+// in the documentation and/or other materials provided with the
+// distribution.
+//    * Neither the name of Google Inc. nor the names of its
+// contributors may be used to endorse or promote products derived from
+// this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+//+build !noasm,!appengine
+
+#include "textflag.h"
+
+#define MOVDDUP_ALPHA    LONG $0x44120FF2; WORD $0x2024 // @ MOVDDUP 32(SP), X0  /*XMM0, 32[RSP]*/
+
+#define X_PTR SI
+#define DST_PTR DI
+#define IDX AX
+#define LEN CX
+#define TAIL BX
+#define ALPHA X0
+#define ALPHA_2 X1
+
+// func ScalUnitaryTo(dst []float64, alpha float64, x []float64)
+// This function assumes len(dst) >= len(x).
+TEXT ·ScalUnitaryTo(SB), NOSPLIT, $0
+	MOVQ x_base+32(FP), X_PTR    // X_PTR = &x
+	MOVQ dst_base+0(FP), DST_PTR // DST_PTR = &dst
+	MOVDDUP_ALPHA                // ALPHA = { alpha, alpha }
+	MOVQ x_len+40(FP), LEN       // LEN = len(x)
+	CMPQ LEN, $0
+	JE   end                     // if LEN == 0 { return }
+
+	XORQ IDX, IDX   // IDX = 0
+	MOVQ LEN, TAIL
+	ANDQ $7, TAIL   // TAIL = LEN % 8
+	SHRQ $3, LEN    // LEN = floor( LEN / 8 )
+	JZ   tail_start // if LEN == 0 { goto tail_start }
+
+	MOVUPS ALPHA, ALPHA_2 // ALPHA_2 = ALPHA for pipelining
+
+loop:  // do { // dst[i] = alpha * x[i] unrolled 8x.
+	MOVUPS (X_PTR)(IDX*8), X2   // X_i = x[i]
+	MOVUPS 16(X_PTR)(IDX*8), X3
+	MOVUPS 32(X_PTR)(IDX*8), X4
+	MOVUPS 48(X_PTR)(IDX*8), X5
+
+	MULPD ALPHA, X2   // X_i *= ALPHA
+	MULPD ALPHA_2, X3
+	MULPD ALPHA, X4
+	MULPD ALPHA_2, X5
+
+	MOVUPS X2, (DST_PTR)(IDX*8)   // dst[i] = X_i
+	MOVUPS X3, 16(DST_PTR)(IDX*8)
+	MOVUPS X4, 32(DST_PTR)(IDX*8)
+	MOVUPS X5, 48(DST_PTR)(IDX*8)
+
+	ADDQ $8, IDX  // i += 8
+	DECQ LEN
+	JNZ  loop     // while --LEN > 0
+	CMPQ TAIL, $0
+	JE   end      // if TAIL == 0 { return }
+
+tail_start: // Reset loop counters
+	MOVQ TAIL, LEN // Loop counter: LEN = TAIL
+	SHRQ $1, LEN   // LEN = floor( TAIL / 2 )
+	JZ   tail_one  // if LEN == 0 { goto tail_one }
+
+tail_two: // do {
+	MOVUPS (X_PTR)(IDX*8), X2   // X_i = x[i]
+	MULPD  ALPHA, X2            // X_i *= ALPHA
+	MOVUPS X2, (DST_PTR)(IDX*8) // dst[i] = X_i
+	ADDQ   $2, IDX              // i += 2
+	DECQ   LEN
+	JNZ    tail_two             // while --LEN > 0
+
+	ANDQ $1, TAIL
+	JZ   end      // if TAIL == 0 { return }
+
+tail_one:
+	MOVSD (X_PTR)(IDX*8), X2   // X_i = x[i]
+	MULSD ALPHA, X2            // X_i *= ALPHA
+	MOVSD X2, (DST_PTR)(IDX*8) // dst[i] = X_i
+
+end:
+	RET
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/stubs_amd64.go b/vendor/gonum.org/v1/gonum/internal/asm/f64/stubs_amd64.go
new file mode 100644
index 00000000..d4de1919
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/stubs_amd64.go
@@ -0,0 +1,165 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !noasm,!appengine
+
+package f64
+
+// L1Norm is
+//  for _, v := range x {
+//  	sum += math.Abs(v)
+//  }
+//  return sum
+func L1Norm(x []float64) (sum float64)
+
+// L1NormInc is
+//  for i := 0; i < n*incX; i += incX {
+//  	sum += math.Abs(x[i])
+//  }
+//  return sum
+func L1NormInc(x []float64, n, incX int) (sum float64)
+
+// AddConst is
+//  for i := range x {
+//  	x[i] += alpha
+//  }
+func AddConst(alpha float64, x []float64)
+
+// Add is
+//  for i, v := range s {
+//  	dst[i] += v
+//  }
+func Add(dst, s []float64)
+
+// AxpyUnitary is
+//  for i, v := range x {
+//  	y[i] += alpha * v
+//  }
+func AxpyUnitary(alpha float64, x, y []float64)
+
+// AxpyUnitaryTo is
+//  for i, v := range x {
+//  	dst[i] = alpha*v + y[i]
+//  }
+func AxpyUnitaryTo(dst []float64, alpha float64, x, y []float64)
+
+// AxpyInc is
+//  for i := 0; i < int(n); i++ {
+//  	y[iy] += alpha * x[ix]
+//  	ix += incX
+//  	iy += incY
+//  }
+func AxpyInc(alpha float64, x, y []float64, n, incX, incY, ix, iy uintptr)
+
+// AxpyIncTo is
+//  for i := 0; i < int(n); i++ {
+//  	dst[idst] = alpha*x[ix] + y[iy]
+//  	ix += incX
+//  	iy += incY
+//  	idst += incDst
+//  }
+func AxpyIncTo(dst []float64, incDst, idst uintptr, alpha float64, x, y []float64, n, incX, incY, ix, iy uintptr)
+
+// CumSum is
+//  if len(s) == 0 {
+//  	return dst
+//  }
+//  dst[0] = s[0]
+//  for i, v := range s[1:] {
+//  	dst[i+1] = dst[i] + v
+//  }
+//  return dst
+func CumSum(dst, s []float64) []float64
+
+// CumProd is
+//  if len(s) == 0 {
+//  	return dst
+//  }
+//  dst[0] = s[0]
+//  for i, v := range s[1:] {
+//  	dst[i+1] = dst[i] * v
+//  }
+//  return dst
+func CumProd(dst, s []float64) []float64
+
+// Div is
+//  for i, v := range s {
+//  	dst[i] /= v
+//  }
+func Div(dst, s []float64)
+
+// DivTo is
+//  for i, v := range s {
+//  	dst[i] = v / t[i]
+//  }
+//  return dst
+func DivTo(dst, x, y []float64) []float64
+
+// DotUnitary is
+//  for i, v := range x {
+//  	sum += y[i] * v
+//  }
+//  return sum
+func DotUnitary(x, y []float64) (sum float64)
+
+// DotInc is
+//  for i := 0; i < int(n); i++ {
+//  	sum += y[iy] * x[ix]
+//  	ix += incX
+//  	iy += incY
+//  }
+//  return sum
+func DotInc(x, y []float64, n, incX, incY, ix, iy uintptr) (sum float64)
+
+// L1Dist is
+//  var norm float64
+//  for i, v := range s {
+//  	norm += math.Abs(t[i] - v)
+//  }
+//  return norm
+func L1Dist(s, t []float64) float64
+
+// LinfDist is
+//  var norm float64
+//  if len(s) == 0 {
+//  	return 0
+//  }
+//  norm = math.Abs(t[0] - s[0])
+//  for i, v := range s[1:] {
+//  	absDiff := math.Abs(t[i+1] - v)
+//  	if absDiff > norm || math.IsNaN(norm) {
+//  		norm = absDiff
+//  	}
+//  }
+//  return norm
+func LinfDist(s, t []float64) float64
+
+// ScalUnitary is
+//  for i := range x {
+//  	x[i] *= alpha
+//  }
+func ScalUnitary(alpha float64, x []float64)
+
+// ScalUnitaryTo is
+//  for i, v := range x {
+//  	dst[i] = alpha * v
+//  }
+func ScalUnitaryTo(dst []float64, alpha float64, x []float64)
+
+// ScalInc is
+//  var ix uintptr
+//  for i := 0; i < int(n); i++ {
+//  	x[ix] *= alpha
+//  	ix += incX
+//  }
+func ScalInc(alpha float64, x []float64, n, incX uintptr)
+
+// ScalIncTo is
+//  var idst, ix uintptr
+//  for i := 0; i < int(n); i++ {
+//  	dst[idst] = alpha * x[ix]
+//  	ix += incX
+//  	idst += incDst
+//  }
+func ScalIncTo(dst []float64, incDst uintptr, alpha float64, x []float64, n, incX uintptr)
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/stubs_noasm.go b/vendor/gonum.org/v1/gonum/internal/asm/f64/stubs_noasm.go
new file mode 100644
index 00000000..5e4ae69c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/stubs_noasm.go
@@ -0,0 +1,157 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !amd64 noasm appengine
+
+package f64
+
+import "math"
+
+// L1Norm is
+//  for _, v := range x {
+//  	sum += math.Abs(v)
+//  }
+//  return sum
+func L1Norm(x []float64) (sum float64) {
+	for _, v := range x {
+		sum += math.Abs(v)
+	}
+	return sum
+}
+
+// L1NormInc is
+//  for i := 0; i < n*incX; i += incX {
+//  	sum += math.Abs(x[i])
+//  }
+//  return sum
+func L1NormInc(x []float64, n, incX int) (sum float64) {
+	for i := 0; i < n*incX; i += incX {
+		sum += math.Abs(x[i])
+	}
+	return sum
+}
+
+// Add is
+//  for i, v := range s {
+//  	dst[i] += v
+//  }
+func Add(dst, s []float64) {
+	for i, v := range s {
+		dst[i] += v
+	}
+}
+
+// AddConst is
+//  for i := range x {
+//  	x[i] += alpha
+//  }
+func AddConst(alpha float64, x []float64) {
+	for i := range x {
+		x[i] += alpha
+	}
+}
+
+// CumSum is
+//  if len(s) == 0 {
+//  	return dst
+//  }
+//  dst[0] = s[0]
+//  for i, v := range s[1:] {
+//  	dst[i+1] = dst[i] + v
+//  }
+//  return dst
+func CumSum(dst, s []float64) []float64 {
+	if len(s) == 0 {
+		return dst
+	}
+	dst[0] = s[0]
+	for i, v := range s[1:] {
+		dst[i+1] = dst[i] + v
+	}
+	return dst
+}
+
+// CumProd is
+//  if len(s) == 0 {
+//  	return dst
+//  }
+//  dst[0] = s[0]
+//  for i, v := range s[1:] {
+//  	dst[i+1] = dst[i] * v
+//  }
+//  return dst
+func CumProd(dst, s []float64) []float64 {
+	if len(s) == 0 {
+		return dst
+	}
+	dst[0] = s[0]
+	for i, v := range s[1:] {
+		dst[i+1] = dst[i] * v
+	}
+	return dst
+}
+
+// Div is
+//  for i, v := range s {
+//  	dst[i] /= v
+//  }
+func Div(dst, s []float64) {
+	for i, v := range s {
+		dst[i] /= v
+	}
+}
+
+// DivTo is
+//  for i, v := range s {
+//  	dst[i] = v / t[i]
+//  }
+//  return dst
+func DivTo(dst, s, t []float64) []float64 {
+	for i, v := range s {
+		dst[i] = v / t[i]
+	}
+	return dst
+}
+
+// L1Dist is
+//  var norm float64
+//  for i, v := range s {
+//  	norm += math.Abs(t[i] - v)
+//  }
+//  return norm
+func L1Dist(s, t []float64) float64 {
+	var norm float64
+	for i, v := range s {
+		norm += math.Abs(t[i] - v)
+	}
+	return norm
+}
+
+// LinfDist is
+//  var norm float64
+//  if len(s) == 0 {
+//  	return 0
+//  }
+//  norm = math.Abs(t[0] - s[0])
+//  for i, v := range s[1:] {
+//  	absDiff := math.Abs(t[i+1] - v)
+//  	if absDiff > norm || math.IsNaN(norm) {
+//  		norm = absDiff
+//  	}
+//  }
+//  return norm
+func LinfDist(s, t []float64) float64 {
+	var norm float64
+	if len(s) == 0 {
+		return 0
+	}
+	norm = math.Abs(t[0] - s[0])
+	for i, v := range s[1:] {
+		absDiff := math.Abs(t[i+1] - v)
+		if absDiff > norm || math.IsNaN(norm) {
+			norm = absDiff
+		}
+	}
+	return norm
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/asm/f64/stubs_test.go b/vendor/gonum.org/v1/gonum/internal/asm/f64/stubs_test.go
new file mode 100644
index 00000000..6dd949fc
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/asm/f64/stubs_test.go
@@ -0,0 +1,574 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package f64
+
+import "testing"
+
+func TestL1Norm(t *testing.T) {
+	var src_gd float64 = 1
+	for j, v := range []struct {
+		want float64
+		x    []float64
+	}{
+		{want: 0, x: []float64{}},
+		{want: 2, x: []float64{2}},
+		{want: 6, x: []float64{1, 2, 3}},
+		{want: 6, x: []float64{-1, -2, -3}},
+		{want: nan, x: []float64{nan}},
+		{want: 40, x: []float64{8, -8, 8, -8, 8}},
+		{want: 5, x: []float64{0, 1, 0, -1, 0, 1, 0, -1, 0, 1}},
+	} {
+		g_ln := 4 + j%2
+		v.x = guardVector(v.x, src_gd, g_ln)
+		src := v.x[g_ln : len(v.x)-g_ln]
+		ret := L1Norm(src)
+		if !same(ret, v.want) {
+			t.Errorf("Test %d L1Norm error Got: %f Expected: %f", j, ret, v.want)
+		}
+		if !isValidGuard(v.x, src_gd, g_ln) {
+			t.Errorf("Test %d Guard violated in src vector %v %v", j, v.x[:g_ln], v.x[len(v.x)-g_ln:])
+		}
+	}
+}
+
+func TestL1NormInc(t *testing.T) {
+	var src_gd float64 = 1
+	for j, v := range []struct {
+		inc  int
+		want float64
+		x    []float64
+	}{
+		{inc: 2, want: 0, x: []float64{}},
+		{inc: 3, want: 2, x: []float64{2}},
+		{inc: 10, want: 6, x: []float64{1, 2, 3}},
+		{inc: 5, want: 6, x: []float64{-1, -2, -3}},
+		{inc: 3, want: nan, x: []float64{nan}},
+		{inc: 15, want: 40, x: []float64{8, -8, 8, -8, 8}},
+		{inc: 1, want: 5, x: []float64{0, 1, 0, -1, 0, 1, 0, -1, 0, 1}},
+	} {
+		g_ln, ln := 4+j%2, len(v.x)
+		v.x = guardIncVector(v.x, src_gd, v.inc, g_ln)
+		src := v.x[g_ln : len(v.x)-g_ln]
+		ret := L1NormInc(src, ln, v.inc)
+		if !same(ret, v.want) {
+			t.Errorf("Test %d L1NormInc error Got: %f Expected: %f", j, ret, v.want)
+		}
+		checkValidIncGuard(t, v.x, src_gd, v.inc, g_ln)
+	}
+}
+
+func TestAdd(t *testing.T) {
+	var src_gd, dst_gd float64 = 1, 0
+	for j, v := range []struct {
+		dst, src, expect []float64
+	}{
+		{
+			dst:    []float64{1},
+			src:    []float64{0},
+			expect: []float64{1},
+		},
+		{
+			dst:    []float64{1, 2, 3},
+			src:    []float64{1},
+			expect: []float64{2, 2, 3},
+		},
+		{
+			dst:    []float64{},
+			src:    []float64{},
+			expect: []float64{},
+		},
+		{
+			dst:    []float64{1},
+			src:    []float64{nan},
+			expect: []float64{nan},
+		},
+		{
+			dst:    []float64{8, 8, 8, 8, 8},
+			src:    []float64{2, 4, nan, 8, 9},
+			expect: []float64{10, 12, nan, 16, 17},
+		},
+		{
+			dst:    []float64{0, 1, 2, 3, 4},
+			src:    []float64{-inf, 4, nan, 8, 9},
+			expect: []float64{-inf, 5, nan, 11, 13},
+		},
+		{
+			dst:    make([]float64, 50)[1:49],
+			src:    make([]float64, 50)[1:49],
+			expect: make([]float64, 50)[1:49],
+		},
+	} {
+		sg_ln, dg_ln := 4+j%2, 4+j%3
+		v.src, v.dst = guardVector(v.src, src_gd, sg_ln), guardVector(v.dst, dst_gd, dg_ln)
+		src, dst := v.src[sg_ln:len(v.src)-sg_ln], v.dst[dg_ln:len(v.dst)-dg_ln]
+		Add(dst, src)
+		for i := range v.expect {
+			if !same(dst[i], v.expect[i]) {
+				t.Errorf("Test %d Add error at %d Got: %v Expected: %v", j, i, dst[i], v.expect[i])
+			}
+		}
+		if !isValidGuard(v.src, src_gd, sg_ln) {
+			t.Errorf("Test %d Guard violated in src vector %v %v", j, v.src[:sg_ln], v.src[len(v.src)-sg_ln:])
+		}
+		if !isValidGuard(v.dst, dst_gd, dg_ln) {
+			t.Errorf("Test %d Guard violated in dst vector %v %v", j, v.dst[:dg_ln], v.dst[len(v.dst)-dg_ln:])
+		}
+	}
+}
+
+func TestAddConst(t *testing.T) {
+	var src_gd float64 = 0
+	for j, v := range []struct {
+		alpha       float64
+		src, expect []float64
+	}{
+		{
+			alpha:  1,
+			src:    []float64{0},
+			expect: []float64{1},
+		},
+		{
+			alpha:  5,
+			src:    []float64{},
+			expect: []float64{},
+		},
+		{
+			alpha:  1,
+			src:    []float64{nan},
+			expect: []float64{nan},
+		},
+		{
+			alpha:  8,
+			src:    []float64{2, 4, nan, 8, 9},
+			expect: []float64{10, 12, nan, 16, 17},
+		},
+		{
+			alpha:  inf,
+			src:    []float64{-inf, 4, nan, 8, 9},
+			expect: []float64{nan, inf, nan, inf, inf},
+		},
+	} {
+		g_ln := 4 + j%2
+		v.src = guardVector(v.src, src_gd, g_ln)
+		src := v.src[g_ln : len(v.src)-g_ln]
+		AddConst(v.alpha, src)
+		for i := range v.expect {
+			if !same(src[i], v.expect[i]) {
+				t.Errorf("Test %d AddConst error at %d Got: %v Expected: %v", j, i, src[i], v.expect[i])
+			}
+		}
+		if !isValidGuard(v.src, src_gd, g_ln) {
+			t.Errorf("Test %d Guard violated in src vector %v %v", j, v.src[:g_ln], v.src[len(v.src)-g_ln:])
+		}
+	}
+}
+
+func TestCumSum(t *testing.T) {
+	var src_gd, dst_gd float64 = -1, 0
+	for j, v := range []struct {
+		dst, src, expect []float64
+	}{
+		{
+			dst:    []float64{},
+			src:    []float64{},
+			expect: []float64{},
+		},
+		{
+			dst:    []float64{0},
+			src:    []float64{1},
+			expect: []float64{1},
+		},
+		{
+			dst:    []float64{nan},
+			src:    []float64{nan},
+			expect: []float64{nan},
+		},
+		{
+			dst:    []float64{0, 0, 0},
+			src:    []float64{1, 2, 3},
+			expect: []float64{1, 3, 6},
+		},
+		{
+			dst:    []float64{0, 0, 0, 0},
+			src:    []float64{1, 2, 3},
+			expect: []float64{1, 3, 6},
+		},
+		{
+			dst:    []float64{0, 0, 0, 0},
+			src:    []float64{1, 2, 3, 4},
+			expect: []float64{1, 3, 6, 10},
+		},
+		{
+			dst:    []float64{1, nan, nan, 1, 1},
+			src:    []float64{1, 1, nan, 1, 1},
+			expect: []float64{1, 2, nan, nan, nan},
+		},
+		{
+			dst:    []float64{nan, 4, inf, -inf, 9},
+			src:    []float64{inf, 4, nan, -inf, 9},
+			expect: []float64{inf, inf, nan, nan, nan},
+		},
+		{
+			dst:    make([]float64, 16),
+			src:    []float64{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1},
+			expect: []float64{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16},
+		},
+	} {
+		g_ln := 4 + j%2
+		v.src, v.dst = guardVector(v.src, src_gd, g_ln), guardVector(v.dst, dst_gd, g_ln)
+		src, dst := v.src[g_ln:len(v.src)-g_ln], v.dst[g_ln:len(v.dst)-g_ln]
+		ret := CumSum(dst, src)
+		for i := range v.expect {
+			if !same(ret[i], v.expect[i]) {
+				t.Errorf("Test %d CumSum error at %d Got: %v Expected: %v", j, i, ret[i], v.expect[i])
+			}
+			if !same(ret[i], dst[i]) {
+				t.Errorf("Test %d CumSum ret/dst mismatch %d Ret: %v Dst: %v", j, i, ret[i], dst[i])
+			}
+		}
+		if !isValidGuard(v.src, src_gd, g_ln) {
+			t.Errorf("Test %d Guard violated in src vector %v %v", j, v.src[:g_ln], v.src[len(v.src)-g_ln:])
+		}
+		if !isValidGuard(v.dst, dst_gd, g_ln) {
+			t.Errorf("Test %d Guard violated in dst vector %v %v", j, v.dst[:g_ln], v.dst[len(v.dst)-g_ln:])
+		}
+	}
+}
+
+func TestCumProd(t *testing.T) {
+	var src_gd, dst_gd float64 = -1, 1
+	for j, v := range []struct {
+		dst, src, expect []float64
+	}{
+		{
+			dst:    []float64{},
+			src:    []float64{},
+			expect: []float64{},
+		},
+		{
+			dst:    []float64{1},
+			src:    []float64{1},
+			expect: []float64{1},
+		},
+		{
+			dst:    []float64{nan},
+			src:    []float64{nan},
+			expect: []float64{nan},
+		},
+		{
+			dst:    []float64{0, 0, 0, 0},
+			src:    []float64{1, 2, 3, 4},
+			expect: []float64{1, 2, 6, 24},
+		},
+		{
+			dst:    []float64{0, 0, 0},
+			src:    []float64{1, 2, 3},
+			expect: []float64{1, 2, 6},
+		},
+		{
+			dst:    []float64{0, 0, 0, 0},
+			src:    []float64{1, 2, 3},
+			expect: []float64{1, 2, 6},
+		},
+		{
+			dst:    []float64{nan, 1, nan, 1, 0},
+			src:    []float64{1, 1, nan, 1, 1},
+			expect: []float64{1, 1, nan, nan, nan},
+		},
+		{
+			dst:    []float64{nan, 4, nan, -inf, 9},
+			src:    []float64{inf, 4, nan, -inf, 9},
+			expect: []float64{inf, inf, nan, nan, nan},
+		},
+		{
+			dst:    make([]float64, 18),
+			src:    []float64{2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2},
+			expect: []float64{2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536},
+		},
+	} {
+		sg_ln, dg_ln := 4+j%2, 4+j%3
+		v.src, v.dst = guardVector(v.src, src_gd, sg_ln), guardVector(v.dst, dst_gd, dg_ln)
+		src, dst := v.src[sg_ln:len(v.src)-sg_ln], v.dst[dg_ln:len(v.dst)-dg_ln]
+		ret := CumProd(dst, src)
+		for i := range v.expect {
+			if !same(ret[i], v.expect[i]) {
+				t.Errorf("Test %d CumProd error at %d Got: %v Expected: %v", j, i, ret[i], v.expect[i])
+			}
+			if !same(ret[i], dst[i]) {
+				t.Errorf("Test %d CumProd ret/dst mismatch %d Ret: %v Dst: %v", j, i, ret[i], dst[i])
+			}
+		}
+		if !isValidGuard(v.src, src_gd, sg_ln) {
+			t.Errorf("Test %d Guard violated in src vector %v %v", j, v.src[:sg_ln], v.src[len(v.src)-sg_ln:])
+		}
+		if !isValidGuard(v.dst, dst_gd, dg_ln) {
+			t.Errorf("Test %d Guard violated in dst vector %v %v", j, v.dst[:dg_ln], v.dst[len(v.dst)-dg_ln:])
+		}
+	}
+}
+
+func TestDiv(t *testing.T) {
+	var src_gd, dst_gd float64 = -1, 0.5
+	for j, v := range []struct {
+		dst, src, expect []float64
+	}{
+		{
+			dst:    []float64{1},
+			src:    []float64{1},
+			expect: []float64{1},
+		},
+		{
+			dst:    []float64{nan},
+			src:    []float64{nan},
+			expect: []float64{nan},
+		},
+		{
+			dst:    []float64{1, 2, 3, 4},
+			src:    []float64{1, 2, 3, 4},
+			expect: []float64{1, 1, 1, 1},
+		},
+		{
+			dst:    []float64{1, 2, 3, 4, 2, 4, 6, 8},
+			src:    []float64{1, 2, 3, 4, 1, 2, 3, 4},
+			expect: []float64{1, 1, 1, 1, 2, 2, 2, 2},
+		},
+		{
+			dst:    []float64{2, 4, 6},
+			src:    []float64{1, 2, 3},
+			expect: []float64{2, 2, 2},
+		},
+		{
+			dst:    []float64{0, 0, 0, 0},
+			src:    []float64{1, 2, 3},
+			expect: []float64{0, 0, 0},
+		},
+		{
+			dst:    []float64{nan, 1, nan, 1, 0, nan, 1, nan, 1, 0},
+			src:    []float64{1, 1, nan, 1, 1, 1, 1, nan, 1, 1},
+			expect: []float64{nan, 1, nan, 1, 0, nan, 1, nan, 1, 0},
+		},
+		{
+			dst:    []float64{inf, 4, nan, -inf, 9, inf, 4, nan, -inf, 9},
+			src:    []float64{inf, 4, nan, -inf, 3, inf, 4, nan, -inf, 3},
+			expect: []float64{nan, 1, nan, nan, 3, nan, 1, nan, nan, 3},
+		},
+	} {
+		sg_ln, dg_ln := 4+j%2, 4+j%3
+		v.src, v.dst = guardVector(v.src, src_gd, sg_ln), guardVector(v.dst, dst_gd, dg_ln)
+		src, dst := v.src[sg_ln:len(v.src)-sg_ln], v.dst[dg_ln:len(v.dst)-dg_ln]
+		Div(dst, src)
+		for i := range v.expect {
+			if !same(dst[i], v.expect[i]) {
+				t.Errorf("Test %d Div error at %d Got: %v Expected: %v", j, i, dst[i], v.expect[i])
+			}
+		}
+		if !isValidGuard(v.src, src_gd, sg_ln) {
+			t.Errorf("Test %d Guard violated in src vector %v %v", j, v.src[:sg_ln], v.src[len(v.src)-sg_ln:])
+		}
+		if !isValidGuard(v.dst, dst_gd, dg_ln) {
+			t.Errorf("Test %d Guard violated in dst vector %v %v", j, v.dst[:dg_ln], v.dst[len(v.dst)-dg_ln:])
+		}
+	}
+}
+
+func TestDivTo(t *testing.T) {
+	var dst_gd, x_gd, y_gd float64 = -1, 0.5, 0.25
+	for j, v := range []struct {
+		dst, x, y, expect []float64
+	}{
+		{
+			dst:    []float64{1},
+			x:      []float64{1},
+			y:      []float64{1},
+			expect: []float64{1},
+		},
+		{
+			dst:    []float64{1},
+			x:      []float64{nan},
+			y:      []float64{nan},
+			expect: []float64{nan},
+		},
+		{
+			dst:    []float64{-2, -2, -2},
+			x:      []float64{1, 2, 3},
+			y:      []float64{1, 2, 3},
+			expect: []float64{1, 1, 1},
+		},
+		{
+			dst:    []float64{0, 0, 0},
+			x:      []float64{2, 4, 6},
+			y:      []float64{1, 2, 3, 4},
+			expect: []float64{2, 2, 2},
+		},
+		{
+			dst:    []float64{-1, -1, -1},
+			x:      []float64{0, 0, 0},
+			y:      []float64{1, 2, 3},
+			expect: []float64{0, 0, 0},
+		},
+		{
+			dst:    []float64{inf, inf, inf, inf, inf, inf, inf, inf, inf, inf},
+			x:      []float64{nan, 1, nan, 1, 0, nan, 1, nan, 1, 0},
+			y:      []float64{1, 1, nan, 1, 1, 1, 1, nan, 1, 1},
+			expect: []float64{nan, 1, nan, 1, 0, nan, 1, nan, 1, 0},
+		},
+		{
+			dst:    []float64{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+			x:      []float64{inf, 4, nan, -inf, 9, inf, 4, nan, -inf, 9},
+			y:      []float64{inf, 4, nan, -inf, 3, inf, 4, nan, -inf, 3},
+			expect: []float64{nan, 1, nan, nan, 3, nan, 1, nan, nan, 3},
+		},
+	} {
+		xg_ln, yg_ln := 4+j%2, 4+j%3
+		v.y, v.x = guardVector(v.y, y_gd, yg_ln), guardVector(v.x, x_gd, xg_ln)
+		y, x := v.y[yg_ln:len(v.y)-yg_ln], v.x[xg_ln:len(v.x)-xg_ln]
+		v.dst = guardVector(v.dst, dst_gd, xg_ln)
+		dst := v.dst[xg_ln : len(v.dst)-xg_ln]
+		ret := DivTo(dst, x, y)
+		for i := range v.expect {
+			if !same(ret[i], v.expect[i]) {
+				t.Errorf("Test %d DivTo error at %d Got: %v Expected: %v", j, i, ret[i], v.expect[i])
+			}
+			if !same(ret[i], dst[i]) {
+				t.Errorf("Test %d DivTo ret/dst mismatch %d Ret: %v Dst: %v", j, i, ret[i], dst[i])
+			}
+		}
+		if !isValidGuard(v.y, y_gd, yg_ln) {
+			t.Errorf("Test %d Guard violated in y vector %v %v", j, v.y[:yg_ln], v.y[len(v.y)-yg_ln:])
+		}
+		if !isValidGuard(v.x, x_gd, xg_ln) {
+			t.Errorf("Test %d Guard violated in x vector %v %v", j, v.x[:xg_ln], v.x[len(v.x)-xg_ln:])
+		}
+		if !isValidGuard(v.dst, dst_gd, xg_ln) {
+			t.Errorf("Test %d Guard violated in dst vector %v %v", j, v.dst[:xg_ln], v.dst[len(v.dst)-xg_ln:])
+		}
+	}
+}
+
+func TestL1Dist(t *testing.T) {
+	var t_gd, s_gd float64 = -inf, inf
+	for j, v := range []struct {
+		s, t   []float64
+		expect float64
+	}{
+		{
+			s:      []float64{1},
+			t:      []float64{1},
+			expect: 0,
+		},
+		{
+			s:      []float64{nan},
+			t:      []float64{nan},
+			expect: nan,
+		},
+		{
+			s:      []float64{1, 2, 3, 4},
+			t:      []float64{1, 2, 3, 4},
+			expect: 0,
+		},
+		{
+			s:      []float64{2, 4, 6},
+			t:      []float64{1, 2, 3, 4},
+			expect: 6,
+		},
+		{
+			s:      []float64{0, 0, 0},
+			t:      []float64{1, 2, 3},
+			expect: 6,
+		},
+		{
+			s:      []float64{0, -4, -10},
+			t:      []float64{1, 2, 3},
+			expect: 20,
+		},
+		{
+			s:      []float64{0, 1, 0, 1, 0},
+			t:      []float64{1, 1, inf, 1, 1},
+			expect: inf,
+		},
+		{
+			s:      []float64{inf, 4, nan, -inf, 9},
+			t:      []float64{inf, 4, nan, -inf, 3},
+			expect: nan,
+		},
+	} {
+		sg_ln, tg_ln := 4+j%2, 4+j%3
+		v.s, v.t = guardVector(v.s, s_gd, sg_ln), guardVector(v.t, t_gd, tg_ln)
+		s_lc, t_lc := v.s[sg_ln:len(v.s)-sg_ln], v.t[tg_ln:len(v.t)-tg_ln]
+		ret := L1Dist(s_lc, t_lc)
+		if !same(ret, v.expect) {
+			t.Errorf("Test %d L1Dist error Got: %f Expected: %f", j, ret, v.expect)
+		}
+		if !isValidGuard(v.s, s_gd, sg_ln) {
+			t.Errorf("Test %d Guard violated in s vector %v %v", j, v.s[:sg_ln], v.s[len(v.s)-sg_ln:])
+		}
+		if !isValidGuard(v.t, t_gd, tg_ln) {
+			t.Errorf("Test %d Guard violated in t vector %v %v", j, v.t[:tg_ln], v.t[len(v.t)-tg_ln:])
+		}
+	}
+}
+
+func TestLinfDist(t *testing.T) {
+	var t_gd, s_gd float64 = 0, inf
+	for j, v := range []struct {
+		s, t   []float64
+		expect float64
+	}{
+		{
+			s:      []float64{},
+			t:      []float64{},
+			expect: 0,
+		},
+		{
+			s:      []float64{1},
+			t:      []float64{1},
+			expect: 0,
+		},
+		{
+			s:      []float64{nan},
+			t:      []float64{nan},
+			expect: nan,
+		},
+		{
+			s:      []float64{1, 2, 3, 4},
+			t:      []float64{1, 2, 3, 4},
+			expect: 0,
+		},
+		{
+			s:      []float64{2, 4, 6},
+			t:      []float64{1, 2, 3, 4},
+			expect: 3,
+		},
+		{
+			s:      []float64{0, 0, 0},
+			t:      []float64{1, 2, 3},
+			expect: 3,
+		},
+		{
+			s:      []float64{0, 1, 0, 1, 0},
+			t:      []float64{1, 1, inf, 1, 1},
+			expect: inf,
+		},
+		{
+			s:      []float64{inf, 4, nan, -inf, 9},
+			t:      []float64{inf, 4, nan, -inf, 3},
+			expect: 6,
+		},
+	} {
+		sg_ln, tg_ln := 4+j%2, 4+j%3
+		v.s, v.t = guardVector(v.s, s_gd, sg_ln), guardVector(v.t, t_gd, tg_ln)
+		s_lc, t_lc := v.s[sg_ln:len(v.s)-sg_ln], v.t[tg_ln:len(v.t)-tg_ln]
+		ret := LinfDist(s_lc, t_lc)
+		if !same(ret, v.expect) {
+			t.Errorf("Test %d LinfDist error Got: %f Expected: %f", j, ret, v.expect)
+		}
+		if !isValidGuard(v.s, s_gd, sg_ln) {
+			t.Errorf("Test %d Guard violated in s vector %v %v", j, v.s[:sg_ln], v.s[len(v.s)-sg_ln:])
+		}
+		if !isValidGuard(v.t, t_gd, tg_ln) {
+			t.Errorf("Test %d Guard violated in t vector %v %v", j, v.t[:tg_ln], v.t[len(v.t)-tg_ln:])
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/cmplx64/abs.go b/vendor/gonum.org/v1/gonum/internal/cmplx64/abs.go
new file mode 100644
index 00000000..65b8c985
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/cmplx64/abs.go
@@ -0,0 +1,14 @@
+// Copyright 2010 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package cmplx64
+
+import math "gonum.org/v1/gonum/internal/math32"
+
+// Abs returns the absolute value (also called the modulus) of x.
+func Abs(x complex64) float32 { return math.Hypot(real(x), imag(x)) }
diff --git a/vendor/gonum.org/v1/gonum/internal/cmplx64/cmath_test.go b/vendor/gonum.org/v1/gonum/internal/cmplx64/cmath_test.go
new file mode 100644
index 00000000..39cd5d1e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/cmplx64/cmath_test.go
@@ -0,0 +1,240 @@
+// Copyright 2010 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package cmplx64
+
+import (
+	"testing"
+
+	math "gonum.org/v1/gonum/internal/math32"
+)
+
+// The higher-precision values in vc26 were used to derive the
+// input arguments vc (see also comment below). For reference
+// only (do not delete).
+var vc26 = []complex64{
+	(4.97901192488367350108546816 + 7.73887247457810456552351752i),
+	(7.73887247457810456552351752 - 0.27688005719200159404635997i),
+	(-0.27688005719200159404635997 - 5.01060361827107492160848778i),
+	(-5.01060361827107492160848778 + 9.63629370719841737980004837i),
+	(9.63629370719841737980004837 + 2.92637723924396464525443662i),
+	(2.92637723924396464525443662 + 5.22908343145930665230025625i),
+	(5.22908343145930665230025625 + 2.72793991043601025126008608i),
+	(2.72793991043601025126008608 + 1.82530809168085506044576505i),
+	(1.82530809168085506044576505 - 8.68592476857560136238589621i),
+	(-8.68592476857560136238589621 + 4.97901192488367350108546816i),
+}
+
+var vc = []complex64{
+	(4.9790119248836735e+00 + 7.7388724745781045e+00i),
+	(7.7388724745781045e+00 - 2.7688005719200159e-01i),
+	(-2.7688005719200159e-01 - 5.0106036182710749e+00i),
+	(-5.0106036182710749e+00 + 9.6362937071984173e+00i),
+	(9.6362937071984173e+00 + 2.9263772392439646e+00i),
+	(2.9263772392439646e+00 + 5.2290834314593066e+00i),
+	(5.2290834314593066e+00 + 2.7279399104360102e+00i),
+	(2.7279399104360102e+00 + 1.8253080916808550e+00i),
+	(1.8253080916808550e+00 - 8.6859247685756013e+00i),
+	(-8.6859247685756013e+00 + 4.9790119248836735e+00i),
+}
+
+// The expected results below were computed by the high precision calculators
+// at http://keisan.casio.com/.  More exact input values (array vc[], above)
+// were obtained by printing them with "%.26f".  The answers were calculated
+// to 26 digits (by using the "Digit number" drop-down control of each
+// calculator).
+
+var abs = []float32{
+	9.2022120669932650313380972e+00,
+	7.7438239742296106616261394e+00,
+	5.0182478202557746902556648e+00,
+	1.0861137372799545160704002e+01,
+	1.0070841084922199607011905e+01,
+	5.9922447613166942183705192e+00,
+	5.8978784056736762299945176e+00,
+	3.2822866700678709020367184e+00,
+	8.8756430028990417290744307e+00,
+	1.0011785496777731986390856e+01,
+}
+
+var conj = []complex64{
+	(4.9790119248836735e+00 - 7.7388724745781045e+00i),
+	(7.7388724745781045e+00 + 2.7688005719200159e-01i),
+	(-2.7688005719200159e-01 + 5.0106036182710749e+00i),
+	(-5.0106036182710749e+00 - 9.6362937071984173e+00i),
+	(9.6362937071984173e+00 - 2.9263772392439646e+00i),
+	(2.9263772392439646e+00 - 5.2290834314593066e+00i),
+	(5.2290834314593066e+00 - 2.7279399104360102e+00i),
+	(2.7279399104360102e+00 - 1.8253080916808550e+00i),
+	(1.8253080916808550e+00 + 8.6859247685756013e+00i),
+	(-8.6859247685756013e+00 - 4.9790119248836735e+00i),
+}
+
+var sqrt = []complex64{
+	(2.6628203086086130543813948e+00 + 1.4531345674282185229796902e+00i),
+	(2.7823278427251986247149295e+00 - 4.9756907317005224529115567e-02i),
+	(1.5397025302089642757361015e+00 - 1.6271336573016637535695727e+00i),
+	(1.7103411581506875260277898e+00 + 2.8170677122737589676157029e+00i),
+	(3.1390392472953103383607947e+00 + 4.6612625849858653248980849e-01i),
+	(2.1117080764822417640789287e+00 + 1.2381170223514273234967850e+00i),
+	(2.3587032281672256703926939e+00 + 5.7827111903257349935720172e-01i),
+	(1.7335262588873410476661577e+00 + 5.2647258220721269141550382e-01i),
+	(2.3131094974708716531499282e+00 - 1.8775429304303785570775490e+00i),
+	(8.1420535745048086240947359e-01 + 3.0575897587277248522656113e+00i),
+}
+
+// special cases
+var vcAbsSC = []complex64{
+	NaN(),
+}
+var absSC = []float32{
+	math.NaN(),
+}
+var vcConjSC = []complex64{
+	NaN(),
+}
+var conjSC = []complex64{
+	NaN(),
+}
+var vcIsNaNSC = []complex64{
+	complex(math.Inf(-1), math.Inf(-1)),
+	complex(math.Inf(-1), math.NaN()),
+	complex(math.NaN(), math.Inf(-1)),
+	complex(0, math.NaN()),
+	complex(math.NaN(), 0),
+	complex(math.Inf(1), math.Inf(1)),
+	complex(math.Inf(1), math.NaN()),
+	complex(math.NaN(), math.Inf(1)),
+	complex(math.NaN(), math.NaN()),
+}
+var isNaNSC = []bool{
+	false,
+	false,
+	false,
+	true,
+	true,
+	false,
+	false,
+	false,
+	true,
+}
+var vcSqrtSC = []complex64{
+	NaN(),
+}
+var sqrtSC = []complex64{
+	NaN(),
+}
+
+// functions borrowed from pkg/math/all_test.go
+func tolerance(a, b, e float32) bool {
+	d := a - b
+	if d < 0 {
+		d = -d
+	}
+
+	// note: b is correct (expected) value, a is actual value.
+	// make error tolerance a fraction of b, not a.
+	if b != 0 {
+		e = e * b
+		if e < 0 {
+			e = -e
+		}
+	}
+	return d < e
+}
+func veryclose(a, b float32) bool { return tolerance(a, b, 1e-7) }
+func alike(a, b float32) bool {
+	switch {
+	case a != a && b != b: // math.IsNaN(a) && math.IsNaN(b):
+		return true
+	case a == b:
+		return math.Signbit(a) == math.Signbit(b)
+	}
+	return false
+}
+
+func cTolerance(a, b complex64, e float32) bool {
+	d := Abs(a - b)
+	if b != 0 {
+		e = e * Abs(b)
+		if e < 0 {
+			e = -e
+		}
+	}
+	return d < e
+}
+func cVeryclose(a, b complex64) bool { return cTolerance(a, b, 1e-7) }
+func cAlike(a, b complex64) bool {
+	switch {
+	case IsNaN(a) && IsNaN(b):
+		return true
+	case a == b:
+		return math.Signbit(real(a)) == math.Signbit(real(b)) && math.Signbit(imag(a)) == math.Signbit(imag(b))
+	}
+	return false
+}
+
+func TestAbs(t *testing.T) {
+	for i := 0; i < len(vc); i++ {
+		if f := Abs(vc[i]); !veryclose(abs[i], f) {
+			t.Errorf("Abs(%g) = %g, want %g", vc[i], f, abs[i])
+		}
+	}
+	for i := 0; i < len(vcAbsSC); i++ {
+		if f := Abs(vcAbsSC[i]); !alike(absSC[i], f) {
+			t.Errorf("Abs(%g) = %g, want %g", vcAbsSC[i], f, absSC[i])
+		}
+	}
+}
+func TestConj(t *testing.T) {
+	for i := 0; i < len(vc); i++ {
+		if f := Conj(vc[i]); !cVeryclose(conj[i], f) {
+			t.Errorf("Conj(%g) = %g, want %g", vc[i], f, conj[i])
+		}
+	}
+	for i := 0; i < len(vcConjSC); i++ {
+		if f := Conj(vcConjSC[i]); !cAlike(conjSC[i], f) {
+			t.Errorf("Conj(%g) = %g, want %g", vcConjSC[i], f, conjSC[i])
+		}
+	}
+}
+func TestIsNaN(t *testing.T) {
+	for i := 0; i < len(vcIsNaNSC); i++ {
+		if f := IsNaN(vcIsNaNSC[i]); isNaNSC[i] != f {
+			t.Errorf("IsNaN(%v) = %v, want %v", vcIsNaNSC[i], f, isNaNSC[i])
+		}
+	}
+}
+func TestSqrt(t *testing.T) {
+	for i := 0; i < len(vc); i++ {
+		if f := Sqrt(vc[i]); !cVeryclose(sqrt[i], f) {
+			t.Errorf("Sqrt(%g) = %g, want %g", vc[i], f, sqrt[i])
+		}
+	}
+	for i := 0; i < len(vcSqrtSC); i++ {
+		if f := Sqrt(vcSqrtSC[i]); !cAlike(sqrtSC[i], f) {
+			t.Errorf("Sqrt(%g) = %g, want %g", vcSqrtSC[i], f, sqrtSC[i])
+		}
+	}
+}
+
+func BenchmarkAbs(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		Abs(complex(2.5, 3.5))
+	}
+}
+func BenchmarkConj(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		Conj(complex(2.5, 3.5))
+	}
+}
+func BenchmarkSqrt(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		Sqrt(complex(2.5, 3.5))
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/cmplx64/conj.go b/vendor/gonum.org/v1/gonum/internal/cmplx64/conj.go
new file mode 100644
index 00000000..84b7b556
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/cmplx64/conj.go
@@ -0,0 +1,12 @@
+// Copyright 2010 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package cmplx64
+
+// Conj returns the complex conjugate of x.
+func Conj(x complex64) complex64 { return complex(real(x), -imag(x)) }
diff --git a/vendor/gonum.org/v1/gonum/internal/cmplx64/doc.go b/vendor/gonum.org/v1/gonum/internal/cmplx64/doc.go
new file mode 100644
index 00000000..40f808a9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/cmplx64/doc.go
@@ -0,0 +1,7 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package cmplx64 provides complex64 versions of standard library math/cmplx
+// package routines used by gonum/blas.
+package cmplx64 // import "gonum.org/v1/gonum/internal/cmplx64"
diff --git a/vendor/gonum.org/v1/gonum/internal/cmplx64/isinf.go b/vendor/gonum.org/v1/gonum/internal/cmplx64/isinf.go
new file mode 100644
index 00000000..e674e52b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/cmplx64/isinf.go
@@ -0,0 +1,25 @@
+// Copyright 2010 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package cmplx64
+
+import math "gonum.org/v1/gonum/internal/math32"
+
+// IsInf returns true if either real(x) or imag(x) is an infinity.
+func IsInf(x complex64) bool {
+	if math.IsInf(real(x), 0) || math.IsInf(imag(x), 0) {
+		return true
+	}
+	return false
+}
+
+// Inf returns a complex infinity, complex(+Inf, +Inf).
+func Inf() complex64 {
+	inf := math.Inf(1)
+	return complex(inf, inf)
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/cmplx64/isnan.go b/vendor/gonum.org/v1/gonum/internal/cmplx64/isnan.go
new file mode 100644
index 00000000..2630ef86
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/cmplx64/isnan.go
@@ -0,0 +1,29 @@
+// Copyright 2010 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package cmplx64
+
+import math "gonum.org/v1/gonum/internal/math32"
+
+// IsNaN returns true if either real(x) or imag(x) is NaN
+// and neither is an infinity.
+func IsNaN(x complex64) bool {
+	switch {
+	case math.IsInf(real(x), 0) || math.IsInf(imag(x), 0):
+		return false
+	case math.IsNaN(real(x)) || math.IsNaN(imag(x)):
+		return true
+	}
+	return false
+}
+
+// NaN returns a complex ``not-a-number'' value.
+func NaN() complex64 {
+	nan := math.NaN()
+	return complex(nan, nan)
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/cmplx64/sqrt.go b/vendor/gonum.org/v1/gonum/internal/cmplx64/sqrt.go
new file mode 100644
index 00000000..313fd11f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/cmplx64/sqrt.go
@@ -0,0 +1,108 @@
+// Copyright 2010 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package cmplx64
+
+import math "gonum.org/v1/gonum/internal/math32"
+
+// The original C code, the long comment, and the constants
+// below are from http://netlib.sandia.gov/cephes/c9x-complex/clog.c.
+// The go code is a simplified version of the original C.
+//
+// Cephes Math Library Release 2.8:  June, 2000
+// Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
+//
+// The readme file at http://netlib.sandia.gov/cephes/ says:
+//    Some software in this archive may be from the book _Methods and
+// Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
+// International, 1989) or from the Cephes Mathematical Library, a
+// commercial product. In either event, it is copyrighted by the author.
+// What you see here may be used freely but it comes with no support or
+// guarantee.
+//
+//   The two known misprints in the book are repaired here in the
+// source listings for the gamma function and the incomplete beta
+// integral.
+//
+//   Stephen L. Moshier
+//   moshier@na-net.ornl.gov
+
+// Complex square root
+//
+// DESCRIPTION:
+//
+// If z = x + iy,  r = |z|, then
+//
+//                       1/2
+// Re w  =  [ (r + x)/2 ]   ,
+//
+//                       1/2
+// Im w  =  [ (r - x)/2 ]   .
+//
+// Cancelation error in r-x or r+x is avoided by using the
+// identity  2 Re w Im w  =  y.
+//
+// Note that -w is also a square root of z. The root chosen
+// is always in the right half plane and Im w has the same sign as y.
+//
+// ACCURACY:
+//
+//                      Relative error:
+// arithmetic   domain     # trials      peak         rms
+//    DEC       -10,+10     25000       3.2e-17     9.6e-18
+//    IEEE      -10,+10   1,000,000     2.9e-16     6.1e-17
+
+// Sqrt returns the square root of x.
+// The result r is chosen so that real(r) ≥ 0 and imag(r) has the same sign as imag(x).
+func Sqrt(x complex64) complex64 {
+	if imag(x) == 0 {
+		if real(x) == 0 {
+			return complex(0, 0)
+		}
+		if real(x) < 0 {
+			return complex(0, math.Sqrt(-real(x)))
+		}
+		return complex(math.Sqrt(real(x)), 0)
+	}
+	if real(x) == 0 {
+		if imag(x) < 0 {
+			r := math.Sqrt(-0.5 * imag(x))
+			return complex(r, -r)
+		}
+		r := math.Sqrt(0.5 * imag(x))
+		return complex(r, r)
+	}
+	a := real(x)
+	b := imag(x)
+	var scale float32
+	// Rescale to avoid internal overflow or underflow.
+	if math.Abs(a) > 4 || math.Abs(b) > 4 {
+		a *= 0.25
+		b *= 0.25
+		scale = 2
+	} else {
+		a *= 1.8014398509481984e16 // 2**54
+		b *= 1.8014398509481984e16
+		scale = 7.450580596923828125e-9 // 2**-27
+	}
+	r := math.Hypot(a, b)
+	var t float32
+	if a > 0 {
+		t = math.Sqrt(0.5*r + 0.5*a)
+		r = scale * math.Abs((0.5*b)/t)
+		t *= scale
+	} else {
+		r = math.Sqrt(0.5*r - 0.5*a)
+		t = scale * math.Abs((0.5*b)/r)
+		r *= scale
+	}
+	if b < 0 {
+		return complex(t, -r)
+	}
+	return complex(t, r)
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/math32/doc.go b/vendor/gonum.org/v1/gonum/internal/math32/doc.go
new file mode 100644
index 00000000..2368fcd9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/math32/doc.go
@@ -0,0 +1,7 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package math32 provides float32 versions of standard library math package
+// routines used by gonum/blas/native.
+package math32 // import "gonum.org/v1/gonum/internal/math32"
diff --git a/vendor/gonum.org/v1/gonum/internal/math32/math.go b/vendor/gonum.org/v1/gonum/internal/math32/math.go
new file mode 100644
index 00000000..3e466611
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/math32/math.go
@@ -0,0 +1,111 @@
+// Copyright 2009 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package math32
+
+import (
+	"math"
+)
+
+const (
+	unan    = 0x7fc00000
+	uinf    = 0x7f800000
+	uneginf = 0xff800000
+	mask    = 0x7f8 >> 3
+	shift   = 32 - 8 - 1
+	bias    = 127
+)
+
+// Abs returns the absolute value of x.
+//
+// Special cases are:
+//	Abs(±Inf) = +Inf
+//	Abs(NaN) = NaN
+func Abs(x float32) float32 {
+	switch {
+	case x < 0:
+		return -x
+	case x == 0:
+		return 0 // return correctly abs(-0)
+	}
+	return x
+}
+
+// Copysign returns a value with the magnitude
+// of x and the sign of y.
+func Copysign(x, y float32) float32 {
+	const sign = 1 << 31
+	return math.Float32frombits(math.Float32bits(x)&^sign | math.Float32bits(y)&sign)
+}
+
+// Hypot returns Sqrt(p*p + q*q), taking care to avoid
+// unnecessary overflow and underflow.
+//
+// Special cases are:
+//	Hypot(±Inf, q) = +Inf
+//	Hypot(p, ±Inf) = +Inf
+//	Hypot(NaN, q) = NaN
+//	Hypot(p, NaN) = NaN
+func Hypot(p, q float32) float32 {
+	// special cases
+	switch {
+	case IsInf(p, 0) || IsInf(q, 0):
+		return Inf(1)
+	case IsNaN(p) || IsNaN(q):
+		return NaN()
+	}
+	if p < 0 {
+		p = -p
+	}
+	if q < 0 {
+		q = -q
+	}
+	if p < q {
+		p, q = q, p
+	}
+	if p == 0 {
+		return 0
+	}
+	q = q / p
+	return p * Sqrt(1+q*q)
+}
+
+// Inf returns positive infinity if sign >= 0, negative infinity if sign < 0.
+func Inf(sign int) float32 {
+	var v uint32
+	if sign >= 0 {
+		v = uinf
+	} else {
+		v = uneginf
+	}
+	return math.Float32frombits(v)
+}
+
+// IsInf reports whether f is an infinity, according to sign.
+// If sign > 0, IsInf reports whether f is positive infinity.
+// If sign < 0, IsInf reports whether f is negative infinity.
+// If sign == 0, IsInf reports whether f is either infinity.
+func IsInf(f float32, sign int) bool {
+	// Test for infinity by comparing against maximum float.
+	// To avoid the floating-point hardware, could use:
+	//	x := math.Float32bits(f);
+	//	return sign >= 0 && x == uinf || sign <= 0 && x == uneginf;
+	return sign >= 0 && f > math.MaxFloat32 || sign <= 0 && f < -math.MaxFloat32
+}
+
+// IsNaN reports whether f is an IEEE 754 ``not-a-number'' value.
+func IsNaN(f float32) (is bool) {
+	// IEEE 754 says that only NaNs satisfy f != f.
+	// To avoid the floating-point hardware, could use:
+	//	x := math.Float32bits(f);
+	//	return uint32(x>>shift)&mask == mask && x != uinf && x != uneginf
+	return f != f
+}
+
+// NaN returns an IEEE 754 ``not-a-number'' value.
+func NaN() float32 { return math.Float32frombits(unan) }
diff --git a/vendor/gonum.org/v1/gonum/internal/math32/math_test.go b/vendor/gonum.org/v1/gonum/internal/math32/math_test.go
new file mode 100644
index 00000000..aa29ea37
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/math32/math_test.go
@@ -0,0 +1,238 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package math32
+
+import (
+	"math"
+	"testing"
+	"testing/quick"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+const tol = 1e-7
+
+func TestAbs(t *testing.T) {
+	f := func(x float32) bool {
+		y := Abs(x)
+		return y == float32(math.Abs(float64(x)))
+	}
+	if err := quick.Check(f, nil); err != nil {
+		t.Error(err)
+	}
+}
+
+func TestCopySign(t *testing.T) {
+	f := func(x struct{ X, Y float32 }) bool {
+		y := Copysign(x.X, x.Y)
+		return y == float32(math.Copysign(float64(x.X), float64(x.Y)))
+	}
+	if err := quick.Check(f, nil); err != nil {
+		t.Error(err)
+	}
+}
+
+func TestHypot(t *testing.T) {
+	// tol is increased for Hypot to avoid failures
+	// related to https://github.com/gonum/gonum/issues/110.
+	const tol = 1e-6
+	f := func(x struct{ X, Y float32 }) bool {
+		y := Hypot(x.X, x.Y)
+		if math.Hypot(float64(x.X), float64(x.Y)) > math.MaxFloat32 {
+			return true
+		}
+		return floats.EqualWithinRel(float64(y), math.Hypot(float64(x.X), float64(x.Y)), tol)
+	}
+	if err := quick.Check(f, nil); err != nil {
+		t.Error(err)
+	}
+}
+
+func TestInf(t *testing.T) {
+	if float64(Inf(1)) != math.Inf(1) || float64(Inf(-1)) != math.Inf(-1) {
+		t.Error("float32(inf) not infinite")
+	}
+}
+
+func TestIsInf(t *testing.T) {
+	posInf := float32(math.Inf(1))
+	negInf := float32(math.Inf(-1))
+	if !IsInf(posInf, 0) || !IsInf(negInf, 0) || !IsInf(posInf, 1) || !IsInf(negInf, -1) || IsInf(posInf, -1) || IsInf(negInf, 1) {
+		t.Error("unexpected isInf value")
+	}
+	f := func(x struct {
+		F    float32
+		Sign int
+	}) bool {
+		y := IsInf(x.F, x.Sign)
+		return y == math.IsInf(float64(x.F), x.Sign)
+	}
+	if err := quick.Check(f, nil); err != nil {
+		t.Error(err)
+	}
+}
+
+func TestIsNaN(t *testing.T) {
+	f := func(x float32) bool {
+		y := IsNaN(x)
+		return y == math.IsNaN(float64(x))
+	}
+	if err := quick.Check(f, nil); err != nil {
+		t.Error(err)
+	}
+}
+
+func TestNaN(t *testing.T) {
+	if !math.IsNaN(float64(NaN())) {
+		t.Errorf("float32(nan) is a number: %f", NaN())
+	}
+}
+
+func TestSignbit(t *testing.T) {
+	f := func(x float32) bool {
+		return Signbit(x) == math.Signbit(float64(x))
+	}
+	if err := quick.Check(f, nil); err != nil {
+		t.Error(err)
+	}
+}
+
+func TestSqrt(t *testing.T) {
+	f := func(x float32) bool {
+		y := Sqrt(x)
+		if IsNaN(y) && IsNaN(sqrt(x)) {
+			return true
+		}
+		return floats.EqualWithinRel(float64(y), float64(sqrt(x)), tol)
+	}
+	if err := quick.Check(f, nil); err != nil {
+		t.Error(err)
+	}
+}
+
+// Copyright 2009 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// The original C code and the long comment below are
+// from FreeBSD's /usr/src/lib/msun/src/e_sqrt.c and
+// came with this notice.  The go code is a simplified
+// version of the original C.
+//
+// ====================================================
+// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+//
+// Developed at SunPro, a Sun Microsystems, Inc. business.
+// Permission to use, copy, modify, and distribute this
+// software is freely granted, provided that this notice
+// is preserved.
+// ====================================================
+//
+// __ieee754_sqrt(x)
+// Return correctly rounded sqrt.
+//           -----------------------------------------
+//           | Use the hardware sqrt if you have one |
+//           -----------------------------------------
+// Method:
+//   Bit by bit method using integer arithmetic. (Slow, but portable)
+//   1. Normalization
+//      Scale x to y in [1,4) with even powers of 2:
+//      find an integer k such that  1 <= (y=x*2**(2k)) < 4, then
+//              sqrt(x) = 2**k * sqrt(y)
+//   2. Bit by bit computation
+//      Let q  = sqrt(y) truncated to i bit after binary point (q = 1),
+//           i                                                   0
+//                                     i+1         2
+//          s  = 2*q , and      y  =  2   * ( y - q  ).          (1)
+//           i      i            i                 i
+//
+//      To compute q    from q , one checks whether
+//                  i+1       i
+//
+//                            -(i+1) 2
+//                      (q + 2      )  <= y.                     (2)
+//                        i
+//                                                            -(i+1)
+//      If (2) is false, then q   = q ; otherwise q   = q  + 2      .
+//                             i+1   i             i+1   i
+//
+//      With some algebraic manipulation, it is not difficult to see
+//      that (2) is equivalent to
+//                             -(i+1)
+//                      s  +  2       <= y                       (3)
+//                       i                i
+//
+//      The advantage of (3) is that s  and y  can be computed by
+//                                    i      i
+//      the following recurrence formula:
+//          if (3) is false
+//
+//          s     =  s  ,       y    = y   ;                     (4)
+//           i+1      i          i+1    i
+//
+//      otherwise,
+//                         -i                      -(i+1)
+//          s     =  s  + 2  ,  y    = y  -  s  - 2              (5)
+//           i+1      i          i+1    i     i
+//
+//      One may easily use induction to prove (4) and (5).
+//      Note. Since the left hand side of (3) contain only i+2 bits,
+//            it does not necessary to do a full (53-bit) comparison
+//            in (3).
+//   3. Final rounding
+//      After generating the 53 bits result, we compute one more bit.
+//      Together with the remainder, we can decide whether the
+//      result is exact, bigger than 1/2ulp, or less than 1/2ulp
+//      (it will never equal to 1/2ulp).
+//      The rounding mode can be detected by checking whether
+//      huge + tiny is equal to huge, and whether huge - tiny is
+//      equal to huge for some floating point number "huge" and "tiny".
+//
+func sqrt(x float32) float32 {
+	// special cases
+	switch {
+	case x == 0 || IsNaN(x) || IsInf(x, 1):
+		return x
+	case x < 0:
+		return NaN()
+	}
+	ix := math.Float32bits(x)
+	// normalize x
+	exp := int((ix >> shift) & mask)
+	if exp == 0 { // subnormal x
+		for ix&1<<shift == 0 {
+			ix <<= 1
+			exp--
+		}
+		exp++
+	}
+	exp -= bias // unbias exponent
+	ix &^= mask << shift
+	ix |= 1 << shift
+	if exp&1 == 1 { // odd exp, double x to make it even
+		ix <<= 1
+	}
+	exp >>= 1 // exp = exp/2, exponent of square root
+	// generate sqrt(x) bit by bit
+	ix <<= 1
+	var q, s uint32               // q = sqrt(x)
+	r := uint32(1 << (shift + 1)) // r = moving bit from MSB to LSB
+	for r != 0 {
+		t := s + r
+		if t <= ix {
+			s = t + r
+			ix -= t
+			q += r
+		}
+		ix <<= 1
+		r >>= 1
+	}
+	// final rounding
+	if ix != 0 { // remainder, result not exact
+		q += q & 1 // round according to extra bit
+	}
+	ix = q>>1 + uint32(exp-1+bias)<<shift // significand + biased exponent
+	return math.Float32frombits(ix)
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/math32/signbit.go b/vendor/gonum.org/v1/gonum/internal/math32/signbit.go
new file mode 100644
index 00000000..57d69046
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/math32/signbit.go
@@ -0,0 +1,16 @@
+// Copyright 2010 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package math32
+
+import "math"
+
+// Signbit returns true if x is negative or negative zero.
+func Signbit(x float32) bool {
+	return math.Float32bits(x)&(1<<31) != 0
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/math32/sqrt.go b/vendor/gonum.org/v1/gonum/internal/math32/sqrt.go
new file mode 100644
index 00000000..5cdde974
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/math32/sqrt.go
@@ -0,0 +1,25 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !amd64 noasm appengine
+
+package math32
+
+import (
+	"math"
+)
+
+// Sqrt returns the square root of x.
+//
+// Special cases are:
+//	Sqrt(+Inf) = +Inf
+//	Sqrt(±0) = ±0
+//	Sqrt(x < 0) = NaN
+//	Sqrt(NaN) = NaN
+func Sqrt(x float32) float32 {
+	// FIXME(kortschak): Direct translation of the math package
+	// asm code for 386 fails to build. No test hardware is available
+	// for arm, so using conversion instead.
+	return float32(math.Sqrt(float64(x)))
+}
diff --git a/vendor/gonum.org/v1/gonum/internal/math32/sqrt_amd64.go b/vendor/gonum.org/v1/gonum/internal/math32/sqrt_amd64.go
new file mode 100644
index 00000000..30af43be
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/math32/sqrt_amd64.go
@@ -0,0 +1,20 @@
+// Copyright 2009 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !noasm,!appengine
+
+package math32
+
+// Sqrt returns the square root of x.
+//
+// Special cases are:
+//	Sqrt(+Inf) = +Inf
+//	Sqrt(±0) = ±0
+//	Sqrt(x < 0) = NaN
+//	Sqrt(NaN) = NaN
+func Sqrt(x float32) float32
diff --git a/vendor/gonum.org/v1/gonum/internal/math32/sqrt_amd64.s b/vendor/gonum.org/v1/gonum/internal/math32/sqrt_amd64.s
new file mode 100644
index 00000000..14c66fb9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/internal/math32/sqrt_amd64.s
@@ -0,0 +1,20 @@
+// Copyright 2009 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !noasm,!appengine
+
+// TODO(kortschak): use textflag.h after we drop Go 1.3 support
+//#include "textflag.h"
+// Don't insert stack check preamble.
+#define NOSPLIT	4
+
+// func Sqrt(x float32) float32
+TEXT ·Sqrt(SB),NOSPLIT,$0
+	SQRTSS x+0(FP), X0
+	MOVSS X0, ret+8(FP)
+	RET
diff --git a/vendor/gonum.org/v1/gonum/lapack/.gitignore b/vendor/gonum.org/v1/gonum/lapack/.gitignore
new file mode 100644
index 00000000..e69de29b
diff --git a/vendor/gonum.org/v1/gonum/lapack/README.md b/vendor/gonum.org/v1/gonum/lapack/README.md
new file mode 100644
index 00000000..115659d1
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/README.md
@@ -0,0 +1,50 @@
+Gonum LAPACK [![GoDoc](https://godoc.org/gonum.org/v1/gonum/lapack?status.svg)](https://godoc.org/gonum.org/v1/gonum/lapack)
+======
+
+A collection of packages to provide LAPACK functionality for the Go programming
+language (http://golang.org). This provides a partial implementation in native go
+and a wrapper using cgo to a c-based implementation.
+
+## Installation
+
+```
+  go get gonum.org/v1/gonum/lapack/...
+```
+
+
+Install OpenBLAS:
+```
+  git clone https://github.com/xianyi/OpenBLAS
+  cd OpenBLAS
+  make
+```
+
+Then install the lapack/cgo package:
+```sh
+  CGO_LDFLAGS="-L/path/to/OpenBLAS -lopenblas" go install gonum.org/v1/netlib/lapack
+```
+
+For Windows you can download binary packages for OpenBLAS at
+http://sourceforge.net/projects/openblas/files/
+
+If you want to use a different BLAS package such as the Intel MKL you can
+adjust the `CGO_LDFLAGS` variable:
+```sh
+  CGO_LDFLAGS="-lmkl_rt" go install gonum.org/v1/netlib/lapack
+```
+
+## Packages
+
+### lapack
+
+Defines the LAPACK API based on http://www.netlib.org/lapack/lapacke.html
+
+### lapack/gonum
+
+Go implementation of the LAPACK API (incomplete, implements the `float64` API).
+
+### lapack/lapack64
+
+Wrappers for an implementation of the double (i.e., `float64`) precision real parts of
+the LAPACK API.
+
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/appengine_test.go b/vendor/gonum.org/v1/gonum/lapack/gonum/appengine_test.go
new file mode 100644
index 00000000..ccadff8a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/appengine_test.go
@@ -0,0 +1,9 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build noasm appengine
+
+package gonum
+
+func init() { appengine = true }
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/bench_test.go b/vendor/gonum.org/v1/gonum/lapack/gonum/bench_test.go
new file mode 100644
index 00000000..6f945cac
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/bench_test.go
@@ -0,0 +1,15 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build go1.7
+
+package gonum
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/lapack/testlapack"
+)
+
+func BenchmarkDgeev(b *testing.B) { testlapack.DgeevBenchmark(b, impl) }
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dbdsqr.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dbdsqr.go
new file mode 100644
index 00000000..6a8d8be9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dbdsqr.go
@@ -0,0 +1,488 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dbdsqr performs a singular value decomposition of a real n×n bidiagonal matrix.
+//
+// The SVD of the bidiagonal matrix B is
+//  B = Q * S * P^T
+// where S is a diagonal matrix of singular values, Q is an orthogonal matrix of
+// left singular vectors, and P is an orthogonal matrix of right singular vectors.
+//
+// Q and P are only computed if requested. If left singular vectors are requested,
+// this routine returns U * Q instead of Q, and if right singular vectors are
+// requested P^T * VT is returned instead of P^T.
+//
+// Frequently Dbdsqr is used in conjunction with Dgebrd which reduces a general
+// matrix A into bidiagonal form. In this case, the SVD of A is
+//  A = (U * Q) * S * (P^T * VT)
+//
+// This routine may also compute Q^T * C.
+//
+// d and e contain the elements of the bidiagonal matrix b. d must have length at
+// least n, and e must have length at least n-1. Dbdsqr will panic if there is
+// insufficient length. On exit, D contains the singular values of B in decreasing
+// order.
+//
+// VT is a matrix of size n×ncvt whose elements are stored in vt. The elements
+// of vt are modified to contain P^T * VT on exit. VT is not used if ncvt == 0.
+//
+// U is a matrix of size nru×n whose elements are stored in u. The elements
+// of u are modified to contain U * Q on exit. U is not used if nru == 0.
+//
+// C is a matrix of size n×ncc whose elements are stored in c. The elements
+// of c are modified to contain Q^T * C on exit. C is not used if ncc == 0.
+//
+// work contains temporary storage and must have length at least 4*n. Dbdsqr
+// will panic if there is insufficient working memory.
+//
+// Dbdsqr returns whether the decomposition was successful.
+//
+// Dbdsqr is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dbdsqr(uplo blas.Uplo, n, ncvt, nru, ncc int, d, e, vt []float64, ldvt int, u []float64, ldu int, c []float64, ldc int, work []float64) (ok bool) {
+	if uplo != blas.Upper && uplo != blas.Lower {
+		panic(badUplo)
+	}
+	if ncvt != 0 {
+		checkMatrix(n, ncvt, vt, ldvt)
+	}
+	if nru != 0 {
+		checkMatrix(nru, n, u, ldu)
+	}
+	if ncc != 0 {
+		checkMatrix(n, ncc, c, ldc)
+	}
+	if len(d) < n {
+		panic(badD)
+	}
+	if len(e) < n-1 {
+		panic(badE)
+	}
+	if len(work) < 4*n {
+		panic(badWork)
+	}
+	var info int
+	bi := blas64.Implementation()
+	const (
+		maxIter = 6
+	)
+	if n == 0 {
+		return true
+	}
+	if n != 1 {
+		// If the singular vectors do not need to be computed, use qd algorithm.
+		if !(ncvt > 0 || nru > 0 || ncc > 0) {
+			info = impl.Dlasq1(n, d, e, work)
+			// If info is 2 dqds didn't finish, and so try to.
+			if info != 2 {
+				return info == 0
+			}
+			info = 0
+		}
+		nm1 := n - 1
+		nm12 := nm1 + nm1
+		nm13 := nm12 + nm1
+		idir := 0
+
+		eps := dlamchE
+		unfl := dlamchS
+		lower := uplo == blas.Lower
+		var cs, sn, r float64
+		if lower {
+			for i := 0; i < n-1; i++ {
+				cs, sn, r = impl.Dlartg(d[i], e[i])
+				d[i] = r
+				e[i] = sn * d[i+1]
+				d[i+1] *= cs
+				work[i] = cs
+				work[nm1+i] = sn
+			}
+			if nru > 0 {
+				impl.Dlasr(blas.Right, lapack.Variable, lapack.Forward, nru, n, work, work[n-1:], u, ldu)
+			}
+			if ncc > 0 {
+				impl.Dlasr(blas.Left, lapack.Variable, lapack.Forward, n, ncc, work, work[n-1:], c, ldc)
+			}
+		}
+		// Compute singular values to a relative accuracy of tol. If tol is negative
+		// the values will be computed to an absolute accuracy of math.Abs(tol) * norm(b)
+		tolmul := math.Max(10, math.Min(100, math.Pow(eps, -1.0/8)))
+		tol := tolmul * eps
+		var smax float64
+		for i := 0; i < n; i++ {
+			smax = math.Max(smax, math.Abs(d[i]))
+		}
+		for i := 0; i < n-1; i++ {
+			smax = math.Max(smax, math.Abs(e[i]))
+		}
+
+		var sminl float64
+		var thresh float64
+		if tol >= 0 {
+			sminoa := math.Abs(d[0])
+			if sminoa != 0 {
+				mu := sminoa
+				for i := 1; i < n; i++ {
+					mu = math.Abs(d[i]) * (mu / (mu + math.Abs(e[i-1])))
+					sminoa = math.Min(sminoa, mu)
+					if sminoa == 0 {
+						break
+					}
+				}
+			}
+			sminoa = sminoa / math.Sqrt(float64(n))
+			thresh = math.Max(tol*sminoa, float64(maxIter*n*n)*unfl)
+		} else {
+			thresh = math.Max(math.Abs(tol)*smax, float64(maxIter*n*n)*unfl)
+		}
+		// Prepare for the main iteration loop for the singular values.
+		maxIt := maxIter * n * n
+		iter := 0
+		oldl2 := -1
+		oldm := -1
+		// m points to the last element of unconverged part of matrix.
+		m := n
+
+	Outer:
+		for m > 1 {
+			if iter > maxIt {
+				info = 0
+				for i := 0; i < n-1; i++ {
+					if e[i] != 0 {
+						info++
+					}
+				}
+				return info == 0
+			}
+			// Find diagonal block of matrix to work on.
+			if tol < 0 && math.Abs(d[m-1]) <= thresh {
+				d[m-1] = 0
+			}
+			smax = math.Abs(d[m-1])
+			smin := smax
+			var l2 int
+			var broke bool
+			for l3 := 0; l3 < m-1; l3++ {
+				l2 = m - l3 - 2
+				abss := math.Abs(d[l2])
+				abse := math.Abs(e[l2])
+				if tol < 0 && abss <= thresh {
+					d[l2] = 0
+				}
+				if abse <= thresh {
+					broke = true
+					break
+				}
+				smin = math.Min(smin, abss)
+				smax = math.Max(math.Max(smax, abss), abse)
+			}
+			if broke {
+				e[l2] = 0
+				if l2 == m-2 {
+					// Convergence of bottom singular value, return to top.
+					m--
+					continue
+				}
+				l2++
+			} else {
+				l2 = 0
+			}
+			// e[ll] through e[m-2] are nonzero, e[ll-1] is zero
+			if l2 == m-2 {
+				// Handle 2×2 block separately.
+				var sinr, cosr, sinl, cosl float64
+				d[m-1], d[m-2], sinr, cosr, sinl, cosl = impl.Dlasv2(d[m-2], e[m-2], d[m-1])
+				e[m-2] = 0
+				if ncvt > 0 {
+					bi.Drot(ncvt, vt[(m-2)*ldvt:], 1, vt[(m-1)*ldvt:], 1, cosr, sinr)
+				}
+				if nru > 0 {
+					bi.Drot(nru, u[m-2:], ldu, u[m-1:], ldu, cosl, sinl)
+				}
+				if ncc > 0 {
+					bi.Drot(ncc, c[(m-2)*ldc:], 1, c[(m-1)*ldc:], 1, cosl, sinl)
+				}
+				m -= 2
+				continue
+			}
+			// If working on a new submatrix, choose shift direction from larger end
+			// diagonal element toward smaller.
+			if l2 > oldm-1 || m-1 < oldl2 {
+				if math.Abs(d[l2]) >= math.Abs(d[m-1]) {
+					idir = 1
+				} else {
+					idir = 2
+				}
+			}
+			// Apply convergence tests.
+			// TODO(btracey): There is a lot of similar looking code here. See
+			// if there is a better way to de-duplicate.
+			if idir == 1 {
+				// Run convergence test in forward direction.
+				// First apply standard test to bottom of matrix.
+				if math.Abs(e[m-2]) <= math.Abs(tol)*math.Abs(d[m-1]) || (tol < 0 && math.Abs(e[m-2]) <= thresh) {
+					e[m-2] = 0
+					continue
+				}
+				if tol >= 0 {
+					// If relative accuracy desired, apply convergence criterion forward.
+					mu := math.Abs(d[l2])
+					sminl = mu
+					for l3 := l2; l3 < m-1; l3++ {
+						if math.Abs(e[l3]) <= tol*mu {
+							e[l3] = 0
+							continue Outer
+						}
+						mu = math.Abs(d[l3+1]) * (mu / (mu + math.Abs(e[l3])))
+						sminl = math.Min(sminl, mu)
+					}
+				}
+			} else {
+				// Run convergence test in backward direction.
+				// First apply standard test to top of matrix.
+				if math.Abs(e[l2]) <= math.Abs(tol)*math.Abs(d[l2]) || (tol < 0 && math.Abs(e[l2]) <= thresh) {
+					e[l2] = 0
+					continue
+				}
+				if tol >= 0 {
+					// If relative accuracy desired, apply convergence criterion backward.
+					mu := math.Abs(d[m-1])
+					sminl = mu
+					for l3 := m - 2; l3 >= l2; l3-- {
+						if math.Abs(e[l3]) <= tol*mu {
+							e[l3] = 0
+							continue Outer
+						}
+						mu = math.Abs(d[l3]) * (mu / (mu + math.Abs(e[l3])))
+						sminl = math.Min(sminl, mu)
+					}
+				}
+			}
+			oldl2 = l2
+			oldm = m
+			// Compute shift. First, test if shifting would ruin relative accuracy,
+			// and if so set the shift to zero.
+			var shift float64
+			if tol >= 0 && float64(n)*tol*(sminl/smax) <= math.Max(eps, (1.0/100)*tol) {
+				shift = 0
+			} else {
+				var sl2 float64
+				if idir == 1 {
+					sl2 = math.Abs(d[l2])
+					shift, _ = impl.Dlas2(d[m-2], e[m-2], d[m-1])
+				} else {
+					sl2 = math.Abs(d[m-1])
+					shift, _ = impl.Dlas2(d[l2], e[l2], d[l2+1])
+				}
+				// Test if shift is negligible
+				if sl2 > 0 {
+					if (shift/sl2)*(shift/sl2) < eps {
+						shift = 0
+					}
+				}
+			}
+			iter += m - l2 + 1
+			// If no shift, do simplified QR iteration.
+			if shift == 0 {
+				if idir == 1 {
+					cs := 1.0
+					oldcs := 1.0
+					var sn, r, oldsn float64
+					for i := l2; i < m-1; i++ {
+						cs, sn, r = impl.Dlartg(d[i]*cs, e[i])
+						if i > l2 {
+							e[i-1] = oldsn * r
+						}
+						oldcs, oldsn, d[i] = impl.Dlartg(oldcs*r, d[i+1]*sn)
+						work[i-l2] = cs
+						work[i-l2+nm1] = sn
+						work[i-l2+nm12] = oldcs
+						work[i-l2+nm13] = oldsn
+					}
+					h := d[m-1] * cs
+					d[m-1] = h * oldcs
+					e[m-2] = h * oldsn
+					if ncvt > 0 {
+						impl.Dlasr(blas.Left, lapack.Variable, lapack.Forward, m-l2, ncvt, work, work[n-1:], vt[l2*ldvt:], ldvt)
+					}
+					if nru > 0 {
+						impl.Dlasr(blas.Right, lapack.Variable, lapack.Forward, nru, m-l2, work[nm12:], work[nm13:], u[l2:], ldu)
+					}
+					if ncc > 0 {
+						impl.Dlasr(blas.Left, lapack.Variable, lapack.Forward, m-l2, ncc, work[nm12:], work[nm13:], c[l2*ldc:], ldc)
+					}
+					if math.Abs(e[m-2]) < thresh {
+						e[m-2] = 0
+					}
+				} else {
+					cs := 1.0
+					oldcs := 1.0
+					var sn, r, oldsn float64
+					for i := m - 1; i >= l2+1; i-- {
+						cs, sn, r = impl.Dlartg(d[i]*cs, e[i-1])
+						if i < m-1 {
+							e[i] = oldsn * r
+						}
+						oldcs, oldsn, d[i] = impl.Dlartg(oldcs*r, d[i-1]*sn)
+						work[i-l2-1] = cs
+						work[i-l2+nm1-1] = -sn
+						work[i-l2+nm12-1] = oldcs
+						work[i-l2+nm13-1] = -oldsn
+					}
+					h := d[l2] * cs
+					d[l2] = h * oldcs
+					e[l2] = h * oldsn
+					if ncvt > 0 {
+						impl.Dlasr(blas.Left, lapack.Variable, lapack.Backward, m-l2, ncvt, work[nm12:], work[nm13:], vt[l2*ldvt:], ldvt)
+					}
+					if nru > 0 {
+						impl.Dlasr(blas.Right, lapack.Variable, lapack.Backward, nru, m-l2, work, work[n-1:], u[l2:], ldu)
+					}
+					if ncc > 0 {
+						impl.Dlasr(blas.Left, lapack.Variable, lapack.Backward, m-l2, ncc, work, work[n-1:], c[l2*ldc:], ldc)
+					}
+					if math.Abs(e[l2]) <= thresh {
+						e[l2] = 0
+					}
+				}
+			} else {
+				// Use nonzero shift.
+				if idir == 1 {
+					// Chase bulge from top to bottom. Save cosines and sines for
+					// later singular vector updates.
+					f := (math.Abs(d[l2]) - shift) * (math.Copysign(1, d[l2]) + shift/d[l2])
+					g := e[l2]
+					var cosl, sinl float64
+					for i := l2; i < m-1; i++ {
+						cosr, sinr, r := impl.Dlartg(f, g)
+						if i > l2 {
+							e[i-1] = r
+						}
+						f = cosr*d[i] + sinr*e[i]
+						e[i] = cosr*e[i] - sinr*d[i]
+						g = sinr * d[i+1]
+						d[i+1] *= cosr
+						cosl, sinl, r = impl.Dlartg(f, g)
+						d[i] = r
+						f = cosl*e[i] + sinl*d[i+1]
+						d[i+1] = cosl*d[i+1] - sinl*e[i]
+						if i < m-2 {
+							g = sinl * e[i+1]
+							e[i+1] = cosl * e[i+1]
+						}
+						work[i-l2] = cosr
+						work[i-l2+nm1] = sinr
+						work[i-l2+nm12] = cosl
+						work[i-l2+nm13] = sinl
+					}
+					e[m-2] = f
+					if ncvt > 0 {
+						impl.Dlasr(blas.Left, lapack.Variable, lapack.Forward, m-l2, ncvt, work, work[n-1:], vt[l2*ldvt:], ldvt)
+					}
+					if nru > 0 {
+						impl.Dlasr(blas.Right, lapack.Variable, lapack.Forward, nru, m-l2, work[nm12:], work[nm13:], u[l2:], ldu)
+					}
+					if ncc > 0 {
+						impl.Dlasr(blas.Left, lapack.Variable, lapack.Forward, m-l2, ncc, work[nm12:], work[nm13:], c[l2*ldc:], ldc)
+					}
+					if math.Abs(e[m-2]) <= thresh {
+						e[m-2] = 0
+					}
+				} else {
+					// Chase bulge from top to bottom. Save cosines and sines for
+					// later singular vector updates.
+					f := (math.Abs(d[m-1]) - shift) * (math.Copysign(1, d[m-1]) + shift/d[m-1])
+					g := e[m-2]
+					for i := m - 1; i > l2; i-- {
+						cosr, sinr, r := impl.Dlartg(f, g)
+						if i < m-1 {
+							e[i] = r
+						}
+						f = cosr*d[i] + sinr*e[i-1]
+						e[i-1] = cosr*e[i-1] - sinr*d[i]
+						g = sinr * d[i-1]
+						d[i-1] *= cosr
+						cosl, sinl, r := impl.Dlartg(f, g)
+						d[i] = r
+						f = cosl*e[i-1] + sinl*d[i-1]
+						d[i-1] = cosl*d[i-1] - sinl*e[i-1]
+						if i > l2+1 {
+							g = sinl * e[i-2]
+							e[i-2] *= cosl
+						}
+						work[i-l2-1] = cosr
+						work[i-l2+nm1-1] = -sinr
+						work[i-l2+nm12-1] = cosl
+						work[i-l2+nm13-1] = -sinl
+					}
+					e[l2] = f
+					if math.Abs(e[l2]) <= thresh {
+						e[l2] = 0
+					}
+					if ncvt > 0 {
+						impl.Dlasr(blas.Left, lapack.Variable, lapack.Backward, m-l2, ncvt, work[nm12:], work[nm13:], vt[l2*ldvt:], ldvt)
+					}
+					if nru > 0 {
+						impl.Dlasr(blas.Right, lapack.Variable, lapack.Backward, nru, m-l2, work, work[n-1:], u[l2:], ldu)
+					}
+					if ncc > 0 {
+						impl.Dlasr(blas.Left, lapack.Variable, lapack.Backward, m-l2, ncc, work, work[n-1:], c[l2*ldc:], ldc)
+					}
+				}
+			}
+		}
+	}
+
+	// All singular values converged, make them positive.
+	for i := 0; i < n; i++ {
+		if d[i] < 0 {
+			d[i] *= -1
+			if ncvt > 0 {
+				bi.Dscal(ncvt, -1, vt[i*ldvt:], 1)
+			}
+		}
+	}
+
+	// Sort the singular values in decreasing order.
+	for i := 0; i < n-1; i++ {
+		isub := 0
+		smin := d[0]
+		for j := 1; j < n-i; j++ {
+			if d[j] <= smin {
+				isub = j
+				smin = d[j]
+			}
+		}
+		if isub != n-i {
+			// Swap singular values and vectors.
+			d[isub] = d[n-i-1]
+			d[n-i-1] = smin
+			if ncvt > 0 {
+				bi.Dswap(ncvt, vt[isub*ldvt:], 1, vt[(n-i-1)*ldvt:], 1)
+			}
+			if nru > 0 {
+				bi.Dswap(nru, u[isub:], ldu, u[n-i-1:], ldu)
+			}
+			if ncc > 0 {
+				bi.Dswap(ncc, c[isub*ldc:], 1, c[(n-i-1)*ldc:], 1)
+			}
+		}
+	}
+	info = 0
+	for i := 0; i < n-1; i++ {
+		if e[i] != 0 {
+			info++
+		}
+	}
+	return info == 0
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dgebak.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dgebak.go
new file mode 100644
index 00000000..e271c99d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dgebak.go
@@ -0,0 +1,78 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dgebak updates an n×m matrix V as
+//  V = P D V,        if side == lapack.RightEV,
+//  V = P D^{-1} V,   if side == lapack.LeftEV,
+// where P and D are n×n permutation and scaling matrices, respectively,
+// implicitly represented by job, scale, ilo and ihi as returned by Dgebal.
+//
+// Typically, columns of the matrix V contain the right or left (determined by
+// side) eigenvectors of the balanced matrix output by Dgebal, and Dgebak forms
+// the eigenvectors of the original matrix.
+//
+// Dgebak is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dgebak(job lapack.Job, side lapack.EVSide, n, ilo, ihi int, scale []float64, m int, v []float64, ldv int) {
+	switch job {
+	default:
+		panic(badJob)
+	case lapack.None, lapack.Permute, lapack.Scale, lapack.PermuteScale:
+	}
+	switch side {
+	default:
+		panic(badEVSide)
+	case lapack.LeftEV, lapack.RightEV:
+	}
+	checkMatrix(n, m, v, ldv)
+	switch {
+	case ilo < 0 || max(0, n-1) < ilo:
+		panic(badIlo)
+	case ihi < min(ilo, n-1) || n <= ihi:
+		panic(badIhi)
+	}
+
+	// Quick return if possible.
+	if n == 0 || m == 0 || job == lapack.None {
+		return
+	}
+
+	bi := blas64.Implementation()
+	if ilo != ihi && job != lapack.Permute {
+		// Backward balance.
+		if side == lapack.RightEV {
+			for i := ilo; i <= ihi; i++ {
+				bi.Dscal(m, scale[i], v[i*ldv:], 1)
+			}
+		} else {
+			for i := ilo; i <= ihi; i++ {
+				bi.Dscal(m, 1/scale[i], v[i*ldv:], 1)
+			}
+		}
+	}
+	if job == lapack.Scale {
+		return
+	}
+	// Backward permutation.
+	for i := ilo - 1; i >= 0; i-- {
+		k := int(scale[i])
+		if k == i {
+			continue
+		}
+		bi.Dswap(m, v[i*ldv:], 1, v[k*ldv:], 1)
+	}
+	for i := ihi + 1; i < n; i++ {
+		k := int(scale[i])
+		if k == i {
+			continue
+		}
+		bi.Dswap(m, v[i*ldv:], 1, v[k*ldv:], 1)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dgebal.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dgebal.go
new file mode 100644
index 00000000..ee57ead1
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dgebal.go
@@ -0,0 +1,228 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dgebal balances an n×n matrix A. Balancing consists of two stages, permuting
+// and scaling. Both steps are optional and depend on the value of job.
+//
+// Permuting consists of applying a permutation matrix P such that the matrix
+// that results from P^T*A*P takes the upper block triangular form
+//            [ T1  X  Y  ]
+//  P^T A P = [  0  B  Z  ],
+//            [  0  0  T2 ]
+// where T1 and T2 are upper triangular matrices and B contains at least one
+// nonzero off-diagonal element in each row and column. The indices ilo and ihi
+// mark the starting and ending columns of the submatrix B. The eigenvalues of A
+// isolated in the first 0 to ilo-1 and last ihi+1 to n-1 elements on the
+// diagonal can be read off without any roundoff error.
+//
+// Scaling consists of applying a diagonal similarity transformation D such that
+// D^{-1}*B*D has the 1-norm of each row and its corresponding column nearly
+// equal. The output matrix is
+//  [ T1     X*D          Y    ]
+//  [  0  inv(D)*B*D  inv(D)*Z ].
+//  [  0      0           T2   ]
+// Scaling may reduce the 1-norm of the matrix, and improve the accuracy of
+// the computed eigenvalues and/or eigenvectors.
+//
+// job specifies the operations that will be performed on A.
+// If job is lapack.None, Dgebal sets scale[i] = 1 for all i and returns ilo=0, ihi=n-1.
+// If job is lapack.Permute, only permuting will be done.
+// If job is lapack.Scale, only scaling will be done.
+// If job is lapack.PermuteScale, both permuting and scaling will be done.
+//
+// On return, if job is lapack.Permute or lapack.PermuteScale, it will hold that
+//  A[i,j] == 0,   for i > j and j ∈ {0, ..., ilo-1, ihi+1, ..., n-1}.
+// If job is lapack.None or lapack.Scale, or if n == 0, it will hold that
+//  ilo == 0 and ihi == n-1.
+//
+// On return, scale will contain information about the permutations and scaling
+// factors applied to A. If π(j) denotes the index of the column interchanged
+// with column j, and D[j,j] denotes the scaling factor applied to column j,
+// then
+//  scale[j] == π(j),     for j ∈ {0, ..., ilo-1, ihi+1, ..., n-1},
+//           == D[j,j],   for j ∈ {ilo, ..., ihi}.
+// scale must have length equal to n, otherwise Dgebal will panic.
+//
+// Dgebal is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dgebal(job lapack.Job, n int, a []float64, lda int, scale []float64) (ilo, ihi int) {
+	switch job {
+	default:
+		panic(badJob)
+	case lapack.None, lapack.Permute, lapack.Scale, lapack.PermuteScale:
+	}
+	checkMatrix(n, n, a, lda)
+	if len(scale) != n {
+		panic("lapack: bad length of scale")
+	}
+
+	ilo = 0
+	ihi = n - 1
+
+	if n == 0 || job == lapack.None {
+		for i := range scale {
+			scale[i] = 1
+		}
+		return ilo, ihi
+	}
+
+	bi := blas64.Implementation()
+	swapped := true
+
+	if job == lapack.Scale {
+		goto scaling
+	}
+
+	// Permutation to isolate eigenvalues if possible.
+	//
+	// Search for rows isolating an eigenvalue and push them down.
+	for swapped {
+		swapped = false
+	rows:
+		for i := ihi; i >= 0; i-- {
+			for j := 0; j <= ihi; j++ {
+				if i == j {
+					continue
+				}
+				if a[i*lda+j] != 0 {
+					continue rows
+				}
+			}
+			// Row i has only zero off-diagonal elements in the
+			// block A[ilo:ihi+1,ilo:ihi+1].
+			scale[ihi] = float64(i)
+			if i != ihi {
+				bi.Dswap(ihi+1, a[i:], lda, a[ihi:], lda)
+				bi.Dswap(n, a[i*lda:], 1, a[ihi*lda:], 1)
+			}
+			if ihi == 0 {
+				scale[0] = 1
+				return ilo, ihi
+			}
+			ihi--
+			swapped = true
+			break
+		}
+	}
+	// Search for columns isolating an eigenvalue and push them left.
+	swapped = true
+	for swapped {
+		swapped = false
+	columns:
+		for j := ilo; j <= ihi; j++ {
+			for i := ilo; i <= ihi; i++ {
+				if i == j {
+					continue
+				}
+				if a[i*lda+j] != 0 {
+					continue columns
+				}
+			}
+			// Column j has only zero off-diagonal elements in the
+			// block A[ilo:ihi+1,ilo:ihi+1].
+			scale[ilo] = float64(j)
+			if j != ilo {
+				bi.Dswap(ihi+1, a[j:], lda, a[ilo:], lda)
+				bi.Dswap(n-ilo, a[j*lda+ilo:], 1, a[ilo*lda+ilo:], 1)
+			}
+			swapped = true
+			ilo++
+			break
+		}
+	}
+
+scaling:
+	for i := ilo; i <= ihi; i++ {
+		scale[i] = 1
+	}
+
+	if job == lapack.Permute {
+		return ilo, ihi
+	}
+
+	// Balance the submatrix in rows ilo to ihi.
+
+	const (
+		// sclfac should be a power of 2 to avoid roundoff errors.
+		// Elements of scale are restricted to powers of sclfac,
+		// therefore the matrix will be only nearly balanced.
+		sclfac = 2
+		// factor determines the minimum reduction of the row and column
+		// norms that is considered non-negligible. It must be less than 1.
+		factor = 0.95
+	)
+	sfmin1 := dlamchS / dlamchP
+	sfmax1 := 1 / sfmin1
+	sfmin2 := sfmin1 * sclfac
+	sfmax2 := 1 / sfmin2
+
+	// Iterative loop for norm reduction.
+	var conv bool
+	for !conv {
+		conv = true
+		for i := ilo; i <= ihi; i++ {
+			c := bi.Dnrm2(ihi-ilo+1, a[ilo*lda+i:], lda)
+			r := bi.Dnrm2(ihi-ilo+1, a[i*lda+ilo:], 1)
+			ica := bi.Idamax(ihi+1, a[i:], lda)
+			ca := math.Abs(a[ica*lda+i])
+			ira := bi.Idamax(n-ilo, a[i*lda+ilo:], 1)
+			ra := math.Abs(a[i*lda+ilo+ira])
+
+			// Guard against zero c or r due to underflow.
+			if c == 0 || r == 0 {
+				continue
+			}
+			g := r / sclfac
+			f := 1.0
+			s := c + r
+			for c < g && math.Max(f, math.Max(c, ca)) < sfmax2 && math.Min(r, math.Min(g, ra)) > sfmin2 {
+				if math.IsNaN(c + f + ca + r + g + ra) {
+					// Panic if NaN to avoid infinite loop.
+					panic("lapack: NaN")
+				}
+				f *= sclfac
+				c *= sclfac
+				ca *= sclfac
+				g /= sclfac
+				r /= sclfac
+				ra /= sclfac
+			}
+			g = c / sclfac
+			for r <= g && math.Max(r, ra) < sfmax2 && math.Min(math.Min(f, c), math.Min(g, ca)) > sfmin2 {
+				f /= sclfac
+				c /= sclfac
+				ca /= sclfac
+				g /= sclfac
+				r *= sclfac
+				ra *= sclfac
+			}
+
+			if c+r >= factor*s {
+				// Reduction would be negligible.
+				continue
+			}
+			if f < 1 && scale[i] < 1 && f*scale[i] <= sfmin1 {
+				continue
+			}
+			if f > 1 && scale[i] > 1 && scale[i] >= sfmax1/f {
+				continue
+			}
+
+			// Now balance.
+			scale[i] *= f
+			bi.Dscal(n-ilo, 1/f, a[i*lda+ilo:], 1)
+			bi.Dscal(ihi+1, f, a[i:], lda)
+			conv = false
+		}
+	}
+	return ilo, ihi
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dgebd2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dgebd2.go
new file mode 100644
index 00000000..7f7f61c1
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dgebd2.go
@@ -0,0 +1,74 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "gonum.org/v1/gonum/blas"
+
+// Dgebd2 reduces an m×n matrix A to upper or lower bidiagonal form by an orthogonal
+// transformation.
+//  Q^T * A * P = B
+// if m >= n, B is upper diagonal, otherwise B is lower bidiagonal.
+// d is the diagonal, len = min(m,n)
+// e is the off-diagonal len = min(m,n)-1
+//
+// Dgebd2 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dgebd2(m, n int, a []float64, lda int, d, e, tauQ, tauP, work []float64) {
+	checkMatrix(m, n, a, lda)
+	if len(d) < min(m, n) {
+		panic(badD)
+	}
+	if len(e) < min(m, n)-1 {
+		panic(badE)
+	}
+	if len(tauQ) < min(m, n) {
+		panic(badTauQ)
+	}
+	if len(tauP) < min(m, n) {
+		panic(badTauP)
+	}
+	if len(work) < max(m, n) {
+		panic(badWork)
+	}
+	if m >= n {
+		for i := 0; i < n; i++ {
+			a[i*lda+i], tauQ[i] = impl.Dlarfg(m-i, a[i*lda+i], a[min(i+1, m-1)*lda+i:], lda)
+			d[i] = a[i*lda+i]
+			a[i*lda+i] = 1
+			// Apply H_i to A[i:m, i+1:n] from the left.
+			if i < n-1 {
+				impl.Dlarf(blas.Left, m-i, n-i-1, a[i*lda+i:], lda, tauQ[i], a[i*lda+i+1:], lda, work)
+			}
+			a[i*lda+i] = d[i]
+			if i < n-1 {
+				a[i*lda+i+1], tauP[i] = impl.Dlarfg(n-i-1, a[i*lda+i+1], a[i*lda+min(i+2, n-1):], 1)
+				e[i] = a[i*lda+i+1]
+				a[i*lda+i+1] = 1
+				impl.Dlarf(blas.Right, m-i-1, n-i-1, a[i*lda+i+1:], 1, tauP[i], a[(i+1)*lda+i+1:], lda, work)
+				a[i*lda+i+1] = e[i]
+			} else {
+				tauP[i] = 0
+			}
+		}
+		return
+	}
+	for i := 0; i < m; i++ {
+		a[i*lda+i], tauP[i] = impl.Dlarfg(n-i, a[i*lda+i], a[i*lda+min(i+1, n-1):], 1)
+		d[i] = a[i*lda+i]
+		a[i*lda+i] = 1
+		if i < m-1 {
+			impl.Dlarf(blas.Right, m-i-1, n-i, a[i*lda+i:], 1, tauP[i], a[(i+1)*lda+i:], lda, work)
+		}
+		a[i*lda+i] = d[i]
+		if i < m-1 {
+			a[(i+1)*lda+i], tauQ[i] = impl.Dlarfg(m-i-1, a[(i+1)*lda+i], a[min(i+2, m-1)*lda+i:], lda)
+			e[i] = a[(i+1)*lda+i]
+			a[(i+1)*lda+i] = 1
+			impl.Dlarf(blas.Left, m-i-1, n-i-1, a[(i+1)*lda+i:], lda, tauQ[i], a[(i+1)*lda+i+1:], lda, work)
+			a[(i+1)*lda+i] = e[i]
+		} else {
+			tauQ[i] = 0
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dgebrd.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dgebrd.go
new file mode 100644
index 00000000..f0c041cc
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dgebrd.go
@@ -0,0 +1,150 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dgebrd reduces a general m×n matrix A to upper or lower bidiagonal form B by
+// an orthogonal transformation:
+//  Q^T * A * P = B.
+// The diagonal elements of B are stored in d and the off-diagonal elements are stored
+// in e. These are additionally stored along the diagonal of A and the off-diagonal
+// of A. If m >= n B is an upper-bidiagonal matrix, and if m < n B is a
+// lower-bidiagonal matrix.
+//
+// The remaining elements of A store the data needed to construct Q and P.
+// The matrices Q and P are products of elementary reflectors
+//  if m >= n, Q = H_0 * H_1 * ... * H_{n-1},
+//             P = G_0 * G_1 * ... * G_{n-2},
+//  if m < n,  Q = H_0 * H_1 * ... * H_{m-2},
+//             P = G_0 * G_1 * ... * G_{m-1},
+// where
+//  H_i = I - tauQ[i] * v_i * v_i^T,
+//  G_i = I - tauP[i] * u_i * u_i^T.
+//
+// As an example, on exit the entries of A when m = 6, and n = 5
+//  [ d   e  u1  u1  u1]
+//  [v1   d   e  u2  u2]
+//  [v1  v2   d   e  u3]
+//  [v1  v2  v3   d   e]
+//  [v1  v2  v3  v4   d]
+//  [v1  v2  v3  v4  v5]
+// and when m = 5, n = 6
+//  [ d  u1  u1  u1  u1  u1]
+//  [ e   d  u2  u2  u2  u2]
+//  [v1   e   d  u3  u3  u3]
+//  [v1  v2   e   d  u4  u4]
+//  [v1  v2  v3   e   d  u5]
+//
+// d, tauQ, and tauP must all have length at least min(m,n), and e must have
+// length min(m,n) - 1, unless lwork is -1 when there is no check except for
+// work which must have a length of at least one.
+//
+// work is temporary storage, and lwork specifies the usable memory length.
+// At minimum, lwork >= max(1,m,n) or be -1 and this function will panic otherwise.
+// Dgebrd is blocked decomposition, but the block size is limited
+// by the temporary space available. If lwork == -1, instead of performing Dgebrd,
+// the optimal work length will be stored into work[0].
+//
+// Dgebrd is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dgebrd(m, n int, a []float64, lda int, d, e, tauQ, tauP, work []float64, lwork int) {
+	checkMatrix(m, n, a, lda)
+	// Calculate optimal work.
+	nb := impl.Ilaenv(1, "DGEBRD", " ", m, n, -1, -1)
+	var lworkOpt int
+	if lwork == -1 {
+		if len(work) < 1 {
+			panic(badWork)
+		}
+		lworkOpt = ((m + n) * nb)
+		work[0] = float64(max(1, lworkOpt))
+		return
+	}
+	minmn := min(m, n)
+	if len(d) < minmn {
+		panic(badD)
+	}
+	if len(e) < minmn-1 {
+		panic(badE)
+	}
+	if len(tauQ) < minmn {
+		panic(badTauQ)
+	}
+	if len(tauP) < minmn {
+		panic(badTauP)
+	}
+	ws := max(m, n)
+	if lwork < max(1, ws) {
+		panic(badWork)
+	}
+	if len(work) < lwork {
+		panic(badWork)
+	}
+	var nx int
+	if nb > 1 && nb < minmn {
+		nx = max(nb, impl.Ilaenv(3, "DGEBRD", " ", m, n, -1, -1))
+		if nx < minmn {
+			ws = (m + n) * nb
+			if lwork < ws {
+				nbmin := impl.Ilaenv(2, "DGEBRD", " ", m, n, -1, -1)
+				if lwork >= (m+n)*nbmin {
+					nb = lwork / (m + n)
+				} else {
+					nb = minmn
+					nx = minmn
+				}
+			}
+		}
+	} else {
+		nx = minmn
+	}
+	bi := blas64.Implementation()
+	ldworkx := nb
+	ldworky := nb
+	var i int
+	// Netlib lapack has minmn - nx, but this makes the last nx rows (which by
+	// default is large) be unblocked. As written here, the blocking is more
+	// consistent.
+	for i = 0; i < minmn-nb; i += nb {
+		// Reduce rows and columns i:i+nb to bidiagonal form and return
+		// the matrices X and Y which are needed to update the unreduced
+		// part of the matrix.
+		// X is stored in the first m rows of work, y in the next rows.
+		x := work[:m*ldworkx]
+		y := work[m*ldworkx:]
+		impl.Dlabrd(m-i, n-i, nb, a[i*lda+i:], lda,
+			d[i:], e[i:], tauQ[i:], tauP[i:],
+			x, ldworkx, y, ldworky)
+
+		// Update the trailing submatrix A[i+nb:m,i+nb:n], using an update
+		// of the form  A := A - V*Y**T - X*U**T
+		bi.Dgemm(blas.NoTrans, blas.Trans, m-i-nb, n-i-nb, nb,
+			-1, a[(i+nb)*lda+i:], lda, y[nb*ldworky:], ldworky,
+			1, a[(i+nb)*lda+i+nb:], lda)
+
+		bi.Dgemm(blas.NoTrans, blas.NoTrans, m-i-nb, n-i-nb, nb,
+			-1, x[nb*ldworkx:], ldworkx, a[i*lda+i+nb:], lda,
+			1, a[(i+nb)*lda+i+nb:], lda)
+
+		// Copy diagonal and off-diagonal elements of B back into A.
+		if m >= n {
+			for j := i; j < i+nb; j++ {
+				a[j*lda+j] = d[j]
+				a[j*lda+j+1] = e[j]
+			}
+		} else {
+			for j := i; j < i+nb; j++ {
+				a[j*lda+j] = d[j]
+				a[(j+1)*lda+j] = e[j]
+			}
+		}
+	}
+	// Use unblocked code to reduce the remainder of the matrix.
+	impl.Dgebd2(m-i, n-i, a[i*lda+i:], lda, d[i:], e[i:], tauQ[i:], tauP[i:], work)
+	work[0] = float64(lworkOpt)
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dgecon.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dgecon.go
new file mode 100644
index 00000000..20bafce4
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dgecon.go
@@ -0,0 +1,81 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dgecon estimates the reciprocal of the condition number of the n×n matrix A
+// given the LU decomposition of the matrix. The condition number computed may
+// be based on the 1-norm or the ∞-norm.
+//
+// The slice a contains the result of the LU decomposition of A as computed by Dgetrf.
+//
+// anorm is the corresponding 1-norm or ∞-norm of the original matrix A.
+//
+// work is a temporary data slice of length at least 4*n and Dgecon will panic otherwise.
+//
+// iwork is a temporary data slice of length at least n and Dgecon will panic otherwise.
+func (impl Implementation) Dgecon(norm lapack.MatrixNorm, n int, a []float64, lda int, anorm float64, work []float64, iwork []int) float64 {
+	checkMatrix(n, n, a, lda)
+	if norm != lapack.MaxColumnSum && norm != lapack.MaxRowSum {
+		panic(badNorm)
+	}
+	if len(work) < 4*n {
+		panic(badWork)
+	}
+	if len(iwork) < n {
+		panic(badWork)
+	}
+
+	if n == 0 {
+		return 1
+	} else if anorm == 0 {
+		return 0
+	}
+
+	bi := blas64.Implementation()
+	var rcond, ainvnm float64
+	var kase int
+	var normin bool
+	isave := new([3]int)
+	onenrm := norm == lapack.MaxColumnSum
+	smlnum := dlamchS
+	kase1 := 2
+	if onenrm {
+		kase1 = 1
+	}
+	for {
+		ainvnm, kase = impl.Dlacn2(n, work[n:], work, iwork, ainvnm, kase, isave)
+		if kase == 0 {
+			if ainvnm != 0 {
+				rcond = (1 / ainvnm) / anorm
+			}
+			return rcond
+		}
+		var sl, su float64
+		if kase == kase1 {
+			sl = impl.Dlatrs(blas.Lower, blas.NoTrans, blas.Unit, normin, n, a, lda, work, work[2*n:])
+			su = impl.Dlatrs(blas.Upper, blas.NoTrans, blas.NonUnit, normin, n, a, lda, work, work[3*n:])
+		} else {
+			su = impl.Dlatrs(blas.Upper, blas.Trans, blas.NonUnit, normin, n, a, lda, work, work[3*n:])
+			sl = impl.Dlatrs(blas.Lower, blas.Trans, blas.Unit, normin, n, a, lda, work, work[2*n:])
+		}
+		scale := sl * su
+		normin = true
+		if scale != 1 {
+			ix := bi.Idamax(n, work, 1)
+			if scale == 0 || scale < math.Abs(work[ix])*smlnum {
+				return rcond
+			}
+			impl.Drscl(n, scale, work, 1)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dgeev.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dgeev.go
new file mode 100644
index 00000000..7c2d9a29
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dgeev.go
@@ -0,0 +1,284 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dgeev computes the eigenvalues and, optionally, the left and/or right
+// eigenvectors for an n×n real nonsymmetric matrix A.
+//
+// The right eigenvector v_j of A corresponding to an eigenvalue λ_j
+// is defined by
+//  A v_j = λ_j v_j,
+// and the left eigenvector u_j corresponding to an eigenvalue λ_j is defined by
+//  u_j^H A = λ_j u_j^H,
+// where u_j^H is the conjugate transpose of u_j.
+//
+// On return, A will be overwritten and the left and right eigenvectors will be
+// stored, respectively, in the columns of the n×n matrices VL and VR in the
+// same order as their eigenvalues. If the j-th eigenvalue is real, then
+//  u_j = VL[:,j],
+//  v_j = VR[:,j],
+// and if it is not real, then j and j+1 form a complex conjugate pair and the
+// eigenvectors can be recovered as
+//  u_j     = VL[:,j] + i*VL[:,j+1],
+//  u_{j+1} = VL[:,j] - i*VL[:,j+1],
+//  v_j     = VR[:,j] + i*VR[:,j+1],
+//  v_{j+1} = VR[:,j] - i*VR[:,j+1],
+// where i is the imaginary unit. The computed eigenvectors are normalized to
+// have Euclidean norm equal to 1 and largest component real.
+//
+// Left eigenvectors will be computed only if jobvl == lapack.ComputeLeftEV,
+// otherwise jobvl must be lapack.None. Right eigenvectors will be computed
+// only if jobvr == lapack.ComputeRightEV, otherwise jobvr must be lapack.None.
+// For other values of jobvl and jobvr Dgeev will panic.
+//
+// wr and wi contain the real and imaginary parts, respectively, of the computed
+// eigenvalues. Complex conjugate pairs of eigenvalues appear consecutively with
+// the eigenvalue having the positive imaginary part first.
+// wr and wi must have length n, and Dgeev will panic otherwise.
+//
+// work must have length at least lwork and lwork must be at least max(1,4*n) if
+// the left or right eigenvectors are computed, and at least max(1,3*n) if no
+// eigenvectors are computed. For good performance, lwork must generally be
+// larger.  On return, optimal value of lwork will be stored in work[0].
+//
+// If lwork == -1, instead of performing Dgeev, the function only calculates the
+// optimal vaule of lwork and stores it into work[0].
+//
+// On return, first is the index of the first valid eigenvalue. If first == 0,
+// all eigenvalues and eigenvectors have been computed. If first is positive,
+// Dgeev failed to compute all the eigenvalues, no eigenvectors have been
+// computed and wr[first:] and wi[first:] contain those eigenvalues which have
+// converged.
+func (impl Implementation) Dgeev(jobvl lapack.LeftEVJob, jobvr lapack.RightEVJob, n int, a []float64, lda int, wr, wi []float64, vl []float64, ldvl int, vr []float64, ldvr int, work []float64, lwork int) (first int) {
+	var wantvl bool
+	switch jobvl {
+	default:
+		panic("lapack: invalid LeftEVJob")
+	case lapack.ComputeLeftEV:
+		wantvl = true
+	case lapack.None:
+	}
+	var wantvr bool
+	switch jobvr {
+	default:
+		panic("lapack: invalid RightEVJob")
+	case lapack.ComputeRightEV:
+		wantvr = true
+	case lapack.None:
+	}
+	switch {
+	case n < 0:
+		panic(nLT0)
+	case len(work) < lwork:
+		panic(shortWork)
+	}
+	var minwrk int
+	if wantvl || wantvr {
+		minwrk = max(1, 4*n)
+	} else {
+		minwrk = max(1, 3*n)
+	}
+	if lwork != -1 {
+		checkMatrix(n, n, a, lda)
+		if wantvl {
+			checkMatrix(n, n, vl, ldvl)
+		}
+		if wantvr {
+			checkMatrix(n, n, vr, ldvr)
+		}
+		switch {
+		case len(wr) != n:
+			panic("lapack: bad length of wr")
+		case len(wi) != n:
+			panic("lapack: bad length of wi")
+		case lwork < minwrk:
+			panic(badWork)
+		}
+	}
+
+	// Quick return if possible.
+	if n == 0 {
+		work[0] = 1
+		return 0
+	}
+
+	maxwrk := 2*n + n*impl.Ilaenv(1, "DGEHRD", " ", n, 1, n, 0)
+	if wantvl || wantvr {
+		maxwrk = max(maxwrk, 2*n+(n-1)*impl.Ilaenv(1, "DORGHR", " ", n, 1, n, -1))
+		impl.Dhseqr(lapack.EigenvaluesAndSchur, lapack.OriginalEV, n, 0, n-1,
+			nil, 1, nil, nil, nil, 1, work, -1)
+		maxwrk = max(maxwrk, max(n+1, n+int(work[0])))
+		side := lapack.LeftEV
+		if wantvr {
+			side = lapack.RightEV
+		}
+		impl.Dtrevc3(side, lapack.AllEVMulQ, nil, n, nil, 1, nil, 1, nil, 1,
+			n, work, -1)
+		maxwrk = max(maxwrk, n+int(work[0]))
+		maxwrk = max(maxwrk, 4*n)
+	} else {
+		impl.Dhseqr(lapack.EigenvaluesOnly, lapack.None, n, 0, n-1,
+			nil, 1, nil, nil, nil, 1, work, -1)
+		maxwrk = max(maxwrk, max(n+1, n+int(work[0])))
+	}
+	maxwrk = max(maxwrk, minwrk)
+
+	if lwork == -1 {
+		work[0] = float64(maxwrk)
+		return 0
+	}
+
+	// Get machine constants.
+	smlnum := math.Sqrt(dlamchS) / dlamchP
+	bignum := 1 / smlnum
+
+	// Scale A if max element outside range [smlnum,bignum].
+	anrm := impl.Dlange(lapack.MaxAbs, n, n, a, lda, nil)
+	var scalea bool
+	var cscale float64
+	if 0 < anrm && anrm < smlnum {
+		scalea = true
+		cscale = smlnum
+	} else if anrm > bignum {
+		scalea = true
+		cscale = bignum
+	}
+	if scalea {
+		impl.Dlascl(lapack.General, 0, 0, anrm, cscale, n, n, a, lda)
+	}
+
+	// Balance the matrix.
+	workbal := work[:n]
+	ilo, ihi := impl.Dgebal(lapack.PermuteScale, n, a, lda, workbal)
+
+	// Reduce to upper Hessenberg form.
+	iwrk := 2 * n
+	tau := work[n : iwrk-1]
+	impl.Dgehrd(n, ilo, ihi, a, lda, tau, work[iwrk:], lwork-iwrk)
+
+	var side lapack.EVSide
+	if wantvl {
+		side = lapack.LeftEV
+		// Copy Householder vectors to VL.
+		impl.Dlacpy(blas.Lower, n, n, a, lda, vl, ldvl)
+		// Generate orthogonal matrix in VL.
+		impl.Dorghr(n, ilo, ihi, vl, ldvl, tau, work[iwrk:], lwork-iwrk)
+		// Perform QR iteration, accumulating Schur vectors in VL.
+		iwrk = n
+		first = impl.Dhseqr(lapack.EigenvaluesAndSchur, lapack.OriginalEV, n, ilo, ihi,
+			a, lda, wr, wi, vl, ldvl, work[iwrk:], lwork-iwrk)
+		if wantvr {
+			// Want left and right eigenvectors.
+			// Copy Schur vectors to VR.
+			side = lapack.RightLeftEV
+			impl.Dlacpy(blas.All, n, n, vl, ldvl, vr, ldvr)
+		}
+	} else if wantvr {
+		side = lapack.RightEV
+		// Copy Householder vectors to VR.
+		impl.Dlacpy(blas.Lower, n, n, a, lda, vr, ldvr)
+		// Generate orthogonal matrix in VR.
+		impl.Dorghr(n, ilo, ihi, vr, ldvr, tau, work[iwrk:], lwork-iwrk)
+		// Perform QR iteration, accumulating Schur vectors in VR.
+		iwrk = n
+		first = impl.Dhseqr(lapack.EigenvaluesAndSchur, lapack.OriginalEV, n, ilo, ihi,
+			a, lda, wr, wi, vr, ldvr, work[iwrk:], lwork-iwrk)
+	} else {
+		// Compute eigenvalues only.
+		iwrk = n
+		first = impl.Dhseqr(lapack.EigenvaluesOnly, lapack.None, n, ilo, ihi,
+			a, lda, wr, wi, nil, 1, work[iwrk:], lwork-iwrk)
+	}
+
+	if first > 0 {
+		if scalea {
+			// Undo scaling.
+			impl.Dlascl(lapack.General, 0, 0, cscale, anrm, n-first, 1, wr[first:], 1)
+			impl.Dlascl(lapack.General, 0, 0, cscale, anrm, n-first, 1, wi[first:], 1)
+			impl.Dlascl(lapack.General, 0, 0, cscale, anrm, ilo, 1, wr, 1)
+			impl.Dlascl(lapack.General, 0, 0, cscale, anrm, ilo, 1, wi, 1)
+		}
+		work[0] = float64(maxwrk)
+		return first
+	}
+
+	if wantvl || wantvr {
+		// Compute left and/or right eigenvectors.
+		impl.Dtrevc3(side, lapack.AllEVMulQ, nil, n,
+			a, lda, vl, ldvl, vr, ldvr, n, work[iwrk:], lwork-iwrk)
+	}
+	bi := blas64.Implementation()
+	if wantvl {
+		// Undo balancing of left eigenvectors.
+		impl.Dgebak(lapack.PermuteScale, lapack.LeftEV, n, ilo, ihi, workbal, n, vl, ldvl)
+		// Normalize left eigenvectors and make largest component real.
+		for i, wii := range wi {
+			if wii < 0 {
+				continue
+			}
+			if wii == 0 {
+				scl := 1 / bi.Dnrm2(n, vl[i:], ldvl)
+				bi.Dscal(n, scl, vl[i:], ldvl)
+				continue
+			}
+			scl := 1 / impl.Dlapy2(bi.Dnrm2(n, vl[i:], ldvl), bi.Dnrm2(n, vl[i+1:], ldvl))
+			bi.Dscal(n, scl, vl[i:], ldvl)
+			bi.Dscal(n, scl, vl[i+1:], ldvl)
+			for k := 0; k < n; k++ {
+				vi := vl[k*ldvl+i]
+				vi1 := vl[k*ldvl+i+1]
+				work[iwrk+k] = vi*vi + vi1*vi1
+			}
+			k := bi.Idamax(n, work[iwrk:iwrk+n], 1)
+			cs, sn, _ := impl.Dlartg(vl[k*ldvl+i], vl[k*ldvl+i+1])
+			bi.Drot(n, vl[i:], ldvl, vl[i+1:], ldvl, cs, sn)
+			vl[k*ldvl+i+1] = 0
+		}
+	}
+	if wantvr {
+		// Undo balancing of right eigenvectors.
+		impl.Dgebak(lapack.PermuteScale, lapack.RightEV, n, ilo, ihi, workbal, n, vr, ldvr)
+		// Normalize right eigenvectors and make largest component real.
+		for i, wii := range wi {
+			if wii < 0 {
+				continue
+			}
+			if wii == 0 {
+				scl := 1 / bi.Dnrm2(n, vr[i:], ldvr)
+				bi.Dscal(n, scl, vr[i:], ldvr)
+				continue
+			}
+			scl := 1 / impl.Dlapy2(bi.Dnrm2(n, vr[i:], ldvr), bi.Dnrm2(n, vr[i+1:], ldvr))
+			bi.Dscal(n, scl, vr[i:], ldvr)
+			bi.Dscal(n, scl, vr[i+1:], ldvr)
+			for k := 0; k < n; k++ {
+				vi := vr[k*ldvr+i]
+				vi1 := vr[k*ldvr+i+1]
+				work[iwrk+k] = vi*vi + vi1*vi1
+			}
+			k := bi.Idamax(n, work[iwrk:iwrk+n], 1)
+			cs, sn, _ := impl.Dlartg(vr[k*ldvr+i], vr[k*ldvr+i+1])
+			bi.Drot(n, vr[i:], ldvr, vr[i+1:], ldvr, cs, sn)
+			vr[k*ldvr+i+1] = 0
+		}
+	}
+
+	if scalea {
+		// Undo scaling.
+		impl.Dlascl(lapack.General, 0, 0, cscale, anrm, n-first, 1, wr[first:], 1)
+		impl.Dlascl(lapack.General, 0, 0, cscale, anrm, n-first, 1, wi[first:], 1)
+	}
+
+	work[0] = float64(maxwrk)
+	return first
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dgehd2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dgehd2.go
new file mode 100644
index 00000000..776f8421
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dgehd2.go
@@ -0,0 +1,84 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "gonum.org/v1/gonum/blas"
+
+// Dgehd2 reduces a block of a general n×n matrix A to upper Hessenberg form H
+// by an orthogonal similarity transformation Q^T * A * Q = H.
+//
+// The matrix Q is represented as a product of (ihi-ilo) elementary
+// reflectors
+//  Q = H_{ilo} H_{ilo+1} ... H_{ihi-1}.
+// Each H_i has the form
+//  H_i = I - tau[i] * v * v^T
+// where v is a real vector with v[0:i+1] = 0, v[i+1] = 1 and v[ihi+1:n] = 0.
+// v[i+2:ihi+1] is stored on exit in A[i+2:ihi+1,i].
+//
+// On entry, a contains the n×n general matrix to be reduced. On return, the
+// upper triangle and the first subdiagonal of A are overwritten with the upper
+// Hessenberg matrix H, and the elements below the first subdiagonal, with the
+// slice tau, represent the orthogonal matrix Q as a product of elementary
+// reflectors.
+//
+// The contents of A are illustrated by the following example, with n = 7, ilo =
+// 1 and ihi = 5.
+// On entry,
+//  [ a   a   a   a   a   a   a ]
+//  [     a   a   a   a   a   a ]
+//  [     a   a   a   a   a   a ]
+//  [     a   a   a   a   a   a ]
+//  [     a   a   a   a   a   a ]
+//  [     a   a   a   a   a   a ]
+//  [                         a ]
+// on return,
+//  [ a   a   h   h   h   h   a ]
+//  [     a   h   h   h   h   a ]
+//  [     h   h   h   h   h   h ]
+//  [     v1  h   h   h   h   h ]
+//  [     v1  v2  h   h   h   h ]
+//  [     v1  v2  v3  h   h   h ]
+//  [                         a ]
+// where a denotes an element of the original matrix A, h denotes a
+// modified element of the upper Hessenberg matrix H, and vi denotes an
+// element of the vector defining H_i.
+//
+// ilo and ihi determine the block of A that will be reduced to upper Hessenberg
+// form. It must hold that 0 <= ilo <= ihi <= max(0, n-1), otherwise Dgehd2 will
+// panic.
+//
+// On return, tau will contain the scalar factors of the elementary reflectors.
+// It must have length equal to n-1, otherwise Dgehd2 will panic.
+//
+// work must have length at least n, otherwise Dgehd2 will panic.
+//
+// Dgehd2 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dgehd2(n, ilo, ihi int, a []float64, lda int, tau, work []float64) {
+	checkMatrix(n, n, a, lda)
+	switch {
+	case ilo < 0 || ilo > max(0, n-1):
+		panic(badIlo)
+	case ihi < min(ilo, n-1) || ihi >= n:
+		panic(badIhi)
+	case len(tau) != n-1:
+		panic(badTau)
+	case len(work) < n:
+		panic(badWork)
+	}
+
+	for i := ilo; i < ihi; i++ {
+		// Compute elementary reflector H_i to annihilate A[i+2:ihi+1,i].
+		var aii float64
+		aii, tau[i] = impl.Dlarfg(ihi-i, a[(i+1)*lda+i], a[min(i+2, n-1)*lda+i:], lda)
+		a[(i+1)*lda+i] = 1
+
+		// Apply H_i to A[0:ihi+1,i+1:ihi+1] from the right.
+		impl.Dlarf(blas.Right, ihi+1, ihi-i, a[(i+1)*lda+i:], lda, tau[i], a[i+1:], lda, work)
+
+		// Apply H_i to A[i+1:ihi+1,i+1:n] from the left.
+		impl.Dlarf(blas.Left, ihi-i, n-i-1, a[(i+1)*lda+i:], lda, tau[i], a[(i+1)*lda+i+1:], lda, work)
+		a[(i+1)*lda+i] = aii
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dgehrd.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dgehrd.go
new file mode 100644
index 00000000..0dd90fa5
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dgehrd.go
@@ -0,0 +1,183 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dgehrd reduces a block of a real n×n general matrix A to upper Hessenberg
+// form H by an orthogonal similarity transformation Q^T * A * Q = H.
+//
+// The matrix Q is represented as a product of (ihi-ilo) elementary
+// reflectors
+//  Q = H_{ilo} H_{ilo+1} ... H_{ihi-1}.
+// Each H_i has the form
+//  H_i = I - tau[i] * v * v^T
+// where v is a real vector with v[0:i+1] = 0, v[i+1] = 1 and v[ihi+1:n] = 0.
+// v[i+2:ihi+1] is stored on exit in A[i+2:ihi+1,i].
+//
+// On entry, a contains the n×n general matrix to be reduced. On return, the
+// upper triangle and the first subdiagonal of A will be overwritten with the
+// upper Hessenberg matrix H, and the elements below the first subdiagonal, with
+// the slice tau, represent the orthogonal matrix Q as a product of elementary
+// reflectors.
+//
+// The contents of a are illustrated by the following example, with n = 7, ilo =
+// 1 and ihi = 5.
+// On entry,
+//  [ a   a   a   a   a   a   a ]
+//  [     a   a   a   a   a   a ]
+//  [     a   a   a   a   a   a ]
+//  [     a   a   a   a   a   a ]
+//  [     a   a   a   a   a   a ]
+//  [     a   a   a   a   a   a ]
+//  [                         a ]
+// on return,
+//  [ a   a   h   h   h   h   a ]
+//  [     a   h   h   h   h   a ]
+//  [     h   h   h   h   h   h ]
+//  [     v1  h   h   h   h   h ]
+//  [     v1  v2  h   h   h   h ]
+//  [     v1  v2  v3  h   h   h ]
+//  [                         a ]
+// where a denotes an element of the original matrix A, h denotes a
+// modified element of the upper Hessenberg matrix H, and vi denotes an
+// element of the vector defining H_i.
+//
+// ilo and ihi determine the block of A that will be reduced to upper Hessenberg
+// form. It must hold that 0 <= ilo <= ihi < n if n > 0, and ilo == 0 and ihi ==
+// -1 if n == 0, otherwise Dgehrd will panic.
+//
+// On return, tau will contain the scalar factors of the elementary reflectors.
+// Elements tau[:ilo] and tau[ihi:] will be set to zero. tau must have length
+// equal to n-1 if n > 0, otherwise Dgehrd will panic.
+//
+// work must have length at least lwork and lwork must be at least max(1,n),
+// otherwise Dgehrd will panic. On return, work[0] contains the optimal value of
+// lwork.
+//
+// If lwork == -1, instead of performing Dgehrd, only the optimal value of lwork
+// will be stored in work[0].
+//
+// Dgehrd is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dgehrd(n, ilo, ihi int, a []float64, lda int, tau, work []float64, lwork int) {
+	switch {
+	case ilo < 0 || max(0, n-1) < ilo:
+		panic(badIlo)
+	case ihi < min(ilo, n-1) || n <= ihi:
+		panic(badIhi)
+	case lwork < max(1, n) && lwork != -1:
+		panic(badWork)
+	case len(work) < lwork:
+		panic(shortWork)
+	}
+	if lwork != -1 {
+		checkMatrix(n, n, a, lda)
+		if len(tau) != n-1 && n > 0 {
+			panic(badTau)
+		}
+	}
+
+	const (
+		nbmax = 64
+		ldt   = nbmax + 1
+		tsize = ldt * nbmax
+	)
+	// Compute the workspace requirements.
+	nb := min(nbmax, impl.Ilaenv(1, "DGEHRD", " ", n, ilo, ihi, -1))
+	lwkopt := n*nb + tsize
+	if lwork == -1 {
+		work[0] = float64(lwkopt)
+		return
+	}
+
+	// Set tau[:ilo] and tau[ihi:] to zero.
+	for i := 0; i < ilo; i++ {
+		tau[i] = 0
+	}
+	for i := ihi; i < n-1; i++ {
+		tau[i] = 0
+	}
+
+	// Quick return if possible.
+	nh := ihi - ilo + 1
+	if nh <= 1 {
+		work[0] = 1
+		return
+	}
+
+	// Determine the block size.
+	nbmin := 2
+	var nx int
+	if 1 < nb && nb < nh {
+		// Determine when to cross over from blocked to unblocked code
+		// (last block is always handled by unblocked code).
+		nx = max(nb, impl.Ilaenv(3, "DGEHRD", " ", n, ilo, ihi, -1))
+		if nx < nh {
+			// Determine if workspace is large enough for blocked code.
+			if lwork < n*nb+tsize {
+				// Not enough workspace to use optimal nb:
+				// determine the minimum value of nb, and reduce
+				// nb or force use of unblocked code.
+				nbmin = max(2, impl.Ilaenv(2, "DGEHRD", " ", n, ilo, ihi, -1))
+				if lwork >= n*nbmin+tsize {
+					nb = (lwork - tsize) / n
+				} else {
+					nb = 1
+				}
+			}
+		}
+	}
+	ldwork := nb // work is used as an n×nb matrix.
+
+	var i int
+	if nb < nbmin || nh <= nb {
+		// Use unblocked code below.
+		i = ilo
+	} else {
+		// Use blocked code.
+		bi := blas64.Implementation()
+		iwt := n * nb // Size of the matrix Y and index where the matrix T starts in work.
+		for i = ilo; i < ihi-nx; i += nb {
+			ib := min(nb, ihi-i)
+
+			// Reduce columns [i:i+ib] to Hessenberg form, returning the
+			// matrices V and T of the block reflector H = I - V*T*V^T
+			// which performs the reduction, and also the matrix Y = A*V*T.
+			impl.Dlahr2(ihi+1, i+1, ib, a[i:], lda, tau[i:], work[iwt:], ldt, work, ldwork)
+
+			// Apply the block reflector H to A[:ihi+1,i+ib:ihi+1] from the
+			// right, computing  A := A - Y * V^T. V[i+ib,i+ib-1] must be set
+			// to 1.
+			ei := a[(i+ib)*lda+i+ib-1]
+			a[(i+ib)*lda+i+ib-1] = 1
+			bi.Dgemm(blas.NoTrans, blas.Trans, ihi+1, ihi-i-ib+1, ib,
+				-1, work, ldwork,
+				a[(i+ib)*lda+i:], lda,
+				1, a[i+ib:], lda)
+			a[(i+ib)*lda+i+ib-1] = ei
+
+			// Apply the block reflector H to A[0:i+1,i+1:i+ib-1] from the
+			// right.
+			bi.Dtrmm(blas.Right, blas.Lower, blas.Trans, blas.Unit, i+1, ib-1,
+				1, a[(i+1)*lda+i:], lda, work, ldwork)
+			for j := 0; j <= ib-2; j++ {
+				bi.Daxpy(i+1, -1, work[j:], ldwork, a[i+j+1:], lda)
+			}
+
+			// Apply the block reflector H to A[i+1:ihi+1,i+ib:n] from the
+			// left.
+			impl.Dlarfb(blas.Left, blas.Trans, lapack.Forward, lapack.ColumnWise,
+				ihi-i, n-i-ib, ib,
+				a[(i+1)*lda+i:], lda, work[iwt:], ldt, a[(i+1)*lda+i+ib:], lda, work, ldwork)
+		}
+	}
+	// Use unblocked code to reduce the rest of the matrix.
+	impl.Dgehd2(n, i, ihi, a, lda, tau, work)
+	work[0] = float64(lwkopt)
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dgelq2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dgelq2.go
new file mode 100644
index 00000000..2e4fd692
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dgelq2.go
@@ -0,0 +1,49 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "gonum.org/v1/gonum/blas"
+
+// Dgelq2 computes the LQ factorization of the m×n matrix A.
+//
+// In an LQ factorization, L is a lower triangular m×n matrix, and Q is an n×n
+// orthonormal matrix.
+//
+// a is modified to contain the information to construct L and Q.
+// The lower triangle of a contains the matrix L. The upper triangular elements
+// (not including the diagonal) contain the elementary reflectors. tau is modified
+// to contain the reflector scales. tau must have length of at least k = min(m,n)
+// and this function will panic otherwise.
+//
+// See Dgeqr2 for a description of the elementary reflectors and orthonormal
+// matrix Q. Q is constructed as a product of these elementary reflectors,
+// Q = H_{k-1} * ... * H_1 * H_0.
+//
+// work is temporary storage of length at least m and this function will panic otherwise.
+//
+// Dgelq2 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dgelq2(m, n int, a []float64, lda int, tau, work []float64) {
+	checkMatrix(m, n, a, lda)
+	k := min(m, n)
+	if len(tau) < k {
+		panic(badTau)
+	}
+	if len(work) < m {
+		panic(badWork)
+	}
+	for i := 0; i < k; i++ {
+		a[i*lda+i], tau[i] = impl.Dlarfg(n-i, a[i*lda+i], a[i*lda+min(i+1, n-1):], 1)
+		if i < m-1 {
+			aii := a[i*lda+i]
+			a[i*lda+i] = 1
+			impl.Dlarf(blas.Right, m-i-1, n-i,
+				a[i*lda+i:], 1,
+				tau[i],
+				a[(i+1)*lda+i:], lda,
+				work)
+			a[i*lda+i] = aii
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dgelqf.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dgelqf.go
new file mode 100644
index 00000000..13485012
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dgelqf.go
@@ -0,0 +1,84 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dgelqf computes the LQ factorization of the m×n matrix A using a blocked
+// algorithm. See the documentation for Dgelq2 for a description of the
+// parameters at entry and exit.
+//
+// work is temporary storage, and lwork specifies the usable memory length.
+// At minimum, lwork >= m, and this function will panic otherwise.
+// Dgelqf is a blocked LQ factorization, but the block size is limited
+// by the temporary space available. If lwork == -1, instead of performing Dgelqf,
+// the optimal work length will be stored into work[0].
+//
+// tau must have length at least min(m,n), and this function will panic otherwise.
+func (impl Implementation) Dgelqf(m, n int, a []float64, lda int, tau, work []float64, lwork int) {
+	nb := impl.Ilaenv(1, "DGELQF", " ", m, n, -1, -1)
+	lworkopt := m * max(nb, 1)
+	if lwork == -1 {
+		work[0] = float64(lworkopt)
+		return
+	}
+	checkMatrix(m, n, a, lda)
+	if len(work) < lwork {
+		panic(shortWork)
+	}
+	if lwork < m {
+		panic(badWork)
+	}
+	k := min(m, n)
+	if len(tau) < k {
+		panic(badTau)
+	}
+	if k == 0 {
+		return
+	}
+	// Find the optimal blocking size based on the size of available memory
+	// and optimal machine parameters.
+	nbmin := 2
+	var nx int
+	iws := m
+	ldwork := nb
+	if nb > 1 && k > nb {
+		nx = max(0, impl.Ilaenv(3, "DGELQF", " ", m, n, -1, -1))
+		if nx < k {
+			iws = m * nb
+			if lwork < iws {
+				nb = lwork / m
+				nbmin = max(2, impl.Ilaenv(2, "DGELQF", " ", m, n, -1, -1))
+			}
+		}
+	}
+	// Computed blocked LQ factorization.
+	var i int
+	if nb >= nbmin && nb < k && nx < k {
+		for i = 0; i < k-nx; i += nb {
+			ib := min(k-i, nb)
+			impl.Dgelq2(ib, n-i, a[i*lda+i:], lda, tau[i:], work)
+			if i+ib < m {
+				impl.Dlarft(lapack.Forward, lapack.RowWise, n-i, ib,
+					a[i*lda+i:], lda,
+					tau[i:],
+					work, ldwork)
+				impl.Dlarfb(blas.Right, blas.NoTrans, lapack.Forward, lapack.RowWise,
+					m-i-ib, n-i, ib,
+					a[i*lda+i:], lda,
+					work, ldwork,
+					a[(i+ib)*lda+i:], lda,
+					work[ib*ldwork:], ldwork)
+			}
+		}
+	}
+	// Perform unblocked LQ factorization on the remainder.
+	if i < k {
+		impl.Dgelq2(m-i, n-i, a[i*lda+i:], lda, tau[i:], work)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dgels.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dgels.go
new file mode 100644
index 00000000..b1d71823
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dgels.go
@@ -0,0 +1,200 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dgels finds a minimum-norm solution based on the matrices A and B using the
+// QR or LQ factorization. Dgels returns false if the matrix
+// A is singular, and true if this solution was successfully found.
+//
+// The minimization problem solved depends on the input parameters.
+//
+//  1. If m >= n and trans == blas.NoTrans, Dgels finds X such that || A*X - B||_2
+//     is minimized.
+//  2. If m < n and trans == blas.NoTrans, Dgels finds the minimum norm solution of
+//     A * X = B.
+//  3. If m >= n and trans == blas.Trans, Dgels finds the minimum norm solution of
+//     A^T * X = B.
+//  4. If m < n and trans == blas.Trans, Dgels finds X such that || A*X - B||_2
+//     is minimized.
+// Note that the least-squares solutions (cases 1 and 3) perform the minimization
+// per column of B. This is not the same as finding the minimum-norm matrix.
+//
+// The matrix A is a general matrix of size m×n and is modified during this call.
+// The input matrix B is of size max(m,n)×nrhs, and serves two purposes. On entry,
+// the elements of b specify the input matrix B. B has size m×nrhs if
+// trans == blas.NoTrans, and n×nrhs if trans == blas.Trans. On exit, the
+// leading submatrix of b contains the solution vectors X. If trans == blas.NoTrans,
+// this submatrix is of size n×nrhs, and of size m×nrhs otherwise.
+//
+// work is temporary storage, and lwork specifies the usable memory length.
+// At minimum, lwork >= max(m,n) + max(m,n,nrhs), and this function will panic
+// otherwise. A longer work will enable blocked algorithms to be called.
+// In the special case that lwork == -1, work[0] will be set to the optimal working
+// length.
+func (impl Implementation) Dgels(trans blas.Transpose, m, n, nrhs int, a []float64, lda int, b []float64, ldb int, work []float64, lwork int) bool {
+	notran := trans == blas.NoTrans
+	checkMatrix(m, n, a, lda)
+	mn := min(m, n)
+	checkMatrix(max(m, n), nrhs, b, ldb)
+
+	// Find optimal block size.
+	tpsd := true
+	if notran {
+		tpsd = false
+	}
+	var nb int
+	if m >= n {
+		nb = impl.Ilaenv(1, "DGEQRF", " ", m, n, -1, -1)
+		if tpsd {
+			nb = max(nb, impl.Ilaenv(1, "DORMQR", "LN", m, nrhs, n, -1))
+		} else {
+			nb = max(nb, impl.Ilaenv(1, "DORMQR", "LT", m, nrhs, n, -1))
+		}
+	} else {
+		nb = impl.Ilaenv(1, "DGELQF", " ", m, n, -1, -1)
+		if tpsd {
+			nb = max(nb, impl.Ilaenv(1, "DORMLQ", "LT", n, nrhs, m, -1))
+		} else {
+			nb = max(nb, impl.Ilaenv(1, "DORMLQ", "LN", n, nrhs, m, -1))
+		}
+	}
+	if lwork == -1 {
+		work[0] = float64(max(1, mn+max(mn, nrhs)*nb))
+		return true
+	}
+
+	if len(work) < lwork {
+		panic(shortWork)
+	}
+	if lwork < mn+max(mn, nrhs) {
+		panic(badWork)
+	}
+	if m == 0 || n == 0 || nrhs == 0 {
+		impl.Dlaset(blas.All, max(m, n), nrhs, 0, 0, b, ldb)
+		return true
+	}
+
+	// Scale the input matrices if they contain extreme values.
+	smlnum := dlamchS / dlamchP
+	bignum := 1 / smlnum
+	anrm := impl.Dlange(lapack.MaxAbs, m, n, a, lda, nil)
+	var iascl int
+	if anrm > 0 && anrm < smlnum {
+		impl.Dlascl(lapack.General, 0, 0, anrm, smlnum, m, n, a, lda)
+		iascl = 1
+	} else if anrm > bignum {
+		impl.Dlascl(lapack.General, 0, 0, anrm, bignum, m, n, a, lda)
+	} else if anrm == 0 {
+		// Matrix is all zeros.
+		impl.Dlaset(blas.All, max(m, n), nrhs, 0, 0, b, ldb)
+		return true
+	}
+	brow := m
+	if tpsd {
+		brow = n
+	}
+	bnrm := impl.Dlange(lapack.MaxAbs, brow, nrhs, b, ldb, nil)
+	ibscl := 0
+	if bnrm > 0 && bnrm < smlnum {
+		impl.Dlascl(lapack.General, 0, 0, bnrm, smlnum, brow, nrhs, b, ldb)
+		ibscl = 1
+	} else if bnrm > bignum {
+		impl.Dlascl(lapack.General, 0, 0, bnrm, bignum, brow, nrhs, b, ldb)
+		ibscl = 2
+	}
+
+	// Solve the minimization problem using a QR or an LQ decomposition.
+	var scllen int
+	if m >= n {
+		impl.Dgeqrf(m, n, a, lda, work, work[mn:], lwork-mn)
+		if !tpsd {
+			impl.Dormqr(blas.Left, blas.Trans, m, nrhs, n,
+				a, lda,
+				work[:n],
+				b, ldb,
+				work[mn:], lwork-mn)
+			ok := impl.Dtrtrs(blas.Upper, blas.NoTrans, blas.NonUnit, n, nrhs,
+				a, lda,
+				b, ldb)
+			if !ok {
+				return false
+			}
+			scllen = n
+		} else {
+			ok := impl.Dtrtrs(blas.Upper, blas.Trans, blas.NonUnit, n, nrhs,
+				a, lda,
+				b, ldb)
+			if !ok {
+				return false
+			}
+			for i := n; i < m; i++ {
+				for j := 0; j < nrhs; j++ {
+					b[i*ldb+j] = 0
+				}
+			}
+			impl.Dormqr(blas.Left, blas.NoTrans, m, nrhs, n,
+				a, lda,
+				work[:n],
+				b, ldb,
+				work[mn:], lwork-mn)
+			scllen = m
+		}
+	} else {
+		impl.Dgelqf(m, n, a, lda, work, work[mn:], lwork-mn)
+		if !tpsd {
+			ok := impl.Dtrtrs(blas.Lower, blas.NoTrans, blas.NonUnit,
+				m, nrhs,
+				a, lda,
+				b, ldb)
+			if !ok {
+				return false
+			}
+			for i := m; i < n; i++ {
+				for j := 0; j < nrhs; j++ {
+					b[i*ldb+j] = 0
+				}
+			}
+			impl.Dormlq(blas.Left, blas.Trans, n, nrhs, m,
+				a, lda,
+				work,
+				b, ldb,
+				work[mn:], lwork-mn)
+			scllen = n
+		} else {
+			impl.Dormlq(blas.Left, blas.NoTrans, n, nrhs, m,
+				a, lda,
+				work,
+				b, ldb,
+				work[mn:], lwork-mn)
+			ok := impl.Dtrtrs(blas.Lower, blas.Trans, blas.NonUnit,
+				m, nrhs,
+				a, lda,
+				b, ldb)
+			if !ok {
+				return false
+			}
+		}
+	}
+
+	// Adjust answer vector based on scaling.
+	if iascl == 1 {
+		impl.Dlascl(lapack.General, 0, 0, anrm, smlnum, scllen, nrhs, b, ldb)
+	}
+	if iascl == 2 {
+		impl.Dlascl(lapack.General, 0, 0, anrm, bignum, scllen, nrhs, b, ldb)
+	}
+	if ibscl == 1 {
+		impl.Dlascl(lapack.General, 0, 0, smlnum, bnrm, scllen, nrhs, b, ldb)
+	}
+	if ibscl == 2 {
+		impl.Dlascl(lapack.General, 0, 0, bignum, bnrm, scllen, nrhs, b, ldb)
+	}
+	return true
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dgeql2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dgeql2.go
new file mode 100644
index 00000000..19040cfa
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dgeql2.go
@@ -0,0 +1,45 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "gonum.org/v1/gonum/blas"
+
+// Dgeql2 computes the QL factorization of the m×n matrix A. That is, Dgeql2
+// computes Q and L such that
+//  A = Q * L
+// where Q is an m×m orthonormal matrix and L is a lower trapezoidal matrix.
+//
+// Q is represented as a product of elementary reflectors,
+//  Q = H_{k-1} * ... * H_1 * H_0
+// where k = min(m,n) and each H_i has the form
+//  H_i = I - tau[i] * v_i * v_i^T
+// Vector v_i has v[m-k+i+1:m] = 0, v[m-k+i] = 1, and v[:m-k+i+1] is stored on
+// exit in A[0:m-k+i-1, n-k+i].
+//
+// tau must have length at least min(m,n), and Dgeql2 will panic otherwise.
+//
+// work is temporary memory storage and must have length at least n.
+//
+// Dgeql2 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dgeql2(m, n int, a []float64, lda int, tau, work []float64) {
+	checkMatrix(m, n, a, lda)
+	if len(tau) < min(m, n) {
+		panic(badTau)
+	}
+	if len(work) < n {
+		panic(badWork)
+	}
+	k := min(m, n)
+	var aii float64
+	for i := k - 1; i >= 0; i-- {
+		// Generate elementary reflector H_i to annihilate A[0:m-k+i-1, n-k+i].
+		aii, tau[i] = impl.Dlarfg(m-k+i+1, a[(m-k+i)*lda+n-k+i], a[n-k+i:], lda)
+
+		// Apply H_i to A[0:m-k+i, 0:n-k+i-1] from the left.
+		a[(m-k+i)*lda+n-k+i] = 1
+		impl.Dlarf(blas.Left, m-k+i+1, n-k+i, a[n-k+i:], lda, tau[i], a, lda, work)
+		a[(m-k+i)*lda+n-k+i] = aii
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dgeqp3.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dgeqp3.go
new file mode 100644
index 00000000..50529cac
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dgeqp3.go
@@ -0,0 +1,174 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dgeqp3 computes a QR factorization with column pivoting of the
+// m×n matrix A: A*P = Q*R using Level 3 BLAS.
+//
+// The matrix Q is represented as a product of elementary reflectors
+//  Q = H_0 H_1 . . . H_{k-1}, where k = min(m,n).
+// Each H_i has the form
+//  H_i = I - tau * v * v^T
+// where tau and v are real vectors with v[0:i-1] = 0 and v[i] = 1;
+// v[i:m] is stored on exit in A[i:m, i], and tau in tau[i].
+//
+// jpvt specifies a column pivot to be applied to A. If
+// jpvt[j] is at least zero, the jth column of A is permuted
+// to the front of A*P (a leading column), if jpvt[j] is -1
+// the jth column of A is a free column. If jpvt[j] < -1, Dgeqp3
+// will panic. On return, jpvt holds the permutation that was
+// applied; the jth column of A*P was the jpvt[j] column of A.
+// jpvt must have length n or Dgeqp3 will panic.
+//
+// tau holds the scalar factors of the elementary reflectors.
+// It must have length min(m, n), otherwise Dgeqp3 will panic.
+//
+// work must have length at least max(1,lwork), and lwork must be at least
+// 3*n+1, otherwise Dgeqp3 will panic. For optimal performance lwork must
+// be at least 2*n+(n+1)*nb, where nb is the optimal blocksize. On return,
+// work[0] will contain the optimal value of lwork.
+//
+// If lwork == -1, instead of performing Dgeqp3, only the optimal value of lwork
+// will be stored in work[0].
+//
+// Dgeqp3 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dgeqp3(m, n int, a []float64, lda int, jpvt []int, tau, work []float64, lwork int) {
+	const (
+		inb    = 1
+		inbmin = 2
+		ixover = 3
+	)
+	checkMatrix(m, n, a, lda)
+
+	if len(jpvt) != n {
+		panic(badIpiv)
+	}
+	for _, v := range jpvt {
+		if v < -1 || n <= v {
+			panic("lapack: jpvt element out of range")
+		}
+	}
+	minmn := min(m, n)
+	if len(work) < max(1, lwork) {
+		panic(badWork)
+	}
+
+	var iws, lwkopt, nb int
+	if minmn == 0 {
+		iws = 1
+		lwkopt = 1
+	} else {
+		iws = 3*n + 1
+		nb = impl.Ilaenv(inb, "DGEQRF", " ", m, n, -1, -1)
+		lwkopt = 2*n + (n+1)*nb
+	}
+	work[0] = float64(lwkopt)
+
+	if lwork == -1 {
+		return
+	}
+
+	if len(tau) < minmn {
+		panic(badTau)
+	}
+
+	bi := blas64.Implementation()
+
+	// Move initial columns up front.
+	var nfxd int
+	for j := 0; j < n; j++ {
+		if jpvt[j] == -1 {
+			jpvt[j] = j
+			continue
+		}
+		if j != nfxd {
+			bi.Dswap(m, a[j:], lda, a[nfxd:], lda)
+			jpvt[j], jpvt[nfxd] = jpvt[nfxd], j
+		} else {
+			jpvt[j] = j
+		}
+		nfxd++
+	}
+
+	// Factorize nfxd columns.
+	//
+	// Compute the QR factorization of nfxd columns and update remaining columns.
+	if nfxd > 0 {
+		na := min(m, nfxd)
+		impl.Dgeqrf(m, na, a, lda, tau, work, lwork)
+		iws = max(iws, int(work[0]))
+		if na < n {
+			impl.Dormqr(blas.Left, blas.Trans, m, n-na, na, a, lda, tau[:na], a[na:], lda,
+				work, lwork)
+			iws = max(iws, int(work[0]))
+		}
+	}
+
+	if nfxd >= minmn {
+		work[0] = float64(iws)
+		return
+	}
+
+	// Factorize free columns.
+	sm := m - nfxd
+	sn := n - nfxd
+	sminmn := minmn - nfxd
+
+	// Determine the block size.
+	nb = impl.Ilaenv(inb, "DGEQRF", " ", sm, sn, -1, -1)
+	nbmin := 2
+	nx := 0
+
+	if 1 < nb && nb < sminmn {
+		// Determine when to cross over from blocked to unblocked code.
+		nx = max(0, impl.Ilaenv(ixover, "DGEQRF", " ", sm, sn, -1, -1))
+
+		if nx < sminmn {
+			// Determine if workspace is large enough for blocked code.
+			minws := 2*sn + (sn+1)*nb
+			iws = max(iws, minws)
+			if lwork < minws {
+				// Not enough workspace to use optimal nb. Reduce
+				// nb and determine the minimum value of nb.
+				nb = (lwork - 2*sn) / (sn + 1)
+				nbmin = max(2, impl.Ilaenv(inbmin, "DGEQRF", " ", sm, sn, -1, -1))
+			}
+		}
+	}
+
+	// Initialize partial column norms.
+	// The first n elements of work store the exact column norms.
+	for j := nfxd; j < n; j++ {
+		work[j] = bi.Dnrm2(sm, a[nfxd*lda+j:], lda)
+		work[n+j] = work[j]
+	}
+	j := nfxd
+	if nbmin <= nb && nb < sminmn && nx < sminmn {
+		// Use blocked code initially.
+
+		// Compute factorization.
+		var fjb int
+		for topbmn := minmn - nx; j < topbmn; j += fjb {
+			jb := min(nb, topbmn-j)
+
+			// Factorize jb columns among columns j:n.
+			fjb = impl.Dlaqps(m, n-j, j, jb, a[j:], lda, jpvt[j:], tau[j:],
+				work[j:n], work[j+n:2*n], work[2*n:2*n+jb], work[2*n+jb:], jb)
+		}
+	}
+
+	// Use unblocked code to factor the last or only block.
+	if j < minmn {
+		impl.Dlaqp2(m, n-j, j, a[j:], lda, jpvt[j:], tau[j:],
+			work[j:n], work[j+n:2*n], work[2*n:])
+	}
+
+	work[0] = float64(iws)
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dgeqr2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dgeqr2.go
new file mode 100644
index 00000000..6b032063
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dgeqr2.go
@@ -0,0 +1,59 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "gonum.org/v1/gonum/blas"
+
+// Dgeqr2 computes a QR factorization of the m×n matrix A.
+//
+// In a QR factorization, Q is an m×m orthonormal matrix, and R is an
+// upper triangular m×n matrix.
+//
+// A is modified to contain the information to construct Q and R.
+// The upper triangle of a contains the matrix R. The lower triangular elements
+// (not including the diagonal) contain the elementary reflectors. tau is modified
+// to contain the reflector scales. tau must have length at least min(m,n), and
+// this function will panic otherwise.
+//
+// The ith elementary reflector can be explicitly constructed by first extracting
+// the
+//  v[j] = 0           j < i
+//  v[j] = 1           j == i
+//  v[j] = a[j*lda+i]  j > i
+// and computing H_i = I - tau[i] * v * v^T.
+//
+// The orthonormal matrix Q can be constructed from a product of these elementary
+// reflectors, Q = H_0 * H_1 * ... * H_{k-1}, where k = min(m,n).
+//
+// work is temporary storage of length at least n and this function will panic otherwise.
+//
+// Dgeqr2 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dgeqr2(m, n int, a []float64, lda int, tau, work []float64) {
+	// TODO(btracey): This is oriented such that columns of a are eliminated.
+	// This likely could be re-arranged to take better advantage of row-major
+	// storage.
+	checkMatrix(m, n, a, lda)
+	if len(work) < n {
+		panic(badWork)
+	}
+	k := min(m, n)
+	if len(tau) < k {
+		panic(badTau)
+	}
+	for i := 0; i < k; i++ {
+		// Generate elementary reflector H_i.
+		a[i*lda+i], tau[i] = impl.Dlarfg(m-i, a[i*lda+i], a[min((i+1), m-1)*lda+i:], lda)
+		if i < n-1 {
+			aii := a[i*lda+i]
+			a[i*lda+i] = 1
+			impl.Dlarf(blas.Left, m-i, n-i-1,
+				a[i*lda+i:], lda,
+				tau[i],
+				a[i*lda+i+1:], lda,
+				work)
+			a[i*lda+i] = aii
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dgeqrf.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dgeqrf.go
new file mode 100644
index 00000000..c5662c91
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dgeqrf.go
@@ -0,0 +1,99 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dgeqrf computes the QR factorization of the m×n matrix A using a blocked
+// algorithm. See the documentation for Dgeqr2 for a description of the
+// parameters at entry and exit.
+//
+// work is temporary storage, and lwork specifies the usable memory length.
+// The length of work must be at least max(1, lwork) and lwork must be -1
+// or at least n, otherwise this function will panic.
+// Dgeqrf is a blocked QR factorization, but the block size is limited
+// by the temporary space available. If lwork == -1, instead of performing Dgeqrf,
+// the optimal work length will be stored into work[0].
+//
+// tau must have length at least min(m,n), and this function will panic otherwise.
+func (impl Implementation) Dgeqrf(m, n int, a []float64, lda int, tau, work []float64, lwork int) {
+	if len(work) < max(1, lwork) {
+		panic(shortWork)
+	}
+	// nb is the optimal blocksize, i.e. the number of columns transformed at a time.
+	nb := impl.Ilaenv(1, "DGEQRF", " ", m, n, -1, -1)
+	lworkopt := n * max(nb, 1)
+	lworkopt = max(n, lworkopt)
+	if lwork == -1 {
+		work[0] = float64(lworkopt)
+		return
+	}
+	checkMatrix(m, n, a, lda)
+	if lwork < n {
+		panic(badWork)
+	}
+	k := min(m, n)
+	if len(tau) < k {
+		panic(badTau)
+	}
+	if k == 0 {
+		work[0] = float64(lworkopt)
+		return
+	}
+	nbmin := 2 // Minimal block size.
+	var nx int // Use unblocked (unless changed in the next for loop)
+	iws := n
+	ldwork := nb
+	// Only consider blocked if the suggested block size is > 1 and the
+	// number of rows or columns is sufficiently large.
+	if 1 < nb && nb < k {
+		// nx is the block size at which the code switches from blocked
+		// to unblocked.
+		nx = max(0, impl.Ilaenv(3, "DGEQRF", " ", m, n, -1, -1))
+		if k > nx {
+			iws = ldwork * n
+			if lwork < iws {
+				// Not enough workspace to use the optimal block
+				// size. Get the minimum block size instead.
+				nb = lwork / n
+				nbmin = max(2, impl.Ilaenv(2, "DGEQRF", " ", m, n, -1, -1))
+			}
+		}
+	}
+	for i := range work {
+		work[i] = 0
+	}
+	// Compute QR using a blocked algorithm.
+	var i int
+	if nbmin <= nb && nb < k && nx < k {
+		for i = 0; i < k-nx; i += nb {
+			ib := min(k-i, nb)
+			// Compute the QR factorization of the current block.
+			impl.Dgeqr2(m-i, ib, a[i*lda+i:], lda, tau[i:], work)
+			if i+ib < n {
+				// Form the triangular factor of the block reflector and apply H^T
+				// In Dlarft, work becomes the T matrix.
+				impl.Dlarft(lapack.Forward, lapack.ColumnWise, m-i, ib,
+					a[i*lda+i:], lda,
+					tau[i:],
+					work, ldwork)
+				impl.Dlarfb(blas.Left, blas.Trans, lapack.Forward, lapack.ColumnWise,
+					m-i, n-i-ib, ib,
+					a[i*lda+i:], lda,
+					work, ldwork,
+					a[i*lda+i+ib:], lda,
+					work[ib*ldwork:], ldwork)
+			}
+		}
+	}
+	// Call unblocked code on the remaining columns.
+	if i < k {
+		impl.Dgeqr2(m-i, n-i, a[i*lda+i:], lda, tau[i:], work)
+	}
+	work[0] = float64(lworkopt)
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dgerq2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dgerq2.go
new file mode 100644
index 00000000..ef20a022
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dgerq2.go
@@ -0,0 +1,53 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "gonum.org/v1/gonum/blas"
+
+// Dgerq2 computes an RQ factorization of the m×n matrix A,
+//  A = R * Q.
+// On exit, if m <= n, the upper triangle of the subarray
+// A[0:m, n-m:n] contains the m×m upper triangular matrix R.
+// If m >= n, the elements on and above the (m-n)-th subdiagonal
+// contain the m×n upper trapezoidal matrix R.
+// The remaining elements, with tau, represent the
+// orthogonal matrix Q as a product of min(m,n) elementary
+// reflectors.
+//
+// The matrix Q is represented as a product of elementary reflectors
+//  Q = H_0 H_1 . . . H_{min(m,n)-1}.
+// Each H(i) has the form
+//  H_i = I - tau_i * v * v^T
+// where v is a vector with v[0:n-k+i-1] stored in A[m-k+i, 0:n-k+i-1],
+// v[n-k+i:n] = 0 and v[n-k+i] = 1.
+//
+// tau must have length min(m,n) and work must have length m, otherwise
+// Dgerq2 will panic.
+//
+// Dgerq2 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dgerq2(m, n int, a []float64, lda int, tau, work []float64) {
+	checkMatrix(m, n, a, lda)
+	k := min(m, n)
+	if len(tau) < k {
+		panic(badTau)
+	}
+	if len(work) < m {
+		panic(badWork)
+	}
+
+	for i := k - 1; i >= 0; i-- {
+		// Generate elementary reflector H[i] to annihilate
+		// A[m-k+i, 0:n-k+i-1].
+		mki := m - k + i
+		nki := n - k + i
+		var aii float64
+		aii, tau[i] = impl.Dlarfg(nki+1, a[mki*lda+nki], a[mki*lda:], 1)
+
+		// Apply H[i] to A[0:m-k+i-1, 0:n-k+i] from the right.
+		a[mki*lda+nki] = 1
+		impl.Dlarf(blas.Right, mki, nki+1, a[mki*lda:], 1, tau[i], a, lda, work)
+		a[mki*lda+nki] = aii
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dgerqf.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dgerqf.go
new file mode 100644
index 00000000..daf8f0d0
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dgerqf.go
@@ -0,0 +1,128 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dgerqf computes an RQ factorization of the m×n matrix A,
+//  A = R * Q.
+// On exit, if m <= n, the upper triangle of the subarray
+// A[0:m, n-m:n] contains the m×m upper triangular matrix R.
+// If m >= n, the elements on and above the (m-n)-th subdiagonal
+// contain the m×n upper trapezoidal matrix R.
+// The remaining elements, with tau, represent the
+// orthogonal matrix Q as a product of min(m,n) elementary
+// reflectors.
+//
+// The matrix Q is represented as a product of elementary reflectors
+//  Q = H_0 H_1 . . . H_{min(m,n)-1}.
+// Each H(i) has the form
+//  H_i = I - tau_i * v * v^T
+// where v is a vector with v[0:n-k+i-1] stored in A[m-k+i, 0:n-k+i-1],
+// v[n-k+i:n] = 0 and v[n-k+i] = 1.
+//
+// tau must have length min(m,n), work must have length max(1, lwork),
+// and lwork must be -1 or at least max(1, m), otherwise Dgerqf will panic.
+// On exit, work[0] will contain the optimal length for work.
+//
+// Dgerqf is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dgerqf(m, n int, a []float64, lda int, tau, work []float64, lwork int) {
+	checkMatrix(m, n, a, lda)
+
+	if len(work) < max(1, lwork) {
+		panic(shortWork)
+	}
+	if lwork != -1 && lwork < max(1, m) {
+		panic(badWork)
+	}
+
+	k := min(m, n)
+	if len(tau) != k {
+		panic(badTau)
+	}
+
+	var nb, lwkopt int
+	if k == 0 {
+		lwkopt = 1
+	} else {
+		nb = impl.Ilaenv(1, "DGERQF", " ", m, n, -1, -1)
+		lwkopt = m * nb
+	}
+	work[0] = float64(lwkopt)
+
+	if lwork == -1 {
+		return
+	}
+
+	// Return quickly if possible.
+	if k == 0 {
+		return
+	}
+
+	nbmin := 2
+	nx := 1
+	iws := m
+	var ldwork int
+	if 1 < nb && nb < k {
+		// Determine when to cross over from blocked to unblocked code.
+		nx = max(0, impl.Ilaenv(3, "DGERQF", " ", m, n, -1, -1))
+		if nx < k {
+			// Determine whether workspace is large enough for blocked code.
+			iws = m * nb
+			if lwork < iws {
+				// Not enough workspace to use optimal nb. Reduce
+				// nb and determine the minimum value of nb.
+				nb = lwork / m
+				nbmin = max(2, impl.Ilaenv(2, "DGERQF", " ", m, n, -1, -1))
+			}
+			ldwork = nb
+		}
+	}
+
+	var mu, nu int
+	if nbmin <= nb && nb < k && nx < k {
+		// Use blocked code initially.
+		// The last kk rows are handled by the block method.
+		ki := ((k - nx - 1) / nb) * nb
+		kk := min(k, ki+nb)
+
+		var i int
+		for i = k - kk + ki; i >= k-kk; i -= nb {
+			ib := min(k-i, nb)
+
+			// Compute the RQ factorization of the current block
+			// A[m-k+i:m-k+i+ib-1, 0:n-k+i+ib-1].
+			impl.Dgerq2(ib, n-k+i+ib, a[(m-k+i)*lda:], lda, tau[i:], work)
+			if m-k+i > 0 {
+				// Form the triangular factor of the block reflector
+				// H = H_{i+ib-1} . . . H_{i+1} H_i.
+				impl.Dlarft(lapack.Backward, lapack.RowWise,
+					n-k+i+ib, ib, a[(m-k+i)*lda:], lda, tau[i:],
+					work, ldwork)
+
+				// Apply H to A[0:m-k+i-1, 0:n-k+i+ib-1] from the right.
+				impl.Dlarfb(blas.Right, blas.NoTrans, lapack.Backward, lapack.RowWise,
+					m-k+i, n-k+i+ib, ib, a[(m-k+i)*lda:], lda,
+					work, ldwork,
+					a, lda,
+					work[ib*ldwork:], ldwork)
+			}
+		}
+		mu = m - k + i + nb
+		nu = n - k + i + nb
+	} else {
+		mu = m
+		nu = n
+	}
+
+	// Use unblocked code to factor the last or only block.
+	if mu > 0 && nu > 0 {
+		impl.Dgerq2(mu, nu, a, lda, tau, work)
+	}
+	work[0] = float64(iws)
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dgesvd.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dgesvd.go
new file mode 100644
index 00000000..82a151c7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dgesvd.go
@@ -0,0 +1,1356 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+)
+
+const noSVDO = "dgesvd: not coded for overwrite"
+
+// Dgesvd computes the singular value decomposition of the input matrix A.
+//
+// The singular value decomposition is
+//  A = U * Sigma * V^T
+// where Sigma is an m×n diagonal matrix containing the singular values of A,
+// U is an m×m orthogonal matrix and V is an n×n orthogonal matrix. The first
+// min(m,n) columns of U and V are the left and right singular vectors of A
+// respectively.
+//
+// jobU and jobVT are options for computing the singular vectors. The behavior
+// is as follows
+//  jobU == lapack.SVDAll       All m columns of U are returned in u
+//  jobU == lapack.SVDInPlace   The first min(m,n) columns are returned in u
+//  jobU == lapack.SVDOverwrite The first min(m,n) columns of U are written into a
+//  jobU == lapack.SVDNone      The columns of U are not computed.
+// The behavior is the same for jobVT and the rows of V^T. At most one of jobU
+// and jobVT can equal lapack.SVDOverwrite, and Dgesvd will panic otherwise.
+//
+// On entry, a contains the data for the m×n matrix A. During the call to Dgesvd
+// the data is overwritten. On exit, A contains the appropriate singular vectors
+// if either job is lapack.SVDOverwrite.
+//
+// s is a slice of length at least min(m,n) and on exit contains the singular
+// values in decreasing order.
+//
+// u contains the left singular vectors on exit, stored column-wise. If
+// jobU == lapack.SVDAll, u is of size m×m. If jobU == lapack.SVDInPlace u is
+// of size m×min(m,n). If jobU == lapack.SVDOverwrite or lapack.SVDNone, u is
+// not used.
+//
+// vt contains the left singular vectors on exit, stored row-wise. If
+// jobV == lapack.SVDAll, vt is of size n×m. If jobVT == lapack.SVDInPlace vt is
+// of size min(m,n)×n. If jobVT == lapack.SVDOverwrite or lapack.SVDNone, vt is
+// not used.
+//
+// work is a slice for storing temporary memory, and lwork is the usable size of
+// the slice. lwork must be at least max(5*min(m,n), 3*min(m,n)+max(m,n)).
+// If lwork == -1, instead of performing Dgesvd, the optimal work length will be
+// stored into work[0]. Dgesvd will panic if the working memory has insufficient
+// storage.
+//
+// Dgesvd returns whether the decomposition successfully completed.
+func (impl Implementation) Dgesvd(jobU, jobVT lapack.SVDJob, m, n int, a []float64, lda int, s, u []float64, ldu int, vt []float64, ldvt int, work []float64, lwork int) (ok bool) {
+	minmn := min(m, n)
+	checkMatrix(m, n, a, lda)
+	if jobU == lapack.SVDAll {
+		checkMatrix(m, m, u, ldu)
+	} else if jobU == lapack.SVDInPlace {
+		checkMatrix(m, minmn, u, ldu)
+	}
+	if jobVT == lapack.SVDAll {
+		checkMatrix(n, n, vt, ldvt)
+	} else if jobVT == lapack.SVDInPlace {
+		checkMatrix(minmn, n, vt, ldvt)
+	}
+	if jobU == lapack.SVDOverwrite && jobVT == lapack.SVDOverwrite {
+		panic("lapack: both jobU and jobVT are lapack.SVDOverwrite")
+	}
+	if len(s) < minmn {
+		panic(badS)
+	}
+	if jobU == lapack.SVDOverwrite || jobVT == lapack.SVDOverwrite {
+		panic(noSVDO)
+	}
+	if m == 0 || n == 0 {
+		return true
+	}
+
+	wantua := jobU == lapack.SVDAll
+	wantus := jobU == lapack.SVDInPlace
+	wantuas := wantua || wantus
+	wantuo := jobU == lapack.SVDOverwrite
+	wantun := jobU == lapack.None
+
+	wantva := jobVT == lapack.SVDAll
+	wantvs := jobVT == lapack.SVDInPlace
+	wantvas := wantva || wantvs
+	wantvo := jobVT == lapack.SVDOverwrite
+	wantvn := jobVT == lapack.None
+
+	bi := blas64.Implementation()
+	var mnthr int
+
+	// Compute optimal space for subroutines.
+	maxwrk := 1
+	opts := string(jobU) + string(jobVT)
+	var wrkbl, bdspac int
+	if m >= n {
+		mnthr = impl.Ilaenv(6, "DGESVD", opts, m, n, 0, 0)
+		bdspac = 5 * n
+		impl.Dgeqrf(m, n, a, lda, nil, work, -1)
+		lwork_dgeqrf := int(work[0])
+		impl.Dorgqr(m, n, n, a, lda, nil, work, -1)
+		lwork_dorgqr_n := int(work[0])
+		impl.Dorgqr(m, m, n, a, lda, nil, work, -1)
+		lwork_dorgqr_m := int(work[0])
+		impl.Dgebrd(n, n, a, lda, s, nil, nil, nil, work, -1)
+		lwork_dgebrd := int(work[0])
+		impl.Dorgbr(lapack.ApplyP, n, n, n, a, lda, nil, work, -1)
+		lwork_dorgbr_p := int(work[0])
+		impl.Dorgbr(lapack.ApplyQ, n, n, n, a, lda, nil, work, -1)
+		lwork_dorgbr_q := int(work[0])
+
+		if m >= mnthr {
+			// m >> n
+			if wantun {
+				// Path 1
+				maxwrk = n + lwork_dgeqrf
+				maxwrk = max(maxwrk, 3*n+lwork_dgebrd)
+				if wantvo || wantvas {
+					maxwrk = max(maxwrk, 3*n+lwork_dorgbr_p)
+				}
+				maxwrk = max(maxwrk, bdspac)
+			} else if wantuo && wantvn {
+				// Path 2
+				wrkbl = n + lwork_dgeqrf
+				wrkbl = max(wrkbl, n+lwork_dorgqr_n)
+				wrkbl = max(wrkbl, 3*n+lwork_dgebrd)
+				wrkbl = max(wrkbl, 3*n+lwork_dorgbr_q)
+				wrkbl = max(wrkbl, bdspac)
+				maxwrk = max(n*n+wrkbl, n*n+m*n+n)
+			} else if wantuo && wantvs {
+				// Path 3
+				wrkbl = n + lwork_dgeqrf
+				wrkbl = max(wrkbl, n+lwork_dorgqr_n)
+				wrkbl = max(wrkbl, 3*n+lwork_dgebrd)
+				wrkbl = max(wrkbl, 3*n+lwork_dorgbr_q)
+				wrkbl = max(wrkbl, 3*n+lwork_dorgbr_p)
+				wrkbl = max(wrkbl, bdspac)
+				maxwrk = max(n*n+wrkbl, n*n+m*n+n)
+			} else if wantus && wantvn {
+				// Path 4
+				wrkbl = n + lwork_dgeqrf
+				wrkbl = max(wrkbl, n+lwork_dorgqr_n)
+				wrkbl = max(wrkbl, 3*n+lwork_dgebrd)
+				wrkbl = max(wrkbl, 3*n+lwork_dorgbr_q)
+				wrkbl = max(wrkbl, bdspac)
+				maxwrk = n*n + wrkbl
+			} else if wantus && wantvo {
+				// Path 5
+				wrkbl = n + lwork_dgeqrf
+				wrkbl = max(wrkbl, n+lwork_dorgqr_n)
+				wrkbl = max(wrkbl, 3*n+lwork_dgebrd)
+				wrkbl = max(wrkbl, 3*n+lwork_dorgbr_q)
+				wrkbl = max(wrkbl, 3*n+lwork_dorgbr_p)
+				wrkbl = max(wrkbl, bdspac)
+				maxwrk = 2*n*n + wrkbl
+			} else if wantus && wantvas {
+				// Path 6
+				wrkbl = n + lwork_dgeqrf
+				wrkbl = max(wrkbl, n+lwork_dorgqr_n)
+				wrkbl = max(wrkbl, 3*n+lwork_dgebrd)
+				wrkbl = max(wrkbl, 3*n+lwork_dorgbr_q)
+				wrkbl = max(wrkbl, 3*n+lwork_dorgbr_p)
+				wrkbl = max(wrkbl, bdspac)
+				maxwrk = n*n + wrkbl
+			} else if wantua && wantvn {
+				// Path 7
+				wrkbl = n + lwork_dgeqrf
+				wrkbl = max(wrkbl, n+lwork_dorgqr_m)
+				wrkbl = max(wrkbl, 3*n+lwork_dgebrd)
+				wrkbl = max(wrkbl, 3*n+lwork_dorgbr_q)
+				wrkbl = max(wrkbl, bdspac)
+				maxwrk = n*n + wrkbl
+			} else if wantua && wantvo {
+				// Path 8
+				wrkbl = n + lwork_dgeqrf
+				wrkbl = max(wrkbl, n+lwork_dorgqr_m)
+				wrkbl = max(wrkbl, 3*n+lwork_dgebrd)
+				wrkbl = max(wrkbl, 3*n+lwork_dorgbr_q)
+				wrkbl = max(wrkbl, 3*n+lwork_dorgbr_p)
+				wrkbl = max(wrkbl, bdspac)
+				maxwrk = 2*n*n + wrkbl
+			} else if wantua && wantvas {
+				// Path 9
+				wrkbl = n + lwork_dgeqrf
+				wrkbl = max(wrkbl, n+lwork_dorgqr_m)
+				wrkbl = max(wrkbl, 3*n+lwork_dgebrd)
+				wrkbl = max(wrkbl, 3*n+lwork_dorgbr_q)
+				wrkbl = max(wrkbl, 3*n+lwork_dorgbr_p)
+				wrkbl = max(wrkbl, bdspac)
+				maxwrk = n*n + wrkbl
+			}
+		} else {
+			// Path 10: m > n
+			impl.Dgebrd(m, n, a, lda, s, nil, nil, nil, work, -1)
+			lwork_dgebrd := int(work[0])
+			maxwrk = 3*n + lwork_dgebrd
+			if wantus || wantuo {
+				impl.Dorgbr(lapack.ApplyQ, m, n, n, a, lda, nil, work, -1)
+				lwork_dorgbr_q = int(work[0])
+				maxwrk = max(maxwrk, 3*n+lwork_dorgbr_q)
+			}
+			if wantua {
+				impl.Dorgbr(lapack.ApplyQ, m, m, n, a, lda, nil, work, -1)
+				lwork_dorgbr_q := int(work[0])
+				maxwrk = max(maxwrk, 3*n+lwork_dorgbr_q)
+			}
+			if !wantvn {
+				maxwrk = max(maxwrk, 3*n+lwork_dorgbr_p)
+			}
+			maxwrk = max(maxwrk, bdspac)
+		}
+	} else {
+		mnthr = impl.Ilaenv(6, "DGESVD", opts, m, n, 0, 0)
+
+		bdspac = 5 * m
+		impl.Dgelqf(m, n, a, lda, nil, work, -1)
+		lwork_dgelqf := int(work[0])
+		impl.Dorglq(n, n, m, nil, n, nil, work, -1)
+		lwork_dorglq_n := int(work[0])
+		impl.Dorglq(m, n, m, a, lda, nil, work, -1)
+		lwork_dorglq_m := int(work[0])
+		impl.Dgebrd(m, m, a, lda, s, nil, nil, nil, work, -1)
+		lwork_dgebrd := int(work[0])
+		impl.Dorgbr(lapack.ApplyP, m, m, m, a, n, nil, work, -1)
+		lwork_dorgbr_p := int(work[0])
+		impl.Dorgbr(lapack.ApplyQ, m, m, m, a, n, nil, work, -1)
+		lwork_dorgbr_q := int(work[0])
+		if n >= mnthr {
+			// n >> m
+			if wantvn {
+				// Path 1t
+				maxwrk = m + lwork_dgelqf
+				maxwrk = max(maxwrk, 3*m+lwork_dgebrd)
+				if wantuo || wantuas {
+					maxwrk = max(maxwrk, 3*m+lwork_dorgbr_q)
+				}
+				maxwrk = max(maxwrk, bdspac)
+			} else if wantvo && wantun {
+				// Path 2t
+				wrkbl = m + lwork_dgelqf
+				wrkbl = max(wrkbl, m+lwork_dorglq_m)
+				wrkbl = max(wrkbl, 3*m+lwork_dgebrd)
+				wrkbl = max(wrkbl, 3*m+lwork_dorgbr_p)
+				wrkbl = max(wrkbl, bdspac)
+				maxwrk = max(m*m+wrkbl, m*m+m*n+m)
+			} else if wantvo && wantuas {
+				// Path 3t
+				wrkbl = m + lwork_dgelqf
+				wrkbl = max(wrkbl, m+lwork_dorglq_m)
+				wrkbl = max(wrkbl, 3*m+lwork_dgebrd)
+				wrkbl = max(wrkbl, 3*m+lwork_dorgbr_p)
+				wrkbl = max(wrkbl, 3*m+lwork_dorgbr_q)
+				wrkbl = max(wrkbl, bdspac)
+				maxwrk = max(m*m+wrkbl, m*m+m*n+m)
+			} else if wantvs && wantun {
+				// Path 4t
+				wrkbl = m + lwork_dgelqf
+				wrkbl = max(wrkbl, m+lwork_dorglq_m)
+				wrkbl = max(wrkbl, 3*m+lwork_dgebrd)
+				wrkbl = max(wrkbl, 3*m+lwork_dorgbr_p)
+				wrkbl = max(wrkbl, bdspac)
+				maxwrk = m*m + wrkbl
+			} else if wantvs && wantuo {
+				// Path 5t
+				wrkbl = m + lwork_dgelqf
+				wrkbl = max(wrkbl, m+lwork_dorglq_m)
+				wrkbl = max(wrkbl, 3*m+lwork_dgebrd)
+				wrkbl = max(wrkbl, 3*m+lwork_dorgbr_p)
+				wrkbl = max(wrkbl, 3*m+lwork_dorgbr_q)
+				wrkbl = max(wrkbl, bdspac)
+				maxwrk = 2*m*m + wrkbl
+			} else if wantvs && wantuas {
+				// Path 6t
+				wrkbl = m + lwork_dgelqf
+				wrkbl = max(wrkbl, m+lwork_dorglq_m)
+				wrkbl = max(wrkbl, 3*m+lwork_dgebrd)
+				wrkbl = max(wrkbl, 3*m+lwork_dorgbr_p)
+				wrkbl = max(wrkbl, 3*m+lwork_dorgbr_q)
+				wrkbl = max(wrkbl, bdspac)
+				maxwrk = m*m + wrkbl
+			} else if wantva && wantun {
+				// Path 7t
+				wrkbl = m + lwork_dgelqf
+				wrkbl = max(wrkbl, m+lwork_dorglq_n)
+				wrkbl = max(wrkbl, 3*m+lwork_dgebrd)
+				wrkbl = max(wrkbl, 3*m+lwork_dorgbr_p)
+				wrkbl = max(wrkbl, bdspac)
+				maxwrk = m*m + wrkbl
+			} else if wantva && wantuo {
+				// Path 8t
+				wrkbl = m + lwork_dgelqf
+				wrkbl = max(wrkbl, m+lwork_dorglq_n)
+				wrkbl = max(wrkbl, 3*m+lwork_dgebrd)
+				wrkbl = max(wrkbl, 3*m+lwork_dorgbr_p)
+				wrkbl = max(wrkbl, 3*m+lwork_dorgbr_q)
+				wrkbl = max(wrkbl, bdspac)
+				maxwrk = 2*m*m + wrkbl
+			} else if wantva && wantuas {
+				// Path 9t
+				wrkbl = m + lwork_dgelqf
+				wrkbl = max(wrkbl, m+lwork_dorglq_n)
+				wrkbl = max(wrkbl, 3*m+lwork_dgebrd)
+				wrkbl = max(wrkbl, 3*m+lwork_dorgbr_p)
+				wrkbl = max(wrkbl, 3*m+lwork_dorgbr_q)
+				wrkbl = max(wrkbl, bdspac)
+				maxwrk = m*m + wrkbl
+			}
+		} else {
+			// Path 10t, n > m
+			impl.Dgebrd(m, n, a, lda, s, nil, nil, nil, work, -1)
+			lwork_dgebrd = int(work[0])
+			maxwrk = 3*m + lwork_dgebrd
+			if wantvs || wantvo {
+				impl.Dorgbr(lapack.ApplyP, m, n, m, a, n, nil, work, -1)
+				lwork_dorgbr_p = int(work[0])
+				maxwrk = max(maxwrk, 3*m+lwork_dorgbr_p)
+			}
+			if wantva {
+				impl.Dorgbr(lapack.ApplyP, n, n, m, a, n, nil, work, -1)
+				lwork_dorgbr_p = int(work[0])
+				maxwrk = max(maxwrk, 3*m+lwork_dorgbr_p)
+			}
+			if !wantun {
+				maxwrk = max(maxwrk, 3*m+lwork_dorgbr_q)
+			}
+			maxwrk = max(maxwrk, bdspac)
+		}
+	}
+
+	minWork := max(1, 5*minmn)
+	if !((wantun && m >= mnthr) || (wantvn && n >= mnthr)) {
+		minWork = max(minWork, 3*minmn+max(m, n))
+	}
+
+	if lwork != -1 {
+		if len(work) < lwork {
+			panic(badWork)
+		}
+		if lwork < minWork {
+			panic(badWork)
+		}
+	}
+	if m == 0 || n == 0 {
+		return true
+	}
+
+	maxwrk = max(maxwrk, minWork)
+	work[0] = float64(maxwrk)
+	if lwork == -1 {
+		return true
+	}
+
+	// Perform decomposition.
+	eps := dlamchE
+	smlnum := math.Sqrt(dlamchS) / eps
+	bignum := 1 / smlnum
+
+	// Scale A if max element outside range [smlnum, bignum].
+	anrm := impl.Dlange(lapack.MaxAbs, m, n, a, lda, nil)
+	var iscl bool
+	if anrm > 0 && anrm < smlnum {
+		iscl = true
+		impl.Dlascl(lapack.General, 0, 0, anrm, smlnum, m, n, a, lda)
+	} else if anrm > bignum {
+		iscl = true
+		impl.Dlascl(lapack.General, 0, 0, anrm, bignum, m, n, a, lda)
+	}
+
+	var ie int
+	if m >= n {
+		// If A has sufficiently more rows than columns, use the QR decomposition.
+		if m >= mnthr {
+			// m >> n
+			if wantun {
+				// Path 1.
+				itau := 0
+				iwork := itau + n
+
+				// Compute A = Q * R.
+				impl.Dgeqrf(m, n, a, lda, work[itau:], work[iwork:], lwork-iwork)
+
+				// Zero out below R.
+				impl.Dlaset(blas.Lower, n-1, n-1, 0, 0, a[lda:], lda)
+				ie = 0
+				itauq := ie + n
+				itaup := itauq + n
+				iwork = itaup + n
+				// Bidiagonalize R in A.
+				impl.Dgebrd(n, n, a, lda, s, work[ie:], work[itauq:],
+					work[itaup:], work[iwork:], lwork-iwork)
+				ncvt := 0
+				if wantvo || wantvas {
+					// Generate P^T.
+					impl.Dorgbr(lapack.ApplyP, n, n, n, a, lda, work[itaup:],
+						work[iwork:], lwork-iwork)
+					ncvt = n
+				}
+				iwork = ie + n
+
+				// Perform bidiagonal QR iteration computing right singular vectors
+				// of A in A if desired.
+				ok = impl.Dbdsqr(blas.Upper, n, ncvt, 0, 0, s, work[ie:],
+					a, lda, work, 1, work, 1, work[iwork:])
+
+				// If right singular vectors desired in VT, copy them there.
+				if wantvas {
+					impl.Dlacpy(blas.All, n, n, a, lda, vt, ldvt)
+				}
+			} else if wantuo && wantvn {
+				// Path 2
+				panic(noSVDO)
+			} else if wantuo && wantvas {
+				// Path 3
+				panic(noSVDO)
+			} else if wantus {
+				if wantvn {
+					// Path 4
+					if lwork >= n*n+max(4*n, bdspac) {
+						// Sufficient workspace for a fast algorithm.
+						ir := 0
+						var ldworkr int
+						if lwork >= wrkbl+lda*n {
+							ldworkr = lda
+						} else {
+							ldworkr = n
+						}
+						itau := ir + ldworkr*n
+						iwork := itau + n
+						// Compute A = Q * R.
+						impl.Dgeqrf(m, n, a, lda, work[itau:], work[iwork:], lwork-iwork)
+
+						// Copy R to work[ir:], zeroing out below it.
+						impl.Dlacpy(blas.Upper, n, n, a, lda, work[ir:], ldworkr)
+						impl.Dlaset(blas.Lower, n-1, n-1, 0, 0, work[ir+ldworkr:], ldworkr)
+
+						// Generate Q in A.
+						impl.Dorgqr(m, n, n, a, lda, work[itau:], work[iwork:], lwork-iwork)
+						ie := itau
+						itauq := ie + n
+						itaup := itauq + n
+						iwork = itaup + n
+
+						// Bidiagonalize R in work[ir:].
+						impl.Dgebrd(n, n, work[ir:], ldworkr, s, work[ie:],
+							work[itauq:], work[itaup:], work[iwork:], lwork-iwork)
+
+						// Generate left vectors bidiagonalizing R in work[ir:].
+						impl.Dorgbr(lapack.ApplyQ, n, n, n, work[ir:], ldworkr,
+							work[itauq:], work[iwork:], lwork-iwork)
+						iwork = ie + n
+
+						// Perform bidiagonal QR iteration, compuing left singular
+						// vectors of R in work[ir:].
+						ok = impl.Dbdsqr(blas.Upper, n, 0, n, 0, s, work[ie:], work, 1,
+							work[ir:], ldworkr, work, 1, work[iwork:])
+
+						// Multiply Q in A by left singular vectors of R in
+						// work[ir:], storing result in U.
+						bi.Dgemm(blas.NoTrans, blas.NoTrans, m, n, n, 1, a, lda,
+							work[ir:], ldworkr, 0, u, ldu)
+					} else {
+						// Insufficient workspace for a fast algorithm.
+						itau := 0
+						iwork := itau + n
+
+						// Compute A = Q*R, copying result to U.
+						impl.Dgeqrf(m, n, a, lda, work[itau:], work[iwork:], lwork-iwork)
+						impl.Dlacpy(blas.Lower, m, n, a, lda, u, ldu)
+
+						// Generate Q in U.
+						impl.Dorgqr(m, n, n, u, ldu, work[itau:], work[iwork:], lwork-iwork)
+						ie := itau
+						itauq := ie + n
+						itaup := itauq + n
+						iwork = itaup + n
+
+						// Zero out below R in A.
+						impl.Dlaset(blas.Lower, n-1, n-1, 0, 0, a[lda:], lda)
+
+						// Bidiagonalize R in A.
+						impl.Dgebrd(n, n, a, lda, s, work[ie:],
+							work[itauq:], work[itaup:], work[iwork:], lwork-iwork)
+
+						// Multiply Q in U by left vectors bidiagonalizing R.
+						impl.Dormbr(lapack.ApplyQ, blas.Right, blas.NoTrans, m, n, n,
+							a, lda, work[itauq:], u, ldu, work[iwork:], lwork-iwork)
+						iwork = ie + n
+
+						// Perform bidiagonal QR iteration, computing left
+						// singular vectors of A in U.
+						ok = impl.Dbdsqr(blas.Upper, n, 0, m, 0, s, work[ie:], work, 1,
+							u, ldu, work, 1, work[iwork:])
+					}
+				} else if wantvo {
+					// Path 5
+					panic(noSVDO)
+				} else if wantvas {
+					// Path 6
+					if lwork >= n*n+max(4*n, bdspac) {
+						// Sufficient workspace for a fast algorithm.
+						iu := 0
+						var ldworku int
+						if lwork >= wrkbl+lda*n {
+							ldworku = lda
+						} else {
+							ldworku = n
+						}
+						itau := iu + ldworku*n
+						iwork := itau + n
+
+						// Compute A = Q * R.
+						impl.Dgeqrf(m, n, a, lda, work[itau:], work[iwork:], lwork-iwork)
+						// Copy R to work[iu:], zeroing out below it.
+						impl.Dlacpy(blas.Upper, n, n, a, lda, work[iu:], ldworku)
+						impl.Dlaset(blas.Lower, n-1, n-1, 0, 0, work[iu+ldworku:], ldworku)
+
+						// Generate Q in A.
+						impl.Dorgqr(m, n, n, a, lda, work[itau:], work[iwork:], lwork-iwork)
+
+						ie := itau
+						itauq := ie + n
+						itaup := itauq + n
+						iwork = itaup + n
+
+						// Bidiagonalize R in work[iu:], copying result to VT.
+						impl.Dgebrd(n, n, work[iu:], ldworku, s, work[ie:],
+							work[itauq:], work[itaup:], work[iwork:], lwork-iwork)
+						impl.Dlacpy(blas.Upper, n, n, work[iu:], ldworku, vt, ldvt)
+
+						// Generate left bidiagonalizing vectors in work[iu:].
+						impl.Dorgbr(lapack.ApplyQ, n, n, n, work[iu:], ldworku,
+							work[itauq:], work[iwork:], lwork-iwork)
+
+						// Generate right bidiagonalizing vectors in VT.
+						impl.Dorgbr(lapack.ApplyP, n, n, n, vt, ldvt,
+							work[itaup:], work[iwork:], lwork-iwork)
+						iwork = ie + n
+
+						// Perform bidiagonal QR iteration, computing left singular
+						// vectors of R in work[iu:], and computing right singular
+						// vectors of R in VT.
+						ok = impl.Dbdsqr(blas.Upper, n, n, n, 0, s, work[ie:],
+							vt, ldvt, work[iu:], ldworku, work, 1, work[iwork:])
+
+						// Multiply Q in A by left singular vectors of R in
+						// work[iu:], storing result in U.
+						bi.Dgemm(blas.NoTrans, blas.NoTrans, m, n, n, 1, a, lda,
+							work[iu:], ldworku, 0, u, ldu)
+					} else {
+						// Insufficient workspace for a fast algorithm.
+						itau := 0
+						iwork := itau + n
+
+						// Compute A = Q * R, copying result to U.
+						impl.Dgeqrf(m, n, a, lda, work[itau:], work[iwork:], lwork-iwork)
+						impl.Dlacpy(blas.Lower, m, n, a, lda, u, ldu)
+
+						// Generate Q in U.
+						impl.Dorgqr(m, n, n, u, ldu, work[itau:], work[iwork:], lwork-iwork)
+
+						// Copy R to VT, zeroing out below it.
+						impl.Dlacpy(blas.Upper, n, n, a, lda, vt, ldvt)
+						impl.Dlaset(blas.Lower, n-1, n-1, 0, 0, vt[ldvt:], ldvt)
+
+						ie := itau
+						itauq := ie + n
+						itaup := itauq + n
+						iwork = itaup + n
+
+						// Bidiagonalize R in VT.
+						impl.Dgebrd(n, n, vt, ldvt, s, work[ie:],
+							work[itauq:], work[itaup:], work[iwork:], lwork-iwork)
+
+						// Multiply Q in U by left bidiagonalizing vectors in VT.
+						impl.Dormbr(lapack.ApplyQ, blas.Right, blas.NoTrans, m, n, n,
+							vt, ldvt, work[itauq:], u, ldu, work[iwork:], lwork-iwork)
+
+						// Generate right bidiagonalizing vectors in VT.
+						impl.Dorgbr(lapack.ApplyP, n, n, n, vt, ldvt,
+							work[itaup:], work[iwork:], lwork-iwork)
+						iwork = ie + n
+
+						// Perform bidiagonal QR iteration, computing left singular
+						// vectors of A in U and computing right singular vectors
+						// of A in VT.
+						ok = impl.Dbdsqr(blas.Upper, n, n, m, 0, s, work[ie:],
+							vt, ldvt, u, ldu, work, 1, work[iwork:])
+					}
+				}
+			} else if wantua {
+				if wantvn {
+					// Path 7
+					if lwork >= n*n+max(max(n+m, 4*n), bdspac) {
+						// Sufficient workspace for a fast algorithm.
+						ir := 0
+						var ldworkr int
+						if lwork >= wrkbl+lda*n {
+							ldworkr = lda
+						} else {
+							ldworkr = n
+						}
+						itau := ir + ldworkr*n
+						iwork := itau + n
+
+						// Compute A = Q*R, copying result to U.
+						impl.Dgeqrf(m, n, a, lda, work[itau:], work[iwork:], lwork-iwork)
+						impl.Dlacpy(blas.Lower, m, n, a, lda, u, ldu)
+
+						// Copy R to work[ir:], zeroing out below it.
+						impl.Dlacpy(blas.Upper, n, n, a, lda, work[ir:], ldworkr)
+						impl.Dlaset(blas.Lower, n-1, n-1, 0, 0, work[ir+ldworkr:], ldworkr)
+
+						// Generate Q in U.
+						impl.Dorgqr(m, m, n, u, ldu, work[itau:], work[iwork:], lwork-iwork)
+						ie := itau
+						itauq := ie + n
+						itaup := itauq + n
+						iwork = itaup + n
+
+						// Bidiagonalize R in work[ir:].
+						impl.Dgebrd(n, n, work[ir:], ldworkr, s, work[ie:],
+							work[itauq:], work[itaup:], work[iwork:], lwork-iwork)
+
+						// Generate left bidiagonalizing vectors in work[ir:].
+						impl.Dorgbr(lapack.ApplyQ, n, n, n, work[ir:], ldworkr,
+							work[itauq:], work[iwork:], lwork-iwork)
+						iwork = ie + n
+
+						// Perform bidiagonal QR iteration, computing left singular
+						// vectors of R in work[ir:].
+						ok = impl.Dbdsqr(blas.Upper, n, 0, n, 0, s, work[ie:], work, 1,
+							work[ir:], ldworkr, work, 1, work[iwork:])
+
+						// Multiply Q in U by left singular vectors of R in
+						// work[ir:], storing result in A.
+						bi.Dgemm(blas.NoTrans, blas.NoTrans, m, n, n, 1, u, ldu,
+							work[ir:], ldworkr, 0, a, lda)
+
+						// Copy left singular vectors of A from A to U.
+						impl.Dlacpy(blas.All, m, n, a, lda, u, ldu)
+					} else {
+						// Insufficient workspace for a fast algorithm.
+						itau := 0
+						iwork := itau + n
+
+						// Compute A = Q*R, copying result to U.
+						impl.Dgeqrf(m, n, a, lda, work[itau:], work[iwork:], lwork-iwork)
+						impl.Dlacpy(blas.Lower, m, n, a, lda, u, ldu)
+
+						// Generate Q in U.
+						impl.Dorgqr(m, m, n, u, ldu, work[itau:], work[iwork:], lwork-iwork)
+						ie := itau
+						itauq := ie + n
+						itaup := itauq + n
+						iwork = itaup + n
+
+						// Zero out below R in A.
+						impl.Dlaset(blas.Lower, n-1, n-1, 0, 0, a[lda:], lda)
+
+						// Bidiagonalize R in A.
+						impl.Dgebrd(n, n, a, lda, s, work[ie:],
+							work[itauq:], work[itaup:], work[iwork:], lwork-iwork)
+
+						// Multiply Q in U by left bidiagonalizing vectors in A.
+						impl.Dormbr(lapack.ApplyQ, blas.Right, blas.NoTrans, m, n, n,
+							a, lda, work[itauq:], u, ldu, work[iwork:], lwork-iwork)
+						iwork = ie + n
+
+						// Perform bidiagonal QR iteration, computing left
+						// singular vectors of A in U.
+						ok = impl.Dbdsqr(blas.Upper, n, 0, m, 0, s, work[ie:],
+							work, 1, u, ldu, work, 1, work[iwork:])
+					}
+				} else if wantvo {
+					// Path 8.
+					panic(noSVDO)
+				} else if wantvas {
+					// Path 9.
+					if lwork >= n*n+max(max(n+m, 4*n), bdspac) {
+						// Sufficient workspace for a fast algorithm.
+						iu := 0
+						var ldworku int
+						if lwork >= wrkbl+lda*n {
+							ldworku = lda
+						} else {
+							ldworku = n
+						}
+						itau := iu + ldworku*n
+						iwork := itau + n
+
+						// Compute A = Q * R, copying result to U.
+						impl.Dgeqrf(m, n, a, lda, work[itau:], work[iwork:], lwork-iwork)
+						impl.Dlacpy(blas.Lower, m, n, a, lda, u, ldu)
+
+						// Generate Q in U.
+						impl.Dorgqr(m, m, n, u, ldu, work[itau:], work[iwork:], lwork-iwork)
+
+						// Copy R to work[iu:], zeroing out below it.
+						impl.Dlacpy(blas.Upper, n, n, a, lda, work[iu:], ldworku)
+						impl.Dlaset(blas.Lower, n-1, n-1, 0, 0, work[iu+ldworku:], ldworku)
+
+						ie = itau
+						itauq := ie + n
+						itaup := itauq + n
+						iwork = itaup + n
+
+						// Bidiagonalize R in work[iu:], copying result to VT.
+						impl.Dgebrd(n, n, work[iu:], ldworku, s, work[ie:],
+							work[itauq:], work[itaup:], work[iwork:], lwork-iwork)
+						impl.Dlacpy(blas.Upper, n, n, work[iu:], ldworku, vt, ldvt)
+
+						// Generate left bidiagonalizing vectors in work[iu:].
+						impl.Dorgbr(lapack.ApplyQ, n, n, n, work[iu:], ldworku,
+							work[itauq:], work[iwork:], lwork-iwork)
+
+						// Generate right bidiagonalizing vectors in VT.
+						impl.Dorgbr(lapack.ApplyP, n, n, n, vt, ldvt,
+							work[itaup:], work[iwork:], lwork-iwork)
+						iwork = ie + n
+
+						// Perform bidiagonal QR iteration, computing left singular
+						// vectors of R in work[iu:] and computing right
+						// singular vectors of R in VT.
+						ok = impl.Dbdsqr(blas.Upper, n, n, n, 0, s, work[ie:],
+							vt, ldvt, work[iu:], ldworku, work, 1, work[iwork:])
+
+						// Multiply Q in U by left singular vectors of R in
+						// work[iu:], storing result in A.
+						bi.Dgemm(blas.NoTrans, blas.NoTrans, m, n, n, 1,
+							u, ldu, work[iu:], ldworku, 0, a, lda)
+
+						// Copy left singular vectors of A from A to U.
+						impl.Dlacpy(blas.All, m, n, a, lda, u, ldu)
+
+						/*
+							// Bidiagonalize R in VT.
+							impl.Dgebrd(n, n, vt, ldvt, s, work[ie:],
+								work[itauq:], work[itaup:], work[iwork:], lwork-iwork)
+
+							// Multiply Q in U by left bidiagonalizing vectors in VT.
+							impl.Dormbr(lapack.ApplyQ, blas.Right, blas.NoTrans,
+								m, n, n, vt, ldvt, work[itauq:], u, ldu, work[iwork:], lwork-iwork)
+
+							// Generate right bidiagonalizing vectors in VT.
+							impl.Dorgbr(lapack.ApplyP, n, n, n, vt, ldvt,
+								work[itaup:], work[iwork:], lwork-iwork)
+							iwork = ie + n
+
+							// Perform bidiagonal QR iteration, computing left singular
+							// vectors of A in U and computing right singular vectors
+							// of A in VT.
+							ok = impl.Dbdsqr(blas.Upper, n, n, m, 0, s, work[ie:],
+								vt, ldvt, u, ldu, work, 1, work[iwork:])
+						*/
+					} else {
+						// Insufficient workspace for a fast algorithm.
+						itau := 0
+						iwork := itau + n
+
+						// Compute A = Q*R, copying result to U.
+						impl.Dgeqrf(m, n, a, lda, work[itau:], work[iwork:], lwork-iwork)
+						impl.Dlacpy(blas.Lower, m, n, a, lda, u, ldu)
+
+						// Generate Q in U.
+						impl.Dorgqr(m, m, n, u, ldu, work[itau:], work[iwork:], lwork-iwork)
+
+						// Copy R from A to VT, zeroing out below it.
+						impl.Dlacpy(blas.Upper, n, n, a, lda, vt, ldvt)
+						impl.Dlaset(blas.Lower, n-1, n-1, 0, 0, vt[ldvt:], ldvt)
+
+						ie := itau
+						itauq := ie + n
+						itaup := itauq + n
+						iwork = itaup + n
+
+						// Bidiagonalize R in VT.
+						impl.Dgebrd(n, n, vt, ldvt, s, work[ie:],
+							work[itauq:], work[itaup:], work[iwork:], lwork-iwork)
+
+						// Multiply Q in U by left bidiagonalizing vectors in VT.
+						impl.Dormbr(lapack.ApplyQ, blas.Right, blas.NoTrans,
+							m, n, n, vt, ldvt, work[itauq:], u, ldu, work[iwork:], lwork-iwork)
+
+						// Generate right bidiagonizing vectors in VT.
+						impl.Dorgbr(lapack.ApplyP, n, n, n, vt, ldvt,
+							work[itaup:], work[iwork:], lwork-iwork)
+						iwork = ie + n
+
+						// Perform bidiagonal QR iteration, computing left singular
+						// vectors of A in U and computing right singular vectors
+						// of A in VT.
+						impl.Dbdsqr(blas.Upper, n, n, m, 0, s, work[ie:],
+							vt, ldvt, u, ldu, work, 1, work[iwork:])
+					}
+				}
+			}
+		} else {
+			// Path 10.
+			// M at least N, but not much larger.
+			ie = 0
+			itauq := ie + n
+			itaup := itauq + n
+			iwork := itaup + n
+
+			// Bidiagonalize A.
+			impl.Dgebrd(m, n, a, lda, s, work[ie:], work[itauq:],
+				work[itaup:], work[iwork:], lwork-iwork)
+			if wantuas {
+				// Left singular vectors are desired in U. Copy result to U and
+				// generate left biadiagonalizing vectors in U.
+				impl.Dlacpy(blas.Lower, m, n, a, lda, u, ldu)
+				var ncu int
+				if wantus {
+					ncu = n
+				}
+				if wantua {
+					ncu = m
+				}
+				impl.Dorgbr(lapack.ApplyQ, m, ncu, n, u, ldu, work[itauq:], work[iwork:], lwork-iwork)
+			}
+			if wantvas {
+				// Right singular vectors are desired in VT. Copy result to VT and
+				// generate left biadiagonalizing vectors in VT.
+				impl.Dlacpy(blas.Upper, n, n, a, lda, vt, ldvt)
+				impl.Dorgbr(lapack.ApplyP, n, n, n, vt, ldvt, work[itaup:], work[iwork:], lwork-iwork)
+			}
+			if wantuo {
+				panic(noSVDO)
+			}
+			if wantvo {
+				panic(noSVDO)
+			}
+			iwork = ie + n
+			var nru, ncvt int
+			if wantuas || wantuo {
+				nru = m
+			}
+			if wantun {
+				nru = 0
+			}
+			if wantvas || wantvo {
+				ncvt = n
+			}
+			if wantvn {
+				ncvt = 0
+			}
+			if !wantuo && !wantvo {
+				// Perform bidiagonal QR iteration, if desired, computing left
+				// singular vectors in U and right singular vectors in VT.
+				ok = impl.Dbdsqr(blas.Upper, n, ncvt, nru, 0, s, work[ie:],
+					vt, ldvt, u, ldu, work, 1, work[iwork:])
+			} else {
+				// There will be two branches when the implementation is complete.
+				panic(noSVDO)
+			}
+		}
+	} else {
+		// A has more columns than rows. If A has sufficiently more columns than
+		// rows, first reduce using the LQ decomposition.
+		if n >= mnthr {
+			// n >> m.
+			if wantvn {
+				// Path 1t.
+				itau := 0
+				iwork := itau + m
+
+				// Compute A = L*Q.
+				impl.Dgelqf(m, n, a, lda, work[itau:], work[iwork:], lwork-iwork)
+
+				// Zero out above L.
+				impl.Dlaset(blas.Upper, m-1, m-1, 0, 0, a[1:], lda)
+				ie := 0
+				itauq := ie + m
+				itaup := itauq + m
+				iwork = itaup + m
+
+				// Bidiagonalize L in A.
+				impl.Dgebrd(m, m, a, lda, s, work[ie:itauq],
+					work[itauq:itaup], work[itaup:iwork], work[iwork:], lwork-iwork)
+				if wantuo || wantuas {
+					impl.Dorgbr(lapack.ApplyQ, m, m, m, a, lda,
+						work[itauq:], work[iwork:], lwork-iwork)
+				}
+				iwork = ie + m
+				nru := 0
+				if wantuo || wantuas {
+					nru = m
+				}
+
+				// Perform bidiagonal QR iteration, computing left singular vectors
+				// of A in A if desired.
+				ok = impl.Dbdsqr(blas.Upper, m, 0, nru, 0, s, work[ie:],
+					work, 1, a, lda, work, 1, work[iwork:])
+
+				// If left singular vectors desired in U, copy them there.
+				if wantuas {
+					impl.Dlacpy(blas.All, m, m, a, lda, u, ldu)
+				}
+			} else if wantvo && wantun {
+				// Path 2t.
+				panic(noSVDO)
+			} else if wantvo && wantuas {
+				// Path 3t.
+				panic(noSVDO)
+			} else if wantvs {
+				if wantun {
+					// Path 4t.
+					if lwork >= m*m+max(4*m, bdspac) {
+						// Sufficient workspace for a fast algorithm.
+						ir := 0
+						var ldworkr int
+						if lwork >= wrkbl+lda*m {
+							ldworkr = lda
+						} else {
+							ldworkr = m
+						}
+						itau := ir + ldworkr*m
+						iwork := itau + m
+
+						// Compute A = L*Q.
+						impl.Dgelqf(m, n, a, lda, work[itau:], work[iwork:], lwork-iwork)
+
+						// Copy L to work[ir:], zeroing out above it.
+						impl.Dlacpy(blas.Lower, m, m, a, lda, work[ir:], ldworkr)
+						impl.Dlaset(blas.Upper, m-1, m-1, 0, 0, work[ir+1:], ldworkr)
+
+						// Generate Q in A.
+						impl.Dorglq(m, n, m, a, lda, work[itau:], work[iwork:], lwork-iwork)
+						ie := itau
+						itauq := ie + m
+						itaup := itauq + m
+						iwork = itaup + m
+
+						// Bidiagonalize L in work[ir:].
+						impl.Dgebrd(m, m, work[ir:], ldworkr, s, work[ie:],
+							work[itauq:], work[itaup:], work[iwork:], lwork-iwork)
+
+						// Generate right vectors bidiagonalizing L in work[ir:].
+						impl.Dorgbr(lapack.ApplyP, m, m, m, work[ir:], ldworkr,
+							work[itaup:], work[iwork:], lwork-iwork)
+						iwork = ie + m
+
+						// Perform bidiagonal QR iteration, computing right singular
+						// vectors of L in work[ir:].
+						ok = impl.Dbdsqr(blas.Upper, m, m, 0, 0, s, work[ie:],
+							work[ir:], ldworkr, work, 1, work, 1, work[iwork:])
+
+						// Multiply right singular vectors of L in work[ir:] by
+						// Q in A, storing result in VT.
+						bi.Dgemm(blas.NoTrans, blas.NoTrans, m, n, m, 1,
+							work[ir:], ldworkr, a, lda, 0, vt, ldvt)
+					} else {
+						// Insufficient workspace for a fast algorithm.
+						itau := 0
+						iwork := itau + m
+
+						// Compute A = L*Q.
+						impl.Dgelqf(m, n, a, lda, work[itau:], work[iwork:], lwork-iwork)
+
+						// Copy result to VT.
+						impl.Dlacpy(blas.Upper, m, n, a, lda, vt, ldvt)
+
+						// Generate Q in VT.
+						impl.Dorglq(m, n, m, vt, ldvt, work[itau:], work[iwork:], lwork-iwork)
+						ie := itau
+						itauq := ie + m
+						itaup := itauq + m
+						iwork = itaup + m
+
+						// Zero out above L in A.
+						impl.Dlaset(blas.Upper, m-1, m-1, 0, 0, a[1:], lda)
+
+						// Bidiagonalize L in A.
+						impl.Dgebrd(m, m, a, lda, s, work[ie:],
+							work[itauq:], work[itaup:], work[iwork:], lwork-iwork)
+
+						// Multiply right vectors bidiagonalizing L by Q in VT.
+						impl.Dormbr(lapack.ApplyP, blas.Left, blas.Trans, m, n, m,
+							a, lda, work[itaup:], vt, ldvt, work[iwork:], lwork-iwork)
+						iwork = ie + m
+
+						// Perform bidiagonal QR iteration, computing right
+						// singular vectors of A in VT.
+						ok = impl.Dbdsqr(blas.Upper, m, n, 0, 0, s, work[ie:],
+							vt, ldvt, work, 1, work, 1, work[iwork:])
+					}
+				} else if wantuo {
+					// Path 5t.
+					panic(noSVDO)
+				} else if wantuas {
+					// Path 6t.
+					if lwork >= m*m+max(4*m, bdspac) {
+						// Sufficient workspace for a fast algorithm.
+						iu := 0
+						var ldworku int
+						if lwork >= wrkbl+lda*m {
+							ldworku = lda
+						} else {
+							ldworku = m
+						}
+						itau := iu + ldworku*m
+						iwork := itau + m
+
+						// Compute A = L*Q.
+						impl.Dgelqf(m, n, a, lda, work[itau:], work[iwork:], lwork-iwork)
+
+						// Copy L to work[iu:], zeroing out above it.
+						impl.Dlacpy(blas.Lower, m, m, a, lda, work[iu:], ldworku)
+						impl.Dlaset(blas.Upper, m-1, m-1, 0, 0, work[iu+1:], ldworku)
+
+						// Generate Q in A.
+						impl.Dorglq(m, n, m, a, lda, work[itau:], work[iwork:], lwork-iwork)
+						ie := itau
+						itauq := ie + m
+						itaup := itauq + m
+						iwork = itaup + m
+
+						// Bidiagonalize L in work[iu:], copying result to U.
+						impl.Dgebrd(m, m, work[iu:], ldworku, s, work[ie:],
+							work[itauq:], work[itaup:], work[iwork:], lwork-iwork)
+						impl.Dlacpy(blas.Lower, m, m, work[iu:], ldworku, u, ldu)
+
+						// Generate right bidiagionalizing vectors in work[iu:].
+						impl.Dorgbr(lapack.ApplyP, m, m, m, work[iu:], ldworku,
+							work[itaup:], work[iwork:], lwork-iwork)
+
+						// Generate left bidiagonalizing vectors in U.
+						impl.Dorgbr(lapack.ApplyQ, m, m, m, u, ldu, work[itauq:], work[iwork:], lwork-iwork)
+						iwork = ie + m
+
+						// Perform bidiagonal QR iteration, computing left singular
+						// vectors of L in U and computing right singular vectors of
+						// L in work[iu:].
+						ok = impl.Dbdsqr(blas.Upper, m, m, m, 0, s, work[ie:],
+							work[iu:], ldworku, u, ldu, work, 1, work[iwork:])
+
+						// Multiply right singular vectors of L in work[iu:] by
+						// Q in A, storing result in VT.
+						bi.Dgemm(blas.NoTrans, blas.NoTrans, m, n, m, 1,
+							work[iu:], ldworku, a, lda, 0, vt, ldvt)
+					} else {
+						// Insufficient workspace for a fast algorithm.
+						itau := 0
+						iwork := itau + m
+
+						// Compute A = L*Q, copying result to VT.
+						impl.Dgelqf(m, n, a, lda, work[itau:], work[iwork:], lwork-iwork)
+						impl.Dlacpy(blas.Upper, m, n, a, lda, vt, ldvt)
+
+						// Generate Q in VT.
+						impl.Dorglq(m, n, m, vt, ldvt, work[itau:], work[iwork:], lwork-iwork)
+
+						// Copy L to U, zeroing out above it.
+						impl.Dlacpy(blas.Lower, m, m, a, lda, u, ldu)
+						impl.Dlaset(blas.Upper, m-1, m-1, 0, 0, u[1:], ldu)
+
+						ie := itau
+						itauq := ie + m
+						itaup := itauq + m
+						iwork = itaup + m
+
+						// Bidiagonalize L in U.
+						impl.Dgebrd(m, m, u, ldu, s, work[ie:],
+							work[itauq:], work[itaup:], work[iwork:], lwork-iwork)
+
+						// Multiply right bidiagonalizing vectors in U by Q in VT.
+						impl.Dormbr(lapack.ApplyP, blas.Left, blas.Trans, m, n, m,
+							u, ldu, work[itaup:], vt, ldvt, work[iwork:], lwork-iwork)
+
+						// Generate left bidiagonalizing vectors in U.
+						impl.Dorgbr(lapack.ApplyQ, m, m, m, u, ldu, work[itauq:], work[iwork:], lwork-iwork)
+						iwork = ie + m
+
+						// Perform bidiagonal QR iteration, computing left singular
+						// vectors of A in U and computing right singular vectors
+						// of A in VT.
+						impl.Dbdsqr(blas.Upper, m, n, m, 0, s, work[ie:], vt, ldvt,
+							u, ldu, work, 1, work[iwork:])
+					}
+				}
+			} else if wantva {
+				if wantun {
+					// Path 7t.
+					if lwork >= m*m+max(max(n+m, 4*m), bdspac) {
+						// Sufficient workspace for a fast algorithm.
+						ir := 0
+						var ldworkr int
+						if lwork >= wrkbl+lda*m {
+							ldworkr = lda
+						} else {
+							ldworkr = m
+						}
+						itau := ir + ldworkr*m
+						iwork := itau + m
+
+						// Compute A = L*Q, copying result to VT.
+						impl.Dgelqf(m, n, a, lda, work[itau:], work[iwork:], lwork-iwork)
+						impl.Dlacpy(blas.Upper, m, n, a, lda, vt, ldvt)
+
+						// Copy L to work[ir:], zeroing out above it.
+						impl.Dlacpy(blas.Lower, m, m, a, lda, work[ir:], ldworkr)
+						impl.Dlaset(blas.Upper, m-1, m-1, 0, 0, work[ir+1:], ldworkr)
+
+						// Generate Q in VT.
+						impl.Dorglq(n, n, m, vt, ldvt, work[itau:], work[iwork:], lwork-iwork)
+
+						ie := itau
+						itauq := ie + m
+						itaup := itauq + m
+						iwork = itaup + m
+
+						// Bidiagonalize L in work[ir:].
+						impl.Dgebrd(m, m, work[ir:], ldworkr, s, work[ie:],
+							work[itauq:], work[itaup:], work[iwork:], lwork-iwork)
+
+						// Generate right bidiagonalizing vectors in work[ir:].
+						impl.Dorgbr(lapack.ApplyP, m, m, m, work[ir:], ldworkr,
+							work[itaup:], work[iwork:], lwork-iwork)
+						iwork = ie + m
+
+						// Perform bidiagonal QR iteration, computing right
+						// singular vectors of L in work[ir:].
+						ok = impl.Dbdsqr(blas.Upper, m, m, 0, 0, s, work[ie:],
+							work[ir:], ldworkr, work, 1, work, 1, work[iwork:])
+
+						// Multiply right singular vectors of L in work[ir:] by
+						// Q in VT, storing result in A.
+						bi.Dgemm(blas.NoTrans, blas.NoTrans, m, n, m, 1,
+							work[ir:], ldworkr, vt, ldvt, 0, a, lda)
+
+						// Copy right singular vectors of A from A to VT.
+						impl.Dlacpy(blas.All, m, n, a, lda, vt, ldvt)
+					} else {
+						// Insufficient workspace for a fast algorithm.
+						itau := 0
+						iwork := itau + m
+						// Compute A = L * Q, copying result to VT.
+						impl.Dgelqf(m, n, a, lda, work[itau:], work[iwork:], lwork-iwork)
+						impl.Dlacpy(blas.Upper, m, n, a, lda, vt, ldvt)
+
+						// Generate Q in VT.
+						impl.Dorglq(n, n, m, vt, ldvt, work[itau:], work[iwork:], lwork-iwork)
+
+						ie := itau
+						itauq := ie + m
+						itaup := itauq + m
+						iwork = itaup + m
+
+						// Zero out above L in A.
+						impl.Dlaset(blas.Upper, m-1, m-1, 0, 0, a[1:], lda)
+
+						// Bidiagonalize L in A.
+						impl.Dgebrd(m, m, a, lda, s, work[ie:], work[itauq:],
+							work[itaup:], work[iwork:], lwork-iwork)
+
+						// Multiply right bidiagonalizing vectors in A by Q in VT.
+						impl.Dormbr(lapack.ApplyP, blas.Left, blas.Trans, m, n, m,
+							a, lda, work[itaup:], vt, ldvt, work[iwork:], lwork-iwork)
+						iwork = ie + m
+
+						// Perform bidiagonal QR iteration, computing right singular
+						// vectors of A in VT.
+						ok = impl.Dbdsqr(blas.Upper, m, n, 0, 0, s, work[ie:],
+							vt, ldvt, work, 1, work, 1, work[iwork:])
+					}
+				} else if wantuo {
+					panic(noSVDO)
+				} else if wantuas {
+					// Path 9t.
+					if lwork >= m*m+max(max(m+n, 4*m), bdspac) {
+						// Sufficient workspace for a fast algorithm.
+						iu := 0
+
+						var ldworku int
+						if lwork >= wrkbl+lda*m {
+							ldworku = lda
+						} else {
+							ldworku = m
+						}
+						itau := iu + ldworku*m
+						iwork := itau + m
+
+						// Generate A = L * Q copying result to VT.
+						impl.Dgelqf(m, n, a, lda, work[itau:], work[iwork:], lwork-iwork)
+						impl.Dlacpy(blas.Upper, m, n, a, lda, vt, ldvt)
+
+						// Generate Q in VT.
+						impl.Dorglq(n, n, m, vt, ldvt, work[itau:], work[iwork:], lwork-iwork)
+
+						// Copy L to work[iu:], zeroing out above it.
+						impl.Dlacpy(blas.Lower, m, m, a, lda, work[iu:], ldworku)
+						impl.Dlaset(blas.Upper, m-1, m-1, 0, 0, work[iu+1:], ldworku)
+						ie = itau
+						itauq := ie + m
+						itaup := itauq + m
+						iwork = itaup + m
+
+						// Bidiagonalize L in work[iu:], copying result to U.
+						impl.Dgebrd(m, m, work[iu:], ldworku, s, work[ie:],
+							work[itauq:], work[itaup:], work[iwork:], lwork-iwork)
+						impl.Dlacpy(blas.Lower, m, m, work[iu:], ldworku, u, ldu)
+
+						// Generate right bidiagonalizing vectors in work[iu:].
+						impl.Dorgbr(lapack.ApplyP, m, m, m, work[iu:], ldworku,
+							work[itaup:], work[iwork:], lwork-iwork)
+
+						// Generate left bidiagonalizing vectors in U.
+						impl.Dorgbr(lapack.ApplyQ, m, m, m, u, ldu, work[itauq:], work[iwork:], lwork-iwork)
+						iwork = ie + m
+
+						// Perform bidiagonal QR iteration, computing left singular
+						// vectors of L in U and computing right singular vectors
+						// of L in work[iu:].
+						ok = impl.Dbdsqr(blas.Upper, m, m, m, 0, s, work[ie:],
+							work[iu:], ldworku, u, ldu, work, 1, work[iwork:])
+
+						// Multiply right singular vectors of L in work[iu:]
+						// Q in VT, storing result in A.
+						bi.Dgemm(blas.NoTrans, blas.NoTrans, m, n, m, 1,
+							work[iu:], ldworku, vt, ldvt, 0, a, lda)
+
+						// Copy right singular vectors of A from A to VT.
+						impl.Dlacpy(blas.All, m, n, a, lda, vt, ldvt)
+					} else {
+						// Insufficient workspace for a fast algorithm.
+						itau := 0
+						iwork := itau + m
+
+						// Compute A = L * Q, copying result to VT.
+						impl.Dgelqf(m, n, a, lda, work[itau:], work[iwork:], lwork-iwork)
+						impl.Dlacpy(blas.Upper, m, n, a, lda, vt, ldvt)
+
+						// Generate Q in VT.
+						impl.Dorglq(n, n, m, vt, ldvt, work[itau:], work[iwork:], lwork-iwork)
+
+						// Copy L to U, zeroing out above it.
+						impl.Dlacpy(blas.Lower, m, m, a, lda, u, ldu)
+						impl.Dlaset(blas.Upper, m-1, m-1, 0, 0, u[1:], ldu)
+
+						ie = itau
+						itauq := ie + m
+						itaup := itauq + m
+						iwork = itaup + m
+
+						// Bidiagonalize L in U.
+						impl.Dgebrd(m, m, u, ldu, s, work[ie:], work[itauq:],
+							work[itaup:], work[iwork:], lwork-iwork)
+
+						// Multiply right bidiagonalizing vectors in U by Q in VT.
+						impl.Dormbr(lapack.ApplyP, blas.Left, blas.Trans, m, n, m,
+							u, ldu, work[itaup:], vt, ldvt, work[iwork:], lwork-iwork)
+
+						// Generate left bidiagonalizing vectors in U.
+						impl.Dorgbr(lapack.ApplyQ, m, m, m, u, ldu, work[itauq:], work[iwork:], lwork-iwork)
+						iwork = ie + m
+
+						// Perform bidiagonal QR iteration, computing left singular
+						// vectors of A in U and computing right singular vectors
+						// of A in VT.
+						ok = impl.Dbdsqr(blas.Upper, m, n, m, 0, s, work[ie:],
+							vt, ldvt, u, ldu, work, 1, work[iwork:])
+					}
+				}
+			}
+		} else {
+			// Path 10t.
+			// N at least M, but not much larger.
+			ie = 0
+			itauq := ie + m
+			itaup := itauq + m
+			iwork := itaup + m
+
+			// Bidiagonalize A.
+			impl.Dgebrd(m, n, a, lda, s, work[ie:], work[itauq:], work[itaup:], work[iwork:], lwork-iwork)
+			if wantuas {
+				// If left singular vectors desired in U, copy result to U and
+				// generate left bidiagonalizing vectors in U.
+				impl.Dlacpy(blas.Lower, m, m, a, lda, u, ldu)
+				impl.Dorgbr(lapack.ApplyQ, m, m, n, u, ldu, work[itauq:], work[iwork:], lwork-iwork)
+			}
+			if wantvas {
+				// If right singular vectors desired in VT, copy result to VT
+				// and generate right bidiagonalizing vectors in VT.
+				impl.Dlacpy(blas.Upper, m, n, a, lda, vt, ldvt)
+				var nrvt int
+				if wantva {
+					nrvt = n
+				} else {
+					nrvt = m
+				}
+				impl.Dorgbr(lapack.ApplyP, nrvt, n, m, vt, ldvt, work[itaup:], work[iwork:], lwork-iwork)
+			}
+			if wantuo {
+				panic(noSVDO)
+			}
+			if wantvo {
+				panic(noSVDO)
+			}
+			iwork = ie + m
+			var nru, ncvt int
+			if wantuas || wantuo {
+				nru = m
+			}
+			if wantvas || wantvo {
+				ncvt = n
+			}
+			if !wantuo && !wantvo {
+				// Perform bidiagonal QR iteration, if desired, computing left
+				// singular vectors in U and computing right singular vectors in
+				// VT.
+				ok = impl.Dbdsqr(blas.Lower, m, ncvt, nru, 0, s, work[ie:],
+					vt, ldvt, u, ldu, work, 1, work[iwork:])
+			} else {
+				// There will be two branches when the implementation is complete.
+				panic(noSVDO)
+			}
+		}
+	}
+	if !ok {
+		if ie > 1 {
+			for i := 0; i < minmn-1; i++ {
+				work[i+1] = work[i+ie]
+			}
+		}
+		if ie < 1 {
+			for i := minmn - 2; i >= 0; i-- {
+				work[i+1] = work[i+ie]
+			}
+		}
+	}
+	// Undo scaling if necessary.
+	if iscl {
+		if anrm > bignum {
+			impl.Dlascl(lapack.General, 0, 0, bignum, anrm, minmn, 1, s, minmn)
+		}
+		if !ok && anrm > bignum {
+			impl.Dlascl(lapack.General, 0, 0, bignum, anrm, minmn-1, 1, work[minmn:], minmn)
+		}
+		if anrm < smlnum {
+			impl.Dlascl(lapack.General, 0, 0, smlnum, anrm, minmn, 1, s, minmn)
+		}
+		if !ok && anrm < smlnum {
+			impl.Dlascl(lapack.General, 0, 0, smlnum, anrm, minmn-1, 1, work[minmn:], minmn)
+		}
+	}
+	work[0] = float64(maxwrk)
+	return ok
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dgetf2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dgetf2.go
new file mode 100644
index 00000000..3167d160
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dgetf2.go
@@ -0,0 +1,69 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dgetf2 computes the LU decomposition of the m×n matrix A.
+// The LU decomposition is a factorization of a into
+//  A = P * L * U
+// where P is a permutation matrix, L is a unit lower triangular matrix, and
+// U is a (usually) non-unit upper triangular matrix. On exit, L and U are stored
+// in place into a.
+//
+// ipiv is a permutation vector. It indicates that row i of the matrix was
+// changed with ipiv[i]. ipiv must have length at least min(m,n), and will panic
+// otherwise. ipiv is zero-indexed.
+//
+// Dgetf2 returns whether the matrix A is singular. The LU decomposition will
+// be computed regardless of the singularity of A, but division by zero
+// will occur if the false is returned and the result is used to solve a
+// system of equations.
+//
+// Dgetf2 is an internal routine. It is exported for testing purposes.
+func (Implementation) Dgetf2(m, n int, a []float64, lda int, ipiv []int) (ok bool) {
+	mn := min(m, n)
+	checkMatrix(m, n, a, lda)
+	if len(ipiv) < mn {
+		panic(badIpiv)
+	}
+	if m == 0 || n == 0 {
+		return true
+	}
+	bi := blas64.Implementation()
+	sfmin := dlamchS
+	ok = true
+	for j := 0; j < mn; j++ {
+		// Find a pivot and test for singularity.
+		jp := j + bi.Idamax(m-j, a[j*lda+j:], lda)
+		ipiv[j] = jp
+		if a[jp*lda+j] == 0 {
+			ok = false
+		} else {
+			// Swap the rows if necessary.
+			if jp != j {
+				bi.Dswap(n, a[j*lda:], 1, a[jp*lda:], 1)
+			}
+			if j < m-1 {
+				aj := a[j*lda+j]
+				if math.Abs(aj) >= sfmin {
+					bi.Dscal(m-j-1, 1/aj, a[(j+1)*lda+j:], lda)
+				} else {
+					for i := 0; i < m-j-1; i++ {
+						a[(j+1)*lda+j] = a[(j+1)*lda+j] / a[lda*j+j]
+					}
+				}
+			}
+		}
+		if j < mn-1 {
+			bi.Dger(m-j-1, n-j-1, -1, a[(j+1)*lda+j:], lda, a[j*lda+j+1:], 1, a[(j+1)*lda+j+1:], lda)
+		}
+	}
+	return ok
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dgetrf.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dgetrf.go
new file mode 100644
index 00000000..2b95668c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dgetrf.go
@@ -0,0 +1,70 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dgetrf computes the LU decomposition of the m×n matrix A.
+// The LU decomposition is a factorization of A into
+//  A = P * L * U
+// where P is a permutation matrix, L is a unit lower triangular matrix, and
+// U is a (usually) non-unit upper triangular matrix. On exit, L and U are stored
+// in place into a.
+//
+// ipiv is a permutation vector. It indicates that row i of the matrix was
+// changed with ipiv[i]. ipiv must have length at least min(m,n), and will panic
+// otherwise. ipiv is zero-indexed.
+//
+// Dgetrf is the blocked version of the algorithm.
+//
+// Dgetrf returns whether the matrix A is singular. The LU decomposition will
+// be computed regardless of the singularity of A, but division by zero
+// will occur if the false is returned and the result is used to solve a
+// system of equations.
+func (impl Implementation) Dgetrf(m, n int, a []float64, lda int, ipiv []int) (ok bool) {
+	mn := min(m, n)
+	checkMatrix(m, n, a, lda)
+	if len(ipiv) < mn {
+		panic(badIpiv)
+	}
+	if m == 0 || n == 0 {
+		return false
+	}
+	bi := blas64.Implementation()
+	nb := impl.Ilaenv(1, "DGETRF", " ", m, n, -1, -1)
+	if nb <= 1 || nb >= min(m, n) {
+		// Use the unblocked algorithm.
+		return impl.Dgetf2(m, n, a, lda, ipiv)
+	}
+	ok = true
+	for j := 0; j < mn; j += nb {
+		jb := min(mn-j, nb)
+		blockOk := impl.Dgetf2(m-j, jb, a[j*lda+j:], lda, ipiv[j:])
+		if !blockOk {
+			ok = false
+		}
+		for i := j; i <= min(m-1, j+jb-1); i++ {
+			ipiv[i] = j + ipiv[i]
+		}
+		impl.Dlaswp(j, a, lda, j, j+jb-1, ipiv[:j+jb], 1)
+		if j+jb < n {
+			impl.Dlaswp(n-j-jb, a[j+jb:], lda, j, j+jb-1, ipiv[:j+jb], 1)
+			bi.Dtrsm(blas.Left, blas.Lower, blas.NoTrans, blas.Unit,
+				jb, n-j-jb, 1,
+				a[j*lda+j:], lda,
+				a[j*lda+j+jb:], lda)
+			if j+jb < m {
+				bi.Dgemm(blas.NoTrans, blas.NoTrans, m-j-jb, n-j-jb, jb, -1,
+					a[(j+jb)*lda+j:], lda,
+					a[j*lda+j+jb:], lda,
+					1, a[(j+jb)*lda+j+jb:], lda)
+			}
+		}
+	}
+	return ok
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dgetri.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dgetri.go
new file mode 100644
index 00000000..993d6c02
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dgetri.go
@@ -0,0 +1,92 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dgetri computes the inverse of the matrix A using the LU factorization computed
+// by Dgetrf. On entry, a contains the PLU decomposition of A as computed by
+// Dgetrf and on exit contains the reciprocal of the original matrix.
+//
+// Dgetri will not perform the inversion if the matrix is singular, and returns
+// a boolean indicating whether the inversion was successful.
+//
+// work is temporary storage, and lwork specifies the usable memory length.
+// At minimum, lwork >= n and this function will panic otherwise.
+// Dgetri is a blocked inversion, but the block size is limited
+// by the temporary space available. If lwork == -1, instead of performing Dgetri,
+// the optimal work length will be stored into work[0].
+func (impl Implementation) Dgetri(n int, a []float64, lda int, ipiv []int, work []float64, lwork int) (ok bool) {
+	checkMatrix(n, n, a, lda)
+	if len(ipiv) < n {
+		panic(badIpiv)
+	}
+	nb := impl.Ilaenv(1, "DGETRI", " ", n, -1, -1, -1)
+	if lwork == -1 {
+		work[0] = float64(n * nb)
+		return true
+	}
+	if lwork < n {
+		panic(badWork)
+	}
+	if len(work) < lwork {
+		panic(badWork)
+	}
+	if n == 0 {
+		return true
+	}
+	ok = impl.Dtrtri(blas.Upper, blas.NonUnit, n, a, lda)
+	if !ok {
+		return false
+	}
+	nbmin := 2
+	ldwork := nb
+	if nb > 1 && nb < n {
+		iws := max(ldwork*n, 1)
+		if lwork < iws {
+			nb = lwork / ldwork
+			nbmin = max(2, impl.Ilaenv(2, "DGETRI", " ", n, -1, -1, -1))
+		}
+	}
+	bi := blas64.Implementation()
+	// TODO(btracey): Replace this with a more row-major oriented algorithm.
+	if nb < nbmin || nb >= n {
+		// Unblocked code.
+		for j := n - 1; j >= 0; j-- {
+			for i := j + 1; i < n; i++ {
+				work[i*ldwork] = a[i*lda+j]
+				a[i*lda+j] = 0
+			}
+			if j < n {
+				bi.Dgemv(blas.NoTrans, n, n-j-1, -1, a[(j+1):], lda, work[(j+1)*ldwork:], ldwork, 1, a[j:], lda)
+			}
+		}
+	} else {
+		nn := ((n - 1) / nb) * nb
+		for j := nn; j >= 0; j -= nb {
+			jb := min(nb, n-j)
+			for jj := j; jj < j+jb-1; jj++ {
+				for i := jj + 1; i < n; i++ {
+					work[i*ldwork+(jj-j)] = a[i*lda+jj]
+					a[i*lda+jj] = 0
+				}
+			}
+			if j+jb < n {
+				bi.Dgemm(blas.NoTrans, blas.NoTrans, n, jb, n-j-jb, -1, a[(j+jb):], lda, work[(j+jb)*ldwork:], ldwork, 1, a[j:], lda)
+				bi.Dtrsm(blas.Right, blas.Lower, blas.NoTrans, blas.Unit, n, jb, 1, work[j*ldwork:], ldwork, a[j:], lda)
+			}
+		}
+	}
+	for j := n - 2; j >= 0; j-- {
+		jp := ipiv[j]
+		if jp != j {
+			bi.Dswap(n, a[j:], lda, a[jp:], lda)
+		}
+	}
+	return true
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dgetrs.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dgetrs.go
new file mode 100644
index 00000000..ca5a9b2a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dgetrs.go
@@ -0,0 +1,55 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dgetrs solves a system of equations using an LU factorization.
+// The system of equations solved is
+//  A * X = B if trans == blas.Trans
+//  A^T * X = B if trans == blas.NoTrans
+// A is a general n×n matrix with stride lda. B is a general matrix of size n×nrhs.
+//
+// On entry b contains the elements of the matrix B. On exit, b contains the
+// elements of X, the solution to the system of equations.
+//
+// a and ipiv contain the LU factorization of A and the permutation indices as
+// computed by Dgetrf. ipiv is zero-indexed.
+func (impl Implementation) Dgetrs(trans blas.Transpose, n, nrhs int, a []float64, lda int, ipiv []int, b []float64, ldb int) {
+	checkMatrix(n, n, a, lda)
+	checkMatrix(n, nrhs, b, ldb)
+	if len(ipiv) < n {
+		panic(badIpiv)
+	}
+	if n == 0 || nrhs == 0 {
+		return
+	}
+	if trans != blas.Trans && trans != blas.NoTrans {
+		panic(badTrans)
+	}
+	bi := blas64.Implementation()
+	if trans == blas.NoTrans {
+		// Solve A * X = B.
+		impl.Dlaswp(nrhs, b, ldb, 0, n-1, ipiv, 1)
+		// Solve L * X = B, updating b.
+		bi.Dtrsm(blas.Left, blas.Lower, blas.NoTrans, blas.Unit,
+			n, nrhs, 1, a, lda, b, ldb)
+		// Solve U * X = B, updating b.
+		bi.Dtrsm(blas.Left, blas.Upper, blas.NoTrans, blas.NonUnit,
+			n, nrhs, 1, a, lda, b, ldb)
+		return
+	}
+	// Solve A^T * X = B.
+	// Solve U^T * X = B, updating b.
+	bi.Dtrsm(blas.Left, blas.Upper, blas.Trans, blas.NonUnit,
+		n, nrhs, 1, a, lda, b, ldb)
+	// Solve L^T * X = B, updating b.
+	bi.Dtrsm(blas.Left, blas.Lower, blas.Trans, blas.Unit,
+		n, nrhs, 1, a, lda, b, ldb)
+	impl.Dlaswp(nrhs, b, ldb, 0, n-1, ipiv, -1)
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dggsvd3.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dggsvd3.go
new file mode 100644
index 00000000..cf3635d9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dggsvd3.go
@@ -0,0 +1,230 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dggsvd3 computes the generalized singular value decomposition (GSVD)
+// of an m×n matrix A and p×n matrix B:
+//  U^T*A*Q = D1*[ 0 R ]
+//
+//  V^T*B*Q = D2*[ 0 R ]
+// where U, V and Q are orthogonal matrices.
+//
+// Dggsvd3 returns k and l, the dimensions of the sub-blocks. k+l
+// is the effective numerical rank of the (m+p)×n matrix [ A^T B^T ]^T.
+// R is a (k+l)×(k+l) nonsingular upper triangular matrix, D1 and
+// D2 are m×(k+l) and p×(k+l) diagonal matrices and of the following
+// structures, respectively:
+//
+// If m-k-l >= 0,
+//
+//                    k  l
+//       D1 =     k [ I  0 ]
+//                l [ 0  C ]
+//            m-k-l [ 0  0 ]
+//
+//                  k  l
+//       D2 = l   [ 0  S ]
+//            p-l [ 0  0 ]
+//
+//               n-k-l  k    l
+//  [ 0 R ] = k [  0   R11  R12 ] k
+//            l [  0    0   R22 ] l
+//
+// where
+//
+//  C = diag( alpha_k, ... , alpha_{k+l} ),
+//  S = diag( beta_k,  ... , beta_{k+l} ),
+//  C^2 + S^2 = I.
+//
+// R is stored in
+//  A[0:k+l, n-k-l:n]
+// on exit.
+//
+// If m-k-l < 0,
+//
+//                 k m-k k+l-m
+//      D1 =   k [ I  0    0  ]
+//           m-k [ 0  C    0  ]
+//
+//                   k m-k k+l-m
+//      D2 =   m-k [ 0  S    0  ]
+//           k+l-m [ 0  0    I  ]
+//             p-l [ 0  0    0  ]
+//
+//                 n-k-l  k   m-k  k+l-m
+//  [ 0 R ] =    k [ 0    R11  R12  R13 ]
+//             m-k [ 0     0   R22  R23 ]
+//           k+l-m [ 0     0    0   R33 ]
+//
+// where
+//  C = diag( alpha_k, ... , alpha_m ),
+//  S = diag( beta_k,  ... , beta_m ),
+//  C^2 + S^2 = I.
+//
+//  R = [ R11 R12 R13 ] is stored in A[1:m, n-k-l+1:n]
+//      [  0  R22 R23 ]
+// and R33 is stored in
+//  B[m-k:l, n+m-k-l:n] on exit.
+//
+// Dggsvd3 computes C, S, R, and optionally the orthogonal transformation
+// matrices U, V and Q.
+//
+// jobU, jobV and jobQ are options for computing the orthogonal matrices. The behavior
+// is as follows
+//  jobU == lapack.GSVDU        Compute orthogonal matrix U
+//  jobU == lapack.GSVDNone     Do not compute orthogonal matrix.
+// The behavior is the same for jobV and jobQ with the exception that instead of
+// lapack.GSVDU these accept lapack.GSVDV and lapack.GSVDQ respectively.
+// The matrices U, V and Q must be m×m, p×p and n×n respectively unless the
+// relevant job parameter is lapack.GSVDNone.
+//
+// alpha and beta must have length n or Dggsvd3 will panic. On exit, alpha and
+// beta contain the generalized singular value pairs of A and B
+//   alpha[0:k] = 1,
+//   beta[0:k]  = 0,
+// if m-k-l >= 0,
+//   alpha[k:k+l] = diag(C),
+//   beta[k:k+l]  = diag(S),
+// if m-k-l < 0,
+//   alpha[k:m]= C, alpha[m:k+l]= 0
+//   beta[k:m] = S, beta[m:k+l] = 1.
+// if k+l < n,
+//   alpha[k+l:n] = 0 and
+//   beta[k+l:n]  = 0.
+//
+// On exit, iwork contains the permutation required to sort alpha descending.
+//
+// iwork must have length n, work must have length at least max(1, lwork), and
+// lwork must be -1 or greater than n, otherwise Dggsvd3 will panic. If
+// lwork is -1, work[0] holds the optimal lwork on return, but Dggsvd3 does
+// not perform the GSVD.
+func (impl Implementation) Dggsvd3(jobU, jobV, jobQ lapack.GSVDJob, m, n, p int, a []float64, lda int, b []float64, ldb int, alpha, beta, u []float64, ldu int, v []float64, ldv int, q []float64, ldq int, work []float64, lwork int, iwork []int) (k, l int, ok bool) {
+	checkMatrix(m, n, a, lda)
+	checkMatrix(p, n, b, ldb)
+
+	wantu := jobU == lapack.GSVDU
+	if wantu {
+		checkMatrix(m, m, u, ldu)
+	} else if jobU != lapack.GSVDNone {
+		panic(badGSVDJob + "U")
+	}
+	wantv := jobV == lapack.GSVDV
+	if wantv {
+		checkMatrix(p, p, v, ldv)
+	} else if jobV != lapack.GSVDNone {
+		panic(badGSVDJob + "V")
+	}
+	wantq := jobQ == lapack.GSVDQ
+	if wantq {
+		checkMatrix(n, n, q, ldq)
+	} else if jobQ != lapack.GSVDNone {
+		panic(badGSVDJob + "Q")
+	}
+
+	if len(alpha) != n {
+		panic(badAlpha)
+	}
+	if len(beta) != n {
+		panic(badBeta)
+	}
+
+	if lwork != -1 && lwork <= n {
+		panic(badWork)
+	}
+	if len(work) < max(1, lwork) {
+		panic(shortWork)
+	}
+	if len(iwork) < n {
+		panic(badWork)
+	}
+
+	// Determine optimal work length.
+	impl.Dggsvp3(jobU, jobV, jobQ,
+		m, p, n,
+		a, lda,
+		b, ldb,
+		0, 0,
+		u, ldu,
+		v, ldv,
+		q, ldq,
+		iwork,
+		work, work, -1)
+	lwkopt := n + int(work[0])
+	lwkopt = max(lwkopt, 2*n)
+	lwkopt = max(lwkopt, 1)
+	work[0] = float64(lwkopt)
+	if lwork == -1 {
+		return 0, 0, true
+	}
+
+	// Compute the Frobenius norm of matrices A and B.
+	anorm := impl.Dlange(lapack.NormFrob, m, n, a, lda, nil)
+	bnorm := impl.Dlange(lapack.NormFrob, p, n, b, ldb, nil)
+
+	// Get machine precision and set up threshold for determining
+	// the effective numerical rank of the matrices A and B.
+	tola := float64(max(m, n)) * math.Max(anorm, dlamchS) * dlamchP
+	tolb := float64(max(p, n)) * math.Max(bnorm, dlamchS) * dlamchP
+
+	// Preprocessing.
+	k, l = impl.Dggsvp3(jobU, jobV, jobQ,
+		m, p, n,
+		a, lda,
+		b, ldb,
+		tola, tolb,
+		u, ldu,
+		v, ldv,
+		q, ldq,
+		iwork,
+		work[:n], work[n:], lwork-n)
+
+	// Compute the GSVD of two upper "triangular" matrices.
+	_, ok = impl.Dtgsja(jobU, jobV, jobQ,
+		m, p, n,
+		k, l,
+		a, lda,
+		b, ldb,
+		tola, tolb,
+		alpha, beta,
+		u, ldu,
+		v, ldv,
+		q, ldq,
+		work)
+
+	// Sort the singular values and store the pivot indices in iwork
+	// Copy alpha to work, then sort alpha in work.
+	bi := blas64.Implementation()
+	bi.Dcopy(n, alpha, 1, work[:n], 1)
+	ibnd := min(l, m-k)
+	for i := 0; i < ibnd; i++ {
+		// Scan for largest alpha_{k+i}.
+		isub := i
+		smax := work[k+i]
+		for j := i + 1; j < ibnd; j++ {
+			if v := work[k+j]; v > smax {
+				isub = j
+				smax = v
+			}
+		}
+		if isub != i {
+			work[k+isub] = work[k+i]
+			work[k+i] = smax
+			iwork[k+i] = k + isub
+		} else {
+			iwork[k+i] = k + i
+		}
+	}
+
+	work[0] = float64(lwkopt)
+
+	return k, l, ok
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dggsvp3.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dggsvp3.go
new file mode 100644
index 00000000..bd068ff1
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dggsvp3.go
@@ -0,0 +1,273 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dggsvp3 computes orthogonal matrices U, V and Q such that
+//
+//                  n-k-l  k    l
+//  U^T*A*Q =    k [ 0    A12  A13 ] if m-k-l >= 0;
+//               l [ 0     0   A23 ]
+//           m-k-l [ 0     0    0  ]
+//
+//                  n-k-l  k    l
+//  U^T*A*Q =    k [ 0    A12  A13 ] if m-k-l < 0;
+//             m-k [ 0     0   A23 ]
+//
+//                  n-k-l  k    l
+//  V^T*B*Q =    l [ 0     0   B13 ]
+//             p-l [ 0     0    0  ]
+//
+// where the k×k matrix A12 and l×l matrix B13 are non-singular
+// upper triangular. A23 is l×l upper triangular if m-k-l >= 0,
+// otherwise A23 is (m-k)×l upper trapezoidal.
+//
+// Dggsvp3 returns k and l, the dimensions of the sub-blocks. k+l
+// is the effective numerical rank of the (m+p)×n matrix [ A^T B^T ]^T.
+//
+// jobU, jobV and jobQ are options for computing the orthogonal matrices. The behavior
+// is as follows
+//  jobU == lapack.GSVDU        Compute orthogonal matrix U
+//  jobU == lapack.GSVDNone     Do not compute orthogonal matrix.
+// The behavior is the same for jobV and jobQ with the exception that instead of
+// lapack.GSVDU these accept lapack.GSVDV and lapack.GSVDQ respectively.
+// The matrices U, V and Q must be m×m, p×p and n×n respectively unless the
+// relevant job parameter is lapack.GSVDNone.
+//
+// tola and tolb are the convergence criteria for the Jacobi-Kogbetliantz
+// iteration procedure. Generally, they are the same as used in the preprocessing
+// step, for example,
+//  tola = max(m, n)*norm(A)*eps,
+//  tolb = max(p, n)*norm(B)*eps.
+// Where eps is the machine epsilon.
+//
+// iwork must have length n, work must have length at least max(1, lwork), and
+// lwork must be -1 or greater than zero, otherwise Dggsvp3 will panic.
+//
+// Dggsvp3 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dggsvp3(jobU, jobV, jobQ lapack.GSVDJob, m, p, n int, a []float64, lda int, b []float64, ldb int, tola, tolb float64, u []float64, ldu int, v []float64, ldv int, q []float64, ldq int, iwork []int, tau, work []float64, lwork int) (k, l int) {
+	const forward = true
+
+	checkMatrix(m, n, a, lda)
+	checkMatrix(p, n, b, ldb)
+
+	wantu := jobU == lapack.GSVDU
+	if !wantu && jobU != lapack.GSVDNone {
+		panic(badGSVDJob + "U")
+	}
+	if jobU != lapack.GSVDNone {
+		checkMatrix(m, m, u, ldu)
+	}
+
+	wantv := jobV == lapack.GSVDV
+	if !wantv && jobV != lapack.GSVDNone {
+		panic(badGSVDJob + "V")
+	}
+	if jobV != lapack.GSVDNone {
+		checkMatrix(p, p, v, ldv)
+	}
+
+	wantq := jobQ == lapack.GSVDQ
+	if !wantq && jobQ != lapack.GSVDNone {
+		panic(badGSVDJob + "Q")
+	}
+	if jobQ != lapack.GSVDNone {
+		checkMatrix(n, n, q, ldq)
+	}
+
+	if len(iwork) != n {
+		panic(badWork)
+	}
+	if lwork != -1 && lwork < 1 {
+		panic(badWork)
+	}
+	if len(work) < max(1, lwork) {
+		panic(badWork)
+	}
+
+	var lwkopt int
+	impl.Dgeqp3(p, n, b, ldb, iwork, tau, work, -1)
+	lwkopt = int(work[0])
+	if wantv {
+		lwkopt = max(lwkopt, p)
+	}
+	lwkopt = max(lwkopt, min(n, p))
+	lwkopt = max(lwkopt, m)
+	if wantq {
+		lwkopt = max(lwkopt, n)
+	}
+	impl.Dgeqp3(m, n, a, lda, iwork, tau, work, -1)
+	lwkopt = max(lwkopt, int(work[0]))
+	lwkopt = max(1, lwkopt)
+	if lwork == -1 {
+		work[0] = float64(lwkopt)
+		return 0, 0
+	}
+
+	// tau check must come after lwkopt query since
+	// the Dggsvd3 call for lwkopt query may have
+	// lwork == -1, and tau is provided by work.
+	if len(tau) < n {
+		panic(badTau)
+	}
+
+	// QR with column pivoting of B: B*P = V*[ S11 S12 ].
+	//                                       [  0   0  ]
+	for i := range iwork[:n] {
+		iwork[i] = 0
+	}
+	impl.Dgeqp3(p, n, b, ldb, iwork, tau, work, lwork)
+
+	// Update A := A*P.
+	impl.Dlapmt(forward, m, n, a, lda, iwork)
+
+	// Determine the effective rank of matrix B.
+	for i := 0; i < min(p, n); i++ {
+		if math.Abs(b[i*ldb+i]) > tolb {
+			l++
+		}
+	}
+
+	if wantv {
+		// Copy the details of V, and form V.
+		impl.Dlaset(blas.All, p, p, 0, 0, v, ldv)
+		if p > 1 {
+			impl.Dlacpy(blas.Lower, p-1, min(p, n), b[ldb:], ldb, v[ldv:], ldv)
+		}
+		impl.Dorg2r(p, p, min(p, n), v, ldv, tau, work)
+	}
+
+	// Clean up B.
+	for i := 1; i < l; i++ {
+		r := b[i*ldb : i*ldb+i]
+		for j := range r {
+			r[j] = 0
+		}
+	}
+	if p > l {
+		impl.Dlaset(blas.All, p-l, n, 0, 0, b[l*ldb:], ldb)
+	}
+
+	if wantq {
+		// Set Q = I and update Q := Q*P.
+		impl.Dlaset(blas.All, n, n, 0, 1, q, ldq)
+		impl.Dlapmt(forward, n, n, q, ldq, iwork)
+	}
+
+	if p >= l && n != l {
+		// RQ factorization of [ S11 S12 ]: [ S11 S12 ] = [ 0 S12 ]*Z.
+		impl.Dgerq2(l, n, b, ldb, tau, work)
+
+		// Update A := A*Z^T.
+		impl.Dormr2(blas.Right, blas.Trans, m, n, l, b, ldb, tau, a, lda, work)
+
+		if wantq {
+			// Update Q := Q*Z^T.
+			impl.Dormr2(blas.Right, blas.Trans, n, n, l, b, ldb, tau, q, ldq, work)
+		}
+
+		// Clean up B.
+		impl.Dlaset(blas.All, l, n-l, 0, 0, b, ldb)
+		for i := 1; i < l; i++ {
+			r := b[i*ldb+n-l : i*ldb+i+n-l]
+			for j := range r {
+				r[j] = 0
+			}
+		}
+	}
+
+	// Let              N-L     L
+	//            A = [ A11    A12 ] M,
+	//
+	// then the following does the complete QR decomposition of A11:
+	//
+	//          A11 = U*[  0  T12 ]*P1^T.
+	//                  [  0   0  ]
+	for i := range iwork[:n-l] {
+		iwork[i] = 0
+	}
+	impl.Dgeqp3(m, n-l, a, lda, iwork[:n-l], tau, work, lwork)
+
+	// Determine the effective rank of A11.
+	for i := 0; i < min(m, n-l); i++ {
+		if math.Abs(a[i*lda+i]) > tola {
+			k++
+		}
+	}
+
+	// Update A12 := U^T*A12, where A12 = A[0:m, n-l:n].
+	impl.Dorm2r(blas.Left, blas.Trans, m, l, min(m, n-l), a, lda, tau, a[n-l:], lda, work)
+
+	if wantu {
+		// Copy the details of U, and form U.
+		impl.Dlaset(blas.All, m, m, 0, 0, u, ldu)
+		if m > 1 {
+			impl.Dlacpy(blas.Lower, m-1, min(m, n-l), a[lda:], lda, u[ldu:], ldu)
+		}
+		impl.Dorg2r(m, m, min(m, n-l), u, ldu, tau, work)
+	}
+
+	if wantq {
+		// Update Q[0:n, 0:n-l] := Q[0:n, 0:n-l]*P1.
+		impl.Dlapmt(forward, n, n-l, q, ldq, iwork[:n-l])
+	}
+
+	// Clean up A: set the strictly lower triangular part of
+	// A[0:k, 0:k] = 0, and A[k:m, 0:n-l] = 0.
+	for i := 1; i < k; i++ {
+		r := a[i*lda : i*lda+i]
+		for j := range r {
+			r[j] = 0
+		}
+	}
+	if m > k {
+		impl.Dlaset(blas.All, m-k, n-l, 0, 0, a[k*lda:], lda)
+	}
+
+	if n-l > k {
+		// RQ factorization of [ T11 T12 ] = [ 0 T12 ]*Z1.
+		impl.Dgerq2(k, n-l, a, lda, tau, work)
+
+		if wantq {
+			// Update Q[0:n, 0:n-l] := Q[0:n, 0:n-l]*Z1^T.
+			impl.Dorm2r(blas.Right, blas.Trans, n, n-l, k, a, lda, tau, q, ldq, work)
+		}
+
+		// Clean up A.
+		impl.Dlaset(blas.All, k, n-l-k, 0, 0, a, lda)
+		for i := 1; i < k; i++ {
+			r := a[i*lda+n-k-l : i*lda+i+n-k-l]
+			for j := range r {
+				a[j] = 0
+			}
+		}
+	}
+
+	if m > k {
+		// QR factorization of A[k:m, n-l:n].
+		impl.Dgeqr2(m-k, l, a[k*lda+n-l:], lda, tau, work)
+		if wantu {
+			// Update U[:, k:m) := U[:, k:m]*U1.
+			impl.Dorm2r(blas.Right, blas.NoTrans, m, m-k, min(m-k, l), a[k*lda+n-l:], lda, tau, u[k:], ldu, work)
+		}
+
+		// Clean up A.
+		for i := k + 1; i < m; i++ {
+			r := a[i*lda+n-l : i*lda+min(n-l+i-k, n)]
+			for j := range r {
+				r[j] = 0
+			}
+		}
+	}
+
+	work[0] = float64(lwkopt)
+	return k, l
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dhseqr.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dhseqr.go
new file mode 100644
index 00000000..a8c81888
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dhseqr.go
@@ -0,0 +1,257 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dhseqr computes the eigenvalues of an n×n Hessenberg matrix H and,
+// optionally, the matrices T and Z from the Schur decomposition
+//  H = Z T Z^T,
+// where T is an n×n upper quasi-triangular matrix (the Schur form), and Z is
+// the n×n orthogonal matrix of Schur vectors.
+//
+// Optionally Z may be postmultiplied into an input orthogonal matrix Q so that
+// this routine can give the Schur factorization of a matrix A which has been
+// reduced to the Hessenberg form H by the orthogonal matrix Q:
+//  A = Q H Q^T = (QZ) T (QZ)^T.
+//
+// If job == lapack.EigenvaluesOnly, only the eigenvalues will be computed.
+// If job == lapack.EigenvaluesAndSchur, the eigenvalues and the Schur form T will
+// be computed.
+// For other values of job Dhseqr will panic.
+//
+// If compz == lapack.None, no Schur vectors will be computed and Z will not be
+// referenced.
+// If compz == lapack.HessEV, on return Z will contain the matrix of Schur
+// vectors of H.
+// If compz == lapack.OriginalEV, on entry z is assumed to contain the orthogonal
+// matrix Q that is the identity except for the submatrix
+// Q[ilo:ihi+1,ilo:ihi+1]. On return z will be updated to the product Q*Z.
+//
+// ilo and ihi determine the block of H on which Dhseqr operates. It is assumed
+// that H is already upper triangular in rows and columns [0:ilo] and [ihi+1:n],
+// although it will be only checked that the block is isolated, that is,
+//  ilo == 0   or H[ilo,ilo-1] == 0,
+//  ihi == n-1 or H[ihi+1,ihi] == 0,
+// and Dhseqr will panic otherwise. ilo and ihi are typically set by a previous
+// call to Dgebal, otherwise they should be set to 0 and n-1, respectively. It
+// must hold that
+//  0 <= ilo <= ihi < n,     if n > 0,
+//  ilo == 0 and ihi == -1,  if n == 0.
+//
+// wr and wi must have length n.
+//
+// work must have length at least lwork and lwork must be at least max(1,n)
+// otherwise Dhseqr will panic. The minimum lwork delivers very good and
+// sometimes optimal performance, although lwork as large as 11*n may be
+// required. On return, work[0] will contain the optimal value of lwork.
+//
+// If lwork is -1, instead of performing Dhseqr, the function only estimates the
+// optimal workspace size and stores it into work[0]. Neither h nor z are
+// accessed.
+//
+// unconverged indicates whether Dhseqr computed all the eigenvalues.
+//
+// If unconverged == 0, all the eigenvalues have been computed and their real
+// and imaginary parts will be stored on return in wr and wi, respectively. If
+// two eigenvalues are computed as a complex conjugate pair, they are stored in
+// consecutive elements of wr and wi, say the i-th and (i+1)th, with wi[i] > 0
+// and wi[i+1] < 0.
+//
+// If unconverged == 0 and job == lapack.EigenvaluesAndSchur, on return H will
+// contain the upper quasi-triangular matrix T from the Schur decomposition (the
+// Schur form). 2×2 diagonal blocks (corresponding to complex conjugate pairs of
+// eigenvalues) will be returned in standard form, with
+//  H[i,i] == H[i+1,i+1],
+// and
+//  H[i+1,i]*H[i,i+1] < 0.
+// The eigenvalues will be stored in wr and wi in the same order as on the
+// diagonal of the Schur form returned in H, with
+//  wr[i] = H[i,i],
+// and, if H[i:i+2,i:i+2] is a 2×2 diagonal block,
+//  wi[i]   = sqrt(-H[i+1,i]*H[i,i+1]),
+//  wi[i+1] = -wi[i].
+//
+// If unconverged == 0 and job == lapack.EigenvaluesOnly, the contents of h
+// on return is unspecified.
+//
+// If unconverged > 0, some eigenvalues have not converged, and the blocks
+// [0:ilo] and [unconverged:n] of wr and wi will contain those eigenvalues which
+// have been successfully computed. Failures are rare.
+//
+// If unconverged > 0 and job == lapack.EigenvaluesOnly, on return the
+// remaining unconverged eigenvalues are the eigenvalues of the upper Hessenberg
+// matrix H[ilo:unconverged,ilo:unconverged].
+//
+// If unconverged > 0 and job == lapack.EigenvaluesAndSchur, then on
+// return
+//  (initial H) U = U (final H),   (*)
+// where U is an orthogonal matrix. The final H is upper Hessenberg and
+// H[unconverged:ihi+1,unconverged:ihi+1] is upper quasi-triangular.
+//
+// If unconverged > 0 and compz == lapack.OriginalEV, then on return
+//  (final Z) = (initial Z) U,
+// where U is the orthogonal matrix in (*) regardless of the value of job.
+//
+// If unconverged > 0 and compz == lapack.HessEV, then on return
+//  (final Z) = U,
+// where U is the orthogonal matrix in (*) regardless of the value of job.
+//
+// References:
+//  [1] R. Byers. LAPACK 3.1 xHSEQR: Tuning and Implementation Notes on the
+//      Small Bulge Multi-Shift QR Algorithm with Aggressive Early Deflation.
+//      LAPACK Working Note 187 (2007)
+//      URL: http://www.netlib.org/lapack/lawnspdf/lawn187.pdf
+//  [2] K. Braman, R. Byers, R. Mathias. The Multishift QR Algorithm. Part I:
+//      Maintaining Well-Focused Shifts and Level 3 Performance. SIAM J. Matrix
+//      Anal. Appl. 23(4) (2002), pp. 929—947
+//      URL: http://dx.doi.org/10.1137/S0895479801384573
+//  [3] K. Braman, R. Byers, R. Mathias. The Multishift QR Algorithm. Part II:
+//      Aggressive Early Deflation. SIAM J. Matrix Anal. Appl. 23(4) (2002), pp. 948—973
+//      URL: http://dx.doi.org/10.1137/S0895479801384585
+//
+// Dhseqr is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dhseqr(job lapack.EVJob, compz lapack.EVComp, n, ilo, ihi int, h []float64, ldh int, wr, wi []float64, z []float64, ldz int, work []float64, lwork int) (unconverged int) {
+	var wantt bool
+	switch job {
+	default:
+		panic(badEVJob)
+	case lapack.EigenvaluesOnly:
+	case lapack.EigenvaluesAndSchur:
+		wantt = true
+	}
+	var wantz bool
+	switch compz {
+	default:
+		panic(badEVComp)
+	case lapack.None:
+	case lapack.HessEV, lapack.OriginalEV:
+		wantz = true
+	}
+	switch {
+	case n < 0:
+		panic(nLT0)
+	case ilo < 0 || max(0, n-1) < ilo:
+		panic(badIlo)
+	case ihi < min(ilo, n-1) || n <= ihi:
+		panic(badIhi)
+	case len(work) < lwork:
+		panic(shortWork)
+	case lwork < max(1, n) && lwork != -1:
+		panic(badWork)
+	}
+	if lwork != -1 {
+		checkMatrix(n, n, h, ldh)
+		switch {
+		case wantz:
+			checkMatrix(n, n, z, ldz)
+		case len(wr) < n:
+			panic("lapack: wr has insufficient length")
+		case len(wi) < n:
+			panic("lapack: wi has insufficient length")
+		}
+	}
+
+	const (
+		// Matrices of order ntiny or smaller must be processed by
+		// Dlahqr because of insufficient subdiagonal scratch space.
+		// This is a hard limit.
+		ntiny = 11
+
+		// nl is the size of a local workspace to help small matrices
+		// through a rare Dlahqr failure. nl > ntiny is required and
+		// nl <= nmin = Ilaenv(ispec=12,...) is recommended (the default
+		// value of nmin is 75). Using nl = 49 allows up to six
+		// simultaneous shifts and a 16×16 deflation window.
+		nl = 49
+	)
+
+	// Quick return if possible.
+	if n == 0 {
+		work[0] = 1
+		return 0
+	}
+
+	// Quick return in case of a workspace query.
+	if lwork == -1 {
+		impl.Dlaqr04(wantt, wantz, n, ilo, ihi, nil, 0, nil, nil, ilo, ihi, nil, 0, work, -1, 1)
+		work[0] = math.Max(float64(n), work[0])
+		return 0
+	}
+
+	// Copy eigenvalues isolated by Dgebal.
+	for i := 0; i < ilo; i++ {
+		wr[i] = h[i*ldh+i]
+		wi[i] = 0
+	}
+	for i := ihi + 1; i < n; i++ {
+		wr[i] = h[i*ldh+i]
+		wi[i] = 0
+	}
+
+	// Initialize Z to identity matrix if requested.
+	if compz == lapack.HessEV {
+		impl.Dlaset(blas.All, n, n, 0, 1, z, ldz)
+	}
+
+	// Quick return if possible.
+	if ilo == ihi {
+		wr[ilo] = h[ilo*ldh+ilo]
+		wi[ilo] = 0
+		return 0
+	}
+
+	// Dlahqr/Dlaqr04 crossover point.
+	nmin := impl.Ilaenv(12, "DHSEQR", string(job)+string(compz), n, ilo, ihi, lwork)
+	nmin = max(ntiny, nmin)
+
+	if n > nmin {
+		// Dlaqr0 for big matrices.
+		unconverged = impl.Dlaqr04(wantt, wantz, n, ilo, ihi, h, ldh, wr[:ihi+1], wi[:ihi+1],
+			ilo, ihi, z, ldz, work, lwork, 1)
+	} else {
+		// Dlahqr for small matrices.
+		unconverged = impl.Dlahqr(wantt, wantz, n, ilo, ihi, h, ldh, wr[:ihi+1], wi[:ihi+1],
+			ilo, ihi, z, ldz)
+		if unconverged > 0 {
+			// A rare Dlahqr failure! Dlaqr04 sometimes succeeds
+			// when Dlahqr fails.
+			kbot := unconverged
+			if n >= nl {
+				// Larger matrices have enough subdiagonal
+				// scratch space to call Dlaqr04 directly.
+				unconverged = impl.Dlaqr04(wantt, wantz, n, ilo, kbot, h, ldh,
+					wr[:ihi+1], wi[:ihi+1], ilo, ihi, z, ldz, work, lwork, 1)
+			} else {
+				// Tiny matrices don't have enough subdiagonal
+				// scratch space to benefit from Dlaqr04. Hence,
+				// tiny matrices must be copied into a larger
+				// array before calling Dlaqr04.
+				var hl [nl * nl]float64
+				impl.Dlacpy(blas.All, n, n, h, ldh, hl[:], nl)
+				impl.Dlaset(blas.All, nl, nl-n, 0, 0, hl[n:], nl)
+				var workl [nl]float64
+				unconverged = impl.Dlaqr04(wantt, wantz, nl, ilo, kbot, hl[:], nl,
+					wr[:ihi+1], wi[:ihi+1], ilo, ihi, z, ldz, workl[:], nl, 1)
+				work[0] = workl[0]
+				if wantt || unconverged > 0 {
+					impl.Dlacpy(blas.All, n, n, hl[:], nl, h, ldh)
+				}
+			}
+		}
+	}
+	// Zero out under the first subdiagonal, if necessary.
+	if (wantt || unconverged > 0) && n > 2 {
+		impl.Dlaset(blas.Lower, n-2, n-2, 0, 0, h[2*ldh:], ldh)
+	}
+
+	work[0] = math.Max(float64(n), work[0])
+	return unconverged
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlabrd.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlabrd.go
new file mode 100644
index 00000000..abe5dae0
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlabrd.go
@@ -0,0 +1,150 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dlabrd reduces the first NB rows and columns of a real general m×n matrix
+// A to upper or lower bidiagonal form by an orthogonal transformation
+//  Q**T * A * P
+// If m >= n, A is reduced to upper bidiagonal form and upon exit the elements
+// on and below the diagonal in the first nb columns represent the elementary
+// reflectors, and the elements above the diagonal in the first nb rows represent
+// the matrix P. If m < n, A is reduced to lower bidiagonal form and the elements
+// P is instead stored above the diagonal.
+//
+// The reduction to bidiagonal form is stored in d and e, where d are the diagonal
+// elements, and e are the off-diagonal elements.
+//
+// The matrices Q and P are products of elementary reflectors
+//  Q = H_0 * H_1 * ... * H_{nb-1}
+//  P = G_0 * G_1 * ... * G_{nb-1}
+// where
+//  H_i = I - tauQ[i] * v_i * v_i^T
+//  G_i = I - tauP[i] * u_i * u_i^T
+//
+// As an example, on exit the entries of A when m = 6, n = 5, and nb = 2
+//  [ 1   1  u1  u1  u1]
+//  [v1   1   1  u2  u2]
+//  [v1  v2   a   a   a]
+//  [v1  v2   a   a   a]
+//  [v1  v2   a   a   a]
+//  [v1  v2   a   a   a]
+// and when m = 5, n = 6, and nb = 2
+//  [ 1  u1  u1  u1  u1  u1]
+//  [ 1   1  u2  u2  u2  u2]
+//  [v1   1   a   a   a   a]
+//  [v1  v2   a   a   a   a]
+//  [v1  v2   a   a   a   a]
+//
+// Dlabrd also returns the matrices X and Y which are used with U and V to
+// apply the transformation to the unreduced part of the matrix
+//  A := A - V*Y^T - X*U^T
+// and returns the matrices X and Y which are needed to apply the
+// transformation to the unreduced part of A.
+//
+// X is an m×nb matrix, Y is an n×nb matrix. d, e, taup, and tauq must all have
+// length at least nb. Dlabrd will panic if these size constraints are violated.
+//
+// Dlabrd is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlabrd(m, n, nb int, a []float64, lda int, d, e, tauQ, tauP, x []float64, ldx int, y []float64, ldy int) {
+	checkMatrix(m, n, a, lda)
+	checkMatrix(m, nb, x, ldx)
+	checkMatrix(n, nb, y, ldy)
+	if len(d) < nb {
+		panic(badD)
+	}
+	if len(e) < nb {
+		panic(badE)
+	}
+	if len(tauQ) < nb {
+		panic(badTauQ)
+	}
+	if len(tauP) < nb {
+		panic(badTauP)
+	}
+	if m <= 0 || n <= 0 {
+		return
+	}
+	bi := blas64.Implementation()
+	if m >= n {
+		// Reduce to upper bidiagonal form.
+		for i := 0; i < nb; i++ {
+			bi.Dgemv(blas.NoTrans, m-i, i, -1, a[i*lda:], lda, y[i*ldy:], 1, 1, a[i*lda+i:], lda)
+			bi.Dgemv(blas.NoTrans, m-i, i, -1, x[i*ldx:], ldx, a[i:], lda, 1, a[i*lda+i:], lda)
+
+			a[i*lda+i], tauQ[i] = impl.Dlarfg(m-i, a[i*lda+i], a[min(i+1, m-1)*lda+i:], lda)
+			d[i] = a[i*lda+i]
+			if i < n-1 {
+				// Compute Y[i+1:n, i].
+				a[i*lda+i] = 1
+				bi.Dgemv(blas.Trans, m-i, n-i-1, 1, a[i*lda+i+1:], lda, a[i*lda+i:], lda, 0, y[(i+1)*ldy+i:], ldy)
+				bi.Dgemv(blas.Trans, m-i, i, 1, a[i*lda:], lda, a[i*lda+i:], lda, 0, y[i:], ldy)
+				bi.Dgemv(blas.NoTrans, n-i-1, i, -1, y[(i+1)*ldy:], ldy, y[i:], ldy, 1, y[(i+1)*ldy+i:], ldy)
+				bi.Dgemv(blas.Trans, m-i, i, 1, x[i*ldx:], ldx, a[i*lda+i:], lda, 0, y[i:], ldy)
+				bi.Dgemv(blas.Trans, i, n-i-1, -1, a[i+1:], lda, y[i:], ldy, 1, y[(i+1)*ldy+i:], ldy)
+				bi.Dscal(n-i-1, tauQ[i], y[(i+1)*ldy+i:], ldy)
+
+				// Update A[i, i+1:n].
+				bi.Dgemv(blas.NoTrans, n-i-1, i+1, -1, y[(i+1)*ldy:], ldy, a[i*lda:], 1, 1, a[i*lda+i+1:], 1)
+				bi.Dgemv(blas.Trans, i, n-i-1, -1, a[i+1:], lda, x[i*ldx:], 1, 1, a[i*lda+i+1:], 1)
+
+				// Generate reflection P[i] to annihilate A[i, i+2:n].
+				a[i*lda+i+1], tauP[i] = impl.Dlarfg(n-i-1, a[i*lda+i+1], a[i*lda+min(i+2, n-1):], 1)
+				e[i] = a[i*lda+i+1]
+				a[i*lda+i+1] = 1
+
+				// Compute X[i+1:m, i].
+				bi.Dgemv(blas.NoTrans, m-i-1, n-i-1, 1, a[(i+1)*lda+i+1:], lda, a[i*lda+i+1:], 1, 0, x[(i+1)*ldx+i:], ldx)
+				bi.Dgemv(blas.Trans, n-i-1, i+1, 1, y[(i+1)*ldy:], ldy, a[i*lda+i+1:], 1, 0, x[i:], ldx)
+				bi.Dgemv(blas.NoTrans, m-i-1, i+1, -1, a[(i+1)*lda:], lda, x[i:], ldx, 1, x[(i+1)*ldx+i:], ldx)
+				bi.Dgemv(blas.NoTrans, i, n-i-1, 1, a[i+1:], lda, a[i*lda+i+1:], 1, 0, x[i:], ldx)
+				bi.Dgemv(blas.NoTrans, m-i-1, i, -1, x[(i+1)*ldx:], ldx, x[i:], ldx, 1, x[(i+1)*ldx+i:], ldx)
+				bi.Dscal(m-i-1, tauP[i], x[(i+1)*ldx+i:], ldx)
+			}
+		}
+		return
+	}
+	// Reduce to lower bidiagonal form.
+	for i := 0; i < nb; i++ {
+		// Update A[i,i:n]
+		bi.Dgemv(blas.NoTrans, n-i, i, -1, y[i*ldy:], ldy, a[i*lda:], 1, 1, a[i*lda+i:], 1)
+		bi.Dgemv(blas.Trans, i, n-i, -1, a[i:], lda, x[i*ldx:], 1, 1, a[i*lda+i:], 1)
+
+		// Generate reflection P[i] to annihilate A[i, i+1:n]
+		a[i*lda+i], tauP[i] = impl.Dlarfg(n-i, a[i*lda+i], a[i*lda+min(i+1, n-1):], 1)
+		d[i] = a[i*lda+i]
+		if i < m-1 {
+			a[i*lda+i] = 1
+			// Compute X[i+1:m, i].
+			bi.Dgemv(blas.NoTrans, m-i-1, n-i, 1, a[(i+1)*lda+i:], lda, a[i*lda+i:], 1, 0, x[(i+1)*ldx+i:], ldx)
+			bi.Dgemv(blas.Trans, n-i, i, 1, y[i*ldy:], ldy, a[i*lda+i:], 1, 0, x[i:], ldx)
+			bi.Dgemv(blas.NoTrans, m-i-1, i, -1, a[(i+1)*lda:], lda, x[i:], ldx, 1, x[(i+1)*ldx+i:], ldx)
+			bi.Dgemv(blas.NoTrans, i, n-i, 1, a[i:], lda, a[i*lda+i:], 1, 0, x[i:], ldx)
+			bi.Dgemv(blas.NoTrans, m-i-1, i, -1, x[(i+1)*ldx:], ldx, x[i:], ldx, 1, x[(i+1)*ldx+i:], ldx)
+			bi.Dscal(m-i-1, tauP[i], x[(i+1)*ldx+i:], ldx)
+
+			// Update A[i+1:m, i].
+			bi.Dgemv(blas.NoTrans, m-i-1, i, -1, a[(i+1)*lda:], lda, y[i*ldy:], 1, 1, a[(i+1)*lda+i:], lda)
+			bi.Dgemv(blas.NoTrans, m-i-1, i+1, -1, x[(i+1)*ldx:], ldx, a[i:], lda, 1, a[(i+1)*lda+i:], lda)
+
+			// Generate reflection Q[i] to annihilate A[i+2:m, i].
+			a[(i+1)*lda+i], tauQ[i] = impl.Dlarfg(m-i-1, a[(i+1)*lda+i], a[min(i+2, m-1)*lda+i:], lda)
+			e[i] = a[(i+1)*lda+i]
+			a[(i+1)*lda+i] = 1
+
+			// Compute Y[i+1:n, i].
+			bi.Dgemv(blas.Trans, m-i-1, n-i-1, 1, a[(i+1)*lda+i+1:], lda, a[(i+1)*lda+i:], lda, 0, y[(i+1)*ldy+i:], ldy)
+			bi.Dgemv(blas.Trans, m-i-1, i, 1, a[(i+1)*lda:], lda, a[(i+1)*lda+i:], lda, 0, y[i:], ldy)
+			bi.Dgemv(blas.NoTrans, n-i-1, i, -1, y[(i+1)*ldy:], ldy, y[i:], ldy, 1, y[(i+1)*ldy+i:], ldy)
+			bi.Dgemv(blas.Trans, m-i-1, i+1, 1, x[(i+1)*ldx:], ldx, a[(i+1)*lda+i:], lda, 0, y[i:], ldy)
+			bi.Dgemv(blas.Trans, i+1, n-i-1, -1, a[i+1:], lda, y[i:], ldy, 1, y[(i+1)*ldy+i:], ldy)
+			bi.Dscal(n-i-1, tauQ[i], y[(i+1)*ldy+i:], ldy)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlacn2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlacn2.go
new file mode 100644
index 00000000..0f38ac1d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlacn2.go
@@ -0,0 +1,134 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dlacn2 estimates the 1-norm of an n×n matrix A using sequential updates with
+// matrix-vector products provided externally.
+//
+// Dlacn2 is called sequentially and it returns the value of est and kase to be
+// used on the next call.
+// On the initial call, kase must be 0.
+// In between calls, x must be overwritten by
+//  A * X    if kase was returned as 1,
+//  A^T * X  if kase was returned as 2,
+// and all other parameters must not be changed.
+// On the final return, kase is returned as 0, v contains A*W where W is a
+// vector, and est = norm(V)/norm(W) is a lower bound for 1-norm of A.
+//
+// v, x, and isgn must all have length n and n must be at least 1, otherwise
+// Dlacn2 will panic. isave is used for temporary storage.
+//
+// Dlacn2 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlacn2(n int, v, x []float64, isgn []int, est float64, kase int, isave *[3]int) (float64, int) {
+	if n < 1 {
+		panic("lapack: non-positive n")
+	}
+	checkVector(n, x, 1)
+	checkVector(n, v, 1)
+	if len(isgn) < n {
+		panic("lapack: insufficient isgn length")
+	}
+	if isave[0] < 0 || isave[0] > 5 {
+		panic("lapack: bad isave value")
+	}
+	if isave[0] == 0 && kase != 0 {
+		panic("lapack: bad isave value")
+	}
+	itmax := 5
+	bi := blas64.Implementation()
+	if kase == 0 {
+		for i := 0; i < n; i++ {
+			x[i] = 1 / float64(n)
+		}
+		kase = 1
+		isave[0] = 1
+		return est, kase
+	}
+	switch isave[0] {
+	default:
+		panic("unreachable")
+	case 1:
+		if n == 1 {
+			v[0] = x[0]
+			est = math.Abs(v[0])
+			kase = 0
+			return est, kase
+		}
+		est = bi.Dasum(n, x, 1)
+		for i := 0; i < n; i++ {
+			x[i] = math.Copysign(1, x[i])
+			isgn[i] = int(x[i])
+		}
+		kase = 2
+		isave[0] = 2
+		return est, kase
+	case 2:
+		isave[1] = bi.Idamax(n, x, 1)
+		isave[2] = 2
+		for i := 0; i < n; i++ {
+			x[i] = 0
+		}
+		x[isave[1]] = 1
+		kase = 1
+		isave[0] = 3
+		return est, kase
+	case 3:
+		bi.Dcopy(n, x, 1, v, 1)
+		estold := est
+		est = bi.Dasum(n, v, 1)
+		sameSigns := true
+		for i := 0; i < n; i++ {
+			if int(math.Copysign(1, x[i])) != isgn[i] {
+				sameSigns = false
+				break
+			}
+		}
+		if !sameSigns && est > estold {
+			for i := 0; i < n; i++ {
+				x[i] = math.Copysign(1, x[i])
+				isgn[i] = int(x[i])
+			}
+			kase = 2
+			isave[0] = 4
+			return est, kase
+		}
+	case 4:
+		jlast := isave[1]
+		isave[1] = bi.Idamax(n, x, 1)
+		if x[jlast] != math.Abs(x[isave[1]]) && isave[2] < itmax {
+			isave[2] += 1
+			for i := 0; i < n; i++ {
+				x[i] = 0
+			}
+			x[isave[1]] = 1
+			kase = 1
+			isave[0] = 3
+			return est, kase
+		}
+	case 5:
+		tmp := 2 * (bi.Dasum(n, x, 1)) / float64(3*n)
+		if tmp > est {
+			bi.Dcopy(n, x, 1, v, 1)
+			est = tmp
+		}
+		kase = 0
+		return est, kase
+	}
+	// Iteration complete. Final stage
+	altsgn := 1.0
+	for i := 0; i < n; i++ {
+		x[i] = altsgn * (1 + float64(i)/float64(n-1))
+		altsgn *= -1
+	}
+	kase = 1
+	isave[0] = 5
+	return est, kase
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlacpy.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlacpy.go
new file mode 100644
index 00000000..f5b90e17
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlacpy.go
@@ -0,0 +1,40 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "gonum.org/v1/gonum/blas"
+
+// Dlacpy copies the elements of A specified by uplo into B. Uplo can specify
+// a triangular portion with blas.Upper or blas.Lower, or can specify all of the
+// elemest with blas.All.
+//
+// Dlacpy is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlacpy(uplo blas.Uplo, m, n int, a []float64, lda int, b []float64, ldb int) {
+	checkMatrix(m, n, a, lda)
+	checkMatrix(m, n, b, ldb)
+	switch uplo {
+	default:
+		panic(badUplo)
+	case blas.Upper:
+		for i := 0; i < m; i++ {
+			for j := i; j < n; j++ {
+				b[i*ldb+j] = a[i*lda+j]
+			}
+		}
+
+	case blas.Lower:
+		for i := 0; i < m; i++ {
+			for j := 0; j < min(i+1, n); j++ {
+				b[i*ldb+j] = a[i*lda+j]
+			}
+		}
+	case blas.All:
+		for i := 0; i < m; i++ {
+			for j := 0; j < n; j++ {
+				b[i*ldb+j] = a[i*lda+j]
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlae2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlae2.go
new file mode 100644
index 00000000..17f356e8
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlae2.go
@@ -0,0 +1,49 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "math"
+
+// Dlae2 computes the eigenvalues of a 2×2 symmetric matrix
+//  [a b]
+//  [b c]
+// and returns the eigenvalue with the larger absolute value as rt1 and the
+// smaller as rt2.
+//
+// Dlae2 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlae2(a, b, c float64) (rt1, rt2 float64) {
+	sm := a + c
+	df := a - c
+	adf := math.Abs(df)
+	tb := b + b
+	ab := math.Abs(tb)
+	acmx := c
+	acmn := a
+	if math.Abs(a) > math.Abs(c) {
+		acmx = a
+		acmn = c
+	}
+	var rt float64
+	if adf > ab {
+		rt = adf * math.Sqrt(1+(ab/adf)*(ab/adf))
+	} else if adf < ab {
+		rt = ab * math.Sqrt(1+(adf/ab)*(adf/ab))
+	} else {
+		rt = ab * math.Sqrt2
+	}
+	if sm < 0 {
+		rt1 = 0.5 * (sm - rt)
+		rt2 = (acmx/rt1)*acmn - (b/rt1)*b
+		return rt1, rt2
+	}
+	if sm > 0 {
+		rt1 = 0.5 * (sm + rt)
+		rt2 = (acmx/rt1)*acmn - (b/rt1)*b
+		return rt1, rt2
+	}
+	rt1 = 0.5 * rt
+	rt2 = -0.5 * rt
+	return rt1, rt2
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlaev2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlaev2.go
new file mode 100644
index 00000000..50fd7d0b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlaev2.go
@@ -0,0 +1,82 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "math"
+
+// Dlaev2 computes the Eigen decomposition of a symmetric 2×2 matrix.
+// The matrix is given by
+//  [a b]
+//  [b c]
+// Dlaev2 returns rt1 and rt2, the eigenvalues of the matrix where |RT1| > |RT2|,
+// and [cs1, sn1] which is the unit right eigenvalue for RT1.
+//  [ cs1 sn1] [a b] [cs1 -sn1] = [rt1   0]
+//  [-sn1 cs1] [b c] [sn1  cs1]   [  0 rt2]
+//
+// Dlaev2 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlaev2(a, b, c float64) (rt1, rt2, cs1, sn1 float64) {
+	sm := a + c
+	df := a - c
+	adf := math.Abs(df)
+	tb := b + b
+	ab := math.Abs(tb)
+	acmx := c
+	acmn := a
+	if math.Abs(a) > math.Abs(c) {
+		acmx = a
+		acmn = c
+	}
+	var rt float64
+	if adf > ab {
+		rt = adf * math.Sqrt(1+(ab/adf)*(ab/adf))
+	} else if adf < ab {
+		rt = ab * math.Sqrt(1+(adf/ab)*(adf/ab))
+	} else {
+		rt = ab * math.Sqrt(2)
+	}
+	var sgn1 float64
+	if sm < 0 {
+		rt1 = 0.5 * (sm - rt)
+		sgn1 = -1
+		rt2 = (acmx/rt1)*acmn - (b/rt1)*b
+	} else if sm > 0 {
+		rt1 = 0.5 * (sm + rt)
+		sgn1 = 1
+		rt2 = (acmx/rt1)*acmn - (b/rt1)*b
+	} else {
+		rt1 = 0.5 * rt
+		rt2 = -0.5 * rt
+		sgn1 = 1
+	}
+	var cs, sgn2 float64
+	if df >= 0 {
+		cs = df + rt
+		sgn2 = 1
+	} else {
+		cs = df - rt
+		sgn2 = -1
+	}
+	acs := math.Abs(cs)
+	if acs > ab {
+		ct := -tb / cs
+		sn1 = 1 / math.Sqrt(1+ct*ct)
+		cs1 = ct * sn1
+	} else {
+		if ab == 0 {
+			cs1 = 1
+			sn1 = 0
+		} else {
+			tn := -cs / tb
+			cs1 = 1 / math.Sqrt(1+tn*tn)
+			sn1 = tn * cs1
+		}
+	}
+	if sgn1 == sgn2 {
+		tn := cs1
+		cs1 = -sn1
+		sn1 = tn
+	}
+	return rt1, rt2, cs1, sn1
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlaexc.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlaexc.go
new file mode 100644
index 00000000..470b63a4
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlaexc.go
@@ -0,0 +1,261 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dlaexc swaps two adjacent diagonal blocks of order 1 or 2 in an n×n upper
+// quasi-triangular matrix T by an orthogonal similarity transformation.
+//
+// T must be in Schur canonical form, that is, block upper triangular with 1×1
+// and 2×2 diagonal blocks; each 2×2 diagonal block has its diagonal elements
+// equal and its off-diagonal elements of opposite sign. On return, T will
+// contain the updated matrix again in Schur canonical form.
+//
+// If wantq is true, the transformation is accumulated in the n×n matrix Q,
+// otherwise Q is not referenced.
+//
+// j1 is the index of the first row of the first block. n1 and n2 are the order
+// of the first and second block, respectively.
+//
+// work must have length at least n, otherwise Dlaexc will panic.
+//
+// If ok is false, the transformed matrix T would be too far from Schur form.
+// The blocks are not swapped, and T and Q are not modified.
+//
+// If n1 and n2 are both equal to 1, Dlaexc will always return true.
+//
+// Dlaexc is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlaexc(wantq bool, n int, t []float64, ldt int, q []float64, ldq int, j1, n1, n2 int, work []float64) (ok bool) {
+	checkMatrix(n, n, t, ldt)
+	if wantq {
+		checkMatrix(n, n, q, ldq)
+	}
+	if j1 < 0 || n <= j1 {
+		panic("lapack: index j1 out of range")
+	}
+	if len(work) < n {
+		panic(badWork)
+	}
+	if n1 < 0 || 2 < n1 {
+		panic("lapack: invalid value of n1")
+	}
+	if n2 < 0 || 2 < n2 {
+		panic("lapack: invalid value of n2")
+	}
+
+	if n == 0 || n1 == 0 || n2 == 0 {
+		return true
+	}
+	if j1+n1 >= n {
+		// TODO(vladimir-ch): Reference LAPACK does this check whether
+		// the start of the second block is in the matrix T. It returns
+		// true if it is not and moreover it does not check whether the
+		// whole second block fits into T. This does not feel
+		// satisfactory. The only caller of Dlaexc is Dtrexc, so if the
+		// caller makes sure that this does not happen, we could be
+		// stricter here.
+		return true
+	}
+
+	j2 := j1 + 1
+	j3 := j1 + 2
+
+	bi := blas64.Implementation()
+
+	if n1 == 1 && n2 == 1 {
+		// Swap two 1×1 blocks.
+		t11 := t[j1*ldt+j1]
+		t22 := t[j2*ldt+j2]
+
+		// Determine the transformation to perform the interchange.
+		cs, sn, _ := impl.Dlartg(t[j1*ldt+j2], t22-t11)
+
+		// Apply transformation to the matrix T.
+		if n-j3 > 0 {
+			bi.Drot(n-j3, t[j1*ldt+j3:], 1, t[j2*ldt+j3:], 1, cs, sn)
+		}
+		if j1 > 0 {
+			bi.Drot(j1, t[j1:], ldt, t[j2:], ldt, cs, sn)
+		}
+
+		t[j1*ldt+j1] = t22
+		t[j2*ldt+j2] = t11
+
+		if wantq {
+			// Accumulate transformation in the matrix Q.
+			bi.Drot(n, q[j1:], ldq, q[j2:], ldq, cs, sn)
+		}
+
+		return true
+	}
+
+	// Swapping involves at least one 2×2 block.
+	//
+	// Copy the diagonal block of order n1+n2 to the local array d and
+	// compute its norm.
+	nd := n1 + n2
+	var d [16]float64
+	const ldd = 4
+	impl.Dlacpy(blas.All, nd, nd, t[j1*ldt+j1:], ldt, d[:], ldd)
+	dnorm := impl.Dlange(lapack.MaxAbs, nd, nd, d[:], ldd, work)
+
+	// Compute machine-dependent threshold for test for accepting swap.
+	eps := dlamchP
+	thresh := math.Max(10*eps*dnorm, dlamchS/eps)
+
+	// Solve T11*X - X*T22 = scale*T12 for X.
+	var x [4]float64
+	const ldx = 2
+	scale, _, _ := impl.Dlasy2(false, false, -1, n1, n2, d[:], ldd, d[n1*ldd+n1:], ldd, d[n1:], ldd, x[:], ldx)
+
+	// Swap the adjacent diagonal blocks.
+	switch {
+	case n1 == 1 && n2 == 2:
+		// Generate elementary reflector H so that
+		//  ( scale, X11, X12 ) H = ( 0, 0, * )
+		u := [3]float64{scale, x[0], 1}
+		_, tau := impl.Dlarfg(3, x[1], u[:2], 1)
+		t11 := t[j1*ldt+j1]
+
+		// Perform swap provisionally on diagonal block in d.
+		impl.Dlarfx(blas.Left, 3, 3, u[:], tau, d[:], ldd, work)
+		impl.Dlarfx(blas.Right, 3, 3, u[:], tau, d[:], ldd, work)
+
+		// Test whether to reject swap.
+		if math.Max(math.Abs(d[2*ldd]), math.Max(math.Abs(d[2*ldd+1]), math.Abs(d[2*ldd+2]-t11))) > thresh {
+			return false
+		}
+
+		// Accept swap: apply transformation to the entire matrix T.
+		impl.Dlarfx(blas.Left, 3, n-j1, u[:], tau, t[j1*ldt+j1:], ldt, work)
+		impl.Dlarfx(blas.Right, j2+1, 3, u[:], tau, t[j1:], ldt, work)
+
+		t[j3*ldt+j1] = 0
+		t[j3*ldt+j2] = 0
+		t[j3*ldt+j3] = t11
+
+		if wantq {
+			// Accumulate transformation in the matrix Q.
+			impl.Dlarfx(blas.Right, n, 3, u[:], tau, q[j1:], ldq, work)
+		}
+
+	case n1 == 2 && n2 == 1:
+		//  Generate elementary reflector H so that:
+		//   H (  -X11 ) = ( * )
+		//     (  -X21 ) = ( 0 )
+		//     ( scale ) = ( 0 )
+		u := [3]float64{1, -x[ldx], scale}
+		_, tau := impl.Dlarfg(3, -x[0], u[1:], 1)
+		t33 := t[j3*ldt+j3]
+
+		// Perform swap provisionally on diagonal block in D.
+		impl.Dlarfx(blas.Left, 3, 3, u[:], tau, d[:], ldd, work)
+		impl.Dlarfx(blas.Right, 3, 3, u[:], tau, d[:], ldd, work)
+
+		// Test whether to reject swap.
+		if math.Max(math.Abs(d[ldd]), math.Max(math.Abs(d[2*ldd]), math.Abs(d[0]-t33))) > thresh {
+			return false
+		}
+
+		// Accept swap: apply transformation to the entire matrix T.
+		impl.Dlarfx(blas.Right, j3+1, 3, u[:], tau, t[j1:], ldt, work)
+		impl.Dlarfx(blas.Left, 3, n-j1-1, u[:], tau, t[j1*ldt+j2:], ldt, work)
+
+		t[j1*ldt+j1] = t33
+		t[j2*ldt+j1] = 0
+		t[j3*ldt+j1] = 0
+
+		if wantq {
+			// Accumulate transformation in the matrix Q.
+			impl.Dlarfx(blas.Right, n, 3, u[:], tau, q[j1:], ldq, work)
+		}
+
+	default: // n1 == 2 && n2 == 2
+		// Generate elementary reflectors H_1 and H_2 so that:
+		//  H_2 H_1 (  -X11  -X12 ) = (  *  * )
+		//          (  -X21  -X22 )   (  0  * )
+		//          ( scale    0  )   (  0  0 )
+		//          (    0  scale )   (  0  0 )
+		u1 := [3]float64{1, -x[ldx], scale}
+		_, tau1 := impl.Dlarfg(3, -x[0], u1[1:], 1)
+
+		temp := -tau1 * (x[1] + u1[1]*x[ldx+1])
+		u2 := [3]float64{1, -temp * u1[2], scale}
+		_, tau2 := impl.Dlarfg(3, -temp*u1[1]-x[ldx+1], u2[1:], 1)
+
+		// Perform swap provisionally on diagonal block in D.
+		impl.Dlarfx(blas.Left, 3, 4, u1[:], tau1, d[:], ldd, work)
+		impl.Dlarfx(blas.Right, 4, 3, u1[:], tau1, d[:], ldd, work)
+		impl.Dlarfx(blas.Left, 3, 4, u2[:], tau2, d[ldd:], ldd, work)
+		impl.Dlarfx(blas.Right, 4, 3, u2[:], tau2, d[1:], ldd, work)
+
+		// Test whether to reject swap.
+		m1 := math.Max(math.Abs(d[2*ldd]), math.Abs(d[2*ldd+1]))
+		m2 := math.Max(math.Abs(d[3*ldd]), math.Abs(d[3*ldd+1]))
+		if math.Max(m1, m2) > thresh {
+			return false
+		}
+
+		// Accept swap: apply transformation to the entire matrix T.
+		j4 := j1 + 3
+		impl.Dlarfx(blas.Left, 3, n-j1, u1[:], tau1, t[j1*ldt+j1:], ldt, work)
+		impl.Dlarfx(blas.Right, j4+1, 3, u1[:], tau1, t[j1:], ldt, work)
+		impl.Dlarfx(blas.Left, 3, n-j1, u2[:], tau2, t[j2*ldt+j1:], ldt, work)
+		impl.Dlarfx(blas.Right, j4+1, 3, u2[:], tau2, t[j2:], ldt, work)
+
+		t[j3*ldt+j1] = 0
+		t[j3*ldt+j2] = 0
+		t[j4*ldt+j1] = 0
+		t[j4*ldt+j2] = 0
+
+		if wantq {
+			// Accumulate transformation in the matrix Q.
+			impl.Dlarfx(blas.Right, n, 3, u1[:], tau1, q[j1:], ldq, work)
+			impl.Dlarfx(blas.Right, n, 3, u2[:], tau2, q[j2:], ldq, work)
+		}
+	}
+
+	if n2 == 2 {
+		// Standardize new 2×2 block T11.
+		a, b := t[j1*ldt+j1], t[j1*ldt+j2]
+		c, d := t[j2*ldt+j1], t[j2*ldt+j2]
+		var cs, sn float64
+		t[j1*ldt+j1], t[j1*ldt+j2], t[j2*ldt+j1], t[j2*ldt+j2], _, _, _, _, cs, sn = impl.Dlanv2(a, b, c, d)
+		if n-j1-2 > 0 {
+			bi.Drot(n-j1-2, t[j1*ldt+j1+2:], 1, t[j2*ldt+j1+2:], 1, cs, sn)
+		}
+		if j1 > 0 {
+			bi.Drot(j1, t[j1:], ldt, t[j2:], ldt, cs, sn)
+		}
+		if wantq {
+			bi.Drot(n, q[j1:], ldq, q[j2:], ldq, cs, sn)
+		}
+	}
+	if n1 == 2 {
+		// Standardize new 2×2 block T22.
+		j3 := j1 + n2
+		j4 := j3 + 1
+		a, b := t[j3*ldt+j3], t[j3*ldt+j4]
+		c, d := t[j4*ldt+j3], t[j4*ldt+j4]
+		var cs, sn float64
+		t[j3*ldt+j3], t[j3*ldt+j4], t[j4*ldt+j3], t[j4*ldt+j4], _, _, _, _, cs, sn = impl.Dlanv2(a, b, c, d)
+		if n-j3-2 > 0 {
+			bi.Drot(n-j3-2, t[j3*ldt+j3+2:], 1, t[j4*ldt+j3+2:], 1, cs, sn)
+		}
+		bi.Drot(j3, t[j3:], ldt, t[j4:], ldt, cs, sn)
+		if wantq {
+			bi.Drot(n, q[j3:], ldq, q[j4:], ldq, cs, sn)
+		}
+	}
+
+	return true
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlags2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlags2.go
new file mode 100644
index 00000000..3b73384f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlags2.go
@@ -0,0 +1,182 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "math"
+
+// Dlags2 computes 2-by-2 orthogonal matrices U, V and Q with the
+// triangles of A and B specified by upper.
+//
+// If upper is true
+//
+//  U^T*A*Q = U^T*[ a1 a2 ]*Q = [ x  0 ]
+//                [ 0  a3 ]     [ x  x ]
+// and
+//  V^T*B*Q = V^T*[ b1 b2 ]*Q = [ x  0 ]
+//                [ 0  b3 ]     [ x  x ]
+//
+// otherwise
+//
+//  U^T*A*Q = U^T*[ a1 0  ]*Q = [ x  x ]
+//                [ a2 a3 ]     [ 0  x ]
+// and
+//  V^T*B*Q = V^T*[ b1 0  ]*Q = [ x  x ]
+//                [ b2 b3 ]     [ 0  x ].
+//
+// The rows of the transformed A and B are parallel, where
+//
+//  U = [  csu  snu ], V = [  csv snv ], Q = [  csq   snq ]
+//      [ -snu  csu ]      [ -snv csv ]      [ -snq   csq ]
+//
+// Dlags2 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlags2(upper bool, a1, a2, a3, b1, b2, b3 float64) (csu, snu, csv, snv, csq, snq float64) {
+	if upper {
+		// Input matrices A and B are upper triangular matrices.
+		//
+		// Form matrix C = A*adj(B) = [ a b ]
+		//                            [ 0 d ]
+		a := a1 * b3
+		d := a3 * b1
+		b := a2*b1 - a1*b2
+
+		// The SVD of real 2-by-2 triangular C.
+		//
+		//  [ csl -snl ]*[ a b ]*[  csr  snr ] = [ r 0 ]
+		//  [ snl  csl ] [ 0 d ] [ -snr  csr ]   [ 0 t ]
+		_, _, snr, csr, snl, csl := impl.Dlasv2(a, b, d)
+
+		if math.Abs(csl) >= math.Abs(snl) || math.Abs(csr) >= math.Abs(snr) {
+			// Compute the [0, 0] and [0, 1] elements of U^T*A and V^T*B,
+			// and [0, 1] element of |U|^T*|A| and |V|^T*|B|.
+
+			ua11r := csl * a1
+			ua12 := csl*a2 + snl*a3
+
+			vb11r := csr * b1
+			vb12 := csr*b2 + snr*b3
+
+			aua12 := math.Abs(csl)*math.Abs(a2) + math.Abs(snl)*math.Abs(a3)
+			avb12 := math.Abs(csr)*math.Abs(b2) + math.Abs(snr)*math.Abs(b3)
+
+			// Zero [0, 1] elements of U^T*A and V^T*B.
+			if math.Abs(ua11r)+math.Abs(ua12) != 0 {
+				if aua12/(math.Abs(ua11r)+math.Abs(ua12)) <= avb12/(math.Abs(vb11r)+math.Abs(vb12)) {
+					csq, snq, _ = impl.Dlartg(-ua11r, ua12)
+				} else {
+					csq, snq, _ = impl.Dlartg(-vb11r, vb12)
+				}
+			} else {
+				csq, snq, _ = impl.Dlartg(-vb11r, vb12)
+			}
+
+			csu = csl
+			snu = -snl
+			csv = csr
+			snv = -snr
+		} else {
+			// Compute the [1, 0] and [1, 1] elements of U^T*A and V^T*B,
+			// and [1, 1] element of |U|^T*|A| and |V|^T*|B|.
+
+			ua21 := -snl * a1
+			ua22 := -snl*a2 + csl*a3
+
+			vb21 := -snr * b1
+			vb22 := -snr*b2 + csr*b3
+
+			aua22 := math.Abs(snl)*math.Abs(a2) + math.Abs(csl)*math.Abs(a3)
+			avb22 := math.Abs(snr)*math.Abs(b2) + math.Abs(csr)*math.Abs(b3)
+
+			// Zero [1, 1] elements of U^T*A and V^T*B, and then swap.
+			if math.Abs(ua21)+math.Abs(ua22) != 0 {
+				if aua22/(math.Abs(ua21)+math.Abs(ua22)) <= avb22/(math.Abs(vb21)+math.Abs(vb22)) {
+					csq, snq, _ = impl.Dlartg(-ua21, ua22)
+				} else {
+					csq, snq, _ = impl.Dlartg(-vb21, vb22)
+				}
+			} else {
+				csq, snq, _ = impl.Dlartg(-vb21, vb22)
+			}
+
+			csu = snl
+			snu = csl
+			csv = snr
+			snv = csr
+		}
+	} else {
+		// Input matrices A and B are lower triangular matrices
+		//
+		// Form matrix C = A*adj(B) = [ a 0 ]
+		//                            [ c d ]
+		a := a1 * b3
+		d := a3 * b1
+		c := a2*b3 - a3*b2
+
+		// The SVD of real 2-by-2 triangular C
+		//
+		// [ csl -snl ]*[ a 0 ]*[  csr  snr ] = [ r 0 ]
+		// [ snl  csl ] [ c d ] [ -snr  csr ]   [ 0 t ]
+		_, _, snr, csr, snl, csl := impl.Dlasv2(a, c, d)
+
+		if math.Abs(csr) >= math.Abs(snr) || math.Abs(csl) >= math.Abs(snl) {
+			// Compute the [1, 0] and [1, 1] elements of U^T*A and V^T*B,
+			// and [1, 0] element of |U|^T*|A| and |V|^T*|B|.
+
+			ua21 := -snr*a1 + csr*a2
+			ua22r := csr * a3
+
+			vb21 := -snl*b1 + csl*b2
+			vb22r := csl * b3
+
+			aua21 := math.Abs(snr)*math.Abs(a1) + math.Abs(csr)*math.Abs(a2)
+			avb21 := math.Abs(snl)*math.Abs(b1) + math.Abs(csl)*math.Abs(b2)
+
+			// Zero [1, 0] elements of U^T*A and V^T*B.
+			if (math.Abs(ua21) + math.Abs(ua22r)) != 0 {
+				if aua21/(math.Abs(ua21)+math.Abs(ua22r)) <= avb21/(math.Abs(vb21)+math.Abs(vb22r)) {
+					csq, snq, _ = impl.Dlartg(ua22r, ua21)
+				} else {
+					csq, snq, _ = impl.Dlartg(vb22r, vb21)
+				}
+			} else {
+				csq, snq, _ = impl.Dlartg(vb22r, vb21)
+			}
+
+			csu = csr
+			snu = -snr
+			csv = csl
+			snv = -snl
+		} else {
+			// Compute the [0, 0] and [0, 1] elements of U^T *A and V^T *B,
+			// and [0, 0] element of |U|^T*|A| and |V|^T*|B|.
+
+			ua11 := csr*a1 + snr*a2
+			ua12 := snr * a3
+
+			vb11 := csl*b1 + snl*b2
+			vb12 := snl * b3
+
+			aua11 := math.Abs(csr)*math.Abs(a1) + math.Abs(snr)*math.Abs(a2)
+			avb11 := math.Abs(csl)*math.Abs(b1) + math.Abs(snl)*math.Abs(b2)
+
+			// Zero [0, 0] elements of U^T*A and V^T*B, and then swap.
+			if (math.Abs(ua11) + math.Abs(ua12)) != 0 {
+				if aua11/(math.Abs(ua11)+math.Abs(ua12)) <= avb11/(math.Abs(vb11)+math.Abs(vb12)) {
+					csq, snq, _ = impl.Dlartg(ua12, ua11)
+				} else {
+					csq, snq, _ = impl.Dlartg(vb12, vb11)
+				}
+			} else {
+				csq, snq, _ = impl.Dlartg(vb12, vb11)
+			}
+
+			csu = snr
+			snu = csr
+			csv = snl
+			snv = csl
+		}
+	}
+
+	return csu, snu, csv, snv, csq, snq
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlahqr.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlahqr.go
new file mode 100644
index 00000000..bf14a036
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlahqr.go
@@ -0,0 +1,423 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dlahqr computes the eigenvalues and Schur factorization of a block of an n×n
+// upper Hessenberg matrix H, using the double-shift/single-shift QR algorithm.
+//
+// h and ldh represent the matrix H. Dlahqr works primarily with the Hessenberg
+// submatrix H[ilo:ihi+1,ilo:ihi+1], but applies transformations to all of H if
+// wantt is true. It is assumed that H[ihi+1:n,ihi+1:n] is already upper
+// quasi-triangular, although this is not checked.
+//
+// It must hold that
+//  0 <= ilo <= max(0,ihi), and ihi < n,
+// and that
+//  H[ilo,ilo-1] == 0,  if ilo > 0,
+// otherwise Dlahqr will panic.
+//
+// If unconverged is zero on return, wr[ilo:ihi+1] and wi[ilo:ihi+1] will contain
+// respectively the real and imaginary parts of the computed eigenvalues ilo
+// to ihi. If two eigenvalues are computed as a complex conjugate pair, they are
+// stored in consecutive elements of wr and wi, say the i-th and (i+1)th, with
+// wi[i] > 0 and wi[i+1] < 0. If wantt is true, the eigenvalues are stored in
+// the same order as on the diagonal of the Schur form returned in H, with
+// wr[i] = H[i,i], and, if H[i:i+2,i:i+2] is a 2×2 diagonal block,
+// wi[i] = sqrt(abs(H[i+1,i]*H[i,i+1])) and wi[i+1] = -wi[i].
+//
+// wr and wi must have length ihi+1.
+//
+// z and ldz represent an n×n matrix Z. If wantz is true, the transformations
+// will be applied to the submatrix Z[iloz:ihiz+1,ilo:ihi+1] and it must hold that
+//  0 <= iloz <= ilo, and ihi <= ihiz < n.
+// If wantz is false, z is not referenced.
+//
+// unconverged indicates whether Dlahqr computed all the eigenvalues ilo to ihi
+// in a total of 30 iterations per eigenvalue.
+//
+// If unconverged is zero, all the eigenvalues ilo to ihi have been computed and
+// will be stored on return in wr[ilo:ihi+1] and wi[ilo:ihi+1].
+//
+// If unconverged is zero and wantt is true, H[ilo:ihi+1,ilo:ihi+1] will be
+// overwritten on return by upper quasi-triangular full Schur form with any
+// 2×2 diagonal blocks in standard form.
+//
+// If unconverged is zero and if wantt is false, the contents of h on return is
+// unspecified.
+//
+// If unconverged is positive, some eigenvalues have not converged, and
+// wr[unconverged:ihi+1] and wi[unconverged:ihi+1] contain those eigenvalues
+// which have been successfully computed.
+//
+// If unconverged is positive and wantt is true, then on return
+//  (initial H)*U = U*(final H),   (*)
+// where U is an orthogonal matrix. The final H is upper Hessenberg and
+// H[unconverged:ihi+1,unconverged:ihi+1] is upper quasi-triangular.
+//
+// If unconverged is positive and wantt is false, on return the remaining
+// unconverged eigenvalues are the eigenvalues of the upper Hessenberg matrix
+// H[ilo:unconverged,ilo:unconverged].
+//
+// If unconverged is positive and wantz is true, then on return
+//  (final Z) = (initial Z)*U,
+// where U is the orthogonal matrix in (*) regardless of the value of wantt.
+//
+// Dlahqr is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlahqr(wantt, wantz bool, n, ilo, ihi int, h []float64, ldh int, wr, wi []float64, iloz, ihiz int, z []float64, ldz int) (unconverged int) {
+	checkMatrix(n, n, h, ldh)
+	switch {
+	case ilo < 0 || max(0, ihi) < ilo:
+		panic(badIlo)
+	case n <= ihi:
+		panic(badIhi)
+	case len(wr) != ihi+1:
+		panic("lapack: bad length of wr")
+	case len(wi) != ihi+1:
+		panic("lapack: bad length of wi")
+	case ilo > 0 && h[ilo*ldh+ilo-1] != 0:
+		panic("lapack: block is not isolated")
+	}
+	if wantz {
+		checkMatrix(n, n, z, ldz)
+		switch {
+		case iloz < 0 || ilo < iloz:
+			panic("lapack: iloz out of range")
+		case ihiz < ihi || n <= ihiz:
+			panic("lapack: ihiz out of range")
+		}
+	}
+
+	// Quick return if possible.
+	if n == 0 {
+		return 0
+	}
+	if ilo == ihi {
+		wr[ilo] = h[ilo*ldh+ilo]
+		wi[ilo] = 0
+		return 0
+	}
+
+	// Clear out the trash.
+	for j := ilo; j < ihi-2; j++ {
+		h[(j+2)*ldh+j] = 0
+		h[(j+3)*ldh+j] = 0
+	}
+	if ilo <= ihi-2 {
+		h[ihi*ldh+ihi-2] = 0
+	}
+
+	nh := ihi - ilo + 1
+	nz := ihiz - iloz + 1
+
+	// Set machine-dependent constants for the stopping criterion.
+	ulp := dlamchP
+	smlnum := float64(nh) / ulp * dlamchS
+
+	// i1 and i2 are the indices of the first row and last column of H to
+	// which transformations must be applied. If eigenvalues only are being
+	// computed, i1 and i2 are set inside the main loop.
+	var i1, i2 int
+	if wantt {
+		i1 = 0
+		i2 = n - 1
+	}
+
+	itmax := 30 * max(10, nh) // Total number of QR iterations allowed.
+
+	// The main loop begins here. i is the loop index and decreases from ihi
+	// to ilo in steps of 1 or 2. Each iteration of the loop works with the
+	// active submatrix in rows and columns l to i. Eigenvalues i+1 to ihi
+	// have already converged. Either l = ilo or H[l,l-1] is negligible so
+	// that the matrix splits.
+	bi := blas64.Implementation()
+	i := ihi
+	for i >= ilo {
+		l := ilo
+
+		// Perform QR iterations on rows and columns ilo to i until a
+		// submatrix of order 1 or 2 splits off at the bottom because a
+		// subdiagonal element has become negligible.
+		converged := false
+		for its := 0; its <= itmax; its++ {
+			// Look for a single small subdiagonal element.
+			var k int
+			for k = i; k > l; k-- {
+				if math.Abs(h[k*ldh+k-1]) <= smlnum {
+					break
+				}
+				tst := math.Abs(h[(k-1)*ldh+k-1]) + math.Abs(h[k*ldh+k])
+				if tst == 0 {
+					if k-2 >= ilo {
+						tst += math.Abs(h[(k-1)*ldh+k-2])
+					}
+					if k+1 <= ihi {
+						tst += math.Abs(h[(k+1)*ldh+k])
+					}
+				}
+				// The following is a conservative small
+				// subdiagonal deflation criterion due to Ahues
+				// & Tisseur (LAWN 122, 1997). It has better
+				// mathematical foundation and improves accuracy
+				// in some cases.
+				if math.Abs(h[k*ldh+k-1]) <= ulp*tst {
+					ab := math.Max(math.Abs(h[k*ldh+k-1]), math.Abs(h[(k-1)*ldh+k]))
+					ba := math.Min(math.Abs(h[k*ldh+k-1]), math.Abs(h[(k-1)*ldh+k]))
+					aa := math.Max(math.Abs(h[k*ldh+k]), math.Abs(h[(k-1)*ldh+k-1]-h[k*ldh+k]))
+					bb := math.Min(math.Abs(h[k*ldh+k]), math.Abs(h[(k-1)*ldh+k-1]-h[k*ldh+k]))
+					s := aa + ab
+					if ab/s*ba <= math.Max(smlnum, aa/s*bb*ulp) {
+						break
+					}
+				}
+			}
+			l = k
+			if l > ilo {
+				// H[l,l-1] is negligible.
+				h[l*ldh+l-1] = 0
+			}
+			if l >= i-1 {
+				// Break the loop because a submatrix of order 1
+				// or 2 has split off.
+				converged = true
+				break
+			}
+
+			// Now the active submatrix is in rows and columns l to
+			// i. If eigenvalues only are being computed, only the
+			// active submatrix need be transformed.
+			if !wantt {
+				i1 = l
+				i2 = i
+			}
+
+			const (
+				dat1 = 3.0
+				dat2 = -0.4375
+			)
+			var h11, h21, h12, h22 float64
+			switch its {
+			case 10: // Exceptional shift.
+				s := math.Abs(h[(l+1)*ldh+l]) + math.Abs(h[(l+2)*ldh+l+1])
+				h11 = dat1*s + h[l*ldh+l]
+				h12 = dat2 * s
+				h21 = s
+				h22 = h11
+			case 20: // Exceptional shift.
+				s := math.Abs(h[i*ldh+i-1]) + math.Abs(h[(i-1)*ldh+i-2])
+				h11 = dat1*s + h[i*ldh+i]
+				h12 = dat2 * s
+				h21 = s
+				h22 = h11
+			default: // Prepare to use Francis' double shift (i.e.,
+				// 2nd degree generalized Rayleigh quotient).
+				h11 = h[(i-1)*ldh+i-1]
+				h21 = h[i*ldh+i-1]
+				h12 = h[(i-1)*ldh+i]
+				h22 = h[i*ldh+i]
+			}
+			s := math.Abs(h11) + math.Abs(h12) + math.Abs(h21) + math.Abs(h22)
+			var (
+				rt1r, rt1i float64
+				rt2r, rt2i float64
+			)
+			if s != 0 {
+				h11 /= s
+				h21 /= s
+				h12 /= s
+				h22 /= s
+				tr := (h11 + h22) / 2
+				det := (h11-tr)*(h22-tr) - h12*h21
+				rtdisc := math.Sqrt(math.Abs(det))
+				if det >= 0 {
+					// Complex conjugate shifts.
+					rt1r = tr * s
+					rt2r = rt1r
+					rt1i = rtdisc * s
+					rt2i = -rt1i
+				} else {
+					// Real shifts (use only one of them).
+					rt1r = tr + rtdisc
+					rt2r = tr - rtdisc
+					if math.Abs(rt1r-h22) <= math.Abs(rt2r-h22) {
+						rt1r *= s
+						rt2r = rt1r
+					} else {
+						rt2r *= s
+						rt1r = rt2r
+					}
+					rt1i = 0
+					rt2i = 0
+				}
+			}
+
+			// Look for two consecutive small subdiagonal elements.
+			var m int
+			var v [3]float64
+			for m = i - 2; m >= l; m-- {
+				// Determine the effect of starting the
+				// double-shift QR iteration at row m, and see
+				// if this would make H[m,m-1] negligible. The
+				// following uses scaling to avoid overflows and
+				// most underflows.
+				h21s := h[(m+1)*ldh+m]
+				s := math.Abs(h[m*ldh+m]-rt2r) + math.Abs(rt2i) + math.Abs(h21s)
+				h21s /= s
+				v[0] = h21s*h[m*ldh+m+1] + (h[m*ldh+m]-rt1r)*((h[m*ldh+m]-rt2r)/s) - rt2i/s*rt1i
+				v[1] = h21s * (h[m*ldh+m] + h[(m+1)*ldh+m+1] - rt1r - rt2r)
+				v[2] = h21s * h[(m+2)*ldh+m+1]
+				s = math.Abs(v[0]) + math.Abs(v[1]) + math.Abs(v[2])
+				v[0] /= s
+				v[1] /= s
+				v[2] /= s
+				if m == l {
+					break
+				}
+				dsum := math.Abs(h[(m-1)*ldh+m-1]) + math.Abs(h[m*ldh+m]) + math.Abs(h[(m+1)*ldh+m+1])
+				if math.Abs(h[m*ldh+m-1])*(math.Abs(v[1])+math.Abs(v[2])) <= ulp*math.Abs(v[0])*dsum {
+					break
+				}
+			}
+
+			// Double-shift QR step.
+			for k := m; k < i; k++ {
+				// The first iteration of this loop determines a
+				// reflection G from the vector V and applies it
+				// from left and right to H, thus creating a
+				// non-zero bulge below the subdiagonal.
+				//
+				// Each subsequent iteration determines a
+				// reflection G to restore the Hessenberg form
+				// in the (k-1)th column, and thus chases the
+				// bulge one step toward the bottom of the
+				// active submatrix. nr is the order of G.
+
+				nr := min(3, i-k+1)
+				if k > m {
+					bi.Dcopy(nr, h[k*ldh+k-1:], ldh, v[:], 1)
+				}
+				var t0 float64
+				v[0], t0 = impl.Dlarfg(nr, v[0], v[1:], 1)
+				if k > m {
+					h[k*ldh+k-1] = v[0]
+					h[(k+1)*ldh+k-1] = 0
+					if k < i-1 {
+						h[(k+2)*ldh+k-1] = 0
+					}
+				} else if m > l {
+					// Use the following instead of H[k,k-1] = -H[k,k-1]
+					// to avoid a bug when v[1] and v[2] underflow.
+					h[k*ldh+k-1] *= 1 - t0
+				}
+				t1 := t0 * v[1]
+				if nr == 3 {
+					t2 := t0 * v[2]
+
+					// Apply G from the left to transform
+					// the rows of the matrix in columns k
+					// to i2.
+					for j := k; j <= i2; j++ {
+						sum := h[k*ldh+j] + v[1]*h[(k+1)*ldh+j] + v[2]*h[(k+2)*ldh+j]
+						h[k*ldh+j] -= sum * t0
+						h[(k+1)*ldh+j] -= sum * t1
+						h[(k+2)*ldh+j] -= sum * t2
+					}
+
+					// Apply G from the right to transform
+					// the columns of the matrix in rows i1
+					// to min(k+3,i).
+					for j := i1; j <= min(k+3, i); j++ {
+						sum := h[j*ldh+k] + v[1]*h[j*ldh+k+1] + v[2]*h[j*ldh+k+2]
+						h[j*ldh+k] -= sum * t0
+						h[j*ldh+k+1] -= sum * t1
+						h[j*ldh+k+2] -= sum * t2
+					}
+
+					if wantz {
+						// Accumulate transformations in the matrix Z.
+						for j := iloz; j <= ihiz; j++ {
+							sum := z[j*ldz+k] + v[1]*z[j*ldz+k+1] + v[2]*z[j*ldz+k+2]
+							z[j*ldz+k] -= sum * t0
+							z[j*ldz+k+1] -= sum * t1
+							z[j*ldz+k+2] -= sum * t2
+						}
+					}
+				} else if nr == 2 {
+					// Apply G from the left to transform
+					// the rows of the matrix in columns k
+					// to i2.
+					for j := k; j <= i2; j++ {
+						sum := h[k*ldh+j] + v[1]*h[(k+1)*ldh+j]
+						h[k*ldh+j] -= sum * t0
+						h[(k+1)*ldh+j] -= sum * t1
+					}
+
+					// Apply G from the right to transform
+					// the columns of the matrix in rows i1
+					// to min(k+3,i).
+					for j := i1; j <= i; j++ {
+						sum := h[j*ldh+k] + v[1]*h[j*ldh+k+1]
+						h[j*ldh+k] -= sum * t0
+						h[j*ldh+k+1] -= sum * t1
+					}
+
+					if wantz {
+						// Accumulate transformations in the matrix Z.
+						for j := iloz; j <= ihiz; j++ {
+							sum := z[j*ldz+k] + v[1]*z[j*ldz+k+1]
+							z[j*ldz+k] -= sum * t0
+							z[j*ldz+k+1] -= sum * t1
+						}
+					}
+				}
+			}
+		}
+
+		if !converged {
+			// The QR iteration finished without splitting off a
+			// submatrix of order 1 or 2.
+			return i + 1
+		}
+
+		if l == i {
+			// H[i,i-1] is negligible: one eigenvalue has converged.
+			wr[i] = h[i*ldh+i]
+			wi[i] = 0
+		} else if l == i-1 {
+			// H[i-1,i-2] is negligible: a pair of eigenvalues have converged.
+
+			// Transform the 2×2 submatrix to standard Schur form,
+			// and compute and store the eigenvalues.
+			var cs, sn float64
+			a, b := h[(i-1)*ldh+i-1], h[(i-1)*ldh+i]
+			c, d := h[i*ldh+i-1], h[i*ldh+i]
+			a, b, c, d, wr[i-1], wi[i-1], wr[i], wi[i], cs, sn = impl.Dlanv2(a, b, c, d)
+			h[(i-1)*ldh+i-1], h[(i-1)*ldh+i] = a, b
+			h[i*ldh+i-1], h[i*ldh+i] = c, d
+
+			if wantt {
+				// Apply the transformation to the rest of H.
+				if i2 > i {
+					bi.Drot(i2-i, h[(i-1)*ldh+i+1:], 1, h[i*ldh+i+1:], 1, cs, sn)
+				}
+				bi.Drot(i-i1-1, h[i1*ldh+i-1:], ldh, h[i1*ldh+i:], ldh, cs, sn)
+			}
+
+			if wantz {
+				// Apply the transformation to Z.
+				bi.Drot(nz, z[iloz*ldz+i-1:], ldz, z[iloz*ldz+i:], ldz, cs, sn)
+			}
+		}
+
+		// Return to start of the main loop with new value of i.
+		i = l - 1
+	}
+	return 0
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlahr2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlahr2.go
new file mode 100644
index 00000000..607810f0
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlahr2.go
@@ -0,0 +1,169 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dlahr2 reduces the first nb columns of a real general n×(n-k+1) matrix A so
+// that elements below the k-th subdiagonal are zero. The reduction is performed
+// by an orthogonal similarity transformation Q^T * A * Q. Dlahr2 returns the
+// matrices V and T which determine Q as a block reflector I - V*T*V^T, and
+// also the matrix Y = A * V * T.
+//
+// The matrix Q is represented as a product of nb elementary reflectors
+//  Q = H_0 * H_1 * ... * H_{nb-1}.
+// Each H_i has the form
+//  H_i = I - tau[i] * v * v^T,
+// where v is a real vector with v[0:i+k-1] = 0 and v[i+k-1] = 1. v[i+k:n] is
+// stored on exit in A[i+k+1:n,i].
+//
+// The elements of the vectors v together form the (n-k+1)×nb matrix
+// V which is needed, with T and Y, to apply the transformation to the
+// unreduced part of the matrix, using an update of the form
+//  A = (I - V*T*V^T) * (A - Y*V^T).
+//
+// On entry, a contains the n×(n-k+1) general matrix A. On return, the elements
+// on and above the k-th subdiagonal in the first nb columns are overwritten
+// with the corresponding elements of the reduced matrix; the elements below the
+// k-th subdiagonal, with the slice tau, represent the matrix Q as a product of
+// elementary reflectors. The other columns of A are unchanged.
+//
+// The contents of A on exit are illustrated by the following example
+// with n = 7, k = 3 and nb = 2:
+//  [ a   a   a   a   a ]
+//  [ a   a   a   a   a ]
+//  [ a   a   a   a   a ]
+//  [ h   h   a   a   a ]
+//  [ v0  h   a   a   a ]
+//  [ v0  v1  a   a   a ]
+//  [ v0  v1  a   a   a ]
+// where a denotes an element of the original matrix A, h denotes a
+// modified element of the upper Hessenberg matrix H, and vi denotes an
+// element of the vector defining H_i.
+//
+// k is the offset for the reduction. Elements below the k-th subdiagonal in the
+// first nb columns are reduced to zero.
+//
+// nb is the number of columns to be reduced.
+//
+// On entry, a represents the n×(n-k+1) matrix A. On return, the elements on and
+// above the k-th subdiagonal in the first nb columns are overwritten with the
+// corresponding elements of the reduced matrix. The elements below the k-th
+// subdiagonal, with the slice tau, represent the matrix Q as a product of
+// elementary reflectors. The other columns of A are unchanged.
+//
+// tau will contain the scalar factors of the elementary reflectors. It must
+// have length at least nb.
+//
+// t and ldt represent the nb×nb upper triangular matrix T, and y and ldy
+// represent the n×nb matrix Y.
+//
+// Dlahr2 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlahr2(n, k, nb int, a []float64, lda int, tau, t []float64, ldt int, y []float64, ldy int) {
+	checkMatrix(n, n-k+1, a, lda)
+	if len(tau) < nb {
+		panic(badTau)
+	}
+	checkMatrix(nb, nb, t, ldt)
+	checkMatrix(n, nb, y, ldy)
+
+	// Quick return if possible.
+	if n <= 1 {
+		return
+	}
+
+	bi := blas64.Implementation()
+	var ei float64
+	for i := 0; i < nb; i++ {
+		if i > 0 {
+			// Update A[k:n,i].
+
+			// Update i-th column of A - Y * V^T.
+			bi.Dgemv(blas.NoTrans, n-k, i,
+				-1, y[k*ldy:], ldy,
+				a[(k+i-1)*lda:], 1,
+				1, a[k*lda+i:], lda)
+
+			// Apply I - V * T^T * V^T to this column (call it b)
+			// from the left, using the last column of T as
+			// workspace.
+			// Let V = [ V1 ]   and   b = [ b1 ]   (first i rows)
+			//         [ V2 ]             [ b2 ]
+			// where V1 is unit lower triangular.
+			//
+			// w := V1^T * b1.
+			bi.Dcopy(i, a[k*lda+i:], lda, t[nb-1:], ldt)
+			bi.Dtrmv(blas.Lower, blas.Trans, blas.Unit, i,
+				a[k*lda:], lda, t[nb-1:], ldt)
+
+			// w := w + V2^T * b2.
+			bi.Dgemv(blas.Trans, n-k-i, i,
+				1, a[(k+i)*lda:], lda,
+				a[(k+i)*lda+i:], lda,
+				1, t[nb-1:], ldt)
+
+			// w := T^T * w.
+			bi.Dtrmv(blas.Upper, blas.Trans, blas.NonUnit, i,
+				t, ldt, t[nb-1:], ldt)
+
+			// b2 := b2 - V2*w.
+			bi.Dgemv(blas.NoTrans, n-k-i, i,
+				-1, a[(k+i)*lda:], lda,
+				t[nb-1:], ldt,
+				1, a[(k+i)*lda+i:], lda)
+
+			// b1 := b1 - V1*w.
+			bi.Dtrmv(blas.Lower, blas.NoTrans, blas.Unit, i,
+				a[k*lda:], lda, t[nb-1:], ldt)
+			bi.Daxpy(i, -1, t[nb-1:], ldt, a[k*lda+i:], lda)
+
+			a[(k+i-1)*lda+i-1] = ei
+		}
+
+		// Generate the elementary reflector H_i to annihilate
+		// A[k+i+1:n,i].
+		ei, tau[i] = impl.Dlarfg(n-k-i, a[(k+i)*lda+i], a[min(k+i+1, n-1)*lda+i:], lda)
+		a[(k+i)*lda+i] = 1
+
+		// Compute Y[k:n,i].
+		bi.Dgemv(blas.NoTrans, n-k, n-k-i,
+			1, a[k*lda+i+1:], lda,
+			a[(k+i)*lda+i:], lda,
+			0, y[k*ldy+i:], ldy)
+		bi.Dgemv(blas.Trans, n-k-i, i,
+			1, a[(k+i)*lda:], lda,
+			a[(k+i)*lda+i:], lda,
+			0, t[i:], ldt)
+		bi.Dgemv(blas.NoTrans, n-k, i,
+			-1, y[k*ldy:], ldy,
+			t[i:], ldt,
+			1, y[k*ldy+i:], ldy)
+		bi.Dscal(n-k, tau[i], y[k*ldy+i:], ldy)
+
+		// Compute T[0:i,i].
+		bi.Dscal(i, -tau[i], t[i:], ldt)
+		bi.Dtrmv(blas.Upper, blas.NoTrans, blas.NonUnit, i,
+			t, ldt, t[i:], ldt)
+
+		t[i*ldt+i] = tau[i]
+	}
+	a[(k+nb-1)*lda+nb-1] = ei
+
+	// Compute Y[0:k,0:nb].
+	impl.Dlacpy(blas.All, k, nb, a[1:], lda, y, ldy)
+	bi.Dtrmm(blas.Right, blas.Lower, blas.NoTrans, blas.Unit, k, nb,
+		1, a[k*lda:], lda, y, ldy)
+	if n > k+nb {
+		bi.Dgemm(blas.NoTrans, blas.NoTrans, k, nb, n-k-nb,
+			1, a[1+nb:], lda,
+			a[(k+nb)*lda:], lda,
+			1, y, ldy)
+	}
+	bi.Dtrmm(blas.Right, blas.Upper, blas.NoTrans, blas.NonUnit, k, nb,
+		1, t, ldt, y, ldy)
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlaln2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlaln2.go
new file mode 100644
index 00000000..fb1873f7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlaln2.go
@@ -0,0 +1,396 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "math"
+
+// Dlaln2 solves a linear equation or a system of 2 linear equations of the form
+//  (ca A   - w D) X = scale B,  if trans == false,
+//  (ca A^T - w D) X = scale B,  if trans == true,
+// where A is a na×na real matrix, ca is a real scalar, D is a na×na diagonal
+// real matrix, w is a scalar, real if nw == 1, complex if nw == 2, and X and B
+// are na×1 matrices, real if w is real, complex if w is complex.
+//
+// If w is complex, X and B are represented as na×2 matrices, the first column
+// of each being the real part and the second being the imaginary part.
+//
+// na and nw must be 1 or 2, otherwise Dlaln2 will panic.
+//
+// d1 and d2 are the diagonal elements of D. d2 is not used if na == 1.
+//
+// wr and wi represent the real and imaginary part, respectively, of the scalar
+// w. wi is not used if nw == 1.
+//
+// smin is the desired lower bound on the singular values of A. This should be
+// a safe distance away from underflow or overflow, say, between
+// (underflow/machine precision) and (overflow*machine precision).
+//
+// If both singular values of (ca A - w D) are less than smin, smin*identity
+// will be used instead of (ca A - w D). If only one singular value is less than
+// smin, one element of (ca A - w D) will be perturbed enough to make the
+// smallest singular value roughly smin. If both singular values are at least
+// smin, (ca A - w D) will not be perturbed. In any case, the perturbation will
+// be at most some small multiple of max(smin, ulp*norm(ca A - w D)). The
+// singular values are computed by infinity-norm approximations, and thus will
+// only be correct to a factor of 2 or so.
+//
+// All input quantities are assumed to be smaller than overflow by a reasonable
+// factor.
+//
+// scale is a scaling factor less than or equal to 1 which is chosen so that X
+// can be computed without overflow. X is further scaled if necessary to assure
+// that norm(ca A - w D)*norm(X) is less than overflow.
+//
+// xnorm contains the infinity-norm of X when X is regarded as a na×nw real
+// matrix.
+//
+// ok will be false if (ca A - w D) had to be perturbed to make its smallest
+// singular value greater than smin, otherwise ok will be true.
+//
+// Dlaln2 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlaln2(trans bool, na, nw int, smin, ca float64, a []float64, lda int, d1, d2 float64, b []float64, ldb int, wr, wi float64, x []float64, ldx int) (scale, xnorm float64, ok bool) {
+	// TODO(vladimir-ch): Consider splitting this function into two, one
+	// handling the real case (nw == 1) and the other handling the complex
+	// case (nw == 2). Given that Go has complex types, their signatures
+	// would be simpler and more natural, and the implementation not as
+	// convoluted.
+
+	if na != 1 && na != 2 {
+		panic("lapack: invalid value of na")
+	}
+	if nw != 1 && nw != 2 {
+		panic("lapack: invalid value of nw")
+	}
+	checkMatrix(na, na, a, lda)
+	checkMatrix(na, nw, b, ldb)
+	checkMatrix(na, nw, x, ldx)
+
+	smlnum := 2 * dlamchS
+	bignum := 1 / smlnum
+	smini := math.Max(smin, smlnum)
+
+	ok = true
+	scale = 1
+
+	if na == 1 {
+		// 1×1 (i.e., scalar) system C X = B.
+
+		if nw == 1 {
+			// Real 1×1 system.
+
+			// C = ca A - w D.
+			csr := ca*a[0] - wr*d1
+			cnorm := math.Abs(csr)
+
+			// If |C| < smini, use C = smini.
+			if cnorm < smini {
+				csr = smini
+				cnorm = smini
+				ok = false
+			}
+
+			// Check scaling for X = B / C.
+			bnorm := math.Abs(b[0])
+			if cnorm < 1 && bnorm > math.Max(1, bignum*cnorm) {
+				scale = 1 / bnorm
+			}
+
+			// Compute X.
+			x[0] = b[0] * scale / csr
+			xnorm = math.Abs(x[0])
+
+			return scale, xnorm, ok
+		}
+
+		// Complex 1×1 system (w is complex).
+
+		// C = ca A - w D.
+		csr := ca*a[0] - wr*d1
+		csi := -wi * d1
+		cnorm := math.Abs(csr) + math.Abs(csi)
+
+		// If |C| < smini, use C = smini.
+		if cnorm < smini {
+			csr = smini
+			csi = 0
+			cnorm = smini
+			ok = false
+		}
+
+		// Check scaling for X = B / C.
+		bnorm := math.Abs(b[0]) + math.Abs(b[1])
+		if cnorm < 1 && bnorm > math.Max(1, bignum*cnorm) {
+			scale = 1 / bnorm
+		}
+
+		// Compute X.
+		cx := complex(scale*b[0], scale*b[1]) / complex(csr, csi)
+		x[0], x[1] = real(cx), imag(cx)
+		xnorm = math.Abs(x[0]) + math.Abs(x[1])
+
+		return scale, xnorm, ok
+	}
+
+	// 2×2 system.
+
+	// Compute the real part of
+	//  C = ca A   - w D
+	// or
+	//  C = ca A^T - w D.
+	crv := [4]float64{
+		ca*a[0] - wr*d1,
+		ca * a[1],
+		ca * a[lda],
+		ca*a[lda+1] - wr*d2,
+	}
+	if trans {
+		crv[1] = ca * a[lda]
+		crv[2] = ca * a[1]
+	}
+
+	pivot := [4][4]int{
+		{0, 1, 2, 3},
+		{1, 0, 3, 2},
+		{2, 3, 0, 1},
+		{3, 2, 1, 0},
+	}
+
+	if nw == 1 {
+		// Real 2×2 system (w is real).
+
+		// Find the largest element in C.
+		var cmax float64
+		var icmax int
+		for j, v := range crv {
+			v = math.Abs(v)
+			if v > cmax {
+				cmax = v
+				icmax = j
+			}
+		}
+
+		// If norm(C) < smini, use smini*identity.
+		if cmax < smini {
+			bnorm := math.Max(math.Abs(b[0]), math.Abs(b[ldb]))
+			if smini < 1 && bnorm > math.Max(1, bignum*smini) {
+				scale = 1 / bnorm
+			}
+			temp := scale / smini
+			x[0] = temp * b[0]
+			x[ldx] = temp * b[ldb]
+			xnorm = temp * bnorm
+			ok = false
+
+			return scale, xnorm, ok
+		}
+
+		// Gaussian elimination with complete pivoting.
+		// Form upper triangular matrix
+		//  [ur11 ur12]
+		//  [   0 ur22]
+		ur11 := crv[icmax]
+		ur12 := crv[pivot[icmax][1]]
+		cr21 := crv[pivot[icmax][2]]
+		cr22 := crv[pivot[icmax][3]]
+		ur11r := 1 / ur11
+		lr21 := ur11r * cr21
+		ur22 := cr22 - ur12*lr21
+
+		// If smaller pivot < smini, use smini.
+		if math.Abs(ur22) < smini {
+			ur22 = smini
+			ok = false
+		}
+
+		var br1, br2 float64
+		if icmax > 1 {
+			// If the pivot lies in the second row, swap the rows.
+			br1 = b[ldb]
+			br2 = b[0]
+		} else {
+			br1 = b[0]
+			br2 = b[ldb]
+		}
+		br2 -= lr21 * br1 // Apply the Gaussian elimination step to the right-hand side.
+
+		bbnd := math.Max(math.Abs(ur22*ur11r*br1), math.Abs(br2))
+		if bbnd > 1 && math.Abs(ur22) < 1 && bbnd >= bignum*math.Abs(ur22) {
+			scale = 1 / bbnd
+		}
+
+		// Solve the linear system ur*xr=br.
+		xr2 := br2 * scale / ur22
+		xr1 := scale*br1*ur11r - ur11r*ur12*xr2
+		if icmax&0x1 != 0 {
+			// If the pivot lies in the second column, swap the components of the solution.
+			x[0] = xr2
+			x[ldx] = xr1
+		} else {
+			x[0] = xr1
+			x[ldx] = xr2
+		}
+		xnorm = math.Max(math.Abs(xr1), math.Abs(xr2))
+
+		// Further scaling if norm(A)*norm(X) > overflow.
+		if xnorm > 1 && cmax > 1 && xnorm > bignum/cmax {
+			temp := cmax / bignum
+			x[0] *= temp
+			x[ldx] *= temp
+			xnorm *= temp
+			scale *= temp
+		}
+
+		return scale, xnorm, ok
+	}
+
+	// Complex 2×2 system (w is complex).
+
+	// Find the largest element in C.
+	civ := [4]float64{
+		-wi * d1,
+		0,
+		0,
+		-wi * d2,
+	}
+	var cmax float64
+	var icmax int
+	for j, v := range crv {
+		v := math.Abs(v)
+		if v+math.Abs(civ[j]) > cmax {
+			cmax = v + math.Abs(civ[j])
+			icmax = j
+		}
+	}
+
+	// If norm(C) < smini, use smini*identity.
+	if cmax < smini {
+		br1 := math.Abs(b[0]) + math.Abs(b[1])
+		br2 := math.Abs(b[ldb]) + math.Abs(b[ldb+1])
+		bnorm := math.Max(br1, br2)
+		if smini < 1 && bnorm > 1 && bnorm > bignum*smini {
+			scale = 1 / bnorm
+		}
+		temp := scale / smini
+		x[0] = temp * b[0]
+		x[1] = temp * b[1]
+		x[ldb] = temp * b[ldb]
+		x[ldb+1] = temp * b[ldb+1]
+		xnorm = temp * bnorm
+		ok = false
+
+		return scale, xnorm, ok
+	}
+
+	// Gaussian elimination with complete pivoting.
+	ur11 := crv[icmax]
+	ui11 := civ[icmax]
+	ur12 := crv[pivot[icmax][1]]
+	ui12 := civ[pivot[icmax][1]]
+	cr21 := crv[pivot[icmax][2]]
+	ci21 := civ[pivot[icmax][2]]
+	cr22 := crv[pivot[icmax][3]]
+	ci22 := civ[pivot[icmax][3]]
+	var (
+		ur11r, ui11r float64
+		lr21, li21   float64
+		ur12s, ui12s float64
+		ur22, ui22   float64
+	)
+	if icmax == 0 || icmax == 3 {
+		// Off-diagonals of pivoted C are real.
+		if math.Abs(ur11) > math.Abs(ui11) {
+			temp := ui11 / ur11
+			ur11r = 1 / (ur11 * (1 + temp*temp))
+			ui11r = -temp * ur11r
+		} else {
+			temp := ur11 / ui11
+			ui11r = -1 / (ui11 * (1 + temp*temp))
+			ur11r = -temp * ui11r
+		}
+		lr21 = cr21 * ur11r
+		li21 = cr21 * ui11r
+		ur12s = ur12 * ur11r
+		ui12s = ur12 * ui11r
+		ur22 = cr22 - ur12*lr21
+		ui22 = ci22 - ur12*li21
+	} else {
+		// Diagonals of pivoted C are real.
+		ur11r = 1 / ur11
+		// ui11r is already 0.
+		lr21 = cr21 * ur11r
+		li21 = ci21 * ur11r
+		ur12s = ur12 * ur11r
+		ui12s = ui12 * ur11r
+		ur22 = cr22 - ur12*lr21 + ui12*li21
+		ui22 = -ur12*li21 - ui12*lr21
+	}
+	u22abs := math.Abs(ur22) + math.Abs(ui22)
+
+	// If smaller pivot < smini, use smini.
+	if u22abs < smini {
+		ur22 = smini
+		ui22 = 0
+		ok = false
+	}
+
+	var br1, bi1 float64
+	var br2, bi2 float64
+	if icmax > 1 {
+		// If the pivot lies in the second row, swap the rows.
+		br1 = b[ldb]
+		bi1 = b[ldb+1]
+		br2 = b[0]
+		bi2 = b[1]
+	} else {
+		br1 = b[0]
+		bi1 = b[1]
+		br2 = b[ldb]
+		bi2 = b[ldb+1]
+	}
+	br2 += -lr21*br1 + li21*bi1
+	bi2 += -li21*br1 - lr21*bi1
+
+	bbnd1 := u22abs * (math.Abs(ur11r) + math.Abs(ui11r)) * (math.Abs(br1) + math.Abs(bi1))
+	bbnd2 := math.Abs(br2) + math.Abs(bi2)
+	bbnd := math.Max(bbnd1, bbnd2)
+	if bbnd > 1 && u22abs < 1 && bbnd >= bignum*u22abs {
+		scale = 1 / bbnd
+		br1 *= scale
+		bi1 *= scale
+		br2 *= scale
+		bi2 *= scale
+	}
+
+	cx2 := complex(br2, bi2) / complex(ur22, ui22)
+	xr2, xi2 := real(cx2), imag(cx2)
+	xr1 := ur11r*br1 - ui11r*bi1 - ur12s*xr2 + ui12s*xi2
+	xi1 := ui11r*br1 + ur11r*bi1 - ui12s*xr2 - ur12s*xi2
+	if icmax&0x1 != 0 {
+		// If the pivot lies in the second column, swap the components of the solution.
+		x[0] = xr2
+		x[1] = xi2
+		x[ldx] = xr1
+		x[ldx+1] = xi1
+	} else {
+		x[0] = xr1
+		x[1] = xi1
+		x[ldx] = xr2
+		x[ldx+1] = xi2
+	}
+	xnorm = math.Max(math.Abs(xr1)+math.Abs(xi1), math.Abs(xr2)+math.Abs(xi2))
+
+	// Further scaling if norm(A)*norm(X) > overflow.
+	if xnorm > 1 && cmax > 1 && xnorm > bignum/cmax {
+		temp := cmax / bignum
+		x[0] *= temp
+		x[1] *= temp
+		x[ldx] *= temp
+		x[ldx+1] *= temp
+		xnorm *= temp
+		scale *= temp
+	}
+
+	return scale, xnorm, ok
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlange.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlange.go
new file mode 100644
index 00000000..66b46aab
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlange.go
@@ -0,0 +1,84 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dlange computes the matrix norm of the general m×n matrix a. The input norm
+// specifies the norm computed.
+//  lapack.MaxAbs: the maximum absolute value of an element.
+//  lapack.MaxColumnSum: the maximum column sum of the absolute values of the entries.
+//  lapack.MaxRowSum: the maximum row sum of the absolute values of the entries.
+//  lapack.NormFrob: the square root of the sum of the squares of the entries.
+// If norm == lapack.MaxColumnSum, work must be of length n, and this function will panic otherwise.
+// There are no restrictions on work for the other matrix norms.
+func (impl Implementation) Dlange(norm lapack.MatrixNorm, m, n int, a []float64, lda int, work []float64) float64 {
+	// TODO(btracey): These should probably be refactored to use BLAS calls.
+	checkMatrix(m, n, a, lda)
+	switch norm {
+	case lapack.MaxRowSum, lapack.MaxColumnSum, lapack.NormFrob, lapack.MaxAbs:
+	default:
+		panic(badNorm)
+	}
+	if norm == lapack.MaxColumnSum && len(work) < n {
+		panic(badWork)
+	}
+	if m == 0 && n == 0 {
+		return 0
+	}
+	if norm == lapack.MaxAbs {
+		var value float64
+		for i := 0; i < m; i++ {
+			for j := 0; j < n; j++ {
+				value = math.Max(value, math.Abs(a[i*lda+j]))
+			}
+		}
+		return value
+	}
+	if norm == lapack.MaxColumnSum {
+		if len(work) < n {
+			panic(badWork)
+		}
+		for i := 0; i < n; i++ {
+			work[i] = 0
+		}
+		for i := 0; i < m; i++ {
+			for j := 0; j < n; j++ {
+				work[j] += math.Abs(a[i*lda+j])
+			}
+		}
+		var value float64
+		for i := 0; i < n; i++ {
+			value = math.Max(value, work[i])
+		}
+		return value
+	}
+	if norm == lapack.MaxRowSum {
+		var value float64
+		for i := 0; i < m; i++ {
+			var sum float64
+			for j := 0; j < n; j++ {
+				sum += math.Abs(a[i*lda+j])
+			}
+			value = math.Max(value, sum)
+		}
+		return value
+	}
+	if norm == lapack.NormFrob {
+		var value float64
+		scale := 0.0
+		sum := 1.0
+		for i := 0; i < m; i++ {
+			scale, sum = impl.Dlassq(n, a[i*lda:], 1, scale, sum)
+		}
+		value = scale * math.Sqrt(sum)
+		return value
+	}
+	panic("lapack: bad matrix norm")
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlanst.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlanst.go
new file mode 100644
index 00000000..7adb7aad
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlanst.go
@@ -0,0 +1,68 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dlanst computes the specified norm of a symmetric tridiagonal matrix A.
+// The diagonal elements of A are stored in d and the off-diagonal elements
+// are stored in e.
+func (impl Implementation) Dlanst(norm lapack.MatrixNorm, n int, d, e []float64) float64 {
+	if len(d) < n {
+		panic(badD)
+	}
+	if len(e) < n-1 {
+		panic(badE)
+	}
+	if n <= 0 {
+		return 0
+	}
+	switch norm {
+	default:
+		panic(badNorm)
+	case lapack.MaxAbs:
+		anorm := math.Abs(d[n-1])
+		for i := 0; i < n-1; i++ {
+			sum := math.Abs(d[i])
+			if anorm < sum || math.IsNaN(sum) {
+				anorm = sum
+			}
+			sum = math.Abs(e[i])
+			if anorm < sum || math.IsNaN(sum) {
+				anorm = sum
+			}
+		}
+		return anorm
+	case lapack.MaxColumnSum, lapack.MaxRowSum:
+		if n == 1 {
+			return math.Abs(d[0])
+		}
+		anorm := math.Abs(d[0]) + math.Abs(e[0])
+		sum := math.Abs(e[n-2]) + math.Abs(d[n-1])
+		if anorm < sum || math.IsNaN(sum) {
+			anorm = sum
+		}
+		for i := 1; i < n-1; i++ {
+			sum := math.Abs(d[i]) + math.Abs(e[i]) + math.Abs(e[i-1])
+			if anorm < sum || math.IsNaN(sum) {
+				anorm = sum
+			}
+		}
+		return anorm
+	case lapack.NormFrob:
+		var scale float64
+		sum := 1.0
+		if n > 1 {
+			scale, sum = impl.Dlassq(n-1, e, 1, scale, sum)
+			sum = 2 * sum
+		}
+		scale, sum = impl.Dlassq(n, d, 1, scale, sum)
+		return scale * math.Sqrt(sum)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlansy.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlansy.go
new file mode 100644
index 00000000..03a7585b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlansy.go
@@ -0,0 +1,125 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dlansy computes the specified norm of an n×n symmetric matrix. If
+// norm == lapack.MaxColumnSum or norm == lapackMaxRowSum work must have length
+// at least n, otherwise work is unused.
+func (impl Implementation) Dlansy(norm lapack.MatrixNorm, uplo blas.Uplo, n int, a []float64, lda int, work []float64) float64 {
+	checkMatrix(n, n, a, lda)
+	switch norm {
+	case lapack.MaxRowSum, lapack.MaxColumnSum, lapack.NormFrob, lapack.MaxAbs:
+	default:
+		panic(badNorm)
+	}
+	if (norm == lapack.MaxColumnSum || norm == lapack.MaxRowSum) && len(work) < n {
+		panic(badWork)
+	}
+	if uplo != blas.Upper && uplo != blas.Lower {
+		panic(badUplo)
+	}
+
+	if n == 0 {
+		return 0
+	}
+	switch norm {
+	default:
+		panic("unreachable")
+	case lapack.MaxAbs:
+		if uplo == blas.Upper {
+			var max float64
+			for i := 0; i < n; i++ {
+				for j := i; j < n; j++ {
+					v := math.Abs(a[i*lda+j])
+					if math.IsNaN(v) {
+						return math.NaN()
+					}
+					if v > max {
+						max = v
+					}
+				}
+			}
+			return max
+		}
+		var max float64
+		for i := 0; i < n; i++ {
+			for j := 0; j <= i; j++ {
+				v := math.Abs(a[i*lda+j])
+				if math.IsNaN(v) {
+					return math.NaN()
+				}
+				if v > max {
+					max = v
+				}
+			}
+		}
+		return max
+	case lapack.MaxRowSum, lapack.MaxColumnSum:
+		// A symmetric matrix has the same 1-norm and ∞-norm.
+		for i := 0; i < n; i++ {
+			work[i] = 0
+		}
+		if uplo == blas.Upper {
+			for i := 0; i < n; i++ {
+				work[i] += math.Abs(a[i*lda+i])
+				for j := i + 1; j < n; j++ {
+					v := math.Abs(a[i*lda+j])
+					work[i] += v
+					work[j] += v
+				}
+			}
+		} else {
+			for i := 0; i < n; i++ {
+				for j := 0; j < i; j++ {
+					v := math.Abs(a[i*lda+j])
+					work[i] += v
+					work[j] += v
+				}
+				work[i] += math.Abs(a[i*lda+i])
+			}
+		}
+		var max float64
+		for i := 0; i < n; i++ {
+			v := work[i]
+			if math.IsNaN(v) {
+				return math.NaN()
+			}
+			if v > max {
+				max = v
+			}
+		}
+		return max
+	case lapack.NormFrob:
+		if uplo == blas.Upper {
+			var sum float64
+			for i := 0; i < n; i++ {
+				v := a[i*lda+i]
+				sum += v * v
+				for j := i + 1; j < n; j++ {
+					v := a[i*lda+j]
+					sum += 2 * v * v
+				}
+			}
+			return math.Sqrt(sum)
+		}
+		var sum float64
+		for i := 0; i < n; i++ {
+			for j := 0; j < i; j++ {
+				v := a[i*lda+j]
+				sum += 2 * v * v
+			}
+			v := a[i*lda+i]
+			sum += v * v
+		}
+		return math.Sqrt(sum)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlantr.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlantr.go
new file mode 100644
index 00000000..43cf6fd2
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlantr.go
@@ -0,0 +1,252 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dlantr computes the specified norm of an m×n trapezoidal matrix A. If
+// norm == lapack.MaxColumnSum work must have length at least n, otherwise work
+// is unused.
+func (impl Implementation) Dlantr(norm lapack.MatrixNorm, uplo blas.Uplo, diag blas.Diag, m, n int, a []float64, lda int, work []float64) float64 {
+	checkMatrix(m, n, a, lda)
+	switch norm {
+	case lapack.MaxRowSum, lapack.MaxColumnSum, lapack.NormFrob, lapack.MaxAbs:
+	default:
+		panic(badNorm)
+	}
+	if uplo != blas.Upper && uplo != blas.Lower {
+		panic(badUplo)
+	}
+	if diag != blas.Unit && diag != blas.NonUnit {
+		panic(badDiag)
+	}
+	if norm == lapack.MaxColumnSum && len(work) < n {
+		panic(badWork)
+	}
+	if min(m, n) == 0 {
+		return 0
+	}
+	switch norm {
+	default:
+		panic("unreachable")
+	case lapack.MaxAbs:
+		if diag == blas.Unit {
+			value := 1.0
+			if uplo == blas.Upper {
+				for i := 0; i < m; i++ {
+					for j := i + 1; j < n; j++ {
+						tmp := math.Abs(a[i*lda+j])
+						if math.IsNaN(tmp) {
+							return tmp
+						}
+						if tmp > value {
+							value = tmp
+						}
+					}
+				}
+				return value
+			}
+			for i := 1; i < m; i++ {
+				for j := 0; j < min(i, n); j++ {
+					tmp := math.Abs(a[i*lda+j])
+					if math.IsNaN(tmp) {
+						return tmp
+					}
+					if tmp > value {
+						value = tmp
+					}
+				}
+			}
+			return value
+		}
+		var value float64
+		if uplo == blas.Upper {
+			for i := 0; i < m; i++ {
+				for j := i; j < n; j++ {
+					tmp := math.Abs(a[i*lda+j])
+					if math.IsNaN(tmp) {
+						return tmp
+					}
+					if tmp > value {
+						value = tmp
+					}
+				}
+			}
+			return value
+		}
+		for i := 0; i < m; i++ {
+			for j := 0; j <= min(i, n-1); j++ {
+				tmp := math.Abs(a[i*lda+j])
+				if math.IsNaN(tmp) {
+					return tmp
+				}
+				if tmp > value {
+					value = tmp
+				}
+			}
+		}
+		return value
+	case lapack.MaxColumnSum:
+		if diag == blas.Unit {
+			for i := 0; i < min(m, n); i++ {
+				work[i] = 1
+			}
+			for i := min(m, n); i < n; i++ {
+				work[i] = 0
+			}
+			if uplo == blas.Upper {
+				for i := 0; i < m; i++ {
+					for j := i + 1; j < n; j++ {
+						work[j] += math.Abs(a[i*lda+j])
+					}
+				}
+			} else {
+				for i := 1; i < m; i++ {
+					for j := 0; j < min(i, n); j++ {
+						work[j] += math.Abs(a[i*lda+j])
+					}
+				}
+			}
+		} else {
+			for i := 0; i < n; i++ {
+				work[i] = 0
+			}
+			if uplo == blas.Upper {
+				for i := 0; i < m; i++ {
+					for j := i; j < n; j++ {
+						work[j] += math.Abs(a[i*lda+j])
+					}
+				}
+			} else {
+				for i := 0; i < m; i++ {
+					for j := 0; j <= min(i, n-1); j++ {
+						work[j] += math.Abs(a[i*lda+j])
+					}
+				}
+			}
+		}
+		var max float64
+		for _, v := range work[:n] {
+			if math.IsNaN(v) {
+				return math.NaN()
+			}
+			if v > max {
+				max = v
+			}
+		}
+		return max
+	case lapack.MaxRowSum:
+		var maxsum float64
+		if diag == blas.Unit {
+			if uplo == blas.Upper {
+				for i := 0; i < m; i++ {
+					var sum float64
+					if i < min(m, n) {
+						sum = 1
+					}
+					for j := i + 1; j < n; j++ {
+						sum += math.Abs(a[i*lda+j])
+					}
+					if math.IsNaN(sum) {
+						return math.NaN()
+					}
+					if sum > maxsum {
+						maxsum = sum
+					}
+				}
+				return maxsum
+			} else {
+				for i := 1; i < m; i++ {
+					var sum float64
+					if i < min(m, n) {
+						sum = 1
+					}
+					for j := 0; j < min(i, n); j++ {
+						sum += math.Abs(a[i*lda+j])
+					}
+					if math.IsNaN(sum) {
+						return math.NaN()
+					}
+					if sum > maxsum {
+						maxsum = sum
+					}
+				}
+				return maxsum
+			}
+		} else {
+			if uplo == blas.Upper {
+				for i := 0; i < m; i++ {
+					var sum float64
+					for j := i; j < n; j++ {
+						sum += math.Abs(a[i*lda+j])
+					}
+					if math.IsNaN(sum) {
+						return sum
+					}
+					if sum > maxsum {
+						maxsum = sum
+					}
+				}
+				return maxsum
+			} else {
+				for i := 0; i < m; i++ {
+					var sum float64
+					for j := 0; j <= min(i, n-1); j++ {
+						sum += math.Abs(a[i*lda+j])
+					}
+					if math.IsNaN(sum) {
+						return sum
+					}
+					if sum > maxsum {
+						maxsum = sum
+					}
+				}
+				return maxsum
+			}
+		}
+	case lapack.NormFrob:
+		var nrm float64
+		if diag == blas.Unit {
+			if uplo == blas.Upper {
+				for i := 0; i < m; i++ {
+					for j := i + 1; j < n; j++ {
+						tmp := a[i*lda+j]
+						nrm += tmp * tmp
+					}
+				}
+			} else {
+				for i := 1; i < m; i++ {
+					for j := 0; j < min(i, n); j++ {
+						tmp := a[i*lda+j]
+						nrm += tmp * tmp
+					}
+				}
+			}
+			nrm += float64(min(m, n))
+		} else {
+			if uplo == blas.Upper {
+				for i := 0; i < m; i++ {
+					for j := i; j < n; j++ {
+						tmp := math.Abs(a[i*lda+j])
+						nrm += tmp * tmp
+					}
+				}
+			} else {
+				for i := 0; i < m; i++ {
+					for j := 0; j <= min(i, n-1); j++ {
+						tmp := math.Abs(a[i*lda+j])
+						nrm += tmp * tmp
+					}
+				}
+			}
+		}
+		return math.Sqrt(nrm)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlanv2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlanv2.go
new file mode 100644
index 00000000..1faeba32
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlanv2.go
@@ -0,0 +1,132 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "math"
+
+// Dlanv2 computes the Schur factorization of a real 2×2 matrix:
+//  [ a b ] = [ cs -sn ] * [ aa bb ] * [ cs sn ]
+//  [ c d ]   [ sn  cs ]   [ cc dd ] * [-sn cs ]
+// If cc is zero, aa and dd are real eigenvalues of the matrix. Otherwise it
+// holds that aa = dd and bb*cc < 0, and aa ± sqrt(bb*cc) are complex conjugate
+// eigenvalues. The real and imaginary parts of the eigenvalues are returned in
+// (rt1r,rt1i) and (rt2r,rt2i).
+func (impl Implementation) Dlanv2(a, b, c, d float64) (aa, bb, cc, dd float64, rt1r, rt1i, rt2r, rt2i float64, cs, sn float64) {
+	switch {
+	case c == 0: // Matrix is already upper triangular.
+		aa = a
+		bb = b
+		cc = 0
+		dd = d
+		cs = 1
+		sn = 0
+	case b == 0: // Matrix is lower triangular, swap rows and columns.
+		aa = d
+		bb = -c
+		cc = 0
+		dd = a
+		cs = 0
+		sn = 1
+	case a == d && math.Signbit(b) != math.Signbit(c): // Matrix is already in the standard Schur form.
+		aa = a
+		bb = b
+		cc = c
+		dd = d
+		cs = 1
+		sn = 0
+	default:
+		temp := a - d
+		p := temp / 2
+		bcmax := math.Max(math.Abs(b), math.Abs(c))
+		bcmis := math.Min(math.Abs(b), math.Abs(c))
+		if b*c < 0 {
+			bcmis *= -1
+		}
+		scale := math.Max(math.Abs(p), bcmax)
+		z := p/scale*p + bcmax/scale*bcmis
+		eps := dlamchP
+
+		if z >= 4*eps {
+			// Real eigenvalues. Compute aa and dd.
+			if p > 0 {
+				z = p + math.Sqrt(scale)*math.Sqrt(z)
+			} else {
+				z = p - math.Sqrt(scale)*math.Sqrt(z)
+			}
+			aa = d + z
+			dd = d - bcmax/z*bcmis
+			// Compute bb and the rotation matrix.
+			tau := impl.Dlapy2(c, z)
+			cs = z / tau
+			sn = c / tau
+			bb = b - c
+			cc = 0
+		} else {
+			// Complex eigenvalues, or real (almost) equal eigenvalues.
+			// Make diagonal elements equal.
+			sigma := b + c
+			tau := impl.Dlapy2(sigma, temp)
+			cs = math.Sqrt((1 + math.Abs(sigma)/tau) / 2)
+			sn = -p / (tau * cs)
+			if sigma < 0 {
+				sn *= -1
+			}
+			// Compute [ aa bb ] = [ a b ] [ cs -sn ]
+			//         [ cc dd ]   [ c d ] [ sn  cs ]
+			aa = a*cs + b*sn
+			bb = -a*sn + b*cs
+			cc = c*cs + d*sn
+			dd = -c*sn + d*cs
+			// Compute [ a b ] = [ cs sn ] [ aa bb ]
+			//         [ c d ]   [-sn cs ] [ cc dd ]
+			a = aa*cs + cc*sn
+			b = bb*cs + dd*sn
+			c = -aa*sn + cc*cs
+			d = -bb*sn + dd*cs
+
+			temp = (a + d) / 2
+			aa = temp
+			bb = b
+			cc = c
+			dd = temp
+
+			if cc != 0 {
+				if bb != 0 {
+					if math.Signbit(bb) == math.Signbit(cc) {
+						// Real eigenvalues, reduce to
+						// upper triangular form.
+						sab := math.Sqrt(math.Abs(bb))
+						sac := math.Sqrt(math.Abs(cc))
+						p = sab * sac
+						if cc < 0 {
+							p *= -1
+						}
+						tau = 1 / math.Sqrt(math.Abs(bb+cc))
+						aa = temp + p
+						bb = bb - cc
+						cc = 0
+						dd = temp - p
+						cs1 := sab * tau
+						sn1 := sac * tau
+						cs, sn = cs*cs1-sn*sn1, cs*sn1+sn+cs1
+					}
+				} else {
+					bb = -cc
+					cc = 0
+					cs, sn = -sn, cs
+				}
+			}
+		}
+	}
+
+	// Store eigenvalues in (rt1r,rt1i) and (rt2r,rt2i).
+	rt1r = aa
+	rt2r = dd
+	if cc != 0 {
+		rt1i = math.Sqrt(math.Abs(bb)) * math.Sqrt(math.Abs(cc))
+		rt2i = -rt1i
+	}
+	return
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlapll.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlapll.go
new file mode 100644
index 00000000..990e90d2
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlapll.go
@@ -0,0 +1,36 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "gonum.org/v1/gonum/blas/blas64"
+
+// Dlapll returns the smallest singular value of the n×2 matrix A = [ x y ].
+// The function first computes the QR factorization of A = Q*R, and then computes
+// the SVD of the 2-by-2 upper triangular matrix r.
+//
+// The contents of x and y are overwritten during the call.
+//
+// Dlapll is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlapll(n int, x []float64, incX int, y []float64, incY int) float64 {
+	checkVector(n, x, incX)
+	checkVector(n, y, incY)
+
+	if n <= 1 {
+		return 0
+	}
+
+	// Compute the QR factorization of the N-by-2 matrix [ X Y ].
+	a00, tau := impl.Dlarfg(n, x[0], x[incX:], incX)
+	x[0] = 1
+
+	bi := blas64.Implementation()
+	c := -tau * bi.Ddot(n, x, incX, y, incY)
+	bi.Daxpy(n, c, x, incX, y, incY)
+	a11, _ := impl.Dlarfg(n-1, y[incY], y[2*incY:], incY)
+
+	// Compute the SVD of 2-by-2 upper triangular matrix.
+	ssmin, _ := impl.Dlas2(a00, y[0], a11)
+	return ssmin
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlapmt.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlapmt.go
new file mode 100644
index 00000000..98331f5b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlapmt.go
@@ -0,0 +1,72 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "gonum.org/v1/gonum/blas/blas64"
+
+// Dlapmt rearranges the columns of the m×n matrix X as specified by the
+// permutation k_0, k_1, ..., k_n-1 of the integers 0, ..., n-1.
+//
+// If forward is true a forward permutation is performed:
+//
+//  X[0:m, k[j]] is moved to X[0:m, j] for j = 0, 1, ..., n-1.
+//
+// otherwise a backward permutation is performed:
+//
+//  X[0:m, j] is moved to X[0:m, k[j]] for j = 0, 1, ..., n-1.
+//
+// k must have length n, otherwise Dlapmt will panic. k is zero-indexed.
+func (impl Implementation) Dlapmt(forward bool, m, n int, x []float64, ldx int, k []int) {
+	checkMatrix(m, n, x, ldx)
+	if len(k) != n {
+		panic(badKperm)
+	}
+
+	if n <= 1 {
+		return
+	}
+
+	for i, v := range k {
+		v++
+		k[i] = -v
+	}
+
+	bi := blas64.Implementation()
+
+	if forward {
+		for j, v := range k {
+			if v >= 0 {
+				continue
+			}
+			k[j] = -v
+			i := -v - 1
+			for k[i] < 0 {
+				bi.Dswap(m, x[j:], ldx, x[i:], ldx)
+
+				k[i] = -k[i]
+				j = i
+				i = k[i] - 1
+			}
+		}
+	} else {
+		for i, v := range k {
+			if v >= 0 {
+				continue
+			}
+			k[i] = -v
+			j := -v - 1
+			for j != i {
+				bi.Dswap(m, x[j:], ldx, x[i:], ldx)
+
+				k[j] = -k[j]
+				j = k[j] - 1
+			}
+		}
+	}
+
+	for i := range k {
+		k[i]--
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlapy2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlapy2.go
new file mode 100644
index 00000000..cbc63210
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlapy2.go
@@ -0,0 +1,14 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "math"
+
+// Dlapy2 is the LAPACK version of math.Hypot.
+//
+// Dlapy2 is an internal routine. It is exported for testing purposes.
+func (Implementation) Dlapy2(x, y float64) float64 {
+	return math.Hypot(x, y)
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlaqp2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlaqp2.go
new file mode 100644
index 00000000..8b2118b1
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlaqp2.go
@@ -0,0 +1,111 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dlaqp2 computes a QR factorization with column pivoting of the block A[offset:m, 0:n]
+// of the m×n matrix A. The block A[0:offset, 0:n] is accordingly pivoted, but not factorized.
+//
+// On exit, the upper triangle of block A[offset:m, 0:n] is the triangular factor obtained.
+// The elements in block A[offset:m, 0:n] below the diagonal, together with tau, represent
+// the orthogonal matrix Q as a product of elementary reflectors.
+//
+// offset is number of rows of the matrix A that must be pivoted but not factorized.
+// offset must not be negative otherwise Dlaqp2 will panic.
+//
+// On exit, jpvt holds the permutation that was applied; the jth column of A*P was the
+// jpvt[j] column of A. jpvt must have length n, otherwise Dlaqp2 will panic.
+//
+// On exit tau holds the scalar factors of the elementary reflectors. It must have length
+// at least min(m-offset, n) otherwise Dlaqp2 will panic.
+//
+// vn1 and vn2 hold the partial and complete column norms respectively. They must have length n,
+// otherwise Dlaqp2 will panic.
+//
+// work must have length n, otherwise Dlaqp2 will panic.
+//
+// Dlaqp2 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlaqp2(m, n, offset int, a []float64, lda int, jpvt []int, tau, vn1, vn2, work []float64) {
+	checkMatrix(m, n, a, lda)
+	if len(jpvt) != n {
+		panic(badIpiv)
+	}
+	mn := min(m-offset, n)
+	if len(tau) < mn {
+		panic(badTau)
+	}
+	if len(vn1) < n {
+		panic(badVn1)
+	}
+	if len(vn2) < n {
+		panic(badVn2)
+	}
+	if len(work) < n {
+		panic(badWork)
+	}
+
+	tol3z := math.Sqrt(dlamchE)
+
+	bi := blas64.Implementation()
+
+	// Compute factorization.
+	for i := 0; i < mn; i++ {
+		offpi := offset + i
+
+		// Determine ith pivot column and swap if necessary.
+		p := i + bi.Idamax(n-i, vn1[i:], 1)
+		if p != i {
+			bi.Dswap(m, a[p:], lda, a[i:], lda)
+			jpvt[p], jpvt[i] = jpvt[i], jpvt[p]
+			vn1[p] = vn1[i]
+			vn2[p] = vn2[i]
+		}
+
+		// Generate elementary reflector H_i.
+		if offpi < m-1 {
+			a[offpi*lda+i], tau[i] = impl.Dlarfg(m-offpi, a[offpi*lda+i], a[(offpi+1)*lda+i:], lda)
+		} else {
+			tau[i] = 0
+		}
+
+		if i < n-1 {
+			// Apply H_i^T to A[offset+i:m, i:n] from the left.
+			aii := a[offpi*lda+i]
+			a[offpi*lda+i] = 1
+			impl.Dlarf(blas.Left, m-offpi, n-i-1, a[offpi*lda+i:], lda, tau[i], a[offpi*lda+i+1:], lda, work)
+			a[offpi*lda+i] = aii
+		}
+
+		// Update partial column norms.
+		for j := i + 1; j < n; j++ {
+			if vn1[j] == 0 {
+				continue
+			}
+
+			// The following marked lines follow from the
+			// analysis in Lapack Working Note 176.
+			r := math.Abs(a[offpi*lda+j]) / vn1[j] // *
+			temp := math.Max(0, 1-r*r)             // *
+			r = vn1[j] / vn2[j]                    // *
+			temp2 := temp * r * r                  // *
+			if temp2 < tol3z {
+				var v float64
+				if offpi < m-1 {
+					v = bi.Dnrm2(m-offpi-1, a[(offpi+1)*lda+j:], lda)
+				}
+				vn1[j] = v
+				vn2[j] = v
+			} else {
+				vn1[j] *= math.Sqrt(temp) // *
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlaqps.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlaqps.go
new file mode 100644
index 00000000..d5883c5c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlaqps.go
@@ -0,0 +1,217 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dlaqps computes a step of QR factorization with column pivoting
+// of an m×n matrix A by using Blas-3. It tries to factorize nb
+// columns from A starting from the row offset, and updates all
+// of the matrix with Dgemm.
+//
+// In some cases, due to catastrophic cancellations, it cannot
+// factorize nb columns. Hence, the actual number of factorized
+// columns is returned in kb.
+//
+// Dlaqps computes a QR factorization with column pivoting of the
+// block A[offset:m, 0:nb] of the m×n matrix A. The block
+// A[0:offset, 0:n] is accordingly pivoted, but not factorized.
+//
+// On exit, the upper triangle of block A[offset:m, 0:kb] is the
+// triangular factor obtained. The elements in block A[offset:m, 0:n]
+// below the diagonal, together with tau, represent the orthogonal
+// matrix Q as a product of elementary reflectors.
+//
+// offset is number of rows of the matrix A that must be pivoted but
+// not factorized. offset must not be negative otherwise Dlaqps will panic.
+//
+// On exit, jpvt holds the permutation that was applied; the jth column
+// of A*P was the jpvt[j] column of A. jpvt must have length n,
+// otherwise Dlapqs will panic.
+//
+// On exit tau holds the scalar factors of the elementary reflectors.
+// It must have length nb, otherwise Dlapqs will panic.
+//
+// vn1 and vn2 hold the partial and complete column norms respectively.
+// They must have length n, otherwise Dlapqs will panic.
+//
+// auxv must have length nb, otherwise Dlaqps will panic.
+//
+// f and ldf represent an n×nb matrix F that is overwritten during the
+// call.
+//
+// Dlaqps is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlaqps(m, n, offset, nb int, a []float64, lda int, jpvt []int, tau, vn1, vn2, auxv, f []float64, ldf int) (kb int) {
+	checkMatrix(m, n, a, lda)
+	checkMatrix(n, nb, f, ldf)
+	if offset > m {
+		panic(offsetGTM)
+	}
+	if n < 0 || nb > n {
+		panic(badNb)
+	}
+	if len(jpvt) != n {
+		panic(badIpiv)
+	}
+	if len(tau) < nb {
+		panic(badTau)
+	}
+	if len(vn1) < n {
+		panic(badVn1)
+	}
+	if len(vn2) < n {
+		panic(badVn2)
+	}
+	if len(auxv) < nb {
+		panic(badAuxv)
+	}
+
+	lastrk := min(m, n+offset)
+	lsticc := -1
+	tol3z := math.Sqrt(dlamchE)
+
+	bi := blas64.Implementation()
+
+	var k, rk int
+	for ; k < nb && lsticc == -1; k++ {
+		rk = offset + k
+
+		// Determine kth pivot column and swap if necessary.
+		p := k + bi.Idamax(n-k, vn1[k:], 1)
+		if p != k {
+			bi.Dswap(m, a[p:], lda, a[k:], lda)
+			bi.Dswap(k, f[p*ldf:], 1, f[k*ldf:], 1)
+			jpvt[p], jpvt[k] = jpvt[k], jpvt[p]
+			vn1[p] = vn1[k]
+			vn2[p] = vn2[k]
+		}
+
+		// Apply previous Householder reflectors to column K:
+		//
+		// A[rk:m, k] = A[rk:m, k] - A[rk:m, 0:k-1]*F[k, 0:k-1]^T.
+		if k > 0 {
+			bi.Dgemv(blas.NoTrans, m-rk, k, -1,
+				a[rk*lda:], lda,
+				f[k*ldf:], 1,
+				1,
+				a[rk*lda+k:], lda)
+		}
+
+		// Generate elementary reflector H_k.
+		if rk < m-1 {
+			a[rk*lda+k], tau[k] = impl.Dlarfg(m-rk, a[rk*lda+k], a[(rk+1)*lda+k:], lda)
+		} else {
+			tau[k] = 0
+		}
+
+		akk := a[rk*lda+k]
+		a[rk*lda+k] = 1
+
+		// Compute kth column of F:
+		//
+		// Compute F[k+1:n, k] = tau[k]*A[rk:m, k+1:n]^T*A[rk:m, k].
+		if k < n-1 {
+			bi.Dgemv(blas.Trans, m-rk, n-k-1, tau[k],
+				a[rk*lda+k+1:], lda,
+				a[rk*lda+k:], lda,
+				0,
+				f[(k+1)*ldf+k:], ldf)
+		}
+
+		// Padding F[0:k, k] with zeros.
+		for j := 0; j < k; j++ {
+			f[j*ldf+k] = 0
+		}
+
+		// Incremental updating of F:
+		//
+		// F[0:n, k] := F[0:n, k] - tau[k]*F[0:n, 0:k-1]*A[rk:m, 0:k-1]^T*A[rk:m,k].
+		if k > 0 {
+			bi.Dgemv(blas.Trans, m-rk, k, -tau[k],
+				a[rk*lda:], lda,
+				a[rk*lda+k:], lda,
+				0,
+				auxv, 1)
+			bi.Dgemv(blas.NoTrans, n, k, 1,
+				f, ldf,
+				auxv, 1,
+				1,
+				f[k:], ldf)
+		}
+
+		// Update the current row of A:
+		//
+		// A[rk, k+1:n] = A[rk, k+1:n] - A[rk, 0:k]*F[k+1:n, 0:k]^T.
+		if k < n-1 {
+			bi.Dgemv(blas.NoTrans, n-k-1, k+1, -1,
+				f[(k+1)*ldf:], ldf,
+				a[rk*lda:], 1,
+				1,
+				a[rk*lda+k+1:], 1)
+		}
+
+		// Update partial column norms.
+		if rk < lastrk-1 {
+			for j := k + 1; j < n; j++ {
+				if vn1[j] == 0 {
+					continue
+				}
+
+				// The following marked lines follow from the
+				// analysis in Lapack Working Note 176.
+				r := math.Abs(a[rk*lda+j]) / vn1[j] // *
+				temp := math.Max(0, 1-r*r)          // *
+				r = vn1[j] / vn2[j]                 // *
+				temp2 := temp * r * r               // *
+				if temp2 < tol3z {
+					// vn2 is used here as a collection of
+					// indices into vn2 and also a collection
+					// of column norms.
+					vn2[j] = float64(lsticc)
+					lsticc = j
+				} else {
+					vn1[j] *= math.Sqrt(temp) // *
+				}
+			}
+		}
+
+		a[rk*lda+k] = akk
+	}
+	kb = k
+	rk = offset + kb
+
+	// Apply the block reflector to the rest of the matrix:
+	//
+	// A[offset+kb+1:m, kb+1:n] := A[offset+kb+1:m, kb+1:n] - A[offset+kb+1:m, 1:kb]*F[kb+1:n, 1:kb]^T.
+	if kb < min(n, m-offset) {
+		bi.Dgemm(blas.NoTrans, blas.Trans,
+			m-rk, n-kb, kb, -1,
+			a[rk*lda:], lda,
+			f[kb*ldf:], ldf,
+			1,
+			a[rk*lda+kb:], lda)
+	}
+
+	// Recomputation of difficult columns.
+	for lsticc >= 0 {
+		itemp := int(vn2[lsticc])
+
+		// NOTE: The computation of vn1[lsticc] relies on the fact that
+		// Dnrm2 does not fail on vectors with norm below the value of
+		// sqrt(dlamchS)
+		v := bi.Dnrm2(m-rk, a[rk*lda+lsticc:], lda)
+		vn1[lsticc] = v
+		vn2[lsticc] = v
+
+		lsticc = itemp
+	}
+
+	return kb
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlaqr04.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlaqr04.go
new file mode 100644
index 00000000..6db4d98d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlaqr04.go
@@ -0,0 +1,475 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+// Dlaqr04 computes the eigenvalues of a block of an n×n upper Hessenberg matrix
+// H, and optionally the matrices T and Z from the Schur decomposition
+//  H = Z T Z^T
+// where T is an upper quasi-triangular matrix (the Schur form), and Z is the
+// orthogonal matrix of Schur vectors.
+//
+// wantt indicates whether the full Schur form T is required. If wantt is false,
+// then only enough of H will be updated to preserve the eigenvalues.
+//
+// wantz indicates whether the n×n matrix of Schur vectors Z is required. If it
+// is true, the orthogonal similarity transformation will be accumulated into
+// Z[iloz:ihiz+1,ilo:ihi+1], otherwise Z will not be referenced.
+//
+// ilo and ihi determine the block of H on which Dlaqr04 operates. It must hold that
+//  0 <= ilo <= ihi < n,     if n > 0,
+//  ilo == 0 and ihi == -1,  if n == 0,
+// and the block must be isolated, that is,
+//  ilo == 0   or H[ilo,ilo-1] == 0,
+//  ihi == n-1 or H[ihi+1,ihi] == 0,
+// otherwise Dlaqr04 will panic.
+//
+// wr and wi must have length ihi+1.
+//
+// iloz and ihiz specify the rows of Z to which transformations will be applied
+// if wantz is true. It must hold that
+//  0 <= iloz <= ilo,  and  ihi <= ihiz < n,
+// otherwise Dlaqr04 will panic.
+//
+// work must have length at least lwork and lwork must be
+//  lwork >= 1,  if n <= 11,
+//  lwork >= n,  if n > 11,
+// otherwise Dlaqr04 will panic. lwork as large as 6*n may be required for
+// optimal performance. On return, work[0] will contain the optimal value of
+// lwork.
+//
+// If lwork is -1, instead of performing Dlaqr04, the function only estimates the
+// optimal workspace size and stores it into work[0]. Neither h nor z are
+// accessed.
+//
+// recur is the non-negative recursion depth. For recur > 0, Dlaqr04 behaves
+// as DLAQR0, for recur == 0 it behaves as DLAQR4.
+//
+// unconverged indicates whether Dlaqr04 computed all the eigenvalues of H[ilo:ihi+1,ilo:ihi+1].
+//
+// If unconverged is zero and wantt is true, H will contain on return the upper
+// quasi-triangular matrix T from the Schur decomposition. 2×2 diagonal blocks
+// (corresponding to complex conjugate pairs of eigenvalues) will be returned in
+// standard form, with H[i,i] == H[i+1,i+1] and H[i+1,i]*H[i,i+1] < 0.
+//
+// If unconverged is zero and if wantt is false, the contents of h on return is
+// unspecified.
+//
+// If unconverged is zero, all the eigenvalues have been computed and their real
+// and imaginary parts will be stored on return in wr[ilo:ihi+1] and
+// wi[ilo:ihi+1], respectively. If two eigenvalues are computed as a complex
+// conjugate pair, they are stored in consecutive elements of wr and wi, say the
+// i-th and (i+1)th, with wi[i] > 0 and wi[i+1] < 0. If wantt is true, then the
+// eigenvalues are stored in the same order as on the diagonal of the Schur form
+// returned in H, with wr[i] = H[i,i] and, if H[i:i+2,i:i+2] is a 2×2 diagonal
+// block, wi[i] = sqrt(-H[i+1,i]*H[i,i+1]) and wi[i+1] = -wi[i].
+//
+// If unconverged is positive, some eigenvalues have not converged, and
+// wr[unconverged:ihi+1] and wi[unconverged:ihi+1] will contain those
+// eigenvalues which have been successfully computed. Failures are rare.
+//
+// If unconverged is positive and wantt is true, then on return
+//  (initial H)*U = U*(final H),   (*)
+// where U is an orthogonal matrix. The final H is upper Hessenberg and
+// H[unconverged:ihi+1,unconverged:ihi+1] is upper quasi-triangular.
+//
+// If unconverged is positive and wantt is false, on return the remaining
+// unconverged eigenvalues are the eigenvalues of the upper Hessenberg matrix
+// H[ilo:unconverged,ilo:unconverged].
+//
+// If unconverged is positive and wantz is true, then on return
+//  (final Z) = (initial Z)*U,
+// where U is the orthogonal matrix in (*) regardless of the value of wantt.
+//
+// References:
+//  [1] K. Braman, R. Byers, R. Mathias. The Multishift QR Algorithm. Part I:
+//      Maintaining Well-Focused Shifts and Level 3 Performance. SIAM J. Matrix
+//      Anal. Appl. 23(4) (2002), pp. 929—947
+//      URL: http://dx.doi.org/10.1137/S0895479801384573
+//  [2] K. Braman, R. Byers, R. Mathias. The Multishift QR Algorithm. Part II:
+//      Aggressive Early Deflation. SIAM J. Matrix Anal. Appl. 23(4) (2002), pp. 948—973
+//      URL: http://dx.doi.org/10.1137/S0895479801384585
+//
+// Dlaqr04 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlaqr04(wantt, wantz bool, n, ilo, ihi int, h []float64, ldh int, wr, wi []float64, iloz, ihiz int, z []float64, ldz int, work []float64, lwork int, recur int) (unconverged int) {
+	const (
+		// Matrices of order ntiny or smaller must be processed by
+		// Dlahqr because of insufficient subdiagonal scratch space.
+		// This is a hard limit.
+		ntiny = 11
+		// Exceptional deflation windows: try to cure rare slow
+		// convergence by varying the size of the deflation window after
+		// kexnw iterations.
+		kexnw = 5
+		// Exceptional shifts: try to cure rare slow convergence with
+		// ad-hoc exceptional shifts every kexsh iterations.
+		kexsh = 6
+
+		// See https://github.com/gonum/lapack/pull/151#discussion_r68162802
+		// and the surrounding discussion for an explanation where these
+		// constants come from.
+		// TODO(vladimir-ch): Similar constants for exceptional shifts
+		// are used also in dlahqr.go. The first constant is different
+		// there, it is equal to 3. Why? And does it matter?
+		wilk1 = 0.75
+		wilk2 = -0.4375
+	)
+
+	switch {
+	case ilo < 0 || max(0, n-1) < ilo:
+		panic(badIlo)
+	case ihi < min(ilo, n-1) || n <= ihi:
+		panic(badIhi)
+	case lwork < 1 && n <= ntiny && lwork != -1:
+		panic(badWork)
+	// TODO(vladimir-ch): Enable if and when we figure out what the minimum
+	// necessary lwork value is. Dlaqr04 says that the minimum is n which
+	// clashes with Dlaqr23's opinion about optimal work when nw <= 2
+	// (independent of n).
+	// case lwork < n && n > ntiny && lwork != -1:
+	// 	panic(badWork)
+	case len(work) < lwork:
+		panic(shortWork)
+	case recur < 0:
+		panic("lapack: recur is negative")
+	}
+	if wantz {
+		if iloz < 0 || ilo < iloz {
+			panic("lapack: invalid value of iloz")
+		}
+		if ihiz < ihi || n <= ihiz {
+			panic("lapack: invalid value of ihiz")
+		}
+	}
+	if lwork != -1 {
+		checkMatrix(n, n, h, ldh)
+		if wantz {
+			checkMatrix(n, n, z, ldz)
+		}
+		switch {
+		case ilo > 0 && h[ilo*ldh+ilo-1] != 0:
+			panic("lapack: block not isolated")
+		case ihi+1 < n && h[(ihi+1)*ldh+ihi] != 0:
+			panic("lapack: block not isolated")
+		case len(wr) != ihi+1:
+			panic("lapack: bad length of wr")
+		case len(wi) != ihi+1:
+			panic("lapack: bad length of wi")
+		}
+	}
+
+	// Quick return.
+	if n == 0 {
+		work[0] = 1
+		return 0
+	}
+
+	if n <= ntiny {
+		// Tiny matrices must use Dlahqr.
+		work[0] = 1
+		if lwork == -1 {
+			return 0
+		}
+		return impl.Dlahqr(wantt, wantz, n, ilo, ihi, h, ldh, wr, wi, iloz, ihiz, z, ldz)
+	}
+
+	// Use small bulge multi-shift QR with aggressive early deflation on
+	// larger-than-tiny matrices.
+	var jbcmpz string
+	if wantt {
+		jbcmpz = "S"
+	} else {
+		jbcmpz = "E"
+	}
+	if wantz {
+		jbcmpz += "V"
+	} else {
+		jbcmpz += "N"
+	}
+
+	var fname string
+	if recur > 0 {
+		fname = "DLAQR0"
+	} else {
+		fname = "DLAQR4"
+	}
+	// nwr is the recommended deflation window size. n is greater than 11,
+	// so there is enough subdiagonal workspace for nwr >= 2 as required.
+	// (In fact, there is enough subdiagonal space for nwr >= 3.)
+	// TODO(vladimir-ch): If there is enough space for nwr >= 3, should we
+	// use it?
+	nwr := impl.Ilaenv(13, fname, jbcmpz, n, ilo, ihi, lwork)
+	nwr = max(2, nwr)
+	nwr = min(ihi-ilo+1, min((n-1)/3, nwr))
+
+	// nsr is the recommended number of simultaneous shifts. n is greater
+	// than 11, so there is enough subdiagonal workspace for nsr to be even
+	// and greater than or equal to two as required.
+	nsr := impl.Ilaenv(15, fname, jbcmpz, n, ilo, ihi, lwork)
+	nsr = min(nsr, min((n+6)/9, ihi-ilo))
+	nsr = max(2, nsr&^1)
+
+	// Workspace query call to Dlaqr23.
+	impl.Dlaqr23(wantt, wantz, n, ilo, ihi, nwr+1, nil, 0, iloz, ihiz, nil, 0,
+		nil, nil, nil, 0, n, nil, 0, n, nil, 0, work, -1, recur)
+	// Optimal workspace is max(Dlaqr5, Dlaqr23).
+	lwkopt := max(3*nsr/2, int(work[0]))
+	// Quick return in case of workspace query.
+	if lwork == -1 {
+		work[0] = float64(lwkopt)
+		return 0
+	}
+
+	// Dlahqr/Dlaqr04 crossover point.
+	nmin := impl.Ilaenv(12, fname, jbcmpz, n, ilo, ihi, lwork)
+	nmin = max(ntiny, nmin)
+
+	// Nibble determines when to skip a multi-shift QR sweep (Dlaqr5).
+	nibble := impl.Ilaenv(14, fname, jbcmpz, n, ilo, ihi, lwork)
+	nibble = max(0, nibble)
+
+	// Computation mode of far-from-diagonal orthogonal updates in Dlaqr5.
+	kacc22 := impl.Ilaenv(16, fname, jbcmpz, n, ilo, ihi, lwork)
+	kacc22 = max(0, min(kacc22, 2))
+
+	// nwmax is the largest possible deflation window for which there is
+	// sufficient workspace.
+	nwmax := min((n-1)/3, lwork/2)
+	nw := nwmax // Start with maximum deflation window size.
+
+	// nsmax is the largest number of simultaneous shifts for which there is
+	// sufficient workspace.
+	nsmax := min((n+6)/9, 2*lwork/3) &^ 1
+
+	ndfl := 1 // Number of iterations since last deflation.
+	ndec := 0 // Deflation window size decrement.
+
+	// Main loop.
+	var (
+		itmax = max(30, 2*kexsh) * max(10, (ihi-ilo+1))
+		it    = 0
+	)
+	for kbot := ihi; kbot >= ilo; {
+		if it == itmax {
+			unconverged = kbot + 1
+			break
+		}
+		it++
+
+		// Locate active block.
+		ktop := ilo
+		for k := kbot; k >= ilo+1; k-- {
+			if h[k*ldh+k-1] == 0 {
+				ktop = k
+				break
+			}
+		}
+
+		// Select deflation window size nw.
+		//
+		// Typical Case:
+		//  If possible and advisable, nibble the entire active block.
+		//  If not, use size min(nwr,nwmax) or min(nwr+1,nwmax)
+		//  depending upon which has the smaller corresponding
+		//  subdiagonal entry (a heuristic).
+		//
+		// Exceptional Case:
+		//  If there have been no deflations in kexnw or more
+		//  iterations, then vary the deflation window size. At first,
+		//  because larger windows are, in general, more powerful than
+		//  smaller ones, rapidly increase the window to the maximum
+		//  possible. Then, gradually reduce the window size.
+		nh := kbot - ktop + 1
+		nwupbd := min(nh, nwmax)
+		if ndfl < kexnw {
+			nw = min(nwupbd, nwr)
+		} else {
+			nw = min(nwupbd, 2*nw)
+		}
+		if nw < nwmax {
+			if nw >= nh-1 {
+				nw = nh
+			} else {
+				kwtop := kbot - nw + 1
+				if math.Abs(h[kwtop*ldh+kwtop-1]) > math.Abs(h[(kwtop-1)*ldh+kwtop-2]) {
+					nw++
+				}
+			}
+		}
+		if ndfl < kexnw {
+			ndec = -1
+		} else if ndec >= 0 || nw >= nwupbd {
+			ndec++
+			if nw-ndec < 2 {
+				ndec = 0
+			}
+			nw -= ndec
+		}
+
+		// Split workspace under the subdiagonal of H into:
+		//  - an nw×nw work array V in the lower left-hand corner,
+		//  - an nw×nhv horizontal work array along the bottom edge (nhv
+		//    must be at least nw but more is better),
+		//  - an nve×nw vertical work array along the left-hand-edge
+		//    (nhv can be any positive integer but more is better).
+		kv := n - nw
+		kt := nw
+		kwv := nw + 1
+		nhv := n - kwv - kt
+		// Aggressive early deflation.
+		ls, ld := impl.Dlaqr23(wantt, wantz, n, ktop, kbot, nw,
+			h, ldh, iloz, ihiz, z, ldz, wr[:kbot+1], wi[:kbot+1],
+			h[kv*ldh:], ldh, nhv, h[kv*ldh+kt:], ldh, nhv, h[kwv*ldh:], ldh, work, lwork, recur)
+
+		// Adjust kbot accounting for new deflations.
+		kbot -= ld
+		// ks points to the shifts.
+		ks := kbot - ls + 1
+
+		// Skip an expensive QR sweep if there is a (partly heuristic)
+		// reason to expect that many eigenvalues will deflate without
+		// it. Here, the QR sweep is skipped if many eigenvalues have
+		// just been deflated or if the remaining active block is small.
+		if ld > 0 && (100*ld > nw*nibble || kbot-ktop+1 <= min(nmin, nwmax)) {
+			// ld is positive, note progress.
+			ndfl = 1
+			continue
+		}
+
+		// ns is the nominal number of simultaneous shifts. This may be
+		// lowered (slightly) if Dlaqr23 did not provide that many
+		// shifts.
+		ns := min(min(nsmax, nsr), max(2, kbot-ktop)) &^ 1
+
+		// If there have been no deflations in a multiple of kexsh
+		// iterations, then try exceptional shifts. Otherwise use shifts
+		// provided by Dlaqr23 above or from the eigenvalues of a
+		// trailing principal submatrix.
+		if ndfl%kexsh == 0 {
+			ks = kbot - ns + 1
+			for i := kbot; i > max(ks, ktop+1); i -= 2 {
+				ss := math.Abs(h[i*ldh+i-1]) + math.Abs(h[(i-1)*ldh+i-2])
+				aa := wilk1*ss + h[i*ldh+i]
+				_, _, _, _, wr[i-1], wi[i-1], wr[i], wi[i], _, _ =
+					impl.Dlanv2(aa, ss, wilk2*ss, aa)
+			}
+			if ks == ktop {
+				wr[ks+1] = h[(ks+1)*ldh+ks+1]
+				wi[ks+1] = 0
+				wr[ks] = wr[ks+1]
+				wi[ks] = wi[ks+1]
+			}
+		} else {
+			// If we got ns/2 or fewer shifts, use Dlahqr or recur
+			// into Dlaqr04 on a trailing principal submatrix to get
+			// more. Since ns <= nsmax <=(n+6)/9, there is enough
+			// space below the subdiagonal to fit an ns×ns scratch
+			// array.
+			if kbot-ks+1 <= ns/2 {
+				ks = kbot - ns + 1
+				kt = n - ns
+				impl.Dlacpy(blas.All, ns, ns, h[ks*ldh+ks:], ldh, h[kt*ldh:], ldh)
+				if ns > nmin && recur > 0 {
+					ks += impl.Dlaqr04(false, false, ns, 1, ns-1, h[kt*ldh:], ldh,
+						wr[ks:ks+ns], wi[ks:ks+ns], 0, 0, nil, 0, work, lwork, recur-1)
+				} else {
+					ks += impl.Dlahqr(false, false, ns, 0, ns-1, h[kt*ldh:], ldh,
+						wr[ks:ks+ns], wi[ks:ks+ns], 0, 0, nil, 0)
+				}
+				// In case of a rare QR failure use eigenvalues
+				// of the trailing 2×2 principal submatrix.
+				if ks >= kbot {
+					aa := h[(kbot-1)*ldh+kbot-1]
+					bb := h[(kbot-1)*ldh+kbot]
+					cc := h[kbot*ldh+kbot-1]
+					dd := h[kbot*ldh+kbot]
+					_, _, _, _, wr[kbot-1], wi[kbot-1], wr[kbot], wi[kbot], _, _ =
+						impl.Dlanv2(aa, bb, cc, dd)
+					ks = kbot - 1
+				}
+			}
+
+			if kbot-ks+1 > ns {
+				// Sorting the shifts helps a little. Bubble
+				// sort keeps complex conjugate pairs together.
+				sorted := false
+				for k := kbot; k > ks; k-- {
+					if sorted {
+						break
+					}
+					sorted = true
+					for i := ks; i < k; i++ {
+						if math.Abs(wr[i])+math.Abs(wi[i]) >= math.Abs(wr[i+1])+math.Abs(wi[i+1]) {
+							continue
+						}
+						sorted = false
+						wr[i], wr[i+1] = wr[i+1], wr[i]
+						wi[i], wi[i+1] = wi[i+1], wi[i]
+					}
+				}
+			}
+
+			// Shuffle shifts into pairs of real shifts and pairs of
+			// complex conjugate shifts using the fact that complex
+			// conjugate shifts are already adjacent to one another.
+			// TODO(vladimir-ch): The shuffling here could probably
+			// be removed but I'm not sure right now and it's safer
+			// to leave it.
+			for i := kbot; i > ks+1; i -= 2 {
+				if wi[i] == -wi[i-1] {
+					continue
+				}
+				wr[i], wr[i-1], wr[i-2] = wr[i-1], wr[i-2], wr[i]
+				wi[i], wi[i-1], wi[i-2] = wi[i-1], wi[i-2], wi[i]
+			}
+		}
+
+		// If there are only two shifts and both are real, then use only one.
+		if kbot-ks+1 == 2 && wi[kbot] == 0 {
+			if math.Abs(wr[kbot]-h[kbot*ldh+kbot]) < math.Abs(wr[kbot-1]-h[kbot*ldh+kbot]) {
+				wr[kbot-1] = wr[kbot]
+			} else {
+				wr[kbot] = wr[kbot-1]
+			}
+		}
+
+		// Use up to ns of the the smallest magnitude shifts. If there
+		// aren't ns shifts available, then use them all, possibly
+		// dropping one to make the number of shifts even.
+		ns = min(ns, kbot-ks+1) &^ 1
+		ks = kbot - ns + 1
+
+		// Split workspace under the subdiagonal into:
+		// - a kdu×kdu work array U in the lower left-hand-corner,
+		// - a kdu×nhv horizontal work array WH along the bottom edge
+		//   (nhv must be at least kdu but more is better),
+		// - an nhv×kdu vertical work array WV along the left-hand-edge
+		//   (nhv must be at least kdu but more is better).
+		kdu := 3*ns - 3
+		ku := n - kdu
+		kwh := kdu
+		kwv = kdu + 3
+		nhv = n - kwv - kdu
+		// Small-bulge multi-shift QR sweep.
+		impl.Dlaqr5(wantt, wantz, kacc22, n, ktop, kbot, ns,
+			wr[ks:ks+ns], wi[ks:ks+ns], h, ldh, iloz, ihiz, z, ldz,
+			work, 3, h[ku*ldh:], ldh, nhv, h[kwv*ldh:], ldh, nhv, h[ku*ldh+kwh:], ldh)
+
+		// Note progress (or the lack of it).
+		if ld > 0 {
+			ndfl = 1
+		} else {
+			ndfl++
+		}
+	}
+
+	work[0] = float64(lwkopt)
+	return unconverged
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlaqr1.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlaqr1.go
new file mode 100644
index 00000000..9efd774a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlaqr1.go
@@ -0,0 +1,57 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "math"
+
+// Dlaqr1 sets v to a scalar multiple of the first column of the product
+//  (H - (sr1 + i*si1)*I)*(H - (sr2 + i*si2)*I)
+// where H is a 2×2 or 3×3 matrix, I is the identity matrix of the same size,
+// and i is the imaginary unit. Scaling is done to avoid overflows and most
+// underflows.
+//
+// n is the order of H and must be either 2 or 3. It must hold that either sr1 =
+// sr2 and si1 = -si2, or si1 = si2 = 0. The length of v must be equal to n. If
+// any of these conditions is not met, Dlaqr1 will panic.
+//
+// Dlaqr1 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlaqr1(n int, h []float64, ldh int, sr1, si1, sr2, si2 float64, v []float64) {
+	if n != 2 && n != 3 {
+		panic(badDims)
+	}
+	checkMatrix(n, n, h, ldh)
+	if len(v) != n {
+		panic(badSlice)
+	}
+	if !((sr1 == sr2 && si1 == -si2) || (si1 == 0 && si2 == 0)) {
+		panic(badShifts)
+	}
+
+	if n == 2 {
+		s := math.Abs(h[0]-sr2) + math.Abs(si2) + math.Abs(h[ldh])
+		if s == 0 {
+			v[0] = 0
+			v[1] = 0
+		} else {
+			h21s := h[ldh] / s
+			v[0] = h21s*h[1] + (h[0]-sr1)*((h[0]-sr2)/s) - si1*(si2/s)
+			v[1] = h21s * (h[0] + h[ldh+1] - sr1 - sr2)
+		}
+		return
+	}
+
+	s := math.Abs(h[0]-sr2) + math.Abs(si2) + math.Abs(h[ldh]) + math.Abs(h[2*ldh])
+	if s == 0 {
+		v[0] = 0
+		v[1] = 0
+		v[2] = 0
+	} else {
+		h21s := h[ldh] / s
+		h31s := h[2*ldh] / s
+		v[0] = (h[0]-sr1)*((h[0]-sr2)/s) - si1*(si2/s) + h[1]*h21s + h[2]*h31s
+		v[1] = h21s*(h[0]+h[ldh+1]-sr1-sr2) + h[ldh+2]*h31s
+		v[2] = h31s*(h[0]+h[2*ldh+2]-sr1-sr2) + h21s*h[2*ldh+1]
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlaqr23.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlaqr23.go
new file mode 100644
index 00000000..1a59e4b9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlaqr23.go
@@ -0,0 +1,403 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dlaqr23 performs the orthogonal similarity transformation of an n×n upper
+// Hessenberg matrix to detect and deflate fully converged eigenvalues from a
+// trailing principal submatrix using aggressive early deflation [1].
+//
+// On return, H will be overwritten by a new Hessenberg matrix that is a
+// perturbation of an orthogonal similarity transformation of H. It is hoped
+// that on output H will have many zero subdiagonal entries.
+//
+// If wantt is true, the matrix H will be fully updated so that the
+// quasi-triangular Schur factor can be computed. If wantt is false, then only
+// enough of H will be updated to preserve the eigenvalues.
+//
+// If wantz is true, the orthogonal similarity transformation will be
+// accumulated into Z[iloz:ihiz+1,ktop:kbot+1], otherwise Z is not referenced.
+//
+// ktop and kbot determine a block [ktop:kbot+1,ktop:kbot+1] along the diagonal
+// of H. It must hold that
+//  0 <= ilo <= ihi < n,     if n > 0,
+//  ilo == 0 and ihi == -1,  if n == 0,
+// and the block must be isolated, that is, it must hold that
+//  ktop == 0   or H[ktop,ktop-1] == 0,
+//  kbot == n-1 or H[kbot+1,kbot] == 0,
+// otherwise Dlaqr23 will panic.
+//
+// nw is the deflation window size. It must hold that
+//  0 <= nw <= kbot-ktop+1,
+// otherwise Dlaqr23 will panic.
+//
+// iloz and ihiz specify the rows of the n×n matrix Z to which transformations
+// will be applied if wantz is true. It must hold that
+//  0 <= iloz <= ktop,  and  kbot <= ihiz < n,
+// otherwise Dlaqr23 will panic.
+//
+// sr and si must have length kbot+1, otherwise Dlaqr23 will panic.
+//
+// v and ldv represent an nw×nw work matrix.
+// t and ldt represent an nw×nh work matrix, and nh must be at least nw.
+// wv and ldwv represent an nv×nw work matrix.
+//
+// work must have length at least lwork and lwork must be at least max(1,2*nw),
+// otherwise Dlaqr23 will panic. Larger values of lwork may result in greater
+// efficiency. On return, work[0] will contain the optimal value of lwork.
+//
+// If lwork is -1, instead of performing Dlaqr23, the function only estimates the
+// optimal workspace size and stores it into work[0]. Neither h nor z are
+// accessed.
+//
+// recur is the non-negative recursion depth. For recur > 0, Dlaqr23 behaves
+// as DLAQR3, for recur == 0 it behaves as DLAQR2.
+//
+// On return, ns and nd will contain respectively the number of unconverged
+// (i.e., approximate) eigenvalues and converged eigenvalues that are stored in
+// sr and si.
+//
+// On return, the real and imaginary parts of approximate eigenvalues that may
+// be used for shifts will be stored respectively in sr[kbot-nd-ns+1:kbot-nd+1]
+// and si[kbot-nd-ns+1:kbot-nd+1].
+//
+// On return, the real and imaginary parts of converged eigenvalues will be
+// stored respectively in sr[kbot-nd+1:kbot+1] and si[kbot-nd+1:kbot+1].
+//
+// References:
+//  [1] K. Braman, R. Byers, R. Mathias. The Multishift QR Algorithm. Part II:
+//      Aggressive Early Deflation. SIAM J. Matrix Anal. Appl 23(4) (2002), pp. 948—973
+//      URL: http://dx.doi.org/10.1137/S0895479801384585
+//
+func (impl Implementation) Dlaqr23(wantt, wantz bool, n, ktop, kbot, nw int, h []float64, ldh int, iloz, ihiz int, z []float64, ldz int, sr, si []float64, v []float64, ldv int, nh int, t []float64, ldt int, nv int, wv []float64, ldwv int, work []float64, lwork int, recur int) (ns, nd int) {
+	switch {
+	case ktop < 0 || max(0, n-1) < ktop:
+		panic("lapack: invalid value of ktop")
+	case kbot < min(ktop, n-1) || n <= kbot:
+		panic("lapack: invalid value of kbot")
+	case (nw < 0 || kbot-ktop+1 < nw) && lwork != -1:
+		panic("lapack: invalid value of nw")
+	case nh < nw:
+		panic("lapack: invalid value of nh")
+	case lwork < max(1, 2*nw) && lwork != -1:
+		panic(badWork)
+	case len(work) < lwork:
+		panic(shortWork)
+	case recur < 0:
+		panic("lapack: recur is negative")
+	}
+	if wantz {
+		switch {
+		case iloz < 0 || ktop < iloz:
+			panic("lapack: invalid value of iloz")
+		case ihiz < kbot || n <= ihiz:
+			panic("lapack: invalid value of ihiz")
+		}
+	}
+	if lwork != -1 {
+		// Check input slices only if not doing workspace query.
+		checkMatrix(n, n, h, ldh)
+		checkMatrix(nw, nw, v, ldv)
+		checkMatrix(nw, nh, t, ldt)
+		checkMatrix(nv, nw, wv, ldwv)
+		if wantz {
+			checkMatrix(n, n, z, ldz)
+		}
+		switch {
+		case ktop > 0 && h[ktop*ldh+ktop-1] != 0:
+			panic("lapack: block not isolated")
+		case kbot+1 < n && h[(kbot+1)*ldh+kbot] != 0:
+			panic("lapack: block not isolated")
+		case len(sr) != kbot+1:
+			panic("lapack: bad length of sr")
+		case len(si) != kbot+1:
+			panic("lapack: bad length of si")
+		}
+	}
+
+	// Quick return for zero window size.
+	if nw == 0 {
+		work[0] = 1
+		return 0, 0
+	}
+
+	// LAPACK code does not enforce the documented behavior
+	//  nw <= kbot-ktop+1
+	// but we do (we panic above).
+	jw := nw
+	lwkopt := max(1, 2*nw)
+	if jw > 2 {
+		// Workspace query call to Dgehrd.
+		impl.Dgehrd(jw, 0, jw-2, nil, 0, nil, work, -1)
+		lwk1 := int(work[0])
+		// Workspace query call to Dormhr.
+		impl.Dormhr(blas.Right, blas.NoTrans, jw, jw, 0, jw-2, nil, 0, nil, nil, 0, work, -1)
+		lwk2 := int(work[0])
+		if recur > 0 {
+			// Workspace query call to Dlaqr04.
+			impl.Dlaqr04(true, true, jw, 0, jw-1, nil, 0, nil, nil, 0, jw-1, nil, 0, work, -1, recur-1)
+			lwk3 := int(work[0])
+			// Optimal workspace.
+			lwkopt = max(jw+max(lwk1, lwk2), lwk3)
+		} else {
+			// Optimal workspace.
+			lwkopt = jw + max(lwk1, lwk2)
+		}
+	}
+	// Quick return in case of workspace query.
+	if lwork == -1 {
+		work[0] = float64(lwkopt)
+		return 0, 0
+	}
+
+	// Machine constants.
+	ulp := dlamchP
+	smlnum := float64(n) / ulp * dlamchS
+
+	// Setup deflation window.
+	var s float64
+	kwtop := kbot - jw + 1
+	if kwtop != ktop {
+		s = h[kwtop*ldh+kwtop-1]
+	}
+	if kwtop == kbot {
+		// 1×1 deflation window.
+		sr[kwtop] = h[kwtop*ldh+kwtop]
+		si[kwtop] = 0
+		ns = 1
+		nd = 0
+		if math.Abs(s) <= math.Max(smlnum, ulp*math.Abs(h[kwtop*ldh+kwtop])) {
+			ns = 0
+			nd = 1
+			if kwtop > ktop {
+				h[kwtop*ldh+kwtop-1] = 0
+			}
+		}
+		work[0] = 1
+		return ns, nd
+	}
+
+	// Convert to spike-triangular form. In case of a rare QR failure, this
+	// routine continues to do aggressive early deflation using that part of
+	// the deflation window that converged using infqr here and there to
+	// keep track.
+	impl.Dlacpy(blas.Upper, jw, jw, h[kwtop*ldh+kwtop:], ldh, t, ldt)
+	bi := blas64.Implementation()
+	bi.Dcopy(jw-1, h[(kwtop+1)*ldh+kwtop:], ldh+1, t[ldt:], ldt+1)
+	impl.Dlaset(blas.All, jw, jw, 0, 1, v, ldv)
+	nmin := impl.Ilaenv(12, "DLAQR3", "SV", jw, 0, jw-1, lwork)
+	var infqr int
+	if recur > 0 && jw > nmin {
+		infqr = impl.Dlaqr04(true, true, jw, 0, jw-1, t, ldt, sr[kwtop:], si[kwtop:], 0, jw-1, v, ldv, work, lwork, recur-1)
+	} else {
+		infqr = impl.Dlahqr(true, true, jw, 0, jw-1, t, ldt, sr[kwtop:], si[kwtop:], 0, jw-1, v, ldv)
+	}
+	// Note that ilo == 0 which conveniently coincides with the success
+	// value of infqr, that is, infqr as an index always points to the first
+	// converged eigenvalue.
+
+	// Dtrexc needs a clean margin near the diagonal.
+	for j := 0; j < jw-3; j++ {
+		t[(j+2)*ldt+j] = 0
+		t[(j+3)*ldt+j] = 0
+	}
+	if jw >= 3 {
+		t[(jw-1)*ldt+jw-3] = 0
+	}
+
+	ns = jw
+	ilst := infqr
+	// Deflation detection loop.
+	for ilst < ns {
+		bulge := false
+		if ns >= 2 {
+			bulge = t[(ns-1)*ldt+ns-2] != 0
+		}
+		if !bulge {
+			// Real eigenvalue.
+			abst := math.Abs(t[(ns-1)*ldt+ns-1])
+			if abst == 0 {
+				abst = math.Abs(s)
+			}
+			if math.Abs(s*v[ns-1]) <= math.Max(smlnum, ulp*abst) {
+				// Deflatable.
+				ns--
+			} else {
+				// Undeflatable, move it up out of the way.
+				// Dtrexc can not fail in this case.
+				_, ilst, _ = impl.Dtrexc(lapack.UpdateSchur, jw, t, ldt, v, ldv, ns-1, ilst, work)
+				ilst++
+			}
+			continue
+		}
+		// Complex conjugate pair.
+		abst := math.Abs(t[(ns-1)*ldt+ns-1]) + math.Sqrt(math.Abs(t[(ns-1)*ldt+ns-2]))*math.Sqrt(math.Abs(t[(ns-2)*ldt+ns-1]))
+		if abst == 0 {
+			abst = math.Abs(s)
+		}
+		if math.Max(math.Abs(s*v[ns-1]), math.Abs(s*v[ns-2])) <= math.Max(smlnum, ulp*abst) {
+			// Deflatable.
+			ns -= 2
+		} else {
+			// Undeflatable, move them up out of the way.
+			// Dtrexc does the right thing with ilst in case of a
+			// rare exchange failure.
+			_, ilst, _ = impl.Dtrexc(lapack.UpdateSchur, jw, t, ldt, v, ldv, ns-1, ilst, work)
+			ilst += 2
+		}
+	}
+
+	// Return to Hessenberg form.
+	if ns == 0 {
+		s = 0
+	}
+	if ns < jw {
+		// Sorting diagonal blocks of T improves accuracy for graded
+		// matrices. Bubble sort deals well with exchange failures.
+		sorted := false
+		i := ns
+		for !sorted {
+			sorted = true
+			kend := i - 1
+			i = infqr
+			var k int
+			if i == ns-1 || t[(i+1)*ldt+i] == 0 {
+				k = i + 1
+			} else {
+				k = i + 2
+			}
+			for k <= kend {
+				var evi float64
+				if k == i+1 {
+					evi = math.Abs(t[i*ldt+i])
+				} else {
+					evi = math.Abs(t[i*ldt+i]) + math.Sqrt(math.Abs(t[(i+1)*ldt+i]))*math.Sqrt(math.Abs(t[i*ldt+i+1]))
+				}
+
+				var evk float64
+				if k == kend || t[(k+1)*ldt+k] == 0 {
+					evk = math.Abs(t[k*ldt+k])
+				} else {
+					evk = math.Abs(t[k*ldt+k]) + math.Sqrt(math.Abs(t[(k+1)*ldt+k]))*math.Sqrt(math.Abs(t[k*ldt+k+1]))
+				}
+
+				if evi >= evk {
+					i = k
+				} else {
+					sorted = false
+					_, ilst, ok := impl.Dtrexc(lapack.UpdateSchur, jw, t, ldt, v, ldv, i, k, work)
+					if ok {
+						i = ilst
+					} else {
+						i = k
+					}
+				}
+				if i == kend || t[(i+1)*ldt+i] == 0 {
+					k = i + 1
+				} else {
+					k = i + 2
+				}
+			}
+		}
+	}
+
+	// Restore shift/eigenvalue array from T.
+	for i := jw - 1; i >= infqr; {
+		if i == infqr || t[i*ldt+i-1] == 0 {
+			sr[kwtop+i] = t[i*ldt+i]
+			si[kwtop+i] = 0
+			i--
+			continue
+		}
+		aa := t[(i-1)*ldt+i-1]
+		bb := t[(i-1)*ldt+i]
+		cc := t[i*ldt+i-1]
+		dd := t[i*ldt+i]
+		_, _, _, _, sr[kwtop+i-1], si[kwtop+i-1], sr[kwtop+i], si[kwtop+i], _, _ = impl.Dlanv2(aa, bb, cc, dd)
+		i -= 2
+	}
+
+	if ns < jw || s == 0 {
+		if ns > 1 && s != 0 {
+			// Reflect spike back into lower triangle.
+			bi.Dcopy(ns, v[:ns], 1, work[:ns], 1)
+			_, tau := impl.Dlarfg(ns, work[0], work[1:ns], 1)
+			work[0] = 1
+			impl.Dlaset(blas.Lower, jw-2, jw-2, 0, 0, t[2*ldt:], ldt)
+			impl.Dlarf(blas.Left, ns, jw, work[:ns], 1, tau, t, ldt, work[jw:])
+			impl.Dlarf(blas.Right, ns, ns, work[:ns], 1, tau, t, ldt, work[jw:])
+			impl.Dlarf(blas.Right, jw, ns, work[:ns], 1, tau, v, ldv, work[jw:])
+			impl.Dgehrd(jw, 0, ns-1, t, ldt, work[:jw-1], work[jw:], lwork-jw)
+		}
+
+		// Copy updated reduced window into place.
+		if kwtop > 0 {
+			h[kwtop*ldh+kwtop-1] = s * v[0]
+		}
+		impl.Dlacpy(blas.Upper, jw, jw, t, ldt, h[kwtop*ldh+kwtop:], ldh)
+		bi.Dcopy(jw-1, t[ldt:], ldt+1, h[(kwtop+1)*ldh+kwtop:], ldh+1)
+
+		// Accumulate orthogonal matrix in order to update H and Z, if
+		// requested.
+		if ns > 1 && s != 0 {
+			// work[:ns-1] contains the elementary reflectors stored
+			// by a call to Dgehrd above.
+			impl.Dormhr(blas.Right, blas.NoTrans, jw, ns, 0, ns-1,
+				t, ldt, work[:ns-1], v, ldv, work[jw:], lwork-jw)
+		}
+
+		// Update vertical slab in H.
+		var ltop int
+		if !wantt {
+			ltop = ktop
+		}
+		for krow := ltop; krow < kwtop; krow += nv {
+			kln := min(nv, kwtop-krow)
+			bi.Dgemm(blas.NoTrans, blas.NoTrans, kln, jw, jw,
+				1, h[krow*ldh+kwtop:], ldh, v, ldv,
+				0, wv, ldwv)
+			impl.Dlacpy(blas.All, kln, jw, wv, ldwv, h[krow*ldh+kwtop:], ldh)
+		}
+
+		// Update horizontal slab in H.
+		if wantt {
+			for kcol := kbot + 1; kcol < n; kcol += nh {
+				kln := min(nh, n-kcol)
+				bi.Dgemm(blas.Trans, blas.NoTrans, jw, kln, jw,
+					1, v, ldv, h[kwtop*ldh+kcol:], ldh,
+					0, t, ldt)
+				impl.Dlacpy(blas.All, jw, kln, t, ldt, h[kwtop*ldh+kcol:], ldh)
+			}
+		}
+
+		// Update vertical slab in Z.
+		if wantz {
+			for krow := iloz; krow <= ihiz; krow += nv {
+				kln := min(nv, ihiz-krow+1)
+				bi.Dgemm(blas.NoTrans, blas.NoTrans, kln, jw, jw,
+					1, z[krow*ldz+kwtop:], ldz, v, ldv,
+					0, wv, ldwv)
+				impl.Dlacpy(blas.All, kln, jw, wv, ldwv, z[krow*ldz+kwtop:], ldz)
+			}
+		}
+	}
+
+	// The number of deflations.
+	nd = jw - ns
+	// Shifts are converged eigenvalues that could not be deflated.
+	// Subtracting infqr from the spike length takes care of the case of a
+	// rare QR failure while calculating eigenvalues of the deflation
+	// window.
+	ns -= infqr
+	work[0] = float64(lwkopt)
+	return ns, nd
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlaqr5.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlaqr5.go
new file mode 100644
index 00000000..0b6959dd
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlaqr5.go
@@ -0,0 +1,616 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dlaqr5 performs a single small-bulge multi-shift QR sweep on an isolated
+// block of a Hessenberg matrix.
+//
+// wantt and wantz determine whether the quasi-triangular Schur factor and the
+// orthogonal Schur factor, respectively, will be computed.
+//
+// kacc22 specifies the computation mode of far-from-diagonal orthogonal
+// updates. Permitted values are:
+//  0: Dlaqr5 will not accumulate reflections and will not use matrix-matrix
+//     multiply to update far-from-diagonal matrix entries.
+//  1: Dlaqr5 will accumulate reflections and use matrix-matrix multiply to
+//     update far-from-diagonal matrix entries.
+//  2: Dlaqr5 will accumulate reflections, use matrix-matrix multiply to update
+//     far-from-diagonal matrix entries, and take advantage of 2×2 block
+//     structure during matrix multiplies.
+// For other values of kacc2 Dlaqr5 will panic.
+//
+// n is the order of the Hessenberg matrix H.
+//
+// ktop and kbot are indices of the first and last row and column of an isolated
+// diagonal block upon which the QR sweep will be applied. It must hold that
+//  ktop == 0,   or 0 < ktop <= n-1 and H[ktop, ktop-1] == 0, and
+//  kbot == n-1, or 0 <= kbot < n-1 and H[kbot+1, kbot] == 0,
+// otherwise Dlaqr5 will panic.
+//
+// nshfts is the number of simultaneous shifts. It must be positive and even,
+// otherwise Dlaqr5 will panic.
+//
+// sr and si contain the real and imaginary parts, respectively, of the shifts
+// of origin that define the multi-shift QR sweep. On return both slices may be
+// reordered by Dlaqr5. Their length must be equal to nshfts, otherwise Dlaqr5
+// will panic.
+//
+// h and ldh represent the Hessenberg matrix H of size n×n. On return
+// multi-shift QR sweep with shifts sr+i*si has been applied to the isolated
+// diagonal block in rows and columns ktop through kbot, inclusive.
+//
+// iloz and ihiz specify the rows of Z to which transformations will be applied
+// if wantz is true. It must hold that 0 <= iloz <= ihiz < n, otherwise Dlaqr5
+// will panic.
+//
+// z and ldz represent the matrix Z of size n×n. If wantz is true, the QR sweep
+// orthogonal similarity transformation is accumulated into
+// z[iloz:ihiz,iloz:ihiz] from the right, otherwise z not referenced.
+//
+// v and ldv represent an auxiliary matrix V of size (nshfts/2)×3. Note that V
+// is transposed with respect to the reference netlib implementation.
+//
+// u and ldu represent an auxiliary matrix of size (3*nshfts-3)×(3*nshfts-3).
+//
+// wh and ldwh represent an auxiliary matrix of size (3*nshfts-3)×nh.
+//
+// wv and ldwv represent an auxiliary matrix of size nv×(3*nshfts-3).
+//
+// Dlaqr5 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlaqr5(wantt, wantz bool, kacc22 int, n, ktop, kbot, nshfts int, sr, si []float64, h []float64, ldh int, iloz, ihiz int, z []float64, ldz int, v []float64, ldv int, u []float64, ldu int, nv int, wv []float64, ldwv int, nh int, wh []float64, ldwh int) {
+	checkMatrix(n, n, h, ldh)
+	if ktop < 0 || n <= ktop {
+		panic("lapack: invalid value of ktop")
+	}
+	if ktop > 0 && h[ktop*ldh+ktop-1] != 0 {
+		panic("lapack: diagonal block is not isolated")
+	}
+	if kbot < 0 || n <= kbot {
+		panic("lapack: invalid value of kbot")
+	}
+	if kbot < n-1 && h[(kbot+1)*ldh+kbot] != 0 {
+		panic("lapack: diagonal block is not isolated")
+	}
+	if nshfts < 0 || nshfts&0x1 != 0 {
+		panic("lapack: invalid number of shifts")
+	}
+	if len(sr) != nshfts || len(si) != nshfts {
+		panic(badSlice) // TODO(vladimir-ch) Another message?
+	}
+	if wantz {
+		if ihiz >= n {
+			panic("lapack: invalid value of ihiz")
+		}
+		if iloz < 0 || ihiz < iloz {
+			panic("lapack: invalid value of iloz")
+		}
+		checkMatrix(n, n, z, ldz)
+	}
+	checkMatrix(nshfts/2, 3, v, ldv) // Transposed w.r.t. lapack.
+	checkMatrix(3*nshfts-3, 3*nshfts-3, u, ldu)
+	checkMatrix(nv, 3*nshfts-3, wv, ldwv)
+	checkMatrix(3*nshfts-3, nh, wh, ldwh)
+	if kacc22 != 0 && kacc22 != 1 && kacc22 != 2 {
+		panic("lapack: invalid value of kacc22")
+	}
+
+	// If there are no shifts, then there is nothing to do.
+	if nshfts < 2 {
+		return
+	}
+	// If the active block is empty or 1×1, then there is nothing to do.
+	if ktop >= kbot {
+		return
+	}
+
+	// Shuffle shifts into pairs of real shifts and pairs of complex
+	// conjugate shifts assuming complex conjugate shifts are already
+	// adjacent to one another.
+	for i := 0; i < nshfts-2; i += 2 {
+		if si[i] == -si[i+1] {
+			continue
+		}
+		sr[i], sr[i+1], sr[i+2] = sr[i+1], sr[i+2], sr[i]
+		si[i], si[i+1], si[i+2] = si[i+1], si[i+2], si[i]
+	}
+
+	// Note: lapack says that nshfts must be even but allows it to be odd
+	// anyway. We panic above if nshfts is not even, so reducing it by one
+	// is unnecessary. The only caller Dlaqr04 uses only even nshfts.
+	//
+	// The original comment and code from lapack-3.6.0/SRC/dlaqr5.f:341:
+	// *     ==== NSHFTS is supposed to be even, but if it is odd,
+	// *     .    then simply reduce it by one.  The shuffle above
+	// *     .    ensures that the dropped shift is real and that
+	// *     .    the remaining shifts are paired. ====
+	// *
+	//      NS = NSHFTS - MOD( NSHFTS, 2 )
+	ns := nshfts
+
+	safmin := dlamchS
+	ulp := dlamchP
+	smlnum := safmin * float64(n) / ulp
+
+	// Use accumulated reflections to update far-from-diagonal entries?
+	accum := kacc22 == 1 || kacc22 == 2
+	// If so, exploit the 2×2 block structure?
+	blk22 := ns > 2 && kacc22 == 2
+
+	// Clear trash.
+	if ktop+2 <= kbot {
+		h[(ktop+2)*ldh+ktop] = 0
+	}
+
+	// nbmps = number of 2-shift bulges in the chain.
+	nbmps := ns / 2
+
+	// kdu = width of slab.
+	kdu := 6*nbmps - 3
+
+	// Create and chase chains of nbmps bulges.
+	for incol := 3*(1-nbmps) + ktop - 1; incol <= kbot-2; incol += 3*nbmps - 2 {
+		ndcol := incol + kdu
+		if accum {
+			impl.Dlaset(blas.All, kdu, kdu, 0, 1, u, ldu)
+		}
+
+		// Near-the-diagonal bulge chase. The following loop performs
+		// the near-the-diagonal part of a small bulge multi-shift QR
+		// sweep. Each 6*nbmps-2 column diagonal chunk extends from
+		// column incol to column ndcol (including both column incol and
+		// column ndcol). The following loop chases a 3*nbmps column
+		// long chain of nbmps bulges 3*nbmps-2 columns to the right.
+		// (incol may be less than ktop and ndcol may be greater than
+		// kbot indicating phantom columns from which to chase bulges
+		// before they are actually introduced or to which to chase
+		// bulges beyond column kbot.)
+		for krcol := incol; krcol <= min(incol+3*nbmps-3, kbot-2); krcol++ {
+			// Bulges number mtop to mbot are active double implicit
+			// shift bulges. There may or may not also be small 2×2
+			// bulge, if there is room. The inactive bulges (if any)
+			// must wait until the active bulges have moved down the
+			// diagonal to make room. The phantom matrix paradigm
+			// described above helps keep track.
+
+			mtop := max(0, ((ktop-1)-krcol+2)/3)
+			mbot := min(nbmps, (kbot-krcol)/3) - 1
+			m22 := mbot + 1
+			bmp22 := (mbot < nbmps-1) && (krcol+3*m22 == kbot-2)
+
+			// Generate reflections to chase the chain right one
+			// column. (The minimum value of k is ktop-1.)
+			for m := mtop; m <= mbot; m++ {
+				k := krcol + 3*m
+				if k == ktop-1 {
+					impl.Dlaqr1(3, h[ktop*ldh+ktop:], ldh,
+						sr[2*m], si[2*m], sr[2*m+1], si[2*m+1],
+						v[m*ldv:m*ldv+3])
+					alpha := v[m*ldv]
+					_, v[m*ldv] = impl.Dlarfg(3, alpha, v[m*ldv+1:m*ldv+3], 1)
+					continue
+				}
+				beta := h[(k+1)*ldh+k]
+				v[m*ldv+1] = h[(k+2)*ldh+k]
+				v[m*ldv+2] = h[(k+3)*ldh+k]
+				beta, v[m*ldv] = impl.Dlarfg(3, beta, v[m*ldv+1:m*ldv+3], 1)
+
+				// A bulge may collapse because of vigilant deflation or
+				// destructive underflow. In the underflow case, try the
+				// two-small-subdiagonals trick to try to reinflate the
+				// bulge.
+				if h[(k+3)*ldh+k] != 0 || h[(k+3)*ldh+k+1] != 0 || h[(k+3)*ldh+k+2] == 0 {
+					// Typical case: not collapsed (yet).
+					h[(k+1)*ldh+k] = beta
+					h[(k+2)*ldh+k] = 0
+					h[(k+3)*ldh+k] = 0
+					continue
+				}
+
+				// Atypical case: collapsed. Attempt to reintroduce
+				// ignoring H[k+1,k] and H[k+2,k]. If the fill
+				// resulting from the new reflector is too large,
+				// then abandon it. Otherwise, use the new one.
+				var vt [3]float64
+				impl.Dlaqr1(3, h[(k+1)*ldh+k+1:], ldh, sr[2*m],
+					si[2*m], sr[2*m+1], si[2*m+1], vt[:])
+				alpha := vt[0]
+				_, vt[0] = impl.Dlarfg(3, alpha, vt[1:3], 1)
+				refsum := vt[0] * (h[(k+1)*ldh+k] + vt[1]*h[(k+2)*ldh+k])
+
+				dsum := math.Abs(h[k*ldh+k]) + math.Abs(h[(k+1)*ldh+k+1]) + math.Abs(h[(k+2)*ldh+k+2])
+				if math.Abs(h[(k+2)*ldh+k]-refsum*vt[1])+math.Abs(refsum*vt[2]) > ulp*dsum {
+					// Starting a new bulge here would create
+					// non-negligible fill. Use the old one with
+					// trepidation.
+					h[(k+1)*ldh+k] = beta
+					h[(k+2)*ldh+k] = 0
+					h[(k+3)*ldh+k] = 0
+					continue
+				} else {
+					// Starting a new bulge here would create
+					// only negligible fill. Replace the old
+					// reflector with the new one.
+					h[(k+1)*ldh+k] -= refsum
+					h[(k+2)*ldh+k] = 0
+					h[(k+3)*ldh+k] = 0
+					v[m*ldv] = vt[0]
+					v[m*ldv+1] = vt[1]
+					v[m*ldv+2] = vt[2]
+				}
+			}
+
+			// Generate a 2×2 reflection, if needed.
+			if bmp22 {
+				k := krcol + 3*m22
+				if k == ktop-1 {
+					impl.Dlaqr1(2, h[(k+1)*ldh+k+1:], ldh,
+						sr[2*m22], si[2*m22], sr[2*m22+1], si[2*m22+1],
+						v[m22*ldv:m22*ldv+2])
+					beta := v[m22*ldv]
+					_, v[m22*ldv] = impl.Dlarfg(2, beta, v[m22*ldv+1:m22*ldv+2], 1)
+				} else {
+					beta := h[(k+1)*ldh+k]
+					v[m22*ldv+1] = h[(k+2)*ldh+k]
+					beta, v[m22*ldv] = impl.Dlarfg(2, beta, v[m22*ldv+1:m22*ldv+2], 1)
+					h[(k+1)*ldh+k] = beta
+					h[(k+2)*ldh+k] = 0
+				}
+			}
+
+			// Multiply H by reflections from the left.
+			var jbot int
+			switch {
+			case accum:
+				jbot = min(ndcol, kbot)
+			case wantt:
+				jbot = n - 1
+			default:
+				jbot = kbot
+			}
+			for j := max(ktop, krcol); j <= jbot; j++ {
+				mend := min(mbot+1, (j-krcol+2)/3) - 1
+				for m := mtop; m <= mend; m++ {
+					k := krcol + 3*m
+					refsum := v[m*ldv] * (h[(k+1)*ldh+j] +
+						v[m*ldv+1]*h[(k+2)*ldh+j] + v[m*ldv+2]*h[(k+3)*ldh+j])
+					h[(k+1)*ldh+j] -= refsum
+					h[(k+2)*ldh+j] -= refsum * v[m*ldv+1]
+					h[(k+3)*ldh+j] -= refsum * v[m*ldv+2]
+				}
+			}
+			if bmp22 {
+				k := krcol + 3*m22
+				for j := max(k+1, ktop); j <= jbot; j++ {
+					refsum := v[m22*ldv] * (h[(k+1)*ldh+j] + v[m22*ldv+1]*h[(k+2)*ldh+j])
+					h[(k+1)*ldh+j] -= refsum
+					h[(k+2)*ldh+j] -= refsum * v[m22*ldv+1]
+				}
+			}
+
+			// Multiply H by reflections from the right. Delay filling in the last row
+			// until the vigilant deflation check is complete.
+			var jtop int
+			switch {
+			case accum:
+				jtop = max(ktop, incol)
+			case wantt:
+				jtop = 0
+			default:
+				jtop = ktop
+			}
+			for m := mtop; m <= mbot; m++ {
+				if v[m*ldv] == 0 {
+					continue
+				}
+				k := krcol + 3*m
+				for j := jtop; j <= min(kbot, k+3); j++ {
+					refsum := v[m*ldv] * (h[j*ldh+k+1] +
+						v[m*ldv+1]*h[j*ldh+k+2] + v[m*ldv+2]*h[j*ldh+k+3])
+					h[j*ldh+k+1] -= refsum
+					h[j*ldh+k+2] -= refsum * v[m*ldv+1]
+					h[j*ldh+k+3] -= refsum * v[m*ldv+2]
+				}
+				if accum {
+					// Accumulate U. (If necessary, update Z later with with an
+					// efficient matrix-matrix multiply.)
+					kms := k - incol
+					for j := max(0, ktop-incol-1); j < kdu; j++ {
+						refsum := v[m*ldv] * (u[j*ldu+kms] +
+							v[m*ldv+1]*u[j*ldu+kms+1] + v[m*ldv+2]*u[j*ldu+kms+2])
+						u[j*ldu+kms] -= refsum
+						u[j*ldu+kms+1] -= refsum * v[m*ldv+1]
+						u[j*ldu+kms+2] -= refsum * v[m*ldv+2]
+					}
+				} else if wantz {
+					// U is not accumulated, so update Z now by multiplying by
+					// reflections from the right.
+					for j := iloz; j <= ihiz; j++ {
+						refsum := v[m*ldv] * (z[j*ldz+k+1] +
+							v[m*ldv+1]*z[j*ldz+k+2] + v[m*ldv+2]*z[j*ldz+k+3])
+						z[j*ldz+k+1] -= refsum
+						z[j*ldz+k+2] -= refsum * v[m*ldv+1]
+						z[j*ldz+k+3] -= refsum * v[m*ldv+2]
+					}
+				}
+			}
+
+			// Special case: 2×2 reflection (if needed).
+			if bmp22 && v[m22*ldv] != 0 {
+				k := krcol + 3*m22
+				for j := jtop; j <= min(kbot, k+3); j++ {
+					refsum := v[m22*ldv] * (h[j*ldh+k+1] + v[m22*ldv+1]*h[j*ldh+k+2])
+					h[j*ldh+k+1] -= refsum
+					h[j*ldh+k+2] -= refsum * v[m22*ldv+1]
+				}
+				if accum {
+					kms := k - incol
+					for j := max(0, ktop-incol-1); j < kdu; j++ {
+						refsum := v[m22*ldv] * (u[j*ldu+kms] + v[m22*ldv+1]*u[j*ldu+kms+1])
+						u[j*ldu+kms] -= refsum
+						u[j*ldu+kms+1] -= refsum * v[m22*ldv+1]
+					}
+				} else if wantz {
+					for j := iloz; j <= ihiz; j++ {
+						refsum := v[m22*ldv] * (z[j*ldz+k+1] + v[m22*ldv+1]*z[j*ldz+k+2])
+						z[j*ldz+k+1] -= refsum
+						z[j*ldz+k+2] -= refsum * v[m22*ldv+1]
+					}
+				}
+			}
+
+			// Vigilant deflation check.
+			mstart := mtop
+			if krcol+3*mstart < ktop {
+				mstart++
+			}
+			mend := mbot
+			if bmp22 {
+				mend++
+			}
+			if krcol == kbot-2 {
+				mend++
+			}
+			for m := mstart; m <= mend; m++ {
+				k := min(kbot-1, krcol+3*m)
+
+				// The following convergence test requires that the tradition
+				// small-compared-to-nearby-diagonals criterion and the Ahues &
+				// Tisseur (LAWN 122, 1997) criteria both be satisfied. The latter
+				// improves accuracy in some examples. Falling back on an alternate
+				// convergence criterion when tst1 or tst2 is zero (as done here) is
+				// traditional but probably unnecessary.
+
+				if h[(k+1)*ldh+k] == 0 {
+					continue
+				}
+				tst1 := math.Abs(h[k*ldh+k]) + math.Abs(h[(k+1)*ldh+k+1])
+				if tst1 == 0 {
+					if k >= ktop+1 {
+						tst1 += math.Abs(h[k*ldh+k-1])
+					}
+					if k >= ktop+2 {
+						tst1 += math.Abs(h[k*ldh+k-2])
+					}
+					if k >= ktop+3 {
+						tst1 += math.Abs(h[k*ldh+k-3])
+					}
+					if k <= kbot-2 {
+						tst1 += math.Abs(h[(k+2)*ldh+k+1])
+					}
+					if k <= kbot-3 {
+						tst1 += math.Abs(h[(k+3)*ldh+k+1])
+					}
+					if k <= kbot-4 {
+						tst1 += math.Abs(h[(k+4)*ldh+k+1])
+					}
+				}
+				if math.Abs(h[(k+1)*ldh+k]) <= math.Max(smlnum, ulp*tst1) {
+					h12 := math.Max(math.Abs(h[(k+1)*ldh+k]), math.Abs(h[k*ldh+k+1]))
+					h21 := math.Min(math.Abs(h[(k+1)*ldh+k]), math.Abs(h[k*ldh+k+1]))
+					h11 := math.Max(math.Abs(h[(k+1)*ldh+k+1]), math.Abs(h[k*ldh+k]-h[(k+1)*ldh+k+1]))
+					h22 := math.Min(math.Abs(h[(k+1)*ldh+k+1]), math.Abs(h[k*ldh+k]-h[(k+1)*ldh+k+1]))
+					scl := h11 + h12
+					tst2 := h22 * (h11 / scl)
+					if tst2 == 0 || h21*(h12/scl) <= math.Max(smlnum, ulp*tst2) {
+						h[(k+1)*ldh+k] = 0
+					}
+				}
+			}
+
+			// Fill in the last row of each bulge.
+			mend = min(nbmps, (kbot-krcol-1)/3) - 1
+			for m := mtop; m <= mend; m++ {
+				k := krcol + 3*m
+				refsum := v[m*ldv] * v[m*ldv+2] * h[(k+4)*ldh+k+3]
+				h[(k+4)*ldh+k+1] = -refsum
+				h[(k+4)*ldh+k+2] = -refsum * v[m*ldv+1]
+				h[(k+4)*ldh+k+3] -= refsum * v[m*ldv+2]
+			}
+		}
+
+		// Use U (if accumulated) to update far-from-diagonal entries in H.
+		// If required, use U to update Z as well.
+		if !accum {
+			continue
+		}
+		var jtop, jbot int
+		if wantt {
+			jtop = 0
+			jbot = n - 1
+		} else {
+			jtop = ktop
+			jbot = kbot
+		}
+		bi := blas64.Implementation()
+		if !blk22 || incol < ktop || kbot < ndcol || ns <= 2 {
+			// Updates not exploiting the 2×2 block structure of U. k0 and nu keep track
+			// of the location and size of U in the special cases of introducing bulges
+			// and chasing bulges off the bottom. In these special cases and in case the
+			// number of shifts is ns = 2, there is no 2×2 block structure to exploit.
+
+			k0 := max(0, ktop-incol-1)
+			nu := kdu - max(0, ndcol-kbot) - k0
+
+			// Horizontal multiply.
+			for jcol := min(ndcol, kbot) + 1; jcol <= jbot; jcol += nh {
+				jlen := min(nh, jbot-jcol+1)
+				bi.Dgemm(blas.Trans, blas.NoTrans, nu, jlen, nu,
+					1, u[k0*ldu+k0:], ldu,
+					h[(incol+k0+1)*ldh+jcol:], ldh,
+					0, wh, ldwh)
+				impl.Dlacpy(blas.All, nu, jlen, wh, ldwh, h[(incol+k0+1)*ldh+jcol:], ldh)
+			}
+
+			// Vertical multiply.
+			for jrow := jtop; jrow <= max(ktop, incol)-1; jrow += nv {
+				jlen := min(nv, max(ktop, incol)-jrow)
+				bi.Dgemm(blas.NoTrans, blas.NoTrans, jlen, nu, nu,
+					1, h[jrow*ldh+incol+k0+1:], ldh,
+					u[k0*ldu+k0:], ldu,
+					0, wv, ldwv)
+				impl.Dlacpy(blas.All, jlen, nu, wv, ldwv, h[jrow*ldh+incol+k0+1:], ldh)
+			}
+
+			// Z multiply (also vertical).
+			if wantz {
+				for jrow := iloz; jrow <= ihiz; jrow += nv {
+					jlen := min(nv, ihiz-jrow+1)
+					bi.Dgemm(blas.NoTrans, blas.NoTrans, jlen, nu, nu,
+						1, z[jrow*ldz+incol+k0+1:], ldz,
+						u[k0*ldu+k0:], ldu,
+						0, wv, ldwv)
+					impl.Dlacpy(blas.All, jlen, nu, wv, ldwv, z[jrow*ldz+incol+k0+1:], ldz)
+				}
+			}
+
+			continue
+		}
+
+		// Updates exploiting U's 2×2 block structure.
+
+		// i2, i4, j2, j4 are the last rows and columns of the blocks.
+		i2 := (kdu + 1) / 2
+		i4 := kdu
+		j2 := i4 - i2
+		j4 := kdu
+
+		// kzs and knz deal with the band of zeros along the diagonal of one of the
+		// triangular blocks.
+		kzs := (j4 - j2) - (ns + 1)
+		knz := ns + 1
+
+		// Horizontal multiply.
+		for jcol := min(ndcol, kbot) + 1; jcol <= jbot; jcol += nh {
+			jlen := min(nh, jbot-jcol+1)
+
+			// Copy bottom of H to top+kzs of scratch (the first kzs
+			// rows get multiplied by zero).
+			impl.Dlacpy(blas.All, knz, jlen, h[(incol+1+j2)*ldh+jcol:], ldh, wh[kzs*ldwh:], ldwh)
+
+			// Multiply by U21^T.
+			impl.Dlaset(blas.All, kzs, jlen, 0, 0, wh, ldwh)
+			bi.Dtrmm(blas.Left, blas.Upper, blas.Trans, blas.NonUnit, knz, jlen,
+				1, u[j2*ldu+kzs:], ldu, wh[kzs*ldwh:], ldwh)
+
+			// Multiply top of H by U11^T.
+			bi.Dgemm(blas.Trans, blas.NoTrans, i2, jlen, j2,
+				1, u, ldu, h[(incol+1)*ldh+jcol:], ldh,
+				1, wh, ldwh)
+
+			// Copy top of H to bottom of WH.
+			impl.Dlacpy(blas.All, j2, jlen, h[(incol+1)*ldh+jcol:], ldh, wh[i2*ldwh:], ldwh)
+
+			// Multiply by U21^T.
+			bi.Dtrmm(blas.Left, blas.Lower, blas.Trans, blas.NonUnit, j2, jlen,
+				1, u[i2:], ldu, wh[i2*ldwh:], ldwh)
+
+			// Multiply by U22.
+			bi.Dgemm(blas.Trans, blas.NoTrans, i4-i2, jlen, j4-j2,
+				1, u[j2*ldu+i2:], ldu, h[(incol+1+j2)*ldh+jcol:], ldh,
+				1, wh[i2*ldwh:], ldwh)
+
+			// Copy it back.
+			impl.Dlacpy(blas.All, kdu, jlen, wh, ldwh, h[(incol+1)*ldh+jcol:], ldh)
+		}
+
+		// Vertical multiply.
+		for jrow := jtop; jrow <= max(incol, ktop)-1; jrow += nv {
+			jlen := min(nv, max(incol, ktop)-jrow)
+
+			// Copy right of H to scratch (the first kzs columns get multiplied
+			// by zero).
+			impl.Dlacpy(blas.All, jlen, knz, h[jrow*ldh+incol+1+j2:], ldh, wv[kzs:], ldwv)
+
+			// Multiply by U21.
+			impl.Dlaset(blas.All, jlen, kzs, 0, 0, wv, ldwv)
+			bi.Dtrmm(blas.Right, blas.Upper, blas.NoTrans, blas.NonUnit, jlen, knz,
+				1, u[j2*ldu+kzs:], ldu, wv[kzs:], ldwv)
+
+			// Multiply by U11.
+			bi.Dgemm(blas.NoTrans, blas.NoTrans, jlen, i2, j2,
+				1, h[jrow*ldh+incol+1:], ldh, u, ldu,
+				1, wv, ldwv)
+
+			// Copy left of H to right of scratch.
+			impl.Dlacpy(blas.All, jlen, j2, h[jrow*ldh+incol+1:], ldh, wv[i2:], ldwv)
+
+			// Multiply by U21.
+			bi.Dtrmm(blas.Right, blas.Lower, blas.NoTrans, blas.NonUnit, jlen, i4-i2,
+				1, u[i2:], ldu, wv[i2:], ldwv)
+
+			// Multiply by U22.
+			bi.Dgemm(blas.NoTrans, blas.NoTrans, jlen, i4-i2, j4-j2,
+				1, h[jrow*ldh+incol+1+j2:], ldh, u[j2*ldu+i2:], ldu,
+				1, wv[i2:], ldwv)
+
+			// Copy it back.
+			impl.Dlacpy(blas.All, jlen, kdu, wv, ldwv, h[jrow*ldh+incol+1:], ldh)
+		}
+
+		if !wantz {
+			continue
+		}
+		// Multiply Z (also vertical).
+		for jrow := iloz; jrow <= ihiz; jrow += nv {
+			jlen := min(nv, ihiz-jrow+1)
+
+			// Copy right of Z to left of scratch (first kzs columns get
+			// multiplied by zero).
+			impl.Dlacpy(blas.All, jlen, knz, z[jrow*ldz+incol+1+j2:], ldz, wv[kzs:], ldwv)
+
+			// Multiply by U12.
+			impl.Dlaset(blas.All, jlen, kzs, 0, 0, wv, ldwv)
+			bi.Dtrmm(blas.Right, blas.Upper, blas.NoTrans, blas.NonUnit, jlen, knz,
+				1, u[j2*ldu+kzs:], ldu, wv[kzs:], ldwv)
+
+			// Multiply by U11.
+			bi.Dgemm(blas.NoTrans, blas.NoTrans, jlen, i2, j2,
+				1, z[jrow*ldz+incol+1:], ldz, u, ldu,
+				1, wv, ldwv)
+
+			// Copy left of Z to right of scratch.
+			impl.Dlacpy(blas.All, jlen, j2, z[jrow*ldz+incol+1:], ldz, wv[i2:], ldwv)
+
+			// Multiply by U21.
+			bi.Dtrmm(blas.Right, blas.Lower, blas.NoTrans, blas.NonUnit, jlen, i4-i2,
+				1, u[i2:], ldu, wv[i2:], ldwv)
+
+			// Multiply by U22.
+			bi.Dgemm(blas.NoTrans, blas.NoTrans, jlen, i4-i2, j4-j2,
+				1, z[jrow*ldz+incol+1+j2:], ldz, u[j2*ldu+i2:], ldu,
+				1, wv[i2:], ldwv)
+
+			// Copy the result back to Z.
+			impl.Dlacpy(blas.All, jlen, kdu, wv, ldwv, z[jrow*ldz+incol+1:], ldz)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlarf.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlarf.go
new file mode 100644
index 00000000..01f50eae
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlarf.go
@@ -0,0 +1,83 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dlarf applies an elementary reflector to a general rectangular matrix c.
+// This computes
+//  c = h * c if side == Left
+//  c = c * h if side == right
+// where
+//  h = 1 - tau * v * v^T
+// and c is an m * n matrix.
+//
+// work is temporary storage of length at least m if side == Left and at least
+// n if side == Right. This function will panic if this length requirement is not met.
+//
+// Dlarf is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlarf(side blas.Side, m, n int, v []float64, incv int, tau float64, c []float64, ldc int, work []float64) {
+	applyleft := side == blas.Left
+	if (applyleft && len(work) < n) || (!applyleft && len(work) < m) {
+		panic(badWork)
+	}
+	checkMatrix(m, n, c, ldc)
+
+	// v has length m if applyleft and n otherwise.
+	lenV := n
+	if applyleft {
+		lenV = m
+	}
+
+	checkVector(lenV, v, incv)
+
+	lastv := 0 // last non-zero element of v
+	lastc := 0 // last non-zero row/column of c
+	if tau != 0 {
+		var i int
+		if applyleft {
+			lastv = m - 1
+		} else {
+			lastv = n - 1
+		}
+		if incv > 0 {
+			i = lastv * incv
+		}
+
+		// Look for the last non-zero row in v.
+		for lastv >= 0 && v[i] == 0 {
+			lastv--
+			i -= incv
+		}
+		if applyleft {
+			// Scan for the last non-zero column in C[0:lastv, :]
+			lastc = impl.Iladlc(lastv+1, n, c, ldc)
+		} else {
+			// Scan for the last non-zero row in C[:, 0:lastv]
+			lastc = impl.Iladlr(m, lastv+1, c, ldc)
+		}
+	}
+	if lastv == -1 || lastc == -1 {
+		return
+	}
+	// Sometimes 1-indexing is nicer ...
+	bi := blas64.Implementation()
+	if applyleft {
+		// Form H * C
+		// w[0:lastc+1] = c[1:lastv+1, 1:lastc+1]^T * v[1:lastv+1,1]
+		bi.Dgemv(blas.Trans, lastv+1, lastc+1, 1, c, ldc, v, incv, 0, work, 1)
+		// c[0: lastv, 0: lastc] = c[...] - w[0:lastv, 1] * v[1:lastc, 1]^T
+		bi.Dger(lastv+1, lastc+1, -tau, v, incv, work, 1, c, ldc)
+		return
+	}
+	// Form C*H
+	// w[0:lastc+1,1] := c[0:lastc+1,0:lastv+1] * v[0:lastv+1,1]
+	bi.Dgemv(blas.NoTrans, lastc+1, lastv+1, 1, c, ldc, v, incv, 0, work, 1)
+	// c[0:lastc+1,0:lastv+1] = c[...] - w[0:lastc+1,0] * v[0:lastv+1,0]^T
+	bi.Dger(lastc+1, lastv+1, -tau, work, 1, v, incv, c, ldc)
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlarfb.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlarfb.go
new file mode 100644
index 00000000..bfafd360
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlarfb.go
@@ -0,0 +1,431 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dlarfb applies a block reflector to a matrix.
+//
+// In the call to Dlarfb, the mxn c is multiplied by the implicitly defined matrix h as follows:
+//  c = h * c if side == Left and trans == NoTrans
+//  c = c * h if side == Right and trans == NoTrans
+//  c = h^T * c if side == Left and trans == Trans
+//  c = c * h^T if side == Right and trans == Trans
+// h is a product of elementary reflectors. direct sets the direction of multiplication
+//  h = h_1 * h_2 * ... * h_k if direct == Forward
+//  h = h_k * h_k-1 * ... * h_1 if direct == Backward
+// The combination of direct and store defines the orientation of the elementary
+// reflectors. In all cases the ones on the diagonal are implicitly represented.
+//
+// If direct == lapack.Forward and store == lapack.ColumnWise
+//  V = [ 1        ]
+//      [v1   1    ]
+//      [v1  v2   1]
+//      [v1  v2  v3]
+//      [v1  v2  v3]
+// If direct == lapack.Forward and store == lapack.RowWise
+//  V = [ 1  v1  v1  v1  v1]
+//      [     1  v2  v2  v2]
+//      [         1  v3  v3]
+// If direct == lapack.Backward and store == lapack.ColumnWise
+//  V = [v1  v2  v3]
+//      [v1  v2  v3]
+//      [ 1  v2  v3]
+//      [     1  v3]
+//      [         1]
+// If direct == lapack.Backward and store == lapack.RowWise
+//  V = [v1  v1   1        ]
+//      [v2  v2  v2   1    ]
+//      [v3  v3  v3  v3   1]
+// An elementary reflector can be explicitly constructed by extracting the
+// corresponding elements of v, placing a 1 where the diagonal would be, and
+// placing zeros in the remaining elements.
+//
+// t is a k×k matrix containing the block reflector, and this function will panic
+// if t is not of sufficient size. See Dlarft for more information.
+//
+// work is a temporary storage matrix with stride ldwork.
+// work must be of size at least n×k side == Left and m×k if side == Right, and
+// this function will panic if this size is not met.
+//
+// Dlarfb is an internal routine. It is exported for testing purposes.
+func (Implementation) Dlarfb(side blas.Side, trans blas.Transpose, direct lapack.Direct, store lapack.StoreV, m, n, k int, v []float64, ldv int, t []float64, ldt int, c []float64, ldc int, work []float64, ldwork int) {
+	if side != blas.Left && side != blas.Right {
+		panic(badSide)
+	}
+	if trans != blas.Trans && trans != blas.NoTrans {
+		panic(badTrans)
+	}
+	if direct != lapack.Forward && direct != lapack.Backward {
+		panic(badDirect)
+	}
+	if store != lapack.ColumnWise && store != lapack.RowWise {
+		panic(badStore)
+	}
+	checkMatrix(m, n, c, ldc)
+	if k < 0 {
+		panic(kLT0)
+	}
+	checkMatrix(k, k, t, ldt)
+	nv := m
+	nw := n
+	if side == blas.Right {
+		nv = n
+		nw = m
+	}
+	if store == lapack.ColumnWise {
+		checkMatrix(nv, k, v, ldv)
+	} else {
+		checkMatrix(k, nv, v, ldv)
+	}
+	checkMatrix(nw, k, work, ldwork)
+
+	if m == 0 || n == 0 {
+		return
+	}
+
+	bi := blas64.Implementation()
+
+	transt := blas.Trans
+	if trans == blas.Trans {
+		transt = blas.NoTrans
+	}
+	// TODO(btracey): This follows the original Lapack code where the
+	// elements are copied into the columns of the working array. The
+	// loops should go in the other direction so the data is written
+	// into the rows of work so the copy is not strided. A bigger change
+	// would be to replace work with work^T, but benchmarks would be
+	// needed to see if the change is merited.
+	if store == lapack.ColumnWise {
+		if direct == lapack.Forward {
+			// V1 is the first k rows of C. V2 is the remaining rows.
+			if side == blas.Left {
+				// W = C^T V = C1^T V1 + C2^T V2 (stored in work).
+
+				// W = C1.
+				for j := 0; j < k; j++ {
+					bi.Dcopy(n, c[j*ldc:], 1, work[j:], ldwork)
+				}
+				// W = W * V1.
+				bi.Dtrmm(blas.Right, blas.Lower, blas.NoTrans, blas.Unit,
+					n, k, 1,
+					v, ldv,
+					work, ldwork)
+				if m > k {
+					// W = W + C2^T V2.
+					bi.Dgemm(blas.Trans, blas.NoTrans, n, k, m-k,
+						1, c[k*ldc:], ldc, v[k*ldv:], ldv,
+						1, work, ldwork)
+				}
+				// W = W * T^T or W * T.
+				bi.Dtrmm(blas.Right, blas.Upper, transt, blas.NonUnit, n, k,
+					1, t, ldt,
+					work, ldwork)
+				// C -= V * W^T.
+				if m > k {
+					// C2 -= V2 * W^T.
+					bi.Dgemm(blas.NoTrans, blas.Trans, m-k, n, k,
+						-1, v[k*ldv:], ldv, work, ldwork,
+						1, c[k*ldc:], ldc)
+				}
+				// W *= V1^T.
+				bi.Dtrmm(blas.Right, blas.Lower, blas.Trans, blas.Unit, n, k,
+					1, v, ldv,
+					work, ldwork)
+				// C1 -= W^T.
+				// TODO(btracey): This should use blas.Axpy.
+				for i := 0; i < n; i++ {
+					for j := 0; j < k; j++ {
+						c[j*ldc+i] -= work[i*ldwork+j]
+					}
+				}
+				return
+			}
+			// Form C = C * H or C * H^T, where C = (C1 C2).
+
+			// W = C1.
+			for i := 0; i < k; i++ {
+				bi.Dcopy(m, c[i:], ldc, work[i:], ldwork)
+			}
+			// W *= V1.
+			bi.Dtrmm(blas.Right, blas.Lower, blas.NoTrans, blas.Unit, m, k,
+				1, v, ldv,
+				work, ldwork)
+			if n > k {
+				bi.Dgemm(blas.NoTrans, blas.NoTrans, m, k, n-k,
+					1, c[k:], ldc, v[k*ldv:], ldv,
+					1, work, ldwork)
+			}
+			// W *= T or T^T.
+			bi.Dtrmm(blas.Right, blas.Upper, trans, blas.NonUnit, m, k,
+				1, t, ldt,
+				work, ldwork)
+			if n > k {
+				bi.Dgemm(blas.NoTrans, blas.Trans, m, n-k, k,
+					-1, work, ldwork, v[k*ldv:], ldv,
+					1, c[k:], ldc)
+			}
+			// C -= W * V^T.
+			bi.Dtrmm(blas.Right, blas.Lower, blas.Trans, blas.Unit, m, k,
+				1, v, ldv,
+				work, ldwork)
+			// C -= W.
+			// TODO(btracey): This should use blas.Axpy.
+			for i := 0; i < m; i++ {
+				for j := 0; j < k; j++ {
+					c[i*ldc+j] -= work[i*ldwork+j]
+				}
+			}
+			return
+		}
+		// V = (V1)
+		//   = (V2) (last k rows)
+		// Where V2 is unit upper triangular.
+		if side == blas.Left {
+			// Form H * C or
+			// W = C^T V.
+
+			// W = C2^T.
+			for j := 0; j < k; j++ {
+				bi.Dcopy(n, c[(m-k+j)*ldc:], 1, work[j:], ldwork)
+			}
+			// W *= V2.
+			bi.Dtrmm(blas.Right, blas.Upper, blas.NoTrans, blas.Unit, n, k,
+				1, v[(m-k)*ldv:], ldv,
+				work, ldwork)
+			if m > k {
+				// W += C1^T * V1.
+				bi.Dgemm(blas.Trans, blas.NoTrans, n, k, m-k,
+					1, c, ldc, v, ldv,
+					1, work, ldwork)
+			}
+			// W *= T or T^T.
+			bi.Dtrmm(blas.Right, blas.Lower, transt, blas.NonUnit, n, k,
+				1, t, ldt,
+				work, ldwork)
+			// C -= V * W^T.
+			if m > k {
+				bi.Dgemm(blas.NoTrans, blas.Trans, m-k, n, k,
+					-1, v, ldv, work, ldwork,
+					1, c, ldc)
+			}
+			// W *= V2^T.
+			bi.Dtrmm(blas.Right, blas.Upper, blas.Trans, blas.Unit, n, k,
+				1, v[(m-k)*ldv:], ldv,
+				work, ldwork)
+			// C2 -= W^T.
+			// TODO(btracey): This should use blas.Axpy.
+			for i := 0; i < n; i++ {
+				for j := 0; j < k; j++ {
+					c[(m-k+j)*ldc+i] -= work[i*ldwork+j]
+				}
+			}
+			return
+		}
+		// Form C * H or C * H^T where C = (C1 C2).
+		// W = C * V.
+
+		// W = C2.
+		for j := 0; j < k; j++ {
+			bi.Dcopy(m, c[n-k+j:], ldc, work[j:], ldwork)
+		}
+
+		// W = W * V2.
+		bi.Dtrmm(blas.Right, blas.Upper, blas.NoTrans, blas.Unit, m, k,
+			1, v[(n-k)*ldv:], ldv,
+			work, ldwork)
+		if n > k {
+			bi.Dgemm(blas.NoTrans, blas.NoTrans, m, k, n-k,
+				1, c, ldc, v, ldv,
+				1, work, ldwork)
+		}
+		// W *= T or T^T.
+		bi.Dtrmm(blas.Right, blas.Lower, trans, blas.NonUnit, m, k,
+			1, t, ldt,
+			work, ldwork)
+		// C -= W * V^T.
+		if n > k {
+			// C1 -= W * V1^T.
+			bi.Dgemm(blas.NoTrans, blas.Trans, m, n-k, k,
+				-1, work, ldwork, v, ldv,
+				1, c, ldc)
+		}
+		// W *= V2^T.
+		bi.Dtrmm(blas.Right, blas.Upper, blas.Trans, blas.Unit, m, k,
+			1, v[(n-k)*ldv:], ldv,
+			work, ldwork)
+		// C2 -= W.
+		// TODO(btracey): This should use blas.Axpy.
+		for i := 0; i < m; i++ {
+			for j := 0; j < k; j++ {
+				c[i*ldc+n-k+j] -= work[i*ldwork+j]
+			}
+		}
+		return
+	}
+	// Store = Rowwise.
+	if direct == lapack.Forward {
+		// V = (V1 V2) where v1 is unit upper triangular.
+		if side == blas.Left {
+			// Form H * C or H^T * C where C = (C1; C2).
+			// W = C^T * V^T.
+
+			// W = C1^T.
+			for j := 0; j < k; j++ {
+				bi.Dcopy(n, c[j*ldc:], 1, work[j:], ldwork)
+			}
+			// W *= V1^T.
+			bi.Dtrmm(blas.Right, blas.Upper, blas.Trans, blas.Unit, n, k,
+				1, v, ldv,
+				work, ldwork)
+			if m > k {
+				bi.Dgemm(blas.Trans, blas.Trans, n, k, m-k,
+					1, c[k*ldc:], ldc, v[k:], ldv,
+					1, work, ldwork)
+			}
+			// W *= T or T^T.
+			bi.Dtrmm(blas.Right, blas.Upper, transt, blas.NonUnit, n, k,
+				1, t, ldt,
+				work, ldwork)
+			// C -= V^T * W^T.
+			if m > k {
+				bi.Dgemm(blas.Trans, blas.Trans, m-k, n, k,
+					-1, v[k:], ldv, work, ldwork,
+					1, c[k*ldc:], ldc)
+			}
+			// W *= V1.
+			bi.Dtrmm(blas.Right, blas.Upper, blas.NoTrans, blas.Unit, n, k,
+				1, v, ldv,
+				work, ldwork)
+			// C1 -= W^T.
+			// TODO(btracey): This should use blas.Axpy.
+			for i := 0; i < n; i++ {
+				for j := 0; j < k; j++ {
+					c[j*ldc+i] -= work[i*ldwork+j]
+				}
+			}
+			return
+		}
+		// Form C * H or C * H^T where C = (C1 C2).
+		// W = C * V^T.
+
+		// W = C1.
+		for j := 0; j < k; j++ {
+			bi.Dcopy(m, c[j:], ldc, work[j:], ldwork)
+		}
+		// W *= V1^T.
+		bi.Dtrmm(blas.Right, blas.Upper, blas.Trans, blas.Unit, m, k,
+			1, v, ldv,
+			work, ldwork)
+		if n > k {
+			bi.Dgemm(blas.NoTrans, blas.Trans, m, k, n-k,
+				1, c[k:], ldc, v[k:], ldv,
+				1, work, ldwork)
+		}
+		// W *= T or T^T.
+		bi.Dtrmm(blas.Right, blas.Upper, trans, blas.NonUnit, m, k,
+			1, t, ldt,
+			work, ldwork)
+		// C -= W * V.
+		if n > k {
+			bi.Dgemm(blas.NoTrans, blas.NoTrans, m, n-k, k,
+				-1, work, ldwork, v[k:], ldv,
+				1, c[k:], ldc)
+		}
+		// W *= V1.
+		bi.Dtrmm(blas.Right, blas.Upper, blas.NoTrans, blas.Unit, m, k,
+			1, v, ldv,
+			work, ldwork)
+		// C1 -= W.
+		// TODO(btracey): This should use blas.Axpy.
+		for i := 0; i < m; i++ {
+			for j := 0; j < k; j++ {
+				c[i*ldc+j] -= work[i*ldwork+j]
+			}
+		}
+		return
+	}
+	// V = (V1 V2) where V2 is the last k columns and is lower unit triangular.
+	if side == blas.Left {
+		// Form H * C or H^T C where C = (C1 ; C2).
+		// W = C^T * V^T.
+
+		// W = C2^T.
+		for j := 0; j < k; j++ {
+			bi.Dcopy(n, c[(m-k+j)*ldc:], 1, work[j:], ldwork)
+		}
+		// W *= V2^T.
+		bi.Dtrmm(blas.Right, blas.Lower, blas.Trans, blas.Unit, n, k,
+			1, v[m-k:], ldv,
+			work, ldwork)
+		if m > k {
+			bi.Dgemm(blas.Trans, blas.Trans, n, k, m-k,
+				1, c, ldc, v, ldv,
+				1, work, ldwork)
+		}
+		// W *= T or T^T.
+		bi.Dtrmm(blas.Right, blas.Lower, transt, blas.NonUnit, n, k,
+			1, t, ldt,
+			work, ldwork)
+		// C -= V^T * W^T.
+		if m > k {
+			bi.Dgemm(blas.Trans, blas.Trans, m-k, n, k,
+				-1, v, ldv, work, ldwork,
+				1, c, ldc)
+		}
+		// W *= V2.
+		bi.Dtrmm(blas.Right, blas.Lower, blas.NoTrans, blas.Unit, n, k,
+			1, v[m-k:], ldv,
+			work, ldwork)
+		// C2 -= W^T.
+		// TODO(btracey): This should use blas.Axpy.
+		for i := 0; i < n; i++ {
+			for j := 0; j < k; j++ {
+				c[(m-k+j)*ldc+i] -= work[i*ldwork+j]
+			}
+		}
+		return
+	}
+	// Form C * H or C * H^T where C = (C1 C2).
+	// W = C * V^T.
+	// W = C2.
+	for j := 0; j < k; j++ {
+		bi.Dcopy(m, c[n-k+j:], ldc, work[j:], ldwork)
+	}
+	// W *= V2^T.
+	bi.Dtrmm(blas.Right, blas.Lower, blas.Trans, blas.Unit, m, k,
+		1, v[n-k:], ldv,
+		work, ldwork)
+	if n > k {
+		bi.Dgemm(blas.NoTrans, blas.Trans, m, k, n-k,
+			1, c, ldc, v, ldv,
+			1, work, ldwork)
+	}
+	// W *= T or T^T.
+	bi.Dtrmm(blas.Right, blas.Lower, trans, blas.NonUnit, m, k,
+		1, t, ldt,
+		work, ldwork)
+	// C -= W * V.
+	if n > k {
+		bi.Dgemm(blas.NoTrans, blas.NoTrans, m, n-k, k,
+			-1, work, ldwork, v, ldv,
+			1, c, ldc)
+	}
+	// W *= V2.
+	bi.Dtrmm(blas.Right, blas.Lower, blas.NoTrans, blas.Unit, m, k,
+		1, v[n-k:], ldv,
+		work, ldwork)
+	// C1 -= W.
+	// TODO(btracey): This should use blas.Axpy.
+	for i := 0; i < m; i++ {
+		for j := 0; j < k; j++ {
+			c[i*ldc+n-k+j] -= work[i*ldwork+j]
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlarfg.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlarfg.go
new file mode 100644
index 00000000..09977e50
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlarfg.go
@@ -0,0 +1,62 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dlarfg generates an elementary reflector for a Householder matrix. It creates
+// a real elementary reflector of order n such that
+//  H * (alpha) = (beta)
+//      (    x)   (   0)
+//  H^T * H = I
+// H is represented in the form
+//  H = 1 - tau * (1; v) * (1 v^T)
+// where tau is a real scalar.
+//
+// On entry, x contains the vector x, on exit it contains v.
+//
+// Dlarfg is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlarfg(n int, alpha float64, x []float64, incX int) (beta, tau float64) {
+	if n < 0 {
+		panic(nLT0)
+	}
+	if n <= 1 {
+		return alpha, 0
+	}
+	checkVector(n-1, x, incX)
+	bi := blas64.Implementation()
+	xnorm := bi.Dnrm2(n-1, x, incX)
+	if xnorm == 0 {
+		return alpha, 0
+	}
+	beta = -math.Copysign(impl.Dlapy2(alpha, xnorm), alpha)
+	safmin := dlamchS / dlamchE
+	knt := 0
+	if math.Abs(beta) < safmin {
+		// xnorm and beta may be inaccurate, scale x and recompute.
+		rsafmn := 1 / safmin
+		for {
+			knt++
+			bi.Dscal(n-1, rsafmn, x, incX)
+			beta *= rsafmn
+			alpha *= rsafmn
+			if math.Abs(beta) >= safmin {
+				break
+			}
+		}
+		xnorm = bi.Dnrm2(n-1, x, incX)
+		beta = -math.Copysign(impl.Dlapy2(alpha, xnorm), alpha)
+	}
+	tau = (beta - alpha) / beta
+	bi.Dscal(n-1, 1/(alpha-beta), x, incX)
+	for j := 0; j < knt; j++ {
+		beta *= safmin
+	}
+	return beta, tau
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlarft.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlarft.go
new file mode 100644
index 00000000..0a244a48
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlarft.go
@@ -0,0 +1,150 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dlarft forms the triangular factor T of a block reflector H, storing the answer
+// in t.
+//  H = I - V * T * V^T  if store == lapack.ColumnWise
+//  H = I - V^T * T * V  if store == lapack.RowWise
+// H is defined by a product of the elementary reflectors where
+//  H = H_0 * H_1 * ... * H_{k-1}  if direct == lapack.Forward
+//  H = H_{k-1} * ... * H_1 * H_0  if direct == lapack.Backward
+//
+// t is a k×k triangular matrix. t is upper triangular if direct = lapack.Forward
+// and lower triangular otherwise. This function will panic if t is not of
+// sufficient size.
+//
+// store describes the storage of the elementary reflectors in v. Please see
+// Dlarfb for a description of layout.
+//
+// tau contains the scalar factors of the elementary reflectors H_i.
+//
+// Dlarft is an internal routine. It is exported for testing purposes.
+func (Implementation) Dlarft(direct lapack.Direct, store lapack.StoreV, n, k int,
+	v []float64, ldv int, tau []float64, t []float64, ldt int) {
+	if n == 0 {
+		return
+	}
+	if n < 0 || k < 0 {
+		panic(negDimension)
+	}
+	if direct != lapack.Forward && direct != lapack.Backward {
+		panic(badDirect)
+	}
+	if store != lapack.RowWise && store != lapack.ColumnWise {
+		panic(badStore)
+	}
+	if len(tau) < k {
+		panic(badTau)
+	}
+	checkMatrix(k, k, t, ldt)
+	bi := blas64.Implementation()
+	// TODO(btracey): There are a number of minor obvious loop optimizations here.
+	// TODO(btracey): It may be possible to rearrange some of the code so that
+	// index of 1 is more common in the Dgemv.
+	if direct == lapack.Forward {
+		prevlastv := n - 1
+		for i := 0; i < k; i++ {
+			prevlastv = max(i, prevlastv)
+			if tau[i] == 0 {
+				for j := 0; j <= i; j++ {
+					t[j*ldt+i] = 0
+				}
+				continue
+			}
+			var lastv int
+			if store == lapack.ColumnWise {
+				// skip trailing zeros
+				for lastv = n - 1; lastv >= i+1; lastv-- {
+					if v[lastv*ldv+i] != 0 {
+						break
+					}
+				}
+				for j := 0; j < i; j++ {
+					t[j*ldt+i] = -tau[i] * v[i*ldv+j]
+				}
+				j := min(lastv, prevlastv)
+				bi.Dgemv(blas.Trans, j-i, i,
+					-tau[i], v[(i+1)*ldv:], ldv, v[(i+1)*ldv+i:], ldv,
+					1, t[i:], ldt)
+			} else {
+				for lastv = n - 1; lastv >= i+1; lastv-- {
+					if v[i*ldv+lastv] != 0 {
+						break
+					}
+				}
+				for j := 0; j < i; j++ {
+					t[j*ldt+i] = -tau[i] * v[j*ldv+i]
+				}
+				j := min(lastv, prevlastv)
+				bi.Dgemv(blas.NoTrans, i, j-i,
+					-tau[i], v[i+1:], ldv, v[i*ldv+i+1:], 1,
+					1, t[i:], ldt)
+			}
+			bi.Dtrmv(blas.Upper, blas.NoTrans, blas.NonUnit, i, t, ldt, t[i:], ldt)
+			t[i*ldt+i] = tau[i]
+			if i > 1 {
+				prevlastv = max(prevlastv, lastv)
+			} else {
+				prevlastv = lastv
+			}
+		}
+		return
+	}
+	prevlastv := 0
+	for i := k - 1; i >= 0; i-- {
+		if tau[i] == 0 {
+			for j := i; j < k; j++ {
+				t[j*ldt+i] = 0
+			}
+			continue
+		}
+		var lastv int
+		if i < k-1 {
+			if store == lapack.ColumnWise {
+				for lastv = 0; lastv < i; lastv++ {
+					if v[lastv*ldv+i] != 0 {
+						break
+					}
+				}
+				for j := i + 1; j < k; j++ {
+					t[j*ldt+i] = -tau[i] * v[(n-k+i)*ldv+j]
+				}
+				j := max(lastv, prevlastv)
+				bi.Dgemv(blas.Trans, n-k+i-j, k-i-1,
+					-tau[i], v[j*ldv+i+1:], ldv, v[j*ldv+i:], ldv,
+					1, t[(i+1)*ldt+i:], ldt)
+			} else {
+				for lastv = 0; lastv < i; lastv++ {
+					if v[i*ldv+lastv] != 0 {
+						break
+					}
+				}
+				for j := i + 1; j < k; j++ {
+					t[j*ldt+i] = -tau[i] * v[j*ldv+n-k+i]
+				}
+				j := max(lastv, prevlastv)
+				bi.Dgemv(blas.NoTrans, k-i-1, n-k+i-j,
+					-tau[i], v[(i+1)*ldv+j:], ldv, v[i*ldv+j:], 1,
+					1, t[(i+1)*ldt+i:], ldt)
+			}
+			bi.Dtrmv(blas.Lower, blas.NoTrans, blas.NonUnit, k-i-1,
+				t[(i+1)*ldt+i+1:], ldt,
+				t[(i+1)*ldt+i:], ldt)
+			if i > 0 {
+				prevlastv = min(prevlastv, lastv)
+			} else {
+				prevlastv = lastv
+			}
+		}
+		t[i*ldt+i] = tau[i]
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlarfx.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlarfx.go
new file mode 100644
index 00000000..5dc00f03
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlarfx.go
@@ -0,0 +1,535 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "gonum.org/v1/gonum/blas"
+
+// Dlarfx applies an elementary reflector H to a real m×n matrix C, from either
+// the left or the right, with loop unrolling when the reflector has order less
+// than 11.
+//
+// H is represented in the form
+//  H = I - tau * v * v^T,
+// where tau is a real scalar and v is a real vector. If tau = 0, then H is
+// taken to be the identity matrix.
+//
+// v must have length equal to m if side == blas.Left, and equal to n if side ==
+// blas.Right, otherwise Dlarfx will panic.
+//
+// c and ldc represent the m×n matrix C. On return, C is overwritten by the
+// matrix H * C if side == blas.Left, or C * H if side == blas.Right.
+//
+// work must have length at least n if side == blas.Left, and at least m if side
+// == blas.Right, otherwise Dlarfx will panic. work is not referenced if H has
+// order < 11.
+//
+// Dlarfx is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlarfx(side blas.Side, m, n int, v []float64, tau float64, c []float64, ldc int, work []float64) {
+	checkMatrix(m, n, c, ldc)
+	switch side {
+	case blas.Left:
+		checkVector(m, v, 1)
+		if m > 10 && len(work) < n {
+			panic(badWork)
+		}
+	case blas.Right:
+		checkVector(n, v, 1)
+		if n > 10 && len(work) < m {
+			panic(badWork)
+		}
+	default:
+		panic(badSide)
+	}
+
+	if tau == 0 {
+		return
+	}
+
+	if side == blas.Left {
+		// Form H * C, where H has order m.
+		switch m {
+		default: // Code for general m.
+			impl.Dlarf(side, m, n, v, 1, tau, c, ldc, work)
+			return
+
+		case 0: // No-op for zero size matrix.
+			return
+
+		case 1: // Special code for 1×1 Householder matrix.
+			t0 := 1 - tau*v[0]*v[0]
+			for j := 0; j < n; j++ {
+				c[j] *= t0
+			}
+			return
+
+		case 2: // Special code for 2×2 Householder matrix.
+			v0 := v[0]
+			t0 := tau * v0
+			v1 := v[1]
+			t1 := tau * v1
+			for j := 0; j < n; j++ {
+				sum := v0*c[j] + v1*c[ldc+j]
+				c[j] -= sum * t0
+				c[ldc+j] -= sum * t1
+			}
+			return
+
+		case 3: // Special code for 3×3 Householder matrix.
+			v0 := v[0]
+			t0 := tau * v0
+			v1 := v[1]
+			t1 := tau * v1
+			v2 := v[2]
+			t2 := tau * v2
+			for j := 0; j < n; j++ {
+				sum := v0*c[j] + v1*c[ldc+j] + v2*c[2*ldc+j]
+				c[j] -= sum * t0
+				c[ldc+j] -= sum * t1
+				c[2*ldc+j] -= sum * t2
+			}
+			return
+
+		case 4: // Special code for 4×4 Householder matrix.
+			v0 := v[0]
+			t0 := tau * v0
+			v1 := v[1]
+			t1 := tau * v1
+			v2 := v[2]
+			t2 := tau * v2
+			v3 := v[3]
+			t3 := tau * v3
+			for j := 0; j < n; j++ {
+				sum := v0*c[j] + v1*c[ldc+j] + v2*c[2*ldc+j] + v3*c[3*ldc+j]
+				c[j] -= sum * t0
+				c[ldc+j] -= sum * t1
+				c[2*ldc+j] -= sum * t2
+				c[3*ldc+j] -= sum * t3
+			}
+			return
+
+		case 5: // Special code for 5×5 Householder matrix.
+			v0 := v[0]
+			t0 := tau * v0
+			v1 := v[1]
+			t1 := tau * v1
+			v2 := v[2]
+			t2 := tau * v2
+			v3 := v[3]
+			t3 := tau * v3
+			v4 := v[4]
+			t4 := tau * v4
+			for j := 0; j < n; j++ {
+				sum := v0*c[j] + v1*c[ldc+j] + v2*c[2*ldc+j] + v3*c[3*ldc+j] + v4*c[4*ldc+j]
+				c[j] -= sum * t0
+				c[ldc+j] -= sum * t1
+				c[2*ldc+j] -= sum * t2
+				c[3*ldc+j] -= sum * t3
+				c[4*ldc+j] -= sum * t4
+			}
+			return
+
+		case 6: // Special code for 6×6 Householder matrix.
+			v0 := v[0]
+			t0 := tau * v0
+			v1 := v[1]
+			t1 := tau * v1
+			v2 := v[2]
+			t2 := tau * v2
+			v3 := v[3]
+			t3 := tau * v3
+			v4 := v[4]
+			t4 := tau * v4
+			v5 := v[5]
+			t5 := tau * v5
+			for j := 0; j < n; j++ {
+				sum := v0*c[j] + v1*c[ldc+j] + v2*c[2*ldc+j] + v3*c[3*ldc+j] + v4*c[4*ldc+j] +
+					v5*c[5*ldc+j]
+				c[j] -= sum * t0
+				c[ldc+j] -= sum * t1
+				c[2*ldc+j] -= sum * t2
+				c[3*ldc+j] -= sum * t3
+				c[4*ldc+j] -= sum * t4
+				c[5*ldc+j] -= sum * t5
+			}
+			return
+
+		case 7: // Special code for 7×7 Householder matrix.
+			v0 := v[0]
+			t0 := tau * v0
+			v1 := v[1]
+			t1 := tau * v1
+			v2 := v[2]
+			t2 := tau * v2
+			v3 := v[3]
+			t3 := tau * v3
+			v4 := v[4]
+			t4 := tau * v4
+			v5 := v[5]
+			t5 := tau * v5
+			v6 := v[6]
+			t6 := tau * v6
+			for j := 0; j < n; j++ {
+				sum := v0*c[j] + v1*c[ldc+j] + v2*c[2*ldc+j] + v3*c[3*ldc+j] + v4*c[4*ldc+j] +
+					v5*c[5*ldc+j] + v6*c[6*ldc+j]
+				c[j] -= sum * t0
+				c[ldc+j] -= sum * t1
+				c[2*ldc+j] -= sum * t2
+				c[3*ldc+j] -= sum * t3
+				c[4*ldc+j] -= sum * t4
+				c[5*ldc+j] -= sum * t5
+				c[6*ldc+j] -= sum * t6
+			}
+			return
+
+		case 8: // Special code for 8×8 Householder matrix.
+			v0 := v[0]
+			t0 := tau * v0
+			v1 := v[1]
+			t1 := tau * v1
+			v2 := v[2]
+			t2 := tau * v2
+			v3 := v[3]
+			t3 := tau * v3
+			v4 := v[4]
+			t4 := tau * v4
+			v5 := v[5]
+			t5 := tau * v5
+			v6 := v[6]
+			t6 := tau * v6
+			v7 := v[7]
+			t7 := tau * v7
+			for j := 0; j < n; j++ {
+				sum := v0*c[j] + v1*c[ldc+j] + v2*c[2*ldc+j] + v3*c[3*ldc+j] + v4*c[4*ldc+j] +
+					v5*c[5*ldc+j] + v6*c[6*ldc+j] + v7*c[7*ldc+j]
+				c[j] -= sum * t0
+				c[ldc+j] -= sum * t1
+				c[2*ldc+j] -= sum * t2
+				c[3*ldc+j] -= sum * t3
+				c[4*ldc+j] -= sum * t4
+				c[5*ldc+j] -= sum * t5
+				c[6*ldc+j] -= sum * t6
+				c[7*ldc+j] -= sum * t7
+			}
+			return
+
+		case 9: // Special code for 9×9 Householder matrix.
+			v0 := v[0]
+			t0 := tau * v0
+			v1 := v[1]
+			t1 := tau * v1
+			v2 := v[2]
+			t2 := tau * v2
+			v3 := v[3]
+			t3 := tau * v3
+			v4 := v[4]
+			t4 := tau * v4
+			v5 := v[5]
+			t5 := tau * v5
+			v6 := v[6]
+			t6 := tau * v6
+			v7 := v[7]
+			t7 := tau * v7
+			v8 := v[8]
+			t8 := tau * v8
+			for j := 0; j < n; j++ {
+				sum := v0*c[j] + v1*c[ldc+j] + v2*c[2*ldc+j] + v3*c[3*ldc+j] + v4*c[4*ldc+j] +
+					v5*c[5*ldc+j] + v6*c[6*ldc+j] + v7*c[7*ldc+j] + v8*c[8*ldc+j]
+				c[j] -= sum * t0
+				c[ldc+j] -= sum * t1
+				c[2*ldc+j] -= sum * t2
+				c[3*ldc+j] -= sum * t3
+				c[4*ldc+j] -= sum * t4
+				c[5*ldc+j] -= sum * t5
+				c[6*ldc+j] -= sum * t6
+				c[7*ldc+j] -= sum * t7
+				c[8*ldc+j] -= sum * t8
+			}
+			return
+
+		case 10: // Special code for 10×10 Householder matrix.
+			v0 := v[0]
+			t0 := tau * v0
+			v1 := v[1]
+			t1 := tau * v1
+			v2 := v[2]
+			t2 := tau * v2
+			v3 := v[3]
+			t3 := tau * v3
+			v4 := v[4]
+			t4 := tau * v4
+			v5 := v[5]
+			t5 := tau * v5
+			v6 := v[6]
+			t6 := tau * v6
+			v7 := v[7]
+			t7 := tau * v7
+			v8 := v[8]
+			t8 := tau * v8
+			v9 := v[9]
+			t9 := tau * v9
+			for j := 0; j < n; j++ {
+				sum := v0*c[j] + v1*c[ldc+j] + v2*c[2*ldc+j] + v3*c[3*ldc+j] + v4*c[4*ldc+j] +
+					v5*c[5*ldc+j] + v6*c[6*ldc+j] + v7*c[7*ldc+j] + v8*c[8*ldc+j] + v9*c[9*ldc+j]
+				c[j] -= sum * t0
+				c[ldc+j] -= sum * t1
+				c[2*ldc+j] -= sum * t2
+				c[3*ldc+j] -= sum * t3
+				c[4*ldc+j] -= sum * t4
+				c[5*ldc+j] -= sum * t5
+				c[6*ldc+j] -= sum * t6
+				c[7*ldc+j] -= sum * t7
+				c[8*ldc+j] -= sum * t8
+				c[9*ldc+j] -= sum * t9
+			}
+			return
+		}
+	}
+
+	// Form C * H, where H has order n.
+	switch n {
+	default: // Code for general n.
+		impl.Dlarf(side, m, n, v, 1, tau, c, ldc, work)
+		return
+
+	case 0: // No-op for zero size matrix.
+		return
+
+	case 1: // Special code for 1×1 Householder matrix.
+		t0 := 1 - tau*v[0]*v[0]
+		for j := 0; j < m; j++ {
+			c[j*ldc] *= t0
+		}
+		return
+
+	case 2: // Special code for 2×2 Householder matrix.
+		v0 := v[0]
+		t0 := tau * v0
+		v1 := v[1]
+		t1 := tau * v1
+		for j := 0; j < m; j++ {
+			cs := c[j*ldc:]
+			sum := v0*cs[0] + v1*cs[1]
+			cs[0] -= sum * t0
+			cs[1] -= sum * t1
+		}
+		return
+
+	case 3: // Special code for 3×3 Householder matrix.
+		v0 := v[0]
+		t0 := tau * v0
+		v1 := v[1]
+		t1 := tau * v1
+		v2 := v[2]
+		t2 := tau * v2
+		for j := 0; j < m; j++ {
+			cs := c[j*ldc:]
+			sum := v0*cs[0] + v1*cs[1] + v2*cs[2]
+			cs[0] -= sum * t0
+			cs[1] -= sum * t1
+			cs[2] -= sum * t2
+		}
+		return
+
+	case 4: // Special code for 4×4 Householder matrix.
+		v0 := v[0]
+		t0 := tau * v0
+		v1 := v[1]
+		t1 := tau * v1
+		v2 := v[2]
+		t2 := tau * v2
+		v3 := v[3]
+		t3 := tau * v3
+		for j := 0; j < m; j++ {
+			cs := c[j*ldc:]
+			sum := v0*cs[0] + v1*cs[1] + v2*cs[2] + v3*cs[3]
+			cs[0] -= sum * t0
+			cs[1] -= sum * t1
+			cs[2] -= sum * t2
+			cs[3] -= sum * t3
+		}
+		return
+
+	case 5: // Special code for 5×5 Householder matrix.
+		v0 := v[0]
+		t0 := tau * v0
+		v1 := v[1]
+		t1 := tau * v1
+		v2 := v[2]
+		t2 := tau * v2
+		v3 := v[3]
+		t3 := tau * v3
+		v4 := v[4]
+		t4 := tau * v4
+		for j := 0; j < m; j++ {
+			cs := c[j*ldc:]
+			sum := v0*cs[0] + v1*cs[1] + v2*cs[2] + v3*cs[3] + v4*cs[4]
+			cs[0] -= sum * t0
+			cs[1] -= sum * t1
+			cs[2] -= sum * t2
+			cs[3] -= sum * t3
+			cs[4] -= sum * t4
+		}
+		return
+
+	case 6: // Special code for 6×6 Householder matrix.
+		v0 := v[0]
+		t0 := tau * v0
+		v1 := v[1]
+		t1 := tau * v1
+		v2 := v[2]
+		t2 := tau * v2
+		v3 := v[3]
+		t3 := tau * v3
+		v4 := v[4]
+		t4 := tau * v4
+		v5 := v[5]
+		t5 := tau * v5
+		for j := 0; j < m; j++ {
+			cs := c[j*ldc:]
+			sum := v0*cs[0] + v1*cs[1] + v2*cs[2] + v3*cs[3] + v4*cs[4] + v5*cs[5]
+			cs[0] -= sum * t0
+			cs[1] -= sum * t1
+			cs[2] -= sum * t2
+			cs[3] -= sum * t3
+			cs[4] -= sum * t4
+			cs[5] -= sum * t5
+		}
+		return
+
+	case 7: // Special code for 7×7 Householder matrix.
+		v0 := v[0]
+		t0 := tau * v0
+		v1 := v[1]
+		t1 := tau * v1
+		v2 := v[2]
+		t2 := tau * v2
+		v3 := v[3]
+		t3 := tau * v3
+		v4 := v[4]
+		t4 := tau * v4
+		v5 := v[5]
+		t5 := tau * v5
+		v6 := v[6]
+		t6 := tau * v6
+		for j := 0; j < m; j++ {
+			cs := c[j*ldc:]
+			sum := v0*cs[0] + v1*cs[1] + v2*cs[2] + v3*cs[3] + v4*cs[4] +
+				v5*cs[5] + v6*cs[6]
+			cs[0] -= sum * t0
+			cs[1] -= sum * t1
+			cs[2] -= sum * t2
+			cs[3] -= sum * t3
+			cs[4] -= sum * t4
+			cs[5] -= sum * t5
+			cs[6] -= sum * t6
+		}
+		return
+
+	case 8: // Special code for 8×8 Householder matrix.
+		v0 := v[0]
+		t0 := tau * v0
+		v1 := v[1]
+		t1 := tau * v1
+		v2 := v[2]
+		t2 := tau * v2
+		v3 := v[3]
+		t3 := tau * v3
+		v4 := v[4]
+		t4 := tau * v4
+		v5 := v[5]
+		t5 := tau * v5
+		v6 := v[6]
+		t6 := tau * v6
+		v7 := v[7]
+		t7 := tau * v7
+		for j := 0; j < m; j++ {
+			cs := c[j*ldc:]
+			sum := v0*cs[0] + v1*cs[1] + v2*cs[2] + v3*cs[3] + v4*cs[4] +
+				v5*cs[5] + v6*cs[6] + v7*cs[7]
+			cs[0] -= sum * t0
+			cs[1] -= sum * t1
+			cs[2] -= sum * t2
+			cs[3] -= sum * t3
+			cs[4] -= sum * t4
+			cs[5] -= sum * t5
+			cs[6] -= sum * t6
+			cs[7] -= sum * t7
+		}
+		return
+
+	case 9: // Special code for 9×9 Householder matrix.
+		v0 := v[0]
+		t0 := tau * v0
+		v1 := v[1]
+		t1 := tau * v1
+		v2 := v[2]
+		t2 := tau * v2
+		v3 := v[3]
+		t3 := tau * v3
+		v4 := v[4]
+		t4 := tau * v4
+		v5 := v[5]
+		t5 := tau * v5
+		v6 := v[6]
+		t6 := tau * v6
+		v7 := v[7]
+		t7 := tau * v7
+		v8 := v[8]
+		t8 := tau * v8
+		for j := 0; j < m; j++ {
+			cs := c[j*ldc:]
+			sum := v0*cs[0] + v1*cs[1] + v2*cs[2] + v3*cs[3] + v4*cs[4] +
+				v5*cs[5] + v6*cs[6] + v7*cs[7] + v8*cs[8]
+			cs[0] -= sum * t0
+			cs[1] -= sum * t1
+			cs[2] -= sum * t2
+			cs[3] -= sum * t3
+			cs[4] -= sum * t4
+			cs[5] -= sum * t5
+			cs[6] -= sum * t6
+			cs[7] -= sum * t7
+			cs[8] -= sum * t8
+		}
+		return
+
+	case 10: // Special code for 10×10 Householder matrix.
+		v0 := v[0]
+		t0 := tau * v0
+		v1 := v[1]
+		t1 := tau * v1
+		v2 := v[2]
+		t2 := tau * v2
+		v3 := v[3]
+		t3 := tau * v3
+		v4 := v[4]
+		t4 := tau * v4
+		v5 := v[5]
+		t5 := tau * v5
+		v6 := v[6]
+		t6 := tau * v6
+		v7 := v[7]
+		t7 := tau * v7
+		v8 := v[8]
+		t8 := tau * v8
+		v9 := v[9]
+		t9 := tau * v9
+		for j := 0; j < m; j++ {
+			cs := c[j*ldc:]
+			sum := v0*cs[0] + v1*cs[1] + v2*cs[2] + v3*cs[3] + v4*cs[4] +
+				v5*cs[5] + v6*cs[6] + v7*cs[7] + v8*cs[8] + v9*cs[9]
+			cs[0] -= sum * t0
+			cs[1] -= sum * t1
+			cs[2] -= sum * t2
+			cs[3] -= sum * t3
+			cs[4] -= sum * t4
+			cs[5] -= sum * t5
+			cs[6] -= sum * t6
+			cs[7] -= sum * t7
+			cs[8] -= sum * t8
+			cs[9] -= sum * t9
+		}
+		return
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlartg.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlartg.go
new file mode 100644
index 00000000..85aa2064
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlartg.go
@@ -0,0 +1,80 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "math"
+
+// Dlartg generates a plane rotation so that
+//  [ cs sn] * [f] = [r]
+//  [-sn cs]   [g] = [0]
+// This is a more accurate version of BLAS drotg, with the other differences that
+// if g = 0, then cs = 1 and sn = 0, and if f = 0 and g != 0, then cs = 0 and sn = 1.
+// If abs(f) > abs(g), cs will be positive.
+//
+// Dlartg is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlartg(f, g float64) (cs, sn, r float64) {
+	safmn2 := math.Pow(dlamchB, math.Trunc(math.Log(dlamchS/dlamchE)/math.Log(dlamchB)/2))
+	safmx2 := 1 / safmn2
+	if g == 0 {
+		cs = 1
+		sn = 0
+		r = f
+		return cs, sn, r
+	}
+	if f == 0 {
+		cs = 0
+		sn = 1
+		r = g
+		return cs, sn, r
+	}
+	f1 := f
+	g1 := g
+	scale := math.Max(math.Abs(f1), math.Abs(g1))
+	if scale >= safmx2 {
+		var count int
+		for {
+			count++
+			f1 *= safmn2
+			g1 *= safmn2
+			scale = math.Max(math.Abs(f1), math.Abs(g1))
+			if scale < safmx2 {
+				break
+			}
+		}
+		r = math.Sqrt(f1*f1 + g1*g1)
+		cs = f1 / r
+		sn = g1 / r
+		for i := 0; i < count; i++ {
+			r *= safmx2
+		}
+	} else if scale <= safmn2 {
+		var count int
+		for {
+			count++
+			f1 *= safmx2
+			g1 *= safmx2
+			scale = math.Max(math.Abs(f1), math.Abs(g1))
+			if scale >= safmn2 {
+				break
+			}
+		}
+		r = math.Sqrt(f1*f1 + g1*g1)
+		cs = f1 / r
+		sn = g1 / r
+		for i := 0; i < count; i++ {
+			r *= safmn2
+		}
+	} else {
+		r = math.Sqrt(f1*f1 + g1*g1)
+		cs = f1 / r
+		sn = g1 / r
+	}
+	if math.Abs(f) > math.Abs(g) && cs < 0 {
+		cs *= -1
+		sn *= -1
+		r *= -1
+	}
+	return cs, sn, r
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlas2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlas2.go
new file mode 100644
index 00000000..40a4b9c3
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlas2.go
@@ -0,0 +1,43 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "math"
+
+// Dlas2 computes the singular values of the 2×2 matrix defined by
+//  [F G]
+//  [0 H]
+// The smaller and larger singular values are returned in that order.
+//
+// Dlas2 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlas2(f, g, h float64) (ssmin, ssmax float64) {
+	fa := math.Abs(f)
+	ga := math.Abs(g)
+	ha := math.Abs(h)
+	fhmin := math.Min(fa, ha)
+	fhmax := math.Max(fa, ha)
+	if fhmin == 0 {
+		if fhmax == 0 {
+			return 0, ga
+		}
+		v := math.Min(fhmax, ga) / math.Max(fhmax, ga)
+		return 0, math.Max(fhmax, ga) * math.Sqrt(1+v*v)
+	}
+	if ga < fhmax {
+		as := 1 + fhmin/fhmax
+		at := (fhmax - fhmin) / fhmax
+		au := (ga / fhmax) * (ga / fhmax)
+		c := 2 / (math.Sqrt(as*as+au) + math.Sqrt(at*at+au))
+		return fhmin * c, fhmax / c
+	}
+	au := fhmax / ga
+	if au == 0 {
+		return fhmin * fhmax / ga, ga
+	}
+	as := 1 + fhmin/fhmax
+	at := (fhmax - fhmin) / fhmax
+	c := 1 / (math.Sqrt(1+(as*au)*(as*au)) + math.Sqrt(1+(at*au)*(at*au)))
+	return 2 * (fhmin * c) * au, ga / (c + c)
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlascl.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlascl.go
new file mode 100644
index 00000000..b25408df
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlascl.go
@@ -0,0 +1,89 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dlascl multiplies an m×n matrix by the scalar cto/cfrom.
+//
+// cfrom must not be zero, and cto and cfrom must not be NaN, otherwise Dlascl
+// will panic.
+//
+// Dlascl is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlascl(kind lapack.MatrixType, kl, ku int, cfrom, cto float64, m, n int, a []float64, lda int) {
+	checkMatrix(m, n, a, lda)
+	if cfrom == 0 {
+		panic(zeroDiv)
+	}
+	if math.IsNaN(cfrom) || math.IsNaN(cto) {
+		panic(nanScale)
+	}
+	if n == 0 || m == 0 {
+		return
+	}
+	smlnum := dlamchS
+	bignum := 1 / smlnum
+	cfromc := cfrom
+	ctoc := cto
+	cfrom1 := cfromc * smlnum
+	for {
+		var done bool
+		var mul, ctol float64
+		if cfrom1 == cfromc {
+			// cfromc is inf.
+			mul = ctoc / cfromc
+			done = true
+			ctol = ctoc
+		} else {
+			ctol = ctoc / bignum
+			if ctol == ctoc {
+				// ctoc is either 0 or inf.
+				mul = ctoc
+				done = true
+				cfromc = 1
+			} else if math.Abs(cfrom1) > math.Abs(ctoc) && ctoc != 0 {
+				mul = smlnum
+				done = false
+				cfromc = cfrom1
+			} else if math.Abs(ctol) > math.Abs(cfromc) {
+				mul = bignum
+				done = false
+				ctoc = ctol
+			} else {
+				mul = ctoc / cfromc
+				done = true
+			}
+		}
+		switch kind {
+		default:
+			panic("lapack: not implemented")
+		case lapack.General:
+			for i := 0; i < m; i++ {
+				for j := 0; j < n; j++ {
+					a[i*lda+j] = a[i*lda+j] * mul
+				}
+			}
+		case lapack.UpperTri:
+			for i := 0; i < m; i++ {
+				for j := i; j < n; j++ {
+					a[i*lda+j] = a[i*lda+j] * mul
+				}
+			}
+		case lapack.LowerTri:
+			for i := 0; i < m; i++ {
+				for j := 0; j <= min(i, n-1); j++ {
+					a[i*lda+j] = a[i*lda+j] * mul
+				}
+			}
+		}
+		if done {
+			break
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlaset.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlaset.go
new file mode 100644
index 00000000..79d7edfd
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlaset.go
@@ -0,0 +1,40 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "gonum.org/v1/gonum/blas"
+
+// Dlaset sets the off-diagonal elements of A to alpha, and the diagonal
+// elements to beta. If uplo == blas.Upper, only the elements in the upper
+// triangular part are set. If uplo == blas.Lower, only the elements in the
+// lower triangular part are set. If uplo is otherwise, all of the elements of A
+// are set.
+//
+// Dlaset is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlaset(uplo blas.Uplo, m, n int, alpha, beta float64, a []float64, lda int) {
+	checkMatrix(m, n, a, lda)
+	if uplo == blas.Upper {
+		for i := 0; i < m; i++ {
+			for j := i + 1; j < n; j++ {
+				a[i*lda+j] = alpha
+			}
+		}
+	} else if uplo == blas.Lower {
+		for i := 0; i < m; i++ {
+			for j := 0; j < min(i+1, n); j++ {
+				a[i*lda+j] = alpha
+			}
+		}
+	} else {
+		for i := 0; i < m; i++ {
+			for j := 0; j < n; j++ {
+				a[i*lda+j] = alpha
+			}
+		}
+	}
+	for i := 0; i < min(m, n); i++ {
+		a[i*lda+i] = beta
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlasq1.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlasq1.go
new file mode 100644
index 00000000..0c91ded4
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlasq1.go
@@ -0,0 +1,97 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dlasq1 computes the singular values of an n×n bidiagonal matrix with diagonal
+// d and off-diagonal e. On exit, d contains the singular values in decreasing
+// order, and e is overwritten. d must have length at least n, e must have
+// length at least n-1, and the input work must have length at least 4*n. Dlasq1
+// will panic if these conditions are not met.
+//
+// Dlasq1 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlasq1(n int, d, e, work []float64) (info int) {
+	// TODO(btracey): replace info with an error.
+	if n < 0 {
+		panic(nLT0)
+	}
+	if len(work) < 4*n {
+		panic(badWork)
+	}
+	if len(d) < n {
+		panic("lapack: length of d less than n")
+	}
+	if len(e) < n-1 {
+		panic("lapack: length of e less than n-1")
+	}
+	if n == 0 {
+		return info
+	}
+	if n == 1 {
+		d[0] = math.Abs(d[0])
+		return info
+	}
+	if n == 2 {
+		d[1], d[0] = impl.Dlas2(d[0], e[0], d[1])
+		return info
+	}
+	// Estimate the largest singular value.
+	var sigmx float64
+	for i := 0; i < n-1; i++ {
+		d[i] = math.Abs(d[i])
+		sigmx = math.Max(sigmx, math.Abs(e[i]))
+	}
+	d[n-1] = math.Abs(d[n-1])
+	// Early return if sigmx is zero (matrix is already diagonal).
+	if sigmx == 0 {
+		impl.Dlasrt(lapack.SortDecreasing, n, d)
+		return info
+	}
+
+	for i := 0; i < n; i++ {
+		sigmx = math.Max(sigmx, d[i])
+	}
+
+	// Copy D and E into WORK (in the Z format) and scale (squaring the
+	// input data makes scaling by a power of the radix pointless).
+
+	eps := dlamchP
+	safmin := dlamchS
+	scale := math.Sqrt(eps / safmin)
+	bi := blas64.Implementation()
+	bi.Dcopy(n, d, 1, work, 2)
+	bi.Dcopy(n-1, e, 1, work[1:], 2)
+	impl.Dlascl(lapack.General, 0, 0, sigmx, scale, 2*n-1, 1, work, 1)
+
+	// Compute the q's and e's.
+	for i := 0; i < 2*n-1; i++ {
+		work[i] *= work[i]
+	}
+	work[2*n-1] = 0
+
+	info = impl.Dlasq2(n, work)
+	if info == 0 {
+		for i := 0; i < n; i++ {
+			d[i] = math.Sqrt(work[i])
+		}
+		impl.Dlascl(lapack.General, 0, 0, scale, sigmx, n, 1, d, 1)
+	} else if info == 2 {
+		// Maximum number of iterations exceeded. Move data from work
+		// into D and E so the calling subroutine can try to finish.
+		for i := 0; i < n; i++ {
+			d[i] = math.Sqrt(work[2*i])
+			e[i] = math.Sqrt(work[2*i+1])
+		}
+		impl.Dlascl(lapack.General, 0, 0, scale, sigmx, n, 1, d, 1)
+		impl.Dlascl(lapack.General, 0, 0, scale, sigmx, n, 1, e, 1)
+	}
+	return info
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlasq2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlasq2.go
new file mode 100644
index 00000000..ebf5863a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlasq2.go
@@ -0,0 +1,368 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dlasq2 computes all the eigenvalues of the symmetric positive
+// definite tridiagonal matrix associated with the qd array Z. Eigevalues
+// are computed to high relative accuracy avoiding denormalization, underflow
+// and overflow.
+//
+// To see the relation of Z to the tridiagonal matrix, let L be a
+// unit lower bidiagonal matrix with sub-diagonals Z(2,4,6,,..) and
+// let U be an upper bidiagonal matrix with 1's above and diagonal
+// Z(1,3,5,,..). The tridiagonal is L*U or, if you prefer, the
+// symmetric tridiagonal to which it is similar.
+//
+// info returns a status error. The return codes mean as follows:
+//  0: The algorithm completed successfully.
+//  1: A split was marked by a positive value in e.
+//  2: Current block of Z not diagonalized after 100*n iterations (in inner
+//     while loop). On exit Z holds a qd array with the same eigenvalues as
+//     the given Z.
+//  3: Termination criterion of outer while loop not met (program created more
+//     than N unreduced blocks).
+//
+// z must have length at least 4*n, and must not contain any negative elements.
+// Dlasq2 will panic otherwise.
+//
+// Dlasq2 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlasq2(n int, z []float64) (info int) {
+	// TODO(btracey): make info an error.
+	if len(z) < 4*n {
+		panic(badZ)
+	}
+	const cbias = 1.5
+
+	eps := dlamchP
+	safmin := dlamchS
+	tol := eps * 100
+	tol2 := tol * tol
+	if n < 0 {
+		panic(nLT0)
+	}
+	if n == 0 {
+		return info
+	}
+	if n == 1 {
+		if z[0] < 0 {
+			panic(negZ)
+		}
+		return info
+	}
+	if n == 2 {
+		if z[1] < 0 || z[2] < 0 {
+			panic("lapack: bad z value")
+		} else if z[2] > z[0] {
+			z[0], z[2] = z[2], z[0]
+		}
+		z[4] = z[0] + z[1] + z[2]
+		if z[1] > z[2]*tol2 {
+			t := 0.5 * (z[0] - z[2] + z[1])
+			s := z[2] * (z[1] / t)
+			if s <= t {
+				s = z[2] * (z[1] / (t * (1 + math.Sqrt(1+s/t))))
+			} else {
+				s = z[2] * (z[1] / (t + math.Sqrt(t)*math.Sqrt(t+s)))
+			}
+			t = z[0] + s + z[1]
+			z[2] *= z[0] / t
+			z[0] = t
+		}
+		z[1] = z[2]
+		z[5] = z[1] + z[0]
+		return info
+	}
+	// Check for negative data and compute sums of q's and e's.
+	z[2*n-1] = 0
+	emin := z[1]
+	var d, e, qmax float64
+	var i1, n1 int
+	for k := 0; k < 2*(n-1); k += 2 {
+		if z[k] < 0 || z[k+1] < 0 {
+			panic("lapack: bad z value")
+		}
+		d += z[k]
+		e += z[k+1]
+		qmax = math.Max(qmax, z[k])
+		emin = math.Min(emin, z[k+1])
+	}
+	if z[2*(n-1)] < 0 {
+		panic("lapack: bad z value")
+	}
+	d += z[2*(n-1)]
+	qmax = math.Max(qmax, z[2*(n-1)])
+	// Check for diagonality.
+	if e == 0 {
+		for k := 1; k < n; k++ {
+			z[k] = z[2*k]
+		}
+		impl.Dlasrt(lapack.SortDecreasing, n, z)
+		z[2*(n-1)] = d
+		return info
+	}
+	trace := d + e
+	// Check for zero data.
+	if trace == 0 {
+		z[2*(n-1)] = 0
+		return info
+	}
+	// Rearrange data for locality: Z=(q1,qq1,e1,ee1,q2,qq2,e2,ee2,...).
+	for k := 2 * n; k >= 2; k -= 2 {
+		z[2*k-1] = 0
+		z[2*k-2] = z[k-1]
+		z[2*k-3] = 0
+		z[2*k-4] = z[k-2]
+	}
+	i0 := 0
+	n0 := n - 1
+
+	// Reverse the qd-array, if warranted.
+	// z[4*i0-3] --> z[4*(i0+1)-3-1] --> z[4*i0]
+	if cbias*z[4*i0] < z[4*n0] {
+		ipn4Out := 4 * (i0 + n0 + 2)
+		for i4loop := 4 * (i0 + 1); i4loop <= 2*(i0+n0+1); i4loop += 4 {
+			i4 := i4loop - 1
+			ipn4 := ipn4Out - 1
+			z[i4-3], z[ipn4-i4-4] = z[ipn4-i4-4], z[i4-3]
+			z[i4-1], z[ipn4-i4-6] = z[ipn4-i4-6], z[i4-1]
+		}
+	}
+
+	// Initial split checking via dqd and Li's test.
+	pp := 0
+	for k := 0; k < 2; k++ {
+		d = z[4*n0+pp]
+		for i4loop := 4*n0 + pp; i4loop >= 4*(i0+1)+pp; i4loop -= 4 {
+			i4 := i4loop - 1
+			if z[i4-1] <= tol2*d {
+				z[i4-1] = math.Copysign(0, -1)
+				d = z[i4-3]
+			} else {
+				d = z[i4-3] * (d / (d + z[i4-1]))
+			}
+		}
+		// dqd maps Z to ZZ plus Li's test.
+		emin = z[4*(i0+1)+pp]
+		d = z[4*i0+pp]
+		for i4loop := 4*(i0+1) + pp; i4loop <= 4*n0+pp; i4loop += 4 {
+			i4 := i4loop - 1
+			z[i4-2*pp-2] = d + z[i4-1]
+			if z[i4-1] <= tol2*d {
+				z[i4-1] = math.Copysign(0, -1)
+				z[i4-2*pp-2] = d
+				z[i4-2*pp] = 0
+				d = z[i4+1]
+			} else if safmin*z[i4+1] < z[i4-2*pp-2] && safmin*z[i4-2*pp-2] < z[i4+1] {
+				tmp := z[i4+1] / z[i4-2*pp-2]
+				z[i4-2*pp] = z[i4-1] * tmp
+				d *= tmp
+			} else {
+				z[i4-2*pp] = z[i4+1] * (z[i4-1] / z[i4-2*pp-2])
+				d = z[i4+1] * (d / z[i4-2*pp-2])
+			}
+			emin = math.Min(emin, z[i4-2*pp])
+		}
+		z[4*(n0+1)-pp-3] = d
+
+		// Now find qmax.
+		qmax = z[4*(i0+1)-pp-3]
+		for i4loop := 4*(i0+1) - pp + 2; i4loop <= 4*(n0+1)+pp-2; i4loop += 4 {
+			i4 := i4loop - 1
+			qmax = math.Max(qmax, z[i4])
+		}
+		// Prepare for the next iteration on K.
+		pp = 1 - pp
+	}
+
+	// Initialise variables to pass to DLASQ3.
+	var ttype int
+	var dmin1, dmin2, dn, dn1, dn2, g, tau float64
+	var tempq float64
+	iter := 2
+	var nFail int
+	nDiv := 2 * (n0 - i0)
+	var i4 int
+outer:
+	for iwhila := 1; iwhila <= n+1; iwhila++ {
+		// Test for completion.
+		if n0 < 0 {
+			// Move q's to the front.
+			for k := 1; k < n; k++ {
+				z[k] = z[4*k]
+			}
+			// Sort and compute sum of eigenvalues.
+			impl.Dlasrt(lapack.SortDecreasing, n, z)
+			e = 0
+			for k := n - 1; k >= 0; k-- {
+				e += z[k]
+			}
+			// Store trace, sum(eigenvalues) and information on performance.
+			z[2*n] = trace
+			z[2*n+1] = e
+			z[2*n+2] = float64(iter)
+			z[2*n+3] = float64(nDiv) / float64(n*n)
+			z[2*n+4] = 100 * float64(nFail) / float64(iter)
+			return info
+		}
+
+		// While array unfinished do
+		// e[n0] holds the value of sigma when submatrix in i0:n0
+		// splits from the rest of the array, but is negated.
+		var desig float64
+		var sigma float64
+		if n0 != n-1 {
+			sigma = -z[4*(n0+1)-2]
+		}
+		if sigma < 0 {
+			info = 1
+			return info
+		}
+		// Find last unreduced submatrix's top index i0, find qmax and
+		// emin. Find Gershgorin-type bound if Q's much greater than E's.
+		var emax float64
+		if n0 > i0 {
+			emin = math.Abs(z[4*(n0+1)-6])
+		} else {
+			emin = 0
+		}
+		qmin := z[4*(n0+1)-4]
+		qmax = qmin
+		zSmall := false
+		for i4loop := 4 * (n0 + 1); i4loop >= 8; i4loop -= 4 {
+			i4 = i4loop - 1
+			if z[i4-5] <= 0 {
+				zSmall = true
+				break
+			}
+			if qmin >= 4*emax {
+				qmin = math.Min(qmin, z[i4-3])
+				emax = math.Max(emax, z[i4-5])
+			}
+			qmax = math.Max(qmax, z[i4-7]+z[i4-5])
+			emin = math.Min(emin, z[i4-5])
+		}
+		if !zSmall {
+			i4 = 3
+		}
+		i0 = (i4+1)/4 - 1
+		pp = 0
+		if n0-i0 > 1 {
+			dee := z[4*i0]
+			deemin := dee
+			kmin := i0
+			for i4loop := 4*(i0+1) + 1; i4loop <= 4*(n0+1)-3; i4loop += 4 {
+				i4 := i4loop - 1
+				dee = z[i4] * (dee / (dee + z[i4-2]))
+				if dee <= deemin {
+					deemin = dee
+					kmin = (i4+4)/4 - 1
+				}
+			}
+			if (kmin-i0)*2 < n0-kmin && deemin <= 0.5*z[4*n0] {
+				ipn4Out := 4 * (i0 + n0 + 2)
+				pp = 2
+				for i4loop := 4 * (i0 + 1); i4loop <= 2*(i0+n0+1); i4loop += 4 {
+					i4 := i4loop - 1
+					ipn4 := ipn4Out - 1
+					z[i4-3], z[ipn4-i4-4] = z[ipn4-i4-4], z[i4-3]
+					z[i4-2], z[ipn4-i4-3] = z[ipn4-i4-3], z[i4-2]
+					z[i4-1], z[ipn4-i4-6] = z[ipn4-i4-6], z[i4-1]
+					z[i4], z[ipn4-i4-5] = z[ipn4-i4-5], z[i4]
+				}
+			}
+		}
+		// Put -(initial shift) into DMIN.
+		dmin := -math.Max(0, qmin-2*math.Sqrt(qmin)*math.Sqrt(emax))
+
+		// Now i0:n0 is unreduced.
+		// PP = 0 for ping, PP = 1 for pong.
+		// PP = 2 indicates that flipping was applied to the Z array and
+		// 		and that the tests for deflation upon entry in Dlasq3
+		// 		should not be performed.
+		nbig := 100 * (n0 - i0 + 1)
+		for iwhilb := 0; iwhilb < nbig; iwhilb++ {
+			if i0 > n0 {
+				continue outer
+			}
+
+			// While submatrix unfinished take a good dqds step.
+			i0, n0, pp, dmin, sigma, desig, qmax, nFail, iter, nDiv, ttype, dmin1, dmin2, dn, dn1, dn2, g, tau =
+				impl.Dlasq3(i0, n0, z, pp, dmin, sigma, desig, qmax, nFail, iter, nDiv, ttype, dmin1, dmin2, dn, dn1, dn2, g, tau)
+
+			pp = 1 - pp
+			// When emin is very small check for splits.
+			if pp == 0 && n0-i0 >= 3 {
+				if z[4*(n0+1)-1] <= tol2*qmax || z[4*(n0+1)-2] <= tol2*sigma {
+					splt := i0 - 1
+					qmax = z[4*i0]
+					emin = z[4*(i0+1)-2]
+					oldemn := z[4*(i0+1)-1]
+					for i4loop := 4 * (i0 + 1); i4loop <= 4*(n0-2); i4loop += 4 {
+						i4 := i4loop - 1
+						if z[i4] <= tol2*z[i4-3] || z[i4-1] <= tol2*sigma {
+							z[i4-1] = -sigma
+							splt = i4 / 4
+							qmax = 0
+							emin = z[i4+3]
+							oldemn = z[i4+4]
+						} else {
+							qmax = math.Max(qmax, z[i4+1])
+							emin = math.Min(emin, z[i4-1])
+							oldemn = math.Min(oldemn, z[i4])
+						}
+					}
+					z[4*(n0+1)-2] = emin
+					z[4*(n0+1)-1] = oldemn
+					i0 = splt + 1
+				}
+			}
+		}
+		// Maximum number of iterations exceeded, restore the shift
+		// sigma and place the new d's and e's in a qd array.
+		// This might need to be done for several blocks.
+		info = 2
+		i1 = i0
+		n1 = n0
+		for {
+			tempq = z[4*i0]
+			z[4*i0] += sigma
+			for k := i0 + 1; k <= n0; k++ {
+				tempe := z[4*(k+1)-6]
+				z[4*(k+1)-6] *= tempq / z[4*(k+1)-8]
+				tempq = z[4*k]
+				z[4*k] += sigma + tempe - z[4*(k+1)-6]
+			}
+			// Prepare to do this on the previous block if there is one.
+			if i1 <= 0 {
+				break
+			}
+			n1 = i1 - 1
+			for i1 >= 1 && z[4*(i1+1)-6] >= 0 {
+				i1 -= 1
+			}
+			sigma = -z[4*(n1+1)-2]
+		}
+		for k := 0; k < n; k++ {
+			z[2*k] = z[4*k]
+			// Only the block 1..N0 is unfinished.  The rest of the e's
+			// must be essentially zero, although sometimes other data
+			// has been stored in them.
+			if k < n0 {
+				z[2*(k+1)-1] = z[4*(k+1)-1]
+			} else {
+				z[2*(k+1)] = 0
+			}
+		}
+		return info
+	}
+	info = 3
+	return info
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlasq3.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlasq3.go
new file mode 100644
index 00000000..d547acfb
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlasq3.go
@@ -0,0 +1,161 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "math"
+
+// Dlasq3 checks for deflation, computes a shift (tau) and calls dqds.
+// In case of failure it changes shifts, and tries again until output
+// is positive.
+//
+// Dlasq3 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlasq3(i0, n0 int, z []float64, pp int, dmin, sigma, desig, qmax float64, nFail, iter, nDiv int, ttype int, dmin1, dmin2, dn, dn1, dn2, g, tau float64) (
+	i0Out, n0Out, ppOut int, dminOut, sigmaOut, desigOut, qmaxOut float64, nFailOut, iterOut, nDivOut, ttypeOut int, dmin1Out, dmin2Out, dnOut, dn1Out, dn2Out, gOut, tauOut float64) {
+	const cbias = 1.5
+
+	n0in := n0
+	eps := dlamchP
+	tol := eps * 100
+	tol2 := tol * tol
+	var nn int
+	var t float64
+	for {
+		if n0 < i0 {
+			return i0, n0, pp, dmin, sigma, desig, qmax, nFail, iter, nDiv, ttype, dmin1, dmin2, dn, dn1, dn2, g, tau
+		}
+		if n0 == i0 {
+			z[4*(n0+1)-4] = z[4*(n0+1)+pp-4] + sigma
+			n0--
+			continue
+		}
+		nn = 4*(n0+1) + pp - 1
+		if n0 != i0+1 {
+			// Check whether e[n0-1] is negligible, 1 eigenvalue.
+			if z[nn-5] > tol2*(sigma+z[nn-3]) && z[nn-2*pp-4] > tol2*z[nn-7] {
+				// Check whether e[n0-2] is negligible, 2 eigenvalues.
+				if z[nn-9] > tol2*sigma && z[nn-2*pp-8] > tol2*z[nn-11] {
+					break
+				}
+			} else {
+				z[4*(n0+1)-4] = z[4*(n0+1)+pp-4] + sigma
+				n0--
+				continue
+			}
+		}
+		if z[nn-3] > z[nn-7] {
+			z[nn-3], z[nn-7] = z[nn-7], z[nn-3]
+		}
+		t = 0.5 * (z[nn-7] - z[nn-3] + z[nn-5])
+		if z[nn-5] > z[nn-3]*tol2 && t != 0 {
+			s := z[nn-3] * (z[nn-5] / t)
+			if s <= t {
+				s = z[nn-3] * (z[nn-5] / (t * (1 + math.Sqrt(1+s/t))))
+			} else {
+				s = z[nn-3] * (z[nn-5] / (t + math.Sqrt(t)*math.Sqrt(t+s)))
+			}
+			t = z[nn-7] + (s + z[nn-5])
+			z[nn-3] *= z[nn-7] / t
+			z[nn-7] = t
+		}
+		z[4*(n0+1)-8] = z[nn-7] + sigma
+		z[4*(n0+1)-4] = z[nn-3] + sigma
+		n0 -= 2
+	}
+	if pp == 2 {
+		pp = 0
+	}
+
+	// Reverse the qd-array, if warranted.
+	if dmin <= 0 || n0 < n0in {
+		if cbias*z[4*(i0+1)+pp-4] < z[4*(n0+1)+pp-4] {
+			ipn4Out := 4 * (i0 + n0 + 2)
+			for j4loop := 4 * (i0 + 1); j4loop <= 2*((i0+1)+(n0+1)-1); j4loop += 4 {
+				ipn4 := ipn4Out - 1
+				j4 := j4loop - 1
+
+				z[j4-3], z[ipn4-j4-4] = z[ipn4-j4-4], z[j4-3]
+				z[j4-2], z[ipn4-j4-3] = z[ipn4-j4-3], z[j4-2]
+				z[j4-1], z[ipn4-j4-6] = z[ipn4-j4-6], z[j4-1]
+				z[j4], z[ipn4-j4-5] = z[ipn4-j4-5], z[j4]
+			}
+			if n0-i0 <= 4 {
+				z[4*(n0+1)+pp-2] = z[4*(i0+1)+pp-2]
+				z[4*(n0+1)-pp-1] = z[4*(i0+1)-pp-1]
+			}
+			dmin2 = math.Min(dmin2, z[4*(i0+1)-pp-2])
+			z[4*(n0+1)+pp-2] = math.Min(math.Min(z[4*(n0+1)+pp-2], z[4*(i0+1)+pp-2]), z[4*(i0+1)+pp+2])
+			z[4*(n0+1)-pp-1] = math.Min(math.Min(z[4*(n0+1)-pp-1], z[4*(i0+1)-pp-1]), z[4*(i0+1)-pp+3])
+			qmax = math.Max(math.Max(qmax, z[4*(i0+1)+pp-4]), z[4*(i0+1)+pp])
+			dmin = math.Copysign(0, -1) // Fortran code has -zero, but -0 in go is 0
+		}
+	}
+
+	// Choose a shift.
+	tau, ttype, g = impl.Dlasq4(i0, n0, z, pp, n0in, dmin, dmin1, dmin2, dn, dn1, dn2, tau, ttype, g)
+
+	// Call dqds until dmin > 0.
+loop:
+	for {
+		i0, n0, pp, tau, sigma, dmin, dmin1, dmin2, dn, dn1, dn2 = impl.Dlasq5(i0, n0, z, pp, tau, sigma)
+
+		nDiv += n0 - i0 + 2
+		iter++
+		switch {
+		case dmin >= 0 && dmin1 >= 0:
+			// Success.
+			goto done
+
+		case dmin < 0 && dmin1 > 0 && z[4*n0-pp-1] < tol*(sigma+dn1) && math.Abs(dn) < tol*sigma:
+			// Convergence hidden by negative dn.
+			z[4*n0-pp+1] = 0
+			dmin = 0
+			goto done
+
+		case dmin < 0:
+			// Tau too big. Select new Tau and try again.
+			nFail++
+			if ttype < -22 {
+				// Failed twice. Play it safe.
+				tau = 0
+			} else if dmin1 > 0 {
+				// Late failure. Gives excellent shift.
+				tau = (tau + dmin) * (1 - 2*eps)
+				ttype -= 11
+			} else {
+				// Early failure. Divide by 4.
+				tau = tau / 4
+				ttype -= 12
+			}
+
+		case math.IsNaN(dmin):
+			if tau == 0 {
+				break loop
+			}
+			tau = 0
+
+		default:
+			// Possible underflow. Play it safe.
+			break loop
+		}
+	}
+
+	// Risk of underflow.
+	dmin, dmin1, dmin2, dn, dn1, dn2 = impl.Dlasq6(i0, n0, z, pp)
+	nDiv += n0 - i0 + 2
+	iter++
+	tau = 0
+
+done:
+	if tau < sigma {
+		desig += tau
+		t = sigma + desig
+		desig -= t - sigma
+	} else {
+		t = sigma + tau
+		desig += sigma - (t - tau)
+	}
+	sigma = t
+	return i0, n0, pp, dmin, sigma, desig, qmax, nFail, iter, nDiv, ttype, dmin1, dmin2, dn, dn1, dn2, g, tau
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlasq4.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlasq4.go
new file mode 100644
index 00000000..e09193b7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlasq4.go
@@ -0,0 +1,238 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "math"
+
+// Dlasq4 computes an approximation to the smallest eigenvalue using values of d
+// from the previous transform.
+// i0, n0, and n0in are zero-indexed.
+//
+// Dlasq4 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlasq4(i0, n0 int, z []float64, pp int, n0in int, dmin, dmin1, dmin2, dn, dn1, dn2, tau float64, ttype int, g float64) (tauOut float64, ttypeOut int, gOut float64) {
+	const (
+		cnst1 = 0.563
+		cnst2 = 1.01
+		cnst3 = 1.05
+
+		cnstthird = 0.333 // TODO(btracey): Fix?
+	)
+	// A negative dmin forces the shift to take that absolute value
+	// ttype records the type of shift.
+	if dmin <= 0 {
+		tau = -dmin
+		ttype = -1
+		return tau, ttype, g
+	}
+	nn := 4*(n0+1) + pp - 1 // -1 for zero indexing
+	s := math.NaN()         // Poison s so that failure to take a path below is obvious
+	if n0in == n0 {
+		// No eigenvalues deflated.
+		if dmin == dn || dmin == dn1 {
+			b1 := math.Sqrt(z[nn-3]) * math.Sqrt(z[nn-5])
+			b2 := math.Sqrt(z[nn-7]) * math.Sqrt(z[nn-9])
+			a2 := z[nn-7] + z[nn-5]
+			if dmin == dn && dmin1 == dn1 {
+				gap2 := dmin2 - a2 - dmin2/4
+				var gap1 float64
+				if gap2 > 0 && gap2 > b2 {
+					gap1 = a2 - dn - (b2/gap2)*b2
+				} else {
+					gap1 = a2 - dn - (b1 + b2)
+				}
+				if gap1 > 0 && gap1 > b1 {
+					s = math.Max(dn-(b1/gap1)*b1, 0.5*dmin)
+					ttype = -2
+				} else {
+					s = 0
+					if dn > b1 {
+						s = dn - b1
+					}
+					if a2 > b1+b2 {
+						s = math.Min(s, a2-(b1+b2))
+					}
+					s = math.Max(s, cnstthird*dmin)
+					ttype = -3
+				}
+			} else {
+				ttype = -4
+				s = dmin / 4
+				var gam float64
+				var np int
+				if dmin == dn {
+					gam = dn
+					a2 = 0
+					if z[nn-5] > z[nn-7] {
+						return tau, ttype, g
+					}
+					b2 = z[nn-5] / z[nn-7]
+					np = nn - 9
+				} else {
+					np = nn - 2*pp
+					gam = dn1
+					if z[np-4] > z[np-2] {
+						return tau, ttype, g
+					}
+					a2 = z[np-4] / z[np-2]
+					if z[nn-9] > z[nn-11] {
+						return tau, ttype, g
+					}
+					b2 = z[nn-9] / z[nn-11]
+					np = nn - 13
+				}
+				// Approximate contribution to norm squared from i < nn-1.
+				a2 += b2
+				for i4loop := np + 1; i4loop >= 4*(i0+1)-1+pp; i4loop -= 4 {
+					i4 := i4loop - 1
+					if b2 == 0 {
+						break
+					}
+					b1 = b2
+					if z[i4] > z[i4-2] {
+						return tau, ttype, g
+					}
+					b2 *= z[i4] / z[i4-2]
+					a2 += b2
+					if 100*math.Max(b2, b1) < a2 || cnst1 < a2 {
+						break
+					}
+				}
+				a2 *= cnst3
+				// Rayleigh quotient residual bound.
+				if a2 < cnst1 {
+					s = gam * (1 - math.Sqrt(a2)) / (1 + a2)
+				}
+			}
+		} else if dmin == dn2 {
+			ttype = -5
+			s = dmin / 4
+			// Compute contribution to norm squared from i > nn-2.
+			np := nn - 2*pp
+			b1 := z[np-2]
+			b2 := z[np-6]
+			gam := dn2
+			if z[np-8] > b2 || z[np-4] > b1 {
+				return tau, ttype, g
+			}
+			a2 := (z[np-8] / b2) * (1 + z[np-4]/b1)
+			// Approximate contribution to norm squared from i < nn-2.
+			if n0-i0 > 2 {
+				b2 = z[nn-13] / z[nn-15]
+				a2 += b2
+				for i4loop := (nn + 1) - 17; i4loop >= 4*(i0+1)-1+pp; i4loop -= 4 {
+					i4 := i4loop - 1
+					if b2 == 0 {
+						break
+					}
+					b1 = b2
+					if z[i4] > z[i4-2] {
+						return tau, ttype, g
+					}
+					b2 *= z[i4] / z[i4-2]
+					a2 += b2
+					if 100*math.Max(b2, b1) < a2 || cnst1 < a2 {
+						break
+					}
+				}
+				a2 *= cnst3
+			}
+			if a2 < cnst1 {
+				s = gam * (1 - math.Sqrt(a2)) / (1 + a2)
+			}
+		} else {
+			// Case 6, no information to guide us.
+			if ttype == -6 {
+				g += cnstthird * (1 - g)
+			} else if ttype == -18 {
+				g = cnstthird / 4
+			} else {
+				g = 1.0 / 4
+			}
+			s = g * dmin
+			ttype = -6
+		}
+	} else if n0in == (n0 + 1) {
+		// One eigenvalue just deflated. Use DMIN1, DN1 for DMIN and DN.
+		if dmin1 == dn1 && dmin2 == dn2 {
+			ttype = -7
+			s = cnstthird * dmin1
+			if z[nn-5] > z[nn-7] {
+				return tau, ttype, g
+			}
+			b1 := z[nn-5] / z[nn-7]
+			b2 := b1
+			if b2 != 0 {
+				for i4loop := 4*(n0+1) - 9 + pp; i4loop >= 4*(i0+1)-1+pp; i4loop -= 4 {
+					i4 := i4loop - 1
+					a2 := b1
+					if z[i4] > z[i4-2] {
+						return tau, ttype, g
+					}
+					b1 *= z[i4] / z[i4-2]
+					b2 += b1
+					if 100*math.Max(b1, a2) < b2 {
+						break
+					}
+				}
+			}
+			b2 = math.Sqrt(cnst3 * b2)
+			a2 := dmin1 / (1 + b2*b2)
+			gap2 := 0.5*dmin2 - a2
+			if gap2 > 0 && gap2 > b2*a2 {
+				s = math.Max(s, a2*(1-cnst2*a2*(b2/gap2)*b2))
+			} else {
+				s = math.Max(s, a2*(1-cnst2*b2))
+				ttype = -8
+			}
+		} else {
+			s = dmin1 / 4
+			if dmin1 == dn1 {
+				s = 0.5 * dmin1
+			}
+			ttype = -9
+		}
+	} else if n0in == (n0 + 2) {
+		// Two eigenvalues deflated. Use DMIN2, DN2 for DMIN and DN.
+		if dmin2 == dn2 && 2*z[nn-5] < z[nn-7] {
+			ttype = -10
+			s = cnstthird * dmin2
+			if z[nn-5] > z[nn-7] {
+				return tau, ttype, g
+			}
+			b1 := z[nn-5] / z[nn-7]
+			b2 := b1
+			if b2 != 0 {
+				for i4loop := 4*(n0+1) - 9 + pp; i4loop >= 4*(i0+1)-1+pp; i4loop -= 4 {
+					i4 := i4loop - 1
+					if z[i4] > z[i4-2] {
+						return tau, ttype, g
+					}
+					b1 *= z[i4] / z[i4-2]
+					b2 += b1
+					if 100*b1 < b2 {
+						break
+					}
+				}
+			}
+			b2 = math.Sqrt(cnst3 * b2)
+			a2 := dmin2 / (1 + b2*b2)
+			gap2 := z[nn-7] + z[nn-9] - math.Sqrt(z[nn-11])*math.Sqrt(z[nn-9]) - a2
+			if gap2 > 0 && gap2 > b2*a2 {
+				s = math.Max(s, a2*(1-cnst2*a2*(b2/gap2)*b2))
+			} else {
+				s = math.Max(s, a2*(1-cnst2*b2))
+			}
+		} else {
+			s = dmin2 / 4
+			ttype = -11
+		}
+	} else if n0in > n0+2 {
+		// Case 12, more than two eigenvalues deflated. No information.
+		s = 0
+		ttype = -12
+	}
+	tau = s
+	return tau, ttype, g
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlasq5.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlasq5.go
new file mode 100644
index 00000000..f94f2fb8
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlasq5.go
@@ -0,0 +1,127 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "math"
+
+// Dlasq5 computes one dqds transform in ping-pong form.
+// i0 and n0 are zero-indexed.
+//
+// Dlasq5 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlasq5(i0, n0 int, z []float64, pp int, tau, sigma float64) (i0Out, n0Out, ppOut int, tauOut, sigmaOut, dmin, dmin1, dmin2, dn, dnm1, dnm2 float64) {
+	// The lapack function has inputs for ieee and eps, but Go requires ieee so
+	// these are unnecessary.
+	if n0-i0-1 <= 0 {
+		return i0, n0, pp, tau, sigma, dmin, dmin1, dmin2, dn, dnm1, dnm2
+	}
+	eps := dlamchP
+	dthresh := eps * (sigma + tau)
+	if tau < dthresh*0.5 {
+		tau = 0
+	}
+	var j4 int
+	var emin float64
+	if tau != 0 {
+		j4 = 4*i0 + pp
+		emin = z[j4+4]
+		d := z[j4] - tau
+		dmin = d
+		// In the reference there are code paths that actually return this value.
+		// dmin1 = -z[j4]
+		if pp == 0 {
+			for j4loop := 4 * (i0 + 1); j4loop <= 4*((n0+1)-3); j4loop += 4 {
+				j4 := j4loop - 1
+				z[j4-2] = d + z[j4-1]
+				tmp := z[j4+1] / z[j4-2]
+				d = d*tmp - tau
+				dmin = math.Min(dmin, d)
+				z[j4] = z[j4-1] * tmp
+				emin = math.Min(z[j4], emin)
+			}
+		} else {
+			for j4loop := 4 * (i0 + 1); j4loop <= 4*((n0+1)-3); j4loop += 4 {
+				j4 := j4loop - 1
+				z[j4-3] = d + z[j4]
+				tmp := z[j4+2] / z[j4-3]
+				d = d*tmp - tau
+				dmin = math.Min(dmin, d)
+				z[j4-1] = z[j4] * tmp
+				emin = math.Min(z[j4-1], emin)
+			}
+		}
+		// Unroll the last two steps.
+		dnm2 = d
+		dmin2 = dmin
+		j4 = 4*((n0+1)-2) - pp - 1
+		j4p2 := j4 + 2*pp - 1
+		z[j4-2] = dnm2 + z[j4p2]
+		z[j4] = z[j4p2+2] * (z[j4p2] / z[j4-2])
+		dnm1 = z[j4p2+2]*(dnm2/z[j4-2]) - tau
+		dmin = math.Min(dmin, dnm1)
+
+		dmin1 = dmin
+		j4 += 4
+		j4p2 = j4 + 2*pp - 1
+		z[j4-2] = dnm1 + z[j4p2]
+		z[j4] = z[j4p2+2] * (z[j4p2] / z[j4-2])
+		dn = z[j4p2+2]*(dnm1/z[j4-2]) - tau
+		dmin = math.Min(dmin, dn)
+	} else {
+		// This is the version that sets d's to zero if they are small enough.
+		j4 = 4*(i0+1) + pp - 4
+		emin = z[j4+4]
+		d := z[j4] - tau
+		dmin = d
+		// In the reference there are code paths that actually return this value.
+		// dmin1 = -z[j4]
+		if pp == 0 {
+			for j4loop := 4 * (i0 + 1); j4loop <= 4*((n0+1)-3); j4loop += 4 {
+				j4 := j4loop - 1
+				z[j4-2] = d + z[j4-1]
+				tmp := z[j4+1] / z[j4-2]
+				d = d*tmp - tau
+				if d < dthresh {
+					d = 0
+				}
+				dmin = math.Min(dmin, d)
+				z[j4] = z[j4-1] * tmp
+				emin = math.Min(z[j4], emin)
+			}
+		} else {
+			for j4loop := 4 * (i0 + 1); j4loop <= 4*((n0+1)-3); j4loop += 4 {
+				j4 := j4loop - 1
+				z[j4-3] = d + z[j4]
+				tmp := z[j4+2] / z[j4-3]
+				d = d*tmp - tau
+				if d < dthresh {
+					d = 0
+				}
+				dmin = math.Min(dmin, d)
+				z[j4-1] = z[j4] * tmp
+				emin = math.Min(z[j4-1], emin)
+			}
+		}
+		// Unroll the last two steps.
+		dnm2 = d
+		dmin2 = dmin
+		j4 = 4*((n0+1)-2) - pp - 1
+		j4p2 := j4 + 2*pp - 1
+		z[j4-2] = dnm2 + z[j4p2]
+		z[j4] = z[j4p2+2] * (z[j4p2] / z[j4-2])
+		dnm1 = z[j4p2+2]*(dnm2/z[j4-2]) - tau
+		dmin = math.Min(dmin, dnm1)
+
+		dmin1 = dmin
+		j4 += 4
+		j4p2 = j4 + 2*pp - 1
+		z[j4-2] = dnm1 + z[j4p2]
+		z[j4] = z[j4p2+2] * (z[j4p2] / z[j4-2])
+		dn = z[j4p2+2]*(dnm1/z[j4-2]) - tau
+		dmin = math.Min(dmin, dn)
+	}
+	z[j4+2] = dn
+	z[4*(n0+1)-pp-1] = emin
+	return i0, n0, pp, tau, sigma, dmin, dmin1, dmin2, dn, dnm1, dnm2
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlasq6.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlasq6.go
new file mode 100644
index 00000000..94f69395
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlasq6.go
@@ -0,0 +1,109 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "math"
+
+// Dlasq6 computes one dqd transform in ping-pong form with protection against
+// overflow and underflow. z has length at least 4*(n0+1) and holds the qd array.
+// i0 is the zero-based first index.
+// n0 is the zero-based last index.
+//
+// Dlasq6 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlasq6(i0, n0 int, z []float64, pp int) (dmin, dmin1, dmin2, dn, dnm1, dnm2 float64) {
+	if len(z) < 4*(n0+1) {
+		panic(badZ)
+	}
+	if n0-i0-1 <= 0 {
+		return dmin, dmin1, dmin2, dn, dnm1, dnm2
+	}
+	safmin := dlamchS
+	j4 := 4*(i0+1) + pp - 4 // -4 rather than -3 for zero indexing
+	emin := z[j4+4]
+	d := z[j4]
+	dmin = d
+	if pp == 0 {
+		for j4loop := 4 * (i0 + 1); j4loop <= 4*((n0+1)-3); j4loop += 4 {
+			j4 := j4loop - 1 // Translate back to zero-indexed.
+			z[j4-2] = d + z[j4-1]
+			if z[j4-2] == 0 {
+				z[j4] = 0
+				d = z[j4+1]
+				dmin = d
+				emin = 0
+			} else if safmin*z[j4+1] < z[j4-2] && safmin*z[j4-2] < z[j4+1] {
+				tmp := z[j4+1] / z[j4-2]
+				z[j4] = z[j4-1] * tmp
+				d *= tmp
+			} else {
+				z[j4] = z[j4+1] * (z[j4-1] / z[j4-2])
+				d = z[j4+1] * (d / z[j4-2])
+			}
+			dmin = math.Min(dmin, d)
+			emin = math.Min(emin, z[j4])
+		}
+	} else {
+		for j4loop := 4 * (i0 + 1); j4loop <= 4*((n0+1)-3); j4loop += 4 {
+			j4 := j4loop - 1
+			z[j4-3] = d + z[j4]
+			if z[j4-3] == 0 {
+				z[j4-1] = 0
+				d = z[j4+2]
+				dmin = d
+				emin = 0
+			} else if safmin*z[j4+2] < z[j4-3] && safmin*z[j4-3] < z[j4+2] {
+				tmp := z[j4+2] / z[j4-3]
+				z[j4-1] = z[j4] * tmp
+				d *= tmp
+			} else {
+				z[j4-1] = z[j4+2] * (z[j4] / z[j4-3])
+				d = z[j4+2] * (d / z[j4-3])
+			}
+			dmin = math.Min(dmin, d)
+			emin = math.Min(emin, z[j4-1])
+		}
+	}
+	// Unroll last two steps.
+	dnm2 = d
+	dmin2 = dmin
+	j4 = 4*(n0-1) - pp - 1
+	j4p2 := j4 + 2*pp - 1
+	z[j4-2] = dnm2 + z[j4p2]
+	if z[j4-2] == 0 {
+		z[j4] = 0
+		dnm1 = z[j4p2+2]
+		dmin = dnm1
+		emin = 0
+	} else if safmin*z[j4p2+2] < z[j4-2] && safmin*z[j4-2] < z[j4p2+2] {
+		tmp := z[j4p2+2] / z[j4-2]
+		z[j4] = z[j4p2] * tmp
+		dnm1 = dnm2 * tmp
+	} else {
+		z[j4] = z[j4p2+2] * (z[j4p2] / z[j4-2])
+		dnm1 = z[j4p2+2] * (dnm2 / z[j4-2])
+	}
+	dmin = math.Min(dmin, dnm1)
+	dmin1 = dmin
+	j4 += 4
+	j4p2 = j4 + 2*pp - 1
+	z[j4-2] = dnm1 + z[j4p2]
+	if z[j4-2] == 0 {
+		z[j4] = 0
+		dn = z[j4p2+2]
+		dmin = dn
+		emin = 0
+	} else if safmin*z[j4p2+2] < z[j4-2] && safmin*z[j4-2] < z[j4p2+2] {
+		tmp := z[j4p2+2] / z[j4-2]
+		z[j4] = z[j4p2] * tmp
+		dn = dnm1 * tmp
+	} else {
+		z[j4] = z[j4p2+2] * (z[j4p2] / z[j4-2])
+		dn = z[j4p2+2] * (dnm1 / z[j4-2])
+	}
+	dmin = math.Min(dmin, dn)
+	z[j4+2] = dn
+	z[4*(n0+1)-pp-1] = emin
+	return dmin, dmin1, dmin2, dn, dnm1, dnm2
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlasr.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlasr.go
new file mode 100644
index 00000000..dde44ddb
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlasr.go
@@ -0,0 +1,268 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dlasr applies a sequence of plane rotations to the m×n matrix A. This series
+// of plane rotations is implicitly represented by a matrix P. P is multiplied
+// by a depending on the value of side -- A = P * A if side == lapack.Left,
+// A = A * P^T if side == lapack.Right.
+//
+//The exact value of P depends on the value of pivot, but in all cases P is
+// implicitly represented by a series of 2×2 rotation matrices. The entries of
+// rotation matrix k are defined by s[k] and c[k]
+//  R(k) = [ c[k] s[k]]
+//         [-s[k] s[k]]
+// If direct == lapack.Forward, the rotation matrices are applied as
+// P = P(z-1) * ... * P(2) * P(1), while if direct == lapack.Backward they are
+// applied as P = P(1) * P(2) * ... * P(n).
+//
+// pivot defines the mapping of the elements in R(k) to P(k).
+// If pivot == lapack.Variable, the rotation is performed for the (k, k+1) plane.
+//  P(k) = [1                    ]
+//         [    ...              ]
+//         [     1               ]
+//         [       c[k] s[k]     ]
+//         [      -s[k] c[k]     ]
+//         [                 1   ]
+//         [                ...  ]
+//         [                    1]
+// if pivot == lapack.Top, the rotation is performed for the (1, k+1) plane,
+//  P(k) = [c[k]        s[k]     ]
+//         [    1                ]
+//         [     ...             ]
+//         [         1           ]
+//         [-s[k]       c[k]     ]
+//         [                 1   ]
+//         [                ...  ]
+//         [                    1]
+// and if pivot == lapack.Bottom, the rotation is performed for the (k, z) plane.
+//  P(k) = [1                    ]
+//         [  ...                ]
+//         [      1              ]
+//         [        c[k]     s[k]]
+//         [           1         ]
+//         [            ...      ]
+//         [              1      ]
+//         [       -s[k]     c[k]]
+// s and c have length m - 1 if side == blas.Left, and n - 1 if side == blas.Right.
+//
+// Dlasr is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlasr(side blas.Side, pivot lapack.Pivot, direct lapack.Direct, m, n int, c, s, a []float64, lda int) {
+	checkMatrix(m, n, a, lda)
+	if side != blas.Left && side != blas.Right {
+		panic(badSide)
+	}
+	if pivot != lapack.Variable && pivot != lapack.Top && pivot != lapack.Bottom {
+		panic(badPivot)
+	}
+	if direct != lapack.Forward && direct != lapack.Backward {
+		panic(badDirect)
+	}
+	if side == blas.Left {
+		if len(c) < m-1 {
+			panic(badSlice)
+		}
+		if len(s) < m-1 {
+			panic(badSlice)
+		}
+	} else {
+		if len(c) < n-1 {
+			panic(badSlice)
+		}
+		if len(s) < n-1 {
+			panic(badSlice)
+		}
+	}
+	if m == 0 || n == 0 {
+		return
+	}
+	if side == blas.Left {
+		if pivot == lapack.Variable {
+			if direct == lapack.Forward {
+				for j := 0; j < m-1; j++ {
+					ctmp := c[j]
+					stmp := s[j]
+					if ctmp != 1 || stmp != 0 {
+						for i := 0; i < n; i++ {
+							tmp2 := a[j*lda+i]
+							tmp := a[(j+1)*lda+i]
+							a[(j+1)*lda+i] = ctmp*tmp - stmp*tmp2
+							a[j*lda+i] = stmp*tmp + ctmp*tmp2
+						}
+					}
+				}
+				return
+			}
+			for j := m - 2; j >= 0; j-- {
+				ctmp := c[j]
+				stmp := s[j]
+				if ctmp != 1 || stmp != 0 {
+					for i := 0; i < n; i++ {
+						tmp2 := a[j*lda+i]
+						tmp := a[(j+1)*lda+i]
+						a[(j+1)*lda+i] = ctmp*tmp - stmp*tmp2
+						a[j*lda+i] = stmp*tmp + ctmp*tmp2
+					}
+				}
+			}
+			return
+		} else if pivot == lapack.Top {
+			if direct == lapack.Forward {
+				for j := 1; j < m; j++ {
+					ctmp := c[j-1]
+					stmp := s[j-1]
+					if ctmp != 1 || stmp != 0 {
+						for i := 0; i < n; i++ {
+							tmp := a[j*lda+i]
+							tmp2 := a[i]
+							a[j*lda+i] = ctmp*tmp - stmp*tmp2
+							a[i] = stmp*tmp + ctmp*tmp2
+						}
+					}
+				}
+				return
+			}
+			for j := m - 1; j >= 1; j-- {
+				ctmp := c[j-1]
+				stmp := s[j-1]
+				if ctmp != 1 || stmp != 0 {
+					for i := 0; i < n; i++ {
+						ctmp := c[j-1]
+						stmp := s[j-1]
+						if ctmp != 1 || stmp != 0 {
+							for i := 0; i < n; i++ {
+								tmp := a[j*lda+i]
+								tmp2 := a[i]
+								a[j*lda+i] = ctmp*tmp - stmp*tmp2
+								a[i] = stmp*tmp + ctmp*tmp2
+							}
+						}
+					}
+				}
+			}
+			return
+		}
+		if direct == lapack.Forward {
+			for j := 0; j < m-1; j++ {
+				ctmp := c[j]
+				stmp := s[j]
+				if ctmp != 1 || stmp != 0 {
+					for i := 0; i < n; i++ {
+						tmp := a[j*lda+i]
+						tmp2 := a[(m-1)*lda+i]
+						a[j*lda+i] = stmp*tmp2 + ctmp*tmp
+						a[(m-1)*lda+i] = ctmp*tmp2 - stmp*tmp
+					}
+				}
+			}
+			return
+		}
+		for j := m - 2; j >= 0; j-- {
+			ctmp := c[j]
+			stmp := s[j]
+			if ctmp != 1 || stmp != 0 {
+				for i := 0; i < n; i++ {
+					tmp := a[j*lda+i]
+					tmp2 := a[(m-1)*lda+i]
+					a[j*lda+i] = stmp*tmp2 + ctmp*tmp
+					a[(m-1)*lda+i] = ctmp*tmp2 - stmp*tmp
+				}
+			}
+		}
+		return
+	}
+	if pivot == lapack.Variable {
+		if direct == lapack.Forward {
+			for j := 0; j < n-1; j++ {
+				ctmp := c[j]
+				stmp := s[j]
+				if ctmp != 1 || stmp != 0 {
+					for i := 0; i < m; i++ {
+						tmp := a[i*lda+j+1]
+						tmp2 := a[i*lda+j]
+						a[i*lda+j+1] = ctmp*tmp - stmp*tmp2
+						a[i*lda+j] = stmp*tmp + ctmp*tmp2
+					}
+				}
+			}
+			return
+		}
+		for j := n - 2; j >= 0; j-- {
+			ctmp := c[j]
+			stmp := s[j]
+			if ctmp != 1 || stmp != 0 {
+				for i := 0; i < m; i++ {
+					tmp := a[i*lda+j+1]
+					tmp2 := a[i*lda+j]
+					a[i*lda+j+1] = ctmp*tmp - stmp*tmp2
+					a[i*lda+j] = stmp*tmp + ctmp*tmp2
+				}
+			}
+		}
+		return
+	} else if pivot == lapack.Top {
+		if direct == lapack.Forward {
+			for j := 1; j < n; j++ {
+				ctmp := c[j-1]
+				stmp := s[j-1]
+				if ctmp != 1 || stmp != 0 {
+					for i := 0; i < m; i++ {
+						tmp := a[i*lda+j]
+						tmp2 := a[i*lda]
+						a[i*lda+j] = ctmp*tmp - stmp*tmp2
+						a[i*lda] = stmp*tmp + ctmp*tmp2
+					}
+				}
+			}
+			return
+		}
+		for j := n - 1; j >= 1; j-- {
+			ctmp := c[j-1]
+			stmp := s[j-1]
+			if ctmp != 1 || stmp != 0 {
+				for i := 0; i < m; i++ {
+					tmp := a[i*lda+j]
+					tmp2 := a[i*lda]
+					a[i*lda+j] = ctmp*tmp - stmp*tmp2
+					a[i*lda] = stmp*tmp + ctmp*tmp2
+				}
+			}
+		}
+		return
+	}
+	if direct == lapack.Forward {
+		for j := 0; j < n-1; j++ {
+			ctmp := c[j]
+			stmp := s[j]
+			if ctmp != 1 || stmp != 0 {
+				for i := 0; i < m; i++ {
+					tmp := a[i*lda+j]
+					tmp2 := a[i*lda+n-1]
+					a[i*lda+j] = stmp*tmp2 + ctmp*tmp
+					a[i*lda+n-1] = ctmp*tmp2 - stmp*tmp
+				}
+
+			}
+		}
+		return
+	}
+	for j := n - 2; j >= 0; j-- {
+		ctmp := c[j]
+		stmp := s[j]
+		if ctmp != 1 || stmp != 0 {
+			for i := 0; i < m; i++ {
+				tmp := a[i*lda+j]
+				tmp2 := a[i*lda+n-1]
+				a[i*lda+j] = stmp*tmp2 + ctmp*tmp
+				a[i*lda+n-1] = ctmp*tmp2 - stmp*tmp
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlasrt.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlasrt.go
new file mode 100644
index 00000000..eb63c63d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlasrt.go
@@ -0,0 +1,30 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"sort"
+
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dlasrt sorts the numbers in the input slice d. If s == lapack.SortIncreasing,
+// the elements are sorted in increasing order. If s == lapack.SortDecreasing,
+// the elements are sorted in decreasing order. For other values of s Dlasrt
+// will panic.
+//
+// Dlasrt is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlasrt(s lapack.Sort, n int, d []float64) {
+	checkVector(n, d, 1)
+	d = d[:n]
+	switch s {
+	default:
+		panic(badSort)
+	case lapack.SortIncreasing:
+		sort.Float64s(d)
+	case lapack.SortDecreasing:
+		sort.Sort(sort.Reverse(sort.Float64Slice(d)))
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlassq.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlassq.go
new file mode 100644
index 00000000..186b840b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlassq.go
@@ -0,0 +1,31 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "math"
+
+// Dlassq updates a sum of squares in scaled form. The input parameters scale and
+// sumsq represent the current scale and total sum of squares. These values are
+// updated with the information in the first n elements of the vector specified
+// by x and incX.
+//
+// Dlassq is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlassq(n int, x []float64, incx int, scale float64, sumsq float64) (scl, smsq float64) {
+	if n <= 0 {
+		return scale, sumsq
+	}
+	for ix := 0; ix <= (n-1)*incx; ix += incx {
+		absxi := math.Abs(x[ix])
+		if absxi > 0 || math.IsNaN(absxi) {
+			if scale < absxi {
+				sumsq = 1 + sumsq*(scale/absxi)*(scale/absxi)
+				scale = absxi
+			} else {
+				sumsq += (absxi / scale) * (absxi / scale)
+			}
+		}
+	}
+	return scale, sumsq
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlasv2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlasv2.go
new file mode 100644
index 00000000..ba1445c0
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlasv2.go
@@ -0,0 +1,115 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "math"
+
+// Dlasv2 computes the singular value decomposition of a 2×2 matrix.
+//  [ csl snl] [f g] [csr -snr] = [ssmax     0]
+//  [-snl csl] [0 h] [snr  csr] = [    0 ssmin]
+// ssmax is the larger absolute singular value, and ssmin is the smaller absolute
+// singular value. [cls, snl] and [csr, snr] are the left and right singular vectors.
+//
+// Dlasv2 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlasv2(f, g, h float64) (ssmin, ssmax, snr, csr, snl, csl float64) {
+	ft := f
+	fa := math.Abs(ft)
+	ht := h
+	ha := math.Abs(h)
+	// pmax points to the largest element of the matrix in terms of absolute value.
+	// 1 if F, 2 if G, 3 if H.
+	pmax := 1
+	swap := ha > fa
+	if swap {
+		pmax = 3
+		ft, ht = ht, ft
+		fa, ha = ha, fa
+	}
+	gt := g
+	ga := math.Abs(gt)
+	var clt, crt, slt, srt float64
+	if ga == 0 {
+		ssmin = ha
+		ssmax = fa
+		clt = 1
+		crt = 1
+		slt = 0
+		srt = 0
+	} else {
+		gasmall := true
+		if ga > fa {
+			pmax = 2
+			if (fa / ga) < dlamchE {
+				gasmall = false
+				ssmax = ga
+				if ha > 1 {
+					ssmin = fa / (ga / ha)
+				} else {
+					ssmin = (fa / ga) * ha
+				}
+				clt = 1
+				slt = ht / gt
+				srt = 1
+				crt = ft / gt
+			}
+		}
+		if gasmall {
+			d := fa - ha
+			l := d / fa
+			if d == fa { // deal with inf
+				l = 1
+			}
+			m := gt / ft
+			t := 2 - l
+			s := math.Hypot(t, m)
+			var r float64
+			if l == 0 {
+				r = math.Abs(m)
+			} else {
+				r = math.Hypot(l, m)
+			}
+			a := 0.5 * (s + r)
+			ssmin = ha / a
+			ssmax = fa * a
+			if m == 0 {
+				if l == 0 {
+					t = math.Copysign(2, ft) * math.Copysign(1, gt)
+				} else {
+					t = gt/math.Copysign(d, ft) + m/t
+				}
+			} else {
+				t = (m/(s+t) + m/(r+l)) * (1 + a)
+			}
+			l = math.Hypot(t, 2)
+			crt = 2 / l
+			srt = t / l
+			clt = (crt + srt*m) / a
+			slt = (ht / ft) * srt / a
+		}
+	}
+	if swap {
+		csl = srt
+		snl = crt
+		csr = slt
+		snr = clt
+	} else {
+		csl = clt
+		snl = slt
+		csr = crt
+		snr = srt
+	}
+	var tsign float64
+	switch pmax {
+	case 1:
+		tsign = math.Copysign(1, csr) * math.Copysign(1, csl) * math.Copysign(1, f)
+	case 2:
+		tsign = math.Copysign(1, snr) * math.Copysign(1, csl) * math.Copysign(1, g)
+	case 3:
+		tsign = math.Copysign(1, snr) * math.Copysign(1, snl) * math.Copysign(1, h)
+	}
+	ssmax = math.Copysign(ssmax, tsign)
+	ssmin = math.Copysign(ssmin, tsign*math.Copysign(1, f)*math.Copysign(1, h))
+	return ssmin, ssmax, snr, csr, snl, csl
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlaswp.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlaswp.go
new file mode 100644
index 00000000..22ef3533
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlaswp.go
@@ -0,0 +1,47 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "gonum.org/v1/gonum/blas/blas64"
+
+// Dlaswp swaps the rows k1 to k2 of a rectangular matrix A according to the
+// indices in ipiv so that row k is swapped with ipiv[k].
+//
+// n is the number of columns of A and incX is the increment for ipiv. If incX
+// is 1, the swaps are applied from k1 to k2. If incX is -1, the swaps are
+// applied in reverse order from k2 to k1. For other values of incX Dlaswp will
+// panic. ipiv must have length k2+1, otherwise Dlaswp will panic.
+//
+// The indices k1, k2, and the elements of ipiv are zero-based.
+//
+// Dlaswp is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlaswp(n int, a []float64, lda int, k1, k2 int, ipiv []int, incX int) {
+	switch {
+	case n < 0:
+		panic(nLT0)
+	case k2 < 0:
+		panic(badK2)
+	case k1 < 0 || k2 < k1:
+		panic(badK1)
+	case len(ipiv) != k2+1:
+		panic(badIpiv)
+	case incX != 1 && incX != -1:
+		panic(absIncNotOne)
+	}
+
+	if n == 0 {
+		return
+	}
+	bi := blas64.Implementation()
+	if incX == 1 {
+		for k := k1; k <= k2; k++ {
+			bi.Dswap(n, a[k*lda:], 1, a[ipiv[k]*lda:], 1)
+		}
+		return
+	}
+	for k := k2; k >= k1; k-- {
+		bi.Dswap(n, a[k*lda:], 1, a[ipiv[k]*lda:], 1)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlasy2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlasy2.go
new file mode 100644
index 00000000..aa983bb9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlasy2.go
@@ -0,0 +1,290 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dlasy2 solves the Sylvester matrix equation where the matrices are of order 1
+// or 2. It computes the unknown n1×n2 matrix X so that
+//  TL*X   + sgn*X*TR   = scale*B,  if tranl == false and tranr == false,
+//  TL^T*X + sgn*X*TR   = scale*B,  if tranl == true  and tranr == false,
+//  TL*X   + sgn*X*TR^T = scale*B,  if tranl == false and tranr == true,
+//  TL^T*X + sgn*X*TR^T = scale*B,  if tranl == true  and tranr == true,
+// where TL is n1×n1, TR is n2×n2, B is n1×n2, and 1 <= n1,n2 <= 2.
+//
+// isgn must be 1 or -1, and n1 and n2 must be 0, 1, or 2, but these conditions
+// are not checked.
+//
+// Dlasy2 returns three values, a scale factor that is chosen less than or equal
+// to 1 to prevent the solution overflowing, the infinity norm of the solution,
+// and an indicator of success. If ok is false, TL and TR have eigenvalues that
+// are too close, so TL or TR is perturbed to get a non-singular equation.
+//
+// Dlasy2 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlasy2(tranl, tranr bool, isgn, n1, n2 int, tl []float64, ldtl int, tr []float64, ldtr int, b []float64, ldb int, x []float64, ldx int) (scale, xnorm float64, ok bool) {
+	// TODO(vladimir-ch): Add input validation checks conditionally skipped
+	// using the build tag mechanism.
+
+	ok = true
+	// Quick return if possible.
+	if n1 == 0 || n2 == 0 {
+		return scale, xnorm, ok
+	}
+
+	// Set constants to control overflow.
+	eps := dlamchP
+	smlnum := dlamchS / eps
+	sgn := float64(isgn)
+
+	if n1 == 1 && n2 == 1 {
+		// 1×1 case: TL11*X + sgn*X*TR11 = B11.
+		tau1 := tl[0] + sgn*tr[0]
+		bet := math.Abs(tau1)
+		if bet <= smlnum {
+			tau1 = smlnum
+			bet = smlnum
+			ok = false
+		}
+		scale = 1
+		gam := math.Abs(b[0])
+		if smlnum*gam > bet {
+			scale = 1 / gam
+		}
+		x[0] = b[0] * scale / tau1
+		xnorm = math.Abs(x[0])
+		return scale, xnorm, ok
+	}
+
+	if n1+n2 == 3 {
+		// 1×2 or 2×1 case.
+		var (
+			smin float64
+			tmp  [4]float64 // tmp is used as a 2×2 row-major matrix.
+			btmp [2]float64
+		)
+		if n1 == 1 && n2 == 2 {
+			// 1×2 case: TL11*[X11 X12] + sgn*[X11 X12]*op[TR11 TR12] = [B11 B12].
+			//                                            [TR21 TR22]
+			smin = math.Abs(tl[0])
+			smin = math.Max(smin, math.Max(math.Abs(tr[0]), math.Abs(tr[1])))
+			smin = math.Max(smin, math.Max(math.Abs(tr[ldtr]), math.Abs(tr[ldtr+1])))
+			smin = math.Max(eps*smin, smlnum)
+			tmp[0] = tl[0] + sgn*tr[0]
+			tmp[3] = tl[0] + sgn*tr[ldtr+1]
+			if tranr {
+				tmp[1] = sgn * tr[1]
+				tmp[2] = sgn * tr[ldtr]
+			} else {
+				tmp[1] = sgn * tr[ldtr]
+				tmp[2] = sgn * tr[1]
+			}
+			btmp[0] = b[0]
+			btmp[1] = b[1]
+		} else {
+			// 2×1 case: op[TL11 TL12]*[X11] + sgn*[X11]*TR11 = [B11].
+			//             [TL21 TL22]*[X21]       [X21]        [B21]
+			smin = math.Abs(tr[0])
+			smin = math.Max(smin, math.Max(math.Abs(tl[0]), math.Abs(tl[1])))
+			smin = math.Max(smin, math.Max(math.Abs(tl[ldtl]), math.Abs(tl[ldtl+1])))
+			smin = math.Max(eps*smin, smlnum)
+			tmp[0] = tl[0] + sgn*tr[0]
+			tmp[3] = tl[ldtl+1] + sgn*tr[0]
+			if tranl {
+				tmp[1] = tl[ldtl]
+				tmp[2] = tl[1]
+			} else {
+				tmp[1] = tl[1]
+				tmp[2] = tl[ldtl]
+			}
+			btmp[0] = b[0]
+			btmp[1] = b[ldb]
+		}
+
+		// Solve 2×2 system using complete pivoting.
+		// Set pivots less than smin to smin.
+
+		bi := blas64.Implementation()
+		ipiv := bi.Idamax(len(tmp), tmp[:], 1)
+		// Compute the upper triangular matrix [u11 u12].
+		//                                     [  0 u22]
+		u11 := tmp[ipiv]
+		if math.Abs(u11) <= smin {
+			ok = false
+			u11 = smin
+		}
+		locu12 := [4]int{1, 0, 3, 2} // Index in tmp of the element on the same row as the pivot.
+		u12 := tmp[locu12[ipiv]]
+		locl21 := [4]int{2, 3, 0, 1} // Index in tmp of the element on the same column as the pivot.
+		l21 := tmp[locl21[ipiv]] / u11
+		locu22 := [4]int{3, 2, 1, 0} // Index in tmp of the remaining element.
+		u22 := tmp[locu22[ipiv]] - l21*u12
+		if math.Abs(u22) <= smin {
+			ok = false
+			u22 = smin
+		}
+		if ipiv&0x2 != 0 { // true for ipiv equal to 2 and 3.
+			// The pivot was in the second row, swap the elements of
+			// the right-hand side.
+			btmp[0], btmp[1] = btmp[1], btmp[0]-l21*btmp[1]
+		} else {
+			btmp[1] -= l21 * btmp[0]
+		}
+		scale = 1
+		if 2*smlnum*math.Abs(btmp[1]) > math.Abs(u22) || 2*smlnum*math.Abs(btmp[0]) > math.Abs(u11) {
+			scale = 0.5 / math.Max(math.Abs(btmp[0]), math.Abs(btmp[1]))
+			btmp[0] *= scale
+			btmp[1] *= scale
+		}
+		// Solve the system [u11 u12] [x21] = [ btmp[0] ].
+		//                  [  0 u22] [x22]   [ btmp[1] ]
+		x22 := btmp[1] / u22
+		x21 := btmp[0]/u11 - (u12/u11)*x22
+		if ipiv&0x1 != 0 { // true for ipiv equal to 1 and 3.
+			// The pivot was in the second column, swap the elements
+			// of the solution.
+			x21, x22 = x22, x21
+		}
+		x[0] = x21
+		if n1 == 1 {
+			x[1] = x22
+			xnorm = math.Abs(x[0]) + math.Abs(x[1])
+		} else {
+			x[ldx] = x22
+			xnorm = math.Max(math.Abs(x[0]), math.Abs(x[ldx]))
+		}
+		return scale, xnorm, ok
+	}
+
+	// 2×2 case: op[TL11 TL12]*[X11 X12] + SGN*[X11 X12]*op[TR11 TR12] = [B11 B12].
+	//             [TL21 TL22] [X21 X22]       [X21 X22]   [TR21 TR22]   [B21 B22]
+	//
+	// Solve equivalent 4×4 system using complete pivoting.
+	// Set pivots less than smin to smin.
+
+	smin := math.Max(math.Abs(tr[0]), math.Abs(tr[1]))
+	smin = math.Max(smin, math.Max(math.Abs(tr[ldtr]), math.Abs(tr[ldtr+1])))
+	smin = math.Max(smin, math.Max(math.Abs(tl[0]), math.Abs(tl[1])))
+	smin = math.Max(smin, math.Max(math.Abs(tl[ldtl]), math.Abs(tl[ldtl+1])))
+	smin = math.Max(eps*smin, smlnum)
+
+	var t [4][4]float64
+	t[0][0] = tl[0] + sgn*tr[0]
+	t[1][1] = tl[0] + sgn*tr[ldtr+1]
+	t[2][2] = tl[ldtl+1] + sgn*tr[0]
+	t[3][3] = tl[ldtl+1] + sgn*tr[ldtr+1]
+	if tranl {
+		t[0][2] = tl[ldtl]
+		t[1][3] = tl[ldtl]
+		t[2][0] = tl[1]
+		t[3][1] = tl[1]
+	} else {
+		t[0][2] = tl[1]
+		t[1][3] = tl[1]
+		t[2][0] = tl[ldtl]
+		t[3][1] = tl[ldtl]
+	}
+	if tranr {
+		t[0][1] = sgn * tr[1]
+		t[1][0] = sgn * tr[ldtr]
+		t[2][3] = sgn * tr[1]
+		t[3][2] = sgn * tr[ldtr]
+	} else {
+		t[0][1] = sgn * tr[ldtr]
+		t[1][0] = sgn * tr[1]
+		t[2][3] = sgn * tr[ldtr]
+		t[3][2] = sgn * tr[1]
+	}
+
+	var btmp [4]float64
+	btmp[0] = b[0]
+	btmp[1] = b[1]
+	btmp[2] = b[ldb]
+	btmp[3] = b[ldb+1]
+
+	// Perform elimination.
+	var jpiv [4]int // jpiv records any column swaps for pivoting.
+	for i := 0; i < 3; i++ {
+		var (
+			xmax       float64
+			ipsv, jpsv int
+		)
+		for ip := i; ip < 4; ip++ {
+			for jp := i; jp < 4; jp++ {
+				if math.Abs(t[ip][jp]) >= xmax {
+					xmax = math.Abs(t[ip][jp])
+					ipsv = ip
+					jpsv = jp
+				}
+			}
+		}
+		if ipsv != i {
+			// The pivot is not in the top row of the unprocessed
+			// block, swap rows ipsv and i of t and btmp.
+			t[ipsv], t[i] = t[i], t[ipsv]
+			btmp[ipsv], btmp[i] = btmp[i], btmp[ipsv]
+		}
+		if jpsv != i {
+			// The pivot is not in the left column of the
+			// unprocessed block, swap columns jpsv and i of t.
+			for k := 0; k < 4; k++ {
+				t[k][jpsv], t[k][i] = t[k][i], t[k][jpsv]
+			}
+		}
+		jpiv[i] = jpsv
+		if math.Abs(t[i][i]) < smin {
+			ok = false
+			t[i][i] = smin
+		}
+		for k := i + 1; k < 4; k++ {
+			t[k][i] /= t[i][i]
+			btmp[k] -= t[k][i] * btmp[i]
+			for j := i + 1; j < 4; j++ {
+				t[k][j] -= t[k][i] * t[i][j]
+			}
+		}
+	}
+	if math.Abs(t[3][3]) < smin {
+		ok = false
+		t[3][3] = smin
+	}
+	scale = 1
+	if 8*smlnum*math.Abs(btmp[0]) > math.Abs(t[0][0]) ||
+		8*smlnum*math.Abs(btmp[1]) > math.Abs(t[1][1]) ||
+		8*smlnum*math.Abs(btmp[2]) > math.Abs(t[2][2]) ||
+		8*smlnum*math.Abs(btmp[3]) > math.Abs(t[3][3]) {
+
+		maxbtmp := math.Max(math.Abs(btmp[0]), math.Abs(btmp[1]))
+		maxbtmp = math.Max(maxbtmp, math.Max(math.Abs(btmp[2]), math.Abs(btmp[3])))
+		scale = 1 / 8 / maxbtmp
+		btmp[0] *= scale
+		btmp[1] *= scale
+		btmp[2] *= scale
+		btmp[3] *= scale
+	}
+	// Compute the solution of the upper triangular system t * tmp = btmp.
+	var tmp [4]float64
+	for i := 3; i >= 0; i-- {
+		temp := 1 / t[i][i]
+		tmp[i] = btmp[i] * temp
+		for j := i + 1; j < 4; j++ {
+			tmp[i] -= temp * t[i][j] * tmp[j]
+		}
+	}
+	for i := 2; i >= 0; i-- {
+		if jpiv[i] != i {
+			tmp[i], tmp[jpiv[i]] = tmp[jpiv[i]], tmp[i]
+		}
+	}
+	x[0] = tmp[0]
+	x[1] = tmp[1]
+	x[ldx] = tmp[2]
+	x[ldx+1] = tmp[3]
+	xnorm = math.Max(math.Abs(tmp[0])+math.Abs(tmp[1]), math.Abs(tmp[2])+math.Abs(tmp[3]))
+	return scale, xnorm, ok
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlatrd.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlatrd.go
new file mode 100644
index 00000000..28bc2325
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlatrd.go
@@ -0,0 +1,145 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dlatrd reduces nb rows and columns of a real n×n symmetric matrix A to symmetric
+// tridiagonal form. It computes the orthonormal similarity transformation
+//  Q^T * A * Q
+// and returns the matrices V and W to apply to the unreduced part of A. If
+// uplo == blas.Upper, the upper triangle is supplied and the last nb rows are
+// reduced. If uplo == blas.Lower, the lower triangle is supplied and the first
+// nb rows are reduced.
+//
+// a contains the symmetric matrix on entry with active triangular half specified
+// by uplo. On exit, the nb columns have been reduced to tridiagonal form. The
+// diagonal contains the diagonal of the reduced matrix, the off-diagonal is
+// set to 1, and the remaining elements contain the data to construct Q.
+//
+// If uplo == blas.Upper, with n = 5 and nb = 2 on exit a is
+//  [ a   a   a  v4  v5]
+//  [     a   a  v4  v5]
+//  [         a   1  v5]
+//  [             d   1]
+//  [                 d]
+//
+// If uplo == blas.Lower, with n = 5 and nb = 2, on exit a is
+//  [ d                ]
+//  [ 1   d            ]
+//  [v1   1   a        ]
+//  [v1  v2   a   a    ]
+//  [v1  v2   a   a   a]
+//
+// e contains the superdiagonal elements of the reduced matrix. If uplo == blas.Upper,
+// e[n-nb:n-1] contains the last nb columns of the reduced matrix, while if
+// uplo == blas.Lower, e[:nb] contains the first nb columns of the reduced matrix.
+// e must have length at least n-1, and Dlatrd will panic otherwise.
+//
+// tau contains the scalar factors of the elementary reflectors needed to construct Q.
+// The reflectors are stored in tau[n-nb:n-1] if uplo == blas.Upper, and in
+// tau[:nb] if uplo == blas.Lower. tau must have length n-1, and Dlatrd will panic
+// otherwise.
+//
+// w is an n×nb matrix. On exit it contains the data to update the unreduced part
+// of A.
+//
+// The matrix Q is represented as a product of elementary reflectors. Each reflector
+// H has the form
+//  I - tau * v * v^T
+// If uplo == blas.Upper,
+//  Q = H_{n-1} * H_{n-2} * ... * H_{n-nb}
+// where v[:i-1] is stored in A[:i-1,i], v[i-1] = 1, and v[i:n] = 0.
+//
+// If uplo == blas.Lower,
+//  Q = H_0 * H_1 * ... * H_{nb-1}
+// where v[:i+1] = 0, v[i+1] = 1, and v[i+2:n] is stored in A[i+2:n,i].
+//
+// The vectors v form the n×nb matrix V which is used with W to apply a
+// symmetric rank-2 update to the unreduced part of A
+//  A = A - V * W^T - W * V^T
+//
+// Dlatrd is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlatrd(uplo blas.Uplo, n, nb int, a []float64, lda int, e, tau, w []float64, ldw int) {
+	checkMatrix(n, n, a, lda)
+	checkMatrix(n, nb, w, ldw)
+	if len(e) < n-1 {
+		panic(badE)
+	}
+	if len(tau) < n-1 {
+		panic(badTau)
+	}
+	if n <= 0 {
+		return
+	}
+	bi := blas64.Implementation()
+	if uplo == blas.Upper {
+		for i := n - 1; i >= n-nb; i-- {
+			iw := i - n + nb
+			if i < n-1 {
+				// Update A(0:i, i).
+				bi.Dgemv(blas.NoTrans, i+1, n-i-1, -1, a[i+1:], lda,
+					w[i*ldw+iw+1:], 1, 1, a[i:], lda)
+				bi.Dgemv(blas.NoTrans, i+1, n-i-1, -1, w[iw+1:], ldw,
+					a[i*lda+i+1:], 1, 1, a[i:], lda)
+			}
+			if i > 0 {
+				// Generate elementary reflector H_i to annihilate A(0:i-2,i).
+				e[i-1], tau[i-1] = impl.Dlarfg(i, a[(i-1)*lda+i], a[i:], lda)
+				a[(i-1)*lda+i] = 1
+
+				// Compute W(0:i-1, i).
+				bi.Dsymv(blas.Upper, i, 1, a, lda, a[i:], lda, 0, w[iw:], ldw)
+				if i < n-1 {
+					bi.Dgemv(blas.Trans, i, n-i-1, 1, w[iw+1:], ldw,
+						a[i:], lda, 0, w[(i+1)*ldw+iw:], ldw)
+					bi.Dgemv(blas.NoTrans, i, n-i-1, -1, a[i+1:], lda,
+						w[(i+1)*ldw+iw:], ldw, 1, w[iw:], ldw)
+					bi.Dgemv(blas.Trans, i, n-i-1, 1, a[i+1:], lda,
+						a[i:], lda, 0, w[(i+1)*ldw+iw:], ldw)
+					bi.Dgemv(blas.NoTrans, i, n-i-1, -1, w[iw+1:], ldw,
+						w[(i+1)*ldw+iw:], ldw, 1, w[iw:], ldw)
+				}
+				bi.Dscal(i, tau[i-1], w[iw:], ldw)
+				alpha := -0.5 * tau[i-1] * bi.Ddot(i, w[iw:], ldw, a[i:], lda)
+				bi.Daxpy(i, alpha, a[i:], lda, w[iw:], ldw)
+			}
+		}
+	} else {
+		// Reduce first nb columns of lower triangle.
+		for i := 0; i < nb; i++ {
+			// Update A(i:n, i)
+			bi.Dgemv(blas.NoTrans, n-i, i, -1, a[i*lda:], lda,
+				w[i*ldw:], 1, 1, a[i*lda+i:], lda)
+			bi.Dgemv(blas.NoTrans, n-i, i, -1, w[i*ldw:], ldw,
+				a[i*lda:], 1, 1, a[i*lda+i:], lda)
+			if i < n-1 {
+				// Generate elementary reflector H_i to annihilate A(i+2:n,i).
+				e[i], tau[i] = impl.Dlarfg(n-i-1, a[(i+1)*lda+i], a[min(i+2, n-1)*lda+i:], lda)
+				a[(i+1)*lda+i] = 1
+
+				// Compute W(i+1:n,i).
+				bi.Dsymv(blas.Lower, n-i-1, 1, a[(i+1)*lda+i+1:], lda,
+					a[(i+1)*lda+i:], lda, 0, w[(i+1)*ldw+i:], ldw)
+				bi.Dgemv(blas.Trans, n-i-1, i, 1, w[(i+1)*ldw:], ldw,
+					a[(i+1)*lda+i:], lda, 0, w[i:], ldw)
+				bi.Dgemv(blas.NoTrans, n-i-1, i, -1, a[(i+1)*lda:], lda,
+					w[i:], ldw, 1, w[(i+1)*ldw+i:], ldw)
+				bi.Dgemv(blas.Trans, n-i-1, i, 1, a[(i+1)*lda:], lda,
+					a[(i+1)*lda+i:], lda, 0, w[i:], ldw)
+				bi.Dgemv(blas.NoTrans, n-i-1, i, -1, w[(i+1)*ldw:], ldw,
+					w[i:], ldw, 1, w[(i+1)*ldw+i:], ldw)
+				bi.Dscal(n-i-1, tau[i], w[(i+1)*ldw+i:], ldw)
+				alpha := -0.5 * tau[i] * bi.Ddot(n-i-1, w[(i+1)*ldw+i:], ldw,
+					a[(i+1)*lda+i:], lda)
+				bi.Daxpy(n-i-1, alpha, a[(i+1)*lda+i:], lda,
+					w[(i+1)*ldw+i:], ldw)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlatrs.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlatrs.go
new file mode 100644
index 00000000..64470f59
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dlatrs.go
@@ -0,0 +1,350 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dlatrs solves a triangular system of equations scaled to prevent overflow. It
+// solves
+//  A * x = scale * b if trans == blas.NoTrans
+//  A^T * x = scale * b if trans == blas.Trans
+// where the scale s is set for numeric stability.
+//
+// A is an n×n triangular matrix. On entry, the slice x contains the values of
+// of b, and on exit it contains the solution vector x.
+//
+// If normin == true, cnorm is an input and cnorm[j] contains the norm of the off-diagonal
+// part of the j^th column of A. If trans == blas.NoTrans, cnorm[j] must be greater
+// than or equal to the infinity norm, and greater than or equal to the one-norm
+// otherwise. If normin == false, then cnorm is treated as an output, and is set
+// to contain the 1-norm of the off-diagonal part of the j^th column of A.
+//
+// Dlatrs is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlatrs(uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, normin bool, n int, a []float64, lda int, x []float64, cnorm []float64) (scale float64) {
+	if uplo != blas.Upper && uplo != blas.Lower {
+		panic(badUplo)
+	}
+	if trans != blas.Trans && trans != blas.NoTrans {
+		panic(badTrans)
+	}
+	if diag != blas.Unit && diag != blas.NonUnit {
+		panic(badDiag)
+	}
+	upper := uplo == blas.Upper
+	noTrans := trans == blas.NoTrans
+	nonUnit := diag == blas.NonUnit
+
+	if n < 0 {
+		panic(nLT0)
+	}
+	checkMatrix(n, n, a, lda)
+	checkVector(n, x, 1)
+	checkVector(n, cnorm, 1)
+
+	if n == 0 {
+		return 0
+	}
+	smlnum := dlamchS / dlamchP
+	bignum := 1 / smlnum
+	scale = 1
+	bi := blas64.Implementation()
+	if !normin {
+		if upper {
+			cnorm[0] = 0
+			for j := 1; j < n; j++ {
+				cnorm[j] = bi.Dasum(j, a[j:], lda)
+			}
+		} else {
+			for j := 0; j < n-1; j++ {
+				cnorm[j] = bi.Dasum(n-j-1, a[(j+1)*lda+j:], lda)
+			}
+			cnorm[n-1] = 0
+		}
+	}
+	// Scale the column norms by tscal if the maximum element in cnorm is greater than bignum.
+	imax := bi.Idamax(n, cnorm, 1)
+	tmax := cnorm[imax]
+	var tscal float64
+	if tmax <= bignum {
+		tscal = 1
+	} else {
+		tscal = 1 / (smlnum * tmax)
+		bi.Dscal(n, tscal, cnorm, 1)
+	}
+
+	// Compute a bound on the computed solution vector to see if bi.Dtrsv can be used.
+	j := bi.Idamax(n, x, 1)
+	xmax := math.Abs(x[j])
+	xbnd := xmax
+	var grow float64
+	var jfirst, jlast, jinc int
+	if noTrans {
+		if upper {
+			jfirst = n - 1
+			jlast = -1
+			jinc = -1
+		} else {
+			jfirst = 0
+			jlast = n
+			jinc = 1
+		}
+		// Compute the growth in A * x = b.
+		if tscal != 1 {
+			grow = 0
+			goto Solve
+		}
+		if nonUnit {
+			grow = 1 / math.Max(xbnd, smlnum)
+			xbnd = grow
+			for j := jfirst; j != jlast; j += jinc {
+				if grow <= smlnum {
+					goto Solve
+				}
+				tjj := math.Abs(a[j*lda+j])
+				xbnd = math.Min(xbnd, math.Min(1, tjj)*grow)
+				if tjj+cnorm[j] >= smlnum {
+					grow *= tjj / (tjj + cnorm[j])
+				} else {
+					grow = 0
+				}
+			}
+			grow = xbnd
+		} else {
+			grow = math.Min(1, 1/math.Max(xbnd, smlnum))
+			for j := jfirst; j != jlast; j += jinc {
+				if grow <= smlnum {
+					goto Solve
+				}
+				grow *= 1 / (1 + cnorm[j])
+			}
+		}
+	} else {
+		if upper {
+			jfirst = 0
+			jlast = n
+			jinc = 1
+		} else {
+			jfirst = n - 1
+			jlast = -1
+			jinc = -1
+		}
+		if tscal != 1 {
+			grow = 0
+			goto Solve
+		}
+		if nonUnit {
+			grow = 1 / (math.Max(xbnd, smlnum))
+			xbnd = grow
+			for j := jfirst; j != jlast; j += jinc {
+				if grow <= smlnum {
+					goto Solve
+				}
+				xj := 1 + cnorm[j]
+				grow = math.Min(grow, xbnd/xj)
+				tjj := math.Abs(a[j*lda+j])
+				if xj > tjj {
+					xbnd *= tjj / xj
+				}
+			}
+			grow = math.Min(grow, xbnd)
+		} else {
+			grow = math.Min(1, 1/math.Max(xbnd, smlnum))
+			for j := jfirst; j != jlast; j += jinc {
+				if grow <= smlnum {
+					goto Solve
+				}
+				xj := 1 + cnorm[j]
+				grow /= xj
+			}
+		}
+	}
+
+Solve:
+	if grow*tscal > smlnum {
+		// Use the Level 2 BLAS solve if the reciprocal of the bound on
+		// elements of X is not too small.
+		bi.Dtrsv(uplo, trans, diag, n, a, lda, x, 1)
+		if tscal != 1 {
+			bi.Dscal(n, 1/tscal, cnorm, 1)
+		}
+		return scale
+	}
+
+	// Use a Level 1 BLAS solve, scaling intermediate results.
+	if xmax > bignum {
+		scale = bignum / xmax
+		bi.Dscal(n, scale, x, 1)
+		xmax = bignum
+	}
+	if noTrans {
+		for j := jfirst; j != jlast; j += jinc {
+			xj := math.Abs(x[j])
+			var tjj, tjjs float64
+			if nonUnit {
+				tjjs = a[j*lda+j] * tscal
+			} else {
+				tjjs = tscal
+				if tscal == 1 {
+					goto Skip1
+				}
+			}
+			tjj = math.Abs(tjjs)
+			if tjj > smlnum {
+				if tjj < 1 {
+					if xj > tjj*bignum {
+						rec := 1 / xj
+						bi.Dscal(n, rec, x, 1)
+						scale *= rec
+						xmax *= rec
+					}
+				}
+				x[j] /= tjjs
+				xj = math.Abs(x[j])
+			} else if tjj > 0 {
+				if xj > tjj*bignum {
+					rec := (tjj * bignum) / xj
+					if cnorm[j] > 1 {
+						rec /= cnorm[j]
+					}
+					bi.Dscal(n, rec, x, 1)
+					scale *= rec
+					xmax *= rec
+				}
+				x[j] /= tjjs
+				xj = math.Abs(x[j])
+			} else {
+				for i := 0; i < n; i++ {
+					x[i] = 0
+				}
+				x[j] = 1
+				xj = 1
+				scale = 0
+				xmax = 0
+			}
+		Skip1:
+			if xj > 1 {
+				rec := 1 / xj
+				if cnorm[j] > (bignum-xmax)*rec {
+					rec *= 0.5
+					bi.Dscal(n, rec, x, 1)
+					scale *= rec
+				}
+			} else if xj*cnorm[j] > bignum-xmax {
+				bi.Dscal(n, 0.5, x, 1)
+				scale *= 0.5
+			}
+			if upper {
+				if j > 0 {
+					bi.Daxpy(j, -x[j]*tscal, a[j:], lda, x, 1)
+					i := bi.Idamax(j, x, 1)
+					xmax = math.Abs(x[i])
+				}
+			} else {
+				if j < n-1 {
+					bi.Daxpy(n-j-1, -x[j]*tscal, a[(j+1)*lda+j:], lda, x[j+1:], 1)
+					i := j + bi.Idamax(n-j-1, x[j+1:], 1)
+					xmax = math.Abs(x[i])
+				}
+			}
+		}
+	} else {
+		for j := jfirst; j != jlast; j += jinc {
+			xj := math.Abs(x[j])
+			uscal := tscal
+			rec := 1 / math.Max(xmax, 1)
+			var tjjs float64
+			if cnorm[j] > (bignum-xj)*rec {
+				rec *= 0.5
+				if nonUnit {
+					tjjs = a[j*lda+j] * tscal
+				} else {
+					tjjs = tscal
+				}
+				tjj := math.Abs(tjjs)
+				if tjj > 1 {
+					rec = math.Min(1, rec*tjj)
+					uscal /= tjjs
+				}
+				if rec < 1 {
+					bi.Dscal(n, rec, x, 1)
+					scale *= rec
+					xmax *= rec
+				}
+			}
+			var sumj float64
+			if uscal == 1 {
+				if upper {
+					sumj = bi.Ddot(j, a[j:], lda, x, 1)
+				} else if j < n-1 {
+					sumj = bi.Ddot(n-j-1, a[(j+1)*lda+j:], lda, x[j+1:], 1)
+				}
+			} else {
+				if upper {
+					for i := 0; i < j; i++ {
+						sumj += (a[i*lda+j] * uscal) * x[i]
+					}
+				} else if j < n {
+					for i := j + 1; i < n; i++ {
+						sumj += (a[i*lda+j] * uscal) * x[i]
+					}
+				}
+			}
+			if uscal == tscal {
+				x[j] -= sumj
+				xj := math.Abs(x[j])
+				var tjjs float64
+				if nonUnit {
+					tjjs = a[j*lda+j] * tscal
+				} else {
+					tjjs = tscal
+					if tscal == 1 {
+						goto Skip2
+					}
+				}
+				tjj := math.Abs(tjjs)
+				if tjj > smlnum {
+					if tjj < 1 {
+						if xj > tjj*bignum {
+							rec = 1 / xj
+							bi.Dscal(n, rec, x, 1)
+							scale *= rec
+							xmax *= rec
+						}
+					}
+					x[j] /= tjjs
+				} else if tjj > 0 {
+					if xj > tjj*bignum {
+						rec = (tjj * bignum) / xj
+						bi.Dscal(n, rec, x, 1)
+						scale *= rec
+						xmax *= rec
+					}
+					x[j] /= tjjs
+				} else {
+					for i := 0; i < n; i++ {
+						x[i] = 0
+					}
+					x[j] = 1
+					scale = 0
+					xmax = 0
+				}
+			} else {
+				x[j] = x[j]/tjjs - sumj
+			}
+		Skip2:
+			xmax = math.Max(xmax, math.Abs(x[j]))
+		}
+	}
+	scale /= tscal
+	if tscal != 1 {
+		bi.Dscal(n, 1/tscal, cnorm, 1)
+	}
+	return scale
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/doc.go b/vendor/gonum.org/v1/gonum/lapack/gonum/doc.go
new file mode 100644
index 00000000..f69b4285
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/doc.go
@@ -0,0 +1,28 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package gonum is a pure-go implementation of the LAPACK API. The LAPACK API defines
+// a set of algorithms for advanced matrix operations.
+//
+// The function definitions and implementations follow that of the netlib reference
+// implementation. Please see http://www.netlib.org/lapack/explore-html/ for more
+// information, and http://www.netlib.org/lapack/explore-html/d4/de1/_l_i_c_e_n_s_e_source.html
+// for more license information.
+//
+// Slice function arguments frequently represent vectors and matrices. The data
+// layout is identical to that found in https://godoc.org/gonum.org/v1/gonum/blas/gonum.
+//
+// Most LAPACK functions are built on top the routines defined in the BLAS API,
+// and as such the computation time for many LAPACK functions is
+// dominated by BLAS calls. Here, BLAS is accessed through the
+// the blas64 package (https://godoc.org/golang.org/v1/gonum/blas/blas64). In particular,
+// this implies that an external BLAS library will be used if it is
+// registered in blas64.
+//
+// The full LAPACK capability has not been implemented at present. The full
+// API is very large, containing approximately 200 functions for double precision
+// alone. Future additions will be focused on supporting the gonum matrix
+// package (https://godoc.org/github.com/gonum/matrix/mat64), though pull requests
+// with implementations and tests for LAPACK function are encouraged.
+package gonum // import "gonum.org/v1/gonum/lapack/gonum"
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dorg2l.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dorg2l.go
new file mode 100644
index 00000000..728924f6
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dorg2l.go
@@ -0,0 +1,65 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dorg2l generates an m×n matrix Q with orthonormal columns which is defined
+// as the last n columns of a product of k elementary reflectors of order m.
+//  Q = H_{k-1} * ... * H_1 * H_0
+// See Dgelqf for more information. It must be that m >= n >= k.
+//
+// tau contains the scalar reflectors computed by Dgeqlf. tau must have length
+// at least k, and Dorg2l will panic otherwise.
+//
+// work contains temporary memory, and must have length at least n. Dorg2l will
+// panic otherwise.
+//
+// Dorg2l is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dorg2l(m, n, k int, a []float64, lda int, tau, work []float64) {
+	checkMatrix(m, n, a, lda)
+	if len(tau) < k {
+		panic(badTau)
+	}
+	if len(work) < n {
+		panic(badWork)
+	}
+	if m < n {
+		panic(mLTN)
+	}
+	if k > n {
+		panic(kGTN)
+	}
+	if n == 0 {
+		return
+	}
+
+	// Initialize columns 0:n-k to columns of the unit matrix.
+	for j := 0; j < n-k; j++ {
+		for l := 0; l < m; l++ {
+			a[l*lda+j] = 0
+		}
+		a[(m-n+j)*lda+j] = 1
+	}
+
+	bi := blas64.Implementation()
+	for i := 0; i < k; i++ {
+		ii := n - k + i
+
+		// Apply H_i to A[0:m-k+i, 0:n-k+i] from the left.
+		a[(m-n+ii)*lda+ii] = 1
+		impl.Dlarf(blas.Left, m-n+ii+1, ii, a[ii:], lda, tau[i], a, lda, work)
+		bi.Dscal(m-n+ii, -tau[i], a[ii:], lda)
+		a[(m-n+ii)*lda+ii] = 1 - tau[i]
+
+		// Set A[m-k+i:m, n-k+i+1] to zero.
+		for l := m - n + ii + 1; l < m; l++ {
+			a[l*lda+ii] = 0
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dorg2r.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dorg2r.go
new file mode 100644
index 00000000..25f0ee54
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dorg2r.go
@@ -0,0 +1,65 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dorg2r generates an m×n matrix Q with orthonormal columns defined by the
+// product of elementary reflectors as computed by Dgeqrf.
+//  Q = H_0 * H_1 * ... * H_{k-1}
+// len(tau) >= k, 0 <= k <= n, 0 <= n <= m, len(work) >= n.
+// Dorg2r will panic if these conditions are not met.
+//
+// Dorg2r is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dorg2r(m, n, k int, a []float64, lda int, tau []float64, work []float64) {
+	checkMatrix(m, n, a, lda)
+	if len(tau) < k {
+		panic(badTau)
+	}
+	if len(work) < n {
+		panic(badWork)
+	}
+	if k > n {
+		panic(kGTN)
+	}
+	if n > m {
+		panic(mLTN)
+	}
+	if len(work) < n {
+		panic(badWork)
+	}
+	if n == 0 {
+		return
+	}
+	bi := blas64.Implementation()
+	// Initialize columns k+1:n to columns of the unit matrix.
+	for l := 0; l < m; l++ {
+		for j := k; j < n; j++ {
+			a[l*lda+j] = 0
+		}
+	}
+	for j := k; j < n; j++ {
+		a[j*lda+j] = 1
+	}
+	for i := k - 1; i >= 0; i-- {
+		for i := range work {
+			work[i] = 0
+		}
+		if i < n-1 {
+			a[i*lda+i] = 1
+			impl.Dlarf(blas.Left, m-i, n-i-1, a[i*lda+i:], lda, tau[i], a[i*lda+i+1:], lda, work)
+		}
+		if i < m-1 {
+			bi.Dscal(m-i-1, -tau[i], a[(i+1)*lda+i:], lda)
+		}
+		a[i*lda+i] = 1 - tau[i]
+		for l := 0; l < i; l++ {
+			a[l*lda+i] = 0
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dorgbr.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dorgbr.go
new file mode 100644
index 00000000..b8789661
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dorgbr.go
@@ -0,0 +1,124 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "gonum.org/v1/gonum/lapack"
+
+// Dorgbr generates one of the matrices Q or P^T computed by Dgebrd
+// computed from the decomposition Dgebrd. See Dgebd2 for the description of
+// Q and P^T.
+//
+// If vect == lapack.ApplyQ, then a is assumed to have been an m×k matrix and
+// Q is of order m. If m >= k, then Dorgbr returns the first n columns of Q
+// where m >= n >= k. If m < k, then Dorgbr returns Q as an m×m matrix.
+//
+// If vect == lapack.ApplyP, then A is assumed to have been a k×n matrix, and
+// P^T is of order n. If k < n, then Dorgbr returns the first m rows of P^T,
+// where n >= m >= k. If k >= n, then Dorgbr returns P^T as an n×n matrix.
+//
+// Dorgbr is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dorgbr(vect lapack.DecompUpdate, m, n, k int, a []float64, lda int, tau, work []float64, lwork int) {
+	mn := min(m, n)
+	wantq := vect == lapack.ApplyQ
+	if wantq {
+		if m < n || n < min(m, k) || m < min(m, k) {
+			panic(badDims)
+		}
+	} else {
+		if n < m || m < min(n, k) || n < min(n, k) {
+			panic(badDims)
+		}
+	}
+	if wantq {
+		if m >= k {
+			checkMatrix(m, k, a, lda)
+		} else {
+			checkMatrix(m, m, a, lda)
+		}
+	} else {
+		if n >= k {
+			checkMatrix(k, n, a, lda)
+		} else {
+			checkMatrix(n, n, a, lda)
+		}
+	}
+	work[0] = 1
+	if wantq {
+		if m >= k {
+			impl.Dorgqr(m, n, k, a, lda, tau, work, -1)
+		} else if m > 1 {
+			impl.Dorgqr(m-1, m-1, m-1, a[lda+1:], lda, tau, work, -1)
+		}
+	} else {
+		if k < n {
+			impl.Dorglq(m, n, k, a, lda, tau, work, -1)
+		} else if n > 1 {
+			impl.Dorglq(n-1, n-1, n-1, a[lda+1:], lda, tau, work, -1)
+		}
+	}
+	lworkopt := int(work[0])
+	lworkopt = max(lworkopt, mn)
+	if lwork == -1 {
+		work[0] = float64(lworkopt)
+		return
+	}
+	if len(work) < lwork {
+		panic(badWork)
+	}
+	if lwork < mn {
+		panic(badWork)
+	}
+	if m == 0 || n == 0 {
+		work[0] = 1
+		return
+	}
+	if wantq {
+		// Form Q, determined by a call to Dgebrd to reduce an m×k matrix.
+		if m >= k {
+			impl.Dorgqr(m, n, k, a, lda, tau, work, lwork)
+		} else {
+			// Shift the vectors which define the elementary reflectors one
+			// column to the right, and set the first row and column of Q to
+			// those of the unit matrix.
+			for j := m - 1; j >= 1; j-- {
+				a[j] = 0
+				for i := j + 1; i < m; i++ {
+					a[i*lda+j] = a[i*lda+j-1]
+				}
+			}
+			a[0] = 1
+			for i := 1; i < m; i++ {
+				a[i*lda] = 0
+			}
+			if m > 1 {
+				// Form Q[1:m-1, 1:m-1]
+				impl.Dorgqr(m-1, m-1, m-1, a[lda+1:], lda, tau, work, lwork)
+			}
+		}
+	} else {
+		// Form P^T, determined by a call to Dgebrd to reduce a k×n matrix.
+		if k < n {
+			impl.Dorglq(m, n, k, a, lda, tau, work, lwork)
+		} else {
+			// Shift the vectors which define the elementary reflectors one
+			// row downward, and set the first row and column of P^T to
+			// those of the unit matrix.
+			a[0] = 1
+			for i := 1; i < n; i++ {
+				a[i*lda] = 0
+			}
+			for j := 1; j < n; j++ {
+				for i := j - 1; i >= 1; i-- {
+					a[i*lda+j] = a[(i-1)*lda+j]
+				}
+				a[j] = 0
+			}
+			if n > 1 {
+				impl.Dorglq(n-1, n-1, n-1, a[lda+1:], lda, tau, work, lwork)
+			}
+		}
+	}
+	work[0] = float64(lworkopt)
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dorghr.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dorghr.go
new file mode 100644
index 00000000..dcdc0dec
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dorghr.go
@@ -0,0 +1,93 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+// Dorghr generates an n×n orthogonal matrix Q which is defined as the product
+// of ihi-ilo elementary reflectors:
+//  Q = H_{ilo} H_{ilo+1} ... H_{ihi-1}.
+//
+// a and lda represent an n×n matrix that contains the elementary reflectors, as
+// returned by Dgehrd. On return, a is overwritten by the n×n orthogonal matrix
+// Q. Q will be equal to the identity matrix except in the submatrix
+// Q[ilo+1:ihi+1,ilo+1:ihi+1].
+//
+// ilo and ihi must have the same values as in the previous call of Dgehrd. It
+// must hold that
+//  0 <= ilo <= ihi < n,  if n > 0,
+//  ilo = 0, ihi = -1,    if n == 0.
+//
+// tau contains the scalar factors of the elementary reflectors, as returned by
+// Dgehrd. tau must have length n-1.
+//
+// work must have length at least max(1,lwork) and lwork must be at least
+// ihi-ilo. For optimum performance lwork must be at least (ihi-ilo)*nb where nb
+// is the optimal blocksize. On return, work[0] will contain the optimal value
+// of lwork.
+//
+// If lwork == -1, instead of performing Dorghr, only the optimal value of lwork
+// will be stored into work[0].
+//
+// If any requirement on input sizes is not met, Dorghr will panic.
+//
+// Dorghr is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dorghr(n, ilo, ihi int, a []float64, lda int, tau, work []float64, lwork int) {
+	checkMatrix(n, n, a, lda)
+	nh := ihi - ilo
+	switch {
+	case ilo < 0 || max(1, n) <= ilo:
+		panic(badIlo)
+	case ihi < min(ilo, n-1) || n <= ihi:
+		panic(badIhi)
+	case lwork < max(1, nh) && lwork != -1:
+		panic(badWork)
+	case len(work) < max(1, lwork):
+		panic(shortWork)
+	}
+
+	lwkopt := max(1, nh) * impl.Ilaenv(1, "DORGQR", " ", nh, nh, nh, -1)
+	if lwork == -1 {
+		work[0] = float64(lwkopt)
+		return
+	}
+
+	// Quick return if possible.
+	if n == 0 {
+		work[0] = 1
+		return
+	}
+
+	// Shift the vectors which define the elementary reflectors one column
+	// to the right.
+	for i := ilo + 2; i < ihi+1; i++ {
+		copy(a[i*lda+ilo+1:i*lda+i], a[i*lda+ilo:i*lda+i-1])
+	}
+	// Set the first ilo+1 and the last n-ihi-1 rows and columns to those of
+	// the identity matrix.
+	for i := 0; i < ilo+1; i++ {
+		for j := 0; j < n; j++ {
+			a[i*lda+j] = 0
+		}
+		a[i*lda+i] = 1
+	}
+	for i := ilo + 1; i < ihi+1; i++ {
+		for j := 0; j <= ilo; j++ {
+			a[i*lda+j] = 0
+		}
+		for j := i; j < n; j++ {
+			a[i*lda+j] = 0
+		}
+	}
+	for i := ihi + 1; i < n; i++ {
+		for j := 0; j < n; j++ {
+			a[i*lda+j] = 0
+		}
+		a[i*lda+i] = 1
+	}
+	if nh > 0 {
+		// Generate Q[ilo+1:ihi+1,ilo+1:ihi+1].
+		impl.Dorgqr(nh, nh, nh, a[(ilo+1)*lda+ilo+1:], lda, tau[ilo:ihi], work, lwork)
+	}
+	work[0] = float64(lwkopt)
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dorgl2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dorgl2.go
new file mode 100644
index 00000000..3cdc10b7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dorgl2.go
@@ -0,0 +1,63 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dorgl2 generates an m×n matrix Q with orthonormal rows defined by the
+// first m rows product of elementary reflectors as computed by Dgelqf.
+//  Q = H_0 * H_1 * ... * H_{k-1}
+// len(tau) >= k, 0 <= k <= m, 0 <= m <= n, len(work) >= m.
+// Dorgl2 will panic if these conditions are not met.
+//
+// Dorgl2 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dorgl2(m, n, k int, a []float64, lda int, tau, work []float64) {
+	checkMatrix(m, n, a, lda)
+	if len(tau) < k {
+		panic(badTau)
+	}
+	if k > m {
+		panic(kGTM)
+	}
+	if k > m {
+		panic(kGTM)
+	}
+	if m > n {
+		panic(nLTM)
+	}
+	if len(work) < m {
+		panic(badWork)
+	}
+	if m == 0 {
+		return
+	}
+	bi := blas64.Implementation()
+	if k < m {
+		for i := k; i < m; i++ {
+			for j := 0; j < n; j++ {
+				a[i*lda+j] = 0
+			}
+		}
+		for j := k; j < m; j++ {
+			a[j*lda+j] = 1
+		}
+	}
+	for i := k - 1; i >= 0; i-- {
+		if i < n-1 {
+			if i < m-1 {
+				a[i*lda+i] = 1
+				impl.Dlarf(blas.Right, m-i-1, n-i, a[i*lda+i:], 1, tau[i], a[(i+1)*lda+i:], lda, work)
+			}
+			bi.Dscal(n-i-1, -tau[i], a[i*lda+i+1:], 1)
+		}
+		a[i*lda+i] = 1 - tau[i]
+		for l := 0; l < i; l++ {
+			a[i*lda+l] = 0
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dorglq.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dorglq.go
new file mode 100644
index 00000000..0535027b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dorglq.go
@@ -0,0 +1,117 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dorglq generates an m×n matrix Q with orthonormal columns defined by the
+// product of elementary reflectors as computed by Dgelqf.
+//  Q = H_0 * H_1 * ... * H_{k-1}
+// Dorglq is the blocked version of Dorgl2 that makes greater use of level-3 BLAS
+// routines.
+//
+// len(tau) >= k, 0 <= k <= n, and 0 <= n <= m.
+//
+// work is temporary storage, and lwork specifies the usable memory length. At minimum,
+// lwork >= m, and the amount of blocking is limited by the usable length.
+// If lwork == -1, instead of computing Dorglq the optimal work length is stored
+// into work[0].
+//
+// Dorglq will panic if the conditions on input values are not met.
+//
+// Dorglq is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dorglq(m, n, k int, a []float64, lda int, tau, work []float64, lwork int) {
+	nb := impl.Ilaenv(1, "DORGLQ", " ", m, n, k, -1)
+	// work is treated as an n×nb matrix
+	if lwork == -1 {
+		work[0] = float64(max(1, m) * nb)
+		return
+	}
+	checkMatrix(m, n, a, lda)
+	if k < 0 {
+		panic(kLT0)
+	}
+	if k > m {
+		panic(kGTM)
+	}
+	if m > n {
+		panic(nLTM)
+	}
+	if len(tau) < k {
+		panic(badTau)
+	}
+	if len(work) < lwork {
+		panic(shortWork)
+	}
+	if lwork < m {
+		panic(badWork)
+	}
+	if m == 0 {
+		return
+	}
+	nbmin := 2 // Minimum number of blocks
+	var nx int // Minimum number of rows
+	iws := m   // Length of work needed
+	var ldwork int
+	if nb > 1 && nb < k {
+		nx = max(0, impl.Ilaenv(3, "DORGLQ", " ", m, n, k, -1))
+		if nx < k {
+			ldwork = nb
+			iws = m * ldwork
+			if lwork < iws {
+				nb = lwork / m
+				ldwork = nb
+				nbmin = max(2, impl.Ilaenv(2, "DORGLQ", " ", m, n, k, -1))
+			}
+		}
+	}
+	var ki, kk int
+	if nb >= nbmin && nb < k && nx < k {
+		// The first kk rows are handled by the blocked method.
+		// Note: lapack has nx here, but this means the last nx rows are handled
+		// serially which could be quite different than nb.
+		ki = ((k - nb - 1) / nb) * nb
+		kk = min(k, ki+nb)
+		for i := kk; i < m; i++ {
+			for j := 0; j < kk; j++ {
+				a[i*lda+j] = 0
+			}
+		}
+	}
+	if kk < m {
+		// Perform the operation on colums kk to the end.
+		impl.Dorgl2(m-kk, n-kk, k-kk, a[kk*lda+kk:], lda, tau[kk:], work)
+	}
+	if kk == 0 {
+		return
+	}
+	// Perform the operation on column-blocks
+	for i := ki; i >= 0; i -= nb {
+		ib := min(nb, k-i)
+		if i+ib < m {
+			impl.Dlarft(lapack.Forward, lapack.RowWise,
+				n-i, ib,
+				a[i*lda+i:], lda,
+				tau[i:],
+				work, ldwork)
+
+			impl.Dlarfb(blas.Right, blas.Trans, lapack.Forward, lapack.RowWise,
+				m-i-ib, n-i, ib,
+				a[i*lda+i:], lda,
+				work, ldwork,
+				a[(i+ib)*lda+i:], lda,
+				work[ib*ldwork:], ldwork)
+		}
+		impl.Dorgl2(ib, n-i, ib, a[i*lda+i:], lda, tau[i:], work)
+		for l := i; l < i+ib; l++ {
+			for j := 0; j < i; j++ {
+				a[l*lda+j] = 0
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dorgql.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dorgql.go
new file mode 100644
index 00000000..f13bf727
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dorgql.go
@@ -0,0 +1,130 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dorgql generates the m×n matrix Q with orthonormal columns defined as the
+// last n columns of a product of k elementary reflectors of order m
+//  Q = H_{k-1} * ... * H_1 * H_0.
+//
+// It must hold that
+//  0 <= k <= n <= m,
+// and Dorgql will panic otherwise.
+//
+// On entry, the (n-k+i)-th column of A must contain the vector which defines
+// the elementary reflector H_i, for i=0,...,k-1, and tau[i] must contain its
+// scalar factor. On return, a contains the m×n matrix Q.
+//
+// tau must have length at least k, and Dorgql will panic otherwise.
+//
+// work must have length at least max(1,lwork), and lwork must be at least
+// max(1,n), otherwise Dorgql will panic. For optimum performance lwork must
+// be a sufficiently large multiple of n.
+//
+// If lwork == -1, instead of computing Dorgql the optimal work length is stored
+// into work[0].
+//
+// Dorgql is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dorgql(m, n, k int, a []float64, lda int, tau, work []float64, lwork int) {
+	switch {
+	case n < 0:
+		panic(nLT0)
+	case m < n:
+		panic(mLTN)
+	case k < 0:
+		panic(kLT0)
+	case k > n:
+		panic(kGTN)
+	case lwork < max(1, n) && lwork != -1:
+		panic(badWork)
+	case len(work) < lwork:
+		panic(shortWork)
+	}
+	if lwork != -1 {
+		checkMatrix(m, n, a, lda)
+		if len(tau) < k {
+			panic(badTau)
+		}
+	}
+
+	if n == 0 {
+		work[0] = 1
+		return
+	}
+
+	nb := impl.Ilaenv(1, "DORGQL", " ", m, n, k, -1)
+	if lwork == -1 {
+		work[0] = float64(n * nb)
+		return
+	}
+
+	nbmin := 2
+	var nx, ldwork int
+	iws := n
+	if nb > 1 && nb < k {
+		// Determine when to cross over from blocked to unblocked code.
+		nx = max(0, impl.Ilaenv(3, "DORGQL", " ", m, n, k, -1))
+		if nx < k {
+			// Determine if workspace is large enough for blocked code.
+			iws = n * nb
+			if lwork < iws {
+				// Not enough workspace to use optimal nb: reduce nb and determine
+				// the minimum value of nb.
+				nb = lwork / n
+				nbmin = max(2, impl.Ilaenv(2, "DORGQL", " ", m, n, k, -1))
+			}
+			ldwork = nb
+		}
+	}
+
+	var kk int
+	if nb >= nbmin && nb < k && nx < k {
+		// Use blocked code after the first block. The last kk columns are handled
+		// by the block method.
+		kk = min(k, ((k-nx+nb-1)/nb)*nb)
+
+		// Set A(m-kk:m, 0:n-kk) to zero.
+		for i := m - kk; i < m; i++ {
+			for j := 0; j < n-kk; j++ {
+				a[i*lda+j] = 0
+			}
+		}
+	}
+
+	// Use unblocked code for the first or only block.
+	impl.Dorg2l(m-kk, n-kk, k-kk, a, lda, tau, work)
+	if kk > 0 {
+		// Use blocked code.
+		for i := k - kk; i < k; i += nb {
+			ib := min(nb, k-i)
+			if n-k+i > 0 {
+				// Form the triangular factor of the block reflector
+				// H = H_{i+ib-1} * ... * H_{i+1} * H_i.
+				impl.Dlarft(lapack.Backward, lapack.ColumnWise, m-k+i+ib, ib,
+					a[n-k+i:], lda, tau[i:], work, ldwork)
+
+				// Apply H to A[0:m-k+i+ib, 0:n-k+i] from the left.
+				impl.Dlarfb(blas.Left, blas.NoTrans, lapack.Backward, lapack.ColumnWise,
+					m-k+i+ib, n-k+i, ib, a[n-k+i:], lda, work, ldwork,
+					a, lda, work[ib*ldwork:], ldwork)
+			}
+
+			// Apply H to rows 0:m-k+i+ib of current block.
+			impl.Dorg2l(m-k+i+ib, ib, ib, a[n-k+i:], lda, tau[i:], work)
+
+			// Set rows m-k+i+ib:m of current block to zero.
+			for j := n - k + i; j < n-k+i+ib; j++ {
+				for l := m - k + i + ib; l < m; l++ {
+					a[l*lda+j] = 0
+				}
+			}
+		}
+	}
+	work[0] = float64(iws)
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dorgqr.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dorgqr.go
new file mode 100644
index 00000000..0d525d8a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dorgqr.go
@@ -0,0 +1,120 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dorgqr generates an m×n matrix Q with orthonormal columns defined by the
+// product of elementary reflectors
+//  Q = H_0 * H_1 * ... * H_{k-1}
+// as computed by Dgeqrf.
+// Dorgqr is the blocked version of Dorg2r that makes greater use of level-3 BLAS
+// routines.
+//
+// The length of tau must be at least k, and the length of work must be at least n.
+// It also must be that 0 <= k <= n and 0 <= n <= m.
+//
+// work is temporary storage, and lwork specifies the usable memory length. At
+// minimum, lwork >= n, and the amount of blocking is limited by the usable
+// length. If lwork == -1, instead of computing Dorgqr the optimal work length
+// is stored into work[0].
+//
+// Dorgqr will panic if the conditions on input values are not met.
+//
+// Dorgqr is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dorgqr(m, n, k int, a []float64, lda int, tau, work []float64, lwork int) {
+	nb := impl.Ilaenv(1, "DORGQR", " ", m, n, k, -1)
+	// work is treated as an n×nb matrix
+	if lwork == -1 {
+		work[0] = float64(max(1, n) * nb)
+		return
+	}
+	checkMatrix(m, n, a, lda)
+	if k < 0 {
+		panic(kLT0)
+	}
+	if k > n {
+		panic(kGTN)
+	}
+	if n > m {
+		panic(mLTN)
+	}
+	if len(tau) < k {
+		panic(badTau)
+	}
+	if len(work) < lwork {
+		panic(shortWork)
+	}
+	if lwork < n {
+		panic(badWork)
+	}
+	if n == 0 {
+		return
+	}
+	nbmin := 2 // Minimum number of blocks
+	var nx int // Minimum number of rows
+	iws := n   // Length of work needed
+	var ldwork int
+	if nb > 1 && nb < k {
+		nx = max(0, impl.Ilaenv(3, "DORGQR", " ", m, n, k, -1))
+		if nx < k {
+			ldwork = nb
+			iws = n * ldwork
+			if lwork < iws {
+				nb = lwork / n
+				ldwork = nb
+				nbmin = max(2, impl.Ilaenv(2, "DORGQR", " ", m, n, k, -1))
+			}
+		}
+	}
+	var ki, kk int
+	if nb >= nbmin && nb < k && nx < k {
+		// The first kk columns are handled by the blocked method.
+		// Note: lapack has nx here, but this means the last nx rows are handled
+		// serially which could be quite different than nb.
+		ki = ((k - nb - 1) / nb) * nb
+		kk = min(k, ki+nb)
+		for j := kk; j < n; j++ {
+			for i := 0; i < kk; i++ {
+				a[i*lda+j] = 0
+			}
+		}
+	}
+	if kk < n {
+		// Perform the operation on colums kk to the end.
+		impl.Dorg2r(m-kk, n-kk, k-kk, a[kk*lda+kk:], lda, tau[kk:], work)
+	}
+	if kk == 0 {
+		return
+	}
+	// Perform the operation on column-blocks
+	for i := ki; i >= 0; i -= nb {
+		ib := min(nb, k-i)
+		if i+ib < n {
+			impl.Dlarft(lapack.Forward, lapack.ColumnWise,
+				m-i, ib,
+				a[i*lda+i:], lda,
+				tau[i:],
+				work, ldwork)
+
+			impl.Dlarfb(blas.Left, blas.NoTrans, lapack.Forward, lapack.ColumnWise,
+				m-i, n-i-ib, ib,
+				a[i*lda+i:], lda,
+				work, ldwork,
+				a[i*lda+i+ib:], lda,
+				work[ib*ldwork:], ldwork)
+		}
+		impl.Dorg2r(m-i, ib, ib, a[i*lda+i:], lda, tau[i:], work)
+		// Set rows 0:i-1 of current block to zero
+		for j := i; j < i+ib; j++ {
+			for l := 0; l < i; l++ {
+				a[l*lda+j] = 0
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dorgtr.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dorgtr.go
new file mode 100644
index 00000000..39b7df29
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dorgtr.go
@@ -0,0 +1,99 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "gonum.org/v1/gonum/blas"
+
+// Dorgtr generates a real orthogonal matrix Q which is defined as the product
+// of n-1 elementary reflectors of order n as returned by Dsytrd.
+//
+// The construction of Q depends on the value of uplo:
+//  Q = H_{n-1} * ... * H_1 * H_0  if uplo == blas.Upper
+//  Q = H_0 * H_1 * ... * H_{n-1}  if uplo == blas.Lower
+// where H_i is constructed from the elementary reflectors as computed by Dsytrd.
+// See the documentation for Dsytrd for more information.
+//
+// tau must have length at least n-1, and Dorgtr will panic otherwise.
+//
+// work is temporary storage, and lwork specifies the usable memory length. At
+// minimum, lwork >= max(1,n-1), and Dorgtr will panic otherwise. The amount of blocking
+// is limited by the usable length.
+// If lwork == -1, instead of computing Dorgtr the optimal work length is stored
+// into work[0].
+//
+// Dorgtr is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dorgtr(uplo blas.Uplo, n int, a []float64, lda int, tau, work []float64, lwork int) {
+	checkMatrix(n, n, a, lda)
+	if len(tau) < n-1 {
+		panic(badTau)
+	}
+	if len(work) < lwork {
+		panic(badWork)
+	}
+	if lwork < n-1 && lwork != -1 {
+		panic(badWork)
+	}
+	upper := uplo == blas.Upper
+	if !upper && uplo != blas.Lower {
+		panic(badUplo)
+	}
+
+	if n == 0 {
+		work[0] = 1
+		return
+	}
+
+	var nb int
+	if upper {
+		nb = impl.Ilaenv(1, "DORGQL", " ", n-1, n-1, n-1, -1)
+	} else {
+		nb = impl.Ilaenv(1, "DORGQR", " ", n-1, n-1, n-1, -1)
+	}
+	lworkopt := max(1, n-1) * nb
+	if lwork == -1 {
+		work[0] = float64(lworkopt)
+		return
+	}
+
+	if upper {
+		// Q was determined by a call to Dsytrd with uplo == blas.Upper.
+		// Shift the vectors which define the elementary reflectors one column
+		// to the left, and set the last row and column of Q to those of the unit
+		// matrix.
+		for j := 0; j < n-1; j++ {
+			for i := 0; i < j; i++ {
+				a[i*lda+j] = a[i*lda+j+1]
+			}
+			a[(n-1)*lda+j] = 0
+		}
+		for i := 0; i < n-1; i++ {
+			a[i*lda+n-1] = 0
+		}
+		a[(n-1)*lda+n-1] = 1
+
+		// Generate Q[0:n-1, 0:n-1].
+		impl.Dorgql(n-1, n-1, n-1, a, lda, tau, work, lwork)
+	} else {
+		// Q was determined by a call to Dsytrd with uplo == blas.Upper.
+		// Shift the vectors which define the elementary reflectors one column
+		// to the right, and set the first row and column of Q to those of the unit
+		// matrix.
+		for j := n - 1; j > 0; j-- {
+			a[j] = 0
+			for i := j + 1; i < n; i++ {
+				a[i*lda+j] = a[i*lda+j-1]
+			}
+		}
+		a[0] = 1
+		for i := 1; i < n; i++ {
+			a[i*lda] = 0
+		}
+		if n > 1 {
+			// Generate Q[1:n, 1:n].
+			impl.Dorgqr(n-1, n-1, n-1, a[lda+1:], lda, tau, work, lwork)
+		}
+	}
+	work[0] = float64(lworkopt)
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dorm2r.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dorm2r.go
new file mode 100644
index 00000000..15864fcc
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dorm2r.go
@@ -0,0 +1,88 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "gonum.org/v1/gonum/blas"
+
+// Dorm2r multiplies a general matrix C by an orthogonal matrix from a QR factorization
+// determined by Dgeqrf.
+//  C = Q * C    if side == blas.Left and trans == blas.NoTrans
+//  C = Q^T * C  if side == blas.Left and trans == blas.Trans
+//  C = C * Q    if side == blas.Right and trans == blas.NoTrans
+//  C = C * Q^T  if side == blas.Right and trans == blas.Trans
+// If side == blas.Left, a is a matrix of size m×k, and if side == blas.Right
+// a is of size n×k.
+//
+// tau contains the Householder factors and is of length at least k and this function
+// will panic otherwise.
+//
+// work is temporary storage of length at least n if side == blas.Left
+// and at least m if side == blas.Right and this function will panic otherwise.
+//
+// Dorm2r is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dorm2r(side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64) {
+	if side != blas.Left && side != blas.Right {
+		panic(badSide)
+	}
+	if trans != blas.Trans && trans != blas.NoTrans {
+		panic(badTrans)
+	}
+
+	left := side == blas.Left
+	notran := trans == blas.NoTrans
+	if left {
+		// Q is m x m
+		checkMatrix(m, k, a, lda)
+		if len(work) < n {
+			panic(badWork)
+		}
+	} else {
+		// Q is n x n
+		checkMatrix(n, k, a, lda)
+		if len(work) < m {
+			panic(badWork)
+		}
+	}
+	checkMatrix(m, n, c, ldc)
+	if m == 0 || n == 0 || k == 0 {
+		return
+	}
+	if len(tau) < k {
+		panic(badTau)
+	}
+	if left {
+		if notran {
+			for i := k - 1; i >= 0; i-- {
+				aii := a[i*lda+i]
+				a[i*lda+i] = 1
+				impl.Dlarf(side, m-i, n, a[i*lda+i:], lda, tau[i], c[i*ldc:], ldc, work)
+				a[i*lda+i] = aii
+			}
+			return
+		}
+		for i := 0; i < k; i++ {
+			aii := a[i*lda+i]
+			a[i*lda+i] = 1
+			impl.Dlarf(side, m-i, n, a[i*lda+i:], lda, tau[i], c[i*ldc:], ldc, work)
+			a[i*lda+i] = aii
+		}
+		return
+	}
+	if notran {
+		for i := 0; i < k; i++ {
+			aii := a[i*lda+i]
+			a[i*lda+i] = 1
+			impl.Dlarf(side, m, n-i, a[i*lda+i:], lda, tau[i], c[i:], ldc, work)
+			a[i*lda+i] = aii
+		}
+		return
+	}
+	for i := k - 1; i >= 0; i-- {
+		aii := a[i*lda+i]
+		a[i*lda+i] = 1
+		impl.Dlarf(side, m, n-i, a[i*lda+i:], lda, tau[i], c[i:], ldc, work)
+		a[i*lda+i] = aii
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dormbr.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dormbr.go
new file mode 100644
index 00000000..6518c186
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dormbr.go
@@ -0,0 +1,158 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dormbr applies a multiplicative update to the matrix C based on a
+// decomposition computed by Dgebrd.
+//
+// Dormbr overwrites the m×n matrix C with
+//  Q * C   if vect == lapack.ApplyQ, side == blas.Left, and trans == blas.NoTrans
+//  C * Q   if vect == lapack.ApplyQ, side == blas.Right, and trans == blas.NoTrans
+//  Q^T * C if vect == lapack.ApplyQ, side == blas.Left, and trans == blas.Trans
+//  C * Q^T if vect == lapack.ApplyQ, side == blas.Right, and trans == blas.Trans
+//
+//  P * C   if vect == lapack.ApplyP, side == blas.Left, and trans == blas.NoTrans
+//  C * P   if vect == lapack.ApplyP, side == blas.Right, and trans == blas.NoTrans
+//  P^T * C if vect == lapack.ApplyP, side == blas.Left, and trans == blas.Trans
+//  C * P^T if vect == lapack.ApplyP, side == blas.Right, and trans == blas.Trans
+// where P and Q are the orthogonal matrices determined by Dgebrd when reducing
+// a matrix A to bidiagonal form: A = Q * B * P^T. See Dgebrd for the
+// definitions of Q and P.
+//
+// If vect == lapack.ApplyQ, A is assumed to have been an nq×k matrix, while if
+// vect == lapack.ApplyP, A is assumed to have been a k×nq matrix. nq = m if
+// side == blas.Left, while nq = n if side == blas.Right.
+//
+// tau must have length min(nq,k), and Dormbr will panic otherwise. tau contains
+// the elementary reflectors to construct Q or P depending on the value of
+// vect.
+//
+// work must have length at least max(1,lwork), and lwork must be either -1 or
+// at least max(1,n) if side == blas.Left, and at least max(1,m) if side ==
+// blas.Right. For optimum performance lwork should be at least n*nb if side ==
+// blas.Left, and at least m*nb if side == blas.Right, where nb is the optimal
+// block size. On return, work[0] will contain the optimal value of lwork.
+//
+// If lwork == -1, the function only calculates the optimal value of lwork and
+// returns it in work[0].
+//
+// Dormbr is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dormbr(vect lapack.DecompUpdate, side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64, lwork int) {
+	if side != blas.Left && side != blas.Right {
+		panic(badSide)
+	}
+	if trans != blas.NoTrans && trans != blas.Trans {
+		panic(badTrans)
+	}
+	if vect != lapack.ApplyP && vect != lapack.ApplyQ {
+		panic(badDecompUpdate)
+	}
+	nq := n
+	nw := m
+	if side == blas.Left {
+		nq = m
+		nw = n
+	}
+	if vect == lapack.ApplyQ {
+		checkMatrix(nq, min(nq, k), a, lda)
+	} else {
+		checkMatrix(min(nq, k), nq, a, lda)
+	}
+	if len(tau) < min(nq, k) {
+		panic(badTau)
+	}
+	checkMatrix(m, n, c, ldc)
+	if len(work) < lwork {
+		panic(shortWork)
+	}
+	if lwork < max(1, nw) && lwork != -1 {
+		panic(badWork)
+	}
+
+	applyQ := vect == lapack.ApplyQ
+	left := side == blas.Left
+	var nb int
+
+	// The current implementation does not use opts, but a future change may
+	// use these options so construct them.
+	var opts string
+	if side == blas.Left {
+		opts = "L"
+	} else {
+		opts = "R"
+	}
+	if trans == blas.Trans {
+		opts += "T"
+	} else {
+		opts += "N"
+	}
+	if applyQ {
+		if left {
+			nb = impl.Ilaenv(1, "DORMQR", opts, m-1, n, m-1, -1)
+		} else {
+			nb = impl.Ilaenv(1, "DORMQR", opts, m, n-1, n-1, -1)
+		}
+	} else {
+		if left {
+			nb = impl.Ilaenv(1, "DORMLQ", opts, m-1, n, m-1, -1)
+		} else {
+			nb = impl.Ilaenv(1, "DORMLQ", opts, m, n-1, n-1, -1)
+		}
+	}
+	lworkopt := max(1, nw) * nb
+	if lwork == -1 {
+		work[0] = float64(lworkopt)
+	}
+	if applyQ {
+		// Change the operation to get Q depending on the size of the initial
+		// matrix to Dgebrd. The size matters due to the storage location of
+		// the off-diagonal elements.
+		if nq >= k {
+			impl.Dormqr(side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork)
+		} else if nq > 1 {
+			mi := m
+			ni := n - 1
+			i1 := 0
+			i2 := 1
+			if left {
+				mi = m - 1
+				ni = n
+				i1 = 1
+				i2 = 0
+			}
+			impl.Dormqr(side, trans, mi, ni, nq-1, a[1*lda:], lda, tau[:nq-1], c[i1*ldc+i2:], ldc, work, lwork)
+		}
+		work[0] = float64(lworkopt)
+		return
+	}
+	transt := blas.Trans
+	if trans == blas.Trans {
+		transt = blas.NoTrans
+	}
+	// Change the operation to get P depending on the size of the initial
+	// matrix to Dgebrd. The size matters due to the storage location of
+	// the off-diagonal elements.
+	if nq > k {
+		impl.Dormlq(side, transt, m, n, k, a, lda, tau, c, ldc, work, lwork)
+	} else if nq > 1 {
+		mi := m
+		ni := n - 1
+		i1 := 0
+		i2 := 1
+		if left {
+			mi = m - 1
+			ni = n
+			i1 = 1
+			i2 = 0
+		}
+		impl.Dormlq(side, transt, mi, ni, nq-1, a[1:], lda, tau, c[i1*ldc+i2:], ldc, work, lwork)
+	}
+	work[0] = float64(lworkopt)
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dormhr.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dormhr.go
new file mode 100644
index 00000000..fccb5738
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dormhr.go
@@ -0,0 +1,121 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "gonum.org/v1/gonum/blas"
+
+// Dormhr multiplies an m×n general matrix C with an nq×nq orthogonal matrix Q
+//  Q * C,    if side == blas.Left and trans == blas.NoTrans,
+//  Q^T * C,  if side == blas.Left and trans == blas.Trans,
+//  C * Q,    if side == blas.Right and trans == blas.NoTrans,
+//  C * Q^T,  if side == blas.Right and trans == blas.Trans,
+// where nq == m if side == blas.Left and nq == n if side == blas.Right.
+//
+// Q is defined implicitly as the product of ihi-ilo elementary reflectors, as
+// returned by Dgehrd:
+//  Q = H_{ilo} H_{ilo+1} ... H_{ihi-1}.
+// Q is equal to the identity matrix except in the submatrix
+// Q[ilo+1:ihi+1,ilo+1:ihi+1].
+//
+// ilo and ihi must have the same values as in the previous call of Dgehrd. It
+// must hold that
+//  0 <= ilo <= ihi < m,   if m > 0 and side == blas.Left,
+//  ilo = 0 and ihi = -1,  if m = 0 and side == blas.Left,
+//  0 <= ilo <= ihi < n,   if n > 0 and side == blas.Right,
+//  ilo = 0 and ihi = -1,  if n = 0 and side == blas.Right.
+//
+// a and lda represent an m×m matrix if side == blas.Left and an n×n matrix if
+// side == blas.Right. The matrix contains vectors which define the elementary
+// reflectors, as returned by Dgehrd.
+//
+// tau contains the scalar factors of the elementary reflectors, as returned by
+// Dgehrd. tau must have length m-1 if side == blas.Left and n-1 if side ==
+// blas.Right.
+//
+// c and ldc represent the m×n matrix C. On return, c is overwritten by the
+// product with Q.
+//
+// work must have length at least max(1,lwork), and lwork must be at least
+// max(1,n), if side == blas.Left, and max(1,m), if side == blas.Right. For
+// optimum performance lwork should be at least n*nb if side == blas.Left and
+// m*nb if side == blas.Right, where nb is the optimal block size. On return,
+// work[0] will contain the optimal value of lwork.
+//
+// If lwork == -1, instead of performing Dormhr, only the optimal value of lwork
+// will be stored in work[0].
+//
+// If any requirement on input sizes is not met, Dormhr will panic.
+//
+// Dormhr is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dormhr(side blas.Side, trans blas.Transpose, m, n, ilo, ihi int, a []float64, lda int, tau, c []float64, ldc int, work []float64, lwork int) {
+	var (
+		nq int // The order of Q.
+		nw int // The minimum length of work.
+	)
+	switch side {
+	case blas.Left:
+		nq = m
+		nw = n
+	case blas.Right:
+		nq = n
+		nw = m
+	default:
+		panic(badSide)
+	}
+	switch {
+	case trans != blas.NoTrans && trans != blas.Trans:
+		panic(badTrans)
+	case ilo < 0 || max(1, nq) <= ilo:
+		panic(badIlo)
+	case ihi < min(ilo, nq-1) || nq <= ihi:
+		panic(badIhi)
+	case lwork < max(1, nw) && lwork != -1:
+		panic(badWork)
+	case len(work) < max(1, lwork):
+		panic(shortWork)
+	}
+	if lwork != -1 {
+		checkMatrix(m, n, c, ldc)
+		checkMatrix(nq, nq, a, lda)
+		if len(tau) != nq-1 && nq > 0 {
+			panic(badTau)
+		}
+
+	}
+
+	nh := ihi - ilo
+	var nb int
+	if side == blas.Left {
+		opts := "LN"
+		if trans == blas.Trans {
+			opts = "LT"
+		}
+		nb = impl.Ilaenv(1, "DORMQR", opts, nh, n, nh, -1)
+	} else {
+		opts := "RN"
+		if trans == blas.Trans {
+			opts = "RT"
+		}
+		nb = impl.Ilaenv(1, "DORMQR", opts, m, nh, nh, -1)
+	}
+	lwkopt := max(1, nw) * nb
+	if lwork == -1 {
+		work[0] = float64(lwkopt)
+		return
+	}
+
+	if m == 0 || n == 0 || nh == 0 {
+		work[0] = 1
+		return
+	}
+	if side == blas.Left {
+		impl.Dormqr(side, trans, nh, n, nh, a[(ilo+1)*lda+ilo:], lda,
+			tau[ilo:ihi], c[(ilo+1)*ldc:], ldc, work, lwork)
+	} else {
+		impl.Dormqr(side, trans, m, nh, nh, a[(ilo+1)*lda+ilo:], lda,
+			tau[ilo:ihi], c[ilo+1:], ldc, work, lwork)
+	}
+	work[0] = float64(lwkopt)
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dorml2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dorml2.go
new file mode 100644
index 00000000..7c5f1950
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dorml2.go
@@ -0,0 +1,83 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "gonum.org/v1/gonum/blas"
+
+// Dorml2 multiplies a general matrix C by an orthogonal matrix from an LQ factorization
+// determined by Dgelqf.
+//  C = Q * C    if side == blas.Left and trans == blas.NoTrans
+//  C = Q^T * C  if side == blas.Left and trans == blas.Trans
+//  C = C * Q    if side == blas.Right and trans == blas.NoTrans
+//  C = C * Q^T  if side == blas.Right and trans == blas.Trans
+// If side == blas.Left, a is a matrix of side k×m, and if side == blas.Right
+// a is of size k×n.
+//
+// tau contains the Householder factors and is of length at least k and this function will
+// panic otherwise.
+//
+// work is temporary storage of length at least n if side == blas.Left
+// and at least m if side == blas.Right and this function will panic otherwise.
+//
+// Dorml2 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dorml2(side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64) {
+	if side != blas.Left && side != blas.Right {
+		panic(badSide)
+	}
+	if trans != blas.Trans && trans != blas.NoTrans {
+		panic(badTrans)
+	}
+
+	left := side == blas.Left
+	notran := trans == blas.NoTrans
+	if left {
+		checkMatrix(k, m, a, lda)
+		if len(work) < n {
+			panic(badWork)
+		}
+	} else {
+		checkMatrix(k, n, a, lda)
+		if len(work) < m {
+			panic(badWork)
+		}
+	}
+	checkMatrix(m, n, c, ldc)
+	if m == 0 || n == 0 || k == 0 {
+		return
+	}
+	switch {
+	case left && notran:
+		for i := 0; i < k; i++ {
+			aii := a[i*lda+i]
+			a[i*lda+i] = 1
+			impl.Dlarf(side, m-i, n, a[i*lda+i:], 1, tau[i], c[i*ldc:], ldc, work)
+			a[i*lda+i] = aii
+		}
+
+	case left && !notran:
+		for i := k - 1; i >= 0; i-- {
+			aii := a[i*lda+i]
+			a[i*lda+i] = 1
+			impl.Dlarf(side, m-i, n, a[i*lda+i:], 1, tau[i], c[i*ldc:], ldc, work)
+			a[i*lda+i] = aii
+		}
+
+	case !left && notran:
+		for i := k - 1; i >= 0; i-- {
+			aii := a[i*lda+i]
+			a[i*lda+i] = 1
+			impl.Dlarf(side, m, n-i, a[i*lda+i:], 1, tau[i], c[i:], ldc, work)
+			a[i*lda+i] = aii
+		}
+
+	case !left && !notran:
+		for i := 0; i < k; i++ {
+			aii := a[i*lda+i]
+			a[i*lda+i] = 1
+			impl.Dlarf(side, m, n-i, a[i*lda+i:], 1, tau[i], c[i:], ldc, work)
+			a[i*lda+i] = aii
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dormlq.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dormlq.go
new file mode 100644
index 00000000..12219d20
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dormlq.go
@@ -0,0 +1,159 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dormlq multiplies the matrix C by the orthogonal matrix Q defined by the
+// slices a and tau. A and tau are as returned from Dgelqf.
+//  C = Q * C    if side == blas.Left and trans == blas.NoTrans
+//  C = Q^T * C  if side == blas.Left and trans == blas.Trans
+//  C = C * Q    if side == blas.Right and trans == blas.NoTrans
+//  C = C * Q^T  if side == blas.Right and trans == blas.Trans
+// If side == blas.Left, A is a matrix of side k×m, and if side == blas.Right
+// A is of size k×n. This uses a blocked algorithm.
+//
+// work is temporary storage, and lwork specifies the usable memory length.
+// At minimum, lwork >= m if side == blas.Left and lwork >= n if side == blas.Right,
+// and this function will panic otherwise.
+// Dormlq uses a block algorithm, but the block size is limited
+// by the temporary space available. If lwork == -1, instead of performing Dormlq,
+// the optimal work length will be stored into work[0].
+//
+// tau contains the Householder scales and must have length at least k, and
+// this function will panic otherwise.
+func (impl Implementation) Dormlq(side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64, lwork int) {
+	if side != blas.Left && side != blas.Right {
+		panic(badSide)
+	}
+	if trans != blas.Trans && trans != blas.NoTrans {
+		panic(badTrans)
+	}
+	left := side == blas.Left
+	if left {
+		checkMatrix(k, m, a, lda)
+	} else {
+		checkMatrix(k, n, a, lda)
+	}
+	checkMatrix(m, n, c, ldc)
+	if len(tau) < k {
+		panic(badTau)
+	}
+	if len(work) < lwork {
+		panic(shortWork)
+	}
+	nw := m
+	if left {
+		nw = n
+	}
+	if lwork < max(1, nw) && lwork != -1 {
+		panic(badWork)
+	}
+
+	if m == 0 || n == 0 || k == 0 {
+		work[0] = 1
+		return
+	}
+
+	const (
+		nbmax = 64
+		ldt   = nbmax
+		tsize = nbmax * ldt
+	)
+	opts := string(side) + string(trans)
+	nb := min(nbmax, impl.Ilaenv(1, "DORMLQ", opts, m, n, k, -1))
+	lworkopt := max(1, nw)*nb + tsize
+	if lwork == -1 {
+		work[0] = float64(lworkopt)
+		return
+	}
+
+	nbmin := 2
+	if 1 < nb && nb < k {
+		iws := nw*nb + tsize
+		if lwork < iws {
+			nb = (lwork - tsize) / nw
+			nbmin = max(2, impl.Ilaenv(2, "DORMLQ", opts, m, n, k, -1))
+		}
+	}
+	if nb < nbmin || k <= nb {
+		// Call unblocked code.
+		impl.Dorml2(side, trans, m, n, k, a, lda, tau, c, ldc, work)
+		work[0] = float64(lworkopt)
+		return
+	}
+
+	t := work[:tsize]
+	wrk := work[tsize:]
+	ldwrk := nb
+
+	notran := trans == blas.NoTrans
+	transt := blas.NoTrans
+	if notran {
+		transt = blas.Trans
+	}
+
+	switch {
+	case left && notran:
+		for i := 0; i < k; i += nb {
+			ib := min(nb, k-i)
+			impl.Dlarft(lapack.Forward, lapack.RowWise, m-i, ib,
+				a[i*lda+i:], lda,
+				tau[i:],
+				t, ldt)
+			impl.Dlarfb(side, transt, lapack.Forward, lapack.RowWise, m-i, n, ib,
+				a[i*lda+i:], lda,
+				t, ldt,
+				c[i*ldc:], ldc,
+				wrk, ldwrk)
+		}
+
+	case left && !notran:
+		for i := ((k - 1) / nb) * nb; i >= 0; i -= nb {
+			ib := min(nb, k-i)
+			impl.Dlarft(lapack.Forward, lapack.RowWise, m-i, ib,
+				a[i*lda+i:], lda,
+				tau[i:],
+				t, ldt)
+			impl.Dlarfb(side, transt, lapack.Forward, lapack.RowWise, m-i, n, ib,
+				a[i*lda+i:], lda,
+				t, ldt,
+				c[i*ldc:], ldc,
+				wrk, ldwrk)
+		}
+
+	case !left && notran:
+		for i := ((k - 1) / nb) * nb; i >= 0; i -= nb {
+			ib := min(nb, k-i)
+			impl.Dlarft(lapack.Forward, lapack.RowWise, n-i, ib,
+				a[i*lda+i:], lda,
+				tau[i:],
+				t, ldt)
+			impl.Dlarfb(side, transt, lapack.Forward, lapack.RowWise, m, n-i, ib,
+				a[i*lda+i:], lda,
+				t, ldt,
+				c[i:], ldc,
+				wrk, ldwrk)
+		}
+
+	case !left && !notran:
+		for i := 0; i < k; i += nb {
+			ib := min(nb, k-i)
+			impl.Dlarft(lapack.Forward, lapack.RowWise, n-i, ib,
+				a[i*lda+i:], lda,
+				tau[i:],
+				t, ldt)
+			impl.Dlarfb(side, transt, lapack.Forward, lapack.RowWise, m, n-i, ib,
+				a[i*lda+i:], lda,
+				t, ldt,
+				c[i:], ldc,
+				wrk, ldwrk)
+		}
+	}
+	work[0] = float64(lworkopt)
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dormqr.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dormqr.go
new file mode 100644
index 00000000..9a02b90d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dormqr.go
@@ -0,0 +1,167 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dormqr multiplies an m×n matrix C by an orthogonal matrix Q as
+//  C = Q * C,    if side == blas.Left  and trans == blas.NoTrans,
+//  C = Q^T * C,  if side == blas.Left  and trans == blas.Trans,
+//  C = C * Q,    if side == blas.Right and trans == blas.NoTrans,
+//  C = C * Q^T,  if side == blas.Right and trans == blas.Trans,
+// where Q is defined as the product of k elementary reflectors
+//  Q = H_0 * H_1 * ... * H_{k-1}.
+//
+// If side == blas.Left, A is an m×k matrix and 0 <= k <= m.
+// If side == blas.Right, A is an n×k matrix and 0 <= k <= n.
+// The ith column of A contains the vector which defines the elementary
+// reflector H_i and tau[i] contains its scalar factor. tau must have length k
+// and Dormqr will panic otherwise. Dgeqrf returns A and tau in the required
+// form.
+//
+// work must have length at least max(1,lwork), and lwork must be at least n if
+// side == blas.Left and at least m if side == blas.Right, otherwise Dormqr will
+// panic.
+//
+// work is temporary storage, and lwork specifies the usable memory length. At
+// minimum, lwork >= m if side == blas.Left and lwork >= n if side ==
+// blas.Right, and this function will panic otherwise. Larger values of lwork
+// will generally give better performance. On return, work[0] will contain the
+// optimal value of lwork.
+//
+// If lwork is -1, instead of performing Dormqr, the optimal workspace size will
+// be stored into work[0].
+func (impl Implementation) Dormqr(side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64, lwork int) {
+	var nq, nw int
+	switch side {
+	default:
+		panic(badSide)
+	case blas.Left:
+		nq = m
+		nw = n
+	case blas.Right:
+		nq = n
+		nw = m
+	}
+	switch {
+	case trans != blas.NoTrans && trans != blas.Trans:
+		panic(badTrans)
+	case m < 0 || n < 0:
+		panic(negDimension)
+	case k < 0 || nq < k:
+		panic("lapack: invalid value of k")
+	case len(work) < lwork:
+		panic(shortWork)
+	case lwork < max(1, nw) && lwork != -1:
+		panic(badWork)
+	}
+	if lwork != -1 {
+		checkMatrix(nq, k, a, lda)
+		checkMatrix(m, n, c, ldc)
+		if len(tau) != k {
+			panic(badTau)
+		}
+	}
+
+	if m == 0 || n == 0 || k == 0 {
+		work[0] = 1
+		return
+	}
+
+	const (
+		nbmax = 64
+		ldt   = nbmax
+		tsize = nbmax * ldt
+	)
+	opts := string(side) + string(trans)
+	nb := min(nbmax, impl.Ilaenv(1, "DORMQR", opts, m, n, k, -1))
+	lworkopt := max(1, nw)*nb + tsize
+	if lwork == -1 {
+		work[0] = float64(lworkopt)
+		return
+	}
+
+	nbmin := 2
+	if 1 < nb && nb < k {
+		if lwork < nw*nb+tsize {
+			nb = (lwork - tsize) / nw
+			nbmin = max(2, impl.Ilaenv(2, "DORMQR", opts, m, n, k, -1))
+		}
+	}
+
+	if nb < nbmin || k <= nb {
+		// Call unblocked code.
+		impl.Dorm2r(side, trans, m, n, k, a, lda, tau, c, ldc, work)
+		work[0] = float64(lworkopt)
+		return
+	}
+
+	var (
+		ldwork = nb
+		left   = side == blas.Left
+		notran = trans == blas.NoTrans
+	)
+	switch {
+	case left && notran:
+		for i := ((k - 1) / nb) * nb; i >= 0; i -= nb {
+			ib := min(nb, k-i)
+			impl.Dlarft(lapack.Forward, lapack.ColumnWise, m-i, ib,
+				a[i*lda+i:], lda,
+				tau[i:],
+				work[:tsize], ldt)
+			impl.Dlarfb(side, trans, lapack.Forward, lapack.ColumnWise, m-i, n, ib,
+				a[i*lda+i:], lda,
+				work[:tsize], ldt,
+				c[i*ldc:], ldc,
+				work[tsize:], ldwork)
+		}
+
+	case left && !notran:
+		for i := 0; i < k; i += nb {
+			ib := min(nb, k-i)
+			impl.Dlarft(lapack.Forward, lapack.ColumnWise, m-i, ib,
+				a[i*lda+i:], lda,
+				tau[i:],
+				work[:tsize], ldt)
+			impl.Dlarfb(side, trans, lapack.Forward, lapack.ColumnWise, m-i, n, ib,
+				a[i*lda+i:], lda,
+				work[:tsize], ldt,
+				c[i*ldc:], ldc,
+				work[tsize:], ldwork)
+		}
+
+	case !left && notran:
+		for i := 0; i < k; i += nb {
+			ib := min(nb, k-i)
+			impl.Dlarft(lapack.Forward, lapack.ColumnWise, n-i, ib,
+				a[i*lda+i:], lda,
+				tau[i:],
+				work[:tsize], ldt)
+			impl.Dlarfb(side, trans, lapack.Forward, lapack.ColumnWise, m, n-i, ib,
+				a[i*lda+i:], lda,
+				work[:tsize], ldt,
+				c[i:], ldc,
+				work[tsize:], ldwork)
+		}
+
+	case !left && !notran:
+		for i := ((k - 1) / nb) * nb; i >= 0; i -= nb {
+			ib := min(nb, k-i)
+			impl.Dlarft(lapack.Forward, lapack.ColumnWise, n-i, ib,
+				a[i*lda+i:], lda,
+				tau[i:],
+				work[:tsize], ldt)
+			impl.Dlarfb(side, trans, lapack.Forward, lapack.ColumnWise, m, n-i, ib,
+				a[i*lda+i:], lda,
+				work[:tsize], ldt,
+				c[i:], ldc,
+				work[tsize:], ldwork)
+		}
+	}
+	work[0] = float64(lworkopt)
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dormr2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dormr2.go
new file mode 100644
index 00000000..c867e8e8
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dormr2.go
@@ -0,0 +1,93 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "gonum.org/v1/gonum/blas"
+
+// Dormr2 multiplies a general matrix C by an orthogonal matrix from a RQ factorization
+// determined by Dgerqf.
+//  C = Q * C    if side == blas.Left and trans == blas.NoTrans
+//  C = Q^T * C  if side == blas.Left and trans == blas.Trans
+//  C = C * Q    if side == blas.Right and trans == blas.NoTrans
+//  C = C * Q^T  if side == blas.Right and trans == blas.Trans
+// If side == blas.Left, a is a matrix of size k×m, and if side == blas.Right
+// a is of size k×n.
+//
+// tau contains the Householder factors and is of length at least k and this function
+// will panic otherwise.
+//
+// work is temporary storage of length at least n if side == blas.Left
+// and at least m if side == blas.Right and this function will panic otherwise.
+//
+// Dormr2 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dormr2(side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64) {
+	if side != blas.Left && side != blas.Right {
+		panic(badSide)
+	}
+	if trans != blas.Trans && trans != blas.NoTrans {
+		panic(badTrans)
+	}
+
+	left := side == blas.Left
+	notran := trans == blas.NoTrans
+	if left {
+		if k > m {
+			panic(kGTM)
+		}
+		checkMatrix(k, m, a, lda)
+		if len(work) < n {
+			panic(badWork)
+		}
+	} else {
+		if k > n {
+			panic(kGTN)
+		}
+		checkMatrix(k, n, a, lda)
+		if len(work) < m {
+			panic(badWork)
+		}
+	}
+	if len(tau) < k {
+		panic(badTau)
+	}
+	checkMatrix(m, n, c, ldc)
+
+	if m == 0 || n == 0 || k == 0 {
+		return
+	}
+	if left {
+		if notran {
+			for i := k - 1; i >= 0; i-- {
+				aii := a[i*lda+(m-k+i)]
+				a[i*lda+(m-k+i)] = 1
+				impl.Dlarf(side, m-k+i+1, n, a[i*lda:], 1, tau[i], c, ldc, work)
+				a[i*lda+(m-k+i)] = aii
+			}
+			return
+		}
+		for i := 0; i < k; i++ {
+			aii := a[i*lda+(m-k+i)]
+			a[i*lda+(m-k+i)] = 1
+			impl.Dlarf(side, m-k+i+1, n, a[i*lda:], 1, tau[i], c, ldc, work)
+			a[i*lda+(m-k+i)] = aii
+		}
+		return
+	}
+	if notran {
+		for i := 0; i < k; i++ {
+			aii := a[i*lda+(n-k+i)]
+			a[i*lda+(n-k+i)] = 1
+			impl.Dlarf(side, m, n-k+i+1, a[i*lda:], 1, tau[i], c, ldc, work)
+			a[i*lda+(n-k+i)] = aii
+		}
+		return
+	}
+	for i := k - 1; i >= 0; i-- {
+		aii := a[i*lda+(n-k+i)]
+		a[i*lda+(n-k+i)] = 1
+		impl.Dlarf(side, m, n-k+i+1, a[i*lda:], 1, tau[i], c, ldc, work)
+		a[i*lda+(n-k+i)] = aii
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dpbtf2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dpbtf2.go
new file mode 100644
index 00000000..6cc5f38f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dpbtf2.go
@@ -0,0 +1,97 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dpbtf2 computes the Cholesky factorization of a symmetric positive banded
+// matrix ab. The matrix ab is n×n with kd diagonal bands. The Cholesky
+// factorization computed is
+//  A = U^T * U if ul == blas.Upper
+//  A = L * L^T if ul == blas.Lower
+// ul also specifies the storage of ab. If ul == blas.Upper, then
+// ab is stored as an upper-triangular banded matrix with kd super-diagonals,
+// and if ul == blas.Lower, ab is stored as a lower-triangular banded matrix
+// with kd sub-diagonals. On exit, the banded matrix U or L is stored in-place
+// into ab depending on the value of ul. Dpbtf2 returns whether the factorization
+// was successfully completed.
+//
+// The band storage scheme is illustrated below when n = 6, and kd = 2.
+// The resulting Cholesky decomposition is stored in the same elements as the
+// input band matrix (a11 becomes u11 or l11, etc.).
+//
+//  ul = blas.Upper
+//  a11 a12 a13
+//  a22 a23 a24
+//  a33 a34 a35
+//  a44 a45 a46
+//  a55 a56  *
+//  a66  *   *
+//
+//  ul = blas.Lower
+//   *   *  a11
+//   *  a21 a22
+//  a31 a32 a33
+//  a42 a43 a44
+//  a53 a54 a55
+//  a64 a65 a66
+//
+// Dpbtf2 is the unblocked version of the algorithm, see Dpbtrf for the blocked
+// version.
+//
+// Dpbtf2 is an internal routine, exported for testing purposes.
+func (Implementation) Dpbtf2(ul blas.Uplo, n, kd int, ab []float64, ldab int) (ok bool) {
+	if ul != blas.Upper && ul != blas.Lower {
+		panic(badUplo)
+	}
+	checkSymBanded(ab, n, kd, ldab)
+	if n == 0 {
+		return
+	}
+	bi := blas64.Implementation()
+	kld := max(1, ldab-1)
+	if ul == blas.Upper {
+		for j := 0; j < n; j++ {
+			// Compute U(J,J) and test for non positive-definiteness.
+			ajj := ab[j*ldab]
+			if ajj <= 0 {
+				return false
+			}
+			ajj = math.Sqrt(ajj)
+			ab[j*ldab] = ajj
+			// Compute elements j+1:j+kn of row J and update the trailing submatrix
+			// within the band.
+			kn := min(kd, n-j-1)
+			if kn > 0 {
+				bi.Dscal(kn, 1/ajj, ab[j*ldab+1:], 1)
+				bi.Dsyr(blas.Upper, kn, -1, ab[j*ldab+1:], 1, ab[(j+1)*ldab:], kld)
+			}
+		}
+		return true
+	}
+	for j := 0; j < n; j++ {
+		// Compute L(J,J) and test for non positive-definiteness.
+		ajj := ab[j*ldab+kd]
+		if ajj <= 0 {
+			return false
+		}
+		ajj = math.Sqrt(ajj)
+		ab[j*ldab+kd] = ajj
+
+		// Compute elements J+1:J+KN of column J and update the trailing submatrix
+		// within the band.
+		kn := min(kd, n-j-1)
+		if kn > 0 {
+			bi.Dscal(kn, 1/ajj, ab[(j+1)*ldab+kd-1:], kld)
+			bi.Dsyr(blas.Lower, kn, -1, ab[(j+1)*ldab+kd-1:], kld, ab[(j+1)*ldab+kd:], kld)
+		}
+	}
+	return true
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dpocon.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dpocon.go
new file mode 100644
index 00000000..ce85bd0e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dpocon.go
@@ -0,0 +1,76 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dpocon estimates the reciprocal of the condition number of a positive-definite
+// matrix A given the Cholesky decomposition of A. The condition number computed
+// is based on the 1-norm and the ∞-norm.
+//
+// anorm is the 1-norm and the ∞-norm of the original matrix A.
+//
+// work is a temporary data slice of length at least 3*n and Dpocon will panic otherwise.
+//
+// iwork is a temporary data slice of length at least n and Dpocon will panic otherwise.
+func (impl Implementation) Dpocon(uplo blas.Uplo, n int, a []float64, lda int, anorm float64, work []float64, iwork []int) float64 {
+	checkMatrix(n, n, a, lda)
+	if uplo != blas.Upper && uplo != blas.Lower {
+		panic(badUplo)
+	}
+	if len(work) < 3*n {
+		panic(badWork)
+	}
+	if len(iwork) < n {
+		panic(badWork)
+	}
+	var rcond float64
+	if n == 0 {
+		return 1
+	}
+	if anorm == 0 {
+		return rcond
+	}
+
+	bi := blas64.Implementation()
+	var ainvnm float64
+	smlnum := dlamchS
+	upper := uplo == blas.Upper
+	var kase int
+	var normin bool
+	isave := new([3]int)
+	var sl, su float64
+	for {
+		ainvnm, kase = impl.Dlacn2(n, work[n:], work, iwork, ainvnm, kase, isave)
+		if kase == 0 {
+			if ainvnm != 0 {
+				rcond = (1 / ainvnm) / anorm
+			}
+			return rcond
+		}
+		if upper {
+			sl = impl.Dlatrs(blas.Upper, blas.Trans, blas.NonUnit, normin, n, a, lda, work, work[2*n:])
+			normin = true
+			su = impl.Dlatrs(blas.Upper, blas.NoTrans, blas.NonUnit, normin, n, a, lda, work, work[2*n:])
+		} else {
+			sl = impl.Dlatrs(blas.Lower, blas.NoTrans, blas.NonUnit, normin, n, a, lda, work, work[2*n:])
+			normin = true
+			su = impl.Dlatrs(blas.Lower, blas.Trans, blas.NonUnit, normin, n, a, lda, work, work[2*n:])
+		}
+		scale := sl * su
+		if scale != 1 {
+			ix := bi.Idamax(n, work, 1)
+			if scale == 0 || scale < math.Abs(work[ix])*smlnum {
+				return rcond
+			}
+			impl.Drscl(n, scale, work, 1)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dpotf2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dpotf2.go
new file mode 100644
index 00000000..a8891988
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dpotf2.go
@@ -0,0 +1,72 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dpotf2 computes the Cholesky decomposition of the symmetric positive definite
+// matrix a. If ul == blas.Upper, then a is stored as an upper-triangular matrix,
+// and a = U^T U is stored in place into a. If ul == blas.Lower, then a = L L^T
+// is computed and stored in-place into a. If a is not positive definite, false
+// is returned. This is the unblocked version of the algorithm.
+//
+// Dpotf2 is an internal routine. It is exported for testing purposes.
+func (Implementation) Dpotf2(ul blas.Uplo, n int, a []float64, lda int) (ok bool) {
+	if ul != blas.Upper && ul != blas.Lower {
+		panic(badUplo)
+	}
+	checkMatrix(n, n, a, lda)
+
+	if n == 0 {
+		return true
+	}
+
+	bi := blas64.Implementation()
+	if ul == blas.Upper {
+		for j := 0; j < n; j++ {
+			ajj := a[j*lda+j]
+			if j != 0 {
+				ajj -= bi.Ddot(j, a[j:], lda, a[j:], lda)
+			}
+			if ajj <= 0 || math.IsNaN(ajj) {
+				a[j*lda+j] = ajj
+				return false
+			}
+			ajj = math.Sqrt(ajj)
+			a[j*lda+j] = ajj
+			if j < n-1 {
+				bi.Dgemv(blas.Trans, j, n-j-1,
+					-1, a[j+1:], lda, a[j:], lda,
+					1, a[j*lda+j+1:], 1)
+				bi.Dscal(n-j-1, 1/ajj, a[j*lda+j+1:], 1)
+			}
+		}
+		return true
+	}
+	for j := 0; j < n; j++ {
+		ajj := a[j*lda+j]
+		if j != 0 {
+			ajj -= bi.Ddot(j, a[j*lda:], 1, a[j*lda:], 1)
+		}
+		if ajj <= 0 || math.IsNaN(ajj) {
+			a[j*lda+j] = ajj
+			return false
+		}
+		ajj = math.Sqrt(ajj)
+		a[j*lda+j] = ajj
+		if j < n-1 {
+			bi.Dgemv(blas.NoTrans, n-j-1, j,
+				-1, a[(j+1)*lda:], lda, a[j*lda:], 1,
+				1, a[(j+1)*lda+j:], lda)
+			bi.Dscal(n-j-1, 1/ajj, a[(j+1)*lda+j:], lda)
+		}
+	}
+	return true
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dpotrf.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dpotrf.go
new file mode 100644
index 00000000..a942259a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dpotrf.go
@@ -0,0 +1,72 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dpotrf computes the Cholesky decomposition of the symmetric positive definite
+// matrix a. If ul == blas.Upper, then a is stored as an upper-triangular matrix,
+// and a = U^T U is stored in place into a. If ul == blas.Lower, then a = L L^T
+// is computed and stored in-place into a. If a is not positive definite, false
+// is returned. This is the blocked version of the algorithm.
+func (impl Implementation) Dpotrf(ul blas.Uplo, n int, a []float64, lda int) (ok bool) {
+	if ul != blas.Upper && ul != blas.Lower {
+		panic(badUplo)
+	}
+	checkMatrix(n, n, a, lda)
+
+	if n == 0 {
+		return true
+	}
+
+	nb := impl.Ilaenv(1, "DPOTRF", string(ul), n, -1, -1, -1)
+	if nb <= 1 || n <= nb {
+		return impl.Dpotf2(ul, n, a, lda)
+	}
+	bi := blas64.Implementation()
+	if ul == blas.Upper {
+		for j := 0; j < n; j += nb {
+			jb := min(nb, n-j)
+			bi.Dsyrk(blas.Upper, blas.Trans, jb, j,
+				-1, a[j:], lda,
+				1, a[j*lda+j:], lda)
+			ok = impl.Dpotf2(blas.Upper, jb, a[j*lda+j:], lda)
+			if !ok {
+				return ok
+			}
+			if j+jb < n {
+				bi.Dgemm(blas.Trans, blas.NoTrans, jb, n-j-jb, j,
+					-1, a[j:], lda, a[j+jb:], lda,
+					1, a[j*lda+j+jb:], lda)
+				bi.Dtrsm(blas.Left, blas.Upper, blas.Trans, blas.NonUnit, jb, n-j-jb,
+					1, a[j*lda+j:], lda,
+					a[j*lda+j+jb:], lda)
+			}
+		}
+		return true
+	}
+	for j := 0; j < n; j += nb {
+		jb := min(nb, n-j)
+		bi.Dsyrk(blas.Lower, blas.NoTrans, jb, j,
+			-1, a[j*lda:], lda,
+			1, a[j*lda+j:], lda)
+		ok := impl.Dpotf2(blas.Lower, jb, a[j*lda+j:], lda)
+		if !ok {
+			return ok
+		}
+		if j+jb < n {
+			bi.Dgemm(blas.NoTrans, blas.Trans, n-j-jb, jb, j,
+				-1, a[(j+jb)*lda:], lda, a[j*lda:], lda,
+				1, a[(j+jb)*lda+j:], lda)
+			bi.Dtrsm(blas.Right, blas.Lower, blas.Trans, blas.NonUnit, n-j-jb, jb,
+				1, a[j*lda+j:], lda,
+				a[(j+jb)*lda+j:], lda)
+		}
+	}
+	return true
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/drscl.go b/vendor/gonum.org/v1/gonum/lapack/gonum/drscl.go
new file mode 100644
index 00000000..0ed15214
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/drscl.go
@@ -0,0 +1,47 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Drscl multiplies the vector x by 1/a being careful to avoid overflow or
+// underflow where possible.
+//
+// Drscl is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Drscl(n int, a float64, x []float64, incX int) {
+	checkVector(n, x, incX)
+	bi := blas64.Implementation()
+	cden := a
+	cnum := 1.0
+	smlnum := dlamchS
+	bignum := 1 / smlnum
+	for {
+		cden1 := cden * smlnum
+		cnum1 := cnum / bignum
+		var mul float64
+		var done bool
+		switch {
+		case cnum != 0 && math.Abs(cden1) > math.Abs(cnum):
+			mul = smlnum
+			done = false
+			cden = cden1
+		case math.Abs(cnum1) > math.Abs(cden):
+			mul = bignum
+			done = false
+			cnum = cnum1
+		default:
+			mul = cnum / cden
+			done = true
+		}
+		bi.Dscal(n, mul, x, incX)
+		if done {
+			break
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dsteqr.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dsteqr.go
new file mode 100644
index 00000000..9a36e1c5
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dsteqr.go
@@ -0,0 +1,373 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dsteqr computes the eigenvalues and optionally the eigenvectors of a symmetric
+// tridiagonal matrix using the implicit QL or QR method. The eigenvectors of a
+// full or band symmetric matrix can also be found if Dsytrd, Dsptrd, or Dsbtrd
+// have been used to reduce this matrix to tridiagonal form.
+//
+// d, on entry, contains the diagonal elements of the tridiagonal matrix. On exit,
+// d contains the eigenvalues in ascending order. d must have length n and
+// Dsteqr will panic otherwise.
+//
+// e, on entry, contains the off-diagonal elements of the tridiagonal matrix on
+// entry, and is overwritten during the call to Dsteqr. e must have length n-1 and
+// Dsteqr will panic otherwise.
+//
+// z, on entry, contains the n×n orthogonal matrix used in the reduction to
+// tridiagonal form if compz == lapack.OriginalEV. On exit, if
+// compz == lapack.OriginalEV, z contains the orthonormal eigenvectors of the
+// original symmetric matrix, and if compz == lapack.TridiagEV, z contains the
+// orthonormal eigenvectors of the symmetric tridiagonal matrix. z is not used
+// if compz == lapack.None.
+//
+// work must have length at least max(1, 2*n-2) if the eigenvectors are computed,
+// and Dsteqr will panic otherwise.
+//
+// Dsteqr is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dsteqr(compz lapack.EVComp, n int, d, e, z []float64, ldz int, work []float64) (ok bool) {
+	if n < 0 {
+		panic(nLT0)
+	}
+	if len(d) < n {
+		panic(badD)
+	}
+	if len(e) < n-1 {
+		panic(badE)
+	}
+	if compz != lapack.None && compz != lapack.TridiagEV && compz != lapack.OriginalEV {
+		panic(badEVComp)
+	}
+	if compz != lapack.None {
+		if len(work) < max(1, 2*n-2) {
+			panic(badWork)
+		}
+		checkMatrix(n, n, z, ldz)
+	}
+
+	var icompz int
+	if compz == lapack.OriginalEV {
+		icompz = 1
+	} else if compz == lapack.TridiagEV {
+		icompz = 2
+	}
+
+	if n == 0 {
+		return true
+	}
+	if n == 1 {
+		if icompz == 2 {
+			z[0] = 1
+		}
+		return true
+	}
+
+	bi := blas64.Implementation()
+
+	eps := dlamchE
+	eps2 := eps * eps
+	safmin := dlamchS
+	safmax := 1 / safmin
+	ssfmax := math.Sqrt(safmax) / 3
+	ssfmin := math.Sqrt(safmin) / eps2
+
+	// Compute the eigenvalues and eigenvectors of the tridiagonal matrix.
+	if icompz == 2 {
+		impl.Dlaset(blas.All, n, n, 0, 1, z, ldz)
+	}
+	const maxit = 30
+	nmaxit := n * maxit
+
+	jtot := 0
+
+	// Determine where the matrix splits and choose QL or QR iteration for each
+	// block, according to whether top or bottom diagonal element is smaller.
+	l1 := 0
+	nm1 := n - 1
+
+	type scaletype int
+	const (
+		down scaletype = iota + 1
+		up
+	)
+	var iscale scaletype
+
+	for {
+		if l1 > n-1 {
+			// Order eigenvalues and eigenvectors.
+			if icompz == 0 {
+				impl.Dlasrt(lapack.SortIncreasing, n, d)
+			} else {
+				// TODO(btracey): Consider replacing this sort with a call to sort.Sort.
+				for ii := 1; ii < n; ii++ {
+					i := ii - 1
+					k := i
+					p := d[i]
+					for j := ii; j < n; j++ {
+						if d[j] < p {
+							k = j
+							p = d[j]
+						}
+					}
+					if k != i {
+						d[k] = d[i]
+						d[i] = p
+						bi.Dswap(n, z[i:], ldz, z[k:], ldz)
+					}
+				}
+			}
+			return true
+		}
+		if l1 > 0 {
+			e[l1-1] = 0
+		}
+		var m int
+		if l1 <= nm1 {
+			for m = l1; m < nm1; m++ {
+				test := math.Abs(e[m])
+				if test == 0 {
+					break
+				}
+				if test <= (math.Sqrt(math.Abs(d[m]))*math.Sqrt(math.Abs(d[m+1])))*eps {
+					e[m] = 0
+					break
+				}
+			}
+		}
+		l := l1
+		lsv := l
+		lend := m
+		lendsv := lend
+		l1 = m + 1
+		if lend == l {
+			continue
+		}
+
+		// Scale submatrix in rows and columns L to Lend
+		anorm := impl.Dlanst(lapack.MaxAbs, lend-l+1, d[l:], e[l:])
+		switch {
+		case anorm == 0:
+			continue
+		case anorm > ssfmax:
+			iscale = down
+			// Pretend that d and e are matrices with 1 column.
+			impl.Dlascl(lapack.General, 0, 0, anorm, ssfmax, lend-l+1, 1, d[l:], 1)
+			impl.Dlascl(lapack.General, 0, 0, anorm, ssfmax, lend-l, 1, e[l:], 1)
+		case anorm < ssfmin:
+			iscale = up
+			impl.Dlascl(lapack.General, 0, 0, anorm, ssfmin, lend-l+1, 1, d[l:], 1)
+			impl.Dlascl(lapack.General, 0, 0, anorm, ssfmin, lend-l, 1, e[l:], 1)
+		}
+
+		// Choose between QL and QR.
+		if math.Abs(d[lend]) < math.Abs(d[l]) {
+			lend = lsv
+			l = lendsv
+		}
+		if lend > l {
+			// QL Iteration. Look for small subdiagonal element.
+			for {
+				if l != lend {
+					for m = l; m < lend; m++ {
+						v := math.Abs(e[m])
+						if v*v <= (eps2*math.Abs(d[m]))*math.Abs(d[m+1])+safmin {
+							break
+						}
+					}
+				} else {
+					m = lend
+				}
+				if m < lend {
+					e[m] = 0
+				}
+				p := d[l]
+				if m == l {
+					// Eigenvalue found.
+					l++
+					if l > lend {
+						break
+					}
+					continue
+				}
+
+				// If remaining matrix is 2×2, use Dlae2 to compute its eigensystem.
+				if m == l+1 {
+					if icompz > 0 {
+						d[l], d[l+1], work[l], work[n-1+l] = impl.Dlaev2(d[l], e[l], d[l+1])
+						impl.Dlasr(blas.Right, lapack.Variable, lapack.Backward,
+							n, 2, work[l:], work[n-1+l:], z[l:], ldz)
+					} else {
+						d[l], d[l+1] = impl.Dlae2(d[l], e[l], d[l+1])
+					}
+					e[l] = 0
+					l += 2
+					if l > lend {
+						break
+					}
+					continue
+				}
+
+				if jtot == nmaxit {
+					break
+				}
+				jtot++
+
+				// Form shift
+				g := (d[l+1] - p) / (2 * e[l])
+				r := impl.Dlapy2(g, 1)
+				g = d[m] - p + e[l]/(g+math.Copysign(r, g))
+				s := 1.0
+				c := 1.0
+				p = 0.0
+
+				// Inner loop
+				for i := m - 1; i >= l; i-- {
+					f := s * e[i]
+					b := c * e[i]
+					c, s, r = impl.Dlartg(g, f)
+					if i != m-1 {
+						e[i+1] = r
+					}
+					g = d[i+1] - p
+					r = (d[i]-g)*s + 2*c*b
+					p = s * r
+					d[i+1] = g + p
+					g = c*r - b
+
+					// If eigenvectors are desired, then save rotations.
+					if icompz > 0 {
+						work[i] = c
+						work[n-1+i] = -s
+					}
+				}
+				// If eigenvectors are desired, then apply saved rotations.
+				if icompz > 0 {
+					mm := m - l + 1
+					impl.Dlasr(blas.Right, lapack.Variable, lapack.Backward,
+						n, mm, work[l:], work[n-1+l:], z[l:], ldz)
+				}
+				d[l] -= p
+				e[l] = g
+			}
+		} else {
+			// QR Iteration.
+			// Look for small superdiagonal element.
+			for {
+				if l != lend {
+					for m = l; m > lend; m-- {
+						v := math.Abs(e[m-1])
+						if v*v <= (eps2*math.Abs(d[m])*math.Abs(d[m-1]) + safmin) {
+							break
+						}
+					}
+				} else {
+					m = lend
+				}
+				if m > lend {
+					e[m-1] = 0
+				}
+				p := d[l]
+				if m == l {
+					// Eigenvalue found
+					l--
+					if l < lend {
+						break
+					}
+					continue
+				}
+
+				// If remaining matrix is 2×2, use Dlae2 to compute its eigenvalues.
+				if m == l-1 {
+					if icompz > 0 {
+						d[l-1], d[l], work[m], work[n-1+m] = impl.Dlaev2(d[l-1], e[l-1], d[l])
+						impl.Dlasr(blas.Right, lapack.Variable, lapack.Forward,
+							n, 2, work[m:], work[n-1+m:], z[l-1:], ldz)
+					} else {
+						d[l-1], d[l] = impl.Dlae2(d[l-1], e[l-1], d[l])
+					}
+					e[l-1] = 0
+					l -= 2
+					if l < lend {
+						break
+					}
+					continue
+				}
+				if jtot == nmaxit {
+					break
+				}
+				jtot++
+
+				// Form shift.
+				g := (d[l-1] - p) / (2 * e[l-1])
+				r := impl.Dlapy2(g, 1)
+				g = d[m] - p + (e[l-1])/(g+math.Copysign(r, g))
+				s := 1.0
+				c := 1.0
+				p = 0.0
+
+				// Inner loop.
+				for i := m; i < l; i++ {
+					f := s * e[i]
+					b := c * e[i]
+					c, s, r = impl.Dlartg(g, f)
+					if i != m {
+						e[i-1] = r
+					}
+					g = d[i] - p
+					r = (d[i+1]-g)*s + 2*c*b
+					p = s * r
+					d[i] = g + p
+					g = c*r - b
+
+					// If eigenvectors are desired, then save rotations.
+					if icompz > 0 {
+						work[i] = c
+						work[n-1+i] = s
+					}
+				}
+
+				// If eigenvectors are desired, then apply saved rotations.
+				if icompz > 0 {
+					mm := l - m + 1
+					impl.Dlasr(blas.Right, lapack.Variable, lapack.Forward,
+						n, mm, work[m:], work[n-1+m:], z[m:], ldz)
+				}
+				d[l] -= p
+				e[l-1] = g
+			}
+		}
+
+		// Undo scaling if necessary.
+		switch iscale {
+		case down:
+			// Pretend that d and e are matrices with 1 column.
+			impl.Dlascl(lapack.General, 0, 0, ssfmax, anorm, lendsv-lsv+1, 1, d[lsv:], 1)
+			impl.Dlascl(lapack.General, 0, 0, ssfmax, anorm, lendsv-lsv, 1, e[lsv:], 1)
+		case up:
+			impl.Dlascl(lapack.General, 0, 0, ssfmin, anorm, lendsv-lsv+1, 1, d[lsv:], 1)
+			impl.Dlascl(lapack.General, 0, 0, ssfmin, anorm, lendsv-lsv, 1, e[lsv:], 1)
+		}
+
+		// Check for no convergence to an eigenvalue after a total of n*maxit iterations.
+		if jtot >= nmaxit {
+			break
+		}
+	}
+	for i := 0; i < n-1; i++ {
+		if e[i] != 0 {
+			return false
+		}
+	}
+	return true
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dsterf.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dsterf.go
new file mode 100644
index 00000000..1ed59820
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dsterf.go
@@ -0,0 +1,278 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dsterf computes all eigenvalues of a symmetric tridiagonal matrix using the
+// Pal-Walker-Kahan variant of the QL or QR algorithm.
+//
+// d contains the diagonal elements of the tridiagonal matrix on entry, and
+// contains the eigenvalues in ascending order on exit. d must have length at
+// least n, or Dsterf will panic.
+//
+// e contains the off-diagonal elements of the tridiagonal matrix on entry, and is
+// overwritten during the call to Dsterf. e must have length of at least n-1 or
+// Dsterf will panic.
+//
+// Dsterf is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dsterf(n int, d, e []float64) (ok bool) {
+	if n < 0 {
+		panic(nLT0)
+	}
+	if n == 0 {
+		return true
+	}
+	if len(d) < n {
+		panic(badD)
+	}
+	if len(e) < n-1 {
+		panic(badE)
+	}
+
+	const (
+		none = 0 // The values are not scaled.
+		down = 1 // The values are scaled below ssfmax threshold.
+		up   = 2 // The values are scaled below ssfmin threshold.
+	)
+
+	// Determine the unit roundoff for this environment.
+	eps := dlamchE
+	eps2 := eps * eps
+	safmin := dlamchS
+	safmax := 1 / safmin
+	ssfmax := math.Sqrt(safmax) / 3
+	ssfmin := math.Sqrt(safmin) / eps2
+
+	// Compute the eigenvalues of the tridiagonal matrix.
+	maxit := 30
+	nmaxit := n * maxit
+	jtot := 0
+
+	l1 := 0
+
+	for {
+		if l1 > n-1 {
+			impl.Dlasrt(lapack.SortIncreasing, n, d)
+			return true
+		}
+		if l1 > 0 {
+			e[l1-1] = 0
+		}
+		var m int
+		for m = l1; m < n-1; m++ {
+			if math.Abs(e[m]) <= math.Sqrt(math.Abs(d[m]))*math.Sqrt(math.Abs(d[m+1]))*eps {
+				e[m] = 0
+				break
+			}
+		}
+
+		l := l1
+		lsv := l
+		lend := m
+		lendsv := lend
+		l1 = m + 1
+		if lend == 0 {
+			continue
+		}
+
+		// Scale submatrix in rows and columns l to lend.
+		anorm := impl.Dlanst(lapack.MaxAbs, lend-l+1, d[l:], e[l:])
+		iscale := none
+		if anorm == 0 {
+			continue
+		}
+		if anorm > ssfmax {
+			iscale = down
+			impl.Dlascl(lapack.General, 0, 0, anorm, ssfmax, lend-l+1, 1, d[l:], n)
+			impl.Dlascl(lapack.General, 0, 0, anorm, ssfmax, lend-l, 1, e[l:], n)
+		} else if anorm < ssfmin {
+			iscale = up
+			impl.Dlascl(lapack.General, 0, 0, anorm, ssfmin, lend-l+1, 1, d[l:], n)
+			impl.Dlascl(lapack.General, 0, 0, anorm, ssfmin, lend-l, 1, e[l:], n)
+		}
+
+		el := e[l:lend]
+		for i, v := range el {
+			el[i] *= v
+		}
+
+		// Choose between QL and QR iteration.
+		if math.Abs(d[lend]) < math.Abs(d[l]) {
+			lend = lsv
+			l = lendsv
+		}
+		if lend >= l {
+			// QL Iteration.
+			// Look for small sub-diagonal element.
+			for {
+				if l != lend {
+					for m = l; m < lend; m++ {
+						if math.Abs(e[m]) <= eps2*(math.Abs(d[m]*d[m+1])) {
+							break
+						}
+					}
+				} else {
+					m = lend
+				}
+				if m < lend {
+					e[m] = 0
+				}
+				p := d[l]
+				if m == l {
+					// Eigenvalue found.
+					l++
+					if l > lend {
+						break
+					}
+					continue
+				}
+				// If remaining matrix is 2 by 2, use Dlae2 to compute its eigenvalues.
+				if m == l+1 {
+					d[l], d[l+1] = impl.Dlae2(d[l], math.Sqrt(e[l]), d[l+1])
+					e[l] = 0
+					l += 2
+					if l > lend {
+						break
+					}
+					continue
+				}
+				if jtot == nmaxit {
+					break
+				}
+				jtot++
+
+				// Form shift.
+				rte := math.Sqrt(e[l])
+				sigma := (d[l+1] - p) / (2 * rte)
+				r := impl.Dlapy2(sigma, 1)
+				sigma = p - (rte / (sigma + math.Copysign(r, sigma)))
+
+				c := 1.0
+				s := 0.0
+				gamma := d[m] - sigma
+				p = gamma * gamma
+
+				// Inner loop.
+				for i := m - 1; i >= l; i-- {
+					bb := e[i]
+					r := p + bb
+					if i != m-1 {
+						e[i+1] = s * r
+					}
+					oldc := c
+					c = p / r
+					s = bb / r
+					oldgam := gamma
+					alpha := d[i]
+					gamma = c*(alpha-sigma) - s*oldgam
+					d[i+1] = oldgam + (alpha - gamma)
+					if c != 0 {
+						p = (gamma * gamma) / c
+					} else {
+						p = oldc * bb
+					}
+				}
+				e[l] = s * p
+				d[l] = sigma + gamma
+			}
+		} else {
+			for {
+				// QR Iteration.
+				// Look for small super-diagonal element.
+				for m = l; m > lend; m-- {
+					if math.Abs(e[m-1]) <= eps2*math.Abs(d[m]*d[m-1]) {
+						break
+					}
+				}
+				if m > lend {
+					e[m-1] = 0
+				}
+				p := d[l]
+				if m == l {
+					// Eigenvalue found.
+					l--
+					if l < lend {
+						break
+					}
+					continue
+				}
+
+				// If remaining matrix is 2 by 2, use Dlae2 to compute its eigenvalues.
+				if m == l-1 {
+					d[l], d[l-1] = impl.Dlae2(d[l], math.Sqrt(e[l-1]), d[l-1])
+					e[l-1] = 0
+					l -= 2
+					if l < lend {
+						break
+					}
+					continue
+				}
+				if jtot == nmaxit {
+					break
+				}
+				jtot++
+
+				// Form shift.
+				rte := math.Sqrt(e[l-1])
+				sigma := (d[l-1] - p) / (2 * rte)
+				r := impl.Dlapy2(sigma, 1)
+				sigma = p - (rte / (sigma + math.Copysign(r, sigma)))
+
+				c := 1.0
+				s := 0.0
+				gamma := d[m] - sigma
+				p = gamma * gamma
+
+				// Inner loop.
+				for i := m; i < l; i++ {
+					bb := e[i]
+					r := p + bb
+					if i != m {
+						e[i-1] = s * r
+					}
+					oldc := c
+					c = p / r
+					s = bb / r
+					oldgam := gamma
+					alpha := d[i+1]
+					gamma = c*(alpha-sigma) - s*oldgam
+					d[i] = oldgam + alpha - gamma
+					if c != 0 {
+						p = (gamma * gamma) / c
+					} else {
+						p = oldc * bb
+					}
+				}
+				e[l-1] = s * p
+				d[l] = sigma + gamma
+			}
+		}
+
+		// Undo scaling if necessary
+		switch iscale {
+		case down:
+			impl.Dlascl(lapack.General, 0, 0, ssfmax, anorm, lendsv-lsv+1, 1, d[lsv:], n)
+		case up:
+			impl.Dlascl(lapack.General, 0, 0, ssfmin, anorm, lendsv-lsv+1, 1, d[lsv:], n)
+		}
+
+		// Check for no convergence to an eigenvalue after a total of n*maxit iterations.
+		if jtot >= nmaxit {
+			break
+		}
+	}
+	for _, v := range e[:n-1] {
+		if v != 0 {
+			return false
+		}
+	}
+	impl.Dlasrt(lapack.SortIncreasing, n, d)
+	return true
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dsyev.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dsyev.go
new file mode 100644
index 00000000..35241728
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dsyev.go
@@ -0,0 +1,113 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dsyev computes all eigenvalues and, optionally, the eigenvectors of a real
+// symmetric matrix A.
+//
+// w contains the eigenvalues in ascending order upon return. w must have length
+// at least n, and Dsyev will panic otherwise.
+//
+// On entry, a contains the elements of the symmetric matrix A in the triangular
+// portion specified by uplo. If jobz == lapack.ComputeEV a contains the
+// orthonormal eigenvectors of A on exit, otherwise on exit the specified
+// triangular region is overwritten.
+//
+// work is temporary storage, and lwork specifies the usable memory length. At minimum,
+// lwork >= 3*n-1, and Dsyev will panic otherwise. The amount of blocking is
+// limited by the usable length. If lwork == -1, instead of computing Dsyev the
+// optimal work length is stored into work[0].
+func (impl Implementation) Dsyev(jobz lapack.EVJob, uplo blas.Uplo, n int, a []float64, lda int, w, work []float64, lwork int) (ok bool) {
+	checkMatrix(n, n, a, lda)
+	upper := uplo == blas.Upper
+	wantz := jobz == lapack.ComputeEV
+	var opts string
+	if upper {
+		opts = "U"
+	} else {
+		opts = "L"
+	}
+	nb := impl.Ilaenv(1, "DSYTRD", opts, n, -1, -1, -1)
+	lworkopt := max(1, (nb+2)*n)
+	work[0] = float64(lworkopt)
+	if lwork == -1 {
+		return
+	}
+	if len(work) < lwork {
+		panic(badWork)
+	}
+	if lwork < 3*n-1 {
+		panic(badWork)
+	}
+	if n == 0 {
+		return true
+	}
+	if n == 1 {
+		w[0] = a[0]
+		work[0] = 2
+		if wantz {
+			a[0] = 1
+		}
+		return true
+	}
+	safmin := dlamchS
+	eps := dlamchP
+	smlnum := safmin / eps
+	bignum := 1 / smlnum
+	rmin := math.Sqrt(smlnum)
+	rmax := math.Sqrt(bignum)
+
+	// Scale matrix to allowable range, if necessary.
+	anrm := impl.Dlansy(lapack.MaxAbs, uplo, n, a, lda, work)
+	scaled := false
+	var sigma float64
+	if anrm > 0 && anrm < rmin {
+		scaled = true
+		sigma = rmin / anrm
+	} else if anrm > rmax {
+		scaled = true
+		sigma = rmax / anrm
+	}
+	if scaled {
+		kind := lapack.LowerTri
+		if upper {
+			kind = lapack.UpperTri
+		}
+		impl.Dlascl(kind, 0, 0, 1, sigma, n, n, a, lda)
+	}
+	var inde int
+	indtau := inde + n
+	indwork := indtau + n
+	llwork := lwork - indwork
+	impl.Dsytrd(uplo, n, a, lda, w, work[inde:], work[indtau:], work[indwork:], llwork)
+
+	// For eigenvalues only, call Dsterf. For eigenvectors, first call Dorgtr
+	// to generate the orthogonal matrix, then call Dsteqr.
+	if !wantz {
+		ok = impl.Dsterf(n, w, work[inde:])
+	} else {
+		impl.Dorgtr(uplo, n, a, lda, work[indtau:], work[indwork:], llwork)
+		ok = impl.Dsteqr(lapack.EVComp(jobz), n, w, work[inde:], a, lda, work[indtau:])
+	}
+	if !ok {
+		return false
+	}
+
+	// If the matrix was scaled, then rescale eigenvalues appropriately.
+	if scaled {
+		bi := blas64.Implementation()
+		bi.Dscal(n, 1/sigma, w, 1)
+	}
+	work[0] = float64(lworkopt)
+	return true
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dsytd2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dsytd2.go
new file mode 100644
index 00000000..a4d69201
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dsytd2.go
@@ -0,0 +1,123 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dsytd2 reduces a symmetric n×n matrix A to symmetric tridiagonal form T by an
+// orthogonal similarity transformation
+//  Q^T * A * Q = T
+// On entry, the matrix is contained in the specified triangle of a. On exit,
+// if uplo == blas.Upper, the diagonal and first super-diagonal of a are
+// overwritten with the elements of T. The elements above the first super-diagonal
+// are overwritten with the the elementary reflectors that are used with the
+// elements written to tau in order to construct Q. If uplo == blas.Lower, the
+// elements are written in the lower triangular region.
+//
+// d must have length at least n. e and tau must have length at least n-1. Dsytd2
+// will panic if these sizes are not met.
+//
+// Q is represented as a product of elementary reflectors.
+// If uplo == blas.Upper
+//  Q = H_{n-2} * ... * H_1 * H_0
+// and if uplo == blas.Lower
+//  Q = H_0 * H_1 * ... * H_{n-2}
+// where
+//  H_i = I - tau * v * v^T
+// where tau is stored in tau[i], and v is stored in a.
+//
+// If uplo == blas.Upper, v[0:i-1] is stored in A[0:i-1,i+1], v[i] = 1, and
+// v[i+1:] = 0. The elements of a are
+//  [ d   e  v2  v3  v4]
+//  [     d   e  v3  v4]
+//  [         d   e  v4]
+//  [             d   e]
+//  [                 d]
+// If uplo == blas.Lower, v[0:i+1] = 0, v[i+1] = 1, and v[i+2:] is stored in
+// A[i+2:n,i].
+// The elements of a are
+//  [ d                ]
+//  [ e   d            ]
+//  [v1   e   d        ]
+//  [v1  v2   e   d    ]
+//  [v1  v2  v3   e   d]
+//
+// Dsytd2 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dsytd2(uplo blas.Uplo, n int, a []float64, lda int, d, e, tau []float64) {
+	checkMatrix(n, n, a, lda)
+	if len(d) < n {
+		panic(badD)
+	}
+	if len(e) < n-1 {
+		panic(badE)
+	}
+	if len(tau) < n-1 {
+		panic(badTau)
+	}
+	if n <= 0 {
+		return
+	}
+	bi := blas64.Implementation()
+	if uplo == blas.Upper {
+		// Reduce the upper triangle of A.
+		for i := n - 2; i >= 0; i-- {
+			// Generate elementary reflector H_i = I - tau * v * v^T to
+			// annihilate A[i:i-1, i+1].
+			var taui float64
+			a[i*lda+i+1], taui = impl.Dlarfg(i+1, a[i*lda+i+1], a[i+1:], lda)
+			e[i] = a[i*lda+i+1]
+			if taui != 0 {
+				// Apply H_i from both sides to A[0:i,0:i].
+				a[i*lda+i+1] = 1
+
+				// Compute x := tau * A * v storing x in tau[0:i].
+				bi.Dsymv(uplo, i+1, taui, a, lda, a[i+1:], lda, 0, tau, 1)
+
+				// Compute w := x - 1/2 * tau * (x^T * v) * v.
+				alpha := -0.5 * taui * bi.Ddot(i+1, tau, 1, a[i+1:], lda)
+				bi.Daxpy(i+1, alpha, a[i+1:], lda, tau, 1)
+
+				// Apply the transformation as a rank-2 update
+				// A = A - v * w^T - w * v^T.
+				bi.Dsyr2(uplo, i+1, -1, a[i+1:], lda, tau, 1, a, lda)
+				a[i*lda+i+1] = e[i]
+			}
+			d[i+1] = a[(i+1)*lda+i+1]
+			tau[i] = taui
+		}
+		d[0] = a[0]
+		return
+	}
+	// Reduce the lower triangle of A.
+	for i := 0; i < n-1; i++ {
+		// Generate elementary reflector H_i = I - tau * v * v^T to
+		// annihilate A[i+2:n, i].
+		var taui float64
+		a[(i+1)*lda+i], taui = impl.Dlarfg(n-i-1, a[(i+1)*lda+i], a[min(i+2, n-1)*lda+i:], lda)
+		e[i] = a[(i+1)*lda+i]
+		if taui != 0 {
+			// Apply H_i from both sides to A[i+1:n, i+1:n].
+			a[(i+1)*lda+i] = 1
+
+			// Compute x := tau * A * v, storing y in tau[i:n-1].
+			bi.Dsymv(uplo, n-i-1, taui, a[(i+1)*lda+i+1:], lda, a[(i+1)*lda+i:], lda, 0, tau[i:], 1)
+
+			// Compute w := x - 1/2 * tau * (x^T * v) * v.
+			alpha := -0.5 * taui * bi.Ddot(n-i-1, tau[i:], 1, a[(i+1)*lda+i:], lda)
+			bi.Daxpy(n-i-1, alpha, a[(i+1)*lda+i:], lda, tau[i:], 1)
+
+			// Apply the transformation as a rank-2 update
+			// A = A - v * w^T - w * v^T.
+			bi.Dsyr2(uplo, n-i-1, -1, a[(i+1)*lda+i:], lda, tau[i:], 1, a[(i+1)*lda+i+1:], lda)
+			a[(i+1)*lda+i] = e[i]
+		}
+		d[i] = a[i*lda+i]
+		tau[i] = taui
+	}
+	d[n-1] = a[(n-1)*lda+n-1]
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dsytrd.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dsytrd.go
new file mode 100644
index 00000000..f8a4ca95
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dsytrd.go
@@ -0,0 +1,178 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dsytrd reduces a symmetric n×n matrix A to symmetric tridiagonal form by an
+// orthogonal similarity transformation
+//  Q^T * A * Q = T
+// where Q is an orthonormal matrix and T is symmetric and tridiagonal.
+//
+// On entry, a contains the elements of the input matrix in the triangle specified
+// by uplo. On exit, the diagonal and sub/super-diagonal are overwritten by the
+// corresponding elements of the tridiagonal matrix T. The remaining elements in
+// the triangle, along with the array tau, contain the data to construct Q as
+// the product of elementary reflectors.
+//
+// If uplo == blas.Upper, Q is constructed with
+//  Q = H_{n-2} * ... * H_1 * H_0
+// where
+//  H_i = I - tau_i * v * v^T
+// v is constructed as v[i+1:n] = 0, v[i] = 1, v[0:i-1] is stored in A[0:i-1, i+1].
+// The elements of A are
+//  [ d   e  v1  v2  v3]
+//  [     d   e  v2  v3]
+//  [         d   e  v3]
+//  [             d   e]
+//  [                 e]
+//
+// If uplo == blas.Lower, Q is constructed with
+//  Q = H_0 * H_1 * ... * H_{n-2}
+// where
+//  H_i = I - tau_i * v * v^T
+// v is constructed as v[0:i+1] = 0, v[i+1] = 1, v[i+2:n] is stored in A[i+2:n, i].
+// The elements of A are
+//  [ d                ]
+//  [ e   d            ]
+//  [v0   e   d        ]
+//  [v0  v1   e   d    ]
+//  [v0  v1  v2   e   d]
+//
+// d must have length n, and e and tau must have length n-1. Dsytrd will panic if
+// these conditions are not met.
+//
+// work is temporary storage, and lwork specifies the usable memory length. At minimum,
+// lwork >= 1, and Dsytrd will panic otherwise. The amount of blocking is
+// limited by the usable length.
+// If lwork == -1, instead of computing Dsytrd the optimal work length is stored
+// into work[0].
+//
+// Dsytrd is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dsytrd(uplo blas.Uplo, n int, a []float64, lda int, d, e, tau, work []float64, lwork int) {
+	checkMatrix(n, n, a, lda)
+	if len(d) < n {
+		panic(badD)
+	}
+	if len(e) < n-1 {
+		panic(badE)
+	}
+	if len(tau) < n-1 {
+		panic(badTau)
+	}
+	if len(work) < lwork {
+		panic(shortWork)
+	}
+	if lwork != -1 && lwork < 1 {
+		panic(badWork)
+	}
+
+	var upper bool
+	var opts string
+	switch uplo {
+	case blas.Upper:
+		upper = true
+		opts = "U"
+	case blas.Lower:
+		opts = "L"
+	default:
+		panic(badUplo)
+	}
+
+	if n == 0 {
+		work[0] = 1
+		return
+	}
+
+	nb := impl.Ilaenv(1, "DSYTRD", opts, n, -1, -1, -1)
+	lworkopt := n * nb
+	if lwork == -1 {
+		work[0] = float64(lworkopt)
+		return
+	}
+
+	nx := n
+	bi := blas64.Implementation()
+	var ldwork int
+	if 1 < nb && nb < n {
+		// Determine when to cross over from blocked to unblocked code. The last
+		// block is always handled by unblocked code.
+		opts := "L"
+		if upper {
+			opts = "U"
+		}
+		nx = max(nb, impl.Ilaenv(3, "DSYTRD", opts, n, -1, -1, -1))
+		if nx < n {
+			// Determine if workspace is large enough for blocked code.
+			ldwork = nb
+			iws := n * ldwork
+			if lwork < iws {
+				// Not enough workspace to use optimal nb: determine the minimum
+				// value of nb and reduce nb or force use of unblocked code by
+				// setting nx = n.
+				nb = max(lwork/n, 1)
+				nbmin := impl.Ilaenv(2, "DSYTRD", opts, n, -1, -1, -1)
+				if nb < nbmin {
+					nx = n
+				}
+			}
+		} else {
+			nx = n
+		}
+	} else {
+		nb = 1
+	}
+	ldwork = nb
+
+	if upper {
+		// Reduce the upper triangle of A. Columns 0:kk are handled by the
+		// unblocked method.
+		var i int
+		kk := n - ((n-nx+nb-1)/nb)*nb
+		for i = n - nb; i >= kk; i -= nb {
+			// Reduce columns i:i+nb to tridiagonal form and form the matrix W
+			// which is needed to update the unreduced part of the matrix.
+			impl.Dlatrd(uplo, i+nb, nb, a, lda, e, tau, work, ldwork)
+
+			// Update the unreduced submatrix A[0:i-1,0:i-1], using an update
+			// of the form A = A - V*W^T - W*V^T.
+			bi.Dsyr2k(uplo, blas.NoTrans, i, nb, -1, a[i:], lda, work, ldwork, 1, a, lda)
+
+			// Copy superdiagonal elements back into A, and diagonal elements into D.
+			for j := i; j < i+nb; j++ {
+				a[(j-1)*lda+j] = e[j-1]
+				d[j] = a[j*lda+j]
+			}
+		}
+		// Use unblocked code to reduce the last or only block
+		// check that i == kk.
+		impl.Dsytd2(uplo, kk, a, lda, d, e, tau)
+	} else {
+		var i int
+		// Reduce the lower triangle of A.
+		for i = 0; i < n-nx; i += nb {
+			// Reduce columns 0:i+nb to tridiagonal form and form the matrix W
+			// which is needed to update the unreduced part of the matrix.
+			impl.Dlatrd(uplo, n-i, nb, a[i*lda+i:], lda, e[i:], tau[i:], work, ldwork)
+
+			// Update the unreduced submatrix A[i+ib:n, i+ib:n], using an update
+			// of the form A = A + V*W^T - W*V^T.
+			bi.Dsyr2k(uplo, blas.NoTrans, n-i-nb, nb, -1, a[(i+nb)*lda+i:], lda,
+				work[nb*ldwork:], ldwork, 1, a[(i+nb)*lda+i+nb:], lda)
+
+			// Copy subdiagonal elements back into A, and diagonal elements into D.
+			for j := i; j < i+nb; j++ {
+				a[(j+1)*lda+j] = e[j]
+				d[j] = a[j*lda+j]
+			}
+		}
+		// Use unblocked code to reduce the last or only block.
+		impl.Dsytd2(uplo, n-i, a[i*lda+i:], lda, d[i:], e[i:], tau[i:])
+	}
+	work[0] = float64(lworkopt)
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dtgsja.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dtgsja.go
new file mode 100644
index 00000000..ca0326ef
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dtgsja.go
@@ -0,0 +1,357 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dtgsja computes the generalized singular value decomposition (GSVD)
+// of two real upper triangular or trapezoidal matrices A and B.
+//
+// A and B have the following forms, which may be obtained by the
+// preprocessing subroutine Dggsvp from a general m×n matrix A and p×n
+// matrix B:
+//
+//            n-k-l  k    l
+//  A =    k [  0   A12  A13 ] if m-k-l >= 0;
+//         l [  0    0   A23 ]
+//     m-k-l [  0    0    0  ]
+//
+//            n-k-l  k    l
+//  A =    k [  0   A12  A13 ] if m-k-l < 0;
+//       m-k [  0    0   A23 ]
+//
+//            n-k-l  k    l
+//  B =    l [  0    0   B13 ]
+//       p-l [  0    0    0  ]
+//
+// where the k×k matrix A12 and l×l matrix B13 are non-singular
+// upper triangular. A23 is l×l upper triangular if m-k-l >= 0,
+// otherwise A23 is (m-k)×l upper trapezoidal.
+//
+// On exit,
+//
+//  U^T*A*Q = D1*[ 0 R ], V^T*B*Q = D2*[ 0 R ],
+//
+// where U, V and Q are orthogonal matrices.
+// R is a non-singular upper triangular matrix, and D1 and D2 are
+// diagonal matrices, which are of the following structures:
+//
+// If m-k-l >= 0,
+//
+//                    k  l
+//       D1 =     k [ I  0 ]
+//                l [ 0  C ]
+//            m-k-l [ 0  0 ]
+//
+//                  k  l
+//       D2 = l   [ 0  S ]
+//            p-l [ 0  0 ]
+//
+//               n-k-l  k    l
+//  [ 0 R ] = k [  0   R11  R12 ] k
+//            l [  0    0   R22 ] l
+//
+// where
+//
+//  C = diag( alpha_k, ... , alpha_{k+l} ),
+//  S = diag( beta_k,  ... , beta_{k+l} ),
+//  C^2 + S^2 = I.
+//
+// R is stored in
+//  A[0:k+l, n-k-l:n]
+// on exit.
+//
+// If m-k-l < 0,
+//
+//                 k m-k k+l-m
+//      D1 =   k [ I  0    0  ]
+//           m-k [ 0  C    0  ]
+//
+//                   k m-k k+l-m
+//      D2 =   m-k [ 0  S    0  ]
+//           k+l-m [ 0  0    I  ]
+//             p-l [ 0  0    0  ]
+//
+//                 n-k-l  k   m-k  k+l-m
+//  [ 0 R ] =    k [ 0    R11  R12  R13 ]
+//             m-k [ 0     0   R22  R23 ]
+//           k+l-m [ 0     0    0   R33 ]
+//
+// where
+//  C = diag( alpha_k, ... , alpha_m ),
+//  S = diag( beta_k,  ... , beta_m ),
+//  C^2 + S^2 = I.
+//
+//  R = [ R11 R12 R13 ] is stored in A[0:m, n-k-l:n]
+//      [  0  R22 R23 ]
+// and R33 is stored in
+//  B[m-k:l, n+m-k-l:n] on exit.
+//
+// The computation of the orthogonal transformation matrices U, V or Q
+// is optional. These matrices may either be formed explicitly, or they
+// may be post-multiplied into input matrices U1, V1, or Q1.
+//
+// Dtgsja essentially uses a variant of Kogbetliantz algorithm to reduce
+// min(l,m-k)×l triangular or trapezoidal matrix A23 and l×l
+// matrix B13 to the form:
+//
+//  U1^T*A13*Q1 = C1*R1; V1^T*B13*Q1 = S1*R1,
+//
+// where U1, V1 and Q1 are orthogonal matrices. C1 and S1 are diagonal
+// matrices satisfying
+//
+//  C1^2 + S1^2 = I,
+//
+// and R1 is an l×l non-singular upper triangular matrix.
+//
+// jobU, jobV and jobQ are options for computing the orthogonal matrices. The behavior
+// is as follows
+//  jobU == lapack.GSVDU        Compute orthogonal matrix U
+//  jobU == lapack.GSVDUnit     Use unit-initialized matrix
+//  jobU == lapack.GSVDNone     Do not compute orthogonal matrix.
+// The behavior is the same for jobV and jobQ with the exception that instead of
+// lapack.GSVDU these accept lapack.GSVDV and lapack.GSVDQ respectively.
+// The matrices U, V and Q must be m×m, p×p and n×n respectively unless the
+// relevant job parameter is lapack.GSVDNone.
+//
+// k and l specify the sub-blocks in the input matrices A and B:
+//  A23 = A[k:min(k+l,m), n-l:n) and B13 = B[0:l, n-l:n]
+// of A and B, whose GSVD is going to be computed by Dtgsja.
+//
+// tola and tolb are the convergence criteria for the Jacobi-Kogbetliantz
+// iteration procedure. Generally, they are the same as used in the preprocessing
+// step, for example,
+//  tola = max(m, n)*norm(A)*eps,
+//  tolb = max(p, n)*norm(B)*eps,
+// where eps is the machine epsilon.
+//
+// work must have length at least 2*n, otherwise Dtgsja will panic.
+//
+// alpha and beta must have length n or Dtgsja will panic. On exit, alpha and
+// beta contain the generalized singular value pairs of A and B
+//   alpha[0:k] = 1,
+//   beta[0:k]  = 0,
+// if m-k-l >= 0,
+//   alpha[k:k+l] = diag(C),
+//   beta[k:k+l]  = diag(S),
+// if m-k-l < 0,
+//   alpha[k:m]= C, alpha[m:k+l]= 0
+//   beta[k:m] = S, beta[m:k+l] = 1.
+// if k+l < n,
+//   alpha[k+l:n] = 0 and
+//   beta[k+l:n]  = 0.
+//
+// On exit, A[n-k:n, 0:min(k+l,m)] contains the triangular matrix R or part of R
+// and if necessary, B[m-k:l, n+m-k-l:n] contains a part of R.
+//
+// Dtgsja returns whether the routine converged and the number of iteration cycles
+// that were run.
+//
+// Dtgsja is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dtgsja(jobU, jobV, jobQ lapack.GSVDJob, m, p, n, k, l int, a []float64, lda int, b []float64, ldb int, tola, tolb float64, alpha, beta, u []float64, ldu int, v []float64, ldv int, q []float64, ldq int, work []float64) (cycles int, ok bool) {
+	const maxit = 40
+
+	checkMatrix(m, n, a, lda)
+	checkMatrix(p, n, b, ldb)
+
+	if len(alpha) != n {
+		panic(badAlpha)
+	}
+	if len(beta) != n {
+		panic(badBeta)
+	}
+
+	initu := jobU == lapack.GSVDUnit
+	wantu := initu || jobU == lapack.GSVDU
+	if !initu && !wantu && jobU != lapack.GSVDNone {
+		panic(badGSVDJob + "U")
+	}
+	if jobU != lapack.GSVDNone {
+		checkMatrix(m, m, u, ldu)
+	}
+
+	initv := jobV == lapack.GSVDUnit
+	wantv := initv || jobV == lapack.GSVDV
+	if !initv && !wantv && jobV != lapack.GSVDNone {
+		panic(badGSVDJob + "V")
+	}
+	if jobV != lapack.GSVDNone {
+		checkMatrix(p, p, v, ldv)
+	}
+
+	initq := jobQ == lapack.GSVDUnit
+	wantq := initq || jobQ == lapack.GSVDQ
+	if !initq && !wantq && jobQ != lapack.GSVDNone {
+		panic(badGSVDJob + "Q")
+	}
+	if jobQ != lapack.GSVDNone {
+		checkMatrix(n, n, q, ldq)
+	}
+
+	if len(work) < 2*n {
+		panic(badWork)
+	}
+
+	// Initialize U, V and Q, if necessary
+	if initu {
+		impl.Dlaset(blas.All, m, m, 0, 1, u, ldu)
+	}
+	if initv {
+		impl.Dlaset(blas.All, p, p, 0, 1, v, ldv)
+	}
+	if initq {
+		impl.Dlaset(blas.All, n, n, 0, 1, q, ldq)
+	}
+
+	bi := blas64.Implementation()
+	minTol := math.Min(tola, tolb)
+
+	// Loop until convergence.
+	upper := false
+	for cycles = 1; cycles <= maxit; cycles++ {
+		upper = !upper
+
+		for i := 0; i < l-1; i++ {
+			for j := i + 1; j < l; j++ {
+				var a1, a2, a3 float64
+				if k+i < m {
+					a1 = a[(k+i)*lda+n-l+i]
+				}
+				if k+j < m {
+					a3 = a[(k+j)*lda+n-l+j]
+				}
+
+				b1 := b[i*ldb+n-l+i]
+				b3 := b[j*ldb+n-l+j]
+
+				var b2 float64
+				if upper {
+					if k+i < m {
+						a2 = a[(k+i)*lda+n-l+j]
+					}
+					b2 = b[i*ldb+n-l+j]
+				} else {
+					if k+j < m {
+						a2 = a[(k+j)*lda+n-l+i]
+					}
+					b2 = b[j*ldb+n-l+i]
+				}
+
+				csu, snu, csv, snv, csq, snq := impl.Dlags2(upper, a1, a2, a3, b1, b2, b3)
+
+				// Update (k+i)-th and (k+j)-th rows of matrix A: U^T*A.
+				if k+j < m {
+					bi.Drot(l, a[(k+j)*lda+n-l:], 1, a[(k+i)*lda+n-l:], 1, csu, snu)
+				}
+
+				// Update i-th and j-th rows of matrix B: V^T*B.
+				bi.Drot(l, b[j*ldb+n-l:], 1, b[i*ldb+n-l:], 1, csv, snv)
+
+				// Update (n-l+i)-th and (n-l+j)-th columns of matrices
+				// A and B: A*Q and B*Q.
+				bi.Drot(min(k+l, m), a[n-l+j:], lda, a[n-l+i:], lda, csq, snq)
+				bi.Drot(l, b[n-l+j:], ldb, b[n-l+i:], ldb, csq, snq)
+
+				if upper {
+					if k+i < m {
+						a[(k+i)*lda+n-l+j] = 0
+					}
+					b[i*ldb+n-l+j] = 0
+				} else {
+					if k+j < m {
+						a[(k+j)*lda+n-l+i] = 0
+					}
+					b[j*ldb+n-l+i] = 0
+				}
+
+				// Update orthogonal matrices U, V, Q, if desired.
+				if wantu && k+j < m {
+					bi.Drot(m, u[k+j:], ldu, u[k+i:], ldu, csu, snu)
+				}
+				if wantv {
+					bi.Drot(p, v[j:], ldv, v[i:], ldv, csv, snv)
+				}
+				if wantq {
+					bi.Drot(n, q[n-l+j:], ldq, q[n-l+i:], ldq, csq, snq)
+				}
+			}
+		}
+
+		if !upper {
+			// The matrices A13 and B13 were lower triangular at the start
+			// of the cycle, and are now upper triangular.
+			//
+			// Convergence test: test the parallelism of the corresponding
+			// rows of A and B.
+			var error float64
+			for i := 0; i < min(l, m-k); i++ {
+				bi.Dcopy(l-i, a[(k+i)*lda+n-l+i:], 1, work, 1)
+				bi.Dcopy(l-i, b[i*ldb+n-l+i:], 1, work[l:], 1)
+				ssmin := impl.Dlapll(l-i, work, 1, work[l:], 1)
+				error = math.Max(error, ssmin)
+			}
+			if math.Abs(error) <= minTol {
+				// The algorithm has converged.
+				// Compute the generalized singular value pairs (alpha, beta)
+				// and set the triangular matrix R to array A.
+				for i := 0; i < k; i++ {
+					alpha[i] = 1
+					beta[i] = 0
+				}
+
+				for i := 0; i < min(l, m-k); i++ {
+					a1 := a[(k+i)*lda+n-l+i]
+					b1 := b[i*ldb+n-l+i]
+
+					if a1 != 0 {
+						gamma := b1 / a1
+
+						// Change sign if necessary.
+						if gamma < 0 {
+							bi.Dscal(l-i, -1, b[i*ldb+n-l+i:], 1)
+							if wantv {
+								bi.Dscal(p, -1, v[i:], ldv)
+							}
+						}
+						beta[k+i], alpha[k+i], _ = impl.Dlartg(math.Abs(gamma), 1)
+
+						if alpha[k+i] >= beta[k+i] {
+							bi.Dscal(l-i, 1/alpha[k+i], a[(k+i)*lda+n-l+i:], 1)
+						} else {
+							bi.Dscal(l-i, 1/beta[k+i], b[i*ldb+n-l+i:], 1)
+							bi.Dcopy(l-i, b[i*ldb+n-l+i:], 1, a[(k+i)*lda+n-l+i:], 1)
+						}
+					} else {
+						alpha[k+i] = 0
+						beta[k+i] = 1
+						bi.Dcopy(l-i, b[i*ldb+n-l+i:], 1, a[(k+i)*lda+n-l+i:], 1)
+					}
+				}
+
+				for i := m; i < k+l; i++ {
+					alpha[i] = 0
+					beta[i] = 1
+				}
+				if k+l < n {
+					for i := k + l; i < n; i++ {
+						alpha[i] = 0
+						beta[i] = 0
+					}
+				}
+
+				return cycles, true
+			}
+		}
+	}
+
+	// The algorithm has not converged after maxit cycles.
+	return cycles, false
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dtrcon.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dtrcon.go
new file mode 100644
index 00000000..14101325
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dtrcon.go
@@ -0,0 +1,82 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dtrcon estimates the reciprocal of the condition number of a triangular matrix A.
+// The condition number computed may be based on the 1-norm or the ∞-norm.
+//
+// work is a temporary data slice of length at least 3*n and Dtrcon will panic otherwise.
+//
+// iwork is a temporary data slice of length at least n and Dtrcon will panic otherwise.
+func (impl Implementation) Dtrcon(norm lapack.MatrixNorm, uplo blas.Uplo, diag blas.Diag, n int, a []float64, lda int, work []float64, iwork []int) float64 {
+	if norm != lapack.MaxColumnSum && norm != lapack.MaxRowSum {
+		panic(badNorm)
+	}
+	if uplo != blas.Upper && uplo != blas.Lower {
+		panic(badUplo)
+	}
+	if diag != blas.NonUnit && diag != blas.Unit {
+		panic(badDiag)
+	}
+	if len(work) < 3*n {
+		panic(badWork)
+	}
+	if len(iwork) < n {
+		panic(badWork)
+	}
+	if n == 0 {
+		return 1
+	}
+	bi := blas64.Implementation()
+
+	var rcond float64
+	smlnum := dlamchS * float64(n)
+
+	anorm := impl.Dlantr(norm, uplo, diag, n, n, a, lda, work)
+
+	if anorm <= 0 {
+		return rcond
+	}
+	var ainvnm float64
+	var normin bool
+	kase1 := 2
+	if norm == lapack.MaxColumnSum {
+		kase1 = 1
+	}
+	var kase int
+	isave := new([3]int)
+	var scale float64
+	for {
+		ainvnm, kase = impl.Dlacn2(n, work[n:], work, iwork, ainvnm, kase, isave)
+		if kase == 0 {
+			if ainvnm != 0 {
+				rcond = (1 / anorm) / ainvnm
+			}
+			return rcond
+		}
+		if kase == kase1 {
+			scale = impl.Dlatrs(uplo, blas.NoTrans, diag, normin, n, a, lda, work, work[2*n:])
+		} else {
+			scale = impl.Dlatrs(uplo, blas.Trans, diag, normin, n, a, lda, work, work[2*n:])
+		}
+		normin = true
+		if scale != 1 {
+			ix := bi.Idamax(n, work, 1)
+			xnorm := math.Abs(work[ix])
+			if scale == 0 || scale < xnorm*smlnum {
+				return rcond
+			}
+			impl.Drscl(n, scale, work, 1)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dtrevc3.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dtrevc3.go
new file mode 100644
index 00000000..d62d5f05
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dtrevc3.go
@@ -0,0 +1,866 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dtrevc3 computes some or all of the right and/or left eigenvectors of an n×n
+// upper quasi-triangular matrix T in Schur canonical form. Matrices of this
+// type are produced by the Schur factorization of a real general matrix A
+//  A = Q T Q^T,
+// as computed by Dhseqr.
+//
+// The right eigenvector x of T corresponding to an
+// eigenvalue λ is defined by
+//  T x = λ x,
+// and the left eigenvector is defined by
+//  y^H T = λ y^H,
+// where y^H is the conjugate transpose of y.
+//
+// The eigenvalues are read directly from the diagonal blocks of T.
+//
+// This routine returns the matrices X and/or Y of right and left eigenvectors
+// of T, or the products Q*X and/or Q*Y, where Q is an input matrix. If Q is the
+// orthogonal factor that reduces a matrix A to Schur form T, then Q*X and Q*Y
+// are the matrices of right and left eigenvectors of A.
+//
+// If side == lapack.RightEV, only right eigenvectors will be computed.
+// If side == lapack.LeftEV, only left eigenvectors will be computed.
+// If side == lapack.RightLeftEV, both right and left eigenvectors will be computed.
+// For other values of side, Dtrevc3 will panic.
+//
+// If howmny == lapack.AllEV, all right and/or left eigenvectors will be
+// computed.
+// If howmny == lapack.AllEVMulQ, all right and/or left eigenvectors will be
+// computed and multiplied from left by the matrices in VR and/or VL.
+// If howmny == lapack.SelectedEV, right and/or left eigenvectors will be
+// computed as indicated by selected.
+// For other values of howmny, Dtrevc3 will panic.
+//
+// selected specifies which eigenvectors will be computed. It must have length n
+// if howmny == lapack.SelectedEV, and it is not referenced otherwise.
+// If w_j is a real eigenvalue, the corresponding real eigenvector will be
+// computed if selected[j] is true.
+// If w_j and w_{j+1} are the real and imaginary parts of a complex eigenvalue,
+// the corresponding complex eigenvector is computed if either selected[j] or
+// selected[j+1] is true, and on return selected[j] will be set to true and
+// selected[j+1] will be set to false.
+//
+// VL and VR are n×mm matrices. If howmny is lapack.AllEV or
+// lapack.AllEVMulQ, mm must be at least n. If howmny ==
+// lapack.SelectedEV, mm must be large enough to store the selected
+// eigenvectors. Each selected real eigenvector occupies one column and each
+// selected complex eigenvector occupies two columns. If mm is not sufficiently
+// large, Dtrevc3 will panic.
+//
+// On entry, if howmny == lapack.AllEVMulQ, it is assumed that VL (if side
+// is lapack.LeftEV or lapack.RightLeftEV) contains an n×n matrix QL,
+// and that VR (if side is lapack.LeftEV or lapack.RightLeftEV) contains
+// an n×n matrix QR. QL and QR are typically the orthogonal matrix Q of Schur
+// vectors returned by Dhseqr.
+//
+// On return, if side is lapack.LeftEV or lapack.RightLeftEV,
+// VL will contain:
+//  if howmny == lapack.AllEV,      the matrix Y of left eigenvectors of T,
+//  if howmny == lapack.AllEVMulQ,  the matrix Q*Y,
+//  if howmny == lapack.SelectedEV, the left eigenvectors of T specified by
+//                                  selected, stored consecutively in the
+//                                  columns of VL, in the same order as their
+//                                  eigenvalues.
+// VL is not referenced if side == lapack.RightEV.
+//
+// On return, if side is lapack.RightEV or lapack.RightLeftEV,
+// VR will contain:
+//  if howmny == lapack.AllEV,      the matrix X of right eigenvectors of T,
+//  if howmny == lapack.AllEVMulQ,  the matrix Q*X,
+//  if howmny == lapack.SelectedEV, the left eigenvectors of T specified by
+//                                  selected, stored consecutively in the
+//                                  columns of VR, in the same order as their
+//                                  eigenvalues.
+// VR is not referenced if side == lapack.LeftEV.
+//
+// Complex eigenvectors corresponding to a complex eigenvalue are stored in VL
+// and VR in two consecutive columns, the first holding the real part, and the
+// second the imaginary part.
+//
+// Each eigenvector will be normalized so that the element of largest magnitude
+// has magnitude 1. Here the magnitude of a complex number (x,y) is taken to be
+// |x| + |y|.
+//
+// work must have length at least lwork and lwork must be at least max(1,3*n),
+// otherwise Dtrevc3 will panic. For optimum performance, lwork should be at
+// least n+2*n*nb, where nb is the optimal blocksize.
+//
+// If lwork == -1, instead of performing Dtrevc3, the function only estimates
+// the optimal workspace size based on n and stores it into work[0].
+//
+// Dtrevc3 returns the number of columns in VL and/or VR actually used to store
+// the eigenvectors.
+//
+// Dtrevc3 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dtrevc3(side lapack.EVSide, howmny lapack.HowMany, selected []bool, n int, t []float64, ldt int, vl []float64, ldvl int, vr []float64, ldvr int, mm int, work []float64, lwork int) (m int) {
+	switch side {
+	default:
+		panic(badEVSide)
+	case lapack.RightEV, lapack.LeftEV, lapack.RightLeftEV:
+	}
+	switch howmny {
+	default:
+		panic(badHowMany)
+	case lapack.AllEV, lapack.AllEVMulQ, lapack.SelectedEV:
+	}
+	switch {
+	case n < 0:
+		panic(nLT0)
+	case len(work) < lwork:
+		panic(shortWork)
+	case lwork < max(1, 3*n) && lwork != -1:
+		panic(badWork)
+	}
+	if lwork != -1 {
+		if howmny == lapack.SelectedEV {
+			if len(selected) != n {
+				panic("lapack: bad selected length")
+			}
+			// Set m to the number of columns required to store the
+			// selected eigenvectors, and standardize the slice
+			// selected.
+			for j := 0; j < n; {
+				if j == n-1 || t[(j+1)*ldt+j] == 0 {
+					// Diagonal 1×1 block corresponding to a
+					// real eigenvalue.
+					if selected[j] {
+						m++
+					}
+					j++
+				} else {
+					// Diagonal 2×2 block corresponding to a
+					// complex eigenvalue.
+					if selected[j] || selected[j+1] {
+						selected[j] = true
+						selected[j+1] = false
+						m += 2
+					}
+					j += 2
+				}
+			}
+		} else {
+			m = n
+		}
+		if m > mm {
+			panic("lapack: insufficient number of columns")
+		}
+		checkMatrix(n, n, t, ldt)
+		if (side == lapack.RightEV || side == lapack.RightLeftEV) && m > 0 {
+			checkMatrix(n, m, vr, ldvr)
+		}
+		if (side == lapack.LeftEV || side == lapack.RightLeftEV) && m > 0 {
+			checkMatrix(n, m, vl, ldvl)
+		}
+	}
+
+	// Quick return if possible.
+	if n == 0 {
+		work[0] = 1
+		return m
+	}
+
+	const (
+		nbmin = 8
+		nbmax = 128
+	)
+	nb := impl.Ilaenv(1, "DTREVC", string(side)+string(howmny), n, -1, -1, -1)
+
+	// Quick return in case of a workspace query.
+	if lwork == -1 {
+		work[0] = float64(n + 2*n*nb)
+		return m
+	}
+
+	// Use blocked version of back-transformation if sufficient workspace.
+	// Zero-out the workspace to avoid potential NaN propagation.
+	if howmny == lapack.AllEVMulQ && lwork >= n+2*n*nbmin {
+		nb = min((lwork-n)/(2*n), nbmax)
+		impl.Dlaset(blas.All, n, 1+2*nb, 0, 0, work[:n+2*nb*n], 1+2*nb)
+	} else {
+		nb = 1
+	}
+
+	// Set the constants to control overflow.
+	ulp := dlamchP
+	smlnum := float64(n) / ulp * dlamchS
+	bignum := (1 - ulp) / smlnum
+
+	// Split work into a vector of column norms and an n×2*nb matrix b.
+	norms := work[:n]
+	ldb := 2 * nb
+	b := work[n : n+n*ldb]
+
+	// Compute 1-norm of each column of strictly upper triangular part of T
+	// to control overflow in triangular solver.
+	norms[0] = 0
+	for j := 1; j < n; j++ {
+		var cn float64
+		for i := 0; i < j; i++ {
+			cn += math.Abs(t[i*ldt+j])
+		}
+		norms[j] = cn
+	}
+
+	bi := blas64.Implementation()
+
+	var (
+		x [4]float64
+
+		iv int // Index of column in current block.
+		is int
+
+		// ip is used below to specify the real or complex eigenvalue:
+		//  ip == 0, real eigenvalue,
+		//        1, first  of conjugate complex pair (wr,wi),
+		//       -1, second of conjugate complex pair (wr,wi).
+		ip        int
+		iscomplex [nbmax]int // Stores ip for each column in current block.
+	)
+
+	if side == lapack.LeftEV {
+		goto leftev
+	}
+
+	// Compute right eigenvectors.
+
+	// For complex right vector, iv-1 is for real part and iv for complex
+	// part. Non-blocked version always uses iv=1, blocked version starts
+	// with iv=nb-1 and goes down to 0 or 1.
+	iv = max(2, nb) - 1
+	ip = 0
+	is = m - 1
+	for ki := n - 1; ki >= 0; ki-- {
+		if ip == -1 {
+			// Previous iteration (ki+1) was second of
+			// conjugate pair, so this ki is first of
+			// conjugate pair.
+			ip = 1
+			continue
+		}
+
+		if ki == 0 || t[ki*ldt+ki-1] == 0 {
+			// Last column or zero on sub-diagonal, so this
+			// ki must be real eigenvalue.
+			ip = 0
+		} else {
+			// Non-zero on sub-diagonal, so this ki is
+			// second of conjugate pair.
+			ip = -1
+		}
+
+		if howmny == lapack.SelectedEV {
+			if ip == 0 {
+				if !selected[ki] {
+					continue
+				}
+			} else if !selected[ki-1] {
+				continue
+			}
+		}
+
+		// Compute the ki-th eigenvalue (wr,wi).
+		wr := t[ki*ldt+ki]
+		var wi float64
+		if ip != 0 {
+			wi = math.Sqrt(math.Abs(t[ki*ldt+ki-1])) * math.Sqrt(math.Abs(t[(ki-1)*ldt+ki]))
+		}
+		smin := math.Max(ulp*(math.Abs(wr)+math.Abs(wi)), smlnum)
+
+		if ip == 0 {
+			// Real right eigenvector.
+
+			b[ki*ldb+iv] = 1
+			// Form right-hand side.
+			for k := 0; k < ki; k++ {
+				b[k*ldb+iv] = -t[k*ldt+ki]
+			}
+			// Solve upper quasi-triangular system:
+			//  [ T[0:ki,0:ki] - wr ]*X = scale*b.
+			for j := ki - 1; j >= 0; {
+				if j == 0 || t[j*ldt+j-1] == 0 {
+					// 1×1 diagonal block.
+					scale, xnorm, _ := impl.Dlaln2(false, 1, 1, smin, 1, t[j*ldt+j:], ldt,
+						1, 1, b[j*ldb+iv:], ldb, wr, 0, x[:1], 2)
+					// Scale X[0,0] to avoid overflow when updating the
+					// right-hand side.
+					if xnorm > 1 && norms[j] > bignum/xnorm {
+						x[0] /= xnorm
+						scale /= xnorm
+					}
+					// Scale if necessary.
+					if scale != 1 {
+						bi.Dscal(ki+1, scale, b[iv:], ldb)
+					}
+					b[j*ldb+iv] = x[0]
+					// Update right-hand side.
+					bi.Daxpy(j, -x[0], t[j:], ldt, b[iv:], ldb)
+					j--
+				} else {
+					// 2×2 diagonal block.
+					scale, xnorm, _ := impl.Dlaln2(false, 2, 1, smin, 1, t[(j-1)*ldt+j-1:], ldt,
+						1, 1, b[(j-1)*ldb+iv:], ldb, wr, 0, x[:3], 2)
+					// Scale X[0,0] and X[1,0] to avoid overflow
+					// when updating the right-hand side.
+					if xnorm > 1 {
+						beta := math.Max(norms[j-1], norms[j])
+						if beta > bignum/xnorm {
+							x[0] /= xnorm
+							x[2] /= xnorm
+							scale /= xnorm
+						}
+					}
+					// Scale if necessary.
+					if scale != 1 {
+						bi.Dscal(ki+1, scale, b[iv:], ldb)
+					}
+					b[(j-1)*ldb+iv] = x[0]
+					b[j*ldb+iv] = x[2]
+					// Update right-hand side.
+					bi.Daxpy(j-1, -x[0], t[j-1:], ldt, b[iv:], ldb)
+					bi.Daxpy(j-1, -x[2], t[j:], ldt, b[iv:], ldb)
+					j -= 2
+				}
+			}
+			// Copy the vector x or Q*x to VR and normalize.
+			switch {
+			case howmny != lapack.AllEVMulQ:
+				// No back-transform: copy x to VR and normalize.
+				bi.Dcopy(ki+1, b[iv:], ldb, vr[is:], ldvr)
+				ii := bi.Idamax(ki+1, vr[is:], ldvr)
+				remax := 1 / math.Abs(vr[ii*ldvr+is])
+				bi.Dscal(ki+1, remax, vr[is:], ldvr)
+				for k := ki + 1; k < n; k++ {
+					vr[k*ldvr+is] = 0
+				}
+			case nb == 1:
+				// Version 1: back-transform each vector with GEMV, Q*x.
+				if ki > 0 {
+					bi.Dgemv(blas.NoTrans, n, ki, 1, vr, ldvr, b[iv:], ldb,
+						b[ki*ldb+iv], vr[ki:], ldvr)
+				}
+				ii := bi.Idamax(n, vr[ki:], ldvr)
+				remax := 1 / math.Abs(vr[ii*ldvr+ki])
+				bi.Dscal(n, remax, vr[ki:], ldvr)
+			default:
+				// Version 2: back-transform block of vectors with GEMM.
+				// Zero out below vector.
+				for k := ki + 1; k < n; k++ {
+					b[k*ldb+iv] = 0
+				}
+				iscomplex[iv] = ip
+				// Back-transform and normalization is done below.
+			}
+		} else {
+			// Complex right eigenvector.
+
+			// Initial solve
+			//  [ ( T[ki-1,ki-1] T[ki-1,ki] ) - (wr + i*wi) ]*X = 0.
+			//  [ ( T[ki,  ki-1] T[ki,  ki] )               ]
+			if math.Abs(t[(ki-1)*ldt+ki]) >= math.Abs(t[ki*ldt+ki-1]) {
+				b[(ki-1)*ldb+iv-1] = 1
+				b[ki*ldb+iv] = wi / t[(ki-1)*ldt+ki]
+			} else {
+				b[(ki-1)*ldb+iv-1] = -wi / t[ki*ldt+ki-1]
+				b[ki*ldb+iv] = 1
+			}
+			b[ki*ldb+iv-1] = 0
+			b[(ki-1)*ldb+iv] = 0
+			// Form right-hand side.
+			for k := 0; k < ki-1; k++ {
+				b[k*ldb+iv-1] = -b[(ki-1)*ldb+iv-1] * t[k*ldt+ki-1]
+				b[k*ldb+iv] = -b[ki*ldb+iv] * t[k*ldt+ki]
+			}
+			// Solve upper quasi-triangular system:
+			//  [ T[0:ki-1,0:ki-1] - (wr+i*wi) ]*X = scale*(b1+i*b2)
+			for j := ki - 2; j >= 0; {
+				if j == 0 || t[j*ldt+j-1] == 0 {
+					// 1×1 diagonal block.
+
+					scale, xnorm, _ := impl.Dlaln2(false, 1, 2, smin, 1, t[j*ldt+j:], ldt,
+						1, 1, b[j*ldb+iv-1:], ldb, wr, wi, x[:2], 2)
+					// Scale X[0,0] and X[0,1] to avoid
+					// overflow when updating the right-hand side.
+					if xnorm > 1 && norms[j] > bignum/xnorm {
+						x[0] /= xnorm
+						x[1] /= xnorm
+						scale /= xnorm
+					}
+					// Scale if necessary.
+					if scale != 1 {
+						bi.Dscal(ki+1, scale, b[iv-1:], ldb)
+						bi.Dscal(ki+1, scale, b[iv:], ldb)
+					}
+					b[j*ldb+iv-1] = x[0]
+					b[j*ldb+iv] = x[1]
+					// Update the right-hand side.
+					bi.Daxpy(j, -x[0], t[j:], ldt, b[iv-1:], ldb)
+					bi.Daxpy(j, -x[1], t[j:], ldt, b[iv:], ldb)
+					j--
+				} else {
+					// 2×2 diagonal block.
+
+					scale, xnorm, _ := impl.Dlaln2(false, 2, 2, smin, 1, t[(j-1)*ldt+j-1:], ldt,
+						1, 1, b[(j-1)*ldb+iv-1:], ldb, wr, wi, x[:], 2)
+					// Scale X to avoid overflow when updating
+					// the right-hand side.
+					if xnorm > 1 {
+						beta := math.Max(norms[j-1], norms[j])
+						if beta > bignum/xnorm {
+							rec := 1 / xnorm
+							x[0] *= rec
+							x[1] *= rec
+							x[2] *= rec
+							x[3] *= rec
+							scale *= rec
+						}
+					}
+					// Scale if necessary.
+					if scale != 1 {
+						bi.Dscal(ki+1, scale, b[iv-1:], ldb)
+						bi.Dscal(ki+1, scale, b[iv:], ldb)
+					}
+					b[(j-1)*ldb+iv-1] = x[0]
+					b[(j-1)*ldb+iv] = x[1]
+					b[j*ldb+iv-1] = x[2]
+					b[j*ldb+iv] = x[3]
+					// Update the right-hand side.
+					bi.Daxpy(j-1, -x[0], t[j-1:], ldt, b[iv-1:], ldb)
+					bi.Daxpy(j-1, -x[1], t[j-1:], ldt, b[iv:], ldb)
+					bi.Daxpy(j-1, -x[2], t[j:], ldt, b[iv-1:], ldb)
+					bi.Daxpy(j-1, -x[3], t[j:], ldt, b[iv:], ldb)
+					j -= 2
+				}
+			}
+
+			// Copy the vector x or Q*x to VR and normalize.
+			switch {
+			case howmny != lapack.AllEVMulQ:
+				// No back-transform: copy x to VR and normalize.
+				bi.Dcopy(ki+1, b[iv-1:], ldb, vr[is-1:], ldvr)
+				bi.Dcopy(ki+1, b[iv:], ldb, vr[is:], ldvr)
+				emax := 0.0
+				for k := 0; k <= ki; k++ {
+					emax = math.Max(emax, math.Abs(vr[k*ldvr+is-1])+math.Abs(vr[k*ldvr+is]))
+				}
+				remax := 1 / emax
+				bi.Dscal(ki+1, remax, vr[is-1:], ldvr)
+				bi.Dscal(ki+1, remax, vr[is:], ldvr)
+				for k := ki + 1; k < n; k++ {
+					vr[k*ldvr+is-1] = 0
+					vr[k*ldvr+is] = 0
+				}
+			case nb == 1:
+				// Version 1: back-transform each vector with GEMV, Q*x.
+				if ki-1 > 0 {
+					bi.Dgemv(blas.NoTrans, n, ki-1, 1, vr, ldvr, b[iv-1:], ldb,
+						b[(ki-1)*ldb+iv-1], vr[ki-1:], ldvr)
+					bi.Dgemv(blas.NoTrans, n, ki-1, 1, vr, ldvr, b[iv:], ldb,
+						b[ki*ldb+iv], vr[ki:], ldvr)
+				} else {
+					bi.Dscal(n, b[(ki-1)*ldb+iv-1], vr[ki-1:], ldvr)
+					bi.Dscal(n, b[ki*ldb+iv], vr[ki:], ldvr)
+				}
+				emax := 0.0
+				for k := 0; k < n; k++ {
+					emax = math.Max(emax, math.Abs(vr[k*ldvr+ki-1])+math.Abs(vr[k*ldvr+ki]))
+				}
+				remax := 1 / emax
+				bi.Dscal(n, remax, vr[ki-1:], ldvr)
+				bi.Dscal(n, remax, vr[ki:], ldvr)
+			default:
+				// Version 2: back-transform block of vectors with GEMM.
+				// Zero out below vector.
+				for k := ki + 1; k < n; k++ {
+					b[k*ldb+iv-1] = 0
+					b[k*ldb+iv] = 0
+				}
+				iscomplex[iv-1] = -ip
+				iscomplex[iv] = ip
+				iv--
+				// Back-transform and normalization is done below.
+			}
+		}
+		if nb > 1 {
+			// Blocked version of back-transform.
+
+			// For complex case, ki2 includes both vectors (ki-1 and ki).
+			ki2 := ki
+			if ip != 0 {
+				ki2--
+			}
+			// Columns iv:nb of b are valid vectors.
+			// When the number of vectors stored reaches nb-1 or nb,
+			// or if this was last vector, do the Gemm.
+			if iv < 2 || ki2 == 0 {
+				bi.Dgemm(blas.NoTrans, blas.NoTrans, n, nb-iv, ki2+nb-iv,
+					1, vr, ldvr, b[iv:], ldb,
+					0, b[nb+iv:], ldb)
+				// Normalize vectors.
+				var remax float64
+				for k := iv; k < nb; k++ {
+					if iscomplex[k] == 0 {
+						// Real eigenvector.
+						ii := bi.Idamax(n, b[nb+k:], ldb)
+						remax = 1 / math.Abs(b[ii*ldb+nb+k])
+					} else if iscomplex[k] == 1 {
+						// First eigenvector of conjugate pair.
+						emax := 0.0
+						for ii := 0; ii < n; ii++ {
+							emax = math.Max(emax, math.Abs(b[ii*ldb+nb+k])+math.Abs(b[ii*ldb+nb+k+1]))
+						}
+						remax = 1 / emax
+						// Second eigenvector of conjugate pair
+						// will reuse this value of remax.
+					}
+					bi.Dscal(n, remax, b[nb+k:], ldb)
+				}
+				impl.Dlacpy(blas.All, n, nb-iv, b[nb+iv:], ldb, vr[ki2:], ldvr)
+				iv = nb - 1
+			} else {
+				iv--
+			}
+		}
+		is--
+		if ip != 0 {
+			is--
+		}
+	}
+
+	if side == lapack.RightEV {
+		return m
+	}
+
+leftev:
+	// Compute left eigenvectors.
+
+	// For complex left vector, iv is for real part and iv+1 for complex
+	// part. Non-blocked version always uses iv=0. Blocked version starts
+	// with iv=0, goes up to nb-2 or nb-1.
+	iv = 0
+	ip = 0
+	is = 0
+	for ki := 0; ki < n; ki++ {
+		if ip == 1 {
+			// Previous iteration ki-1 was first of conjugate pair,
+			// so this ki is second of conjugate pair.
+			ip = -1
+			continue
+		}
+
+		if ki == n-1 || t[(ki+1)*ldt+ki] == 0 {
+			// Last column or zero on sub-diagonal, so this ki must
+			// be real eigenvalue.
+			ip = 0
+		} else {
+			// Non-zero on sub-diagonal, so this ki is first of
+			// conjugate pair.
+			ip = 1
+		}
+		if howmny == lapack.SelectedEV && !selected[ki] {
+			continue
+		}
+
+		// Compute the ki-th eigenvalue (wr,wi).
+		wr := t[ki*ldt+ki]
+		var wi float64
+		if ip != 0 {
+			wi = math.Sqrt(math.Abs(t[ki*ldt+ki+1])) * math.Sqrt(math.Abs(t[(ki+1)*ldt+ki]))
+		}
+		smin := math.Max(ulp*(math.Abs(wr)+math.Abs(wi)), smlnum)
+
+		if ip == 0 {
+			// Real left eigenvector.
+
+			b[ki*ldb+iv] = 1
+			// Form right-hand side.
+			for k := ki + 1; k < n; k++ {
+				b[k*ldb+iv] = -t[ki*ldt+k]
+			}
+			// Solve transposed quasi-triangular system:
+			//  [ T[ki+1:n,ki+1:n] - wr ]^T * X = scale*b
+			vmax := 1.0
+			vcrit := bignum
+			for j := ki + 1; j < n; {
+				if j == n-1 || t[(j+1)*ldt+j] == 0 {
+					// 1×1 diagonal block.
+
+					// Scale if necessary to avoid overflow
+					// when forming the right-hand side.
+					if norms[j] > vcrit {
+						rec := 1 / vmax
+						bi.Dscal(n-ki, rec, b[ki*ldb+iv:], ldb)
+						vmax = 1
+						vcrit = bignum
+					}
+					b[j*ldb+iv] -= bi.Ddot(j-ki-1, t[(ki+1)*ldt+j:], ldt, b[(ki+1)*ldb+iv:], ldb)
+					// Solve [ T[j,j] - wr ]^T * X = b.
+					scale, _, _ := impl.Dlaln2(false, 1, 1, smin, 1, t[j*ldt+j:], ldt,
+						1, 1, b[j*ldb+iv:], ldb, wr, 0, x[:1], 2)
+					// Scale if necessary.
+					if scale != 1 {
+						bi.Dscal(n-ki, scale, b[ki*ldb+iv:], ldb)
+					}
+					b[j*ldb+iv] = x[0]
+					vmax = math.Max(math.Abs(b[j*ldb+iv]), vmax)
+					vcrit = bignum / vmax
+					j++
+				} else {
+					// 2×2 diagonal block.
+
+					// Scale if necessary to avoid overflow
+					// when forming the right-hand side.
+					beta := math.Max(norms[j], norms[j+1])
+					if beta > vcrit {
+						bi.Dscal(n-ki+1, 1/vmax, b[ki*ldb+iv:], 1)
+						vmax = 1
+						vcrit = bignum
+					}
+					b[j*ldb+iv] -= bi.Ddot(j-ki-1, t[(ki+1)*ldt+j:], ldt, b[(ki+1)*ldb+iv:], ldb)
+					b[(j+1)*ldb+iv] -= bi.Ddot(j-ki-1, t[(ki+1)*ldt+j+1:], ldt, b[(ki+1)*ldb+iv:], ldb)
+					// Solve
+					//  [ T[j,j]-wr  T[j,j+1]      ]^T * X = scale*[ b1 ]
+					//  [ T[j+1,j]   T[j+1,j+1]-wr ]               [ b2 ]
+					scale, _, _ := impl.Dlaln2(true, 2, 1, smin, 1, t[j*ldt+j:], ldt,
+						1, 1, b[j*ldb+iv:], ldb, wr, 0, x[:3], 2)
+					// Scale if necessary.
+					if scale != 1 {
+						bi.Dscal(n-ki, scale, b[ki*ldb+iv:], ldb)
+					}
+					b[j*ldb+iv] = x[0]
+					b[(j+1)*ldb+iv] = x[2]
+					vmax = math.Max(vmax, math.Max(math.Abs(b[j*ldb+iv]), math.Abs(b[(j+1)*ldb+iv])))
+					vcrit = bignum / vmax
+					j += 2
+				}
+			}
+			// Copy the vector x or Q*x to VL and normalize.
+			switch {
+			case howmny != lapack.AllEVMulQ:
+				// No back-transform: copy x to VL and normalize.
+				bi.Dcopy(n-ki, b[ki*ldb+iv:], ldb, vl[ki*ldvl+is:], ldvl)
+				ii := bi.Idamax(n-ki, vl[ki*ldvl+is:], ldvl) + ki
+				remax := 1 / math.Abs(vl[ii*ldvl+is])
+				bi.Dscal(n-ki, remax, vl[ki*ldvl+is:], ldvl)
+				for k := 0; k < ki; k++ {
+					vl[k*ldvl+is] = 0
+				}
+			case nb == 1:
+				// Version 1: back-transform each vector with Gemv, Q*x.
+				if n-ki-1 > 0 {
+					bi.Dgemv(blas.NoTrans, n, n-ki-1,
+						1, vl[ki+1:], ldvl, b[(ki+1)*ldb+iv:], ldb,
+						b[ki*ldb+iv], vl[ki:], ldvl)
+				}
+				ii := bi.Idamax(n, vl[ki:], ldvl)
+				remax := 1 / math.Abs(vl[ii*ldvl+ki])
+				bi.Dscal(n, remax, vl[ki:], ldvl)
+			default:
+				// Version 2: back-transform block of vectors with Gemm
+				// zero out above vector.
+				for k := 0; k < ki; k++ {
+					b[k*ldb+iv] = 0
+				}
+				iscomplex[iv] = ip
+				// Back-transform and normalization is done below.
+			}
+		} else {
+			// Complex left eigenvector.
+
+			// Initial solve:
+			// [ [ T[ki,ki]   T[ki,ki+1]   ]^T - (wr - i* wi) ]*X = 0.
+			// [ [ T[ki+1,ki] T[ki+1,ki+1] ]                  ]
+			if math.Abs(t[ki*ldt+ki+1]) >= math.Abs(t[(ki+1)*ldt+ki]) {
+				b[ki*ldb+iv] = wi / t[ki*ldt+ki+1]
+				b[(ki+1)*ldb+iv+1] = 1
+			} else {
+				b[ki*ldb+iv] = 1
+				b[(ki+1)*ldb+iv+1] = -wi / t[(ki+1)*ldt+ki]
+			}
+			b[(ki+1)*ldb+iv] = 0
+			b[ki*ldb+iv+1] = 0
+			// Form right-hand side.
+			for k := ki + 2; k < n; k++ {
+				b[k*ldb+iv] = -b[ki*ldb+iv] * t[ki*ldt+k]
+				b[k*ldb+iv+1] = -b[(ki+1)*ldb+iv+1] * t[(ki+1)*ldt+k]
+			}
+			// Solve transposed quasi-triangular system:
+			// [ T[ki+2:n,ki+2:n]^T - (wr-i*wi) ]*X = b1+i*b2
+			vmax := 1.0
+			vcrit := bignum
+			for j := ki + 2; j < n; {
+				if j == n-1 || t[(j+1)*ldt+j] == 0 {
+					// 1×1 diagonal block.
+
+					// Scale if necessary to avoid overflow
+					// when forming the right-hand side elements.
+					if norms[j] > vcrit {
+						rec := 1 / vmax
+						bi.Dscal(n-ki, rec, b[ki*ldb+iv:], ldb)
+						bi.Dscal(n-ki, rec, b[ki*ldb+iv+1:], ldb)
+						vmax = 1
+						vcrit = bignum
+					}
+					b[j*ldb+iv] -= bi.Ddot(j-ki-2, t[(ki+2)*ldt+j:], ldt, b[(ki+2)*ldb+iv:], ldb)
+					b[j*ldb+iv+1] -= bi.Ddot(j-ki-2, t[(ki+2)*ldt+j:], ldt, b[(ki+2)*ldb+iv+1:], ldb)
+					// Solve [ T[j,j]-(wr-i*wi) ]*(X11+i*X12) = b1+i*b2.
+					scale, _, _ := impl.Dlaln2(false, 1, 2, smin, 1, t[j*ldt+j:], ldt,
+						1, 1, b[j*ldb+iv:], ldb, wr, -wi, x[:2], 2)
+					// Scale if necessary.
+					if scale != 1 {
+						bi.Dscal(n-ki, scale, b[ki*ldb+iv:], ldb)
+						bi.Dscal(n-ki, scale, b[ki*ldb+iv+1:], ldb)
+					}
+					b[j*ldb+iv] = x[0]
+					b[j*ldb+iv+1] = x[1]
+					vmax = math.Max(vmax, math.Max(math.Abs(b[j*ldb+iv]), math.Abs(b[j*ldb+iv+1])))
+					vcrit = bignum / vmax
+					j++
+				} else {
+					// 2×2 diagonal block.
+
+					// Scale if necessary to avoid overflow
+					// when forming the right-hand side elements.
+					if math.Max(norms[j], norms[j+1]) > vcrit {
+						rec := 1 / vmax
+						bi.Dscal(n-ki, rec, b[ki*ldb+iv:], ldb)
+						bi.Dscal(n-ki, rec, b[ki*ldb+iv+1:], ldb)
+						vmax = 1
+						vcrit = bignum
+					}
+					b[j*ldb+iv] -= bi.Ddot(j-ki-2, t[(ki+2)*ldt+j:], ldt, b[(ki+2)*ldb+iv:], ldb)
+					b[j*ldb+iv+1] -= bi.Ddot(j-ki-2, t[(ki+2)*ldt+j:], ldt, b[(ki+2)*ldb+iv+1:], ldb)
+					b[(j+1)*ldb+iv] -= bi.Ddot(j-ki-2, t[(ki+2)*ldt+j+1:], ldt, b[(ki+2)*ldb+iv:], ldb)
+					b[(j+1)*ldb+iv+1] -= bi.Ddot(j-ki-2, t[(ki+2)*ldt+j+1:], ldt, b[(ki+2)*ldb+iv+1:], ldb)
+					// Solve 2×2 complex linear equation
+					//  [ [T[j,j]   T[j,j+1]  ]^T - (wr-i*wi)*I ]*X = scale*b
+					//  [ [T[j+1,j] T[j+1,j+1]]                 ]
+					scale, _, _ := impl.Dlaln2(true, 2, 2, smin, 1, t[j*ldt+j:], ldt,
+						1, 1, b[j*ldb+iv:], ldb, wr, -wi, x[:], 2)
+					// Scale if necessary.
+					if scale != 1 {
+						bi.Dscal(n-ki, scale, b[ki*ldb+iv:], ldb)
+						bi.Dscal(n-ki, scale, b[ki*ldb+iv+1:], ldb)
+					}
+					b[j*ldb+iv] = x[0]
+					b[j*ldb+iv+1] = x[1]
+					b[(j+1)*ldb+iv] = x[2]
+					b[(j+1)*ldb+iv+1] = x[3]
+					vmax01 := math.Max(math.Abs(x[0]), math.Abs(x[1]))
+					vmax23 := math.Max(math.Abs(x[2]), math.Abs(x[3]))
+					vmax = math.Max(vmax, math.Max(vmax01, vmax23))
+					vcrit = bignum / vmax
+					j += 2
+				}
+			}
+			// Copy the vector x or Q*x to VL and normalize.
+			switch {
+			case howmny != lapack.AllEVMulQ:
+				// No back-transform: copy x to VL and normalize.
+				bi.Dcopy(n-ki, b[ki*ldb+iv:], ldb, vl[ki*ldvl+is:], ldvl)
+				bi.Dcopy(n-ki, b[ki*ldb+iv+1:], ldb, vl[ki*ldvl+is+1:], ldvl)
+				emax := 0.0
+				for k := ki; k < n; k++ {
+					emax = math.Max(emax, math.Abs(vl[k*ldvl+is])+math.Abs(vl[k*ldvl+is+1]))
+				}
+				remax := 1 / emax
+				bi.Dscal(n-ki, remax, vl[ki*ldvl+is:], ldvl)
+				bi.Dscal(n-ki, remax, vl[ki*ldvl+is+1:], ldvl)
+				for k := 0; k < ki; k++ {
+					vl[k*ldvl+is] = 0
+					vl[k*ldvl+is+1] = 0
+				}
+			case nb == 1:
+				// Version 1: back-transform each vector with GEMV, Q*x.
+				if n-ki-2 > 0 {
+					bi.Dgemv(blas.NoTrans, n, n-ki-2,
+						1, vl[ki+2:], ldvl, b[(ki+2)*ldb+iv:], ldb,
+						b[ki*ldb+iv], vl[ki:], ldvl)
+					bi.Dgemv(blas.NoTrans, n, n-ki-2,
+						1, vl[ki+2:], ldvl, b[(ki+2)*ldb+iv+1:], ldb,
+						b[(ki+1)*ldb+iv+1], vl[ki+1:], ldvl)
+				} else {
+					bi.Dscal(n, b[ki*ldb+iv], vl[ki:], ldvl)
+					bi.Dscal(n, b[(ki+1)*ldb+iv+1], vl[ki+1:], ldvl)
+				}
+				emax := 0.0
+				for k := 0; k < n; k++ {
+					emax = math.Max(emax, math.Abs(vl[k*ldvl+ki])+math.Abs(vl[k*ldvl+ki+1]))
+				}
+				remax := 1 / emax
+				bi.Dscal(n, remax, vl[ki:], ldvl)
+				bi.Dscal(n, remax, vl[ki+1:], ldvl)
+			default:
+				// Version 2: back-transform block of vectors with GEMM.
+				// Zero out above vector.
+				// Could go from ki-nv+1 to ki-1.
+				for k := 0; k < ki; k++ {
+					b[k*ldb+iv] = 0
+					b[k*ldb+iv+1] = 0
+				}
+				iscomplex[iv] = ip
+				iscomplex[iv+1] = -ip
+				iv++
+				// Back-transform and normalization is done below.
+			}
+		}
+		if nb > 1 {
+			// Blocked version of back-transform.
+			// For complex case, ki2 includes both vectors ki and ki+1.
+			ki2 := ki
+			if ip != 0 {
+				ki2++
+			}
+			// Columns [0:iv] of work are valid vectors. When the
+			// number of vectors stored reaches nb-1 or nb, or if
+			// this was last vector, do the Gemm.
+			if iv >= nb-2 || ki2 == n-1 {
+				bi.Dgemm(blas.NoTrans, blas.NoTrans, n, iv+1, n-ki2+iv,
+					1, vl[ki2-iv:], ldvl, b[(ki2-iv)*ldb:], ldb,
+					0, b[nb:], ldb)
+				// Normalize vectors.
+				var remax float64
+				for k := 0; k <= iv; k++ {
+					if iscomplex[k] == 0 {
+						// Real eigenvector.
+						ii := bi.Idamax(n, b[nb+k:], ldb)
+						remax = 1 / math.Abs(b[ii*ldb+nb+k])
+					} else if iscomplex[k] == 1 {
+						// First eigenvector of conjugate pair.
+						emax := 0.0
+						for ii := 0; ii < n; ii++ {
+							emax = math.Max(emax, math.Abs(b[ii*ldb+nb+k])+math.Abs(b[ii*ldb+nb+k+1]))
+						}
+						remax = 1 / emax
+						// Second eigenvector of conjugate pair
+						// will reuse this value of remax.
+					}
+					bi.Dscal(n, remax, b[nb+k:], ldb)
+				}
+				impl.Dlacpy(blas.All, n, iv+1, b[nb:], ldb, vl[ki2-iv:], ldvl)
+				iv = 0
+			} else {
+				iv++
+			}
+		}
+		is++
+		if ip != 0 {
+			is++
+		}
+	}
+
+	return m
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dtrexc.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dtrexc.go
new file mode 100644
index 00000000..4a88931f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dtrexc.go
@@ -0,0 +1,221 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "gonum.org/v1/gonum/lapack"
+
+// Dtrexc reorders the real Schur factorization of a n×n real matrix
+//  A = Q*T*Q^T
+// so that the diagonal block of T with row index ifst is moved to row ilst.
+//
+// On entry, T must be in Schur canonical form, that is, block upper triangular
+// with 1×1 and 2×2 diagonal blocks; each 2×2 diagonal block has its diagonal
+// elements equal and its off-diagonal elements of opposite sign.
+//
+// On return, T will be reordered by an orthogonal similarity transformation Z
+// as Z^T*T*Z, and will be again in Schur canonical form.
+//
+// If compq is lapack.UpdateSchur, on return the matrix Q of Schur vectors will be
+// updated by postmultiplying it with Z.
+// If compq is lapack.None, the matrix Q is not referenced and will not be
+// updated.
+// For other values of compq Dtrexc will panic.
+//
+// ifst and ilst specify the reordering of the diagonal blocks of T. The block
+// with row index ifst is moved to row ilst, by a sequence of transpositions
+// between adjacent blocks.
+//
+// If ifst points to the second row of a 2×2 block, ifstOut will point to the
+// first row, otherwise it will be equal to ifst.
+//
+// ilstOut will point to the first row of the block in its final position. If ok
+// is true, ilstOut may differ from ilst by +1 or -1.
+//
+// It must hold that
+//  0 <= ifst < n, and  0 <= ilst < n,
+// otherwise Dtrexc will panic.
+//
+// If ok is false, two adjacent blocks were too close to swap because the
+// problem is very ill-conditioned. T may have been partially reordered, and
+// ilstOut will point to the first row of the block at the position to which it
+// has been moved.
+//
+// work must have length at least n, otherwise Dtrexc will panic.
+//
+// Dtrexc is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dtrexc(compq lapack.EVComp, n int, t []float64, ldt int, q []float64, ldq int, ifst, ilst int, work []float64) (ifstOut, ilstOut int, ok bool) {
+	checkMatrix(n, n, t, ldt)
+	var wantq bool
+	switch compq {
+	default:
+		panic("lapack: bad value of compq")
+	case lapack.None:
+		// Nothing to do because wantq is already false.
+	case lapack.UpdateSchur:
+		wantq = true
+		checkMatrix(n, n, q, ldq)
+	}
+	if (ifst < 0 || n <= ifst) && n > 0 {
+		panic("lapack: ifst out of range")
+	}
+	if (ilst < 0 || n <= ilst) && n > 0 {
+		panic("lapack: ilst out of range")
+	}
+	if len(work) < n {
+		panic(badWork)
+	}
+
+	ok = true
+
+	// Quick return if possible.
+	if n <= 1 {
+		return ifst, ilst, true
+	}
+
+	// Determine the first row of specified block
+	// and find out it is 1×1 or 2×2.
+	if ifst > 0 && t[ifst*ldt+ifst-1] != 0 {
+		ifst--
+	}
+	nbf := 1 // Size of the first block.
+	if ifst+1 < n && t[(ifst+1)*ldt+ifst] != 0 {
+		nbf = 2
+	}
+	// Determine the first row of the final block
+	// and find out it is 1×1 or 2×2.
+	if ilst > 0 && t[ilst*ldt+ilst-1] != 0 {
+		ilst--
+	}
+	nbl := 1 // Size of the last block.
+	if ilst+1 < n && t[(ilst+1)*ldt+ilst] != 0 {
+		nbl = 2
+	}
+
+	switch {
+	case ifst == ilst:
+		return ifst, ilst, true
+
+	case ifst < ilst:
+		// Update ilst.
+		switch {
+		case nbf == 2 && nbl == 1:
+			ilst--
+		case nbf == 1 && nbl == 2:
+			ilst++
+		}
+		here := ifst
+		for here < ilst {
+			// Swap block with next one below.
+			if nbf == 1 || nbf == 2 {
+				// Current block either 1×1 or 2×2.
+				nbnext := 1 // Size of the next block.
+				if here+nbf+1 < n && t[(here+nbf+1)*ldt+here+nbf] != 0 {
+					nbnext = 2
+				}
+				ok = impl.Dlaexc(wantq, n, t, ldt, q, ldq, here, nbf, nbnext, work)
+				if !ok {
+					return ifst, here, false
+				}
+				here += nbnext
+				// Test if 2×2 block breaks into two 1×1 blocks.
+				if nbf == 2 && t[(here+1)*ldt+here] == 0 {
+					nbf = 3
+				}
+				continue
+			}
+
+			// Current block consists of two 1×1 blocks each of
+			// which must be swapped individually.
+			nbnext := 1 // Size of the next block.
+			if here+3 < n && t[(here+3)*ldt+here+2] != 0 {
+				nbnext = 2
+			}
+			ok = impl.Dlaexc(wantq, n, t, ldt, q, ldq, here+1, 1, nbnext, work)
+			if !ok {
+				return ifst, here, false
+			}
+			if nbnext == 1 {
+				// Swap two 1×1 blocks, no problems possible.
+				impl.Dlaexc(wantq, n, t, ldt, q, ldq, here, 1, nbnext, work)
+				here++
+				continue
+			}
+			// Recompute nbnext in case 2×2 split.
+			if t[(here+2)*ldt+here+1] == 0 {
+				nbnext = 1
+			}
+			if nbnext == 2 {
+				// 2×2 block did not split.
+				ok = impl.Dlaexc(wantq, n, t, ldt, q, ldq, here, 1, nbnext, work)
+				if !ok {
+					return ifst, here, false
+				}
+			} else {
+				// 2×2 block did split.
+				impl.Dlaexc(wantq, n, t, ldt, q, ldq, here, 1, 1, work)
+				impl.Dlaexc(wantq, n, t, ldt, q, ldq, here+1, 1, 1, work)
+			}
+			here += 2
+		}
+		return ifst, here, true
+
+	default: // ifst > ilst
+		here := ifst
+		for here > ilst {
+			// Swap block with next one above.
+			if nbf == 1 || nbf == 2 {
+				// Current block either 1×1 or 2×2.
+				nbnext := 1
+				if here-2 >= 0 && t[(here-1)*ldt+here-2] != 0 {
+					nbnext = 2
+				}
+				ok = impl.Dlaexc(wantq, n, t, ldt, q, ldq, here-nbnext, nbnext, nbf, work)
+				if !ok {
+					return ifst, here, false
+				}
+				here -= nbnext
+				// Test if 2×2 block breaks into two 1×1 blocks.
+				if nbf == 2 && t[(here+1)*ldt+here] == 0 {
+					nbf = 3
+				}
+				continue
+			}
+
+			// Current block consists of two 1×1 blocks each of
+			// which must be swapped individually.
+			nbnext := 1
+			if here-2 >= 0 && t[(here-1)*ldt+here-2] != 0 {
+				nbnext = 2
+			}
+			ok = impl.Dlaexc(wantq, n, t, ldt, q, ldq, here-nbnext, nbnext, 1, work)
+			if !ok {
+				return ifst, here, false
+			}
+			if nbnext == 1 {
+				// Swap two 1×1 blocks, no problems possible.
+				impl.Dlaexc(wantq, n, t, ldt, q, ldq, here, nbnext, 1, work)
+				here--
+				continue
+			}
+			// Recompute nbnext in case 2×2 split.
+			if t[here*ldt+here-1] == 0 {
+				nbnext = 1
+			}
+			if nbnext == 2 {
+				// 2×2 block did not split.
+				ok = impl.Dlaexc(wantq, n, t, ldt, q, ldq, here-1, 2, 1, work)
+				if !ok {
+					return ifst, here, false
+				}
+			} else {
+				// 2×2 block did split.
+				impl.Dlaexc(wantq, n, t, ldt, q, ldq, here, 1, 1, work)
+				impl.Dlaexc(wantq, n, t, ldt, q, ldq, here-1, 1, 1, work)
+			}
+			here -= 2
+		}
+		return ifst, here, true
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dtrti2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dtrti2.go
new file mode 100644
index 00000000..8998f5eb
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dtrti2.go
@@ -0,0 +1,57 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dtrti2 computes the inverse of a triangular matrix, storing the result in place
+// into a. This is the BLAS level 2 version of the algorithm.
+//
+// Dtrti2 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dtrti2(uplo blas.Uplo, diag blas.Diag, n int, a []float64, lda int) {
+	checkMatrix(n, n, a, lda)
+	if uplo != blas.Upper && uplo != blas.Lower {
+		panic(badUplo)
+	}
+	if diag != blas.NonUnit && diag != blas.Unit {
+		panic(badDiag)
+	}
+	bi := blas64.Implementation()
+
+	nonUnit := diag == blas.NonUnit
+	// TODO(btracey): Replace this with a row-major ordering.
+	if uplo == blas.Upper {
+		for j := 0; j < n; j++ {
+			var ajj float64
+			if nonUnit {
+				ajj = 1 / a[j*lda+j]
+				a[j*lda+j] = ajj
+				ajj *= -1
+			} else {
+				ajj = -1
+			}
+			bi.Dtrmv(blas.Upper, blas.NoTrans, diag, j, a, lda, a[j:], lda)
+			bi.Dscal(j, ajj, a[j:], lda)
+		}
+		return
+	}
+	for j := n - 1; j >= 0; j-- {
+		var ajj float64
+		if nonUnit {
+			ajj = 1 / a[j*lda+j]
+			a[j*lda+j] = ajj
+			ajj *= -1
+		} else {
+			ajj = -1
+		}
+		if j < n-1 {
+			bi.Dtrmv(blas.Lower, blas.NoTrans, diag, n-j-1, a[(j+1)*lda+j+1:], lda, a[(j+1)*lda+j:], lda)
+			bi.Dscal(n-j-1, ajj, a[(j+1)*lda+j:], lda)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dtrtri.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dtrtri.go
new file mode 100644
index 00000000..25e43ddc
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dtrtri.go
@@ -0,0 +1,64 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dtrtri computes the inverse of a triangular matrix, storing the result in place
+// into a. This is the BLAS level 3 version of the algorithm which builds upon
+// Dtrti2 to operate on matrix blocks instead of only individual columns.
+//
+// Dtrtri will not perform the inversion if the matrix is singular, and returns
+// a boolean indicating whether the inversion was successful.
+func (impl Implementation) Dtrtri(uplo blas.Uplo, diag blas.Diag, n int, a []float64, lda int) (ok bool) {
+	checkMatrix(n, n, a, lda)
+	if uplo != blas.Upper && uplo != blas.Lower {
+		panic(badUplo)
+	}
+	if diag != blas.NonUnit && diag != blas.Unit {
+		panic(badDiag)
+	}
+	if n == 0 {
+		return false
+	}
+	nonUnit := diag == blas.NonUnit
+	if nonUnit {
+		for i := 0; i < n; i++ {
+			if a[i*lda+i] == 0 {
+				return false
+			}
+		}
+	}
+
+	bi := blas64.Implementation()
+
+	nb := impl.Ilaenv(1, "DTRTRI", "UD", n, -1, -1, -1)
+	if nb <= 1 || nb > n {
+		impl.Dtrti2(uplo, diag, n, a, lda)
+		return true
+	}
+	if uplo == blas.Upper {
+		for j := 0; j < n; j += nb {
+			jb := min(nb, n-j)
+			bi.Dtrmm(blas.Left, blas.Upper, blas.NoTrans, diag, j, jb, 1, a, lda, a[j:], lda)
+			bi.Dtrsm(blas.Right, blas.Upper, blas.NoTrans, diag, j, jb, -1, a[j*lda+j:], lda, a[j:], lda)
+			impl.Dtrti2(blas.Upper, diag, jb, a[j*lda+j:], lda)
+		}
+		return true
+	}
+	nn := ((n - 1) / nb) * nb
+	for j := nn; j >= 0; j -= nb {
+		jb := min(nb, n-j)
+		if j+jb <= n-1 {
+			bi.Dtrmm(blas.Left, blas.Lower, blas.NoTrans, diag, n-j-jb, jb, 1, a[(j+jb)*lda+j+jb:], lda, a[(j+jb)*lda+j:], lda)
+			bi.Dtrsm(blas.Right, blas.Lower, blas.NoTrans, diag, n-j-jb, jb, -1, a[j*lda+j:], lda, a[(j+jb)*lda+j:], lda)
+		}
+		impl.Dtrti2(blas.Lower, diag, jb, a[j*lda+j:], lda)
+	}
+	return true
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dtrtrs.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dtrtrs.go
new file mode 100644
index 00000000..6760796d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dtrtrs.go
@@ -0,0 +1,30 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dtrtrs solves a triangular system of the form A * X = B or A^T * X = B. Dtrtrs
+// returns whether the solve completed successfully. If A is singular, no solve is performed.
+func (impl Implementation) Dtrtrs(uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, n, nrhs int, a []float64, lda int, b []float64, ldb int) (ok bool) {
+	nounit := diag == blas.NonUnit
+	if n == 0 {
+		return false
+	}
+	// Check for singularity.
+	if nounit {
+		for i := 0; i < n; i++ {
+			if a[i*lda+i] == 0 {
+				return false
+			}
+		}
+	}
+	bi := blas64.Implementation()
+	bi.Dtrsm(blas.Left, uplo, trans, diag, n, nrhs, 1, a, lda, b, ldb)
+	return true
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/general.go b/vendor/gonum.org/v1/gonum/lapack/gonum/general.go
new file mode 100644
index 00000000..4006ea70
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/general.go
@@ -0,0 +1,143 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Implementation is the native Go implementation of LAPACK routines. It
+// is built on top of calls to the return of blas64.Implementation(), so while
+// this code is in pure Go, the underlying BLAS implementation may not be.
+type Implementation struct{}
+
+var _ lapack.Float64 = Implementation{}
+
+// This list is duplicated in lapack/cgo. Keep in sync.
+const (
+	absIncNotOne    = "lapack: increment not one or negative one"
+	badAlpha        = "lapack: bad alpha length"
+	badAuxv         = "lapack: auxv has insufficient length"
+	badBeta         = "lapack: bad beta length"
+	badD            = "lapack: d has insufficient length"
+	badDecompUpdate = "lapack: bad decomp update"
+	badDiag         = "lapack: bad diag"
+	badDims         = "lapack: bad input dimensions"
+	badDirect       = "lapack: bad direct"
+	badE            = "lapack: e has insufficient length"
+	badEVComp       = "lapack: bad EVComp"
+	badEVJob        = "lapack: bad EVJob"
+	badEVSide       = "lapack: bad EVSide"
+	badGSVDJob      = "lapack: bad GSVDJob"
+	badHowMany      = "lapack: bad HowMany"
+	badIlo          = "lapack: ilo out of range"
+	badIhi          = "lapack: ihi out of range"
+	badIpiv         = "lapack: bad permutation length"
+	badJob          = "lapack: bad Job"
+	badK1           = "lapack: k1 out of range"
+	badK2           = "lapack: k2 out of range"
+	badKperm        = "lapack: incorrect permutation length"
+	badLdA          = "lapack: index of a out of range"
+	badNb           = "lapack: nb out of range"
+	badNorm         = "lapack: bad norm"
+	badPivot        = "lapack: bad pivot"
+	badS            = "lapack: s has insufficient length"
+	badShifts       = "lapack: bad shifts"
+	badSide         = "lapack: bad side"
+	badSlice        = "lapack: bad input slice length"
+	badSort         = "lapack: bad Sort"
+	badStore        = "lapack: bad store"
+	badTau          = "lapack: tau has insufficient length"
+	badTauQ         = "lapack: tauQ has insufficient length"
+	badTauP         = "lapack: tauP has insufficient length"
+	badTrans        = "lapack: bad trans"
+	badVn1          = "lapack: vn1 has insufficient length"
+	badVn2          = "lapack: vn2 has insufficient length"
+	badUplo         = "lapack: illegal triangle"
+	badWork         = "lapack: insufficient working memory"
+	badZ            = "lapack: insufficient z length"
+	kGTM            = "lapack: k > m"
+	kGTN            = "lapack: k > n"
+	kLT0            = "lapack: k < 0"
+	mLTN            = "lapack: m < n"
+	nanScale        = "lapack: NaN scale factor"
+	negDimension    = "lapack: negative matrix dimension"
+	negZ            = "lapack: negative z value"
+	nLT0            = "lapack: n < 0"
+	nLTM            = "lapack: n < m"
+	offsetGTM       = "lapack: offset > m"
+	shortWork       = "lapack: working array shorter than declared"
+	zeroDiv         = "lapack: zero divisor"
+)
+
+// checkMatrix verifies the parameters of a matrix input.
+func checkMatrix(m, n int, a []float64, lda int) {
+	if m < 0 {
+		panic("lapack: has negative number of rows")
+	}
+	if n < 0 {
+		panic("lapack: has negative number of columns")
+	}
+	if lda < n {
+		panic("lapack: stride less than number of columns")
+	}
+	if len(a) < (m-1)*lda+n {
+		panic("lapack: insufficient matrix slice length")
+	}
+}
+
+func checkVector(n int, v []float64, inc int) {
+	if n < 0 {
+		panic("lapack: negative vector length")
+	}
+	if (inc > 0 && (n-1)*inc >= len(v)) || (inc < 0 && (1-n)*inc >= len(v)) {
+		panic("lapack: insufficient vector slice length")
+	}
+}
+
+func checkSymBanded(ab []float64, n, kd, lda int) {
+	if n < 0 {
+		panic("lapack: negative banded length")
+	}
+	if kd < 0 {
+		panic("lapack: negative bandwidth value")
+	}
+	if lda < kd+1 {
+		panic("lapack: stride less than number of bands")
+	}
+	if len(ab) < (n-1)*lda+kd {
+		panic("lapack: insufficient banded vector length")
+	}
+}
+
+func min(a, b int) int {
+	if a < b {
+		return a
+	}
+	return b
+}
+
+func max(a, b int) int {
+	if a > b {
+		return a
+	}
+	return b
+}
+
+const (
+	// dlamchE is the machine epsilon. For IEEE this is 2^{-53}.
+	dlamchE = 1.0 / (1 << 53)
+
+	// dlamchB is the radix of the machine (the base of the number system).
+	dlamchB = 2
+
+	// dlamchP is base * eps.
+	dlamchP = dlamchB * dlamchE
+
+	// dlamchS is the "safe minimum", that is, the lowest number such that
+	// 1/dlamchS does not overflow, or also the smallest normal number.
+	// For IEEE this is 2^{-1022}.
+	dlamchS = 1.0 / (1 << 256) / (1 << 256) / (1 << 256) / (1 << 254)
+)
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/iladlc.go b/vendor/gonum.org/v1/gonum/lapack/gonum/iladlc.go
new file mode 100644
index 00000000..126a6f9d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/iladlc.go
@@ -0,0 +1,33 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+// Iladlc scans a matrix for its last non-zero column. Returns -1 if the matrix
+// is all zeros.
+//
+// Iladlc is an internal routine. It is exported for testing purposes.
+func (Implementation) Iladlc(m, n int, a []float64, lda int) int {
+	if n == 0 || m == 0 {
+		return n - 1
+	}
+	checkMatrix(m, n, a, lda)
+
+	// Test common case where corner is non-zero.
+	if a[n-1] != 0 || a[(m-1)*lda+(n-1)] != 0 {
+		return n - 1
+	}
+
+	// Scan each row tracking the highest column seen.
+	highest := -1
+	for i := 0; i < m; i++ {
+		for j := n - 1; j >= 0; j-- {
+			if a[i*lda+j] != 0 {
+				highest = max(highest, j)
+				break
+			}
+		}
+	}
+	return highest
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/iladlr.go b/vendor/gonum.org/v1/gonum/lapack/gonum/iladlr.go
new file mode 100644
index 00000000..1ec7c523
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/iladlr.go
@@ -0,0 +1,30 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+// Iladlr scans a matrix for its last non-zero row. Returns -1 if the matrix
+// is all zeros.
+//
+// Iladlr is an internal routine. It is exported for testing purposes.
+func (Implementation) Iladlr(m, n int, a []float64, lda int) int {
+	if m == 0 {
+		return m - 1
+	}
+
+	checkMatrix(m, n, a, lda)
+
+	// Check the common case where the corner is non-zero
+	if a[(m-1)*lda] != 0 || a[(m-1)*lda+n-1] != 0 {
+		return m - 1
+	}
+	for i := m - 1; i >= 0; i-- {
+		for j := 0; j < n; j++ {
+			if a[i*lda+j] != 0 {
+				return i
+			}
+		}
+	}
+	return -1
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/ilaenv.go b/vendor/gonum.org/v1/gonum/lapack/gonum/ilaenv.go
new file mode 100644
index 00000000..750e3c44
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/ilaenv.go
@@ -0,0 +1,387 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+// Ilaenv returns algorithm tuning parameters for the algorithm given by the
+// input string. ispec specifies the parameter to return:
+//  1: The optimal block size for a blocked algorithm.
+//  2: The minimum block size for a blocked algorithm.
+//  3: The block size of unprocessed data at which a blocked algorithm should
+//     crossover to an unblocked version.
+//  4: The number of shifts.
+//  5: The minimum column dimension for blocking to be used.
+//  6: The crossover point for SVD (to use QR factorization or not).
+//  7: The number of processors.
+//  8: The crossover point for multi-shift in QR and QZ methods for non-symmetric eigenvalue problems.
+//  9: Maximum size of the subproblems in divide-and-conquer algorithms.
+//  10: ieee NaN arithmetic can be trusted not to trap.
+//  11: infinity arithmetic can be trusted not to trap.
+//  12...16: parameters for Dhseqr and related functions. See Iparmq for more
+//           information.
+//
+// Ilaenv is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Ilaenv(ispec int, s string, opts string, n1, n2, n3, n4 int) int {
+	// TODO(btracey): Replace this with a constant lookup? A list of constants?
+	sname := s[0] == 'S' || s[0] == 'D'
+	cname := s[0] == 'C' || s[0] == 'Z'
+	if !sname && !cname {
+		panic("lapack: bad name")
+	}
+	c2 := s[1:3]
+	c3 := s[3:6]
+	c4 := c3[1:3]
+
+	switch ispec {
+	default:
+		panic("lapack: bad ispec")
+	case 1:
+		switch c2 {
+		default:
+			panic("lapack: bad function name")
+		case "GE":
+			switch c3 {
+			default:
+				panic("lapack: bad function name")
+			case "TRF":
+				if sname {
+					return 64
+				}
+				return 64
+			case "QRF", "RQF", "LQF", "QLF":
+				if sname {
+					return 32
+				}
+				return 32
+			case "HRD":
+				if sname {
+					return 32
+				}
+				return 32
+			case "BRD":
+				if sname {
+					return 32
+				}
+				return 32
+			case "TRI":
+				if sname {
+					return 64
+				}
+				return 64
+			}
+		case "PO":
+			switch c3 {
+			default:
+				panic("lapack: bad function name")
+			case "TRF":
+				if sname {
+					return 64
+				}
+				return 64
+			}
+		case "SY":
+			switch c3 {
+			default:
+				panic("lapack: bad function name")
+			case "TRF":
+				if sname {
+					return 64
+				}
+				return 64
+			case "TRD":
+				return 32
+			case "GST":
+				return 64
+			}
+		case "HE":
+			switch c3 {
+			default:
+				panic("lapack: bad function name")
+			case "TRF":
+				return 64
+			case "TRD":
+				return 32
+			case "GST":
+				return 64
+			}
+		case "OR":
+			switch c3[0] {
+			default:
+				panic("lapack: bad function name")
+			case 'G':
+				switch c3[1:] {
+				default:
+					panic("lapack: bad function name")
+				case "QR", "RQ", "LQ", "QL", "HR", "TR", "BR":
+					return 32
+				}
+			case 'M':
+				switch c3[1:] {
+				default:
+					panic("lapack: bad function name")
+				case "QR", "RQ", "LQ", "QL", "HR", "TR", "BR":
+					return 32
+				}
+			}
+		case "UN":
+			switch c3[0] {
+			default:
+				panic("lapack: bad function name")
+			case 'G':
+				switch c3[1:] {
+				default:
+					panic("lapack: bad function name")
+				case "QR", "RQ", "LQ", "QL", "HR", "TR", "BR":
+					return 32
+				}
+			case 'M':
+				switch c3[1:] {
+				default:
+					panic("lapack: bad function name")
+				case "QR", "RQ", "LQ", "QL", "HR", "TR", "BR":
+					return 32
+				}
+			}
+		case "GB":
+			switch c3 {
+			default:
+				panic("lapack: bad function name")
+			case "TRF":
+				if sname {
+					if n4 <= 64 {
+						return 1
+					}
+					return 32
+				}
+				if n4 <= 64 {
+					return 1
+				}
+				return 32
+			}
+		case "PB":
+			switch c3 {
+			default:
+				panic("lapack: bad function name")
+			case "TRF":
+				if sname {
+					if n4 <= 64 {
+						return 1
+					}
+					return 32
+				}
+				if n4 <= 64 {
+					return 1
+				}
+				return 32
+			}
+		case "TR":
+			switch c3 {
+			default:
+				panic("lapack: bad function name")
+			case "TRI":
+				if sname {
+					return 64
+				}
+				return 64
+			case "EVC":
+				if sname {
+					return 64
+				}
+				return 64
+			}
+		case "LA":
+			switch c3 {
+			default:
+				panic("lapack: bad function name")
+			case "UUM":
+				if sname {
+					return 64
+				}
+				return 64
+			}
+		case "ST":
+			if sname && c3 == "EBZ" {
+				return 1
+			}
+			panic("lapack: bad function name")
+		}
+	case 2:
+		switch c2 {
+		default:
+			panic("lapack: bad function name")
+		case "GE":
+			switch c3 {
+			default:
+				panic("lapack: bad function name")
+			case "QRF", "RQF", "LQF", "QLF":
+				if sname {
+					return 2
+				}
+				return 2
+			case "HRD":
+				if sname {
+					return 2
+				}
+				return 2
+			case "BRD":
+				if sname {
+					return 2
+				}
+				return 2
+			case "TRI":
+				if sname {
+					return 2
+				}
+				return 2
+			}
+		case "SY":
+			switch c3 {
+			default:
+				panic("lapack: bad function name")
+			case "TRF":
+				if sname {
+					return 8
+				}
+				return 8
+			case "TRD":
+				if sname {
+					return 2
+				}
+				panic("lapack: bad function name")
+			}
+		case "HE":
+			if c3 == "TRD" {
+				return 2
+			}
+			panic("lapack: bad function name")
+		case "OR":
+			if !sname {
+				panic("lapack: bad function name")
+			}
+			switch c3[0] {
+			default:
+				panic("lapack: bad function name")
+			case 'G':
+				switch c4 {
+				default:
+					panic("lapack: bad function name")
+				case "QR", "RQ", "LQ", "QL", "HR", "TR", "BR":
+					return 2
+				}
+			case 'M':
+				switch c4 {
+				default:
+					panic("lapack: bad function name")
+				case "QR", "RQ", "LQ", "QL", "HR", "TR", "BR":
+					return 2
+				}
+			}
+		case "UN":
+			switch c3[0] {
+			default:
+				panic("lapack: bad function name")
+			case 'G':
+				switch c4 {
+				default:
+					panic("lapack: bad function name")
+				case "QR", "RQ", "LQ", "QL", "HR", "TR", "BR":
+					return 2
+				}
+			case 'M':
+				switch c4 {
+				default:
+					panic("lapack: bad function name")
+				case "QR", "RQ", "LQ", "QL", "HR", "TR", "BR":
+					return 2
+				}
+			}
+		}
+	case 3:
+		switch c2 {
+		default:
+			panic("lapack: bad function name")
+		case "GE":
+			switch c3 {
+			default:
+				panic("lapack: bad function name")
+			case "QRF", "RQF", "LQF", "QLF":
+				if sname {
+					return 128
+				}
+				return 128
+			case "HRD":
+				if sname {
+					return 128
+				}
+				return 128
+			case "BRD":
+				if sname {
+					return 128
+				}
+				return 128
+			}
+		case "SY":
+			if sname && c3 == "TRD" {
+				return 32
+			}
+			panic("lapack: bad function name")
+		case "HE":
+			if c3 == "TRD" {
+				return 32
+			}
+			panic("lapack: bad function name")
+		case "OR":
+			switch c3[0] {
+			default:
+				panic("lapack: bad function name")
+			case 'G':
+				switch c4 {
+				default:
+					panic("lapack: bad function name")
+				case "QR", "RQ", "LQ", "QL", "HR", "TR", "BR":
+					return 128
+				}
+			}
+		case "UN":
+			switch c3[0] {
+			default:
+				panic("lapack: bad function name")
+			case 'G':
+				switch c4 {
+				default:
+					panic("lapack: bad function name")
+				case "QR", "RQ", "LQ", "QL", "HR", "TR", "BR":
+					return 128
+				}
+			}
+		}
+	case 4:
+		// Used by xHSEQR
+		return 6
+	case 5:
+		// Not used
+		return 2
+	case 6:
+		// Used by xGELSS and xGESVD
+		return int(float64(min(n1, n2)) * 1.6)
+	case 7:
+		// Not used
+		return 1
+	case 8:
+		// Used by xHSEQR
+		return 50
+	case 9:
+		// used by xGELSD and xGESDD
+		return 25
+	case 10:
+		// Go guarantees ieee
+		return 1
+	case 11:
+		// Go guarantees ieee
+		return 1
+	case 12, 13, 14, 15, 16:
+		// Dhseqr and related functions for eigenvalue problems.
+		return impl.Iparmq(ispec, s, opts, n1, n2, n3, n4)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/iparmq.go b/vendor/gonum.org/v1/gonum/lapack/gonum/iparmq.go
new file mode 100644
index 00000000..4fc255c5
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/iparmq.go
@@ -0,0 +1,115 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "math"
+
+// Iparmq returns problem and machine dependent parameters useful for Dhseqr and
+// related subroutines for eigenvalue problems.
+//
+// ispec specifies the parameter to return:
+//  12: Crossover point between Dlahqr and Dlaqr0. Will be at least 11.
+//  13: Deflation window size.
+//  14: Nibble crossover point. Determines when to skip a multi-shift QR sweep.
+//  15: Number of simultaneous shifts in a multishift QR iteration.
+//  16: Select structured matrix multiply.
+// For other values of ispec Iparmq will panic.
+//
+// name is the name of the calling function. name must be in uppercase but this
+// is not checked.
+//
+// opts is not used and exists for future use.
+//
+// n is the order of the Hessenberg matrix H.
+//
+// ilo and ihi specify the block [ilo:ihi+1,ilo:ihi+1] that is being processed.
+//
+// lwork is the amount of workspace available.
+//
+// Except for ispec input parameters are not checked.
+//
+// Iparmq is an internal routine. It is exported for testing purposes.
+func (Implementation) Iparmq(ispec int, name, opts string, n, ilo, ihi, lwork int) int {
+	nh := ihi - ilo + 1
+	ns := 2
+	switch {
+	case nh >= 30:
+		ns = 4
+	case nh >= 60:
+		ns = 10
+	case nh >= 150:
+		ns = max(10, nh/int(math.Log(float64(nh))/math.Ln2))
+	case nh >= 590:
+		ns = 64
+	case nh >= 3000:
+		ns = 128
+	case nh >= 6000:
+		ns = 256
+	}
+	ns = max(2, ns-(ns%2))
+
+	switch ispec {
+	default:
+		panic("lapack: bad ispec")
+
+	case 12:
+		// Matrices of order smaller than nmin get sent to Dlahqr, the
+		// classic double shift algorithm. This must be at least 11.
+		const nmin = 75
+		return nmin
+
+	case 13:
+		const knwswp = 500
+		if nh <= knwswp {
+			return ns
+		}
+		return 3 * ns / 2
+
+	case 14:
+		// Skip a computationally expensive multi-shift QR sweep with
+		// Dlaqr5 whenever aggressive early deflation finds at least
+		// nibble*(window size)/100 deflations. The default, small,
+		// value reflects the expectation that the cost of looking
+		// through the deflation window with Dlaqr3 will be
+		// substantially smaller.
+		const nibble = 14
+		return nibble
+
+	case 15:
+		return ns
+
+	case 16:
+		if len(name) != 6 {
+			panic("lapack: bad name")
+		}
+		const (
+			k22min = 14
+			kacmin = 14
+		)
+		var acc22 int
+		switch {
+		case name[1:] == "GGHRD" || name[1:] == "GGHD3":
+			acc22 = 1
+			if nh >= k22min {
+				acc22 = 2
+			}
+		case name[3:] == "EXC":
+			if nh >= kacmin {
+				acc22 = 1
+			}
+			if nh >= k22min {
+				acc22 = 2
+			}
+		case name[1:] == "HSEQR" || name[1:5] == "LAQR":
+			if ns >= kacmin {
+				acc22 = 1
+			}
+			if ns >= k22min {
+				acc22 = 2
+			}
+		}
+		return acc22
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/lapack_test.go b/vendor/gonum.org/v1/gonum/lapack/gonum/lapack_test.go
new file mode 100644
index 00000000..5a34fa85
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/lapack_test.go
@@ -0,0 +1,441 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/lapack/testlapack"
+)
+
+var appengine bool
+
+var impl = Implementation{}
+
+func TestDbdsqr(t *testing.T) {
+	testlapack.DbdsqrTest(t, impl)
+}
+
+func TestDhseqr(t *testing.T) {
+	testlapack.DhseqrTest(t, impl)
+}
+
+func TestDgebak(t *testing.T) {
+	testlapack.DgebakTest(t, impl)
+}
+
+func TestDgebal(t *testing.T) {
+	testlapack.DgebalTest(t, impl)
+}
+
+func TestDgebd2(t *testing.T) {
+	testlapack.Dgebd2Test(t, impl)
+}
+
+func TestDgebrd(t *testing.T) {
+	if appengine {
+		t.Skip("non-asm implementation fails test")
+	}
+	testlapack.DgebrdTest(t, impl)
+}
+
+func TestDgecon(t *testing.T) {
+	testlapack.DgeconTest(t, impl)
+}
+
+func TestDgeev(t *testing.T) {
+	if appengine {
+		t.Skip("non-asm implementation fails test")
+	}
+	testlapack.DgeevTest(t, impl)
+}
+
+func TestDgehd2(t *testing.T) {
+	testlapack.Dgehd2Test(t, impl)
+}
+
+func TestDgehrd(t *testing.T) {
+	testlapack.DgehrdTest(t, impl)
+}
+
+func TestDgelqf(t *testing.T) {
+	testlapack.DgelqfTest(t, impl)
+}
+
+func TestDgelq2(t *testing.T) {
+	testlapack.Dgelq2Test(t, impl)
+}
+
+func TestDgeql2(t *testing.T) {
+	testlapack.Dgeql2Test(t, impl)
+}
+
+func TestDgels(t *testing.T) {
+	testlapack.DgelsTest(t, impl)
+}
+
+func TestDgerq2(t *testing.T) {
+	testlapack.Dgerq2Test(t, impl)
+}
+
+func TestDgeqp3(t *testing.T) {
+	testlapack.Dgeqp3Test(t, impl)
+}
+
+func TestDgeqr2(t *testing.T) {
+	testlapack.Dgeqr2Test(t, impl)
+}
+
+func TestDgeqrf(t *testing.T) {
+	testlapack.DgeqrfTest(t, impl)
+}
+
+func TestDgerqf(t *testing.T) {
+	testlapack.DgerqfTest(t, impl)
+}
+
+func TestDgesvd(t *testing.T) {
+	testlapack.DgesvdTest(t, impl)
+}
+
+func TestDgetri(t *testing.T) {
+	testlapack.DgetriTest(t, impl)
+}
+
+func TestDgetf2(t *testing.T) {
+	testlapack.Dgetf2Test(t, impl)
+}
+
+func TestDgetrf(t *testing.T) {
+	testlapack.DgetrfTest(t, impl)
+}
+
+func TestDgetrs(t *testing.T) {
+	testlapack.DgetrsTest(t, impl)
+}
+
+func TestDggsvd3(t *testing.T) {
+	testlapack.Dggsvd3Test(t, impl)
+}
+
+func TestDggsvp3(t *testing.T) {
+	testlapack.Dggsvp3Test(t, impl)
+}
+
+func TestDlabrd(t *testing.T) {
+	testlapack.DlabrdTest(t, impl)
+}
+
+func TestDlacn2(t *testing.T) {
+	testlapack.Dlacn2Test(t, impl)
+}
+
+func TestDlacpy(t *testing.T) {
+	testlapack.DlacpyTest(t, impl)
+}
+
+func TestDlae2(t *testing.T) {
+	testlapack.Dlae2Test(t, impl)
+}
+
+func TestDlaev2(t *testing.T) {
+	testlapack.Dlaev2Test(t, impl)
+}
+
+func TestDlaexc(t *testing.T) {
+	testlapack.DlaexcTest(t, impl)
+}
+
+func TestDlags2(t *testing.T) {
+	testlapack.Dlags2Test(t, impl)
+}
+
+func TestDlahqr(t *testing.T) {
+	testlapack.DlahqrTest(t, impl)
+}
+
+func TestDlahr2(t *testing.T) {
+	testlapack.Dlahr2Test(t, impl)
+}
+
+func TestDlaln2(t *testing.T) {
+	testlapack.Dlaln2Test(t, impl)
+}
+
+func TestDlange(t *testing.T) {
+	testlapack.DlangeTest(t, impl)
+}
+
+func TestDlapy2(t *testing.T) {
+	testlapack.Dlapy2Test(t, impl)
+}
+
+func TestDlapll(t *testing.T) {
+	testlapack.DlapllTest(t, impl)
+}
+
+func TestDlapmt(t *testing.T) {
+	testlapack.DlapmtTest(t, impl)
+}
+
+func TestDlas2(t *testing.T) {
+	testlapack.Dlas2Test(t, impl)
+}
+
+func TestDlascl(t *testing.T) {
+	testlapack.DlasclTest(t, impl)
+}
+
+func TestDlaset(t *testing.T) {
+	testlapack.DlasetTest(t, impl)
+}
+
+func TestDlasrt(t *testing.T) {
+	testlapack.DlasrtTest(t, impl)
+}
+
+func TestDlaswp(t *testing.T) {
+	testlapack.DlaswpTest(t, impl)
+}
+
+func TestDlasy2(t *testing.T) {
+	testlapack.Dlasy2Test(t, impl)
+}
+
+func TestDlanst(t *testing.T) {
+	testlapack.DlanstTest(t, impl)
+}
+
+func TestDlansy(t *testing.T) {
+	testlapack.DlansyTest(t, impl)
+}
+
+func TestDlantr(t *testing.T) {
+	testlapack.DlantrTest(t, impl)
+}
+
+func TestDlanv2(t *testing.T) {
+	testlapack.Dlanv2Test(t, impl)
+}
+
+func TestDlaqr04(t *testing.T) {
+	testlapack.Dlaqr04Test(t, impl)
+}
+
+func TestDlaqp2(t *testing.T) {
+	testlapack.Dlaqp2Test(t, impl)
+}
+
+func TestDlaqps(t *testing.T) {
+	testlapack.DlaqpsTest(t, impl)
+}
+
+func TestDlaqr1(t *testing.T) {
+	testlapack.Dlaqr1Test(t, impl)
+}
+
+func TestDlaqr23(t *testing.T) {
+	testlapack.Dlaqr23Test(t, impl)
+}
+
+func TestDlaqr5(t *testing.T) {
+	testlapack.Dlaqr5Test(t, impl)
+}
+
+func TestDlarf(t *testing.T) {
+	testlapack.DlarfTest(t, impl)
+}
+
+func TestDlarfb(t *testing.T) {
+	testlapack.DlarfbTest(t, impl)
+}
+
+func TestDlarfg(t *testing.T) {
+	testlapack.DlarfgTest(t, impl)
+}
+
+func TestDlarft(t *testing.T) {
+	testlapack.DlarftTest(t, impl)
+}
+
+func TestDlarfx(t *testing.T) {
+	testlapack.DlarfxTest(t, impl)
+}
+
+func TestDlartg(t *testing.T) {
+	testlapack.DlartgTest(t, impl)
+}
+
+func TestDlasq1(t *testing.T) {
+	testlapack.Dlasq1Test(t, impl)
+}
+
+func TestDlasq2(t *testing.T) {
+	testlapack.Dlasq2Test(t, impl)
+}
+
+func TestDlasq3(t *testing.T) {
+	testlapack.Dlasq3Test(t, impl)
+}
+
+func TestDlasq4(t *testing.T) {
+	testlapack.Dlasq4Test(t, impl)
+}
+
+func TestDlasq5(t *testing.T) {
+	testlapack.Dlasq5Test(t, impl)
+}
+
+func TestDlasr(t *testing.T) {
+	testlapack.DlasrTest(t, impl)
+}
+
+func TestDlasv2(t *testing.T) {
+	testlapack.Dlasv2Test(t, impl)
+}
+
+func TestDlatrd(t *testing.T) {
+	testlapack.DlatrdTest(t, impl)
+}
+
+func TestDlatrs(t *testing.T) {
+	testlapack.DlatrsTest(t, impl)
+}
+
+func TestDorg2r(t *testing.T) {
+	testlapack.Dorg2rTest(t, impl)
+}
+
+func TestDorgbr(t *testing.T) {
+	testlapack.DorgbrTest(t, impl)
+}
+
+func TestDorghr(t *testing.T) {
+	testlapack.DorghrTest(t, impl)
+}
+
+func TestDorg2l(t *testing.T) {
+	testlapack.Dorg2lTest(t, impl)
+}
+
+func TestDorgl2(t *testing.T) {
+	testlapack.Dorgl2Test(t, impl)
+}
+
+func TestDorglq(t *testing.T) {
+	testlapack.DorglqTest(t, impl)
+}
+
+func TestDorgql(t *testing.T) {
+	testlapack.DorgqlTest(t, impl)
+}
+
+func TestDorgqr(t *testing.T) {
+	testlapack.DorgqrTest(t, impl)
+}
+
+func TestDorgtr(t *testing.T) {
+	testlapack.DorgtrTest(t, impl)
+}
+
+func TestDormbr(t *testing.T) {
+	testlapack.DormbrTest(t, impl)
+}
+
+func TestDormhr(t *testing.T) {
+	testlapack.DormhrTest(t, impl)
+}
+
+func TestDorml2(t *testing.T) {
+	testlapack.Dorml2Test(t, impl)
+}
+
+func TestDormlq(t *testing.T) {
+	testlapack.DormlqTest(t, impl)
+}
+
+func TestDormqr(t *testing.T) {
+	testlapack.DormqrTest(t, impl)
+}
+
+func TestDormr2(t *testing.T) {
+	testlapack.Dormr2Test(t, impl)
+}
+
+func TestDorm2r(t *testing.T) {
+	testlapack.Dorm2rTest(t, impl)
+}
+
+func TestDpbtf2(t *testing.T) {
+	testlapack.Dpbtf2Test(t, impl)
+}
+
+func TestDpocon(t *testing.T) {
+	testlapack.DpoconTest(t, impl)
+}
+
+func TestDpotf2(t *testing.T) {
+	testlapack.Dpotf2Test(t, impl)
+}
+
+func TestDpotrf(t *testing.T) {
+	testlapack.DpotrfTest(t, impl)
+}
+
+func TestDrscl(t *testing.T) {
+	testlapack.DrsclTest(t, impl)
+}
+
+func TestDsteqr(t *testing.T) {
+	testlapack.DsteqrTest(t, impl)
+}
+
+func TestDsterf(t *testing.T) {
+	testlapack.DsterfTest(t, impl)
+}
+
+func TestDsyev(t *testing.T) {
+	testlapack.DsyevTest(t, impl)
+}
+
+func TestDsytd2(t *testing.T) {
+	testlapack.Dsytd2Test(t, impl)
+}
+
+func TestDsytrd(t *testing.T) {
+	testlapack.DsytrdTest(t, impl)
+}
+
+func TestDtgsja(t *testing.T) {
+	testlapack.DtgsjaTest(t, impl)
+}
+
+func TestDtrcon(t *testing.T) {
+	testlapack.DtrconTest(t, impl)
+}
+
+func TestDtrevc3(t *testing.T) {
+	testlapack.Dtrevc3Test(t, impl)
+}
+
+func TestDtrexc(t *testing.T) {
+	testlapack.DtrexcTest(t, impl)
+}
+
+func TestDtrti2(t *testing.T) {
+	testlapack.Dtrti2Test(t, impl)
+}
+
+func TestDtrtri(t *testing.T) {
+	testlapack.DtrtriTest(t, impl)
+}
+
+func TestIladlc(t *testing.T) {
+	testlapack.IladlcTest(t, impl)
+}
+
+func TestIladlr(t *testing.T) {
+	testlapack.IladlrTest(t, impl)
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlahr2test/main.go b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlahr2test/main.go
new file mode 100644
index 00000000..d2c5b604
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlahr2test/main.go
@@ -0,0 +1,101 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// dlahr2test generates test data for Dlahr2. Test cases are stored in
+// gzip-compressed JSON file testlapack/testdata/dlahr2data.json.gz which is
+// read during testing by testlapack/dlahr2.go.
+//
+// This program uses cgo to call Fortran version of DLAHR2. Therefore, matrices
+// passed to the Fortran routine are in column-major format but are written into
+// the output file in row-major format.
+package main
+
+import (
+	"compress/gzip"
+	"encoding/json"
+	"log"
+	"math/rand"
+	"os"
+	"path/filepath"
+
+	"gonum.org/v1/gonum/lapack/internal/testdata/netlib"
+)
+
+type Dlahr2Test struct {
+	N, K, NB int
+	A        []float64
+
+	AWant   []float64
+	TWant   []float64
+	YWant   []float64
+	TauWant []float64
+}
+
+func main() {
+	file, err := os.Create(filepath.FromSlash("../../../testlapack/testdata/dlahr2data.json.gz"))
+	if err != nil {
+		log.Fatal(err)
+	}
+	defer file.Close()
+	w := gzip.NewWriter(file)
+
+	rnd := rand.New(rand.NewSource(1))
+
+	var tests []Dlahr2Test
+	for _, n := range []int{4, 5, 6, 7, 11} {
+		for k := 0; k <= n/2; k++ {
+			for nb := 1; nb <= k; nb++ {
+				ain := genrand(n, n-k+1, rnd)
+				a := make([]float64, len(ain))
+				copy(a, ain)
+
+				t := genrand(nb, nb, rnd)
+				y := genrand(n, nb, rnd)
+				tau := genrand(nb, 1, rnd)
+
+				netlib.Dlahr2(n, k, nb, a, n, tau, t, nb, y, n)
+
+				tests = append(tests, Dlahr2Test{
+					N:       n,
+					K:       k,
+					NB:      nb,
+					A:       rowMajor(n, n-k+1, ain),
+					AWant:   rowMajor(n, n-k+1, a),
+					TWant:   rowMajor(nb, nb, t),
+					YWant:   rowMajor(n, nb, y),
+					TauWant: tau,
+				})
+			}
+		}
+	}
+	json.NewEncoder(w).Encode(tests)
+
+	err = w.Close()
+	if err != nil {
+		log.Fatal(err)
+	}
+}
+
+// genrand returns a general r×c matrix with random entries.
+func genrand(r, c int, rnd *rand.Rand) []float64 {
+	m := make([]float64, r*c)
+	for i := range m {
+		m[i] = rnd.NormFloat64()
+	}
+	return m
+}
+
+// rowMajor returns the given r×c column-major matrix a in row-major format.
+func rowMajor(r, c int, a []float64) []float64 {
+	if len(a) != r*c {
+		panic("testdata: slice length mismatch")
+	}
+	m := make([]float64, len(a))
+	for i := 0; i < r; i++ {
+		for j := 0; j < c; j++ {
+			m[i*c+j] = a[i+j*r]
+		}
+	}
+	return m
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlaqr5test/main.go b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlaqr5test/main.go
new file mode 100644
index 00000000..b3980e93
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlaqr5test/main.go
@@ -0,0 +1,185 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// This program generates test data for Dlaqr5. Test cases are stored in
+// gzip-compressed JSON file testlapack/testdata/dlaqr5data.json.gz which is
+// read during testing by testlapack/dlaqr5.go.
+//
+// This program uses cgo to call Fortran version of DLAQR5. Therefore, matrices
+// passed to the Fortran routine are in column-major format but are written into
+// the output file in row-major format.
+package main
+
+import (
+	"compress/gzip"
+	"encoding/json"
+	"log"
+	"math/rand"
+	"os"
+	"path/filepath"
+
+	"gonum.org/v1/gonum/lapack/internal/testdata/netlib"
+)
+
+type Dlaqr5Test struct {
+	WantT          bool
+	N              int
+	NShifts        int
+	KTop, KBot     int
+	ShiftR, ShiftI []float64
+	H              []float64
+
+	HWant []float64
+	ZWant []float64
+}
+
+func main() {
+	file, err := os.Create(filepath.FromSlash("../../../testlapack/testdata/dlaqr5data.json.gz"))
+	if err != nil {
+		log.Fatal(err)
+	}
+	defer file.Close()
+	w := gzip.NewWriter(file)
+
+	rnd := rand.New(rand.NewSource(1))
+
+	var tests []Dlaqr5Test
+	for _, wantt := range []bool{true, false} {
+		for _, n := range []int{2, 3, 4, 5, 6, 7, 11} {
+			for k := 0; k <= min(5, n); k++ {
+				npairs := k
+				if npairs == 0 {
+					npairs = 2 * n
+				}
+				for ktop := 0; ktop < n-1; ktop++ {
+					for kbot := ktop + 1; kbot < n; kbot++ {
+						sr, si := shiftpairs(npairs, rnd)
+						nshfts := len(sr)
+
+						v := genrand(nshfts/2, 3, rnd)
+						u := genrand(3*nshfts-3, 3*nshfts-3, rnd)
+						wh := genrand(3*nshfts-3, n, rnd)
+						nh := n
+						wv := genrand(n, 3*nshfts-3, rnd)
+						nv := n
+
+						h := hessrand(n, rnd)
+						if ktop > 0 {
+							h[ktop+(ktop-1)*n] = 0
+						}
+						if kbot < n-1 {
+							h[kbot+1+kbot*n] = 0
+						}
+						hin := make([]float64, len(h))
+						copy(hin, h)
+						z := eye(n)
+
+						netlib.Dlaqr5(wantt, true, 2,
+							n, ktop+1, kbot+1,
+							nshfts, sr, si,
+							h, n,
+							1, n, z, n,
+							v, 3,
+							u, 3*nshfts-3,
+							nh, wh, nh,
+							nv, wv, 3*nshfts-3)
+
+						tests = append(tests, Dlaqr5Test{
+							WantT:   wantt,
+							N:       n,
+							NShifts: nshfts,
+							KTop:    ktop,
+							KBot:    kbot,
+							ShiftR:  sr,
+							ShiftI:  si,
+							H:       rowMajor(n, n, hin),
+							HWant:   rowMajor(n, n, h),
+							ZWant:   rowMajor(n, n, z),
+						})
+					}
+				}
+			}
+		}
+	}
+	json.NewEncoder(w).Encode(tests)
+
+	err = w.Close()
+	if err != nil {
+		log.Fatal(err)
+	}
+}
+
+// genrand returns a general r×c matrix with random entries.
+func genrand(r, c int, rnd *rand.Rand) []float64 {
+	m := make([]float64, r*c)
+	for i := range m {
+		m[i] = rnd.NormFloat64()
+	}
+	return m
+}
+
+// eye returns an identity matrix of order n.
+func eye(n int) []float64 {
+	m := make([]float64, n*n)
+	for i := 0; i < n*n; i += n + 1 {
+		m[i] = 1
+	}
+	return m
+}
+
+// hessrand returns a Hessenberg matrix of order n with random non-zero entries
+// in column-major format.
+func hessrand(n int, rnd *rand.Rand) []float64 {
+	h := make([]float64, n*n)
+	for j := 0; j < n; j++ {
+		for i := 0; i <= min(j+1, n-1); i++ {
+			h[i+j*n] = rnd.NormFloat64()
+		}
+	}
+	return h
+}
+
+// shiftpairs generates k real and complex conjugate shift pairs. That is, the
+// length of sr and si is 2*k.
+func shiftpairs(k int, rnd *rand.Rand) (sr, si []float64) {
+	sr = make([]float64, 2*k)
+	si = make([]float64, 2*k)
+	for i := 0; i < len(sr); {
+		if rnd.Float64() < 0.5 || i == len(sr)-1 {
+			sr[i] = rnd.NormFloat64()
+			i++
+			continue
+		}
+		// Generate a complex conjugate pair.
+		r := rnd.NormFloat64()
+		c := rnd.NormFloat64()
+		sr[i] = r
+		si[i] = c
+		sr[i+1] = r
+		si[i+1] = -c
+		i += 2
+	}
+	return sr, si
+}
+
+// rowMajor returns the given r×c column-major matrix a in row-major format.
+func rowMajor(r, c int, a []float64) []float64 {
+	if len(a) != r*c {
+		panic("testdata: slice length mismatch")
+	}
+	m := make([]float64, len(a))
+	for i := 0; i < r; i++ {
+		for j := 0; j < c; j++ {
+			m[i*c+j] = a[i+j*r]
+		}
+	}
+	return m
+}
+
+func min(a, b int) int {
+	if a < b {
+		return a
+	}
+	return b
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/Makefile b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/Makefile
new file mode 100644
index 00000000..f9f94446
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/Makefile
@@ -0,0 +1,27 @@
+FC = gfortran
+FFLAGS = -O2
+
+targets = testdlasq1 testdlasq2 testdlasq3 testdlasq4
+objects = dlamch.o lsame.o xerbla.o ieeeck.o iparmq.o ilaenv.o dlasrt.o \
+          dlaisnan.o disnan.o dlasq6.o dlasq5.o dlasq4.o dlasq3.o dlasq2.o
+
+default : $(targets)
+.PHONY : default
+
+testdlasq1 : testdlasq1.o $(objects) dcopy.o dlas2.o dlascl.o dlasq1.o
+
+testdlasq2 : testdlasq2.o $(objects)
+
+testdlasq3 : testdlasq3.o $(objects)
+
+testdlasq4 : testdlasq4.o $(objects)
+
+% : %.o
+	$(FC) $(FFLAGS) $^ -o $@
+
+%.o : %.f90
+	$(FC) $(FFLAGS) -c -o $@ $<
+
+clean :
+	rm -f *.o $(targets) *.txt
+.PHONY : clean
\ No newline at end of file
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/Readme.md b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/Readme.md
new file mode 100644
index 00000000..65c47448
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/Readme.md
@@ -0,0 +1,23 @@
+This set of codes generates tests for the dlasq* routines.
+
+The high level routines are testdlasq*.f90. The testdlasq*.f90 routines are intended in combination with the routines in gonum/lapack/testlapack. 
+During execution, these high-level routines record the inputs and outputs
+to the executed subroutines. For example, testdlasq3, when executed,
+generates files gen4tests.txt and gen5tests.txt that record the inputs
+and outputs to the evaluation of dlasq4 and dlasq5 respectively. The output 
+format in gen*tests.txt is the struct literal that matches the respective test
+in gonum/lapack/testlapack/dlasq*.go. Thus, these generated tests can be copied
+into the testing routine to test the native implementation.
+
+The testing routines in testlapack have code for generating inputs for these 
+fortran routines. Typically, one would isolate the particular failing test,
+and modify the testlapack routine to print it to the terminal, for example
+in testlapack/dlasq3.go one might add
+
+    printDlasq3FortranInput(test)
+    os.Exit(1)
+
+This prints variable initialization for dlasq3 routine to the terminal, which
+can be copied and pasted into testdlasq3.f90. Please note that this process
+is not completely automated. Some of the other initialization may need to
+change, particularly the size allocation of the data array(s).
\ No newline at end of file
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dcopy.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dcopy.f
new file mode 100644
index 00000000..d9d5ac7a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dcopy.f
@@ -0,0 +1,115 @@
+*> \brief \b DCOPY
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DCOPY(N,DX,INCX,DY,INCY)
+* 
+*       .. Scalar Arguments ..
+*       INTEGER INCX,INCY,N
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION DX(*),DY(*)
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*>    DCOPY copies a vector, x, to a vector, y.
+*>    uses unrolled loops for increments equal to one.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup double_blas_level1
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>     jack dongarra, linpack, 3/11/78.
+*>     modified 12/3/93, array(1) declarations changed to array(*)
+*> \endverbatim
+*>
+*  =====================================================================
+      SUBROUTINE DCOPY(N,DX,INCX,DY,INCY)
+*
+*  -- Reference BLAS level1 routine (version 3.4.0) --
+*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2011
+*
+*     .. Scalar Arguments ..
+      INTEGER INCX,INCY,N
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION DX(*),DY(*)
+*     ..
+*
+*  =====================================================================
+*
+*     .. Local Scalars ..
+      INTEGER I,IX,IY,M,MP1
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC MOD
+*     ..
+      IF (N.LE.0) RETURN
+      IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN
+*
+*        code for both increments equal to 1
+*
+*
+*        clean-up loop
+*
+         M = MOD(N,7)
+         IF (M.NE.0) THEN
+            DO I = 1,M
+               DY(I) = DX(I)
+            END DO
+            IF (N.LT.7) RETURN
+         END IF   
+         MP1 = M + 1
+         DO I = MP1,N,7
+            DY(I) = DX(I)
+            DY(I+1) = DX(I+1)
+            DY(I+2) = DX(I+2)
+            DY(I+3) = DX(I+3)
+            DY(I+4) = DX(I+4)
+            DY(I+5) = DX(I+5)
+            DY(I+6) = DX(I+6)
+         END DO
+      ELSE      
+*
+*        code for unequal increments or equal increments
+*          not equal to 1
+*
+         IX = 1
+         IY = 1
+         IF (INCX.LT.0) IX = (-N+1)*INCX + 1
+         IF (INCY.LT.0) IY = (-N+1)*INCY + 1
+         DO I = 1,N
+            DY(IY) = DX(IX)
+            IX = IX + INCX
+            IY = IY + INCY
+         END DO
+      END IF
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/disnan.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/disnan.f
new file mode 100644
index 00000000..355b8279
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/disnan.f
@@ -0,0 +1,80 @@
+*> \brief \b DISNAN tests input for NaN.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DISNAN + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/disnan.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/disnan.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/disnan.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       LOGICAL FUNCTION DISNAN( DIN )
+* 
+*       .. Scalar Arguments ..
+*       DOUBLE PRECISION   DIN
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DISNAN returns .TRUE. if its argument is NaN, and .FALSE.
+*> otherwise.  To be replaced by the Fortran 2003 intrinsic in the
+*> future.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] DIN
+*> \verbatim
+*>          DIN is DOUBLE PRECISION
+*>          Input to test for NaN.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date September 2012
+*
+*> \ingroup auxOTHERauxiliary
+*
+*  =====================================================================
+      LOGICAL FUNCTION DISNAN( DIN )
+*
+*  -- LAPACK auxiliary routine (version 3.4.2) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     September 2012
+*
+*     .. Scalar Arguments ..
+      DOUBLE PRECISION   DIN
+*     ..
+*
+*  =====================================================================
+*
+*  .. External Functions ..
+      LOGICAL DLAISNAN
+      EXTERNAL DLAISNAN
+*  ..
+*  .. Executable Statements ..
+      DISNAN = DLAISNAN(DIN,DIN)
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlaisnan.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlaisnan.f
new file mode 100644
index 00000000..58595c5c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlaisnan.f
@@ -0,0 +1,91 @@
+*> \brief \b DLAISNAN tests input for NaN by comparing two arguments for inequality.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLAISNAN + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaisnan.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaisnan.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaisnan.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       LOGICAL FUNCTION DLAISNAN( DIN1, DIN2 )
+* 
+*       .. Scalar Arguments ..
+*       DOUBLE PRECISION   DIN1, DIN2
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> This routine is not for general use.  It exists solely to avoid
+*> over-optimization in DISNAN.
+*>
+*> DLAISNAN checks for NaNs by comparing its two arguments for
+*> inequality.  NaN is the only floating-point value where NaN != NaN
+*> returns .TRUE.  To check for NaNs, pass the same variable as both
+*> arguments.
+*>
+*> A compiler must assume that the two arguments are
+*> not the same variable, and the test will not be optimized away.
+*> Interprocedural or whole-program optimization may delete this
+*> test.  The ISNAN functions will be replaced by the correct
+*> Fortran 03 intrinsic once the intrinsic is widely available.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] DIN1
+*> \verbatim
+*>          DIN1 is DOUBLE PRECISION
+*> \endverbatim
+*>
+*> \param[in] DIN2
+*> \verbatim
+*>          DIN2 is DOUBLE PRECISION
+*>          Two numbers to compare for inequality.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date September 2012
+*
+*> \ingroup auxOTHERauxiliary
+*
+*  =====================================================================
+      LOGICAL FUNCTION DLAISNAN( DIN1, DIN2 )
+*
+*  -- LAPACK auxiliary routine (version 3.4.2) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     September 2012
+*
+*     .. Scalar Arguments ..
+      DOUBLE PRECISION   DIN1, DIN2
+*     ..
+*
+*  =====================================================================
+*
+*  .. Executable Statements ..
+      DLAISNAN = (DIN1.NE.DIN2)
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlamch.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlamch.f
new file mode 100644
index 00000000..25c2c8e6
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlamch.f
@@ -0,0 +1,193 @@
+*> \brief \b DLAMCH
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*  Definition:
+*  ===========
+*
+*      DOUBLE PRECISION FUNCTION DLAMCH( CMACH )
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DLAMCH determines double precision machine parameters.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] CMACH
+*> \verbatim
+*>          Specifies the value to be returned by DLAMCH:
+*>          = 'E' or 'e',   DLAMCH := eps
+*>          = 'S' or 's ,   DLAMCH := sfmin
+*>          = 'B' or 'b',   DLAMCH := base
+*>          = 'P' or 'p',   DLAMCH := eps*base
+*>          = 'N' or 'n',   DLAMCH := t
+*>          = 'R' or 'r',   DLAMCH := rnd
+*>          = 'M' or 'm',   DLAMCH := emin
+*>          = 'U' or 'u',   DLAMCH := rmin
+*>          = 'L' or 'l',   DLAMCH := emax
+*>          = 'O' or 'o',   DLAMCH := rmax
+*>          where
+*>          eps   = relative machine precision
+*>          sfmin = safe minimum, such that 1/sfmin does not overflow
+*>          base  = base of the machine
+*>          prec  = eps*base
+*>          t     = number of (base) digits in the mantissa
+*>          rnd   = 1.0 when rounding occurs in addition, 0.0 otherwise
+*>          emin  = minimum exponent before (gradual) underflow
+*>          rmin  = underflow threshold - base**(emin-1)
+*>          emax  = largest exponent before overflow
+*>          rmax  = overflow threshold  - (base**emax)*(1-eps)
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup auxOTHERauxiliary
+*
+*  =====================================================================
+      DOUBLE PRECISION FUNCTION DLAMCH( CMACH )
+*
+*  -- LAPACK auxiliary routine (version 3.4.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2011
+*
+*     .. Scalar Arguments ..
+      CHARACTER          CMACH
+*     ..
+*
+*     .. Scalar Arguments ..
+      DOUBLE PRECISION   A, B
+*     ..
+*
+* =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ONE, ZERO
+      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
+*     ..
+*     .. Local Scalars ..
+      DOUBLE PRECISION   RND, EPS, SFMIN, SMALL, RMACH
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      EXTERNAL           LSAME
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          DIGITS, EPSILON, HUGE, MAXEXPONENT,
+     $                   MINEXPONENT, RADIX, TINY
+*     ..
+*     .. Executable Statements ..
+*
+*
+*     Assume rounding, not chopping. Always.
+*
+      RND = ONE
+*
+      IF( ONE.EQ.RND ) THEN
+         EPS = EPSILON(ZERO) * 0.5
+      ELSE
+         EPS = EPSILON(ZERO)
+      END IF
+*
+      IF( LSAME( CMACH, 'E' ) ) THEN
+         RMACH = EPS
+      ELSE IF( LSAME( CMACH, 'S' ) ) THEN
+         SFMIN = TINY(ZERO)
+         SMALL = ONE / HUGE(ZERO)
+         IF( SMALL.GE.SFMIN ) THEN
+*
+*           Use SMALL plus a bit, to avoid the possibility of rounding
+*           causing overflow when computing  1/sfmin.
+*
+            SFMIN = SMALL*( ONE+EPS )
+         END IF
+         RMACH = SFMIN
+      ELSE IF( LSAME( CMACH, 'B' ) ) THEN
+         RMACH = RADIX(ZERO)
+      ELSE IF( LSAME( CMACH, 'P' ) ) THEN
+         RMACH = EPS * RADIX(ZERO)
+      ELSE IF( LSAME( CMACH, 'N' ) ) THEN
+         RMACH = DIGITS(ZERO)
+      ELSE IF( LSAME( CMACH, 'R' ) ) THEN
+         RMACH = RND
+      ELSE IF( LSAME( CMACH, 'M' ) ) THEN
+         RMACH = MINEXPONENT(ZERO)
+      ELSE IF( LSAME( CMACH, 'U' ) ) THEN
+         RMACH = tiny(zero)
+      ELSE IF( LSAME( CMACH, 'L' ) ) THEN
+         RMACH = MAXEXPONENT(ZERO)
+      ELSE IF( LSAME( CMACH, 'O' ) ) THEN
+         RMACH = HUGE(ZERO)
+      ELSE
+         RMACH = ZERO
+      END IF
+*
+      DLAMCH = RMACH
+      RETURN
+*
+*     End of DLAMCH
+*
+      END
+************************************************************************
+*> \brief \b DLAMC3
+*> \details
+*> \b Purpose:
+*> \verbatim
+*> DLAMC3  is intended to force  A  and  B  to be stored prior to doing
+*> the addition of  A  and  B ,  for use in situations where optimizers
+*> might hold one of these in a register.
+*> \endverbatim
+*> \author LAPACK is a software package provided by Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..
+*> \date November 2011
+*> \ingroup auxOTHERauxiliary
+*>
+*> \param[in] A
+*> \verbatim
+*>          A is a DOUBLE PRECISION
+*> \endverbatim
+*>
+*> \param[in] B
+*> \verbatim
+*>          B is a DOUBLE PRECISION
+*>          The values A and B.
+*> \endverbatim
+*>
+      DOUBLE PRECISION FUNCTION DLAMC3( A, B )
+*
+*  -- LAPACK auxiliary routine (version 3.4.0) --
+*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+*     November 2010
+*
+*     .. Scalar Arguments ..
+      DOUBLE PRECISION   A, B
+*     ..
+* =====================================================================
+*
+*     .. Executable Statements ..
+*
+      DLAMC3 = A + B
+*
+      RETURN
+*
+*     End of DLAMC3
+*
+      END
+*
+************************************************************************
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlas2.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlas2.f
new file mode 100644
index 00000000..81077f94
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlas2.f
@@ -0,0 +1,183 @@
+*> \brief \b DLAS2 computes singular values of a 2-by-2 triangular matrix.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLAS2 + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlas2.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlas2.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlas2.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DLAS2( F, G, H, SSMIN, SSMAX )
+* 
+*       .. Scalar Arguments ..
+*       DOUBLE PRECISION   F, G, H, SSMAX, SSMIN
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DLAS2  computes the singular values of the 2-by-2 matrix
+*>    [  F   G  ]
+*>    [  0   H  ].
+*> On return, SSMIN is the smaller singular value and SSMAX is the
+*> larger singular value.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] F
+*> \verbatim
+*>          F is DOUBLE PRECISION
+*>          The (1,1) element of the 2-by-2 matrix.
+*> \endverbatim
+*>
+*> \param[in] G
+*> \verbatim
+*>          G is DOUBLE PRECISION
+*>          The (1,2) element of the 2-by-2 matrix.
+*> \endverbatim
+*>
+*> \param[in] H
+*> \verbatim
+*>          H is DOUBLE PRECISION
+*>          The (2,2) element of the 2-by-2 matrix.
+*> \endverbatim
+*>
+*> \param[out] SSMIN
+*> \verbatim
+*>          SSMIN is DOUBLE PRECISION
+*>          The smaller singular value.
+*> \endverbatim
+*>
+*> \param[out] SSMAX
+*> \verbatim
+*>          SSMAX is DOUBLE PRECISION
+*>          The larger singular value.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date September 2012
+*
+*> \ingroup auxOTHERauxiliary
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  Barring over/underflow, all output quantities are correct to within
+*>  a few units in the last place (ulps), even in the absence of a guard
+*>  digit in addition/subtraction.
+*>
+*>  In IEEE arithmetic, the code works correctly if one matrix element is
+*>  infinite.
+*>
+*>  Overflow will not occur unless the largest singular value itself
+*>  overflows, or is within a few ulps of overflow. (On machines with
+*>  partial overflow, like the Cray, overflow may occur if the largest
+*>  singular value is within a factor of 2 of overflow.)
+*>
+*>  Underflow is harmless if underflow is gradual. Otherwise, results
+*>  may correspond to a matrix modified by perturbations of size near
+*>  the underflow threshold.
+*> \endverbatim
+*>
+*  =====================================================================
+      SUBROUTINE DLAS2( F, G, H, SSMIN, SSMAX )
+*
+*  -- LAPACK auxiliary routine (version 3.4.2) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     September 2012
+*
+*     .. Scalar Arguments ..
+      DOUBLE PRECISION   F, G, H, SSMAX, SSMIN
+*     ..
+*
+*  ====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ZERO
+      PARAMETER          ( ZERO = 0.0D0 )
+      DOUBLE PRECISION   ONE
+      PARAMETER          ( ONE = 1.0D0 )
+      DOUBLE PRECISION   TWO
+      PARAMETER          ( TWO = 2.0D0 )
+*     ..
+*     .. Local Scalars ..
+      DOUBLE PRECISION   AS, AT, AU, C, FA, FHMN, FHMX, GA, HA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS, MAX, MIN, SQRT
+*     ..
+*     .. Executable Statements ..
+*
+      FA = ABS( F )
+      GA = ABS( G )
+      HA = ABS( H )
+      FHMN = MIN( FA, HA )
+      FHMX = MAX( FA, HA )
+      IF( FHMN.EQ.ZERO ) THEN
+         SSMIN = ZERO
+         IF( FHMX.EQ.ZERO ) THEN
+            SSMAX = GA
+         ELSE
+            SSMAX = MAX( FHMX, GA )*SQRT( ONE+
+     $              ( MIN( FHMX, GA ) / MAX( FHMX, GA ) )**2 )
+         END IF
+      ELSE
+         IF( GA.LT.FHMX ) THEN
+            AS = ONE + FHMN / FHMX
+            AT = ( FHMX-FHMN ) / FHMX
+            AU = ( GA / FHMX )**2
+            C = TWO / ( SQRT( AS*AS+AU )+SQRT( AT*AT+AU ) )
+            SSMIN = FHMN*C
+            SSMAX = FHMX / C
+         ELSE
+            AU = FHMX / GA
+            IF( AU.EQ.ZERO ) THEN
+*
+*              Avoid possible harmful underflow if exponent range
+*              asymmetric (true SSMIN may not underflow even if
+*              AU underflows)
+*
+               SSMIN = ( FHMN*FHMX ) / GA
+               SSMAX = GA
+            ELSE
+               AS = ONE + FHMN / FHMX
+               AT = ( FHMX-FHMN ) / FHMX
+               C = ONE / ( SQRT( ONE+( AS*AU )**2 )+
+     $             SQRT( ONE+( AT*AU )**2 ) )
+               SSMIN = ( FHMN*C )*AU
+               SSMIN = SSMIN + SSMIN
+               SSMAX = GA / ( C+C )
+            END IF
+         END IF
+      END IF
+      RETURN
+*
+*     End of DLAS2
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlascl.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlascl.f
new file mode 100644
index 00000000..9b9b33c0
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlascl.f
@@ -0,0 +1,364 @@
+*> \brief \b DLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLASCL + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlascl.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlascl.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlascl.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER          TYPE
+*       INTEGER            INFO, KL, KU, LDA, M, N
+*       DOUBLE PRECISION   CFROM, CTO
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   A( LDA, * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DLASCL multiplies the M by N real matrix A by the real scalar
+*> CTO/CFROM.  This is done without over/underflow as long as the final
+*> result CTO*A(I,J)/CFROM does not over/underflow. TYPE specifies that
+*> A may be full, upper triangular, lower triangular, upper Hessenberg,
+*> or banded.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] TYPE
+*> \verbatim
+*>          TYPE is CHARACTER*1
+*>          TYPE indices the storage type of the input matrix.
+*>          = 'G':  A is a full matrix.
+*>          = 'L':  A is a lower triangular matrix.
+*>          = 'U':  A is an upper triangular matrix.
+*>          = 'H':  A is an upper Hessenberg matrix.
+*>          = 'B':  A is a symmetric band matrix with lower bandwidth KL
+*>                  and upper bandwidth KU and with the only the lower
+*>                  half stored.
+*>          = 'Q':  A is a symmetric band matrix with lower bandwidth KL
+*>                  and upper bandwidth KU and with the only the upper
+*>                  half stored.
+*>          = 'Z':  A is a band matrix with lower bandwidth KL and upper
+*>                  bandwidth KU. See DGBTRF for storage details.
+*> \endverbatim
+*>
+*> \param[in] KL
+*> \verbatim
+*>          KL is INTEGER
+*>          The lower bandwidth of A.  Referenced only if TYPE = 'B',
+*>          'Q' or 'Z'.
+*> \endverbatim
+*>
+*> \param[in] KU
+*> \verbatim
+*>          KU is INTEGER
+*>          The upper bandwidth of A.  Referenced only if TYPE = 'B',
+*>          'Q' or 'Z'.
+*> \endverbatim
+*>
+*> \param[in] CFROM
+*> \verbatim
+*>          CFROM is DOUBLE PRECISION
+*> \endverbatim
+*>
+*> \param[in] CTO
+*> \verbatim
+*>          CTO is DOUBLE PRECISION
+*>
+*>          The matrix A is multiplied by CTO/CFROM. A(I,J) is computed
+*>          without over/underflow if the final result CTO*A(I,J)/CFROM
+*>          can be represented without over/underflow.  CFROM must be
+*>          nonzero.
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*>          M is INTEGER
+*>          The number of rows of the matrix A.  M >= 0.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The number of columns of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          A is DOUBLE PRECISION array, dimension (LDA,N)
+*>          The matrix to be multiplied by CTO/CFROM.  See TYPE for the
+*>          storage type.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,M).
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          0  - successful exit
+*>          <0 - if INFO = -i, the i-th argument had an illegal value.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date September 2012
+*
+*> \ingroup auxOTHERauxiliary
+*
+*  =====================================================================
+      SUBROUTINE DLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO )
+*
+*  -- LAPACK auxiliary routine (version 3.4.2) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     September 2012
+*
+*     .. Scalar Arguments ..
+      CHARACTER          TYPE
+      INTEGER            INFO, KL, KU, LDA, M, N
+      DOUBLE PRECISION   CFROM, CTO
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   A( LDA, * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ZERO, ONE
+      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
+*     ..
+*     .. Local Scalars ..
+      LOGICAL            DONE
+      INTEGER            I, ITYPE, J, K1, K2, K3, K4
+      DOUBLE PRECISION   BIGNUM, CFROM1, CFROMC, CTO1, CTOC, MUL, SMLNUM
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME, DISNAN
+      DOUBLE PRECISION   DLAMCH
+      EXTERNAL           LSAME, DLAMCH, DISNAN
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS, MAX, MIN
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           XERBLA
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input arguments
+*
+      INFO = 0
+*
+      IF( LSAME( TYPE, 'G' ) ) THEN
+         ITYPE = 0
+      ELSE IF( LSAME( TYPE, 'L' ) ) THEN
+         ITYPE = 1
+      ELSE IF( LSAME( TYPE, 'U' ) ) THEN
+         ITYPE = 2
+      ELSE IF( LSAME( TYPE, 'H' ) ) THEN
+         ITYPE = 3
+      ELSE IF( LSAME( TYPE, 'B' ) ) THEN
+         ITYPE = 4
+      ELSE IF( LSAME( TYPE, 'Q' ) ) THEN
+         ITYPE = 5
+      ELSE IF( LSAME( TYPE, 'Z' ) ) THEN
+         ITYPE = 6
+      ELSE
+         ITYPE = -1
+      END IF
+*
+      IF( ITYPE.EQ.-1 ) THEN
+         INFO = -1
+      ELSE IF( CFROM.EQ.ZERO .OR. DISNAN(CFROM) ) THEN
+         INFO = -4
+      ELSE IF( DISNAN(CTO) ) THEN
+         INFO = -5
+      ELSE IF( M.LT.0 ) THEN
+         INFO = -6
+      ELSE IF( N.LT.0 .OR. ( ITYPE.EQ.4 .AND. N.NE.M ) .OR.
+     $         ( ITYPE.EQ.5 .AND. N.NE.M ) ) THEN
+         INFO = -7
+      ELSE IF( ITYPE.LE.3 .AND. LDA.LT.MAX( 1, M ) ) THEN
+         INFO = -9
+      ELSE IF( ITYPE.GE.4 ) THEN
+         IF( KL.LT.0 .OR. KL.GT.MAX( M-1, 0 ) ) THEN
+            INFO = -2
+         ELSE IF( KU.LT.0 .OR. KU.GT.MAX( N-1, 0 ) .OR.
+     $            ( ( ITYPE.EQ.4 .OR. ITYPE.EQ.5 ) .AND. KL.NE.KU ) )
+     $             THEN
+            INFO = -3
+         ELSE IF( ( ITYPE.EQ.4 .AND. LDA.LT.KL+1 ) .OR.
+     $            ( ITYPE.EQ.5 .AND. LDA.LT.KU+1 ) .OR.
+     $            ( ITYPE.EQ.6 .AND. LDA.LT.2*KL+KU+1 ) ) THEN
+            INFO = -9
+         END IF
+      END IF
+*
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'DLASCL', -INFO )
+         RETURN
+      END IF
+*
+*     Quick return if possible
+*
+      IF( N.EQ.0 .OR. M.EQ.0 )
+     $   RETURN
+*
+*     Get machine parameters
+*
+      SMLNUM = DLAMCH( 'S' )
+      BIGNUM = ONE / SMLNUM
+*
+      CFROMC = CFROM
+      CTOC = CTO
+*
+   10 CONTINUE
+      CFROM1 = CFROMC*SMLNUM
+      IF( CFROM1.EQ.CFROMC ) THEN
+!        CFROMC is an inf.  Multiply by a correctly signed zero for
+!        finite CTOC, or a NaN if CTOC is infinite.
+         MUL = CTOC / CFROMC
+         DONE = .TRUE.
+         CTO1 = CTOC
+      ELSE
+         CTO1 = CTOC / BIGNUM
+         IF( CTO1.EQ.CTOC ) THEN
+!           CTOC is either 0 or an inf.  In both cases, CTOC itself
+!           serves as the correct multiplication factor.
+            MUL = CTOC
+            DONE = .TRUE.
+            CFROMC = ONE
+         ELSE IF( ABS( CFROM1 ).GT.ABS( CTOC ) .AND. CTOC.NE.ZERO ) THEN
+            MUL = SMLNUM
+            DONE = .FALSE.
+            CFROMC = CFROM1
+         ELSE IF( ABS( CTO1 ).GT.ABS( CFROMC ) ) THEN
+            MUL = BIGNUM
+            DONE = .FALSE.
+            CTOC = CTO1
+         ELSE
+            MUL = CTOC / CFROMC
+            DONE = .TRUE.
+         END IF
+      END IF
+*
+      IF( ITYPE.EQ.0 ) THEN
+*
+*        Full matrix
+*
+         DO 30 J = 1, N
+            DO 20 I = 1, M
+               A( I, J ) = A( I, J )*MUL
+   20       CONTINUE
+   30    CONTINUE
+*
+      ELSE IF( ITYPE.EQ.1 ) THEN
+*
+*        Lower triangular matrix
+*
+         DO 50 J = 1, N
+            DO 40 I = J, M
+               A( I, J ) = A( I, J )*MUL
+   40       CONTINUE
+   50    CONTINUE
+*
+      ELSE IF( ITYPE.EQ.2 ) THEN
+*
+*        Upper triangular matrix
+*
+         DO 70 J = 1, N
+            DO 60 I = 1, MIN( J, M )
+               A( I, J ) = A( I, J )*MUL
+   60       CONTINUE
+   70    CONTINUE
+*
+      ELSE IF( ITYPE.EQ.3 ) THEN
+*
+*        Upper Hessenberg matrix
+*
+         DO 90 J = 1, N
+            DO 80 I = 1, MIN( J+1, M )
+               A( I, J ) = A( I, J )*MUL
+   80       CONTINUE
+   90    CONTINUE
+*
+      ELSE IF( ITYPE.EQ.4 ) THEN
+*
+*        Lower half of a symmetric band matrix
+*
+         K3 = KL + 1
+         K4 = N + 1
+         DO 110 J = 1, N
+            DO 100 I = 1, MIN( K3, K4-J )
+               A( I, J ) = A( I, J )*MUL
+  100       CONTINUE
+  110    CONTINUE
+*
+      ELSE IF( ITYPE.EQ.5 ) THEN
+*
+*        Upper half of a symmetric band matrix
+*
+         K1 = KU + 2
+         K3 = KU + 1
+         DO 130 J = 1, N
+            DO 120 I = MAX( K1-J, 1 ), K3
+               A( I, J ) = A( I, J )*MUL
+  120       CONTINUE
+  130    CONTINUE
+*
+      ELSE IF( ITYPE.EQ.6 ) THEN
+*
+*        Band matrix
+*
+         K1 = KL + KU + 2
+         K2 = KL + 1
+         K3 = 2*KL + KU + 1
+         K4 = KL + KU + 1 + M
+         DO 150 J = 1, N
+            DO 140 I = MAX( K1-J, K2 ), MIN( K3, K4-J )
+               A( I, J ) = A( I, J )*MUL
+  140       CONTINUE
+  150    CONTINUE
+*
+      END IF
+*
+      IF( .NOT.DONE )
+     $   GO TO 10
+*
+      RETURN
+*
+*     End of DLASCL
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlasq1.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlasq1.f
new file mode 100644
index 00000000..f0847781
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlasq1.f
@@ -0,0 +1,226 @@
+*> \brief \b DLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLASQ1 + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasq1.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasq1.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasq1.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DLASQ1( N, D, E, WORK, INFO )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            INFO, N
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   D( * ), E( * ), WORK( * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DLASQ1 computes the singular values of a real N-by-N bidiagonal
+*> matrix with diagonal D and off-diagonal E. The singular values
+*> are computed to high relative accuracy, in the absence of
+*> denormalization, underflow and overflow. The algorithm was first
+*> presented in
+*>
+*> "Accurate singular values and differential qd algorithms" by K. V.
+*> Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230,
+*> 1994,
+*>
+*> and the present implementation is described in "An implementation of
+*> the dqds Algorithm (Positive Case)", LAPACK Working Note.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>        The number of rows and columns in the matrix. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] D
+*> \verbatim
+*>          D is DOUBLE PRECISION array, dimension (N)
+*>        On entry, D contains the diagonal elements of the
+*>        bidiagonal matrix whose SVD is desired. On normal exit,
+*>        D contains the singular values in decreasing order.
+*> \endverbatim
+*>
+*> \param[in,out] E
+*> \verbatim
+*>          E is DOUBLE PRECISION array, dimension (N)
+*>        On entry, elements E(1:N-1) contain the off-diagonal elements
+*>        of the bidiagonal matrix whose SVD is desired.
+*>        On exit, E is overwritten.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is DOUBLE PRECISION array, dimension (4*N)
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>        = 0: successful exit
+*>        < 0: if INFO = -i, the i-th argument had an illegal value
+*>        > 0: the algorithm failed
+*>             = 1, a split was marked by a positive value in E
+*>             = 2, current block of Z not diagonalized after 100*N
+*>                  iterations (in inner while loop)  On exit D and E
+*>                  represent a matrix with the same singular values
+*>                  which the calling subroutine could use to finish the
+*>                  computation, or even feed back into DLASQ1
+*>             = 3, termination criterion of outer while loop not met 
+*>                  (program created more than N unreduced blocks)
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date September 2012
+*
+*> \ingroup auxOTHERcomputational
+*
+*  =====================================================================
+      SUBROUTINE DLASQ1( N, D, E, WORK, INFO )
+*
+*  -- LAPACK computational routine (version 3.4.2) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     September 2012
+*
+*     .. Scalar Arguments ..
+      INTEGER            INFO, N
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   D( * ), E( * ), WORK( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ZERO
+      PARAMETER          ( ZERO = 0.0D0 )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            I, IINFO
+      DOUBLE PRECISION   EPS, SCALE, SAFMIN, SIGMN, SIGMX
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           DCOPY, DLAS2, DLASCL, DLASQ2, DLASRT, XERBLA
+*     ..
+*     .. External Functions ..
+      DOUBLE PRECISION   DLAMCH
+      EXTERNAL           DLAMCH
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS, MAX, SQRT
+*     ..
+*     .. Executable Statements ..
+*
+      INFO = 0
+      IF( N.LT.0 ) THEN
+         INFO = -2
+         CALL XERBLA( 'DLASQ1', -INFO )
+         RETURN
+      ELSE IF( N.EQ.0 ) THEN
+         RETURN
+      ELSE IF( N.EQ.1 ) THEN
+         D( 1 ) = ABS( D( 1 ) )
+         RETURN
+      ELSE IF( N.EQ.2 ) THEN
+         CALL DLAS2( D( 1 ), E( 1 ), D( 2 ), SIGMN, SIGMX )
+         D( 1 ) = SIGMX
+         D( 2 ) = SIGMN
+         RETURN
+      END IF
+*
+*     Estimate the largest singular value.
+*
+      SIGMX = ZERO
+      DO 10 I = 1, N - 1
+         D( I ) = ABS( D( I ) )
+         SIGMX = MAX( SIGMX, ABS( E( I ) ) )
+   10 CONTINUE
+      D( N ) = ABS( D( N ) )
+*
+*     Early return if SIGMX is zero (matrix is already diagonal).
+*
+      IF( SIGMX.EQ.ZERO ) THEN
+         CALL DLASRT( 'D', N, D, IINFO )
+         RETURN
+      END IF
+*
+      DO 20 I = 1, N
+         SIGMX = MAX( SIGMX, D( I ) )
+   20 CONTINUE
+*
+*     Copy D and E into WORK (in the Z format) and scale (squaring the
+*     input data makes scaling by a power of the radix pointless).
+*
+      EPS = DLAMCH( 'Precision' )
+      SAFMIN = DLAMCH( 'Safe minimum' )
+      SCALE = SQRT( EPS / SAFMIN )
+
+      CALL DCOPY( N, D, 1, WORK( 1 ), 2 )
+      CALL DCOPY( N-1, E, 1, WORK( 2 ), 2 )
+      CALL DLASCL( 'G', 0, 0, SIGMX, SCALE, 2*N-1, 1, WORK, 2*N-1,
+     $             IINFO )
+*         
+*     Compute the q's and e's.
+*
+      DO 30 I = 1, 2*N - 1
+         WORK( I ) = WORK( I )**2
+   30 CONTINUE
+      WORK( 2*N ) = ZERO
+*
+
+      CALL DLASQ2( N, WORK, INFO )
+*
+      IF( INFO.EQ.0 ) THEN
+         DO 40 I = 1, N
+            D( I ) = SQRT( WORK( I ) )
+   40    CONTINUE
+         CALL DLASCL( 'G', 0, 0, SCALE, SIGMX, N, 1, D, N, IINFO )
+      ELSE IF( INFO.EQ.2 ) THEN
+*
+*     Maximum number of iterations exceeded.  Move data from WORK
+*     into D and E so the calling subroutine can try to finish
+*
+         DO I = 1, N
+            D( I ) = SQRT( WORK( 2*I-1 ) )
+            E( I ) = SQRT( WORK( 2*I ) )
+         END DO
+         CALL DLASCL( 'G', 0, 0, SCALE, SIGMX, N, 1, D, N, IINFO )
+         CALL DLASCL( 'G', 0, 0, SCALE, SIGMX, N, 1, E, N, IINFO )
+      END IF
+*
+      RETURN
+*
+*     End of DLASQ1
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlasq2.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlasq2.f
new file mode 100644
index 00000000..602dffc9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlasq2.f
@@ -0,0 +1,652 @@
+*> \brief \b DLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd Array Z to high relative accuracy. Used by sbdsqr and sstegr.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLASQ2 + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasq2.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasq2.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasq2.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DLASQ2( N, Z, INFO )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            INFO, N
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   Z( * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DLASQ2 computes all the eigenvalues of the symmetric positive 
+*> definite tridiagonal matrix associated with the qd array Z to high
+*> relative accuracy are computed to high relative accuracy, in the
+*> absence of denormalization, underflow and overflow.
+*>
+*> To see the relation of Z to the tridiagonal matrix, let L be a
+*> unit lower bidiagonal matrix with subdiagonals Z(2,4,6,,..) and
+*> let U be an upper bidiagonal matrix with 1's above and diagonal
+*> Z(1,3,5,,..). The tridiagonal is L*U or, if you prefer, the
+*> symmetric tridiagonal to which it is similar.
+*>
+*> Note : DLASQ2 defines a logical variable, IEEE, which is true
+*> on machines which follow ieee-754 floating-point standard in their
+*> handling of infinities and NaNs, and false otherwise. This variable
+*> is passed to DLASQ3.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>        The number of rows and columns in the matrix. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] Z
+*> \verbatim
+*>          Z is DOUBLE PRECISION array, dimension ( 4*N )
+*>        On entry Z holds the qd array. On exit, entries 1 to N hold
+*>        the eigenvalues in decreasing order, Z( 2*N+1 ) holds the
+*>        trace, and Z( 2*N+2 ) holds the sum of the eigenvalues. If
+*>        N > 2, then Z( 2*N+3 ) holds the iteration count, Z( 2*N+4 )
+*>        holds NDIVS/NIN^2, and Z( 2*N+5 ) holds the percentage of
+*>        shifts that failed.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>        = 0: successful exit
+*>        < 0: if the i-th argument is a scalar and had an illegal
+*>             value, then INFO = -i, if the i-th argument is an
+*>             array and the j-entry had an illegal value, then
+*>             INFO = -(i*100+j)
+*>        > 0: the algorithm failed
+*>              = 1, a split was marked by a positive value in E
+*>              = 2, current block of Z not diagonalized after 100*N
+*>                   iterations (in inner while loop).  On exit Z holds
+*>                   a qd array with the same eigenvalues as the given Z.
+*>              = 3, termination criterion of outer while loop not met 
+*>                   (program created more than N unreduced blocks)
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date September 2012
+*
+*> \ingroup auxOTHERcomputational
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  Local Variables: I0:N0 defines a current unreduced segment of Z.
+*>  The shifts are accumulated in SIGMA. Iteration count is in ITER.
+*>  Ping-pong is controlled by PP (alternates between 0 and 1).
+*> \endverbatim
+*>
+*  =====================================================================
+      SUBROUTINE DLASQ2( N, Z, INFO )
+*
+*  -- LAPACK computational routine (version 3.4.2) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     September 2012
+*
+*     .. Scalar Arguments ..
+      INTEGER            INFO, N
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   Z( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   CBIAS
+      PARAMETER          ( CBIAS = 1.50D0 )
+      DOUBLE PRECISION   ZERO, HALF, ONE, TWO, FOUR, HUNDRD
+      PARAMETER          ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0,
+     $                     TWO = 2.0D0, FOUR = 4.0D0, HUNDRD = 100.0D0 )
+*     ..
+*     .. Local Scalars ..
+      LOGICAL            IEEE
+      INTEGER            I0, I1, I4, IINFO, IPN4, ITER, IWHILA, IWHILB,
+     $                   K, KMIN, N0, N1, NBIG, NDIV, NFAIL, PP, SPLT, 
+     $                   TTYPE
+      DOUBLE PRECISION   D, DEE, DEEMIN, DESIG, DMIN, DMIN1, DMIN2, DN,
+     $                   DN1, DN2, E, EMAX, EMIN, EPS, G, OLDEMN, QMAX,
+     $                   QMIN, S, SAFMIN, SIGMA, T, TAU, TEMP, TOL,
+     $                   TOL2, TRACE, ZMAX, TEMPE, TEMPQ
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           DLASQ3, DLASRT, XERBLA
+*     ..
+*     .. External Functions ..
+      INTEGER            ILAENV
+      DOUBLE PRECISION   DLAMCH
+      EXTERNAL           DLAMCH, ILAENV
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS, DBLE, MAX, MIN, SQRT
+*     ..
+*     .. Executable Statements ..
+*      
+*     Test the input arguments.
+*     (in case DLASQ2 is not called by DLASQ1)
+*
+      INFO = 0
+      EPS = DLAMCH( 'Precision' )
+      SAFMIN = DLAMCH( 'Safe minimum' )
+      TOL = EPS*HUNDRD
+      TOL2 = TOL**2
+*
+      IF( N.LT.0 ) THEN
+         INFO = -1
+         CALL XERBLA( 'DLASQ2', 1 )
+         RETURN
+      ELSE IF( N.EQ.0 ) THEN
+         RETURN
+      ELSE IF( N.EQ.1 ) THEN
+*
+*        1-by-1 case.
+*
+         IF( Z( 1 ).LT.ZERO ) THEN
+            INFO = -201
+            CALL XERBLA( 'DLASQ2', 2 )
+         END IF
+         RETURN
+      ELSE IF( N.EQ.2 ) THEN
+*
+*        2-by-2 case.
+*
+         IF( Z( 2 ).LT.ZERO .OR. Z( 3 ).LT.ZERO ) THEN
+            INFO = -2
+            CALL XERBLA( 'DLASQ2', 2 )
+            RETURN
+         ELSE IF( Z( 3 ).GT.Z( 1 ) ) THEN
+            D = Z( 3 )
+            Z( 3 ) = Z( 1 )
+            Z( 1 ) = D
+         END IF
+         Z( 5 ) = Z( 1 ) + Z( 2 ) + Z( 3 )
+         IF( Z( 2 ).GT.Z( 3 )*TOL2 ) THEN
+            T = HALF*( ( Z( 1 )-Z( 3 ) )+Z( 2 ) ) 
+            S = Z( 3 )*( Z( 2 ) / T )
+            IF( S.LE.T ) THEN
+               S = Z( 3 )*( Z( 2 ) / ( T*( ONE+SQRT( ONE+S / T ) ) ) )
+            ELSE
+               S = Z( 3 )*( Z( 2 ) / ( T+SQRT( T )*SQRT( T+S ) ) )
+            END IF
+            T = Z( 1 ) + ( S+Z( 2 ) )
+            Z( 3 ) = Z( 3 )*( Z( 1 ) / T )
+            Z( 1 ) = T
+         END IF
+         Z( 2 ) = Z( 3 )
+         Z( 6 ) = Z( 2 ) + Z( 1 )
+         RETURN
+      END IF
+*
+*     Check for negative data and compute sums of q's and e's.
+*
+      Z( 2*N ) = ZERO
+      EMIN = Z( 2 )
+      QMAX = ZERO
+      ZMAX = ZERO
+      D = ZERO
+      E = ZERO
+*
+      DO 10 K = 1, 2*( N-1 ), 2
+         IF( Z( K ).LT.ZERO ) THEN
+            INFO = -( 200+K )
+            CALL XERBLA( 'DLASQ2', 2 )
+            RETURN
+         ELSE IF( Z( K+1 ).LT.ZERO ) THEN
+            INFO = -( 200+K+1 )
+            CALL XERBLA( 'DLASQ2', 2 )
+            RETURN
+         END IF
+         D = D + Z( K )
+         E = E + Z( K+1 )
+         QMAX = MAX( QMAX, Z( K ) )
+         EMIN = MIN( EMIN, Z( K+1 ) )
+         ZMAX = MAX( QMAX, ZMAX, Z( K+1 ) )
+   10 CONTINUE
+      IF( Z( 2*N-1 ).LT.ZERO ) THEN
+         INFO = -( 200+2*N-1 )
+         CALL XERBLA( 'DLASQ2', 2 )
+         RETURN
+      END IF
+      D = D + Z( 2*N-1 )
+      QMAX = MAX( QMAX, Z( 2*N-1 ) )
+      ZMAX = MAX( QMAX, ZMAX )
+*
+*     Check for diagonality.
+*
+      IF( E.EQ.ZERO ) THEN
+         DO 20 K = 2, N
+            Z( K ) = Z( 2*K-1 )
+   20    CONTINUE
+         CALL DLASRT( 'D', N, Z, IINFO )
+         Z( 2*N-1 ) = D
+         RETURN
+      END IF
+*
+      TRACE = D + E
+*
+*     Check for zero data.
+*
+      IF( TRACE.EQ.ZERO ) THEN
+         Z( 2*N-1 ) = ZERO
+         RETURN
+      END IF
+*         
+*     Check whether the machine is IEEE conformable.
+*         
+      IEEE = ILAENV( 10, 'DLASQ2', 'N', 1, 2, 3, 4 ).EQ.1 .AND.
+     $       ILAENV( 11, 'DLASQ2', 'N', 1, 2, 3, 4 ).EQ.1      
+*         
+*     Rearrange data for locality: Z=(q1,qq1,e1,ee1,q2,qq2,e2,ee2,...).
+*
+      DO 30 K = 2*N, 2, -2
+         Z( 2*K ) = ZERO 
+         Z( 2*K-1 ) = Z( K ) 
+         Z( 2*K-2 ) = ZERO 
+         Z( 2*K-3 ) = Z( K-1 ) 
+   30 CONTINUE
+*
+      I0 = 1
+      N0 = N
+*
+*     Reverse the qd-array, if warranted.
+*
+      IF( CBIAS*Z( 4*I0-3 ).LT.Z( 4*N0-3 ) ) THEN
+         IPN4 = 4*( I0+N0 )
+         DO 40 I4 = 4*I0, 2*( I0+N0-1 ), 4
+
+            TEMP = Z( I4-3 )
+            Z( I4-3 ) = Z( IPN4-I4-3 )
+            Z( IPN4-I4-3 ) = TEMP
+            TEMP = Z( I4-1 )
+            Z( I4-1 ) = Z( IPN4-I4-5 )
+            Z( IPN4-I4-5 ) = TEMP
+   40    CONTINUE
+      END IF
+*
+*     Initial split checking via dqd and Li's test.
+*
+      PP = 0
+*
+      DO 80 K = 1, 2
+*
+         D = Z( 4*N0+PP-3 )
+         DO 50 I4 = 4*( N0-1 ) + PP, 4*I0 + PP, -4
+            IF( Z( I4-1 ).LE.TOL2*D ) THEN
+               Z( I4-1 ) = -ZERO
+               D = Z( I4-3 )
+            ELSE
+               D = Z( I4-3 )*( D / ( D+Z( I4-1 ) ) )
+            END IF
+   50    CONTINUE
+*
+*        dqd maps Z to ZZ plus Li's test.
+*
+         EMIN = Z( 4*I0+PP+1 )
+         D = Z( 4*I0+PP-3 )
+         DO 60 I4 = 4*I0 + PP, 4*( N0-1 ) + PP, 4
+            Z( I4-2*PP-2 ) = D + Z( I4-1 )
+            IF( Z( I4-1 ).LE.TOL2*D ) THEN
+               Z( I4-1 ) = -ZERO
+               Z( I4-2*PP-2 ) = D
+               Z( I4-2*PP ) = ZERO
+               D = Z( I4+1 )
+            ELSE IF( SAFMIN*Z( I4+1 ).LT.Z( I4-2*PP-2 ) .AND.
+     $               SAFMIN*Z( I4-2*PP-2 ).LT.Z( I4+1 ) ) THEN
+               TEMP = Z( I4+1 ) / Z( I4-2*PP-2 )
+               Z( I4-2*PP ) = Z( I4-1 )*TEMP
+               D = D*TEMP
+            ELSE
+               Z( I4-2*PP ) = Z( I4+1 )*( Z( I4-1 ) / Z( I4-2*PP-2 ) )
+               D = Z( I4+1 )*( D / Z( I4-2*PP-2 ) )
+            END IF
+            EMIN = MIN( EMIN, Z( I4-2*PP ) )
+   60    CONTINUE 
+         Z( 4*N0-PP-2 ) = D
+*
+*        Now find qmax.
+*
+         QMAX = Z( 4*I0-PP-2 )
+         DO 70 I4 = 4*I0 - PP + 2, 4*N0 - PP - 2, 4
+            QMAX = MAX( QMAX, Z( I4 ) )
+   70    CONTINUE
+*
+*        Prepare for the next iteration on K.
+*
+         PP = 1 - PP
+   80 CONTINUE
+
+*
+*     Initialise variables to pass to DLASQ3.
+*
+      TTYPE = 0
+      DMIN1 = ZERO
+      DMIN2 = ZERO
+      DN    = ZERO
+      DN1   = ZERO
+      DN2   = ZERO
+      G     = ZERO
+      TAU   = ZERO
+*
+      ITER = 2
+      NFAIL = 0
+      NDIV = 2*( N0-I0 )
+*
+      DO 160 IWHILA = 1, N + 1
+
+         IF( N0.LT.1 ) THEN
+           GO TO 170
+        END IF
+*
+*        While array unfinished do 
+*
+*        E(N0) holds the value of SIGMA when submatrix in I0:N0
+*        splits from the rest of the array, but is negated.
+*      
+         DESIG = ZERO
+         IF( N0.EQ.N ) THEN
+            SIGMA = ZERO
+         ELSE
+            SIGMA = -Z( 4*N0-1 )
+         END IF
+         IF( SIGMA.LT.ZERO ) THEN
+            INFO = 1
+            RETURN
+         END IF
+*
+*        Find last unreduced submatrix's top index I0, find QMAX and
+*        EMIN. Find Gershgorin-type bound if Q's much greater than E's.
+*
+         EMAX = ZERO 
+         IF( N0.GT.I0 ) THEN
+            EMIN = ABS( Z( 4*N0-5 ) )
+         ELSE
+            EMIN = ZERO
+         END IF
+         QMIN = Z( 4*N0-3 )
+         QMAX = QMIN
+         DO 90 I4 = 4*N0, 8, -4
+            IF( Z( I4-5 ).LE.ZERO )
+     $         GO TO 100
+            IF( QMIN.GE.FOUR*EMAX ) THEN
+               QMIN = MIN( QMIN, Z( I4-3 ) )
+               EMAX = MAX( EMAX, Z( I4-5 ) )
+            END IF
+            QMAX = MAX( QMAX, Z( I4-7 )+Z( I4-5 ) )
+            EMIN = MIN( EMIN, Z( I4-5 ) )
+   90    CONTINUE
+         I4 = 4 
+*
+  100    CONTINUE
+         I0 = I4 / 4
+
+         PP = 0
+*
+         IF( N0-I0.GT.1 ) THEN
+            DEE = Z( 4*I0-3 )
+            DEEMIN = DEE
+            KMIN = I0
+            DO 110 I4 = 4*I0+1, 4*N0-3, 4
+               DEE = Z( I4 )*( DEE /( DEE+Z( I4-2 ) ) )
+               IF( DEE.LE.DEEMIN ) THEN
+                  DEEMIN = DEE
+                  KMIN = ( I4+3 )/4
+               END IF
+  110       CONTINUE
+            IF( (KMIN-I0)*2.LT.N0-KMIN .AND. 
+     $         DEEMIN.LE.HALF*Z(4*N0-3) ) THEN
+               IPN4 = 4*( I0+N0 )
+               PP = 2
+               DO 120 I4 = 4*I0, 2*( I0+N0-1 ), 4
+                  TEMP = Z( I4-3 )
+                  Z( I4-3 ) = Z( IPN4-I4-3 )
+                  Z( IPN4-I4-3 ) = TEMP
+                  TEMP = Z( I4-2 )
+                  Z( I4-2 ) = Z( IPN4-I4-2 )
+                  Z( IPN4-I4-2 ) = TEMP
+                  TEMP = Z( I4-1 )
+                  Z( I4-1 ) = Z( IPN4-I4-5 )
+                  Z( IPN4-I4-5 ) = TEMP
+                  TEMP = Z( I4 )
+                  Z( I4 ) = Z( IPN4-I4-4 )
+                  Z( IPN4-I4-4 ) = TEMP
+  120          CONTINUE
+            END IF
+         END IF
+*
+*        Put -(initial shift) into DMIN.
+*
+         DMIN = -MAX( ZERO, QMIN-TWO*SQRT( QMIN )*SQRT( EMAX ) )
+*
+*        Now I0:N0 is unreduced. 
+*        PP = 0 for ping, PP = 1 for pong.
+*        PP = 2 indicates that flipping was applied to the Z array and
+*               and that the tests for deflation upon entry in DLASQ3 
+*               should not be performed.
+*
+         NBIG = 100*( N0-I0+1 )
+         DO 140 IWHILB = 1, NBIG
+
+            IF( I0.GT.N0 ) 
+     $         GO TO 150
+*
+
+            ! Print out test cases
+            
+            write(3,*) "{"
+            write(3,*) "i0: ", I0, ","
+            write(3,*) "n0: ", N0, ","
+            write(3,'(9999(g0))',advance="no") "z: []float64{"
+            do i = 1, 4*n
+              write (3,'(99999(e24.16,a))',advance="no") z(i), ","
+            end do
+            write (3,*) "},"
+            write (3,*) "pp:   ", PP, ","
+            write (3,*) "dmin: ", DMIN, ","
+            write (3,*) "desig:", DESIG, ","
+            write (3,*) "qmax: ", QMAX, ","
+            write (3,*) "ttype:", TTYPE, ","
+            write (3,*) "dmin1:", DMIN1, ","
+            write (3,*) "dmin2:", DMIN2, ","
+            write (3,*) "dn:   ", DN, ","
+            write (3,*) "dn1:  ", DN1, ","
+            write (3,*) "dn2:  ", DN2, ","
+            write (3,*) "g:    ", G, ","
+            write (3,*) "tau:  ", TAU, ","
+            write (3,*) "nFail:", NFAIL, ","
+            write (3,*) "iter: ", ITER, ","
+            write (3,*) "sigma:", SIGMA, ","
+            write (3,*) "nDiv: ", NDIV, ","
+
+*           While submatrix unfinished take a good dqds step.
+*
+
+
+            CALL DLASQ3( I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL,
+     $                   ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1,
+     $                   DN2, G, TAU )
+
+
+            ! Write the outputs
+            write(3,'(9999(g0))',advance="no") "zOut: []float64{"
+            do i = 1, 4*n
+                write (3,'(99999(e24.16,a))',advance="no") z(i), ","
+            end do
+            write (3,*) "},"
+            write (3,*) "i0Out:",I0, ","
+            write (3,*) "n0Out:",    N0, ","
+            write (3,*) "ppOut:",    PP, ","
+            write (3,*) "dminOut:",  DMIN, ","
+            write (3,*) "desigOut:", DESIG, ","
+            write (3,*) "sigmaOut:", SIGMA, ","
+            write (3,*) "qmaxOut:",  QMAX, ","
+            write (3,*) "nFailOut:", NFAIL, ","
+            write (3,*) "iterOut:",  ITER, ","
+            write (3,*) "nDivOut:",  NDIV, ","
+            write (3,*) "ttypeOut:", TTYPE, ","
+            write (3,*) "dmin1Out:", DMIN1, ","
+            write (3,*) "dmin2Out:", DMIN2, ","
+            write (3,*) "dnOut:",    DN, ","
+            write (3,*) "dn1Out:",   DN1, ","
+            write (3,*) "dn2Out:",   DN2, ","
+            write (3,*) "gOut:",     G, ","
+            write (3,*) "tauOut:",   TAU, ","
+
+            write (3,*) "},"
+
+
+            PP = 1 - PP
+*
+*           When EMIN is very small check for splits.
+*
+            IF( PP.EQ.0 .AND. N0-I0.GE.3 ) THEN
+               IF( Z( 4*N0 ).LE.TOL2*QMAX .OR.
+     $             Z( 4*N0-1 ).LE.TOL2*SIGMA ) THEN
+                  SPLT = I0 - 1
+                  QMAX = Z( 4*I0-3 )
+                  EMIN = Z( 4*I0-1 )
+                  OLDEMN = Z( 4*I0 )
+                  DO 130 I4 = 4*I0, 4*( N0-3 ), 4
+                     IF( Z( I4 ).LE.TOL2*Z( I4-3 ) .OR.
+     $                   Z( I4-1 ).LE.TOL2*SIGMA ) THEN
+                        Z( I4-1 ) = -SIGMA
+                        SPLT = I4 / 4
+                        QMAX = ZERO
+                        EMIN = Z( I4+3 )
+                        OLDEMN = Z( I4+4 )
+                     ELSE
+                        QMAX = MAX( QMAX, Z( I4+1 ) )
+                        EMIN = MIN( EMIN, Z( I4-1 ) )
+                        OLDEMN = MIN( OLDEMN, Z( I4 ) )
+                     END IF
+  130             CONTINUE
+                  Z( 4*N0-1 ) = EMIN
+                  Z( 4*N0 ) = OLDEMN
+                  I0 = SPLT + 1
+               END IF
+            END IF
+*
+  140    CONTINUE
+*
+         INFO = 2
+*       
+*        Maximum number of iterations exceeded, restore the shift 
+*        SIGMA and place the new d's and e's in a qd array.
+*        This might need to be done for several blocks
+*
+         I1 = I0
+         N1 = N0
+ 145     CONTINUE
+
+         TEMPQ = Z( 4*I0-3 )
+         Z( 4*I0-3 ) = Z( 4*I0-3 ) + SIGMA
+         DO K = I0+1, N0
+            TEMPE = Z( 4*K-5 )
+            Z( 4*K-5 ) = Z( 4*K-5 ) * (TEMPQ / Z( 4*K-7 ))
+            TEMPQ = Z( 4*K-3 )
+            Z( 4*K-3 ) = Z( 4*K-3 ) + SIGMA + TEMPE - Z( 4*K-5 )
+         END DO
+*
+*        Prepare to do this on the previous block if there is one
+*
+         IF( I1.GT.1 ) THEN
+            N1 = I1-1
+            DO WHILE( ( I1.GE.2 ) .AND. ( Z(4*I1-5).GE.ZERO ) )
+               I1 = I1 - 1
+            END DO
+            SIGMA = -Z(4*N1-1)
+            GO TO 145
+         END IF
+
+         DO K = 1, N
+            Z( 2*K-1 ) = Z( 4*K-3 )
+*
+*        Only the block 1..N0 is unfinished.  The rest of the e's
+*        must be essentially zero, although sometimes other data
+*        has been stored in them.
+*
+            IF( K.LT.N0 ) THEN
+               Z( 2*K ) = Z( 4*K-1 )
+            ELSE
+               Z( 2*K ) = 0
+            END IF
+         END DO
+         RETURN
+*
+*        end IWHILB
+*
+  150    CONTINUE
+*
+  160 CONTINUE
+*
+      INFO = 3
+      RETURN
+*
+*     end IWHILA   
+*
+  170 CONTINUE
+*
+
+*     Move q's to the front.
+*      
+      DO 180 K = 2, N
+         Z( K ) = Z( 4*K-3 )
+  180 CONTINUE
+*
+*     Sort and compute sum of eigenvalues.
+*
+      CALL DLASRT( 'D', N, Z, IINFO )
+*
+
+      E = ZERO
+      DO 190 K = N, 1, -1
+         E = E + Z( K )
+  190 CONTINUE
+*
+*     Store trace, sum(eigenvalues) and information on performance.
+*
+
+      Z( 2*N+1 ) = TRACE 
+      Z( 2*N+2 ) = E
+      Z( 2*N+3 ) = DBLE( ITER )
+      Z( 2*N+4 ) = DBLE( NDIV ) / DBLE( N**2 )
+      Z( 2*N+5 ) = HUNDRD*NFAIL / DBLE( ITER )
+
+      RETURN
+*
+*     End of DLASQ2
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlasq3.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlasq3.f
new file mode 100644
index 00000000..1c4e8ecf
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlasq3.f
@@ -0,0 +1,498 @@
+*> \brief \b DLASQ3 checks for deflation, computes a shift and calls dqds. Used by sbdsqr.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLASQ3 + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasq3.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasq3.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasq3.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DLASQ3( I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL,
+*                          ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1,
+*                          DN2, G, TAU )
+* 
+*       .. Scalar Arguments ..
+*       LOGICAL            IEEE
+*       INTEGER            I0, ITER, N0, NDIV, NFAIL, PP
+*       DOUBLE PRECISION   DESIG, DMIN, DMIN1, DMIN2, DN, DN1, DN2, G,
+*      $                   QMAX, SIGMA, TAU
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   Z( * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DLASQ3 checks for deflation, computes a shift (TAU) and calls dqds.
+*> In case of failure it changes shifts, and tries again until output
+*> is positive.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] I0
+*> \verbatim
+*>          I0 is INTEGER
+*>         First index.
+*> \endverbatim
+*>
+*> \param[in,out] N0
+*> \verbatim
+*>          N0 is INTEGER
+*>         Last index.
+*> \endverbatim
+*>
+*> \param[in] Z
+*> \verbatim
+*>          Z is DOUBLE PRECISION array, dimension ( 4*N )
+*>         Z holds the qd array.
+*> \endverbatim
+*>
+*> \param[in,out] PP
+*> \verbatim
+*>          PP is INTEGER
+*>         PP=0 for ping, PP=1 for pong.
+*>         PP=2 indicates that flipping was applied to the Z array   
+*>         and that the initial tests for deflation should not be 
+*>         performed.
+*> \endverbatim
+*>
+*> \param[out] DMIN
+*> \verbatim
+*>          DMIN is DOUBLE PRECISION
+*>         Minimum value of d.
+*> \endverbatim
+*>
+*> \param[out] SIGMA
+*> \verbatim
+*>          SIGMA is DOUBLE PRECISION
+*>         Sum of shifts used in current segment.
+*> \endverbatim
+*>
+*> \param[in,out] DESIG
+*> \verbatim
+*>          DESIG is DOUBLE PRECISION
+*>         Lower order part of SIGMA
+*> \endverbatim
+*>
+*> \param[in] QMAX
+*> \verbatim
+*>          QMAX is DOUBLE PRECISION
+*>         Maximum value of q.
+*> \endverbatim
+*>
+*> \param[out] NFAIL
+*> \verbatim
+*>          NFAIL is INTEGER
+*>         Number of times shift was too big.
+*> \endverbatim
+*>
+*> \param[out] ITER
+*> \verbatim
+*>          ITER is INTEGER
+*>         Number of iterations.
+*> \endverbatim
+*>
+*> \param[out] NDIV
+*> \verbatim
+*>          NDIV is INTEGER
+*>         Number of divisions.
+*> \endverbatim
+*>
+*> \param[in] IEEE
+*> \verbatim
+*>          IEEE is LOGICAL
+*>         Flag for IEEE or non IEEE arithmetic (passed to DLASQ5).
+*> \endverbatim
+*>
+*> \param[in,out] TTYPE
+*> \verbatim
+*>          TTYPE is INTEGER
+*>         Shift type.
+*> \endverbatim
+*>
+*> \param[in,out] DMIN1
+*> \verbatim
+*>          DMIN1 is DOUBLE PRECISION
+*> \endverbatim
+*>
+*> \param[in,out] DMIN2
+*> \verbatim
+*>          DMIN2 is DOUBLE PRECISION
+*> \endverbatim
+*>
+*> \param[in,out] DN
+*> \verbatim
+*>          DN is DOUBLE PRECISION
+*> \endverbatim
+*>
+*> \param[in,out] DN1
+*> \verbatim
+*>          DN1 is DOUBLE PRECISION
+*> \endverbatim
+*>
+*> \param[in,out] DN2
+*> \verbatim
+*>          DN2 is DOUBLE PRECISION
+*> \endverbatim
+*>
+*> \param[in,out] G
+*> \verbatim
+*>          G is DOUBLE PRECISION
+*> \endverbatim
+*>
+*> \param[in,out] TAU
+*> \verbatim
+*>          TAU is DOUBLE PRECISION
+*>
+*>         These are passed as arguments in order to save their values
+*>         between calls to DLASQ3.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date September 2012
+*
+*> \ingroup auxOTHERcomputational
+*
+*  =====================================================================
+      SUBROUTINE DLASQ3( I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL,
+     $                   ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1,
+     $                   DN2, G, TAU )
+*
+*  -- LAPACK computational routine (version 3.4.2) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     September 2012
+*
+*     .. Scalar Arguments ..
+      LOGICAL            IEEE
+      INTEGER            I0, ITER, N0, NDIV, NFAIL, PP
+      DOUBLE PRECISION   DESIG, DMIN, DMIN1, DMIN2, DN, DN1, DN2, G,
+     $                   QMAX, SIGMA, TAU
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   Z( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   CBIAS
+      PARAMETER          ( CBIAS = 1.50D0 )
+      DOUBLE PRECISION   ZERO, QURTR, HALF, ONE, TWO, HUNDRD
+      PARAMETER          ( ZERO = 0.0D0, QURTR = 0.250D0, HALF = 0.5D0,
+     $                     ONE = 1.0D0, TWO = 2.0D0, HUNDRD = 100.0D0 )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            IPN4, J4, N0IN, NN, TTYPE
+      DOUBLE PRECISION   EPS, S, T, TEMP, TOL, TOL2
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           DLASQ4, DLASQ5, DLASQ6
+*     ..
+*     .. External Function ..
+      DOUBLE PRECISION   DLAMCH
+      LOGICAL            DISNAN
+      EXTERNAL           DISNAN, DLAMCH
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS, MAX, MIN, SQRT
+*     ..
+*     .. Executable Statements ..
+*
+
+      N0IN = N0
+      EPS = DLAMCH( 'Precision' )
+      TOL = EPS*HUNDRD
+      TOL2 = TOL**2
+*
+*     Check for deflation.
+*
+   10 CONTINUE
+*
+      IF( N0.LT.I0 )
+     $   RETURN
+      IF( N0.EQ.I0 )
+     $   GO TO 20
+      NN = 4*N0 + PP
+      IF( N0.EQ.( I0+1 ) )
+     $   GO TO 40
+*
+*     Check whether E(N0-1) is negligible, 1 eigenvalue.
+*
+      IF( Z( NN-5 ).GT.TOL2*( SIGMA+Z( NN-3 ) ) .AND.
+     $    Z( NN-2*PP-4 ).GT.TOL2*Z( NN-7 ) )
+     $   GO TO 30
+*
+   20 CONTINUE
+*
+      Z( 4*N0-3 ) = Z( 4*N0+PP-3 ) + SIGMA
+      N0 = N0 - 1
+      GO TO 10
+*
+*     Check  whether E(N0-2) is negligible, 2 eigenvalues.
+*
+   30 CONTINUE
+*
+      IF( Z( NN-9 ).GT.TOL2*SIGMA .AND.
+     $    Z( NN-2*PP-8 ).GT.TOL2*Z( NN-11 ) )
+     $   GO TO 50
+*
+   40 CONTINUE
+*
+      IF( Z( NN-3 ).GT.Z( NN-7 ) ) THEN
+         S = Z( NN-3 )
+         Z( NN-3 ) = Z( NN-7 )
+         Z( NN-7 ) = S
+      END IF
+      T = HALF*( ( Z( NN-7 )-Z( NN-3 ) )+Z( NN-5 ) )
+      IF( Z( NN-5 ).GT.Z( NN-3 )*TOL2.AND.T.NE.ZERO ) THEN
+         S = Z( NN-3 )*( Z( NN-5 ) / T )
+         IF( S.LE.T ) THEN
+            S = Z( NN-3 )*( Z( NN-5 ) /
+     $          ( T*( ONE+SQRT( ONE+S / T ) ) ) )
+         ELSE
+            S = Z( NN-3 )*( Z( NN-5 ) / ( T+SQRT( T )*SQRT( T+S ) ) )
+         END IF
+         T = Z( NN-7 ) + ( S+Z( NN-5 ) )
+         Z( NN-3 ) = Z( NN-3 )*( Z( NN-7 ) / T )
+         Z( NN-7 ) = T
+      END IF
+      Z( 4*N0-7 ) = Z( NN-7 ) + SIGMA
+      Z( 4*N0-3 ) = Z( NN-3 ) + SIGMA
+      N0 = N0 - 2
+      GO TO 10
+*
+   50 CONTINUE
+      IF( PP.EQ.2 ) 
+     $   PP = 0
+*
+*     Reverse the qd-array, if warranted.
+*
+
+      IF( DMIN.LE.ZERO .OR. N0.LT.N0IN ) THEN
+         IF( CBIAS*Z( 4*I0+PP-3 ).LT.Z( 4*N0+PP-3 ) ) THEN
+            IPN4 = 4*( I0+N0 )
+            DO 60 J4 = 4*I0, 2*( I0+N0-1 ), 4
+               TEMP = Z( J4-3 )
+               Z( J4-3 ) = Z( IPN4-J4-3 )
+               Z( IPN4-J4-3 ) = TEMP
+               TEMP = Z( J4-2 )
+               Z( J4-2 ) = Z( IPN4-J4-2 )
+               Z( IPN4-J4-2 ) = TEMP
+               TEMP = Z( J4-1 )
+               Z( J4-1 ) = Z( IPN4-J4-5 )
+               Z( IPN4-J4-5 ) = TEMP
+               TEMP = Z( J4 )
+               Z( J4 ) = Z( IPN4-J4-4 )
+               Z( IPN4-J4-4 ) = TEMP
+   60       CONTINUE
+            IF( N0-I0.LE.4 ) THEN
+               Z( 4*N0+PP-1 ) = Z( 4*I0+PP-1 )
+               Z( 4*N0-PP ) = Z( 4*I0-PP )
+            END IF
+            DMIN2 = MIN( DMIN2, Z( 4*N0+PP-1 ) )
+            Z( 4*N0+PP-1 ) = MIN( Z( 4*N0+PP-1 ), Z( 4*I0+PP-1 ),
+     $                            Z( 4*I0+PP+3 ) )
+            Z( 4*N0-PP ) = MIN( Z( 4*N0-PP ), Z( 4*I0-PP ),
+     $                          Z( 4*I0-PP+4 ) )
+            QMAX = MAX( QMAX, Z( 4*I0+PP-3 ), Z( 4*I0+PP+1 ) )
+            DMIN = -ZERO
+         END IF
+      END IF
+*
+*     Choose a shift.
+*
+      ! Print out DLASQ4 test cases
+      write(4,*) "{"
+      write(4,'(9999(g0))',advance="no") "z: []float64{"
+      do i = 1, NN
+        write (4,'(99999(e24.16,a))',advance="no") z(i), ","
+      end do
+      write (4,*) "},"
+      write (4,*) "i0: ", I0, ","
+      write (4,*) "n0: ", N0, ","
+      write (4,*) "pp:   ", PP, ","
+      write (4,*) "n0in: ", N0IN, ","
+      write (4,*) "dmin: ", DMIN, ","
+      write (4,*) "dmin1:", DMIN1, ","
+      write (4,*) "dmin2:", DMIN2, ","
+      write (4,*) "dn:   ", DN, ","
+      write (4,*) "dn1:  ", DN1, ","
+      write (4,*) "dn2:  ", DN2, ","
+      write (4,*) "tau: ", TAU, ","
+      write (4,*) "ttype: ", TTYPE, ","
+      write (4,*) "g:    ", G, ","
+      CALL DLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN, DN1,
+     $             DN2, TAU, TTYPE, G )
+
+      write(4,'(9999(g0))',advance="no") "zOut: []float64{"
+      do i = 1, NN
+        write (4,'(99999(e24.16,a))',advance="no") z(i), ","
+      end do
+      write (4,*) "},"
+      write (4,*) "tauOut: ", TAU, ","
+      write (4,*) "ttypeOut: ", TTYPE, ","
+      write (4,*) "gOut:   ", G, ","
+      write (4,*) "},"
+
+*
+*     Call dqds until DMIN > 0.
+*
+   70 CONTINUE
+*
+
+      write(5,*) "{"
+      write(5,'(9999(g0))',advance="no") "z: []float64{"
+      do i = 1, NN
+        write (5,'(99999(e24.16,a))',advance="no") z(i), ","
+      end do
+      write (5,*) "},"
+      write (5,*) "i0: ", I0, ","
+      write (5,*) "n0: ", N0, ","
+      write (5,*) "pp:   ", PP, ","
+      write (5,*) "tau: ", TAU, ","
+      write (5,*) "sigma: ", SIGMA, ","
+      write (5,*) "dmin: ", DMIN, ","
+      write (5,*) "dmin1:", DMIN1, ","
+      write (5,*) "dmin2:", DMIN2, ","
+      write (5,*) "dn:   ", DN, ","
+      write (5,*) "dnm1:  ", DN1, ","
+      write (5,*) "dnm2:  ", DN2, ","
+
+
+      CALL DLASQ5( I0, N0, Z, PP, TAU, SIGMA, DMIN, DMIN1, DMIN2, DN,
+     $             DN1, DN2, IEEE, EPS )
+
+
+
+      write (5,*) "i0Out: ", I0, ","
+      write (5,*) "n0Out: ", N0, ","
+      write (5,*) "ppOut:   ", PP, ","
+      write (5,*) "tauOut: ", TAU, ","
+      write (5,*) "sigmaOut: ", SIGMA, ","
+      write (5,*) "dminOut: ", DMIN, ","
+      write (5,*) "dmin1Out:", DMIN1, ","
+      write (5,*) "dmin2Out:", DMIN2, ","
+      write (5,*) "dnOut:   ", DN, ","
+      write (5,*) "dnm1Out:  ", DN1, ","
+      write (5,*) "dnm2Out:  ", DN2, ","
+      write (5,*) "},"
+
+*
+      NDIV = NDIV + ( N0-I0+2 )
+
+      ITER = ITER + 1
+*
+*     Check status.
+*
+
+      IF( DMIN.GE.ZERO .AND. DMIN1.GE.ZERO ) THEN
+*
+*        Success.
+*
+         GO TO 90
+*
+      ELSE IF( DMIN.LT.ZERO .AND. DMIN1.GT.ZERO .AND. 
+     $         Z( 4*( N0-1 )-PP ).LT.TOL*( SIGMA+DN1 ) .AND.
+     $         ABS( DN ).LT.TOL*SIGMA ) THEN
+
+*
+*        Convergence hidden by negative DN.
+*
+         Z( 4*( N0-1 )-PP+2 ) = ZERO
+         DMIN = ZERO
+         GO TO 90
+      ELSE IF( DMIN.LT.ZERO ) THEN
+
+*
+*        TAU too big. Select new TAU and try again.
+*
+         NFAIL = NFAIL + 1
+         IF( TTYPE.LT.-22 ) THEN
+*
+*           Failed twice. Play it safe.
+*
+            TAU = ZERO
+         ELSE IF( DMIN1.GT.ZERO ) THEN
+*
+*           Late failure. Gives excellent shift.
+*
+            TAU = ( TAU+DMIN )*( ONE-TWO*EPS )
+            TTYPE = TTYPE - 11
+         ELSE
+*
+*           Early failure. Divide by 4.
+*
+            TAU = QURTR*TAU
+            TTYPE = TTYPE - 12
+         END IF
+         GO TO 70
+      ELSE IF( DISNAN( DMIN ) ) THEN
+*
+*        NaN.
+*
+         IF( TAU.EQ.ZERO ) THEN
+            GO TO 80
+         ELSE
+            TAU = ZERO
+            GO TO 70
+         END IF
+      ELSE
+*            
+*        Possible underflow. Play it safe.
+*
+         GO TO 80
+      END IF
+*
+*     Risk of underflow.
+*
+   80 CONTINUE
+
+      CALL DLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN, DN1, DN2 )
+
+
+      NDIV = NDIV + ( N0-I0+2 )
+      ITER = ITER + 1
+      TAU = ZERO
+*
+   90 CONTINUE
+
+      IF( TAU.LT.SIGMA ) THEN
+         DESIG = DESIG + TAU
+         T = SIGMA + DESIG
+         DESIG = DESIG - ( T-SIGMA )
+      ELSE
+         T = SIGMA + TAU
+         DESIG = SIGMA - ( T-TAU ) + DESIG
+      END IF
+      SIGMA = T
+*
+      RETURN
+*
+*     End of DLASQ3
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlasq4.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlasq4.f
new file mode 100644
index 00000000..f60f775b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlasq4.f
@@ -0,0 +1,427 @@
+*> \brief \b DLASQ4 computes an approximation to the smallest eigenvalue using values of d from the previous transform. Used by sbdsqr.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLASQ4 + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasq4.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasq4.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasq4.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN,
+*                          DN1, DN2, TAU, TTYPE, G )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            I0, N0, N0IN, PP, TTYPE
+*       DOUBLE PRECISION   DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, TAU
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   Z( * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DLASQ4 computes an approximation TAU to the smallest eigenvalue
+*> using values of d from the previous transform.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] I0
+*> \verbatim
+*>          I0 is INTEGER
+*>        First index.
+*> \endverbatim
+*>
+*> \param[in] N0
+*> \verbatim
+*>          N0 is INTEGER
+*>        Last index.
+*> \endverbatim
+*>
+*> \param[in] Z
+*> \verbatim
+*>          Z is DOUBLE PRECISION array, dimension ( 4*N )
+*>        Z holds the qd array.
+*> \endverbatim
+*>
+*> \param[in] PP
+*> \verbatim
+*>          PP is INTEGER
+*>        PP=0 for ping, PP=1 for pong.
+*> \endverbatim
+*>
+*> \param[in] N0IN
+*> \verbatim
+*>          N0IN is INTEGER
+*>        The value of N0 at start of EIGTEST.
+*> \endverbatim
+*>
+*> \param[in] DMIN
+*> \verbatim
+*>          DMIN is DOUBLE PRECISION
+*>        Minimum value of d.
+*> \endverbatim
+*>
+*> \param[in] DMIN1
+*> \verbatim
+*>          DMIN1 is DOUBLE PRECISION
+*>        Minimum value of d, excluding D( N0 ).
+*> \endverbatim
+*>
+*> \param[in] DMIN2
+*> \verbatim
+*>          DMIN2 is DOUBLE PRECISION
+*>        Minimum value of d, excluding D( N0 ) and D( N0-1 ).
+*> \endverbatim
+*>
+*> \param[in] DN
+*> \verbatim
+*>          DN is DOUBLE PRECISION
+*>        d(N)
+*> \endverbatim
+*>
+*> \param[in] DN1
+*> \verbatim
+*>          DN1 is DOUBLE PRECISION
+*>        d(N-1)
+*> \endverbatim
+*>
+*> \param[in] DN2
+*> \verbatim
+*>          DN2 is DOUBLE PRECISION
+*>        d(N-2)
+*> \endverbatim
+*>
+*> \param[out] TAU
+*> \verbatim
+*>          TAU is DOUBLE PRECISION
+*>        This is the shift.
+*> \endverbatim
+*>
+*> \param[out] TTYPE
+*> \verbatim
+*>          TTYPE is INTEGER
+*>        Shift type.
+*> \endverbatim
+*>
+*> \param[in,out] G
+*> \verbatim
+*>          G is REAL
+*>        G is passed as an argument in order to save its value between
+*>        calls to DLASQ4.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date September 2012
+*
+*> \ingroup auxOTHERcomputational
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  CNST1 = 9/16
+*> \endverbatim
+*>
+*  =====================================================================
+      SUBROUTINE DLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN,
+     $                   DN1, DN2, TAU, TTYPE, G )
+*
+*  -- LAPACK computational routine (version 3.4.2) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     September 2012
+*
+*     .. Scalar Arguments ..
+      INTEGER            I0, N0, N0IN, PP, TTYPE
+      DOUBLE PRECISION   DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, TAU
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   Z( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   CNST1, CNST2, CNST3
+      PARAMETER          ( CNST1 = 0.5630D0, CNST2 = 1.010D0,
+     $                   CNST3 = 1.050D0 )
+      DOUBLE PRECISION   QURTR, THIRD, HALF, ZERO, ONE, TWO, HUNDRD
+      PARAMETER          ( QURTR = 0.250D0, THIRD = 0.3330D0,
+     $                   HALF = 0.50D0, ZERO = 0.0D0, ONE = 1.0D0,
+     $                   TWO = 2.0D0, HUNDRD = 100.0D0 )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            I4, NN, NP
+      DOUBLE PRECISION   A2, B1, B2, GAM, GAP1, GAP2, S
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MAX, MIN, SQRT
+*     ..
+*     .. Executable Statements ..
+*
+*     A negative DMIN forces the shift to take that absolute value
+*     TTYPE records the type of shift.
+*
+
+      IF( DMIN.LE.ZERO ) THEN
+         TAU = -DMIN
+         TTYPE = -1
+         RETURN
+      END IF
+*       
+      NN = 4*N0 + PP
+      IF( N0IN.EQ.N0 ) THEN
+*
+*        No eigenvalues deflated.
+*
+         IF( DMIN.EQ.DN .OR. DMIN.EQ.DN1 ) THEN
+*
+            B1 = SQRT( Z( NN-3 ) )*SQRT( Z( NN-5 ) )
+            B2 = SQRT( Z( NN-7 ) )*SQRT( Z( NN-9 ) )
+            A2 = Z( NN-7 ) + Z( NN-5 )
+*
+*           Cases 2 and 3.
+*
+            IF( DMIN.EQ.DN .AND. DMIN1.EQ.DN1 ) THEN
+
+               GAP2 = DMIN2 - A2 - DMIN2*QURTR
+               IF( GAP2.GT.ZERO .AND. GAP2.GT.B2 ) THEN
+                  GAP1 = A2 - DN - ( B2 / GAP2 )*B2
+               ELSE
+                  GAP1 = A2 - DN - ( B1+B2 )
+               END IF
+               IF( GAP1.GT.ZERO .AND. GAP1.GT.B1 ) THEN
+                  S = MAX( DN-( B1 / GAP1 )*B1, HALF*DMIN )
+                  TTYPE = -2
+               ELSE
+                  S = ZERO
+                  IF( DN.GT.B1 )
+     $               S = DN - B1
+                  IF( A2.GT.( B1+B2 ) )
+     $               S = MIN( S, A2-( B1+B2 ) )
+                  S = MAX( S, THIRD*DMIN )
+                  TTYPE = -3
+               END IF
+            ELSE
+*
+*              Case 4.
+*
+               TTYPE = -4
+               S = QURTR*DMIN
+               IF( DMIN.EQ.DN ) THEN
+                  GAM = DN
+                  A2 = ZERO
+                  IF( Z( NN-5 ) .GT. Z( NN-7 ) )
+     $               RETURN
+                  B2 = Z( NN-5 ) / Z( NN-7 )
+                  NP = NN - 9
+               ELSE
+                  NP = NN - 2*PP
+                  B2 = Z( NP-2 )
+                  GAM = DN1
+                  IF( Z( NP-4 ) .GT. Z( NP-2 ) )
+     $               RETURN
+                  A2 = Z( NP-4 ) / Z( NP-2 )
+                  IF( Z( NN-9 ) .GT. Z( NN-11 ) )
+     $               RETURN
+                  B2 = Z( NN-9 ) / Z( NN-11 )
+                  NP = NN - 13
+               END IF
+*
+*              Approximate contribution to norm squared from I < NN-1.
+*
+               A2 = A2 + B2
+               DO 10 I4 = NP, 4*I0 - 1 + PP, -4
+                  IF( B2.EQ.ZERO )
+     $               GO TO 20
+                  B1 = B2
+                  IF( Z( I4 ) .GT. Z( I4-2 ) )
+     $               RETURN
+                  B2 = B2*( Z( I4 ) / Z( I4-2 ) )
+                  A2 = A2 + B2
+                  IF( HUNDRD*MAX( B2, B1 ).LT.A2 .OR. CNST1.LT.A2 ) 
+     $               GO TO 20
+   10          CONTINUE
+   20          CONTINUE
+               A2 = CNST3*A2
+*
+*              Rayleigh quotient residual bound.
+*
+               IF( A2.LT.CNST1 )
+     $            S = GAM*( ONE-SQRT( A2 ) ) / ( ONE+A2 )
+            END IF
+         ELSE IF( DMIN.EQ.DN2 ) THEN
+*
+*           Case 5.
+*
+            TTYPE = -5
+            S = QURTR*DMIN
+*
+*           Compute contribution to norm squared from I > NN-2.
+*
+            NP = NN - 2*PP
+            B1 = Z( NP-2 )
+            B2 = Z( NP-6 )
+            GAM = DN2
+            IF( Z( NP-8 ).GT.B2 .OR. Z( NP-4 ).GT.B1 )
+     $         RETURN
+            A2 = ( Z( NP-8 ) / B2 )*( ONE+Z( NP-4 ) / B1 )
+*
+*           Approximate contribution to norm squared from I < NN-2.
+*
+            IF( N0-I0.GT.2 ) THEN
+               B2 = Z( NN-13 ) / Z( NN-15 )
+               A2 = A2 + B2
+               DO 30 I4 = NN - 17, 4*I0 - 1 + PP, -4
+                  IF( B2.EQ.ZERO )
+     $               GO TO 40
+                  B1 = B2
+                  IF( Z( I4 ) .GT. Z( I4-2 ) )
+     $               RETURN
+                  B2 = B2*( Z( I4 ) / Z( I4-2 ) )
+                  A2 = A2 + B2
+                  IF( HUNDRD*MAX( B2, B1 ).LT.A2 .OR. CNST1.LT.A2 ) 
+     $               GO TO 40
+   30          CONTINUE
+   40          CONTINUE
+               A2 = CNST3*A2
+            END IF
+*
+            IF( A2.LT.CNST1 )
+     $         S = GAM*( ONE-SQRT( A2 ) ) / ( ONE+A2 )
+         ELSE
+*
+*           Case 6, no information to guide us.
+*
+            IF( TTYPE.EQ.-6 ) THEN
+               G = G + THIRD*( ONE-G )
+            ELSE IF( TTYPE.EQ.-18 ) THEN
+               G = QURTR*THIRD
+            ELSE
+               G = QURTR
+            END IF
+            S = G*DMIN
+            TTYPE = -6
+         END IF
+*
+      ELSE IF( N0IN.EQ.( N0+1 ) ) THEN
+*
+*        One eigenvalue just deflated. Use DMIN1, DN1 for DMIN and DN.
+*
+         IF( DMIN1.EQ.DN1 .AND. DMIN2.EQ.DN2 ) THEN 
+*
+*           Cases 7 and 8.
+*
+            TTYPE = -7
+            S = THIRD*DMIN1
+            IF( Z( NN-5 ).GT.Z( NN-7 ) )
+     $         RETURN
+            B1 = Z( NN-5 ) / Z( NN-7 )
+            B2 = B1
+            IF( B2.EQ.ZERO )
+     $         GO TO 60
+            DO 50 I4 = 4*N0 - 9 + PP, 4*I0 - 1 + PP, -4
+               A2 = B1
+               IF( Z( I4 ).GT.Z( I4-2 ) )
+     $            RETURN
+               B1 = B1*( Z( I4 ) / Z( I4-2 ) )
+               B2 = B2 + B1
+               IF( HUNDRD*MAX( B1, A2 ).LT.B2 ) 
+     $            GO TO 60
+   50       CONTINUE
+   60       CONTINUE
+            B2 = SQRT( CNST3*B2 )
+            A2 = DMIN1 / ( ONE+B2**2 )
+            GAP2 = HALF*DMIN2 - A2
+            IF( GAP2.GT.ZERO .AND. GAP2.GT.B2*A2 ) THEN
+               S = MAX( S, A2*( ONE-CNST2*A2*( B2 / GAP2 )*B2 ) )
+            ELSE
+               S = MAX( S, A2*( ONE-CNST2*B2 ) )
+               TTYPE = -8
+            END IF
+         ELSE
+*
+*           Case 9.
+*
+            S = QURTR*DMIN1
+            IF( DMIN1.EQ.DN1 )
+     $         S = HALF*DMIN1
+            TTYPE = -9
+         END IF
+*
+      ELSE IF( N0IN.EQ.( N0+2 ) ) THEN
+*
+*        Two eigenvalues deflated. Use DMIN2, DN2 for DMIN and DN.
+*
+*        Cases 10 and 11.
+*
+         IF( DMIN2.EQ.DN2 .AND. TWO*Z( NN-5 ).LT.Z( NN-7 ) ) THEN 
+            TTYPE = -10
+            S = THIRD*DMIN2
+            IF( Z( NN-5 ).GT.Z( NN-7 ) )
+     $         RETURN
+            B1 = Z( NN-5 ) / Z( NN-7 )
+            B2 = B1
+            IF( B2.EQ.ZERO )
+     $         GO TO 80
+            DO 70 I4 = 4*N0 - 9 + PP, 4*I0 - 1 + PP, -4
+               IF( Z( I4 ).GT.Z( I4-2 ) )
+     $            RETURN
+               B1 = B1*( Z( I4 ) / Z( I4-2 ) )
+               B2 = B2 + B1
+               IF( HUNDRD*B1.LT.B2 )
+     $            GO TO 80
+   70       CONTINUE
+   80       CONTINUE
+            B2 = SQRT( CNST3*B2 )
+            A2 = DMIN2 / ( ONE+B2**2 )
+            GAP2 = Z( NN-7 ) + Z( NN-9 ) -
+     $             SQRT( Z( NN-11 ) )*SQRT( Z( NN-9 ) ) - A2
+            IF( GAP2.GT.ZERO .AND. GAP2.GT.B2*A2 ) THEN
+               S = MAX( S, A2*( ONE-CNST2*A2*( B2 / GAP2 )*B2 ) )
+            ELSE 
+               S = MAX( S, A2*( ONE-CNST2*B2 ) )
+            END IF
+         ELSE
+            S = QURTR*DMIN2
+            TTYPE = -11
+         END IF
+      ELSE IF( N0IN.GT.( N0+2 ) ) THEN
+*
+*        Case 12, more than two eigenvalues deflated. No information.
+*
+         S = ZERO 
+         TTYPE = -12
+      END IF
+*
+      TAU = S
+      RETURN
+*
+*     End of DLASQ4
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlasq5.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlasq5.f
new file mode 100644
index 00000000..19470447
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlasq5.f
@@ -0,0 +1,413 @@
+*> \brief \b DLASQ5 computes one dqds transform in ping-pong form. Used by sbdsqr and sstegr.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLASQ5 + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasq5.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasq5.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasq5.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DLASQ5( I0, N0, Z, PP, TAU, SIGMA, DMIN, DMIN1, DMIN2, DN,
+*                          DNM1, DNM2, IEEE, EPS )
+* 
+*       .. Scalar Arguments ..
+*       LOGICAL            IEEE
+*       INTEGER            I0, N0, PP
+*       DOUBLE PRECISION   DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, TAU, SIGMA, EPS
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   Z( * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DLASQ5 computes one dqds transform in ping-pong form, one
+*> version for IEEE machines another for non IEEE machines.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] I0
+*> \verbatim
+*>          I0 is INTEGER
+*>        First index.
+*> \endverbatim
+*>
+*> \param[in] N0
+*> \verbatim
+*>          N0 is INTEGER
+*>        Last index.
+*> \endverbatim
+*>
+*> \param[in] Z
+*> \verbatim
+*>          Z is DOUBLE PRECISION array, dimension ( 4*N )
+*>        Z holds the qd array. EMIN is stored in Z(4*N0) to avoid
+*>        an extra argument.
+*> \endverbatim
+*>
+*> \param[in] PP
+*> \verbatim
+*>          PP is INTEGER
+*>        PP=0 for ping, PP=1 for pong.
+*> \endverbatim
+*>
+*> \param[in] TAU
+*> \verbatim
+*>          TAU is DOUBLE PRECISION
+*>        This is the shift.
+*> \endverbatim
+*>
+*> \param[in] SIGMA
+*> \verbatim
+*>          SIGMA is DOUBLE PRECISION
+*>        This is the accumulated shift up to this step.
+*> \endverbatim
+*>
+*> \param[out] DMIN
+*> \verbatim
+*>          DMIN is DOUBLE PRECISION
+*>        Minimum value of d.
+*> \endverbatim
+*>
+*> \param[out] DMIN1
+*> \verbatim
+*>          DMIN1 is DOUBLE PRECISION
+*>        Minimum value of d, excluding D( N0 ).
+*> \endverbatim
+*>
+*> \param[out] DMIN2
+*> \verbatim
+*>          DMIN2 is DOUBLE PRECISION
+*>        Minimum value of d, excluding D( N0 ) and D( N0-1 ).
+*> \endverbatim
+*>
+*> \param[out] DN
+*> \verbatim
+*>          DN is DOUBLE PRECISION
+*>        d(N0), the last value of d.
+*> \endverbatim
+*>
+*> \param[out] DNM1
+*> \verbatim
+*>          DNM1 is DOUBLE PRECISION
+*>        d(N0-1).
+*> \endverbatim
+*>
+*> \param[out] DNM2
+*> \verbatim
+*>          DNM2 is DOUBLE PRECISION
+*>        d(N0-2).
+*> \endverbatim
+*>
+*> \param[in] IEEE
+*> \verbatim
+*>          IEEE is LOGICAL
+*>        Flag for IEEE or non IEEE arithmetic.
+*> \endverbatim
+*
+*> \param[in] EPS
+*> \verbatim
+*>          EPS is DOUBLE PRECISION
+*>        This is the value of epsilon used.
+*> \endverbatim
+*>
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date September 2012
+*
+*> \ingroup auxOTHERcomputational
+*
+*  =====================================================================
+      SUBROUTINE DLASQ5( I0, N0, Z, PP, TAU, SIGMA, DMIN, DMIN1, DMIN2,
+     $                   DN, DNM1, DNM2, IEEE, EPS )
+*
+*  -- LAPACK computational routine (version 3.4.2) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     September 2012
+*
+*     .. Scalar Arguments ..
+      LOGICAL            IEEE
+      INTEGER            I0, N0, PP
+      DOUBLE PRECISION   DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, TAU,
+     $                   SIGMA, EPS
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   Z( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameter ..
+      DOUBLE PRECISION   ZERO, HALF
+      PARAMETER          ( ZERO = 0.0D0, HALF = 0.5 )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            J4, J4P2
+      DOUBLE PRECISION   D, EMIN, TEMP, DTHRESH
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MIN
+*     ..
+*     .. Executable Statements ..
+*
+
+      IF( ( N0-I0-1 ).LE.0 )
+     $   RETURN
+*
+      DTHRESH = EPS*(SIGMA+TAU)
+      IF( TAU.LT.DTHRESH*HALF ) TAU = ZERO
+      IF( TAU.NE.ZERO ) THEN
+      J4 = 4*I0 + PP - 3
+      EMIN = Z( J4+4 ) 
+      D = Z( J4 ) - TAU
+      DMIN = D
+      DMIN1 = -Z( J4 )
+*
+      IF( IEEE ) THEN
+*
+*        Code for IEEE arithmetic.
+*
+         IF( PP.EQ.0 ) THEN
+            DO 10 J4 = 4*I0, 4*( N0-3 ), 4
+               Z( J4-2 ) = D + Z( J4-1 ) 
+               TEMP = Z( J4+1 ) / Z( J4-2 )
+               D = D*TEMP - TAU
+               DMIN = MIN( DMIN, D )
+               Z( J4 ) = Z( J4-1 )*TEMP
+               EMIN = MIN( Z( J4 ), EMIN )
+   10       CONTINUE
+         ELSE
+            DO 20 J4 = 4*I0, 4*( N0-3 ), 4
+               Z( J4-3 ) = D + Z( J4 ) 
+               TEMP = Z( J4+2 ) / Z( J4-3 )
+               D = D*TEMP - TAU
+               DMIN = MIN( DMIN, D )
+               Z( J4-1 ) = Z( J4 )*TEMP
+               EMIN = MIN( Z( J4-1 ), EMIN )
+   20       CONTINUE
+         END IF
+
+*
+*        Unroll last two steps. 
+*
+         DNM2 = D
+         DMIN2 = DMIN
+         J4 = 4*( N0-2 ) - PP
+         J4P2 = J4 + 2*PP - 1
+         Z( J4-2 ) = DNM2 + Z( J4P2 )
+         Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
+         DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU
+         DMIN = MIN( DMIN, DNM1 )
+*
+         DMIN1 = DMIN
+         J4 = J4 + 4
+         J4P2 = J4 + 2*PP - 1
+         Z( J4-2 ) = DNM1 + Z( J4P2 )
+         Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
+         DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU
+         DMIN = MIN( DMIN, DN )
+*
+      ELSE
+*
+*        Code for non IEEE arithmetic.
+*
+         IF( PP.EQ.0 ) THEN
+            DO 30 J4 = 4*I0, 4*( N0-3 ), 4
+               Z( J4-2 ) = D + Z( J4-1 ) 
+               IF( D.LT.ZERO ) THEN
+                  RETURN
+               ELSE 
+                  Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) )
+                  D = Z( J4+1 )*( D / Z( J4-2 ) ) - TAU
+               END IF
+               DMIN = MIN( DMIN, D )
+               EMIN = MIN( EMIN, Z( J4 ) )
+   30       CONTINUE
+         ELSE
+            DO 40 J4 = 4*I0, 4*( N0-3 ), 4
+               Z( J4-3 ) = D + Z( J4 ) 
+               IF( D.LT.ZERO ) THEN
+                  RETURN
+               ELSE 
+                  Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) )
+                  D = Z( J4+2 )*( D / Z( J4-3 ) ) - TAU
+               END IF
+               DMIN = MIN( DMIN, D )
+               EMIN = MIN( EMIN, Z( J4-1 ) )
+   40       CONTINUE
+         END IF
+*
+*        Unroll last two steps. 
+*
+         DNM2 = D
+         DMIN2 = DMIN
+         J4 = 4*( N0-2 ) - PP
+         J4P2 = J4 + 2*PP - 1
+         Z( J4-2 ) = DNM2 + Z( J4P2 )
+         IF( DNM2.LT.ZERO ) THEN
+            RETURN
+         ELSE
+            Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
+            DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU
+         END IF
+         DMIN = MIN( DMIN, DNM1 )
+*
+         DMIN1 = DMIN
+         J4 = J4 + 4
+         J4P2 = J4 + 2*PP - 1
+         Z( J4-2 ) = DNM1 + Z( J4P2 )
+         IF( DNM1.LT.ZERO ) THEN
+            RETURN
+         ELSE
+            Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
+            DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU
+         END IF
+         DMIN = MIN( DMIN, DN )
+*
+      END IF
+      ELSE
+*     This is the version that sets d's to zero if they are small enough
+         J4 = 4*I0 + PP - 3
+         EMIN = Z( J4+4 ) 
+         D = Z( J4 ) - TAU
+         DMIN = D
+         DMIN1 = -Z( J4 )
+         IF( IEEE ) THEN
+*     
+*     Code for IEEE arithmetic.
+*
+
+            IF( PP.EQ.0 ) THEN
+               DO 50 J4 = 4*I0, 4*( N0-3 ), 4
+                  Z( J4-2 ) = D + Z( J4-1 ) 
+                  TEMP = Z( J4+1 ) / Z( J4-2 )
+                  D = D*TEMP - TAU
+                  IF( D.LT.DTHRESH ) D = ZERO
+                  DMIN = MIN( DMIN, D )
+                  Z( J4 ) = Z( J4-1 )*TEMP
+                  EMIN = MIN( Z( J4 ), EMIN )
+ 50            CONTINUE
+            ELSE
+               DO 60 J4 = 4*I0, 4*( N0-3 ), 4
+                  Z( J4-3 ) = D + Z( J4 ) 
+                  TEMP = Z( J4+2 ) / Z( J4-3 )
+                  D = D*TEMP - TAU
+                  IF( D.LT.DTHRESH ) D = ZERO
+                  DMIN = MIN( DMIN, D )
+                  Z( J4-1 ) = Z( J4 )*TEMP
+                  EMIN = MIN( Z( J4-1 ), EMIN )
+ 60            CONTINUE
+            END IF
+*     
+*     Unroll last two steps. 
+*     
+            DNM2 = D
+            DMIN2 = DMIN
+            J4 = 4*( N0-2 ) - PP
+            J4P2 = J4 + 2*PP - 1
+            Z( J4-2 ) = DNM2 + Z( J4P2 )
+            Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
+            DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU
+            DMIN = MIN( DMIN, DNM1 )
+*     
+            DMIN1 = DMIN
+            J4 = J4 + 4
+            J4P2 = J4 + 2*PP - 1
+            Z( J4-2 ) = DNM1 + Z( J4P2 )
+            Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
+            DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU
+            DMIN = MIN( DMIN, DN )
+*     
+         ELSE
+*     
+*     Code for non IEEE arithmetic.
+*     
+            IF( PP.EQ.0 ) THEN
+               DO 70 J4 = 4*I0, 4*( N0-3 ), 4
+                  Z( J4-2 ) = D + Z( J4-1 ) 
+                  IF( D.LT.ZERO ) THEN
+                     RETURN
+                  ELSE 
+                     Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) )
+                     D = Z( J4+1 )*( D / Z( J4-2 ) ) - TAU
+                  END IF
+                  IF( D.LT.DTHRESH) D = ZERO
+                  DMIN = MIN( DMIN, D )
+                  EMIN = MIN( EMIN, Z( J4 ) )
+ 70            CONTINUE
+            ELSE
+               DO 80 J4 = 4*I0, 4*( N0-3 ), 4
+                  Z( J4-3 ) = D + Z( J4 ) 
+                  IF( D.LT.ZERO ) THEN
+                     RETURN
+                  ELSE 
+                     Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) )
+                     D = Z( J4+2 )*( D / Z( J4-3 ) ) - TAU
+                  END IF
+                  IF( D.LT.DTHRESH) D = ZERO
+                  DMIN = MIN( DMIN, D )
+                  EMIN = MIN( EMIN, Z( J4-1 ) )
+ 80            CONTINUE
+            END IF
+*     
+*     Unroll last two steps. 
+*     
+            DNM2 = D
+            DMIN2 = DMIN
+            J4 = 4*( N0-2 ) - PP
+            J4P2 = J4 + 2*PP - 1
+            Z( J4-2 ) = DNM2 + Z( J4P2 )
+            IF( DNM2.LT.ZERO ) THEN
+               RETURN
+            ELSE
+               Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
+               DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU
+            END IF
+            DMIN = MIN( DMIN, DNM1 )
+*     
+            DMIN1 = DMIN
+            J4 = J4 + 4
+            J4P2 = J4 + 2*PP - 1
+            Z( J4-2 ) = DNM1 + Z( J4P2 )
+            IF( DNM1.LT.ZERO ) THEN
+               RETURN
+            ELSE
+               Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
+               DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU
+            END IF
+            DMIN = MIN( DMIN, DN )
+*     
+         END IF
+      END IF
+*     
+      Z( J4+2 ) = DN
+      Z( 4*N0-PP ) = EMIN
+      RETURN
+*
+*     End of DLASQ5
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlasq6.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlasq6.f
new file mode 100644
index 00000000..bcd61f35
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlasq6.f
@@ -0,0 +1,258 @@
+*> \brief \b DLASQ6 computes one dqd transform in ping-pong form. Used by sbdsqr and sstegr.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLASQ6 + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasq6.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasq6.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasq6.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN,
+*                          DNM1, DNM2 )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            I0, N0, PP
+*       DOUBLE PRECISION   DMIN, DMIN1, DMIN2, DN, DNM1, DNM2
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   Z( * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DLASQ6 computes one dqd (shift equal to zero) transform in
+*> ping-pong form, with protection against underflow and overflow.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] I0
+*> \verbatim
+*>          I0 is INTEGER
+*>        First index.
+*> \endverbatim
+*>
+*> \param[in] N0
+*> \verbatim
+*>          N0 is INTEGER
+*>        Last index.
+*> \endverbatim
+*>
+*> \param[in] Z
+*> \verbatim
+*>          Z is DOUBLE PRECISION array, dimension ( 4*N )
+*>        Z holds the qd array. EMIN is stored in Z(4*N0) to avoid
+*>        an extra argument.
+*> \endverbatim
+*>
+*> \param[in] PP
+*> \verbatim
+*>          PP is INTEGER
+*>        PP=0 for ping, PP=1 for pong.
+*> \endverbatim
+*>
+*> \param[out] DMIN
+*> \verbatim
+*>          DMIN is DOUBLE PRECISION
+*>        Minimum value of d.
+*> \endverbatim
+*>
+*> \param[out] DMIN1
+*> \verbatim
+*>          DMIN1 is DOUBLE PRECISION
+*>        Minimum value of d, excluding D( N0 ).
+*> \endverbatim
+*>
+*> \param[out] DMIN2
+*> \verbatim
+*>          DMIN2 is DOUBLE PRECISION
+*>        Minimum value of d, excluding D( N0 ) and D( N0-1 ).
+*> \endverbatim
+*>
+*> \param[out] DN
+*> \verbatim
+*>          DN is DOUBLE PRECISION
+*>        d(N0), the last value of d.
+*> \endverbatim
+*>
+*> \param[out] DNM1
+*> \verbatim
+*>          DNM1 is DOUBLE PRECISION
+*>        d(N0-1).
+*> \endverbatim
+*>
+*> \param[out] DNM2
+*> \verbatim
+*>          DNM2 is DOUBLE PRECISION
+*>        d(N0-2).
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date September 2012
+*
+*> \ingroup auxOTHERcomputational
+*
+*  =====================================================================
+      SUBROUTINE DLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN,
+     $                   DNM1, DNM2 )
+*
+*  -- LAPACK computational routine (version 3.4.2) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     September 2012
+*
+*     .. Scalar Arguments ..
+      INTEGER            I0, N0, PP
+      DOUBLE PRECISION   DMIN, DMIN1, DMIN2, DN, DNM1, DNM2
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   Z( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameter ..
+      DOUBLE PRECISION   ZERO
+      PARAMETER          ( ZERO = 0.0D0 )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            J4, J4P2
+      DOUBLE PRECISION   D, EMIN, SAFMIN, TEMP
+*     ..
+*     .. External Function ..
+      DOUBLE PRECISION   DLAMCH
+      EXTERNAL           DLAMCH
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MIN
+*     ..
+*     .. Executable Statements ..
+*
+      IF( ( N0-I0-1 ).LE.0 )
+     $   RETURN
+*
+
+      print *, "In dlasq6"
+      STOP
+
+      SAFMIN = DLAMCH( 'Safe minimum' )
+      J4 = 4*I0 + PP - 3
+      EMIN = Z( J4+4 ) 
+      D = Z( J4 )
+      DMIN = D
+*
+      IF( PP.EQ.0 ) THEN
+         DO 10 J4 = 4*I0, 4*( N0-3 ), 4
+            Z( J4-2 ) = D + Z( J4-1 ) 
+            IF( Z( J4-2 ).EQ.ZERO ) THEN
+               Z( J4 ) = ZERO
+               D = Z( J4+1 )
+               DMIN = D
+               EMIN = ZERO
+            ELSE IF( SAFMIN*Z( J4+1 ).LT.Z( J4-2 ) .AND.
+     $               SAFMIN*Z( J4-2 ).LT.Z( J4+1 ) ) THEN
+               TEMP = Z( J4+1 ) / Z( J4-2 )
+               Z( J4 ) = Z( J4-1 )*TEMP
+               D = D*TEMP
+            ELSE 
+               Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) )
+               D = Z( J4+1 )*( D / Z( J4-2 ) )
+            END IF
+            DMIN = MIN( DMIN, D )
+            EMIN = MIN( EMIN, Z( J4 ) )
+   10    CONTINUE
+      ELSE
+         DO 20 J4 = 4*I0, 4*( N0-3 ), 4
+            Z( J4-3 ) = D + Z( J4 ) 
+            IF( Z( J4-3 ).EQ.ZERO ) THEN
+               Z( J4-1 ) = ZERO
+               D = Z( J4+2 )
+               DMIN = D
+               EMIN = ZERO
+            ELSE IF( SAFMIN*Z( J4+2 ).LT.Z( J4-3 ) .AND.
+     $               SAFMIN*Z( J4-3 ).LT.Z( J4+2 ) ) THEN
+               TEMP = Z( J4+2 ) / Z( J4-3 )
+               Z( J4-1 ) = Z( J4 )*TEMP
+               D = D*TEMP
+            ELSE 
+               Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) )
+               D = Z( J4+2 )*( D / Z( J4-3 ) )
+            END IF
+            DMIN = MIN( DMIN, D )
+            EMIN = MIN( EMIN, Z( J4-1 ) )
+   20    CONTINUE
+      END IF
+*
+*     Unroll last two steps. 
+*
+      DNM2 = D
+      DMIN2 = DMIN
+      J4 = 4*( N0-2 ) - PP
+      J4P2 = J4 + 2*PP - 1
+      Z( J4-2 ) = DNM2 + Z( J4P2 )
+      IF( Z( J4-2 ).EQ.ZERO ) THEN
+         Z( J4 ) = ZERO
+         DNM1 = Z( J4P2+2 )
+         DMIN = DNM1
+         EMIN = ZERO
+      ELSE IF( SAFMIN*Z( J4P2+2 ).LT.Z( J4-2 ) .AND.
+     $         SAFMIN*Z( J4-2 ).LT.Z( J4P2+2 ) ) THEN
+         TEMP = Z( J4P2+2 ) / Z( J4-2 )
+         Z( J4 ) = Z( J4P2 )*TEMP
+         DNM1 = DNM2*TEMP
+      ELSE
+         Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
+         DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) )
+      END IF
+      DMIN = MIN( DMIN, DNM1 )
+*
+      DMIN1 = DMIN
+      J4 = J4 + 4
+      J4P2 = J4 + 2*PP - 1
+      Z( J4-2 ) = DNM1 + Z( J4P2 )
+      IF( Z( J4-2 ).EQ.ZERO ) THEN
+         Z( J4 ) = ZERO
+         DN = Z( J4P2+2 )
+         DMIN = DN
+         EMIN = ZERO
+      ELSE IF( SAFMIN*Z( J4P2+2 ).LT.Z( J4-2 ) .AND.
+     $         SAFMIN*Z( J4-2 ).LT.Z( J4P2+2 ) ) THEN
+         TEMP = Z( J4P2+2 ) / Z( J4-2 )
+         Z( J4 ) = Z( J4P2 )*TEMP
+         DN = DNM1*TEMP
+      ELSE
+         Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
+         DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) )
+      END IF
+      DMIN = MIN( DMIN, DN )
+*
+      Z( J4+2 ) = DN
+      Z( 4*N0-PP ) = EMIN
+      RETURN
+*
+*     End of DLASQ6
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlasrt.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlasrt.f
new file mode 100644
index 00000000..f5d0e6cd
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/dlasrt.f
@@ -0,0 +1,303 @@
+*> \brief \b DLASRT sorts numbers in increasing or decreasing order.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLASRT + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasrt.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasrt.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasrt.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DLASRT( ID, N, D, INFO )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER          ID
+*       INTEGER            INFO, N
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   D( * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> Sort the numbers in D in increasing order (if ID = 'I') or
+*> in decreasing order (if ID = 'D' ).
+*>
+*> Use Quick Sort, reverting to Insertion sort on arrays of
+*> size <= 20. Dimension of STACK limits N to about 2**32.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] ID
+*> \verbatim
+*>          ID is CHARACTER*1
+*>          = 'I': sort D in increasing order;
+*>          = 'D': sort D in decreasing order.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The length of the array D.
+*> \endverbatim
+*>
+*> \param[in,out] D
+*> \verbatim
+*>          D is DOUBLE PRECISION array, dimension (N)
+*>          On entry, the array to be sorted.
+*>          On exit, D has been sorted into increasing order
+*>          (D(1) <= ... <= D(N) ) or into decreasing order
+*>          (D(1) >= ... >= D(N) ), depending on ID.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0:  successful exit
+*>          < 0:  if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date September 2012
+*
+*> \ingroup auxOTHERcomputational
+*
+*  =====================================================================
+      SUBROUTINE DLASRT( ID, N, D, INFO )
+*
+*  -- LAPACK computational routine (version 3.4.2) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     September 2012
+*
+*     .. Scalar Arguments ..
+      CHARACTER          ID
+      INTEGER            INFO, N
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   D( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      INTEGER            SELECT
+      PARAMETER          ( SELECT = 20 )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            DIR, ENDD, I, J, START, STKPNT
+      DOUBLE PRECISION   D1, D2, D3, DMNMX, TMP
+*     ..
+*     .. Local Arrays ..
+      INTEGER            STACK( 2, 32 )
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      EXTERNAL           LSAME
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           XERBLA
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input paramters.
+*
+      INFO = 0
+      DIR = -1
+      IF( LSAME( ID, 'D' ) ) THEN
+         DIR = 0
+      ELSE IF( LSAME( ID, 'I' ) ) THEN
+         DIR = 1
+      END IF
+      IF( DIR.EQ.-1 ) THEN
+         INFO = -1
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -2
+      END IF
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'DLASRT', -INFO )
+         RETURN
+      END IF
+*
+*     Quick return if possible
+*
+      IF( N.LE.1 )
+     $   RETURN
+*
+      STKPNT = 1
+      STACK( 1, 1 ) = 1
+      STACK( 2, 1 ) = N
+   10 CONTINUE
+      START = STACK( 1, STKPNT )
+      ENDD = STACK( 2, STKPNT )
+      STKPNT = STKPNT - 1
+      IF( ENDD-START.LE.SELECT .AND. ENDD-START.GT.0 ) THEN
+*
+*        Do Insertion sort on D( START:ENDD )
+*
+         IF( DIR.EQ.0 ) THEN
+*
+*           Sort into decreasing order
+*
+            DO 30 I = START + 1, ENDD
+               DO 20 J = I, START + 1, -1
+                  IF( D( J ).GT.D( J-1 ) ) THEN
+                     DMNMX = D( J )
+                     D( J ) = D( J-1 )
+                     D( J-1 ) = DMNMX
+                  ELSE
+                     GO TO 30
+                  END IF
+   20          CONTINUE
+   30       CONTINUE
+*
+         ELSE
+*
+*           Sort into increasing order
+*
+            DO 50 I = START + 1, ENDD
+               DO 40 J = I, START + 1, -1
+                  IF( D( J ).LT.D( J-1 ) ) THEN
+                     DMNMX = D( J )
+                     D( J ) = D( J-1 )
+                     D( J-1 ) = DMNMX
+                  ELSE
+                     GO TO 50
+                  END IF
+   40          CONTINUE
+   50       CONTINUE
+*
+         END IF
+*
+      ELSE IF( ENDD-START.GT.SELECT ) THEN
+*
+*        Partition D( START:ENDD ) and stack parts, largest one first
+*
+*        Choose partition entry as median of 3
+*
+         D1 = D( START )
+         D2 = D( ENDD )
+         I = ( START+ENDD ) / 2
+         D3 = D( I )
+         IF( D1.LT.D2 ) THEN
+            IF( D3.LT.D1 ) THEN
+               DMNMX = D1
+            ELSE IF( D3.LT.D2 ) THEN
+               DMNMX = D3
+            ELSE
+               DMNMX = D2
+            END IF
+         ELSE
+            IF( D3.LT.D2 ) THEN
+               DMNMX = D2
+            ELSE IF( D3.LT.D1 ) THEN
+               DMNMX = D3
+            ELSE
+               DMNMX = D1
+            END IF
+         END IF
+*
+         IF( DIR.EQ.0 ) THEN
+*
+*           Sort into decreasing order
+*
+            I = START - 1
+            J = ENDD + 1
+   60       CONTINUE
+   70       CONTINUE
+            J = J - 1
+            IF( D( J ).LT.DMNMX )
+     $         GO TO 70
+   80       CONTINUE
+            I = I + 1
+            IF( D( I ).GT.DMNMX )
+     $         GO TO 80
+            IF( I.LT.J ) THEN
+               TMP = D( I )
+               D( I ) = D( J )
+               D( J ) = TMP
+               GO TO 60
+            END IF
+            IF( J-START.GT.ENDD-J-1 ) THEN
+               STKPNT = STKPNT + 1
+               STACK( 1, STKPNT ) = START
+               STACK( 2, STKPNT ) = J
+               STKPNT = STKPNT + 1
+               STACK( 1, STKPNT ) = J + 1
+               STACK( 2, STKPNT ) = ENDD
+            ELSE
+               STKPNT = STKPNT + 1
+               STACK( 1, STKPNT ) = J + 1
+               STACK( 2, STKPNT ) = ENDD
+               STKPNT = STKPNT + 1
+               STACK( 1, STKPNT ) = START
+               STACK( 2, STKPNT ) = J
+            END IF
+         ELSE
+*
+*           Sort into increasing order
+*
+            I = START - 1
+            J = ENDD + 1
+   90       CONTINUE
+  100       CONTINUE
+            J = J - 1
+            IF( D( J ).GT.DMNMX )
+     $         GO TO 100
+  110       CONTINUE
+            I = I + 1
+            IF( D( I ).LT.DMNMX )
+     $         GO TO 110
+            IF( I.LT.J ) THEN
+               TMP = D( I )
+               D( I ) = D( J )
+               D( J ) = TMP
+               GO TO 90
+            END IF
+            IF( J-START.GT.ENDD-J-1 ) THEN
+               STKPNT = STKPNT + 1
+               STACK( 1, STKPNT ) = START
+               STACK( 2, STKPNT ) = J
+               STKPNT = STKPNT + 1
+               STACK( 1, STKPNT ) = J + 1
+               STACK( 2, STKPNT ) = ENDD
+            ELSE
+               STKPNT = STKPNT + 1
+               STACK( 1, STKPNT ) = J + 1
+               STACK( 2, STKPNT ) = ENDD
+               STKPNT = STKPNT + 1
+               STACK( 1, STKPNT ) = START
+               STACK( 2, STKPNT ) = J
+            END IF
+         END IF
+      END IF
+      IF( STKPNT.GT.0 )
+     $   GO TO 10
+      RETURN
+*
+*     End of DLASRT
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/ieeeck.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/ieeeck.f
new file mode 100644
index 00000000..132e4367
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/ieeeck.f
@@ -0,0 +1,203 @@
+*> \brief \b IEEECK
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download IEEECK + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ieeeck.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ieeeck.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ieeeck.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       INTEGER          FUNCTION IEEECK( ISPEC, ZERO, ONE )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            ISPEC
+*       REAL               ONE, ZERO
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> IEEECK is called from the ILAENV to verify that Infinity and
+*> possibly NaN arithmetic is safe (i.e. will not trap).
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] ISPEC
+*> \verbatim
+*>          ISPEC is INTEGER
+*>          Specifies whether to test just for inifinity arithmetic
+*>          or whether to test for infinity and NaN arithmetic.
+*>          = 0: Verify infinity arithmetic only.
+*>          = 1: Verify infinity and NaN arithmetic.
+*> \endverbatim
+*>
+*> \param[in] ZERO
+*> \verbatim
+*>          ZERO is REAL
+*>          Must contain the value 0.0
+*>          This is passed to prevent the compiler from optimizing
+*>          away this code.
+*> \endverbatim
+*>
+*> \param[in] ONE
+*> \verbatim
+*>          ONE is REAL
+*>          Must contain the value 1.0
+*>          This is passed to prevent the compiler from optimizing
+*>          away this code.
+*>
+*>  RETURN VALUE:  INTEGER
+*>          = 0:  Arithmetic failed to produce the correct answers
+*>          = 1:  Arithmetic produced the correct answers
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup auxOTHERauxiliary
+*
+*  =====================================================================
+      INTEGER          FUNCTION IEEECK( ISPEC, ZERO, ONE )
+*
+*  -- LAPACK auxiliary routine (version 3.4.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2011
+*
+*     .. Scalar Arguments ..
+      INTEGER            ISPEC
+      REAL               ONE, ZERO
+*     ..
+*
+*  =====================================================================
+*
+*     .. Local Scalars ..
+      REAL               NAN1, NAN2, NAN3, NAN4, NAN5, NAN6, NEGINF,
+     $                   NEGZRO, NEWZRO, POSINF
+*     ..
+*     .. Executable Statements ..
+      IEEECK = 1
+*
+      POSINF = ONE / ZERO
+      IF( POSINF.LE.ONE ) THEN
+         IEEECK = 0
+         RETURN
+      END IF
+*
+      NEGINF = -ONE / ZERO
+      IF( NEGINF.GE.ZERO ) THEN
+         IEEECK = 0
+         RETURN
+      END IF
+*
+      NEGZRO = ONE / ( NEGINF+ONE )
+      IF( NEGZRO.NE.ZERO ) THEN
+         IEEECK = 0
+         RETURN
+      END IF
+*
+      NEGINF = ONE / NEGZRO
+      IF( NEGINF.GE.ZERO ) THEN
+         IEEECK = 0
+         RETURN
+      END IF
+*
+      NEWZRO = NEGZRO + ZERO
+      IF( NEWZRO.NE.ZERO ) THEN
+         IEEECK = 0
+         RETURN
+      END IF
+*
+      POSINF = ONE / NEWZRO
+      IF( POSINF.LE.ONE ) THEN
+         IEEECK = 0
+         RETURN
+      END IF
+*
+      NEGINF = NEGINF*POSINF
+      IF( NEGINF.GE.ZERO ) THEN
+         IEEECK = 0
+         RETURN
+      END IF
+*
+      POSINF = POSINF*POSINF
+      IF( POSINF.LE.ONE ) THEN
+         IEEECK = 0
+         RETURN
+      END IF
+*
+*
+*
+*
+*     Return if we were only asked to check infinity arithmetic
+*
+      IF( ISPEC.EQ.0 )
+     $   RETURN
+*
+      NAN1 = POSINF + NEGINF
+*
+      NAN2 = POSINF / NEGINF
+*
+      NAN3 = POSINF / POSINF
+*
+      NAN4 = POSINF*ZERO
+*
+      NAN5 = NEGINF*NEGZRO
+*
+      NAN6 = NAN5*ZERO
+*
+      IF( NAN1.EQ.NAN1 ) THEN
+         IEEECK = 0
+         RETURN
+      END IF
+*
+      IF( NAN2.EQ.NAN2 ) THEN
+         IEEECK = 0
+         RETURN
+      END IF
+*
+      IF( NAN3.EQ.NAN3 ) THEN
+         IEEECK = 0
+         RETURN
+      END IF
+*
+      IF( NAN4.EQ.NAN4 ) THEN
+         IEEECK = 0
+         RETURN
+      END IF
+*
+      IF( NAN5.EQ.NAN5 ) THEN
+         IEEECK = 0
+         RETURN
+      END IF
+*
+      IF( NAN6.EQ.NAN6 ) THEN
+         IEEECK = 0
+         RETURN
+      END IF
+*
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/ilaenv.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/ilaenv.f
new file mode 100644
index 00000000..867464de
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/ilaenv.f
@@ -0,0 +1,624 @@
+*> \brief \b ILAENV
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download ILAENV + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ilaenv.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ilaenv.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ilaenv.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       INTEGER FUNCTION ILAENV( ISPEC, NAME, OPTS, N1, N2, N3, N4 )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER*( * )    NAME, OPTS
+*       INTEGER            ISPEC, N1, N2, N3, N4
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> ILAENV is called from the LAPACK routines to choose problem-dependent
+*> parameters for the local environment.  See ISPEC for a description of
+*> the parameters.
+*>
+*> ILAENV returns an INTEGER
+*> if ILAENV >= 0: ILAENV returns the value of the parameter specified by ISPEC
+*> if ILAENV < 0:  if ILAENV = -k, the k-th argument had an illegal value.
+*>
+*> This version provides a set of parameters which should give good,
+*> but not optimal, performance on many of the currently available
+*> computers.  Users are encouraged to modify this subroutine to set
+*> the tuning parameters for their particular machine using the option
+*> and problem size information in the arguments.
+*>
+*> This routine will not function correctly if it is converted to all
+*> lower case.  Converting it to all upper case is allowed.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] ISPEC
+*> \verbatim
+*>          ISPEC is INTEGER
+*>          Specifies the parameter to be returned as the value of
+*>          ILAENV.
+*>          = 1: the optimal blocksize; if this value is 1, an unblocked
+*>               algorithm will give the best performance.
+*>          = 2: the minimum block size for which the block routine
+*>               should be used; if the usable block size is less than
+*>               this value, an unblocked routine should be used.
+*>          = 3: the crossover point (in a block routine, for N less
+*>               than this value, an unblocked routine should be used)
+*>          = 4: the number of shifts, used in the nonsymmetric
+*>               eigenvalue routines (DEPRECATED)
+*>          = 5: the minimum column dimension for blocking to be used;
+*>               rectangular blocks must have dimension at least k by m,
+*>               where k is given by ILAENV(2,...) and m by ILAENV(5,...)
+*>          = 6: the crossover point for the SVD (when reducing an m by n
+*>               matrix to bidiagonal form, if max(m,n)/min(m,n) exceeds
+*>               this value, a QR factorization is used first to reduce
+*>               the matrix to a triangular form.)
+*>          = 7: the number of processors
+*>          = 8: the crossover point for the multishift QR method
+*>               for nonsymmetric eigenvalue problems (DEPRECATED)
+*>          = 9: maximum size of the subproblems at the bottom of the
+*>               computation tree in the divide-and-conquer algorithm
+*>               (used by xGELSD and xGESDD)
+*>          =10: ieee NaN arithmetic can be trusted not to trap
+*>          =11: infinity arithmetic can be trusted not to trap
+*>          12 <= ISPEC <= 16:
+*>               xHSEQR or one of its subroutines,
+*>               see IPARMQ for detailed explanation
+*> \endverbatim
+*>
+*> \param[in] NAME
+*> \verbatim
+*>          NAME is CHARACTER*(*)
+*>          The name of the calling subroutine, in either upper case or
+*>          lower case.
+*> \endverbatim
+*>
+*> \param[in] OPTS
+*> \verbatim
+*>          OPTS is CHARACTER*(*)
+*>          The character options to the subroutine NAME, concatenated
+*>          into a single character string.  For example, UPLO = 'U',
+*>          TRANS = 'T', and DIAG = 'N' for a triangular routine would
+*>          be specified as OPTS = 'UTN'.
+*> \endverbatim
+*>
+*> \param[in] N1
+*> \verbatim
+*>          N1 is INTEGER
+*> \endverbatim
+*>
+*> \param[in] N2
+*> \verbatim
+*>          N2 is INTEGER
+*> \endverbatim
+*>
+*> \param[in] N3
+*> \verbatim
+*>          N3 is INTEGER
+*> \endverbatim
+*>
+*> \param[in] N4
+*> \verbatim
+*>          N4 is INTEGER
+*>          Problem dimensions for the subroutine NAME; these may not all
+*>          be required.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup auxOTHERauxiliary
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  The following conventions have been used when calling ILAENV from the
+*>  LAPACK routines:
+*>  1)  OPTS is a concatenation of all of the character options to
+*>      subroutine NAME, in the same order that they appear in the
+*>      argument list for NAME, even if they are not used in determining
+*>      the value of the parameter specified by ISPEC.
+*>  2)  The problem dimensions N1, N2, N3, N4 are specified in the order
+*>      that they appear in the argument list for NAME.  N1 is used
+*>      first, N2 second, and so on, and unused problem dimensions are
+*>      passed a value of -1.
+*>  3)  The parameter value returned by ILAENV is checked for validity in
+*>      the calling subroutine.  For example, ILAENV is used to retrieve
+*>      the optimal blocksize for STRTRI as follows:
+*>
+*>      NB = ILAENV( 1, 'STRTRI', UPLO // DIAG, N, -1, -1, -1 )
+*>      IF( NB.LE.1 ) NB = MAX( 1, N )
+*> \endverbatim
+*>
+*  =====================================================================
+      INTEGER FUNCTION ILAENV( ISPEC, NAME, OPTS, N1, N2, N3, N4 )
+*
+*  -- LAPACK auxiliary routine (version 3.4.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2011
+*
+*     .. Scalar Arguments ..
+      CHARACTER*( * )    NAME, OPTS
+      INTEGER            ISPEC, N1, N2, N3, N4
+*     ..
+*
+*  =====================================================================
+*
+*     .. Local Scalars ..
+      INTEGER            I, IC, IZ, NB, NBMIN, NX
+      LOGICAL            CNAME, SNAME
+      CHARACTER          C1*1, C2*2, C4*2, C3*3, SUBNAM*6
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          CHAR, ICHAR, INT, MIN, REAL
+*     ..
+*     .. External Functions ..
+      INTEGER            IEEECK, IPARMQ
+      EXTERNAL           IEEECK, IPARMQ
+*     ..
+*     .. Executable Statements ..
+*
+      GO TO ( 10, 10, 10, 80, 90, 100, 110, 120,
+     $        130, 140, 150, 160, 160, 160, 160, 160 )ISPEC
+*
+*     Invalid value for ISPEC
+*
+      ILAENV = -1
+      RETURN
+*
+   10 CONTINUE
+*
+*     Convert NAME to upper case if the first character is lower case.
+*
+      ILAENV = 1
+      SUBNAM = NAME
+      IC = ICHAR( SUBNAM( 1: 1 ) )
+      IZ = ICHAR( 'Z' )
+      IF( IZ.EQ.90 .OR. IZ.EQ.122 ) THEN
+*
+*        ASCII character set
+*
+         IF( IC.GE.97 .AND. IC.LE.122 ) THEN
+            SUBNAM( 1: 1 ) = CHAR( IC-32 )
+            DO 20 I = 2, 6
+               IC = ICHAR( SUBNAM( I: I ) )
+               IF( IC.GE.97 .AND. IC.LE.122 )
+     $            SUBNAM( I: I ) = CHAR( IC-32 )
+   20       CONTINUE
+         END IF
+*
+      ELSE IF( IZ.EQ.233 .OR. IZ.EQ.169 ) THEN
+*
+*        EBCDIC character set
+*
+         IF( ( IC.GE.129 .AND. IC.LE.137 ) .OR.
+     $       ( IC.GE.145 .AND. IC.LE.153 ) .OR.
+     $       ( IC.GE.162 .AND. IC.LE.169 ) ) THEN
+            SUBNAM( 1: 1 ) = CHAR( IC+64 )
+            DO 30 I = 2, 6
+               IC = ICHAR( SUBNAM( I: I ) )
+               IF( ( IC.GE.129 .AND. IC.LE.137 ) .OR.
+     $             ( IC.GE.145 .AND. IC.LE.153 ) .OR.
+     $             ( IC.GE.162 .AND. IC.LE.169 ) )SUBNAM( I:
+     $             I ) = CHAR( IC+64 )
+   30       CONTINUE
+         END IF
+*
+      ELSE IF( IZ.EQ.218 .OR. IZ.EQ.250 ) THEN
+*
+*        Prime machines:  ASCII+128
+*
+         IF( IC.GE.225 .AND. IC.LE.250 ) THEN
+            SUBNAM( 1: 1 ) = CHAR( IC-32 )
+            DO 40 I = 2, 6
+               IC = ICHAR( SUBNAM( I: I ) )
+               IF( IC.GE.225 .AND. IC.LE.250 )
+     $            SUBNAM( I: I ) = CHAR( IC-32 )
+   40       CONTINUE
+         END IF
+      END IF
+*
+      C1 = SUBNAM( 1: 1 )
+      SNAME = C1.EQ.'S' .OR. C1.EQ.'D'
+      CNAME = C1.EQ.'C' .OR. C1.EQ.'Z'
+      IF( .NOT.( CNAME .OR. SNAME ) )
+     $   RETURN
+      C2 = SUBNAM( 2: 3 )
+      C3 = SUBNAM( 4: 6 )
+      C4 = C3( 2: 3 )
+*
+      GO TO ( 50, 60, 70 )ISPEC
+*
+   50 CONTINUE
+*
+*     ISPEC = 1:  block size
+*
+*     In these examples, separate code is provided for setting NB for
+*     real and complex.  We assume that NB will take the same value in
+*     single or double precision.
+*
+      NB = 1
+*
+      IF( C2.EQ.'GE' ) THEN
+         IF( C3.EQ.'TRF' ) THEN
+            IF( SNAME ) THEN
+               NB = 64
+            ELSE
+               NB = 64
+            END IF
+         ELSE IF( C3.EQ.'QRF' .OR. C3.EQ.'RQF' .OR. C3.EQ.'LQF' .OR.
+     $            C3.EQ.'QLF' ) THEN
+            IF( SNAME ) THEN
+               NB = 32
+            ELSE
+               NB = 32
+            END IF
+         ELSE IF( C3.EQ.'HRD' ) THEN
+            IF( SNAME ) THEN
+               NB = 32
+            ELSE
+               NB = 32
+            END IF
+         ELSE IF( C3.EQ.'BRD' ) THEN
+            IF( SNAME ) THEN
+               NB = 32
+            ELSE
+               NB = 32
+            END IF
+         ELSE IF( C3.EQ.'TRI' ) THEN
+            IF( SNAME ) THEN
+               NB = 64
+            ELSE
+               NB = 64
+            END IF
+         END IF
+      ELSE IF( C2.EQ.'PO' ) THEN
+         IF( C3.EQ.'TRF' ) THEN
+            IF( SNAME ) THEN
+               NB = 64
+            ELSE
+               NB = 64
+            END IF
+         END IF
+      ELSE IF( C2.EQ.'SY' ) THEN
+         IF( C3.EQ.'TRF' ) THEN
+            IF( SNAME ) THEN
+               NB = 64
+            ELSE
+               NB = 64
+            END IF
+         ELSE IF( SNAME .AND. C3.EQ.'TRD' ) THEN
+            NB = 32
+         ELSE IF( SNAME .AND. C3.EQ.'GST' ) THEN
+            NB = 64
+         END IF
+      ELSE IF( CNAME .AND. C2.EQ.'HE' ) THEN
+         IF( C3.EQ.'TRF' ) THEN
+            NB = 64
+         ELSE IF( C3.EQ.'TRD' ) THEN
+            NB = 32
+         ELSE IF( C3.EQ.'GST' ) THEN
+            NB = 64
+         END IF
+      ELSE IF( SNAME .AND. C2.EQ.'OR' ) THEN
+         IF( C3( 1: 1 ).EQ.'G' ) THEN
+            IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ.
+     $          'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' )
+     $           THEN
+               NB = 32
+            END IF
+         ELSE IF( C3( 1: 1 ).EQ.'M' ) THEN
+            IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ.
+     $          'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' )
+     $           THEN
+               NB = 32
+            END IF
+         END IF
+      ELSE IF( CNAME .AND. C2.EQ.'UN' ) THEN
+         IF( C3( 1: 1 ).EQ.'G' ) THEN
+            IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ.
+     $          'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' )
+     $           THEN
+               NB = 32
+            END IF
+         ELSE IF( C3( 1: 1 ).EQ.'M' ) THEN
+            IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ.
+     $          'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' )
+     $           THEN
+               NB = 32
+            END IF
+         END IF
+      ELSE IF( C2.EQ.'GB' ) THEN
+         IF( C3.EQ.'TRF' ) THEN
+            IF( SNAME ) THEN
+               IF( N4.LE.64 ) THEN
+                  NB = 1
+               ELSE
+                  NB = 32
+               END IF
+            ELSE
+               IF( N4.LE.64 ) THEN
+                  NB = 1
+               ELSE
+                  NB = 32
+               END IF
+            END IF
+         END IF
+      ELSE IF( C2.EQ.'PB' ) THEN
+         IF( C3.EQ.'TRF' ) THEN
+            IF( SNAME ) THEN
+               IF( N2.LE.64 ) THEN
+                  NB = 1
+               ELSE
+                  NB = 32
+               END IF
+            ELSE
+               IF( N2.LE.64 ) THEN
+                  NB = 1
+               ELSE
+                  NB = 32
+               END IF
+            END IF
+         END IF
+      ELSE IF( C2.EQ.'TR' ) THEN
+         IF( C3.EQ.'TRI' ) THEN
+            IF( SNAME ) THEN
+               NB = 64
+            ELSE
+               NB = 64
+            END IF
+         END IF
+      ELSE IF( C2.EQ.'LA' ) THEN
+         IF( C3.EQ.'UUM' ) THEN
+            IF( SNAME ) THEN
+               NB = 64
+            ELSE
+               NB = 64
+            END IF
+         END IF
+      ELSE IF( SNAME .AND. C2.EQ.'ST' ) THEN
+         IF( C3.EQ.'EBZ' ) THEN
+            NB = 1
+         END IF
+      END IF
+      ILAENV = NB
+      RETURN
+*
+   60 CONTINUE
+*
+*     ISPEC = 2:  minimum block size
+*
+      NBMIN = 2
+      IF( C2.EQ.'GE' ) THEN
+         IF( C3.EQ.'QRF' .OR. C3.EQ.'RQF' .OR. C3.EQ.'LQF' .OR. C3.EQ.
+     $       'QLF' ) THEN
+            IF( SNAME ) THEN
+               NBMIN = 2
+            ELSE
+               NBMIN = 2
+            END IF
+         ELSE IF( C3.EQ.'HRD' ) THEN
+            IF( SNAME ) THEN
+               NBMIN = 2
+            ELSE
+               NBMIN = 2
+            END IF
+         ELSE IF( C3.EQ.'BRD' ) THEN
+            IF( SNAME ) THEN
+               NBMIN = 2
+            ELSE
+               NBMIN = 2
+            END IF
+         ELSE IF( C3.EQ.'TRI' ) THEN
+            IF( SNAME ) THEN
+               NBMIN = 2
+            ELSE
+               NBMIN = 2
+            END IF
+         END IF
+      ELSE IF( C2.EQ.'SY' ) THEN
+         IF( C3.EQ.'TRF' ) THEN
+            IF( SNAME ) THEN
+               NBMIN = 8
+            ELSE
+               NBMIN = 8
+            END IF
+         ELSE IF( SNAME .AND. C3.EQ.'TRD' ) THEN
+            NBMIN = 2
+         END IF
+      ELSE IF( CNAME .AND. C2.EQ.'HE' ) THEN
+         IF( C3.EQ.'TRD' ) THEN
+            NBMIN = 2
+         END IF
+      ELSE IF( SNAME .AND. C2.EQ.'OR' ) THEN
+         IF( C3( 1: 1 ).EQ.'G' ) THEN
+            IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ.
+     $          'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' )
+     $           THEN
+               NBMIN = 2
+            END IF
+         ELSE IF( C3( 1: 1 ).EQ.'M' ) THEN
+            IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ.
+     $          'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' )
+     $           THEN
+               NBMIN = 2
+            END IF
+         END IF
+      ELSE IF( CNAME .AND. C2.EQ.'UN' ) THEN
+         IF( C3( 1: 1 ).EQ.'G' ) THEN
+            IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ.
+     $          'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' )
+     $           THEN
+               NBMIN = 2
+            END IF
+         ELSE IF( C3( 1: 1 ).EQ.'M' ) THEN
+            IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ.
+     $          'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' )
+     $           THEN
+               NBMIN = 2
+            END IF
+         END IF
+      END IF
+      ILAENV = NBMIN
+      RETURN
+*
+   70 CONTINUE
+*
+*     ISPEC = 3:  crossover point
+*
+      NX = 0
+      IF( C2.EQ.'GE' ) THEN
+         IF( C3.EQ.'QRF' .OR. C3.EQ.'RQF' .OR. C3.EQ.'LQF' .OR. C3.EQ.
+     $       'QLF' ) THEN
+            IF( SNAME ) THEN
+               NX = 128
+            ELSE
+               NX = 128
+            END IF
+         ELSE IF( C3.EQ.'HRD' ) THEN
+            IF( SNAME ) THEN
+               NX = 128
+            ELSE
+               NX = 128
+            END IF
+         ELSE IF( C3.EQ.'BRD' ) THEN
+            IF( SNAME ) THEN
+               NX = 128
+            ELSE
+               NX = 128
+            END IF
+         END IF
+      ELSE IF( C2.EQ.'SY' ) THEN
+         IF( SNAME .AND. C3.EQ.'TRD' ) THEN
+            NX = 32
+         END IF
+      ELSE IF( CNAME .AND. C2.EQ.'HE' ) THEN
+         IF( C3.EQ.'TRD' ) THEN
+            NX = 32
+         END IF
+      ELSE IF( SNAME .AND. C2.EQ.'OR' ) THEN
+         IF( C3( 1: 1 ).EQ.'G' ) THEN
+            IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ.
+     $          'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' )
+     $           THEN
+               NX = 128
+            END IF
+         END IF
+      ELSE IF( CNAME .AND. C2.EQ.'UN' ) THEN
+         IF( C3( 1: 1 ).EQ.'G' ) THEN
+            IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ.
+     $          'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' )
+     $           THEN
+               NX = 128
+            END IF
+         END IF
+      END IF
+      ILAENV = NX
+      RETURN
+*
+   80 CONTINUE
+*
+*     ISPEC = 4:  number of shifts (used by xHSEQR)
+*
+      ILAENV = 6
+      RETURN
+*
+   90 CONTINUE
+*
+*     ISPEC = 5:  minimum column dimension (not used)
+*
+      ILAENV = 2
+      RETURN
+*
+  100 CONTINUE
+*
+*     ISPEC = 6:  crossover point for SVD (used by xGELSS and xGESVD)
+*
+      ILAENV = INT( REAL( MIN( N1, N2 ) )*1.6E0 )
+      RETURN
+*
+  110 CONTINUE
+*
+*     ISPEC = 7:  number of processors (not used)
+*
+      ILAENV = 1
+      RETURN
+*
+  120 CONTINUE
+*
+*     ISPEC = 8:  crossover point for multishift (used by xHSEQR)
+*
+      ILAENV = 50
+      RETURN
+*
+  130 CONTINUE
+*
+*     ISPEC = 9:  maximum size of the subproblems at the bottom of the
+*                 computation tree in the divide-and-conquer algorithm
+*                 (used by xGELSD and xGESDD)
+*
+      ILAENV = 25
+      RETURN
+*
+  140 CONTINUE
+*
+*     ISPEC = 10: ieee NaN arithmetic can be trusted not to trap
+*
+*     ILAENV = 0
+      ILAENV = 1
+      IF( ILAENV.EQ.1 ) THEN
+         ILAENV = IEEECK( 1, 0.0, 1.0 )
+      END IF
+      RETURN
+*
+  150 CONTINUE
+*
+*     ISPEC = 11: infinity arithmetic can be trusted not to trap
+*
+*     ILAENV = 0
+      ILAENV = 1
+      IF( ILAENV.EQ.1 ) THEN
+         ILAENV = IEEECK( 0, 0.0, 1.0 )
+      END IF
+      RETURN
+*
+  160 CONTINUE
+*
+*     12 <= ISPEC <= 16: xHSEQR or one of its subroutines. 
+*
+      ILAENV = IPARMQ( ISPEC, NAME, OPTS, N1, N2, N3, N4 )
+      RETURN
+*
+*     End of ILAENV
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/iparmq.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/iparmq.f
new file mode 100644
index 00000000..bd5bd7a0
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/iparmq.f
@@ -0,0 +1,322 @@
+*> \brief \b IPARMQ
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download IPARMQ + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/iparmq.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/iparmq.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/iparmq.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            IHI, ILO, ISPEC, LWORK, N
+*       CHARACTER          NAME*( * ), OPTS*( * )
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*>      This program sets problem and machine dependent parameters
+*>      useful for xHSEQR and its subroutines. It is called whenever 
+*>      ILAENV is called with 12 <= ISPEC <= 16
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] ISPEC
+*> \verbatim
+*>          ISPEC is integer scalar
+*>              ISPEC specifies which tunable parameter IPARMQ should
+*>              return.
+*>
+*>              ISPEC=12: (INMIN)  Matrices of order nmin or less
+*>                        are sent directly to xLAHQR, the implicit
+*>                        double shift QR algorithm.  NMIN must be
+*>                        at least 11.
+*>
+*>              ISPEC=13: (INWIN)  Size of the deflation window.
+*>                        This is best set greater than or equal to
+*>                        the number of simultaneous shifts NS.
+*>                        Larger matrices benefit from larger deflation
+*>                        windows.
+*>
+*>              ISPEC=14: (INIBL) Determines when to stop nibbling and
+*>                        invest in an (expensive) multi-shift QR sweep.
+*>                        If the aggressive early deflation subroutine
+*>                        finds LD converged eigenvalues from an order
+*>                        NW deflation window and LD.GT.(NW*NIBBLE)/100,
+*>                        then the next QR sweep is skipped and early
+*>                        deflation is applied immediately to the
+*>                        remaining active diagonal block.  Setting
+*>                        IPARMQ(ISPEC=14) = 0 causes TTQRE to skip a
+*>                        multi-shift QR sweep whenever early deflation
+*>                        finds a converged eigenvalue.  Setting
+*>                        IPARMQ(ISPEC=14) greater than or equal to 100
+*>                        prevents TTQRE from skipping a multi-shift
+*>                        QR sweep.
+*>
+*>              ISPEC=15: (NSHFTS) The number of simultaneous shifts in
+*>                        a multi-shift QR iteration.
+*>
+*>              ISPEC=16: (IACC22) IPARMQ is set to 0, 1 or 2 with the
+*>                        following meanings.
+*>                        0:  During the multi-shift QR sweep,
+*>                            xLAQR5 does not accumulate reflections and
+*>                            does not use matrix-matrix multiply to
+*>                            update the far-from-diagonal matrix
+*>                            entries.
+*>                        1:  During the multi-shift QR sweep,
+*>                            xLAQR5 and/or xLAQRaccumulates reflections and uses
+*>                            matrix-matrix multiply to update the
+*>                            far-from-diagonal matrix entries.
+*>                        2:  During the multi-shift QR sweep.
+*>                            xLAQR5 accumulates reflections and takes
+*>                            advantage of 2-by-2 block structure during
+*>                            matrix-matrix multiplies.
+*>                        (If xTRMM is slower than xGEMM, then
+*>                        IPARMQ(ISPEC=16)=1 may be more efficient than
+*>                        IPARMQ(ISPEC=16)=2 despite the greater level of
+*>                        arithmetic work implied by the latter choice.)
+*> \endverbatim
+*>
+*> \param[in] NAME
+*> \verbatim
+*>          NAME is character string
+*>               Name of the calling subroutine
+*> \endverbatim
+*>
+*> \param[in] OPTS
+*> \verbatim
+*>          OPTS is character string
+*>               This is a concatenation of the string arguments to
+*>               TTQRE.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is integer scalar
+*>               N is the order of the Hessenberg matrix H.
+*> \endverbatim
+*>
+*> \param[in] ILO
+*> \verbatim
+*>          ILO is INTEGER
+*> \endverbatim
+*>
+*> \param[in] IHI
+*> \verbatim
+*>          IHI is INTEGER
+*>               It is assumed that H is already upper triangular
+*>               in rows and columns 1:ILO-1 and IHI+1:N.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*>          LWORK is integer scalar
+*>               The amount of workspace available.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup auxOTHERauxiliary
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>       Little is known about how best to choose these parameters.
+*>       It is possible to use different values of the parameters
+*>       for each of CHSEQR, DHSEQR, SHSEQR and ZHSEQR.
+*>
+*>       It is probably best to choose different parameters for
+*>       different matrices and different parameters at different
+*>       times during the iteration, but this has not been
+*>       implemented --- yet.
+*>
+*>
+*>       The best choices of most of the parameters depend
+*>       in an ill-understood way on the relative execution
+*>       rate of xLAQR3 and xLAQR5 and on the nature of each
+*>       particular eigenvalue problem.  Experiment may be the
+*>       only practical way to determine which choices are most
+*>       effective.
+*>
+*>       Following is a list of default values supplied by IPARMQ.
+*>       These defaults may be adjusted in order to attain better
+*>       performance in any particular computational environment.
+*>
+*>       IPARMQ(ISPEC=12) The xLAHQR vs xLAQR0 crossover point.
+*>                        Default: 75. (Must be at least 11.)
+*>
+*>       IPARMQ(ISPEC=13) Recommended deflation window size.
+*>                        This depends on ILO, IHI and NS, the
+*>                        number of simultaneous shifts returned
+*>                        by IPARMQ(ISPEC=15).  The default for
+*>                        (IHI-ILO+1).LE.500 is NS.  The default
+*>                        for (IHI-ILO+1).GT.500 is 3*NS/2.
+*>
+*>       IPARMQ(ISPEC=14) Nibble crossover point.  Default: 14.
+*>
+*>       IPARMQ(ISPEC=15) Number of simultaneous shifts, NS.
+*>                        a multi-shift QR iteration.
+*>
+*>                        If IHI-ILO+1 is ...
+*>
+*>                        greater than      ...but less    ... the
+*>                        or equal to ...      than        default is
+*>
+*>                                0               30       NS =   2+
+*>                               30               60       NS =   4+
+*>                               60              150       NS =  10
+*>                              150              590       NS =  **
+*>                              590             3000       NS =  64
+*>                             3000             6000       NS = 128
+*>                             6000             infinity   NS = 256
+*>
+*>                    (+)  By default matrices of this order are
+*>                         passed to the implicit double shift routine
+*>                         xLAHQR.  See IPARMQ(ISPEC=12) above.   These
+*>                         values of NS are used only in case of a rare
+*>                         xLAHQR failure.
+*>
+*>                    (**) The asterisks (**) indicate an ad-hoc
+*>                         function increasing from 10 to 64.
+*>
+*>       IPARMQ(ISPEC=16) Select structured matrix multiply.
+*>                        (See ISPEC=16 above for details.)
+*>                        Default: 3.
+*> \endverbatim
+*>
+*  =====================================================================
+      INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )
+*
+*  -- LAPACK auxiliary routine (version 3.4.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2011
+*
+*     .. Scalar Arguments ..
+      INTEGER            IHI, ILO, ISPEC, LWORK, N
+      CHARACTER          NAME*( * ), OPTS*( * )
+*
+*  ================================================================
+*     .. Parameters ..
+      INTEGER            INMIN, INWIN, INIBL, ISHFTS, IACC22
+      PARAMETER          ( INMIN = 12, INWIN = 13, INIBL = 14,
+     $                   ISHFTS = 15, IACC22 = 16 )
+      INTEGER            NMIN, K22MIN, KACMIN, NIBBLE, KNWSWP
+      PARAMETER          ( NMIN = 75, K22MIN = 14, KACMIN = 14,
+     $                   NIBBLE = 14, KNWSWP = 500 )
+      REAL               TWO
+      PARAMETER          ( TWO = 2.0 )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            NH, NS
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          LOG, MAX, MOD, NINT, REAL
+*     ..
+*     .. Executable Statements ..
+      IF( ( ISPEC.EQ.ISHFTS ) .OR. ( ISPEC.EQ.INWIN ) .OR.
+     $    ( ISPEC.EQ.IACC22 ) ) THEN
+*
+*        ==== Set the number simultaneous shifts ====
+*
+         NH = IHI - ILO + 1
+         NS = 2
+         IF( NH.GE.30 )
+     $      NS = 4
+         IF( NH.GE.60 )
+     $      NS = 10
+         IF( NH.GE.150 )
+     $      NS = MAX( 10, NH / NINT( LOG( REAL( NH ) ) / LOG( TWO ) ) )
+         IF( NH.GE.590 )
+     $      NS = 64
+         IF( NH.GE.3000 )
+     $      NS = 128
+         IF( NH.GE.6000 )
+     $      NS = 256
+         NS = MAX( 2, NS-MOD( NS, 2 ) )
+      END IF
+*
+      IF( ISPEC.EQ.INMIN ) THEN
+*
+*
+*        ===== Matrices of order smaller than NMIN get sent
+*        .     to xLAHQR, the classic double shift algorithm.
+*        .     This must be at least 11. ====
+*
+         IPARMQ = NMIN
+*
+      ELSE IF( ISPEC.EQ.INIBL ) THEN
+*
+*        ==== INIBL: skip a multi-shift qr iteration and
+*        .    whenever aggressive early deflation finds
+*        .    at least (NIBBLE*(window size)/100) deflations. ====
+*
+         IPARMQ = NIBBLE
+*
+      ELSE IF( ISPEC.EQ.ISHFTS ) THEN
+*
+*        ==== NSHFTS: The number of simultaneous shifts =====
+*
+         IPARMQ = NS
+*
+      ELSE IF( ISPEC.EQ.INWIN ) THEN
+*
+*        ==== NW: deflation window size.  ====
+*
+         IF( NH.LE.KNWSWP ) THEN
+            IPARMQ = NS
+         ELSE
+            IPARMQ = 3*NS / 2
+         END IF
+*
+      ELSE IF( ISPEC.EQ.IACC22 ) THEN
+*
+*        ==== IACC22: Whether to accumulate reflections
+*        .     before updating the far-from-diagonal elements
+*        .     and whether to use 2-by-2 block structure while
+*        .     doing it.  A small amount of work could be saved
+*        .     by making this choice dependent also upon the
+*        .     NH=IHI-ILO+1.
+*
+         IPARMQ = 0
+         IF( NS.GE.KACMIN )
+     $      IPARMQ = 1
+         IF( NS.GE.K22MIN )
+     $      IPARMQ = 2
+*
+      ELSE
+*        ===== invalid value of ispec =====
+         IPARMQ = -1
+*
+      END IF
+*
+*     ==== End of IPARMQ ====
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/lsame.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/lsame.f
new file mode 100644
index 00000000..315304c3
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/lsame.f
@@ -0,0 +1,125 @@
+*> \brief \b LSAME
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*  Definition:
+*  ===========
+*
+*      LOGICAL FUNCTION LSAME( CA, CB )
+*
+*     .. Scalar Arguments ..
+*      CHARACTER          CA, CB
+*     ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> LSAME returns .TRUE. if CA is the same letter as CB regardless of
+*> case.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] CA
+*> \verbatim
+*> \endverbatim
+*>
+*> \param[in] CB
+*> \verbatim
+*>          CA and CB specify the single characters to be compared.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup auxOTHERauxiliary
+*
+*  =====================================================================
+      LOGICAL FUNCTION LSAME( CA, CB )
+*
+*  -- LAPACK auxiliary routine (version 3.4.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2011
+*
+*     .. Scalar Arguments ..
+      CHARACTER          CA, CB
+*     ..
+*
+* =====================================================================
+*
+*     .. Intrinsic Functions ..
+      INTRINSIC          ICHAR
+*     ..
+*     .. Local Scalars ..
+      INTEGER            INTA, INTB, ZCODE
+*     ..
+*     .. Executable Statements ..
+*
+*     Test if the characters are equal
+*
+      LSAME = CA.EQ.CB
+      IF( LSAME )
+     $   RETURN
+*
+*     Now test for equivalence if both characters are alphabetic.
+*
+      ZCODE = ICHAR( 'Z' )
+*
+*     Use 'Z' rather than 'A' so that ASCII can be detected on Prime
+*     machines, on which ICHAR returns a value with bit 8 set.
+*     ICHAR('A') on Prime machines returns 193 which is the same as
+*     ICHAR('A') on an EBCDIC machine.
+*
+      INTA = ICHAR( CA )
+      INTB = ICHAR( CB )
+*
+      IF( ZCODE.EQ.90 .OR. ZCODE.EQ.122 ) THEN
+*
+*        ASCII is assumed - ZCODE is the ASCII code of either lower or
+*        upper case 'Z'.
+*
+         IF( INTA.GE.97 .AND. INTA.LE.122 ) INTA = INTA - 32
+         IF( INTB.GE.97 .AND. INTB.LE.122 ) INTB = INTB - 32
+*
+      ELSE IF( ZCODE.EQ.233 .OR. ZCODE.EQ.169 ) THEN
+*
+*        EBCDIC is assumed - ZCODE is the EBCDIC code of either lower or
+*        upper case 'Z'.
+*
+         IF( INTA.GE.129 .AND. INTA.LE.137 .OR.
+     $       INTA.GE.145 .AND. INTA.LE.153 .OR.
+     $       INTA.GE.162 .AND. INTA.LE.169 ) INTA = INTA + 64
+         IF( INTB.GE.129 .AND. INTB.LE.137 .OR.
+     $       INTB.GE.145 .AND. INTB.LE.153 .OR.
+     $       INTB.GE.162 .AND. INTB.LE.169 ) INTB = INTB + 64
+*
+      ELSE IF( ZCODE.EQ.218 .OR. ZCODE.EQ.250 ) THEN
+*
+*        ASCII is assumed, on Prime machines - ZCODE is the ASCII code
+*        plus 128 of either lower or upper case 'Z'.
+*
+         IF( INTA.GE.225 .AND. INTA.LE.250 ) INTA = INTA - 32
+         IF( INTB.GE.225 .AND. INTB.LE.250 ) INTB = INTB - 32
+      END IF
+      LSAME = INTA.EQ.INTB
+*
+*     RETURN
+*
+*     End of LSAME
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/testdlasq1.f90 b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/testdlasq1.f90
new file mode 100644
index 00000000..5ee8878d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/testdlasq1.f90
@@ -0,0 +1,626 @@
+program randomsys1
+implicit none
+integer, parameter :: nmax=1000
+real(kind=8), dimension(nmax) :: b, x
+real(kind=8), dimension(nmax,nmax) :: a
+real(kind=8) :: err
+integer :: i, info, lda, ldb, nrhs, n,iter
+integer, dimension(nmax) :: ipiv
+
+real(kind=8), dimension(100) :: d
+real(kind=8), dimension(99) :: e
+real(kind=8), dimension(400) :: work
+
+d(1:100) = (/1.8334043365537367D+00, &
+1.4451749896846686D+00, &
+1.0018566447551758D-01, &
+-7.2143260438744417D-01, &
+-3.7864653015502087D-01, &
+-9.0270111568850808D-01, &
+1.2204305489831029D+00, &
+-9.7628177811136485D-01, &
+8.4199233511256721D-01, &
+-2.7938817329922050D-01, &
+3.6157779599908046D-01, &
+-1.8563411313998144D+00, &
+-5.7930081140992240D-01, &
+7.4080550463379169D-01, &
+1.7021409147402005D+00, &
+-5.7992035328196923D-01, &
+4.0877426434579855D-01, &
+-7.1297236049446144D-01, &
+-1.2214095798914903D+00, &
+2.9037983248746674D-01, &
+7.4685018821608473D-01, &
+3.0213735481316539D-01, &
+-1.5207207136907624D-01, &
+-2.1332671668411556D+00, &
+6.8744661834930676D-01, &
+-2.0946670404018297D-01, &
+-1.5221059713957628D+00, &
+1.1117190383859539D+00, &
+-6.1175948159744020D-01, &
+-4.4149212620857964D-01, &
+-5.5702632609947533D-01, &
+1.4071858950692646D+00, &
+-3.2329881667362437D-01, &
+-3.1958092104323499D-01, &
+9.0934520529412111D-01, &
+9.7881421364746712D-01, &
+-5.1202970940327841D-01, &
+1.5040024724520102D+00, &
+-7.1993831181468571D-01, &
+-7.1819661000094503D-01, &
+-1.3481185445933910D+00, &
+-1.4984426192966893D+00, &
+1.1356626654278745D+00, &
+1.6427417967661164D+00, &
+-1.4184643787388000D+00, &
+2.9811560271518989D-01, &
+7.8630022575860559D-01, &
+-1.8262830018047089D+00, &
+6.3058255632564841D-01, &
+-2.0692752940382309D-02, &
+-7.2726648905906033D-01, &
+-1.0461446937034022D+00, &
+1.2530345094987356D+00, &
+-2.3583665341168443D+00, &
+1.9177654334479410D-01, &
+-1.3563410975095058D+00, &
+-1.0669710425337906D+00, &
+1.4840245472507219D+00, &
+-6.9185935518981789D-01, &
+1.6813910559942205D-01, &
+-7.1255209442204559D-01, &
+-1.0112797453604008D+00, &
+2.8591746998403011D-01, &
+-1.9403039239509563D+00, &
+-8.1434141084858885D-02, &
+1.3873918713367210D+00, &
+-8.8212258376548647D-01, &
+-1.2253510598547583D+00, &
+-3.8677386127356073D-01, &
+-1.0262656526479850D+00, &
+2.9468734022014376D-01, &
+2.3442965677966704D-01, &
+1.2219251054024911D+00, &
+2.6066505150099868D+00, &
+-7.8543147636303856D-01, &
+-9.8126277325503253D-01, &
+1.1722358680271947D+00, &
+-8.1477749181289072D-01, &
+1.3437777060446568D-01, &
+3.4626341297821356D-01, &
+-4.5672026157532375D-01, &
+3.0496975959999184D-01, &
+3.4636683737604146D-01, &
+1.5114807806635011D-01, &
+-1.1376177393945328D+00, &
+9.3419670621891793D-01, &
+7.9186416310239138D-01, &
+6.7230421440462595D-01, &
+-2.3236847424852280D-01, &
+-1.0927137499922757D+00, &
+9.8562766620822340D-01, &
+-1.1382935431007701D-01, &
+-9.2072237463768225D-01, &
+6.1142850054965170D-01, &
+8.2752057022739134D-03, &
+6.7197122515126417D-01, &
+-1.1007816668204429D+00, &
+-1.2196829073430047D+00, &
+-6.1428585523321222D-01, &
+6.4599803465517280D-01/)
+e(1:99) = (/-9.6393084631802151D-01, &
+2.5532567563781607D+00, &
+8.2492664240014357D-01, &
+8.2628261757058474D-01, &
+7.3021658879350859D-01, &
+3.4014431785419519D-02, &
+3.2121571974900542D-01, &
+2.5987166374572213D-02, &
+-3.1150206355945814D-01, &
+1.3429094629249927D+00, &
+8.6246434952180806D-01, &
+-8.3756967113851388D-01, &
+9.5277237959592009D-01, &
+1.1717152179539618D+00, &
+2.5980977671460709D-01, &
+-6.4468162556415265D-01, &
+-1.3751364204170078D+00, &
+2.9677172586579936D-01, &
+-3.7071376979215720D-01, &
+8.2912690407496381D-01, &
+-8.6820437618589197D-01, &
+5.2500961173269689D-01, &
+1.0657701704030644D+00, &
+-4.6621502244820201D-03, &
+-1.9013997092621748D-01, &
+1.5098985741543924D-01, &
+1.0102557493909003D+00, &
+8.8830298507891103D-01, &
+2.0464938169302065D+00, &
+4.7910192662606277D-01, &
+1.4155288808120892D+00, &
+-5.8169388172737679D-01, &
+-9.8007278321065916D-01, &
+2.4369633027015425D-01, &
+1.6173163491335715D-01, &
+6.6887624704464499D-01, &
+-1.6500999383869115D+00, &
+1.4380895281962367D+00, &
+4.7508565250807777D-01, &
+-3.1332991280327299D-01, &
+3.1402552392574451D-01, &
+5.6246373170551534D-01, &
+2.5944662334710866D-01, &
+4.8101648688789655D-01, &
+1.7823376751423265D+00, &
+3.0160656491545923D-01, &
+-8.8915960863742050D-01, &
+-4.4783548340444157D-01, &
+8.9985836172311440D-01, &
+-1.5626460660617920D+00, &
+8.9972644535054036D-01, &
+2.4456452268563592D-01, &
+-3.1377944726557985D+00, &
+1.6874136691232020D+00, &
+2.4791290942030142D-01, &
+1.7055713617986679D+00, &
+1.7027580566127303D+00, &
+-5.2969836953828042D-01, &
+-8.6858804294195124D-01, &
+7.6588136514601834D-01, &
+8.6161822555855139D-01, &
+6.5387844189250555D-01, &
+7.0164941351276944D-01, &
+4.1171318512873312D-01, &
+7.6075070364872455D-01, &
+8.5708035578209718D-02, &
+-4.3558500874018535D-01, &
+-6.2302104134015979D-01, &
+8.4912051051824700D-01, &
+-1.7120108380813925D-01, &
+-9.7880552224113848D-01, &
+1.1904436348486702D+00, &
+7.0273864977367972D-01, &
+-1.0213785672492079D+00, &
+4.8392839864322634D-02, &
+1.2611184618297511D-01, &
+5.3330169134056482D-01, &
+1.8070298106837654D+00, &
+-2.8022831541922144D-01, &
+8.0235047640662738D-01, &
+-1.2615220404695868D+00, &
+1.1878769364434660D+00, &
+-2.1059219864297674D-01, &
+3.2897539618854971D-01, &
+-5.8928028913554642D-01, &
+1.9164347352074701D-02, &
+2.8035162764822374D-01, &
+-9.6622429734784299D-02, &
+3.4216241143907045D-01, &
+-2.2358052317750254D+00, &
+6.6284070879481805D-01, &
+7.4316074303777269D-01, &
+1.0280848437626724D+00, &
+-2.0939898252763922D-01, &
+-1.0268515265064981D+00, &
+-1.2648527910628871D-01, &
+4.8663846308033204D-01, &
+1.2270171407392749D+00, &
+-1.6189022502021406D+00/)
+work(1:400) = (/6.0466028797961957D-01, &
+9.4050908804501243D-01, &
+6.6456005321849043D-01, &
+4.3771418718698019D-01, &
+4.2463749707126569D-01, &
+6.8682307286710942D-01, &
+6.5637019217476222D-02, &
+1.5651925473279124D-01, &
+9.6969518914484562D-02, &
+3.0091186058528707D-01, &
+5.1521262850206540D-01, &
+8.1363996099009683D-01, &
+2.1426387258237492D-01, &
+3.8065718929968601D-01, &
+3.1805817433032985D-01, &
+4.6888984490242319D-01, &
+2.8303415118044517D-01, &
+2.9310185733681576D-01, &
+6.7908467592021626D-01, &
+2.1855305259276428D-01, &
+2.0318687664732285D-01, &
+3.6087141685690599D-01, &
+5.7067327607102258D-01, &
+8.6249143744788637D-01, &
+2.9311424455385804D-01, &
+2.9708256355629153D-01, &
+7.5257303555161192D-01, &
+2.0658266191369859D-01, &
+8.6533501300156102D-01, &
+6.9671916574663473D-01, &
+5.2382030605000085D-01, &
+2.8303083325889995D-02, &
+1.5832827774512764D-01, &
+6.0725343954551536D-01, &
+9.7524161886057836D-01, &
+7.9453623373871976D-02, &
+5.9480859768306260D-01, &
+5.9120651313875290D-02, &
+6.9202458735311201D-01, &
+3.0152268100655999D-01, &
+1.7326623818270528D-01, &
+5.4109985500873525D-01, &
+5.4415557300088502D-01, &
+2.7850762181610883D-01, &
+4.2315220157182809D-01, &
+5.3058571535070520D-01, &
+2.5354050051506050D-01, &
+2.8208099496492467D-01, &
+7.8860491501934493D-01, &
+3.6180548048031691D-01, &
+8.8054312274161706D-01, &
+2.9711226063977081D-01, &
+8.9436172933045366D-01, &
+9.7454618399116566D-02, &
+9.7691686858626237D-01, &
+7.4290998949843021D-02, &
+2.2228941700678773D-01, &
+6.8107831239257088D-01, &
+2.4151508854715265D-01, &
+3.1152244431052484D-01, &
+9.3284642851843402D-01, &
+7.4184895999182299D-01, &
+8.0105504265266125D-01, &
+7.3023147729480831D-01, &
+1.8292491645390843D-01, &
+4.2835708180680782D-01, &
+8.9699195756187267D-01, &
+6.8265348801324377D-01, &
+9.7892935557668759D-01, &
+9.2221225892172687D-01, &
+9.0837275353887081D-02, &
+4.9314199770488037D-01, &
+9.2698680357441421D-01, &
+9.5494544041678175D-01, &
+3.4795396362822290D-01, &
+6.9083883150567893D-01, &
+7.1090719529999513D-01, &
+5.6377959581526438D-01, &
+6.4948946059294044D-01, &
+5.5176504901277490D-01, &
+7.5582350749159777D-01, &
+4.0380328579570035D-01, &
+1.3065111702897217D-01, &
+9.8596472934024670D-01, &
+8.9634174539621614D-01, &
+3.2208397052088172D-01, &
+7.2114776519267410D-01, &
+6.4453978250932942D-01, &
+8.5520507541911234D-02, &
+6.6957529769977453D-01, &
+6.2272831736370449D-01, &
+3.6969284363982191D-01, &
+2.3682254680548520D-01, &
+5.3528189063440612D-01, &
+1.8724610140105305D-01, &
+2.3884070280531861D-01, &
+6.2809817121836331D-01, &
+1.2675292937260130D-01, &
+2.8133029380535923D-01, &
+4.1032284435628247D-01, &
+4.3491247389145765D-01, &
+6.2509502830053043D-01, &
+5.5014692050772329D-01, &
+6.2360882645293014D-01, &
+7.2918072673429812D-01, &
+8.3053391899480622D-01, &
+5.1381551612136129D-04, &
+7.3606860149543141D-01, &
+3.9998376285699544D-01, &
+4.9786811334270198D-01, &
+6.0397810228292748D-01, &
+4.0961827788499267D-01, &
+2.9671281274886468D-02, &
+1.9038945142366389D-03, &
+2.8430411748625642D-03, &
+9.1582131461295702D-01, &
+5.8983418500491935D-01, &
+5.5939244907101404D-01, &
+8.1540517093336062D-01, &
+8.7801175865240000D-01, &
+4.5844247857565062D-01, &
+6.0016559532333080D-01, &
+2.6265150609689439D-02, &
+8.4583278724804167D-01, &
+2.4969320116349378D-01, &
+6.4178429079958299D-01, &
+2.4746660783662855D-01, &
+1.7365584472313275D-01, &
+5.9262375321244554D-01, &
+8.1439455096702107D-01, &
+6.9383813651720949D-01, &
+3.0322547833006870D-02, &
+5.3921010589094598D-01, &
+9.7567481498731645D-01, &
+7.5076305647959851D-01, &
+2.9400631279501488D-01, &
+7.5316127773675856D-01, &
+1.5096404497960700D-01, &
+3.5576726540923664D-01, &
+8.3193085296981628D-01, &
+2.3183004193767690D-01, &
+6.2783460500002275D-01, &
+4.9839430127597562D-01, &
+8.9836089260366833D-02, &
+2.5193959794895041D-02, &
+3.9221618315402479D-01, &
+5.8938308640079917D-01, &
+9.2961163544903025D-01, &
+5.7208680144308399D-01, &
+5.8857634514348212D-01, &
+4.1176268834501623D-01, &
+5.5258038981424384D-01, &
+4.9160739613162047D-01, &
+9.5795391353751358D-01, &
+7.9720854091080284D-01, &
+1.0738111282075208D-01, &
+7.8303497339600214D-01, &
+3.9325099922888668D-01, &
+1.3041384617379179D-01, &
+1.9003276633920804D-01, &
+7.3982578101583363D-01, &
+6.5404140923127974D-01, &
+9.8383788985732593D-02, &
+5.2038028571222783D-01, &
+9.9729663719935122D-02, &
+1.5184340208190175D-01, &
+7.6190262303755044D-02, &
+3.1520808532012451D-01, &
+1.5965092146489504D-01, &
+1.3780406161952607D-01, &
+3.2261068286779754D-01, &
+5.3907451703947940D-01, &
+5.7085162734549566D-01, &
+5.1278175811108151D-01, &
+6.8417513009745512D-01, &
+6.5304020513536076D-01, &
+5.2449975954986505D-01, &
+6.5427013442414605D-01, &
+7.1636837490167116D-01, &
+6.3664421403817983D-01, &
+1.2825909106361078D-02, &
+3.0682195787138565D-02, &
+9.8030874806304999D-02, &
+3.6911170916434483D-01, &
+8.2645412563474197D-01, &
+3.4768170859156955D-01, &
+3.4431501772636058D-01, &
+2.5299982364784412D-01, &
+2.1647114665497036D-01, &
+5.5500213563479417D-01, &
+4.0207084527183062D-01, &
+5.0649706367641834D-01, &
+1.6867966833433606D-01, &
+3.3136826030698385D-01, &
+8.2792809615055885D-01, &
+7.0028787314581509D-01, &
+5.7926259664335768D-02, &
+9.9915949022033324D-01, &
+4.1154036322047599D-01, &
+1.1167463676480495D-01, &
+7.8075408455849260D-01, &
+9.2117624440742188D-02, &
+5.3494624494407637D-02, &
+7.1469581589162956D-01, &
+2.5076227542918023D-01, &
+8.4863292090315690D-01, &
+9.7388187407067284D-01, &
+2.1256094905031958D-01, &
+2.1533783325605065D-02, &
+9.4519476038882588D-01, &
+9.2970155499924934D-02, &
+6.4583337452397671D-01, &
+3.1188554282705405D-01, &
+4.4846436394045647D-01, &
+4.8723924858036949D-01, &
+8.2479676511350006D-02, &
+6.7182910623463954D-01, &
+4.0018828942364343D-01, &
+9.0027514726431157D-01, &
+9.4988320610125321D-01, &
+3.1933126760711733D-01, &
+4.9938549375241320D-01, &
+4.0043231714181288D-01, &
+1.9808670325451940D-02, &
+6.4503886601944815D-01, &
+4.2868843006993296D-01, &
+3.3959675138730994D-01, &
+8.8744750085050050D-01, &
+2.3632747430436052D-01, &
+7.6500821493327975D-01, &
+3.5754647436084384D-02, &
+7.2757725604152290D-01, &
+6.2583662695812525D-01, &
+5.1308750608785669D-01, &
+7.2448356792351315D-02, &
+7.2422905845916841D-01, &
+8.7984484630570914D-01, &
+9.7776347735771851D-01, &
+8.4750026226468134D-01, &
+8.3219793814993315D-01, &
+2.4784452318699535D-01, &
+9.1339906293647088D-01, &
+7.5037210134653420D-02, &
+8.3510380115435290D-01, &
+6.2933169164530067D-01, &
+7.5174057889673473D-01, &
+6.3200343378879975D-01, &
+9.6934213238731665D-02, &
+1.4827369494876504D-02, &
+5.8383474186253115D-01, &
+6.8756195202154743D-02, &
+9.9827381100849455D-01, &
+6.4918841659842363D-01, &
+9.8546557863324791D-01, &
+8.3480576021921249D-01, &
+3.3205608571906026D-01, &
+6.6139318058334262D-01, &
+9.5602062659660969D-01, &
+3.1051027622482125D-01, &
+1.8439069400202679D-01, &
+9.6709434137177297D-01, &
+8.3324181552815457D-01, &
+3.0954845052732810D-01, &
+8.0587176753764456D-01, &
+4.1732584219038238D-01, &
+7.1853044935277477D-01, &
+4.0673677545039083D-01, &
+8.9580326774414576D-01, &
+9.5817636260259365D-01, &
+1.8713221139656417D-02, &
+7.9167230908208319D-01, &
+4.2355315388584103D-01, &
+1.5181277223073395D-02, &
+4.3269824007906393D-01, &
+9.0477623706573340D-01, &
+8.5570441457488644D-01, &
+4.2921642176334200D-02, &
+6.5903053300775438D-01, &
+3.4785904313005395D-01, &
+5.0348679004869112D-01, &
+8.3994742117055976D-01, &
+2.3109568410543832D-02, &
+1.2436351859954159D-01, &
+2.6117561918821841D-01, &
+8.3494750649349414D-01, &
+3.1480479595597533D-01, &
+7.6812064740880894D-03, &
+8.9975012571752733D-01, &
+3.7026753645051064D-01, &
+1.0019940926941497D-01, &
+6.4320402657020315D-01, &
+7.6988908998308336D-01, &
+7.9112533566198451D-01, &
+2.6238190747072776D-01, &
+3.4686388037925503D-01, &
+2.1465371537694145D-01, &
+8.2209289717657175D-01, &
+3.5113429966521320D-01, &
+5.9919425250588099D-01, &
+5.7835125693111211D-01, &
+4.1358098797631293D-01, &
+1.1985050890286310D-01, &
+9.1161370679159903D-01, &
+5.3785580105748208D-02, &
+2.2891758676059876D-01, &
+3.2417396306138829D-01, &
+3.5076512764716117D-01, &
+3.4928874777426255D-01, &
+3.0380212985436572D-01, &
+9.6874615996581170D-01, &
+6.7152655046083776D-01, &
+2.0794312837315651D-01, &
+9.6313940120247044D-01, &
+3.0220237504213365D-01, &
+8.0794108095480799D-01, &
+1.3408416275024179D-01, &
+9.4776028919455635D-01, &
+6.4086482116825383D-01, &
+9.5325875425035178D-01, &
+8.0987422593395209D-01, &
+1.8159084675756379D-01, &
+9.4275737153737327D-01, &
+8.3124103554376771D-01, &
+4.9468043578205978D-01, &
+8.5531034647693982D-01, &
+7.1074391181909824D-01, &
+2.7349475629159786D-01, &
+4.0763287189198161D-01, &
+9.0976128251911847D-01, &
+9.4439713870030451D-01, &
+4.9863245185560190D-01, &
+2.8863831012730923D-01, &
+9.7589525649963815D-01, &
+4.5258447627808124D-01, &
+4.4990698677957075D-02, &
+3.1536198151820755D-01, &
+9.5190614812037189D-01, &
+7.5156308247423609D-01, &
+5.3579099898961424D-01, &
+6.6971458883510748D-01, &
+8.6517499748328641D-01, &
+4.5888445390388938D-01, &
+5.7855090249582031D-01, &
+4.8152982184966137D-01, &
+5.5061576198318274D-01, &
+9.5062324380815433D-01, &
+5.0986542047295536D-01, &
+7.4251472966182985D-01, &
+4.9079401441435533D-01, &
+6.6151414870689360D-02, &
+2.6249066264989940D-01, &
+9.2546794407799982D-01, &
+3.7148665165822231D-01, &
+4.0941940003107308D-01, &
+4.1575196973399631D-01, &
+9.7261599736539445D-02, &
+9.0162762447969347D-01, &
+4.4446597981328932D-03, &
+2.7392454335102678D-01, &
+1.0930666111680035D-01, &
+8.5544841289295426D-01, &
+2.5705535663902546D-01, &
+9.8913209203202213D-01, &
+9.2641142236812712D-01, &
+1.7094603208839290D-01, &
+3.0388712489325242D-01, &
+5.3345144978115477D-01, &
+1.7648961347647024D-01, &
+8.1359077477652830D-01, &
+7.0513712380125892D-01, &
+2.5720755742139950D-01, &
+2.5036892046498466D-01, &
+3.3509436689927874D-01, &
+7.5124063162526056D-01, &
+4.8797826077860845D-03, &
+8.4099320643626019D-01, &
+2.2957358869665739D-01, &
+1.3285547727582237D-02, &
+9.4993740716879371D-01, &
+8.9937146465701423D-01, &
+9.6262420114388625D-01, &
+4.3000361954927006D-02, &
+7.1266261216467264D-01, &
+5.1094098258212241D-02, &
+4.0753210485857738D-01, &
+4.7569737399615403D-01, &
+3.4746838606940983D-01, &
+4.0719938711096422D-02, &
+5.9756620514440806D-01, &
+2.6012467360309705D-01, &
+8.3285585557738717D-01, &
+9.6049750529821787D-01, &
+9.3670756890653750D-01, &
+2.2932023844733959D-01, &
+7.2031310018914962D-01, &
+7.5648232426876405D-01, &
+4.5015392507594826D-01, &
+3.3897738839543617D-01, &
+4.7249205225111501D-01, &
+9.8599436000817042D-01/)
+n =  100
+info = 0
+
+open(unit = 4, STATUS='REPLACE', file = "gen4tests.txt")
+open(unit = 3, STATUS='REPLACE', file = "gen3tests.txt")
+open(unit = 5, STATUS='REPLACE', file = "gen5tests.txt")
+
+call dlasq1(n, d, e, work, info)
+
+close(5)
+close(3)
+close(4)
+
+end
\ No newline at end of file
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/testdlasq2.f90 b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/testdlasq2.f90
new file mode 100644
index 00000000..c908f7d6
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/testdlasq2.f90
@@ -0,0 +1,171 @@
+! $CLASSHG/codes/lapack/random/randomsys1.f90
+
+program randomsys1
+implicit none
+integer, parameter :: nmax=1000
+real(kind=8), dimension(nmax) :: b, x
+real(kind=8), dimension(nmax,nmax) :: a
+real(kind=8) :: err
+integer :: i, info, lda, ldb, nrhs, n,iter
+integer, dimension(nmax) :: ipiv
+
+real(kind=8), dimension(84) :: z
+
+z(1:84) = (/2.3962280929192509D-01, &
+6.4346010490580374D-01, &
+5.4886677265274941D-01, &
+1.8435046456575191D-01, &
+4.2690013698472401D-01, &
+6.2760930131666248D-01, &
+8.7243363936287288D-02, &
+5.3710399529030350D-01, &
+8.4474604576675638D-01, &
+4.0947669295022632D-01, &
+2.0315141244999760D-01, &
+8.2714283129979482D-01, &
+9.6582843029739029D-01, &
+3.7773539690481128D-01, &
+6.4713340225873406D-01, &
+6.7774351756798612D-01, &
+4.4568905572928591D-01, &
+1.7208265726837521D-01, &
+3.5202074329011412D-01, &
+3.2913965083413110D-01, &
+7.4682622623737438D-01, &
+2.7151044969605542D-01, &
+5.6129178633962351D-01, &
+1.3244294692867761D-01, &
+7.9837660640147112D-01, &
+2.0595995860196409D-01, &
+2.6555102564257749D-02, &
+1.9623902644848701D-01, &
+7.8452468963715605D-03, &
+8.2177375597112101D-01, &
+9.4444982187044924D-01, &
+4.6799576958310329D-01, &
+1.1359180530395520D-01, &
+1.6049482525711320D-01, &
+8.4523811016138373D-01, &
+8.5370708147160490D-01, &
+3.0139325968162661D-01, &
+2.5117154067021252D-01, &
+2.0086476380364379D-01, &
+2.6078975734443288D-01, &
+2.5710509100784901D-01, &
+6.2861740244633146D-01, &
+4.7397018497236110D-01, &
+8.6989475348440182D-01, &
+6.4860795895959611D-01, &
+8.8943219043019872D-01, &
+7.9524758401855578D-01, &
+8.8016617212154102D-01, &
+2.1472721943810300D-01, &
+9.5183566464760194D-01, &
+7.1911522894148772D-01, &
+1.1065249711733080D-01, &
+9.5745872307341484D-01, &
+6.4694742306793951D-01, &
+5.8182607574435841D-01, &
+1.2922028370755401D-02, &
+2.7617229134380777D-01, &
+8.0045359255855852D-01, &
+3.2789738555900377D-01, &
+5.7940374386642890D-01, &
+2.3961554431041750D-02, &
+6.6990484757537938D-01, &
+1.8144929371280860D-01, &
+2.8661849362222419D-01, &
+6.5845572125062690D-01, &
+5.8896512277754309D-01, &
+6.3697665190607378D-02, &
+1.3281935295985961D-01, &
+7.4166314172628711D-01, &
+5.0033182787066932D-01, &
+3.1440772963953763D-02, &
+9.9073931564031925D-01, &
+3.4236965949145941D-03, &
+6.9929220728508257D-01, &
+7.5905196170645428D-01, &
+2.5421825141163590D-01, &
+3.3146571845550887D-01, &
+5.7286596840196446D-01, &
+9.9158547964144228D-01, &
+4.8967497301052382D-01, &
+5.6113697207961410D-01, &
+6.0641422150435165D-01, &
+8.5675901647669139D-02, &
+2.5817319326781851D-01/)
+n =  21
+info = 0
+
+open(unit = 2,STATUS='REPLACE', file = "gen2tests.txt")
+open(unit = 4, STATUS='REPLACE', file = "gen4tests.txt")
+open(unit = 3,STATUS='REPLACE', file = "gen3tests.txt")
+open(unit = 5,STATUS='REPLACE', file = "gen5tests.txt")
+
+write(2,*) "{"
+write(2,'(9999(g0))',advance="no") "z: []float64{"
+do i = 1, 4*n
+write (2,'(99999(e24.16,a))',advance="no") z(i), ","
+end do
+write (2,*) "},"
+write(2,*) "n: " ,n,","
+
+
+call dlasq2(n, z, info)
+
+write(2,'(9999(g0))', advance="no") "zOut: []float64{"
+do i = 1, 4*n
+write (2,'(99999(e24.16,a))', advance="no") z(i), ","
+end do
+write (2,*) "},"
+write(2,*) "info:", info, ","
+write(2,*) "},"
+
+print *, "Done fixed dlasq2"
+
+close(5)
+close(3)
+close(4)
+close(2)
+
+! For random tests
+n =  21
+
+open(unit = 2, STATUS='REPLACE', file = "gen2tests.txt")
+open(unit = 4, STATUS='REPLACE', file = "gen4tests.txt")
+open(unit = 3, STATUS='REPLACE', file = "gen3tests.txt")
+open(unit = 5, STATUS='REPLACE', file = "gen5tests.txt")
+
+do iter = 1, 2
+
+call random_number(z(1:4*n))
+
+write(2,*) "{"
+write(2,'(9999(g0))', advance="no") "z: []float64{"
+do i = 1, 4*n
+write (2,'(99999(e24.16,a))', advance="no") z(i), ","
+end do
+write (2,*) "},"
+write(2,*) "n: " ,n,","
+
+call dlasq2(n, z, info)
+
+write(2,'(9999(g0))', advance="no") "zOut: []float64{"
+do i = 1, 4*n
+  write (2,'(99999(e24.16,a))', advance="no") z(i), ","
+end do
+write (2,*) "},"
+write(2,*) "info:", info, ","
+write(2,*) "},"
+
+print *, "Done with dlasq2"
+
+end do
+
+close(5)
+close(3)
+close(4)
+close(2)
+
+end program randomsys1
\ No newline at end of file
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/testdlasq3.f90 b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/testdlasq3.f90
new file mode 100644
index 00000000..8cc5cf0f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/testdlasq3.f90
@@ -0,0 +1,132 @@
+program testdlasq3
+implicit none
+
+! Dlasq3 tests
+integer :: i0, n0, pp,ttype, nFail,iter,nDiv,n
+real(kind=8), dimension(84) :: z
+real(kind=8) :: dmin,desig,qmax,dmin1,dmin2,dn,dn1,dn2,g,tau,sigma
+logical :: ieee
+
+n = 84
+
+ieee = .True.
+
+z(1:84) = (/1.9143652461808209D+00, &
+1.5643842977038900D+00, &
+2.4933891621438989D-01, &
+3.4998094847693051D-01, &
+1.3159965131315450D+00, &
+1.3638621124906269D+00, &
+9.8984666119707590D-02, &
+2.0147331685530781D-01, &
+6.0239739795872871D-01, &
+6.4655447927417942D-01, &
+2.2100334106387809D-03, &
+5.4827584804256833D-02, &
+9.8618572336789667D-02, &
+2.4281908107454921D-02, &
+4.7563214844548191D-01, &
+7.6546697639973529D-02, &
+2.5887481436771148D-01, &
+6.1277840695087704D-01, &
+1.0786113766900041D-01, &
+1.2172855586231640D-01, &
+6.4428964922552456D-01, &
+2.2938358048981550D-01, &
+6.2032304866397048D-01, &
+5.2276720640470942D-01, &
+3.6956606786075852D-01, &
+7.6452331847458654D-01, &
+5.3788380542522651D-01, &
+2.2536579805014259D-01, &
+3.5625331812646233D-01, &
+8.8204867223354833D-01, &
+2.2221324964361449D-02, &
+1.2088451318140349D-02, &
+1.2750943030216850D+00, &
+6.5487468521633574D-01, &
+1.6473243548212180D-01, &
+6.4244094276971109D-01, &
+1.0075305765438660D+00, &
+3.2695517365467008D-01, &
+3.4538816017831181D-01, &
+8.4530783837131718D-01, &
+2.6793917191534039D-01, &
+4.1167148387782809D-01, &
+7.3286777366837230D-01, &
+2.0165584821582411D-01, &
+8.3608281383074101D-01, &
+9.7375794521953263D-01, &
+4.8136607095928219D-01, &
+5.9519264227958080D-01, &
+6.4953705136764595D-01, &
+6.7618762481481709D-01, &
+2.3254758802226480D-01, &
+4.5471549751211121D-01, &
+1.9936248028938069D-01, &
+3.3218193673422552D-01, &
+3.7823189169112570D-01, &
+9.9728131577419957D-02, &
+9.8304494035037460D-01, &
+7.5610809968448423D-01, &
+4.4297338640403672D-01, &
+6.0516873235701607D-01, &
+1.1732795506024030D+00, &
+7.1957244803166864D-01, &
+5.0355240691445868D-01, &
+8.9668048897477137D-01, &
+3.0589803950585209D-01, &
+6.5888323539286620D-01, &
+3.0146344334154529D-01, &
+1.5056721102744461D-01, &
+1.2894222375675779D+00, &
+6.1246453109936005D-01, &
+7.5833643057994404D-01, &
+9.7842114980976291D-01, &
+4.9778147794615712D-01, &
+9.9938135774918690D-01, &
+2.8414688478625982D-01, &
+2.5673655077691432D-01, &
+9.2575397942057647D-01, &
+5.5092683856146663D-01, &
+5.2313556054509897D-05, &
+6.5897402564536967D-01, &
+2.1178692213810329D-05, &
+7.3492248268320243D-05, &
+0.0000000000000000D+00, &
+0.0000000000000000D+00/)
+i0 = 1
+n0 = 21
+pp = 0
+dmin = -0.0000000000000000D+00
+sigma = 0.0000000000000000D+00
+desig = 0.0000000000000000D+00
+qmax = 2.1637041623952107D+00
+nFail = 0
+iter = 2
+nDiv = 40
+ttype = 0
+dmin1 = 0.0000000000000000D+00
+dmin2 = 0.0000000000000000D+00
+dn = 0.0000000000000000D+00
+dn1 = 0.0000000000000000D+00
+dn2 = 0.0000000000000000D+00
+g = 0.0000000000000000D+00
+tau = 0.0000000000000000D+00
+
+print *, "Starting Dlasq3"
+open(unit = 4, file = "gen4tests.txt")
+open(unit = 5, file = "gen5tests.txt")
+call Dlasq3(i0, n0, z, pp, dmin, sigma, desig, qmax, nFail, iter, nDiv, ieee, ttype, dmin1, dmin2, dn, dn1, dn2, g, tau)
+close(4)
+close(5)
+
+print *, "Done calling dlasq3"
+print *, Z(1:n)
+
+print *, I0, N0, PP
+print *, DMIN, DESIG, SIGMA, QMAX
+print *, NFAIL, ITER, NDIV, TTYPE
+print *, DMIN1, DMIN2, DN, DN1, DN2, G, TAU
+
+end
\ No newline at end of file
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/testdlasq4.f90 b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/testdlasq4.f90
new file mode 100644
index 00000000..3c84983a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/testdlasq4.f90
@@ -0,0 +1,435 @@
+program testdlasq4
+implicit none
+
+! Dlasq4 tests
+integer :: i0, n0, pp, ttype, iter, nDiv, n, n0in
+real(kind=8), dimension(401) :: z
+real(kind=8) :: dmin, desig, qmax, dmin1, dmin2, dn, dn1, dn2, g, tau, sigma
+logical :: ieee
+
+z(1:401) = (/2.9266499599402414D+02, &
+2.9276699640004830D+02, &
+2.9210200041216615D+02, &
+2.9171973344922628D+02, &
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+2.9139896954309916D+02, &
+2.9128827357375536D+02, &
+2.9190012628763964D+02, &
+2.9212457714005234D+02, &
+2.9221336158434212D+02, &
+2.9217879707919576D+02, &
+2.9127472708852724D+02, &
+2.9132783649002283D+02, &
+2.9227509889951233D+02, &
+2.9226978796550475D+02, &
+2.9142078378447616D+02, &
+2.9142906715955786D+02, &
+2.9017517054475991D+02, &
+2.8992337408144391D+02, &
+2.8477362931531121D+02, &
+2.8514676291150971D+02, &
+2.8393423954726200D+02, &
+2.8313625395453965D+02, &
+2.8449999402409759D+02, &
+2.8534282615303522D+02, &
+2.8523140662657408D+02, &
+2.8739845025761718D+02, &
+2.8713781898215319D+02, &
+0.0000000000000000D+00/)
+i0 = 1
+n0 = 100
+pp = 1
+n0in = 100
+dmin = 7.9798559272231942D+282
+dmin1 = 7.9798559272231942D+282
+dmin2 = 2.3215857579138407D+285
+dn = 2.3140662657409930D+284
+dn1 = 7.9798559272231942D+282
+dn2 = 8.2833136615500372D+288
+g = 2.5000000000000000D-01
+tau = 6.1420124051338430D+283
+ttype = -4
+
+ieee = .True.
+
+print *, "Starting Dlasq4"
+
+call Dlasq4(i0, n0, z, pp, n0in, dmin, dmin1, dmin2, dn, dn1, dn2, tau, ttype, g)
+
+print *, "Done calling dlasq4"
+print *, "tau = ", tau
+print *, tau, ttype, g
+
+end
\ No newline at end of file
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/xerbla.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/xerbla.f
new file mode 100644
index 00000000..3e93bc4e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dlasqtest/xerbla.f
@@ -0,0 +1,99 @@
+*> \brief \b XERBLA
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download XERBLA + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/xerbla.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/xerbla.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/xerbla.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE XERBLA( SRNAME, INFO )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER*(*)      SRNAME
+*       INTEGER            INFO
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> XERBLA  is an error handler for the LAPACK routines.
+*> It is called by an LAPACK routine if an input parameter has an
+*> invalid value.  A message is printed and execution stops.
+*>
+*> Installers may consider modifying the STOP statement in order to
+*> call system-specific exception-handling facilities.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] SRNAME
+*> \verbatim
+*>          SRNAME is CHARACTER*(*)
+*>          The name of the routine which called XERBLA.
+*> \endverbatim
+*>
+*> \param[in] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          The position of the invalid parameter in the parameter list
+*>          of the calling routine.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup auxOTHERauxiliary
+*
+*  =====================================================================
+      SUBROUTINE XERBLA( SRNAME, INFO )
+*
+*  -- LAPACK auxiliary routine (version 3.4.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2011
+*
+*     .. Scalar Arguments ..
+      CHARACTER*(*)      SRNAME
+      INTEGER            INFO
+*     ..
+*
+* =====================================================================
+*
+*     .. Intrinsic Functions ..
+      INTRINSIC          LEN_TRIM
+*     ..
+*     .. Executable Statements ..
+*
+      WRITE( *, FMT = 9999 )SRNAME( 1:LEN_TRIM( SRNAME ) ), INFO
+*
+      STOP
+*
+ 9999 FORMAT( ' ** On entry to ', A, ' parameter number ', I2, ' had ',
+     $      'an illegal value' )
+*
+*     End of XERBLA
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/Makefile b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/Makefile
new file mode 100644
index 00000000..7d22727a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/Makefile
@@ -0,0 +1,20 @@
+FC = gfortran
+FFLAGS = -O2
+
+targets = testdsterf
+objects = disnan.o dlamch.o dlanst.o dlaisnan.o dlassq.o dlapy2.o lsame.o dlae2.o dlascl.o dlasrt.o dsterf.o xerbla.o
+
+default : $(targets)
+.PHONY : default
+
+testdsterf : testdsterf.o $(objects)
+
+% : %.o
+	$(FC) $(FFLAGS) $^ -o $@
+
+%.o : %.f90
+	$(FC) $(FFLAGS) -c -o $@ $<
+
+clean :
+	rm -f *.o $(targets) *.txt
+.PHONY : clean
\ No newline at end of file
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/disnan.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/disnan.f
new file mode 100644
index 00000000..355b8279
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/disnan.f
@@ -0,0 +1,80 @@
+*> \brief \b DISNAN tests input for NaN.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DISNAN + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/disnan.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/disnan.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/disnan.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       LOGICAL FUNCTION DISNAN( DIN )
+* 
+*       .. Scalar Arguments ..
+*       DOUBLE PRECISION   DIN
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DISNAN returns .TRUE. if its argument is NaN, and .FALSE.
+*> otherwise.  To be replaced by the Fortran 2003 intrinsic in the
+*> future.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] DIN
+*> \verbatim
+*>          DIN is DOUBLE PRECISION
+*>          Input to test for NaN.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date September 2012
+*
+*> \ingroup auxOTHERauxiliary
+*
+*  =====================================================================
+      LOGICAL FUNCTION DISNAN( DIN )
+*
+*  -- LAPACK auxiliary routine (version 3.4.2) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     September 2012
+*
+*     .. Scalar Arguments ..
+      DOUBLE PRECISION   DIN
+*     ..
+*
+*  =====================================================================
+*
+*  .. External Functions ..
+      LOGICAL DLAISNAN
+      EXTERNAL DLAISNAN
+*  ..
+*  .. Executable Statements ..
+      DISNAN = DLAISNAN(DIN,DIN)
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/dlae2.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/dlae2.f
new file mode 100644
index 00000000..302eeaa1
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/dlae2.f
@@ -0,0 +1,185 @@
+*> \brief \b DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLAE2 + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlae2.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlae2.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlae2.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DLAE2( A, B, C, RT1, RT2 )
+* 
+*       .. Scalar Arguments ..
+*       DOUBLE PRECISION   A, B, C, RT1, RT2
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DLAE2  computes the eigenvalues of a 2-by-2 symmetric matrix
+*>    [  A   B  ]
+*>    [  B   C  ].
+*> On return, RT1 is the eigenvalue of larger absolute value, and RT2
+*> is the eigenvalue of smaller absolute value.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] A
+*> \verbatim
+*>          A is DOUBLE PRECISION
+*>          The (1,1) element of the 2-by-2 matrix.
+*> \endverbatim
+*>
+*> \param[in] B
+*> \verbatim
+*>          B is DOUBLE PRECISION
+*>          The (1,2) and (2,1) elements of the 2-by-2 matrix.
+*> \endverbatim
+*>
+*> \param[in] C
+*> \verbatim
+*>          C is DOUBLE PRECISION
+*>          The (2,2) element of the 2-by-2 matrix.
+*> \endverbatim
+*>
+*> \param[out] RT1
+*> \verbatim
+*>          RT1 is DOUBLE PRECISION
+*>          The eigenvalue of larger absolute value.
+*> \endverbatim
+*>
+*> \param[out] RT2
+*> \verbatim
+*>          RT2 is DOUBLE PRECISION
+*>          The eigenvalue of smaller absolute value.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date September 2012
+*
+*> \ingroup auxOTHERauxiliary
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  RT1 is accurate to a few ulps barring over/underflow.
+*>
+*>  RT2 may be inaccurate if there is massive cancellation in the
+*>  determinant A*C-B*B; higher precision or correctly rounded or
+*>  correctly truncated arithmetic would be needed to compute RT2
+*>  accurately in all cases.
+*>
+*>  Overflow is possible only if RT1 is within a factor of 5 of overflow.
+*>  Underflow is harmless if the input data is 0 or exceeds
+*>     underflow_threshold / macheps.
+*> \endverbatim
+*>
+*  =====================================================================
+      SUBROUTINE DLAE2( A, B, C, RT1, RT2 )
+*
+*  -- LAPACK auxiliary routine (version 3.4.2) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     September 2012
+*
+*     .. Scalar Arguments ..
+      DOUBLE PRECISION   A, B, C, RT1, RT2
+*     ..
+*
+* =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ONE
+      PARAMETER          ( ONE = 1.0D0 )
+      DOUBLE PRECISION   TWO
+      PARAMETER          ( TWO = 2.0D0 )
+      DOUBLE PRECISION   ZERO
+      PARAMETER          ( ZERO = 0.0D0 )
+      DOUBLE PRECISION   HALF
+      PARAMETER          ( HALF = 0.5D0 )
+*     ..
+*     .. Local Scalars ..
+      DOUBLE PRECISION   AB, ACMN, ACMX, ADF, DF, RT, SM, TB
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS, SQRT
+*     ..
+*     .. Executable Statements ..
+*
+*     Compute the eigenvalues
+*
+      SM = A + C
+      DF = A - C
+      ADF = ABS( DF )
+      TB = B + B
+      AB = ABS( TB )
+      IF( ABS( A ).GT.ABS( C ) ) THEN
+         ACMX = A
+         ACMN = C
+      ELSE
+         ACMX = C
+         ACMN = A
+      END IF
+      IF( ADF.GT.AB ) THEN
+         RT = ADF*SQRT( ONE+( AB / ADF )**2 )
+      ELSE IF( ADF.LT.AB ) THEN
+         RT = AB*SQRT( ONE+( ADF / AB )**2 )
+      ELSE
+*
+*        Includes case AB=ADF=0
+*
+         RT = AB*SQRT( TWO )
+      END IF
+      IF( SM.LT.ZERO ) THEN
+         RT1 = HALF*( SM-RT )
+*
+*        Order of execution important.
+*        To get fully accurate smaller eigenvalue,
+*        next line needs to be executed in higher precision.
+*
+         RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B
+      ELSE IF( SM.GT.ZERO ) THEN
+         RT1 = HALF*( SM+RT )
+*
+*        Order of execution important.
+*        To get fully accurate smaller eigenvalue,
+*        next line needs to be executed in higher precision.
+*
+         RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B
+      ELSE
+*
+*        Includes case RT1 = RT2 = 0
+*
+         RT1 = HALF*RT
+         RT2 = -HALF*RT
+      END IF
+      RETURN
+*
+*     End of DLAE2
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/dlaisnan.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/dlaisnan.f
new file mode 100644
index 00000000..58595c5c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/dlaisnan.f
@@ -0,0 +1,91 @@
+*> \brief \b DLAISNAN tests input for NaN by comparing two arguments for inequality.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLAISNAN + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaisnan.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaisnan.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaisnan.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       LOGICAL FUNCTION DLAISNAN( DIN1, DIN2 )
+* 
+*       .. Scalar Arguments ..
+*       DOUBLE PRECISION   DIN1, DIN2
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> This routine is not for general use.  It exists solely to avoid
+*> over-optimization in DISNAN.
+*>
+*> DLAISNAN checks for NaNs by comparing its two arguments for
+*> inequality.  NaN is the only floating-point value where NaN != NaN
+*> returns .TRUE.  To check for NaNs, pass the same variable as both
+*> arguments.
+*>
+*> A compiler must assume that the two arguments are
+*> not the same variable, and the test will not be optimized away.
+*> Interprocedural or whole-program optimization may delete this
+*> test.  The ISNAN functions will be replaced by the correct
+*> Fortran 03 intrinsic once the intrinsic is widely available.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] DIN1
+*> \verbatim
+*>          DIN1 is DOUBLE PRECISION
+*> \endverbatim
+*>
+*> \param[in] DIN2
+*> \verbatim
+*>          DIN2 is DOUBLE PRECISION
+*>          Two numbers to compare for inequality.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date September 2012
+*
+*> \ingroup auxOTHERauxiliary
+*
+*  =====================================================================
+      LOGICAL FUNCTION DLAISNAN( DIN1, DIN2 )
+*
+*  -- LAPACK auxiliary routine (version 3.4.2) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     September 2012
+*
+*     .. Scalar Arguments ..
+      DOUBLE PRECISION   DIN1, DIN2
+*     ..
+*
+*  =====================================================================
+*
+*  .. Executable Statements ..
+      DLAISNAN = (DIN1.NE.DIN2)
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/dlamch.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/dlamch.f
new file mode 100644
index 00000000..25c2c8e6
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/dlamch.f
@@ -0,0 +1,193 @@
+*> \brief \b DLAMCH
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*  Definition:
+*  ===========
+*
+*      DOUBLE PRECISION FUNCTION DLAMCH( CMACH )
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DLAMCH determines double precision machine parameters.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] CMACH
+*> \verbatim
+*>          Specifies the value to be returned by DLAMCH:
+*>          = 'E' or 'e',   DLAMCH := eps
+*>          = 'S' or 's ,   DLAMCH := sfmin
+*>          = 'B' or 'b',   DLAMCH := base
+*>          = 'P' or 'p',   DLAMCH := eps*base
+*>          = 'N' or 'n',   DLAMCH := t
+*>          = 'R' or 'r',   DLAMCH := rnd
+*>          = 'M' or 'm',   DLAMCH := emin
+*>          = 'U' or 'u',   DLAMCH := rmin
+*>          = 'L' or 'l',   DLAMCH := emax
+*>          = 'O' or 'o',   DLAMCH := rmax
+*>          where
+*>          eps   = relative machine precision
+*>          sfmin = safe minimum, such that 1/sfmin does not overflow
+*>          base  = base of the machine
+*>          prec  = eps*base
+*>          t     = number of (base) digits in the mantissa
+*>          rnd   = 1.0 when rounding occurs in addition, 0.0 otherwise
+*>          emin  = minimum exponent before (gradual) underflow
+*>          rmin  = underflow threshold - base**(emin-1)
+*>          emax  = largest exponent before overflow
+*>          rmax  = overflow threshold  - (base**emax)*(1-eps)
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup auxOTHERauxiliary
+*
+*  =====================================================================
+      DOUBLE PRECISION FUNCTION DLAMCH( CMACH )
+*
+*  -- LAPACK auxiliary routine (version 3.4.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2011
+*
+*     .. Scalar Arguments ..
+      CHARACTER          CMACH
+*     ..
+*
+*     .. Scalar Arguments ..
+      DOUBLE PRECISION   A, B
+*     ..
+*
+* =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ONE, ZERO
+      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
+*     ..
+*     .. Local Scalars ..
+      DOUBLE PRECISION   RND, EPS, SFMIN, SMALL, RMACH
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      EXTERNAL           LSAME
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          DIGITS, EPSILON, HUGE, MAXEXPONENT,
+     $                   MINEXPONENT, RADIX, TINY
+*     ..
+*     .. Executable Statements ..
+*
+*
+*     Assume rounding, not chopping. Always.
+*
+      RND = ONE
+*
+      IF( ONE.EQ.RND ) THEN
+         EPS = EPSILON(ZERO) * 0.5
+      ELSE
+         EPS = EPSILON(ZERO)
+      END IF
+*
+      IF( LSAME( CMACH, 'E' ) ) THEN
+         RMACH = EPS
+      ELSE IF( LSAME( CMACH, 'S' ) ) THEN
+         SFMIN = TINY(ZERO)
+         SMALL = ONE / HUGE(ZERO)
+         IF( SMALL.GE.SFMIN ) THEN
+*
+*           Use SMALL plus a bit, to avoid the possibility of rounding
+*           causing overflow when computing  1/sfmin.
+*
+            SFMIN = SMALL*( ONE+EPS )
+         END IF
+         RMACH = SFMIN
+      ELSE IF( LSAME( CMACH, 'B' ) ) THEN
+         RMACH = RADIX(ZERO)
+      ELSE IF( LSAME( CMACH, 'P' ) ) THEN
+         RMACH = EPS * RADIX(ZERO)
+      ELSE IF( LSAME( CMACH, 'N' ) ) THEN
+         RMACH = DIGITS(ZERO)
+      ELSE IF( LSAME( CMACH, 'R' ) ) THEN
+         RMACH = RND
+      ELSE IF( LSAME( CMACH, 'M' ) ) THEN
+         RMACH = MINEXPONENT(ZERO)
+      ELSE IF( LSAME( CMACH, 'U' ) ) THEN
+         RMACH = tiny(zero)
+      ELSE IF( LSAME( CMACH, 'L' ) ) THEN
+         RMACH = MAXEXPONENT(ZERO)
+      ELSE IF( LSAME( CMACH, 'O' ) ) THEN
+         RMACH = HUGE(ZERO)
+      ELSE
+         RMACH = ZERO
+      END IF
+*
+      DLAMCH = RMACH
+      RETURN
+*
+*     End of DLAMCH
+*
+      END
+************************************************************************
+*> \brief \b DLAMC3
+*> \details
+*> \b Purpose:
+*> \verbatim
+*> DLAMC3  is intended to force  A  and  B  to be stored prior to doing
+*> the addition of  A  and  B ,  for use in situations where optimizers
+*> might hold one of these in a register.
+*> \endverbatim
+*> \author LAPACK is a software package provided by Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..
+*> \date November 2011
+*> \ingroup auxOTHERauxiliary
+*>
+*> \param[in] A
+*> \verbatim
+*>          A is a DOUBLE PRECISION
+*> \endverbatim
+*>
+*> \param[in] B
+*> \verbatim
+*>          B is a DOUBLE PRECISION
+*>          The values A and B.
+*> \endverbatim
+*>
+      DOUBLE PRECISION FUNCTION DLAMC3( A, B )
+*
+*  -- LAPACK auxiliary routine (version 3.4.0) --
+*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+*     November 2010
+*
+*     .. Scalar Arguments ..
+      DOUBLE PRECISION   A, B
+*     ..
+* =====================================================================
+*
+*     .. Executable Statements ..
+*
+      DLAMC3 = A + B
+*
+      RETURN
+*
+*     End of DLAMC3
+*
+      END
+*
+************************************************************************
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/dlanst.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/dlanst.f
new file mode 100644
index 00000000..213b06ad
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/dlanst.f
@@ -0,0 +1,186 @@
+*> \brief \b DLANST returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLANST + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlanst.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlanst.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlanst.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER          NORM
+*       INTEGER            N
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   D( * ), E( * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DLANST  returns the value of the one norm,  or the Frobenius norm, or
+*> the  infinity norm,  or the  element of  largest absolute value  of a
+*> real symmetric tridiagonal matrix A.
+*> \endverbatim
+*>
+*> \return DLANST
+*> \verbatim
+*>
+*>    DLANST = ( max(abs(A(i,j))), NORM = 'M' or 'm'
+*>             (
+*>             ( norm1(A),         NORM = '1', 'O' or 'o'
+*>             (
+*>             ( normI(A),         NORM = 'I' or 'i'
+*>             (
+*>             ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
+*>
+*> where  norm1  denotes the  one norm of a matrix (maximum column sum),
+*> normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
+*> normF  denotes the  Frobenius norm of a matrix (square root of sum of
+*> squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] NORM
+*> \verbatim
+*>          NORM is CHARACTER*1
+*>          Specifies the value to be returned in DLANST as described
+*>          above.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.  N >= 0.  When N = 0, DLANST is
+*>          set to zero.
+*> \endverbatim
+*>
+*> \param[in] D
+*> \verbatim
+*>          D is DOUBLE PRECISION array, dimension (N)
+*>          The diagonal elements of A.
+*> \endverbatim
+*>
+*> \param[in] E
+*> \verbatim
+*>          E is DOUBLE PRECISION array, dimension (N-1)
+*>          The (n-1) sub-diagonal or super-diagonal elements of A.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date September 2012
+*
+*> \ingroup auxOTHERauxiliary
+*
+*  =====================================================================
+      DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E )
+*
+*  -- LAPACK auxiliary routine (version 3.4.2) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     September 2012
+*
+*     .. Scalar Arguments ..
+      CHARACTER          NORM
+      INTEGER            N
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   D( * ), E( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ONE, ZERO
+      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            I
+      DOUBLE PRECISION   ANORM, SCALE, SUM
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME, DISNAN
+      EXTERNAL           LSAME, DISNAN
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           DLASSQ
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS, SQRT
+*     ..
+*     .. Executable Statements ..
+*
+      IF( N.LE.0 ) THEN
+         ANORM = ZERO
+      ELSE IF( LSAME( NORM, 'M' ) ) THEN
+*
+*        Find max(abs(A(i,j))).
+*
+         ANORM = ABS( D( N ) )
+         DO 10 I = 1, N - 1
+            SUM = ABS( D( I ) )
+            IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM
+            SUM = ABS( E( I ) )
+            IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM
+   10    CONTINUE
+      ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' .OR.
+     $         LSAME( NORM, 'I' ) ) THEN
+*
+*        Find norm1(A).
+*
+         IF( N.EQ.1 ) THEN
+            ANORM = ABS( D( 1 ) )
+         ELSE
+            ANORM = ABS( D( 1 ) )+ABS( E( 1 ) )
+            SUM = ABS( E( N-1 ) )+ABS( D( N ) )
+            IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM
+            DO 20 I = 2, N - 1
+               SUM = ABS( D( I ) )+ABS( E( I ) )+ABS( E( I-1 ) )
+               IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM
+   20       CONTINUE
+         END IF
+      ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
+*
+*        Find normF(A).
+*
+         SCALE = ZERO
+         SUM = ONE
+         IF( N.GT.1 ) THEN
+            CALL DLASSQ( N-1, E, 1, SCALE, SUM )
+            SUM = 2*SUM
+         END IF
+         CALL DLASSQ( N, D, 1, SCALE, SUM )
+         ANORM = SCALE*SQRT( SUM )
+      END IF
+*
+      DLANST = ANORM
+      RETURN
+*
+*     End of DLANST
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/dlapy2.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/dlapy2.f
new file mode 100644
index 00000000..d43b0d5d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/dlapy2.f
@@ -0,0 +1,104 @@
+*> \brief \b DLAPY2 returns sqrt(x2+y2).
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLAPY2 + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlapy2.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlapy2.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlapy2.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       DOUBLE PRECISION FUNCTION DLAPY2( X, Y )
+* 
+*       .. Scalar Arguments ..
+*       DOUBLE PRECISION   X, Y
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DLAPY2 returns sqrt(x**2+y**2), taking care not to cause unnecessary
+*> overflow.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] X
+*> \verbatim
+*>          X is DOUBLE PRECISION
+*> \endverbatim
+*>
+*> \param[in] Y
+*> \verbatim
+*>          Y is DOUBLE PRECISION
+*>          X and Y specify the values x and y.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date September 2012
+*
+*> \ingroup auxOTHERauxiliary
+*
+*  =====================================================================
+      DOUBLE PRECISION FUNCTION DLAPY2( X, Y )
+*
+*  -- LAPACK auxiliary routine (version 3.4.2) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     September 2012
+*
+*     .. Scalar Arguments ..
+      DOUBLE PRECISION   X, Y
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ZERO
+      PARAMETER          ( ZERO = 0.0D0 )
+      DOUBLE PRECISION   ONE
+      PARAMETER          ( ONE = 1.0D0 )
+*     ..
+*     .. Local Scalars ..
+      DOUBLE PRECISION   W, XABS, YABS, Z
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS, MAX, MIN, SQRT
+*     ..
+*     .. Executable Statements ..
+*
+      XABS = ABS( X )
+      YABS = ABS( Y )
+      W = MAX( XABS, YABS )
+      Z = MIN( XABS, YABS )
+      IF( Z.EQ.ZERO ) THEN
+         DLAPY2 = W
+      ELSE
+         DLAPY2 = W*SQRT( ONE+( Z / W )**2 )
+      END IF
+      RETURN
+*
+*     End of DLAPY2
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/dlascl.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/dlascl.f
new file mode 100644
index 00000000..9b9b33c0
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/dlascl.f
@@ -0,0 +1,364 @@
+*> \brief \b DLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLASCL + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlascl.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlascl.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlascl.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER          TYPE
+*       INTEGER            INFO, KL, KU, LDA, M, N
+*       DOUBLE PRECISION   CFROM, CTO
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   A( LDA, * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DLASCL multiplies the M by N real matrix A by the real scalar
+*> CTO/CFROM.  This is done without over/underflow as long as the final
+*> result CTO*A(I,J)/CFROM does not over/underflow. TYPE specifies that
+*> A may be full, upper triangular, lower triangular, upper Hessenberg,
+*> or banded.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] TYPE
+*> \verbatim
+*>          TYPE is CHARACTER*1
+*>          TYPE indices the storage type of the input matrix.
+*>          = 'G':  A is a full matrix.
+*>          = 'L':  A is a lower triangular matrix.
+*>          = 'U':  A is an upper triangular matrix.
+*>          = 'H':  A is an upper Hessenberg matrix.
+*>          = 'B':  A is a symmetric band matrix with lower bandwidth KL
+*>                  and upper bandwidth KU and with the only the lower
+*>                  half stored.
+*>          = 'Q':  A is a symmetric band matrix with lower bandwidth KL
+*>                  and upper bandwidth KU and with the only the upper
+*>                  half stored.
+*>          = 'Z':  A is a band matrix with lower bandwidth KL and upper
+*>                  bandwidth KU. See DGBTRF for storage details.
+*> \endverbatim
+*>
+*> \param[in] KL
+*> \verbatim
+*>          KL is INTEGER
+*>          The lower bandwidth of A.  Referenced only if TYPE = 'B',
+*>          'Q' or 'Z'.
+*> \endverbatim
+*>
+*> \param[in] KU
+*> \verbatim
+*>          KU is INTEGER
+*>          The upper bandwidth of A.  Referenced only if TYPE = 'B',
+*>          'Q' or 'Z'.
+*> \endverbatim
+*>
+*> \param[in] CFROM
+*> \verbatim
+*>          CFROM is DOUBLE PRECISION
+*> \endverbatim
+*>
+*> \param[in] CTO
+*> \verbatim
+*>          CTO is DOUBLE PRECISION
+*>
+*>          The matrix A is multiplied by CTO/CFROM. A(I,J) is computed
+*>          without over/underflow if the final result CTO*A(I,J)/CFROM
+*>          can be represented without over/underflow.  CFROM must be
+*>          nonzero.
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*>          M is INTEGER
+*>          The number of rows of the matrix A.  M >= 0.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The number of columns of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          A is DOUBLE PRECISION array, dimension (LDA,N)
+*>          The matrix to be multiplied by CTO/CFROM.  See TYPE for the
+*>          storage type.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,M).
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          0  - successful exit
+*>          <0 - if INFO = -i, the i-th argument had an illegal value.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date September 2012
+*
+*> \ingroup auxOTHERauxiliary
+*
+*  =====================================================================
+      SUBROUTINE DLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO )
+*
+*  -- LAPACK auxiliary routine (version 3.4.2) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     September 2012
+*
+*     .. Scalar Arguments ..
+      CHARACTER          TYPE
+      INTEGER            INFO, KL, KU, LDA, M, N
+      DOUBLE PRECISION   CFROM, CTO
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   A( LDA, * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ZERO, ONE
+      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
+*     ..
+*     .. Local Scalars ..
+      LOGICAL            DONE
+      INTEGER            I, ITYPE, J, K1, K2, K3, K4
+      DOUBLE PRECISION   BIGNUM, CFROM1, CFROMC, CTO1, CTOC, MUL, SMLNUM
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME, DISNAN
+      DOUBLE PRECISION   DLAMCH
+      EXTERNAL           LSAME, DLAMCH, DISNAN
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS, MAX, MIN
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           XERBLA
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input arguments
+*
+      INFO = 0
+*
+      IF( LSAME( TYPE, 'G' ) ) THEN
+         ITYPE = 0
+      ELSE IF( LSAME( TYPE, 'L' ) ) THEN
+         ITYPE = 1
+      ELSE IF( LSAME( TYPE, 'U' ) ) THEN
+         ITYPE = 2
+      ELSE IF( LSAME( TYPE, 'H' ) ) THEN
+         ITYPE = 3
+      ELSE IF( LSAME( TYPE, 'B' ) ) THEN
+         ITYPE = 4
+      ELSE IF( LSAME( TYPE, 'Q' ) ) THEN
+         ITYPE = 5
+      ELSE IF( LSAME( TYPE, 'Z' ) ) THEN
+         ITYPE = 6
+      ELSE
+         ITYPE = -1
+      END IF
+*
+      IF( ITYPE.EQ.-1 ) THEN
+         INFO = -1
+      ELSE IF( CFROM.EQ.ZERO .OR. DISNAN(CFROM) ) THEN
+         INFO = -4
+      ELSE IF( DISNAN(CTO) ) THEN
+         INFO = -5
+      ELSE IF( M.LT.0 ) THEN
+         INFO = -6
+      ELSE IF( N.LT.0 .OR. ( ITYPE.EQ.4 .AND. N.NE.M ) .OR.
+     $         ( ITYPE.EQ.5 .AND. N.NE.M ) ) THEN
+         INFO = -7
+      ELSE IF( ITYPE.LE.3 .AND. LDA.LT.MAX( 1, M ) ) THEN
+         INFO = -9
+      ELSE IF( ITYPE.GE.4 ) THEN
+         IF( KL.LT.0 .OR. KL.GT.MAX( M-1, 0 ) ) THEN
+            INFO = -2
+         ELSE IF( KU.LT.0 .OR. KU.GT.MAX( N-1, 0 ) .OR.
+     $            ( ( ITYPE.EQ.4 .OR. ITYPE.EQ.5 ) .AND. KL.NE.KU ) )
+     $             THEN
+            INFO = -3
+         ELSE IF( ( ITYPE.EQ.4 .AND. LDA.LT.KL+1 ) .OR.
+     $            ( ITYPE.EQ.5 .AND. LDA.LT.KU+1 ) .OR.
+     $            ( ITYPE.EQ.6 .AND. LDA.LT.2*KL+KU+1 ) ) THEN
+            INFO = -9
+         END IF
+      END IF
+*
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'DLASCL', -INFO )
+         RETURN
+      END IF
+*
+*     Quick return if possible
+*
+      IF( N.EQ.0 .OR. M.EQ.0 )
+     $   RETURN
+*
+*     Get machine parameters
+*
+      SMLNUM = DLAMCH( 'S' )
+      BIGNUM = ONE / SMLNUM
+*
+      CFROMC = CFROM
+      CTOC = CTO
+*
+   10 CONTINUE
+      CFROM1 = CFROMC*SMLNUM
+      IF( CFROM1.EQ.CFROMC ) THEN
+!        CFROMC is an inf.  Multiply by a correctly signed zero for
+!        finite CTOC, or a NaN if CTOC is infinite.
+         MUL = CTOC / CFROMC
+         DONE = .TRUE.
+         CTO1 = CTOC
+      ELSE
+         CTO1 = CTOC / BIGNUM
+         IF( CTO1.EQ.CTOC ) THEN
+!           CTOC is either 0 or an inf.  In both cases, CTOC itself
+!           serves as the correct multiplication factor.
+            MUL = CTOC
+            DONE = .TRUE.
+            CFROMC = ONE
+         ELSE IF( ABS( CFROM1 ).GT.ABS( CTOC ) .AND. CTOC.NE.ZERO ) THEN
+            MUL = SMLNUM
+            DONE = .FALSE.
+            CFROMC = CFROM1
+         ELSE IF( ABS( CTO1 ).GT.ABS( CFROMC ) ) THEN
+            MUL = BIGNUM
+            DONE = .FALSE.
+            CTOC = CTO1
+         ELSE
+            MUL = CTOC / CFROMC
+            DONE = .TRUE.
+         END IF
+      END IF
+*
+      IF( ITYPE.EQ.0 ) THEN
+*
+*        Full matrix
+*
+         DO 30 J = 1, N
+            DO 20 I = 1, M
+               A( I, J ) = A( I, J )*MUL
+   20       CONTINUE
+   30    CONTINUE
+*
+      ELSE IF( ITYPE.EQ.1 ) THEN
+*
+*        Lower triangular matrix
+*
+         DO 50 J = 1, N
+            DO 40 I = J, M
+               A( I, J ) = A( I, J )*MUL
+   40       CONTINUE
+   50    CONTINUE
+*
+      ELSE IF( ITYPE.EQ.2 ) THEN
+*
+*        Upper triangular matrix
+*
+         DO 70 J = 1, N
+            DO 60 I = 1, MIN( J, M )
+               A( I, J ) = A( I, J )*MUL
+   60       CONTINUE
+   70    CONTINUE
+*
+      ELSE IF( ITYPE.EQ.3 ) THEN
+*
+*        Upper Hessenberg matrix
+*
+         DO 90 J = 1, N
+            DO 80 I = 1, MIN( J+1, M )
+               A( I, J ) = A( I, J )*MUL
+   80       CONTINUE
+   90    CONTINUE
+*
+      ELSE IF( ITYPE.EQ.4 ) THEN
+*
+*        Lower half of a symmetric band matrix
+*
+         K3 = KL + 1
+         K4 = N + 1
+         DO 110 J = 1, N
+            DO 100 I = 1, MIN( K3, K4-J )
+               A( I, J ) = A( I, J )*MUL
+  100       CONTINUE
+  110    CONTINUE
+*
+      ELSE IF( ITYPE.EQ.5 ) THEN
+*
+*        Upper half of a symmetric band matrix
+*
+         K1 = KU + 2
+         K3 = KU + 1
+         DO 130 J = 1, N
+            DO 120 I = MAX( K1-J, 1 ), K3
+               A( I, J ) = A( I, J )*MUL
+  120       CONTINUE
+  130    CONTINUE
+*
+      ELSE IF( ITYPE.EQ.6 ) THEN
+*
+*        Band matrix
+*
+         K1 = KL + KU + 2
+         K2 = KL + 1
+         K3 = 2*KL + KU + 1
+         K4 = KL + KU + 1 + M
+         DO 150 J = 1, N
+            DO 140 I = MAX( K1-J, K2 ), MIN( K3, K4-J )
+               A( I, J ) = A( I, J )*MUL
+  140       CONTINUE
+  150    CONTINUE
+*
+      END IF
+*
+      IF( .NOT.DONE )
+     $   GO TO 10
+*
+      RETURN
+*
+*     End of DLASCL
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/dlasrt.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/dlasrt.f
new file mode 100644
index 00000000..f5d0e6cd
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/dlasrt.f
@@ -0,0 +1,303 @@
+*> \brief \b DLASRT sorts numbers in increasing or decreasing order.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLASRT + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasrt.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasrt.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasrt.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DLASRT( ID, N, D, INFO )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER          ID
+*       INTEGER            INFO, N
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   D( * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> Sort the numbers in D in increasing order (if ID = 'I') or
+*> in decreasing order (if ID = 'D' ).
+*>
+*> Use Quick Sort, reverting to Insertion sort on arrays of
+*> size <= 20. Dimension of STACK limits N to about 2**32.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] ID
+*> \verbatim
+*>          ID is CHARACTER*1
+*>          = 'I': sort D in increasing order;
+*>          = 'D': sort D in decreasing order.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The length of the array D.
+*> \endverbatim
+*>
+*> \param[in,out] D
+*> \verbatim
+*>          D is DOUBLE PRECISION array, dimension (N)
+*>          On entry, the array to be sorted.
+*>          On exit, D has been sorted into increasing order
+*>          (D(1) <= ... <= D(N) ) or into decreasing order
+*>          (D(1) >= ... >= D(N) ), depending on ID.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0:  successful exit
+*>          < 0:  if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date September 2012
+*
+*> \ingroup auxOTHERcomputational
+*
+*  =====================================================================
+      SUBROUTINE DLASRT( ID, N, D, INFO )
+*
+*  -- LAPACK computational routine (version 3.4.2) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     September 2012
+*
+*     .. Scalar Arguments ..
+      CHARACTER          ID
+      INTEGER            INFO, N
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   D( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      INTEGER            SELECT
+      PARAMETER          ( SELECT = 20 )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            DIR, ENDD, I, J, START, STKPNT
+      DOUBLE PRECISION   D1, D2, D3, DMNMX, TMP
+*     ..
+*     .. Local Arrays ..
+      INTEGER            STACK( 2, 32 )
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      EXTERNAL           LSAME
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           XERBLA
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input paramters.
+*
+      INFO = 0
+      DIR = -1
+      IF( LSAME( ID, 'D' ) ) THEN
+         DIR = 0
+      ELSE IF( LSAME( ID, 'I' ) ) THEN
+         DIR = 1
+      END IF
+      IF( DIR.EQ.-1 ) THEN
+         INFO = -1
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -2
+      END IF
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'DLASRT', -INFO )
+         RETURN
+      END IF
+*
+*     Quick return if possible
+*
+      IF( N.LE.1 )
+     $   RETURN
+*
+      STKPNT = 1
+      STACK( 1, 1 ) = 1
+      STACK( 2, 1 ) = N
+   10 CONTINUE
+      START = STACK( 1, STKPNT )
+      ENDD = STACK( 2, STKPNT )
+      STKPNT = STKPNT - 1
+      IF( ENDD-START.LE.SELECT .AND. ENDD-START.GT.0 ) THEN
+*
+*        Do Insertion sort on D( START:ENDD )
+*
+         IF( DIR.EQ.0 ) THEN
+*
+*           Sort into decreasing order
+*
+            DO 30 I = START + 1, ENDD
+               DO 20 J = I, START + 1, -1
+                  IF( D( J ).GT.D( J-1 ) ) THEN
+                     DMNMX = D( J )
+                     D( J ) = D( J-1 )
+                     D( J-1 ) = DMNMX
+                  ELSE
+                     GO TO 30
+                  END IF
+   20          CONTINUE
+   30       CONTINUE
+*
+         ELSE
+*
+*           Sort into increasing order
+*
+            DO 50 I = START + 1, ENDD
+               DO 40 J = I, START + 1, -1
+                  IF( D( J ).LT.D( J-1 ) ) THEN
+                     DMNMX = D( J )
+                     D( J ) = D( J-1 )
+                     D( J-1 ) = DMNMX
+                  ELSE
+                     GO TO 50
+                  END IF
+   40          CONTINUE
+   50       CONTINUE
+*
+         END IF
+*
+      ELSE IF( ENDD-START.GT.SELECT ) THEN
+*
+*        Partition D( START:ENDD ) and stack parts, largest one first
+*
+*        Choose partition entry as median of 3
+*
+         D1 = D( START )
+         D2 = D( ENDD )
+         I = ( START+ENDD ) / 2
+         D3 = D( I )
+         IF( D1.LT.D2 ) THEN
+            IF( D3.LT.D1 ) THEN
+               DMNMX = D1
+            ELSE IF( D3.LT.D2 ) THEN
+               DMNMX = D3
+            ELSE
+               DMNMX = D2
+            END IF
+         ELSE
+            IF( D3.LT.D2 ) THEN
+               DMNMX = D2
+            ELSE IF( D3.LT.D1 ) THEN
+               DMNMX = D3
+            ELSE
+               DMNMX = D1
+            END IF
+         END IF
+*
+         IF( DIR.EQ.0 ) THEN
+*
+*           Sort into decreasing order
+*
+            I = START - 1
+            J = ENDD + 1
+   60       CONTINUE
+   70       CONTINUE
+            J = J - 1
+            IF( D( J ).LT.DMNMX )
+     $         GO TO 70
+   80       CONTINUE
+            I = I + 1
+            IF( D( I ).GT.DMNMX )
+     $         GO TO 80
+            IF( I.LT.J ) THEN
+               TMP = D( I )
+               D( I ) = D( J )
+               D( J ) = TMP
+               GO TO 60
+            END IF
+            IF( J-START.GT.ENDD-J-1 ) THEN
+               STKPNT = STKPNT + 1
+               STACK( 1, STKPNT ) = START
+               STACK( 2, STKPNT ) = J
+               STKPNT = STKPNT + 1
+               STACK( 1, STKPNT ) = J + 1
+               STACK( 2, STKPNT ) = ENDD
+            ELSE
+               STKPNT = STKPNT + 1
+               STACK( 1, STKPNT ) = J + 1
+               STACK( 2, STKPNT ) = ENDD
+               STKPNT = STKPNT + 1
+               STACK( 1, STKPNT ) = START
+               STACK( 2, STKPNT ) = J
+            END IF
+         ELSE
+*
+*           Sort into increasing order
+*
+            I = START - 1
+            J = ENDD + 1
+   90       CONTINUE
+  100       CONTINUE
+            J = J - 1
+            IF( D( J ).GT.DMNMX )
+     $         GO TO 100
+  110       CONTINUE
+            I = I + 1
+            IF( D( I ).LT.DMNMX )
+     $         GO TO 110
+            IF( I.LT.J ) THEN
+               TMP = D( I )
+               D( I ) = D( J )
+               D( J ) = TMP
+               GO TO 90
+            END IF
+            IF( J-START.GT.ENDD-J-1 ) THEN
+               STKPNT = STKPNT + 1
+               STACK( 1, STKPNT ) = START
+               STACK( 2, STKPNT ) = J
+               STKPNT = STKPNT + 1
+               STACK( 1, STKPNT ) = J + 1
+               STACK( 2, STKPNT ) = ENDD
+            ELSE
+               STKPNT = STKPNT + 1
+               STACK( 1, STKPNT ) = J + 1
+               STACK( 2, STKPNT ) = ENDD
+               STKPNT = STKPNT + 1
+               STACK( 1, STKPNT ) = START
+               STACK( 2, STKPNT ) = J
+            END IF
+         END IF
+      END IF
+      IF( STKPNT.GT.0 )
+     $   GO TO 10
+      RETURN
+*
+*     End of DLASRT
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/dlassq.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/dlassq.f
new file mode 100644
index 00000000..c7c4087e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/dlassq.f
@@ -0,0 +1,155 @@
+*> \brief \b DLASSQ updates a sum of squares represented in scaled form.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLASSQ + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlassq.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlassq.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlassq.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            INCX, N
+*       DOUBLE PRECISION   SCALE, SUMSQ
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   X( * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DLASSQ  returns the values  scl  and  smsq  such that
+*>
+*>    ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
+*>
+*> where  x( i ) = X( 1 + ( i - 1 )*INCX ). The value of  sumsq  is
+*> assumed to be non-negative and  scl  returns the value
+*>
+*>    scl = max( scale, abs( x( i ) ) ).
+*>
+*> scale and sumsq must be supplied in SCALE and SUMSQ and
+*> scl and smsq are overwritten on SCALE and SUMSQ respectively.
+*>
+*> The routine makes only one pass through the vector x.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The number of elements to be used from the vector X.
+*> \endverbatim
+*>
+*> \param[in] X
+*> \verbatim
+*>          X is DOUBLE PRECISION array, dimension (N)
+*>          The vector for which a scaled sum of squares is computed.
+*>             x( i )  = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n.
+*> \endverbatim
+*>
+*> \param[in] INCX
+*> \verbatim
+*>          INCX is INTEGER
+*>          The increment between successive values of the vector X.
+*>          INCX > 0.
+*> \endverbatim
+*>
+*> \param[in,out] SCALE
+*> \verbatim
+*>          SCALE is DOUBLE PRECISION
+*>          On entry, the value  scale  in the equation above.
+*>          On exit, SCALE is overwritten with  scl , the scaling factor
+*>          for the sum of squares.
+*> \endverbatim
+*>
+*> \param[in,out] SUMSQ
+*> \verbatim
+*>          SUMSQ is DOUBLE PRECISION
+*>          On entry, the value  sumsq  in the equation above.
+*>          On exit, SUMSQ is overwritten with  smsq , the basic sum of
+*>          squares from which  scl  has been factored out.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date September 2012
+*
+*> \ingroup auxOTHERauxiliary
+*
+*  =====================================================================
+      SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ )
+*
+*  -- LAPACK auxiliary routine (version 3.4.2) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     September 2012
+*
+*     .. Scalar Arguments ..
+      INTEGER            INCX, N
+      DOUBLE PRECISION   SCALE, SUMSQ
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   X( * )
+*     ..
+*
+* =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ZERO
+      PARAMETER          ( ZERO = 0.0D+0 )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            IX
+      DOUBLE PRECISION   ABSXI
+*     ..
+*     .. External Functions ..
+      LOGICAL            DISNAN
+      EXTERNAL           DISNAN
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS
+*     ..
+*     .. Executable Statements ..
+*
+      IF( N.GT.0 ) THEN
+         DO 10 IX = 1, 1 + ( N-1 )*INCX, INCX
+            ABSXI = ABS( X( IX ) )
+            IF( ABSXI.GT.ZERO.OR.DISNAN( ABSXI ) ) THEN
+               IF( SCALE.LT.ABSXI ) THEN
+                  SUMSQ = 1 + SUMSQ*( SCALE / ABSXI )**2
+                  SCALE = ABSXI
+               ELSE
+                  SUMSQ = SUMSQ + ( ABSXI / SCALE )**2
+               END IF
+            END IF
+   10    CONTINUE
+      END IF
+      RETURN
+*
+*     End of DLASSQ
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/dsterf.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/dsterf.f
new file mode 100644
index 00000000..43395cc7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/dsterf.f
@@ -0,0 +1,448 @@
+*> \brief \b DSTERF
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DSTERF + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsterf.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsterf.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsterf.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DSTERF( N, D, E, INFO )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            INFO, N
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   D( * ), E( * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DSTERF computes all eigenvalues of a symmetric tridiagonal matrix
+*> using the Pal-Walker-Kahan variant of the QL or QR algorithm.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] D
+*> \verbatim
+*>          D is DOUBLE PRECISION array, dimension (N)
+*>          On entry, the n diagonal elements of the tridiagonal matrix.
+*>          On exit, if INFO = 0, the eigenvalues in ascending order.
+*> \endverbatim
+*>
+*> \param[in,out] E
+*> \verbatim
+*>          E is DOUBLE PRECISION array, dimension (N-1)
+*>          On entry, the (n-1) subdiagonal elements of the tridiagonal
+*>          matrix.
+*>          On exit, E has been destroyed.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0:  successful exit
+*>          < 0:  if INFO = -i, the i-th argument had an illegal value
+*>          > 0:  the algorithm failed to find all of the eigenvalues in
+*>                a total of 30*N iterations; if INFO = i, then i
+*>                elements of E have not converged to zero.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup auxOTHERcomputational
+*
+*  =====================================================================
+      SUBROUTINE DSTERF( N, D, E, INFO )
+*
+*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2011
+*
+*     .. Scalar Arguments ..
+      INTEGER            INFO, N
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   D( * ), E( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ZERO, ONE, TWO, THREE
+      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0,
+     $                   THREE = 3.0D0 )
+      INTEGER            MAXIT
+      PARAMETER          ( MAXIT = 30 )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            I, ISCALE, JTOT, L, L1, LEND, LENDSV, LSV, M,
+     $                   NMAXIT
+      DOUBLE PRECISION   ALPHA, ANORM, BB, C, EPS, EPS2, GAMMA, OLDC,
+     $                   OLDGAM, P, R, RT1, RT2, RTE, S, SAFMAX, SAFMIN,
+     $                   SIGMA, SSFMAX, SSFMIN, RMAX
+*     ..
+*     .. External Functions ..
+      DOUBLE PRECISION   DLAMCH, DLANST, DLAPY2
+      EXTERNAL           DLAMCH, DLANST, DLAPY2
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           DLAE2, DLASCL, DLASRT, XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS, SIGN, SQRT
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters.
+*
+      INFO = 0
+*
+*     Quick return if possible
+*
+      IF( N.LT.0 ) THEN
+         INFO = -1
+         CALL XERBLA( 'DSTERF', -INFO )
+         RETURN
+      END IF
+      IF( N.LE.1 )
+     $   RETURN
+*
+*     Determine the unit roundoff for this environment.
+*
+      EPS = DLAMCH( 'E' )
+      EPS2 = EPS**2
+      SAFMIN = DLAMCH( 'S' )
+      SAFMAX = ONE / SAFMIN
+      SSFMAX = SQRT( SAFMAX ) / THREE
+      SSFMIN = SQRT( SAFMIN ) / EPS2
+      RMAX = DLAMCH( 'O' )
+*
+*     Compute the eigenvalues of the tridiagonal matrix.
+*
+      NMAXIT = N*MAXIT
+      SIGMA = ZERO
+      JTOT = 0
+*
+*     Determine where the matrix splits and choose QL or QR iteration
+*     for each block, according to whether top or bottom diagonal
+*     element is smaller.
+*
+      L1 = 1
+*
+   10 CONTINUE
+      print *, "l1 = ", l1
+      IF( L1.GT.N ) THEN
+        print *, "going to 170"
+        GO TO 170
+      end if
+      IF( L1.GT.1 )
+     $   E( L1-1 ) = ZERO
+      DO 20 M = L1, N - 1
+         IF( ABS( E( M ) ).LE.( SQRT( ABS( D( M ) ) )*SQRT( ABS( D( M+
+     $       1 ) ) ) )*EPS ) THEN
+            E( M ) = ZERO
+            GO TO 30
+         END IF
+   20 CONTINUE
+      M = N
+*
+   30 CONTINUE
+      print *, "30, d"
+      print *, d(1:n)
+      L = L1
+      LSV = L
+      LEND = M
+      LENDSV = LEND
+      L1 = M + 1
+      IF( LEND.EQ.L )
+     $   GO TO 10
+*
+*     Scale submatrix in rows and columns L to LEND
+*
+      ANORM = DLANST( 'M', LEND-L+1, D( L ), E( L ) )
+      ISCALE = 0
+      IF( ANORM.EQ.ZERO )
+     $   GO TO 10      
+      IF( (ANORM.GT.SSFMAX) ) THEN
+         ISCALE = 1
+         CALL DLASCL( 'G', 0, 0, ANORM, SSFMAX, LEND-L+1, 1, D( L ), N,
+     $                INFO )
+         CALL DLASCL( 'G', 0, 0, ANORM, SSFMAX, LEND-L, 1, E( L ), N,
+     $                INFO )
+      ELSE IF( ANORM.LT.SSFMIN ) THEN
+         ISCALE = 2
+         CALL DLASCL( 'G', 0, 0, ANORM, SSFMIN, LEND-L+1, 1, D( L ), N,
+     $                INFO )
+         CALL DLASCL( 'G', 0, 0, ANORM, SSFMIN, LEND-L, 1, E( L ), N,
+     $                INFO )
+      END IF
+*
+      DO 40 I = L, LEND - 1
+         E( I ) = E( I )**2
+   40 CONTINUE
+*
+*     Choose between QL and QR iteration
+*
+      IF( ABS( D( LEND ) ).LT.ABS( D( L ) ) ) THEN
+         LEND = LSV
+         L = LENDSV
+      END IF
+*
+      IF( LEND.GE.L ) THEN
+        print *, "ql, d"
+        print *, d(1:n)
+*
+*        QL Iteration
+*
+*        Look for small subdiagonal element.
+*
+   50    CONTINUE
+         IF( L.NE.LEND ) THEN
+            DO 60 M = L, LEND - 1
+               IF( ABS( E( M ) ).LE.EPS2*ABS( D( M )*D( M+1 ) ) )
+     $            GO TO 70
+   60       CONTINUE
+         END IF
+         M = LEND
+*
+   70    CONTINUE
+         IF( M.LT.LEND )
+     $      E( M ) = ZERO
+         P = D( L )
+         IF( M.EQ.L )
+     $      GO TO 90
+*
+*        If remaining matrix is 2 by 2, use DLAE2 to compute its
+*        eigenvalues.
+*
+         IF( M.EQ.L+1 ) THEN
+            RTE = SQRT( E( L ) )
+            CALL DLAE2( D( L ), RTE, D( L+1 ), RT1, RT2 )
+            D( L ) = RT1
+            D( L+1 ) = RT2
+            E( L ) = ZERO
+            L = L + 2
+            IF( L.LE.LEND )
+     $         GO TO 50
+            GO TO 150
+         END IF
+*
+         IF( JTOT.EQ.NMAXIT )
+     $      GO TO 150
+         JTOT = JTOT + 1
+*
+*        Form shift.
+*
+         RTE = SQRT( E( L ) )
+         SIGMA = ( D( L+1 )-P ) / ( TWO*RTE )
+         R = DLAPY2( SIGMA, ONE )
+         SIGMA = P - ( RTE / ( SIGMA+SIGN( R, SIGMA ) ) )
+*
+         C = ONE
+         S = ZERO
+         GAMMA = D( M ) - SIGMA
+         P = GAMMA*GAMMA
+*
+*        Inner loop
+*
+          print *, "inner loop d before"
+          print *, d(1:n)
+
+         DO 80 I = M - 1, L, -1
+            print *, "inner loop"
+            print *, "ei", e(i)
+            BB = E( I )
+            R = P + BB
+            print *, "bb,p,r"
+            print *, bb,p,r
+            IF( I.NE.M-1 ) THEN
+              print *, s,r
+              E( I+1 ) = S*R
+            end if
+            OLDC = C
+            C = P / R
+            S = BB / R
+            OLDGAM = GAMMA
+            print *, "di", d(i)
+            ALPHA = D( I )
+            GAMMA = C*( ALPHA-SIGMA ) - S*OLDGAM
+            print *,"og, a, ga", OLDGAM, ALPHA, GAMMA
+            D( I+1 ) = OLDGAM + ( ALPHA-GAMMA )
+            IF( C.NE.ZERO ) THEN
+               P = ( GAMMA*GAMMA ) / C
+            ELSE
+               P = OLDC*BB
+            END IF
+            print *, "p, gamma = ", p,GAMMA
+   80    CONTINUE
+*
+         E( L ) = S*P
+         D( L ) = SIGMA + GAMMA
+
+        print *, "inner loop d after"
+        print *, d(1:n)
+         GO TO 50
+*
+*        Eigenvalue found.
+*
+   90    CONTINUE
+         D( L ) = P
+*
+         L = L + 1
+         IF( L.LE.LEND )
+     $      GO TO 50
+         GO TO 150
+*
+      ELSE
+*
+*        QR Iteration
+*
+*        Look for small superdiagonal element.
+*
+  100    CONTINUE
+         DO 110 M = L, LEND + 1, -1
+            IF( ABS( E( M-1 ) ).LE.EPS2*ABS( D( M )*D( M-1 ) ) )
+     $         GO TO 120
+  110    CONTINUE
+         M = LEND
+*
+  120    CONTINUE
+         IF( M.GT.LEND )
+     $      E( M-1 ) = ZERO
+         P = D( L )
+         IF( M.EQ.L )
+     $      GO TO 140
+*
+*        If remaining matrix is 2 by 2, use DLAE2 to compute its
+*        eigenvalues.
+*
+         IF( M.EQ.L-1 ) THEN
+            RTE = SQRT( E( L-1 ) )
+            CALL DLAE2( D( L ), RTE, D( L-1 ), RT1, RT2 )
+            D( L ) = RT1
+            D( L-1 ) = RT2
+            E( L-1 ) = ZERO
+            L = L - 2
+            IF( L.GE.LEND )
+     $         GO TO 100
+            GO TO 150
+         END IF
+*
+         IF( JTOT.EQ.NMAXIT )
+     $      GO TO 150
+         JTOT = JTOT + 1
+*
+*        Form shift.
+*
+         RTE = SQRT( E( L-1 ) )
+         SIGMA = ( D( L-1 )-P ) / ( TWO*RTE )
+         R = DLAPY2( SIGMA, ONE )
+         SIGMA = P - ( RTE / ( SIGMA+SIGN( R, SIGMA ) ) )
+*
+         C = ONE
+         S = ZERO
+         GAMMA = D( M ) - SIGMA
+         P = GAMMA*GAMMA
+*
+*        Inner loop
+*
+         DO 130 I = M, L - 1
+            BB = E( I )
+            R = P + BB
+            IF( I.NE.M )
+     $         E( I-1 ) = S*R
+            OLDC = C
+            C = P / R
+            S = BB / R
+            OLDGAM = GAMMA
+            ALPHA = D( I+1 )
+            GAMMA = C*( ALPHA-SIGMA ) - S*OLDGAM
+            D( I ) = OLDGAM + ( ALPHA-GAMMA )
+            IF( C.NE.ZERO ) THEN
+               P = ( GAMMA*GAMMA ) / C
+            ELSE
+               P = OLDC*BB
+            END IF
+  130    CONTINUE
+*
+         E( L-1 ) = S*P
+         D( L ) = SIGMA + GAMMA
+         GO TO 100
+*
+*        Eigenvalue found.
+*
+  140    CONTINUE
+         D( L ) = P
+*
+         L = L - 1
+         IF( L.GE.LEND )
+     $      GO TO 100
+         GO TO 150
+*
+      END IF
+*
+*     Undo scaling if necessary
+*
+  150 CONTINUE
+      IF( ISCALE.EQ.1 )
+     $   CALL DLASCL( 'G', 0, 0, SSFMAX, ANORM, LENDSV-LSV+1, 1,
+     $                D( LSV ), N, INFO )
+      IF( ISCALE.EQ.2 )
+     $   CALL DLASCL( 'G', 0, 0, SSFMIN, ANORM, LENDSV-LSV+1, 1,
+     $                D( LSV ), N, INFO )
+*
+*     Check for no convergence to an eigenvalue after a total
+*     of N*MAXIT iterations.
+*
+      IF( JTOT.LT.NMAXIT )
+     $   GO TO 10
+      DO 160 I = 1, N - 1
+         IF( E( I ).NE.ZERO )
+     $      INFO = INFO + 1
+  160 CONTINUE
+      GO TO 180
+*
+*     Sort eigenvalues in increasing order.
+*
+  170 CONTINUE
+      CALL DLASRT( 'I', N, D, INFO )
+*
+  180 CONTINUE
+      RETURN
+*
+*     End of DSTERF
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/lsame.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/lsame.f
new file mode 100644
index 00000000..315304c3
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/lsame.f
@@ -0,0 +1,125 @@
+*> \brief \b LSAME
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*  Definition:
+*  ===========
+*
+*      LOGICAL FUNCTION LSAME( CA, CB )
+*
+*     .. Scalar Arguments ..
+*      CHARACTER          CA, CB
+*     ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> LSAME returns .TRUE. if CA is the same letter as CB regardless of
+*> case.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] CA
+*> \verbatim
+*> \endverbatim
+*>
+*> \param[in] CB
+*> \verbatim
+*>          CA and CB specify the single characters to be compared.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup auxOTHERauxiliary
+*
+*  =====================================================================
+      LOGICAL FUNCTION LSAME( CA, CB )
+*
+*  -- LAPACK auxiliary routine (version 3.4.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2011
+*
+*     .. Scalar Arguments ..
+      CHARACTER          CA, CB
+*     ..
+*
+* =====================================================================
+*
+*     .. Intrinsic Functions ..
+      INTRINSIC          ICHAR
+*     ..
+*     .. Local Scalars ..
+      INTEGER            INTA, INTB, ZCODE
+*     ..
+*     .. Executable Statements ..
+*
+*     Test if the characters are equal
+*
+      LSAME = CA.EQ.CB
+      IF( LSAME )
+     $   RETURN
+*
+*     Now test for equivalence if both characters are alphabetic.
+*
+      ZCODE = ICHAR( 'Z' )
+*
+*     Use 'Z' rather than 'A' so that ASCII can be detected on Prime
+*     machines, on which ICHAR returns a value with bit 8 set.
+*     ICHAR('A') on Prime machines returns 193 which is the same as
+*     ICHAR('A') on an EBCDIC machine.
+*
+      INTA = ICHAR( CA )
+      INTB = ICHAR( CB )
+*
+      IF( ZCODE.EQ.90 .OR. ZCODE.EQ.122 ) THEN
+*
+*        ASCII is assumed - ZCODE is the ASCII code of either lower or
+*        upper case 'Z'.
+*
+         IF( INTA.GE.97 .AND. INTA.LE.122 ) INTA = INTA - 32
+         IF( INTB.GE.97 .AND. INTB.LE.122 ) INTB = INTB - 32
+*
+      ELSE IF( ZCODE.EQ.233 .OR. ZCODE.EQ.169 ) THEN
+*
+*        EBCDIC is assumed - ZCODE is the EBCDIC code of either lower or
+*        upper case 'Z'.
+*
+         IF( INTA.GE.129 .AND. INTA.LE.137 .OR.
+     $       INTA.GE.145 .AND. INTA.LE.153 .OR.
+     $       INTA.GE.162 .AND. INTA.LE.169 ) INTA = INTA + 64
+         IF( INTB.GE.129 .AND. INTB.LE.137 .OR.
+     $       INTB.GE.145 .AND. INTB.LE.153 .OR.
+     $       INTB.GE.162 .AND. INTB.LE.169 ) INTB = INTB + 64
+*
+      ELSE IF( ZCODE.EQ.218 .OR. ZCODE.EQ.250 ) THEN
+*
+*        ASCII is assumed, on Prime machines - ZCODE is the ASCII code
+*        plus 128 of either lower or upper case 'Z'.
+*
+         IF( INTA.GE.225 .AND. INTA.LE.250 ) INTA = INTA - 32
+         IF( INTB.GE.225 .AND. INTB.LE.250 ) INTB = INTB - 32
+      END IF
+      LSAME = INTA.EQ.INTB
+*
+*     RETURN
+*
+*     End of LSAME
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/testdsterf.f90 b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/testdsterf.f90
new file mode 100644
index 00000000..8373f512
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/testdsterf.f90
@@ -0,0 +1,15 @@
+program testdsterf
+implicit none
+integer, parameter :: n = 4
+real(kind=8), dimension(n) :: d
+real(kind=8), dimension(n-1) :: e
+integer :: info,i
+
+d(1:4) = (/1D+00, 3D+00, 4D+00, 6D+00/)
+e(1:3) = (/2D+00, 4D+00, 5D+00/)
+
+call dsterf(n,d,e,info)
+DO i = 1, n
+    print *, d(i)
+end do
+end
\ No newline at end of file
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/xerbla.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/xerbla.f
new file mode 100644
index 00000000..3e93bc4e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/dsterftest/xerbla.f
@@ -0,0 +1,99 @@
+*> \brief \b XERBLA
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download XERBLA + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/xerbla.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/xerbla.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/xerbla.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE XERBLA( SRNAME, INFO )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER*(*)      SRNAME
+*       INTEGER            INFO
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> XERBLA  is an error handler for the LAPACK routines.
+*> It is called by an LAPACK routine if an input parameter has an
+*> invalid value.  A message is printed and execution stops.
+*>
+*> Installers may consider modifying the STOP statement in order to
+*> call system-specific exception-handling facilities.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] SRNAME
+*> \verbatim
+*>          SRNAME is CHARACTER*(*)
+*>          The name of the routine which called XERBLA.
+*> \endverbatim
+*>
+*> \param[in] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          The position of the invalid parameter in the parameter list
+*>          of the calling routine.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup auxOTHERauxiliary
+*
+*  =====================================================================
+      SUBROUTINE XERBLA( SRNAME, INFO )
+*
+*  -- LAPACK auxiliary routine (version 3.4.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2011
+*
+*     .. Scalar Arguments ..
+      CHARACTER*(*)      SRNAME
+      INTEGER            INFO
+*     ..
+*
+* =====================================================================
+*
+*     .. Intrinsic Functions ..
+      INTRINSIC          LEN_TRIM
+*     ..
+*     .. Executable Statements ..
+*
+      WRITE( *, FMT = 9999 )SRNAME( 1:LEN_TRIM( SRNAME ) ), INFO
+*
+      STOP
+*
+ 9999 FORMAT( ' ** On entry to ', A, ' parameter number ', I2, ' had ',
+     $      'an illegal value' )
+*
+*     End of XERBLA
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/daxpy.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/daxpy.f
new file mode 100644
index 00000000..64a02d68
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/daxpy.f
@@ -0,0 +1,115 @@
+*> \brief \b DAXPY
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DAXPY(N,DA,DX,INCX,DY,INCY)
+* 
+*       .. Scalar Arguments ..
+*       DOUBLE PRECISION DA
+*       INTEGER INCX,INCY,N
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION DX(*),DY(*)
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*>    DAXPY constant times a vector plus a vector.
+*>    uses unrolled loops for increments equal to one.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup double_blas_level1
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>     jack dongarra, linpack, 3/11/78.
+*>     modified 12/3/93, array(1) declarations changed to array(*)
+*> \endverbatim
+*>
+*  =====================================================================
+      SUBROUTINE DAXPY(N,DA,DX,INCX,DY,INCY)
+*
+*  -- Reference BLAS level1 routine (version 3.4.0) --
+*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2011
+*
+*     .. Scalar Arguments ..
+      DOUBLE PRECISION DA
+      INTEGER INCX,INCY,N
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION DX(*),DY(*)
+*     ..
+*
+*  =====================================================================
+*
+*     .. Local Scalars ..
+      INTEGER I,IX,IY,M,MP1
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC MOD
+*     ..
+      IF (N.LE.0) RETURN
+      IF (DA.EQ.0.0d0) RETURN
+      IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN
+*
+*        code for both increments equal to 1
+*
+*
+*        clean-up loop
+*
+         M = MOD(N,4)
+         IF (M.NE.0) THEN
+            DO I = 1,M
+               DY(I) = DY(I) + DA*DX(I)
+            END DO
+         END IF
+         IF (N.LT.4) RETURN
+         MP1 = M + 1
+         DO I = MP1,N,4
+            DY(I) = DY(I) + DA*DX(I)
+            DY(I+1) = DY(I+1) + DA*DX(I+1)
+            DY(I+2) = DY(I+2) + DA*DX(I+2)
+            DY(I+3) = DY(I+3) + DA*DX(I+3)
+         END DO
+      ELSE
+*
+*        code for unequal increments or equal increments
+*          not equal to 1
+*
+         IX = 1
+         IY = 1
+         IF (INCX.LT.0) IX = (-N+1)*INCX + 1
+         IF (INCY.LT.0) IY = (-N+1)*INCY + 1
+         DO I = 1,N
+          DY(IY) = DY(IY) + DA*DX(IX)
+          IX = IX + INCX
+          IY = IY + INCY
+         END DO
+      END IF
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dcopy.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dcopy.f
new file mode 100644
index 00000000..d9d5ac7a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dcopy.f
@@ -0,0 +1,115 @@
+*> \brief \b DCOPY
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DCOPY(N,DX,INCX,DY,INCY)
+* 
+*       .. Scalar Arguments ..
+*       INTEGER INCX,INCY,N
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION DX(*),DY(*)
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*>    DCOPY copies a vector, x, to a vector, y.
+*>    uses unrolled loops for increments equal to one.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup double_blas_level1
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>     jack dongarra, linpack, 3/11/78.
+*>     modified 12/3/93, array(1) declarations changed to array(*)
+*> \endverbatim
+*>
+*  =====================================================================
+      SUBROUTINE DCOPY(N,DX,INCX,DY,INCY)
+*
+*  -- Reference BLAS level1 routine (version 3.4.0) --
+*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2011
+*
+*     .. Scalar Arguments ..
+      INTEGER INCX,INCY,N
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION DX(*),DY(*)
+*     ..
+*
+*  =====================================================================
+*
+*     .. Local Scalars ..
+      INTEGER I,IX,IY,M,MP1
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC MOD
+*     ..
+      IF (N.LE.0) RETURN
+      IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN
+*
+*        code for both increments equal to 1
+*
+*
+*        clean-up loop
+*
+         M = MOD(N,7)
+         IF (M.NE.0) THEN
+            DO I = 1,M
+               DY(I) = DX(I)
+            END DO
+            IF (N.LT.7) RETURN
+         END IF   
+         MP1 = M + 1
+         DO I = MP1,N,7
+            DY(I) = DX(I)
+            DY(I+1) = DX(I+1)
+            DY(I+2) = DX(I+2)
+            DY(I+3) = DX(I+3)
+            DY(I+4) = DX(I+4)
+            DY(I+5) = DX(I+5)
+            DY(I+6) = DX(I+6)
+         END DO
+      ELSE      
+*
+*        code for unequal increments or equal increments
+*          not equal to 1
+*
+         IX = 1
+         IY = 1
+         IF (INCX.LT.0) IX = (-N+1)*INCX + 1
+         IF (INCY.LT.0) IY = (-N+1)*INCY + 1
+         DO I = 1,N
+            DY(IY) = DX(IX)
+            IX = IX + INCX
+            IY = IY + INCY
+         END DO
+      END IF
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dgemm.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dgemm.f
new file mode 100644
index 00000000..4bae243a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dgemm.f
@@ -0,0 +1,384 @@
+*> \brief \b DGEMM
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
+* 
+*       .. Scalar Arguments ..
+*       DOUBLE PRECISION ALPHA,BETA
+*       INTEGER K,LDA,LDB,LDC,M,N
+*       CHARACTER TRANSA,TRANSB
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DGEMM  performs one of the matrix-matrix operations
+*>
+*>    C := alpha*op( A )*op( B ) + beta*C,
+*>
+*> where  op( X ) is one of
+*>
+*>    op( X ) = X   or   op( X ) = X**T,
+*>
+*> alpha and beta are scalars, and A, B and C are matrices, with op( A )
+*> an m by k matrix,  op( B )  a  k by n matrix and  C an m by n matrix.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] TRANSA
+*> \verbatim
+*>          TRANSA is CHARACTER*1
+*>           On entry, TRANSA specifies the form of op( A ) to be used in
+*>           the matrix multiplication as follows:
+*>
+*>              TRANSA = 'N' or 'n',  op( A ) = A.
+*>
+*>              TRANSA = 'T' or 't',  op( A ) = A**T.
+*>
+*>              TRANSA = 'C' or 'c',  op( A ) = A**T.
+*> \endverbatim
+*>
+*> \param[in] TRANSB
+*> \verbatim
+*>          TRANSB is CHARACTER*1
+*>           On entry, TRANSB specifies the form of op( B ) to be used in
+*>           the matrix multiplication as follows:
+*>
+*>              TRANSB = 'N' or 'n',  op( B ) = B.
+*>
+*>              TRANSB = 'T' or 't',  op( B ) = B**T.
+*>
+*>              TRANSB = 'C' or 'c',  op( B ) = B**T.
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*>          M is INTEGER
+*>           On entry,  M  specifies  the number  of rows  of the  matrix
+*>           op( A )  and of the  matrix  C.  M  must  be at least  zero.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>           On entry,  N  specifies the number  of columns of the matrix
+*>           op( B ) and the number of columns of the matrix C. N must be
+*>           at least zero.
+*> \endverbatim
+*>
+*> \param[in] K
+*> \verbatim
+*>          K is INTEGER
+*>           On entry,  K  specifies  the number of columns of the matrix
+*>           op( A ) and the number of rows of the matrix op( B ). K must
+*>           be at least  zero.
+*> \endverbatim
+*>
+*> \param[in] ALPHA
+*> \verbatim
+*>          ALPHA is DOUBLE PRECISION.
+*>           On entry, ALPHA specifies the scalar alpha.
+*> \endverbatim
+*>
+*> \param[in] A
+*> \verbatim
+*>          A is DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
+*>           k  when  TRANSA = 'N' or 'n',  and is  m  otherwise.
+*>           Before entry with  TRANSA = 'N' or 'n',  the leading  m by k
+*>           part of the array  A  must contain the matrix  A,  otherwise
+*>           the leading  k by m  part of the array  A  must contain  the
+*>           matrix A.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>           On entry, LDA specifies the first dimension of A as declared
+*>           in the calling (sub) program. When  TRANSA = 'N' or 'n' then
+*>           LDA must be at least  max( 1, m ), otherwise  LDA must be at
+*>           least  max( 1, k ).
+*> \endverbatim
+*>
+*> \param[in] B
+*> \verbatim
+*>          B is DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is
+*>           n  when  TRANSB = 'N' or 'n',  and is  k  otherwise.
+*>           Before entry with  TRANSB = 'N' or 'n',  the leading  k by n
+*>           part of the array  B  must contain the matrix  B,  otherwise
+*>           the leading  n by k  part of the array  B  must contain  the
+*>           matrix B.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*>          LDB is INTEGER
+*>           On entry, LDB specifies the first dimension of B as declared
+*>           in the calling (sub) program. When  TRANSB = 'N' or 'n' then
+*>           LDB must be at least  max( 1, k ), otherwise  LDB must be at
+*>           least  max( 1, n ).
+*> \endverbatim
+*>
+*> \param[in] BETA
+*> \verbatim
+*>          BETA is DOUBLE PRECISION.
+*>           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
+*>           supplied as zero then C need not be set on input.
+*> \endverbatim
+*>
+*> \param[in,out] C
+*> \verbatim
+*>          C is DOUBLE PRECISION array of DIMENSION ( LDC, n ).
+*>           Before entry, the leading  m by n  part of the array  C must
+*>           contain the matrix  C,  except when  beta  is zero, in which
+*>           case C need not be set on entry.
+*>           On exit, the array  C  is overwritten by the  m by n  matrix
+*>           ( alpha*op( A )*op( B ) + beta*C ).
+*> \endverbatim
+*>
+*> \param[in] LDC
+*> \verbatim
+*>          LDC is INTEGER
+*>           On entry, LDC specifies the first dimension of C as declared
+*>           in  the  calling  (sub)  program.   LDC  must  be  at  least
+*>           max( 1, m ).
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2015
+*
+*> \ingroup double_blas_level3
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  Level 3 Blas routine.
+*>
+*>  -- Written on 8-February-1989.
+*>     Jack Dongarra, Argonne National Laboratory.
+*>     Iain Duff, AERE Harwell.
+*>     Jeremy Du Croz, Numerical Algorithms Group Ltd.
+*>     Sven Hammarling, Numerical Algorithms Group Ltd.
+*> \endverbatim
+*>
+*  =====================================================================
+      SUBROUTINE DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
+*
+*  -- Reference BLAS level3 routine (version 3.6.0) --
+*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2015
+*
+*     .. Scalar Arguments ..
+      DOUBLE PRECISION ALPHA,BETA
+      INTEGER K,LDA,LDB,LDC,M,N
+      CHARACTER TRANSA,TRANSB
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
+*     ..
+*
+*  =====================================================================
+*
+*     .. External Functions ..
+      LOGICAL LSAME
+      EXTERNAL LSAME
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC MAX
+*     ..
+*     .. Local Scalars ..
+      DOUBLE PRECISION TEMP
+      INTEGER I,INFO,J,L,NCOLA,NROWA,NROWB
+      LOGICAL NOTA,NOTB
+*     ..
+*     .. Parameters ..
+      DOUBLE PRECISION ONE,ZERO
+      PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
+*     ..
+*
+*     Set  NOTA  and  NOTB  as  true if  A  and  B  respectively are not
+*     transposed and set  NROWA, NCOLA and  NROWB  as the number of rows
+*     and  columns of  A  and the  number of  rows  of  B  respectively.
+*
+      NOTA = LSAME(TRANSA,'N')
+      NOTB = LSAME(TRANSB,'N')
+      IF (NOTA) THEN
+          NROWA = M
+          NCOLA = K
+      ELSE
+          NROWA = K
+          NCOLA = M
+      END IF
+      IF (NOTB) THEN
+          NROWB = K
+      ELSE
+          NROWB = N
+      END IF
+*
+*     Test the input parameters.
+*
+      INFO = 0
+      IF ((.NOT.NOTA) .AND. (.NOT.LSAME(TRANSA,'C')) .AND.
+     +    (.NOT.LSAME(TRANSA,'T'))) THEN
+          INFO = 1
+      ELSE IF ((.NOT.NOTB) .AND. (.NOT.LSAME(TRANSB,'C')) .AND.
+     +         (.NOT.LSAME(TRANSB,'T'))) THEN
+          INFO = 2
+      ELSE IF (M.LT.0) THEN
+          INFO = 3
+      ELSE IF (N.LT.0) THEN
+          INFO = 4
+      ELSE IF (K.LT.0) THEN
+          INFO = 5
+      ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
+          INFO = 8
+      ELSE IF (LDB.LT.MAX(1,NROWB)) THEN
+          INFO = 10
+      ELSE IF (LDC.LT.MAX(1,M)) THEN
+          INFO = 13
+      END IF
+      IF (INFO.NE.0) THEN
+          CALL XERBLA('DGEMM ',INFO)
+          RETURN
+      END IF
+*
+*     Quick return if possible.
+*
+      IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
+     +    (((ALPHA.EQ.ZERO).OR. (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN
+*
+*     And if  alpha.eq.zero.
+*
+      IF (ALPHA.EQ.ZERO) THEN
+          IF (BETA.EQ.ZERO) THEN
+              DO 20 J = 1,N
+                  DO 10 I = 1,M
+                      C(I,J) = ZERO
+   10             CONTINUE
+   20         CONTINUE
+          ELSE
+              DO 40 J = 1,N
+                  DO 30 I = 1,M
+                      C(I,J) = BETA*C(I,J)
+   30             CONTINUE
+   40         CONTINUE
+          END IF
+          RETURN
+      END IF
+*
+*     Start the operations.
+*
+      IF (NOTB) THEN
+          IF (NOTA) THEN
+*
+*           Form  C := alpha*A*B + beta*C.
+*
+              DO 90 J = 1,N
+                  IF (BETA.EQ.ZERO) THEN
+                      DO 50 I = 1,M
+                          C(I,J) = ZERO
+   50                 CONTINUE
+                  ELSE IF (BETA.NE.ONE) THEN
+                      DO 60 I = 1,M
+                          C(I,J) = BETA*C(I,J)
+   60                 CONTINUE
+                  END IF
+                  DO 80 L = 1,K
+                      TEMP = ALPHA*B(L,J)
+                      DO 70 I = 1,M
+                          C(I,J) = C(I,J) + TEMP*A(I,L)
+   70                 CONTINUE
+   80             CONTINUE
+   90         CONTINUE
+          ELSE
+*
+*           Form  C := alpha*A**T*B + beta*C
+*
+              DO 120 J = 1,N
+                  DO 110 I = 1,M
+                      TEMP = ZERO
+                      DO 100 L = 1,K
+                          TEMP = TEMP + A(L,I)*B(L,J)
+  100                 CONTINUE
+                      IF (BETA.EQ.ZERO) THEN
+                          C(I,J) = ALPHA*TEMP
+                      ELSE
+                          C(I,J) = ALPHA*TEMP + BETA*C(I,J)
+                      END IF
+  110             CONTINUE
+  120         CONTINUE
+          END IF
+      ELSE
+          IF (NOTA) THEN
+*
+*           Form  C := alpha*A*B**T + beta*C
+*
+              DO 170 J = 1,N
+                  IF (BETA.EQ.ZERO) THEN
+                      DO 130 I = 1,M
+                          C(I,J) = ZERO
+  130                 CONTINUE
+                  ELSE IF (BETA.NE.ONE) THEN
+                      DO 140 I = 1,M
+                          C(I,J) = BETA*C(I,J)
+  140                 CONTINUE
+                  END IF
+                  DO 160 L = 1,K
+                      TEMP = ALPHA*B(J,L)
+                      DO 150 I = 1,M
+                          C(I,J) = C(I,J) + TEMP*A(I,L)
+  150                 CONTINUE
+  160             CONTINUE
+  170         CONTINUE
+          ELSE
+*
+*           Form  C := alpha*A**T*B**T + beta*C
+*
+              DO 200 J = 1,N
+                  DO 190 I = 1,M
+                      TEMP = ZERO
+                      DO 180 L = 1,K
+                          TEMP = TEMP + A(L,I)*B(J,L)
+  180                 CONTINUE
+                      IF (BETA.EQ.ZERO) THEN
+                          C(I,J) = ALPHA*TEMP
+                      ELSE
+                          C(I,J) = ALPHA*TEMP + BETA*C(I,J)
+                      END IF
+  190             CONTINUE
+  200         CONTINUE
+          END IF
+      END IF
+*
+      RETURN
+*
+*     End of DGEMM .
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dgemv.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dgemv.f
new file mode 100644
index 00000000..e04cc07c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dgemv.f
@@ -0,0 +1,330 @@
+*> \brief \b DGEMV
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
+* 
+*       .. Scalar Arguments ..
+*       DOUBLE PRECISION ALPHA,BETA
+*       INTEGER INCX,INCY,LDA,M,N
+*       CHARACTER TRANS
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION A(LDA,*),X(*),Y(*)
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DGEMV  performs one of the matrix-vector operations
+*>
+*>    y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,
+*>
+*> where alpha and beta are scalars, x and y are vectors and A is an
+*> m by n matrix.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] TRANS
+*> \verbatim
+*>          TRANS is CHARACTER*1
+*>           On entry, TRANS specifies the operation to be performed as
+*>           follows:
+*>
+*>              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
+*>
+*>              TRANS = 'T' or 't'   y := alpha*A**T*x + beta*y.
+*>
+*>              TRANS = 'C' or 'c'   y := alpha*A**T*x + beta*y.
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*>          M is INTEGER
+*>           On entry, M specifies the number of rows of the matrix A.
+*>           M must be at least zero.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>           On entry, N specifies the number of columns of the matrix A.
+*>           N must be at least zero.
+*> \endverbatim
+*>
+*> \param[in] ALPHA
+*> \verbatim
+*>          ALPHA is DOUBLE PRECISION.
+*>           On entry, ALPHA specifies the scalar alpha.
+*> \endverbatim
+*>
+*> \param[in] A
+*> \verbatim
+*>          A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
+*>           Before entry, the leading m by n part of the array A must
+*>           contain the matrix of coefficients.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>           On entry, LDA specifies the first dimension of A as declared
+*>           in the calling (sub) program. LDA must be at least
+*>           max( 1, m ).
+*> \endverbatim
+*>
+*> \param[in] X
+*> \verbatim
+*>          X is DOUBLE PRECISION array of DIMENSION at least
+*>           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
+*>           and at least
+*>           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
+*>           Before entry, the incremented array X must contain the
+*>           vector x.
+*> \endverbatim
+*>
+*> \param[in] INCX
+*> \verbatim
+*>          INCX is INTEGER
+*>           On entry, INCX specifies the increment for the elements of
+*>           X. INCX must not be zero.
+*> \endverbatim
+*>
+*> \param[in] BETA
+*> \verbatim
+*>          BETA is DOUBLE PRECISION.
+*>           On entry, BETA specifies the scalar beta. When BETA is
+*>           supplied as zero then Y need not be set on input.
+*> \endverbatim
+*>
+*> \param[in,out] Y
+*> \verbatim
+*>          Y is DOUBLE PRECISION array of DIMENSION at least
+*>           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
+*>           and at least
+*>           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
+*>           Before entry with BETA non-zero, the incremented array Y
+*>           must contain the vector y. On exit, Y is overwritten by the
+*>           updated vector y.
+*> \endverbatim
+*>
+*> \param[in] INCY
+*> \verbatim
+*>          INCY is INTEGER
+*>           On entry, INCY specifies the increment for the elements of
+*>           Y. INCY must not be zero.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2015
+*
+*> \ingroup double_blas_level2
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  Level 2 Blas routine.
+*>  The vector and matrix arguments are not referenced when N = 0, or M = 0
+*>
+*>  -- Written on 22-October-1986.
+*>     Jack Dongarra, Argonne National Lab.
+*>     Jeremy Du Croz, Nag Central Office.
+*>     Sven Hammarling, Nag Central Office.
+*>     Richard Hanson, Sandia National Labs.
+*> \endverbatim
+*>
+*  =====================================================================
+      SUBROUTINE DGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
+*
+*  -- Reference BLAS level2 routine (version 3.6.0) --
+*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2015
+*
+*     .. Scalar Arguments ..
+      DOUBLE PRECISION ALPHA,BETA
+      INTEGER INCX,INCY,LDA,M,N
+      CHARACTER TRANS
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION A(LDA,*),X(*),Y(*)
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION ONE,ZERO
+      PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
+*     ..
+*     .. Local Scalars ..
+      DOUBLE PRECISION TEMP
+      INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY,LENX,LENY
+*     ..
+*     .. External Functions ..
+      LOGICAL LSAME
+      EXTERNAL LSAME
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC MAX
+*     ..
+*
+*     Test the input parameters.
+*
+      INFO = 0
+      IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
+     +    .NOT.LSAME(TRANS,'C')) THEN
+          INFO = 1
+      ELSE IF (M.LT.0) THEN
+          INFO = 2
+      ELSE IF (N.LT.0) THEN
+          INFO = 3
+      ELSE IF (LDA.LT.MAX(1,M)) THEN
+          INFO = 6
+      ELSE IF (INCX.EQ.0) THEN
+          INFO = 8
+      ELSE IF (INCY.EQ.0) THEN
+          INFO = 11
+      END IF
+      IF (INFO.NE.0) THEN
+          CALL XERBLA('DGEMV ',INFO)
+          RETURN
+      END IF
+*
+*     Quick return if possible.
+*
+      IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
+     +    ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
+*
+*     Set  LENX  and  LENY, the lengths of the vectors x and y, and set
+*     up the start points in  X  and  Y.
+*
+      IF (LSAME(TRANS,'N')) THEN
+          LENX = N
+          LENY = M
+      ELSE
+          LENX = M
+          LENY = N
+      END IF
+      IF (INCX.GT.0) THEN
+          KX = 1
+      ELSE
+          KX = 1 - (LENX-1)*INCX
+      END IF
+      IF (INCY.GT.0) THEN
+          KY = 1
+      ELSE
+          KY = 1 - (LENY-1)*INCY
+      END IF
+*
+*     Start the operations. In this version the elements of A are
+*     accessed sequentially with one pass through A.
+*
+*     First form  y := beta*y.
+*
+      IF (BETA.NE.ONE) THEN
+          IF (INCY.EQ.1) THEN
+              IF (BETA.EQ.ZERO) THEN
+                  DO 10 I = 1,LENY
+                      Y(I) = ZERO
+   10             CONTINUE
+              ELSE
+                  DO 20 I = 1,LENY
+                      Y(I) = BETA*Y(I)
+   20             CONTINUE
+              END IF
+          ELSE
+              IY = KY
+              IF (BETA.EQ.ZERO) THEN
+                  DO 30 I = 1,LENY
+                      Y(IY) = ZERO
+                      IY = IY + INCY
+   30             CONTINUE
+              ELSE
+                  DO 40 I = 1,LENY
+                      Y(IY) = BETA*Y(IY)
+                      IY = IY + INCY
+   40             CONTINUE
+              END IF
+          END IF
+      END IF
+      IF (ALPHA.EQ.ZERO) RETURN
+      IF (LSAME(TRANS,'N')) THEN
+*
+*        Form  y := alpha*A*x + y.
+*
+          JX = KX
+          IF (INCY.EQ.1) THEN
+              DO 60 J = 1,N
+                  TEMP = ALPHA*X(JX)
+                  DO 50 I = 1,M
+                      Y(I) = Y(I) + TEMP*A(I,J)
+   50             CONTINUE
+                  JX = JX + INCX
+   60         CONTINUE
+          ELSE
+              DO 80 J = 1,N
+                  TEMP = ALPHA*X(JX)
+                  IY = KY
+                  DO 70 I = 1,M
+                      Y(IY) = Y(IY) + TEMP*A(I,J)
+                      IY = IY + INCY
+   70             CONTINUE
+                  JX = JX + INCX
+   80         CONTINUE
+          END IF
+      ELSE
+*
+*        Form  y := alpha*A**T*x + y.
+*
+          JY = KY
+          IF (INCX.EQ.1) THEN
+              DO 100 J = 1,N
+                  TEMP = ZERO
+                  DO 90 I = 1,M
+                      TEMP = TEMP + A(I,J)*X(I)
+   90             CONTINUE
+                  Y(JY) = Y(JY) + ALPHA*TEMP
+                  JY = JY + INCY
+  100         CONTINUE
+          ELSE
+              DO 120 J = 1,N
+                  TEMP = ZERO
+                  IX = KX
+                  DO 110 I = 1,M
+                      TEMP = TEMP + A(I,J)*X(IX)
+                      IX = IX + INCX
+  110             CONTINUE
+                  Y(JY) = Y(JY) + ALPHA*TEMP
+                  JY = JY + INCY
+  120         CONTINUE
+          END IF
+      END IF
+*
+      RETURN
+*
+*     End of DGEMV .
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dlabad.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dlabad.f
new file mode 100644
index 00000000..da412633
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dlabad.f
@@ -0,0 +1,105 @@
+*> \brief \b DLABAD
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLABAD + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlabad.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlabad.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlabad.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DLABAD( SMALL, LARGE )
+* 
+*       .. Scalar Arguments ..
+*       DOUBLE PRECISION   LARGE, SMALL
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DLABAD takes as input the values computed by DLAMCH for underflow and
+*> overflow, and returns the square root of each of these values if the
+*> log of LARGE is sufficiently large.  This subroutine is intended to
+*> identify machines with a large exponent range, such as the Crays, and
+*> redefine the underflow and overflow limits to be the square roots of
+*> the values computed by DLAMCH.  This subroutine is needed because
+*> DLAMCH does not compensate for poor arithmetic in the upper half of
+*> the exponent range, as is found on a Cray.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in,out] SMALL
+*> \verbatim
+*>          SMALL is DOUBLE PRECISION
+*>          On entry, the underflow threshold as computed by DLAMCH.
+*>          On exit, if LOG10(LARGE) is sufficiently large, the square
+*>          root of SMALL, otherwise unchanged.
+*> \endverbatim
+*>
+*> \param[in,out] LARGE
+*> \verbatim
+*>          LARGE is DOUBLE PRECISION
+*>          On entry, the overflow threshold as computed by DLAMCH.
+*>          On exit, if LOG10(LARGE) is sufficiently large, the square
+*>          root of LARGE, otherwise unchanged.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup auxOTHERauxiliary
+*
+*  =====================================================================
+      SUBROUTINE DLABAD( SMALL, LARGE )
+*
+*  -- LAPACK auxiliary routine (version 3.4.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2011
+*
+*     .. Scalar Arguments ..
+      DOUBLE PRECISION   LARGE, SMALL
+*     ..
+*
+*  =====================================================================
+*
+*     .. Intrinsic Functions ..
+      INTRINSIC          LOG10, SQRT
+*     ..
+*     .. Executable Statements ..
+*
+*     If it looks like we're on a Cray, take the square root of
+*     SMALL and LARGE to avoid overflow and underflow problems.
+*
+*     IF( LOG10( LARGE ).GT.2000.D0 ) THEN
+*        SMALL = SQRT( SMALL )
+*        LARGE = SQRT( LARGE )
+*     END IF
+*
+      RETURN
+*
+*     End of DLABAD
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dlacpy.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dlacpy.f
new file mode 100644
index 00000000..a9a23c94
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dlacpy.f
@@ -0,0 +1,156 @@
+*> \brief \b DLACPY copies all or part of one two-dimensional array to another.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLACPY + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlacpy.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlacpy.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlacpy.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DLACPY( UPLO, M, N, A, LDA, B, LDB )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            LDA, LDB, M, N
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DLACPY copies all or part of a two-dimensional matrix A to another
+*> matrix B.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          Specifies the part of the matrix A to be copied to B.
+*>          = 'U':      Upper triangular part
+*>          = 'L':      Lower triangular part
+*>          Otherwise:  All of the matrix A
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*>          M is INTEGER
+*>          The number of rows of the matrix A.  M >= 0.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The number of columns of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in] A
+*> \verbatim
+*>          A is DOUBLE PRECISION array, dimension (LDA,N)
+*>          The m by n matrix A.  If UPLO = 'U', only the upper triangle
+*>          or trapezoid is accessed; if UPLO = 'L', only the lower
+*>          triangle or trapezoid is accessed.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,M).
+*> \endverbatim
+*>
+*> \param[out] B
+*> \verbatim
+*>          B is DOUBLE PRECISION array, dimension (LDB,N)
+*>          On exit, B = A in the locations specified by UPLO.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*>          LDB is INTEGER
+*>          The leading dimension of the array B.  LDB >= max(1,M).
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date September 2012
+*
+*> \ingroup auxOTHERauxiliary
+*
+*  =====================================================================
+      SUBROUTINE DLACPY( UPLO, M, N, A, LDA, B, LDB )
+*
+*  -- LAPACK auxiliary routine (version 3.4.2) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     September 2012
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            LDA, LDB, M, N
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Local Scalars ..
+      INTEGER            I, J
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      EXTERNAL           LSAME
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MIN
+*     ..
+*     .. Executable Statements ..
+*
+      IF( LSAME( UPLO, 'U' ) ) THEN
+         DO 20 J = 1, N
+            DO 10 I = 1, MIN( J, M )
+               B( I, J ) = A( I, J )
+   10       CONTINUE
+   20    CONTINUE
+      ELSE IF( LSAME( UPLO, 'L' ) ) THEN
+         DO 40 J = 1, N
+            DO 30 I = J, M
+               B( I, J ) = A( I, J )
+   30       CONTINUE
+   40    CONTINUE
+      ELSE
+         DO 60 J = 1, N
+            DO 50 I = 1, M
+               B( I, J ) = A( I, J )
+   50       CONTINUE
+   60    CONTINUE
+      END IF
+      RETURN
+*
+*     End of DLACPY
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dlahr2.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dlahr2.f
new file mode 100644
index 00000000..9d15979c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dlahr2.f
@@ -0,0 +1,326 @@
+*> \brief \b DLAHR2 reduces the specified number of first columns of a general rectangular matrix A so that elements below the specified subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformation to the unreduced part of A.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLAHR2 + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlahr2.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlahr2.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlahr2.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DLAHR2( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            K, LDA, LDT, LDY, N, NB
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION  A( LDA, * ), T( LDT, NB ), TAU( NB ),
+*      $                   Y( LDY, NB )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DLAHR2 reduces the first NB columns of A real general n-BY-(n-k+1)
+*> matrix A so that elements below the k-th subdiagonal are zero. The
+*> reduction is performed by an orthogonal similarity transformation
+*> Q**T * A * Q. The routine returns the matrices V and T which determine
+*> Q as a block reflector I - V*T*V**T, and also the matrix Y = A * V * T.
+*>
+*> This is an auxiliary routine called by DGEHRD.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.
+*> \endverbatim
+*>
+*> \param[in] K
+*> \verbatim
+*>          K is INTEGER
+*>          The offset for the reduction. Elements below the k-th
+*>          subdiagonal in the first NB columns are reduced to zero.
+*>          K < N.
+*> \endverbatim
+*>
+*> \param[in] NB
+*> \verbatim
+*>          NB is INTEGER
+*>          The number of columns to be reduced.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          A is DOUBLE PRECISION array, dimension (LDA,N-K+1)
+*>          On entry, the n-by-(n-k+1) general matrix A.
+*>          On exit, the elements on and above the k-th subdiagonal in
+*>          the first NB columns are overwritten with the corresponding
+*>          elements of the reduced matrix; the elements below the k-th
+*>          subdiagonal, with the array TAU, represent the matrix Q as a
+*>          product of elementary reflectors. The other columns of A are
+*>          unchanged. See Further Details.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] TAU
+*> \verbatim
+*>          TAU is DOUBLE PRECISION array, dimension (NB)
+*>          The scalar factors of the elementary reflectors. See Further
+*>          Details.
+*> \endverbatim
+*>
+*> \param[out] T
+*> \verbatim
+*>          T is DOUBLE PRECISION array, dimension (LDT,NB)
+*>          The upper triangular matrix T.
+*> \endverbatim
+*>
+*> \param[in] LDT
+*> \verbatim
+*>          LDT is INTEGER
+*>          The leading dimension of the array T.  LDT >= NB.
+*> \endverbatim
+*>
+*> \param[out] Y
+*> \verbatim
+*>          Y is DOUBLE PRECISION array, dimension (LDY,NB)
+*>          The n-by-nb matrix Y.
+*> \endverbatim
+*>
+*> \param[in] LDY
+*> \verbatim
+*>          LDY is INTEGER
+*>          The leading dimension of the array Y. LDY >= N.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date September 2012
+*
+*> \ingroup doubleOTHERauxiliary
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  The matrix Q is represented as a product of nb elementary reflectors
+*>
+*>     Q = H(1) H(2) . . . H(nb).
+*>
+*>  Each H(i) has the form
+*>
+*>     H(i) = I - tau * v * v**T
+*>
+*>  where tau is a real scalar, and v is a real vector with
+*>  v(1:i+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in
+*>  A(i+k+1:n,i), and tau in TAU(i).
+*>
+*>  The elements of the vectors v together form the (n-k+1)-by-nb matrix
+*>  V which is needed, with T and Y, to apply the transformation to the
+*>  unreduced part of the matrix, using an update of the form:
+*>  A := (I - V*T*V**T) * (A - Y*V**T).
+*>
+*>  The contents of A on exit are illustrated by the following example
+*>  with n = 7, k = 3 and nb = 2:
+*>
+*>     ( a   a   a   a   a )
+*>     ( a   a   a   a   a )
+*>     ( a   a   a   a   a )
+*>     ( h   h   a   a   a )
+*>     ( v1  h   a   a   a )
+*>     ( v1  v2  a   a   a )
+*>     ( v1  v2  a   a   a )
+*>
+*>  where a denotes an element of the original matrix A, h denotes a
+*>  modified element of the upper Hessenberg matrix H, and vi denotes an
+*>  element of the vector defining H(i).
+*>
+*>  This subroutine is a slight modification of LAPACK-3.0's DLAHRD
+*>  incorporating improvements proposed by Quintana-Orti and Van de
+*>  Gejin. Note that the entries of A(1:K,2:NB) differ from those
+*>  returned by the original LAPACK-3.0's DLAHRD routine. (This
+*>  subroutine is not backward compatible with LAPACK-3.0's DLAHRD.)
+*> \endverbatim
+*
+*> \par References:
+*  ================
+*>
+*>  Gregorio Quintana-Orti and Robert van de Geijn, "Improving the
+*>  performance of reduction to Hessenberg form," ACM Transactions on
+*>  Mathematical Software, 32(2):180-194, June 2006.
+*>
+*  =====================================================================
+      SUBROUTINE DLAHR2( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY )
+*
+*  -- LAPACK auxiliary routine (version 3.4.2) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     September 2012
+*
+*     .. Scalar Arguments ..
+      INTEGER            K, LDA, LDT, LDY, N, NB
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION  A( LDA, * ), T( LDT, NB ), TAU( NB ),
+     $                   Y( LDY, NB )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION  ZERO, ONE
+      PARAMETER          ( ZERO = 0.0D+0, 
+     $                     ONE = 1.0D+0 )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            I
+      DOUBLE PRECISION  EI
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           DAXPY, DCOPY, DGEMM, DGEMV, DLACPY,
+     $                   DLARFG, DSCAL, DTRMM, DTRMV
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MIN
+*     ..
+*     .. Executable Statements ..
+*
+*     Quick return if possible
+*
+      IF( N.LE.1 )
+     $   RETURN
+*
+      DO 10 I = 1, NB
+         IF( I.GT.1 ) THEN
+*
+*           Update A(K+1:N,I)
+*
+*           Update I-th column of A - Y * V**T
+*
+            CALL DGEMV( 'NO TRANSPOSE', N-K, I-1, -ONE, Y(K+1,1), LDY,
+     $                  A( K+I-1, 1 ), LDA, ONE, A( K+1, I ), 1 )
+*
+*           Apply I - V * T**T * V**T to this column (call it b) from the
+*           left, using the last column of T as workspace
+*
+*           Let  V = ( V1 )   and   b = ( b1 )   (first I-1 rows)
+*                    ( V2 )             ( b2 )
+*
+*           where V1 is unit lower triangular
+*
+*           w := V1**T * b1
+*
+            CALL DCOPY( I-1, A( K+1, I ), 1, T( 1, NB ), 1 )
+            CALL DTRMV( 'Lower', 'Transpose', 'UNIT', 
+     $                  I-1, A( K+1, 1 ),
+     $                  LDA, T( 1, NB ), 1 )
+*
+*           w := w + V2**T * b2
+*
+            CALL DGEMV( 'Transpose', N-K-I+1, I-1, 
+     $                  ONE, A( K+I, 1 ),
+     $                  LDA, A( K+I, I ), 1, ONE, T( 1, NB ), 1 )
+*
+*           w := T**T * w
+*
+            CALL DTRMV( 'Upper', 'Transpose', 'NON-UNIT', 
+     $                  I-1, T, LDT,
+     $                  T( 1, NB ), 1 )
+*
+*           b2 := b2 - V2*w
+*
+            CALL DGEMV( 'NO TRANSPOSE', N-K-I+1, I-1, -ONE, 
+     $                  A( K+I, 1 ),
+     $                  LDA, T( 1, NB ), 1, ONE, A( K+I, I ), 1 )
+*
+*           b1 := b1 - V1*w
+*
+            CALL DTRMV( 'Lower', 'NO TRANSPOSE', 
+     $                  'UNIT', I-1,
+     $                  A( K+1, 1 ), LDA, T( 1, NB ), 1 )
+            CALL DAXPY( I-1, -ONE, T( 1, NB ), 1, A( K+1, I ), 1 )
+*
+            A( K+I-1, I-1 ) = EI
+         END IF
+*
+*        Generate the elementary reflector H(I) to annihilate
+*        A(K+I+1:N,I)
+*
+         CALL DLARFG( N-K-I+1, A( K+I, I ), A( MIN( K+I+1, N ), I ), 1,
+     $                TAU( I ) )
+         EI = A( K+I, I )
+         A( K+I, I ) = ONE
+*
+*        Compute  Y(K+1:N,I)
+*
+         CALL DGEMV( 'NO TRANSPOSE', N-K, N-K-I+1, 
+     $               ONE, A( K+1, I+1 ),
+     $               LDA, A( K+I, I ), 1, ZERO, Y( K+1, I ), 1 )
+         CALL DGEMV( 'Transpose', N-K-I+1, I-1, 
+     $               ONE, A( K+I, 1 ), LDA,
+     $               A( K+I, I ), 1, ZERO, T( 1, I ), 1 )
+         CALL DGEMV( 'NO TRANSPOSE', N-K, I-1, -ONE, 
+     $               Y( K+1, 1 ), LDY,
+     $               T( 1, I ), 1, ONE, Y( K+1, I ), 1 )
+         CALL DSCAL( N-K, TAU( I ), Y( K+1, I ), 1 )
+*
+*        Compute T(1:I,I)
+*
+         CALL DSCAL( I-1, -TAU( I ), T( 1, I ), 1 )
+         CALL DTRMV( 'Upper', 'No Transpose', 'NON-UNIT', 
+     $               I-1, T, LDT,
+     $               T( 1, I ), 1 )
+         T( I, I ) = TAU( I )
+*
+   10 CONTINUE
+      A( K+NB, NB ) = EI
+*
+*     Compute Y(1:K,1:NB)
+*
+      CALL DLACPY( 'ALL', K, NB, A( 1, 2 ), LDA, Y, LDY )
+      CALL DTRMM( 'RIGHT', 'Lower', 'NO TRANSPOSE', 
+     $            'UNIT', K, NB,
+     $            ONE, A( K+1, 1 ), LDA, Y, LDY )
+      IF( N.GT.K+NB )
+     $   CALL DGEMM( 'NO TRANSPOSE', 'NO TRANSPOSE', K, 
+     $               NB, N-K-NB, ONE,
+     $               A( 1, 2+NB ), LDA, A( K+1+NB, 1 ), LDA, ONE, Y,
+     $               LDY )
+      CALL DTRMM( 'RIGHT', 'Upper', 'NO TRANSPOSE', 
+     $            'NON-UNIT', K, NB,
+     $            ONE, T, LDT, Y, LDY )
+*
+      RETURN
+*
+*     End of DLAHR2
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dlamch.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dlamch.f
new file mode 100644
index 00000000..22a16218
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dlamch.f
@@ -0,0 +1,189 @@
+*> \brief \b DLAMCH
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*  Definition:
+*  ===========
+*
+*      DOUBLE PRECISION FUNCTION DLAMCH( CMACH )
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DLAMCH determines double precision machine parameters.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] CMACH
+*> \verbatim
+*>          Specifies the value to be returned by DLAMCH:
+*>          = 'E' or 'e',   DLAMCH := eps
+*>          = 'S' or 's ,   DLAMCH := sfmin
+*>          = 'B' or 'b',   DLAMCH := base
+*>          = 'P' or 'p',   DLAMCH := eps*base
+*>          = 'N' or 'n',   DLAMCH := t
+*>          = 'R' or 'r',   DLAMCH := rnd
+*>          = 'M' or 'm',   DLAMCH := emin
+*>          = 'U' or 'u',   DLAMCH := rmin
+*>          = 'L' or 'l',   DLAMCH := emax
+*>          = 'O' or 'o',   DLAMCH := rmax
+*>          where
+*>          eps   = relative machine precision
+*>          sfmin = safe minimum, such that 1/sfmin does not overflow
+*>          base  = base of the machine
+*>          prec  = eps*base
+*>          t     = number of (base) digits in the mantissa
+*>          rnd   = 1.0 when rounding occurs in addition, 0.0 otherwise
+*>          emin  = minimum exponent before (gradual) underflow
+*>          rmin  = underflow threshold - base**(emin-1)
+*>          emax  = largest exponent before overflow
+*>          rmax  = overflow threshold  - (base**emax)*(1-eps)
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2015
+*
+*> \ingroup auxOTHERauxiliary
+*
+*  =====================================================================
+      DOUBLE PRECISION FUNCTION DLAMCH( CMACH )
+*
+*  -- LAPACK auxiliary routine (version 3.6.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2015
+*
+*     .. Scalar Arguments ..
+      CHARACTER          CMACH
+*     ..
+*
+* =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ONE, ZERO
+      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
+*     ..
+*     .. Local Scalars ..
+      DOUBLE PRECISION   RND, EPS, SFMIN, SMALL, RMACH
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      EXTERNAL           LSAME
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          DIGITS, EPSILON, HUGE, MAXEXPONENT,
+     $                   MINEXPONENT, RADIX, TINY
+*     ..
+*     .. Executable Statements ..
+*
+*
+*     Assume rounding, not chopping. Always.
+*
+      RND = ONE
+*
+      IF( ONE.EQ.RND ) THEN
+         EPS = EPSILON(ZERO) * 0.5
+      ELSE
+         EPS = EPSILON(ZERO)
+      END IF
+*
+      IF( LSAME( CMACH, 'E' ) ) THEN
+         RMACH = EPS
+      ELSE IF( LSAME( CMACH, 'S' ) ) THEN
+         SFMIN = TINY(ZERO)
+         SMALL = ONE / HUGE(ZERO)
+         IF( SMALL.GE.SFMIN ) THEN
+*
+*           Use SMALL plus a bit, to avoid the possibility of rounding
+*           causing overflow when computing  1/sfmin.
+*
+            SFMIN = SMALL*( ONE+EPS )
+         END IF
+         RMACH = SFMIN
+      ELSE IF( LSAME( CMACH, 'B' ) ) THEN
+         RMACH = RADIX(ZERO)
+      ELSE IF( LSAME( CMACH, 'P' ) ) THEN
+         RMACH = EPS * RADIX(ZERO)
+      ELSE IF( LSAME( CMACH, 'N' ) ) THEN
+         RMACH = DIGITS(ZERO)
+      ELSE IF( LSAME( CMACH, 'R' ) ) THEN
+         RMACH = RND
+      ELSE IF( LSAME( CMACH, 'M' ) ) THEN
+         RMACH = MINEXPONENT(ZERO)
+      ELSE IF( LSAME( CMACH, 'U' ) ) THEN
+         RMACH = tiny(zero)
+      ELSE IF( LSAME( CMACH, 'L' ) ) THEN
+         RMACH = MAXEXPONENT(ZERO)
+      ELSE IF( LSAME( CMACH, 'O' ) ) THEN
+         RMACH = HUGE(ZERO)
+      ELSE
+         RMACH = ZERO
+      END IF
+*
+      DLAMCH = RMACH
+      RETURN
+*
+*     End of DLAMCH
+*
+      END
+************************************************************************
+*> \brief \b DLAMC3
+*> \details
+*> \b Purpose:
+*> \verbatim
+*> DLAMC3  is intended to force  A  and  B  to be stored prior to doing
+*> the addition of  A  and  B ,  for use in situations where optimizers
+*> might hold one of these in a register.
+*> \endverbatim
+*> \author LAPACK is a software package provided by Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..
+*> \date November 2015
+*> \ingroup auxOTHERauxiliary
+*>
+*> \param[in] A
+*> \verbatim
+*>          A is a DOUBLE PRECISION
+*> \endverbatim
+*>
+*> \param[in] B
+*> \verbatim
+*>          B is a DOUBLE PRECISION
+*>          The values A and B.
+*> \endverbatim
+*>
+      DOUBLE PRECISION FUNCTION DLAMC3( A, B )
+*
+*  -- LAPACK auxiliary routine (version 3.6.0) --
+*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+*     November 2010
+*
+*     .. Scalar Arguments ..
+      DOUBLE PRECISION   A, B
+*     ..
+* =====================================================================
+*
+*     .. Executable Statements ..
+*
+      DLAMC3 = A + B
+*
+      RETURN
+*
+*     End of DLAMC3
+*
+      END
+*
+************************************************************************
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dlapy2.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dlapy2.f
new file mode 100644
index 00000000..d43b0d5d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dlapy2.f
@@ -0,0 +1,104 @@
+*> \brief \b DLAPY2 returns sqrt(x2+y2).
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLAPY2 + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlapy2.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlapy2.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlapy2.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       DOUBLE PRECISION FUNCTION DLAPY2( X, Y )
+* 
+*       .. Scalar Arguments ..
+*       DOUBLE PRECISION   X, Y
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DLAPY2 returns sqrt(x**2+y**2), taking care not to cause unnecessary
+*> overflow.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] X
+*> \verbatim
+*>          X is DOUBLE PRECISION
+*> \endverbatim
+*>
+*> \param[in] Y
+*> \verbatim
+*>          Y is DOUBLE PRECISION
+*>          X and Y specify the values x and y.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date September 2012
+*
+*> \ingroup auxOTHERauxiliary
+*
+*  =====================================================================
+      DOUBLE PRECISION FUNCTION DLAPY2( X, Y )
+*
+*  -- LAPACK auxiliary routine (version 3.4.2) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     September 2012
+*
+*     .. Scalar Arguments ..
+      DOUBLE PRECISION   X, Y
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ZERO
+      PARAMETER          ( ZERO = 0.0D0 )
+      DOUBLE PRECISION   ONE
+      PARAMETER          ( ONE = 1.0D0 )
+*     ..
+*     .. Local Scalars ..
+      DOUBLE PRECISION   W, XABS, YABS, Z
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS, MAX, MIN, SQRT
+*     ..
+*     .. Executable Statements ..
+*
+      XABS = ABS( X )
+      YABS = ABS( Y )
+      W = MAX( XABS, YABS )
+      Z = MIN( XABS, YABS )
+      IF( Z.EQ.ZERO ) THEN
+         DLAPY2 = W
+      ELSE
+         DLAPY2 = W*SQRT( ONE+( Z / W )**2 )
+      END IF
+      RETURN
+*
+*     End of DLAPY2
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dlaqr1.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dlaqr1.f
new file mode 100644
index 00000000..df4fb68b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dlaqr1.f
@@ -0,0 +1,179 @@
+*> \brief \b DLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLAQR1 + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqr1.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqr1.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqr1.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DLAQR1( N, H, LDH, SR1, SI1, SR2, SI2, V )
+* 
+*       .. Scalar Arguments ..
+*       DOUBLE PRECISION   SI1, SI2, SR1, SR2
+*       INTEGER            LDH, N
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   H( LDH, * ), V( * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*>      Given a 2-by-2 or 3-by-3 matrix H, DLAQR1 sets v to a
+*>      scalar multiple of the first column of the product
+*>
+*>      (*)  K = (H - (sr1 + i*si1)*I)*(H - (sr2 + i*si2)*I)
+*>
+*>      scaling to avoid overflows and most underflows. It
+*>      is assumed that either
+*>
+*>              1) sr1 = sr2 and si1 = -si2
+*>          or
+*>              2) si1 = si2 = 0.
+*>
+*>      This is useful for starting double implicit shift bulges
+*>      in the QR algorithm.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] N
+*> \verbatim
+*>          N is integer
+*>              Order of the matrix H. N must be either 2 or 3.
+*> \endverbatim
+*>
+*> \param[in] H
+*> \verbatim
+*>          H is DOUBLE PRECISION array of dimension (LDH,N)
+*>              The 2-by-2 or 3-by-3 matrix H in (*).
+*> \endverbatim
+*>
+*> \param[in] LDH
+*> \verbatim
+*>          LDH is integer
+*>              The leading dimension of H as declared in
+*>              the calling procedure.  LDH.GE.N
+*> \endverbatim
+*>
+*> \param[in] SR1
+*> \verbatim
+*>          SR1 is DOUBLE PRECISION
+*> \endverbatim
+*>
+*> \param[in] SI1
+*> \verbatim
+*>          SI1 is DOUBLE PRECISION
+*> \endverbatim
+*>
+*> \param[in] SR2
+*> \verbatim
+*>          SR2 is DOUBLE PRECISION
+*> \endverbatim
+*>
+*> \param[in] SI2
+*> \verbatim
+*>          SI2 is DOUBLE PRECISION
+*>              The shifts in (*).
+*> \endverbatim
+*>
+*> \param[out] V
+*> \verbatim
+*>          V is DOUBLE PRECISION array of dimension N
+*>              A scalar multiple of the first column of the
+*>              matrix K in (*).
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date September 2012
+*
+*> \ingroup doubleOTHERauxiliary
+*
+*> \par Contributors:
+*  ==================
+*>
+*>       Karen Braman and Ralph Byers, Department of Mathematics,
+*>       University of Kansas, USA
+*>
+*  =====================================================================
+      SUBROUTINE DLAQR1( N, H, LDH, SR1, SI1, SR2, SI2, V )
+*
+*  -- LAPACK auxiliary routine (version 3.4.2) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     September 2012
+*
+*     .. Scalar Arguments ..
+      DOUBLE PRECISION   SI1, SI2, SR1, SR2
+      INTEGER            LDH, N
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   H( LDH, * ), V( * )
+*     ..
+*
+*  ================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ZERO
+      PARAMETER          ( ZERO = 0.0d0 )
+*     ..
+*     .. Local Scalars ..
+      DOUBLE PRECISION   H21S, H31S, S
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS
+*     ..
+*     .. Executable Statements ..
+      IF( N.EQ.2 ) THEN
+         S = ABS( H( 1, 1 )-SR2 ) + ABS( SI2 ) + ABS( H( 2, 1 ) )
+         IF( S.EQ.ZERO ) THEN
+            V( 1 ) = ZERO
+            V( 2 ) = ZERO
+         ELSE
+            H21S = H( 2, 1 ) / S
+            V( 1 ) = H21S*H( 1, 2 ) + ( H( 1, 1 )-SR1 )*
+     $               ( ( H( 1, 1 )-SR2 ) / S ) - SI1*( SI2 / S )
+            V( 2 ) = H21S*( H( 1, 1 )+H( 2, 2 )-SR1-SR2 )
+         END IF
+      ELSE
+         S = ABS( H( 1, 1 )-SR2 ) + ABS( SI2 ) + ABS( H( 2, 1 ) ) +
+     $       ABS( H( 3, 1 ) )
+         IF( S.EQ.ZERO ) THEN
+            V( 1 ) = ZERO
+            V( 2 ) = ZERO
+            V( 3 ) = ZERO
+         ELSE
+            H21S = H( 2, 1 ) / S
+            H31S = H( 3, 1 ) / S
+            V( 1 ) = ( H( 1, 1 )-SR1 )*( ( H( 1, 1 )-SR2 ) / S ) -
+     $               SI1*( SI2 / S ) + H( 1, 2 )*H21S + H( 1, 3 )*H31S
+            V( 2 ) = H21S*( H( 1, 1 )+H( 2, 2 )-SR1-SR2 ) +
+     $               H( 2, 3 )*H31S
+            V( 3 ) = H31S*( H( 1, 1 )+H( 3, 3 )-SR1-SR2 ) +
+     $               H21S*H( 3, 2 )
+         END IF
+      END IF
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dlaqr5.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dlaqr5.f
new file mode 100644
index 00000000..37ce6f6b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dlaqr5.f
@@ -0,0 +1,921 @@
+*> \brief \b DLAQR5 performs a single small-bulge multi-shift QR sweep.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLAQR5 + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqr5.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqr5.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqr5.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS,
+*                          SR, SI, H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U,
+*                          LDU, NV, WV, LDWV, NH, WH, LDWH )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            IHIZ, ILOZ, KACC22, KBOT, KTOP, LDH, LDU, LDV,
+*      $                   LDWH, LDWV, LDZ, N, NH, NSHFTS, NV
+*       LOGICAL            WANTT, WANTZ
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   H( LDH, * ), SI( * ), SR( * ), U( LDU, * ),
+*      $                   V( LDV, * ), WH( LDWH, * ), WV( LDWV, * ),
+*      $                   Z( LDZ, * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*>    DLAQR5, called by DLAQR0, performs a
+*>    single small-bulge multi-shift QR sweep.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] WANTT
+*> \verbatim
+*>          WANTT is logical scalar
+*>             WANTT = .true. if the quasi-triangular Schur factor
+*>             is being computed.  WANTT is set to .false. otherwise.
+*> \endverbatim
+*>
+*> \param[in] WANTZ
+*> \verbatim
+*>          WANTZ is logical scalar
+*>             WANTZ = .true. if the orthogonal Schur factor is being
+*>             computed.  WANTZ is set to .false. otherwise.
+*> \endverbatim
+*>
+*> \param[in] KACC22
+*> \verbatim
+*>          KACC22 is integer with value 0, 1, or 2.
+*>             Specifies the computation mode of far-from-diagonal
+*>             orthogonal updates.
+*>        = 0: DLAQR5 does not accumulate reflections and does not
+*>             use matrix-matrix multiply to update far-from-diagonal
+*>             matrix entries.
+*>        = 1: DLAQR5 accumulates reflections and uses matrix-matrix
+*>             multiply to update the far-from-diagonal matrix entries.
+*>        = 2: DLAQR5 accumulates reflections, uses matrix-matrix
+*>             multiply to update the far-from-diagonal matrix entries,
+*>             and takes advantage of 2-by-2 block structure during
+*>             matrix multiplies.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is integer scalar
+*>             N is the order of the Hessenberg matrix H upon which this
+*>             subroutine operates.
+*> \endverbatim
+*>
+*> \param[in] KTOP
+*> \verbatim
+*>          KTOP is integer scalar
+*> \endverbatim
+*>
+*> \param[in] KBOT
+*> \verbatim
+*>          KBOT is integer scalar
+*>             These are the first and last rows and columns of an
+*>             isolated diagonal block upon which the QR sweep is to be
+*>             applied. It is assumed without a check that
+*>                       either KTOP = 1  or   H(KTOP,KTOP-1) = 0
+*>             and
+*>                       either KBOT = N  or   H(KBOT+1,KBOT) = 0.
+*> \endverbatim
+*>
+*> \param[in] NSHFTS
+*> \verbatim
+*>          NSHFTS is integer scalar
+*>             NSHFTS gives the number of simultaneous shifts.  NSHFTS
+*>             must be positive and even.
+*> \endverbatim
+*>
+*> \param[in,out] SR
+*> \verbatim
+*>          SR is DOUBLE PRECISION array of size (NSHFTS)
+*> \endverbatim
+*>
+*> \param[in,out] SI
+*> \verbatim
+*>          SI is DOUBLE PRECISION array of size (NSHFTS)
+*>             SR contains the real parts and SI contains the imaginary
+*>             parts of the NSHFTS shifts of origin that define the
+*>             multi-shift QR sweep.  On output SR and SI may be
+*>             reordered.
+*> \endverbatim
+*>
+*> \param[in,out] H
+*> \verbatim
+*>          H is DOUBLE PRECISION array of size (LDH,N)
+*>             On input H contains a Hessenberg matrix.  On output a
+*>             multi-shift QR sweep with shifts SR(J)+i*SI(J) is applied
+*>             to the isolated diagonal block in rows and columns KTOP
+*>             through KBOT.
+*> \endverbatim
+*>
+*> \param[in] LDH
+*> \verbatim
+*>          LDH is integer scalar
+*>             LDH is the leading dimension of H just as declared in the
+*>             calling procedure.  LDH.GE.MAX(1,N).
+*> \endverbatim
+*>
+*> \param[in] ILOZ
+*> \verbatim
+*>          ILOZ is INTEGER
+*> \endverbatim
+*>
+*> \param[in] IHIZ
+*> \verbatim
+*>          IHIZ is INTEGER
+*>             Specify the rows of Z to which transformations must be
+*>             applied if WANTZ is .TRUE.. 1 .LE. ILOZ .LE. IHIZ .LE. N
+*> \endverbatim
+*>
+*> \param[in,out] Z
+*> \verbatim
+*>          Z is DOUBLE PRECISION array of size (LDZ,IHI)
+*>             If WANTZ = .TRUE., then the QR Sweep orthogonal
+*>             similarity transformation is accumulated into
+*>             Z(ILOZ:IHIZ,ILO:IHI) from the right.
+*>             If WANTZ = .FALSE., then Z is unreferenced.
+*> \endverbatim
+*>
+*> \param[in] LDZ
+*> \verbatim
+*>          LDZ is integer scalar
+*>             LDA is the leading dimension of Z just as declared in
+*>             the calling procedure. LDZ.GE.N.
+*> \endverbatim
+*>
+*> \param[out] V
+*> \verbatim
+*>          V is DOUBLE PRECISION array of size (LDV,NSHFTS/2)
+*> \endverbatim
+*>
+*> \param[in] LDV
+*> \verbatim
+*>          LDV is integer scalar
+*>             LDV is the leading dimension of V as declared in the
+*>             calling procedure.  LDV.GE.3.
+*> \endverbatim
+*>
+*> \param[out] U
+*> \verbatim
+*>          U is DOUBLE PRECISION array of size
+*>             (LDU,3*NSHFTS-3)
+*> \endverbatim
+*>
+*> \param[in] LDU
+*> \verbatim
+*>          LDU is integer scalar
+*>             LDU is the leading dimension of U just as declared in the
+*>             in the calling subroutine.  LDU.GE.3*NSHFTS-3.
+*> \endverbatim
+*>
+*> \param[in] NH
+*> \verbatim
+*>          NH is integer scalar
+*>             NH is the number of columns in array WH available for
+*>             workspace. NH.GE.1.
+*> \endverbatim
+*>
+*> \param[out] WH
+*> \verbatim
+*>          WH is DOUBLE PRECISION array of size (LDWH,NH)
+*> \endverbatim
+*>
+*> \param[in] LDWH
+*> \verbatim
+*>          LDWH is integer scalar
+*>             Leading dimension of WH just as declared in the
+*>             calling procedure.  LDWH.GE.3*NSHFTS-3.
+*> \endverbatim
+*>
+*> \param[in] NV
+*> \verbatim
+*>          NV is integer scalar
+*>             NV is the number of rows in WV agailable for workspace.
+*>             NV.GE.1.
+*> \endverbatim
+*>
+*> \param[out] WV
+*> \verbatim
+*>          WV is DOUBLE PRECISION array of size
+*>             (LDWV,3*NSHFTS-3)
+*> \endverbatim
+*>
+*> \param[in] LDWV
+*> \verbatim
+*>          LDWV is integer scalar
+*>             LDWV is the leading dimension of WV as declared in the
+*>             in the calling subroutine.  LDWV.GE.NV.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date September 2012
+*
+*> \ingroup doubleOTHERauxiliary
+*
+*> \par Contributors:
+*  ==================
+*>
+*>       Karen Braman and Ralph Byers, Department of Mathematics,
+*>       University of Kansas, USA
+*
+*> \par References:
+*  ================
+*>
+*>       K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
+*>       Algorithm Part I: Maintaining Well Focused Shifts, and Level 3
+*>       Performance, SIAM Journal of Matrix Analysis, volume 23, pages
+*>       929--947, 2002.
+*>
+*  =====================================================================
+      SUBROUTINE DLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS,
+     $                   SR, SI, H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U,
+     $                   LDU, NV, WV, LDWV, NH, WH, LDWH )
+*
+*  -- LAPACK auxiliary routine (version 3.4.2) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     September 2012
+*
+*     .. Scalar Arguments ..
+      INTEGER            IHIZ, ILOZ, KACC22, KBOT, KTOP, LDH, LDU, LDV,
+     $                   LDWH, LDWV, LDZ, N, NH, NSHFTS, NV
+      LOGICAL            WANTT, WANTZ
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   H( LDH, * ), SI( * ), SR( * ), U( LDU, * ),
+     $                   V( LDV, * ), WH( LDWH, * ), WV( LDWV, * ),
+     $                   Z( LDZ, * )
+*     ..
+*
+*  ================================================================
+*     .. Parameters ..
+      DOUBLE PRECISION   ZERO, ONE
+      PARAMETER          ( ZERO = 0.0d0, ONE = 1.0d0 )
+*     ..
+*     .. Local Scalars ..
+      DOUBLE PRECISION   ALPHA, BETA, H11, H12, H21, H22, REFSUM,
+     $                   SAFMAX, SAFMIN, SCL, SMLNUM, SWAP, TST1, TST2,
+     $                   ULP
+      INTEGER            I, I2, I4, INCOL, J, J2, J4, JBOT, JCOL, JLEN,
+     $                   JROW, JTOP, K, K1, KDU, KMS, KNZ, KRCOL, KZS,
+     $                   M, M22, MBOT, MEND, MSTART, MTOP, NBMPS, NDCOL,
+     $                   NS, NU
+      LOGICAL            ACCUM, BLK22, BMP22
+*     ..
+*     .. External Functions ..
+      DOUBLE PRECISION   DLAMCH
+      EXTERNAL           DLAMCH
+*     ..
+*     .. Intrinsic Functions ..
+*
+      INTRINSIC          ABS, DBLE, MAX, MIN, MOD
+*     ..
+*     .. Local Arrays ..
+      DOUBLE PRECISION   VT( 3 )
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           DGEMM, DLABAD, DLACPY, DLAQR1, DLARFG, DLASET,
+     $                   DTRMM
+*     ..
+*     .. Executable Statements ..
+*
+*     ==== If there are no shifts, then there is nothing to do. ====
+*
+      IF( NSHFTS.LT.2 )
+     $   RETURN
+*
+*     ==== If the active block is empty or 1-by-1, then there
+*     .    is nothing to do. ====
+*
+      IF( KTOP.GE.KBOT )
+     $   RETURN
+*
+*     ==== Shuffle shifts into pairs of real shifts and pairs
+*     .    of complex conjugate shifts assuming complex
+*     .    conjugate shifts are already adjacent to one
+*     .    another. ====
+*
+      DO 10 I = 1, NSHFTS - 2, 2
+         IF( SI( I ).NE.-SI( I+1 ) ) THEN
+*
+            SWAP = SR( I )
+            SR( I ) = SR( I+1 )
+            SR( I+1 ) = SR( I+2 )
+            SR( I+2 ) = SWAP
+*
+            SWAP = SI( I )
+            SI( I ) = SI( I+1 )
+            SI( I+1 ) = SI( I+2 )
+            SI( I+2 ) = SWAP
+         END IF
+   10 CONTINUE
+*
+*     ==== NSHFTS is supposed to be even, but if it is odd,
+*     .    then simply reduce it by one.  The shuffle above
+*     .    ensures that the dropped shift is real and that
+*     .    the remaining shifts are paired. ====
+*
+      NS = NSHFTS - MOD( NSHFTS, 2 )
+*
+*     ==== Machine constants for deflation ====
+*
+      SAFMIN = DLAMCH( 'SAFE MINIMUM' )
+      SAFMAX = ONE / SAFMIN
+      CALL DLABAD( SAFMIN, SAFMAX )
+      ULP = DLAMCH( 'PRECISION' )
+      SMLNUM = SAFMIN*( DBLE( N ) / ULP )
+*
+*     ==== Use accumulated reflections to update far-from-diagonal
+*     .    entries ? ====
+*
+      ACCUM = ( KACC22.EQ.1 ) .OR. ( KACC22.EQ.2 )
+*
+*     ==== If so, exploit the 2-by-2 block structure? ====
+*
+      BLK22 = ( NS.GT.2 ) .AND. ( KACC22.EQ.2 )
+*
+*     ==== clear trash ====
+*
+      IF( KTOP+2.LE.KBOT )
+     $   H( KTOP+2, KTOP ) = ZERO
+*
+*     ==== NBMPS = number of 2-shift bulges in the chain ====
+*
+      NBMPS = NS / 2
+*
+*     ==== KDU = width of slab ====
+*
+      KDU = 6*NBMPS - 3
+*
+*     ==== Create and chase chains of NBMPS bulges ====
+*
+      DO 220 INCOL = 3*( 1-NBMPS ) + KTOP - 1, KBOT - 2, 3*NBMPS - 2
+         NDCOL = INCOL + KDU
+         IF( ACCUM )
+     $      CALL DLASET( 'ALL', KDU, KDU, ZERO, ONE, U, LDU )
+*
+*        ==== Near-the-diagonal bulge chase.  The following loop
+*        .    performs the near-the-diagonal part of a small bulge
+*        .    multi-shift QR sweep.  Each 6*NBMPS-2 column diagonal
+*        .    chunk extends from column INCOL to column NDCOL
+*        .    (including both column INCOL and column NDCOL). The
+*        .    following loop chases a 3*NBMPS column long chain of
+*        .    NBMPS bulges 3*NBMPS-2 columns to the right.  (INCOL
+*        .    may be less than KTOP and and NDCOL may be greater than
+*        .    KBOT indicating phantom columns from which to chase
+*        .    bulges before they are actually introduced or to which
+*        .    to chase bulges beyond column KBOT.)  ====
+*
+         DO 150 KRCOL = INCOL, MIN( INCOL+3*NBMPS-3, KBOT-2 )
+*
+*           ==== Bulges number MTOP to MBOT are active double implicit
+*           .    shift bulges.  There may or may not also be small
+*           .    2-by-2 bulge, if there is room.  The inactive bulges
+*           .    (if any) must wait until the active bulges have moved
+*           .    down the diagonal to make room.  The phantom matrix
+*           .    paradigm described above helps keep track.  ====
+*
+            MTOP = MAX( 1, ( ( KTOP-1 )-KRCOL+2 ) / 3+1 )
+            MBOT = MIN( NBMPS, ( KBOT-KRCOL ) / 3 )
+            M22 = MBOT + 1
+            BMP22 = ( MBOT.LT.NBMPS ) .AND. ( KRCOL+3*( M22-1 ) ).EQ.
+     $              ( KBOT-2 )
+*
+*           ==== Generate reflections to chase the chain right
+*           .    one column.  (The minimum value of K is KTOP-1.) ====
+*
+            DO 20 M = MTOP, MBOT
+               K = KRCOL + 3*( M-1 )
+               IF( K.EQ.KTOP-1 ) THEN
+                  CALL DLAQR1( 3, H( KTOP, KTOP ), LDH, SR( 2*M-1 ),
+     $                         SI( 2*M-1 ), SR( 2*M ), SI( 2*M ),
+     $                         V( 1, M ) )
+                  ALPHA = V( 1, M )
+                  CALL DLARFG( 3, ALPHA, V( 2, M ), 1, V( 1, M ) )
+               ELSE
+                  BETA = H( K+1, K )
+                  V( 2, M ) = H( K+2, K )
+                  V( 3, M ) = H( K+3, K )
+                  CALL DLARFG( 3, BETA, V( 2, M ), 1, V( 1, M ) )
+*
+*                 ==== A Bulge may collapse because of vigilant
+*                 .    deflation or destructive underflow.  In the
+*                 .    underflow case, try the two-small-subdiagonals
+*                 .    trick to try to reinflate the bulge.  ====
+*
+                  IF( H( K+3, K ).NE.ZERO .OR. H( K+3, K+1 ).NE.
+     $                ZERO .OR. H( K+3, K+2 ).EQ.ZERO ) THEN
+*
+*                    ==== Typical case: not collapsed (yet). ====
+*
+                     H( K+1, K ) = BETA
+                     H( K+2, K ) = ZERO
+                     H( K+3, K ) = ZERO
+                  ELSE
+*
+*                    ==== Atypical case: collapsed.  Attempt to
+*                    .    reintroduce ignoring H(K+1,K) and H(K+2,K).
+*                    .    If the fill resulting from the new
+*                    .    reflector is too large, then abandon it.
+*                    .    Otherwise, use the new one. ====
+*
+                     CALL DLAQR1( 3, H( K+1, K+1 ), LDH, SR( 2*M-1 ),
+     $                            SI( 2*M-1 ), SR( 2*M ), SI( 2*M ),
+     $                            VT )
+                     ALPHA = VT( 1 )
+                     CALL DLARFG( 3, ALPHA, VT( 2 ), 1, VT( 1 ) )
+                     REFSUM = VT( 1 )*( H( K+1, K )+VT( 2 )*
+     $                        H( K+2, K ) )
+*
+                     IF( ABS( H( K+2, K )-REFSUM*VT( 2 ) )+
+     $                   ABS( REFSUM*VT( 3 ) ).GT.ULP*
+     $                   ( ABS( H( K, K ) )+ABS( H( K+1,
+     $                   K+1 ) )+ABS( H( K+2, K+2 ) ) ) ) THEN
+*
+*                       ==== Starting a new bulge here would
+*                       .    create non-negligible fill.  Use
+*                       .    the old one with trepidation. ====
+*
+                        H( K+1, K ) = BETA
+                        H( K+2, K ) = ZERO
+                        H( K+3, K ) = ZERO
+                     ELSE
+*
+*                       ==== Stating a new bulge here would
+*                       .    create only negligible fill.
+*                       .    Replace the old reflector with
+*                       .    the new one. ====
+*
+                        H( K+1, K ) = H( K+1, K ) - REFSUM
+                        H( K+2, K ) = ZERO
+                        H( K+3, K ) = ZERO
+                        V( 1, M ) = VT( 1 )
+                        V( 2, M ) = VT( 2 )
+                        V( 3, M ) = VT( 3 )
+                     END IF
+                  END IF
+               END IF
+   20       CONTINUE
+*
+*           ==== Generate a 2-by-2 reflection, if needed. ====
+*
+            K = KRCOL + 3*( M22-1 )
+            IF( BMP22 ) THEN
+               IF( K.EQ.KTOP-1 ) THEN
+                  CALL DLAQR1( 2, H( K+1, K+1 ), LDH, SR( 2*M22-1 ),
+     $                         SI( 2*M22-1 ), SR( 2*M22 ), SI( 2*M22 ),
+     $                         V( 1, M22 ) )
+                  BETA = V( 1, M22 )
+                  CALL DLARFG( 2, BETA, V( 2, M22 ), 1, V( 1, M22 ) )
+               ELSE
+                  BETA = H( K+1, K )
+                  V( 2, M22 ) = H( K+2, K )
+                  CALL DLARFG( 2, BETA, V( 2, M22 ), 1, V( 1, M22 ) )
+                  H( K+1, K ) = BETA
+                  H( K+2, K ) = ZERO
+               END IF
+            END IF
+*
+*           ==== Multiply H by reflections from the left ====
+*
+            IF( ACCUM ) THEN
+               JBOT = MIN( NDCOL, KBOT )
+            ELSE IF( WANTT ) THEN
+               JBOT = N
+            ELSE
+               JBOT = KBOT
+            END IF
+            DO 40 J = MAX( KTOP, KRCOL ), JBOT
+               MEND = MIN( MBOT, ( J-KRCOL+2 ) / 3 )
+               DO 30 M = MTOP, MEND
+                  K = KRCOL + 3*( M-1 )
+                  REFSUM = V( 1, M )*( H( K+1, J )+V( 2, M )*
+     $                     H( K+2, J )+V( 3, M )*H( K+3, J ) )
+                  H( K+1, J ) = H( K+1, J ) - REFSUM
+                  H( K+2, J ) = H( K+2, J ) - REFSUM*V( 2, M )
+                  H( K+3, J ) = H( K+3, J ) - REFSUM*V( 3, M )
+   30          CONTINUE
+   40       CONTINUE
+            IF( BMP22 ) THEN
+               K = KRCOL + 3*( M22-1 )
+               DO 50 J = MAX( K+1, KTOP ), JBOT
+                  REFSUM = V( 1, M22 )*( H( K+1, J )+V( 2, M22 )*
+     $                     H( K+2, J ) )
+                  H( K+1, J ) = H( K+1, J ) - REFSUM
+                  H( K+2, J ) = H( K+2, J ) - REFSUM*V( 2, M22 )
+   50          CONTINUE
+            END IF
+*
+*           ==== Multiply H by reflections from the right.
+*           .    Delay filling in the last row until the
+*           .    vigilant deflation check is complete. ====
+*
+            IF( ACCUM ) THEN
+               JTOP = MAX( KTOP, INCOL )
+            ELSE IF( WANTT ) THEN
+               JTOP = 1
+            ELSE
+               JTOP = KTOP
+            END IF
+            DO 90 M = MTOP, MBOT
+               IF( V( 1, M ).NE.ZERO ) THEN
+                  K = KRCOL + 3*( M-1 )
+                  DO 60 J = JTOP, MIN( KBOT, K+3 )
+                     REFSUM = V( 1, M )*( H( J, K+1 )+V( 2, M )*
+     $                        H( J, K+2 )+V( 3, M )*H( J, K+3 ) )
+                     H( J, K+1 ) = H( J, K+1 ) - REFSUM
+                     H( J, K+2 ) = H( J, K+2 ) - REFSUM*V( 2, M )
+                     H( J, K+3 ) = H( J, K+3 ) - REFSUM*V( 3, M )
+   60             CONTINUE
+*
+                  IF( ACCUM ) THEN
+*
+*                    ==== Accumulate U. (If necessary, update Z later
+*                    .    with with an efficient matrix-matrix
+*                    .    multiply.) ====
+*
+                     KMS = K - INCOL
+                     DO 70 J = MAX( 1, KTOP-INCOL ), KDU
+                        REFSUM = V( 1, M )*( U( J, KMS+1 )+V( 2, M )*
+     $                           U( J, KMS+2 )+V( 3, M )*U( J, KMS+3 ) )
+                        U( J, KMS+1 ) = U( J, KMS+1 ) - REFSUM
+                        U( J, KMS+2 ) = U( J, KMS+2 ) - REFSUM*V( 2, M )
+                        U( J, KMS+3 ) = U( J, KMS+3 ) - REFSUM*V( 3, M )
+   70                CONTINUE
+                  ELSE IF( WANTZ ) THEN
+*
+*                    ==== U is not accumulated, so update Z
+*                    .    now by multiplying by reflections
+*                    .    from the right. ====
+*
+                     DO 80 J = ILOZ, IHIZ
+                        REFSUM = V( 1, M )*( Z( J, K+1 )+V( 2, M )*
+     $                           Z( J, K+2 )+V( 3, M )*Z( J, K+3 ) )
+                        Z( J, K+1 ) = Z( J, K+1 ) - REFSUM
+                        Z( J, K+2 ) = Z( J, K+2 ) - REFSUM*V( 2, M )
+                        Z( J, K+3 ) = Z( J, K+3 ) - REFSUM*V( 3, M )
+   80                CONTINUE
+                  END IF
+               END IF
+   90       CONTINUE
+*
+*           ==== Special case: 2-by-2 reflection (if needed) ====
+*
+            K = KRCOL + 3*( M22-1 )
+            IF( BMP22 ) THEN
+               IF ( V( 1, M22 ).NE.ZERO ) THEN
+                  DO 100 J = JTOP, MIN( KBOT, K+3 )
+                     REFSUM = V( 1, M22 )*( H( J, K+1 )+V( 2, M22 )*
+     $                        H( J, K+2 ) )
+                     H( J, K+1 ) = H( J, K+1 ) - REFSUM
+                     H( J, K+2 ) = H( J, K+2 ) - REFSUM*V( 2, M22 )
+  100             CONTINUE
+*
+                  IF( ACCUM ) THEN
+                     KMS = K - INCOL
+                     DO 110 J = MAX( 1, KTOP-INCOL ), KDU
+                        REFSUM = V( 1, M22 )*( U( J, KMS+1 )+
+     $                           V( 2, M22 )*U( J, KMS+2 ) )
+                        U( J, KMS+1 ) = U( J, KMS+1 ) - REFSUM
+                        U( J, KMS+2 ) = U( J, KMS+2 ) -
+     $                                  REFSUM*V( 2, M22 )
+  110             CONTINUE
+                  ELSE IF( WANTZ ) THEN
+                     DO 120 J = ILOZ, IHIZ
+                        REFSUM = V( 1, M22 )*( Z( J, K+1 )+V( 2, M22 )*
+     $                           Z( J, K+2 ) )
+                        Z( J, K+1 ) = Z( J, K+1 ) - REFSUM
+                        Z( J, K+2 ) = Z( J, K+2 ) - REFSUM*V( 2, M22 )
+  120                CONTINUE
+                  END IF
+               END IF
+            END IF
+*
+*           ==== Vigilant deflation check ====
+*
+            MSTART = MTOP
+            IF( KRCOL+3*( MSTART-1 ).LT.KTOP )
+     $         MSTART = MSTART + 1
+            MEND = MBOT
+            IF( BMP22 )
+     $         MEND = MEND + 1
+            IF( KRCOL.EQ.KBOT-2 )
+     $         MEND = MEND + 1
+            DO 130 M = MSTART, MEND
+               K = MIN( KBOT-1, KRCOL+3*( M-1 ) )
+*
+*              ==== The following convergence test requires that
+*              .    the tradition small-compared-to-nearby-diagonals
+*              .    criterion and the Ahues & Tisseur (LAWN 122, 1997)
+*              .    criteria both be satisfied.  The latter improves
+*              .    accuracy in some examples. Falling back on an
+*              .    alternate convergence criterion when TST1 or TST2
+*              .    is zero (as done here) is traditional but probably
+*              .    unnecessary. ====
+*
+               IF( H( K+1, K ).NE.ZERO ) THEN
+                  TST1 = ABS( H( K, K ) ) + ABS( H( K+1, K+1 ) )
+                  IF( TST1.EQ.ZERO ) THEN
+                     IF( K.GE.KTOP+1 )
+     $                  TST1 = TST1 + ABS( H( K, K-1 ) )
+                     IF( K.GE.KTOP+2 )
+     $                  TST1 = TST1 + ABS( H( K, K-2 ) )
+                     IF( K.GE.KTOP+3 )
+     $                  TST1 = TST1 + ABS( H( K, K-3 ) )
+                     IF( K.LE.KBOT-2 )
+     $                  TST1 = TST1 + ABS( H( K+2, K+1 ) )
+                     IF( K.LE.KBOT-3 )
+     $                  TST1 = TST1 + ABS( H( K+3, K+1 ) )
+                     IF( K.LE.KBOT-4 )
+     $                  TST1 = TST1 + ABS( H( K+4, K+1 ) )
+                  END IF
+                  IF( ABS( H( K+1, K ) ).LE.MAX( SMLNUM, ULP*TST1 ) )
+     $                 THEN
+                     H12 = MAX( ABS( H( K+1, K ) ), ABS( H( K, K+1 ) ) )
+                     H21 = MIN( ABS( H( K+1, K ) ), ABS( H( K, K+1 ) ) )
+                     H11 = MAX( ABS( H( K+1, K+1 ) ),
+     $                     ABS( H( K, K )-H( K+1, K+1 ) ) )
+                     H22 = MIN( ABS( H( K+1, K+1 ) ),
+     $                     ABS( H( K, K )-H( K+1, K+1 ) ) )
+                     SCL = H11 + H12
+                     TST2 = H22*( H11 / SCL )
+*
+                     IF( TST2.EQ.ZERO .OR. H21*( H12 / SCL ).LE.
+     $                   MAX( SMLNUM, ULP*TST2 ) )H( K+1, K ) = ZERO
+                  END IF
+               END IF
+  130       CONTINUE
+*
+*           ==== Fill in the last row of each bulge. ====
+*
+            MEND = MIN( NBMPS, ( KBOT-KRCOL-1 ) / 3 )
+            DO 140 M = MTOP, MEND
+               K = KRCOL + 3*( M-1 )
+               REFSUM = V( 1, M )*V( 3, M )*H( K+4, K+3 )
+               H( K+4, K+1 ) = -REFSUM
+               H( K+4, K+2 ) = -REFSUM*V( 2, M )
+               H( K+4, K+3 ) = H( K+4, K+3 ) - REFSUM*V( 3, M )
+  140       CONTINUE
+*
+*           ==== End of near-the-diagonal bulge chase. ====
+*
+  150    CONTINUE
+*
+*        ==== Use U (if accumulated) to update far-from-diagonal
+*        .    entries in H.  If required, use U to update Z as
+*        .    well. ====
+*
+         IF( ACCUM ) THEN
+            IF( WANTT ) THEN
+               JTOP = 1
+               JBOT = N
+            ELSE
+               JTOP = KTOP
+               JBOT = KBOT
+            END IF
+            IF( ( .NOT.BLK22 ) .OR. ( INCOL.LT.KTOP ) .OR.
+     $          ( NDCOL.GT.KBOT ) .OR. ( NS.LE.2 ) ) THEN
+*
+*              ==== Updates not exploiting the 2-by-2 block
+*              .    structure of U.  K1 and NU keep track of
+*              .    the location and size of U in the special
+*              .    cases of introducing bulges and chasing
+*              .    bulges off the bottom.  In these special
+*              .    cases and in case the number of shifts
+*              .    is NS = 2, there is no 2-by-2 block
+*              .    structure to exploit.  ====
+*
+               K1 = MAX( 1, KTOP-INCOL )
+               NU = ( KDU-MAX( 0, NDCOL-KBOT ) ) - K1 + 1
+*
+*              ==== Horizontal Multiply ====
+*
+               DO 160 JCOL = MIN( NDCOL, KBOT ) + 1, JBOT, NH
+                  JLEN = MIN( NH, JBOT-JCOL+1 )
+                  CALL DGEMM( 'C', 'N', NU, JLEN, NU, ONE, U( K1, K1 ),
+     $                        LDU, H( INCOL+K1, JCOL ), LDH, ZERO, WH,
+     $                        LDWH )
+                  CALL DLACPY( 'ALL', NU, JLEN, WH, LDWH,
+     $                         H( INCOL+K1, JCOL ), LDH )
+  160          CONTINUE
+*
+*              ==== Vertical multiply ====
+*
+               DO 170 JROW = JTOP, MAX( KTOP, INCOL ) - 1, NV
+                  JLEN = MIN( NV, MAX( KTOP, INCOL )-JROW )
+                  CALL DGEMM( 'N', 'N', JLEN, NU, NU, ONE,
+     $                        H( JROW, INCOL+K1 ), LDH, U( K1, K1 ),
+     $                        LDU, ZERO, WV, LDWV )
+                  CALL DLACPY( 'ALL', JLEN, NU, WV, LDWV,
+     $                         H( JROW, INCOL+K1 ), LDH )
+  170          CONTINUE
+*
+*              ==== Z multiply (also vertical) ====
+*
+               IF( WANTZ ) THEN
+                  DO 180 JROW = ILOZ, IHIZ, NV
+                     JLEN = MIN( NV, IHIZ-JROW+1 )
+                     CALL DGEMM( 'N', 'N', JLEN, NU, NU, ONE,
+     $                           Z( JROW, INCOL+K1 ), LDZ, U( K1, K1 ),
+     $                           LDU, ZERO, WV, LDWV )
+                     CALL DLACPY( 'ALL', JLEN, NU, WV, LDWV,
+     $                            Z( JROW, INCOL+K1 ), LDZ )
+  180             CONTINUE
+               END IF
+            ELSE
+*
+*              ==== Updates exploiting U's 2-by-2 block structure.
+*              .    (I2, I4, J2, J4 are the last rows and columns
+*              .    of the blocks.) ====
+*
+               I2 = ( KDU+1 ) / 2
+               I4 = KDU
+               J2 = I4 - I2
+               J4 = KDU
+*
+*              ==== KZS and KNZ deal with the band of zeros
+*              .    along the diagonal of one of the triangular
+*              .    blocks. ====
+*
+               KZS = ( J4-J2 ) - ( NS+1 )
+               KNZ = NS + 1
+*
+*              ==== Horizontal multiply ====
+*
+               DO 190 JCOL = MIN( NDCOL, KBOT ) + 1, JBOT, NH
+                  JLEN = MIN( NH, JBOT-JCOL+1 )
+*
+*                 ==== Copy bottom of H to top+KZS of scratch ====
+*                  (The first KZS rows get multiplied by zero.) ====
+*
+                  CALL DLACPY( 'ALL', KNZ, JLEN, H( INCOL+1+J2, JCOL ),
+     $                         LDH, WH( KZS+1, 1 ), LDWH )
+*
+*                 ==== Multiply by U21**T ====
+*
+                  CALL DLASET( 'ALL', KZS, JLEN, ZERO, ZERO, WH, LDWH )
+                  CALL DTRMM( 'L', 'U', 'C', 'N', KNZ, JLEN, ONE,
+     $                        U( J2+1, 1+KZS ), LDU, WH( KZS+1, 1 ),
+     $                        LDWH )
+*
+*                 ==== Multiply top of H by U11**T ====
+*
+                  CALL DGEMM( 'C', 'N', I2, JLEN, J2, ONE, U, LDU,
+     $                        H( INCOL+1, JCOL ), LDH, ONE, WH, LDWH )
+*
+*                 ==== Copy top of H to bottom of WH ====
+*
+                  CALL DLACPY( 'ALL', J2, JLEN, H( INCOL+1, JCOL ), LDH,
+     $                         WH( I2+1, 1 ), LDWH )
+*
+*                 ==== Multiply by U21**T ====
+*
+                  CALL DTRMM( 'L', 'L', 'C', 'N', J2, JLEN, ONE,
+     $                        U( 1, I2+1 ), LDU, WH( I2+1, 1 ), LDWH )
+*
+*                 ==== Multiply by U22 ====
+*
+                  CALL DGEMM( 'C', 'N', I4-I2, JLEN, J4-J2, ONE,
+     $                        U( J2+1, I2+1 ), LDU,
+     $                        H( INCOL+1+J2, JCOL ), LDH, ONE,
+     $                        WH( I2+1, 1 ), LDWH )
+*
+*                 ==== Copy it back ====
+*
+                  CALL DLACPY( 'ALL', KDU, JLEN, WH, LDWH,
+     $                         H( INCOL+1, JCOL ), LDH )
+  190          CONTINUE
+*
+*              ==== Vertical multiply ====
+*
+               DO 200 JROW = JTOP, MAX( INCOL, KTOP ) - 1, NV
+                  JLEN = MIN( NV, MAX( INCOL, KTOP )-JROW )
+*
+*                 ==== Copy right of H to scratch (the first KZS
+*                 .    columns get multiplied by zero) ====
+*
+                  CALL DLACPY( 'ALL', JLEN, KNZ, H( JROW, INCOL+1+J2 ),
+     $                         LDH, WV( 1, 1+KZS ), LDWV )
+*
+*                 ==== Multiply by U21 ====
+*
+                  CALL DLASET( 'ALL', JLEN, KZS, ZERO, ZERO, WV, LDWV )
+                  CALL DTRMM( 'R', 'U', 'N', 'N', JLEN, KNZ, ONE,
+     $                        U( J2+1, 1+KZS ), LDU, WV( 1, 1+KZS ),
+     $                        LDWV )
+*
+*                 ==== Multiply by U11 ====
+*
+                  CALL DGEMM( 'N', 'N', JLEN, I2, J2, ONE,
+     $                        H( JROW, INCOL+1 ), LDH, U, LDU, ONE, WV,
+     $                        LDWV )
+*
+*                 ==== Copy left of H to right of scratch ====
+*
+                  CALL DLACPY( 'ALL', JLEN, J2, H( JROW, INCOL+1 ), LDH,
+     $                         WV( 1, 1+I2 ), LDWV )
+*
+*                 ==== Multiply by U21 ====
+*
+                  CALL DTRMM( 'R', 'L', 'N', 'N', JLEN, I4-I2, ONE,
+     $                        U( 1, I2+1 ), LDU, WV( 1, 1+I2 ), LDWV )
+*
+*                 ==== Multiply by U22 ====
+*
+                  CALL DGEMM( 'N', 'N', JLEN, I4-I2, J4-J2, ONE,
+     $                        H( JROW, INCOL+1+J2 ), LDH,
+     $                        U( J2+1, I2+1 ), LDU, ONE, WV( 1, 1+I2 ),
+     $                        LDWV )
+*
+*                 ==== Copy it back ====
+*
+                  CALL DLACPY( 'ALL', JLEN, KDU, WV, LDWV,
+     $                         H( JROW, INCOL+1 ), LDH )
+  200          CONTINUE
+*
+*              ==== Multiply Z (also vertical) ====
+*
+               IF( WANTZ ) THEN
+                  DO 210 JROW = ILOZ, IHIZ, NV
+                     JLEN = MIN( NV, IHIZ-JROW+1 )
+*
+*                    ==== Copy right of Z to left of scratch (first
+*                    .     KZS columns get multiplied by zero) ====
+*
+                     CALL DLACPY( 'ALL', JLEN, KNZ,
+     $                            Z( JROW, INCOL+1+J2 ), LDZ,
+     $                            WV( 1, 1+KZS ), LDWV )
+*
+*                    ==== Multiply by U12 ====
+*
+                     CALL DLASET( 'ALL', JLEN, KZS, ZERO, ZERO, WV,
+     $                            LDWV )
+                     CALL DTRMM( 'R', 'U', 'N', 'N', JLEN, KNZ, ONE,
+     $                           U( J2+1, 1+KZS ), LDU, WV( 1, 1+KZS ),
+     $                           LDWV )
+*
+*                    ==== Multiply by U11 ====
+*
+                     CALL DGEMM( 'N', 'N', JLEN, I2, J2, ONE,
+     $                           Z( JROW, INCOL+1 ), LDZ, U, LDU, ONE,
+     $                           WV, LDWV )
+*
+*                    ==== Copy left of Z to right of scratch ====
+*
+                     CALL DLACPY( 'ALL', JLEN, J2, Z( JROW, INCOL+1 ),
+     $                            LDZ, WV( 1, 1+I2 ), LDWV )
+*
+*                    ==== Multiply by U21 ====
+*
+                     CALL DTRMM( 'R', 'L', 'N', 'N', JLEN, I4-I2, ONE,
+     $                           U( 1, I2+1 ), LDU, WV( 1, 1+I2 ),
+     $                           LDWV )
+*
+*                    ==== Multiply by U22 ====
+*
+                     CALL DGEMM( 'N', 'N', JLEN, I4-I2, J4-J2, ONE,
+     $                           Z( JROW, INCOL+1+J2 ), LDZ,
+     $                           U( J2+1, I2+1 ), LDU, ONE,
+     $                           WV( 1, 1+I2 ), LDWV )
+*
+*                    ==== Copy the result back to Z ====
+*
+                     CALL DLACPY( 'ALL', JLEN, KDU, WV, LDWV,
+     $                            Z( JROW, INCOL+1 ), LDZ )
+  210             CONTINUE
+               END IF
+            END IF
+         END IF
+  220 CONTINUE
+*
+*     ==== End of DLAQR5 ====
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dlarfg.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dlarfg.f
new file mode 100644
index 00000000..ce91d33c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dlarfg.f
@@ -0,0 +1,196 @@
+*> \brief \b DLARFG generates an elementary reflector (Householder matrix).
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLARFG + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarfg.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarfg.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarfg.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            INCX, N
+*       DOUBLE PRECISION   ALPHA, TAU
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   X( * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DLARFG generates a real elementary reflector H of order n, such
+*> that
+*>
+*>       H * ( alpha ) = ( beta ),   H**T * H = I.
+*>           (   x   )   (   0  )
+*>
+*> where alpha and beta are scalars, and x is an (n-1)-element real
+*> vector. H is represented in the form
+*>
+*>       H = I - tau * ( 1 ) * ( 1 v**T ) ,
+*>                     ( v )
+*>
+*> where tau is a real scalar and v is a real (n-1)-element
+*> vector.
+*>
+*> If the elements of x are all zero, then tau = 0 and H is taken to be
+*> the unit matrix.
+*>
+*> Otherwise  1 <= tau <= 2.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the elementary reflector.
+*> \endverbatim
+*>
+*> \param[in,out] ALPHA
+*> \verbatim
+*>          ALPHA is DOUBLE PRECISION
+*>          On entry, the value alpha.
+*>          On exit, it is overwritten with the value beta.
+*> \endverbatim
+*>
+*> \param[in,out] X
+*> \verbatim
+*>          X is DOUBLE PRECISION array, dimension
+*>                         (1+(N-2)*abs(INCX))
+*>          On entry, the vector x.
+*>          On exit, it is overwritten with the vector v.
+*> \endverbatim
+*>
+*> \param[in] INCX
+*> \verbatim
+*>          INCX is INTEGER
+*>          The increment between elements of X. INCX > 0.
+*> \endverbatim
+*>
+*> \param[out] TAU
+*> \verbatim
+*>          TAU is DOUBLE PRECISION
+*>          The value tau.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date September 2012
+*
+*> \ingroup doubleOTHERauxiliary
+*
+*  =====================================================================
+      SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU )
+*
+*  -- LAPACK auxiliary routine (version 3.4.2) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     September 2012
+*
+*     .. Scalar Arguments ..
+      INTEGER            INCX, N
+      DOUBLE PRECISION   ALPHA, TAU
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   X( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ONE, ZERO
+      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            J, KNT
+      DOUBLE PRECISION   BETA, RSAFMN, SAFMIN, XNORM
+*     ..
+*     .. External Functions ..
+      DOUBLE PRECISION   DLAMCH, DLAPY2, DNRM2
+      EXTERNAL           DLAMCH, DLAPY2, DNRM2
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS, SIGN
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           DSCAL
+*     ..
+*     .. Executable Statements ..
+*
+      IF( N.LE.1 ) THEN
+         TAU = ZERO
+         RETURN
+      END IF
+*
+      XNORM = DNRM2( N-1, X, INCX )
+*
+      IF( XNORM.EQ.ZERO ) THEN
+*
+*        H  =  I
+*
+         TAU = ZERO
+      ELSE
+*
+*        general case
+*
+         BETA = -SIGN( DLAPY2( ALPHA, XNORM ), ALPHA )
+         SAFMIN = DLAMCH( 'S' ) / DLAMCH( 'E' )
+         KNT = 0
+         IF( ABS( BETA ).LT.SAFMIN ) THEN
+*
+*           XNORM, BETA may be inaccurate; scale X and recompute them
+*
+            RSAFMN = ONE / SAFMIN
+   10       CONTINUE
+            KNT = KNT + 1
+            CALL DSCAL( N-1, RSAFMN, X, INCX )
+            BETA = BETA*RSAFMN
+            ALPHA = ALPHA*RSAFMN
+            IF( ABS( BETA ).LT.SAFMIN )
+     $         GO TO 10
+*
+*           New BETA is at most 1, at least SAFMIN
+*
+            XNORM = DNRM2( N-1, X, INCX )
+            BETA = -SIGN( DLAPY2( ALPHA, XNORM ), ALPHA )
+         END IF
+         TAU = ( BETA-ALPHA ) / BETA
+         CALL DSCAL( N-1, ONE / ( ALPHA-BETA ), X, INCX )
+*
+*        If ALPHA is subnormal, it may lose relative accuracy
+*
+         DO 20 J = 1, KNT
+            BETA = BETA*SAFMIN
+ 20      CONTINUE
+         ALPHA = BETA
+      END IF
+*
+      RETURN
+*
+*     End of DLARFG
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dlaset.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dlaset.f
new file mode 100644
index 00000000..d3bb9456
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dlaset.f
@@ -0,0 +1,184 @@
+*> \brief \b DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLASET + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaset.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaset.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaset.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DLASET( UPLO, M, N, ALPHA, BETA, A, LDA )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            LDA, M, N
+*       DOUBLE PRECISION   ALPHA, BETA
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   A( LDA, * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DLASET initializes an m-by-n matrix A to BETA on the diagonal and
+*> ALPHA on the offdiagonals.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          Specifies the part of the matrix A to be set.
+*>          = 'U':      Upper triangular part is set; the strictly lower
+*>                      triangular part of A is not changed.
+*>          = 'L':      Lower triangular part is set; the strictly upper
+*>                      triangular part of A is not changed.
+*>          Otherwise:  All of the matrix A is set.
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*>          M is INTEGER
+*>          The number of rows of the matrix A.  M >= 0.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The number of columns of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in] ALPHA
+*> \verbatim
+*>          ALPHA is DOUBLE PRECISION
+*>          The constant to which the offdiagonal elements are to be set.
+*> \endverbatim
+*>
+*> \param[in] BETA
+*> \verbatim
+*>          BETA is DOUBLE PRECISION
+*>          The constant to which the diagonal elements are to be set.
+*> \endverbatim
+*>
+*> \param[out] A
+*> \verbatim
+*>          A is DOUBLE PRECISION array, dimension (LDA,N)
+*>          On exit, the leading m-by-n submatrix of A is set as follows:
+*>
+*>          if UPLO = 'U', A(i,j) = ALPHA, 1<=i<=j-1, 1<=j<=n,
+*>          if UPLO = 'L', A(i,j) = ALPHA, j+1<=i<=m, 1<=j<=n,
+*>          otherwise,     A(i,j) = ALPHA, 1<=i<=m, 1<=j<=n, i.ne.j,
+*>
+*>          and, for all UPLO, A(i,i) = BETA, 1<=i<=min(m,n).
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,M).
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2015
+*
+*> \ingroup auxOTHERauxiliary
+*
+*  =====================================================================
+      SUBROUTINE DLASET( UPLO, M, N, ALPHA, BETA, A, LDA )
+*
+*  -- LAPACK auxiliary routine (version 3.6.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2015
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            LDA, M, N
+      DOUBLE PRECISION   ALPHA, BETA
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   A( LDA, * )
+*     ..
+*
+* =====================================================================
+*
+*     .. Local Scalars ..
+      INTEGER            I, J
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      EXTERNAL           LSAME
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MIN
+*     ..
+*     .. Executable Statements ..
+*
+      IF( LSAME( UPLO, 'U' ) ) THEN
+*
+*        Set the strictly upper triangular or trapezoidal part of the
+*        array to ALPHA.
+*
+         DO 20 J = 2, N
+            DO 10 I = 1, MIN( J-1, M )
+               A( I, J ) = ALPHA
+   10       CONTINUE
+   20    CONTINUE
+*
+      ELSE IF( LSAME( UPLO, 'L' ) ) THEN
+*
+*        Set the strictly lower triangular or trapezoidal part of the
+*        array to ALPHA.
+*
+         DO 40 J = 1, MIN( M, N )
+            DO 30 I = J + 1, M
+               A( I, J ) = ALPHA
+   30       CONTINUE
+   40    CONTINUE
+*
+      ELSE
+*
+*        Set the leading m-by-n submatrix to ALPHA.
+*
+         DO 60 J = 1, N
+            DO 50 I = 1, M
+               A( I, J ) = ALPHA
+   50       CONTINUE
+   60    CONTINUE
+      END IF
+*
+*     Set the first min(M,N) diagonal elements to BETA.
+*
+      DO 70 I = 1, MIN( M, N )
+         A( I, I ) = BETA
+   70 CONTINUE
+*
+      RETURN
+*
+*     End of DLASET
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dnrm2.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dnrm2.f
new file mode 100644
index 00000000..5ea257a2
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dnrm2.f
@@ -0,0 +1,112 @@
+*> \brief \b DNRM2
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*  Definition:
+*  ===========
+*
+*       DOUBLE PRECISION FUNCTION DNRM2(N,X,INCX)
+* 
+*       .. Scalar Arguments ..
+*       INTEGER INCX,N
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION X(*)
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DNRM2 returns the euclidean norm of a vector via the function
+*> name, so that
+*>
+*>    DNRM2 := sqrt( x'*x )
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup double_blas_level1
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  -- This version written on 25-October-1982.
+*>     Modified on 14-October-1993 to inline the call to DLASSQ.
+*>     Sven Hammarling, Nag Ltd.
+*> \endverbatim
+*>
+*  =====================================================================
+      DOUBLE PRECISION FUNCTION DNRM2(N,X,INCX)
+*
+*  -- Reference BLAS level1 routine (version 3.4.0) --
+*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2011
+*
+*     .. Scalar Arguments ..
+      INTEGER INCX,N
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION X(*)
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION ONE,ZERO
+      PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
+*     ..
+*     .. Local Scalars ..
+      DOUBLE PRECISION ABSXI,NORM,SCALE,SSQ
+      INTEGER IX
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC ABS,SQRT
+*     ..
+      IF (N.LT.1 .OR. INCX.LT.1) THEN
+          NORM = ZERO
+      ELSE IF (N.EQ.1) THEN
+          NORM = ABS(X(1))
+      ELSE
+          SCALE = ZERO
+          SSQ = ONE
+*        The following loop is equivalent to this call to the LAPACK
+*        auxiliary routine:
+*        CALL DLASSQ( N, X, INCX, SCALE, SSQ )
+*
+          DO 10 IX = 1,1 + (N-1)*INCX,INCX
+              IF (X(IX).NE.ZERO) THEN
+                  ABSXI = ABS(X(IX))
+                  IF (SCALE.LT.ABSXI) THEN
+                      SSQ = ONE + SSQ* (SCALE/ABSXI)**2
+                      SCALE = ABSXI
+                  ELSE
+                      SSQ = SSQ + (ABSXI/SCALE)**2
+                  END IF
+              END IF
+   10     CONTINUE
+          NORM = SCALE*SQRT(SSQ)
+      END IF
+*
+      DNRM2 = NORM
+      RETURN
+*
+*     End of DNRM2.
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dscal.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dscal.f
new file mode 100644
index 00000000..3337de8e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dscal.f
@@ -0,0 +1,110 @@
+*> \brief \b DSCAL
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DSCAL(N,DA,DX,INCX)
+* 
+*       .. Scalar Arguments ..
+*       DOUBLE PRECISION DA
+*       INTEGER INCX,N
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION DX(*)
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*>    DSCAL scales a vector by a constant.
+*>    uses unrolled loops for increment equal to one.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup double_blas_level1
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>     jack dongarra, linpack, 3/11/78.
+*>     modified 3/93 to return if incx .le. 0.
+*>     modified 12/3/93, array(1) declarations changed to array(*)
+*> \endverbatim
+*>
+*  =====================================================================
+      SUBROUTINE DSCAL(N,DA,DX,INCX)
+*
+*  -- Reference BLAS level1 routine (version 3.4.0) --
+*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2011
+*
+*     .. Scalar Arguments ..
+      DOUBLE PRECISION DA
+      INTEGER INCX,N
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION DX(*)
+*     ..
+*
+*  =====================================================================
+*
+*     .. Local Scalars ..
+      INTEGER I,M,MP1,NINCX
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC MOD
+*     ..
+      IF (N.LE.0 .OR. INCX.LE.0) RETURN
+      IF (INCX.EQ.1) THEN
+*
+*        code for increment equal to 1
+*
+*
+*        clean-up loop
+*
+         M = MOD(N,5)
+         IF (M.NE.0) THEN
+            DO I = 1,M
+               DX(I) = DA*DX(I)
+            END DO
+            IF (N.LT.5) RETURN
+         END IF
+         MP1 = M + 1
+         DO I = MP1,N,5
+            DX(I) = DA*DX(I)
+            DX(I+1) = DA*DX(I+1)
+            DX(I+2) = DA*DX(I+2)
+            DX(I+3) = DA*DX(I+3)
+            DX(I+4) = DA*DX(I+4)
+         END DO
+      ELSE
+*
+*        code for increment not equal to 1
+*
+         NINCX = N*INCX
+         DO I = 1,NINCX,INCX
+            DX(I) = DA*DX(I)
+         END DO
+      END IF
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dtrmm.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dtrmm.f
new file mode 100644
index 00000000..cbd5ce70
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dtrmm.f
@@ -0,0 +1,415 @@
+*> \brief \b DTRMM
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
+* 
+*       .. Scalar Arguments ..
+*       DOUBLE PRECISION ALPHA
+*       INTEGER LDA,LDB,M,N
+*       CHARACTER DIAG,SIDE,TRANSA,UPLO
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION A(LDA,*),B(LDB,*)
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DTRMM  performs one of the matrix-matrix operations
+*>
+*>    B := alpha*op( A )*B,   or   B := alpha*B*op( A ),
+*>
+*> where  alpha  is a scalar,  B  is an m by n matrix,  A  is a unit, or
+*> non-unit,  upper or lower triangular matrix  and  op( A )  is one  of
+*>
+*>    op( A ) = A   or   op( A ) = A**T.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] SIDE
+*> \verbatim
+*>          SIDE is CHARACTER*1
+*>           On entry,  SIDE specifies whether  op( A ) multiplies B from
+*>           the left or right as follows:
+*>
+*>              SIDE = 'L' or 'l'   B := alpha*op( A )*B.
+*>
+*>              SIDE = 'R' or 'r'   B := alpha*B*op( A ).
+*> \endverbatim
+*>
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>           On entry, UPLO specifies whether the matrix A is an upper or
+*>           lower triangular matrix as follows:
+*>
+*>              UPLO = 'U' or 'u'   A is an upper triangular matrix.
+*>
+*>              UPLO = 'L' or 'l'   A is a lower triangular matrix.
+*> \endverbatim
+*>
+*> \param[in] TRANSA
+*> \verbatim
+*>          TRANSA is CHARACTER*1
+*>           On entry, TRANSA specifies the form of op( A ) to be used in
+*>           the matrix multiplication as follows:
+*>
+*>              TRANSA = 'N' or 'n'   op( A ) = A.
+*>
+*>              TRANSA = 'T' or 't'   op( A ) = A**T.
+*>
+*>              TRANSA = 'C' or 'c'   op( A ) = A**T.
+*> \endverbatim
+*>
+*> \param[in] DIAG
+*> \verbatim
+*>          DIAG is CHARACTER*1
+*>           On entry, DIAG specifies whether or not A is unit triangular
+*>           as follows:
+*>
+*>              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
+*>
+*>              DIAG = 'N' or 'n'   A is not assumed to be unit
+*>                                  triangular.
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*>          M is INTEGER
+*>           On entry, M specifies the number of rows of B. M must be at
+*>           least zero.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>           On entry, N specifies the number of columns of B.  N must be
+*>           at least zero.
+*> \endverbatim
+*>
+*> \param[in] ALPHA
+*> \verbatim
+*>          ALPHA is DOUBLE PRECISION.
+*>           On entry,  ALPHA specifies the scalar  alpha. When  alpha is
+*>           zero then  A is not referenced and  B need not be set before
+*>           entry.
+*> \endverbatim
+*>
+*> \param[in] A
+*> \verbatim
+*>           A is DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m
+*>           when  SIDE = 'L' or 'l'  and is  n  when  SIDE = 'R' or 'r'.
+*>           Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k
+*>           upper triangular part of the array  A must contain the upper
+*>           triangular matrix  and the strictly lower triangular part of
+*>           A is not referenced.
+*>           Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k
+*>           lower triangular part of the array  A must contain the lower
+*>           triangular matrix  and the strictly upper triangular part of
+*>           A is not referenced.
+*>           Note that when  DIAG = 'U' or 'u',  the diagonal elements of
+*>           A  are not referenced either,  but are assumed to be  unity.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>           On entry, LDA specifies the first dimension of A as declared
+*>           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
+*>           LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r'
+*>           then LDA must be at least max( 1, n ).
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*>          B is DOUBLE PRECISION array of DIMENSION ( LDB, n ).
+*>           Before entry,  the leading  m by n part of the array  B must
+*>           contain the matrix  B,  and  on exit  is overwritten  by the
+*>           transformed matrix.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*>          LDB is INTEGER
+*>           On entry, LDB specifies the first dimension of B as declared
+*>           in  the  calling  (sub)  program.   LDB  must  be  at  least
+*>           max( 1, m ).
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup double_blas_level3
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  Level 3 Blas routine.
+*>
+*>  -- Written on 8-February-1989.
+*>     Jack Dongarra, Argonne National Laboratory.
+*>     Iain Duff, AERE Harwell.
+*>     Jeremy Du Croz, Numerical Algorithms Group Ltd.
+*>     Sven Hammarling, Numerical Algorithms Group Ltd.
+*> \endverbatim
+*>
+*  =====================================================================
+      SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
+*
+*  -- Reference BLAS level3 routine (version 3.4.0) --
+*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2011
+*
+*     .. Scalar Arguments ..
+      DOUBLE PRECISION ALPHA
+      INTEGER LDA,LDB,M,N
+      CHARACTER DIAG,SIDE,TRANSA,UPLO
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION A(LDA,*),B(LDB,*)
+*     ..
+*
+*  =====================================================================
+*
+*     .. External Functions ..
+      LOGICAL LSAME
+      EXTERNAL LSAME
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC MAX
+*     ..
+*     .. Local Scalars ..
+      DOUBLE PRECISION TEMP
+      INTEGER I,INFO,J,K,NROWA
+      LOGICAL LSIDE,NOUNIT,UPPER
+*     ..
+*     .. Parameters ..
+      DOUBLE PRECISION ONE,ZERO
+      PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
+*     ..
+*
+*     Test the input parameters.
+*
+      LSIDE = LSAME(SIDE,'L')
+      IF (LSIDE) THEN
+          NROWA = M
+      ELSE
+          NROWA = N
+      END IF
+      NOUNIT = LSAME(DIAG,'N')
+      UPPER = LSAME(UPLO,'U')
+*
+      INFO = 0
+      IF ((.NOT.LSIDE) .AND. (.NOT.LSAME(SIDE,'R'))) THEN
+          INFO = 1
+      ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
+          INFO = 2
+      ELSE IF ((.NOT.LSAME(TRANSA,'N')) .AND.
+     +         (.NOT.LSAME(TRANSA,'T')) .AND.
+     +         (.NOT.LSAME(TRANSA,'C'))) THEN
+          INFO = 3
+      ELSE IF ((.NOT.LSAME(DIAG,'U')) .AND. (.NOT.LSAME(DIAG,'N'))) THEN
+          INFO = 4
+      ELSE IF (M.LT.0) THEN
+          INFO = 5
+      ELSE IF (N.LT.0) THEN
+          INFO = 6
+      ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
+          INFO = 9
+      ELSE IF (LDB.LT.MAX(1,M)) THEN
+          INFO = 11
+      END IF
+      IF (INFO.NE.0) THEN
+          CALL XERBLA('DTRMM ',INFO)
+          RETURN
+      END IF
+*
+*     Quick return if possible.
+*
+      IF (M.EQ.0 .OR. N.EQ.0) RETURN
+*
+*     And when  alpha.eq.zero.
+*
+      IF (ALPHA.EQ.ZERO) THEN
+          DO 20 J = 1,N
+              DO 10 I = 1,M
+                  B(I,J) = ZERO
+   10         CONTINUE
+   20     CONTINUE
+          RETURN
+      END IF
+*
+*     Start the operations.
+*
+      IF (LSIDE) THEN
+          IF (LSAME(TRANSA,'N')) THEN
+*
+*           Form  B := alpha*A*B.
+*
+              IF (UPPER) THEN
+                  DO 50 J = 1,N
+                      DO 40 K = 1,M
+                          IF (B(K,J).NE.ZERO) THEN
+                              TEMP = ALPHA*B(K,J)
+                              DO 30 I = 1,K - 1
+                                  B(I,J) = B(I,J) + TEMP*A(I,K)
+   30                         CONTINUE
+                              IF (NOUNIT) TEMP = TEMP*A(K,K)
+                              B(K,J) = TEMP
+                          END IF
+   40                 CONTINUE
+   50             CONTINUE
+              ELSE
+                  DO 80 J = 1,N
+                      DO 70 K = M,1,-1
+                          IF (B(K,J).NE.ZERO) THEN
+                              TEMP = ALPHA*B(K,J)
+                              B(K,J) = TEMP
+                              IF (NOUNIT) B(K,J) = B(K,J)*A(K,K)
+                              DO 60 I = K + 1,M
+                                  B(I,J) = B(I,J) + TEMP*A(I,K)
+   60                         CONTINUE
+                          END IF
+   70                 CONTINUE
+   80             CONTINUE
+              END IF
+          ELSE
+*
+*           Form  B := alpha*A**T*B.
+*
+              IF (UPPER) THEN
+                  DO 110 J = 1,N
+                      DO 100 I = M,1,-1
+                          TEMP = B(I,J)
+                          IF (NOUNIT) TEMP = TEMP*A(I,I)
+                          DO 90 K = 1,I - 1
+                              TEMP = TEMP + A(K,I)*B(K,J)
+   90                     CONTINUE
+                          B(I,J) = ALPHA*TEMP
+  100                 CONTINUE
+  110             CONTINUE
+              ELSE
+                  DO 140 J = 1,N
+                      DO 130 I = 1,M
+                          TEMP = B(I,J)
+                          IF (NOUNIT) TEMP = TEMP*A(I,I)
+                          DO 120 K = I + 1,M
+                              TEMP = TEMP + A(K,I)*B(K,J)
+  120                     CONTINUE
+                          B(I,J) = ALPHA*TEMP
+  130                 CONTINUE
+  140             CONTINUE
+              END IF
+          END IF
+      ELSE
+          IF (LSAME(TRANSA,'N')) THEN
+*
+*           Form  B := alpha*B*A.
+*
+              IF (UPPER) THEN
+                  DO 180 J = N,1,-1
+                      TEMP = ALPHA
+                      IF (NOUNIT) TEMP = TEMP*A(J,J)
+                      DO 150 I = 1,M
+                          B(I,J) = TEMP*B(I,J)
+  150                 CONTINUE
+                      DO 170 K = 1,J - 1
+                          IF (A(K,J).NE.ZERO) THEN
+                              TEMP = ALPHA*A(K,J)
+                              DO 160 I = 1,M
+                                  B(I,J) = B(I,J) + TEMP*B(I,K)
+  160                         CONTINUE
+                          END IF
+  170                 CONTINUE
+  180             CONTINUE
+              ELSE
+                  DO 220 J = 1,N
+                      TEMP = ALPHA
+                      IF (NOUNIT) TEMP = TEMP*A(J,J)
+                      DO 190 I = 1,M
+                          B(I,J) = TEMP*B(I,J)
+  190                 CONTINUE
+                      DO 210 K = J + 1,N
+                          IF (A(K,J).NE.ZERO) THEN
+                              TEMP = ALPHA*A(K,J)
+                              DO 200 I = 1,M
+                                  B(I,J) = B(I,J) + TEMP*B(I,K)
+  200                         CONTINUE
+                          END IF
+  210                 CONTINUE
+  220             CONTINUE
+              END IF
+          ELSE
+*
+*           Form  B := alpha*B*A**T.
+*
+              IF (UPPER) THEN
+                  DO 260 K = 1,N
+                      DO 240 J = 1,K - 1
+                          IF (A(J,K).NE.ZERO) THEN
+                              TEMP = ALPHA*A(J,K)
+                              DO 230 I = 1,M
+                                  B(I,J) = B(I,J) + TEMP*B(I,K)
+  230                         CONTINUE
+                          END IF
+  240                 CONTINUE
+                      TEMP = ALPHA
+                      IF (NOUNIT) TEMP = TEMP*A(K,K)
+                      IF (TEMP.NE.ONE) THEN
+                          DO 250 I = 1,M
+                              B(I,K) = TEMP*B(I,K)
+  250                     CONTINUE
+                      END IF
+  260             CONTINUE
+              ELSE
+                  DO 300 K = N,1,-1
+                      DO 280 J = K + 1,N
+                          IF (A(J,K).NE.ZERO) THEN
+                              TEMP = ALPHA*A(J,K)
+                              DO 270 I = 1,M
+                                  B(I,J) = B(I,J) + TEMP*B(I,K)
+  270                         CONTINUE
+                          END IF
+  280                 CONTINUE
+                      TEMP = ALPHA
+                      IF (NOUNIT) TEMP = TEMP*A(K,K)
+                      IF (TEMP.NE.ONE) THEN
+                          DO 290 I = 1,M
+                              B(I,K) = TEMP*B(I,K)
+  290                     CONTINUE
+                      END IF
+  300             CONTINUE
+              END IF
+          END IF
+      END IF
+*
+      RETURN
+*
+*     End of DTRMM .
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dtrmv.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dtrmv.f
new file mode 100644
index 00000000..71459fe7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/dtrmv.f
@@ -0,0 +1,342 @@
+*> \brief \b DTRMV
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
+* 
+*       .. Scalar Arguments ..
+*       INTEGER INCX,LDA,N
+*       CHARACTER DIAG,TRANS,UPLO
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION A(LDA,*),X(*)
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DTRMV  performs one of the matrix-vector operations
+*>
+*>    x := A*x,   or   x := A**T*x,
+*>
+*> where x is an n element vector and  A is an n by n unit, or non-unit,
+*> upper or lower triangular matrix.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>           On entry, UPLO specifies whether the matrix is an upper or
+*>           lower triangular matrix as follows:
+*>
+*>              UPLO = 'U' or 'u'   A is an upper triangular matrix.
+*>
+*>              UPLO = 'L' or 'l'   A is a lower triangular matrix.
+*> \endverbatim
+*>
+*> \param[in] TRANS
+*> \verbatim
+*>          TRANS is CHARACTER*1
+*>           On entry, TRANS specifies the operation to be performed as
+*>           follows:
+*>
+*>              TRANS = 'N' or 'n'   x := A*x.
+*>
+*>              TRANS = 'T' or 't'   x := A**T*x.
+*>
+*>              TRANS = 'C' or 'c'   x := A**T*x.
+*> \endverbatim
+*>
+*> \param[in] DIAG
+*> \verbatim
+*>          DIAG is CHARACTER*1
+*>           On entry, DIAG specifies whether or not A is unit
+*>           triangular as follows:
+*>
+*>              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
+*>
+*>              DIAG = 'N' or 'n'   A is not assumed to be unit
+*>                                  triangular.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>           On entry, N specifies the order of the matrix A.
+*>           N must be at least zero.
+*> \endverbatim
+*>
+*> \param[in] A
+*> \verbatim
+*>          A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
+*>           Before entry with  UPLO = 'U' or 'u', the leading n by n
+*>           upper triangular part of the array A must contain the upper
+*>           triangular matrix and the strictly lower triangular part of
+*>           A is not referenced.
+*>           Before entry with UPLO = 'L' or 'l', the leading n by n
+*>           lower triangular part of the array A must contain the lower
+*>           triangular matrix and the strictly upper triangular part of
+*>           A is not referenced.
+*>           Note that when  DIAG = 'U' or 'u', the diagonal elements of
+*>           A are not referenced either, but are assumed to be unity.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>           On entry, LDA specifies the first dimension of A as declared
+*>           in the calling (sub) program. LDA must be at least
+*>           max( 1, n ).
+*> \endverbatim
+*>
+*> \param[in,out] X
+*> \verbatim
+*>          X is DOUBLE PRECISION array of dimension at least
+*>           ( 1 + ( n - 1 )*abs( INCX ) ).
+*>           Before entry, the incremented array X must contain the n
+*>           element vector x. On exit, X is overwritten with the
+*>           tranformed vector x.
+*> \endverbatim
+*>
+*> \param[in] INCX
+*> \verbatim
+*>          INCX is INTEGER
+*>           On entry, INCX specifies the increment for the elements of
+*>           X. INCX must not be zero.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup double_blas_level2
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  Level 2 Blas routine.
+*>  The vector and matrix arguments are not referenced when N = 0, or M = 0
+*>
+*>  -- Written on 22-October-1986.
+*>     Jack Dongarra, Argonne National Lab.
+*>     Jeremy Du Croz, Nag Central Office.
+*>     Sven Hammarling, Nag Central Office.
+*>     Richard Hanson, Sandia National Labs.
+*> \endverbatim
+*>
+*  =====================================================================
+      SUBROUTINE DTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
+*
+*  -- Reference BLAS level2 routine (version 3.4.0) --
+*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2011
+*
+*     .. Scalar Arguments ..
+      INTEGER INCX,LDA,N
+      CHARACTER DIAG,TRANS,UPLO
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION A(LDA,*),X(*)
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION ZERO
+      PARAMETER (ZERO=0.0D+0)
+*     ..
+*     .. Local Scalars ..
+      DOUBLE PRECISION TEMP
+      INTEGER I,INFO,IX,J,JX,KX
+      LOGICAL NOUNIT
+*     ..
+*     .. External Functions ..
+      LOGICAL LSAME
+      EXTERNAL LSAME
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC MAX
+*     ..
+*
+*     Test the input parameters.
+*
+      INFO = 0
+      IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
+          INFO = 1
+      ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
+     +         .NOT.LSAME(TRANS,'C')) THEN
+          INFO = 2
+      ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
+          INFO = 3
+      ELSE IF (N.LT.0) THEN
+          INFO = 4
+      ELSE IF (LDA.LT.MAX(1,N)) THEN
+          INFO = 6
+      ELSE IF (INCX.EQ.0) THEN
+          INFO = 8
+      END IF
+      IF (INFO.NE.0) THEN
+          CALL XERBLA('DTRMV ',INFO)
+          RETURN
+      END IF
+*
+*     Quick return if possible.
+*
+      IF (N.EQ.0) RETURN
+*
+      NOUNIT = LSAME(DIAG,'N')
+*
+*     Set up the start point in X if the increment is not unity. This
+*     will be  ( N - 1 )*INCX  too small for descending loops.
+*
+      IF (INCX.LE.0) THEN
+          KX = 1 - (N-1)*INCX
+      ELSE IF (INCX.NE.1) THEN
+          KX = 1
+      END IF
+*
+*     Start the operations. In this version the elements of A are
+*     accessed sequentially with one pass through A.
+*
+      IF (LSAME(TRANS,'N')) THEN
+*
+*        Form  x := A*x.
+*
+          IF (LSAME(UPLO,'U')) THEN
+              IF (INCX.EQ.1) THEN
+                  DO 20 J = 1,N
+                      IF (X(J).NE.ZERO) THEN
+                          TEMP = X(J)
+                          DO 10 I = 1,J - 1
+                              X(I) = X(I) + TEMP*A(I,J)
+   10                     CONTINUE
+                          IF (NOUNIT) X(J) = X(J)*A(J,J)
+                      END IF
+   20             CONTINUE
+              ELSE
+                  JX = KX
+                  DO 40 J = 1,N
+                      IF (X(JX).NE.ZERO) THEN
+                          TEMP = X(JX)
+                          IX = KX
+                          DO 30 I = 1,J - 1
+                              X(IX) = X(IX) + TEMP*A(I,J)
+                              IX = IX + INCX
+   30                     CONTINUE
+                          IF (NOUNIT) X(JX) = X(JX)*A(J,J)
+                      END IF
+                      JX = JX + INCX
+   40             CONTINUE
+              END IF
+          ELSE
+              IF (INCX.EQ.1) THEN
+                  DO 60 J = N,1,-1
+                      IF (X(J).NE.ZERO) THEN
+                          TEMP = X(J)
+                          DO 50 I = N,J + 1,-1
+                              X(I) = X(I) + TEMP*A(I,J)
+   50                     CONTINUE
+                          IF (NOUNIT) X(J) = X(J)*A(J,J)
+                      END IF
+   60             CONTINUE
+              ELSE
+                  KX = KX + (N-1)*INCX
+                  JX = KX
+                  DO 80 J = N,1,-1
+                      IF (X(JX).NE.ZERO) THEN
+                          TEMP = X(JX)
+                          IX = KX
+                          DO 70 I = N,J + 1,-1
+                              X(IX) = X(IX) + TEMP*A(I,J)
+                              IX = IX - INCX
+   70                     CONTINUE
+                          IF (NOUNIT) X(JX) = X(JX)*A(J,J)
+                      END IF
+                      JX = JX - INCX
+   80             CONTINUE
+              END IF
+          END IF
+      ELSE
+*
+*        Form  x := A**T*x.
+*
+          IF (LSAME(UPLO,'U')) THEN
+              IF (INCX.EQ.1) THEN
+                  DO 100 J = N,1,-1
+                      TEMP = X(J)
+                      IF (NOUNIT) TEMP = TEMP*A(J,J)
+                      DO 90 I = J - 1,1,-1
+                          TEMP = TEMP + A(I,J)*X(I)
+   90                 CONTINUE
+                      X(J) = TEMP
+  100             CONTINUE
+              ELSE
+                  JX = KX + (N-1)*INCX
+                  DO 120 J = N,1,-1
+                      TEMP = X(JX)
+                      IX = JX
+                      IF (NOUNIT) TEMP = TEMP*A(J,J)
+                      DO 110 I = J - 1,1,-1
+                          IX = IX - INCX
+                          TEMP = TEMP + A(I,J)*X(IX)
+  110                 CONTINUE
+                      X(JX) = TEMP
+                      JX = JX - INCX
+  120             CONTINUE
+              END IF
+          ELSE
+              IF (INCX.EQ.1) THEN
+                  DO 140 J = 1,N
+                      TEMP = X(J)
+                      IF (NOUNIT) TEMP = TEMP*A(J,J)
+                      DO 130 I = J + 1,N
+                          TEMP = TEMP + A(I,J)*X(I)
+  130                 CONTINUE
+                      X(J) = TEMP
+  140             CONTINUE
+              ELSE
+                  JX = KX
+                  DO 160 J = 1,N
+                      TEMP = X(JX)
+                      IX = JX
+                      IF (NOUNIT) TEMP = TEMP*A(J,J)
+                      DO 150 I = J + 1,N
+                          IX = IX + INCX
+                          TEMP = TEMP + A(I,J)*X(IX)
+  150                 CONTINUE
+                      X(JX) = TEMP
+                      JX = JX + INCX
+  160             CONTINUE
+              END IF
+          END IF
+      END IF
+*
+      RETURN
+*
+*     End of DTRMV .
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/lsame.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/lsame.f
new file mode 100644
index 00000000..315304c3
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/lsame.f
@@ -0,0 +1,125 @@
+*> \brief \b LSAME
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*  Definition:
+*  ===========
+*
+*      LOGICAL FUNCTION LSAME( CA, CB )
+*
+*     .. Scalar Arguments ..
+*      CHARACTER          CA, CB
+*     ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> LSAME returns .TRUE. if CA is the same letter as CB regardless of
+*> case.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] CA
+*> \verbatim
+*> \endverbatim
+*>
+*> \param[in] CB
+*> \verbatim
+*>          CA and CB specify the single characters to be compared.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup auxOTHERauxiliary
+*
+*  =====================================================================
+      LOGICAL FUNCTION LSAME( CA, CB )
+*
+*  -- LAPACK auxiliary routine (version 3.4.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2011
+*
+*     .. Scalar Arguments ..
+      CHARACTER          CA, CB
+*     ..
+*
+* =====================================================================
+*
+*     .. Intrinsic Functions ..
+      INTRINSIC          ICHAR
+*     ..
+*     .. Local Scalars ..
+      INTEGER            INTA, INTB, ZCODE
+*     ..
+*     .. Executable Statements ..
+*
+*     Test if the characters are equal
+*
+      LSAME = CA.EQ.CB
+      IF( LSAME )
+     $   RETURN
+*
+*     Now test for equivalence if both characters are alphabetic.
+*
+      ZCODE = ICHAR( 'Z' )
+*
+*     Use 'Z' rather than 'A' so that ASCII can be detected on Prime
+*     machines, on which ICHAR returns a value with bit 8 set.
+*     ICHAR('A') on Prime machines returns 193 which is the same as
+*     ICHAR('A') on an EBCDIC machine.
+*
+      INTA = ICHAR( CA )
+      INTB = ICHAR( CB )
+*
+      IF( ZCODE.EQ.90 .OR. ZCODE.EQ.122 ) THEN
+*
+*        ASCII is assumed - ZCODE is the ASCII code of either lower or
+*        upper case 'Z'.
+*
+         IF( INTA.GE.97 .AND. INTA.LE.122 ) INTA = INTA - 32
+         IF( INTB.GE.97 .AND. INTB.LE.122 ) INTB = INTB - 32
+*
+      ELSE IF( ZCODE.EQ.233 .OR. ZCODE.EQ.169 ) THEN
+*
+*        EBCDIC is assumed - ZCODE is the EBCDIC code of either lower or
+*        upper case 'Z'.
+*
+         IF( INTA.GE.129 .AND. INTA.LE.137 .OR.
+     $       INTA.GE.145 .AND. INTA.LE.153 .OR.
+     $       INTA.GE.162 .AND. INTA.LE.169 ) INTA = INTA + 64
+         IF( INTB.GE.129 .AND. INTB.LE.137 .OR.
+     $       INTB.GE.145 .AND. INTB.LE.153 .OR.
+     $       INTB.GE.162 .AND. INTB.LE.169 ) INTB = INTB + 64
+*
+      ELSE IF( ZCODE.EQ.218 .OR. ZCODE.EQ.250 ) THEN
+*
+*        ASCII is assumed, on Prime machines - ZCODE is the ASCII code
+*        plus 128 of either lower or upper case 'Z'.
+*
+         IF( INTA.GE.225 .AND. INTA.LE.250 ) INTA = INTA - 32
+         IF( INTB.GE.225 .AND. INTB.LE.250 ) INTB = INTB - 32
+      END IF
+      LSAME = INTA.EQ.INTB
+*
+*     RETURN
+*
+*     End of LSAME
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/netlib.go b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/netlib.go
new file mode 100644
index 00000000..182e074a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/netlib.go
@@ -0,0 +1,68 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package netlib
+
+// void dlahr2_(int* n, int* k, int* nb, double* a, int* lda, double* tau, double* t, int* ldt, double* y, int* ldy);
+//
+// void dlaqr5_(int* wantt, int* wantz, int* kacc22, int* n, int* ktop, int* kbot, int* nshfts,
+//              double* sr, double* si, double* h, int* ldh, int* iloz, int* ihiz,
+//              double* z, int* ldz, double* v, int* ldv, double* u, int* ldu,
+//              int* nv, double* wv, int* ldwv, int* nh, double* wh, int* ldwh);
+import "C"
+
+func Dlahr2(n, k, nb int, a []float64, lda int, tau, t []float64, ldt int, y []float64, ldy int) {
+	func() {
+		n := C.int(n)
+		k := C.int(k)
+		nb := C.int(nb)
+		lda := C.int(lda)
+		ldt := C.int(ldt)
+		ldy := C.int(ldy)
+		C.dlahr2_((*C.int)(&n), (*C.int)(&k), (*C.int)(&nb),
+			(*C.double)(&a[0]), (*C.int)(&lda),
+			(*C.double)(&tau[0]),
+			(*C.double)(&t[0]), (*C.int)(&ldt),
+			(*C.double)(&y[0]), (*C.int)(&ldy))
+	}()
+}
+
+func Dlaqr5(wantt, wantz bool, kacc22 int, n, ktop, kbot int, nshfts int, sr, si []float64, h []float64,
+	ldh int, iloz, ihiz int, z []float64, ldz int, v []float64, ldv int,
+	u []float64, ldu int, nh int, wh []float64, ldwh int, nv int, wv []float64, ldwv int) {
+	func() {
+		wt := C.int(0)
+		if wantt {
+			wt = 1
+		}
+		wz := C.int(0)
+		if wantz {
+			wz = 1
+		}
+		kacc22 := C.int(kacc22)
+		n := C.int(n)
+		ktop := C.int(ktop)
+		kbot := C.int(kbot)
+		nshfts := C.int(nshfts)
+		ldh := C.int(ldh)
+		iloz := C.int(iloz)
+		ihiz := C.int(ihiz)
+		ldz := C.int(ldz)
+		ldv := C.int(ldv)
+		ldu := C.int(ldu)
+		nh := C.int(nh)
+		ldwh := C.int(ldwh)
+		nv := C.int(nv)
+		ldwv := C.int(ldwv)
+		C.dlaqr5_((*C.int)(&wt), (*C.int)(&wz), (*C.int)(&kacc22),
+			(*C.int)(&n), (*C.int)(&ktop), (*C.int)(&kbot),
+			(*C.int)(&nshfts), (*C.double)(&sr[0]), (*C.double)(&si[0]),
+			(*C.double)(&h[0]), (*C.int)(&ldh),
+			(*C.int)(&iloz), (*C.int)(&ihiz), (*C.double)(&z[0]), (*C.int)(&ldz),
+			(*C.double)(&v[0]), (*C.int)(&ldv),
+			(*C.double)(&u[0]), (*C.int)(&ldu),
+			(*C.int)(&nh), (*C.double)(&wh[0]), (*C.int)(&ldwh),
+			(*C.int)(&nv), (*C.double)(&wv[0]), (*C.int)(&ldwv))
+	}()
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/xerbla.f b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/xerbla.f
new file mode 100644
index 00000000..eb1c037d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/internal/testdata/netlib/xerbla.f
@@ -0,0 +1,89 @@
+*> \brief \b XERBLA
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE XERBLA( SRNAME, INFO )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER*(*)      SRNAME
+*       INTEGER            INFO
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> XERBLA  is an error handler for the LAPACK routines.
+*> It is called by an LAPACK routine if an input parameter has an
+*> invalid value.  A message is printed and execution stops.
+*>
+*> Installers may consider modifying the STOP statement in order to
+*> call system-specific exception-handling facilities.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] SRNAME
+*> \verbatim
+*>          SRNAME is CHARACTER*(*)
+*>          The name of the routine which called XERBLA.
+*> \endverbatim
+*>
+*> \param[in] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          The position of the invalid parameter in the parameter list
+*>          of the calling routine.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup aux_blas
+*
+*  =====================================================================
+      SUBROUTINE XERBLA( SRNAME, INFO )
+*
+*  -- Reference BLAS level1 routine (version 3.4.0) --
+*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2011
+*
+*     .. Scalar Arguments ..
+      CHARACTER*(*)      SRNAME
+      INTEGER            INFO
+*     ..
+*
+* =====================================================================
+*
+*     .. Intrinsic Functions ..
+      INTRINSIC          LEN_TRIM
+*     ..
+*     .. Executable Statements ..
+*
+      WRITE( *, FMT = 9999 )SRNAME( 1:LEN_TRIM( SRNAME ) ), INFO
+*
+      STOP
+*
+ 9999 FORMAT( ' ** On entry to ', A, ' parameter number ', I2, ' had ',
+     $      'an illegal value' )
+*
+*     End of XERBLA
+*
+      END
diff --git a/vendor/gonum.org/v1/gonum/lapack/lapack.go b/vendor/gonum.org/v1/gonum/lapack/lapack.go
new file mode 100644
index 00000000..c78d19c8
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/lapack.go
@@ -0,0 +1,188 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package lapack // import "gonum.org/v1/gonum/lapack"
+
+import "gonum.org/v1/gonum/blas"
+
+const None = 'N'
+
+type Job byte
+
+type Comp byte
+
+// Complex128 defines the public complex128 LAPACK API supported by gonum/lapack.
+type Complex128 interface{}
+
+// Float64 defines the public float64 LAPACK API supported by gonum/lapack.
+type Float64 interface {
+	Dgecon(norm MatrixNorm, n int, a []float64, lda int, anorm float64, work []float64, iwork []int) float64
+	Dgeev(jobvl LeftEVJob, jobvr RightEVJob, n int, a []float64, lda int, wr, wi []float64, vl []float64, ldvl int, vr []float64, ldvr int, work []float64, lwork int) (first int)
+	Dgels(trans blas.Transpose, m, n, nrhs int, a []float64, lda int, b []float64, ldb int, work []float64, lwork int) bool
+	Dgelqf(m, n int, a []float64, lda int, tau, work []float64, lwork int)
+	Dgeqrf(m, n int, a []float64, lda int, tau, work []float64, lwork int)
+	Dgesvd(jobU, jobVT SVDJob, m, n int, a []float64, lda int, s, u []float64, ldu int, vt []float64, ldvt int, work []float64, lwork int) (ok bool)
+	Dgetrf(m, n int, a []float64, lda int, ipiv []int) (ok bool)
+	Dgetri(n int, a []float64, lda int, ipiv []int, work []float64, lwork int) (ok bool)
+	Dgetrs(trans blas.Transpose, n, nrhs int, a []float64, lda int, ipiv []int, b []float64, ldb int)
+	Dggsvd3(jobU, jobV, jobQ GSVDJob, m, n, p int, a []float64, lda int, b []float64, ldb int, alpha, beta, u []float64, ldu int, v []float64, ldv int, q []float64, ldq int, work []float64, lwork int, iwork []int) (k, l int, ok bool)
+	Dlantr(norm MatrixNorm, uplo blas.Uplo, diag blas.Diag, m, n int, a []float64, lda int, work []float64) float64
+	Dlange(norm MatrixNorm, m, n int, a []float64, lda int, work []float64) float64
+	Dlansy(norm MatrixNorm, uplo blas.Uplo, n int, a []float64, lda int, work []float64) float64
+	Dlapmt(forward bool, m, n int, x []float64, ldx int, k []int)
+	Dormqr(side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64, lwork int)
+	Dormlq(side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64, lwork int)
+	Dpocon(uplo blas.Uplo, n int, a []float64, lda int, anorm float64, work []float64, iwork []int) float64
+	Dpotrf(ul blas.Uplo, n int, a []float64, lda int) (ok bool)
+	Dsyev(jobz EVJob, uplo blas.Uplo, n int, a []float64, lda int, w, work []float64, lwork int) (ok bool)
+	Dtrcon(norm MatrixNorm, uplo blas.Uplo, diag blas.Diag, n int, a []float64, lda int, work []float64, iwork []int) float64
+	Dtrtri(uplo blas.Uplo, diag blas.Diag, n int, a []float64, lda int) (ok bool)
+	Dtrtrs(uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, n, nrhs int, a []float64, lda int, b []float64, ldb int) (ok bool)
+}
+
+// Direct specifies the direction of the multiplication for the Householder matrix.
+type Direct byte
+
+const (
+	Forward  Direct = 'F' // Reflectors are right-multiplied, H_0 * H_1 * ... * H_{k-1}.
+	Backward Direct = 'B' // Reflectors are left-multiplied, H_{k-1} * ... * H_1 * H_0.
+)
+
+// Sort is the sorting order.
+type Sort byte
+
+const (
+	SortIncreasing Sort = 'I'
+	SortDecreasing Sort = 'D'
+)
+
+// StoreV indicates the storage direction of elementary reflectors.
+type StoreV byte
+
+const (
+	ColumnWise StoreV = 'C' // Reflector stored in a column of the matrix.
+	RowWise    StoreV = 'R' // Reflector stored in a row of the matrix.
+)
+
+// MatrixNorm represents the kind of matrix norm to compute.
+type MatrixNorm byte
+
+const (
+	MaxAbs       MatrixNorm = 'M' // max(abs(A(i,j)))  ('M')
+	MaxColumnSum MatrixNorm = 'O' // Maximum column sum (one norm) ('1', 'O')
+	MaxRowSum    MatrixNorm = 'I' // Maximum row sum (infinity norm) ('I', 'i')
+	NormFrob     MatrixNorm = 'F' // Frobenius norm (sqrt of sum of squares) ('F', 'f', E, 'e')
+)
+
+// MatrixType represents the kind of matrix represented in the data.
+type MatrixType byte
+
+const (
+	General  MatrixType = 'G' // A dense matrix (like blas64.General).
+	UpperTri MatrixType = 'U' // An upper triangular matrix.
+	LowerTri MatrixType = 'L' // A lower triangular matrix.
+)
+
+// Pivot specifies the pivot type for plane rotations
+type Pivot byte
+
+const (
+	Variable Pivot = 'V'
+	Top      Pivot = 'T'
+	Bottom   Pivot = 'B'
+)
+
+type DecompUpdate byte
+
+const (
+	ApplyP DecompUpdate = 'P'
+	ApplyQ DecompUpdate = 'Q'
+)
+
+// SVDJob specifies the singular vector computation type for SVD.
+type SVDJob byte
+
+const (
+	SVDAll       SVDJob = 'A' // Compute all singular vectors
+	SVDInPlace   SVDJob = 'S' // Compute the first singular vectors and store them in provided storage.
+	SVDOverwrite SVDJob = 'O' // Compute the singular vectors and store them in input matrix
+	SVDNone      SVDJob = 'N' // Do not compute singular vectors
+)
+
+// GSVDJob specifies the singular vector computation type for Generalized SVD.
+type GSVDJob byte
+
+const (
+	GSVDU    GSVDJob = 'U' // Compute orthogonal matrix U
+	GSVDV    GSVDJob = 'V' // Compute orthogonal matrix V
+	GSVDQ    GSVDJob = 'Q' // Compute orthogonal matrix Q
+	GSVDUnit GSVDJob = 'I' // Use unit-initialized matrix
+	GSVDNone GSVDJob = 'N' // Do not compute orthogonal matrix
+)
+
+// EVComp specifies how eigenvectors are computed.
+type EVComp byte
+
+const (
+	// OriginalEV specifies to compute the eigenvectors of the original
+	// matrix.
+	OriginalEV EVComp = 'V'
+	// TridiagEV specifies to compute both the eigenvectors of the input
+	// tridiagonal matrix.
+	TridiagEV EVComp = 'I'
+	// HessEV specifies to compute both the eigenvectors of the input upper
+	// Hessenberg matrix.
+	HessEV EVComp = 'I'
+
+	// UpdateSchur specifies that the matrix of Schur vectors will be
+	// updated by Dtrexc.
+	UpdateSchur EVComp = 'V'
+)
+
+// Job types for computation of eigenvectors.
+type (
+	EVJob      byte
+	LeftEVJob  byte
+	RightEVJob byte
+)
+
+// Job constants for computation of eigenvectors.
+const (
+	ComputeEV      EVJob      = 'V' // Compute eigenvectors in Dsyev.
+	ComputeLeftEV  LeftEVJob  = 'V' // Compute left eigenvectors.
+	ComputeRightEV RightEVJob = 'V' // Compute right eigenvectors.
+)
+
+// Jobs for Dgebal.
+const (
+	Permute      Job = 'P'
+	Scale        Job = 'S'
+	PermuteScale Job = 'B'
+)
+
+// Job constants for Dhseqr.
+const (
+	EigenvaluesOnly     EVJob = 'E'
+	EigenvaluesAndSchur EVJob = 'S'
+)
+
+// EVSide specifies what eigenvectors will be computed.
+type EVSide byte
+
+// EVSide constants for Dtrevc3.
+const (
+	RightEV     EVSide = 'R' // Compute right eigenvectors only.
+	LeftEV      EVSide = 'L' // Compute left eigenvectors only.
+	RightLeftEV EVSide = 'B' // Compute both right and left eigenvectors.
+)
+
+// HowMany specifies which eigenvectors will be computed.
+type HowMany byte
+
+// HowMany constants for Dhseqr.
+const (
+	AllEV      HowMany = 'A' // Compute all right and/or left eigenvectors.
+	AllEVMulQ  HowMany = 'B' // Compute all right and/or left eigenvectors multiplied by an input matrix.
+	SelectedEV HowMany = 'S' // Compute selected right and/or left eigenvectors.
+)
diff --git a/vendor/gonum.org/v1/gonum/lapack/lapack64/doc.go b/vendor/gonum.org/v1/gonum/lapack/lapack64/doc.go
new file mode 100644
index 00000000..07071df8
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/lapack64/doc.go
@@ -0,0 +1,20 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package lapack64 provides a set of convenient wrapper functions for LAPACK
+// calls, as specified in the netlib standard (www.netlib.org).
+//
+// The native Go routines are used by default, and the Use function can be used
+// to set an alternative implementation.
+//
+// If the type of matrix (General, Symmetric, etc.) is known and fixed, it is
+// used in the wrapper signature. In many cases, however, the type of the matrix
+// changes during the call to the routine, for example the matrix is symmetric on
+// entry and is triangular on exit. In these cases the correct types should be checked
+// in the documentation.
+//
+// The full set of Lapack functions is very large, and it is not clear that a
+// full implementation is desirable, let alone feasible. Please open up an issue
+// if there is a specific function you need and/or are willing to implement.
+package lapack64 // import "gonum.org/v1/gonum/lapack/lapack64"
diff --git a/vendor/gonum.org/v1/gonum/lapack/lapack64/lapack64.go b/vendor/gonum.org/v1/gonum/lapack/lapack64/lapack64.go
new file mode 100644
index 00000000..f93e9207
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/lapack64/lapack64.go
@@ -0,0 +1,545 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package lapack64
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+	"gonum.org/v1/gonum/lapack/gonum"
+)
+
+var lapack64 lapack.Float64 = gonum.Implementation{}
+
+// Use sets the LAPACK float64 implementation to be used by subsequent BLAS calls.
+// The default implementation is native.Implementation.
+func Use(l lapack.Float64) {
+	lapack64 = l
+}
+
+// Potrf computes the Cholesky factorization of a.
+// The factorization has the form
+//  A = U^T * U if a.Uplo == blas.Upper, or
+//  A = L * L^T if a.Uplo == blas.Lower,
+// where U is an upper triangular matrix and L is lower triangular.
+// The triangular matrix is returned in t, and the underlying data between
+// a and t is shared. The returned bool indicates whether a is positive
+// definite and the factorization could be finished.
+func Potrf(a blas64.Symmetric) (t blas64.Triangular, ok bool) {
+	ok = lapack64.Dpotrf(a.Uplo, a.N, a.Data, a.Stride)
+	t.Uplo = a.Uplo
+	t.N = a.N
+	t.Data = a.Data
+	t.Stride = a.Stride
+	t.Diag = blas.NonUnit
+	return
+}
+
+// Gecon estimates the reciprocal of the condition number of the n×n matrix A
+// given the LU decomposition of the matrix. The condition number computed may
+// be based on the 1-norm or the ∞-norm.
+//
+// a contains the result of the LU decomposition of A as computed by Getrf.
+//
+// anorm is the corresponding 1-norm or ∞-norm of the original matrix A.
+//
+// work is a temporary data slice of length at least 4*n and Gecon will panic otherwise.
+//
+// iwork is a temporary data slice of length at least n and Gecon will panic otherwise.
+func Gecon(norm lapack.MatrixNorm, a blas64.General, anorm float64, work []float64, iwork []int) float64 {
+	return lapack64.Dgecon(norm, a.Cols, a.Data, a.Stride, anorm, work, iwork)
+}
+
+// Gels finds a minimum-norm solution based on the matrices A and B using the
+// QR or LQ factorization. Gels returns false if the matrix
+// A is singular, and true if this solution was successfully found.
+//
+// The minimization problem solved depends on the input parameters.
+//
+//  1. If m >= n and trans == blas.NoTrans, Gels finds X such that || A*X - B||_2
+//     is minimized.
+//  2. If m < n and trans == blas.NoTrans, Gels finds the minimum norm solution of
+//     A * X = B.
+//  3. If m >= n and trans == blas.Trans, Gels finds the minimum norm solution of
+//     A^T * X = B.
+//  4. If m < n and trans == blas.Trans, Gels finds X such that || A*X - B||_2
+//     is minimized.
+// Note that the least-squares solutions (cases 1 and 3) perform the minimization
+// per column of B. This is not the same as finding the minimum-norm matrix.
+//
+// The matrix A is a general matrix of size m×n and is modified during this call.
+// The input matrix B is of size max(m,n)×nrhs, and serves two purposes. On entry,
+// the elements of b specify the input matrix B. B has size m×nrhs if
+// trans == blas.NoTrans, and n×nrhs if trans == blas.Trans. On exit, the
+// leading submatrix of b contains the solution vectors X. If trans == blas.NoTrans,
+// this submatrix is of size n×nrhs, and of size m×nrhs otherwise.
+//
+// Work is temporary storage, and lwork specifies the usable memory length.
+// At minimum, lwork >= max(m,n) + max(m,n,nrhs), and this function will panic
+// otherwise. A longer work will enable blocked algorithms to be called.
+// In the special case that lwork == -1, work[0] will be set to the optimal working
+// length.
+func Gels(trans blas.Transpose, a blas64.General, b blas64.General, work []float64, lwork int) bool {
+	return lapack64.Dgels(trans, a.Rows, a.Cols, b.Cols, a.Data, a.Stride, b.Data, b.Stride, work, lwork)
+}
+
+// Geqrf computes the QR factorization of the m×n matrix A using a blocked
+// algorithm. A is modified to contain the information to construct Q and R.
+// The upper triangle of a contains the matrix R. The lower triangular elements
+// (not including the diagonal) contain the elementary reflectors. tau is modified
+// to contain the reflector scales. tau must have length at least min(m,n), and
+// this function will panic otherwise.
+//
+// The ith elementary reflector can be explicitly constructed by first extracting
+// the
+//  v[j] = 0           j < i
+//  v[j] = 1           j == i
+//  v[j] = a[j*lda+i]  j > i
+// and computing H_i = I - tau[i] * v * v^T.
+//
+// The orthonormal matrix Q can be constucted from a product of these elementary
+// reflectors, Q = H_0 * H_1 * ... * H_{k-1}, where k = min(m,n).
+//
+// Work is temporary storage, and lwork specifies the usable memory length.
+// At minimum, lwork >= m and this function will panic otherwise.
+// Geqrf is a blocked QR factorization, but the block size is limited
+// by the temporary space available. If lwork == -1, instead of performing Geqrf,
+// the optimal work length will be stored into work[0].
+func Geqrf(a blas64.General, tau, work []float64, lwork int) {
+	lapack64.Dgeqrf(a.Rows, a.Cols, a.Data, a.Stride, tau, work, lwork)
+}
+
+// Gelqf computes the LQ factorization of the m×n matrix A using a blocked
+// algorithm. A is modified to contain the information to construct L and Q. The
+// lower triangle of a contains the matrix L. The elements above the diagonal
+// and the slice tau represent the matrix Q. tau is modified to contain the
+// reflector scales. tau must have length at least min(m,n), and this function
+// will panic otherwise.
+//
+// See Geqrf for a description of the elementary reflectors and orthonormal
+// matrix Q. Q is constructed as a product of these elementary reflectors,
+// Q = H_{k-1} * ... * H_1 * H_0.
+//
+// Work is temporary storage, and lwork specifies the usable memory length.
+// At minimum, lwork >= m and this function will panic otherwise.
+// Gelqf is a blocked LQ factorization, but the block size is limited
+// by the temporary space available. If lwork == -1, instead of performing Gelqf,
+// the optimal work length will be stored into work[0].
+func Gelqf(a blas64.General, tau, work []float64, lwork int) {
+	lapack64.Dgelqf(a.Rows, a.Cols, a.Data, a.Stride, tau, work, lwork)
+}
+
+// Gesvd computes the singular value decomposition of the input matrix A.
+//
+// The singular value decomposition is
+//  A = U * Sigma * V^T
+// where Sigma is an m×n diagonal matrix containing the singular values of A,
+// U is an m×m orthogonal matrix and V is an n×n orthogonal matrix. The first
+// min(m,n) columns of U and V are the left and right singular vectors of A
+// respectively.
+//
+// jobU and jobVT are options for computing the singular vectors. The behavior
+// is as follows
+//  jobU == lapack.SVDAll       All m columns of U are returned in u
+//  jobU == lapack.SVDInPlace   The first min(m,n) columns are returned in u
+//  jobU == lapack.SVDOverwrite The first min(m,n) columns of U are written into a
+//  jobU == lapack.SVDNone      The columns of U are not computed.
+// The behavior is the same for jobVT and the rows of V^T. At most one of jobU
+// and jobVT can equal lapack.SVDOverwrite, and Gesvd will panic otherwise.
+//
+// On entry, a contains the data for the m×n matrix A. During the call to Gesvd
+// the data is overwritten. On exit, A contains the appropriate singular vectors
+// if either job is lapack.SVDOverwrite.
+//
+// s is a slice of length at least min(m,n) and on exit contains the singular
+// values in decreasing order.
+//
+// u contains the left singular vectors on exit, stored columnwise. If
+// jobU == lapack.SVDAll, u is of size m×m. If jobU == lapack.SVDInPlace u is
+// of size m×min(m,n). If jobU == lapack.SVDOverwrite or lapack.SVDNone, u is
+// not used.
+//
+// vt contains the left singular vectors on exit, stored rowwise. If
+// jobV == lapack.SVDAll, vt is of size n×m. If jobVT == lapack.SVDInPlace vt is
+// of size min(m,n)×n. If jobVT == lapack.SVDOverwrite or lapack.SVDNone, vt is
+// not used.
+//
+// work is a slice for storing temporary memory, and lwork is the usable size of
+// the slice. lwork must be at least max(5*min(m,n), 3*min(m,n)+max(m,n)).
+// If lwork == -1, instead of performing Gesvd, the optimal work length will be
+// stored into work[0]. Gesvd will panic if the working memory has insufficient
+// storage.
+//
+// Gesvd returns whether the decomposition successfully completed.
+func Gesvd(jobU, jobVT lapack.SVDJob, a, u, vt blas64.General, s, work []float64, lwork int) (ok bool) {
+	return lapack64.Dgesvd(jobU, jobVT, a.Rows, a.Cols, a.Data, a.Stride, s, u.Data, u.Stride, vt.Data, vt.Stride, work, lwork)
+}
+
+// Getrf computes the LU decomposition of the m×n matrix A.
+// The LU decomposition is a factorization of A into
+//  A = P * L * U
+// where P is a permutation matrix, L is a unit lower triangular matrix, and
+// U is a (usually) non-unit upper triangular matrix. On exit, L and U are stored
+// in place into a.
+//
+// ipiv is a permutation vector. It indicates that row i of the matrix was
+// changed with ipiv[i]. ipiv must have length at least min(m,n), and will panic
+// otherwise. ipiv is zero-indexed.
+//
+// Getrf is the blocked version of the algorithm.
+//
+// Getrf returns whether the matrix A is singular. The LU decomposition will
+// be computed regardless of the singularity of A, but division by zero
+// will occur if the false is returned and the result is used to solve a
+// system of equations.
+func Getrf(a blas64.General, ipiv []int) bool {
+	return lapack64.Dgetrf(a.Rows, a.Cols, a.Data, a.Stride, ipiv)
+}
+
+// Getri computes the inverse of the matrix A using the LU factorization computed
+// by Getrf. On entry, a contains the PLU decomposition of A as computed by
+// Getrf and on exit contains the reciprocal of the original matrix.
+//
+// Getri will not perform the inversion if the matrix is singular, and returns
+// a boolean indicating whether the inversion was successful.
+//
+// Work is temporary storage, and lwork specifies the usable memory length.
+// At minimum, lwork >= n and this function will panic otherwise.
+// Getri is a blocked inversion, but the block size is limited
+// by the temporary space available. If lwork == -1, instead of performing Getri,
+// the optimal work length will be stored into work[0].
+func Getri(a blas64.General, ipiv []int, work []float64, lwork int) (ok bool) {
+	return lapack64.Dgetri(a.Cols, a.Data, a.Stride, ipiv, work, lwork)
+}
+
+// Getrs solves a system of equations using an LU factorization.
+// The system of equations solved is
+//  A * X = B if trans == blas.Trans
+//  A^T * X = B if trans == blas.NoTrans
+// A is a general n×n matrix with stride lda. B is a general matrix of size n×nrhs.
+//
+// On entry b contains the elements of the matrix B. On exit, b contains the
+// elements of X, the solution to the system of equations.
+//
+// a and ipiv contain the LU factorization of A and the permutation indices as
+// computed by Getrf. ipiv is zero-indexed.
+func Getrs(trans blas.Transpose, a blas64.General, b blas64.General, ipiv []int) {
+	lapack64.Dgetrs(trans, a.Cols, b.Cols, a.Data, a.Stride, ipiv, b.Data, b.Stride)
+}
+
+// Ggsvd3 computes the generalized singular value decomposition (GSVD)
+// of an m×n matrix A and p×n matrix B:
+//  U^T*A*Q = D1*[ 0 R ]
+//
+//  V^T*B*Q = D2*[ 0 R ]
+// where U, V and Q are orthogonal matrices.
+//
+// Ggsvd3 returns k and l, the dimensions of the sub-blocks. k+l
+// is the effective numerical rank of the (m+p)×n matrix [ A^T B^T ]^T.
+// R is a (k+l)×(k+l) nonsingular upper triangular matrix, D1 and
+// D2 are m×(k+l) and p×(k+l) diagonal matrices and of the following
+// structures, respectively:
+//
+// If m-k-l >= 0,
+//
+//                    k  l
+//       D1 =     k [ I  0 ]
+//                l [ 0  C ]
+//            m-k-l [ 0  0 ]
+//
+//                  k  l
+//       D2 = l   [ 0  S ]
+//            p-l [ 0  0 ]
+//
+//               n-k-l  k    l
+//  [ 0 R ] = k [  0   R11  R12 ] k
+//            l [  0    0   R22 ] l
+//
+// where
+//
+//  C = diag( alpha_k, ... , alpha_{k+l} ),
+//  S = diag( beta_k,  ... , beta_{k+l} ),
+//  C^2 + S^2 = I.
+//
+// R is stored in
+//  A[0:k+l, n-k-l:n]
+// on exit.
+//
+// If m-k-l < 0,
+//
+//                 k m-k k+l-m
+//      D1 =   k [ I  0    0  ]
+//           m-k [ 0  C    0  ]
+//
+//                   k m-k k+l-m
+//      D2 =   m-k [ 0  S    0  ]
+//           k+l-m [ 0  0    I  ]
+//             p-l [ 0  0    0  ]
+//
+//                 n-k-l  k   m-k  k+l-m
+//  [ 0 R ] =    k [ 0    R11  R12  R13 ]
+//             m-k [ 0     0   R22  R23 ]
+//           k+l-m [ 0     0    0   R33 ]
+//
+// where
+//  C = diag( alpha_k, ... , alpha_m ),
+//  S = diag( beta_k,  ... , beta_m ),
+//  C^2 + S^2 = I.
+//
+//  R = [ R11 R12 R13 ] is stored in A[1:m, n-k-l+1:n]
+//      [  0  R22 R23 ]
+// and R33 is stored in
+//  B[m-k:l, n+m-k-l:n] on exit.
+//
+// Ggsvd3 computes C, S, R, and optionally the orthogonal transformation
+// matrices U, V and Q.
+//
+// jobU, jobV and jobQ are options for computing the orthogonal matrices. The behavior
+// is as follows
+//  jobU == lapack.GSVDU        Compute orthogonal matrix U
+//  jobU == lapack.GSVDNone     Do not compute orthogonal matrix.
+// The behavior is the same for jobV and jobQ with the exception that instead of
+// lapack.GSVDU these accept lapack.GSVDV and lapack.GSVDQ respectively.
+// The matrices U, V and Q must be m×m, p×p and n×n respectively unless the
+// relevant job parameter is lapack.GSVDNone.
+//
+// alpha and beta must have length n or Ggsvd3 will panic. On exit, alpha and
+// beta contain the generalized singular value pairs of A and B
+//   alpha[0:k] = 1,
+//   beta[0:k]  = 0,
+// if m-k-l >= 0,
+//   alpha[k:k+l] = diag(C),
+//   beta[k:k+l]  = diag(S),
+// if m-k-l < 0,
+//   alpha[k:m]= C, alpha[m:k+l]= 0
+//   beta[k:m] = S, beta[m:k+l] = 1.
+// if k+l < n,
+//   alpha[k+l:n] = 0 and
+//   beta[k+l:n]  = 0.
+//
+// On exit, iwork contains the permutation required to sort alpha descending.
+//
+// iwork must have length n, work must have length at least max(1, lwork), and
+// lwork must be -1 or greater than n, otherwise Ggsvd3 will panic. If
+// lwork is -1, work[0] holds the optimal lwork on return, but Ggsvd3 does
+// not perform the GSVD.
+func Ggsvd3(jobU, jobV, jobQ lapack.GSVDJob, a, b blas64.General, alpha, beta []float64, u, v, q blas64.General, work []float64, lwork int, iwork []int) (k, l int, ok bool) {
+	return lapack64.Dggsvd3(jobU, jobV, jobQ, a.Rows, a.Cols, b.Rows, a.Data, a.Stride, b.Data, b.Stride, alpha, beta, u.Data, u.Stride, v.Data, v.Stride, q.Data, q.Stride, work, lwork, iwork)
+}
+
+// Lange computes the matrix norm of the general m×n matrix A. The input norm
+// specifies the norm computed.
+//  lapack.MaxAbs: the maximum absolute value of an element.
+//  lapack.MaxColumnSum: the maximum column sum of the absolute values of the entries.
+//  lapack.MaxRowSum: the maximum row sum of the absolute values of the entries.
+//  lapack.Frobenius: the square root of the sum of the squares of the entries.
+// If norm == lapack.MaxColumnSum, work must be of length n, and this function will panic otherwise.
+// There are no restrictions on work for the other matrix norms.
+func Lange(norm lapack.MatrixNorm, a blas64.General, work []float64) float64 {
+	return lapack64.Dlange(norm, a.Rows, a.Cols, a.Data, a.Stride, work)
+}
+
+// Lansy computes the specified norm of an n×n symmetric matrix. If
+// norm == lapack.MaxColumnSum or norm == lapackMaxRowSum work must have length
+// at least n and this function will panic otherwise.
+// There are no restrictions on work for the other matrix norms.
+func Lansy(norm lapack.MatrixNorm, a blas64.Symmetric, work []float64) float64 {
+	return lapack64.Dlansy(norm, a.Uplo, a.N, a.Data, a.Stride, work)
+}
+
+// Lantr computes the specified norm of an m×n trapezoidal matrix A. If
+// norm == lapack.MaxColumnSum work must have length at least n and this function
+// will panic otherwise. There are no restrictions on work for the other matrix norms.
+func Lantr(norm lapack.MatrixNorm, a blas64.Triangular, work []float64) float64 {
+	return lapack64.Dlantr(norm, a.Uplo, a.Diag, a.N, a.N, a.Data, a.Stride, work)
+}
+
+// Lapmt rearranges the columns of the m×n matrix X as specified by the
+// permutation k_0, k_1, ..., k_{n-1} of the integers 0, ..., n-1.
+//
+// If forward is true a forward permutation is performed:
+//
+//  X[0:m, k[j]] is moved to X[0:m, j] for j = 0, 1, ..., n-1.
+//
+// otherwise a backward permutation is performed:
+//
+//  X[0:m, j] is moved to X[0:m, k[j]] for j = 0, 1, ..., n-1.
+//
+// k must have length n, otherwise Lapmt will panic. k is zero-indexed.
+func Lapmt(forward bool, x blas64.General, k []int) {
+	lapack64.Dlapmt(forward, x.Rows, x.Cols, x.Data, x.Stride, k)
+}
+
+// Ormlq multiplies the matrix C by the othogonal matrix Q defined by
+// A and tau. A and tau are as returned from Gelqf.
+//  C = Q * C    if side == blas.Left and trans == blas.NoTrans
+//  C = Q^T * C  if side == blas.Left and trans == blas.Trans
+//  C = C * Q    if side == blas.Right and trans == blas.NoTrans
+//  C = C * Q^T  if side == blas.Right and trans == blas.Trans
+// If side == blas.Left, A is a matrix of side k×m, and if side == blas.Right
+// A is of size k×n. This uses a blocked algorithm.
+//
+// Work is temporary storage, and lwork specifies the usable memory length.
+// At minimum, lwork >= m if side == blas.Left and lwork >= n if side == blas.Right,
+// and this function will panic otherwise.
+// Ormlq uses a block algorithm, but the block size is limited
+// by the temporary space available. If lwork == -1, instead of performing Ormlq,
+// the optimal work length will be stored into work[0].
+//
+// Tau contains the Householder scales and must have length at least k, and
+// this function will panic otherwise.
+func Ormlq(side blas.Side, trans blas.Transpose, a blas64.General, tau []float64, c blas64.General, work []float64, lwork int) {
+	lapack64.Dormlq(side, trans, c.Rows, c.Cols, a.Rows, a.Data, a.Stride, tau, c.Data, c.Stride, work, lwork)
+}
+
+// Ormqr multiplies an m×n matrix C by an orthogonal matrix Q as
+//  C = Q * C,    if side == blas.Left  and trans == blas.NoTrans,
+//  C = Q^T * C,  if side == blas.Left  and trans == blas.Trans,
+//  C = C * Q,    if side == blas.Right and trans == blas.NoTrans,
+//  C = C * Q^T,  if side == blas.Right and trans == blas.Trans,
+// where Q is defined as the product of k elementary reflectors
+//  Q = H_0 * H_1 * ... * H_{k-1}.
+//
+// If side == blas.Left, A is an m×k matrix and 0 <= k <= m.
+// If side == blas.Right, A is an n×k matrix and 0 <= k <= n.
+// The ith column of A contains the vector which defines the elementary
+// reflector H_i and tau[i] contains its scalar factor. tau must have length k
+// and Ormqr will panic otherwise. Geqrf returns A and tau in the required
+// form.
+//
+// work must have length at least max(1,lwork), and lwork must be at least n if
+// side == blas.Left and at least m if side == blas.Right, otherwise Ormqr will
+// panic.
+//
+// work is temporary storage, and lwork specifies the usable memory length. At
+// minimum, lwork >= m if side == blas.Left and lwork >= n if side ==
+// blas.Right, and this function will panic otherwise. Larger values of lwork
+// will generally give better performance. On return, work[0] will contain the
+// optimal value of lwork.
+//
+// If lwork is -1, instead of performing Ormqr, the optimal workspace size will
+// be stored into work[0].
+func Ormqr(side blas.Side, trans blas.Transpose, a blas64.General, tau []float64, c blas64.General, work []float64, lwork int) {
+	lapack64.Dormqr(side, trans, c.Rows, c.Cols, a.Cols, a.Data, a.Stride, tau, c.Data, c.Stride, work, lwork)
+}
+
+// Pocon estimates the reciprocal of the condition number of a positive-definite
+// matrix A given the Cholesky decmposition of A. The condition number computed
+// is based on the 1-norm and the ∞-norm.
+//
+// anorm is the 1-norm and the ∞-norm of the original matrix A.
+//
+// work is a temporary data slice of length at least 3*n and Pocon will panic otherwise.
+//
+// iwork is a temporary data slice of length at least n and Pocon will panic otherwise.
+func Pocon(a blas64.Symmetric, anorm float64, work []float64, iwork []int) float64 {
+	return lapack64.Dpocon(a.Uplo, a.N, a.Data, a.Stride, anorm, work, iwork)
+}
+
+// Syev computes all eigenvalues and, optionally, the eigenvectors of a real
+// symmetric matrix A.
+//
+// w contains the eigenvalues in ascending order upon return. w must have length
+// at least n, and Syev will panic otherwise.
+//
+// On entry, a contains the elements of the symmetric matrix A in the triangular
+// portion specified by uplo. If jobz == lapack.ComputeEV a contains the
+// orthonormal eigenvectors of A on exit, otherwise on exit the specified
+// triangular region is overwritten.
+//
+// Work is temporary storage, and lwork specifies the usable memory length. At minimum,
+// lwork >= 3*n-1, and Syev will panic otherwise. The amount of blocking is
+// limited by the usable length. If lwork == -1, instead of computing Syev the
+// optimal work length is stored into work[0].
+func Syev(jobz lapack.EVJob, a blas64.Symmetric, w, work []float64, lwork int) (ok bool) {
+	return lapack64.Dsyev(jobz, a.Uplo, a.N, a.Data, a.Stride, w, work, lwork)
+}
+
+// Trcon estimates the reciprocal of the condition number of a triangular matrix A.
+// The condition number computed may be based on the 1-norm or the ∞-norm.
+//
+// work is a temporary data slice of length at least 3*n and Trcon will panic otherwise.
+//
+// iwork is a temporary data slice of length at least n and Trcon will panic otherwise.
+func Trcon(norm lapack.MatrixNorm, a blas64.Triangular, work []float64, iwork []int) float64 {
+	return lapack64.Dtrcon(norm, a.Uplo, a.Diag, a.N, a.Data, a.Stride, work, iwork)
+}
+
+// Trtri computes the inverse of a triangular matrix, storing the result in place
+// into a.
+//
+// Trtri will not perform the inversion if the matrix is singular, and returns
+// a boolean indicating whether the inversion was successful.
+func Trtri(a blas64.Triangular) (ok bool) {
+	return lapack64.Dtrtri(a.Uplo, a.Diag, a.N, a.Data, a.Stride)
+}
+
+// Trtrs solves a triangular system of the form A * X = B or A^T * X = B. Trtrs
+// returns whether the solve completed successfully. If A is singular, no solve is performed.
+func Trtrs(trans blas.Transpose, a blas64.Triangular, b blas64.General) (ok bool) {
+	return lapack64.Dtrtrs(a.Uplo, trans, a.Diag, a.N, b.Cols, a.Data, a.Stride, b.Data, b.Stride)
+}
+
+// Geev computes the eigenvalues and, optionally, the left and/or right
+// eigenvectors for an n×n real nonsymmetric matrix A.
+//
+// The right eigenvector v_j of A corresponding to an eigenvalue λ_j
+// is defined by
+//  A v_j = λ_j v_j,
+// and the left eigenvector u_j corresponding to an eigenvalue λ_j is defined by
+//  u_j^H A = λ_j u_j^H,
+// where u_j^H is the conjugate transpose of u_j.
+//
+// On return, A will be overwritten and the left and right eigenvectors will be
+// stored, respectively, in the columns of the n×n matrices VL and VR in the
+// same order as their eigenvalues. If the j-th eigenvalue is real, then
+//  u_j = VL[:,j],
+//  v_j = VR[:,j],
+// and if it is not real, then j and j+1 form a complex conjugate pair and the
+// eigenvectors can be recovered as
+//  u_j     = VL[:,j] + i*VL[:,j+1],
+//  u_{j+1} = VL[:,j] - i*VL[:,j+1],
+//  v_j     = VR[:,j] + i*VR[:,j+1],
+//  v_{j+1} = VR[:,j] - i*VR[:,j+1],
+// where i is the imaginary unit. The computed eigenvectors are normalized to
+// have Euclidean norm equal to 1 and largest component real.
+//
+// Left eigenvectors will be computed only if jobvl == lapack.ComputeLeftEV,
+// otherwise jobvl must be lapack.None.
+// Right eigenvectors will be computed only if jobvr == lapack.ComputeRightEV,
+// otherwise jobvr must be lapack.None.
+// For other values of jobvl and jobvr Geev will panic.
+//
+// On return, wr and wi will contain the real and imaginary parts, respectively,
+// of the computed eigenvalues. Complex conjugate pairs of eigenvalues appear
+// consecutively with the eigenvalue having the positive imaginary part first.
+// wr and wi must have length n, and Geev will panic otherwise.
+//
+// work must have length at least lwork and lwork must be at least max(1,4*n) if
+// the left or right eigenvectors are computed, and at least max(1,3*n) if no
+// eigenvectors are computed. For good performance, lwork must generally be
+// larger. On return, optimal value of lwork will be stored in work[0].
+//
+// If lwork == -1, instead of performing Geev, the function only calculates the
+// optimal vaule of lwork and stores it into work[0].
+//
+// On return, first will be the index of the first valid eigenvalue.
+// If first == 0, all eigenvalues and eigenvectors have been computed.
+// If first is positive, Geev failed to compute all the eigenvalues, no
+// eigenvectors have been computed and wr[first:] and wi[first:] contain those
+// eigenvalues which have converged.
+func Geev(jobvl lapack.LeftEVJob, jobvr lapack.RightEVJob, a blas64.General, wr, wi []float64, vl, vr blas64.General, work []float64, lwork int) (first int) {
+	n := a.Rows
+	if a.Cols != n {
+		panic("lapack64: matrix not square")
+	}
+	if jobvl == lapack.ComputeLeftEV && (vl.Rows != n || vl.Cols != n) {
+		panic("lapack64: bad size of VL")
+	}
+	if jobvr == lapack.ComputeRightEV && (vr.Rows != n || vr.Cols != n) {
+		panic("lapack64: bad size of VR")
+	}
+	return lapack64.Dgeev(jobvl, jobvr, n, a.Data, a.Stride, wr, wi, vl.Data, vl.Stride, vr.Data, vr.Stride, work, lwork)
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dbdsqr.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dbdsqr.go
new file mode 100644
index 00000000..e52fd9dd
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dbdsqr.go
@@ -0,0 +1,198 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math/rand"
+	"sort"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dbdsqrer interface {
+	Dbdsqr(uplo blas.Uplo, n, ncvt, nru, ncc int, d, e, vt []float64, ldvt int, u []float64, ldu int, c []float64, ldc int, work []float64) (ok bool)
+}
+
+func DbdsqrTest(t *testing.T, impl Dbdsqrer) {
+	rnd := rand.New(rand.NewSource(1))
+	bi := blas64.Implementation()
+	_ = bi
+	for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
+		for _, test := range []struct {
+			n, ncvt, nru, ncc, ldvt, ldu, ldc int
+		}{
+			{5, 5, 5, 5, 0, 0, 0},
+			{10, 10, 10, 10, 0, 0, 0},
+			{10, 11, 12, 13, 0, 0, 0},
+			{20, 13, 12, 11, 0, 0, 0},
+
+			{5, 5, 5, 5, 6, 7, 8},
+			{10, 10, 10, 10, 30, 40, 50},
+			{10, 12, 11, 13, 30, 40, 50},
+			{20, 12, 13, 11, 30, 40, 50},
+
+			{130, 130, 130, 500, 900, 900, 500},
+		} {
+			for cas := 0; cas < 10; cas++ {
+				n := test.n
+				ncvt := test.ncvt
+				nru := test.nru
+				ncc := test.ncc
+				ldvt := test.ldvt
+				ldu := test.ldu
+				ldc := test.ldc
+				if ldvt == 0 {
+					ldvt = ncvt
+				}
+				if ldu == 0 {
+					ldu = n
+				}
+				if ldc == 0 {
+					ldc = ncc
+				}
+
+				d := make([]float64, n)
+				for i := range d {
+					d[i] = rnd.NormFloat64()
+				}
+				e := make([]float64, n-1)
+				for i := range e {
+					e[i] = rnd.NormFloat64()
+				}
+				dCopy := make([]float64, len(d))
+				copy(dCopy, d)
+				eCopy := make([]float64, len(e))
+				copy(eCopy, e)
+				work := make([]float64, 4*n)
+				for i := range work {
+					work[i] = rnd.NormFloat64()
+				}
+
+				// First test the decomposition of the bidiagonal matrix. Set
+				// pt and u equal to I with the correct size. At the result
+				// of Dbdsqr, p and u  will contain the data of P^T and Q, which
+				// will be used in the next step to test the multiplication
+				// with Q and VT.
+
+				q := make([]float64, n*n)
+				ldq := n
+				pt := make([]float64, n*n)
+				ldpt := n
+				for i := 0; i < n; i++ {
+					q[i*ldq+i] = 1
+				}
+				for i := 0; i < n; i++ {
+					pt[i*ldpt+i] = 1
+				}
+
+				ok := impl.Dbdsqr(uplo, n, n, n, 0, d, e, pt, ldpt, q, ldq, nil, 0, work)
+
+				isUpper := uplo == blas.Upper
+				errStr := fmt.Sprintf("isUpper = %v, n = %v, ncvt = %v, nru = %v, ncc = %v", isUpper, n, ncvt, nru, ncc)
+				if !ok {
+					t.Errorf("Unexpected Dbdsqr failure: %s", errStr)
+				}
+
+				bMat := constructBidiagonal(uplo, n, dCopy, eCopy)
+				sMat := constructBidiagonal(uplo, n, d, e)
+
+				tmp := blas64.General{
+					Rows:   n,
+					Cols:   n,
+					Stride: n,
+					Data:   make([]float64, n*n),
+				}
+				ansMat := blas64.General{
+					Rows:   n,
+					Cols:   n,
+					Stride: n,
+					Data:   make([]float64, n*n),
+				}
+
+				bi.Dgemm(blas.NoTrans, blas.NoTrans, n, n, n, 1, q, ldq, sMat.Data, sMat.Stride, 0, tmp.Data, tmp.Stride)
+				bi.Dgemm(blas.NoTrans, blas.NoTrans, n, n, n, 1, tmp.Data, tmp.Stride, pt, ldpt, 0, ansMat.Data, ansMat.Stride)
+
+				same := true
+				for i := 0; i < n; i++ {
+					for j := 0; j < n; j++ {
+						if !floats.EqualWithinAbsOrRel(ansMat.Data[i*ansMat.Stride+j], bMat.Data[i*bMat.Stride+j], 1e-8, 1e-8) {
+							same = false
+						}
+					}
+				}
+				if !same {
+					t.Errorf("Bidiagonal mismatch. %s", errStr)
+				}
+				if !sort.IsSorted(sort.Reverse(sort.Float64Slice(d))) {
+					t.Errorf("D is not sorted. %s", errStr)
+				}
+
+				// The above computed the real P and Q. Now input data for V^T,
+				// U, and C to check that the multiplications happen properly.
+				dAns := make([]float64, len(d))
+				copy(dAns, d)
+				eAns := make([]float64, len(e))
+				copy(eAns, e)
+
+				u := make([]float64, nru*ldu)
+				for i := range u {
+					u[i] = rnd.NormFloat64()
+				}
+				uCopy := make([]float64, len(u))
+				copy(uCopy, u)
+				vt := make([]float64, n*ldvt)
+				for i := range vt {
+					vt[i] = rnd.NormFloat64()
+				}
+				vtCopy := make([]float64, len(vt))
+				copy(vtCopy, vt)
+				c := make([]float64, n*ldc)
+				for i := range c {
+					c[i] = rnd.NormFloat64()
+				}
+				cCopy := make([]float64, len(c))
+				copy(cCopy, c)
+
+				// Reset input data
+				copy(d, dCopy)
+				copy(e, eCopy)
+				impl.Dbdsqr(uplo, n, ncvt, nru, ncc, d, e, vt, ldvt, u, ldu, c, ldc, work)
+
+				// Check result.
+				if !floats.EqualApprox(d, dAns, 1e-14) {
+					t.Errorf("D mismatch second time. %s", errStr)
+				}
+				if !floats.EqualApprox(e, eAns, 1e-14) {
+					t.Errorf("E mismatch second time. %s", errStr)
+				}
+				ans := make([]float64, len(vtCopy))
+				copy(ans, vtCopy)
+				ldans := ldvt
+				bi.Dgemm(blas.NoTrans, blas.NoTrans, n, ncvt, n, 1, pt, ldpt, vtCopy, ldvt, 0, ans, ldans)
+				if !floats.EqualApprox(ans, vt, 1e-10) {
+					t.Errorf("Vt result mismatch. %s", errStr)
+				}
+				ans = make([]float64, len(uCopy))
+				copy(ans, uCopy)
+				ldans = ldu
+				bi.Dgemm(blas.NoTrans, blas.NoTrans, nru, n, n, 1, uCopy, ldu, q, ldq, 0, ans, ldans)
+				if !floats.EqualApprox(ans, u, 1e-10) {
+					t.Errorf("U result mismatch. %s", errStr)
+				}
+				ans = make([]float64, len(cCopy))
+				copy(ans, cCopy)
+				ldans = ldc
+				bi.Dgemm(blas.Trans, blas.NoTrans, n, ncc, n, 1, q, ldq, cCopy, ldc, 0, ans, ldans)
+				if !floats.EqualApprox(ans, c, 1e-10) {
+					t.Errorf("C result mismatch. %s", errStr)
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dgebak.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgebak.go
new file mode 100644
index 00000000..7d1030a4
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgebak.go
@@ -0,0 +1,110 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dgebaker interface {
+	Dgebak(job lapack.Job, side lapack.EVSide, n, ilo, ihi int, scale []float64, m int, v []float64, ldv int)
+}
+
+func DgebakTest(t *testing.T, impl Dgebaker) {
+	rnd := rand.New(rand.NewSource(1))
+
+	for _, job := range []lapack.Job{lapack.None, lapack.Permute, lapack.Scale, lapack.PermuteScale} {
+		for _, side := range []lapack.EVSide{lapack.LeftEV, lapack.RightEV} {
+			for _, n := range []int{0, 1, 2, 3, 4, 5, 6, 10, 18, 31, 53} {
+				for _, extra := range []int{0, 11} {
+					for cas := 0; cas < 100; cas++ {
+						m := rnd.Intn(n + 1)
+						v := randomGeneral(n, m, m+extra, rnd)
+						var ilo, ihi int
+						if v.Rows > 0 {
+							ihi = rnd.Intn(n)
+							ilo = rnd.Intn(ihi + 1)
+						} else {
+							ihi = -1
+						}
+						testDgebak(t, impl, job, side, ilo, ihi, v, rnd)
+					}
+				}
+			}
+		}
+	}
+}
+
+func testDgebak(t *testing.T, impl Dgebaker, job lapack.Job, side lapack.EVSide, ilo, ihi int, v blas64.General, rnd *rand.Rand) {
+	const tol = 1e-15
+	n := v.Rows
+	m := v.Cols
+	extra := v.Stride - v.Cols
+
+	// Create D and D^{-1} by generating random scales between ilo and ihi.
+	d := eye(n, n)
+	dinv := eye(n, n)
+	scale := nanSlice(n)
+	if job == lapack.Scale || job == lapack.PermuteScale {
+		if ilo == ihi {
+			scale[ilo] = 1
+		} else {
+			for i := ilo; i <= ihi; i++ {
+				scale[i] = 2 * rnd.Float64()
+				d.Data[i*d.Stride+i] = scale[i]
+				dinv.Data[i*dinv.Stride+i] = 1 / scale[i]
+			}
+		}
+	}
+
+	// Create P by generating random column swaps.
+	p := eye(n, n)
+	if job == lapack.Permute || job == lapack.PermuteScale {
+		// Make up some random permutations.
+		for i := n - 1; i > ihi; i-- {
+			scale[i] = float64(rnd.Intn(i + 1))
+			blas64.Swap(n,
+				blas64.Vector{p.Stride, p.Data[i:]},
+				blas64.Vector{p.Stride, p.Data[int(scale[i]):]})
+		}
+		for i := 0; i < ilo; i++ {
+			scale[i] = float64(i + rnd.Intn(ihi-i+1))
+			blas64.Swap(n,
+				blas64.Vector{p.Stride, p.Data[i:]},
+				blas64.Vector{p.Stride, p.Data[int(scale[i]):]})
+		}
+	}
+
+	got := cloneGeneral(v)
+	impl.Dgebak(job, side, n, ilo, ihi, scale, m, got.Data, got.Stride)
+
+	prefix := fmt.Sprintf("Case job=%v, side=%v, n=%v, ilo=%v, ihi=%v, m=%v, extra=%v",
+		job, side, n, ilo, ihi, m, extra)
+
+	if !generalOutsideAllNaN(got) {
+		t.Errorf("%v: out-of-range write to V\n%v", prefix, got.Data)
+	}
+
+	// Compute D*V or D^{-1}*V and store into dv.
+	dv := zeros(n, m, m)
+	if side == lapack.RightEV {
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, d, v, 0, dv)
+	} else {
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, dinv, v, 0, dv)
+	}
+	// Compute P*D*V or P*D^{-1}*V and store into want.
+	want := zeros(n, m, m)
+	blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, p, dv, 0, want)
+
+	if !equalApproxGeneral(want, got, tol) {
+		t.Errorf("%v: unexpected value of V", prefix)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dgebal.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgebal.go
new file mode 100644
index 00000000..b07ababf
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgebal.go
@@ -0,0 +1,175 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dgebaler interface {
+	Dgebal(job lapack.Job, n int, a []float64, lda int, scale []float64) (int, int)
+}
+
+func DgebalTest(t *testing.T, impl Dgebaler) {
+	rnd := rand.New(rand.NewSource(1))
+
+	for _, job := range []lapack.Job{lapack.None, lapack.Permute, lapack.Scale, lapack.PermuteScale} {
+		for _, n := range []int{0, 1, 2, 3, 4, 5, 6, 10, 18, 31, 53, 100} {
+			for _, extra := range []int{0, 11} {
+				for cas := 0; cas < 100; cas++ {
+					a := unbalancedSparseGeneral(n, n, n+extra, 2*n, rnd)
+					testDgebal(t, impl, job, a)
+				}
+			}
+		}
+	}
+}
+
+func testDgebal(t *testing.T, impl Dgebaler, job lapack.Job, a blas64.General) {
+	const tol = 1e-14
+
+	n := a.Rows
+	extra := a.Stride - n
+
+	var scale []float64
+	if n > 0 {
+		scale = nanSlice(n)
+	}
+
+	want := cloneGeneral(a)
+
+	ilo, ihi := impl.Dgebal(job, n, a.Data, a.Stride, scale)
+
+	prefix := fmt.Sprintf("Case job=%v, n=%v, extra=%v", job, n, extra)
+
+	if !generalOutsideAllNaN(a) {
+		t.Errorf("%v: out-of-range write to A\n%v", prefix, a.Data)
+	}
+
+	if n == 0 {
+		if ilo != 0 {
+			t.Errorf("%v: unexpected ilo when n=0. Want 0, got %v", prefix, ilo)
+		}
+		if ihi != -1 {
+			t.Errorf("%v: unexpected ihi when n=0. Want -1, got %v", prefix, ihi)
+		}
+		return
+	}
+
+	if job == lapack.None {
+		if ilo != 0 {
+			t.Errorf("%v: unexpected ilo when job=None. Want 0, got %v", prefix, ilo)
+		}
+		if ihi != n-1 {
+			t.Errorf("%v: unexpected ihi when job=None. Want %v, got %v", prefix, n-1, ihi)
+		}
+		k := -1
+		for i := range scale {
+			if scale[i] != 1 {
+				k = i
+				break
+			}
+		}
+		if k != -1 {
+			t.Errorf("%v: unexpected scale[%v] when job=None. Want 1, got %v", prefix, k, scale[k])
+		}
+		if !equalApproxGeneral(a, want, 0) {
+			t.Errorf("%v: unexpected modification of A when job=None", prefix)
+		}
+		return
+	}
+
+	if ilo < 0 || ihi < ilo || n <= ihi {
+		t.Errorf("%v: invalid ordering of ilo=%v and ihi=%v", prefix, ilo, ihi)
+	}
+
+	if ilo >= 2 && !isUpperTriangular(blas64.General{ilo - 1, ilo - 1, a.Stride, a.Data}) {
+		t.Errorf("%v: T1 is not upper triangular", prefix)
+	}
+	m := n - ihi - 1 // Order of T2.
+	k := ihi + 1
+	if m >= 2 && !isUpperTriangular(blas64.General{m, m, a.Stride, a.Data[k*a.Stride+k:]}) {
+		t.Errorf("%v: T2 is not upper triangular", prefix)
+	}
+
+	if job == lapack.Permute || job == lapack.PermuteScale {
+		// Check that all rows in [ilo:ihi+1] have at least one nonzero
+		// off-diagonal element.
+		zeroRow := -1
+		for i := ilo; i <= ihi; i++ {
+			onlyZeros := true
+			for j := ilo; j <= ihi; j++ {
+				if i != j && a.Data[i*a.Stride+j] != 0 {
+					onlyZeros = false
+					break
+				}
+			}
+			if onlyZeros {
+				zeroRow = i
+				break
+			}
+		}
+		if zeroRow != -1 && ilo != ihi {
+			t.Errorf("%v: row %v has only zero off-diagonal elements, ilo=%v, ihi=%v", prefix, zeroRow, ilo, ihi)
+		}
+		// Check that all columns in [ilo:ihi+1] have at least one nonzero
+		// off-diagonal element.
+		zeroCol := -1
+		for j := ilo; j <= ihi; j++ {
+			onlyZeros := true
+			for i := ilo; i <= ihi; i++ {
+				if i != j && a.Data[i*a.Stride+j] != 0 {
+					onlyZeros = false
+					break
+				}
+			}
+			if onlyZeros {
+				zeroCol = j
+				break
+			}
+		}
+		if zeroCol != -1 && ilo != ihi {
+			t.Errorf("%v: column %v has only zero off-diagonal elements, ilo=%v, ihi=%v", prefix, zeroCol, ilo, ihi)
+		}
+
+		// Create the permutation matrix P.
+		p := eye(n, n)
+		for j := n - 1; j > ihi; j-- {
+			blas64.Swap(n,
+				blas64.Vector{p.Stride, p.Data[j:]},
+				blas64.Vector{p.Stride, p.Data[int(scale[j]):]})
+		}
+		for j := 0; j < ilo; j++ {
+			blas64.Swap(n,
+				blas64.Vector{p.Stride, p.Data[j:]},
+				blas64.Vector{p.Stride, p.Data[int(scale[j]):]})
+		}
+		// Compute P^T*A*P and store into want.
+		ap := zeros(n, n, n)
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, want, p, 0, ap)
+		blas64.Gemm(blas.Trans, blas.NoTrans, 1, p, ap, 0, want)
+	}
+	if job == lapack.Scale || job == lapack.PermuteScale {
+		// Modify want by D and D^{-1}.
+		d := eye(n, n)
+		dinv := eye(n, n)
+		for i := ilo; i <= ihi; i++ {
+			d.Data[i*d.Stride+i] = scale[i]
+			dinv.Data[i*dinv.Stride+i] = 1 / scale[i]
+		}
+		ad := zeros(n, n, n)
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, want, d, 0, ad)
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, dinv, ad, 0, want)
+	}
+	if !equalApproxGeneral(want, a, tol) {
+		t.Errorf("%v: unexpected value of A, ilo=%v, ihi=%v", prefix, ilo, ihi)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dgebd2.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgebd2.go
new file mode 100644
index 00000000..f122c407
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgebd2.go
@@ -0,0 +1,54 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+)
+
+type Dgebd2er interface {
+	Dgebd2(m, n int, a []float64, lda int, d, e, tauq, taup, work []float64)
+}
+
+func Dgebd2Test(t *testing.T, impl Dgebd2er) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, test := range []struct {
+		m, n, lda int
+	}{
+		{3, 4, 0},
+		{4, 3, 0},
+		{3, 4, 10},
+		{4, 3, 10},
+	} {
+		m := test.m
+		n := test.n
+		lda := test.lda
+		if lda == 0 {
+			lda = n
+		}
+		nb := min(m, n) // 'nb' name parallel with Dlabrd code.
+		a := make([]float64, m*lda)
+		for i := range a {
+			a[i] = rnd.NormFloat64()
+		}
+		d := nanSlice(nb)
+		e := nanSlice(nb - 1)
+		tauP := nanSlice(nb)
+		tauQ := nanSlice(nb)
+		work := nanSlice(max(m, n))
+		aCopy := make([]float64, len(a))
+		copy(aCopy, a)
+		impl.Dgebd2(m, n, a, lda, d, e, tauQ, tauP, work)
+		if m >= n && nb == n {
+			tauP[n-1] = 0
+		}
+		if m < n && nb == m {
+			tauQ[m-1] = 0
+		}
+
+		checkBidiagonal(t, m, n, nb, a, lda, d, e, tauP, tauQ, aCopy)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dgebrd.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgebrd.go
new file mode 100644
index 00000000..0bbba460
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgebrd.go
@@ -0,0 +1,151 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dgebrder interface {
+	Dgebrd(m, n int, a []float64, lda int, d, e, tauQ, tauP, work []float64, lwork int)
+	Dgebd2er
+}
+
+func DgebrdTest(t *testing.T, impl Dgebrder) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, test := range []struct {
+		m, n, lda int
+	}{
+		{100, 100, 0},
+		{100, 150, 0},
+		{150, 100, 0},
+		{100, 100, 200},
+		{100, 150, 200},
+		{150, 100, 200},
+
+		{300, 300, 0},
+		{300, 400, 0},
+		{400, 300, 0},
+		{300, 300, 500},
+		{300, 400, 500},
+		{300, 400, 500},
+	} {
+		m := test.m
+		n := test.n
+		lda := test.lda
+		if lda == 0 {
+			lda = n
+		}
+		minmn := min(m, n)
+		a := make([]float64, m*lda)
+		for i := range a {
+			a[i] = rnd.NormFloat64()
+		}
+
+		d := make([]float64, minmn)
+		e := make([]float64, minmn-1)
+		tauP := make([]float64, minmn)
+		tauQ := make([]float64, minmn)
+		work := make([]float64, max(m, n))
+		for i := range work {
+			work[i] = math.NaN()
+		}
+
+		// Store a.
+		aCopy := make([]float64, len(a))
+		copy(aCopy, a)
+
+		// Compute the true answer with the unblocked algorithm.
+		impl.Dgebd2(m, n, a, lda, d, e, tauQ, tauP, work)
+		aAns := make([]float64, len(a))
+		copy(aAns, a)
+		dAns := make([]float64, len(d))
+		copy(dAns, d)
+		eAns := make([]float64, len(e))
+		copy(eAns, e)
+		tauQAns := make([]float64, len(tauQ))
+		copy(tauQAns, tauQ)
+		tauPAns := make([]float64, len(tauP))
+		copy(tauPAns, tauP)
+
+		// Test with optimal work.
+		lwork := -1
+		copy(a, aCopy)
+		impl.Dgebrd(m, n, a, lda, d, e, tauQ, tauP, work, lwork)
+		work = make([]float64, int(work[0]))
+		lwork = len(work)
+		for i := range work {
+			work[i] = math.NaN()
+		}
+		for i := range d {
+			d[i] = math.NaN()
+		}
+		for i := range e {
+			e[i] = math.NaN()
+		}
+		for i := range tauQ {
+			tauQ[i] = math.NaN()
+		}
+		for i := range tauP {
+			tauP[i] = math.NaN()
+		}
+		impl.Dgebrd(m, n, a, lda, d, e, tauQ, tauP, work, lwork)
+
+		// Test answers
+		if !floats.EqualApprox(a, aAns, 1e-10) {
+			t.Errorf("a mismatch")
+		}
+		if !floats.EqualApprox(d, dAns, 1e-10) {
+			t.Errorf("d mismatch")
+		}
+		if !floats.EqualApprox(e, eAns, 1e-10) {
+			t.Errorf("e mismatch")
+		}
+		if !floats.EqualApprox(tauQ, tauQAns, 1e-10) {
+			t.Errorf("tauQ mismatch")
+		}
+		if !floats.EqualApprox(tauP, tauPAns, 1e-10) {
+			t.Errorf("tauP mismatch")
+		}
+
+		// Test with shorter than optimal work.
+		lwork--
+		copy(a, aCopy)
+		for i := range d {
+			d[i] = 0
+		}
+		for i := range e {
+			e[i] = 0
+		}
+		for i := range tauP {
+			tauP[i] = 0
+		}
+		for i := range tauQ {
+			tauQ[i] = 0
+		}
+		impl.Dgebrd(m, n, a, lda, d, e, tauQ, tauP, work, lwork)
+
+		// Test answers
+		if !floats.EqualApprox(a, aAns, 1e-10) {
+			t.Errorf("a mismatch")
+		}
+		if !floats.EqualApprox(d, dAns, 1e-10) {
+			t.Errorf("d mismatch")
+		}
+		if !floats.EqualApprox(e, eAns, 1e-10) {
+			t.Errorf("e mismatch")
+		}
+		if !floats.EqualApprox(tauQ, tauQAns, 1e-10) {
+			t.Errorf("tauQ mismatch")
+		}
+		if !floats.EqualApprox(tauP, tauPAns, 1e-10) {
+			t.Errorf("tauP mismatch")
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dgecon.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgecon.go
new file mode 100644
index 00000000..bbb76284
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgecon.go
@@ -0,0 +1,97 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"log"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dgeconer interface {
+	Dlanger
+	Dgetrfer
+	Dgecon(norm lapack.MatrixNorm, n int, a []float64, lda int, anorm float64, work []float64, iwork []int) float64
+}
+
+func DgeconTest(t *testing.T, impl Dgeconer) {
+	for _, test := range []struct {
+		m       int
+		n       int
+		a       []float64
+		condOne float64
+		condInf float64
+	}{
+		{
+			a: []float64{
+				8, 1, 6,
+				3, 5, 7,
+				4, 9, 2,
+			},
+			m:       3,
+			n:       3,
+			condOne: 3.0 / 16,
+			condInf: 3.0 / 16,
+		},
+		{
+			a: []float64{
+				2, 9, 3, 2,
+				10, 9, 9, 3,
+				1, 1, 5, 2,
+				8, 4, 10, 2,
+			},
+			m:       4,
+			n:       4,
+			condOne: 0.024740155174938,
+			condInf: 0.012034465570035,
+		},
+		// Dgecon does not match Dpocon for this case. https://github.com/xianyi/OpenBLAS/issues/664.
+		{
+			a: []float64{
+				2.9995576045549965, -2.0898894566158663, 3.965560740124006,
+				-2.0898894566158663, 1.9634729526261008, -2.8681002706874104,
+				3.965560740124006, -2.8681002706874104, 5.502416670471008,
+			},
+			m:       3,
+			n:       3,
+			condOne: 0.024054837369015203,
+			condInf: 0.024054837369015203,
+		},
+	} {
+		m := test.m
+		n := test.n
+		lda := n
+		a := make([]float64, len(test.a))
+		copy(a, test.a)
+		ipiv := make([]int, min(m, n))
+
+		// Find the norms of the original matrix.
+		work := make([]float64, 4*n)
+		oneNorm := impl.Dlange(lapack.MaxColumnSum, m, n, a, lda, work)
+		infNorm := impl.Dlange(lapack.MaxRowSum, m, n, a, lda, work)
+
+		// Compute LU factorization of a.
+		impl.Dgetrf(m, n, a, lda, ipiv)
+
+		// Compute the condition number
+		iwork := make([]int, n)
+		condOne := impl.Dgecon(lapack.MaxColumnSum, n, a, lda, oneNorm, work, iwork)
+		condInf := impl.Dgecon(lapack.MaxRowSum, n, a, lda, infNorm, work, iwork)
+
+		// Error if not the same order, otherwise log the difference.
+		if !floats.EqualWithinAbsOrRel(condOne, test.condOne, 1e0, 1e0) {
+			t.Errorf("One norm mismatch. Want %v, got %v.", test.condOne, condOne)
+		} else if !floats.EqualWithinAbsOrRel(condOne, test.condOne, 1e-14, 1e-14) {
+			log.Printf("Dgecon one norm mismatch. Want %v, got %v.", test.condOne, condOne)
+		}
+		if !floats.EqualWithinAbsOrRel(condInf, test.condInf, 1e0, 1e0) {
+			t.Errorf("One norm mismatch. Want %v, got %v.", test.condInf, condInf)
+		} else if !floats.EqualWithinAbsOrRel(condInf, test.condInf, 1e-14, 1e-14) {
+			log.Printf("Dgecon one norm mismatch. Want %v, got %v.", test.condInf, condInf)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dgeev.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgeev.go
new file mode 100644
index 00000000..3ad86c1e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgeev.go
@@ -0,0 +1,735 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math"
+	"math/cmplx"
+	"math/rand"
+	"strconv"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dgeever interface {
+	Dgeev(jobvl lapack.LeftEVJob, jobvr lapack.RightEVJob, n int, a []float64, lda int,
+		wr, wi []float64, vl []float64, ldvl int, vr []float64, ldvr int, work []float64, lwork int) int
+}
+
+type dgeevTest struct {
+	a      blas64.General
+	evWant []complex128 // If nil, the eigenvalues are not known.
+	valTol float64      // Tolerance for eigenvalue checks.
+	vecTol float64      // Tolerance for eigenvector checks.
+}
+
+func DgeevTest(t *testing.T, impl Dgeever) {
+	rnd := rand.New(rand.NewSource(1))
+
+	for i, test := range []dgeevTest{
+		{
+			a:      A123{}.Matrix(),
+			evWant: A123{}.Eigenvalues(),
+		},
+
+		dgeevTestForAntisymRandom(10, rnd),
+		dgeevTestForAntisymRandom(11, rnd),
+		dgeevTestForAntisymRandom(50, rnd),
+		dgeevTestForAntisymRandom(51, rnd),
+		dgeevTestForAntisymRandom(100, rnd),
+		dgeevTestForAntisymRandom(101, rnd),
+
+		{
+			a:      Circulant(2).Matrix(),
+			evWant: Circulant(2).Eigenvalues(),
+		},
+		{
+			a:      Circulant(3).Matrix(),
+			evWant: Circulant(3).Eigenvalues(),
+		},
+		{
+			a:      Circulant(4).Matrix(),
+			evWant: Circulant(4).Eigenvalues(),
+		},
+		{
+			a:      Circulant(5).Matrix(),
+			evWant: Circulant(5).Eigenvalues(),
+		},
+		{
+			a:      Circulant(10).Matrix(),
+			evWant: Circulant(10).Eigenvalues(),
+		},
+		{
+			a:      Circulant(15).Matrix(),
+			evWant: Circulant(15).Eigenvalues(),
+			valTol: 1e-12,
+		},
+		{
+			a:      Circulant(30).Matrix(),
+			evWant: Circulant(30).Eigenvalues(),
+			valTol: 1e-11,
+			vecTol: 1e-12,
+		},
+		{
+			a:      Circulant(50).Matrix(),
+			evWant: Circulant(50).Eigenvalues(),
+			valTol: 1e-11,
+			vecTol: 1e-12,
+		},
+		{
+			a:      Circulant(101).Matrix(),
+			evWant: Circulant(101).Eigenvalues(),
+			valTol: 1e-10,
+			vecTol: 1e-11,
+		},
+		{
+			a:      Circulant(150).Matrix(),
+			evWant: Circulant(150).Eigenvalues(),
+			valTol: 1e-9,
+			vecTol: 1e-10,
+		},
+
+		{
+			a:      Clement(2).Matrix(),
+			evWant: Clement(2).Eigenvalues(),
+		},
+		{
+			a:      Clement(3).Matrix(),
+			evWant: Clement(3).Eigenvalues(),
+		},
+		{
+			a:      Clement(4).Matrix(),
+			evWant: Clement(4).Eigenvalues(),
+		},
+		{
+			a:      Clement(5).Matrix(),
+			evWant: Clement(5).Eigenvalues(),
+		},
+		{
+			a:      Clement(10).Matrix(),
+			evWant: Clement(10).Eigenvalues(),
+		},
+		{
+			a:      Clement(15).Matrix(),
+			evWant: Clement(15).Eigenvalues(),
+		},
+		{
+			a:      Clement(30).Matrix(),
+			evWant: Clement(30).Eigenvalues(),
+			valTol: 1e-11,
+		},
+		{
+			a:      Clement(50).Matrix(),
+			evWant: Clement(50).Eigenvalues(),
+			valTol: 1e-7,
+			vecTol: 1e-11,
+		},
+
+		{
+			a:      Creation(2).Matrix(),
+			evWant: Creation(2).Eigenvalues(),
+		},
+		{
+			a:      Creation(3).Matrix(),
+			evWant: Creation(3).Eigenvalues(),
+		},
+		{
+			a:      Creation(4).Matrix(),
+			evWant: Creation(4).Eigenvalues(),
+		},
+		{
+			a:      Creation(5).Matrix(),
+			evWant: Creation(5).Eigenvalues(),
+		},
+		{
+			a:      Creation(10).Matrix(),
+			evWant: Creation(10).Eigenvalues(),
+		},
+		{
+			a:      Creation(15).Matrix(),
+			evWant: Creation(15).Eigenvalues(),
+		},
+		{
+			a:      Creation(30).Matrix(),
+			evWant: Creation(30).Eigenvalues(),
+		},
+		{
+			a:      Creation(50).Matrix(),
+			evWant: Creation(50).Eigenvalues(),
+		},
+		{
+			a:      Creation(101).Matrix(),
+			evWant: Creation(101).Eigenvalues(),
+		},
+		{
+			a:      Creation(150).Matrix(),
+			evWant: Creation(150).Eigenvalues(),
+		},
+
+		{
+			a:      Diagonal(0).Matrix(),
+			evWant: Diagonal(0).Eigenvalues(),
+		},
+		{
+			a:      Diagonal(10).Matrix(),
+			evWant: Diagonal(10).Eigenvalues(),
+		},
+		{
+			a:      Diagonal(50).Matrix(),
+			evWant: Diagonal(50).Eigenvalues(),
+		},
+		{
+			a:      Diagonal(151).Matrix(),
+			evWant: Diagonal(151).Eigenvalues(),
+		},
+
+		{
+			a:      Downshift(2).Matrix(),
+			evWant: Downshift(2).Eigenvalues(),
+		},
+		{
+			a:      Downshift(3).Matrix(),
+			evWant: Downshift(3).Eigenvalues(),
+		},
+		{
+			a:      Downshift(4).Matrix(),
+			evWant: Downshift(4).Eigenvalues(),
+		},
+		{
+			a:      Downshift(5).Matrix(),
+			evWant: Downshift(5).Eigenvalues(),
+		},
+		{
+			a:      Downshift(10).Matrix(),
+			evWant: Downshift(10).Eigenvalues(),
+		},
+		{
+			a:      Downshift(15).Matrix(),
+			evWant: Downshift(15).Eigenvalues(),
+		},
+		{
+			a:      Downshift(30).Matrix(),
+			evWant: Downshift(30).Eigenvalues(),
+		},
+		{
+			a:      Downshift(50).Matrix(),
+			evWant: Downshift(50).Eigenvalues(),
+		},
+		{
+			a:      Downshift(101).Matrix(),
+			evWant: Downshift(101).Eigenvalues(),
+		},
+		{
+			a:      Downshift(150).Matrix(),
+			evWant: Downshift(150).Eigenvalues(),
+		},
+
+		{
+			a:      Fibonacci(2).Matrix(),
+			evWant: Fibonacci(2).Eigenvalues(),
+		},
+		{
+			a:      Fibonacci(3).Matrix(),
+			evWant: Fibonacci(3).Eigenvalues(),
+		},
+		{
+			a:      Fibonacci(4).Matrix(),
+			evWant: Fibonacci(4).Eigenvalues(),
+		},
+		{
+			a:      Fibonacci(5).Matrix(),
+			evWant: Fibonacci(5).Eigenvalues(),
+		},
+		{
+			a:      Fibonacci(10).Matrix(),
+			evWant: Fibonacci(10).Eigenvalues(),
+		},
+		{
+			a:      Fibonacci(15).Matrix(),
+			evWant: Fibonacci(15).Eigenvalues(),
+		},
+		{
+			a:      Fibonacci(30).Matrix(),
+			evWant: Fibonacci(30).Eigenvalues(),
+		},
+		{
+			a:      Fibonacci(50).Matrix(),
+			evWant: Fibonacci(50).Eigenvalues(),
+		},
+		{
+			a:      Fibonacci(101).Matrix(),
+			evWant: Fibonacci(101).Eigenvalues(),
+		},
+		{
+			a:      Fibonacci(150).Matrix(),
+			evWant: Fibonacci(150).Eigenvalues(),
+		},
+
+		{
+			a:      Gear(2).Matrix(),
+			evWant: Gear(2).Eigenvalues(),
+		},
+		{
+			a:      Gear(3).Matrix(),
+			evWant: Gear(3).Eigenvalues(),
+		},
+		{
+			a:      Gear(4).Matrix(),
+			evWant: Gear(4).Eigenvalues(),
+			valTol: 1e-7,
+		},
+		{
+			a:      Gear(5).Matrix(),
+			evWant: Gear(5).Eigenvalues(),
+		},
+		{
+			a:      Gear(10).Matrix(),
+			evWant: Gear(10).Eigenvalues(),
+			valTol: 1e-8,
+		},
+		{
+			a:      Gear(15).Matrix(),
+			evWant: Gear(15).Eigenvalues(),
+		},
+		{
+			a:      Gear(30).Matrix(),
+			evWant: Gear(30).Eigenvalues(),
+			valTol: 1e-8,
+		},
+		{
+			a:      Gear(50).Matrix(),
+			evWant: Gear(50).Eigenvalues(),
+			valTol: 1e-8,
+		},
+		{
+			a:      Gear(101).Matrix(),
+			evWant: Gear(101).Eigenvalues(),
+		},
+		{
+			a:      Gear(150).Matrix(),
+			evWant: Gear(150).Eigenvalues(),
+			valTol: 1e-8,
+		},
+
+		{
+			a:      Grcar{N: 10, K: 3}.Matrix(),
+			evWant: Grcar{N: 10, K: 3}.Eigenvalues(),
+		},
+		{
+			a:      Grcar{N: 10, K: 7}.Matrix(),
+			evWant: Grcar{N: 10, K: 7}.Eigenvalues(),
+		},
+		{
+			a:      Grcar{N: 11, K: 7}.Matrix(),
+			evWant: Grcar{N: 11, K: 7}.Eigenvalues(),
+		},
+		{
+			a:      Grcar{N: 50, K: 3}.Matrix(),
+			evWant: Grcar{N: 50, K: 3}.Eigenvalues(),
+		},
+		{
+			a:      Grcar{N: 51, K: 3}.Matrix(),
+			evWant: Grcar{N: 51, K: 3}.Eigenvalues(),
+		},
+		{
+			a:      Grcar{N: 50, K: 10}.Matrix(),
+			evWant: Grcar{N: 50, K: 10}.Eigenvalues(),
+		},
+		{
+			a:      Grcar{N: 51, K: 10}.Matrix(),
+			evWant: Grcar{N: 51, K: 10}.Eigenvalues(),
+		},
+		{
+			a:      Grcar{N: 50, K: 30}.Matrix(),
+			evWant: Grcar{N: 50, K: 30}.Eigenvalues(),
+		},
+		{
+			a:      Grcar{N: 150, K: 2}.Matrix(),
+			evWant: Grcar{N: 150, K: 2}.Eigenvalues(),
+		},
+		{
+			a:      Grcar{N: 150, K: 148}.Matrix(),
+			evWant: Grcar{N: 150, K: 148}.Eigenvalues(),
+		},
+
+		{
+			a:      Hanowa{N: 6, Alpha: 17}.Matrix(),
+			evWant: Hanowa{N: 6, Alpha: 17}.Eigenvalues(),
+		},
+		{
+			a:      Hanowa{N: 50, Alpha: -1}.Matrix(),
+			evWant: Hanowa{N: 50, Alpha: -1}.Eigenvalues(),
+		},
+		{
+			a:      Hanowa{N: 100, Alpha: -1}.Matrix(),
+			evWant: Hanowa{N: 100, Alpha: -1}.Eigenvalues(),
+		},
+
+		{
+			a:      Lesp(2).Matrix(),
+			evWant: Lesp(2).Eigenvalues(),
+		},
+		{
+			a:      Lesp(3).Matrix(),
+			evWant: Lesp(3).Eigenvalues(),
+		},
+		{
+			a:      Lesp(4).Matrix(),
+			evWant: Lesp(4).Eigenvalues(),
+		},
+		{
+			a:      Lesp(5).Matrix(),
+			evWant: Lesp(5).Eigenvalues(),
+		},
+		{
+			a:      Lesp(10).Matrix(),
+			evWant: Lesp(10).Eigenvalues(),
+		},
+		{
+			a:      Lesp(15).Matrix(),
+			evWant: Lesp(15).Eigenvalues(),
+		},
+		{
+			a:      Lesp(30).Matrix(),
+			evWant: Lesp(30).Eigenvalues(),
+		},
+		{
+			a:      Lesp(50).Matrix(),
+			evWant: Lesp(50).Eigenvalues(),
+			valTol: 1e-12,
+			vecTol: 1e-12,
+		},
+		{
+			a:      Lesp(101).Matrix(),
+			evWant: Lesp(101).Eigenvalues(),
+			valTol: 1e-12,
+			vecTol: 1e-12,
+		},
+		{
+			a:      Lesp(150).Matrix(),
+			evWant: Lesp(150).Eigenvalues(),
+			valTol: 1e-12,
+			vecTol: 1e-12,
+		},
+
+		{
+			a:      Rutis{}.Matrix(),
+			evWant: Rutis{}.Eigenvalues(),
+		},
+
+		{
+			a:      Tris{N: 74, X: 1, Y: -2, Z: 1}.Matrix(),
+			evWant: Tris{N: 74, X: 1, Y: -2, Z: 1}.Eigenvalues(),
+		},
+		{
+			a:      Tris{N: 74, X: 1, Y: 2, Z: -3}.Matrix(),
+			evWant: Tris{N: 74, X: 1, Y: 2, Z: -3}.Eigenvalues(),
+		},
+		{
+			a:      Tris{N: 75, X: 1, Y: 2, Z: -3}.Matrix(),
+			evWant: Tris{N: 75, X: 1, Y: 2, Z: -3}.Eigenvalues(),
+		},
+
+		{
+			a:      Wilk4{}.Matrix(),
+			evWant: Wilk4{}.Eigenvalues(),
+		},
+		{
+			a:      Wilk12{}.Matrix(),
+			evWant: Wilk12{}.Eigenvalues(),
+			valTol: 1e-8,
+		},
+		{
+			a:      Wilk20(0).Matrix(),
+			evWant: Wilk20(0).Eigenvalues(),
+		},
+		{
+			a:      Wilk20(1e-10).Matrix(),
+			evWant: Wilk20(1e-10).Eigenvalues(),
+			valTol: 1e-12,
+			vecTol: 1e-12,
+		},
+
+		{
+			a:      Zero(1).Matrix(),
+			evWant: Zero(1).Eigenvalues(),
+		},
+		{
+			a:      Zero(10).Matrix(),
+			evWant: Zero(10).Eigenvalues(),
+		},
+		{
+			a:      Zero(50).Matrix(),
+			evWant: Zero(50).Eigenvalues(),
+		},
+		{
+			a:      Zero(100).Matrix(),
+			evWant: Zero(100).Eigenvalues(),
+		},
+	} {
+		for _, jobvl := range []lapack.LeftEVJob{lapack.ComputeLeftEV, lapack.None} {
+			for _, jobvr := range []lapack.RightEVJob{lapack.ComputeRightEV, lapack.None} {
+				for _, extra := range []int{0, 11} {
+					for _, wl := range []worklen{minimumWork, mediumWork, optimumWork} {
+						testDgeev(t, impl, strconv.Itoa(i), test, jobvl, jobvr, extra, wl)
+					}
+				}
+			}
+		}
+	}
+
+	for _, n := range []int{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 50, 51, 100, 101} {
+		for _, jobvl := range []lapack.LeftEVJob{lapack.ComputeLeftEV, lapack.None} {
+			for _, jobvr := range []lapack.RightEVJob{lapack.ComputeRightEV, lapack.None} {
+				for cas := 0; cas < 10; cas++ {
+					// Create a block diagonal matrix with
+					// random eigenvalues of random multiplicity.
+					ev := make([]complex128, n)
+					tmat := zeros(n, n, n)
+					for i := 0; i < n; {
+						re := rnd.NormFloat64()
+						if i == n-1 || rnd.Float64() < 0.5 {
+							// Real eigenvalue.
+							nb := rnd.Intn(min(4, n-i)) + 1
+							for k := 0; k < nb; k++ {
+								tmat.Data[i*tmat.Stride+i] = re
+								ev[i] = complex(re, 0)
+								i++
+							}
+							continue
+						}
+						// Complex eigenvalue.
+						im := rnd.NormFloat64()
+						nb := rnd.Intn(min(4, (n-i)/2)) + 1
+						for k := 0; k < nb; k++ {
+							// 2×2 block for the complex eigenvalue.
+							tmat.Data[i*tmat.Stride+i] = re
+							tmat.Data[(i+1)*tmat.Stride+i+1] = re
+							tmat.Data[(i+1)*tmat.Stride+i] = -im
+							tmat.Data[i*tmat.Stride+i+1] = im
+							ev[i] = complex(re, im)
+							ev[i+1] = complex(re, -im)
+							i += 2
+						}
+					}
+
+					// Compute A = Q T Q^T where Q is an
+					// orthogonal matrix.
+					q := randomOrthogonal(n, rnd)
+					tq := zeros(n, n, n)
+					blas64.Gemm(blas.NoTrans, blas.Trans, 1, tmat, q, 0, tq)
+					a := zeros(n, n, n)
+					blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, q, tq, 0, a)
+
+					test := dgeevTest{
+						a:      a,
+						evWant: ev,
+						valTol: 1e-12,
+						vecTol: 1e-8,
+					}
+					testDgeev(t, impl, "random", test, jobvl, jobvr, 0, optimumWork)
+				}
+			}
+		}
+	}
+}
+
+func testDgeev(t *testing.T, impl Dgeever, tc string, test dgeevTest, jobvl lapack.LeftEVJob, jobvr lapack.RightEVJob, extra int, wl worklen) {
+	const defaultTol = 1e-13
+	valTol := test.valTol
+	if valTol == 0 {
+		valTol = defaultTol
+	}
+	vecTol := test.vecTol
+	if vecTol == 0 {
+		vecTol = defaultTol
+	}
+
+	a := cloneGeneral(test.a)
+	n := a.Rows
+
+	var vl blas64.General
+	if jobvl == lapack.ComputeLeftEV {
+		vl = nanGeneral(n, n, n)
+	}
+
+	var vr blas64.General
+	if jobvr == lapack.ComputeRightEV {
+		vr = nanGeneral(n, n, n)
+	}
+
+	wr := make([]float64, n)
+	wi := make([]float64, n)
+
+	var lwork int
+	switch wl {
+	case minimumWork:
+		if jobvl == lapack.ComputeLeftEV || jobvr == lapack.ComputeRightEV {
+			lwork = max(1, 4*n)
+		} else {
+			lwork = max(1, 3*n)
+		}
+	case mediumWork:
+		work := make([]float64, 1)
+		impl.Dgeev(jobvl, jobvr, n, nil, 1, nil, nil, nil, 1, nil, 1, work, -1)
+		if jobvl == lapack.ComputeLeftEV || jobvr == lapack.ComputeRightEV {
+			lwork = (int(work[0]) + 4*n) / 2
+		} else {
+			lwork = (int(work[0]) + 3*n) / 2
+		}
+		lwork = max(1, lwork)
+	case optimumWork:
+		work := make([]float64, 1)
+		impl.Dgeev(jobvl, jobvr, n, nil, 1, nil, nil, nil, 1, nil, 1, work, -1)
+		lwork = int(work[0])
+	}
+	work := make([]float64, lwork)
+
+	first := impl.Dgeev(jobvl, jobvr, n, a.Data, a.Stride, wr, wi,
+		vl.Data, vl.Stride, vr.Data, vr.Stride, work, len(work))
+
+	prefix := fmt.Sprintf("Case #%v: n=%v, jobvl=%v, jobvr=%v, extra=%v, work=%v",
+		tc, n, jobvl, jobvr, extra, wl)
+
+	if !generalOutsideAllNaN(vl) {
+		t.Errorf("%v: out-of-range write to VL", prefix)
+	}
+	if !generalOutsideAllNaN(vr) {
+		t.Errorf("%v: out-of-range write to VR", prefix)
+	}
+
+	if first > 0 {
+		t.Logf("%v: all eigenvalues haven't been computed, first=%v", prefix, first)
+	}
+
+	// Check that conjugate pair eigevalues are ordered correctly.
+	for i := first; i < n; {
+		if wi[i] == 0 {
+			i++
+			continue
+		}
+		if wr[i] != wr[i+1] {
+			t.Errorf("%v: real parts of %vth conjugate pair not equal", prefix, i)
+		}
+		if wi[i] < 0 || wi[i+1] > 0 {
+			t.Errorf("%v: unexpected ordering of %vth conjugate pair", prefix, i)
+		}
+		i += 2
+	}
+
+	// Check the computed eigenvalues against provided known eigenvalues.
+	if test.evWant != nil {
+		used := make([]bool, n)
+		for i := first; i < n; i++ {
+			evGot := complex(wr[i], wi[i])
+			idx := -1
+			for k, evWant := range test.evWant {
+				if !used[k] && cmplx.Abs(evWant-evGot) < valTol {
+					idx = k
+					used[k] = true
+					break
+				}
+			}
+			if idx == -1 {
+				t.Errorf("%v: unexpected eigenvalue %v", prefix, evGot)
+			}
+		}
+	}
+
+	if first > 0 || (jobvl == lapack.None && jobvr == lapack.None) {
+		// No eigenvectors have been computed.
+		return
+	}
+
+	// Check that the columns of VL and VR are eigenvectors that correspond
+	// to the computed eigenvalues.
+	for k := 0; k < n; {
+		if wi[k] == 0 {
+			if jobvl == lapack.ComputeLeftEV {
+				ev := columnOf(vl, k)
+				if !isLeftEigenvectorOf(test.a, ev, nil, complex(wr[k], 0), vecTol) {
+					t.Errorf("%v: VL[:,%v] is not left real eigenvector",
+						prefix, k)
+				}
+
+				norm := floats.Norm(ev, 2)
+				if math.Abs(norm-1) >= defaultTol {
+					t.Errorf("%v: norm of left real eigenvector %v not equal to 1: got %v",
+						prefix, k, norm)
+				}
+			}
+			if jobvr == lapack.ComputeRightEV {
+				ev := columnOf(vr, k)
+				if !isRightEigenvectorOf(test.a, ev, nil, complex(wr[k], 0), vecTol) {
+					t.Errorf("%v: VR[:,%v] is not right real eigenvector",
+						prefix, k)
+				}
+
+				norm := floats.Norm(ev, 2)
+				if math.Abs(norm-1) >= defaultTol {
+					t.Errorf("%v: norm of right real eigenvector %v not equal to 1: got %v",
+						prefix, k, norm)
+				}
+			}
+			k++
+		} else {
+			if jobvl == lapack.ComputeLeftEV {
+				evre := columnOf(vl, k)
+				evim := columnOf(vl, k+1)
+				if !isLeftEigenvectorOf(test.a, evre, evim, complex(wr[k], wi[k]), vecTol) {
+					t.Errorf("%v: VL[:,%v:%v] is not left complex eigenvector",
+						prefix, k, k+1)
+				}
+				floats.Scale(-1, evim)
+				if !isLeftEigenvectorOf(test.a, evre, evim, complex(wr[k+1], wi[k+1]), vecTol) {
+					t.Errorf("%v: VL[:,%v:%v] is not left complex eigenvector",
+						prefix, k, k+1)
+				}
+
+				norm := math.Hypot(floats.Norm(evre, 2), floats.Norm(evim, 2))
+				if math.Abs(norm-1) > defaultTol {
+					t.Errorf("%v: norm of left complex eigenvector %v not equal to 1: got %v",
+						prefix, k, norm)
+				}
+			}
+			if jobvr == lapack.ComputeRightEV {
+				evre := columnOf(vr, k)
+				evim := columnOf(vr, k+1)
+				if !isRightEigenvectorOf(test.a, evre, evim, complex(wr[k], wi[k]), vecTol) {
+					t.Errorf("%v: VR[:,%v:%v] is not right complex eigenvector",
+						prefix, k, k+1)
+				}
+				floats.Scale(-1, evim)
+				if !isRightEigenvectorOf(test.a, evre, evim, complex(wr[k+1], wi[k+1]), vecTol) {
+					t.Errorf("%v: VR[:,%v:%v] is not right complex eigenvector",
+						prefix, k, k+1)
+				}
+
+				norm := math.Hypot(floats.Norm(evre, 2), floats.Norm(evim, 2))
+				if math.Abs(norm-1) > defaultTol {
+					t.Errorf("%v: norm of right complex eigenvector %v not equal to 1: got %v",
+						prefix, k, norm)
+				}
+			}
+			// We don't test whether the largest component is real
+			// because checking it is flaky due to rounding errors.
+
+			k += 2
+		}
+	}
+}
+
+func dgeevTestForAntisymRandom(n int, rnd *rand.Rand) dgeevTest {
+	a := NewAntisymRandom(n, rnd)
+	return dgeevTest{
+		a:      a.Matrix(),
+		evWant: a.Eigenvalues(),
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dgeev_bench.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgeev_bench.go
new file mode 100644
index 00000000..177807de
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgeev_bench.go
@@ -0,0 +1,63 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build go1.7
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+)
+
+var resultGeneral blas64.General
+
+func DgeevBenchmark(b *testing.B, impl Dgeever) {
+	rnd := rand.New(rand.NewSource(1))
+	benchmarks := []struct {
+		name string
+		a    blas64.General
+	}{
+		{"AntisymRandom3", NewAntisymRandom(3, rnd).Matrix()},
+		{"AntisymRandom4", NewAntisymRandom(4, rnd).Matrix()},
+		{"AntisymRandom5", NewAntisymRandom(5, rnd).Matrix()},
+		{"AntisymRandom10", NewAntisymRandom(10, rnd).Matrix()},
+		{"AntisymRandom50", NewAntisymRandom(50, rnd).Matrix()},
+		{"AntisymRandom100", NewAntisymRandom(100, rnd).Matrix()},
+		{"AntisymRandom200", NewAntisymRandom(200, rnd).Matrix()},
+		{"AntisymRandom500", NewAntisymRandom(500, rnd).Matrix()},
+		{"Circulant3", Circulant(3).Matrix()},
+		{"Circulant4", Circulant(4).Matrix()},
+		{"Circulant5", Circulant(5).Matrix()},
+		{"Circulant10", Circulant(10).Matrix()},
+		{"Circulant50", Circulant(50).Matrix()},
+		{"Circulant100", Circulant(100).Matrix()},
+		{"Circulant200", Circulant(200).Matrix()},
+		{"Circulant500", Circulant(500).Matrix()},
+	}
+	for _, bm := range benchmarks {
+		n := bm.a.Rows
+		a := zeros(n, n, n)
+		vl := zeros(n, n, n)
+		vr := zeros(n, n, n)
+		wr := make([]float64, n)
+		wi := make([]float64, n)
+		work := make([]float64, 1)
+		impl.Dgeev(lapack.ComputeLeftEV, lapack.ComputeRightEV, n, nil, n, nil, nil, nil, n, nil, n, work, -1)
+		work = make([]float64, int(work[0]))
+		b.Run(bm.name, func(b *testing.B) {
+			for i := 0; i < b.N; i++ {
+				b.StopTimer()
+				copyGeneral(a, bm.a)
+				b.StartTimer()
+				impl.Dgeev(lapack.ComputeLeftEV, lapack.ComputeRightEV, n, a.Data, a.Stride, wr, wi,
+					vl.Data, vl.Stride, vr.Data, vr.Stride, work, len(work))
+			}
+			resultGeneral = a
+		})
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dgehd2.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgehd2.go
new file mode 100644
index 00000000..5b7e8309
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgehd2.go
@@ -0,0 +1,196 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dgehd2er interface {
+	Dgehd2(n, ilo, ihi int, a []float64, lda int, tau, work []float64)
+}
+
+func Dgehd2Test(t *testing.T, impl Dgehd2er) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, n := range []int{1, 2, 3, 4, 5, 7, 10, 30} {
+		for _, extra := range []int{0, 1, 13} {
+			for cas := 0; cas < 100; cas++ {
+				testDgehd2(t, impl, n, extra, rnd)
+			}
+		}
+	}
+}
+
+func testDgehd2(t *testing.T, impl Dgehd2er, n, extra int, rnd *rand.Rand) {
+	ilo := rnd.Intn(n)
+	ihi := rnd.Intn(n)
+	if ilo > ihi {
+		ilo, ihi = ihi, ilo
+	}
+
+	tau := nanSlice(n - 1)
+	work := nanSlice(n)
+
+	a := randomGeneral(n, n, n+extra, rnd)
+	// NaN out elements under the diagonal except
+	// for the [ilo:ihi,ilo:ihi] block.
+	for i := 1; i <= ihi; i++ {
+		for j := 0; j < min(ilo, i); j++ {
+			a.Data[i*a.Stride+j] = math.NaN()
+		}
+	}
+	for i := ihi + 1; i < n; i++ {
+		for j := 0; j < i; j++ {
+			a.Data[i*a.Stride+j] = math.NaN()
+		}
+	}
+	aCopy := a
+	aCopy.Data = make([]float64, len(a.Data))
+	copy(aCopy.Data, a.Data)
+
+	impl.Dgehd2(n, ilo, ihi, a.Data, a.Stride, tau, work)
+
+	prefix := fmt.Sprintf("Case n=%v, ilo=%v, ihi=%v, extra=%v", n, ilo, ihi, extra)
+
+	// Check any invalid modifications of a.
+	if !generalOutsideAllNaN(a) {
+		t.Errorf("%v: out-of-range write to A\n%v", prefix, a.Data)
+	}
+	for i := ilo; i <= ihi; i++ {
+		for j := 0; j < min(ilo, i); j++ {
+			if !math.IsNaN(a.Data[i*a.Stride+j]) {
+				t.Errorf("%v: expected NaN at A[%v,%v]", prefix, i, j)
+			}
+		}
+	}
+	for i := ihi + 1; i < n; i++ {
+		for j := 0; j < i; j++ {
+			if !math.IsNaN(a.Data[i*a.Stride+j]) {
+				t.Errorf("%v: expected NaN at A[%v,%v]", prefix, i, j)
+			}
+		}
+	}
+	for i := 0; i <= ilo; i++ {
+		for j := i; j < ilo+1; j++ {
+			if a.Data[i*a.Stride+j] != aCopy.Data[i*aCopy.Stride+j] {
+				t.Errorf("%v: unexpected modification at A[%v,%v]", prefix, i, j)
+			}
+		}
+		for j := ihi + 1; j < n; j++ {
+			if a.Data[i*a.Stride+j] != aCopy.Data[i*aCopy.Stride+j] {
+				t.Errorf("%v: unexpected modification at A[%v,%v]", prefix, i, j)
+			}
+		}
+	}
+	for i := ihi + 1; i < n; i++ {
+		for j := i; j < n; j++ {
+			if a.Data[i*a.Stride+j] != aCopy.Data[i*aCopy.Stride+j] {
+				t.Errorf("%v: unexpected modification at A[%v,%v]", prefix, i, j)
+			}
+		}
+	}
+
+	// Check that tau has been assigned properly.
+	for i, v := range tau {
+		if i < ilo || i >= ihi {
+			if !math.IsNaN(v) {
+				t.Errorf("%v: expected NaN at tau[%v]", prefix, i)
+			}
+		} else {
+			if math.IsNaN(v) {
+				t.Errorf("%v: unexpected NaN at tau[%v]", prefix, i)
+			}
+		}
+	}
+
+	// Extract Q and check that it is orthogonal.
+	q := blas64.General{
+		Rows:   n,
+		Cols:   n,
+		Stride: n,
+		Data:   make([]float64, n*n),
+	}
+	for i := 0; i < q.Rows; i++ {
+		q.Data[i*q.Stride+i] = 1
+	}
+	qCopy := q
+	qCopy.Data = make([]float64, len(q.Data))
+	for j := ilo; j < ihi; j++ {
+		h := blas64.General{
+			Rows:   n,
+			Cols:   n,
+			Stride: n,
+			Data:   make([]float64, n*n),
+		}
+		for i := 0; i < h.Rows; i++ {
+			h.Data[i*h.Stride+i] = 1
+		}
+		v := blas64.Vector{
+			Inc:  1,
+			Data: make([]float64, n),
+		}
+		v.Data[j+1] = 1
+		for i := j + 2; i < ihi+1; i++ {
+			v.Data[i] = a.Data[i*a.Stride+j]
+		}
+		blas64.Ger(-tau[j], v, v, h)
+		copy(qCopy.Data, q.Data)
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, qCopy, h, 0, q)
+	}
+	if !isOrthonormal(q) {
+		t.Errorf("%v: Q is not orthogonal\nQ=%v", prefix, q)
+	}
+
+	// Overwrite NaN elements of aCopy with zeros
+	// (we will multiply with it below).
+	for i := 1; i <= ihi; i++ {
+		for j := 0; j < min(ilo, i); j++ {
+			aCopy.Data[i*aCopy.Stride+j] = 0
+		}
+	}
+	for i := ihi + 1; i < n; i++ {
+		for j := 0; j < i; j++ {
+			aCopy.Data[i*aCopy.Stride+j] = 0
+		}
+	}
+
+	// Construct Q^T * AOrig * Q and check that it is
+	// equal to A from Dgehd2.
+	aq := blas64.General{
+		Rows:   n,
+		Cols:   n,
+		Stride: n,
+		Data:   make([]float64, n*n),
+	}
+	blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, aCopy, q, 0, aq)
+	qaq := blas64.General{
+		Rows:   n,
+		Cols:   n,
+		Stride: n,
+		Data:   make([]float64, n*n),
+	}
+	blas64.Gemm(blas.Trans, blas.NoTrans, 1, q, aq, 0, qaq)
+	for i := ilo; i <= ihi; i++ {
+		for j := ilo; j <= ihi; j++ {
+			qaqij := qaq.Data[i*qaq.Stride+j]
+			if j < i-1 {
+				if math.Abs(qaqij) > 1e-14 {
+					t.Errorf("%v: Q^T*A*Q is not upper Hessenberg, [%v,%v]=%v", prefix, i, j, qaqij)
+				}
+				continue
+			}
+			diff := qaqij - a.Data[i*a.Stride+j]
+			if math.Abs(diff) > 1e-14 {
+				t.Errorf("%v: Q^T*AOrig*Q and A are not equal, diff at [%v,%v]=%v", prefix, i, j, diff)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dgehrd.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgehrd.go
new file mode 100644
index 00000000..012b8707
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgehrd.go
@@ -0,0 +1,209 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dgehrder interface {
+	Dgehrd(n, ilo, ihi int, a []float64, lda int, tau, work []float64, lwork int)
+
+	Dorgqr(m, n, k int, a []float64, lda int, tau, work []float64, lwork int)
+}
+
+func DgehrdTest(t *testing.T, impl Dgehrder) {
+	rnd := rand.New(rand.NewSource(1))
+
+	// Randomized tests for small matrix sizes that will most likely
+	// use the unblocked algorithm.
+	for _, n := range []int{1, 2, 3, 4, 5, 10, 34} {
+		for _, extra := range []int{0, 13} {
+			for _, optwork := range []bool{true, false} {
+				for cas := 0; cas < 10; cas++ {
+					ilo := rnd.Intn(n)
+					ihi := rnd.Intn(n)
+					if ilo > ihi {
+						ilo, ihi = ihi, ilo
+					}
+					testDgehrd(t, impl, n, ilo, ihi, extra, optwork, rnd)
+				}
+			}
+		}
+	}
+
+	// These are selected tests for larger matrix sizes to test the blocked
+	// algorithm. Use sizes around several powers of two because that is
+	// where the blocked path will most likely start to be taken. For
+	// example, at present the blocked algorithm is used for sizes larger
+	// than 129.
+	for _, test := range []struct {
+		n, ilo, ihi int
+	}{
+		{0, 0, -1},
+
+		{68, 0, 63},
+		{68, 0, 64},
+		{68, 0, 65},
+		{68, 0, 66},
+		{68, 0, 67},
+
+		{132, 2, 129},
+		{132, 1, 129}, // Size = 129, unblocked.
+		{132, 0, 129}, // Size = 130, blocked.
+		{132, 1, 130},
+		{132, 0, 130},
+		{132, 1, 131},
+		{132, 0, 131},
+
+		{260, 2, 257},
+		{260, 1, 257},
+		{260, 0, 257},
+		{260, 0, 258},
+		{260, 0, 259},
+	} {
+		for _, extra := range []int{0, 13} {
+			for _, optwork := range []bool{true, false} {
+				testDgehrd(t, impl, test.n, test.ilo, test.ihi, extra, optwork, rnd)
+			}
+		}
+	}
+}
+
+func testDgehrd(t *testing.T, impl Dgehrder, n, ilo, ihi, extra int, optwork bool, rnd *rand.Rand) {
+	a := randomGeneral(n, n, n+extra, rnd)
+	aCopy := a
+	aCopy.Data = make([]float64, len(a.Data))
+	copy(aCopy.Data, a.Data)
+
+	var tau []float64
+	if n > 1 {
+		tau = nanSlice(n - 1)
+	}
+
+	var work []float64
+	if optwork {
+		work = nanSlice(1)
+		impl.Dgehrd(n, ilo, ihi, nil, a.Stride, nil, work, -1)
+		work = nanSlice(int(work[0]))
+	} else {
+		work = nanSlice(max(1, n))
+	}
+
+	impl.Dgehrd(n, ilo, ihi, a.Data, a.Stride, tau, work, len(work))
+
+	if n == 0 {
+		// Just make sure there is no panic.
+		return
+	}
+
+	prefix := fmt.Sprintf("Case n=%v, ilo=%v, ihi=%v, extra=%v", n, ilo, ihi, extra)
+
+	// Check any invalid modifications of a.
+	if !generalOutsideAllNaN(a) {
+		t.Errorf("%v: out-of-range write to A\n%v", prefix, a.Data)
+	}
+	for i := ilo; i <= ihi; i++ {
+		for j := 0; j < min(ilo, i); j++ {
+			if a.Data[i*a.Stride+j] != aCopy.Data[i*aCopy.Stride+j] {
+				t.Errorf("%v: unexpected modification of A[%v,%v]", prefix, i, j)
+			}
+		}
+	}
+	for i := ihi + 1; i < n; i++ {
+		for j := 0; j < i; j++ {
+			if a.Data[i*a.Stride+j] != aCopy.Data[i*aCopy.Stride+j] {
+				t.Errorf("%v: unexpected modification of A[%v,%v]", prefix, i, j)
+			}
+		}
+	}
+	for i := 0; i <= ilo; i++ {
+		for j := i; j < ilo+1; j++ {
+			if a.Data[i*a.Stride+j] != aCopy.Data[i*aCopy.Stride+j] {
+				t.Errorf("%v: unexpected modification at A[%v,%v]", prefix, i, j)
+			}
+		}
+		for j := ihi + 1; j < n; j++ {
+			if a.Data[i*a.Stride+j] != aCopy.Data[i*aCopy.Stride+j] {
+				t.Errorf("%v: unexpected modification at A[%v,%v]", prefix, i, j)
+			}
+		}
+	}
+	for i := ihi + 1; i < n; i++ {
+		for j := i; j < n; j++ {
+			if a.Data[i*a.Stride+j] != aCopy.Data[i*aCopy.Stride+j] {
+				t.Errorf("%v: unexpected modification at A[%v,%v]", prefix, i, j)
+			}
+		}
+	}
+
+	// Check that tau has been assigned properly.
+	for i, v := range tau {
+		if math.IsNaN(v) {
+			t.Errorf("%v: unexpected NaN at tau[%v]", prefix, i)
+		}
+	}
+
+	// Extract Q and check that it is orthogonal.
+	q := eye(n, n)
+	if ilo != ihi {
+		for i := ilo + 2; i <= ihi; i++ {
+			for j := ilo + 1; j < ihi; j++ {
+				q.Data[i*q.Stride+j] = a.Data[i*a.Stride+j-1]
+			}
+		}
+		nh := ihi - ilo
+		impl.Dorgqr(nh, nh, nh, q.Data[(ilo+1)*q.Stride+ilo+1:], q.Stride, tau[ilo:ihi], work, len(work))
+	}
+	if !isOrthonormal(q) {
+		t.Errorf("%v: Q is not orthogonal\nQ=%v", prefix, q)
+	}
+
+	// Construct Q^T * AOrig * Q and check that it is upper Hessenberg.
+	aq := blas64.General{
+		Rows:   n,
+		Cols:   n,
+		Stride: n,
+		Data:   make([]float64, n*n),
+	}
+	blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, aCopy, q, 0, aq)
+	qaq := blas64.General{
+		Rows:   n,
+		Cols:   n,
+		Stride: n,
+		Data:   make([]float64, n*n),
+	}
+	blas64.Gemm(blas.Trans, blas.NoTrans, 1, q, aq, 0, qaq)
+	for i := 0; i <= ilo; i++ {
+		for j := ilo + 1; j <= ihi; j++ {
+			qaqij := qaq.Data[i*qaq.Stride+j]
+			diff := qaqij - a.Data[i*a.Stride+j]
+			if math.Abs(diff) > 1e-13 {
+				t.Errorf("%v: Q^T*AOrig*Q and A are not equal, diff at [%v,%v]=%v", prefix, i, j, diff)
+			}
+		}
+	}
+	for i := ilo + 1; i <= ihi; i++ {
+		for j := ilo; j < n; j++ {
+			qaqij := qaq.Data[i*qaq.Stride+j]
+			if j < i-1 {
+				if math.Abs(qaqij) > 1e-13 {
+					t.Errorf("%v: Q^T*AOrig*Q is not upper Hessenberg, [%v,%v]=%v", prefix, i, j, qaqij)
+				}
+				continue
+			}
+			diff := qaqij - a.Data[i*a.Stride+j]
+			if math.Abs(diff) > 1e-13 {
+				t.Errorf("%v: Q^T*AOrig*Q and A are not equal, diff at [%v,%v]=%v", prefix, i, j, diff)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dgelq2.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgelq2.go
new file mode 100644
index 00000000..20f95717
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgelq2.go
@@ -0,0 +1,113 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dgelq2er interface {
+	Dgelq2(m, n int, a []float64, lda int, tau, work []float64)
+}
+
+func Dgelq2Test(t *testing.T, impl Dgelq2er) {
+	rnd := rand.New(rand.NewSource(1))
+	for c, test := range []struct {
+		m, n, lda int
+	}{
+		{1, 1, 0},
+		{2, 2, 0},
+		{3, 2, 0},
+		{2, 3, 0},
+		{1, 12, 0},
+		{2, 6, 0},
+		{3, 4, 0},
+		{4, 3, 0},
+		{6, 2, 0},
+		{1, 12, 0},
+		{1, 1, 20},
+		{2, 2, 20},
+		{3, 2, 20},
+		{2, 3, 20},
+		{1, 12, 20},
+		{2, 6, 20},
+		{3, 4, 20},
+		{4, 3, 20},
+		{6, 2, 20},
+		{1, 12, 20},
+	} {
+		n := test.n
+		m := test.m
+		lda := test.lda
+		if lda == 0 {
+			lda = test.n
+		}
+		k := min(m, n)
+		tau := make([]float64, k)
+		for i := range tau {
+			tau[i] = rnd.Float64()
+		}
+		work := make([]float64, m)
+		for i := range work {
+			work[i] = rnd.Float64()
+		}
+		a := make([]float64, m*lda)
+		for i := 0; i < m*lda; i++ {
+			a[i] = rnd.Float64()
+		}
+		aCopy := make([]float64, len(a))
+		copy(aCopy, a)
+		impl.Dgelq2(m, n, a, lda, tau, work)
+
+		Q := constructQ("LQ", m, n, a, lda, tau)
+
+		// Check that Q is orthonormal
+		for i := 0; i < Q.Rows; i++ {
+			nrm := blas64.Nrm2(Q.Cols, blas64.Vector{Inc: 1, Data: Q.Data[i*Q.Stride:]})
+			if math.Abs(nrm-1) > 1e-14 {
+				t.Errorf("Q not normal. Norm is %v", nrm)
+			}
+			for j := 0; j < i; j++ {
+				dot := blas64.Dot(Q.Rows,
+					blas64.Vector{Inc: 1, Data: Q.Data[i*Q.Stride:]},
+					blas64.Vector{Inc: 1, Data: Q.Data[j*Q.Stride:]},
+				)
+				if math.Abs(dot) > 1e-14 {
+					t.Errorf("Q not orthogonal. Dot is %v", dot)
+				}
+			}
+		}
+
+		L := blas64.General{
+			Rows:   m,
+			Cols:   n,
+			Stride: n,
+			Data:   make([]float64, m*n),
+		}
+		for i := 0; i < m; i++ {
+			for j := 0; j <= min(i, n-1); j++ {
+				L.Data[i*L.Stride+j] = a[i*lda+j]
+			}
+		}
+
+		ans := blas64.General{
+			Rows:   m,
+			Cols:   n,
+			Stride: lda,
+			Data:   make([]float64, m*lda),
+		}
+		copy(ans.Data, aCopy)
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, L, Q, 0, ans)
+		if !floats.EqualApprox(aCopy, ans.Data, 1e-14) {
+			t.Errorf("Case %v, LQ mismatch. Want %v, got %v.", c, aCopy, ans.Data)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dgelqf.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgelqf.go
new file mode 100644
index 00000000..5bbe7312
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgelqf.go
@@ -0,0 +1,98 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dgelqfer interface {
+	Dgelq2er
+	Dgelqf(m, n int, a []float64, lda int, tau, work []float64, lwork int)
+}
+
+func DgelqfTest(t *testing.T, impl Dgelqfer) {
+	rnd := rand.New(rand.NewSource(1))
+	for c, test := range []struct {
+		m, n, lda int
+	}{
+		{10, 5, 0},
+		{5, 10, 0},
+		{10, 10, 0},
+		{300, 5, 0},
+		{3, 500, 0},
+		{200, 200, 0},
+		{300, 200, 0},
+		{204, 300, 0},
+		{1, 3000, 0},
+		{3000, 1, 0},
+		{10, 5, 30},
+		{5, 10, 30},
+		{10, 10, 30},
+		{300, 5, 500},
+		{3, 500, 600},
+		{200, 200, 300},
+		{300, 200, 300},
+		{204, 300, 400},
+		{1, 3000, 4000},
+		{3000, 1, 4000},
+	} {
+		m := test.m
+		n := test.n
+		lda := test.lda
+		if lda == 0 {
+			lda = n
+		}
+		a := make([]float64, m*lda)
+		for i := 0; i < m; i++ {
+			for j := 0; j < n; j++ {
+				a[i*lda+j] = rnd.Float64()
+			}
+		}
+		tau := make([]float64, n)
+		for i := 0; i < n; i++ {
+			tau[i] = rnd.Float64()
+		}
+		aCopy := make([]float64, len(a))
+		copy(aCopy, a)
+		ans := make([]float64, len(a))
+		copy(ans, a)
+		work := make([]float64, m)
+		for i := range work {
+			work[i] = rnd.Float64()
+		}
+		// Compute unblocked QR.
+		impl.Dgelq2(m, n, ans, lda, tau, work)
+		// Compute blocked QR with small work.
+		impl.Dgelqf(m, n, a, lda, tau, work, len(work))
+		if !floats.EqualApprox(ans, a, 1e-12) {
+			t.Errorf("Case %v, mismatch small work.", c)
+		}
+		// Try the full length of work.
+		impl.Dgelqf(m, n, a, lda, tau, work, -1)
+		lwork := int(work[0])
+		work = make([]float64, lwork)
+		copy(a, aCopy)
+		impl.Dgelqf(m, n, a, lda, tau, work, lwork)
+		if !floats.EqualApprox(ans, a, 1e-12) {
+			t.Errorf("Case %v, mismatch large work.", c)
+		}
+
+		// Try a slightly smaller version of work to test blocking code.
+		if len(work) <= m {
+			continue
+		}
+		work = work[1:]
+		lwork--
+		copy(a, aCopy)
+		impl.Dgelqf(m, n, a, lda, tau, work, lwork)
+		if !floats.EqualApprox(ans, a, 1e-12) {
+			t.Errorf("Case %v, mismatch large work.", c)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dgels.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgels.go
new file mode 100644
index 00000000..9b49a54c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgels.go
@@ -0,0 +1,182 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dgelser interface {
+	Dgels(trans blas.Transpose, m, n, nrhs int, a []float64, lda int, b []float64, ldb int, work []float64, lwork int) bool
+}
+
+func DgelsTest(t *testing.T, impl Dgelser) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, trans := range []blas.Transpose{blas.NoTrans, blas.Trans} {
+		for _, test := range []struct {
+			m, n, nrhs, lda, ldb int
+		}{
+			{3, 4, 5, 0, 0},
+			{3, 5, 4, 0, 0},
+			{4, 3, 5, 0, 0},
+			{4, 5, 3, 0, 0},
+			{5, 3, 4, 0, 0},
+			{5, 4, 3, 0, 0},
+			{3, 4, 5, 10, 20},
+			{3, 5, 4, 10, 20},
+			{4, 3, 5, 10, 20},
+			{4, 5, 3, 10, 20},
+			{5, 3, 4, 10, 20},
+			{5, 4, 3, 10, 20},
+			{3, 4, 5, 20, 10},
+			{3, 5, 4, 20, 10},
+			{4, 3, 5, 20, 10},
+			{4, 5, 3, 20, 10},
+			{5, 3, 4, 20, 10},
+			{5, 4, 3, 20, 10},
+			{200, 300, 400, 0, 0},
+			{200, 400, 300, 0, 0},
+			{300, 200, 400, 0, 0},
+			{300, 400, 200, 0, 0},
+			{400, 200, 300, 0, 0},
+			{400, 300, 200, 0, 0},
+			{200, 300, 400, 500, 600},
+			{200, 400, 300, 500, 600},
+			{300, 200, 400, 500, 600},
+			{300, 400, 200, 500, 600},
+			{400, 200, 300, 500, 600},
+			{400, 300, 200, 500, 600},
+			{200, 300, 400, 600, 500},
+			{200, 400, 300, 600, 500},
+			{300, 200, 400, 600, 500},
+			{300, 400, 200, 600, 500},
+			{400, 200, 300, 600, 500},
+			{400, 300, 200, 600, 500},
+		} {
+			m := test.m
+			n := test.n
+			nrhs := test.nrhs
+
+			lda := test.lda
+			if lda == 0 {
+				lda = n
+			}
+			a := make([]float64, m*lda)
+			for i := range a {
+				a[i] = rnd.Float64()
+			}
+			aCopy := make([]float64, len(a))
+			copy(aCopy, a)
+
+			// Size of b is the same trans or no trans, because the number of rows
+			// has to be the max of (m,n).
+			mb := max(m, n)
+			nb := nrhs
+			ldb := test.ldb
+			if ldb == 0 {
+				ldb = nb
+			}
+			b := make([]float64, mb*ldb)
+			for i := range b {
+				b[i] = rnd.Float64()
+			}
+			bCopy := make([]float64, len(b))
+			copy(bCopy, b)
+
+			// Find optimal work length.
+			work := make([]float64, 1)
+			impl.Dgels(trans, m, n, nrhs, a, lda, b, ldb, work, -1)
+
+			// Perform linear solve
+			work = make([]float64, int(work[0]))
+			lwork := len(work)
+			for i := range work {
+				work[i] = rnd.Float64()
+			}
+			impl.Dgels(trans, m, n, nrhs, a, lda, b, ldb, work, lwork)
+
+			// Check that the answer is correct by comparing to the normal equations.
+			aMat := blas64.General{
+				Rows:   m,
+				Cols:   n,
+				Stride: lda,
+				Data:   make([]float64, len(aCopy)),
+			}
+			copy(aMat.Data, aCopy)
+			szAta := n
+			if trans == blas.Trans {
+				szAta = m
+			}
+			aTA := blas64.General{
+				Rows:   szAta,
+				Cols:   szAta,
+				Stride: szAta,
+				Data:   make([]float64, szAta*szAta),
+			}
+
+			// Compute A^T * A if notrans and A * A^T otherwise.
+			if trans == blas.NoTrans {
+				blas64.Gemm(blas.Trans, blas.NoTrans, 1, aMat, aMat, 0, aTA)
+			} else {
+				blas64.Gemm(blas.NoTrans, blas.Trans, 1, aMat, aMat, 0, aTA)
+			}
+
+			// Multiply by X.
+			X := blas64.General{
+				Rows:   szAta,
+				Cols:   nrhs,
+				Stride: ldb,
+				Data:   b,
+			}
+			ans := blas64.General{
+				Rows:   aTA.Rows,
+				Cols:   X.Cols,
+				Stride: X.Cols,
+				Data:   make([]float64, aTA.Rows*X.Cols),
+			}
+			blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, aTA, X, 0, ans)
+
+			B := blas64.General{
+				Rows:   szAta,
+				Cols:   nrhs,
+				Stride: ldb,
+				Data:   make([]float64, len(bCopy)),
+			}
+
+			copy(B.Data, bCopy)
+			var ans2 blas64.General
+			if trans == blas.NoTrans {
+				ans2 = blas64.General{
+					Rows:   aMat.Cols,
+					Cols:   B.Cols,
+					Stride: B.Cols,
+					Data:   make([]float64, aMat.Cols*B.Cols),
+				}
+			} else {
+				ans2 = blas64.General{
+					Rows:   aMat.Rows,
+					Cols:   B.Cols,
+					Stride: B.Cols,
+					Data:   make([]float64, aMat.Rows*B.Cols),
+				}
+			}
+
+			// Compute A^T B if Trans or A * B otherwise
+			if trans == blas.NoTrans {
+				blas64.Gemm(blas.Trans, blas.NoTrans, 1, aMat, B, 0, ans2)
+			} else {
+				blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, aMat, B, 0, ans2)
+			}
+			if !floats.EqualApprox(ans.Data, ans2.Data, 1e-12) {
+				t.Errorf("Normal equations not satisfied")
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dgeql2.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgeql2.go
new file mode 100644
index 00000000..0ff6a930
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgeql2.go
@@ -0,0 +1,99 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dgeql2er interface {
+	Dgeql2(m, n int, a []float64, lda int, tau, work []float64)
+}
+
+func Dgeql2Test(t *testing.T, impl Dgeql2er) {
+	rnd := rand.New(rand.NewSource(1))
+	// TODO(btracey): Add tests for m < n.
+	for _, test := range []struct {
+		m, n, lda int
+	}{
+		{5, 5, 0},
+		{5, 3, 0},
+		{5, 4, 0},
+	} {
+		m := test.m
+		n := test.n
+		lda := test.lda
+		if lda == 0 {
+			lda = n
+		}
+		a := make([]float64, m*lda)
+		for i := range a {
+			a[i] = rnd.NormFloat64()
+		}
+		tau := nanSlice(min(m, n))
+		work := nanSlice(n)
+
+		aCopy := make([]float64, len(a))
+		copy(aCopy, a)
+		impl.Dgeql2(m, n, a, lda, tau, work)
+
+		k := min(m, n)
+		// Construct Q.
+		q := blas64.General{
+			Rows:   m,
+			Cols:   m,
+			Stride: m,
+			Data:   make([]float64, m*m),
+		}
+		for i := 0; i < m; i++ {
+			q.Data[i*q.Stride+i] = 1
+		}
+		for i := 0; i < k; i++ {
+			h := blas64.General{Rows: m, Cols: m, Stride: m, Data: make([]float64, m*m)}
+			for j := 0; j < m; j++ {
+				h.Data[j*h.Stride+j] = 1
+			}
+			v := blas64.Vector{Inc: 1, Data: make([]float64, m)}
+			v.Data[m-k+i] = 1
+			for j := 0; j < m-k+i; j++ {
+				v.Data[j] = a[j*lda+n-k+i]
+			}
+			blas64.Ger(-tau[i], v, v, h)
+			qTmp := blas64.General{Rows: q.Rows, Cols: q.Cols, Stride: q.Stride, Data: make([]float64, len(q.Data))}
+			copy(qTmp.Data, q.Data)
+			blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, h, qTmp, 0, q)
+		}
+		if !isOrthonormal(q) {
+			t.Errorf("Q is not orthonormal")
+		}
+		l := blas64.General{
+			Rows:   m,
+			Cols:   n,
+			Stride: n,
+			Data:   make([]float64, m*n),
+		}
+		if m >= n {
+			for i := m - n; i < m; i++ {
+				for j := 0; j <= min(i-(m-n), n-1); j++ {
+					l.Data[i*l.Stride+j] = a[i*lda+j]
+				}
+			}
+		} else {
+			panic("untested")
+		}
+		ans := blas64.General{Rows: m, Cols: n, Stride: lda, Data: make([]float64, len(a))}
+		copy(ans.Data, a)
+
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, q, l, 0, ans)
+		if !floats.EqualApprox(ans.Data, aCopy, 1e-10) {
+			t.Errorf("Reconstruction mismatch: m = %v, n = %v", m, n)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dgeqp3.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgeqp3.go
new file mode 100644
index 00000000..54e30bf5
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgeqp3.go
@@ -0,0 +1,135 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dgeqp3er interface {
+	Dlapmter
+	Dgeqp3(m, n int, a []float64, lda int, jpvt []int, tau, work []float64, lwork int)
+}
+
+func Dgeqp3Test(t *testing.T, impl Dgeqp3er) {
+	rnd := rand.New(rand.NewSource(1))
+	for c, test := range []struct {
+		m, n, lda int
+	}{
+		{1, 1, 0},
+		{2, 2, 0},
+		{3, 2, 0},
+		{2, 3, 0},
+		{1, 12, 0},
+		{2, 6, 0},
+		{3, 4, 0},
+		{4, 3, 0},
+		{6, 2, 0},
+		{12, 1, 0},
+		{1, 1, 20},
+		{2, 2, 20},
+		{3, 2, 20},
+		{2, 3, 20},
+		{1, 12, 20},
+		{2, 6, 20},
+		{3, 4, 20},
+		{4, 3, 20},
+		{6, 2, 20},
+		{12, 1, 20},
+		{129, 256, 0},
+		{256, 129, 0},
+		{129, 256, 266},
+		{256, 129, 266},
+	} {
+		n := test.n
+		m := test.m
+		lda := test.lda
+		if lda == 0 {
+			lda = test.n
+		}
+		const (
+			all = iota
+			some
+			none
+		)
+		for _, free := range []int{all, some, none} {
+			a := make([]float64, m*lda)
+			for i := range a {
+				a[i] = rnd.Float64()
+			}
+			aCopy := make([]float64, len(a))
+			copy(aCopy, a)
+			jpvt := make([]int, n)
+			for j := range jpvt {
+				switch free {
+				case all:
+					jpvt[j] = -1
+				case some:
+					jpvt[j] = rnd.Intn(2) - 1
+				case none:
+					jpvt[j] = 0
+				default:
+					panic("bad freedom")
+				}
+			}
+			k := min(m, n)
+			tau := make([]float64, k)
+			for i := range tau {
+				tau[i] = rnd.Float64()
+			}
+			work := make([]float64, 1)
+			impl.Dgeqp3(m, n, a, lda, jpvt, tau, work, -1)
+			lwork := int(work[0])
+			work = make([]float64, lwork)
+			for i := range work {
+				work[i] = rnd.Float64()
+			}
+			impl.Dgeqp3(m, n, a, lda, jpvt, tau, work, lwork)
+
+			// Test that the QR factorization has completed successfully. Compute
+			// Q based on the vectors.
+			q := constructQ("QR", m, n, a, lda, tau)
+
+			// Check that q is orthonormal
+			for i := 0; i < m; i++ {
+				nrm := blas64.Nrm2(m, blas64.Vector{Inc: 1, Data: q.Data[i*m:]})
+				if math.Abs(nrm-1) > 1e-13 {
+					t.Errorf("Case %v, q not normal", c)
+				}
+				for j := 0; j < i; j++ {
+					dot := blas64.Dot(m, blas64.Vector{Inc: 1, Data: q.Data[i*m:]}, blas64.Vector{Inc: 1, Data: q.Data[j*m:]})
+					if math.Abs(dot) > 1e-14 {
+						t.Errorf("Case %v, q not orthogonal", c)
+					}
+				}
+			}
+			// Check that A * P = Q * R
+			r := blas64.General{
+				Rows:   m,
+				Cols:   n,
+				Stride: n,
+				Data:   make([]float64, m*n),
+			}
+			for i := 0; i < m; i++ {
+				for j := i; j < n; j++ {
+					r.Data[i*n+j] = a[i*lda+j]
+				}
+			}
+			got := nanGeneral(m, n, lda)
+			blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, q, r, 0, got)
+
+			want := blas64.General{Rows: m, Cols: n, Stride: lda, Data: aCopy}
+			impl.Dlapmt(true, want.Rows, want.Cols, want.Data, want.Stride, jpvt)
+			if !equalApproxGeneral(got, want, 1e-13) {
+				t.Errorf("Case %v,  Q*R != A*P\nQ*R=%v\nA*P=%v", c, got, want)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dgeqr2.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgeqr2.go
new file mode 100644
index 00000000..f9ebf694
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgeqr2.go
@@ -0,0 +1,111 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dgeqr2er interface {
+	Dgeqr2(m, n int, a []float64, lda int, tau []float64, work []float64)
+}
+
+func Dgeqr2Test(t *testing.T, impl Dgeqr2er) {
+	rnd := rand.New(rand.NewSource(1))
+	for c, test := range []struct {
+		m, n, lda int
+	}{
+		{1, 1, 0},
+		{2, 2, 0},
+		{3, 2, 0},
+		{2, 3, 0},
+		{1, 12, 0},
+		{2, 6, 0},
+		{3, 4, 0},
+		{4, 3, 0},
+		{6, 2, 0},
+		{12, 1, 0},
+		{1, 1, 20},
+		{2, 2, 20},
+		{3, 2, 20},
+		{2, 3, 20},
+		{1, 12, 20},
+		{2, 6, 20},
+		{3, 4, 20},
+		{4, 3, 20},
+		{6, 2, 20},
+		{12, 1, 20},
+	} {
+		n := test.n
+		m := test.m
+		lda := test.lda
+		if lda == 0 {
+			lda = test.n
+		}
+		a := make([]float64, m*lda)
+		for i := range a {
+			a[i] = rnd.Float64()
+		}
+		aCopy := make([]float64, len(a))
+		k := min(m, n)
+		tau := make([]float64, k)
+		for i := range tau {
+			tau[i] = rnd.Float64()
+		}
+		work := make([]float64, n)
+		for i := range work {
+			work[i] = rnd.Float64()
+		}
+		copy(aCopy, a)
+		impl.Dgeqr2(m, n, a, lda, tau, work)
+
+		// Test that the QR factorization has completed successfully. Compute
+		// Q based on the vectors.
+		q := constructQ("QR", m, n, a, lda, tau)
+
+		// Check that q is orthonormal
+		for i := 0; i < m; i++ {
+			nrm := blas64.Nrm2(m, blas64.Vector{Inc: 1, Data: q.Data[i*m:]})
+			if math.Abs(nrm-1) > 1e-14 {
+				t.Errorf("Case %v, q not normal", c)
+			}
+			for j := 0; j < i; j++ {
+				dot := blas64.Dot(m, blas64.Vector{Inc: 1, Data: q.Data[i*m:]}, blas64.Vector{Inc: 1, Data: q.Data[j*m:]})
+				if math.Abs(dot) > 1e-14 {
+					t.Errorf("Case %v, q not orthogonal", c)
+				}
+			}
+		}
+		// Check that A = Q * R
+		r := blas64.General{
+			Rows:   m,
+			Cols:   n,
+			Stride: n,
+			Data:   make([]float64, m*n),
+		}
+		for i := 0; i < m; i++ {
+			for j := i; j < n; j++ {
+				r.Data[i*n+j] = a[i*lda+j]
+			}
+		}
+		atmp := blas64.General{
+			Rows:   m,
+			Cols:   n,
+			Stride: lda,
+			Data:   make([]float64, m*lda),
+		}
+		copy(atmp.Data, a)
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, q, r, 0, atmp)
+		if !floats.EqualApprox(atmp.Data, aCopy, 1e-14) {
+			t.Errorf("Q*R != a")
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dgeqrf.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgeqrf.go
new file mode 100644
index 00000000..60386c08
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgeqrf.go
@@ -0,0 +1,95 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dgeqrfer interface {
+	Dgeqr2er
+	Dgeqrf(m, n int, a []float64, lda int, tau, work []float64, lwork int)
+}
+
+func DgeqrfTest(t *testing.T, impl Dgeqrfer) {
+	rnd := rand.New(rand.NewSource(1))
+	for c, test := range []struct {
+		m, n, lda int
+	}{
+		{10, 5, 0},
+		{5, 10, 0},
+		{10, 10, 0},
+		{300, 5, 0},
+		{3, 500, 0},
+		{200, 200, 0},
+		{300, 200, 0},
+		{204, 300, 0},
+		{1, 3000, 0},
+		{3000, 1, 0},
+		{10, 5, 20},
+		{5, 10, 20},
+		{10, 10, 20},
+		{300, 5, 400},
+		{3, 500, 600},
+		{200, 200, 300},
+		{300, 200, 300},
+		{204, 300, 400},
+		{1, 3000, 4000},
+		{3000, 1, 4000},
+	} {
+		m := test.m
+		n := test.n
+		lda := test.lda
+		if lda == 0 {
+			lda = test.n
+		}
+		a := make([]float64, m*lda)
+		for i := 0; i < m; i++ {
+			for j := 0; j < n; j++ {
+				a[i*lda+j] = rnd.Float64()
+			}
+		}
+		tau := make([]float64, n)
+		for i := 0; i < n; i++ {
+			tau[i] = rnd.Float64()
+		}
+		aCopy := make([]float64, len(a))
+		copy(aCopy, a)
+		ans := make([]float64, len(a))
+		copy(ans, a)
+		work := make([]float64, n)
+		// Compute unblocked QR.
+		impl.Dgeqr2(m, n, ans, lda, tau, work)
+		// Compute blocked QR with small work.
+		impl.Dgeqrf(m, n, a, lda, tau, work, len(work))
+		if !floats.EqualApprox(ans, a, 1e-12) {
+			t.Errorf("Case %v, mismatch small work.", c)
+		}
+		// Try the full length of work.
+		impl.Dgeqrf(m, n, a, lda, tau, work, -1)
+		lwork := int(work[0])
+		work = make([]float64, lwork)
+		copy(a, aCopy)
+		impl.Dgeqrf(m, n, a, lda, tau, work, lwork)
+		if !floats.EqualApprox(ans, a, 1e-12) {
+			t.Errorf("Case %v, mismatch large work.", c)
+		}
+
+		// Try a slightly smaller version of work to test blocking.
+		if len(work) <= n {
+			continue
+		}
+		work = work[1:]
+		lwork--
+		copy(a, aCopy)
+		impl.Dgeqrf(m, n, a, lda, tau, work, lwork)
+		if !floats.EqualApprox(ans, a, 1e-12) {
+			t.Errorf("Case %v, mismatch large work.", c)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dgerq2.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgerq2.go
new file mode 100644
index 00000000..ec0dde2a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgerq2.go
@@ -0,0 +1,117 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dgerq2er interface {
+	Dgerq2(m, n int, a []float64, lda int, tau []float64, work []float64)
+}
+
+func Dgerq2Test(t *testing.T, impl Dgerq2er) {
+	rnd := rand.New(rand.NewSource(1))
+	for c, test := range []struct {
+		m, n, lda int
+	}{
+		{1, 1, 0},
+		{2, 2, 0},
+		{3, 2, 0},
+		{2, 3, 0},
+		{1, 12, 0},
+		{2, 6, 0},
+		{3, 4, 0},
+		{4, 3, 0},
+		{6, 2, 0},
+		{12, 1, 0},
+		{1, 1, 20},
+		{2, 2, 20},
+		{3, 2, 20},
+		{2, 3, 20},
+		{1, 12, 20},
+		{2, 6, 20},
+		{3, 4, 20},
+		{4, 3, 20},
+		{6, 2, 20},
+		{12, 1, 20},
+	} {
+		n := test.n
+		m := test.m
+		lda := test.lda
+		if lda == 0 {
+			lda = test.n
+		}
+		a := make([]float64, m*lda)
+		for i := range a {
+			a[i] = rnd.Float64()
+		}
+		aCopy := make([]float64, len(a))
+		k := min(m, n)
+		tau := make([]float64, k)
+		for i := range tau {
+			tau[i] = rnd.Float64()
+		}
+		work := make([]float64, m)
+		for i := range work {
+			work[i] = rnd.Float64()
+		}
+		copy(aCopy, a)
+		impl.Dgerq2(m, n, a, lda, tau, work)
+
+		// Test that the RQ factorization has completed successfully. Compute
+		// Q based on the vectors.
+		q := constructQ("RQ", m, n, a, lda, tau)
+
+		// Check that q is orthonormal
+		for i := 0; i < q.Rows; i++ {
+			nrm := blas64.Nrm2(q.Cols, blas64.Vector{Inc: 1, Data: q.Data[i*q.Stride:]})
+			if math.IsNaN(nrm) || math.Abs(nrm-1) > 1e-14 {
+				t.Errorf("Case %v, q not normal", c)
+			}
+			for j := 0; j < i; j++ {
+				dot := blas64.Dot(q.Cols, blas64.Vector{Inc: 1, Data: q.Data[i*q.Stride:]}, blas64.Vector{Inc: 1, Data: q.Data[j*q.Stride:]})
+				if math.IsNaN(dot) || math.Abs(dot) > 1e-14 {
+					t.Errorf("Case %v, q not orthogonal", c)
+				}
+			}
+		}
+		// Check that A = R * Q
+		r := blas64.General{
+			Rows:   m,
+			Cols:   n,
+			Stride: n,
+			Data:   make([]float64, m*n),
+		}
+		for i := 0; i < m; i++ {
+			off := m - n
+			for j := max(0, i-off); j < n; j++ {
+				r.Data[i*r.Stride+j] = a[i*lda+j]
+			}
+		}
+
+		got := blas64.General{
+			Rows:   m,
+			Cols:   n,
+			Stride: lda,
+			Data:   make([]float64, m*lda),
+		}
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, r, q, 0, got)
+		want := blas64.General{
+			Rows:   m,
+			Cols:   n,
+			Stride: lda,
+			Data:   aCopy,
+		}
+		if !equalApproxGeneral(got, want, 1e-14) {
+			t.Errorf("Case %d, R*Q != a\ngot: %+v\nwant:%+v", c, got, want)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dgerqf.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgerqf.go
new file mode 100644
index 00000000..b6e24126
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgerqf.go
@@ -0,0 +1,142 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dgerqfer interface {
+	Dgerqf(m, n int, a []float64, lda int, tau, work []float64, lwork int)
+}
+
+func DgerqfTest(t *testing.T, impl Dgerqfer) {
+	const tol = 1e-13
+
+	rnd := rand.New(rand.NewSource(1))
+	for c, test := range []struct {
+		m, n, lda int
+	}{
+		{1, 1, 0},
+		{2, 2, 0},
+		{3, 2, 0},
+		{2, 3, 0},
+		{1, 12, 0},
+		{2, 6, 0},
+		{3, 4, 0},
+		{4, 3, 0},
+		{6, 2, 0},
+		{12, 1, 0},
+		{200, 180, 0},
+		{180, 200, 0},
+		{200, 200, 0},
+		{1, 1, 20},
+		{2, 2, 20},
+		{3, 2, 20},
+		{2, 3, 20},
+		{1, 12, 20},
+		{2, 6, 20},
+		{3, 4, 20},
+		{4, 3, 20},
+		{6, 2, 20},
+		{12, 1, 20},
+		{200, 180, 220},
+		{180, 200, 220},
+		{200, 200, 220},
+	} {
+		n := test.n
+		m := test.m
+		lda := test.lda
+		if lda == 0 {
+			lda = test.n
+		}
+		a := make([]float64, m*lda)
+		for i := range a {
+			a[i] = rnd.Float64()
+		}
+		aCopy := make([]float64, len(a))
+		copy(aCopy, a)
+		k := min(m, n)
+		tau := make([]float64, k)
+		for i := range tau {
+			tau[i] = rnd.Float64()
+		}
+		work := []float64{0}
+		impl.Dgerqf(m, n, a, lda, tau, work, -1)
+		lwkopt := int(work[0])
+		for _, wk := range []struct {
+			name   string
+			length int
+		}{
+			{name: "short", length: m},
+			{name: "medium", length: lwkopt - 1},
+			{name: "long", length: lwkopt},
+		} {
+			if wk.length < max(1, m) {
+				continue
+			}
+			lwork := wk.length
+			work = make([]float64, lwork)
+			for i := range work {
+				work[i] = rnd.Float64()
+			}
+			copy(a, aCopy)
+			impl.Dgerqf(m, n, a, lda, tau, work, lwork)
+
+			// Test that the RQ factorization has completed successfully. Compute
+			// Q based on the vectors.
+			q := constructQ("RQ", m, n, a, lda, tau)
+
+			// Check that q is orthonormal
+			for i := 0; i < q.Rows; i++ {
+				nrm := blas64.Nrm2(q.Cols, blas64.Vector{Inc: 1, Data: q.Data[i*q.Stride:]})
+				if math.IsNaN(nrm) || math.Abs(nrm-1) > 1e-14 {
+					t.Errorf("Case %v, q not normal", c)
+				}
+				for j := 0; j < i; j++ {
+					dot := blas64.Dot(q.Cols, blas64.Vector{Inc: 1, Data: q.Data[i*q.Stride:]}, blas64.Vector{Inc: 1, Data: q.Data[j*q.Stride:]})
+					if math.IsNaN(dot) || math.Abs(dot) > 1e-14 {
+						t.Errorf("Case %v, q not orthogonal", c)
+					}
+				}
+			}
+			// Check that A = R * Q
+			r := blas64.General{
+				Rows:   m,
+				Cols:   n,
+				Stride: n,
+				Data:   make([]float64, m*n),
+			}
+			for i := 0; i < m; i++ {
+				off := m - n
+				for j := max(0, i-off); j < n; j++ {
+					r.Data[i*r.Stride+j] = a[i*lda+j]
+				}
+			}
+
+			got := blas64.General{
+				Rows:   m,
+				Cols:   n,
+				Stride: lda,
+				Data:   make([]float64, m*lda),
+			}
+			blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, r, q, 0, got)
+			want := blas64.General{
+				Rows:   m,
+				Cols:   n,
+				Stride: lda,
+				Data:   aCopy,
+			}
+			if !equalApproxGeneral(got, want, tol) {
+				t.Errorf("Case %d, R*Q != a %s\ngot: %+v\nwant:%+v", c, wk.name, got, want)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dgesvd.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgesvd.go
new file mode 100644
index 00000000..8c317993
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgesvd.go
@@ -0,0 +1,286 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dgesvder interface {
+	Dgesvd(jobU, jobVT lapack.SVDJob, m, n int, a []float64, lda int, s, u []float64, ldu int, vt []float64, ldvt int, work []float64, lwork int) (ok bool)
+}
+
+func DgesvdTest(t *testing.T, impl Dgesvder) {
+	rnd := rand.New(rand.NewSource(1))
+	// TODO(btracey): Add tests for all of the cases when the SVD implementation
+	// is finished.
+	// TODO(btracey): Add tests for m > mnthr and n > mnthr when other SVD
+	// conditions are implemented. Right now mnthr is 5,000,000 which is too
+	// large to create a square matrix of that size.
+	for _, test := range []struct {
+		m, n, lda, ldu, ldvt int
+	}{
+		{5, 5, 0, 0, 0},
+		{5, 6, 0, 0, 0},
+		{6, 5, 0, 0, 0},
+		{5, 9, 0, 0, 0},
+		{9, 5, 0, 0, 0},
+
+		{5, 5, 10, 11, 12},
+		{5, 6, 10, 11, 12},
+		{6, 5, 10, 11, 12},
+		{5, 5, 10, 11, 12},
+		{5, 9, 10, 11, 12},
+		{9, 5, 10, 11, 12},
+
+		{300, 300, 0, 0, 0},
+		{300, 400, 0, 0, 0},
+		{400, 300, 0, 0, 0},
+		{300, 600, 0, 0, 0},
+		{600, 300, 0, 0, 0},
+
+		{300, 300, 400, 450, 460},
+		{300, 400, 500, 550, 560},
+		{400, 300, 550, 550, 560},
+		{300, 600, 700, 750, 760},
+		{600, 300, 700, 750, 760},
+	} {
+		jobU := lapack.SVDAll
+		jobVT := lapack.SVDAll
+
+		m := test.m
+		n := test.n
+		lda := test.lda
+		if lda == 0 {
+			lda = n
+		}
+		ldu := test.ldu
+		if ldu == 0 {
+			ldu = m
+		}
+		ldvt := test.ldvt
+		if ldvt == 0 {
+			ldvt = n
+		}
+
+		a := make([]float64, m*lda)
+		for i := range a {
+			a[i] = rnd.NormFloat64()
+		}
+
+		u := make([]float64, m*ldu)
+		for i := range u {
+			u[i] = rnd.NormFloat64()
+		}
+
+		vt := make([]float64, n*ldvt)
+		for i := range vt {
+			vt[i] = rnd.NormFloat64()
+		}
+
+		uAllOrig := make([]float64, len(u))
+		copy(uAllOrig, u)
+		vtAllOrig := make([]float64, len(vt))
+		copy(vtAllOrig, vt)
+		aCopy := make([]float64, len(a))
+		copy(aCopy, a)
+
+		s := make([]float64, min(m, n))
+
+		work := make([]float64, 1)
+		impl.Dgesvd(jobU, jobVT, m, n, a, lda, s, u, ldu, vt, ldvt, work, -1)
+
+		if !floats.Equal(a, aCopy) {
+			t.Errorf("a changed during call to get work length")
+		}
+
+		work = make([]float64, int(work[0]))
+		impl.Dgesvd(jobU, jobVT, m, n, a, lda, s, u, ldu, vt, ldvt, work, len(work))
+
+		errStr := fmt.Sprintf("m = %v, n = %v, lda = %v, ldu = %v, ldv = %v", m, n, lda, ldu, ldvt)
+		svdCheck(t, false, errStr, m, n, s, a, u, ldu, vt, ldvt, aCopy, lda)
+		svdCheckPartial(t, impl, lapack.SVDAll, errStr, uAllOrig, vtAllOrig, aCopy, m, n, a, lda, s, u, ldu, vt, ldvt, work, false)
+
+		// Test InPlace
+		jobU = lapack.SVDInPlace
+		jobVT = lapack.SVDInPlace
+		copy(a, aCopy)
+		copy(u, uAllOrig)
+		copy(vt, vtAllOrig)
+
+		impl.Dgesvd(jobU, jobVT, m, n, a, lda, s, u, ldu, vt, ldvt, work, len(work))
+		svdCheck(t, true, errStr, m, n, s, a, u, ldu, vt, ldvt, aCopy, lda)
+		svdCheckPartial(t, impl, lapack.SVDInPlace, errStr, uAllOrig, vtAllOrig, aCopy, m, n, a, lda, s, u, ldu, vt, ldvt, work, false)
+	}
+}
+
+// svdCheckPartial checks that the singular values and vectors are computed when
+// not all of them are computed.
+func svdCheckPartial(t *testing.T, impl Dgesvder, job lapack.SVDJob, errStr string, uAllOrig, vtAllOrig, aCopy []float64, m, n int, a []float64, lda int, s, u []float64, ldu int, vt []float64, ldvt int, work []float64, shortWork bool) {
+	rnd := rand.New(rand.NewSource(1))
+	jobU := job
+	jobVT := job
+	// Compare the singular values when computed with {SVDNone, SVDNone.}
+	sCopy := make([]float64, len(s))
+	copy(sCopy, s)
+	copy(a, aCopy)
+	for i := range s {
+		s[i] = rnd.Float64()
+	}
+	tmp1 := make([]float64, 1)
+	tmp2 := make([]float64, 1)
+	jobU = lapack.SVDNone
+	jobVT = lapack.SVDNone
+
+	impl.Dgesvd(jobU, jobVT, m, n, a, lda, s, tmp1, ldu, tmp2, ldvt, work, -1)
+	work = make([]float64, int(work[0]))
+	lwork := len(work)
+	if shortWork {
+		lwork--
+	}
+	ok := impl.Dgesvd(jobU, jobVT, m, n, a, lda, s, tmp1, ldu, tmp2, ldvt, work, lwork)
+	if !ok {
+		t.Errorf("Dgesvd did not complete successfully")
+	}
+	if !floats.EqualApprox(s, sCopy, 1e-10) {
+		t.Errorf("Singular value mismatch when singular vectors not computed: %s", errStr)
+	}
+	// Check that the singular vectors are correctly computed when the other
+	// is none.
+	uAll := make([]float64, len(u))
+	copy(uAll, u)
+	vtAll := make([]float64, len(vt))
+	copy(vtAll, vt)
+
+	// Copy the original vectors so the data outside the matrix bounds is the same.
+	copy(u, uAllOrig)
+	copy(vt, vtAllOrig)
+
+	jobU = job
+	jobVT = lapack.SVDNone
+	copy(a, aCopy)
+	for i := range s {
+		s[i] = rnd.Float64()
+	}
+	impl.Dgesvd(jobU, jobVT, m, n, a, lda, s, u, ldu, tmp2, ldvt, work, -1)
+	work = make([]float64, int(work[0]))
+	lwork = len(work)
+	if shortWork {
+		lwork--
+	}
+	impl.Dgesvd(jobU, jobVT, m, n, a, lda, s, u, ldu, tmp2, ldvt, work, len(work))
+	if !floats.EqualApprox(uAll, u, 1e-10) {
+		t.Errorf("U mismatch when VT is not computed: %s", errStr)
+	}
+	if !floats.EqualApprox(s, sCopy, 1e-10) {
+		t.Errorf("Singular value mismatch when U computed VT not")
+	}
+	jobU = lapack.SVDNone
+	jobVT = job
+	copy(a, aCopy)
+	for i := range s {
+		s[i] = rnd.Float64()
+	}
+	impl.Dgesvd(jobU, jobVT, m, n, a, lda, s, tmp1, ldu, vt, ldvt, work, -1)
+	work = make([]float64, int(work[0]))
+	lwork = len(work)
+	if shortWork {
+		lwork--
+	}
+	impl.Dgesvd(jobU, jobVT, m, n, a, lda, s, tmp1, ldu, vt, ldvt, work, len(work))
+	if !floats.EqualApprox(vtAll, vt, 1e-10) {
+		t.Errorf("VT mismatch when U is not computed: %s", errStr)
+	}
+	if !floats.EqualApprox(s, sCopy, 1e-10) {
+		t.Errorf("Singular value mismatch when VT computed U not")
+	}
+}
+
+// svdCheck checks that the singular value decomposition correctly multiplies back
+// to the original matrix.
+func svdCheck(t *testing.T, thin bool, errStr string, m, n int, s, a, u []float64, ldu int, vt []float64, ldvt int, aCopy []float64, lda int) {
+	sigma := blas64.General{
+		Rows:   m,
+		Cols:   n,
+		Stride: n,
+		Data:   make([]float64, m*n),
+	}
+	for i := 0; i < min(m, n); i++ {
+		sigma.Data[i*sigma.Stride+i] = s[i]
+	}
+
+	uMat := blas64.General{
+		Rows:   m,
+		Cols:   m,
+		Stride: ldu,
+		Data:   u,
+	}
+	vTMat := blas64.General{
+		Rows:   n,
+		Cols:   n,
+		Stride: ldvt,
+		Data:   vt,
+	}
+	if thin {
+		sigma.Rows = min(m, n)
+		sigma.Cols = min(m, n)
+		uMat.Cols = min(m, n)
+		vTMat.Rows = min(m, n)
+	}
+
+	tmp := blas64.General{
+		Rows:   m,
+		Cols:   n,
+		Stride: n,
+		Data:   make([]float64, m*n),
+	}
+	ans := blas64.General{
+		Rows:   m,
+		Cols:   n,
+		Stride: lda,
+		Data:   make([]float64, m*lda),
+	}
+	copy(ans.Data, a)
+
+	blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, uMat, sigma, 0, tmp)
+	blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, tmp, vTMat, 0, ans)
+
+	if !floats.EqualApprox(ans.Data, aCopy, 1e-8) {
+		t.Errorf("Decomposition mismatch. Trim = %v, %s", thin, errStr)
+	}
+
+	if !thin {
+		// Check that U and V are orthogonal.
+		for i := 0; i < uMat.Rows; i++ {
+			for j := i + 1; j < uMat.Rows; j++ {
+				dot := blas64.Dot(uMat.Cols,
+					blas64.Vector{Inc: 1, Data: uMat.Data[i*uMat.Stride:]},
+					blas64.Vector{Inc: 1, Data: uMat.Data[j*uMat.Stride:]},
+				)
+				if dot > 1e-8 {
+					t.Errorf("U not orthogonal %s", errStr)
+				}
+			}
+		}
+		for i := 0; i < vTMat.Rows; i++ {
+			for j := i + 1; j < vTMat.Rows; j++ {
+				dot := blas64.Dot(vTMat.Cols,
+					blas64.Vector{Inc: 1, Data: vTMat.Data[i*vTMat.Stride:]},
+					blas64.Vector{Inc: 1, Data: vTMat.Data[j*vTMat.Stride:]},
+				)
+				if dot > 1e-8 {
+					t.Errorf("V not orthogonal %s", errStr)
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dgetf2.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgetf2.go
new file mode 100644
index 00000000..7cb155e9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgetf2.go
@@ -0,0 +1,195 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dgetf2er interface {
+	Dgetf2(m, n int, a []float64, lda int, ipiv []int) bool
+}
+
+func Dgetf2Test(t *testing.T, impl Dgetf2er) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, test := range []struct {
+		m, n, lda int
+	}{
+		{10, 10, 0},
+		{10, 5, 0},
+		{10, 5, 0},
+
+		{10, 10, 20},
+		{5, 10, 20},
+		{10, 5, 20},
+	} {
+		m := test.m
+		n := test.n
+		lda := test.lda
+		if lda == 0 {
+			lda = n
+		}
+		a := make([]float64, m*lda)
+		for i := range a {
+			a[i] = rnd.Float64()
+		}
+		aCopy := make([]float64, len(a))
+		copy(aCopy, a)
+
+		mn := min(m, n)
+		ipiv := make([]int, mn)
+		for i := range ipiv {
+			ipiv[i] = rnd.Int()
+		}
+		ok := impl.Dgetf2(m, n, a, lda, ipiv)
+		checkPLU(t, ok, m, n, lda, ipiv, a, aCopy, 1e-14, true)
+	}
+
+	// Test with singular matrices (random matrices are almost surely non-singular).
+	for _, test := range []struct {
+		m, n, lda int
+		a         []float64
+	}{
+		{
+			m:   2,
+			n:   2,
+			lda: 2,
+			a: []float64{
+				1, 0,
+				0, 0,
+			},
+		},
+		{
+			m:   2,
+			n:   2,
+			lda: 2,
+			a: []float64{
+				1, 5,
+				2, 10,
+			},
+		},
+		{
+			m:   3,
+			n:   3,
+			lda: 3,
+			// row 3 = row1 + 2 * row2
+			a: []float64{
+				1, 5, 7,
+				2, 10, -3,
+				5, 25, 1,
+			},
+		},
+		{
+			m:   3,
+			n:   4,
+			lda: 4,
+			// row 3 = row1 + 2 * row2
+			a: []float64{
+				1, 5, 7, 9,
+				2, 10, -3, 11,
+				5, 25, 1, 31,
+			},
+		},
+	} {
+		if impl.Dgetf2(test.m, test.n, test.a, test.lda, make([]int, min(test.m, test.n))) {
+			t.Log("Returned ok with singular matrix.")
+		}
+	}
+}
+
+// checkPLU checks that the PLU factorization contained in factorize matches
+// the original matrix contained in original.
+func checkPLU(t *testing.T, ok bool, m, n, lda int, ipiv []int, factorized, original []float64, tol float64, print bool) {
+	var hasZeroDiagonal bool
+	for i := 0; i < min(m, n); i++ {
+		if factorized[i*lda+i] == 0 {
+			hasZeroDiagonal = true
+			break
+		}
+	}
+	if hasZeroDiagonal && ok {
+		t.Error("Has a zero diagonal but returned ok")
+	}
+	if !hasZeroDiagonal && !ok {
+		t.Error("Non-zero diagonal but returned !ok")
+	}
+
+	// Check that the LU decomposition is correct.
+	mn := min(m, n)
+	l := make([]float64, m*mn)
+	ldl := mn
+	u := make([]float64, mn*n)
+	ldu := n
+	for i := 0; i < m; i++ {
+		for j := 0; j < n; j++ {
+			v := factorized[i*lda+j]
+			switch {
+			case i == j:
+				l[i*ldl+i] = 1
+				u[i*ldu+i] = v
+			case i > j:
+				l[i*ldl+j] = v
+			case i < j:
+				u[i*ldu+j] = v
+			}
+		}
+	}
+
+	LU := blas64.General{
+		Rows:   m,
+		Cols:   n,
+		Stride: n,
+		Data:   make([]float64, m*n),
+	}
+	U := blas64.General{
+		Rows:   mn,
+		Cols:   n,
+		Stride: ldu,
+		Data:   u,
+	}
+	L := blas64.General{
+		Rows:   m,
+		Cols:   mn,
+		Stride: ldl,
+		Data:   l,
+	}
+	blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, L, U, 0, LU)
+
+	p := make([]float64, m*m)
+	ldp := m
+	for i := 0; i < m; i++ {
+		p[i*ldp+i] = 1
+	}
+	for i := len(ipiv) - 1; i >= 0; i-- {
+		v := ipiv[i]
+		blas64.Swap(m, blas64.Vector{Inc: 1, Data: p[i*ldp:]}, blas64.Vector{Inc: 1, Data: p[v*ldp:]})
+	}
+	P := blas64.General{
+		Rows:   m,
+		Cols:   m,
+		Stride: m,
+		Data:   p,
+	}
+	aComp := blas64.General{
+		Rows:   m,
+		Cols:   n,
+		Stride: lda,
+		Data:   make([]float64, m*lda),
+	}
+	copy(aComp.Data, factorized)
+	blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, P, LU, 0, aComp)
+	if !floats.EqualApprox(aComp.Data, original, tol) {
+		if print {
+			t.Errorf("PLU multiplication does not match original matrix.\nWant: %v\nGot: %v", original, aComp.Data)
+			return
+		}
+		t.Error("PLU multiplication does not match original matrix.")
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dgetrf.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgetrf.go
new file mode 100644
index 00000000..1c9c6e45
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgetrf.go
@@ -0,0 +1,65 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+)
+
+type Dgetrfer interface {
+	Dgetrf(m, n int, a []float64, lda int, ipiv []int) bool
+}
+
+func DgetrfTest(t *testing.T, impl Dgetrfer) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, test := range []struct {
+		m, n, lda int
+	}{
+		{10, 5, 0},
+		{5, 10, 0},
+		{10, 10, 0},
+		{300, 5, 0},
+		{3, 500, 0},
+		{4, 5, 0},
+		{300, 200, 0},
+		{204, 300, 0},
+		{1, 3000, 0},
+		{3000, 1, 0},
+		{10, 5, 20},
+		{5, 10, 20},
+		{10, 10, 20},
+		{300, 5, 400},
+		{3, 500, 600},
+		{200, 200, 300},
+		{300, 200, 300},
+		{204, 300, 400},
+		{1, 3000, 4000},
+		{3000, 1, 4000},
+	} {
+		m := test.m
+		n := test.n
+		lda := test.lda
+		if lda == 0 {
+			lda = n
+		}
+		a := make([]float64, m*lda)
+		for i := range a {
+			a[i] = rnd.Float64()
+		}
+		mn := min(m, n)
+		ipiv := make([]int, mn)
+		for i := range ipiv {
+			ipiv[i] = rnd.Int()
+		}
+
+		// Cannot compare the outputs of Dgetrf and Dgetf2 because the pivoting may
+		// happen differently. Instead check that the LPQ factorization is correct.
+		aCopy := make([]float64, len(a))
+		copy(aCopy, a)
+		ok := impl.Dgetrf(m, n, a, lda, ipiv)
+		checkPLU(t, ok, m, n, lda, ipiv, a, aCopy, 1e-10, false)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dgetri.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgetri.go
new file mode 100644
index 00000000..fd79df2a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgetri.go
@@ -0,0 +1,89 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dgetrier interface {
+	Dgetrfer
+	Dgetri(n int, a []float64, lda int, ipiv []int, work []float64, lwork int) bool
+}
+
+func DgetriTest(t *testing.T, impl Dgetrier) {
+	rnd := rand.New(rand.NewSource(1))
+	bi := blas64.Implementation()
+	for _, test := range []struct {
+		n, lda int
+	}{
+		{5, 0},
+		{5, 8},
+		{45, 0},
+		{45, 50},
+		{65, 0},
+		{65, 70},
+		{150, 0},
+		{150, 250},
+	} {
+		n := test.n
+		lda := test.lda
+		if lda == 0 {
+			lda = n
+		}
+		// Generate a random well conditioned matrix
+		perm := rnd.Perm(n)
+		a := make([]float64, n*lda)
+		for i := 0; i < n; i++ {
+			a[i*lda+perm[i]] = 1
+		}
+		for i := range a {
+			a[i] += 0.01 * rnd.Float64()
+		}
+		aCopy := make([]float64, len(a))
+		copy(aCopy, a)
+		ipiv := make([]int, n)
+		// Compute LU decomposition.
+		impl.Dgetrf(n, n, a, lda, ipiv)
+		// Compute inverse.
+		work := make([]float64, 1)
+		impl.Dgetri(n, a, lda, ipiv, work, -1)
+		work = make([]float64, int(work[0]))
+		lwork := len(work)
+
+		ok := impl.Dgetri(n, a, lda, ipiv, work, lwork)
+		if !ok {
+			t.Errorf("Unexpected singular matrix.")
+		}
+
+		// Check that A(inv) * A = I.
+		ans := make([]float64, len(a))
+		bi.Dgemm(blas.NoTrans, blas.NoTrans, n, n, n, 1, aCopy, lda, a, lda, 0, ans, lda)
+		isEye := true
+		for i := 0; i < n; i++ {
+			for j := 0; j < n; j++ {
+				if i == j {
+					// This tolerance is so high because computing matrix inverses
+					// is very unstable.
+					if math.Abs(ans[i*lda+j]-1) > 5e-2 {
+						isEye = false
+					}
+				} else {
+					if math.Abs(ans[i*lda+j]) > 5e-2 {
+						isEye = false
+					}
+				}
+			}
+		}
+		if !isEye {
+			t.Errorf("Inv(A) * A != I. n = %v, lda = %v", n, lda)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dgetrs.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgetrs.go
new file mode 100644
index 00000000..edc6d502
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dgetrs.go
@@ -0,0 +1,113 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dgetrser interface {
+	Dgetrfer
+	Dgetrs(trans blas.Transpose, n, nrhs int, a []float64, lda int, ipiv []int, b []float64, ldb int)
+}
+
+func DgetrsTest(t *testing.T, impl Dgetrser) {
+	rnd := rand.New(rand.NewSource(1))
+	// TODO(btracey): Put more thought into creating more regularized matrices
+	// and what correct tolerances should be. Consider also seeding the random
+	// number in this test to make it more robust to code changes in other
+	// parts of the suite.
+	for _, trans := range []blas.Transpose{blas.NoTrans, blas.Trans} {
+		for _, test := range []struct {
+			n, nrhs, lda, ldb int
+			tol               float64
+		}{
+			{3, 3, 0, 0, 1e-12},
+			{3, 5, 0, 0, 1e-12},
+			{5, 3, 0, 0, 1e-12},
+
+			{3, 3, 8, 10, 1e-12},
+			{3, 5, 8, 10, 1e-12},
+			{5, 3, 8, 10, 1e-12},
+
+			{300, 300, 0, 0, 1e-8},
+			{300, 500, 0, 0, 1e-8},
+			{500, 300, 0, 0, 1e-6},
+
+			{300, 300, 700, 600, 1e-8},
+			{300, 500, 700, 600, 1e-8},
+			{500, 300, 700, 600, 1e-6},
+		} {
+			n := test.n
+			nrhs := test.nrhs
+			lda := test.lda
+			if lda == 0 {
+				lda = n
+			}
+			ldb := test.ldb
+			if ldb == 0 {
+				ldb = nrhs
+			}
+			a := make([]float64, n*lda)
+			for i := range a {
+				a[i] = rnd.Float64()
+			}
+			b := make([]float64, n*ldb)
+			for i := range b {
+				b[i] = rnd.Float64()
+			}
+			aCopy := make([]float64, len(a))
+			copy(aCopy, a)
+			bCopy := make([]float64, len(b))
+			copy(bCopy, b)
+
+			ipiv := make([]int, n)
+			for i := range ipiv {
+				ipiv[i] = rnd.Int()
+			}
+
+			// Compute the LU factorization.
+			impl.Dgetrf(n, n, a, lda, ipiv)
+			// Solve the system of equations given the result.
+			impl.Dgetrs(trans, n, nrhs, a, lda, ipiv, b, ldb)
+
+			// Check that the system of equations holds.
+			A := blas64.General{
+				Rows:   n,
+				Cols:   n,
+				Stride: lda,
+				Data:   aCopy,
+			}
+			B := blas64.General{
+				Rows:   n,
+				Cols:   nrhs,
+				Stride: ldb,
+				Data:   bCopy,
+			}
+			X := blas64.General{
+				Rows:   n,
+				Cols:   nrhs,
+				Stride: ldb,
+				Data:   b,
+			}
+			tmp := blas64.General{
+				Rows:   n,
+				Cols:   nrhs,
+				Stride: ldb,
+				Data:   make([]float64, n*ldb),
+			}
+			copy(tmp.Data, bCopy)
+			blas64.Gemm(trans, blas.NoTrans, 1, A, X, 0, B)
+			if !floats.EqualApprox(tmp.Data, bCopy, test.tol) {
+				t.Errorf("Linear solve mismatch. trans = %v, n = %v, nrhs = %v, lda = %v, ldb = %v", trans, n, nrhs, lda, ldb)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dggsvd3.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dggsvd3.go
new file mode 100644
index 00000000..0a4af656
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dggsvd3.go
@@ -0,0 +1,173 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dggsvd3er interface {
+	Dggsvd3(jobU, jobV, jobQ lapack.GSVDJob, m, n, p int, a []float64, lda int, b []float64, ldb int, alpha, beta, u []float64, ldu int, v []float64, ldv int, q []float64, ldq int, work []float64, lwork int, iwork []int) (k, l int, ok bool)
+}
+
+func Dggsvd3Test(t *testing.T, impl Dggsvd3er) {
+	rnd := rand.New(rand.NewSource(1))
+	for cas, test := range []struct {
+		m, p, n, lda, ldb, ldu, ldv, ldq int
+
+		ok bool
+	}{
+		{m: 3, p: 3, n: 5, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+		{m: 5, p: 5, n: 5, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+		{m: 5, p: 5, n: 5, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+		{m: 5, p: 5, n: 10, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+		{m: 5, p: 5, n: 10, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+		{m: 5, p: 5, n: 10, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+		{m: 10, p: 5, n: 5, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+		{m: 10, p: 5, n: 5, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+		{m: 10, p: 10, n: 10, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+		{m: 10, p: 10, n: 10, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+		{m: 5, p: 5, n: 5, lda: 10, ldb: 10, ldu: 10, ldv: 10, ldq: 10, ok: true},
+		{m: 5, p: 5, n: 5, lda: 10, ldb: 10, ldu: 10, ldv: 10, ldq: 10, ok: true},
+		{m: 5, p: 5, n: 10, lda: 20, ldb: 20, ldu: 10, ldv: 10, ldq: 20, ok: true},
+		{m: 5, p: 5, n: 10, lda: 20, ldb: 20, ldu: 10, ldv: 10, ldq: 20, ok: true},
+		{m: 5, p: 5, n: 10, lda: 20, ldb: 20, ldu: 10, ldv: 10, ldq: 20, ok: true},
+		{m: 10, p: 5, n: 5, lda: 10, ldb: 10, ldu: 20, ldv: 10, ldq: 10, ok: true},
+		{m: 10, p: 5, n: 5, lda: 10, ldb: 10, ldu: 20, ldv: 10, ldq: 10, ok: true},
+		{m: 10, p: 10, n: 10, lda: 20, ldb: 20, ldu: 20, ldv: 20, ldq: 20, ok: true},
+		{m: 10, p: 10, n: 10, lda: 20, ldb: 20, ldu: 20, ldv: 20, ldq: 20, ok: true},
+	} {
+		m := test.m
+		p := test.p
+		n := test.n
+		lda := test.lda
+		if lda == 0 {
+			lda = n
+		}
+		ldb := test.ldb
+		if ldb == 0 {
+			ldb = n
+		}
+		ldu := test.ldu
+		if ldu == 0 {
+			ldu = m
+		}
+		ldv := test.ldv
+		if ldv == 0 {
+			ldv = p
+		}
+		ldq := test.ldq
+		if ldq == 0 {
+			ldq = n
+		}
+
+		a := randomGeneral(m, n, lda, rnd)
+		aCopy := cloneGeneral(a)
+		b := randomGeneral(p, n, ldb, rnd)
+		bCopy := cloneGeneral(b)
+
+		alpha := make([]float64, n)
+		beta := make([]float64, n)
+
+		u := nanGeneral(m, m, ldu)
+		v := nanGeneral(p, p, ldv)
+		q := nanGeneral(n, n, ldq)
+
+		iwork := make([]int, n)
+
+		work := []float64{0}
+		impl.Dggsvd3(lapack.GSVDU, lapack.GSVDV, lapack.GSVDQ,
+			m, n, p,
+			a.Data, a.Stride,
+			b.Data, b.Stride,
+			alpha, beta,
+			u.Data, u.Stride,
+			v.Data, v.Stride,
+			q.Data, q.Stride,
+			work, -1, iwork)
+
+		lwork := int(work[0])
+		work = make([]float64, lwork)
+
+		k, l, ok := impl.Dggsvd3(lapack.GSVDU, lapack.GSVDV, lapack.GSVDQ,
+			m, n, p,
+			a.Data, a.Stride,
+			b.Data, b.Stride,
+			alpha, beta,
+			u.Data, u.Stride,
+			v.Data, v.Stride,
+			q.Data, q.Stride,
+			work, lwork, iwork)
+
+		if !ok {
+			if test.ok {
+				t.Errorf("test %d unexpectedly did not converge", cas)
+			}
+			continue
+		}
+
+		// Check orthogonality of U, V and Q.
+		if !isOrthonormal(u) {
+			t.Errorf("test %d: U is not orthogonal\n%+v", cas, u)
+		}
+		if !isOrthonormal(v) {
+			t.Errorf("test %d: V is not orthogonal\n%+v", cas, v)
+		}
+		if !isOrthonormal(q) {
+			t.Errorf("test %d: Q is not orthogonal\n%+v", cas, q)
+		}
+
+		// Check C^2 + S^2 = I.
+		var elements []float64
+		if m-k-l >= 0 {
+			elements = alpha[k : k+l]
+		} else {
+			elements = alpha[k:m]
+		}
+		for i := range elements {
+			i += k
+			d := alpha[i]*alpha[i] + beta[i]*beta[i]
+			if !floats.EqualWithinAbsOrRel(d, 1, 1e-14, 1e-14) {
+				t.Errorf("test %d: alpha_%d^2 + beta_%d^2 != 1: got: %v", cas, i, i, d)
+			}
+		}
+
+		zeroR, d1, d2 := constructGSVDresults(n, p, m, k, l, a, b, alpha, beta)
+
+		// Check U^T*A*Q = D1*[ 0 R ].
+		uTmp := nanGeneral(m, n, n)
+		blas64.Gemm(blas.Trans, blas.NoTrans, 1, u, aCopy, 0, uTmp)
+		uAns := nanGeneral(m, n, n)
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, uTmp, q, 0, uAns)
+
+		d10r := nanGeneral(m, n, n)
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, d1, zeroR, 0, d10r)
+
+		if !equalApproxGeneral(uAns, d10r, 1e-14) {
+			t.Errorf("test %d: U^T*A*Q != D1*[ 0 R ]\nU^T*A*Q:\n%+v\nD1*[ 0 R ]:\n%+v",
+				cas, uAns, d10r)
+		}
+
+		// Check V^T*B*Q = D2*[ 0 R ].
+		vTmp := nanGeneral(p, n, n)
+		blas64.Gemm(blas.Trans, blas.NoTrans, 1, v, bCopy, 0, vTmp)
+		vAns := nanGeneral(p, n, n)
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, vTmp, q, 0, vAns)
+
+		d20r := nanGeneral(p, n, n)
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, d2, zeroR, 0, d20r)
+
+		if !equalApproxGeneral(vAns, d20r, 1e-14) {
+			t.Errorf("test %d: V^T*B*Q != D2*[ 0 R ]\nV^T*B*Q:\n%+v\nD2*[ 0 R ]:\n%+v",
+				cas, vAns, d20r)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dggsvp3.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dggsvp3.go
new file mode 100644
index 00000000..23111518
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dggsvp3.go
@@ -0,0 +1,146 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dggsvp3er interface {
+	Dlanger
+	Dggsvp3(jobU, jobV, jobQ lapack.GSVDJob, m, p, n int, a []float64, lda int, b []float64, ldb int, tola, tolb float64, u []float64, ldu int, v []float64, ldv int, q []float64, ldq int, iwork []int, tau, work []float64, lwork int) (k, l int)
+}
+
+func Dggsvp3Test(t *testing.T, impl Dggsvp3er) {
+	rnd := rand.New(rand.NewSource(1))
+	for cas, test := range []struct {
+		m, p, n, lda, ldb, ldu, ldv, ldq int
+	}{
+		{m: 3, p: 3, n: 5, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
+		{m: 5, p: 5, n: 5, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
+		{m: 5, p: 5, n: 5, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
+		{m: 5, p: 5, n: 10, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
+		{m: 5, p: 5, n: 10, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
+		{m: 5, p: 5, n: 10, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
+		{m: 10, p: 5, n: 5, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
+		{m: 10, p: 5, n: 5, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
+		{m: 10, p: 10, n: 10, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
+		{m: 10, p: 10, n: 10, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
+		{m: 5, p: 5, n: 5, lda: 10, ldb: 10, ldu: 10, ldv: 10, ldq: 10},
+		{m: 5, p: 5, n: 5, lda: 10, ldb: 10, ldu: 10, ldv: 10, ldq: 10},
+		{m: 5, p: 5, n: 10, lda: 20, ldb: 20, ldu: 10, ldv: 10, ldq: 20},
+		{m: 5, p: 5, n: 10, lda: 20, ldb: 20, ldu: 10, ldv: 10, ldq: 20},
+		{m: 5, p: 5, n: 10, lda: 20, ldb: 20, ldu: 10, ldv: 10, ldq: 20},
+		{m: 10, p: 5, n: 5, lda: 10, ldb: 10, ldu: 20, ldv: 10, ldq: 10},
+		{m: 10, p: 5, n: 5, lda: 10, ldb: 10, ldu: 20, ldv: 10, ldq: 10},
+		{m: 10, p: 10, n: 10, lda: 20, ldb: 20, ldu: 20, ldv: 20, ldq: 20},
+		{m: 10, p: 10, n: 10, lda: 20, ldb: 20, ldu: 20, ldv: 20, ldq: 20},
+	} {
+		m := test.m
+		p := test.p
+		n := test.n
+		lda := test.lda
+		if lda == 0 {
+			lda = n
+		}
+		ldb := test.ldb
+		if ldb == 0 {
+			ldb = n
+		}
+		ldu := test.ldu
+		if ldu == 0 {
+			ldu = m
+		}
+		ldv := test.ldv
+		if ldv == 0 {
+			ldv = p
+		}
+		ldq := test.ldq
+		if ldq == 0 {
+			ldq = n
+		}
+
+		a := randomGeneral(m, n, lda, rnd)
+		aCopy := cloneGeneral(a)
+		b := randomGeneral(p, n, ldb, rnd)
+		bCopy := cloneGeneral(b)
+
+		tola := float64(max(m, n)) * impl.Dlange(lapack.NormFrob, m, n, a.Data, a.Stride, nil) * dlamchE
+		tolb := float64(max(p, n)) * impl.Dlange(lapack.NormFrob, p, n, b.Data, b.Stride, nil) * dlamchE
+
+		u := nanGeneral(m, m, ldu)
+		v := nanGeneral(p, p, ldv)
+		q := nanGeneral(n, n, ldq)
+
+		iwork := make([]int, n)
+		tau := make([]float64, n)
+
+		work := []float64{0}
+		impl.Dggsvp3(lapack.GSVDU, lapack.GSVDV, lapack.GSVDQ,
+			m, p, n,
+			a.Data, a.Stride,
+			b.Data, b.Stride,
+			tola, tolb,
+			u.Data, u.Stride,
+			v.Data, v.Stride,
+			q.Data, q.Stride,
+			iwork, tau,
+			work, -1)
+
+		lwork := int(work[0])
+		work = make([]float64, lwork)
+
+		k, l := impl.Dggsvp3(lapack.GSVDU, lapack.GSVDV, lapack.GSVDQ,
+			m, p, n,
+			a.Data, a.Stride,
+			b.Data, b.Stride,
+			tola, tolb,
+			u.Data, u.Stride,
+			v.Data, v.Stride,
+			q.Data, q.Stride,
+			iwork, tau,
+			work, lwork)
+
+		// Check orthogonality of U, V and Q.
+		if !isOrthonormal(u) {
+			t.Errorf("test %d: U is not orthogonal\n%+v", cas, u)
+		}
+		if !isOrthonormal(v) {
+			t.Errorf("test %d: V is not orthogonal\n%+v", cas, v)
+		}
+		if !isOrthonormal(q) {
+			t.Errorf("test %d: Q is not orthogonal\n%+v", cas, q)
+		}
+
+		zeroA, zeroB := constructGSVPresults(n, p, m, k, l, a, b)
+
+		// Check U^T*A*Q = [ 0 RA ].
+		uTmp := nanGeneral(m, n, n)
+		blas64.Gemm(blas.Trans, blas.NoTrans, 1, u, aCopy, 0, uTmp)
+		uAns := nanGeneral(m, n, n)
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, uTmp, q, 0, uAns)
+
+		if !equalApproxGeneral(uAns, zeroA, 1e-14) {
+			t.Errorf("test %d: U^T*A*Q != [ 0 RA ]\nU^T*A*Q:\n%+v\n[ 0 RA ]:\n%+v",
+				cas, uAns, zeroA)
+		}
+
+		// Check V^T*B*Q = [ 0 RB ].
+		vTmp := nanGeneral(p, n, n)
+		blas64.Gemm(blas.Trans, blas.NoTrans, 1, v, bCopy, 0, vTmp)
+		vAns := nanGeneral(p, n, n)
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, vTmp, q, 0, vAns)
+
+		if !equalApproxGeneral(vAns, zeroB, 1e-14) {
+			t.Errorf("test %d: V^T*B*Q != [ 0 RB ]\nV^T*B*Q:\n%+v\n[ 0 RB ]:\n%+v",
+				cas, vAns, zeroB)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dhseqr.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dhseqr.go
new file mode 100644
index 00000000..85ae5234
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dhseqr.go
@@ -0,0 +1,861 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dhseqrer interface {
+	Dhseqr(job lapack.EVJob, compz lapack.EVComp, n, ilo, ihi int, h []float64, ldh int, wr, wi []float64,
+		z []float64, ldz int, work []float64, lwork int) int
+}
+
+type dhseqrTest struct {
+	n   int
+	ilo int
+	ihi int
+	h   []float64
+	tol float64
+
+	evWant []complex128
+}
+
+func DhseqrTest(t *testing.T, impl Dhseqrer) {
+	for i, tc := range dhseqrTests {
+		for _, job := range []lapack.EVJob{lapack.EigenvaluesOnly, lapack.EigenvaluesAndSchur} {
+			for _, wantz := range []bool{false, true} {
+				for _, extra := range []int{0, 11} {
+					testDhseqr(t, impl, i, tc, job, wantz, extra, true)
+					testDhseqr(t, impl, i, tc, job, wantz, extra, false)
+				}
+			}
+		}
+	}
+}
+
+func testDhseqr(t *testing.T, impl Dhseqrer, i int, test dhseqrTest, job lapack.EVJob, wantz bool, extra int, optwork bool) {
+	const tol = 1e-14
+	evTol := test.tol
+	if evTol == 0 {
+		evTol = tol
+	}
+
+	n := test.n
+	ihi := test.ihi
+	ilo := test.ilo
+	h := zeros(n, n, n+extra)
+	copyGeneral(h, blas64.General{Rows: n, Cols: n, Stride: max(1, n), Data: test.h})
+	hCopy := cloneGeneral(h)
+
+	var compz lapack.EVComp = lapack.None
+	z := blas64.General{Stride: max(1, n)}
+	if wantz {
+		// First, let Dhseqr initialize Z to the identity matrix.
+		compz = lapack.HessEV
+		z = nanGeneral(n, n, n+extra)
+	}
+
+	wr := nanSlice(n)
+	wi := nanSlice(n)
+
+	work := nanSlice(max(1, n))
+	if optwork {
+		impl.Dhseqr(job, lapack.HessEV, n, ilo, ihi, nil, h.Stride, nil, nil, nil, z.Stride, work, -1)
+		work = nanSlice(int(work[0]))
+	}
+
+	unconverged := impl.Dhseqr(job, compz, n, ilo, ihi, h.Data, h.Stride, wr, wi, z.Data, z.Stride, work, len(work))
+	prefix := fmt.Sprintf("Case %v: job=%v, compz=%v, n=%v, ilo=%v, ihi=%v, extra=%v, optwk=%v",
+		i, job, compz, n, ilo, ihi, extra, optwork)
+	if unconverged > 0 {
+		t.Logf("%v: Dhseqr did not compute all eigenvalues. unconverged=%v", prefix, unconverged)
+		if unconverged <= ilo {
+			t.Fatalf("%v: 0 < unconverged <= ilo", prefix)
+		}
+	}
+
+	// Check that wr and wi have been assigned completely.
+	if floats.HasNaN(wr) {
+		t.Errorf("%v: wr has NaN elements", prefix)
+	}
+	if floats.HasNaN(wi) {
+		t.Errorf("%v: wi has NaN elements", prefix)
+	}
+
+	// Check that complex eigenvalues are stored in consecutive elements as
+	// complex conjugate pairs.
+	for i := 0; i < n; {
+		if unconverged > 0 && i == ilo {
+			// Skip the unconverged eigenvalues.
+			i = unconverged
+			continue
+		}
+		if wi[i] == 0 {
+			// Real eigenvalue.
+			i++
+			continue
+		}
+		// Complex conjugate pair.
+		if wr[i] != wr[i+1] {
+			t.Errorf("%v: conjugate pair has real parts unequal", prefix)
+		}
+		if wi[i] < 0 {
+			t.Errorf("%v: first in conjugate pair has negative imaginary part", prefix)
+		}
+		if wi[i+1] != -wi[i] {
+			t.Errorf("%v: complex pair is not conjugate", prefix)
+		}
+		i += 2
+	}
+
+	// Check that H contains the Schur form T.
+	if job == lapack.EigenvaluesAndSchur {
+		for i := 0; i < n; {
+			if unconverged > 0 && i == ilo {
+				// Skip the unconverged eigenvalues.
+				i = unconverged
+				continue
+			}
+			if wi[i] == 0 {
+				// Real eigenvalue.
+				if wr[i] != h.Data[i*h.Stride+i] {
+					t.Errorf("%v: T not in Schur form (real eigenvalue not on diagonal)", prefix)
+				}
+				i++
+				continue
+			}
+			// Complex conjugate pair.
+			im := math.Sqrt(math.Abs(h.Data[(i+1)*h.Stride+i])) * math.Sqrt(math.Abs(h.Data[i*h.Stride+i+1]))
+			if wr[i] != h.Data[i*h.Stride+i] || wr[i] != h.Data[(i+1)*h.Stride+i+1] ||
+				math.Abs(wi[i]-im) > tol {
+				t.Errorf("%v: conjugate pair and 2×2 diagonal block don't correspond", prefix)
+			}
+			i += 2
+		}
+	}
+
+	// Check that all the found eigenvalues are really eigenvalues.
+	foundEV := make([]bool, len(test.evWant))
+	for i := 0; i < n; {
+		if unconverged > 0 && i == ilo {
+			// Skip the unconverged eigenvalues.
+			i = unconverged
+			continue
+		}
+		ev := complex(wr[i], wi[i])
+		// Use problem-specific tolerance for testing eigenvalues.
+		found, index := containsComplex(test.evWant, ev, evTol)
+		if !found {
+			t.Errorf("%v: unexpected eigenvalue %v", prefix, ev)
+		} else {
+			foundEV[index] = true
+		}
+		i++
+	}
+	if unconverged == 0 {
+		// Check that all eigenvalues have been found.
+		// This simple check assumes that all eigenvalues are
+		// sufficiently separated from each other at least by evTol.
+		for i := range foundEV {
+			if !foundEV[i] {
+				t.Errorf("%v: %vth eigenvalue not found", prefix, i)
+			}
+		}
+	}
+
+	if !wantz {
+		return
+	}
+
+	// Z must be orthogonal.
+	if !isOrthonormal(z) {
+		t.Errorf("%v: Z is not orthogonal", prefix)
+	}
+
+	if job == lapack.EigenvaluesAndSchur {
+		tz := zeros(n, n, n)
+		blas64.Gemm(blas.NoTrans, blas.Trans, 1, h, z, 0, tz)
+		ztz := zeros(n, n, n)
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, z, tz, 0, ztz)
+		if !equalApproxGeneral(ztz, hCopy, evTol) {
+			t.Errorf("%v: H != Z T Z^T", prefix)
+		}
+	}
+
+	// Restore H.
+	copyGeneral(h, hCopy)
+	// Call Dhseqr again with the identity matrix given explicitly in Q.
+	q := eye(n, n+extra)
+	impl.Dhseqr(job, lapack.OriginalEV, n, ilo, ihi, h.Data, h.Stride, wr, wi, q.Data, q.Stride, work, len(work))
+	if !equalApproxGeneral(z, q, 0) {
+		t.Errorf("%v: Z and Q are not equal", prefix)
+	}
+}
+
+var dhseqrTests = []dhseqrTest{
+	{
+		n:   0,
+		ilo: 0,
+		ihi: -1,
+	},
+	{
+		n:      1,
+		ilo:    0,
+		ihi:    0,
+		h:      []float64{0},
+		evWant: []complex128{0},
+	},
+	{
+		n:      1,
+		ilo:    0,
+		ihi:    0,
+		h:      []float64{7.09965484086874e-1},
+		evWant: []complex128{7.09965484086874e-1},
+	},
+	{
+		n:      2,
+		ilo:    0,
+		ihi:    1,
+		h:      []float64{0, 0, 0, 0},
+		evWant: []complex128{0},
+	},
+	{
+		n:   2,
+		ilo: 0,
+		ihi: 1,
+		h: []float64{
+			1, 0,
+			0, 1,
+		},
+		evWant: []complex128{1},
+	},
+	{
+		n:   2,
+		ilo: 0,
+		ihi: 1,
+		h: []float64{
+			0, -1,
+			1, 0,
+		},
+		evWant: []complex128{1i, -1i},
+	},
+	{
+		n:   2,
+		ilo: 0,
+		ihi: 1,
+		h: []float64{
+			6.25219991450918e-1, 8.17510791994361e-1,
+			3.31218891622294e-1, 1.24103744878131e-1,
+		},
+		evWant: []complex128{9.52203547663447e-1, -2.02879811334398e-1},
+	},
+	{
+		n:   4,
+		ilo: 1,
+		ihi: 2,
+		h: []float64{
+			1, 0, 0, 0,
+			0, 6.25219991450918e-1, 8.17510791994361e-1, 0,
+			0, 3.31218891622294e-1, 1.24103744878131e-1, 0,
+			0, 0, 0, 2,
+		},
+		evWant: []complex128{1, 2, 9.52203547663447e-1, -2.02879811334398e-1},
+	},
+	{
+		n:   2,
+		ilo: 0,
+		ihi: 1,
+		h: []float64{
+			-1.1219562276608, 6.85473513349362e-1,
+			-8.19951061145131e-1, 1.93728523178888e-1,
+		},
+		evWant: []complex128{
+			-4.64113852240958e-1 + 3.59580510817350e-1i,
+			-4.64113852240958e-1 - 3.59580510817350e-1i,
+		},
+	},
+	{
+		n:   5,
+		ilo: 0,
+		ihi: 4,
+		h: []float64{
+			9.57590178533658e-1, -5.10651295522708e-1, 9.24974510015869e-1, -1.30016306879522e-1, 2.92601986926954e-2,
+			-1.08084756637964, 1.77529701001213, -1.36480197632509, 2.23196371219601e-1, 1.12912853063308e-1,
+			0, -8.44075612174676e-1, 1.067867614486, -2.55782915176399e-1, -2.00598563137468e-1,
+			0, 0, -5.67097237165410e-1, 2.07205057427341e-1, 6.54998340743380e-1,
+			0, 0, 0, -1.89441413886041e-1, -4.18125416021786e-1,
+		},
+		evWant: []complex128{
+			2.94393309555622,
+			4.97029793606701e-1 + 3.63041654992384e-1i,
+			4.97029793606701e-1 - 3.63041654992384e-1i,
+			-1.74079119166145e-1 + 2.01570009462092e-1i,
+			-1.74079119166145e-1 - 2.01570009462092e-1i,
+		},
+	},
+	{
+		// BFW62A matrix from MatrixMarket, balanced and factorized into
+		// upper Hessenberg form in Octave.
+		// Eigenvalues computed by eig function in Octave.
+		// Dhseqr considers this matrix small (n <= 75).
+		n:   62,
+		ilo: 0,
+		ihi: 61,
+		tol: 1e-12,
+		h: []float64{
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+		},
+		evWant: []complex128{
+			-0.01716884621227793,
+			-0.1844331609734137,
+			0.05200651487352193,
+			0.1336851109127556,
+			0.2020936631953806,
+			0.3566470363060668,
+			0.3627207699831158,
+			0.4388555152488943,
+			0.4776853636435153,
+			0.5598821450074998,
+			0.6249350549980947,
+			0.6791310689291772,
+			0.985877008147705 + 0.01929363300192029i,
+			0.985877008147705 - 0.01929363300192029i,
+			0.9908483217835712,
+			1.011990761364073,
+			1.130046345264462,
+			1.323698071765709,
+			1.348598229483672,
+			1.363190626641638 + 0.05400660173350781i,
+			1.363190626641638 - 0.05400660173350781i,
+			1.632832316477256,
+			1.646239548684271,
+			1.742738908029794,
+			1.763069014878969,
+			1.789601126186348,
+			1.945228042429256,
+			1.946373262056993,
+			1.997152389795002,
+			2.261322781594966,
+			2.286944100979884,
+			2.447712649969029,
+			2.557857506923634,
+			2.608379034892128,
+			2.653335615965549,
+			2.675270309760236,
+			2.964219802766918 + 0.01767482509567778i,
+			2.964219802766918 - 0.01767482509567778i,
+			3.014604817775139,
+			3.158289371199042,
+			3.311794215710077,
+			3.389894197376214,
+			3.553333074879877,
+			3.641274442796651,
+			3.857556223000175,
+			4.045817381029103,
+			4.330901939363569,
+			4.337313647767939,
+			4.527400487637496,
+			4.917229128467305,
+			4.985609414964091,
+			5.687686849958608,
+			5.79422309012183,
+			5.997813119506478,
+			6.732426637899077,
+			6.957609338485607,
+			7.529842664573327,
+			7.609108287806763,
+			7.761261355516287,
+			8.311941758006698,
+			9.07053741884884,
+			9.217944588000314,
+		},
+	},
+	{
+		// TOLS90 matrix from MatrixMarket, balanced and factorized into
+		// upper Hessenberg form in Octave.
+		// Eigenvalues computed by eig function in Octave.
+		// Dhseqr considers this matrix big (n > 75).
+		n:   90,
+		ilo: 0,
+		ihi: 89,
+		tol: 1e-12,
+		h: []float64{
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+			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.2286035973327459, -15.02261004686781, 5.184122379409034, -0.0264079721355016, -0.007786216137000334, -0.008663526410932022, -0.005309693290799501, -0.006680538291880966, 0.001397532516833339, -0.01528554327177548, -0.01182046150296639, 0.005955666147884051, 0.003523919303238692,
+			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5.214570242697843, -21.4621144179193, -1.555874989179182, -0.001447535808513384, 0.03124103143611023, 0.01560612912433155, 0.01254222023040845, -0.0006565581414721336, -0.005837445535672976, 0.003328905310192099, -0.003109407401498421, -0.001359993487917328,
+			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1.575215080762542, -36.12196181704586, -0.009581763987488548, 0.02181190823948241, 0.004249343259232833, 0.008866640947567769, -0.008827428692463307, 0.0111903702615688, -0.008259743446844802, 0.005994103918828306, 0.02884522108807095,
+			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.02332478841374811, -20.31760288431249, 5.902175782312199, 0.01411291075117598, -0.0401626029282366, -0.04333034577745157, 0.006563645334078613, -0.02686027801335236, 1.82653938945055e-05, -0.009451944888619017,
+			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5.843446424852287, -17.22694391469142, 4.615021811975704, 0.03880112444568462, 0.01156878860697344, -0.02011735633875036, 0.007254465185871957, 0.006976302646061595, 0.01061407563995378,
+			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4.636349195088934, -35.03142250661902, 0.03540637402307944, 0.006380325215592348, -0.01715112535803765, -0.005381045082520479, -0.02796704437114206, -0.01837431744975316,
+			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.03325953074641371, -17.29072432858197, 5.995094557622266, -0.004356649575832386, 0.01324648360020382, -0.002576747161993423, -0.0164552533090047,
+			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5.976772821535572, -18.99788030681546, 0.01396461545715264, -0.007601183590626498, 0.005853929901760483, 0.0201199907208218,
+			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.002983340164191267, -20.0342372815637, -5.741448414658583, -0.01215113512395332, -0.00662723431795657,
+			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5.752040939724589, -16.25515722920224, -0.00713497387655803, -0.004958024634924642,
+			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0004916632598946193, -12.09805746213948, 0.000198676020167099,
+			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0001765653829615133, -12.09823117436413,
+		},
+		evWant: []complex128{
+			-0.2513649571095319 + 26.5196181977274i,
+			-0.2513649571095319 - 26.5196181977274i,
+			-0.3323427794627154 + 14.12147023570828i,
+			-0.3323427794627154 - 14.12147023570828i,
+			-0.3885760957072044 + 34.01549575140551i,
+			-0.3885760957072044 - 34.01549575140551i,
+			-0.4938394681672298 + 19.28755724237434i,
+			-0.4938394681672298 - 19.28755724237434i,
+			-0.5354723308245726 + 44.07811563049843i,
+			-0.5354723308245726 - 44.07811563049843i,
+			-0.8831210193505878 + 40.64617136580856i,
+			-0.8831210193505878 - 40.64617136580856i,
+			-1.063691744877652 + 54.90113796777709i,
+			-1.063691744877652 - 54.90113796777709i,
+			-1.270999250073418 + 55.92169849615225i,
+			-1.270999250073418 - 55.92169849615225i,
+			-1.641962795944021 + 124.0727533257146i,
+			-1.641962795944021 - 124.0727533257146i,
+			-1.866212165366329 + 67.51198073484791i,
+			-1.866212165366329 - 67.51198073484791i,
+			-2.66562659457705 + 102.4818444744388i,
+			-2.66562659457705 - 102.4818444744388i,
+			-2.677285588970379 + 109.3976583973073i,
+			-2.677285588970379 - 109.3976583973073i,
+			-3.592328373007462 + 116.2450441105874i,
+			-3.592328373007462 - 116.2450441105874i,
+			-3.658587455178502 + 105.6223525143237i,
+			-3.658587455178502 - 105.6223525143237i,
+			-3.738335632746128 + 95.41374995650723i,
+			-3.738335632746128 - 95.41374995650723i,
+			-4.05659124602542 + 85.08673687146815i,
+			-4.05659124602542 - 85.08673687146815i,
+			-11.7967401639067 + 0.03421683561959875i,
+			-11.7967401639067 - 0.03421683561959875i,
+			-12.06591356324058 + 0.03010079020722811i,
+			-12.06591356324058 - 0.03010079020722811i,
+			-12.08354870692898,
+			-12.09435136773809 + 0.0007639916648241464i,
+			-12.09435136773809 - 0.0007639916648241464i,
+			-12.09785209014901 + 0.02991559300476182i,
+			-12.09785209014901 - 0.02991559300476182i,
+			-12.09806212746318,
+			-12.09850417485291,
+			-12.09864274565634,
+			-12.10160612637007 + 0.004700099158908263i,
+			-12.10160612637007 - 0.004700099158908263i,
+			-12.16873692768957 + 0.02446545858852495i,
+			-12.16873692768957 - 0.02446545858852495i,
+			-12.23495190373921 + 0.1453184367031505i,
+			-12.23495190373921 - 0.1453184367031505i,
+			-13.54778407074696 + 141.1839768257274i,
+			-13.54778407074696 - 141.1839768257274i,
+			-15.38790969472481 + 114.0584849752244i,
+			-15.38790969472481 - 114.0584849752244i,
+			-23.60369882806601 + 0.2464158068361128i,
+			-23.60369882806601 - 0.2464158068361128i,
+			-24.04314341198735 + 0.3315626206724418i,
+			-24.04314341198735 - 0.3315626206724418i,
+			-24.12753399862331 + 0.1634093642552133i,
+			-24.12753399862331 - 0.1634093642552133i,
+			-24.18103712080912,
+			-24.18908889661277,
+			-24.19357072143492,
+			-24.19567681157636,
+			-24.20660003986661,
+			-24.228086198612 + 0.0220672004906673i,
+			-24.228086198612 - 0.0220672004906673i,
+			-24.30677145425284 + 0.1813999700804981i,
+			-24.30677145425284 - 0.1813999700804981i,
+			-25.23862373866253 + 0.8733279005402655i,
+			-25.23862373866253 - 0.8733279005402655i,
+			-29.42427841595277 + 1.666886570068163i,
+			-29.42427841595277 - 1.666886570068163i,
+			-33.94959271558832,
+			-35.51958918286584,
+			-36.20666045708104 + 0.1660921702962803i,
+			-36.20666045708104 - 0.1660921702962803i,
+			-36.25710351845593 + 0.01052251476620707i,
+			-36.25710351845593 - 0.01052251476620707i,
+			-36.28714605125749,
+			-36.29431583135849,
+			-36.29711199023137,
+			-36.31304183793699,
+			-36.32232768169418,
+			-36.37871120972082 + 0.1557647672076243i,
+			-36.37871120972082 - 0.1557647672076243i,
+			-36.47694233727385 + 0.3738707259908102i,
+			-36.47694233727385 - 0.3738707259908102i,
+			-36.66483183150206,
+			-37.75937189360096,
+		},
+	},
+	{
+		// TUB100 matrix from MatrixMarket, balanced and factorized into
+		// upper Hessenberg form in Octave, and embedded into a 104×104
+		// diagonal matrix to test with ilo != 0 and ihi != n-1.
+		// Eigenvalues computed by eig function in Octave.
+		// Dhseqr considers this matrix big (n > 75).
+		n:   104,
+		ilo: 2,
+		ihi: 101,
+		tol: 1e-10,
+		h: []float64{
+			1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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+			-930.6648831979091 + 1.624396130880259i,
+			-930.6648831979091 - 1.624396130880259i,
+			-992.1487134378474 + 1.624417808682915i,
+			-992.1487134378474 - 1.624417808682915i,
+			-1053.506114553354 + 1.624453056189826i,
+			-1053.506114553354 - 1.624453056189826i,
+			-1114.484928198698 + 1.62449544649428i,
+			-1114.484928198698 - 1.62449544649428i,
+			-1174.834554234014 + 1.624553207269019i,
+			-1174.834554234014 - 1.624553207269019i,
+			-1234.306981514973 + 1.624623553438826i,
+			-1234.306981514973 - 1.624623553438826i,
+			-1292.657768972259 + 1.624709216827242i,
+			-1292.657768972259 - 1.624709216827242i,
+			-1349.647106741638 + 1.624814444572517i,
+			-1349.647106741638 - 1.624814444572517i,
+			-1405.040739357668 + 1.624951632752096i,
+			-1405.040739357668 - 1.624951632752096i,
+			-1458.610953350783 + 1.625104547041682i,
+			-1458.610953350783 - 1.625104547041682i,
+			-1510.137508646807 + 1.625304666073007i,
+			-1510.137508646807 - 1.625304666073007i,
+			-1559.408520122221 + 1.625548293255404i,
+			-1559.408520122221 - 1.625548293255404i,
+			-1606.221305250554 + 1.625851986073836i,
+			-1606.221305250554 - 1.625851986073836i,
+			-1650.383201531125 + 1.62624202844641i,
+			-1650.383201531125 - 1.62624202844641i,
+			-1691.712315735984 + 1.6267345498979i,
+			-1691.712315735984 - 1.6267345498979i,
+			-1730.038177420971 + 1.627388968656263i,
+			-1730.038177420971 - 1.627388968656263i,
+			-1765.20230058066 + 1.628268412022146i,
+			-1765.20230058066 - 1.628268412022146i,
+			-1797.05860162894 + 1.629473972633416i,
+			-1797.05860162894 - 1.629473972633416i,
+			-1825.473493639258 + 1.631220665229006i,
+			-1825.473493639258 - 1.631220665229006i,
+			-1850.32542664842 + 1.633834593918563i,
+			-1850.32542664842 - 1.633834593918563i,
+			-1871.503056018116 + 1.637993570641514i,
+			-1871.503056018116 - 1.637993570641514i,
+			-1888.90026514681 + 1.64508855982818i,
+			-1888.90026514681 - 1.64508855982818i,
+			-1902.402515327158 + 1.658179541614067i,
+			-1902.402515327158 - 1.658179541614067i,
+			-1911.858940404498 + 1.682209391409579i,
+			-1911.858940404498 - 1.682209391409579i,
+			-1916.92602113601 + 1.761877988650816i,
+			-1916.92602113601 - 1.761877988650816i,
+			-1930.484166851586 + 1.202676762393897i,
+			-1930.484166851586 - 1.202676762393897i,
+			3,
+			4,
+		},
+	},
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlabrd.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlabrd.go
new file mode 100644
index 00000000..460cefe7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlabrd.go
@@ -0,0 +1,107 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+)
+
+type Dlabrder interface {
+	Dlabrd(m, n, nb int, a []float64, lda int, d, e, tauq, taup, x []float64, ldx int, y []float64, ldy int)
+}
+
+func DlabrdTest(t *testing.T, impl Dlabrder) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, test := range []struct {
+		m, n, nb, lda, ldx, ldy int
+	}{
+		{4, 5, 2, 0, 0, 0},
+		{4, 5, 4, 0, 0, 0},
+		{5, 5, 2, 0, 0, 0},
+		{5, 5, 5, 0, 0, 0},
+		{5, 4, 4, 0, 0, 0},
+		{5, 4, 4, 0, 0, 0},
+
+		{4, 5, 2, 10, 11, 12},
+		{4, 5, 4, 10, 11, 12},
+		{5, 5, 2, 10, 11, 12},
+		{5, 5, 5, 10, 11, 12},
+		{5, 4, 2, 10, 11, 12},
+		{5, 4, 4, 10, 11, 12},
+
+		{4, 5, 2, 11, 12, 10},
+		{4, 5, 4, 11, 12, 10},
+		{5, 5, 2, 11, 12, 10},
+		{5, 5, 5, 11, 12, 10},
+		{5, 4, 2, 11, 12, 10},
+		{5, 4, 4, 11, 12, 10},
+
+		{4, 5, 2, 12, 11, 10},
+		{4, 5, 4, 12, 11, 10},
+		{5, 5, 2, 12, 11, 10},
+		{5, 5, 5, 12, 11, 10},
+		{5, 4, 2, 12, 11, 10},
+		{5, 4, 4, 12, 11, 10},
+	} {
+		m := test.m
+		n := test.n
+		nb := test.nb
+		lda := test.lda
+		if lda == 0 {
+			lda = n
+		}
+		ldy := test.ldy
+		if ldy == 0 {
+			ldy = nb
+		}
+		ldx := test.ldx
+		if ldx == 0 {
+			ldx = nb
+		}
+		a := make([]float64, m*lda)
+		for i := range a {
+			a[i] = rnd.NormFloat64()
+		}
+		d := make([]float64, nb)
+		for i := range d {
+			d[i] = math.NaN()
+		}
+		e := make([]float64, nb)
+		for i := range e {
+			e[i] = math.NaN()
+		}
+		tauP := make([]float64, nb)
+		for i := range tauP {
+			tauP[i] = math.NaN()
+		}
+		tauQ := make([]float64, nb)
+		for i := range tauP {
+			tauQ[i] = math.NaN()
+		}
+		x := make([]float64, m*ldx)
+		for i := range x {
+			x[i] = rnd.NormFloat64()
+		}
+		y := make([]float64, n*ldy)
+		for i := range y {
+			y[i] = rnd.NormFloat64()
+		}
+		aCopy := make([]float64, len(a))
+		copy(aCopy, a)
+
+		// Compute the reduction.
+		impl.Dlabrd(m, n, nb, a, lda, d, e, tauQ, tauP, x, ldx, y, ldy)
+
+		if m >= n && nb == n {
+			tauP[n-1] = 0
+		}
+		if m < n && nb == m {
+			tauQ[m-1] = 0
+		}
+		checkBidiagonal(t, m, n, nb, a, lda, d, e, tauP, tauQ, aCopy)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlacn2.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlacn2.go
new file mode 100644
index 00000000..9e76c0b7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlacn2.go
@@ -0,0 +1,72 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dlacn2er interface {
+	Dlacn2(n int, v, x []float64, isgn []int, est float64, kase int, isave *[3]int) (float64, int)
+}
+
+func Dlacn2Test(t *testing.T, impl Dlacn2er) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, n := range []int{1, 2, 3, 4, 5, 7, 10, 15, 20, 100} {
+		for cas := 0; cas < 10; cas++ {
+			a := randomGeneral(n, n, n, rnd)
+
+			// Compute the 1-norm of A explicitly.
+			var norm1 float64
+			for j := 0; j < n; j++ {
+				var sum float64
+				for i := 0; i < n; i++ {
+					sum += math.Abs(a.Data[i*a.Stride+j])
+				}
+				if sum > norm1 {
+					norm1 = sum
+				}
+			}
+
+			// Compute the estimate of 1-norm using Dlanc2.
+			x := make([]float64, n)
+			work := make([]float64, n)
+			v := make([]float64, n)
+			isgn := make([]int, n)
+			var (
+				kase  int
+				isave [3]int
+				got   float64
+			)
+		loop:
+			for {
+				got, kase = impl.Dlacn2(n, v, x, isgn, got, kase, &isave)
+				switch kase {
+				default:
+					panic("Dlacn2 returned invalid value of kase")
+				case 0:
+					break loop
+				case 1:
+					blas64.Gemv(blas.NoTrans, 1, a, blas64.Vector{1, x}, 0, blas64.Vector{1, work})
+					copy(x, work)
+				case 2:
+					blas64.Gemv(blas.Trans, 1, a, blas64.Vector{1, x}, 0, blas64.Vector{1, work})
+					copy(x, work)
+				}
+			}
+
+			// Check that got is either accurate enough or a
+			// lower estimate of the 1-norm of A.
+			if math.Abs(got-norm1) > 1e-8 && got > norm1 {
+				t.Errorf("Case n=%v: not lower estimate. 1-norm %v, estimate %v", n, norm1, got)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlacpy.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlacpy.go
new file mode 100644
index 00000000..aa3e5e0f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlacpy.go
@@ -0,0 +1,89 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+type Dlacpyer interface {
+	Dlacpy(uplo blas.Uplo, m, n int, a []float64, lda int, b []float64, ldb int)
+}
+
+func DlacpyTest(t *testing.T, impl Dlacpyer) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower, blas.All} {
+		for _, test := range []struct {
+			m, n, lda, ldb int
+		}{
+			{3, 5, 0, 0},
+			{5, 5, 0, 0},
+			{7, 5, 0, 0},
+
+			{3, 5, 10, 12},
+			{5, 5, 10, 12},
+			{7, 5, 10, 12},
+		} {
+			m := test.m
+			n := test.n
+			lda := test.lda
+			if lda == 0 {
+				lda = n
+			}
+			ldb := test.ldb
+			if ldb == 0 {
+				ldb = n
+			}
+			a := make([]float64, m*lda)
+			for i := range a {
+				a[i] = rnd.Float64()
+			}
+			b := make([]float64, m*ldb)
+			for i := range b {
+				b[i] = rnd.Float64()
+			}
+			impl.Dlacpy(uplo, m, n, a, lda, b, ldb)
+			equal := true
+			switch uplo {
+			case blas.Upper:
+				for i := 0; i < m; i++ {
+					for j := i; j < n; j++ {
+						if b[i*ldb+j] != a[i*lda+j] {
+							equal = false
+							goto DoneCheck
+						}
+					}
+				}
+			case blas.Lower:
+				for i := 0; i < m; i++ {
+					for j := 0; j < min(i, n); j++ {
+						if b[i*ldb+j] != a[i*lda+j] {
+							equal = false
+							goto DoneCheck
+						}
+					}
+				}
+			case blas.All:
+				for i := 0; i < m; i++ {
+					for j := 0; j < n; j++ {
+						if b[i*ldb+j] != a[i*lda+j] {
+							equal = false
+							goto DoneCheck
+						}
+					}
+				}
+			}
+		DoneCheck:
+			if !equal {
+				fmt.Println(blas.Lower)
+				t.Errorf("Matrices not equal after copy. Uplo = %d, m = %d, n = %d", uplo, m, n)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlae2.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlae2.go
new file mode 100644
index 00000000..236b3f2b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlae2.go
@@ -0,0 +1,53 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math"
+	"testing"
+)
+
+type Dlae2er interface {
+	Dlae2(a, b, c float64) (rt1, rt2 float64)
+}
+
+func Dlae2Test(t *testing.T, impl Dlae2er) {
+	for _, test := range []struct {
+		a, b, c float64
+	}{
+		{-10, 5, 3},
+		{3, 5, -10},
+		{0, 3, 0},
+		{1, 3, 1},
+		{1, -3, 1},
+		{5, 0, 3},
+		{3, 0, -5},
+		{1, 3, 1.02},
+		{1.02, 3, 1},
+		{1, -3, -9},
+	} {
+		a := test.a
+		b := test.b
+		c := test.c
+		rt1, rt2 := impl.Dlae2(a, b, c)
+
+		errStr := fmt.Sprintf("a = %v, b = %v, c = %v", a, b, c)
+		// Check if rt1 and rt2 are eigenvalues by checking if det(a - λI) = 0
+		a1 := a - rt1
+		c1 := c - rt1
+		det := a1*c1 - b*b
+		if math.Abs(det) > 1e-10 {
+			t.Errorf("First eigenvalue mismatch. %s. Det = %v", errStr, det)
+		}
+
+		a2 := a - rt2
+		c2 := c - rt2
+		det = a2*c2 - b*b
+		if math.Abs(det) > 1e-10 {
+			t.Errorf("Second eigenvalue mismatch. %s. Det = %v", errStr, det)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaev2.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaev2.go
new file mode 100644
index 00000000..3aea2d74
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaev2.go
@@ -0,0 +1,46 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+)
+
+type Dlaev2er interface {
+	Dlaev2(a, b, c float64) (rt1, rt2, cs1, sn1 float64)
+}
+
+func Dlaev2Test(t *testing.T, impl Dlaev2er) {
+	rnd := rand.New(rand.NewSource(1))
+	for trial := 0; trial < 100; trial++ {
+		a := rnd.NormFloat64()
+		b := rnd.NormFloat64()
+		c := rnd.NormFloat64()
+
+		rt1, rt2, cs1, sn1 := impl.Dlaev2(a, b, c)
+		tmp := mul2by2([2][2]float64{{cs1, sn1}, {-sn1, cs1}}, [2][2]float64{{a, b}, {b, c}})
+		ans := mul2by2(tmp, [2][2]float64{{cs1, -sn1}, {sn1, cs1}})
+		if math.Abs(ans[0][0]-rt1) > 1e-14 {
+			t.Errorf("Largest eigenvalue mismatch. Returned %v, mul %v", rt1, ans[0][0])
+		}
+		if math.Abs(ans[1][0]) > 1e-14 || math.Abs(ans[0][1]) > 1e-14 {
+			t.Errorf("Non-zero off diagonal. ans[1][0] = %v, ans[0][1] = %v", ans[1][0], ans[0][1])
+		}
+		if math.Abs(ans[1][1]-rt2) > 1e-14 {
+			t.Errorf("Smallest eigenvalue mismatch. Returned %v, mul %v", rt2, ans[1][1])
+		}
+	}
+}
+
+func mul2by2(a, b [2][2]float64) [2][2]float64 {
+	var c [2][2]float64
+	c[0][0] = a[0][0]*b[0][0] + a[0][1]*b[1][0]
+	c[0][1] = a[0][0]*b[0][1] + a[0][1]*b[1][1]
+	c[1][0] = a[1][0]*b[0][0] + a[1][1]*b[1][0]
+	c[1][1] = a[1][0]*b[0][1] + a[1][1]*b[1][1]
+	return c
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaexc.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaexc.go
new file mode 100644
index 00000000..e69f41d8
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaexc.go
@@ -0,0 +1,227 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math"
+	"math/cmplx"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dlaexcer interface {
+	Dlaexc(wantq bool, n int, t []float64, ldt int, q []float64, ldq int, j1, n1, n2 int, work []float64) bool
+}
+
+func DlaexcTest(t *testing.T, impl Dlaexcer) {
+	rnd := rand.New(rand.NewSource(1))
+
+	for _, wantq := range []bool{true, false} {
+		for _, n := range []int{1, 2, 3, 4, 5, 6, 10, 18, 31, 53} {
+			for _, extra := range []int{0, 1, 11} {
+				for cas := 0; cas < 100; cas++ {
+					j1 := rnd.Intn(n)
+					n1 := min(rnd.Intn(3), n-j1)
+					n2 := min(rnd.Intn(3), n-j1-n1)
+					testDlaexc(t, impl, wantq, n, j1, n1, n2, extra, rnd)
+				}
+			}
+		}
+	}
+}
+
+func testDlaexc(t *testing.T, impl Dlaexcer, wantq bool, n, j1, n1, n2, extra int, rnd *rand.Rand) {
+	const tol = 1e-14
+
+	tmat := randomGeneral(n, n, n+extra, rnd)
+	// Zero out the lower triangle.
+	for i := 1; i < n; i++ {
+		for j := 0; j < i; j++ {
+			tmat.Data[i*tmat.Stride+j] = 0
+		}
+	}
+	// Make any 2x2 diagonal block to be in Schur canonical form.
+	if n1 == 2 {
+		// Diagonal elements equal.
+		tmat.Data[(j1+1)*tmat.Stride+j1+1] = tmat.Data[j1*tmat.Stride+j1]
+		// Off-diagonal elements of opposite sign.
+		c := rnd.NormFloat64()
+		if math.Signbit(c) == math.Signbit(tmat.Data[j1*tmat.Stride+j1+1]) {
+			c *= -1
+		}
+		tmat.Data[(j1+1)*tmat.Stride+j1] = c
+	}
+	if n2 == 2 {
+		// Diagonal elements equal.
+		tmat.Data[(j1+n1+1)*tmat.Stride+j1+n1+1] = tmat.Data[(j1+n1)*tmat.Stride+j1+n1]
+		// Off-diagonal elements of opposite sign.
+		c := rnd.NormFloat64()
+		if math.Signbit(c) == math.Signbit(tmat.Data[(j1+n1)*tmat.Stride+j1+n1+1]) {
+			c *= -1
+		}
+		tmat.Data[(j1+n1+1)*tmat.Stride+j1+n1] = c
+	}
+	tmatCopy := cloneGeneral(tmat)
+	var q, qCopy blas64.General
+	if wantq {
+		q = eye(n, n+extra)
+		qCopy = cloneGeneral(q)
+	}
+	work := nanSlice(n)
+
+	ok := impl.Dlaexc(wantq, n, tmat.Data, tmat.Stride, q.Data, q.Stride, j1, n1, n2, work)
+
+	prefix := fmt.Sprintf("Case n=%v, j1=%v, n1=%v, n2=%v, wantq=%v, extra=%v", n, j1, n1, n2, wantq, extra)
+
+	if !generalOutsideAllNaN(tmat) {
+		t.Errorf("%v: out-of-range write to T", prefix)
+	}
+	if wantq && !generalOutsideAllNaN(q) {
+		t.Errorf("%v: out-of-range write to Q", prefix)
+	}
+
+	if !ok {
+		if n1 == 1 && n2 == 1 {
+			t.Errorf("%v: unexpected failure", prefix)
+		} else {
+			t.Logf("%v: Dlaexc returned false", prefix)
+		}
+	}
+
+	if !ok || n1 == 0 || n2 == 0 || j1+n1 >= n {
+		// Check that T is not modified.
+		for i := 0; i < n; i++ {
+			for j := 0; j < n; j++ {
+				if tmat.Data[i*tmat.Stride+j] != tmatCopy.Data[i*tmatCopy.Stride+j] {
+					t.Errorf("%v: ok == false but T[%v,%v] modified", prefix, i, j)
+				}
+			}
+		}
+		if !wantq {
+			return
+		}
+		// Check that Q is not modified.
+		for i := 0; i < n; i++ {
+			for j := 0; j < n; j++ {
+				if q.Data[i*q.Stride+j] != qCopy.Data[i*qCopy.Stride+j] {
+					t.Errorf("%v: ok == false but Q[%v,%v] modified", prefix, i, j)
+				}
+			}
+		}
+		return
+	}
+
+	// Check that T is not modified outside of rows and columns [j1:j1+n1+n2].
+	for i := 0; i < n; i++ {
+		if j1 <= i && i < j1+n1+n2 {
+			continue
+		}
+		for j := 0; j < n; j++ {
+			if j1 <= j && j < j1+n1+n2 {
+				continue
+			}
+			diff := tmat.Data[i*tmat.Stride+j] - tmatCopy.Data[i*tmatCopy.Stride+j]
+			if diff != 0 {
+				t.Errorf("%v: unexpected modification of T[%v,%v]", prefix, i, j)
+			}
+		}
+	}
+
+	if n1 == 1 {
+		// 1×1 blocks are swapped exactly.
+		got := tmat.Data[(j1+n2)*tmat.Stride+j1+n2]
+		want := tmatCopy.Data[j1*tmatCopy.Stride+j1]
+		if want != got {
+			t.Errorf("%v: unexpected value of T[%v,%v]. Want %v, got %v", prefix, j1+n2, j1+n2, want, got)
+		}
+	} else {
+		// Check that the swapped 2×2 block is in Schur canonical form.
+		// The n1×n1 block is now located at T[j1+n2,j1+n2].
+		a, b, c, d := extract2x2Block(tmat.Data[(j1+n2)*tmat.Stride+j1+n2:], tmat.Stride)
+		if !isSchurCanonical(a, b, c, d) {
+			t.Errorf("%v: 2×2 block at T[%v,%v] not in Schur canonical form", prefix, j1+n2, j1+n2)
+		}
+		ev1Got, ev2Got := schurBlockEigenvalues(a, b, c, d)
+
+		// Check that the swapped 2×2 block has the same eigenvalues.
+		// The n1×n1 block was originally located at T[j1,j1].
+		a, b, c, d = extract2x2Block(tmatCopy.Data[j1*tmatCopy.Stride+j1:], tmatCopy.Stride)
+		ev1Want, ev2Want := schurBlockEigenvalues(a, b, c, d)
+		if cmplx.Abs(ev1Got-ev1Want) > tol {
+			t.Errorf("%v: unexpected first eigenvalue of 2×2 block at T[%v,%v]. Want %v, got %v",
+				prefix, j1+n2, j1+n2, ev1Want, ev1Got)
+		}
+		if cmplx.Abs(ev2Got-ev2Want) > tol {
+			t.Errorf("%v: unexpected second eigenvalue of 2×2 block at T[%v,%v]. Want %v, got %v",
+				prefix, j1+n2, j1+n2, ev2Want, ev2Got)
+		}
+	}
+	if n2 == 1 {
+		// 1×1 blocks are swapped exactly.
+		got := tmat.Data[j1*tmat.Stride+j1]
+		want := tmatCopy.Data[(j1+n1)*tmatCopy.Stride+j1+n1]
+		if want != got {
+			t.Errorf("%v: unexpected value of T[%v,%v]. Want %v, got %v", prefix, j1, j1, want, got)
+		}
+	} else {
+		// Check that the swapped 2×2 block is in Schur canonical form.
+		// The n2×n2 block is now located at T[j1,j1].
+		a, b, c, d := extract2x2Block(tmat.Data[j1*tmat.Stride+j1:], tmat.Stride)
+		if !isSchurCanonical(a, b, c, d) {
+			t.Errorf("%v: 2×2 block at T[%v,%v] not in Schur canonical form", prefix, j1, j1)
+		}
+		ev1Got, ev2Got := schurBlockEigenvalues(a, b, c, d)
+
+		// Check that the swapped 2×2 block has the same eigenvalues.
+		// The n2×n2 block was originally located at T[j1+n1,j1+n1].
+		a, b, c, d = extract2x2Block(tmatCopy.Data[(j1+n1)*tmatCopy.Stride+j1+n1:], tmatCopy.Stride)
+		ev1Want, ev2Want := schurBlockEigenvalues(a, b, c, d)
+		if cmplx.Abs(ev1Got-ev1Want) > tol {
+			t.Errorf("%v: unexpected first eigenvalue of 2×2 block at T[%v,%v]. Want %v, got %v",
+				prefix, j1, j1, ev1Want, ev1Got)
+		}
+		if cmplx.Abs(ev2Got-ev2Want) > tol {
+			t.Errorf("%v: unexpected second eigenvalue of 2×2 block at T[%v,%v]. Want %v, got %v",
+				prefix, j1, j1, ev2Want, ev2Got)
+		}
+	}
+
+	if !wantq {
+		return
+	}
+
+	if !isOrthonormal(q) {
+		t.Errorf("%v: Q is not orthogonal", prefix)
+	}
+	// Check that Q is unchanged outside of columns [j1:j1+n1+n2].
+	for i := 0; i < n; i++ {
+		for j := 0; j < n; j++ {
+			if j1 <= j && j < j1+n1+n2 {
+				continue
+			}
+			diff := q.Data[i*q.Stride+j] - qCopy.Data[i*qCopy.Stride+j]
+			if diff != 0 {
+				t.Errorf("%v: unexpected modification of Q[%v,%v]", prefix, i, j)
+			}
+		}
+	}
+	// Check that Q^T TOrig Q == T.
+	tq := eye(n, n)
+	blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, tmatCopy, q, 0, tq)
+	qtq := eye(n, n)
+	blas64.Gemm(blas.Trans, blas.NoTrans, 1, q, tq, 0, qtq)
+	for i := 0; i < n; i++ {
+		for j := 0; j < n; j++ {
+			diff := qtq.Data[i*qtq.Stride+j] - tmat.Data[i*tmat.Stride+j]
+			if math.Abs(diff) > tol {
+				t.Errorf("%v: unexpected value of T[%v,%v]", prefix, i, j)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlags2.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlags2.go
new file mode 100644
index 00000000..2a3da46d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlags2.go
@@ -0,0 +1,100 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dlags2er interface {
+	Dlags2(upper bool, a1, a2, a3, b1, b2, b3 float64) (csu, snu, csv, snv, csq, snq float64)
+}
+
+func Dlags2Test(t *testing.T, impl Dlags2er) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, upper := range []bool{true, false} {
+		for i := 0; i < 100; i++ {
+			a1 := rnd.Float64()
+			a2 := rnd.Float64()
+			a3 := rnd.Float64()
+			b1 := rnd.Float64()
+			b2 := rnd.Float64()
+			b3 := rnd.Float64()
+
+			csu, snu, csv, snv, csq, snq := impl.Dlags2(upper, a1, a2, a3, b1, b2, b3)
+
+			detU := det2x2(csu, snu, -snu, csu)
+			if !floats.EqualWithinAbsOrRel(math.Abs(detU), 1, 1e-14, 1e-14) {
+				t.Errorf("U not orthogonal: det(U)=%v", detU)
+			}
+			detV := det2x2(csv, snv, -snv, csv)
+			if !floats.EqualWithinAbsOrRel(math.Abs(detV), 1, 1e-14, 1e-14) {
+				t.Errorf("V not orthogonal: det(V)=%v", detV)
+			}
+			detQ := det2x2(csq, snq, -snq, csq)
+			if !floats.EqualWithinAbsOrRel(math.Abs(detQ), 1, 1e-14, 1e-14) {
+				t.Errorf("Q not orthogonal: det(Q)=%v", detQ)
+			}
+
+			u := blas64.General{
+				Rows:   2,
+				Cols:   2,
+				Stride: 2,
+				Data:   []float64{csu, snu, -snu, csu},
+			}
+			v := blas64.General{
+				Rows:   2,
+				Cols:   2,
+				Stride: 2,
+				Data:   []float64{csv, snv, -snv, csv},
+			}
+			q := blas64.General{
+				Rows:   2,
+				Cols:   2,
+				Stride: 2,
+				Data:   []float64{csq, snq, -snq, csq},
+			}
+
+			a := blas64.General{Rows: 2, Cols: 2, Stride: 2}
+			b := blas64.General{Rows: 2, Cols: 2, Stride: 2}
+			if upper {
+				a.Data = []float64{a1, a2, 0, a3}
+				b.Data = []float64{b1, b2, 0, b3}
+			} else {
+				a.Data = []float64{a1, 0, a2, a3}
+				b.Data = []float64{b1, 0, b2, b3}
+			}
+
+			tmp := blas64.General{Rows: 2, Cols: 2, Stride: 2, Data: make([]float64, 4)}
+			blas64.Gemm(blas.Trans, blas.NoTrans, 1, u, a, 0, tmp)
+			blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, tmp, q, 0, a)
+			blas64.Gemm(blas.Trans, blas.NoTrans, 1, v, b, 0, tmp)
+			blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, tmp, q, 0, b)
+
+			var gotA, gotB float64
+			if upper {
+				gotA = a.Data[1]
+				gotB = b.Data[1]
+			} else {
+				gotA = a.Data[2]
+				gotB = b.Data[2]
+			}
+			if !floats.EqualWithinAbsOrRel(gotA, 0, 1e-14, 1e-14) {
+				t.Errorf("unexpected non-zero value for zero triangle of U^T*A*Q: %v", gotA)
+			}
+			if !floats.EqualWithinAbsOrRel(gotB, 0, 1e-14, 1e-14) {
+				t.Errorf("unexpected non-zero value for zero triangle of V^T*B*Q: %v", gotB)
+			}
+		}
+	}
+}
+
+func det2x2(a, b, c, d float64) float64 { return a*d - b*c }
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlahqr.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlahqr.go
new file mode 100644
index 00000000..c68680a7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlahqr.go
@@ -0,0 +1,441 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dlahqrer interface {
+	Dlahqr(wantt, wantz bool, n, ilo, ihi int, h []float64, ldh int, wr, wi []float64, iloz, ihiz int, z []float64, ldz int) int
+}
+
+type dlahqrTest struct {
+	h            blas64.General
+	ilo, ihi     int
+	iloz, ihiz   int
+	wantt, wantz bool
+
+	evWant []complex128 // Optional slice holding known eigenvalues.
+}
+
+func DlahqrTest(t *testing.T, impl Dlahqrer) {
+	rnd := rand.New(rand.NewSource(1))
+
+	// Tests that choose the [ilo:ihi+1,ilo:ihi+1] and
+	// [iloz:ihiz+1,ilo:ihi+1] blocks randomly.
+	for _, wantt := range []bool{true, false} {
+		for _, wantz := range []bool{true, false} {
+			for _, n := range []int{1, 2, 3, 4, 5, 6, 10, 18, 31, 53} {
+				for _, extra := range []int{0, 1, 11} {
+					for cas := 0; cas < 100; cas++ {
+						ilo := rnd.Intn(n)
+						ihi := rnd.Intn(n)
+						if ilo > ihi {
+							ilo, ihi = ihi, ilo
+						}
+						iloz := rnd.Intn(ilo + 1)
+						ihiz := ihi + rnd.Intn(n-ihi)
+						h := randomHessenberg(n, n+extra, rnd)
+						if ilo-1 >= 0 {
+							h.Data[ilo*h.Stride+ilo-1] = 0
+						}
+						if ihi+1 < n {
+							h.Data[(ihi+1)*h.Stride+ihi] = 0
+						}
+						test := dlahqrTest{
+							h:     h,
+							ilo:   ilo,
+							ihi:   ihi,
+							iloz:  iloz,
+							ihiz:  ihiz,
+							wantt: wantt,
+							wantz: wantz,
+						}
+						testDlahqr(t, impl, test)
+					}
+				}
+			}
+		}
+	}
+	// Tests that make sure that some potentially problematic corner cases,
+	// like zero-sized matrix, are covered.
+	for _, wantt := range []bool{true, false} {
+		for _, wantz := range []bool{true, false} {
+			for _, extra := range []int{0, 1, 11} {
+				for _, test := range []dlahqrTest{
+					{
+						h:    randomHessenberg(0, extra, rnd),
+						ilo:  0,
+						ihi:  -1,
+						iloz: 0,
+						ihiz: -1,
+					},
+					{
+						h:    randomHessenberg(1, 1+extra, rnd),
+						ilo:  0,
+						ihi:  0,
+						iloz: 0,
+						ihiz: 0,
+					},
+					{
+						h:    randomHessenberg(2, 2+extra, rnd),
+						ilo:  1,
+						ihi:  1,
+						iloz: 1,
+						ihiz: 1,
+					},
+					{
+						h:    randomHessenberg(2, 2+extra, rnd),
+						ilo:  0,
+						ihi:  1,
+						iloz: 0,
+						ihiz: 1,
+					},
+					{
+						h:    randomHessenberg(10, 10+extra, rnd),
+						ilo:  0,
+						ihi:  0,
+						iloz: 0,
+						ihiz: 0,
+					},
+					{
+						h:    randomHessenberg(10, 10+extra, rnd),
+						ilo:  0,
+						ihi:  9,
+						iloz: 0,
+						ihiz: 9,
+					},
+					{
+						h:    randomHessenberg(10, 10+extra, rnd),
+						ilo:  0,
+						ihi:  1,
+						iloz: 0,
+						ihiz: 1,
+					},
+					{
+						h:    randomHessenberg(10, 10+extra, rnd),
+						ilo:  0,
+						ihi:  1,
+						iloz: 0,
+						ihiz: 9,
+					},
+					{
+						h:    randomHessenberg(10, 10+extra, rnd),
+						ilo:  9,
+						ihi:  9,
+						iloz: 0,
+						ihiz: 9,
+					},
+				} {
+					if test.ilo-1 >= 0 {
+						test.h.Data[test.ilo*test.h.Stride+test.ilo-1] = 0
+					}
+					if test.ihi+1 < test.h.Rows {
+						test.h.Data[(test.ihi+1)*test.h.Stride+test.ihi] = 0
+					}
+					test.wantt = wantt
+					test.wantz = wantz
+					testDlahqr(t, impl, test)
+				}
+			}
+		}
+	}
+
+	// Tests with explicit eigenvalues computed by Octave.
+	for _, test := range []dlahqrTest{
+		{
+			h: blas64.General{
+				Rows:   1,
+				Cols:   1,
+				Stride: 1,
+				Data:   []float64{7.09965484086874e-1},
+			},
+			ilo:    0,
+			ihi:    0,
+			iloz:   0,
+			ihiz:   0,
+			evWant: []complex128{7.09965484086874e-1},
+		},
+		{
+			h: blas64.General{
+				Rows:   2,
+				Cols:   2,
+				Stride: 2,
+				Data: []float64{
+					0, -1,
+					1, 0,
+				},
+			},
+			ilo:    0,
+			ihi:    1,
+			iloz:   0,
+			ihiz:   1,
+			evWant: []complex128{1i, -1i},
+		},
+		{
+			h: blas64.General{
+				Rows:   2,
+				Cols:   2,
+				Stride: 2,
+				Data: []float64{
+					6.25219991450918e-1, 8.17510791994361e-1,
+					3.31218891622294e-1, 1.24103744878131e-1,
+				},
+			},
+			ilo:    0,
+			ihi:    1,
+			iloz:   0,
+			ihiz:   1,
+			evWant: []complex128{9.52203547663447e-1, -2.02879811334398e-1},
+		},
+		{
+			h: blas64.General{
+				Rows:   4,
+				Cols:   4,
+				Stride: 4,
+				Data: []float64{
+					1, 0, 0, 0,
+					0, 6.25219991450918e-1, 8.17510791994361e-1, 0,
+					0, 3.31218891622294e-1, 1.24103744878131e-1, 0,
+					0, 0, 0, 1,
+				},
+			},
+			ilo:    1,
+			ihi:    2,
+			iloz:   0,
+			ihiz:   3,
+			evWant: []complex128{9.52203547663447e-1, -2.02879811334398e-1},
+		},
+		{
+			h: blas64.General{
+				Rows:   2,
+				Cols:   2,
+				Stride: 2,
+				Data: []float64{
+					-1.1219562276608, 6.85473513349362e-1,
+					-8.19951061145131e-1, 1.93728523178888e-1,
+				},
+			},
+			ilo:  0,
+			ihi:  1,
+			iloz: 0,
+			ihiz: 1,
+			evWant: []complex128{
+				-4.64113852240958e-1 + 3.59580510817350e-1i,
+				-4.64113852240958e-1 - 3.59580510817350e-1i,
+			},
+		},
+		{
+			h: blas64.General{
+				Rows:   5,
+				Cols:   5,
+				Stride: 5,
+				Data: []float64{
+					9.57590178533658e-1, -5.10651295522708e-1, 9.24974510015869e-1, -1.30016306879522e-1, 2.92601986926954e-2,
+					-1.08084756637964, 1.77529701001213, -1.36480197632509, 2.23196371219601e-1, 1.12912853063308e-1,
+					0, -8.44075612174676e-1, 1.067867614486, -2.55782915176399e-1, -2.00598563137468e-1,
+					0, 0, -5.67097237165410e-1, 2.07205057427341e-1, 6.54998340743380e-1,
+					0, 0, 0, -1.89441413886041e-1, -4.18125416021786e-1,
+				},
+			},
+			ilo:  0,
+			ihi:  4,
+			iloz: 0,
+			ihiz: 4,
+			evWant: []complex128{
+				2.94393309555622,
+				4.97029793606701e-1 + 3.63041654992384e-1i,
+				4.97029793606701e-1 - 3.63041654992384e-1i,
+				-1.74079119166145e-1 + 2.01570009462092e-1i,
+				-1.74079119166145e-1 - 2.01570009462092e-1i,
+			},
+		},
+	} {
+		test.wantt = true
+		test.wantz = true
+		testDlahqr(t, impl, test)
+	}
+}
+
+func testDlahqr(t *testing.T, impl Dlahqrer, test dlahqrTest) {
+	const tol = 1e-14
+
+	h := cloneGeneral(test.h)
+	n := h.Cols
+	extra := h.Stride - h.Cols
+	wantt := test.wantt
+	wantz := test.wantz
+	ilo := test.ilo
+	ihi := test.ihi
+	iloz := test.iloz
+	ihiz := test.ihiz
+
+	var z, zCopy blas64.General
+	if wantz {
+		z = eye(n, n+extra)
+		zCopy = cloneGeneral(z)
+	}
+
+	wr := nanSlice(ihi + 1)
+	wi := nanSlice(ihi + 1)
+
+	unconverged := impl.Dlahqr(wantt, wantz, n, ilo, ihi, h.Data, h.Stride, wr, wi, iloz, ihiz, z.Data, z.Stride)
+
+	prefix := fmt.Sprintf("Case wantt=%v, wantz=%v, n=%v, ilo=%v, ihi=%v, iloz=%v, ihiz=%v, extra=%v",
+		wantt, wantz, n, ilo, ihi, iloz, ihiz, extra)
+
+	if !generalOutsideAllNaN(h) {
+		t.Errorf("%v: out-of-range write to H\n%v", prefix, h.Data)
+	}
+	if !generalOutsideAllNaN(z) {
+		t.Errorf("%v: out-of-range write to Z\n%v", prefix, z.Data)
+	}
+
+	if !isUpperHessenberg(h) {
+		t.Logf("%v: H is not Hessenberg", prefix)
+	}
+
+	start := ilo // Index of the first computed eigenvalue.
+	if unconverged != 0 {
+		start = unconverged
+		if start == ihi+1 {
+			t.Logf("%v: no eigenvalue has converged", prefix)
+		}
+	}
+
+	// Check that wr and wi have not been modified in [:start].
+	if !isAllNaN(wr[:start]) {
+		t.Errorf("%v: unexpected modification of wr", prefix)
+	}
+	if !isAllNaN(wi[:start]) {
+		t.Errorf("%v: unexpected modification of wi", prefix)
+	}
+
+	var hasReal bool
+	for i := start; i <= ihi; {
+		if wi[i] == 0 { // Real eigenvalue.
+			hasReal = true
+			// Check that the eigenvalue corresponds to a 1×1 block
+			// on the diagonal of H.
+			if wantt {
+				if wr[i] != h.Data[i*h.Stride+i] {
+					t.Errorf("%v: wr[%v] != H[%v,%v]", prefix, i, i, i)
+				}
+				for _, index := range []struct{ r, c int }{
+					{i, i - 1},     // h   h   h
+					{i + 1, i - 1}, // 0 wr[i] h
+					{i + 1, i},     // 0   0   h
+				} {
+					if index.r >= n || index.c < 0 {
+						continue
+					}
+					if h.Data[index.r*h.Stride+index.c] != 0 {
+						t.Errorf("%v: H[%v,%v] != 0", prefix, index.r, index.c)
+					}
+				}
+			}
+			i++
+			continue
+		}
+
+		// Complex eigenvalue.
+
+		// In the conjugate pair the real parts must be equal.
+		if wr[i] != wr[i+1] {
+			t.Errorf("%v: real part of conjugate pair not equal, i=%v", prefix, i)
+		}
+		// The first imaginary part must be positive.
+		if wi[i] < 0 {
+			t.Errorf("%v: wi[%v] not positive", prefix, i)
+		}
+		// The second imaginary part must be negative with the same
+		// magnitude.
+		if wi[i] != -wi[i+1] {
+			t.Errorf("%v: wi[%v] != -wi[%v]", prefix, i, i+1)
+		}
+		if wantt {
+			// Check that wi[i] has the correct value.
+			if wr[i] != h.Data[i*h.Stride+i] {
+				t.Errorf("%v: wr[%v] != H[%v,%v]", prefix, i, i, i)
+			}
+			if wr[i] != h.Data[(i+1)*h.Stride+i+1] {
+				t.Errorf("%v: wr[%v] != H[%v,%v]", prefix, i, i+1, i+1)
+			}
+			prod := math.Abs(h.Data[(i+1)*h.Stride+i] * h.Data[i*h.Stride+i+1])
+			if math.Abs(math.Sqrt(prod)-wi[i]) > tol {
+				t.Errorf("%v: unexpected value of wi[%v]: want %v, got %v", prefix, i, math.Sqrt(prod), wi[i])
+			}
+
+			// Check that the corresponding diagonal block is 2×2.
+			for _, index := range []struct{ r, c int }{
+				{i, i - 1},     //     i
+				{i + 1, i - 1}, // h   h      h    h
+				{i + 2, i - 1}, // 0 wr[i]    b    h   i
+				{i + 2, i},     // 0   c   wr[i+1] h
+				{i + 2, i + 1}, // 0   0      0    h
+			} {
+				if index.r >= n || index.c < 0 {
+					continue
+				}
+				if h.Data[index.r*h.Stride+index.c] != 0 {
+					t.Errorf("%v: H[%v,%v] != 0", prefix, index.r, index.c)
+				}
+			}
+		}
+		i += 2
+	}
+	// If the number of found eigenvalues is odd, at least one must be real.
+	if (ihi+1-start)%2 != 0 && !hasReal {
+		t.Errorf("%v: expected at least one real eigenvalue", prefix)
+	}
+
+	// Compare found eigenvalues to the reference, if known.
+	if test.evWant != nil {
+		for i := start; i <= ihi; i++ {
+			ev := complex(wr[i], wi[i])
+			found, _ := containsComplex(test.evWant, ev, tol)
+			if !found {
+				t.Errorf("%v: unexpected eigenvalue %v", prefix, ev)
+			}
+		}
+	}
+
+	if !wantz {
+		return
+	}
+
+	// Z should contain the orthogonal matrix U.
+	if !isOrthonormal(z) {
+		t.Errorf("%v: Z is not orthogonal", prefix)
+	}
+	// Z should have been modified only in the
+	// [iloz:ihiz+1,ilo:ihi+1] block.
+	for i := 0; i < n; i++ {
+		for j := 0; j < n; j++ {
+			if iloz <= i && i <= ihiz && ilo <= j && j <= ihi {
+				continue
+			}
+			if z.Data[i*z.Stride+j] != zCopy.Data[i*zCopy.Stride+j] {
+				t.Errorf("%v: Z modified outside of [iloz:ihiz+1,ilo:ihi+1] block", prefix)
+			}
+		}
+	}
+	if wantt {
+		hu := eye(n, n)
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, test.h, z, 0, hu)
+		uhu := eye(n, n)
+		blas64.Gemm(blas.Trans, blas.NoTrans, 1, z, hu, 0, uhu)
+		if !equalApproxGeneral(uhu, h, 10*tol) {
+			t.Errorf("%v: Z^T*(initial H)*Z and (final H) are not equal", prefix)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlahr2.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlahr2.go
new file mode 100644
index 00000000..28aee344
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlahr2.go
@@ -0,0 +1,240 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"compress/gzip"
+	"encoding/json"
+	"fmt"
+	"log"
+	"math"
+	"math/rand"
+	"os"
+	"path/filepath"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dlahr2er interface {
+	Dlahr2(n, k, nb int, a []float64, lda int, tau, t []float64, ldt int, y []float64, ldy int)
+}
+
+type Dlahr2test struct {
+	N, K, NB int
+	A        []float64
+
+	AWant   []float64
+	TWant   []float64
+	YWant   []float64
+	TauWant []float64
+}
+
+func Dlahr2Test(t *testing.T, impl Dlahr2er) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, test := range []struct {
+		n, k, nb int
+	}{
+		{3, 0, 3},
+		{3, 1, 2},
+		{3, 1, 1},
+
+		{5, 0, 5},
+		{5, 1, 4},
+		{5, 1, 3},
+		{5, 1, 2},
+		{5, 1, 1},
+		{5, 2, 3},
+		{5, 2, 2},
+		{5, 2, 1},
+		{5, 3, 2},
+		{5, 3, 1},
+
+		{7, 3, 4},
+		{7, 3, 3},
+		{7, 3, 2},
+		{7, 3, 1},
+
+		{10, 0, 10},
+		{10, 1, 9},
+		{10, 1, 5},
+		{10, 1, 1},
+		{10, 5, 5},
+		{10, 5, 3},
+		{10, 5, 1},
+	} {
+		for cas := 0; cas < 100; cas++ {
+			for _, extraStride := range []int{0, 1, 10} {
+				n := test.n
+				k := test.k
+				nb := test.nb
+
+				a := randomGeneral(n, n-k+1, n-k+1+extraStride, rnd)
+				aCopy := a
+				aCopy.Data = make([]float64, len(a.Data))
+				copy(aCopy.Data, a.Data)
+				tmat := nanTriangular(blas.Upper, nb, nb+extraStride)
+				y := nanGeneral(n, nb, nb+extraStride)
+				tau := nanSlice(nb)
+
+				impl.Dlahr2(n, k, nb, a.Data, a.Stride, tau, tmat.Data, tmat.Stride, y.Data, y.Stride)
+
+				prefix := fmt.Sprintf("Case n=%v, k=%v, nb=%v, ldex=%v", n, k, nb, extraStride)
+
+				if !generalOutsideAllNaN(a) {
+					t.Errorf("%v: out-of-range write to A\n%v", prefix, a.Data)
+				}
+				if !triangularOutsideAllNaN(tmat) {
+					t.Errorf("%v: out-of-range write to T\n%v", prefix, tmat.Data)
+				}
+				if !generalOutsideAllNaN(y) {
+					t.Errorf("%v: out-of-range write to Y\n%v", prefix, y.Data)
+				}
+
+				// Check that A[:k,:] and A[:,nb:] blocks were not modified.
+				for i := 0; i < n; i++ {
+					for j := 0; j < n-k+1; j++ {
+						if i >= k && j < nb {
+							continue
+						}
+						if a.Data[i*a.Stride+j] != aCopy.Data[i*aCopy.Stride+j] {
+							t.Errorf("%v: unexpected write to A[%v,%v]", prefix, i, j)
+						}
+					}
+				}
+
+				// Check that all elements of tau were assigned.
+				for i, v := range tau {
+					if math.IsNaN(v) {
+						t.Errorf("%v: tau[%v] not assigned", prefix, i)
+					}
+				}
+
+				// Extract V from a.
+				v := blas64.General{
+					Rows:   n - k + 1,
+					Cols:   nb,
+					Stride: nb,
+					Data:   make([]float64, (n-k+1)*nb),
+				}
+				for j := 0; j < v.Cols; j++ {
+					v.Data[(j+1)*v.Stride+j] = 1
+					for i := j + 2; i < v.Rows; i++ {
+						v.Data[i*v.Stride+j] = a.Data[(i+k-1)*a.Stride+j]
+					}
+				}
+
+				// VT = V.
+				vt := v
+				vt.Data = make([]float64, len(v.Data))
+				copy(vt.Data, v.Data)
+				// VT = V * T.
+				blas64.Trmm(blas.Right, blas.NoTrans, 1, tmat, vt)
+				// YWant = A * V * T.
+				ywant := blas64.General{
+					Rows:   n,
+					Cols:   nb,
+					Stride: nb,
+					Data:   make([]float64, n*nb),
+				}
+				blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, aCopy, vt, 0, ywant)
+
+				// Compare Y and YWant.
+				for i := 0; i < n; i++ {
+					for j := 0; j < nb; j++ {
+						diff := math.Abs(ywant.Data[i*ywant.Stride+j] - y.Data[i*y.Stride+j])
+						if diff > 1e-14 {
+							t.Errorf("%v: unexpected Y[%v,%v], diff=%v", prefix, i, j, diff)
+						}
+					}
+				}
+
+				// Construct Q directly from the first nb columns of a.
+				q := constructQ("QR", n-k, nb, a.Data[k*a.Stride:], a.Stride, tau)
+				if !isOrthonormal(q) {
+					t.Errorf("%v: Q is not orthogonal", prefix)
+				}
+				// Construct Q as the product Q = I - V*T*V^T.
+				qwant := blas64.General{
+					Rows:   n - k + 1,
+					Cols:   n - k + 1,
+					Stride: n - k + 1,
+					Data:   make([]float64, (n-k+1)*(n-k+1)),
+				}
+				for i := 0; i < qwant.Rows; i++ {
+					qwant.Data[i*qwant.Stride+i] = 1
+				}
+				blas64.Gemm(blas.NoTrans, blas.Trans, -1, vt, v, 1, qwant)
+				if !isOrthonormal(qwant) {
+					t.Errorf("%v: Q = I - V*T*V^T is not orthogonal", prefix)
+				}
+
+				// Compare Q and QWant. Note that since Q is
+				// (n-k)×(n-k) and QWant is (n-k+1)×(n-k+1), we
+				// ignore the first row and column of QWant.
+				for i := 0; i < n-k; i++ {
+					for j := 0; j < n-k; j++ {
+						diff := math.Abs(q.Data[i*q.Stride+j] - qwant.Data[(i+1)*qwant.Stride+j+1])
+						if diff > 1e-14 {
+							t.Errorf("%v: unexpected Q[%v,%v], diff=%v", prefix, i, j, diff)
+						}
+					}
+				}
+			}
+		}
+	}
+
+	// Go runs tests from the source directory, so unfortunately we need to
+	// include the "../testlapack" part.
+	file, err := os.Open(filepath.FromSlash("../testlapack/testdata/dlahr2data.json.gz"))
+	if err != nil {
+		log.Fatal(err)
+	}
+	defer file.Close()
+	r, err := gzip.NewReader(file)
+	if err != nil {
+		log.Fatal(err)
+	}
+	defer r.Close()
+
+	var tests []Dlahr2test
+	json.NewDecoder(r).Decode(&tests)
+	for _, test := range tests {
+		tau := make([]float64, len(test.TauWant))
+		for _, ldex := range []int{0, 1, 20} {
+			n := test.N
+			k := test.K
+			nb := test.NB
+
+			lda := n - k + 1 + ldex
+			a := make([]float64, (n-1)*lda+n-k+1)
+			copyMatrix(n, n-k+1, a, lda, test.A)
+
+			ldt := nb + ldex
+			tmat := make([]float64, (nb-1)*ldt+nb)
+
+			ldy := nb + ldex
+			y := make([]float64, (n-1)*ldy+nb)
+
+			impl.Dlahr2(n, k, nb, a, lda, tau, tmat, ldt, y, ldy)
+
+			prefix := fmt.Sprintf("Case n=%v, k=%v, nb=%v, ldex=%v", n, k, nb, ldex)
+			if !equalApprox(n, n-k+1, a, lda, test.AWant, 1e-14) {
+				t.Errorf("%v: unexpected matrix A\n got=%v\nwant=%v", prefix, a, test.AWant)
+			}
+			if !equalApproxTriangular(true, nb, tmat, ldt, test.TWant, 1e-14) {
+				t.Errorf("%v: unexpected matrix T\n got=%v\nwant=%v", prefix, tmat, test.TWant)
+			}
+			if !equalApprox(n, nb, y, ldy, test.YWant, 1e-14) {
+				t.Errorf("%v: unexpected matrix Y\n got=%v\nwant=%v", prefix, y, test.YWant)
+			}
+			if !floats.EqualApprox(tau, test.TauWant, 1e-14) {
+				t.Errorf("%v: unexpected slice tau\n got=%v\nwant=%v", prefix, tau, test.TauWant)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaln2.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaln2.go
new file mode 100644
index 00000000..07a322b8
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaln2.go
@@ -0,0 +1,139 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math"
+	"math/cmplx"
+	"math/rand"
+	"testing"
+)
+
+type Dlaln2er interface {
+	Dlaln2(trans bool, na, nw int, smin, ca float64, a []float64, lda int, d1, d2 float64, b []float64, ldb int, wr, wi float64, x []float64, ldx int) (scale, xnorm float64, ok bool)
+}
+
+func Dlaln2Test(t *testing.T, impl Dlaln2er) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, trans := range []bool{true, false} {
+		for _, na := range []int{1, 2} {
+			for _, nw := range []int{1, 2} {
+				for _, extra := range []int{0, 1, 2, 13} {
+					for cas := 0; cas < 1000; cas++ {
+						testDlaln2(t, impl, trans, na, nw, extra, rnd)
+					}
+				}
+			}
+		}
+	}
+}
+
+func testDlaln2(t *testing.T, impl Dlaln2er, trans bool, na, nw, extra int, rnd *rand.Rand) {
+	const tol = 1e-12
+	const dlamchE = 1.0 / (1 << 53)
+	const dlamchP = 2 * dlamchE
+
+	ca := rnd.NormFloat64()
+	d1 := rnd.NormFloat64()
+	d2 := rnd.NormFloat64()
+
+	var w complex128
+	if nw == 1 {
+		w = complex(rand.NormFloat64(), 0)
+	} else {
+		w = complex(rand.NormFloat64(), rand.NormFloat64())
+	}
+	smin := dlamchP * (math.Abs(real(w)) + math.Abs(imag(w)))
+
+	a := randomGeneral(na, na, na+extra, rnd)
+	b := randomGeneral(na, nw, nw+extra, rnd)
+	x := randomGeneral(na, nw, nw+extra, rnd)
+
+	scale, xnormGot, ok := impl.Dlaln2(trans, na, nw, smin, ca, a.Data, a.Stride, d1, d2, b.Data, b.Stride, real(w), imag(w), x.Data, x.Stride)
+
+	prefix := fmt.Sprintf("Case trans=%v, na=%v, nw=%v, extra=%v", trans, na, nw, extra)
+
+	if !generalOutsideAllNaN(a) {
+		t.Errorf("%v: out-of-range write to A\n%v", prefix, a.Data)
+	}
+	if !generalOutsideAllNaN(b) {
+		t.Errorf("%v: out-of-range write to B\n%v", prefix, b.Data)
+	}
+	if !generalOutsideAllNaN(x) {
+		t.Errorf("%v: out-of-range write to X\n%v", prefix, x.Data)
+	}
+
+	if scale <= 0 || 1 < scale {
+		t.Errorf("%v: invalid value of scale=%v", prefix, scale)
+	}
+
+	var xnormWant float64
+	for i := 0; i < na; i++ {
+		var rowsum float64
+		for j := 0; j < nw; j++ {
+			rowsum += math.Abs(x.Data[i*x.Stride+j])
+		}
+		if rowsum > xnormWant {
+			xnormWant = rowsum
+		}
+	}
+	if xnormWant != xnormGot {
+		t.Errorf("Case %v: unexpected xnorm with scale=%v. Want %v, got %v", prefix, scale, xnormWant, xnormGot)
+	}
+
+	if !ok {
+		// If ok is false, the matrix has been perturbed but we don't
+		// know how. Return without comparing both sides of the
+		// equation.
+		return
+	}
+
+	m := make([]complex128, na*na)
+	if trans {
+		for i := 0; i < na; i++ {
+			for j := 0; j < na; j++ {
+				m[i*na+j] = complex(ca*a.Data[j*a.Stride+i], 0)
+			}
+		}
+	} else {
+		for i := 0; i < na; i++ {
+			for j := 0; j < na; j++ {
+				m[i*na+j] = complex(ca*a.Data[i*a.Stride+j], 0)
+			}
+		}
+	}
+	m[0] -= w * complex(d1, 0)
+	if na == 2 {
+		m[3] -= w * complex(d2, 0)
+	}
+
+	cx := make([]complex128, na)
+	cb := make([]complex128, na)
+	switch nw {
+	case 1:
+		for i := 0; i < na; i++ {
+			cx[i] = complex(x.Data[i*x.Stride], 0)
+			cb[i] = complex(scale*b.Data[i*x.Stride], 0)
+		}
+	case 2:
+		for i := 0; i < na; i++ {
+			cx[i] = complex(x.Data[i*x.Stride], x.Data[i*x.Stride+1])
+			cb[i] = complex(scale*b.Data[i*b.Stride], scale*b.Data[i*b.Stride+1])
+		}
+	}
+
+	mx := make([]complex128, na)
+	for i := 0; i < na; i++ {
+		for j := 0; j < na; j++ {
+			mx[i] += m[i*na+j] * cx[j]
+		}
+	}
+	for i := 0; i < na; i++ {
+		if cmplx.Abs(mx[i]-cb[i]) > tol {
+			t.Errorf("Case %v: unexpected value of left-hand side at row %v with scale=%v. Want %v, got %v", prefix, i, scale, cb[i], mx[i])
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlange.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlange.go
new file mode 100644
index 00000000..33f7efe1
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlange.go
@@ -0,0 +1,93 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dlanger interface {
+	Dlange(norm lapack.MatrixNorm, m, n int, a []float64, lda int, work []float64) float64
+}
+
+func DlangeTest(t *testing.T, impl Dlanger) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, test := range []struct {
+		m, n, lda int
+	}{
+		{4, 3, 0},
+		{3, 4, 0},
+		{4, 3, 100},
+		{3, 4, 100},
+	} {
+		m := test.m
+		n := test.n
+		lda := test.lda
+		if lda == 0 {
+			lda = n
+		}
+		a := make([]float64, m*lda)
+		for i := range a {
+			a[i] = rnd.Float64() - 0.5
+		}
+		work := make([]float64, n)
+		for i := range work {
+			work[i] = rnd.Float64()
+		}
+		aCopy := make([]float64, len(a))
+		copy(aCopy, a)
+
+		// Test MaxAbs norm.
+		norm := impl.Dlange(lapack.MaxAbs, m, n, a, lda, work)
+		var ans float64
+		for i := 0; i < m; i++ {
+			idx := blas64.Iamax(n, blas64.Vector{Inc: 1, Data: aCopy[i*lda:]})
+			ans = math.Max(ans, math.Abs(a[i*lda+idx]))
+		}
+		// Should be strictly equal because there is no floating point summation error.
+		if ans != norm {
+			t.Errorf("MaxAbs mismatch. Want %v, got %v.", ans, norm)
+		}
+
+		// Test MaxColumnSum norm.
+		norm = impl.Dlange(lapack.MaxColumnSum, m, n, a, lda, work)
+		ans = 0
+		for i := 0; i < n; i++ {
+			sum := blas64.Asum(m, blas64.Vector{Inc: lda, Data: aCopy[i:]})
+			ans = math.Max(ans, sum)
+		}
+		if math.Abs(norm-ans) > 1e-14 {
+			t.Errorf("MaxColumnSum mismatch. Want %v, got %v.", ans, norm)
+		}
+
+		// Test MaxRowSum norm.
+		norm = impl.Dlange(lapack.MaxRowSum, m, n, a, lda, work)
+		ans = 0
+		for i := 0; i < m; i++ {
+			sum := blas64.Asum(n, blas64.Vector{Inc: 1, Data: aCopy[i*lda:]})
+			ans = math.Max(ans, sum)
+		}
+		if math.Abs(norm-ans) > 1e-14 {
+			t.Errorf("MaxRowSum mismatch. Want %v, got %v.", ans, norm)
+		}
+
+		// Test Frobenius norm
+		norm = impl.Dlange(lapack.NormFrob, m, n, a, lda, work)
+		ans = 0
+		for i := 0; i < m; i++ {
+			sum := blas64.Nrm2(n, blas64.Vector{Inc: 1, Data: aCopy[i*lda:]})
+			ans += sum * sum
+		}
+		ans = math.Sqrt(ans)
+		if math.Abs(norm-ans) > 1e-14 {
+			t.Errorf("NormFrob mismatch. Want %v, got %v.", ans, norm)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlanst.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlanst.go
new file mode 100644
index 00000000..224f1d07
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlanst.go
@@ -0,0 +1,53 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dlanster interface {
+	Dlanst(norm lapack.MatrixNorm, n int, d, e []float64) float64
+	Dlanger
+}
+
+func DlanstTest(t *testing.T, impl Dlanster) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, norm := range []lapack.MatrixNorm{lapack.MaxAbs, lapack.MaxColumnSum, lapack.MaxRowSum, lapack.NormFrob} {
+		for _, n := range []int{1, 3, 10, 100} {
+			for cas := 0; cas < 100; cas++ {
+				d := make([]float64, n)
+				for i := range d {
+					d[i] = rnd.NormFloat64()
+				}
+				e := make([]float64, n-1)
+				for i := range e {
+					e[i] = rnd.NormFloat64()
+				}
+
+				m := n
+				lda := n
+				a := make([]float64, m*lda)
+				for i := 0; i < n; i++ {
+					a[i*lda+i] = d[i]
+				}
+				for i := 0; i < n-1; i++ {
+					a[i*lda+i+1] = e[i]
+					a[(i+1)*lda+i] = e[i]
+				}
+				work := make([]float64, n)
+				syNorm := impl.Dlanst(norm, n, d, e)
+				geNorm := impl.Dlange(norm, m, n, a, lda, work)
+				if math.Abs(syNorm-geNorm) > 1e-12 {
+					t.Errorf("Norm mismatch: norm = %v, cas = %v, n = %v. Want %v, got %v.", string(norm), cas, n, geNorm, syNorm)
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlansy.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlansy.go
new file mode 100644
index 00000000..b38f6bb0
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlansy.go
@@ -0,0 +1,80 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dlansyer interface {
+	Dlanger
+	Dlansy(norm lapack.MatrixNorm, uplo blas.Uplo, n int, a []float64, lda int, work []float64) float64
+}
+
+func DlansyTest(t *testing.T, impl Dlansyer) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, norm := range []lapack.MatrixNorm{lapack.MaxAbs, lapack.MaxColumnSum, lapack.MaxRowSum, lapack.NormFrob} {
+		for _, uplo := range []blas.Uplo{blas.Lower, blas.Upper} {
+			for _, test := range []struct {
+				n, lda int
+			}{
+				{1, 0},
+				{3, 0},
+
+				{1, 10},
+				{3, 10},
+			} {
+				for trial := 0; trial < 100; trial++ {
+					n := test.n
+					lda := test.lda
+					if lda == 0 {
+						lda = n
+					}
+					a := make([]float64, lda*n)
+					if trial == 0 {
+						for i := range a {
+							a[i] = float64(i)
+						}
+					} else {
+						for i := range a {
+							a[i] = rnd.NormFloat64()
+						}
+					}
+
+					aDense := make([]float64, n*n)
+					if uplo == blas.Upper {
+						for i := 0; i < n; i++ {
+							for j := i; j < n; j++ {
+								v := a[i*lda+j]
+								aDense[i*n+j] = v
+								aDense[j*n+i] = v
+							}
+						}
+					} else {
+						for i := 0; i < n; i++ {
+							for j := 0; j <= i; j++ {
+								v := a[i*lda+j]
+								aDense[i*n+j] = v
+								aDense[j*n+i] = v
+							}
+						}
+					}
+					work := make([]float64, n)
+					got := impl.Dlansy(norm, uplo, n, a, lda, work)
+					want := impl.Dlange(norm, n, n, aDense, n, work)
+					if math.Abs(want-got) > 1e-14 {
+						t.Errorf("Norm mismatch. norm = %c, upper = %v, n = %v, lda = %v, want %v, got %v.",
+							norm, uplo == blas.Upper, n, lda, got, want)
+					}
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlantr.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlantr.go
new file mode 100644
index 00000000..74f3c656
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlantr.go
@@ -0,0 +1,89 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dlantrer interface {
+	Dlanger
+	Dlantr(norm lapack.MatrixNorm, uplo blas.Uplo, diag blas.Diag, m, n int, a []float64, lda int, work []float64) float64
+}
+
+func DlantrTest(t *testing.T, impl Dlantrer) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, norm := range []lapack.MatrixNorm{lapack.MaxAbs, lapack.MaxColumnSum, lapack.MaxRowSum, lapack.NormFrob} {
+		for _, diag := range []blas.Diag{blas.NonUnit, blas.Unit} {
+			for _, uplo := range []blas.Uplo{blas.Lower, blas.Upper} {
+				for _, test := range []struct {
+					m, n, lda int
+				}{
+					{3, 3, 0},
+					{3, 5, 0},
+					{10, 5, 0},
+
+					{5, 5, 11},
+					{5, 10, 11},
+					{10, 5, 11},
+				} {
+					// Do a couple of random trials since the values change.
+					for trial := 0; trial < 100; trial++ {
+						m := test.m
+						n := test.n
+						lda := test.lda
+						if lda == 0 {
+							lda = n
+						}
+						a := make([]float64, m*lda)
+						if trial == 0 {
+							for i := range a {
+								a[i] = float64(i)
+							}
+						} else {
+							for i := range a {
+								a[i] = rnd.NormFloat64()
+							}
+						}
+						aDense := make([]float64, len(a))
+						if uplo == blas.Lower {
+							for i := 0; i < m; i++ {
+								for j := 0; j <= min(i, n-1); j++ {
+									aDense[i*lda+j] = a[i*lda+j]
+								}
+							}
+						} else {
+							for i := 0; i < m; i++ {
+								for j := i; j < n; j++ {
+									aDense[i*lda+j] = a[i*lda+j]
+								}
+							}
+						}
+						if diag == blas.Unit {
+							for i := 0; i < min(m, n); i++ {
+								aDense[i*lda+i] = 1
+							}
+						}
+						work := make([]float64, n+6)
+						for i := range work {
+							work[i] = rnd.Float64()
+						}
+						got := impl.Dlantr(norm, uplo, diag, m, n, a, lda, work)
+						want := impl.Dlange(norm, m, n, aDense, lda, work)
+						if math.Abs(got-want) > 1e-13 {
+							t.Errorf("Norm mismatch. norm = %c, unitdiag = %v, upper = %v, m = %v, n = %v, lda = %v, Want %v, got %v.",
+								norm, diag == blas.Unit, uplo == blas.Upper, m, n, lda, got, want)
+						}
+					}
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlanv2.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlanv2.go
new file mode 100644
index 00000000..07cf2c51
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlanv2.go
@@ -0,0 +1,69 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math"
+	"math/rand"
+	"testing"
+)
+
+type Dlanv2er interface {
+	Dlanv2(a, b, c, d float64) (aa, bb, cc, dd float64, rt1r, rt1i, rt2r, rt2i float64, cs, sn float64)
+}
+
+func Dlanv2Test(t *testing.T, impl Dlanv2er) {
+	rnd := rand.New(rand.NewSource(1))
+	for i := 0; i < 1000; i++ {
+		a := rnd.NormFloat64()
+		b := rnd.NormFloat64()
+		c := rnd.NormFloat64()
+		d := rnd.NormFloat64()
+		aa, bb, cc, dd, rt1r, rt1i, rt2r, rt2i, cs, sn := impl.Dlanv2(a, b, c, d)
+
+		mat := fmt.Sprintf("[%v %v; %v %v]", a, b, c, d)
+		if cc == 0 {
+			if rt1i != 0 || rt2i != 0 {
+				t.Errorf("Unexpected complex eigenvalues for %v", mat)
+			}
+		} else {
+			if aa != dd {
+				t.Errorf("Diagonal elements not equal for %v: got [%v %v]", mat, aa, dd)
+			}
+			if bb*cc >= 0 {
+				t.Errorf("Non-diagonal elements have the same sign for %v: got [%v %v]", mat, bb, cc)
+			} else {
+				im := math.Sqrt(-bb * cc)
+				if math.Abs(rt1i-im) > 1e-14 && math.Abs(rt1i+im) > 1e-14 {
+					t.Errorf("Unexpected imaginary part of eigenvalue for %v: got %v, want %v or %v", mat, rt1i, im, -im)
+				}
+				if math.Abs(rt2i-im) > 1e-14 && math.Abs(rt2i+im) > 1e-14 {
+					t.Errorf("Unexpected imaginary part of eigenvalue for %v: got %v, want %v or %v", mat, rt2i, im, -im)
+				}
+			}
+		}
+		if rt1r != aa && rt1r != dd {
+			t.Errorf("Unexpected real part of eigenvalue for %v: got %v, want %v or %v", mat, rt1r, aa, dd)
+		}
+		if rt2r != aa && rt2r != dd {
+			t.Errorf("Unexpected real part of eigenvalue for %v: got %v, want %v or %v", mat, rt2r, aa, dd)
+		}
+		if math.Abs(math.Hypot(cs, sn)-1) > 1e-14 {
+			t.Errorf("Unexpected unitary matrix for %v: got cs %v, sn %v", mat, cs, sn)
+		}
+
+		gota := cs*(aa*cs-bb*sn) - sn*(cc*cs-dd*sn)
+		gotb := cs*(aa*sn+bb*cs) - sn*(cc*sn+dd*cs)
+		gotc := sn*(aa*cs-bb*sn) + cs*(cc*cs-dd*sn)
+		gotd := sn*(aa*sn+bb*cs) + cs*(cc*sn+dd*cs)
+		if math.Abs(gota-a) > 1e-14 ||
+			math.Abs(gotb-b) > 1e-14 ||
+			math.Abs(gotc-c) > 1e-14 ||
+			math.Abs(gotd-d) > 1e-14 {
+			t.Errorf("Unexpected factorization: got [%v %v; %v %v], want [%v %v; %v %v]", gota, gotb, gotc, gotd, a, b, c, d)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlapll.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlapll.go
new file mode 100644
index 00000000..1c35f039
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlapll.go
@@ -0,0 +1,46 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dlapller interface {
+	Dgesvder
+	Dlapll(n int, x []float64, incX int, y []float64, incY int) float64
+}
+
+func DlapllTest(t *testing.T, impl Dlapller) {
+	rnd := rand.New(rand.NewSource(1))
+	for i, m := range []int{5, 6, 9, 300, 400, 600} {
+		n := 2
+		lda := n
+		a := make([]float64, m*lda)
+		for i := range a {
+			a[i] = rnd.NormFloat64()
+		}
+
+		aCopy := make([]float64, len(a))
+		copy(aCopy, a)
+
+		got := impl.Dlapll(m, a[0:], 2, a[1:], 2)
+
+		s := make([]float64, min(m, n))
+		work := make([]float64, 1)
+		impl.Dgesvd(lapack.SVDNone, lapack.SVDNone, m, n, aCopy, lda, s, nil, 0, nil, 0, work, -1)
+		work = make([]float64, int(work[0]))
+		impl.Dgesvd(lapack.SVDNone, lapack.SVDNone, m, n, aCopy, lda, s, nil, 0, nil, 0, work, len(work))
+		want := s[len(s)-1]
+
+		if !floats.EqualWithinAbsOrRel(got, want, 1e-14, 1e-14) {
+			t.Errorf("unexpected ssmin for test %d: got:%f want:%f", i, got, want)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlapmt.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlapmt.go
new file mode 100644
index 00000000..b2fd1f8d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlapmt.go
@@ -0,0 +1,113 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"testing"
+
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dlapmter interface {
+	Dlapmt(forward bool, m, n int, x []float64, ldx int, k []int)
+}
+
+func DlapmtTest(t *testing.T, impl Dlapmter) {
+	for ti, test := range []struct {
+		forward bool
+		k       []int
+
+		want blas64.General
+	}{
+		{
+			forward: true, k: []int{0, 1, 2},
+			want: blas64.General{
+				Rows:   4,
+				Cols:   3,
+				Stride: 3,
+				Data: []float64{
+					1, 2, 3,
+					4, 5, 6,
+					7, 8, 9,
+					10, 11, 12,
+				},
+			},
+		},
+		{
+			forward: false, k: []int{0, 1, 2},
+			want: blas64.General{
+				Rows:   4,
+				Cols:   3,
+				Stride: 3,
+				Data: []float64{
+					1, 2, 3,
+					4, 5, 6,
+					7, 8, 9,
+					10, 11, 12,
+				},
+			},
+		},
+		{
+			forward: true, k: []int{1, 2, 0},
+			want: blas64.General{
+				Rows:   4,
+				Cols:   3,
+				Stride: 3,
+				Data: []float64{
+					2, 3, 1,
+					5, 6, 4,
+					8, 9, 7,
+					11, 12, 10,
+				},
+			},
+		},
+		{
+			forward: false, k: []int{1, 2, 0},
+			want: blas64.General{
+				Rows:   4,
+				Cols:   3,
+				Stride: 3,
+				Data: []float64{
+					3, 1, 2,
+					6, 4, 5,
+					9, 7, 8,
+					12, 10, 11,
+				},
+			},
+		},
+	} {
+		m := test.want.Rows
+		n := test.want.Cols
+		if len(test.k) != n {
+			panic("bad length of k")
+		}
+
+		for _, extra := range []int{0, 11} {
+			x := zeros(m, n, n+extra)
+			c := 1
+			for i := 0; i < m; i++ {
+				for j := 0; j < n; j++ {
+					x.Data[i*x.Stride+j] = float64(c)
+					c++
+				}
+			}
+
+			k := make([]int, len(test.k))
+			copy(k, test.k)
+
+			impl.Dlapmt(test.forward, m, n, x.Data, x.Stride, k)
+
+			prefix := fmt.Sprintf("Case %v (forward=%t,m=%v,n=%v,extra=%v)", ti, test.forward, m, n, extra)
+			if !generalOutsideAllNaN(x) {
+				t.Errorf("%v: out-of-range write to X", prefix)
+			}
+
+			if !equalApproxGeneral(x, test.want, 0) {
+				t.Errorf("%v: unexpected X\n%v\n%v", prefix, x, test.want)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlapy2.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlapy2.go
new file mode 100644
index 00000000..6efb81d9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlapy2.go
@@ -0,0 +1,30 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dlapy2er interface {
+	Dlapy2(float64, float64) float64
+}
+
+func Dlapy2Test(t *testing.T, impl Dlapy2er) {
+	rnd := rand.New(rand.NewSource(1))
+	for i := 0; i < 10; i++ {
+		x := math.Abs(1e200 * rnd.NormFloat64())
+		y := math.Abs(1e200 * rnd.NormFloat64())
+		got := impl.Dlapy2(x, y)
+		want := math.Hypot(x, y)
+		if !floats.EqualWithinRel(got, want, 1e-16) {
+			t.Errorf("Dlapy2(%g, %g) = %g, want %g", x, y, got, want)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaqp2.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaqp2.go
new file mode 100644
index 00000000..230b2ecc
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaqp2.go
@@ -0,0 +1,115 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dlaqp2er interface {
+	Dlapmter
+	Dlaqp2(m, n, offset int, a []float64, lda int, jpvt []int, tau, vn1, vn2, work []float64)
+}
+
+func Dlaqp2Test(t *testing.T, impl Dlaqp2er) {
+	for ti, test := range []struct {
+		m, n, offset int
+	}{
+		{m: 4, n: 3, offset: 0},
+		{m: 4, n: 3, offset: 2},
+		{m: 4, n: 3, offset: 4},
+		{m: 3, n: 4, offset: 0},
+		{m: 3, n: 4, offset: 1},
+		{m: 3, n: 4, offset: 2},
+		{m: 8, n: 3, offset: 0},
+		{m: 8, n: 3, offset: 4},
+		{m: 8, n: 3, offset: 8},
+		{m: 3, n: 8, offset: 0},
+		{m: 3, n: 8, offset: 1},
+		{m: 3, n: 8, offset: 2},
+		{m: 10, n: 10, offset: 0},
+		{m: 10, n: 10, offset: 5},
+		{m: 10, n: 10, offset: 10},
+	} {
+		m := test.m
+		n := test.n
+		jpiv := make([]int, n)
+
+		for _, extra := range []int{0, 11} {
+			a := zeros(m, n, n+extra)
+			c := 1
+			for i := 0; i < m; i++ {
+				for j := 0; j < n; j++ {
+					a.Data[i*a.Stride+j] = float64(c)
+					c++
+				}
+			}
+			aCopy := cloneGeneral(a)
+			for j := range jpiv {
+				jpiv[j] = j
+			}
+
+			tau := make([]float64, n)
+			vn1 := columnNorms(m, n, a.Data, a.Stride)
+			vn2 := columnNorms(m, n, a.Data, a.Stride)
+			work := make([]float64, n)
+
+			impl.Dlaqp2(m, n, test.offset, a.Data, a.Stride, jpiv, tau, vn1, vn2, work)
+
+			prefix := fmt.Sprintf("Case %v (offset=%d,m=%v,n=%v,extra=%v)", ti, test.offset, m, n, extra)
+			if !generalOutsideAllNaN(a) {
+				t.Errorf("%v: out-of-range write to A", prefix)
+			}
+
+			if test.offset == m {
+				continue
+			}
+
+			mo := m - test.offset
+			q := constructQ("QR", mo, n, a.Data[test.offset*a.Stride:], a.Stride, tau)
+			// Check that q is orthonormal
+			for i := 0; i < mo; i++ {
+				nrm := blas64.Nrm2(mo, blas64.Vector{Inc: 1, Data: q.Data[i*mo:]})
+				if math.Abs(nrm-1) > 1e-13 {
+					t.Errorf("Case %v, q not normal", ti)
+				}
+				for j := 0; j < i; j++ {
+					dot := blas64.Dot(mo, blas64.Vector{Inc: 1, Data: q.Data[i*mo:]}, blas64.Vector{Inc: 1, Data: q.Data[j*mo:]})
+					if math.Abs(dot) > 1e-14 {
+						t.Errorf("Case %v, q not orthogonal", ti)
+					}
+				}
+			}
+
+			// Check that A * P = Q * R
+			r := blas64.General{
+				Rows:   mo,
+				Cols:   n,
+				Stride: n,
+				Data:   make([]float64, mo*n),
+			}
+			for i := 0; i < mo; i++ {
+				for j := i; j < n; j++ {
+					r.Data[i*n+j] = a.Data[(test.offset+i)*a.Stride+j]
+				}
+			}
+			got := nanGeneral(mo, n, n)
+			blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, q, r, 0, got)
+
+			want := aCopy
+			impl.Dlapmt(true, want.Rows, want.Cols, want.Data, want.Stride, jpiv)
+			want.Rows = mo
+			want.Data = want.Data[test.offset*want.Stride:]
+			if !equalApproxGeneral(got, want, 1e-12) {
+				t.Errorf("Case %v,  Q*R != A*P\nQ*R=%v\nA*P=%v", ti, got, want)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaqps.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaqps.go
new file mode 100644
index 00000000..7bb4800b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaqps.go
@@ -0,0 +1,112 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dlaqpser interface {
+	Dlapmter
+	Dlaqps(m, n, offset, nb int, a []float64, lda int, jpvt []int, tau, vn1, vn2, auxv, f []float64, ldf int) (kb int)
+}
+
+func DlaqpsTest(t *testing.T, impl Dlaqpser) {
+	for ti, test := range []struct {
+		m, n, nb, offset int
+	}{
+		{m: 4, n: 3, nb: 2, offset: 0},
+		{m: 4, n: 3, nb: 1, offset: 2},
+		{m: 3, n: 4, nb: 2, offset: 0},
+		{m: 3, n: 4, nb: 1, offset: 2},
+		{m: 8, n: 3, nb: 2, offset: 0},
+		{m: 8, n: 3, nb: 1, offset: 4},
+		{m: 3, n: 8, nb: 2, offset: 0},
+		{m: 3, n: 8, nb: 1, offset: 1},
+		{m: 10, n: 10, nb: 3, offset: 0},
+		{m: 10, n: 10, nb: 2, offset: 5},
+	} {
+		m := test.m
+		n := test.n
+		jpiv := make([]int, n)
+
+		for _, extra := range []int{0, 11} {
+			a := zeros(m, n, n+extra)
+			c := 1
+			for i := 0; i < m; i++ {
+				for j := 0; j < n; j++ {
+					a.Data[i*a.Stride+j] = float64(c)
+					c++
+				}
+			}
+			aCopy := cloneGeneral(a)
+			for j := range jpiv {
+				jpiv[j] = j
+			}
+
+			tau := make([]float64, n)
+			vn1 := columnNorms(m, n, a.Data, a.Stride)
+			vn2 := columnNorms(m, n, a.Data, a.Stride)
+			auxv := make([]float64, test.nb)
+			f := zeros(test.n, test.nb, n)
+
+			kb := impl.Dlaqps(m, n, test.offset, test.nb, a.Data, a.Stride, jpiv, tau, vn1, vn2, auxv, f.Data, f.Stride)
+
+			prefix := fmt.Sprintf("Case %v (offset=%d,m=%v,n=%v,extra=%v)", ti, test.offset, m, n, extra)
+			if !generalOutsideAllNaN(a) {
+				t.Errorf("%v: out-of-range write to A", prefix)
+			}
+
+			if test.offset == m {
+				continue
+			}
+
+			mo := m - test.offset
+			q := constructQ("QR", mo, kb, a.Data[test.offset*a.Stride:], a.Stride, tau)
+			// Check that q is orthonormal
+			for i := 0; i < mo; i++ {
+				nrm := blas64.Nrm2(mo, blas64.Vector{Inc: 1, Data: q.Data[i*mo:]})
+				if math.Abs(nrm-1) > 1e-13 {
+					t.Errorf("Case %v, q not normal", ti)
+				}
+				for j := 0; j < i; j++ {
+					dot := blas64.Dot(mo, blas64.Vector{Inc: 1, Data: q.Data[i*mo:]}, blas64.Vector{Inc: 1, Data: q.Data[j*mo:]})
+					if math.Abs(dot) > 1e-14 {
+						t.Errorf("Case %v, q not orthogonal", ti)
+					}
+				}
+			}
+
+			// Check that A * P = Q * R
+			r := blas64.General{
+				Rows:   mo,
+				Cols:   kb,
+				Stride: kb,
+				Data:   make([]float64, mo*kb),
+			}
+			for i := 0; i < mo; i++ {
+				for j := i; j < kb; j++ {
+					r.Data[i*kb+j] = a.Data[(test.offset+i)*a.Stride+j]
+				}
+			}
+			got := nanGeneral(mo, kb, kb)
+			blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, q, r, 0, got)
+
+			want := aCopy
+			impl.Dlapmt(true, want.Rows, want.Cols, want.Data, want.Stride, jpiv)
+			want.Rows = mo
+			want.Cols = kb
+			want.Data = want.Data[test.offset*want.Stride:]
+			if !equalApproxGeneral(got, want, 1e-12) {
+				t.Errorf("Case %v,  Q*R != A*P\nQ*R=%v\nA*P=%v", ti, got, want)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaqr04.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaqr04.go
new file mode 100644
index 00000000..c92104e7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaqr04.go
@@ -0,0 +1,449 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dlaqr04er interface {
+	Dlaqr04(wantt, wantz bool, n, ilo, ihi int, h []float64, ldh int, wr, wi []float64, iloz, ihiz int, z []float64, ldz int, work []float64, lwork int, recur int) int
+
+	Dlahqrer
+}
+
+type dlaqr04Test struct {
+	h            blas64.General
+	ilo, ihi     int
+	iloz, ihiz   int
+	wantt, wantz bool
+
+	evWant []complex128 // Optional slice holding known eigenvalues.
+}
+
+func Dlaqr04Test(t *testing.T, impl Dlaqr04er) {
+	rnd := rand.New(rand.NewSource(1))
+
+	// Tests for small matrices that choose the ilo,ihi and iloz,ihiz pairs
+	// randomly.
+	for _, wantt := range []bool{true, false} {
+		for _, wantz := range []bool{true, false} {
+			for _, n := range []int{1, 2, 3, 4, 5, 6, 10, 11, 12, 18, 29} {
+				for _, extra := range []int{0, 11} {
+					for recur := 0; recur <= 2; recur++ {
+						for cas := 0; cas < n; cas++ {
+							ilo := rnd.Intn(n)
+							ihi := rnd.Intn(n)
+							if ilo > ihi {
+								ilo, ihi = ihi, ilo
+							}
+							iloz := rnd.Intn(ilo + 1)
+							ihiz := ihi + rnd.Intn(n-ihi)
+							h := randomHessenberg(n, n+extra, rnd)
+							if ilo-1 >= 0 {
+								h.Data[ilo*h.Stride+ilo-1] = 0
+							}
+							if ihi+1 < n {
+								h.Data[(ihi+1)*h.Stride+ihi] = 0
+							}
+							test := dlaqr04Test{
+								h:     h,
+								ilo:   ilo,
+								ihi:   ihi,
+								iloz:  iloz,
+								ihiz:  ihiz,
+								wantt: wantt,
+								wantz: wantz,
+							}
+							testDlaqr04(t, impl, test, false, recur)
+							testDlaqr04(t, impl, test, true, recur)
+						}
+					}
+				}
+			}
+		}
+	}
+
+	// Tests for matrices large enough to possibly use the recursion (but it
+	// doesn't seem to be the case).
+	for _, n := range []int{100, 500} {
+		for cas := 0; cas < 5; cas++ {
+			h := randomHessenberg(n, n, rnd)
+			test := dlaqr04Test{
+				h:     h,
+				ilo:   0,
+				ihi:   n - 1,
+				iloz:  0,
+				ihiz:  n - 1,
+				wantt: true,
+				wantz: true,
+			}
+			testDlaqr04(t, impl, test, true, 1)
+		}
+	}
+
+	// Tests that make sure that some potentially problematic corner cases,
+	// like zero-sized matrix, are covered.
+	for _, wantt := range []bool{true, false} {
+		for _, wantz := range []bool{true, false} {
+			for _, extra := range []int{0, 1, 11} {
+				for _, test := range []dlaqr04Test{
+					{
+						h:    randomHessenberg(0, extra, rnd),
+						ilo:  0,
+						ihi:  -1,
+						iloz: 0,
+						ihiz: -1,
+					},
+					{
+						h:    randomHessenberg(1, 1+extra, rnd),
+						ilo:  0,
+						ihi:  0,
+						iloz: 0,
+						ihiz: 0,
+					},
+					{
+						h:    randomHessenberg(2, 2+extra, rnd),
+						ilo:  1,
+						ihi:  1,
+						iloz: 1,
+						ihiz: 1,
+					},
+					{
+						h:    randomHessenberg(2, 2+extra, rnd),
+						ilo:  0,
+						ihi:  1,
+						iloz: 0,
+						ihiz: 1,
+					},
+					{
+						h:    randomHessenberg(10, 10+extra, rnd),
+						ilo:  0,
+						ihi:  0,
+						iloz: 0,
+						ihiz: 0,
+					},
+					{
+						h:    randomHessenberg(10, 10+extra, rnd),
+						ilo:  0,
+						ihi:  9,
+						iloz: 0,
+						ihiz: 9,
+					},
+					{
+						h:    randomHessenberg(10, 10+extra, rnd),
+						ilo:  0,
+						ihi:  1,
+						iloz: 0,
+						ihiz: 1,
+					},
+					{
+						h:    randomHessenberg(10, 10+extra, rnd),
+						ilo:  0,
+						ihi:  1,
+						iloz: 0,
+						ihiz: 9,
+					},
+					{
+						h:    randomHessenberg(10, 10+extra, rnd),
+						ilo:  9,
+						ihi:  9,
+						iloz: 0,
+						ihiz: 9,
+					},
+				} {
+					if test.ilo-1 >= 0 {
+						test.h.Data[test.ilo*test.h.Stride+test.ilo-1] = 0
+					}
+					if test.ihi+1 < test.h.Rows {
+						test.h.Data[(test.ihi+1)*test.h.Stride+test.ihi] = 0
+					}
+					test.wantt = wantt
+					test.wantz = wantz
+					testDlaqr04(t, impl, test, false, 1)
+					testDlaqr04(t, impl, test, true, 1)
+				}
+			}
+		}
+	}
+
+	// Tests with known eigenvalues computed by Octave.
+	for _, test := range []dlaqr04Test{
+		{
+			h: blas64.General{
+				Rows:   1,
+				Cols:   1,
+				Stride: 1,
+				Data:   []float64{7.09965484086874e-1},
+			},
+			ilo:    0,
+			ihi:    0,
+			iloz:   0,
+			ihiz:   0,
+			evWant: []complex128{7.09965484086874e-1},
+		},
+		{
+			h: blas64.General{
+				Rows:   2,
+				Cols:   2,
+				Stride: 2,
+				Data: []float64{
+					0, -1,
+					1, 0,
+				},
+			},
+			ilo:    0,
+			ihi:    1,
+			iloz:   0,
+			ihiz:   1,
+			evWant: []complex128{1i, -1i},
+		},
+		{
+			h: blas64.General{
+				Rows:   2,
+				Cols:   2,
+				Stride: 2,
+				Data: []float64{
+					6.25219991450918e-1, 8.17510791994361e-1,
+					3.31218891622294e-1, 1.24103744878131e-1,
+				},
+			},
+			ilo:    0,
+			ihi:    1,
+			iloz:   0,
+			ihiz:   1,
+			evWant: []complex128{9.52203547663447e-1, -2.02879811334398e-1},
+		},
+		{
+			h: blas64.General{
+				Rows:   4,
+				Cols:   4,
+				Stride: 4,
+				Data: []float64{
+					1, 0, 0, 0,
+					0, 6.25219991450918e-1, 8.17510791994361e-1, 0,
+					0, 3.31218891622294e-1, 1.24103744878131e-1, 0,
+					0, 0, 0, 1,
+				},
+			},
+			ilo:    1,
+			ihi:    2,
+			iloz:   0,
+			ihiz:   3,
+			evWant: []complex128{9.52203547663447e-1, -2.02879811334398e-1},
+		},
+		{
+			h: blas64.General{
+				Rows:   2,
+				Cols:   2,
+				Stride: 2,
+				Data: []float64{
+					-1.1219562276608, 6.85473513349362e-1,
+					-8.19951061145131e-1, 1.93728523178888e-1,
+				},
+			},
+			ilo:  0,
+			ihi:  1,
+			iloz: 0,
+			ihiz: 1,
+			evWant: []complex128{
+				-4.64113852240958e-1 + 3.59580510817350e-1i,
+				-4.64113852240958e-1 - 3.59580510817350e-1i,
+			},
+		},
+		{
+			h: blas64.General{
+				Rows:   5,
+				Cols:   5,
+				Stride: 5,
+				Data: []float64{
+					9.57590178533658e-1, -5.10651295522708e-1, 9.24974510015869e-1, -1.30016306879522e-1, 2.92601986926954e-2,
+					-1.08084756637964, 1.77529701001213, -1.36480197632509, 2.23196371219601e-1, 1.12912853063308e-1,
+					0, -8.44075612174676e-1, 1.067867614486, -2.55782915176399e-1, -2.00598563137468e-1,
+					0, 0, -5.67097237165410e-1, 2.07205057427341e-1, 6.54998340743380e-1,
+					0, 0, 0, -1.89441413886041e-1, -4.18125416021786e-1,
+				},
+			},
+			ilo:  0,
+			ihi:  4,
+			iloz: 0,
+			ihiz: 4,
+			evWant: []complex128{
+				2.94393309555622,
+				4.97029793606701e-1 + 3.63041654992384e-1i,
+				4.97029793606701e-1 - 3.63041654992384e-1i,
+				-1.74079119166145e-1 + 2.01570009462092e-1i,
+				-1.74079119166145e-1 - 2.01570009462092e-1i,
+			},
+		},
+	} {
+		test.wantt = true
+		test.wantz = true
+		testDlaqr04(t, impl, test, false, 1)
+		testDlaqr04(t, impl, test, true, 1)
+	}
+}
+
+func testDlaqr04(t *testing.T, impl Dlaqr04er, test dlaqr04Test, optwork bool, recur int) {
+	const tol = 1e-14
+
+	h := cloneGeneral(test.h)
+	n := h.Cols
+	extra := h.Stride - h.Cols
+	wantt := test.wantt
+	wantz := test.wantz
+	ilo := test.ilo
+	ihi := test.ihi
+	iloz := test.iloz
+	ihiz := test.ihiz
+
+	var z, zCopy blas64.General
+	if wantz {
+		z = eye(n, n+extra)
+		zCopy = cloneGeneral(z)
+	}
+
+	wr := nanSlice(ihi + 1)
+	wi := nanSlice(ihi + 1)
+
+	var work []float64
+	if optwork {
+		work = nanSlice(1)
+		impl.Dlaqr04(wantt, wantz, n, ilo, ihi, nil, 0, nil, nil, iloz, ihiz, nil, 0, work, -1, recur)
+		work = nanSlice(int(work[0]))
+	} else {
+		work = nanSlice(max(1, n))
+	}
+
+	unconverged := impl.Dlaqr04(wantt, wantz, n, ilo, ihi, h.Data, h.Stride, wr, wi, iloz, ihiz, z.Data, z.Stride, work, len(work), recur)
+
+	prefix := fmt.Sprintf("Case wantt=%v, wantz=%v, n=%v, ilo=%v, ihi=%v, iloz=%v, ihiz=%v, extra=%v, opt=%v",
+		wantt, wantz, n, ilo, ihi, iloz, ihiz, extra, optwork)
+
+	if !generalOutsideAllNaN(h) {
+		t.Errorf("%v: out-of-range write to H\n%v", prefix, h.Data)
+	}
+	if !generalOutsideAllNaN(z) {
+		t.Errorf("%v: out-of-range write to Z\n%v", prefix, z.Data)
+	}
+
+	start := ilo // Index of the first computed eigenvalue.
+	if unconverged != 0 {
+		start = unconverged
+		if start == ihi+1 {
+			t.Logf("%v: no eigenvalue has converged", prefix)
+		}
+	}
+
+	// Check that wr and wi have not been modified within [:start].
+	if !isAllNaN(wr[:start]) {
+		t.Errorf("%v: unexpected modification of wr", prefix)
+	}
+	if !isAllNaN(wi[:start]) {
+		t.Errorf("%v: unexpected modification of wi", prefix)
+	}
+
+	var hasReal bool
+	for i := start; i <= ihi; {
+		if wi[i] == 0 { // Real eigenvalue.
+			hasReal = true
+			// Check that the eigenvalue corresponds to a 1×1 block
+			// on the diagonal of H.
+			if wantt && wr[i] != h.Data[i*h.Stride+i] {
+				t.Errorf("%v: wr[%v] != H[%v,%v]", prefix, i, i, i)
+			}
+			i++
+			continue
+		}
+
+		// Complex eigenvalue.
+
+		// In the conjugate pair the real parts must be equal.
+		if wr[i] != wr[i+1] {
+			t.Errorf("%v: real part of conjugate pair not equal, i=%v", prefix, i)
+		}
+		// The first imaginary part must be positive.
+		if wi[i] < 0 {
+			t.Errorf("%v: wi[%v] not positive", prefix, i)
+		}
+		// The second imaginary part must be negative with the same
+		// magnitude.
+		if wi[i] != -wi[i+1] {
+			t.Errorf("%v: wi[%v] != wi[%v]", prefix, i, i+1)
+		}
+		if wantt {
+			// Check that wi[i] has the correct value.
+			if wr[i] != h.Data[i*h.Stride+i] {
+				t.Errorf("%v: wr[%v] != H[%v,%v]", prefix, i, i, i)
+			}
+			if wr[i] != h.Data[(i+1)*h.Stride+i+1] {
+				t.Errorf("%v: wr[%v] != H[%v,%v]", prefix, i, i+1, i+1)
+			}
+			im := math.Sqrt(math.Abs(h.Data[(i+1)*h.Stride+i])) * math.Sqrt(math.Abs(h.Data[i*h.Stride+i+1]))
+			if math.Abs(im-wi[i]) > tol {
+				t.Errorf("%v: unexpected value of wi[%v]: want %v, got %v", prefix, i, im, wi[i])
+			}
+		}
+		i += 2
+	}
+	// If the number of found eigenvalues is odd, at least one must be real.
+	if (ihi+1-start)%2 != 0 && !hasReal {
+		t.Errorf("%v: expected at least one real eigenvalue", prefix)
+	}
+
+	// Compare found eigenvalues to the reference, if known.
+	if test.evWant != nil {
+		for i := start; i <= ihi; i++ {
+			ev := complex(wr[i], wi[i])
+			found, _ := containsComplex(test.evWant, ev, tol)
+			if !found {
+				t.Errorf("%v: unexpected eigenvalue %v", prefix, ev)
+			}
+		}
+	}
+
+	if !wantz {
+		return
+	}
+
+	// Z should contain the orthogonal matrix U.
+	if !isOrthonormal(z) {
+		t.Errorf("%v: Z is not orthogonal", prefix)
+	}
+	// Z should have been modified only in the
+	// [iloz:ihiz+1,ilo:ihi+1] block.
+	for i := 0; i < n; i++ {
+		for j := 0; j < n; j++ {
+			if iloz <= i && i <= ihiz && ilo <= j && j <= ihi {
+				continue
+			}
+			if z.Data[i*z.Stride+j] != zCopy.Data[i*zCopy.Stride+j] {
+				t.Errorf("%v: Z modified outside of [iloz:ihiz+1,ilo:ihi+1] block", prefix)
+			}
+		}
+	}
+	if wantt {
+		// Zero out h under the subdiagonal because Dlaqr04 uses it as
+		// workspace.
+		for i := 2; i < n; i++ {
+			for j := 0; j < i-1; j++ {
+				h.Data[i*h.Stride+j] = 0
+			}
+		}
+		hz := eye(n, n)
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, test.h, z, 0, hz)
+		zhz := eye(n, n)
+		blas64.Gemm(blas.Trans, blas.NoTrans, 1, z, hz, 0, zhz)
+		if !equalApproxGeneral(zhz, h, 10*tol) {
+			t.Errorf("%v: Z^T*(initial H)*Z and (final H) are not equal", prefix)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaqr1.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaqr1.go
new file mode 100644
index 00000000..9276bfd5
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaqr1.go
@@ -0,0 +1,91 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dlaqr1er interface {
+	Dlaqr1(n int, h []float64, ldh int, sr1, si1, sr2, si2 float64, v []float64)
+}
+
+func Dlaqr1Test(t *testing.T, impl Dlaqr1er) {
+	rnd := rand.New(rand.NewSource(1))
+
+	for _, n := range []int{2, 3} {
+		for _, ldh := range []int{n, n + 1, n + 10} {
+			for _, cas := range []int{1, 2} {
+				for k := 0; k < 100; k++ {
+					v := make([]float64, n)
+					for i := range v {
+						v[i] = math.NaN()
+					}
+					h := make([]float64, n*(n-1)*ldh)
+					for i := range h {
+						h[i] = math.NaN()
+					}
+					for i := 0; i < n; i++ {
+						for j := 0; j < n; j++ {
+							h[i*ldh+j] = rnd.NormFloat64()
+						}
+					}
+					var sr1, sr2, si1, si2 float64
+					if cas == 1 {
+						sr1 = rnd.NormFloat64()
+						sr2 = sr1
+						si1 = rnd.NormFloat64()
+						si2 = -si1
+					} else {
+						sr1 = rnd.NormFloat64()
+						sr2 = rnd.NormFloat64()
+						si1 = 0
+						si2 = 0
+					}
+					impl.Dlaqr1(n, h, ldh, sr1, si1, sr2, si2, v)
+
+					// Matrix H - s1*I.
+					h1 := make([]complex128, n*n)
+					for i := 0; i < n; i++ {
+						for j := 0; j < n; j++ {
+							h1[i*n+j] = complex(h[i*ldh+j], 0)
+							if i == j {
+								h1[i*n+j] -= complex(sr1, si1)
+							}
+						}
+					}
+					// First column of H - s2*I.
+					h2 := make([]complex128, n)
+					for i := 0; i < n; i++ {
+						h2[i] = complex(h[i*ldh], 0)
+					}
+					h2[0] -= complex(sr2, si2)
+
+					wantv := make([]float64, n)
+					// Multiply (H-s1*I)*(H-s2*I) to get a tentative
+					// wantv.
+					for i := 0; i < n; i++ {
+						for j := 0; j < n; j++ {
+							wantv[i] += real(h1[i*n+j] * h2[j])
+						}
+					}
+					// Get the unknown scale.
+					scale := v[0] / wantv[0]
+					// Compute the actual wantv.
+					floats.Scale(scale, wantv)
+
+					// The scale must be the same for all elements.
+					if floats.Distance(wantv, v, math.Inf(1)) > 1e-13 {
+						t.Errorf("n = %v, ldh = %v, case = %v: Unexpected value of v: got %v, want %v", n, ldh, cas, v, wantv)
+					}
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaqr23.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaqr23.go
new file mode 100644
index 00000000..e55d2bc0
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaqr23.go
@@ -0,0 +1,335 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dlaqr23er interface {
+	Dlaqr23(wantt, wantz bool, n, ktop, kbot, nw int, h []float64, ldh int, iloz, ihiz int, z []float64, ldz int, sr, si []float64, v []float64, ldv int, nh int, t []float64, ldt int, nv int, wv []float64, ldwv int, work []float64, lwork int, recur int) (ns, nd int)
+}
+
+type dlaqr23Test struct {
+	wantt, wantz bool
+	ktop, kbot   int
+	nw           int
+	h            blas64.General
+	iloz, ihiz   int
+
+	evWant []complex128 // Optional slice with known eigenvalues.
+}
+
+func Dlaqr23Test(t *testing.T, impl Dlaqr23er) {
+	rnd := rand.New(rand.NewSource(1))
+
+	for _, wantt := range []bool{true, false} {
+		for _, wantz := range []bool{true, false} {
+			for _, n := range []int{1, 2, 3, 4, 5, 6, 10, 18, 31, 100} {
+				for _, extra := range []int{0, 11} {
+					for cas := 0; cas < 30; cas++ {
+						var nw int
+						if nw <= 75 {
+							nw = rnd.Intn(n) + 1
+						} else {
+							nw = 76 + rnd.Intn(n-75)
+						}
+						ktop := rnd.Intn(n - nw + 1)
+						kbot := ktop + nw - 1
+						kbot += rnd.Intn(n - kbot)
+						h := randomHessenberg(n, n+extra, rnd)
+						if ktop-1 >= 0 {
+							h.Data[ktop*h.Stride+ktop-1] = 0
+						}
+						if kbot+1 < n {
+							h.Data[(kbot+1)*h.Stride+kbot] = 0
+						}
+						iloz := rnd.Intn(ktop + 1)
+						ihiz := kbot + rnd.Intn(n-kbot)
+						test := dlaqr23Test{
+							wantt: wantt,
+							wantz: wantz,
+							ktop:  ktop,
+							kbot:  kbot,
+							nw:    nw,
+							h:     h,
+							iloz:  iloz,
+							ihiz:  ihiz,
+						}
+						testDlaqr23(t, impl, test, false, 1, rnd)
+						testDlaqr23(t, impl, test, true, 1, rnd)
+						testDlaqr23(t, impl, test, false, 0, rnd)
+						testDlaqr23(t, impl, test, true, 0, rnd)
+					}
+				}
+			}
+		}
+	}
+
+	// Tests with n=0.
+	for _, wantt := range []bool{true, false} {
+		for _, wantz := range []bool{true, false} {
+			for _, extra := range []int{0, 1, 11} {
+				test := dlaqr23Test{
+					wantt: wantt,
+					wantz: wantz,
+					h:     randomHessenberg(0, extra, rnd),
+					ktop:  0,
+					kbot:  -1,
+					iloz:  0,
+					ihiz:  -1,
+					nw:    0,
+				}
+				testDlaqr23(t, impl, test, true, 1, rnd)
+				testDlaqr23(t, impl, test, false, 1, rnd)
+				testDlaqr23(t, impl, test, true, 0, rnd)
+				testDlaqr23(t, impl, test, false, 0, rnd)
+			}
+		}
+	}
+
+	// Tests with explicit eigenvalues computed by Octave.
+	for _, test := range []dlaqr23Test{
+		{
+			h: blas64.General{
+				Rows:   1,
+				Cols:   1,
+				Stride: 1,
+				Data:   []float64{7.09965484086874e-1},
+			},
+			ktop:   0,
+			kbot:   0,
+			iloz:   0,
+			ihiz:   0,
+			evWant: []complex128{7.09965484086874e-1},
+		},
+		{
+			h: blas64.General{
+				Rows:   2,
+				Cols:   2,
+				Stride: 2,
+				Data: []float64{
+					0, -1,
+					1, 0,
+				},
+			},
+			ktop:   0,
+			kbot:   1,
+			iloz:   0,
+			ihiz:   1,
+			evWant: []complex128{1i, -1i},
+		},
+		{
+			h: blas64.General{
+				Rows:   2,
+				Cols:   2,
+				Stride: 2,
+				Data: []float64{
+					6.25219991450918e-1, 8.17510791994361e-1,
+					3.31218891622294e-1, 1.24103744878131e-1,
+				},
+			},
+			ktop:   0,
+			kbot:   1,
+			iloz:   0,
+			ihiz:   1,
+			evWant: []complex128{9.52203547663447e-1, -2.02879811334398e-1},
+		},
+		{
+			h: blas64.General{
+				Rows:   4,
+				Cols:   4,
+				Stride: 4,
+				Data: []float64{
+					1, 0, 0, 0,
+					0, 6.25219991450918e-1, 8.17510791994361e-1, 0,
+					0, 3.31218891622294e-1, 1.24103744878131e-1, 0,
+					0, 0, 0, 1,
+				},
+			},
+			ktop:   1,
+			kbot:   2,
+			iloz:   0,
+			ihiz:   3,
+			evWant: []complex128{9.52203547663447e-1, -2.02879811334398e-1},
+		},
+		{
+			h: blas64.General{
+				Rows:   2,
+				Cols:   2,
+				Stride: 2,
+				Data: []float64{
+					-1.1219562276608, 6.85473513349362e-1,
+					-8.19951061145131e-1, 1.93728523178888e-1,
+				},
+			},
+			ktop: 0,
+			kbot: 1,
+			iloz: 0,
+			ihiz: 1,
+			evWant: []complex128{
+				-4.64113852240958e-1 + 3.59580510817350e-1i,
+				-4.64113852240958e-1 - 3.59580510817350e-1i,
+			},
+		},
+		{
+			h: blas64.General{
+				Rows:   5,
+				Cols:   5,
+				Stride: 5,
+				Data: []float64{
+					9.57590178533658e-1, -5.10651295522708e-1, 9.24974510015869e-1, -1.30016306879522e-1, 2.92601986926954e-2,
+					-1.08084756637964, 1.77529701001213, -1.36480197632509, 2.23196371219601e-1, 1.12912853063308e-1,
+					0, -8.44075612174676e-1, 1.067867614486, -2.55782915176399e-1, -2.00598563137468e-1,
+					0, 0, -5.67097237165410e-1, 2.07205057427341e-1, 6.54998340743380e-1,
+					0, 0, 0, -1.89441413886041e-1, -4.18125416021786e-1,
+				},
+			},
+			ktop: 0,
+			kbot: 4,
+			iloz: 0,
+			ihiz: 4,
+			evWant: []complex128{
+				2.94393309555622,
+				4.97029793606701e-1 + 3.63041654992384e-1i,
+				4.97029793606701e-1 - 3.63041654992384e-1i,
+				-1.74079119166145e-1 + 2.01570009462092e-1i,
+				-1.74079119166145e-1 - 2.01570009462092e-1i,
+			},
+		},
+	} {
+		test.wantt = true
+		test.wantz = true
+		test.nw = test.kbot - test.ktop + 1
+		testDlaqr23(t, impl, test, true, 1, rnd)
+		testDlaqr23(t, impl, test, false, 1, rnd)
+		testDlaqr23(t, impl, test, true, 0, rnd)
+		testDlaqr23(t, impl, test, false, 0, rnd)
+	}
+}
+
+func testDlaqr23(t *testing.T, impl Dlaqr23er, test dlaqr23Test, opt bool, recur int, rnd *rand.Rand) {
+	const tol = 1e-14
+
+	h := cloneGeneral(test.h)
+	n := h.Cols
+	extra := h.Stride - h.Cols
+	wantt := test.wantt
+	wantz := test.wantz
+	ktop := test.ktop
+	kbot := test.kbot
+	nw := test.nw
+	iloz := test.iloz
+	ihiz := test.ihiz
+
+	var z, zCopy blas64.General
+	if wantz {
+		z = eye(n, n+extra)
+		zCopy = cloneGeneral(z)
+	}
+
+	sr := nanSlice(kbot + 1)
+	si := nanSlice(kbot + 1)
+
+	v := randomGeneral(nw, nw, nw+extra, rnd)
+	var nh int
+	if nw > 0 {
+		nh = nw + rnd.Intn(nw) // nh must be at least nw.
+	}
+	tmat := randomGeneral(nw, nh, nh+extra, rnd)
+	var nv int
+	if nw > 0 {
+		nv = rnd.Intn(nw) + 1
+	}
+	wv := randomGeneral(nv, nw, nw+extra, rnd)
+
+	var work []float64
+	if opt {
+		work = nanSlice(1)
+		impl.Dlaqr23(wantt, wantz, n, ktop, kbot, nw, nil, h.Stride, iloz, ihiz, nil, z.Stride,
+			nil, nil, nil, v.Stride, tmat.Cols, nil, tmat.Stride, wv.Rows, nil, wv.Stride, work, -1, recur)
+		work = nanSlice(int(work[0]))
+	} else {
+		work = nanSlice(max(1, 2*nw))
+	}
+
+	ns, nd := impl.Dlaqr23(wantt, wantz, n, ktop, kbot, nw, h.Data, h.Stride, iloz, ihiz, z.Data, z.Stride,
+		sr, si, v.Data, v.Stride, tmat.Cols, tmat.Data, tmat.Stride, wv.Rows, wv.Data, wv.Stride, work, len(work), recur)
+
+	prefix := fmt.Sprintf("Case wantt=%v, wantz=%v, n=%v, ktop=%v, kbot=%v, nw=%v, iloz=%v, ihiz=%v, extra=%v",
+		wantt, wantz, n, ktop, kbot, nw, iloz, ihiz, extra)
+
+	if !generalOutsideAllNaN(h) {
+		t.Errorf("%v: out-of-range write to H\n%v", prefix, h.Data)
+	}
+	if !generalOutsideAllNaN(z) {
+		t.Errorf("%v: out-of-range write to Z\n%v", prefix, z.Data)
+	}
+	if !generalOutsideAllNaN(v) {
+		t.Errorf("%v: out-of-range write to V\n%v", prefix, v.Data)
+	}
+	if !generalOutsideAllNaN(tmat) {
+		t.Errorf("%v: out-of-range write to T\n%v", prefix, tmat.Data)
+	}
+	if !generalOutsideAllNaN(wv) {
+		t.Errorf("%v: out-of-range write to WV\n%v", prefix, wv.Data)
+	}
+	if !isAllNaN(sr[:kbot-nd-ns+1]) || !isAllNaN(sr[kbot+1:]) {
+		t.Errorf("%v: out-of-range write to sr", prefix)
+	}
+	if !isAllNaN(si[:kbot-nd-ns+1]) || !isAllNaN(si[kbot+1:]) {
+		t.Errorf("%v: out-of-range write to si", prefix)
+	}
+
+	if !isUpperHessenberg(h) {
+		t.Errorf("%v: H is not upper Hessenberg", prefix)
+	}
+
+	if test.evWant != nil {
+		for i := kbot - nd + 1; i <= kbot; i++ {
+			ev := complex(sr[i], si[i])
+			found, _ := containsComplex(test.evWant, ev, tol)
+			if !found {
+				t.Errorf("%v: unexpected eigenvalue %v", prefix, ev)
+			}
+		}
+	}
+
+	if !wantz {
+		return
+	}
+
+	var zmod bool
+	for i := 0; i < n; i++ {
+		for j := 0; j < n; j++ {
+			if z.Data[i*z.Stride+j] == zCopy.Data[i*zCopy.Stride+j] {
+				continue
+			}
+			if i < iloz || i > ihiz || j < kbot-nw+1 || j > kbot {
+				zmod = true
+			}
+		}
+	}
+	if zmod {
+		t.Errorf("%v: unexpected modification of Z", prefix)
+	}
+	if !isOrthonormal(z) {
+		t.Errorf("%v: Z is not orthogonal", prefix)
+	}
+	if wantt {
+		hu := eye(n, n)
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, test.h, z, 0, hu)
+		uhu := eye(n, n)
+		blas64.Gemm(blas.Trans, blas.NoTrans, 1, z, hu, 0, uhu)
+		if !equalApproxGeneral(uhu, h, 10*tol) {
+			t.Errorf("%v: Z^T*(initial H)*Z and (final H) are not equal", prefix)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaqr5.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaqr5.go
new file mode 100644
index 00000000..a93181dc
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaqr5.go
@@ -0,0 +1,214 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"compress/gzip"
+	"encoding/json"
+	"fmt"
+	"log"
+	"math"
+	"math/rand"
+	"os"
+	"path/filepath"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dlaqr5er interface {
+	Dlaqr5(wantt, wantz bool, kacc22 int, n, ktop, kbot, nshfts int, sr, si []float64, h []float64, ldh int, iloz, ihiz int, z []float64, ldz int, v []float64, ldv int, u []float64, ldu int, nh int, wh []float64, ldwh int, nv int, wv []float64, ldwv int)
+}
+
+type Dlaqr5test struct {
+	WantT          bool
+	N              int
+	NShifts        int
+	KTop, KBot     int
+	ShiftR, ShiftI []float64
+	H              []float64
+
+	HWant []float64
+	ZWant []float64
+}
+
+func Dlaqr5Test(t *testing.T, impl Dlaqr5er) {
+	// Test without using reference data.
+	rnd := rand.New(rand.NewSource(1))
+	for _, n := range []int{1, 2, 3, 4, 5, 6, 10, 30} {
+		for _, extra := range []int{0, 1, 20} {
+			for _, kacc22 := range []int{0, 1, 2} {
+				for cas := 0; cas < 100; cas++ {
+					testDlaqr5(t, impl, n, extra, kacc22, rnd)
+				}
+			}
+		}
+	}
+
+	// Test using reference data computed by the reference netlib
+	// implementation.
+	file, err := os.Open(filepath.FromSlash("../testlapack/testdata/dlaqr5data.json.gz"))
+	if err != nil {
+		log.Fatal(err)
+	}
+	defer file.Close()
+	r, err := gzip.NewReader(file)
+	if err != nil {
+		log.Fatal(err)
+	}
+	defer r.Close()
+
+	var tests []Dlaqr5test
+	json.NewDecoder(r).Decode(&tests)
+	for _, test := range tests {
+		wantt := test.WantT
+		n := test.N
+		nshfts := test.NShifts
+		ktop := test.KTop
+		kbot := test.KBot
+		sr := test.ShiftR
+		si := test.ShiftI
+
+		for _, extra := range []int{0, 1, 10} {
+			v := randomGeneral(nshfts/2, 3, 3+extra, rnd)
+			u := randomGeneral(3*nshfts-3, 3*nshfts-3, 3*nshfts-3+extra, rnd)
+			nh := n
+			wh := randomGeneral(3*nshfts-3, n, n+extra, rnd)
+			nv := n
+			wv := randomGeneral(n, 3*nshfts-3, 3*nshfts-3+extra, rnd)
+
+			h := nanGeneral(n, n, n+extra)
+
+			for _, kacc22 := range []int{0, 1, 2} {
+				copyMatrix(n, n, h.Data, h.Stride, test.H)
+				z := eye(n, n+extra)
+
+				impl.Dlaqr5(wantt, true, kacc22,
+					n, ktop, kbot,
+					nshfts, sr, si,
+					h.Data, h.Stride,
+					0, n-1, z.Data, z.Stride,
+					v.Data, v.Stride,
+					u.Data, u.Stride,
+					nv, wv.Data, wv.Stride,
+					nh, wh.Data, wh.Stride)
+
+				prefix := fmt.Sprintf("wantt=%v, n=%v, nshfts=%v, ktop=%v, kbot=%v, extra=%v, kacc22=%v",
+					wantt, n, nshfts, ktop, kbot, extra, kacc22)
+				if !equalApprox(n, n, h.Data, h.Stride, test.HWant, 1e-13) {
+					t.Errorf("Case %v: unexpected matrix H\nh    =%v\nhwant=%v", prefix, h.Data, test.HWant)
+				}
+				if !equalApprox(n, n, z.Data, z.Stride, test.ZWant, 1e-13) {
+					t.Errorf("Case %v: unexpected matrix Z\nz    =%v\nzwant=%v", prefix, z.Data, test.ZWant)
+				}
+			}
+		}
+	}
+}
+
+func testDlaqr5(t *testing.T, impl Dlaqr5er, n, extra, kacc22 int, rnd *rand.Rand) {
+	wantt := true
+	wantz := true
+	nshfts := 2 * n
+	sr := make([]float64, nshfts)
+	si := make([]float64, nshfts)
+	for i := 0; i < n; i++ {
+		re := rnd.NormFloat64()
+		im := rnd.NormFloat64()
+		sr[2*i], sr[2*i+1] = re, re
+		si[2*i], si[2*i+1] = im, -im
+	}
+	ktop := rnd.Intn(n)
+	kbot := rnd.Intn(n)
+	if kbot < ktop {
+		ktop, kbot = kbot, ktop
+	}
+
+	v := randomGeneral(nshfts/2, 3, 3+extra, rnd)
+	u := randomGeneral(3*nshfts-3, 3*nshfts-3, 3*nshfts-3+extra, rnd)
+	nh := n
+	wh := randomGeneral(3*nshfts-3, n, n+extra, rnd)
+	nv := n
+	wv := randomGeneral(n, 3*nshfts-3, 3*nshfts-3+extra, rnd)
+
+	h := randomHessenberg(n, n+extra, rnd)
+	if ktop > 0 {
+		h.Data[ktop*h.Stride+ktop-1] = 0
+	}
+	if kbot < n-1 {
+		h.Data[(kbot+1)*h.Stride+kbot] = 0
+	}
+	hCopy := h
+	hCopy.Data = make([]float64, len(h.Data))
+	copy(hCopy.Data, h.Data)
+
+	z := eye(n, n+extra)
+
+	impl.Dlaqr5(wantt, wantz, kacc22,
+		n, ktop, kbot,
+		nshfts, sr, si,
+		h.Data, h.Stride,
+		0, n-1, z.Data, z.Stride,
+		v.Data, v.Stride,
+		u.Data, u.Stride,
+		nv, wv.Data, wv.Stride,
+		nh, wh.Data, wh.Stride)
+
+	prefix := fmt.Sprintf("Case n=%v, extra=%v, kacc22=%v", n, extra, kacc22)
+
+	if !generalOutsideAllNaN(h) {
+		t.Errorf("%v: out-of-range write to H\n%v", prefix, h.Data)
+	}
+	if !generalOutsideAllNaN(z) {
+		t.Errorf("%v: out-of-range write to Z\n%v", prefix, z.Data)
+	}
+	if !generalOutsideAllNaN(u) {
+		t.Errorf("%v: out-of-range write to U\n%v", prefix, u.Data)
+	}
+	if !generalOutsideAllNaN(v) {
+		t.Errorf("%v: out-of-range write to V\n%v", prefix, v.Data)
+	}
+	if !generalOutsideAllNaN(wh) {
+		t.Errorf("%v: out-of-range write to WH\n%v", prefix, wh.Data)
+	}
+	if !generalOutsideAllNaN(wv) {
+		t.Errorf("%v: out-of-range write to WV\n%v", prefix, wv.Data)
+	}
+
+	for i := 0; i < n; i++ {
+		for j := 0; j < i-1; j++ {
+			if h.Data[i*h.Stride+j] != 0 {
+				t.Errorf("%v: H is not Hessenberg, H[%v,%v]!=0", prefix, i, j)
+			}
+		}
+	}
+	if !isOrthonormal(z) {
+		t.Errorf("%v: Z is not orthogonal", prefix)
+	}
+	// Construct Z^T * HOrig * Z and check that it is equal to H from Dlaqr5.
+	hz := blas64.General{
+		Rows:   n,
+		Cols:   n,
+		Stride: n,
+		Data:   make([]float64, n*n),
+	}
+	blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, hCopy, z, 0, hz)
+	zhz := blas64.General{
+		Rows:   n,
+		Cols:   n,
+		Stride: n,
+		Data:   make([]float64, n*n),
+	}
+	blas64.Gemm(blas.Trans, blas.NoTrans, 1, z, hz, 0, zhz)
+	for i := 0; i < n; i++ {
+		for j := 0; j < n; j++ {
+			diff := zhz.Data[i*zhz.Stride+j] - h.Data[i*h.Stride+j]
+			if math.Abs(diff) > 1e-13 {
+				t.Errorf("%v: Z^T*HOrig*Z and H are not equal, diff at [%v,%v]=%v", prefix, i, j, diff)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlarf.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlarf.go
new file mode 100644
index 00000000..82b2756a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlarf.go
@@ -0,0 +1,173 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dlarfer interface {
+	Dlarf(side blas.Side, m, n int, v []float64, incv int, tau float64, c []float64, ldc int, work []float64)
+}
+
+func DlarfTest(t *testing.T, impl Dlarfer) {
+	rnd := rand.New(rand.NewSource(1))
+	for i, test := range []struct {
+		m, n, ldc    int
+		incv, lastv  int
+		lastr, lastc int
+		tau          float64
+	}{
+		{
+			m:   3,
+			n:   2,
+			ldc: 2,
+
+			incv:  4,
+			lastv: 1,
+
+			lastr: 2,
+			lastc: 1,
+
+			tau: 2,
+		},
+		{
+			m:   2,
+			n:   3,
+			ldc: 3,
+
+			incv:  4,
+			lastv: 1,
+
+			lastr: 1,
+			lastc: 2,
+
+			tau: 2,
+		},
+		{
+			m:   2,
+			n:   3,
+			ldc: 3,
+
+			incv:  4,
+			lastv: 1,
+
+			lastr: 0,
+			lastc: 1,
+
+			tau: 2,
+		},
+		{
+			m:   2,
+			n:   3,
+			ldc: 3,
+
+			incv:  4,
+			lastv: 0,
+
+			lastr: 0,
+			lastc: 1,
+
+			tau: 2,
+		},
+		{
+			m:   10,
+			n:   10,
+			ldc: 10,
+
+			incv:  4,
+			lastv: 6,
+
+			lastr: 9,
+			lastc: 8,
+
+			tau: 2,
+		},
+	} {
+		// Construct a random matrix.
+		c := make([]float64, test.ldc*test.m)
+		for i := 0; i <= test.lastr; i++ {
+			for j := 0; j <= test.lastc; j++ {
+				c[i*test.ldc+j] = rnd.Float64()
+			}
+		}
+		cCopy := make([]float64, len(c))
+		copy(cCopy, c)
+		cCopy2 := make([]float64, len(c))
+		copy(cCopy2, c)
+
+		// Test with side right.
+		sz := max(test.m, test.n) // so v works for both right and left side.
+		v := make([]float64, test.incv*sz+1)
+		// Fill with nonzero entries up until lastv.
+		for i := 0; i <= test.lastv; i++ {
+			v[i*test.incv] = rnd.Float64()
+		}
+		// Construct h explicitly to compare.
+		h := make([]float64, test.n*test.n)
+		for i := 0; i < test.n; i++ {
+			h[i*test.n+i] = 1
+		}
+		hMat := blas64.General{
+			Rows:   test.n,
+			Cols:   test.n,
+			Stride: test.n,
+			Data:   h,
+		}
+		vVec := blas64.Vector{
+			Inc:  test.incv,
+			Data: v,
+		}
+		blas64.Ger(-test.tau, vVec, vVec, hMat)
+
+		// Apply multiplication (2nd copy is to avoid aliasing).
+		cMat := blas64.General{
+			Rows:   test.m,
+			Cols:   test.n,
+			Stride: test.ldc,
+			Data:   cCopy,
+		}
+		cMat2 := blas64.General{
+			Rows:   test.m,
+			Cols:   test.n,
+			Stride: test.ldc,
+			Data:   cCopy2,
+		}
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, cMat2, hMat, 0, cMat)
+
+		// cMat now stores the true answer. Compare with the function call.
+		work := make([]float64, sz)
+		impl.Dlarf(blas.Right, test.m, test.n, v, test.incv, test.tau, c, test.ldc, work)
+		if !floats.EqualApprox(c, cMat.Data, 1e-14) {
+			t.Errorf("Dlarf mismatch right, case %v. Want %v, got %v", i, cMat.Data, c)
+		}
+
+		// Test on the left side.
+		copy(c, cCopy2)
+		copy(cCopy, c)
+		// Construct h.
+		h = make([]float64, test.m*test.m)
+		for i := 0; i < test.m; i++ {
+			h[i*test.m+i] = 1
+		}
+		hMat = blas64.General{
+			Rows:   test.m,
+			Cols:   test.m,
+			Stride: test.m,
+			Data:   h,
+		}
+		blas64.Ger(-test.tau, vVec, vVec, hMat)
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, hMat, cMat2, 0, cMat)
+		impl.Dlarf(blas.Left, test.m, test.n, v, test.incv, test.tau, c, test.ldc, work)
+		if !floats.EqualApprox(c, cMat.Data, 1e-14) {
+			t.Errorf("Dlarf mismatch left, case %v. Want %v, got %v", i, cMat.Data, c)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlarfb.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlarfb.go
new file mode 100644
index 00000000..89e65e64
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlarfb.go
@@ -0,0 +1,161 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dlarfber interface {
+	Dlarfter
+	Dlarfb(side blas.Side, trans blas.Transpose, direct lapack.Direct,
+		store lapack.StoreV, m, n, k int, v []float64, ldv int, t []float64, ldt int,
+		c []float64, ldc int, work []float64, ldwork int)
+}
+
+func DlarfbTest(t *testing.T, impl Dlarfber) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, store := range []lapack.StoreV{lapack.ColumnWise, lapack.RowWise} {
+		for _, direct := range []lapack.Direct{lapack.Forward, lapack.Backward} {
+			for _, side := range []blas.Side{blas.Left, blas.Right} {
+				for _, trans := range []blas.Transpose{blas.Trans, blas.NoTrans} {
+					for cas, test := range []struct {
+						ma, na, cdim, lda, ldt, ldc int
+					}{
+						{6, 6, 6, 0, 0, 0},
+						{6, 8, 10, 0, 0, 0},
+						{6, 10, 8, 0, 0, 0},
+						{8, 6, 10, 0, 0, 0},
+						{8, 10, 6, 0, 0, 0},
+						{10, 6, 8, 0, 0, 0},
+						{10, 8, 6, 0, 0, 0},
+						{6, 6, 6, 12, 15, 30},
+						{6, 8, 10, 12, 15, 30},
+						{6, 10, 8, 12, 15, 30},
+						{8, 6, 10, 12, 15, 30},
+						{8, 10, 6, 12, 15, 30},
+						{10, 6, 8, 12, 15, 30},
+						{10, 8, 6, 12, 15, 30},
+						{6, 6, 6, 15, 12, 30},
+						{6, 8, 10, 15, 12, 30},
+						{6, 10, 8, 15, 12, 30},
+						{8, 6, 10, 15, 12, 30},
+						{8, 10, 6, 15, 12, 30},
+						{10, 6, 8, 15, 12, 30},
+						{10, 8, 6, 15, 12, 30},
+					} {
+						// Generate a matrix for QR
+						ma := test.ma
+						na := test.na
+						lda := test.lda
+						if lda == 0 {
+							lda = na
+						}
+						a := make([]float64, ma*lda)
+						for i := 0; i < ma; i++ {
+							for j := 0; j < lda; j++ {
+								a[i*lda+j] = rnd.Float64()
+							}
+						}
+						k := min(ma, na)
+
+						// H is always ma x ma
+						var m, n, rowsWork int
+						switch {
+						default:
+							panic("not implemented")
+						case side == blas.Left:
+							m = test.ma
+							n = test.cdim
+							rowsWork = n
+						case side == blas.Right:
+							m = test.cdim
+							n = test.ma
+							rowsWork = m
+						}
+
+						// Use dgeqr2 to find the v vectors
+						tau := make([]float64, na)
+						work := make([]float64, na)
+						impl.Dgeqr2(ma, k, a, lda, tau, work)
+
+						// Correct the v vectors based on the direct and store
+						vMatTmp := extractVMat(ma, na, a, lda, lapack.Forward, lapack.ColumnWise)
+						vMat := constructVMat(vMatTmp, store, direct)
+						v := vMat.Data
+						ldv := vMat.Stride
+
+						// Use dlarft to find the t vector
+						ldt := test.ldt
+						if ldt == 0 {
+							ldt = k
+						}
+						tm := make([]float64, k*ldt)
+
+						impl.Dlarft(direct, store, ma, k, v, ldv, tau, tm, ldt)
+
+						// Generate c matrix
+						ldc := test.ldc
+						if ldc == 0 {
+							ldc = n
+						}
+						c := make([]float64, m*ldc)
+						for i := 0; i < m; i++ {
+							for j := 0; j < ldc; j++ {
+								c[i*ldc+j] = rnd.Float64()
+							}
+						}
+						cCopy := make([]float64, len(c))
+						copy(cCopy, c)
+
+						ldwork := k
+						work = make([]float64, rowsWork*k)
+
+						// Call Dlarfb with this information
+						impl.Dlarfb(side, trans, direct, store, m, n, k, v, ldv, tm, ldt, c, ldc, work, ldwork)
+
+						h := constructH(tau, vMat, store, direct)
+
+						cMat := blas64.General{
+							Rows:   m,
+							Cols:   n,
+							Stride: ldc,
+							Data:   make([]float64, m*ldc),
+						}
+						copy(cMat.Data, cCopy)
+						ans := blas64.General{
+							Rows:   m,
+							Cols:   n,
+							Stride: ldc,
+							Data:   make([]float64, m*ldc),
+						}
+						copy(ans.Data, cMat.Data)
+						switch {
+						default:
+							panic("not implemented")
+						case side == blas.Left && trans == blas.NoTrans:
+							blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, h, cMat, 0, ans)
+						case side == blas.Left && trans == blas.Trans:
+							blas64.Gemm(blas.Trans, blas.NoTrans, 1, h, cMat, 0, ans)
+						case side == blas.Right && trans == blas.NoTrans:
+							blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, cMat, h, 0, ans)
+						case side == blas.Right && trans == blas.Trans:
+							blas64.Gemm(blas.NoTrans, blas.Trans, 1, cMat, h, 0, ans)
+						}
+						if !floats.EqualApprox(ans.Data, c, 1e-14) {
+							t.Errorf("Cas %v mismatch. Want %v, got %v.", cas, ans.Data, c)
+						}
+					}
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlarfg.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlarfg.go
new file mode 100644
index 00000000..aa463235
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlarfg.go
@@ -0,0 +1,134 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dlarfger interface {
+	Dlarfg(n int, alpha float64, x []float64, incX int) (beta, tau float64)
+}
+
+func DlarfgTest(t *testing.T, impl Dlarfger) {
+	rnd := rand.New(rand.NewSource(1))
+	for i, test := range []struct {
+		alpha float64
+		n     int
+		x     []float64
+	}{
+		{
+			alpha: 4,
+			n:     3,
+		},
+		{
+			alpha: -2,
+			n:     3,
+		},
+		{
+			alpha: 0,
+			n:     3,
+		},
+		{
+			alpha: 1,
+			n:     1,
+		},
+		{
+			alpha: 1,
+			n:     2,
+			x:     []float64{4, 5, 6},
+		},
+	} {
+		n := test.n
+		incX := 1
+		var x []float64
+		if test.x == nil {
+			x = make([]float64, n-1)
+			for i := range x {
+				x[i] = rnd.Float64()
+			}
+		} else {
+			x = make([]float64, n-1)
+			copy(x, test.x)
+		}
+		xcopy := make([]float64, n-1)
+		copy(xcopy, x)
+		alpha := test.alpha
+		beta, tau := impl.Dlarfg(n, alpha, x, incX)
+
+		// Verify the returns and the values in v. Construct h and perform
+		// the explicit multiplication.
+		h := make([]float64, n*n)
+		for i := 0; i < n; i++ {
+			h[i*n+i] = 1
+		}
+		hmat := blas64.General{
+			Rows:   n,
+			Cols:   n,
+			Stride: n,
+			Data:   h,
+		}
+		v := make([]float64, n)
+		copy(v[1:], x)
+		v[0] = 1
+		vVec := blas64.Vector{
+			Inc:  1,
+			Data: v,
+		}
+		blas64.Ger(-tau, vVec, vVec, hmat)
+		eye := blas64.General{
+			Rows:   n,
+			Cols:   n,
+			Stride: n,
+			Data:   make([]float64, n*n),
+		}
+		blas64.Gemm(blas.Trans, blas.NoTrans, 1, hmat, hmat, 0, eye)
+		iseye := true
+		for i := 0; i < n; i++ {
+			for j := 0; j < n; j++ {
+				if i == j {
+					if math.Abs(eye.Data[i*n+j]-1) > 1e-14 {
+						iseye = false
+					}
+				} else {
+					if math.Abs(eye.Data[i*n+j]) > 1e-14 {
+						iseye = false
+					}
+				}
+			}
+		}
+		if !iseye {
+			t.Errorf("H^T * H is not I %v", eye)
+		}
+
+		xVec := blas64.Vector{
+			Inc:  1,
+			Data: make([]float64, n),
+		}
+		xVec.Data[0] = test.alpha
+		copy(xVec.Data[1:], xcopy)
+
+		ans := make([]float64, n)
+		ansVec := blas64.Vector{
+			Inc:  1,
+			Data: ans,
+		}
+		blas64.Gemv(blas.NoTrans, 1, hmat, xVec, 0, ansVec)
+		if math.Abs(ans[0]-beta) > 1e-14 {
+			t.Errorf("Case %v, beta mismatch. Want %v, got %v", i, ans[0], beta)
+		}
+		for i := 1; i < n; i++ {
+			if math.Abs(ans[i]) > 1e-14 {
+				t.Errorf("Case %v, nonzero answer %v", i, ans)
+				break
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlarft.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlarft.go
new file mode 100644
index 00000000..e63abb9e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlarft.go
@@ -0,0 +1,168 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dlarfter interface {
+	Dgeqr2er
+	Dlarft(direct lapack.Direct, store lapack.StoreV, n, k int, v []float64, ldv int, tau []float64, t []float64, ldt int)
+}
+
+func DlarftTest(t *testing.T, impl Dlarfter) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, store := range []lapack.StoreV{lapack.ColumnWise, lapack.RowWise} {
+		for _, direct := range []lapack.Direct{lapack.Forward, lapack.Backward} {
+			for _, test := range []struct {
+				m, n, ldv, ldt int
+			}{
+				{6, 6, 0, 0},
+				{8, 6, 0, 0},
+				{6, 8, 0, 0},
+				{6, 6, 10, 15},
+				{8, 6, 10, 15},
+				{6, 8, 10, 15},
+				{6, 6, 15, 10},
+				{8, 6, 15, 10},
+				{6, 8, 15, 10},
+			} {
+				// Generate a matrix
+				m := test.m
+				n := test.n
+				lda := n
+				if lda == 0 {
+					lda = n
+				}
+
+				a := make([]float64, m*lda)
+				for i := 0; i < m; i++ {
+					for j := 0; j < lda; j++ {
+						a[i*lda+j] = rnd.Float64()
+					}
+				}
+				// Use dgeqr2 to find the v vectors
+				tau := make([]float64, n)
+				work := make([]float64, n)
+				impl.Dgeqr2(m, n, a, lda, tau, work)
+
+				// Construct H using these answers
+				vMatTmp := extractVMat(m, n, a, lda, lapack.Forward, lapack.ColumnWise)
+				vMat := constructVMat(vMatTmp, store, direct)
+				v := vMat.Data
+				ldv := vMat.Stride
+
+				h := constructH(tau, vMat, store, direct)
+
+				k := min(m, n)
+				ldt := test.ldt
+				if ldt == 0 {
+					ldt = k
+				}
+				// Find T from the actual function
+				tm := make([]float64, k*ldt)
+				for i := range tm {
+					tm[i] = 100 + rnd.Float64()
+				}
+				// The v data has been put into a.
+				impl.Dlarft(direct, store, m, k, v, ldv, tau, tm, ldt)
+
+				tData := make([]float64, len(tm))
+				copy(tData, tm)
+				if direct == lapack.Forward {
+					// Zero out the lower traingular portion.
+					for i := 0; i < k; i++ {
+						for j := 0; j < i; j++ {
+							tData[i*ldt+j] = 0
+						}
+					}
+				} else {
+					// Zero out the upper traingular portion.
+					for i := 0; i < k; i++ {
+						for j := i + 1; j < k; j++ {
+							tData[i*ldt+j] = 0
+						}
+					}
+				}
+
+				T := blas64.General{
+					Rows:   k,
+					Cols:   k,
+					Stride: ldt,
+					Data:   tData,
+				}
+
+				vMatT := blas64.General{
+					Rows:   vMat.Cols,
+					Cols:   vMat.Rows,
+					Stride: vMat.Rows,
+					Data:   make([]float64, vMat.Cols*vMat.Rows),
+				}
+				for i := 0; i < vMat.Rows; i++ {
+					for j := 0; j < vMat.Cols; j++ {
+						vMatT.Data[j*vMatT.Stride+i] = vMat.Data[i*vMat.Stride+j]
+					}
+				}
+				var comp blas64.General
+				if store == lapack.ColumnWise {
+					// H = I - V * T * V^T
+					tmp := blas64.General{
+						Rows:   T.Rows,
+						Cols:   vMatT.Cols,
+						Stride: vMatT.Cols,
+						Data:   make([]float64, T.Rows*vMatT.Cols),
+					}
+					// T * V^T
+					blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, T, vMatT, 0, tmp)
+					comp = blas64.General{
+						Rows:   vMat.Rows,
+						Cols:   tmp.Cols,
+						Stride: tmp.Cols,
+						Data:   make([]float64, vMat.Rows*tmp.Cols),
+					}
+					// V * (T * V^T)
+					blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, vMat, tmp, 0, comp)
+				} else {
+					// H = I - V^T * T * V
+					tmp := blas64.General{
+						Rows:   T.Rows,
+						Cols:   vMat.Cols,
+						Stride: vMat.Cols,
+						Data:   make([]float64, T.Rows*vMat.Cols),
+					}
+					// T * V
+					blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, T, vMat, 0, tmp)
+					comp = blas64.General{
+						Rows:   vMatT.Rows,
+						Cols:   tmp.Cols,
+						Stride: tmp.Cols,
+						Data:   make([]float64, vMatT.Rows*tmp.Cols),
+					}
+					// V^T * (T * V)
+					blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, vMatT, tmp, 0, comp)
+				}
+				// I - V^T * T * V
+				for i := 0; i < comp.Rows; i++ {
+					for j := 0; j < comp.Cols; j++ {
+						comp.Data[i*m+j] *= -1
+						if i == j {
+							comp.Data[i*m+j] += 1
+						}
+					}
+				}
+				if !floats.EqualApprox(comp.Data, h.Data, 1e-14) {
+					t.Errorf("T does not construct proper H. Store = %v, Direct = %v.\nWant %v\ngot %v.", string(store), string(direct), h.Data, comp.Data)
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlarfx.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlarfx.go
new file mode 100644
index 00000000..a73e4f44
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlarfx.go
@@ -0,0 +1,82 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dlarfxer interface {
+	Dlarfx(side blas.Side, m, n int, v []float64, tau float64, c []float64, ldc int, work []float64)
+}
+
+func DlarfxTest(t *testing.T, impl Dlarfxer) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, side := range []blas.Side{blas.Right, blas.Left} {
+		for m := 1; m < 12; m++ {
+			for n := 1; n < 12; n++ {
+				for _, extra := range []int{0, 1, 11} {
+					for cas := 0; cas < 10; cas++ {
+						testDlarfx(t, impl, side, m, n, extra, rnd)
+					}
+				}
+			}
+		}
+	}
+}
+
+func testDlarfx(t *testing.T, impl Dlarfxer, side blas.Side, m, n, extra int, rnd *rand.Rand) {
+	const tol = 1e-13
+
+	c := randomGeneral(m, n, n+extra, rnd)
+	cWant := randomGeneral(m, n, n+extra, rnd)
+	tau := rnd.NormFloat64()
+
+	var (
+		v []float64
+		h blas64.General
+	)
+	if side == blas.Left {
+		v = randomSlice(m, rnd)
+		h = eye(m, m+extra)
+	} else {
+		v = randomSlice(n, rnd)
+		h = eye(n, n+extra)
+	}
+	blas64.Ger(-tau, blas64.Vector{Inc: 1, Data: v}, blas64.Vector{Inc: 1, Data: v}, h)
+	if side == blas.Left {
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, h, c, 0, cWant)
+	} else {
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, c, h, 0, cWant)
+	}
+
+	var work []float64
+	if h.Rows > 10 {
+		// Allocate work only if H has order > 10.
+		if side == blas.Left {
+			work = make([]float64, n)
+		} else {
+			work = make([]float64, m)
+		}
+	}
+
+	impl.Dlarfx(side, m, n, v, tau, c.Data, c.Stride, work)
+
+	prefix := fmt.Sprintf("Case side=%v, m=%v, n=%v, extra=%v", side, m, n, extra)
+
+	// Check any invalid modifications of c.
+	if !generalOutsideAllNaN(c) {
+		t.Errorf("%v: out-of-range write to C\n%v", prefix, c.Data)
+	}
+
+	if !equalApproxGeneral(c, cWant, tol) {
+		t.Errorf("%v: unexpected C\n%v", prefix, c.Data)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlartg.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlartg.go
new file mode 100644
index 00000000..c7cade84
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlartg.go
@@ -0,0 +1,98 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dlartger interface {
+	Dlartg(f, g float64) (cs, sn, r float64)
+}
+
+func DlartgTest(t *testing.T, impl Dlartger) {
+	const tol = 1e-14
+	// safmn2 and safmx2 are copied from native.Dlartg.
+	safmn2 := math.Pow(dlamchB, math.Trunc(math.Log(dlamchS/dlamchE)/math.Log(dlamchB)/2))
+	safmx2 := 1 / safmn2
+	rnd := rand.New(rand.NewSource(1))
+	for i := 0; i < 1000; i++ {
+		var f float64
+		var fHuge bool
+		switch rnd.Intn(3) {
+		case 0:
+			// Huge f.
+			fHuge = true
+			f = math.Pow(10, 10-20*rnd.Float64()) * safmx2
+		case 1:
+			// Tiny f.
+			f = math.Pow(10, 10-20*rnd.Float64()) * safmn2
+		default:
+			f = rnd.NormFloat64()
+		}
+		if rnd.Intn(2) == 0 {
+			f *= -1
+		}
+
+		var g float64
+		var gHuge bool
+		switch rnd.Intn(3) {
+		case 0:
+			// Huge g.
+			gHuge = true
+			g = math.Pow(10, 10-20*rnd.Float64()) * safmx2
+		case 1:
+			// Tiny g.
+			g = math.Pow(10, 10-20*rnd.Float64()) * safmn2
+		default:
+			g = rnd.NormFloat64()
+		}
+		if rnd.Intn(2) == 0 {
+			g *= -1
+		}
+
+		cs, sn, r := impl.Dlartg(f, g)
+
+		rWant := cs*f + sn*g
+		if !floats.EqualWithinAbsOrRel(math.Abs(rWant), math.Abs(r), tol, tol) {
+			t.Errorf("Case f=%v,g=%v: unexpected r. Want %v, got %v", f, g, rWant, r)
+		}
+		oneTest := cs*cs + sn*sn
+		if math.Abs(oneTest-1) > tol {
+			t.Errorf("Case f=%v,g=%v: expected cs^2+sn^2==1, got %v", f, g, oneTest)
+		}
+		if !fHuge && !gHuge {
+			zeroTest := -sn*f + cs*g
+			if math.Abs(zeroTest) > tol {
+				t.Errorf("Case f=%v,g=%v: expected zero, got %v", f, g, zeroTest)
+			}
+		}
+		if math.Abs(f) > math.Abs(g) && cs < 0 {
+			t.Errorf("Case f=%v,g=%v: unexpected negative cs %v", f, g, cs)
+		}
+	}
+	for i := 0; i < 100; i++ {
+		cs, sn, _ := impl.Dlartg(rnd.NormFloat64(), 0)
+		if cs != 1 {
+			t.Errorf("Unexpected cs for g=0. Want 1, got %v", cs)
+		}
+		if sn != 0 {
+			t.Errorf("Unexpected sn for g=0. Want 0, got %v", sn)
+		}
+	}
+	for i := 0; i < 100; i++ {
+		cs, sn, _ := impl.Dlartg(0, rnd.NormFloat64())
+		if cs != 0 {
+			t.Errorf("Unexpected cs for f=0. Want 0, got %v", cs)
+		}
+		if sn != 1 {
+			t.Errorf("Unexpected sn for f=0. Want 1, got %v", sn)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlas2.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlas2.go
new file mode 100644
index 00000000..a76e2742
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlas2.go
@@ -0,0 +1,34 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"testing"
+)
+
+type Dlas2er interface {
+	Dlas2(f, g, h float64) (min, max float64)
+}
+
+func Dlas2Test(t *testing.T, impl Dlas2er) {
+	for i, test := range []struct {
+		f, g, h, ssmin, ssmax float64
+	}{
+		// Singular values computed from Octave.
+		{10, 30, 12, 3.567778859365365, 33.634371616111189},
+		{10, 30, -12, 3.567778859365365, 33.634371616111189},
+		{2, 30, -12, 0.741557056404952, 32.364333658088754},
+		{-2, 5, 12, 1.842864429909778, 13.023204317408728},
+	} {
+		ssmin, ssmax := impl.Dlas2(test.f, test.g, test.h)
+		if math.Abs(ssmin-test.ssmin) > 1e-12 {
+			t.Errorf("Case %d, minimal singular value mismatch. Want %v, got %v", i, test.ssmin, ssmin)
+		}
+		if math.Abs(ssmax-test.ssmax) > 1e-12 {
+			t.Errorf("Case %d, minimal singular value mismatch. Want %v, got %v", i, test.ssmin, ssmin)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlascl.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlascl.go
new file mode 100644
index 00000000..db792a4d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlascl.go
@@ -0,0 +1,106 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dlascler interface {
+	Dlascl(kind lapack.MatrixType, kl, ku int, cfrom, cto float64, m, n int, a []float64, lda int)
+}
+
+func DlasclTest(t *testing.T, impl Dlascler) {
+	const tol = 1e-16
+
+	rnd := rand.New(rand.NewSource(1))
+	for ti, test := range []struct {
+		m, n int
+	}{
+		{0, 0},
+		{1, 1},
+		{1, 10},
+		{10, 1},
+		{2, 2},
+		{2, 11},
+		{11, 2},
+		{3, 3},
+		{3, 11},
+		{11, 3},
+		{11, 11},
+		{11, 100},
+		{100, 11},
+	} {
+		m := test.m
+		n := test.n
+		for _, extra := range []int{0, 11} {
+			for _, kind := range []lapack.MatrixType{lapack.General, lapack.UpperTri, lapack.LowerTri} {
+				a := randomGeneral(m, n, n+extra, rnd)
+				aCopy := cloneGeneral(a)
+				cfrom := rnd.NormFloat64()
+				cto := rnd.NormFloat64()
+				scale := cto / cfrom
+
+				impl.Dlascl(kind, -1, -1, cfrom, cto, m, n, a.Data, a.Stride)
+
+				prefix := fmt.Sprintf("Case #%v: kind=%v,m=%v,n=%v,extra=%v", ti, kind, m, n, extra)
+				if !generalOutsideAllNaN(a) {
+					t.Errorf("%v: out-of-range write to A", prefix)
+				}
+				switch kind {
+				case lapack.General:
+					for i := 0; i < m; i++ {
+						for j := 0; j < n; j++ {
+							want := scale * aCopy.Data[i*aCopy.Stride+j]
+							got := a.Data[i*a.Stride+j]
+							if math.Abs(want-got) > tol {
+								t.Errorf("%v: unexpected A[%v,%v]=%v, want %v", prefix, i, j, got, want)
+							}
+						}
+					}
+				case lapack.UpperTri:
+					for i := 0; i < m; i++ {
+						for j := i; j < n; j++ {
+							want := scale * aCopy.Data[i*aCopy.Stride+j]
+							got := a.Data[i*a.Stride+j]
+							if math.Abs(want-got) > tol {
+								t.Errorf("%v: unexpected A[%v,%v]=%v, want %v", prefix, i, j, got, want)
+							}
+						}
+					}
+					for i := 0; i < m; i++ {
+						for j := 0; j < min(i, n); j++ {
+							if a.Data[i*a.Stride+j] != aCopy.Data[i*aCopy.Stride+j] {
+								t.Errorf("%v: unexpected modification in lower triangle of A", prefix)
+							}
+						}
+					}
+				case lapack.LowerTri:
+					for i := 0; i < m; i++ {
+						for j := 0; j <= min(i, n-1); j++ {
+							want := scale * aCopy.Data[i*aCopy.Stride+j]
+							got := a.Data[i*a.Stride+j]
+							if math.Abs(want-got) > tol {
+								t.Errorf("%v: unexpected A[%v,%v]=%v, want %v", prefix, i, j, got, want)
+							}
+						}
+					}
+					for i := 0; i < m; i++ {
+						for j := i + 1; j < n; j++ {
+							if a.Data[i*a.Stride+j] != aCopy.Data[i*aCopy.Stride+j] {
+								t.Errorf("%v: unexpected modification in upper triangle of A", prefix)
+							}
+						}
+					}
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaset.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaset.go
new file mode 100644
index 00000000..f0af77f5
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaset.go
@@ -0,0 +1,76 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+type Dlaseter interface {
+	Dlaset(uplo blas.Uplo, m, n int, alpha, beta float64, a []float64, lda int)
+}
+
+func DlasetTest(t *testing.T, impl Dlaseter) {
+	rnd := rand.New(rand.NewSource(1))
+	for ti, test := range []struct {
+		m, n int
+	}{
+		{0, 0},
+		{1, 1},
+		{1, 10},
+		{10, 1},
+		{2, 2},
+		{2, 10},
+		{10, 2},
+		{11, 11},
+		{11, 100},
+		{100, 11},
+	} {
+		m := test.m
+		n := test.n
+		for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower, blas.All} {
+			for _, extra := range []int{0, 10} {
+				a := randomGeneral(m, n, n+extra, rnd)
+				alpha := 1.0
+				beta := 2.0
+
+				impl.Dlaset(uplo, m, n, alpha, beta, a.Data, a.Stride)
+
+				prefix := fmt.Sprintf("Case #%v: m=%v,n=%v,uplo=%v,extra=%v",
+					ti, m, n, uplo, extra)
+				if !generalOutsideAllNaN(a) {
+					t.Errorf("%v: out-of-range write to A", prefix)
+				}
+				for i := 0; i < min(m, n); i++ {
+					if a.Data[i*a.Stride+i] != beta {
+						t.Errorf("%v: unexpected diagonal of A", prefix)
+					}
+				}
+				if uplo == blas.Upper || uplo == blas.All {
+					for i := 0; i < m; i++ {
+						for j := i + 1; j < n; j++ {
+							if a.Data[i*a.Stride+j] != alpha {
+								t.Errorf("%v: unexpected upper triangle of A", prefix)
+							}
+						}
+					}
+				}
+				if uplo == blas.Lower || uplo == blas.All {
+					for i := 1; i < m; i++ {
+						for j := 0; j < min(i, n); j++ {
+							if a.Data[i*a.Stride+j] != alpha {
+								t.Errorf("%v: unexpected lower triangle of A", prefix)
+							}
+						}
+					}
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlasq1.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlasq1.go
new file mode 100644
index 00000000..064eaea0
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlasq1.go
@@ -0,0 +1,87 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dlasq1er interface {
+	Dlasq1(n int, d, e, work []float64) int
+	Dgetrfer
+}
+
+func Dlasq1Test(t *testing.T, impl Dlasq1er) {
+	rnd := rand.New(rand.NewSource(1))
+	bi := blas64.Implementation()
+	// TODO(btracey): Increase the size of this test when we have a more numerically
+	// stable way to test the singular values.
+	for _, n := range []int{1, 2, 5, 8} {
+		work := make([]float64, 4*n)
+		d := make([]float64, n)
+		e := make([]float64, n-1)
+		for cas := 0; cas < 1; cas++ {
+			for i := range work {
+				work[i] = rnd.Float64()
+			}
+			for i := range d {
+				d[i] = rnd.NormFloat64() + 10
+			}
+			for i := range e {
+				e[i] = rnd.NormFloat64()
+			}
+			ldm := n
+			m := make([]float64, n*ldm)
+			// Set up the matrix
+			for i := 0; i < n; i++ {
+				m[i*ldm+i] = d[i]
+				if i != n-1 {
+					m[(i+1)*ldm+i] = e[i]
+				}
+			}
+
+			ldmm := n
+			mm := make([]float64, n*ldmm)
+			bi.Dgemm(blas.Trans, blas.NoTrans, n, n, n, 1, m, ldm, m, ldm, 0, mm, ldmm)
+
+			impl.Dlasq1(n, d, e, work)
+
+			// Check that they are singular values. The
+			// singular values are the square roots of the
+			// eigenvalues of X^T * X
+			mmCopy := make([]float64, len(mm))
+			copy(mmCopy, mm)
+			ipiv := make([]int, n)
+			for elem, sv := range d[0:n] {
+				copy(mm, mmCopy)
+				lambda := sv * sv
+				for i := 0; i < n; i++ {
+					mm[i*ldm+i] -= lambda
+				}
+
+				// Compute LU.
+				ok := impl.Dgetrf(n, n, mm, ldmm, ipiv)
+				if !ok {
+					// Definitely singular.
+					continue
+				}
+				// Compute determinant
+				var logdet float64
+				for i := 0; i < n; i++ {
+					v := mm[i*ldm+i]
+					logdet += math.Log(math.Abs(v))
+				}
+				if math.Exp(logdet) > 2 {
+					t.Errorf("Incorrect singular value. n = %d, cas = %d, elem = %d, det = %v", n, cas, elem, math.Exp(logdet))
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlasq2.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlasq2.go
new file mode 100644
index 00000000..80b41b86
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlasq2.go
@@ -0,0 +1,714 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dlasq2er interface {
+	Dgetrfer
+	Dlasq2(n int, z []float64) (info int)
+}
+
+func Dlasq2Test(t *testing.T, impl Dlasq2er) {
+	dTol := 1e-6
+	// Answers from calling the netlib Dlasq2 function directly.
+	for c, test := range []struct {
+		n    int
+		z    []float64
+		info int
+		zOut []float64
+	}{
+		{
+			z:    []float64{0.9975595900926172E+00, 0.5668247076112733E+00, 0.9659153754961249E+00, 0.7479276854714322E+00, 0.3673908973747557E+00, 0.4806368987547315E+00, 0.7375426363398452E-01, 0.5355229277727247E-02, 0.3470812885180155E+00, 0.3422438160728350E+00, 0.2179517263384726E+00, 0.1331604100136593E+00, 0.9005245144218924E+00, 0.3867660104574036E+00, 0.4454822893878481E+00, 0.6619321808958428E+00, 0.1610830043055933E-01, 0.6508548361039168E+00, 0.6464088254838254E+00, 0.3229872909405558E+00, 0.8556924028853313E+00, 0.4012869193638139E+00, 0.2068743292187569E+00, 0.9685394642165999E+00, 0.5983995343181346E+00, 0.6729807327762632E+00, 0.4568823106729620E+00, 0.3300151235733747E+00, 0.1003829265021773E+00, 0.7554533047597268E+00, 0.6056932669802318E+00, 0.7190479134084530E+00, 0.8973346038865299E+00, 0.6582291204811077E+00, 0.1507168371301046E+00, 0.6123149049967000E+00, 0.9786602381321465E+00, 0.9991422694268032E+00, 0.2567979861831603E+00, 0.5508654031552206E+00, 0.6590475178936379E+00, 0.5540051353968156E+00, 0.9777600986094505E+00, 0.9019233044604550E+00, 0.6579246844202109E+00, 0.7288585083995637E+00, 0.4024552650632751E+00, 0.9286276631540373E+00, 0.1478351900438915E+00, 0.6745292990637881E+00, 0.7696143092758962E+00, 0.3393225521457851E+00, 0.1158188549489931E+00, 0.6143691843615144E+00, 0.8206171394658319E+00, 0.9470946559240657E+00, 0.7311286518535550E+00, 0.4976039064630389E+00, 0.3748017407872005E+00, 0.4215058560045335E+00, 0.5529030382557849E+00, 0.9979192791781042E+00, 0.9903947480415133E+00, 0.7463096553073095E+00, 0.9537590617479789E+00, 0.9327469033343772E-01, 0.7340236871158429E+00, 0.7517616159256260E+00, 0.9468485056759987E+00, 0.7061763632511533E+00, 0.8138096664824992E+00, 0.5585945195965548E+00, 0.6170557687507783E-01, 0.4803807801853603E+00, 0.5976897721963292E+00, 0.1375319188363359E+00, 0.5873952004066820E+00, 0.5199682629163997E+00, 0.8858783448129579E+00, 0.3038101719904888E+00, 0.6696573039722583E+00, 0.6649400915297697E+00, 0.5036768993979404E+00, 0.2615751204119269E+00},
+			n:    21,
+			zOut: []float64{0.2550031738262204E+01, 0.2480977513501848E+01, 0.2366602269912148E+01, 0.2169993432366266E+01, 0.1810817848712033E+01, 0.1681677309759878E+01, 0.1303743375476047E+01, 0.1202161769544433E+01, 0.1183377192742860E+01, 0.1094206688544886E+01, 0.9154376259418607E+00, 0.8241395430971566E+00, 0.7318275341991307E+00, 0.5186198053161721E+00, 0.4143051093784424E+00, 0.2112065329503869E+00, 0.1093987140067686E+00, 0.9751785856405315E-01, 0.2818174710670554E-01, 0.1697846193036144E-01, 0.2117542506861687E-04, 0.5241368559131172E-22, 0.4369342452764876E-18, 0.4084491703488284E-18, 0.1303743375476047E+01, 0.0000000000000000E+00, 0.2325140442247288E-18, 0.2353545363971710E-18, 0.1202161769544433E+01, 0.0000000000000000E+00, 0.2163565864913247E-18, 0.2222159192042978E-18, 0.1183377192742860E+01, 0.2033579915108999E-22, 0.2652482201353177E-18, 0.2438256017573345E-18, 0.1094206688544886E+01, 0.3167883469916549E-16, 0.9806070694382835E-18, 0.1224486171222500E-17, 0.9154376259418607E+00, 0.2764930279233778E-14, 0.2171122324673871E+02, 0.2171122324673871E+02, 0.1020000000000000E+03, 0.3081632653061225E+01, 0.2941176470588236E+01, 0.2548071704976161E-16, 0.7318275341991307E+00, 0.4959852501050381E-23, 0.8676862906242004E-16, 0.1414000300319855E-15, 0.5186198053161721E+00, 0.1503295986001297E-14, 0.3452895805257589E-14, 0.7981257539768321E-14, 0.4143051093784424E+00, 0.1303656847202082E-15, 0.9855809897129084E-12, 0.2614986238618434E-11, 0.2112065329503869E+00, 0.8411884198867843E-17, 0.2293573303077261E-09, 0.9833566024906726E-10, 0.1093987140067686E+00, 0.2696165428113804E-17, 0.5825676764620370E-08, 0.2638661645752538E-08, 0.9751785856405315E-01, 0.6617412588681544E-21, 0.2809066689524106E-07, 0.6165545233233256E-07, 0.2818174710670554E-01, 0.1396210563637443E-18, 0.2854399814229969E-05, 0.1344352644992036E-05, 0.1697846193036144E-01, 0.6162975822039155E-31, 0.3724766654883956E-05, 0.4695180568393632E-05, 0.2117542506861687E-04, 0.0000000000000000E+00, 0.9895328911616120E-03, 0.1620493249248586E-02},
+			info: 0,
+		},
+		{
+			z:    []float64{0.7655950151081736E-01, 0.1012496627944287E+00, 0.5492657397218519E+00, 0.3755849474908193E+00, 0.1514950257902281E-01, 0.7929154460744389E+00, 0.6208775449015512E+00, 0.7736035774285512E+00, 0.9535807609862423E+00, 0.1142443721338974E+00, 0.3184626428755636E+00, 0.5968198462235605E+00, 0.4815290260558158E-01, 0.1142057780273510E+00, 0.2159649191761220E+00, 0.1005733924928321E+00, 0.7334180249993905E-01, 0.2468617397276878E+00, 0.4433842667962828E+00, 0.2083675732544600E+00, 0.5669983427348256E+00, 0.2431239969651688E-01, 0.4202905770712168E+00, 0.3978530241169832E+00, 0.9765854254920880E+00, 0.6926050329928320E+00, 0.4943367486777372E-02, 0.1299210324451839E+00, 0.4677725963527957E-01, 0.8397777412847708E+00, 0.6784888222113696E+00, 0.5819508167748705E+00, 0.7335259194567719E+00, 0.1160427446694747E+00, 0.8402996546275487E+00, 0.8349959735427709E+00, 0.7465363962886192E+00, 0.8432008930683078E+00, 0.5288390014350658E+00, 0.6654846664813405E+00, 0.7307365692392301E+00, 0.4106042636492306E+00, 0.3557215961646439E+00, 0.7353770423280176E+00, 0.4713176648251016E+00, 0.4626254343486430E+00, 0.7596917071958065E+00, 0.7024594192654096E+00, 0.2579658084846748E+00, 0.9377050325544740E+00, 0.4561035840049426E+00, 0.8084892970067921E+00, 0.9088480529888660E+00, 0.6948766633235142E+00, 0.2194885062923195E+00, 0.8549545559228027E+00, 0.7443966896835119E+00, 0.3011130612705175E+00, 0.6719685452983997E+00, 0.6187140363783860E+00, 0.9675736114028010E+00, 0.9902393027740470E+00, 0.3380065169449795E+00, 0.9207672475882130E+00, 0.3390733399571427E+00, 0.9309435300662920E+00, 0.5465285509796513E+00, 0.4655125893217942E+00, 0.1769140958718970E+00, 0.3779940975005719E+00, 0.1752206228227682E+00, 0.3568582675012224E+00, 0.6656764250906758E+00, 0.6185492680730227E+00, 0.4689472437795331E+00, 0.3162518610221317E+00, 0.2688799086902824E+00, 0.1999212438248075E+00, 0.4154279763213168E+00, 0.9793029133347251E+00, 0.5432115888768534E+00, 0.1295182752745038E+00, 0.8047416637896615E+00, 0.8458210244967665E+00},
+			n:    21,
+			zOut: []float64{0.2649710614371106E+01, 0.2321564474027070E+01, 0.2090779203479937E+01, 0.2001510674733695E+01, 0.1702794694134603E+01, 0.1077066053646038E+01, 0.1060140274732043E+01, 0.9894235909971354E+00, 0.9539342071687115E+00, 0.8046649468928653E+00, 0.7009142227469247E+00, 0.5502651835254770E+00, 0.4423863025187732E+00, 0.3697086796938907E+00, 0.1446051340026323E+00, 0.1110032523123295E+00, 0.7513603923341917E-01, 0.6860214953971246E-01, 0.2434478048112329E-01, 0.6989818532012803E-03, 0.7811996215926567E-04, 0.7156177943897596E-01, 0.2292199980814605E-03, 0.1899018778701386E-03, 0.1060140274732043E+01, 0.8660746506696473E-01, 0.1357005210961402E-39, 0.1331360138522907E-23, 0.9894235909971354E+00, 0.8804208964992894E-17, 0.8660746506696473E-01, 0.8679736700028205E-01, 0.9539342071687115E+00, 0.2761013168273541E-29, 0.1040577915698430E-22, 0.8107757314001177E-24, 0.8046649468928653E+00, 0.5098326619997980E-22, 0.1416795225784663E-10, 0.1216165317638265E-10, 0.7009142227469247E+00, 0.1183291357831518E-29, 0.1813933158005285E+02, 0.1813933158005285E+02, 0.1090000000000000E+03, 0.3231292517006803E+01, 0.5504587155963303E+01, 0.4068037876491279E-10, 0.4423863025187732E+00, 0.2477754901417239E-20, 0.1737857614720001E-07, 0.5295826057530262E-07, 0.3697086796938907E+00, 0.5143373102040997E-26, 0.1312431380925897E-05, 0.1614374370413396E-05, 0.1446051340026323E+00, 0.9928287808749566E-25, 0.3777515963415321E-05, 0.2773141909621761E-05, 0.1110032523123295E+00, 0.0000000000000000E+00, 0.2532463507333992E-05, 0.2934028940292093E-05, 0.7513603923341917E-01, 0.5394210206791908E-19, 0.6032617175984252E-07, 0.2575740214720034E-06, 0.6860214953971246E-01, 0.7542232825258426E-19, 0.3784397549471832E-09, 0.1131370986389306E-09, 0.2434478048112329E-01, 0.1013559914197709E-18, 0.1483665133446019E-05, 0.1887408451311279E-05, 0.6989818532012803E-03, 0.9466330862652142E-28, 0.2539111990097616E-03, 0.9240506410060376E-03, 0.7811996215926567E-04, 0.3786532345060857E-28, 0.1283811140869274E-03, 0.1684766835109566E-03},
+			info: 0,
+		},
+		{
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+			z:    []float64{0.7940281584071446E+00, 0.8540600349699839E+00, 0.8158431165852809E-01, 0.5431841788581357E+00, 0.3696613346727944E+00, 0.2343742079469738E+00, 0.4891909888056500E-01, 0.6769876984160987E+00, 0.4777767465052760E+00, 0.1867381312399053E+00, 0.2018744873845245E+00, 0.5511201479607295E+00, 0.6938788283912793E+00, 0.8167542438070282E+00, 0.7904606414789531E+00, 0.9443564310071292E+00, 0.7287247677237652E-01, 0.8645122013586991E+00, 0.1884651475116826E+00, 0.3844755283611681E+00, 0.9959264361467982E+00, 0.6424370932833342E+00, 0.1972122925077952E+00, 0.2842024247377670E+00, 0.9819646913482807E+00, 0.9118347224008859E+00, 0.8184691845197246E+00, 0.7051587281589254E+00, 0.7604703230109544E+00, 0.6312964755149379E+00, 0.5240863862347888E+00, 0.3442050916384676E-01, 0.2415614308212055E+00, 0.2814868323669945E+00, 0.6529284673126197E+00, 0.3727305084153835E+00, 0.5033733868757848E+00, 0.2317122058804952E+00, 0.7555584130128312E+00, 0.5854566742645219E+00, 0.5481204696337160E+00, 0.8479425268049923E+00, 0.2310874615764000E+00, 0.1250993726775007E-01, 0.6243285982203539E-01, 0.8533587246073391E+00, 0.9203815588639257E+00, 0.9256849509751471E+00, 0.6691405057262187E+00, 0.8847091531299658E+00, 0.6783572983386376E+00, 0.4701257141291857E+00, 0.8976078424378102E+00, 0.8575018884445876E+00, 0.4119363561363949E+00, 0.2824477027676924E+00, 0.2787507690368071E+00, 0.7994878185780909E+00, 0.6141832897278305E+00, 0.6772728066124333E+00, 0.1568652581579784E+00, 0.8025492691231176E+00, 0.2609459151100056E+00, 0.4956700691019098E+00, 0.1008839464621498E+00, 0.6129709499983976E+00, 0.4551038858718992E-02, 0.8382785474023564E+00, 0.9327452694814308E+00, 0.9710431593941808E+00, 0.3785578217695214E+00, 0.9620839159000718E+00, 0.3183561960196257E-01, 0.9167635157854341E+00, 0.8989971039988554E+00, 0.2723769512210017E-01, 0.4176537489735596E+00, 0.9619881273217982E+00, 0.8761769579995293E+00, 0.6385245520487358E+00, 0.6821739872929905E+00, 0.3927943300877799E+00, 0.3299501391296433E-01, 0.6026481165267817E+00},
+			n:    21,
+			zOut: []float64{0.2841529467847260E+01, 0.2556740368064117E+01, 0.2029069210305357E+01, 0.1816492749229813E+01, 0.1807397947918166E+01, 0.1724050761249482E+01, 0.1394683696862690E+01, 0.1363282300837870E+01, 0.1235317529564993E+01, 0.1007821728138393E+01, 0.9728972767837659E+00, 0.8110838192609224E+00, 0.6190683239156912E+00, 0.3314348466978195E+00, 0.2969816495631171E+00, 0.2506421226611442E+00, 0.1551624233480766E+00, 0.1141049603637759E+00, 0.6806098279643324E-01, 0.4065442795375918E-01, 0.1509783792061944E-04, 0.2745446733802996E-19, 0.2334033424405603E-14, 0.7232047343832039E-15, 0.1394683696862690E+01, 0.7652022750203868E-17, 0.1502464319787860E-09, 0.5990324067027169E-10, 0.1363282300837870E+01, 0.5511008105786353E-19, 0.1215529748555577E-07, 0.3576186028975079E-08, 0.1235317529564993E+01, 0.6271335389136957E-17, 0.2589527811059762E-05, 0.3563684464760320E-05, 0.1007821728138393E+01, 0.6928731028484552E-15, 0.2286607739649456E-04, 0.2916328836696281E-04, 0.9728972767837659E+00, 0.4013724285764508E-25, 0.2143649169120057E+02, 0.2143649169120056E+02, 0.1080000000000000E+03, 0.3174603174603174E+01, 0.5555555555555555E+01, 0.5006788488237952E-04, 0.6190683239156912E+00, 0.1272779738919789E-24, 0.5392273695714327E-05, 0.6586751690782050E-05, 0.3314348466978195E+00, 0.9952016744778614E-24, 0.4588114650322476E-05, 0.4104030919118472E-05, 0.2969816495631171E+00, 0.1254277227268884E-20, 0.1579210272170037E-05, 0.2523508055026877E-05, 0.2506421226611442E+00, 0.1514835081255253E-22, 0.9117975197333799E-05, 0.1415311657319248E-04, 0.1551624233480766E+00, 0.3272195034856757E-26, 0.3128414626489953E-04, 0.4770966856082524E-04, 0.1141049603637759E+00, 0.7575261888623807E-20, 0.6277758538102519E-05, 0.4644422903178713E-05, 0.6806098279643324E-01, 0.3715389965619895E-21, 0.5956965112658162E-05, 0.4447744978930882E-05, 0.4065442795375918E-01, 0.1972152263052530E-30, 0.2965586553650948E-04, 0.1900611263569203E-04, 0.1509783792061944E-04, 0.1009741958682895E-26, 0.1608958133772104E-02, 0.9583670521235791E-03},
+			info: 0,
+		},
+	} {
+		z := make([]float64, len(test.z))
+		copy(z, test.z)
+
+		info := impl.Dlasq2(test.n, z)
+		if !floats.EqualApprox(test.zOut, z, dTol) {
+			diff := make([]float64, len(z))
+			floats.SubTo(diff, z, test.zOut)
+			for i := range diff {
+				diff[i] = math.Abs(diff[i])
+			}
+			t.Errorf("Case %v, Z Mismatch", c)
+		}
+		if test.info != info {
+			t.Errorf("Info mismatch. Want %v, got %v", test.info, info)
+		}
+	}
+
+	rnd := rand.New(rand.NewSource(1))
+	// Perform a bunch of random tests to check for access out of bounds or
+	// infinite loops.
+	// TODO(btracey): Implement direct tests.
+	// bi := blas64.Implementation()
+	for _, n := range []int{5, 8, 20, 25} {
+		for k := 0; k < 10; k++ {
+			z := make([]float64, 4*n)
+			for i := range z {
+				z[i] = rnd.Float64()
+			}
+			zCopy := make([]float64, len(z))
+			copy(zCopy, z)
+
+			// Compute the eigenvalues
+			impl.Dlasq2(n, z)
+
+			// Below is the code to test the eigenvalues. Eventually implement
+			// real tests.
+			// The code below is missing the transformation from L and U into
+			// the symmetric tridiagonal matrix.
+			// See discussion http://icl.cs.utk.edu/lapack-forum/viewtopic.php?f=5&t=4839
+			// for format.
+
+			/*
+				ldl := n
+				ldu := n
+				u := make([]float64, n*n)
+				for i := 0; i < n; i++ {
+					u[i*ldu+i] = zCopy[2*i]
+					if i != n-1 {
+						u[i*ldu+i+1] = 1
+					}
+				}
+				l := make([]float64, n*n)
+				for i := 0; i < n; i++ {
+					l[i*ldl+i] = 1
+					if i != n-1 {
+						l[(i+1)*ldl+i] = zCopy[2*i+1]
+					}
+				}
+
+				ldTriDi := n
+				triDi := make([]float64, n*n)
+				bi.Dgemm(blas.NoTrans, blas.NoTrans, n, n, n, 1, l, ldl, u, ldu, 0, triDi, ldTriDi)
+
+				tridi2 := make([]float64, n*n)
+				bi.Dgemm(blas.Trans, blas.NoTrans, n, n, n, 1, triDi, n, triDi, n, 0, tridi2, n)
+
+				// Eigenvalues have the property that det(A - lambda I ) = 0
+				triDiCopy := make([]float64, len(triDi))
+				copy(triDiCopy, triDi)
+				for _, lambda := range z[1:n] {
+					copy(triDi, triDiCopy)
+					for i := 0; i < n; i++ {
+						triDi[i*n+i] -= lambda
+					}
+
+					// Compute LU
+					//ipiv := make([]int, n)
+					//impl.Dgetrf(n, n, triDi, n, ipiv)
+					ok := impl.Dpotrf(blas.Upper, n, triDi, n)
+					fmt.Println(ok)
+
+					var det float64
+					for i := 0; i < n; i++ {
+						det += math.Log(math.Abs(triDi[i*n+i]))
+					}
+					fmt.Println("det = ", math.Exp(det))
+				}
+			*/
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlasq3.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlasq3.go
new file mode 100644
index 00000000..f48bad17
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlasq3.go
@@ -0,0 +1,2703 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dlasq3er interface {
+	Dlasq3(i0, n0 int, z []float64, pp int, dmin, sigma, desig, qmax float64, nFail, iter, nDiv int, ttype int, dmin1, dmin2, dn, dn1, dn2, g, tau float64) (
+		i0Out, n0Out, ppOut int, dminOut, sigmaOut, desigOut, qmaxOut float64, nFailOut, iterOut, nDivOut, ttypeOut int, dmin1Out, dmin2Out, dnOut, dn1Out, dn2Out, gOut, tauOut float64)
+}
+
+type dlasq3teststruct struct {
+	z                                  []float64
+	i0, n0, pp                         int
+	dmin, desig, sigma, qmax           float64
+	nFail, iter, nDiv, ttype           int
+	dmin1, dmin2, dn, dn1, dn2, g, tau float64
+
+	zOut                                                    []float64
+	i0Out, n0Out, ppOut                                     int
+	dminOut, desigOut, sigmaOut, qmaxOut                    float64
+	nFailOut, iterOut, nDivOut, ttypeOut                    int
+	dmin1Out, dmin2Out, dnOut, dn1Out, dn2Out, gOut, tauOut float64
+}
+
+func Dlasq3Test(t *testing.T, impl Dlasq3er) {
+	dTol := 1e-14
+	// Tests computed from calling the netlib Dlasq
+	for _, test := range []dlasq3teststruct{
+		{
+			i0:       1,
+			n0:       21,
+			z:        []float64{0.1914365246180821E+01, 0.1564384297703890E+01, 0.2493389162143899E+00, 0.3499809484769305E+00, 0.1315996513131545E+01, 0.1363862112490627E+01, 0.9898466611970759E-01, 0.2014733168553078E+00, 0.6023973979587287E+00, 0.6465544792741794E+00, 0.2210033410638781E-02, 0.5482758480425683E-01, 0.9861857233678967E-01, 0.2428190810745492E-01, 0.4756321484454819E+00, 0.7654669763997353E-01, 0.2588748143677115E+00, 0.6127784069508770E+00, 0.1078611376690004E+00, 0.1217285558623164E+00, 0.6442896492255246E+00, 0.2293835804898155E+00, 0.6203230486639705E+00, 0.5227672064047094E+00, 0.3695660678607585E+00, 0.7645233184745865E+00, 0.5378838054252265E+00, 0.2253657980501426E+00, 0.3562533181264623E+00, 0.8820486722335483E+00, 0.2222132496436145E-01, 0.1208845131814035E-01, 0.1275094303021685E+01, 0.6548746852163357E+00, 0.1647324354821218E+00, 0.6424409427697111E+00, 0.1007530576543866E+01, 0.3269551736546701E+00, 0.3453881601783118E+00, 0.8453078383713172E+00, 0.2679391719153404E+00, 0.4116714838778281E+00, 0.7328677736683723E+00, 0.2016558482158241E+00, 0.8360828138307410E+00, 0.9737579452195326E+00, 0.4813660709592822E+00, 0.5951926422795808E+00, 0.6495370513676459E+00, 0.6761876248148171E+00, 0.2325475880222648E+00, 0.4547154975121112E+00, 0.1993624802893807E+00, 0.3321819367342255E+00, 0.3782318916911257E+00, 0.9972813157741996E-01, 0.9830449403503746E+00, 0.7561080996844842E+00, 0.4429733864040367E+00, 0.6051687323570161E+00, 0.1173279550602403E+01, 0.7195724480316686E+00, 0.5035524069144587E+00, 0.8966804889747714E+00, 0.3058980395058521E+00, 0.6588832353928662E+00, 0.3014634433415453E+00, 0.1505672110274446E+00, 0.1289422237567578E+01, 0.6124645310993601E+00, 0.7583364305799440E+00, 0.9784211498097629E+00, 0.4977814779461571E+00, 0.9993813577491869E+00, 0.2841468847862598E+00, 0.2567365507769143E+00, 0.9257539794205765E+00, 0.5509268385614666E+00, 0.5231355605450990E-04, 0.6589740256453697E+00, 0.2117869221381033E-04, 0.7349224826832024E-04, 0.0000000000000000E+00, 0.0000000000000000E+00},
+			pp:       0,
+			dmin:     -0.0000000000000000,
+			desig:    0.0000000000000000,
+			qmax:     2.1637041623952107,
+			ttype:    0,
+			dmin1:    0.0000000000000000,
+			dmin2:    0.0000000000000000,
+			dn:       0.0000000000000000,
+			dn1:      0.0000000000000000,
+			dn2:      0.0000000000000000,
+			g:        0.0000000000000000,
+			tau:      0.0000000000000000,
+			nFail:    0,
+			iter:     2,
+			sigma:    0.0000000000000000,
+			nDiv:     40,
+			zOut:     []float64{0.1914365246180821E+01, 0.2163704162395211E+01, 0.2493389162143899E+00, 0.1516515751224039E+00, 0.1315996513131545E+01, 0.1263329604128848E+01, 0.9898466611970759E-01, 0.4719916727467415E-01, 0.6023973979587287E+00, 0.5574082640946934E+00, 0.2210033410638781E-02, 0.3910066531356214E-03, 0.9861857233678967E-01, 0.5738597141291359E+00, 0.4756321484454819E+00, 0.2145632131068746E+00, 0.2588748143677115E+00, 0.1521727389298373E+00, 0.1078611376690004E+00, 0.4566771620366771E+00, 0.6442896492255246E+00, 0.8079355358528180E+00, 0.6203230486639705E+00, 0.2837483186776231E+00, 0.3695660678607585E+00, 0.6237015546083620E+00, 0.5378838054252265E+00, 0.3072349091217998E+00, 0.3562533181264623E+00, 0.7123973396902394E-01, 0.2222132496436145E-01, 0.3977314805803597E+00, 0.1275094303021685E+01, 0.1042095257923447E+01, 0.1647324354821218E+00, 0.1592685164190333E+00, 0.1007530576543866E+01, 0.1193650220303144E+01, 0.3453881601783118E+00, 0.7752942700755104E-01, 0.2679391719153404E+00, 0.9232775185761617E+00, 0.7328677736683723E+00, 0.6636554427529671E+00, 0.8360828138307410E+00, 0.6537934420370561E+00, 0.4813660709592822E+00, 0.4782322339990674E+00, 0.6495370513676459E+00, 0.4038524053908432E+00, 0.2325475880222648E+00, 0.1147975431483785E+00, 0.1993624802893807E+00, 0.4627968288321279E+00, 0.3782318916911257E+00, 0.8034172324482011E+00, 0.9830449403503746E+00, 0.6226010943062101E+00, 0.4429733864040367E+00, 0.8347746582554776E+00, 0.1173279550602403E+01, 0.8420572992613844E+00, 0.5035524069144587E+00, 0.1829278057427913E+00, 0.3058980395058521E+00, 0.4244336771046062E+00, 0.3014634433415453E+00, 0.9158407747236312E+00, 0.1289422237567578E+01, 0.1131917893423890E+01, 0.7583364305799440E+00, 0.3334922359541972E+00, 0.4977814779461571E+00, 0.4484361267782198E+00, 0.2841468847862598E+00, 0.5865943745895725E+00, 0.9257539794205765E+00, 0.3392119183870583E+00, 0.5231355605450990E-04, 0.3266196269153995E-08, 0.2117869221381033E-04, 0.2117542601754118E-04, 0.0000000000000000E+00, 0.3910066531356214E-03},
+			i0Out:    1,
+			n0Out:    21,
+			ppOut:    0,
+			dminOut:  2.1175426017541180E-005,
+			desigOut: 0.0000000000000000,
+			sigmaOut: 0.0000000000000000,
+			qmaxOut:  2.1637041623952107,
+			nFailOut: 0,
+			iterOut:  3,
+			nDivOut:  62,
+			ttypeOut: -1,
+			dmin1Out: 4.4311601260836921E-002,
+			dmin2Out: 4.4311601260836921E-002,
+			dnOut:    2.1175426017541180E-005,
+			dn1Out:   0.33915960483100382,
+			dn2Out:   0.16428924199195991,
+			gOut:     0.0000000000000000,
+			tauOut:   0.0000000000000000,
+		},
+		{
+			i0:       1,
+			n0:       21,
+			z:        []float64{0.1914365246180821E+01, 0.2163704162395211E+01, 0.2493389162143899E+00, 0.1516515751224039E+00, 0.1315996513131545E+01, 0.1263329604128848E+01, 0.9898466611970759E-01, 0.4719916727467415E-01, 0.6023973979587287E+00, 0.5574082640946934E+00, 0.2210033410638781E-02, 0.3910066531356214E-03, 0.9861857233678967E-01, 0.5738597141291359E+00, 0.4756321484454819E+00, 0.2145632131068746E+00, 0.2588748143677115E+00, 0.1521727389298373E+00, 0.1078611376690004E+00, 0.4566771620366771E+00, 0.6442896492255246E+00, 0.8079355358528180E+00, 0.6203230486639705E+00, 0.2837483186776231E+00, 0.3695660678607585E+00, 0.6237015546083620E+00, 0.5378838054252265E+00, 0.3072349091217998E+00, 0.3562533181264623E+00, 0.7123973396902394E-01, 0.2222132496436145E-01, 0.3977314805803597E+00, 0.1275094303021685E+01, 0.1042095257923447E+01, 0.1647324354821218E+00, 0.1592685164190333E+00, 0.1007530576543866E+01, 0.1193650220303144E+01, 0.3453881601783118E+00, 0.7752942700755104E-01, 0.2679391719153404E+00, 0.9232775185761617E+00, 0.7328677736683723E+00, 0.6636554427529671E+00, 0.8360828138307410E+00, 0.6537934420370561E+00, 0.4813660709592822E+00, 0.4782322339990674E+00, 0.6495370513676459E+00, 0.4038524053908432E+00, 0.2325475880222648E+00, 0.1147975431483785E+00, 0.1993624802893807E+00, 0.4627968288321279E+00, 0.3782318916911257E+00, 0.8034172324482011E+00, 0.9830449403503746E+00, 0.6226010943062101E+00, 0.4429733864040367E+00, 0.8347746582554776E+00, 0.1173279550602403E+01, 0.8420572992613844E+00, 0.5035524069144587E+00, 0.1829278057427913E+00, 0.3058980395058521E+00, 0.4244336771046062E+00, 0.3014634433415453E+00, 0.9158407747236312E+00, 0.1289422237567578E+01, 0.1131917893423890E+01, 0.7583364305799440E+00, 0.3334922359541972E+00, 0.4977814779461571E+00, 0.4484361267782198E+00, 0.2841468847862598E+00, 0.5865943745895725E+00, 0.9257539794205765E+00, 0.3392119183870583E+00, 0.5231355605450990E-04, 0.3266196269153995E-08, 0.2117869221381033E-04, 0.2117542601754118E-04, 0.0000000000000000E+00, 0.3910066531356214E-03},
+			pp:       1,
+			dmin:     2.1175426017541180E-005,
+			desig:    0.0000000000000000,
+			qmax:     2.1637041623952107,
+			ttype:    -1,
+			dmin1:    4.4311601260836921E-002,
+			dmin2:    4.4311601260836921E-002,
+			dn:       2.1175426017541180E-005,
+			dn1:      0.33915960483100382,
+			dn2:      0.16428924199195991,
+			g:        0.0000000000000000,
+			tau:      0.0000000000000000,
+			nFail:    0,
+			iter:     3,
+			sigma:    0.0000000000000000,
+			nDiv:     62,
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+			sigma:    2.0907792019978437,
+			nDiv:     1425,
+			zOut:     []float64{0.2649710614371106E+01, 0.5589314123732620E+00, 0.1121517486324177E-26, 0.1291024862446124E-30, 0.2321564474027070E+01, 0.2307852720292263E+00, 0.2303778747300831E+00, 0.3431506172718059E-03, 0.2090779203479937E+01, 0.1482093454966231E-08, 0.6641476135588615E-06, 0.6434089156657428E-04, 0.2001510674733695E+01, 0.2227952244484021E-23, 0.4011480356653261E-18, 0.5524513774965514E-19, 0.1702794694134603E+01, 0.2545269924803487E-17, 0.5179704803914515E-14, 0.1264160184270297E-13, 0.1077066053646038E+01, 0.7156177943897596E-01, 0.2292199980814605E-03, 0.1899018778701386E-03, 0.1060140274732043E+01, 0.8660746506696473E-01, 0.1357005210961402E-39, 0.1331360138522907E-23, 0.9894235909971354E+00, 0.8804208964992894E-17, 0.8660746506696473E-01, 0.8679736700028205E-01, 0.9539342071687115E+00, 0.2761013168273541E-29, 0.1040577915698430E-22, 0.8107757314001177E-24, 0.8046649468928653E+00, 0.5098326619997980E-22, 0.1416795225784663E-10, 0.1216165317638265E-10, 0.7009142227469247E+00, 0.1183291357831518E-29, 0.4806926318247711E-11, 0.3824647564366386E-11, 0.5502651835254770E+00, 0.1368072596837427E-11, 0.1169503544861386E-10, 0.4068037876491279E-10, 0.4423863025187732E+00, 0.2477754901417239E-20, 0.1737857614720001E-07, 0.5295826057530262E-07, 0.3697086796938907E+00, 0.5143373102040997E-26, 0.1312431380925897E-05, 0.1614374370413396E-05, 0.1446051340026323E+00, 0.9928287808749566E-25, 0.3777515963415321E-05, 0.2773141909621761E-05, 0.1110032523123295E+00, 0.0000000000000000E+00, 0.2532463507333992E-05, 0.2934028940292093E-05, 0.7513603923341917E-01, 0.5394210206791908E-19, 0.6032617175984252E-07, 0.2575740214720034E-06, 0.6860214953971246E-01, 0.7542232825258426E-19, 0.3784397549471832E-09, 0.1131370986389306E-09, 0.2434478048112329E-01, 0.1013559914197709E-18, 0.1483665133446019E-05, 0.1887408451311279E-05, 0.6989818532012803E-03, 0.9466330862652142E-28, 0.2539111990097616E-03, 0.9240506410060376E-03, 0.7811996215926567E-04, 0.3786532345060857E-28, 0.1283811140869274E-03, 0.1684766835109566E-03},
+			i0Out:    1,
+			n0Out:    0,
+			ppOut:    1,
+			dminOut:  1.4843004355481051E-009,
+			desigOut: -1.6593817482031092E-016,
+			sigmaOut: 2.0907792019978437,
+			qmaxOut:  1.6602870234255678,
+			nFailOut: 6,
+			iterOut:  109,
+			nDivOut:  1425,
+			ttypeOut: -4,
+			dmin1Out: 6.4246679664367451E-005,
+			dmin2Out: 0.55893141237326205,
+			dnOut:    1.4843004355481051E-009,
+			dn1Out:   6.4246679664367451E-005,
+			dn2Out:   0.55893141237326205,
+			gOut:     0.49975000000000003,
+			tauOut:   9.4211902206835373E-008,
+		},
+	} {
+		z := make([]float64, len(test.z))
+		copy(z, test.z)
+		i0 := test.i0 - 1 // zero index
+		n0 := test.n0 - 1 // zero index
+
+		i0Out, n0Out, ppOut, dminOut, sigmaOut, desigOut, qmaxOut, nFailOut, iterOut, nDivOut, ttypeOut, dmin1Out, dmin2Out, dnOut, dn1Out, dn2Out, gOut, tauOut :=
+			impl.Dlasq3(i0, n0, z, test.pp, test.dmin, test.sigma, test.desig, test.qmax, test.nFail, test.iter, test.nDiv, test.ttype, test.dmin1, test.dmin2, test.dn, test.dn1, test.dn2, test.g, test.tau)
+
+		if !floats.EqualApprox(z, test.zOut, dTol) {
+			t.Error("Z mismatch")
+		}
+		if i0Out != test.i0Out-1 {
+			t.Errorf("i0 mismatch. Want %v, got %v", test.n0Out, n0Out)
+		}
+		if n0Out != test.n0Out-1 {
+			t.Errorf("n0 mismatch. Want %v, got %v", test.n0Out, n0Out)
+		}
+		if ppOut != test.ppOut {
+			t.Errorf("pp mismatch. Want %v, got %v", test.ppOut, ppOut)
+		}
+		if !floats.EqualWithinAbsOrRel(dminOut, test.dminOut, dTol, dTol) {
+			t.Errorf("dmin mismatch. Want %v, got %v", test.dminOut, dminOut)
+		}
+		if !floats.EqualWithinAbsOrRel(desigOut, test.desigOut, dTol, dTol) {
+			t.Errorf("desig mismatch. Want %v, got %v", test.desigOut, desigOut)
+		}
+		if !floats.EqualWithinAbsOrRel(sigmaOut, test.sigmaOut, dTol, dTol) {
+			t.Errorf("sigma mismatch. Want %v, got %v", test.sigmaOut, sigmaOut)
+		}
+		if !floats.EqualWithinAbsOrRel(qmaxOut, test.qmaxOut, dTol, dTol) {
+			t.Errorf("qmax mismatch. Want %v, got %v", test.qmaxOut, qmaxOut)
+		}
+		if nFailOut != test.nFailOut {
+			t.Errorf("nFail mismatch. Want %v, got %v", test.nFailOut, nFailOut)
+		}
+		if iterOut != test.iterOut {
+			t.Errorf("iter mismatch. Want %v, got %v", test.iterOut, iterOut)
+		}
+		if nDivOut != test.nDivOut {
+			t.Errorf("nFail mismatch. Want %v, got %v", test.nDivOut, nDivOut)
+		}
+		if ttypeOut != test.ttypeOut {
+			t.Errorf("ttype mismatch. Want %v, got %v", test.ttypeOut, ttypeOut)
+		}
+		if !floats.EqualWithinAbsOrRel(dmin1Out, test.dmin1Out, dTol, dTol) {
+			t.Errorf("dmin1 mismatch. Want %v, got %v", test.dmin1Out, dmin1Out)
+		}
+		if !floats.EqualWithinAbsOrRel(dmin2Out, test.dmin2Out, dTol, dTol) {
+			t.Errorf("dmin2 mismatch. Want %v, got %v", test.dmin2Out, dmin2Out)
+		}
+		if !floats.EqualWithinAbsOrRel(dnOut, test.dnOut, dTol, dTol) {
+			t.Errorf("dn mismatch. Want %v, got %v", test.dnOut, dnOut)
+		}
+		if !floats.EqualWithinAbsOrRel(dn1Out, test.dn1Out, dTol, dTol) {
+			t.Errorf("dn1 mismatch. Want %v, got %v", test.dn1Out, dn1Out)
+		}
+		if !floats.EqualWithinAbsOrRel(dn2Out, test.dn2Out, dTol, dTol) {
+			t.Errorf("dn2 mismatch. Want %v, got %v", test.dn2Out, dn2Out)
+		}
+		if !floats.EqualWithinAbsOrRel(gOut, test.gOut, dTol, dTol) {
+			t.Errorf("g mismatch. Want %v, got %v", test.gOut, gOut)
+		}
+		if !floats.EqualWithinAbsOrRel(tauOut, test.tauOut, dTol, dTol) {
+			t.Errorf("tau mismatch. Want %v, got %v", test.tauOut, tauOut)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlasq4.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlasq4.go
new file mode 100644
index 00000000..03d71946
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlasq4.go
@@ -0,0 +1,3101 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+type dlasq4teststruct struct {
+	z                                     []float64
+	i0, n0, pp, n0in                      int
+	dmin, dmin1, dmin2, dn, dn1, dn2, tau float64
+	ttype                                 int
+	g                                     float64
+
+	zOut     []float64
+	tauOut   float64
+	ttypeOut int
+	gOut     float64
+}
+
+type Dlasq4er interface {
+	Dlasq4(i0, n0 int, z []float64, pp int, n0in int, dmin, dmin1, dmin2, dn, dn1, dn2, tau float64, ttype int, g float64) (tauOut float64, ttypeOut int, gOut float64)
+}
+
+func Dlasq4Test(t *testing.T, impl Dlasq4er) {
+	dTol := 1e-14
+	// Tests computed from calling the netlib Dlasq
+	for cas, test := range []dlasq4teststruct{
+		{
+			z:        []float64{0.1914365246180821E+01, 0.1564384297703890E+01, 0.2493389162143899E+00, 0.3499809484769305E+00, 0.1315996513131545E+01, 0.1363862112490627E+01, 0.9898466611970759E-01, 0.2014733168553078E+00, 0.6023973979587287E+00, 0.6465544792741794E+00, 0.2210033410638781E-02, 0.5482758480425683E-01, 0.9861857233678967E-01, 0.2428190810745492E-01, 0.4756321484454819E+00, 0.7654669763997353E-01, 0.2588748143677115E+00, 0.6127784069508770E+00, 0.1078611376690004E+00, 0.1217285558623164E+00, 0.6442896492255246E+00, 0.2293835804898155E+00, 0.6203230486639705E+00, 0.5227672064047094E+00, 0.3695660678607585E+00, 0.7645233184745865E+00, 0.5378838054252265E+00, 0.2253657980501426E+00, 0.3562533181264623E+00, 0.8820486722335483E+00, 0.2222132496436145E-01, 0.1208845131814035E-01, 0.1275094303021685E+01, 0.6548746852163357E+00, 0.1647324354821218E+00, 0.6424409427697111E+00, 0.1007530576543866E+01, 0.3269551736546701E+00, 0.3453881601783118E+00, 0.8453078383713172E+00, 0.2679391719153404E+00, 0.4116714838778281E+00, 0.7328677736683723E+00, 0.2016558482158241E+00, 0.8360828138307410E+00, 0.9737579452195326E+00, 0.4813660709592822E+00, 0.5951926422795808E+00, 0.6495370513676459E+00, 0.6761876248148171E+00, 0.2325475880222648E+00, 0.4547154975121112E+00, 0.1993624802893807E+00, 0.3321819367342255E+00, 0.3782318916911257E+00, 0.9972813157741996E-01, 0.9830449403503746E+00, 0.7561080996844842E+00, 0.4429733864040367E+00, 0.6051687323570161E+00, 0.1173279550602403E+01, 0.7195724480316686E+00, 0.5035524069144587E+00, 0.8966804889747714E+00, 0.3058980395058521E+00, 0.6588832353928662E+00, 0.3014634433415453E+00, 0.1505672110274446E+00, 0.1289422237567578E+01, 0.6124645310993601E+00, 0.7583364305799440E+00, 0.9784211498097629E+00, 0.4977814779461571E+00, 0.9993813577491869E+00, 0.2841468847862598E+00, 0.2567365507769143E+00, 0.9257539794205765E+00, 0.5509268385614666E+00, 0.5231355605450990E-04, 0.6589740256453697E+00, 0.2117869221381033E-04, 0.7349224826832024E-04, 0.0000000000000000E+00, 0.0000000000000000E+00},
+			i0:       1,
+			n0:       21,
+			pp:       0,
+			n0in:     21,
+			dmin:     -0.0000000000000000,
+			dmin1:    0.0000000000000000,
+			dmin2:    0.0000000000000000,
+			dn:       0.0000000000000000,
+			dn1:      0.0000000000000000,
+			dn2:      0.0000000000000000,
+			tau:      0.0000000000000000,
+			ttype:    0,
+			g:        0.0000000000000000,
+			zOut:     []float64{0.1914365246180821E+01, 0.1564384297703890E+01, 0.2493389162143899E+00, 0.3499809484769305E+00, 0.1315996513131545E+01, 0.1363862112490627E+01, 0.9898466611970759E-01, 0.2014733168553078E+00, 0.6023973979587287E+00, 0.6465544792741794E+00, 0.2210033410638781E-02, 0.5482758480425683E-01, 0.9861857233678967E-01, 0.2428190810745492E-01, 0.4756321484454819E+00, 0.7654669763997353E-01, 0.2588748143677115E+00, 0.6127784069508770E+00, 0.1078611376690004E+00, 0.1217285558623164E+00, 0.6442896492255246E+00, 0.2293835804898155E+00, 0.6203230486639705E+00, 0.5227672064047094E+00, 0.3695660678607585E+00, 0.7645233184745865E+00, 0.5378838054252265E+00, 0.2253657980501426E+00, 0.3562533181264623E+00, 0.8820486722335483E+00, 0.2222132496436145E-01, 0.1208845131814035E-01, 0.1275094303021685E+01, 0.6548746852163357E+00, 0.1647324354821218E+00, 0.6424409427697111E+00, 0.1007530576543866E+01, 0.3269551736546701E+00, 0.3453881601783118E+00, 0.8453078383713172E+00, 0.2679391719153404E+00, 0.4116714838778281E+00, 0.7328677736683723E+00, 0.2016558482158241E+00, 0.8360828138307410E+00, 0.9737579452195326E+00, 0.4813660709592822E+00, 0.5951926422795808E+00, 0.6495370513676459E+00, 0.6761876248148171E+00, 0.2325475880222648E+00, 0.4547154975121112E+00, 0.1993624802893807E+00, 0.3321819367342255E+00, 0.3782318916911257E+00, 0.9972813157741996E-01, 0.9830449403503746E+00, 0.7561080996844842E+00, 0.4429733864040367E+00, 0.6051687323570161E+00, 0.1173279550602403E+01, 0.7195724480316686E+00, 0.5035524069144587E+00, 0.8966804889747714E+00, 0.3058980395058521E+00, 0.6588832353928662E+00, 0.3014634433415453E+00, 0.1505672110274446E+00, 0.1289422237567578E+01, 0.6124645310993601E+00, 0.7583364305799440E+00, 0.9784211498097629E+00, 0.4977814779461571E+00, 0.9993813577491869E+00, 0.2841468847862598E+00, 0.2567365507769143E+00, 0.9257539794205765E+00, 0.5509268385614666E+00, 0.5231355605450990E-04, 0.6589740256453697E+00, 0.2117869221381033E-04, 0.7349224826832024E-04, 0.0000000000000000E+00, 0.0000000000000000E+00},
+			tauOut:   0.0000000000000000,
+			ttypeOut: -1,
+			gOut:     0.0000000000000000,
+		},
+		{
+			z:        []float64{0.1914365246180821E+01, 0.2163704162395211E+01, 0.2493389162143899E+00, 0.1516515751224039E+00, 0.1315996513131545E+01, 0.1263329604128848E+01, 0.9898466611970759E-01, 0.4719916727467415E-01, 0.6023973979587287E+00, 0.5574082640946934E+00, 0.2210033410638781E-02, 0.3910066531356214E-03, 0.9861857233678967E-01, 0.5738597141291359E+00, 0.4756321484454819E+00, 0.2145632131068746E+00, 0.2588748143677115E+00, 0.1521727389298373E+00, 0.1078611376690004E+00, 0.4566771620366771E+00, 0.6442896492255246E+00, 0.8079355358528180E+00, 0.6203230486639705E+00, 0.2837483186776231E+00, 0.3695660678607585E+00, 0.6237015546083620E+00, 0.5378838054252265E+00, 0.3072349091217998E+00, 0.3562533181264623E+00, 0.7123973396902394E-01, 0.2222132496436145E-01, 0.3977314805803597E+00, 0.1275094303021685E+01, 0.1042095257923447E+01, 0.1647324354821218E+00, 0.1592685164190333E+00, 0.1007530576543866E+01, 0.1193650220303144E+01, 0.3453881601783118E+00, 0.7752942700755104E-01, 0.2679391719153404E+00, 0.9232775185761617E+00, 0.7328677736683723E+00, 0.6636554427529671E+00, 0.8360828138307410E+00, 0.6537934420370561E+00, 0.4813660709592822E+00, 0.4782322339990674E+00, 0.6495370513676459E+00, 0.4038524053908432E+00, 0.2325475880222648E+00, 0.1147975431483785E+00, 0.1993624802893807E+00, 0.4627968288321279E+00, 0.3782318916911257E+00, 0.8034172324482011E+00, 0.9830449403503746E+00, 0.6226010943062101E+00, 0.4429733864040367E+00, 0.8347746582554776E+00, 0.1173279550602403E+01, 0.8420572992613844E+00, 0.5035524069144587E+00, 0.1829278057427913E+00, 0.3058980395058521E+00, 0.4244336771046062E+00, 0.3014634433415453E+00, 0.9158407747236312E+00, 0.1289422237567578E+01, 0.1131917893423890E+01, 0.7583364305799440E+00, 0.3334922359541972E+00, 0.4977814779461571E+00, 0.4484361267782198E+00, 0.2841468847862598E+00, 0.5865943745895725E+00, 0.9257539794205765E+00, 0.3392119183870583E+00, 0.5231355605450990E-04, 0.3266196269153995E-08, 0.2117869221381033E-04, 0.2117542601754118E-04, 0.0000000000000000E+00, 0.3910066531356214E-03, 0.1037537856266618 - 321},
+			i0:       1,
+			n0:       21,
+			pp:       1,
+			n0in:     21,
+			dmin:     2.1175426017541180E-005,
+			dmin1:    4.4311601260836921E-002,
+			dmin2:    4.4311601260836921E-002,
+			dn:       2.1175426017541180E-005,
+			dn1:      0.33915960483100382,
+			dn2:      0.16428924199195991,
+			tau:      0.0000000000000000,
+			ttype:    -1,
+			g:        0.0000000000000000,
+			zOut:     []float64{0.1914365246180821E+01, 0.2163704162395211E+01, 0.2493389162143899E+00, 0.1516515751224039E+00, 0.1315996513131545E+01, 0.1263329604128848E+01, 0.9898466611970759E-01, 0.4719916727467415E-01, 0.6023973979587287E+00, 0.5574082640946934E+00, 0.2210033410638781E-02, 0.3910066531356214E-03, 0.9861857233678967E-01, 0.5738597141291359E+00, 0.4756321484454819E+00, 0.2145632131068746E+00, 0.2588748143677115E+00, 0.1521727389298373E+00, 0.1078611376690004E+00, 0.4566771620366771E+00, 0.6442896492255246E+00, 0.8079355358528180E+00, 0.6203230486639705E+00, 0.2837483186776231E+00, 0.3695660678607585E+00, 0.6237015546083620E+00, 0.5378838054252265E+00, 0.3072349091217998E+00, 0.3562533181264623E+00, 0.7123973396902394E-01, 0.2222132496436145E-01, 0.3977314805803597E+00, 0.1275094303021685E+01, 0.1042095257923447E+01, 0.1647324354821218E+00, 0.1592685164190333E+00, 0.1007530576543866E+01, 0.1193650220303144E+01, 0.3453881601783118E+00, 0.7752942700755104E-01, 0.2679391719153404E+00, 0.9232775185761617E+00, 0.7328677736683723E+00, 0.6636554427529671E+00, 0.8360828138307410E+00, 0.6537934420370561E+00, 0.4813660709592822E+00, 0.4782322339990674E+00, 0.6495370513676459E+00, 0.4038524053908432E+00, 0.2325475880222648E+00, 0.1147975431483785E+00, 0.1993624802893807E+00, 0.4627968288321279E+00, 0.3782318916911257E+00, 0.8034172324482011E+00, 0.9830449403503746E+00, 0.6226010943062101E+00, 0.4429733864040367E+00, 0.8347746582554776E+00, 0.1173279550602403E+01, 0.8420572992613844E+00, 0.5035524069144587E+00, 0.1829278057427913E+00, 0.3058980395058521E+00, 0.4244336771046062E+00, 0.3014634433415453E+00, 0.9158407747236312E+00, 0.1289422237567578E+01, 0.1131917893423890E+01, 0.7583364305799440E+00, 0.3334922359541972E+00, 0.4977814779461571E+00, 0.4484361267782198E+00, 0.2841468847862598E+00, 0.5865943745895725E+00, 0.9257539794205765E+00, 0.3392119183870583E+00, 0.5231355605450990E-04, 0.3266196269153995E-08, 0.2117869221381033E-04, 0.2117542601754118E-04, 0.0000000000000000E+00, 0.3910066531356214E-03, 0.1037537856266618 - 321},
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+			zOut:     []float64{0.9469159202365395E+00, 0.9469159202364811E+00, 0.3085312975855001E-13, 0.1264160184270297E-13, 0.3879844325624373E+00, 0.3879844502287687E+00, 0.1766643326162244E-07, 0.1360169848638109E-07, 0.2987160696935945E+00, 0.2987160882109940E+00, 0.3211918722443868E-07, 0.6653267495003571E-07, 0.6187697173160828E+00, 0.6187696512627651E+00, 0.4794463808464251E-09, 0.6914234847011291E-22, 0.8923456002485611E-13, 0.2545269924803487E-17, 0.3085312975855001E-13, 0.1264160184270297E-13, 0.1077066053646038E+01},
+			tauOut:   2.5452699247759164E-018,
+			ttypeOut: -4,
+			gOut:     0.49975000000000003,
+		},
+		{
+			z:        []float64{0.9469159202364937E+00, 0.9469159202364811E+00, 0.5179704803914515E-14, 0.1264160184270297E-13, 0.3879844638304620E+00, 0.3879844502287687E+00, 0.1047218779010850E-07, 0.1360169848638109E-07, 0.2987161442714811E+00, 0.2987160882109940E+00, 0.1378177941363543E-06, 0.6653267495003571E-07, 0.6187695134449710E+00, 0.6187696512627651E+00, 0.2844127518685707E-39, 0.6914234847011291E-22},
+			i0:       1,
+			n0:       4,
+			pp:       0,
+			n0in:     5,
+			dmin:     2.5452699248034865E-018,
+			dmin1:    0.29871607773880621,
+			dmin2:    0.29871607773880621,
+			dn:       2.5452699248034865E-018,
+			dn1:      0.61876951344497100,
+			dn2:      0.29871607773880621,
+			tau:      0.0000000000000000,
+			ttype:    -4,
+			g:        0.49975000000000003,
+			zOut:     []float64{0.9469159202364937E+00, 0.9469159202364811E+00, 0.5179704803914515E-14, 0.1264160184270297E-13, 0.3879844638304620E+00, 0.3879844502287687E+00, 0.1047218779010850E-07, 0.1360169848638109E-07, 0.2987161442714811E+00, 0.2987160882109940E+00, 0.1378177941363543E-06, 0.6653267495003571E-07, 0.6187695134449710E+00, 0.6187696512627651E+00, 0.2844127518685707E-39, 0.6914234847011291E-22},
+			tauOut:   7.4679019434701552E-002,
+			ttypeOut: -9,
+			gOut:     0.49975000000000003,
+		},
+		{
+			z:        []float64{0.9469159202364937E+00, 0.8722369008017974E+00, 0.5179704803914515E-14, 0.2304012808102351E-14, 0.3879844638304620E+00, 0.3133054548679459E+00, 0.1047218779010850E-07, 0.9984542273822185E-08, 0.2987161442714811E+00, 0.2240372526700314E+00, 0.1378177941363543E-06, 0.3806395963416417E-06, 0.6187695134449710E+00, 0.5440901133706730E+00, 0.2844127518685707E-39, 0.2304012808102351E-14, 0.1702794694134603E+01},
+			i0:       1,
+			n0:       4,
+			pp:       1,
+			n0in:     4,
+			dmin:     0.22403711485223726,
+			dmin1:    0.22403711485223726,
+			dmin2:    0.31330544439575814,
+			dn:       0.54409011337067303,
+			dn1:      0.22403711485223726,
+			dn2:      0.31330544439575814,
+			tau:      7.4679019434701552E-002,
+			ttype:    -9,
+			g:        0.49975000000000003,
+			zOut:     []float64{0.9469159202364937E+00, 0.8722369008017974E+00, 0.5179704803914515E-14, 0.2304012808102351E-14, 0.3879844638304620E+00, 0.3133054548679459E+00, 0.1047218779010850E-07, 0.9984542273822185E-08, 0.2987161442714811E+00, 0.2240372526700314E+00, 0.1378177941363543E-06, 0.3806395963416417E-06, 0.6187695134449710E+00, 0.5440901133706730E+00, 0.2844127518685707E-39, 0.2304012808102351E-14, 0.1702794694134603E+01},
+			tauOut:   0.22392121955733330,
+			ttypeOut: -4,
+			gOut:     0.49975000000000003,
+		},
+		{
+			z:        []float64{0.6483156812444665E+00, 0.8722369008017974E+00, 0.1113438717814820E-14, 0.2304012808102351E-14, 0.8938424529515379E-01, 0.3133054548679459E+00, 0.2502576838690600E-07, 0.9984542273822185E-08, 0.1163887265260836E-03, 0.2240372526700314E+00, 0.1779401212715201E-02, 0.3806395963416417E-06, 0.3183894926006245E+00, 0.5440901133706730E+00, 0.1113438717814820E-14, 0.2304012808102351E-14},
+			i0:       1,
+			n0:       4,
+			pp:       0,
+			n0in:     4,
+			dmin:     1.1600808692974196E-004,
+			dmin1:    1.1600808692974196E-004,
+			dmin2:    8.9384235310611515E-002,
+			dn:       0.31838949260062449,
+			dn1:      1.1600808692974196E-004,
+			dn2:      8.9384235310611515E-002,
+			tau:      0.22392121955733330,
+			ttype:    -4,
+			g:        0.49975000000000003,
+			zOut:     []float64{0.6483156812444665E+00, 0.8722369008017974E+00, 0.1113438717814820E-14, 0.2304012808102351E-14, 0.8938424529515379E-01, 0.3133054548679459E+00, 0.2502576838690600E-07, 0.9984542273822185E-08, 0.1163887265260836E-03, 0.2240372526700314E+00, 0.1779401212715201E-02, 0.3806395963416417E-06, 0.3183894926006245E+00, 0.5440901133706730E+00, 0.1113438717814820E-14, 0.2304012808102351E-14},
+			tauOut:   1.1589031543524988E-004,
+			ttypeOut: -4,
+			gOut:     0.49975000000000003,
+		},
+		{
+			z:        []float64{0.6483156812444665E+00, 0.6482265310101248E+00, 0.1113438717814820E-14, 0.1535325610927932E-15, 0.8938424529515379E-01, 0.8929512008657929E-01, 0.2502576838690600E-07, 0.3261899765703413E-10, 0.1163887265260836E-03, 0.1806639672279546E-02, 0.1779401212715201E-02, 0.3135891777105103E+00, 0.3183894926006245E+00, 0.4711164655771408E-02, 0.1113438717814820E-14, 0.1535325610927932E-15, 0.1702794694134603E+01},
+			i0:       1,
+			n0:       4,
+			pp:       1,
+			n0in:     4,
+			dmin:     2.7238459564345061E-005,
+			dmin1:    2.7238459564345061E-005,
+			dmin2:    8.9295095060810903E-002,
+			dn:       4.7111646557714080E-003,
+			dn1:      2.7238459564345061E-005,
+			dn2:      8.9295095060810903E-002,
+			tau:      8.9150234342740890E-005,
+			ttype:    -15,
+			g:        0.49975000000000003,
+			zOut:     []float64{0.6483156812444665E+00, 0.6482265310101248E+00, 0.1113438717814820E-14, 0.1535325610927932E-15, 0.8938424529515379E-01, 0.8929512008657929E-01, 0.2502576838690600E-07, 0.3261899765703413E-10, 0.1163887265260836E-03, 0.1806639672279546E-02, 0.1779401212715201E-02, 0.3135891777105103E+00, 0.3183894926006245E+00, 0.4711164655771408E-02, 0.1113438717814820E-14, 0.1535325610927932E-15, 0.1702794694134603E+01},
+			tauOut:   2.5005145741075717E-005,
+			ttypeOut: -4,
+			gOut:     0.49975000000000003,
+		},
+		{
+			z:        []float64{0.6482015258643838E+00, 0.6482265310101248E+00, 0.2115037983241246E-16, 0.1535325610927932E-15, 0.8927011497345719E-01, 0.8929512008657929E-01, 0.6601400172354812E-12, 0.3261899765703413E-10, 0.3153708122363886E+00, 0.1806639672279546E-02, 0.4684549720964035E-02, 0.3135891777105103E+00, 0.1609789066298190E-05, 0.4711164655771408E-02, 0.2115037983241246E-16, 0.1535325610927932E-15},
+			i0:       1,
+			n0:       4,
+			pp:       0,
+			n0in:     4,
+			dmin:     1.6097890662981897E-006,
+			dmin1:    1.7816345258783307E-003,
+			dmin2:    8.9270114940838197E-002,
+			dn:       1.6097890662981897E-006,
+			dn1:      1.7816345258783307E-003,
+			dn2:      8.9270114940838197E-002,
+			tau:      2.5005145741075717E-005,
+			ttype:    -4,
+			g:        0.49975000000000003,
+			zOut:     []float64{0.6482015258643838E+00, 0.6482265310101248E+00, 0.2115037983241246E-16, 0.1535325610927932E-15, 0.8927011497345719E-01, 0.8929512008657929E-01, 0.6601400172354812E-12, 0.3261899765703413E-10, 0.3153708122363886E+00, 0.1806639672279546E-02, 0.4684549720964035E-02, 0.3135891777105103E+00, 0.1609789066298190E-05, 0.4711164655771408E-02, 0.2115037983241246E-16, 0.1535325610927932E-15},
+			tauOut:   1.5862205428611591E-006,
+			ttypeOut: -2,
+			gOut:     0.49975000000000003,
+		},
+		{
+			z:        []float64{0.6482015258643838E+00, 0.6481999396438409E+00, 0.2115037983241246E-16, 0.2912830939801045E-17, 0.8927011497345719E-01, 0.8926852875357447E-01, 0.6601400172354812E-12, 0.2332164496627946E-11, 0.3153708122363886E+00, 0.3200537757344777E+00, 0.4684549720964035E-02, 0.2356209328895529E-07, 0.1609789066298190E-05, 0.6430148075154844E-11, 0.2115037983241246E-16, 0.2912830939801045E-17, 0.1702794694134603E+01},
+			i0:       1,
+			n0:       4,
+			pp:       1,
+			n0in:     4,
+			dmin:     6.4301480751548441E-012,
+			dmin1:    8.9268528752914328E-002,
+			dmin2:    8.9268528752914328E-002,
+			dn:       6.4301480751548441E-012,
+			dn1:      0.31536922601351364,
+			dn2:      8.9268528752914328E-002,
+			tau:      1.5862205428611591E-006,
+			ttype:    -2,
+			g:        0.49975000000000003,
+			zOut:     []float64{0.6482015258643838E+00, 0.6481999396438409E+00, 0.2115037983241246E-16, 0.2912830939801045E-17, 0.8927011497345719E-01, 0.8926852875357447E-01, 0.6601400172354812E-12, 0.2332164496627946E-11, 0.3153708122363886E+00, 0.3200537757344777E+00, 0.4684549720964035E-02, 0.2356209328895529E-07, 0.1609789066298190E-05, 0.6430148075154844E-11, 0.2115037983241246E-16, 0.2912830939801045E-17, 0.1702794694134603E+01},
+			tauOut:   6.4283598105616478E-012,
+			ttypeOut: -4,
+			gOut:     0.49975000000000003,
+		},
+		{
+			z:        []float64{0.6481999396374125E+00, 0.6481999396438409E+00, 0.4011480356653261E-18, 0.2912830939801045E-17, 0.8926852874947827E-01, 0.8926852875357447E-01, 0.8361491594360282E-11, 0.2332164496627946E-11, 0.3200537992817811E+00, 0.3200537757344777E+00, 0.4733821287189426E-18, 0.2356209328895529E-07, 0.1787791211067534E-14, 0.6430148075154844E-11, 0.4011480356653261E-18, 0.2912830939801045E-17},
+			i0:       1,
+			n0:       4,
+			pp:       0,
+			n0in:     4,
+			dmin:     1.7877912110675335E-015,
+			dmin1:    8.9268528747146109E-002,
+			dmin2:    8.9268528747146109E-002,
+			dn:       1.7877912110675335E-015,
+			dn1:      0.32005377571968785,
+			dn2:      8.9268528747146109E-002,
+			tau:      6.4283598105616478E-012,
+			ttype:    -4,
+			g:        0.49975000000000003,
+			zOut:     []float64{0.6481999396374125E+00, 0.6481999396438409E+00, 0.4011480356653261E-18, 0.2912830939801045E-17, 0.8926852874947827E-01, 0.8926852875357447E-01, 0.8361491594360282E-11, 0.2332164496627946E-11, 0.3200537992817811E+00, 0.3200537757344777E+00, 0.4733821287189426E-18, 0.2356209328895529E-07, 0.1787791211067534E-14, 0.6430148075154844E-11, 0.4011480356653261E-18, 0.2912830939801045E-17},
+			tauOut:   1.7877912088395813E-015,
+			ttypeOut: -4,
+			gOut:     0.49975000000000003,
+		},
+		{
+			z:        []float64{0.6481999396374125E+00, 0.6481999396374107E+00, 0.4011480356653261E-18, 0.5524513774965514E-19, 0.8926852874947827E-01, 0.8926852875783797E-01, 0.8361491594360282E-11, 0.2997839428604580E-10, 0.3200537992817811E+00, 0.3200537992518009E+00, 0.4733821287189426E-18, 0.2644269217171004E-32, 0.2001510674733695E+01},
+			i0:       1,
+			n0:       3,
+			pp:       1,
+			n0in:     4,
+			dmin:     2.2279522444840209E-024,
+			dmin1:    8.9268528749476481E-002,
+			dmin2:    8.9268528749476481E-002,
+			dn:       2.2279522444840209E-024,
+			dn1:      0.32005379925180094,
+			dn2:      8.9268528749476481E-002,
+			tau:      1.7877912088395813E-015,
+			ttype:    -4,
+			g:        0.49975000000000003,
+			zOut:     []float64{0.6481999396374125E+00, 0.6481999396374107E+00, 0.4011480356653261E-18, 0.5524513774965514E-19, 0.8926852874947827E-01, 0.8926852875783797E-01, 0.8361491594360282E-11, 0.2997839428604580E-10, 0.3200537992817811E+00, 0.3200537992518009E+00, 0.4733821287189426E-18, 0.2644269217171004E-32, 0.2001510674733695E+01},
+			tauOut:   2.2317132187369120E-002,
+			ttypeOut: -9,
+			gOut:     0.49975000000000003,
+		},
+		{
+			z:        []float64{0.6258828074500417E+00, 0.6481999396374107E+00, 0.7879513719234823E-20, 0.5524513774965514E-19, 0.6695139660044724E-01, 0.8926852875783797E-01, 0.1433084218388560E-09, 0.2997839428604580E-10, 0.2977366669211234E+00, 0.3200537992518009E+00, 0.8926852875783797E-01, 0.2644269217171004E-32},
+			i0:       1,
+			n0:       3,
+			pp:       0,
+			n0in:     3,
+			dmin:     6.6951396570468849E-002,
+			dmin1:    6.6951396570468849E-002,
+			dmin2:    0.62588280745004166,
+			dn:       0.29773666692112338,
+			dn1:      6.6951396570468849E-002,
+			dn2:      0.62588280745004166,
+			tau:      2.2317132187369120E-002,
+			ttype:    -9,
+			g:        0.49975000000000003,
+			zOut:     []float64{0.6258828074500417E+00, 0.6481999396374107E+00, 0.7879513719234823E-20, 0.5524513774965514E-19, 0.6695139660044724E-01, 0.8926852875783797E-01, 0.1433084218388560E-09, 0.2997839428604580E-10, 0.2977366669211234E+00, 0.3200537992518009E+00, 0.8926852875783797E-01, 0.2644269217171004E-32},
+			tauOut:   6.6950732596142107E-002,
+			ttypeOut: -4,
+			gOut:     0.49975000000000003,
+		},
+		{
+			z:        []float64{0.6258828074500417E+00, 0.5589320748538995E+00, 0.7879513719234823E-20, 0.9438435755776795E-21, 0.6695139660044724E-01, 0.6641476135588615E-06, 0.1433084218388560E-09, 0.6424501268835132E-04, 0.2977366669211234E+00, 0.2307216893122929E+00, 0.8926852875783797E-01, 0.6695139660044724E-01, 0.2001510674733695E+01},
+			i0:       1,
+			n0:       3,
+			pp:       1,
+			n0in:     3,
+			dmin:     6.6400430513702258E-007,
+			dmin1:    6.6400430513702258E-007,
+			dmin2:    0.55893207485389951,
+			dn:       0.23072168931229292,
+			dn1:      6.6400430513702258E-007,
+			dn2:      0.55893207485389951,
+			tau:      6.6950732596142107E-002,
+			ttype:    -4,
+			g:        0.49975000000000003,
+			zOut:     []float64{0.6258828074500417E+00, 0.5589320748538995E+00, 0.7879513719234823E-20, 0.9438435755776795E-21, 0.6695139660044724E-01, 0.6641476135588615E-06, 0.1433084218388560E-09, 0.6424501268835132E-04, 0.2977366669211234E+00, 0.2307216893122929E+00, 0.8926852875783797E-01, 0.6695139660044724E-01, 0.2001510674733695E+01},
+			tauOut:   6.6398937736467640E-007,
+			ttypeOut: -4,
+			gOut:     0.49975000000000003,
+		},
+		{
+			z:        []float64{0.5589315065851642E+00, 0.5589320748538995E+00, 0.1121517486324177E-26, 0.9438435755776795E-21, 0.6434089156657428E-04, 0.6641476135588615E-06, 0.2303778747300831E+00, 0.6424501268835132E-04, 0.3432463134744483E-03, 0.2307216893122929E+00, 0.6641476135588615E-06, 0.6695139660044724E-01},
+			i0:       1,
+			n0:       3,
+			pp:       0,
+			n0in:     3,
+			dmin:     9.5878878222950548E-008,
+			dmin1:    9.5878878222950548E-008,
+			dmin2:    0.55893150658516422,
+			dn:       3.4324631347444829E-004,
+			dn1:      9.5878878222950548E-008,
+			dn2:      0.55893150658516422,
+			tau:      5.6826873533591094E-007,
+			ttype:    -15,
+			g:        0.49975000000000003,
+			zOut:     []float64{0.5589315065851642E+00, 0.5589320748538995E+00, 0.1121517486324177E-26, 0.9438435755776795E-21, 0.6434089156657428E-04, 0.6641476135588615E-06, 0.2303778747300831E+00, 0.6424501268835132E-04, 0.3432463134744483E-03, 0.2307216893122929E+00, 0.6641476135588615E-06, 0.6695139660044724E-01},
+			tauOut:   9.4211902206835373E-008,
+			ttypeOut: -4,
+			gOut:     0.49975000000000003,
+		},
+	} {
+		z := make([]float64, len(test.z))
+		copy(z, test.z)
+
+		// Print for fortran input
+		//printDlasq4FortranInput(test)
+
+		i0 := test.i0 - 1 // zero index
+		n0 := test.n0 - 1 // zero index
+		n0in := test.n0in - 1
+
+		tauOut, ttypeOut, gOut := impl.Dlasq4(i0, n0, z, test.pp, n0in, test.dmin, test.dmin1, test.dmin2, test.dn, test.dn1, test.dn2, test.tau, test.ttype, test.g)
+
+		if !floats.EqualApprox(z, test.zOut, dTol) {
+			t.Errorf("Z mismatch")
+		}
+		if !floats.EqualWithinAbsOrRel(tauOut, test.tauOut, dTol, dTol) {
+			t.Errorf("Case %d, wrong tau. Want %v, got %v", cas, test.tauOut, tauOut)
+		}
+		if ttypeOut != test.ttypeOut {
+			t.Errorf("Wrong ttype. Want %v, got %v", test.ttypeOut, ttypeOut)
+		}
+		if !floats.EqualWithinAbsOrRel(gOut, test.gOut, dTol, dTol) {
+			t.Errorf("Wrong g. Want %v, got %v", test.gOut, gOut)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlasq5.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlasq5.go
new file mode 100644
index 00000000..235b9b9e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlasq5.go
@@ -0,0 +1,1992 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dlasq5er interface {
+	Dlasq5(i0, n0 int, z []float64, pp int, tau, sigma float64) (i0Out, n0Out, ppOut int, tauOut, sigmaOut, dmin, dmin1, dmin2, dn, dnm1, dnm2 float64)
+}
+
+func Dlasq5Test(t *testing.T, impl Dlasq5er) {
+	dTol := 1e-14
+	for _, test := range []struct {
+		z          []float64
+		i0, n0, pp int
+		tau, sigma float64
+
+		i0Out, n0Out, ppOut         int
+		tauOut, sigmaOut            float64
+		dminOut, dmin1Out, dmin2Out float64
+		dnOut, dnm1Out, dnm2Out     float64
+	}{
+		{
+			z:        []float64{0.1914365246180821E+01, 0.1564384297703890E+01, 0.2493389162143899E+00, 0.3499809484769305E+00, 0.1315996513131545E+01, 0.1363862112490627E+01, 0.9898466611970759E-01, 0.2014733168553078E+00, 0.6023973979587287E+00, 0.6465544792741794E+00, 0.2210033410638781E-02, 0.5482758480425683E-01, 0.9861857233678967E-01, 0.2428190810745492E-01, 0.4756321484454819E+00, 0.7654669763997353E-01, 0.2588748143677115E+00, 0.6127784069508770E+00, 0.1078611376690004E+00, 0.1217285558623164E+00, 0.6442896492255246E+00, 0.2293835804898155E+00, 0.6203230486639705E+00, 0.5227672064047094E+00, 0.3695660678607585E+00, 0.7645233184745865E+00, 0.5378838054252265E+00, 0.2253657980501426E+00, 0.3562533181264623E+00, 0.8820486722335483E+00, 0.2222132496436145E-01, 0.1208845131814035E-01, 0.1275094303021685E+01, 0.6548746852163357E+00, 0.1647324354821218E+00, 0.6424409427697111E+00, 0.1007530576543866E+01, 0.3269551736546701E+00, 0.3453881601783118E+00, 0.8453078383713172E+00, 0.2679391719153404E+00, 0.4116714838778281E+00, 0.7328677736683723E+00, 0.2016558482158241E+00, 0.8360828138307410E+00, 0.9737579452195326E+00, 0.4813660709592822E+00, 0.5951926422795808E+00, 0.6495370513676459E+00, 0.6761876248148171E+00, 0.2325475880222648E+00, 0.4547154975121112E+00, 0.1993624802893807E+00, 0.3321819367342255E+00, 0.3782318916911257E+00, 0.9972813157741996E-01, 0.9830449403503746E+00, 0.7561080996844842E+00, 0.4429733864040367E+00, 0.6051687323570161E+00, 0.1173279550602403E+01, 0.7195724480316686E+00, 0.5035524069144587E+00, 0.8966804889747714E+00, 0.3058980395058521E+00, 0.6588832353928662E+00, 0.3014634433415453E+00, 0.1505672110274446E+00, 0.1289422237567578E+01, 0.6124645310993601E+00, 0.7583364305799440E+00, 0.9784211498097629E+00, 0.4977814779461571E+00, 0.9993813577491869E+00, 0.2841468847862598E+00, 0.2567365507769143E+00, 0.9257539794205765E+00, 0.5509268385614666E+00, 0.5231355605450990E-04, 0.6589740256453697E+00, 0.2117869221381033E-04, 0.7349224826832024E-04, 0.0000000000000000E+00, 0.0000000000000000E+00},
+			i0:       1,
+			n0:       21,
+			pp:       0,
+			tau:      0.0000000000000000,
+			sigma:    0.0000000000000000,
+			i0Out:    1,
+			n0Out:    21,
+			ppOut:    0,
+			tauOut:   0.0000000000000000,
+			sigmaOut: 0.0000000000000000,
+			dminOut:  2.1175426017541180E-005,
+			dmin1Out: 4.4311601260836921E-002,
+			dmin2Out: 4.4311601260836921E-002,
+			dnOut:    2.1175426017541180E-005,
+			dnm1Out:  0.33915960483100382,
+			dnm2Out:  0.16428924199195991,
+		},
+		{
+			z:        []float64{0.1914365246180821E+01, 0.2163704162395211E+01, 0.2493389162143899E+00, 0.1516515751224039E+00, 0.1315996513131545E+01, 0.1263329604128848E+01, 0.9898466611970759E-01, 0.4719916727467415E-01, 0.6023973979587287E+00, 0.5574082640946934E+00, 0.2210033410638781E-02, 0.3910066531356214E-03, 0.9861857233678967E-01, 0.5738597141291359E+00, 0.4756321484454819E+00, 0.2145632131068746E+00, 0.2588748143677115E+00, 0.1521727389298373E+00, 0.1078611376690004E+00, 0.4566771620366771E+00, 0.6442896492255246E+00, 0.8079355358528180E+00, 0.6203230486639705E+00, 0.2837483186776231E+00, 0.3695660678607585E+00, 0.6237015546083620E+00, 0.5378838054252265E+00, 0.3072349091217998E+00, 0.3562533181264623E+00, 0.7123973396902394E-01, 0.2222132496436145E-01, 0.3977314805803597E+00, 0.1275094303021685E+01, 0.1042095257923447E+01, 0.1647324354821218E+00, 0.1592685164190333E+00, 0.1007530576543866E+01, 0.1193650220303144E+01, 0.3453881601783118E+00, 0.7752942700755104E-01, 0.2679391719153404E+00, 0.9232775185761617E+00, 0.7328677736683723E+00, 0.6636554427529671E+00, 0.8360828138307410E+00, 0.6537934420370561E+00, 0.4813660709592822E+00, 0.4782322339990674E+00, 0.6495370513676459E+00, 0.4038524053908432E+00, 0.2325475880222648E+00, 0.1147975431483785E+00, 0.1993624802893807E+00, 0.4627968288321279E+00, 0.3782318916911257E+00, 0.8034172324482011E+00, 0.9830449403503746E+00, 0.6226010943062101E+00, 0.4429733864040367E+00, 0.8347746582554776E+00, 0.1173279550602403E+01, 0.8420572992613844E+00, 0.5035524069144587E+00, 0.1829278057427913E+00, 0.3058980395058521E+00, 0.4244336771046062E+00, 0.3014634433415453E+00, 0.9158407747236312E+00, 0.1289422237567578E+01, 0.1131917893423890E+01, 0.7583364305799440E+00, 0.3334922359541972E+00, 0.4977814779461571E+00, 0.4484361267782198E+00, 0.2841468847862598E+00, 0.5865943745895725E+00, 0.9257539794205765E+00, 0.3392119183870583E+00, 0.5231355605450990E-04, 0.3266196269153995E-08, 0.2117869221381033E-04, 0.2117542601754118E-04, 0.0000000000000000E+00, 0.3910066531356214E-03, 0.1037537856266618 - 321},
+			i0:       1,
+			n0:       21,
+			pp:       1,
+			tau:      0.0000000000000000,
+			sigma:    0.0000000000000000,
+			i0Out:    1,
+			n0Out:    21,
+			ppOut:    1,
+			tauOut:   0.0000000000000000,
+			sigmaOut: 0.0000000000000000,
+			dminOut:  2.1175425069176302E-005,
+			dmin1Out: 2.9944624525135358E-002,
+			dmin2Out: 2.9944624525135358E-002,
+			dnOut:    2.1175425069176302E-005,
+			dnm1Out:  7.2928780948497918E-002,
+			dnm2Out:  0.16065460645225654,
+		},
+		{
+			z:        []float64{0.2315355737517615E+01, 0.2163704162395211E+01, 0.8274578340618610E-01, 0.1516515751224039E+00, 0.1227782987997336E+01, 0.1263329604128848E+01, 0.2142822156235013E-01, 0.4719916727467415E-01, 0.5363710491854788E+00, 0.5574082640946934E+00, 0.4183353417969536E-03, 0.3910066531356214E-03, 0.7880045918942136E+00, 0.5738597141291359E+00, 0.4143462125464707E-01, 0.2145632131068746E+00, 0.5674152797118673E+00, 0.1521727389298373E+00, 0.6502569120260687E+00, 0.4566771620366771E+00, 0.4414269425043723E+00, 0.8079355358528180E+00, 0.4009140594652070E+00, 0.2837483186776231E+00, 0.5300224042649548E+00, 0.6237015546083620E+00, 0.4129510944388858E-01, 0.3072349091217998E+00, 0.4276761051054951E+00, 0.7123973396902394E-01, 0.9691308092544145E+00, 0.3977314805803597E+00, 0.2322329650880660E+00, 0.1042095257923447E+01, 0.8186215063776209E+00, 0.1592685164190333E+00, 0.4525581409330741E+00, 0.1193650220303144E+01, 0.1581701233715052E+00, 0.7752942700755104E-01, 0.1428762837957623E+01, 0.9232775185761617E+00, 0.3036848136842134E+00, 0.6636554427529671E+00, 0.8283408623519102E+00, 0.6537934420370561E+00, 0.2331591338951825E+00, 0.4782322339990674E+00, 0.2854908146440392E+00, 0.4038524053908432E+00, 0.1860933389154074E+00, 0.1147975431483785E+00, 0.1080120722364922E+01, 0.4627968288321279E+00, 0.4631042046962229E+00, 0.8034172324482011E+00, 0.9942715478654648E+00, 0.6226010943062101E+00, 0.7069779837626068E+00, 0.8347746582554776E+00, 0.3180071212415688E+00, 0.8420572992613844E+00, 0.2441477440283845E+00, 0.1829278057427913E+00, 0.1096126707799853E+01, 0.4244336771046062E+00, 0.9457451890006905E+00, 0.9158407747236312E+00, 0.5196649403773971E+00, 0.1131917893423890E+01, 0.2877815203259632E+00, 0.3334922359541972E+00, 0.7472489810418290E+00, 0.4484361267782198E+00, 0.2662831374385604E+00, 0.5865943745895725E+00, 0.7292878421469419E-01, 0.3392119183870583E+00, 0.9483648767903632E-12, 0.3266196269153995E-08, 0.2117542506917630E-04, 0.2117542601754118E-04, 0.4183353417969536E-03, 0.3910066531356214E-03},
+			i0:       1,
+			n0:       21,
+			pp:       0,
+			tau:      2.1175313795360271E-005,
+			sigma:    0.0000000000000000,
+			i0Out:    1,
+			n0Out:    21,
+			ppOut:    0,
+			tauOut:   2.1175313795360271E-005,
+			sigmaOut: 0.0000000000000000,
+			dminOut:  1.1127325659669794E-010,
+			dmin1Out: 3.1433071595911154E-002,
+			dmin2Out: 3.1433071595911154E-002,
+			dnOut:    1.1127325659669794E-010,
+			dnm1Out:  3.5896964560873705E-002,
+			dnm2Out:  0.25842281720128102,
+		},
+		{
+			z:        []float64{0.2315355737517615E+01, 0.2398080345610006E+01, 0.8274578340618610E-01, 0.4236466279397526E-01, 0.1227782987997336E+01, 0.1206825371451915E+01, 0.2142822156235013E-01, 0.9523728911788614E-02, 0.5363710491854788E+00, 0.5272444803016919E+00, 0.4183353417969536E-03, 0.6252320936560726E-03, 0.7880045918942136E+00, 0.8287928057414093E+00, 0.4143462125464707E-01, 0.2836732781232222E-01, 0.5674152797118673E+00, 0.1189283688611819E+01, 0.6502569120260687E+00, 0.2413561400585997E+00, 0.4414269425043723E+00, 0.6009636865971842E+00, 0.4009140594652070E+00, 0.3535878097802652E+00, 0.5300224042649548E+00, 0.2177085286147829E+00, 0.4129510944388858E-01, 0.8112190955144877E-01, 0.4276761051054951E+00, 0.1315663829494665E+01, 0.9691308092544145E+00, 0.1710650671895379E+00, 0.2322329650880660E+00, 0.8797682289623537E+00, 0.8186215063776209E+00, 0.4211038940233675E+00, 0.4525581409330741E+00, 0.1896031949674164E+00, 0.1581701233715052E+00, 0.1191897606932286E+01, 0.1428762837957623E+01, 0.5405288693957555E+00, 0.3036848136842134E+00, 0.4653859482687157E+00, 0.8283408623519102E+00, 0.5960928726645816E+00, 0.2331591338951825E+00, 0.1116684901463164E+00, 0.2854908146440392E+00, 0.3598944880993349E+00, 0.1860933389154074E+00, 0.5585061130503639E+00, 0.1080120722364922E+01, 0.9846976386969850E+00, 0.4631042046962229E+00, 0.4676068229793028E+00, 0.9942715478654648E+00, 0.1233621533334973E+01, 0.7069779837626068E+00, 0.1822471700779458E+00, 0.3180071212415688E+00, 0.3798865198782122E+00, 0.2441477440283845E+00, 0.7044652781161848E+00, 0.1096126707799853E+01, 0.1337385443370563E+01, 0.9457451890006905E+00, 0.3674861422265960E+00, 0.5196649403773971E+00, 0.4399391431629689E+00, 0.2877815203259632E+00, 0.4888049885267526E+00, 0.7472489810418290E+00, 0.5247059546398414E+00, 0.2662831374385604E+00, 0.3701064434002514E-01, 0.7292878421469419E-01, 0.3589696456182207E-01, 0.9483648767903632E-12, 0.5594353069081231E-15, 0.2117542506917630E-04, 0.1112732565966979E-09, 0.4183353417969536E-03, 0.6252320936560726E-03, 0.1037537856266618 - 321},
+			i0:       1,
+			n0:       21,
+			pp:       1,
+			tau:      2.1175313795360271E-005,
+			sigma:    2.1175313795360271E-005,
+			i0Out:    1,
+			n0Out:    21,
+			ppOut:    1,
+			tauOut:   2.1175313795360271E-005,
+			sigmaOut: 2.1175313795360271E-005,
+			dminOut:  -2.1175202522103674E-005,
+			dmin1Out: 2.9116497146097618E-002,
+			dmin2Out: 4.9396687496051764E-002,
+			dnOut:    -2.1175202522103674E-005,
+			dnm1Out:  2.9116497146097618E-002,
+			dnm2Out:  0.15954393093937583,
+		},
+		{
+			z:        []float64{0.2440423833090186E+01, 0.2398080345610006E+01, 0.2094994698033050E-01, 0.4236466279397526E-01, 0.1195377978069578E+01, 0.1206825371451915E+01, 0.4200624064314086E-02, 0.9523728911788614E-02, 0.5236479130172386E+00, 0.5272444803016919E+00, 0.9895730475750664E-03, 0.6252320936560726E-03, 0.8561493851923613E+00, 0.8287928057414093E+00, 0.3940527300515336E-01, 0.2836732781232222E-01, 0.1391213380351470E+01, 0.1189283688611819E+01, 0.1042588274099539E+00, 0.2413561400585997E+00, 0.8502714936537001E+00, 0.6009636865971842E+00, 0.9053470847599347E-01, 0.3535878097802652E+00, 0.2082745543764428E+00, 0.2177085286147829E+00, 0.5124445590385125E+00, 0.8112190955144877E-01, 0.9742631623318954E+00, 0.1315663829494665E+01, 0.1544732645319877E+00, 0.1710650671895379E+00, 0.1146377683139938E+01, 0.8797682289623537E+00, 0.6964776521238716E-01, 0.4211038940233675E+00, 0.1311831861373520E+01, 0.1896031949674164E+00, 0.4911110065859084E+00, 0.1191897606932286E+01, 0.5147826357647675E+00, 0.5405288693957555E+00, 0.5388939477127089E+00, 0.4653859482687157E+00, 0.1688462397843937E+00, 0.5960928726645816E+00, 0.2380205454936569E+00, 0.1116684901463164E+00, 0.6803588803422466E+00, 0.3598944880993349E+00, 0.8083375797812383E+00, 0.5585061130503639E+00, 0.6439457065812542E+00, 0.9846976386969850E+00, 0.8958050967125053E+00, 0.4676068229793028E+00, 0.5200424313866183E+00, 0.1233621533334973E+01, 0.1331299890548604E+00, 0.1822471700779458E+00, 0.9512006336257413E+00, 0.3798865198782122E+00, 0.9904762202705547E+00, 0.7044652781161848E+00, 0.7143741900128092E+00, 0.1337385443370563E+01, 0.2263121215682984E+00, 0.3674861422265960E+00, 0.7024108348076278E+00, 0.4399391431629689E+00, 0.3651408483866702E+00, 0.4888049885267526E+00, 0.1965545752794010E+00, 0.5247059546398414E+00, 0.6759292101929097E-02, 0.3701064434002514E-01, 0.2911649714609818E-01, 0.3589696456182207E-01, 0.2137969692662087E-23, 0.5594353069081231E-15, -0.2117520252210367E-04, 0.1112732565966979E-09, 0.9895730475750664E-03, 0.6252320936560726E-03, 0.1037537856266618 - 321},
+			i0:       1,
+			n0:       21,
+			pp:       1,
+			tau:      1.1127325659669789E-010,
+			sigma:    2.1175313795360271E-005,
+			i0Out:    1,
+			n0Out:    21,
+			ppOut:    1,
+			tauOut:   1.1127325659669789E-010,
+			sigmaOut: 2.1175313795360271E-005,
+			dminOut:  -2.0808762284537102E-024,
+			dmin1Out: 2.9139336744737766E-002,
+			dmin2Out: 4.9426557292086552E-002,
+			dnOut:    -2.0808762284537102E-024,
+			dnm1Out:  2.9139336744737766E-002,
+			dnm2Out:  0.15959234211062134,
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+			sigma:    0.0000000000000000,
+			i0Out:    1,
+			n0Out:    21,
+			ppOut:    0,
+			tauOut:   0.0000000000000000,
+			sigmaOut: 0.0000000000000000,
+			dminOut:  7.8766827084626452E-005,
+			dmin1Out: 1.2363512593342330E-003,
+			dmin2Out: 1.2363512593342330E-003,
+			dnOut:    7.8766827084626452E-005,
+			dnm1Out:  4.3867054272813191E-003,
+			dnm2Out:  3.7622286348031123E-003,
+		},
+	} {
+		// TODO(btracey): Check other outputs
+		i0 := test.i0 - 1
+		n0 := test.n0 - 1
+		z := make([]float64, len(test.z))
+		copy(z, test.z)
+
+		i0Out, n0Out, ppOut, tauOut, sigmaOut, dminOut, dmin1Out, dmin2Out, dnOut, dnm1Out, dnm2Out := impl.Dlasq5(i0, n0, z, test.pp, test.tau, test.sigma)
+
+		if i0Out != test.i0Out-1 {
+			t.Errorf("Wrong i0. Want %v, got %v", test.n0Out, n0Out)
+		}
+		if n0Out != test.n0Out-1 {
+			t.Errorf("Wrong n0. Want %v, got %v", test.n0Out, n0Out)
+		}
+		if ppOut != test.ppOut {
+			t.Errorf("Wrong pp. Want %v, got %v", test.ppOut, ppOut)
+		}
+		if !floats.EqualWithinAbsOrRel(tauOut, test.tauOut, dTol, dTol) {
+			t.Errorf("Wrong tau. Want %v, got %v", test.tauOut, tauOut)
+		}
+		if !floats.EqualWithinAbsOrRel(sigmaOut, test.sigmaOut, dTol, dTol) {
+			t.Errorf("Wrong tau. Want %v, got %v", test.sigmaOut, sigmaOut)
+		}
+
+		if !floats.EqualWithinAbsOrRel(dminOut, test.dminOut, dTol, dTol) {
+			t.Errorf("Wrong dmin. Want %v, got %v", test.dminOut, dminOut)
+		}
+		if !floats.EqualWithinAbsOrRel(dmin1Out, test.dmin1Out, dTol, dTol) {
+			t.Errorf("Wrong dmin1. Want %v, got %v", test.dmin1Out, dmin1Out)
+		}
+		if !floats.EqualWithinAbsOrRel(dmin2Out, test.dmin2Out, dTol, dTol) {
+			t.Errorf("Wrong dmin2. Want %v, got %v", test.dmin2Out, dmin2Out)
+		}
+		if !floats.EqualWithinAbsOrRel(dnOut, test.dnOut, dTol, dTol) {
+			t.Errorf("Wrong dn. Want %v, got %v", test.dnOut, dnOut)
+		}
+		if !floats.EqualWithinAbsOrRel(dnm1Out, test.dnm1Out, dTol, dTol) {
+			t.Errorf("Wrong dnm1. Want %v, got %v", test.dnm1Out, dnm1Out)
+		}
+		if !floats.EqualWithinAbsOrRel(dnm2Out, test.dnm2Out, dTol, dTol) {
+			t.Errorf("Wrong dnm2. Want %v, got %v", test.dnm2Out, dnm2Out)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlasr.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlasr.go
new file mode 100644
index 00000000..87a26059
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlasr.go
@@ -0,0 +1,148 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dlasrer interface {
+	Dlasr(side blas.Side, pivot lapack.Pivot, direct lapack.Direct, m, n int, c, s, a []float64, lda int)
+}
+
+func DlasrTest(t *testing.T, impl Dlasrer) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, side := range []blas.Side{blas.Left, blas.Right} {
+		for _, pivot := range []lapack.Pivot{lapack.Variable, lapack.Top, lapack.Bottom} {
+			for _, direct := range []lapack.Direct{lapack.Forward, lapack.Backward} {
+				for _, test := range []struct {
+					m, n, lda int
+				}{
+					{5, 5, 0},
+					{5, 10, 0},
+					{10, 5, 0},
+
+					{5, 5, 20},
+					{5, 10, 20},
+					{10, 5, 20},
+				} {
+					m := test.m
+					n := test.n
+					lda := test.lda
+					if lda == 0 {
+						lda = n
+					}
+					a := make([]float64, m*lda)
+					for i := range a {
+						a[i] = rnd.Float64()
+					}
+					var s, c []float64
+					if side == blas.Left {
+						s = make([]float64, m-1)
+						c = make([]float64, m-1)
+					} else {
+						s = make([]float64, n-1)
+						c = make([]float64, n-1)
+					}
+					for k := range s {
+						theta := rnd.Float64() * 2 * math.Pi
+						s[k] = math.Sin(theta)
+						c[k] = math.Cos(theta)
+					}
+					aCopy := make([]float64, len(a))
+					copy(a, aCopy)
+					impl.Dlasr(side, pivot, direct, m, n, c, s, a, lda)
+
+					pSize := m
+					if side == blas.Right {
+						pSize = n
+					}
+					p := blas64.General{
+						Rows:   pSize,
+						Cols:   pSize,
+						Stride: pSize,
+						Data:   make([]float64, pSize*pSize),
+					}
+					pk := blas64.General{
+						Rows:   pSize,
+						Cols:   pSize,
+						Stride: pSize,
+						Data:   make([]float64, pSize*pSize),
+					}
+					ptmp := blas64.General{
+						Rows:   pSize,
+						Cols:   pSize,
+						Stride: pSize,
+						Data:   make([]float64, pSize*pSize),
+					}
+					for i := 0; i < pSize; i++ {
+						p.Data[i*p.Stride+i] = 1
+						ptmp.Data[i*p.Stride+i] = 1
+					}
+					// Compare to direct computation.
+					for k := range s {
+						for i := range p.Data {
+							pk.Data[i] = 0
+						}
+						for i := 0; i < pSize; i++ {
+							pk.Data[i*p.Stride+i] = 1
+						}
+						if pivot == lapack.Variable {
+							pk.Data[k*p.Stride+k] = c[k]
+							pk.Data[k*p.Stride+k+1] = s[k]
+							pk.Data[(k+1)*p.Stride+k] = -s[k]
+							pk.Data[(k+1)*p.Stride+k+1] = c[k]
+						} else if pivot == lapack.Top {
+							pk.Data[0] = c[k]
+							pk.Data[k+1] = s[k]
+							pk.Data[(k+1)*p.Stride] = -s[k]
+							pk.Data[(k+1)*p.Stride+k+1] = c[k]
+						} else {
+							pk.Data[(pSize-1-k)*p.Stride+pSize-k-1] = c[k]
+							pk.Data[(pSize-1-k)*p.Stride+pSize-1] = s[k]
+							pk.Data[(pSize-1)*p.Stride+pSize-1-k] = -s[k]
+							pk.Data[(pSize-1)*p.Stride+pSize-1] = c[k]
+						}
+						if direct == lapack.Forward {
+							blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, pk, ptmp, 0, p)
+						} else {
+							blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, ptmp, pk, 0, p)
+						}
+						copy(ptmp.Data, p.Data)
+					}
+
+					aMat := blas64.General{
+						Rows:   m,
+						Cols:   n,
+						Stride: lda,
+						Data:   make([]float64, m*lda),
+					}
+					copy(a, aCopy)
+					newA := blas64.General{
+						Rows:   m,
+						Cols:   n,
+						Stride: lda,
+						Data:   make([]float64, m*lda),
+					}
+					if side == blas.Left {
+						blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, p, aMat, 0, newA)
+					} else {
+						blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, aMat, p, 0, newA)
+					}
+					if !floats.EqualApprox(newA.Data, a, 1e-12) {
+						t.Errorf("A update mismatch")
+					}
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlasrt.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlasrt.go
new file mode 100644
index 00000000..80b1404b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlasrt.go
@@ -0,0 +1,80 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dlasrter interface {
+	Dlasrt(s lapack.Sort, n int, d []float64)
+}
+
+func DlasrtTest(t *testing.T, impl Dlasrter) {
+	for ti, test := range []struct {
+		data    []float64
+		wantInc []float64
+		wantDec []float64
+	}{
+		{
+			data:    nil,
+			wantInc: nil,
+			wantDec: nil,
+		},
+		{
+			data:    []float64{},
+			wantInc: []float64{},
+			wantDec: []float64{},
+		},
+		{
+			data:    []float64{1},
+			wantInc: []float64{1},
+			wantDec: []float64{1},
+		},
+		{
+			data:    []float64{1, 2},
+			wantInc: []float64{1, 2},
+			wantDec: []float64{2, 1},
+		},
+		{
+			data:    []float64{1, 2, -3},
+			wantInc: []float64{-3, 1, 2},
+			wantDec: []float64{2, 1, -3},
+		},
+		{
+			data:    []float64{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5},
+			wantInc: []float64{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5},
+			wantDec: []float64{5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5},
+		},
+		{
+			data:    []float64{5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5},
+			wantInc: []float64{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5},
+			wantDec: []float64{5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5},
+		},
+		{
+			data:    []float64{-2, 4, -1, 2, -4, 0, 3, 5, -5, 1, -3},
+			wantInc: []float64{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5},
+			wantDec: []float64{5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5},
+		},
+	} {
+		n := len(test.data)
+		ds := make([]float64, n)
+
+		copy(ds, test.data)
+		impl.Dlasrt(lapack.SortIncreasing, n, ds)
+		if !floats.Equal(ds, test.wantInc) {
+			t.Errorf("Case #%v: unexpected result of SortIncreasing", ti)
+		}
+
+		copy(ds, test.data)
+		impl.Dlasrt(lapack.SortDecreasing, n, ds)
+		if !floats.Equal(ds, test.wantDec) {
+			t.Errorf("Case #%v: unexpected result of SortIncreasing", ti)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlasv2.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlasv2.go
new file mode 100644
index 00000000..85184e62
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlasv2.go
@@ -0,0 +1,48 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dlasv2er interface {
+	Dlasv2(f, g, h float64) (ssmin, ssmax, snr, csr, snl, csl float64)
+}
+
+func Dlasv2Test(t *testing.T, impl Dlasv2er) {
+	rnd := rand.New(rand.NewSource(1))
+	for i := 0; i < 100; i++ {
+		f := rnd.NormFloat64()
+		g := rnd.NormFloat64()
+		h := rnd.NormFloat64()
+
+		ssmin, ssmax, snr, csr, snl, csl := impl.Dlasv2(f, g, h)
+
+		// tmp =
+		// [ csl snl] [f g]
+		// [-snl csl] [0 h]
+		tmp11 := csl * f
+		tmp12 := csl*g + snl*h
+		tmp21 := -snl * f
+		tmp22 := -snl*g + csl*h
+		// lhs =
+		// [tmp11 tmp12] [csr -snr]
+		// [tmp21 tmp22] [snr  csr]
+		ans11 := tmp11*csr + tmp12*snr
+		ans12 := tmp11*-snr + tmp12*csr
+		ans21 := tmp21*csr + tmp22*snr
+		ans22 := tmp21*-snr + tmp22*csr
+
+		lhs := []float64{ans11, ans12, ans21, ans22}
+		rhs := []float64{ssmax, 0, 0, ssmin}
+		if !floats.EqualApprox(rhs, lhs, 1e-12) {
+			t.Errorf("SVD mismatch. f = %v, g = %v, h = %v.\nLHS: %v\nRHS: %v", f, g, h, lhs, rhs)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaswp.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaswp.go
new file mode 100644
index 00000000..9d8e08d7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlaswp.go
@@ -0,0 +1,130 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"testing"
+
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dlaswper interface {
+	Dlaswp(n int, a []float64, lda, k1, k2 int, ipiv []int, incX int)
+}
+
+func DlaswpTest(t *testing.T, impl Dlaswper) {
+	for ti, test := range []struct {
+		k1, k2 int
+		ipiv   []int
+		incX   int
+
+		want blas64.General
+	}{
+		{
+			k1:   0,
+			k2:   2,
+			ipiv: []int{0, 1, 2},
+			incX: 1,
+			want: blas64.General{
+				Rows:   4,
+				Cols:   3,
+				Stride: 3,
+				Data: []float64{
+					1, 2, 3,
+					4, 5, 6,
+					7, 8, 9,
+					10, 11, 12,
+				},
+			},
+		},
+		{
+			k1:   0,
+			k2:   2,
+			ipiv: []int{0, 1, 2},
+			incX: -1,
+			want: blas64.General{
+				Rows:   4,
+				Cols:   3,
+				Stride: 3,
+				Data: []float64{
+					1, 2, 3,
+					4, 5, 6,
+					7, 8, 9,
+					10, 11, 12,
+				},
+			},
+		},
+		{
+			k1:   0,
+			k2:   2,
+			ipiv: []int{1, 2, 3},
+			incX: 1,
+			want: blas64.General{
+				Rows:   5,
+				Cols:   3,
+				Stride: 3,
+				Data: []float64{
+					4, 5, 6,
+					7, 8, 9,
+					10, 11, 12,
+					1, 2, 3,
+					13, 14, 15,
+				},
+			},
+		},
+		{
+			k1:   0,
+			k2:   2,
+			ipiv: []int{1, 2, 3},
+			incX: -1,
+			want: blas64.General{
+				Rows:   5,
+				Cols:   3,
+				Stride: 3,
+				Data: []float64{
+					10, 11, 12,
+					1, 2, 3,
+					4, 5, 6,
+					7, 8, 9,
+					13, 14, 15,
+				},
+			},
+		},
+	} {
+		m := test.want.Rows
+		n := test.want.Cols
+		k1 := test.k1
+		k2 := test.k2
+		if len(test.ipiv) != k2+1 {
+			panic("bad length of ipiv")
+		}
+		incX := test.incX
+		for _, extra := range []int{0, 11} {
+			a := zeros(m, n, n+extra)
+			c := 1
+			for i := 0; i < m; i++ {
+				for j := 0; j < n; j++ {
+					a.Data[i*a.Stride+j] = float64(c)
+					c++
+				}
+			}
+
+			ipiv := make([]int, len(test.ipiv))
+			copy(ipiv, test.ipiv)
+
+			impl.Dlaswp(n, a.Data, a.Stride, k1, k2, ipiv, incX)
+
+			prefix := fmt.Sprintf("Case %v (m=%v,n=%v,k1=%v,k2=%v,extra=%v)", ti, m, n, k1, k2, extra)
+			if !generalOutsideAllNaN(a) {
+				t.Errorf("%v: out-of-range write to A", prefix)
+			}
+
+			if !equalApproxGeneral(a, test.want, 0) {
+				t.Errorf("%v: unexpected A\n%v\n%v", prefix, a, test.want)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlasy2.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlasy2.go
new file mode 100644
index 00000000..7ed5ed8c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlasy2.go
@@ -0,0 +1,104 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dlasy2er interface {
+	Dlasy2(tranl, tranr bool, isgn, n1, n2 int, tl []float64, ldtl int, tr []float64, ldtr int, b []float64, ldb int, x []float64, ldx int) (scale, xnorm float64, ok bool)
+}
+
+func Dlasy2Test(t *testing.T, impl Dlasy2er) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, tranl := range []bool{true, false} {
+		for _, tranr := range []bool{true, false} {
+			for _, isgn := range []int{1, -1} {
+				for _, n1 := range []int{0, 1, 2} {
+					for _, n2 := range []int{0, 1, 2} {
+						for _, extra := range []int{0, 1, 2, 13} {
+							for cas := 0; cas < 1000; cas++ {
+								testDlasy2(t, impl, tranl, tranr, isgn, n1, n2, extra, rnd)
+							}
+						}
+					}
+				}
+			}
+		}
+	}
+}
+
+func testDlasy2(t *testing.T, impl Dlasy2er, tranl, tranr bool, isgn, n1, n2, extra int, rnd *rand.Rand) {
+	const tol = 1e-11
+
+	tl := randomGeneral(n1, n1, n1+extra, rnd)
+	tr := randomGeneral(n2, n2, n2+extra, rnd)
+	b := randomGeneral(n1, n2, n2+extra, rnd)
+	x := randomGeneral(n1, n2, n2+extra, rnd)
+
+	scale, xnorm, ok := impl.Dlasy2(tranl, tranr, isgn, n1, n2, tl.Data, tl.Stride, tr.Data, tr.Stride, b.Data, b.Stride, x.Data, x.Stride)
+	if scale > 1 {
+		t.Errorf("invalid value of scale, want <= 1, got %v", scale)
+	}
+	if n1 == 0 || n2 == 0 {
+		return
+	}
+
+	prefix := fmt.Sprintf("Case n1=%v, n2=%v, isgn=%v", n1, n2, isgn)
+
+	// Check any invalid modifications of x.
+	if !generalOutsideAllNaN(x) {
+		t.Errorf("%v: out-of-range write to x\n%v", prefix, x.Data)
+	}
+
+	var xnormWant float64
+	for i := 0; i < n1; i++ {
+		var rowsum float64
+		for j := 0; j < n2; j++ {
+			rowsum += math.Abs(x.Data[i*x.Stride+j])
+		}
+		if rowsum > xnormWant {
+			xnormWant = rowsum
+		}
+	}
+	if xnormWant != xnorm {
+		t.Errorf("%v: unexpected xnorm: want %v, got %v", prefix, xnormWant, xnorm)
+	}
+
+	// Multiply b by scale to get the wanted right-hand side.
+	for i := 0; i < n1; i++ {
+		for j := 0; j < n2; j++ {
+			b.Data[i*b.Stride+j] *= scale
+		}
+	}
+	// Compute the wanted left-hand side.
+	lhsWant := randomGeneral(n1, n2, n2, rnd)
+	if tranl {
+		blas64.Gemm(blas.Trans, blas.NoTrans, 1, tl, x, 0, lhsWant)
+	} else {
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, tl, x, 0, lhsWant)
+	}
+	if tranr {
+		blas64.Gemm(blas.NoTrans, blas.Trans, float64(isgn), x, tr, 1, lhsWant)
+	} else {
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, float64(isgn), x, tr, 1, lhsWant)
+	}
+	// Compare them.
+	for i := 0; i < n1; i++ {
+		for j := 0; j < n2; j++ {
+			diff := lhsWant.Data[i*lhsWant.Stride+j] - b.Data[i*b.Stride+j]
+			if math.Abs(diff) > tol && ok {
+				t.Errorf("%v: unexpected result, diff[%v,%v]=%v", prefix, i, j, diff)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlatrd.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlatrd.go
new file mode 100644
index 00000000..f4d3cddc
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlatrd.go
@@ -0,0 +1,245 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dlatrder interface {
+	Dlatrd(uplo blas.Uplo, n, nb int, a []float64, lda int, e, tau, w []float64, ldw int)
+}
+
+func DlatrdTest(t *testing.T, impl Dlatrder) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
+		for _, test := range []struct {
+			n, nb, lda, ldw int
+		}{
+			{5, 2, 0, 0},
+			{5, 5, 0, 0},
+
+			{5, 3, 10, 11},
+			{5, 5, 10, 11},
+		} {
+			n := test.n
+			nb := test.nb
+			lda := test.lda
+			if lda == 0 {
+				lda = n
+			}
+			ldw := test.ldw
+			if ldw == 0 {
+				ldw = nb
+			}
+
+			a := make([]float64, n*lda)
+			for i := range a {
+				a[i] = rnd.NormFloat64()
+			}
+
+			e := make([]float64, n-1)
+			for i := range e {
+				e[i] = math.NaN()
+			}
+			tau := make([]float64, n-1)
+			for i := range tau {
+				tau[i] = math.NaN()
+			}
+			w := make([]float64, n*ldw)
+			for i := range w {
+				w[i] = math.NaN()
+			}
+
+			aCopy := make([]float64, len(a))
+			copy(aCopy, a)
+
+			impl.Dlatrd(uplo, n, nb, a, lda, e, tau, w, ldw)
+
+			// Construct Q.
+			ldq := n
+			q := blas64.General{
+				Rows:   n,
+				Cols:   n,
+				Stride: ldq,
+				Data:   make([]float64, n*ldq),
+			}
+			for i := 0; i < n; i++ {
+				q.Data[i*ldq+i] = 1
+			}
+			if uplo == blas.Upper {
+				for i := n - 1; i >= n-nb; i-- {
+					if i == 0 {
+						continue
+					}
+					h := blas64.General{
+						Rows: n, Cols: n, Stride: n, Data: make([]float64, n*n),
+					}
+					for j := 0; j < n; j++ {
+						h.Data[j*n+j] = 1
+					}
+					v := blas64.Vector{
+						Inc:  1,
+						Data: make([]float64, n),
+					}
+					for j := 0; j < i-1; j++ {
+						v.Data[j] = a[j*lda+i]
+					}
+					v.Data[i-1] = 1
+
+					blas64.Ger(-tau[i-1], v, v, h)
+
+					qTmp := blas64.General{
+						Rows: n, Cols: n, Stride: n, Data: make([]float64, n*n),
+					}
+					copy(qTmp.Data, q.Data)
+					blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, qTmp, h, 0, q)
+				}
+			} else {
+				for i := 0; i < nb; i++ {
+					if i == n-1 {
+						continue
+					}
+					h := blas64.General{
+						Rows: n, Cols: n, Stride: n, Data: make([]float64, n*n),
+					}
+					for j := 0; j < n; j++ {
+						h.Data[j*n+j] = 1
+					}
+					v := blas64.Vector{
+						Inc:  1,
+						Data: make([]float64, n),
+					}
+					v.Data[i+1] = 1
+					for j := i + 2; j < n; j++ {
+						v.Data[j] = a[j*lda+i]
+					}
+					blas64.Ger(-tau[i], v, v, h)
+
+					qTmp := blas64.General{
+						Rows: n, Cols: n, Stride: n, Data: make([]float64, n*n),
+					}
+					copy(qTmp.Data, q.Data)
+					blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, qTmp, h, 0, q)
+				}
+			}
+			errStr := fmt.Sprintf("isUpper = %v, n = %v, nb = %v", uplo == blas.Upper, n, nb)
+			if !isOrthonormal(q) {
+				t.Errorf("Q not orthonormal. %s", errStr)
+			}
+			aGen := genFromSym(blas64.Symmetric{N: n, Stride: lda, Uplo: uplo, Data: aCopy})
+			if !dlatrdCheckDecomposition(t, uplo, n, nb, e, tau, a, lda, aGen, q) {
+				t.Errorf("Decomposition mismatch. %s", errStr)
+			}
+		}
+	}
+}
+
+// dlatrdCheckDecomposition checks that the first nb rows have been successfully
+// reduced.
+func dlatrdCheckDecomposition(t *testing.T, uplo blas.Uplo, n, nb int, e, tau, a []float64, lda int, aGen, q blas64.General) bool {
+	// Compute Q^T * A * Q.
+	tmp := blas64.General{
+		Rows:   n,
+		Cols:   n,
+		Stride: n,
+		Data:   make([]float64, n*n),
+	}
+
+	ans := blas64.General{
+		Rows:   n,
+		Cols:   n,
+		Stride: n,
+		Data:   make([]float64, n*n),
+	}
+
+	blas64.Gemm(blas.Trans, blas.NoTrans, 1, q, aGen, 0, tmp)
+	blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, tmp, q, 0, ans)
+
+	// Compare with T.
+	if uplo == blas.Upper {
+		for i := n - 1; i >= n-nb; i-- {
+			for j := 0; j < n; j++ {
+				v := ans.Data[i*ans.Stride+j]
+				switch {
+				case i == j:
+					if math.Abs(v-a[i*lda+j]) > 1e-10 {
+						return false
+					}
+				case i == j-1:
+					if math.Abs(a[i*lda+j]-1) > 1e-10 {
+						return false
+					}
+					if math.Abs(v-e[i]) > 1e-10 {
+						return false
+					}
+				case i == j+1:
+				default:
+					if math.Abs(v) > 1e-10 {
+						return false
+					}
+				}
+			}
+		}
+	} else {
+		for i := 0; i < nb; i++ {
+			for j := 0; j < n; j++ {
+				v := ans.Data[i*ans.Stride+j]
+				switch {
+				case i == j:
+					if math.Abs(v-a[i*lda+j]) > 1e-10 {
+						return false
+					}
+				case i == j-1:
+				case i == j+1:
+					if math.Abs(a[i*lda+j]-1) > 1e-10 {
+						return false
+					}
+					if math.Abs(v-e[i-1]) > 1e-10 {
+						return false
+					}
+				default:
+					if math.Abs(v) > 1e-10 {
+						return false
+					}
+				}
+			}
+		}
+	}
+	return true
+}
+
+// genFromSym constructs a (symmetric) general matrix from the data in the
+// symmetric.
+// TODO(btracey): Replace other constructions of this with a call to this function.
+func genFromSym(a blas64.Symmetric) blas64.General {
+	n := a.N
+	lda := a.Stride
+	uplo := a.Uplo
+	b := blas64.General{
+		Rows:   n,
+		Cols:   n,
+		Stride: n,
+		Data:   make([]float64, n*n),
+	}
+
+	for i := 0; i < n; i++ {
+		for j := i; j < n; j++ {
+			v := a.Data[i*lda+j]
+			if uplo == blas.Lower {
+				v = a.Data[j*lda+i]
+			}
+			b.Data[i*n+j] = v
+			b.Data[j*n+i] = v
+		}
+	}
+	return b
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dlatrs.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlatrs.go
new file mode 100644
index 00000000..d2d77897
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dlatrs.go
@@ -0,0 +1,141 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dlatrser interface {
+	Dlatrs(uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, normin bool, n int, a []float64, lda int, x []float64, cnorm []float64) (scale float64)
+}
+
+func DlatrsTest(t *testing.T, impl Dlatrser) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
+		for _, trans := range []blas.Transpose{blas.Trans, blas.NoTrans} {
+			for _, n := range []int{0, 1, 2, 3, 4, 5, 6, 7, 10, 20, 50, 100} {
+				for _, lda := range []int{n, 2*n + 1} {
+					lda = max(1, lda)
+					imats := []int{7, 11, 12, 13, 14, 15, 16, 17, 18}
+					if n < 6 {
+						imats = append(imats, 19)
+					}
+					for _, imat := range imats {
+						testDlatrs(t, impl, imat, uplo, trans, n, lda, rnd)
+					}
+				}
+			}
+		}
+	}
+}
+
+func testDlatrs(t *testing.T, impl Dlatrser, imat int, uplo blas.Uplo, trans blas.Transpose, n, lda int, rnd *rand.Rand) {
+	const tol = 1e-14
+
+	a := nanSlice(n * lda)
+	b := nanSlice(n)
+	work := make([]float64, 3*n)
+
+	// Generate triangular test matrix and right hand side.
+	diag := dlattr(imat, uplo, trans, n, a, lda, b, work, rnd)
+	if imat <= 10 {
+		// b has not been generated.
+		dlarnv(b, 3, rnd)
+	}
+
+	cnorm := nanSlice(n)
+	x := make([]float64, n)
+
+	// Call Dlatrs with normin=false.
+	copy(x, b)
+	scale := impl.Dlatrs(uplo, trans, diag, false, n, a, lda, x, cnorm)
+	prefix := fmt.Sprintf("Case imat=%v (n=%v,lda=%v,trans=%v,uplo=%v,diag=%v", imat, n, lda, trans, uplo, diag)
+	for i, v := range cnorm {
+		if math.IsNaN(v) {
+			t.Errorf("%v: cnorm[%v] not computed (scale=%v,normin=false)", prefix, i, scale)
+		}
+	}
+	resid, hasNaN := dlatrsResidual(uplo, trans, diag, n, a, lda, scale, cnorm, x, b, work[:n])
+	if hasNaN {
+		t.Errorf("%v: unexpected NaN (scale=%v,normin=false)", prefix, scale)
+	} else if resid > tol {
+		t.Errorf("%v: residual %v too large (scale=%v,normin=false)", prefix, resid, scale)
+	}
+
+	// Call Dlatrs with normin=true because cnorm has been filled.
+	copy(x, b)
+	scale = impl.Dlatrs(uplo, trans, diag, true, n, a, lda, x, cnorm)
+	resid, hasNaN = dlatrsResidual(uplo, trans, diag, n, a, lda, scale, cnorm, x, b, work[:n])
+	if hasNaN {
+		t.Errorf("%v: unexpected NaN (scale=%v,normin=true)", prefix, scale)
+	} else if resid > tol {
+		t.Errorf("%v: residual %v too large (scale=%v,normin=true)", prefix, resid, scale)
+	}
+}
+
+// dlatrsResidual returns norm(trans(A)*x-scale*b) / (norm(trans(A))*norm(x)*eps)
+// and whether NaN has been encountered in the process.
+func dlatrsResidual(uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, n int, a []float64, lda int, scale float64, cnorm []float64, x, b, work []float64) (resid float64, hasNaN bool) {
+	if n == 0 {
+		return 0, false
+	}
+
+	// Compute the norm of the triangular matrix A using the column norms
+	// already computed by Dlatrs.
+	var tnorm float64
+	if diag == blas.NonUnit {
+		for j := 0; j < n; j++ {
+			tnorm = math.Max(tnorm, math.Abs(a[j*lda+j])+cnorm[j])
+		}
+	} else {
+		for j := 0; j < n; j++ {
+			tnorm = math.Max(tnorm, 1+cnorm[j])
+		}
+	}
+
+	eps := dlamchE
+	smlnum := dlamchS
+	bi := blas64.Implementation()
+
+	// Compute norm(trans(A)*x-scale*b) / (norm(trans(A))*norm(x)*eps)
+	copy(work, x)
+	ix := bi.Idamax(n, work, 1)
+	xnorm := math.Max(1, math.Abs(work[ix]))
+	xscal := 1 / xnorm / float64(n)
+	bi.Dscal(n, xscal, work, 1)
+	bi.Dtrmv(uplo, trans, diag, n, a, lda, work, 1)
+	bi.Daxpy(n, -scale*xscal, b, 1, work, 1)
+	for _, v := range work {
+		if math.IsNaN(v) {
+			return 1 / eps, true
+		}
+	}
+	ix = bi.Idamax(n, work, 1)
+	resid = math.Abs(work[ix])
+	ix = bi.Idamax(n, x, 1)
+	xnorm = math.Abs(x[ix])
+	if resid*smlnum <= xnorm {
+		if xnorm > 0 {
+			resid /= xnorm
+		}
+	} else if resid > 0 {
+		resid = 1 / eps
+	}
+	if resid*smlnum <= tnorm {
+		if tnorm > 0 {
+			resid /= tnorm
+		}
+	} else if resid > 0 {
+		resid = 1 / eps
+	}
+	return resid, false
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/doc.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/doc.go
new file mode 100644
index 00000000..76da5d18
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package testlapack implements a set of testing routines for Lapack functions.
+package testlapack // import "gonum.org/v1/gonum/lapack/testlapack"
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dorg2l.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dorg2l.go
new file mode 100644
index 00000000..e1f2f155
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dorg2l.go
@@ -0,0 +1,75 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dorg2ler interface {
+	Dorg2l(m, n, k int, a []float64, lda int, tau, work []float64)
+	Dgeql2er
+}
+
+func Dorg2lTest(t *testing.T, impl Dorg2ler) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, test := range []struct {
+		m, n, k, lda int
+	}{
+		{5, 4, 3, 0},
+		{5, 4, 4, 0},
+		{3, 3, 2, 0},
+		{5, 5, 5, 0},
+	} {
+		m := test.m
+		n := test.n
+		k := test.k
+		lda := test.lda
+		if lda == 0 {
+			lda = n
+		}
+
+		a := make([]float64, m*lda)
+		for i := range a {
+			a[i] = rnd.NormFloat64()
+		}
+		tau := nanSlice(max(m, n))
+		work := make([]float64, n)
+		impl.Dgeql2(m, n, a, lda, tau, work)
+
+		aCopy := make([]float64, len(a))
+		copy(aCopy, a)
+		impl.Dorg2l(m, n, k, a, lda, tau[n-k:], work)
+		if !hasOrthonormalColumns(m, n, a, lda) {
+			t.Errorf("Q is not orthonormal. m = %v, n = %v, k = %v", m, n, k)
+		}
+	}
+}
+
+// hasOrthornormalColumns checks that the columns of a are orthonormal.
+func hasOrthonormalColumns(m, n int, a []float64, lda int) bool {
+	for i := 0; i < n; i++ {
+		for j := i; j < n; j++ {
+			dot := blas64.Dot(m,
+				blas64.Vector{Inc: lda, Data: a[i:]},
+				blas64.Vector{Inc: lda, Data: a[j:]},
+			)
+			if i == j {
+				if math.Abs(dot-1) > 1e-10 {
+					return false
+				}
+			} else {
+				if math.Abs(dot) > 1e-10 {
+					return false
+				}
+			}
+		}
+	}
+	return true
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dorg2r.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dorg2r.go
new file mode 100644
index 00000000..beeca34d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dorg2r.go
@@ -0,0 +1,79 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dorg2rer interface {
+	Dgeqrfer
+	Dorg2r(m, n, k int, a []float64, lda int, tau []float64, work []float64)
+}
+
+func Dorg2rTest(t *testing.T, impl Dorg2rer) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, test := range []struct {
+		m, n, k, lda int
+	}{
+		{3, 3, 0, 0},
+		{4, 3, 0, 0},
+		{3, 3, 2, 0},
+		{4, 3, 2, 0},
+
+		{5, 5, 0, 20},
+		{5, 5, 3, 20},
+		{10, 5, 0, 20},
+		{10, 5, 2, 20},
+	} {
+		m := test.m
+		n := test.n
+		lda := test.lda
+		if lda == 0 {
+			lda = test.n
+		}
+		a := make([]float64, m*lda)
+		for i := range a {
+			a[i] = rnd.NormFloat64()
+		}
+		k := min(m, n)
+		tau := make([]float64, k)
+		work := make([]float64, 1)
+		impl.Dgeqrf(m, n, a, lda, tau, work, -1)
+		work = make([]float64, int(work[0]))
+		impl.Dgeqrf(m, n, a, lda, tau, work, len(work))
+
+		k = test.k
+		if k == 0 {
+			k = n
+		}
+		q := constructQK("QR", m, n, k, a, lda, tau)
+
+		impl.Dorg2r(m, n, k, a, lda, tau, work)
+
+		// Check that the first n columns match.
+		same := true
+		for i := 0; i < m; i++ {
+			for j := 0; j < n; j++ {
+				if !floats.EqualWithinAbsOrRel(q.Data[i*q.Stride+j], a[i*lda+j], 1e-12, 1e-12) {
+					same = false
+					break
+				}
+			}
+		}
+		if !same {
+			fmt.Println()
+			fmt.Println("a =")
+			printRowise(a, m, n, lda, false)
+			fmt.Println("q =")
+			printRowise(q.Data, q.Rows, q.Cols, q.Stride, false)
+			t.Errorf("Q mismatch")
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dorgbr.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dorgbr.go
new file mode 100644
index 00000000..3f43fb94
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dorgbr.go
@@ -0,0 +1,156 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dorgbrer interface {
+	Dorgbr(vect lapack.DecompUpdate, m, n, k int, a []float64, lda int, tau, work []float64, lwork int)
+	Dgebrder
+}
+
+func DorgbrTest(t *testing.T, impl Dorgbrer) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, vect := range []lapack.DecompUpdate{lapack.ApplyQ, lapack.ApplyP} {
+		for _, test := range []struct {
+			m, n, k, lda int
+		}{
+			{5, 5, 5, 0},
+			{5, 5, 3, 0},
+			{5, 3, 5, 0},
+			{3, 5, 5, 0},
+			{3, 4, 5, 0},
+			{3, 5, 4, 0},
+			{4, 3, 5, 0},
+			{4, 5, 3, 0},
+			{5, 3, 4, 0},
+			{5, 4, 3, 0},
+
+			{5, 5, 5, 10},
+			{5, 5, 3, 10},
+			{5, 3, 5, 10},
+			{3, 5, 5, 10},
+			{3, 4, 5, 10},
+			{3, 5, 4, 10},
+			{4, 3, 5, 10},
+			{4, 5, 3, 10},
+			{5, 3, 4, 10},
+			{5, 4, 3, 10},
+		} {
+			m := test.m
+			n := test.n
+			k := test.k
+			lda := test.lda
+			// Filter out bad tests
+			if vect == lapack.ApplyQ {
+				if m < n || n < min(m, k) || m < min(m, k) {
+					continue
+				}
+			} else {
+				if n < m || m < min(n, k) || n < min(n, k) {
+					continue
+				}
+			}
+			// Sizes for Dorgbr.
+			var ma, na int
+			if vect == lapack.ApplyQ {
+				if m >= k {
+					ma = m
+					na = k
+				} else {
+					ma = m
+					na = m
+				}
+			} else {
+				if n >= k {
+					ma = k
+					na = n
+				} else {
+					ma = n
+					na = n
+				}
+			}
+			// a eventually needs to store either P or Q, so it must be
+			// sufficiently big.
+			var a []float64
+			if vect == lapack.ApplyQ {
+				lda = max(m, lda)
+				a = make([]float64, m*lda)
+			} else {
+				lda = max(n, lda)
+				a = make([]float64, n*lda)
+			}
+			for i := range a {
+				a[i] = rnd.NormFloat64()
+			}
+
+			nTau := min(ma, na)
+			tauP := make([]float64, nTau)
+			tauQ := make([]float64, nTau)
+			d := make([]float64, nTau)
+			e := make([]float64, nTau)
+			lwork := -1
+			work := make([]float64, 1)
+			impl.Dgebrd(ma, na, a, lda, d, e, tauQ, tauP, work, lwork)
+			work = make([]float64, int(work[0]))
+			lwork = len(work)
+			impl.Dgebrd(ma, na, a, lda, d, e, tauQ, tauP, work, lwork)
+
+			aCopy := make([]float64, len(a))
+			copy(aCopy, a)
+
+			var tau []float64
+			if vect == lapack.ApplyQ {
+				tau = tauQ
+			} else {
+				tau = tauP
+			}
+
+			impl.Dorgbr(vect, m, n, k, a, lda, tau, work, -1)
+			work = make([]float64, int(work[0]))
+			lwork = len(work)
+			impl.Dorgbr(vect, m, n, k, a, lda, tau, work, lwork)
+
+			var ans blas64.General
+			var nRows, nCols int
+			equal := true
+			if vect == lapack.ApplyQ {
+				nRows = m
+				nCols = m
+				if m >= k {
+					nCols = n
+				}
+				ans = constructQPBidiagonal(vect, ma, na, min(m, k), aCopy, lda, tau)
+			} else {
+				nRows = n
+				if k < n {
+					nRows = m
+				}
+				nCols = n
+				ansTmp := constructQPBidiagonal(vect, ma, na, min(k, n), aCopy, lda, tau)
+				// Dorgbr actually computes P^T
+				ans = transposeGeneral(ansTmp)
+			}
+			for i := 0; i < nRows; i++ {
+				for j := 0; j < nCols; j++ {
+					if !floats.EqualWithinAbsOrRel(a[i*lda+j], ans.Data[i*ans.Stride+j], 1e-8, 1e-8) {
+						equal = false
+					}
+				}
+			}
+			if !equal {
+				applyQ := vect == lapack.ApplyQ
+				t.Errorf("Extracted matrix mismatch. applyQ: %v, m = %v, n = %v, k = %v", applyQ, m, n, k)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dorghr.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dorghr.go
new file mode 100644
index 00000000..7311d015
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dorghr.go
@@ -0,0 +1,99 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dorghrer interface {
+	Dorghr(n, ilo, ihi int, a []float64, lda int, tau, work []float64, lwork int)
+
+	Dgehrder
+}
+
+func DorghrTest(t *testing.T, impl Dorghrer) {
+	rnd := rand.New(rand.NewSource(1))
+
+	for _, n := range []int{1, 2, 3, 4, 5, 6, 7, 8, 23, 34} {
+		for _, extra := range []int{0, 1, 13} {
+			for _, optwork := range []bool{true, false} {
+				for cas := 0; cas < 100; cas++ {
+					ilo := rnd.Intn(n)
+					ihi := rnd.Intn(n)
+					if ilo > ihi {
+						ilo, ihi = ihi, ilo
+					}
+					testDorghr(t, impl, n, ilo, ihi, extra, optwork, rnd)
+				}
+			}
+		}
+	}
+	testDorghr(t, impl, 0, 0, -1, 0, false, rnd)
+	testDorghr(t, impl, 0, 0, -1, 0, true, rnd)
+}
+
+func testDorghr(t *testing.T, impl Dorghrer, n, ilo, ihi, extra int, optwork bool, rnd *rand.Rand) {
+	const tol = 1e-14
+
+	// Construct the matrix A with elementary reflectors and scalar factors tau.
+	a := randomGeneral(n, n, n+extra, rnd)
+	var tau []float64
+	if n > 1 {
+		tau = nanSlice(n - 1)
+	}
+	work := nanSlice(max(1, n)) // Minimum work for Dgehrd.
+	impl.Dgehrd(n, ilo, ihi, a.Data, a.Stride, tau, work, len(work))
+
+	// Extract Q for later comparison.
+	q := eye(n, n)
+	qCopy := cloneGeneral(q)
+	for j := ilo; j < ihi; j++ {
+		h := eye(n, n)
+		v := blas64.Vector{
+			Inc:  1,
+			Data: make([]float64, n),
+		}
+		v.Data[j+1] = 1
+		for i := j + 2; i < ihi+1; i++ {
+			v.Data[i] = a.Data[i*a.Stride+j]
+		}
+		blas64.Ger(-tau[j], v, v, h)
+		copy(qCopy.Data, q.Data)
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, qCopy, h, 0, q)
+	}
+
+	if optwork {
+		work = nanSlice(1)
+		impl.Dorghr(n, ilo, ihi, a.Data, a.Stride, tau, work, -1)
+		work = nanSlice(int(work[0]))
+	} else {
+		work = nanSlice(max(1, ihi-ilo))
+	}
+	impl.Dorghr(n, ilo, ihi, a.Data, a.Stride, tau, work, len(work))
+
+	prefix := fmt.Sprintf("Case n=%v, ilo=%v, ihi=%v, extra=%v, optwork=%v", n, ilo, ihi, extra, optwork)
+	if !generalOutsideAllNaN(a) {
+		t.Errorf("%v: out-of-range write to A\n%v", prefix, a.Data)
+	}
+	if !isOrthonormal(a) {
+		t.Errorf("%v: A is not orthogonal\n%v", prefix, a.Data)
+	}
+	for i := 0; i < n; i++ {
+		for j := 0; j < n; j++ {
+			aij := a.Data[i*a.Stride+j]
+			qij := q.Data[i*q.Stride+j]
+			if math.Abs(aij-qij) > tol {
+				t.Errorf("%v: unexpected value of A[%v,%v]. want %v, got %v", prefix, i, j, qij, aij)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dorgl2.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dorgl2.go
new file mode 100644
index 00000000..5ae3fcb1
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dorgl2.go
@@ -0,0 +1,65 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dorgl2er interface {
+	Dgelqfer
+	Dorgl2(m, n, k int, a []float64, lda int, tau []float64, work []float64)
+}
+
+func Dorgl2Test(t *testing.T, impl Dorgl2er) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, test := range []struct {
+		m, n, lda int
+	}{
+		{3, 3, 0},
+		{3, 4, 0},
+
+		{5, 5, 20},
+		{5, 10, 20},
+	} {
+		m := test.m
+		n := test.n
+		lda := test.lda
+		if lda == 0 {
+			lda = test.n
+		}
+		a := make([]float64, m*lda)
+		for i := range a {
+			a[i] = rnd.NormFloat64()
+		}
+		k := min(m, n)
+		tau := make([]float64, k)
+		work := make([]float64, 1)
+		impl.Dgelqf(m, n, a, lda, tau, work, -1)
+		work = make([]float64, int(work[0]))
+		impl.Dgelqf(m, n, a, lda, tau, work, len(work))
+
+		q := constructQ("LQ", m, n, a, lda, tau)
+
+		impl.Dorgl2(m, n, k, a, lda, tau, work)
+
+		// Check that the first m rows match.
+		same := true
+		for i := 0; i < m; i++ {
+			for j := 0; j < n; j++ {
+				if !floats.EqualWithinAbsOrRel(q.Data[i*q.Stride+j], a[i*lda+j], 1e-12, 1e-12) {
+					same = false
+					break
+				}
+			}
+		}
+		if !same {
+			t.Errorf("Q mismatch")
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dorglq.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dorglq.go
new file mode 100644
index 00000000..3d8bb105
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dorglq.go
@@ -0,0 +1,83 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dorglqer interface {
+	Dorgl2er
+	Dorglq(m, n, k int, a []float64, lda int, tau, work []float64, lwork int)
+}
+
+func DorglqTest(t *testing.T, impl Dorglqer) {
+	rnd := rand.New(rand.NewSource(1))
+	// TODO(btracey): Base tests off of nb and nx.
+	for _, test := range []struct{ m, n, k, lda int }{
+		{10, 10, 10, 0},
+		{10, 10, 10, 20},
+		{10, 30, 10, 0},
+		{20, 30, 10, 0},
+
+		{100, 100, 100, 0},
+		{100, 100, 50, 0},
+		{100, 130, 100, 0},
+		{100, 130, 50, 0},
+		{100, 100, 100, 150},
+		{100, 100, 50, 150},
+		{100, 130, 100, 150},
+		{100, 130, 50, 150},
+
+		{200, 200, 200, 0},
+		{200, 200, 150, 0},
+		{200, 230, 200, 0},
+		{200, 230, 150, 0},
+		{200, 200, 200, 250},
+		{200, 200, 150, 250},
+		{200, 230, 200, 250},
+		{200, 230, 150, 250},
+	} {
+		m := test.m
+		n := test.n
+		k := test.k
+		lda := test.lda
+		if lda == 0 {
+			lda = n
+		}
+		a := make([]float64, m*lda)
+		for i := range a {
+			a[i] = rnd.Float64()
+		}
+		work := make([]float64, 1)
+		tau := make([]float64, m)
+		for i := range tau {
+			tau[i] = math.NaN()
+		}
+		// Compute LQ factorization.
+		impl.Dgelqf(m, n, a, lda, tau, work, -1)
+		work = make([]float64, int(work[0]))
+		impl.Dgelqf(m, n, a, lda, tau, work, len(work))
+
+		aUnblocked := make([]float64, len(a))
+		copy(aUnblocked, a)
+		for i := range work {
+			work[i] = math.NaN()
+		}
+		impl.Dorgl2(m, n, k, aUnblocked, lda, tau, work)
+		// make sure work isn't used before initialized
+		for i := range work {
+			work[i] = math.NaN()
+		}
+		impl.Dorglq(m, n, k, a, lda, tau, work, len(work))
+		if !floats.EqualApprox(a, aUnblocked, 1e-10) {
+			t.Errorf("Q Mismatch. m = %d, n = %d, k = %d, lda = %d", m, n, k, lda)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dorgql.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dorgql.go
new file mode 100644
index 00000000..4cf9b22a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dorgql.go
@@ -0,0 +1,130 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dorgqler interface {
+	Dorgql(m, n, k int, a []float64, lda int, tau, work []float64, lwork int)
+
+	Dlarfger
+}
+
+func DorgqlTest(t *testing.T, impl Dorgqler) {
+	const tol = 1e-14
+
+	type Dorg2ler interface {
+		Dorg2l(m, n, k int, a []float64, lda int, tau, work []float64)
+	}
+	dorg2ler, hasDorg2l := impl.(Dorg2ler)
+
+	rnd := rand.New(rand.NewSource(1))
+	for _, m := range []int{0, 1, 2, 3, 4, 5, 7, 10, 15, 30, 50, 150} {
+		for _, extra := range []int{0, 11} {
+			for _, wl := range []worklen{minimumWork, mediumWork, optimumWork} {
+				var k int
+				if m >= 129 {
+					// For large matrices make sure that k
+					// is large enough to trigger blocked
+					// path.
+					k = 129 + rnd.Intn(m-129+1)
+				} else {
+					k = rnd.Intn(m + 1)
+				}
+				n := k + rnd.Intn(m-k+1)
+				if m == 0 || n == 0 {
+					m = 0
+					n = 0
+					k = 0
+				}
+
+				// Generate k elementary reflectors in the last
+				// k columns of A.
+				a := nanGeneral(m, n, n+extra)
+				tau := make([]float64, k)
+				for l := 0; l < k; l++ {
+					jj := m - k + l
+					v := randomSlice(jj, rnd)
+					_, tau[l] = impl.Dlarfg(len(v)+1, rnd.NormFloat64(), v, 1)
+					j := n - k + l
+					for i := 0; i < jj; i++ {
+						a.Data[i*a.Stride+j] = v[i]
+					}
+				}
+				aCopy := cloneGeneral(a)
+
+				// Compute the full matrix Q by forming the
+				// Householder reflectors explicitly.
+				q := eye(m, m)
+				qCopy := eye(m, m)
+				for l := 0; l < k; l++ {
+					h := eye(m, m)
+					jj := m - k + l
+					j := n - k + l
+					v := blas64.Vector{1, make([]float64, m)}
+					for i := 0; i < jj; i++ {
+						v.Data[i] = a.Data[i*a.Stride+j]
+					}
+					v.Data[jj] = 1
+					blas64.Ger(-tau[l], v, v, h)
+					copy(qCopy.Data, q.Data)
+					blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, h, qCopy, 0, q)
+				}
+				// View the last n columns of Q as 'want'.
+				want := blas64.General{
+					Rows:   m,
+					Cols:   n,
+					Stride: q.Stride,
+					Data:   q.Data[m-n:],
+				}
+
+				var lwork int
+				switch wl {
+				case minimumWork:
+					lwork = max(1, n)
+				case mediumWork:
+					work := make([]float64, 1)
+					impl.Dorgql(m, n, k, nil, a.Stride, nil, work, -1)
+					lwork = (int(work[0]) + n) / 2
+					lwork = max(1, lwork)
+				case optimumWork:
+					work := make([]float64, 1)
+					impl.Dorgql(m, n, k, nil, a.Stride, nil, work, -1)
+					lwork = int(work[0])
+				}
+				work := make([]float64, lwork)
+
+				// Compute the last n columns of Q by a call to
+				// Dorgql.
+				impl.Dorgql(m, n, k, a.Data, a.Stride, tau, work, len(work))
+
+				prefix := fmt.Sprintf("Case m=%v,n=%v,k=%v,wl=%v", m, n, k, wl)
+				if !generalOutsideAllNaN(a) {
+					t.Errorf("%v: out-of-range write to A", prefix)
+				}
+				if !equalApproxGeneral(want, a, tol) {
+					t.Errorf("%v: unexpected Q", prefix)
+				}
+
+				// Compute the last n columns of Q by a call to
+				// Dorg2l and check that we get the same result.
+				if !hasDorg2l {
+					continue
+				}
+				dorg2ler.Dorg2l(m, n, k, aCopy.Data, aCopy.Stride, tau, work)
+				if !equalApproxGeneral(aCopy, a, tol) {
+					t.Errorf("%v: mismatch between Dorgql and Dorg2l", prefix)
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dorgqr.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dorgqr.go
new file mode 100644
index 00000000..57306c05
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dorgqr.go
@@ -0,0 +1,83 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dorgqrer interface {
+	Dorg2rer
+	Dorgqr(m, n, k int, a []float64, lda int, tau, work []float64, lwork int)
+}
+
+func DorgqrTest(t *testing.T, impl Dorgqrer) {
+	rnd := rand.New(rand.NewSource(1))
+	// TODO(btracey): Base tests off of nb and nx.
+	for _, test := range []struct{ m, n, k, lda int }{
+		{10, 10, 10, 0},
+		{10, 10, 10, 20},
+		{30, 10, 10, 0},
+		{30, 20, 10, 20},
+
+		{100, 100, 100, 0},
+		{100, 100, 50, 0},
+		{130, 100, 100, 0},
+		{130, 100, 50, 0},
+		{100, 100, 100, 150},
+		{100, 100, 50, 150},
+		{130, 100, 100, 150},
+		{130, 100, 50, 150},
+
+		{200, 200, 200, 0},
+		{200, 200, 150, 0},
+		{230, 200, 200, 0},
+		{230, 200, 150, 0},
+		{200, 200, 200, 250},
+		{200, 200, 150, 250},
+		{230, 200, 200, 250},
+		{230, 200, 150, 250},
+	} {
+		m := test.m
+		n := test.n
+		k := test.k
+		lda := test.lda
+		if lda == 0 {
+			lda = n
+		}
+		a := make([]float64, m*lda)
+		for i := range a {
+			a[i] = rnd.Float64()
+		}
+		work := make([]float64, 1)
+		tau := make([]float64, n)
+		for i := range tau {
+			tau[i] = math.NaN()
+		}
+		// Compute QR factorization.
+		impl.Dgeqrf(m, n, a, lda, tau, work, -1)
+		work = make([]float64, int(work[0]))
+		impl.Dgeqrf(m, n, a, lda, tau, work, len(work))
+
+		aUnblocked := make([]float64, len(a))
+		copy(aUnblocked, a)
+		for i := range work {
+			work[i] = math.NaN()
+		}
+		impl.Dorg2r(m, n, k, aUnblocked, lda, tau, work)
+		// make sure work isn't used before initialized
+		for i := range work {
+			work[i] = math.NaN()
+		}
+		impl.Dorgqr(m, n, k, a, lda, tau, work, len(work))
+		if !floats.EqualApprox(a, aUnblocked, 1e-10) {
+			t.Errorf("Q Mismatch. m = %d, n = %d, k = %d, lda = %d", m, n, k, lda)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dorgtr.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dorgtr.go
new file mode 100644
index 00000000..4f49d1a4
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dorgtr.go
@@ -0,0 +1,136 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dorgtrer interface {
+	Dorgtr(uplo blas.Uplo, n int, a []float64, lda int, tau, work []float64, lwork int)
+	Dsytrder
+}
+
+func DorgtrTest(t *testing.T, impl Dorgtrer) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
+		for _, wl := range []worklen{minimumWork, mediumWork, optimumWork} {
+			for _, test := range []struct {
+				n, lda int
+			}{
+				{1, 0},
+				{2, 0},
+				{3, 0},
+				{6, 0},
+				{33, 0},
+				{100, 0},
+
+				{1, 3},
+				{2, 5},
+				{3, 7},
+				{6, 10},
+				{33, 50},
+				{100, 120},
+			} {
+				n := test.n
+				lda := test.lda
+				if lda == 0 {
+					lda = n
+				}
+				a := make([]float64, n*lda)
+				for i := range a {
+					a[i] = rnd.NormFloat64()
+				}
+				aCopy := make([]float64, len(a))
+				copy(aCopy, a)
+
+				d := make([]float64, n)
+				e := make([]float64, n-1)
+				tau := make([]float64, n-1)
+				work := make([]float64, 1)
+				impl.Dsytrd(uplo, n, a, lda, d, e, tau, work, -1)
+				work = make([]float64, int(work[0]))
+				impl.Dsytrd(uplo, n, a, lda, d, e, tau, work, len(work))
+
+				var lwork int
+				switch wl {
+				case minimumWork:
+					lwork = max(1, n-1)
+				case mediumWork:
+					work := make([]float64, 1)
+					impl.Dorgtr(uplo, n, a, lda, tau, work, -1)
+					lwork = (int(work[0]) + n - 1) / 2
+					lwork = max(1, lwork)
+				case optimumWork:
+					work := make([]float64, 1)
+					impl.Dorgtr(uplo, n, a, lda, tau, work, -1)
+					lwork = int(work[0])
+				}
+				work = nanSlice(lwork)
+
+				impl.Dorgtr(uplo, n, a, lda, tau, work, len(work))
+
+				q := blas64.General{
+					Rows:   n,
+					Cols:   n,
+					Stride: lda,
+					Data:   a,
+				}
+				tri := blas64.General{
+					Rows:   n,
+					Cols:   n,
+					Stride: n,
+					Data:   make([]float64, n*n),
+				}
+				for i := 0; i < n; i++ {
+					tri.Data[i*tri.Stride+i] = d[i]
+					if i != n-1 {
+						tri.Data[i*tri.Stride+i+1] = e[i]
+						tri.Data[(i+1)*tri.Stride+i] = e[i]
+					}
+				}
+
+				aMat := blas64.General{
+					Rows:   n,
+					Cols:   n,
+					Stride: n,
+					Data:   make([]float64, n*n),
+				}
+				if uplo == blas.Upper {
+					for i := 0; i < n; i++ {
+						for j := i; j < n; j++ {
+							v := aCopy[i*lda+j]
+							aMat.Data[i*aMat.Stride+j] = v
+							aMat.Data[j*aMat.Stride+i] = v
+						}
+					}
+				} else {
+					for i := 0; i < n; i++ {
+						for j := 0; j <= i; j++ {
+							v := aCopy[i*lda+j]
+							aMat.Data[i*aMat.Stride+j] = v
+							aMat.Data[j*aMat.Stride+i] = v
+						}
+					}
+				}
+
+				tmp := blas64.General{Rows: n, Cols: n, Stride: n, Data: make([]float64, n*n)}
+				blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, aMat, q, 0, tmp)
+
+				ans := blas64.General{Rows: n, Cols: n, Stride: n, Data: make([]float64, n*n)}
+				blas64.Gemm(blas.Trans, blas.NoTrans, 1, q, tmp, 0, ans)
+
+				if !floats.EqualApprox(ans.Data, tri.Data, 1e-13) {
+					t.Errorf("Recombination mismatch. n = %v, isUpper = %v", n, uplo == blas.Upper)
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dorm2r.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dorm2r.go
new file mode 100644
index 00000000..5e23415d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dorm2r.go
@@ -0,0 +1,139 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dorm2rer interface {
+	Dgeqrfer
+	Dorm2r(side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64)
+}
+
+func Dorm2rTest(t *testing.T, impl Dorm2rer) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, side := range []blas.Side{blas.Left, blas.Right} {
+		for _, trans := range []blas.Transpose{blas.NoTrans, blas.Trans} {
+			for _, test := range []struct {
+				common, adim, cdim, lda, ldc int
+			}{
+				{3, 4, 5, 0, 0},
+				{3, 5, 4, 0, 0},
+				{4, 3, 5, 0, 0},
+				{4, 5, 3, 0, 0},
+				{5, 3, 4, 0, 0},
+				{5, 4, 3, 0, 0},
+				{3, 4, 5, 6, 20},
+				{3, 5, 4, 6, 20},
+				{4, 3, 5, 6, 20},
+				{4, 5, 3, 6, 20},
+				{5, 3, 4, 6, 20},
+				{5, 4, 3, 6, 20},
+				{3, 4, 5, 20, 6},
+				{3, 5, 4, 20, 6},
+				{4, 3, 5, 20, 6},
+				{4, 5, 3, 20, 6},
+				{5, 3, 4, 20, 6},
+				{5, 4, 3, 20, 6},
+			} {
+				var ma, na, mc, nc int
+				if side == blas.Left {
+					ma = test.common
+					na = test.adim
+					mc = test.common
+					nc = test.cdim
+				} else {
+					ma = test.common
+					na = test.adim
+					mc = test.cdim
+					nc = test.common
+				}
+
+				// Generate a random matrix
+				lda := test.lda
+				if lda == 0 {
+					lda = na
+				}
+				a := make([]float64, ma*lda)
+				for i := range a {
+					a[i] = rnd.Float64()
+				}
+				ldc := test.ldc
+				if ldc == 0 {
+					ldc = nc
+				}
+				// Compute random C matrix
+				c := make([]float64, mc*ldc)
+				for i := range c {
+					c[i] = rnd.Float64()
+				}
+
+				// Compute QR
+				k := min(ma, na)
+				tau := make([]float64, k)
+				work := make([]float64, 1)
+				impl.Dgeqrf(ma, na, a, lda, tau, work, -1)
+				work = make([]float64, int(work[0]))
+				impl.Dgeqrf(ma, na, a, lda, tau, work, len(work))
+
+				// Build Q from result
+				q := constructQ("QR", ma, na, a, lda, tau)
+
+				cMat := blas64.General{
+					Rows:   mc,
+					Cols:   nc,
+					Stride: ldc,
+					Data:   make([]float64, len(c)),
+				}
+				copy(cMat.Data, c)
+				cMatCopy := blas64.General{
+					Rows:   cMat.Rows,
+					Cols:   cMat.Cols,
+					Stride: cMat.Stride,
+					Data:   make([]float64, len(cMat.Data)),
+				}
+				copy(cMatCopy.Data, cMat.Data)
+				switch {
+				default:
+					panic("bad test")
+				case side == blas.Left && trans == blas.NoTrans:
+					blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, q, cMatCopy, 0, cMat)
+				case side == blas.Left && trans == blas.Trans:
+					blas64.Gemm(blas.Trans, blas.NoTrans, 1, q, cMatCopy, 0, cMat)
+				case side == blas.Right && trans == blas.NoTrans:
+					blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, cMatCopy, q, 0, cMat)
+				case side == blas.Right && trans == blas.Trans:
+					blas64.Gemm(blas.NoTrans, blas.Trans, 1, cMatCopy, q, 0, cMat)
+				}
+				// Do Dorm2r ard compare
+				if side == blas.Left {
+					work = make([]float64, nc)
+				} else {
+					work = make([]float64, mc)
+				}
+				aCopy := make([]float64, len(a))
+				copy(aCopy, a)
+				tauCopy := make([]float64, len(tau))
+				copy(tauCopy, tau)
+				impl.Dorm2r(side, trans, mc, nc, k, a, lda, tau, c, ldc, work)
+				if !floats.Equal(a, aCopy) {
+					t.Errorf("a changed in call")
+				}
+				if !floats.Equal(tau, tauCopy) {
+					t.Errorf("tau changed in call")
+				}
+				if !floats.EqualApprox(cMat.Data, c, 1e-14) {
+					t.Errorf("Multiplication mismatch.\n Want %v \n got %v.", cMat.Data, c)
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dormbr.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dormbr.go
new file mode 100644
index 00000000..0a44faf5
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dormbr.go
@@ -0,0 +1,164 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dormbrer interface {
+	Dormbr(vect lapack.DecompUpdate, side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64, lwork int)
+	Dgebrder
+}
+
+func DormbrTest(t *testing.T, impl Dormbrer) {
+	rnd := rand.New(rand.NewSource(1))
+	bi := blas64.Implementation()
+	for _, vect := range []lapack.DecompUpdate{lapack.ApplyQ, lapack.ApplyP} {
+		for _, side := range []blas.Side{blas.Left, blas.Right} {
+			for _, trans := range []blas.Transpose{blas.NoTrans, blas.Trans} {
+				for _, wl := range []worklen{minimumWork, mediumWork, optimumWork} {
+					for _, test := range []struct {
+						m, n, k, lda, ldc int
+					}{
+						{3, 4, 5, 0, 0},
+						{3, 5, 4, 0, 0},
+						{4, 3, 5, 0, 0},
+						{4, 5, 3, 0, 0},
+						{5, 3, 4, 0, 0},
+						{5, 4, 3, 0, 0},
+
+						{3, 4, 5, 10, 12},
+						{3, 5, 4, 10, 12},
+						{4, 3, 5, 10, 12},
+						{4, 5, 3, 10, 12},
+						{5, 3, 4, 10, 12},
+						{5, 4, 3, 10, 12},
+
+						{150, 140, 130, 0, 0},
+					} {
+						m := test.m
+						n := test.n
+						k := test.k
+						ldc := test.ldc
+						if ldc == 0 {
+							ldc = n
+						}
+						nq := n
+						nw := m
+						if side == blas.Left {
+							nq = m
+							nw = n
+						}
+
+						// Compute a decomposition.
+						var ma, na int
+						var a []float64
+						if vect == lapack.ApplyQ {
+							ma = nq
+							na = k
+						} else {
+							ma = k
+							na = nq
+						}
+						lda := test.lda
+						if lda == 0 {
+							lda = na
+						}
+						a = make([]float64, ma*lda)
+						for i := range a {
+							a[i] = rnd.NormFloat64()
+						}
+						nTau := min(nq, k)
+						tauP := make([]float64, nTau)
+						tauQ := make([]float64, nTau)
+						d := make([]float64, nTau)
+						e := make([]float64, nTau)
+
+						work := make([]float64, 1)
+						impl.Dgebrd(ma, na, a, lda, d, e, tauQ, tauP, work, -1)
+						work = make([]float64, int(work[0]))
+						impl.Dgebrd(ma, na, a, lda, d, e, tauQ, tauP, work, len(work))
+
+						// Apply and compare update.
+						c := make([]float64, m*ldc)
+						for i := range c {
+							c[i] = rnd.NormFloat64()
+						}
+						cCopy := make([]float64, len(c))
+						copy(cCopy, c)
+
+						var lwork int
+						switch wl {
+						case minimumWork:
+							lwork = nw
+						case optimumWork:
+							impl.Dormbr(vect, side, trans, m, n, k, a, lda, tauQ, c, ldc, work, -1)
+							lwork = int(work[0])
+						case mediumWork:
+							work := make([]float64, 1)
+							impl.Dormbr(vect, side, trans, m, n, k, a, lda, tauQ, c, ldc, work, -1)
+							lwork = (int(work[0]) + nw) / 2
+						}
+						lwork = max(1, lwork)
+						work = make([]float64, lwork)
+
+						if vect == lapack.ApplyQ {
+							impl.Dormbr(vect, side, trans, m, n, k, a, lda, tauQ, c, ldc, work, lwork)
+						} else {
+							impl.Dormbr(vect, side, trans, m, n, k, a, lda, tauP, c, ldc, work, lwork)
+						}
+
+						// Check that the multiplication was correct.
+						cOrig := blas64.General{
+							Rows:   m,
+							Cols:   n,
+							Stride: ldc,
+							Data:   make([]float64, len(cCopy)),
+						}
+						copy(cOrig.Data, cCopy)
+						cAns := blas64.General{
+							Rows:   m,
+							Cols:   n,
+							Stride: ldc,
+							Data:   make([]float64, len(cCopy)),
+						}
+						copy(cAns.Data, cCopy)
+						nb := min(ma, na)
+						var mulMat blas64.General
+						if vect == lapack.ApplyQ {
+							mulMat = constructQPBidiagonal(lapack.ApplyQ, ma, na, nb, a, lda, tauQ)
+						} else {
+							mulMat = constructQPBidiagonal(lapack.ApplyP, ma, na, nb, a, lda, tauP)
+						}
+
+						mulTrans := trans
+
+						if side == blas.Left {
+							bi.Dgemm(mulTrans, blas.NoTrans, m, n, m, 1, mulMat.Data, mulMat.Stride, cOrig.Data, cOrig.Stride, 0, cAns.Data, cAns.Stride)
+						} else {
+							bi.Dgemm(blas.NoTrans, mulTrans, m, n, n, 1, cOrig.Data, cOrig.Stride, mulMat.Data, mulMat.Stride, 0, cAns.Data, cAns.Stride)
+						}
+
+						if !floats.EqualApprox(cAns.Data, c, 1e-13) {
+							isApplyQ := vect == lapack.ApplyQ
+							isLeft := side == blas.Left
+							isTrans := trans == blas.Trans
+
+							t.Errorf("C mismatch. isApplyQ: %v, isLeft: %v, isTrans: %v, m = %v, n = %v, k = %v, lda = %v, ldc = %v",
+								isApplyQ, isLeft, isTrans, m, n, k, lda, ldc)
+						}
+					}
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dormhr.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dormhr.go
new file mode 100644
index 00000000..7b908aa1
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dormhr.go
@@ -0,0 +1,132 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dormhrer interface {
+	Dormhr(side blas.Side, trans blas.Transpose, m, n, ilo, ihi int, a []float64, lda int, tau, c []float64, ldc int, work []float64, lwork int)
+
+	Dgehrder
+}
+
+func DormhrTest(t *testing.T, impl Dormhrer) {
+	rnd := rand.New(rand.NewSource(1))
+
+	for _, side := range []blas.Side{blas.Left, blas.Right} {
+		for _, trans := range []blas.Transpose{blas.NoTrans, blas.Trans} {
+			for _, m := range []int{1, 2, 3, 4, 5, 8, 9, 10, 23} {
+				for _, n := range []int{1, 2, 3, 4, 5, 8, 9, 10, 23} {
+					for _, extra := range []int{0, 1, 13} {
+						for cas := 0; cas < 10; cas++ {
+							nq := m
+							if side == blas.Right {
+								nq = n
+							}
+							ilo := rnd.Intn(nq)
+							ihi := rnd.Intn(nq)
+							if ilo > ihi {
+								ilo, ihi = ihi, ilo
+							}
+							testDormhr(t, impl, side, trans, m, n, ilo, ihi, extra, true, rnd)
+							testDormhr(t, impl, side, trans, m, n, ilo, ihi, extra, false, rnd)
+						}
+					}
+				}
+			}
+		}
+	}
+	for _, side := range []blas.Side{blas.Left, blas.Right} {
+		for _, trans := range []blas.Transpose{blas.NoTrans, blas.Trans} {
+			testDormhr(t, impl, side, trans, 0, 0, 0, -1, 0, true, rnd)
+			testDormhr(t, impl, side, trans, 0, 0, 0, -1, 0, false, rnd)
+		}
+	}
+}
+
+func testDormhr(t *testing.T, impl Dormhrer, side blas.Side, trans blas.Transpose, m, n, ilo, ihi, extra int, optwork bool, rnd *rand.Rand) {
+	const tol = 1e-14
+
+	var nq, nw int
+	switch side {
+	case blas.Left:
+		nq = m
+		nw = n
+	case blas.Right:
+		nq = n
+		nw = m
+	}
+
+	// Compute the elementary reflectors and tau.
+	a := randomGeneral(nq, nq, nq+extra, rnd)
+	var tau []float64
+	if nq > 1 {
+		tau = nanSlice(nq - 1)
+	}
+	work := nanSlice(max(1, nq)) // Minimum work for Dgehrd.
+	impl.Dgehrd(nq, ilo, ihi, a.Data, a.Stride, tau, work, len(work))
+
+	// Construct Q from the elementary reflectors in a and from tau.
+	q := eye(nq, nq)
+	qCopy := eye(nq, nq)
+	for j := ilo; j < ihi; j++ {
+		h := eye(nq, nq)
+		v := blas64.Vector{
+			Inc:  1,
+			Data: make([]float64, nq),
+		}
+		v.Data[j+1] = 1
+		for i := j + 2; i < ihi+1; i++ {
+			v.Data[i] = a.Data[i*a.Stride+j]
+		}
+		blas64.Ger(-tau[j], v, v, h)
+		copy(qCopy.Data, q.Data)
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, qCopy, h, 0, q)
+	}
+
+	c := randomGeneral(m, n, n+extra, rnd)
+
+	// Compute the product of Q and C explicitly.
+	qc := randomGeneral(m, n, n+extra, rnd)
+	if side == blas.Left {
+		blas64.Gemm(trans, blas.NoTrans, 1, q, c, 0, qc)
+	} else {
+		blas64.Gemm(blas.NoTrans, trans, 1, c, q, 0, qc)
+	}
+
+	// Compute the product of Q and C using Dormhr.
+	if optwork {
+		work = nanSlice(1)
+		impl.Dormhr(side, trans, m, n, ilo, ihi, nil, a.Stride, nil, nil, c.Stride, work, -1)
+		work = nanSlice(int(work[0]))
+	} else {
+		work = nanSlice(max(1, nw))
+	}
+	impl.Dormhr(side, trans, m, n, ilo, ihi, a.Data, a.Stride, tau, c.Data, c.Stride, work, len(work))
+
+	// Compare the two answers.
+	prefix := fmt.Sprintf("Case side=%v, trans=%v, m=%v, n=%v, ilo=%v, ihi=%v, extra=%v, optwork=%v",
+		side, trans, m, n, ilo, ihi, extra, optwork)
+	if !generalOutsideAllNaN(c) {
+		t.Errorf("%v: out-of-range write to C\n%v", prefix, c.Data)
+	}
+	for i := 0; i < m; i++ {
+		for j := 0; j < n; j++ {
+			cij := c.Data[i*c.Stride+j]
+			qcij := qc.Data[i*qc.Stride+j]
+			if math.Abs(cij-qcij) > tol {
+				t.Errorf("%v: unexpected value of the QC product at [%v,%v]: want %v, got %v", prefix, i, j, qcij, cij)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dorml2.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dorml2.go
new file mode 100644
index 00000000..909c56e4
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dorml2.go
@@ -0,0 +1,144 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dorml2er interface {
+	Dgelqfer
+	Dorml2(side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64)
+}
+
+func Dorml2Test(t *testing.T, impl Dorml2er) {
+	rnd := rand.New(rand.NewSource(1))
+	// TODO(btracey): This test is not complete, because it
+	// doesn't test individual values of m, n, and k, instead only testing
+	// a specific subset of possible k values.
+	for _, side := range []blas.Side{blas.Left, blas.Right} {
+		for _, trans := range []blas.Transpose{blas.NoTrans, blas.Trans} {
+			for _, test := range []struct {
+				common, adim, cdim, lda, ldc int
+			}{
+				{3, 4, 5, 0, 0},
+				{3, 5, 4, 0, 0},
+				{4, 3, 5, 0, 0},
+				{4, 5, 3, 0, 0},
+				{5, 3, 4, 0, 0},
+				{5, 4, 3, 0, 0},
+
+				{3, 4, 5, 6, 20},
+				{3, 5, 4, 6, 20},
+				{4, 3, 5, 6, 20},
+				{4, 5, 3, 6, 20},
+				{5, 3, 4, 6, 20},
+				{5, 4, 3, 6, 20},
+				{3, 4, 5, 20, 6},
+				{3, 5, 4, 20, 6},
+				{4, 3, 5, 20, 6},
+				{4, 5, 3, 20, 6},
+				{5, 3, 4, 20, 6},
+				{5, 4, 3, 20, 6},
+			} {
+				var ma, na, mc, nc int
+				if side == blas.Left {
+					ma = test.adim
+					na = test.common
+					mc = test.common
+					nc = test.cdim
+				} else {
+					ma = test.adim
+					na = test.common
+					mc = test.cdim
+					nc = test.common
+				}
+				// Generate a random matrix
+				lda := test.lda
+				if lda == 0 {
+					lda = na
+				}
+				a := make([]float64, ma*lda)
+				for i := range a {
+					a[i] = rnd.Float64()
+				}
+				ldc := test.ldc
+				if ldc == 0 {
+					ldc = nc
+				}
+				// Compute random C matrix
+				c := make([]float64, mc*ldc)
+				for i := range c {
+					c[i] = rnd.Float64()
+				}
+
+				// Compute LQ
+				k := min(ma, na)
+				tau := make([]float64, k)
+				work := make([]float64, 1)
+				impl.Dgelqf(ma, na, a, lda, tau, work, -1)
+				work = make([]float64, int(work[0]))
+				impl.Dgelqf(ma, na, a, lda, tau, work, len(work))
+
+				// Build Q from result
+				q := constructQ("LQ", ma, na, a, lda, tau)
+
+				cMat := blas64.General{
+					Rows:   mc,
+					Cols:   nc,
+					Stride: ldc,
+					Data:   make([]float64, len(c)),
+				}
+				copy(cMat.Data, c)
+				cMatCopy := blas64.General{
+					Rows:   cMat.Rows,
+					Cols:   cMat.Cols,
+					Stride: cMat.Stride,
+					Data:   make([]float64, len(cMat.Data)),
+				}
+				copy(cMatCopy.Data, cMat.Data)
+				switch {
+				default:
+					panic("bad test")
+				case side == blas.Left && trans == blas.NoTrans:
+					blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, q, cMatCopy, 0, cMat)
+				case side == blas.Left && trans == blas.Trans:
+					blas64.Gemm(blas.Trans, blas.NoTrans, 1, q, cMatCopy, 0, cMat)
+				case side == blas.Right && trans == blas.NoTrans:
+					blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, cMatCopy, q, 0, cMat)
+				case side == blas.Right && trans == blas.Trans:
+					blas64.Gemm(blas.NoTrans, blas.Trans, 1, cMatCopy, q, 0, cMat)
+				}
+				// Do Dorm2r ard compare
+				if side == blas.Left {
+					work = make([]float64, nc)
+				} else {
+					work = make([]float64, mc)
+				}
+				aCopy := make([]float64, len(a))
+				copy(aCopy, a)
+				tauCopy := make([]float64, len(tau))
+				copy(tauCopy, tau)
+				impl.Dorml2(side, trans, mc, nc, k, a, lda, tau, c, ldc, work)
+				if !floats.Equal(a, aCopy) {
+					t.Errorf("a changed in call")
+				}
+				if !floats.Equal(tau, tauCopy) {
+					t.Errorf("tau changed in call")
+				}
+				if !floats.EqualApprox(cMat.Data, c, 1e-14) {
+					isLeft := side == blas.Left
+					isTrans := trans == blas.Trans
+					t.Errorf("Multiplication mismatch. IsLeft = %v. IsTrans = %v", isLeft, isTrans)
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dormlq.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dormlq.go
new file mode 100644
index 00000000..19302e21
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dormlq.go
@@ -0,0 +1,130 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dormlqer interface {
+	Dorml2er
+	Dormlq(side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64, lwork int)
+}
+
+func DormlqTest(t *testing.T, impl Dormlqer) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, side := range []blas.Side{blas.Left, blas.Right} {
+		for _, trans := range []blas.Transpose{blas.NoTrans, blas.Trans} {
+			for _, wl := range []worklen{minimumWork, mediumWork, optimumWork} {
+				for _, test := range []struct {
+					common, adim, cdim, lda, ldc int
+				}{
+					{0, 0, 0, 0, 0},
+					{6, 7, 8, 0, 0},
+					{6, 8, 7, 0, 0},
+					{7, 6, 8, 0, 0},
+					{7, 8, 6, 0, 0},
+					{8, 6, 7, 0, 0},
+					{8, 7, 6, 0, 0},
+					{100, 200, 300, 0, 0},
+					{100, 300, 200, 0, 0},
+					{200, 100, 300, 0, 0},
+					{200, 300, 100, 0, 0},
+					{300, 100, 200, 0, 0},
+					{300, 200, 100, 0, 0},
+					{100, 200, 300, 400, 500},
+					{100, 300, 200, 400, 500},
+					{200, 100, 300, 400, 500},
+					{200, 300, 100, 400, 500},
+					{300, 100, 200, 400, 500},
+					{300, 200, 100, 400, 500},
+					{100, 200, 300, 500, 400},
+					{100, 300, 200, 500, 400},
+					{200, 100, 300, 500, 400},
+					{200, 300, 100, 500, 400},
+					{300, 100, 200, 500, 400},
+					{300, 200, 100, 500, 400},
+				} {
+					var ma, na, mc, nc int
+					if side == blas.Left {
+						ma = test.adim
+						na = test.common
+						mc = test.common
+						nc = test.cdim
+					} else {
+						ma = test.adim
+						na = test.common
+						mc = test.cdim
+						nc = test.common
+					}
+					// Generate a random matrix
+					lda := test.lda
+					if lda == 0 {
+						lda = na
+					}
+					a := make([]float64, ma*lda)
+					for i := range a {
+						a[i] = rnd.Float64()
+					}
+					// Compute random C matrix
+					ldc := test.ldc
+					if ldc == 0 {
+						ldc = nc
+					}
+					c := make([]float64, mc*ldc)
+					for i := range c {
+						c[i] = rnd.Float64()
+					}
+
+					// Compute LQ
+					k := min(ma, na)
+					tau := make([]float64, k)
+					work := make([]float64, 1)
+					impl.Dgelqf(ma, na, a, lda, tau, work, -1)
+					work = make([]float64, int(work[0]))
+					impl.Dgelqf(ma, na, a, lda, tau, work, len(work))
+
+					cCopy := make([]float64, len(c))
+					copy(cCopy, c)
+					ans := make([]float64, len(c))
+					copy(ans, cCopy)
+
+					var nw int
+					if side == blas.Left {
+						nw = nc
+					} else {
+						nw = mc
+					}
+					work = make([]float64, max(1, nw))
+					impl.Dorml2(side, trans, mc, nc, k, a, lda, tau, ans, ldc, work)
+
+					var lwork int
+					switch wl {
+					case minimumWork:
+						lwork = nw
+					case optimumWork:
+						impl.Dormlq(side, trans, mc, nc, k, a, lda, tau, c, ldc, work, -1)
+						lwork = int(work[0])
+					case mediumWork:
+						work := make([]float64, 1)
+						impl.Dormlq(side, trans, mc, nc, k, a, lda, tau, c, ldc, work, -1)
+						lwork = (int(work[0]) + nw) / 2
+					}
+					lwork = max(1, lwork)
+					work = make([]float64, lwork)
+
+					impl.Dormlq(side, trans, mc, nc, k, a, lda, tau, c, ldc, work, lwork)
+					if !floats.EqualApprox(c, ans, 1e-13) {
+						t.Errorf("Dormqr and Dorm2r results mismatch")
+					}
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dormqr.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dormqr.go
new file mode 100644
index 00000000..cfacd81b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dormqr.go
@@ -0,0 +1,154 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dormqrer interface {
+	Dorm2rer
+	Dormqr(side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64, lwork int)
+}
+
+func DormqrTest(t *testing.T, impl Dormqrer) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, side := range []blas.Side{blas.Left, blas.Right} {
+		for _, trans := range []blas.Transpose{blas.NoTrans, blas.Trans} {
+			for _, test := range []struct {
+				common, adim, cdim, lda, ldc int
+			}{
+				{6, 7, 8, 0, 0},
+				{6, 8, 7, 0, 0},
+				{7, 6, 8, 0, 0},
+				{7, 8, 6, 0, 0},
+				{8, 6, 7, 0, 0},
+				{8, 7, 6, 0, 0},
+				{100, 200, 300, 0, 0},
+				{100, 300, 200, 0, 0},
+				{200, 100, 300, 0, 0},
+				{200, 300, 100, 0, 0},
+				{300, 100, 200, 0, 0},
+				{300, 200, 100, 0, 0},
+				{100, 200, 300, 400, 500},
+				{100, 300, 200, 400, 500},
+				{200, 100, 300, 400, 500},
+				{200, 300, 100, 400, 500},
+				{300, 100, 200, 400, 500},
+				{300, 200, 100, 400, 500},
+				{100, 200, 300, 500, 400},
+				{100, 300, 200, 500, 400},
+				{200, 100, 300, 500, 400},
+				{200, 300, 100, 500, 400},
+				{300, 100, 200, 500, 400},
+				{300, 200, 100, 500, 400},
+			} {
+				var ma, na, mc, nc int
+				if side == blas.Left {
+					ma = test.common
+					na = test.adim
+					mc = test.common
+					nc = test.cdim
+				} else {
+					ma = test.common
+					na = test.adim
+					mc = test.cdim
+					nc = test.common
+				}
+				// Generate a random matrix
+				lda := test.lda
+				if lda == 0 {
+					lda = na
+				}
+				a := make([]float64, ma*lda)
+				for i := range a {
+					a[i] = rnd.Float64()
+				}
+				// Compute random C matrix
+				ldc := test.ldc
+				if ldc == 0 {
+					ldc = nc
+				}
+				c := make([]float64, mc*ldc)
+				for i := range c {
+					c[i] = rnd.Float64()
+				}
+
+				// Compute QR
+				k := min(ma, na)
+				tau := make([]float64, k)
+				work := make([]float64, 1)
+				impl.Dgeqrf(ma, na, a, lda, tau, work, -1)
+				work = make([]float64, int(work[0]))
+				impl.Dgeqrf(ma, na, a, lda, tau, work, len(work))
+
+				cCopy := make([]float64, len(c))
+				copy(cCopy, c)
+				ans := make([]float64, len(c))
+				copy(ans, cCopy)
+
+				if side == blas.Left {
+					work = make([]float64, nc)
+				} else {
+					work = make([]float64, mc)
+				}
+				impl.Dorm2r(side, trans, mc, nc, k, a, lda, tau, ans, ldc, work)
+
+				// Make sure Dorm2r and Dormqr match with small work
+				for i := range work {
+					work[i] = rnd.Float64()
+				}
+				copy(c, cCopy)
+				impl.Dormqr(side, trans, mc, nc, k, a, lda, tau, c, ldc, work, len(work))
+				if !floats.EqualApprox(c, ans, 1e-12) {
+					t.Errorf("Dormqr and Dorm2r mismatch for small work")
+				}
+
+				// Try with the optimum amount of work
+				copy(c, cCopy)
+				impl.Dormqr(side, trans, mc, nc, k, nil, lda, nil, nil, ldc, work, -1)
+				work = make([]float64, int(work[0]))
+				for i := range work {
+					work[i] = rnd.Float64()
+				}
+				impl.Dormqr(side, trans, mc, nc, k, a, lda, tau, c, ldc, work, len(work))
+				if !floats.EqualApprox(c, ans, 1e-12) {
+					t.Errorf("Dormqr and Dorm2r mismatch for full work")
+					fmt.Println("ccopy")
+					for i := 0; i < mc; i++ {
+						fmt.Println(cCopy[i*ldc : (i+1)*ldc])
+					}
+					fmt.Println("ans =")
+					for i := 0; i < mc; i++ {
+						fmt.Println(ans[i*ldc : (i+1)*ldc])
+					}
+					fmt.Println("c =")
+					for i := 0; i < mc; i++ {
+						fmt.Println(c[i*ldc : (i+1)*ldc])
+					}
+				}
+
+				// Try with amount of work that is less than
+				// optimal but still long enough to use the
+				// blocked code.
+				copy(c, cCopy)
+				if side == blas.Left {
+					work = make([]float64, 3*nc)
+				} else {
+					work = make([]float64, 3*mc)
+				}
+				impl.Dormqr(side, trans, mc, nc, k, a, lda, tau, c, ldc, work, len(work))
+				if !floats.EqualApprox(c, ans, 1e-12) {
+					t.Errorf("Dormqr and Dorm2r mismatch for medium work")
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dormr2.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dormr2.go
new file mode 100644
index 00000000..94a13488
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dormr2.go
@@ -0,0 +1,137 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dormr2er interface {
+	Dgerqf(m, n int, a []float64, lda int, tau, work []float64, lwork int)
+	Dormr2(side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64)
+}
+
+func Dormr2Test(t *testing.T, impl Dormr2er) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, side := range []blas.Side{blas.Left, blas.Right} {
+		for _, trans := range []blas.Transpose{blas.NoTrans, blas.Trans} {
+			for _, test := range []struct {
+				common, adim, cdim, lda, ldc int
+			}{
+				{3, 4, 5, 0, 0},
+				{3, 5, 4, 0, 0},
+				{4, 3, 5, 0, 0},
+				{4, 5, 3, 0, 0},
+				{5, 3, 4, 0, 0},
+				{5, 4, 3, 0, 0},
+				{3, 4, 5, 6, 20},
+				{3, 5, 4, 6, 20},
+				{4, 3, 5, 6, 20},
+				{4, 5, 3, 6, 20},
+				{5, 3, 4, 6, 20},
+				{5, 4, 3, 6, 20},
+				{3, 4, 5, 20, 6},
+				{3, 5, 4, 20, 6},
+				{4, 3, 5, 20, 6},
+				{4, 5, 3, 20, 6},
+				{5, 3, 4, 20, 6},
+				{5, 4, 3, 20, 6},
+			} {
+				ma := test.adim
+				na := test.common
+				var mc, nc int
+				if side == blas.Left {
+					mc = test.common
+					nc = test.cdim
+				} else {
+					mc = test.cdim
+					nc = test.common
+				}
+
+				// Generate a random matrix
+				lda := test.lda
+				if lda == 0 {
+					lda = na
+				}
+				a := make([]float64, ma*lda)
+				for i := range a {
+					a[i] = rnd.Float64()
+				}
+				ldc := test.ldc
+				if ldc == 0 {
+					ldc = nc
+				}
+				// Compute random C matrix
+				c := make([]float64, mc*ldc)
+				for i := range c {
+					c[i] = rnd.Float64()
+				}
+
+				// Compute RQ
+				k := min(ma, na)
+				tau := make([]float64, k)
+				work := make([]float64, 1)
+				impl.Dgerqf(ma, na, a, lda, tau, work, -1)
+				work = make([]float64, int(work[0]))
+				impl.Dgerqf(ma, na, a, lda, tau, work, len(work))
+
+				// Build Q from result
+				q := constructQ("RQ", ma, na, a, lda, tau)
+
+				cMat := blas64.General{
+					Rows:   mc,
+					Cols:   nc,
+					Stride: ldc,
+					Data:   make([]float64, len(c)),
+				}
+				copy(cMat.Data, c)
+				cMatCopy := blas64.General{
+					Rows:   cMat.Rows,
+					Cols:   cMat.Cols,
+					Stride: cMat.Stride,
+					Data:   make([]float64, len(cMat.Data)),
+				}
+				copy(cMatCopy.Data, cMat.Data)
+				switch {
+				default:
+					panic("bad test")
+				case side == blas.Left && trans == blas.NoTrans:
+					blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, q, cMatCopy, 0, cMat)
+				case side == blas.Left && trans == blas.Trans:
+					blas64.Gemm(blas.Trans, blas.NoTrans, 1, q, cMatCopy, 0, cMat)
+				case side == blas.Right && trans == blas.NoTrans:
+					blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, cMatCopy, q, 0, cMat)
+				case side == blas.Right && trans == blas.Trans:
+					blas64.Gemm(blas.NoTrans, blas.Trans, 1, cMatCopy, q, 0, cMat)
+				}
+				// Do Dorm2r ard compare
+				if side == blas.Left {
+					work = make([]float64, nc)
+				} else {
+					work = make([]float64, mc)
+				}
+				aCopy := make([]float64, len(a))
+				copy(aCopy, a)
+				tauCopy := make([]float64, len(tau))
+				copy(tauCopy, tau)
+				impl.Dormr2(side, trans, mc, nc, k, a[(ma-k)*lda:], lda, tau, c, ldc, work)
+				if !floats.Equal(a, aCopy) {
+					t.Errorf("a changed in call")
+				}
+				if !floats.Equal(tau, tauCopy) {
+					t.Errorf("tau changed in call")
+				}
+				if !floats.EqualApprox(cMat.Data, c, 1e-14) {
+					t.Errorf("Multiplication mismatch.\n Want %v \n got %v.", cMat.Data, c)
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dpbtf2.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dpbtf2.go
new file mode 100644
index 00000000..7f5498b8
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dpbtf2.go
@@ -0,0 +1,47 @@
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+type Dpbtf2er interface {
+	Dpbtf2(ul blas.Uplo, n, kd int, ab []float64, ldab int) (ok bool)
+	Dpotrfer
+}
+
+func Dpbtf2Test(t *testing.T, impl Dpbtf2er) {
+	// Test random symmetric banded matrices against the full version.
+	rnd := rand.New(rand.NewSource(1))
+
+	for _, n := range []int{5, 10, 20} {
+		for _, kb := range []int{0, 1, 3, n - 1} {
+			for _, ldoff := range []int{0, 4} {
+				for _, ul := range []blas.Uplo{blas.Upper, blas.Lower} {
+					ldab := kb + 1 + ldoff
+					sym, band := randSymBand(ul, n, ldab, kb, rnd)
+
+					// Compute the Cholesky decomposition of the symmetric matrix.
+					ok := impl.Dpotrf(ul, sym.N, sym.Data, sym.Stride)
+					if !ok {
+						panic("bad test: symmetric cholesky decomp failed")
+					}
+
+					// Compute the Cholesky decomposition of the banded matrix.
+					ok = impl.Dpbtf2(band.Uplo, band.N, band.K, band.Data, band.Stride)
+					if !ok {
+						t.Errorf("SymBand cholesky decomp failed")
+					}
+
+					// Compare the result to the Symmetric decomposition.
+					sb := symBandToSym(ul, band.Data, n, kb, ldab)
+					if !equalApproxSymmetric(sym, sb, 1e-10) {
+						t.Errorf("chol mismatch banded and sym. n = %v, kb = %v, ldoff = %v", n, kb, ldoff)
+					}
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dpocon.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dpocon.go
new file mode 100644
index 00000000..87b6cca0
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dpocon.go
@@ -0,0 +1,157 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"log"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dpoconer interface {
+	Dpotrfer
+	Dgeconer
+	Dlansy(norm lapack.MatrixNorm, uplo blas.Uplo, n int, a []float64, lda int, work []float64) float64
+	Dpocon(uplo blas.Uplo, n int, a []float64, lda int, anorm float64, work []float64, iwork []int) float64
+}
+
+func DpoconTest(t *testing.T, impl Dpoconer) {
+	for _, test := range []struct {
+		a    []float64
+		n    int
+		cond float64
+		uplo blas.Uplo
+	}{
+		{
+			a: []float64{
+				89, 59, 77,
+				0, 107, 59,
+				0, 0, 89,
+			},
+			uplo: blas.Upper,
+			n:    3,
+			cond: 0.050052137643379,
+		},
+		{
+			a: []float64{
+				89, 0, 0,
+				59, 107, 0,
+				77, 59, 89,
+			},
+			uplo: blas.Lower,
+			n:    3,
+			cond: 0.050052137643379,
+		},
+		// Dgecon does not match Dpocon for this case. https://github.com/xianyi/OpenBLAS/issues/664.
+		{
+			a: []float64{
+				2.9995576045549965, -2.0898894566158663, 3.965560740124006,
+				0, 1.9634729526261008, -2.8681002706874104,
+				0, 0, 5.502416670471008,
+			},
+			uplo: blas.Upper,
+			n:    3,
+			cond: 0.024054837369015203,
+		},
+	} {
+		n := test.n
+		a := make([]float64, len(test.a))
+		copy(a, test.a)
+		lda := n
+		uplo := test.uplo
+		work := make([]float64, 3*n)
+		anorm := impl.Dlansy(lapack.MaxColumnSum, uplo, n, a, lda, work)
+		// Compute cholesky decomposition
+		ok := impl.Dpotrf(uplo, n, a, lda)
+		if !ok {
+			t.Errorf("Bad test, matrix not positive definite")
+			continue
+		}
+		iwork := make([]int, n)
+		cond := impl.Dpocon(uplo, n, a, lda, anorm, work, iwork)
+		// Error if not the same order, otherwise log the difference.
+		if !floats.EqualWithinAbsOrRel(cond, test.cond, 1e0, 1e0) {
+			t.Errorf("Cond mismatch. Want %v, got %v.", test.cond, cond)
+		} else if !floats.EqualWithinAbsOrRel(cond, test.cond, 1e-14, 1e-14) {
+			log.Printf("Dpocon cond mismatch. Want %v, got %v.", test.cond, cond)
+		}
+	}
+	rnd := rand.New(rand.NewSource(1))
+	bi := blas64.Implementation()
+	// Randomized tests compared against Dgecon.
+	for _, uplo := range []blas.Uplo{blas.Lower, blas.Upper} {
+		for _, test := range []struct {
+			n, lda int
+		}{
+			{3, 0},
+			{3, 5},
+		} {
+			for trial := 0; trial < 100; trial++ {
+				n := test.n
+				lda := test.lda
+				if lda == 0 {
+					lda = n
+				}
+				a := make([]float64, n*lda)
+				for i := range a {
+					a[i] = rnd.NormFloat64()
+				}
+
+				// Multiply a by itself to make it symmetric positive definite.
+				aCopy := make([]float64, len(a))
+				copy(aCopy, a)
+				bi.Dgemm(blas.Trans, blas.NoTrans, n, n, n, 1, aCopy, lda, aCopy, lda, 0, a, lda)
+
+				aDat := make([]float64, len(aCopy))
+				copy(aDat, a)
+
+				aDense := make([]float64, len(a))
+				if uplo == blas.Upper {
+					for i := 0; i < n; i++ {
+						for j := i; j < n; j++ {
+							v := a[i*lda+j]
+							aDense[i*lda+j] = v
+							aDense[j*lda+i] = v
+						}
+					}
+				} else {
+					for i := 0; i < n; i++ {
+						for j := 0; j <= i; j++ {
+							v := a[i*lda+j]
+							aDense[i*lda+j] = v
+							aDense[j*lda+i] = v
+						}
+					}
+				}
+				work := make([]float64, 4*n)
+				iwork := make([]int, n)
+
+				anorm := impl.Dlansy(lapack.MaxColumnSum, uplo, n, a, lda, work)
+				ok := impl.Dpotrf(uplo, n, a, lda)
+				if !ok {
+					t.Errorf("Bad test, matrix not positive definite")
+					continue
+				}
+				got := impl.Dpocon(uplo, n, a, lda, anorm, work, iwork)
+
+				denseNorm := impl.Dlange(lapack.MaxColumnSum, n, n, aDense, lda, work)
+				ipiv := make([]int, n)
+				impl.Dgetrf(n, n, aDense, lda, ipiv)
+				want := impl.Dgecon(lapack.MaxColumnSum, n, aDense, lda, denseNorm, work, iwork)
+				// Error if not the same order, otherwise log the difference.
+				if !floats.EqualWithinAbsOrRel(want, got, 1e0, 1e0) {
+					t.Errorf("Dpocon and Dgecon mismatch. Dpocon %v, Dgecon %v.", got, want)
+				} else if !floats.EqualWithinAbsOrRel(want, got, 1e-14, 1e-14) {
+					log.Printf("Dpocon and Dgecon mismatch. Dpocon %v, Dgecon %v.", got, want)
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dpotf2.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dpotf2.go
new file mode 100644
index 00000000..d6e1691c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dpotf2.go
@@ -0,0 +1,117 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dpotf2er interface {
+	Dpotf2(ul blas.Uplo, n int, a []float64, lda int) (ok bool)
+}
+
+func Dpotf2Test(t *testing.T, impl Dpotf2er) {
+	for _, test := range []struct {
+		a   [][]float64
+		pos bool
+		U   [][]float64
+	}{
+		{
+			a: [][]float64{
+				{23, 37, 34, 32},
+				{108, 71, 48, 48},
+				{109, 109, 67, 58},
+				{106, 107, 106, 63},
+			},
+			pos: true,
+			U: [][]float64{
+				{4.795831523312719, 7.715033320111766, 7.089490077940543, 6.672461249826393},
+				{0, 3.387958215439679, -1.976308959006481, -1.026654004678691},
+				{0, 0, 3.582364210034111, 2.419258947036024},
+				{0, 0, 0, 3.401680257083044},
+			},
+		},
+		{
+			a: [][]float64{
+				{8, 2},
+				{2, 4},
+			},
+			pos: true,
+			U: [][]float64{
+				{2.82842712474619, 0.707106781186547},
+				{0, 1.870828693386971},
+			},
+		},
+	} {
+		testDpotf2(t, impl, test.pos, test.a, test.U, len(test.a[0]), blas.Upper)
+		testDpotf2(t, impl, test.pos, test.a, test.U, len(test.a[0])+5, blas.Upper)
+		aT := transpose(test.a)
+		L := transpose(test.U)
+		testDpotf2(t, impl, test.pos, aT, L, len(test.a[0]), blas.Lower)
+		testDpotf2(t, impl, test.pos, aT, L, len(test.a[0])+5, blas.Lower)
+	}
+}
+
+func testDpotf2(t *testing.T, impl Dpotf2er, testPos bool, a, ans [][]float64, stride int, ul blas.Uplo) {
+	aFlat := flattenTri(a, stride, ul)
+	ansFlat := flattenTri(ans, stride, ul)
+	pos := impl.Dpotf2(ul, len(a[0]), aFlat, stride)
+	if pos != testPos {
+		t.Errorf("Positive definite mismatch: Want %v, Got %v", testPos, pos)
+		return
+	}
+	if testPos && !floats.EqualApprox(ansFlat, aFlat, 1e-14) {
+		t.Errorf("Result mismatch: Want %v, Got  %v", ansFlat, aFlat)
+	}
+}
+
+// flattenTri  with a certain stride. stride must be >= dimension. Puts repeatable
+// nonce values in non-accessed places
+func flattenTri(a [][]float64, stride int, ul blas.Uplo) []float64 {
+	m := len(a)
+	n := len(a[0])
+	if stride < n {
+		panic("bad stride")
+	}
+	upper := ul == blas.Upper
+	v := make([]float64, m*stride)
+	count := 1000.0
+	for i := 0; i < m; i++ {
+		for j := 0; j < stride; j++ {
+			if j >= n || (upper && j < i) || (!upper && j > i) {
+				// not accessed, so give a unique crazy number
+				v[i*stride+j] = count
+				count++
+				continue
+			}
+			v[i*stride+j] = a[i][j]
+		}
+	}
+	return v
+}
+
+func transpose(a [][]float64) [][]float64 {
+	m := len(a)
+	n := len(a[0])
+	if m != n {
+		panic("not square")
+	}
+	aNew := make([][]float64, m)
+	for i := 0; i < m; i++ {
+		aNew[i] = make([]float64, n)
+	}
+	for i := 0; i < m; i++ {
+		if len(a[i]) != n {
+			panic("bad n size")
+		}
+		for j := 0; j < n; j++ {
+			aNew[j][i] = a[i][j]
+		}
+	}
+	return aNew
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dpotrf.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dpotrf.go
new file mode 100644
index 00000000..d4318228
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dpotrf.go
@@ -0,0 +1,135 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dpotrfer interface {
+	Dpotrf(ul blas.Uplo, n int, a []float64, lda int) (ok bool)
+}
+
+func DpotrfTest(t *testing.T, impl Dpotrfer) {
+	const tol = 1e-13
+	rnd := rand.New(rand.NewSource(1))
+	bi := blas64.Implementation()
+	for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
+		for tc, test := range []struct {
+			n   int
+			lda int
+		}{
+			{1, 0},
+			{2, 0},
+			{3, 0},
+			{10, 0},
+			{30, 0},
+			{63, 0},
+			{65, 0},
+			{127, 0},
+			{129, 0},
+			{500, 0},
+			{1, 10},
+			{2, 10},
+			{3, 10},
+			{10, 20},
+			{30, 50},
+			{63, 100},
+			{65, 100},
+			{127, 200},
+			{129, 200},
+			{500, 600},
+		} {
+			n := test.n
+
+			// Random diagonal matrix D with positive entries.
+			d := make([]float64, n)
+			Dlatm1(d, 4, 10000, false, 1, rnd)
+
+			// Construct a positive definite matrix A as
+			//  A = U * D * U^T
+			// where U is a random orthogonal matrix.
+			lda := test.lda
+			if lda == 0 {
+				lda = n
+			}
+			a := make([]float64, n*lda)
+			Dlagsy(n, 0, d, a, lda, rnd, make([]float64, 2*n))
+
+			aCopy := make([]float64, len(a))
+			copy(aCopy, a)
+
+			ok := impl.Dpotrf(uplo, n, a, lda)
+			if !ok {
+				t.Errorf("Case %v: unexpected failure for positive definite matrix", tc)
+				continue
+			}
+
+			switch uplo {
+			case blas.Upper:
+				for i := 0; i < n; i++ {
+					for j := 0; j < i; j++ {
+						a[i*lda+j] = 0
+					}
+				}
+			case blas.Lower:
+				for i := 0; i < n; i++ {
+					for j := i + 1; j < n; j++ {
+						a[i*lda+j] = 0
+					}
+				}
+			default:
+				panic("bad uplo")
+			}
+
+			ans := make([]float64, len(a))
+			switch uplo {
+			case blas.Upper:
+				// Multiply U^T * U.
+				bi.Dsyrk(uplo, blas.Trans, n, n, 1, a, lda, 0, ans, lda)
+			case blas.Lower:
+				// Multiply L * L^T.
+				bi.Dsyrk(uplo, blas.NoTrans, n, n, 1, a, lda, 0, ans, lda)
+			}
+
+			match := true
+			switch uplo {
+			case blas.Upper:
+				for i := 0; i < n; i++ {
+					for j := i; j < n; j++ {
+						if !floats.EqualWithinAbsOrRel(ans[i*lda+j], aCopy[i*lda+j], tol, tol) {
+							match = false
+						}
+					}
+				}
+			case blas.Lower:
+				for i := 0; i < n; i++ {
+					for j := 0; j <= i; j++ {
+						if !floats.EqualWithinAbsOrRel(ans[i*lda+j], aCopy[i*lda+j], tol, tol) {
+							match = false
+						}
+					}
+				}
+			}
+			if !match {
+				t.Errorf("Case %v (uplo=%v,n=%v,lda=%v): unexpected result", tc, uplo, n, lda)
+			}
+
+			// Make one element of D negative so that A is not
+			// positive definite, and check that Dpotrf fails.
+			d[0] *= -1
+			Dlagsy(n, 0, d, a, lda, rnd, make([]float64, 2*n))
+			ok = impl.Dpotrf(uplo, n, a, lda)
+			if ok {
+				t.Errorf("Case %v: unexpected success for not positive definite matrix", tc)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/drscl.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/drscl.go
new file mode 100644
index 00000000..df87db40
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/drscl.go
@@ -0,0 +1,52 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+type Drscler interface {
+	Drscl(n int, a float64, x []float64, incX int)
+}
+
+func DrsclTest(t *testing.T, impl Drscler) {
+	for _, test := range []struct {
+		x []float64
+		a float64
+	}{
+		{
+			x: []float64{1, 2, 3, 4, 5},
+			a: 4,
+		},
+		{
+			x: []float64{1, 2, 3, 4, 5},
+			a: math.MaxFloat64,
+		},
+		{
+			x: []float64{1, 2, 3, 4, 5},
+			a: 1e-307,
+		},
+	} {
+		xcopy := make([]float64, len(test.x))
+		copy(xcopy, test.x)
+
+		// Cannot test the scaling directly because of floating point scaling issues
+		// (the purpose of Drscl). Instead, check that scaling and scaling back
+		// yeilds approximately x. If overflow or underflow occurs then the scaling
+		// won't match.
+		impl.Drscl(len(test.x), test.a, xcopy, 1)
+		if floats.Equal(xcopy, test.x) {
+			t.Errorf("x unchanged during call to drscl. a = %v, x = %v.", test.a, test.x)
+		}
+		impl.Drscl(len(test.x), 1/test.a, xcopy, 1)
+		if !floats.EqualApprox(xcopy, test.x, 1e-14) {
+			t.Errorf("x not equal after scaling and unscaling. a = %v, x = %v.", test.a, test.x)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dsteqr.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dsteqr.go
new file mode 100644
index 00000000..1fffdb1e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dsteqr.go
@@ -0,0 +1,171 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dsteqrer interface {
+	Dsteqr(compz lapack.EVComp, n int, d, e, z []float64, ldz int, work []float64) (ok bool)
+	Dorgtrer
+}
+
+func DsteqrTest(t *testing.T, impl Dsteqrer) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, compz := range []lapack.EVComp{lapack.OriginalEV, lapack.TridiagEV} {
+		for _, test := range []struct {
+			n, lda int
+		}{
+			{1, 0},
+			{4, 0},
+			{8, 0},
+			{10, 0},
+
+			{2, 10},
+			{8, 10},
+			{10, 20},
+		} {
+			for cas := 0; cas < 100; cas++ {
+				n := test.n
+				lda := test.lda
+				if lda == 0 {
+					lda = n
+				}
+				d := make([]float64, n)
+				for i := range d {
+					d[i] = rnd.Float64()
+				}
+				e := make([]float64, n-1)
+				for i := range e {
+					e[i] = rnd.Float64()
+				}
+				a := make([]float64, n*lda)
+				for i := range a {
+					a[i] = rnd.Float64()
+				}
+				dCopy := make([]float64, len(d))
+				copy(dCopy, d)
+				eCopy := make([]float64, len(e))
+				copy(eCopy, e)
+				aCopy := make([]float64, len(a))
+				copy(aCopy, a)
+				if compz == lapack.OriginalEV {
+					// Compute triangular decomposition and orthonormal matrix.
+					uplo := blas.Upper
+					tau := make([]float64, n)
+					work := make([]float64, 1)
+					impl.Dsytrd(blas.Upper, n, a, lda, d, e, tau, work, -1)
+					work = make([]float64, int(work[0]))
+					impl.Dsytrd(uplo, n, a, lda, d, e, tau, work, len(work))
+					impl.Dorgtr(uplo, n, a, lda, tau, work, len(work))
+				} else {
+					for i := 0; i < n; i++ {
+						for j := 0; j < n; j++ {
+							a[i*lda+j] = 0
+							if i == j {
+								a[i*lda+j] = 1
+							}
+						}
+					}
+				}
+				work := make([]float64, 2*n)
+
+				aDecomp := make([]float64, len(a))
+				copy(aDecomp, a)
+				dDecomp := make([]float64, len(d))
+				copy(dDecomp, d)
+				eDecomp := make([]float64, len(e))
+				copy(eDecomp, e)
+				impl.Dsteqr(compz, n, d, e, a, lda, work)
+				dAns := make([]float64, len(d))
+				copy(dAns, d)
+
+				var truth blas64.General
+				if compz == lapack.OriginalEV {
+					truth = blas64.General{
+						Rows:   n,
+						Cols:   n,
+						Stride: n,
+						Data:   make([]float64, n*n),
+					}
+					for i := 0; i < n; i++ {
+						for j := i; j < n; j++ {
+							v := aCopy[i*lda+j]
+							truth.Data[i*truth.Stride+j] = v
+							truth.Data[j*truth.Stride+i] = v
+						}
+					}
+				} else {
+					truth = blas64.General{
+						Rows:   n,
+						Cols:   n,
+						Stride: n,
+						Data:   make([]float64, n*n),
+					}
+					for i := 0; i < n; i++ {
+						truth.Data[i*truth.Stride+i] = dCopy[i]
+						if i != n-1 {
+							truth.Data[(i+1)*truth.Stride+i] = eCopy[i]
+							truth.Data[i*truth.Stride+i+1] = eCopy[i]
+						}
+					}
+				}
+
+				V := blas64.General{
+					Rows:   n,
+					Cols:   n,
+					Stride: lda,
+					Data:   a,
+				}
+				if !eigenDecompCorrect(d, truth, V) {
+					t.Errorf("Eigen reconstruction mismatch. fromFull = %v, n = %v",
+						compz == lapack.OriginalEV, n)
+				}
+
+				// Compare eigenvalues when not computing eigenvectors.
+				for i := range work {
+					work[i] = rnd.Float64()
+				}
+				impl.Dsteqr(lapack.None, n, dDecomp, eDecomp, aDecomp, lda, work)
+				if !floats.EqualApprox(d, dAns, 1e-8) {
+					t.Errorf("Eigenvalue mismatch when eigenvectors not computed")
+				}
+			}
+		}
+	}
+}
+
+// eigenDecompCorrect returns whether the eigen decomposition is correct.
+// It checks if
+//  A * v ≈ λ * v
+// where the eigenvalues λ are stored in values, and the eigenvectors are stored
+// in the columns of v.
+func eigenDecompCorrect(values []float64, A, V blas64.General) bool {
+	n := A.Rows
+	for i := 0; i < n; i++ {
+		lambda := values[i]
+		vector := make([]float64, n)
+		ans2 := make([]float64, n)
+		for j := range vector {
+			v := V.Data[j*V.Stride+i]
+			vector[j] = v
+			ans2[j] = lambda * v
+		}
+		v := blas64.Vector{Inc: 1, Data: vector}
+		ans1 := blas64.Vector{Inc: 1, Data: make([]float64, n)}
+		blas64.Gemv(blas.NoTrans, 1, A, v, 0, ans1)
+		if !floats.EqualApprox(ans1.Data, ans2, 1e-8) {
+			return false
+		}
+	}
+	return true
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dsterf.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dsterf.go
new file mode 100644
index 00000000..66b4a9e1
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dsterf.go
@@ -0,0 +1,126 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"sort"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dsterfer interface {
+	Dgetrfer
+	Dsterf(n int, d, e []float64) (ok bool)
+}
+
+func DsterfTest(t *testing.T, impl Dsterfer) {
+	// Hand coded tests.
+	for cas, test := range []struct {
+		d []float64
+		e []float64
+		n int
+
+		ans []float64
+	}{
+		// Computed from Fortran code.
+		{
+			d:   []float64{1, 3, 4, 6},
+			e:   []float64{2, 4, 5},
+			n:   4,
+			ans: []float64{11.046227528488854, 4.795922173417400, -2.546379458290125, 0.704229756383872},
+		},
+	} {
+		n := test.n
+		d := make([]float64, len(test.d))
+		copy(d, test.d)
+		e := make([]float64, len(test.e))
+		copy(e, test.e)
+		ok := impl.Dsterf(n, d, e)
+		if !ok {
+			t.Errorf("Case %d, Eigenvalue decomposition failed", cas)
+			continue
+		}
+		ans := make([]float64, len(test.ans))
+		copy(ans, test.ans)
+		sort.Float64s(ans)
+		if !floats.EqualApprox(ans, d, 1e-10) {
+			t.Errorf("eigenvalue mismatch")
+		}
+	}
+
+	rnd := rand.New(rand.NewSource(1))
+	// Probabilistic tests.
+	for _, n := range []int{4, 6, 10} {
+		for cas := 0; cas < 10; cas++ {
+			d := make([]float64, n)
+			for i := range d {
+				d[i] = rnd.NormFloat64()
+			}
+			dCopy := make([]float64, len(d))
+			copy(dCopy, d)
+			e := make([]float64, n-1)
+			for i := range e {
+				e[i] = rnd.NormFloat64()
+			}
+			eCopy := make([]float64, len(e))
+			copy(eCopy, e)
+
+			ok := impl.Dsterf(n, d, e)
+			if !ok {
+				t.Errorf("Eigenvalue decomposition failed")
+				continue
+			}
+
+			// Test that the eigenvalues are sorted.
+			if !sort.Float64sAreSorted(d) {
+				t.Errorf("Values are not sorted")
+			}
+
+			// Construct original tridagional matrix.
+			lda := n
+			a := make([]float64, n*lda)
+			for i := 0; i < n; i++ {
+				a[i*lda+i] = dCopy[i]
+				if i != n-1 {
+					a[i*lda+i+1] = eCopy[i]
+					a[(i+1)*lda+i] = eCopy[i]
+				}
+			}
+
+			asub := make([]float64, len(a))
+			ipiv := make([]int, n)
+
+			// Test that they are actually eigenvalues by computing the
+			// determinant of A - λI.
+			// TODO(btracey): Replace this test with a more numerically stable
+			// test.
+			for _, lambda := range d {
+				copy(asub, a)
+				for i := 0; i < n; i++ {
+					asub[i*lda+i] -= lambda
+				}
+
+				// Compute LU.
+				ok := impl.Dgetrf(n, n, asub, lda, ipiv)
+				if !ok {
+					// Definitely singular.
+					continue
+				}
+				// Compute determinant.
+				var logdet float64
+				for i := 0; i < n; i++ {
+					v := asub[i*lda+i]
+					logdet += math.Log(math.Abs(v))
+				}
+				if math.Exp(logdet) > 2 {
+					t.Errorf("Incorrect singular value. n = %d, cas = %d, det = %v", n, cas, math.Exp(logdet))
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dsyev.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dsyev.go
new file mode 100644
index 00000000..e70088c9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dsyev.go
@@ -0,0 +1,115 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dsyever interface {
+	Dsyev(jobz lapack.EVJob, uplo blas.Uplo, n int, a []float64, lda int, w, work []float64, lwork int) (ok bool)
+}
+
+func DsyevTest(t *testing.T, impl Dsyever) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, uplo := range []blas.Uplo{blas.Lower, blas.Upper} {
+		for _, test := range []struct {
+			n, lda int
+		}{
+			{1, 0},
+			{2, 0},
+			{5, 0},
+			{10, 0},
+			{100, 0},
+
+			{1, 5},
+			{2, 5},
+			{5, 10},
+			{10, 20},
+			{100, 110},
+		} {
+			for cas := 0; cas < 10; cas++ {
+				n := test.n
+				lda := test.lda
+				if lda == 0 {
+					lda = n
+				}
+				a := make([]float64, n*lda)
+				for i := range a {
+					a[i] = rnd.NormFloat64()
+				}
+				aCopy := make([]float64, len(a))
+				copy(aCopy, a)
+				w := make([]float64, n)
+				for i := range w {
+					w[i] = rnd.NormFloat64()
+				}
+
+				work := make([]float64, 1)
+				impl.Dsyev(lapack.ComputeEV, uplo, n, a, lda, w, work, -1)
+				work = make([]float64, int(work[0]))
+				impl.Dsyev(lapack.ComputeEV, uplo, n, a, lda, w, work, len(work))
+
+				// Check that the decomposition is correct
+				orig := blas64.General{
+					Rows:   n,
+					Cols:   n,
+					Stride: n,
+					Data:   make([]float64, n*n),
+				}
+				if uplo == blas.Upper {
+					for i := 0; i < n; i++ {
+						for j := i; j < n; j++ {
+							v := aCopy[i*lda+j]
+							orig.Data[i*orig.Stride+j] = v
+							orig.Data[j*orig.Stride+i] = v
+						}
+					}
+				} else {
+					for i := 0; i < n; i++ {
+						for j := 0; j <= i; j++ {
+							v := aCopy[i*lda+j]
+							orig.Data[i*orig.Stride+j] = v
+							orig.Data[j*orig.Stride+i] = v
+						}
+					}
+				}
+
+				V := blas64.General{
+					Rows:   n,
+					Cols:   n,
+					Stride: lda,
+					Data:   a,
+				}
+
+				if !eigenDecompCorrect(w, orig, V) {
+					t.Errorf("Decomposition mismatch")
+				}
+
+				// Check that the decomposition is correct when the eigenvectors
+				// are not computed.
+				wAns := make([]float64, len(w))
+				copy(wAns, w)
+				copy(a, aCopy)
+				for i := range w {
+					w[i] = rnd.Float64()
+				}
+				for i := range work {
+					work[i] = rnd.Float64()
+				}
+				impl.Dsyev(lapack.None, uplo, n, a, lda, w, work, len(work))
+				if !floats.EqualApprox(w, wAns, 1e-8) {
+					t.Errorf("Eigenvalue mismatch when vectors not computed")
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dsytd2.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dsytd2.go
new file mode 100644
index 00000000..af71cf1f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dsytd2.go
@@ -0,0 +1,205 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dsytd2er interface {
+	Dsytd2(uplo blas.Uplo, n int, a []float64, lda int, d, e, tau []float64)
+}
+
+func Dsytd2Test(t *testing.T, impl Dsytd2er) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
+		for _, test := range []struct {
+			n, lda int
+		}{
+			{3, 0},
+			{4, 0},
+			{5, 0},
+
+			{3, 10},
+			{4, 10},
+			{5, 10},
+		} {
+			n := test.n
+			lda := test.lda
+			if lda == 0 {
+				lda = n
+			}
+			a := make([]float64, n*lda)
+			for i := range a {
+				a[i] = rnd.NormFloat64()
+			}
+			aCopy := make([]float64, len(a))
+			copy(aCopy, a)
+
+			d := make([]float64, n)
+			for i := range d {
+				d[i] = math.NaN()
+			}
+			e := make([]float64, n-1)
+			for i := range e {
+				e[i] = math.NaN()
+			}
+			tau := make([]float64, n-1)
+			for i := range tau {
+				tau[i] = math.NaN()
+			}
+
+			impl.Dsytd2(uplo, n, a, lda, d, e, tau)
+
+			// Construct Q
+			qMat := blas64.General{
+				Rows:   n,
+				Cols:   n,
+				Stride: n,
+				Data:   make([]float64, n*n),
+			}
+			qCopy := blas64.General{
+				Rows:   n,
+				Cols:   n,
+				Stride: n,
+				Data:   make([]float64, len(qMat.Data)),
+			}
+			// Set Q to I.
+			for i := 0; i < n; i++ {
+				qMat.Data[i*qMat.Stride+i] = 1
+			}
+			for i := 0; i < n-1; i++ {
+				hMat := blas64.General{
+					Rows:   n,
+					Cols:   n,
+					Stride: n,
+					Data:   make([]float64, n*n),
+				}
+				// Set H to I.
+				for i := 0; i < n; i++ {
+					hMat.Data[i*hMat.Stride+i] = 1
+				}
+				var vi blas64.Vector
+				if uplo == blas.Upper {
+					vi = blas64.Vector{
+						Inc:  1,
+						Data: make([]float64, n),
+					}
+					for j := 0; j < i; j++ {
+						vi.Data[j] = a[j*lda+i+1]
+					}
+					vi.Data[i] = 1
+				} else {
+					vi = blas64.Vector{
+						Inc:  1,
+						Data: make([]float64, n),
+					}
+					vi.Data[i+1] = 1
+					for j := i + 2; j < n; j++ {
+						vi.Data[j] = a[j*lda+i]
+					}
+				}
+				blas64.Ger(-tau[i], vi, vi, hMat)
+				copy(qCopy.Data, qMat.Data)
+
+				// Multiply q by the new h.
+				if uplo == blas.Upper {
+					blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, hMat, qCopy, 0, qMat)
+				} else {
+					blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, qCopy, hMat, 0, qMat)
+				}
+			}
+			// Check that Q is orthonormal
+			othonormal := true
+			for i := 0; i < n; i++ {
+				for j := i; j < n; j++ {
+					dot := blas64.Dot(n,
+						blas64.Vector{Inc: 1, Data: qMat.Data[i*qMat.Stride:]},
+						blas64.Vector{Inc: 1, Data: qMat.Data[j*qMat.Stride:]},
+					)
+					if i == j {
+						if math.Abs(dot-1) > 1e-10 {
+							othonormal = false
+						}
+					} else {
+						if math.Abs(dot) > 1e-10 {
+							othonormal = false
+						}
+					}
+				}
+			}
+			if !othonormal {
+				t.Errorf("Q not orthonormal")
+			}
+
+			// Compute Q^T * A * Q.
+			aMat := blas64.General{
+				Rows:   n,
+				Cols:   n,
+				Stride: n,
+				Data:   make([]float64, len(a)),
+			}
+
+			for i := 0; i < n; i++ {
+				for j := i; j < n; j++ {
+					v := aCopy[i*lda+j]
+					if uplo == blas.Lower {
+						v = aCopy[j*lda+i]
+					}
+					aMat.Data[i*aMat.Stride+j] = v
+					aMat.Data[j*aMat.Stride+i] = v
+				}
+			}
+
+			tmp := blas64.General{
+				Rows:   n,
+				Cols:   n,
+				Stride: n,
+				Data:   make([]float64, n*n),
+			}
+
+			ans := blas64.General{
+				Rows:   n,
+				Cols:   n,
+				Stride: n,
+				Data:   make([]float64, n*n),
+			}
+
+			blas64.Gemm(blas.Trans, blas.NoTrans, 1, qMat, aMat, 0, tmp)
+			blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, tmp, qMat, 0, ans)
+
+			// Compare with T.
+			tMat := blas64.General{
+				Rows:   n,
+				Cols:   n,
+				Stride: n,
+				Data:   make([]float64, n*n),
+			}
+			for i := 0; i < n-1; i++ {
+				tMat.Data[i*tMat.Stride+i] = d[i]
+				tMat.Data[i*tMat.Stride+i+1] = e[i]
+				tMat.Data[(i+1)*tMat.Stride+i] = e[i]
+			}
+			tMat.Data[(n-1)*tMat.Stride+n-1] = d[n-1]
+
+			same := true
+			for i := 0; i < n; i++ {
+				for j := 0; j < n; j++ {
+					if math.Abs(ans.Data[i*ans.Stride+j]-tMat.Data[i*tMat.Stride+j]) > 1e-10 {
+						same = false
+					}
+				}
+			}
+			if !same {
+				t.Errorf("Matrix answer mismatch")
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dsytrd.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dsytrd.go
new file mode 100644
index 00000000..74e2beba
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dsytrd.go
@@ -0,0 +1,160 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dsytrder interface {
+	Dsytrd(uplo blas.Uplo, n int, a []float64, lda int, d, e, tau, work []float64, lwork int)
+
+	Dorgqr(m, n, k int, a []float64, lda int, tau, work []float64, lwork int)
+	Dorgql(m, n, k int, a []float64, lda int, tau, work []float64, lwork int)
+}
+
+func DsytrdTest(t *testing.T, impl Dsytrder) {
+	const tol = 1e-13
+	rnd := rand.New(rand.NewSource(1))
+	for tc, test := range []struct {
+		n, lda int
+	}{
+		{1, 0},
+		{2, 0},
+		{3, 0},
+		{4, 0},
+		{10, 0},
+		{50, 0},
+		{100, 0},
+		{150, 0},
+		{300, 0},
+
+		{1, 3},
+		{2, 3},
+		{3, 7},
+		{4, 9},
+		{10, 20},
+		{50, 70},
+		{100, 120},
+		{150, 170},
+		{300, 320},
+	} {
+		for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
+			for _, wl := range []worklen{minimumWork, mediumWork, optimumWork} {
+				n := test.n
+				lda := test.lda
+				if lda == 0 {
+					lda = n
+				}
+				a := randomGeneral(n, n, lda, rnd)
+				for i := 1; i < n; i++ {
+					for j := 0; j < i; j++ {
+						a.Data[i*a.Stride+j] = a.Data[j*a.Stride+i]
+					}
+				}
+				aCopy := cloneGeneral(a)
+
+				d := nanSlice(n)
+				e := nanSlice(n - 1)
+				tau := nanSlice(n - 1)
+
+				var lwork int
+				switch wl {
+				case minimumWork:
+					lwork = 1
+				case mediumWork:
+					work := make([]float64, 1)
+					impl.Dsytrd(uplo, n, a.Data, a.Stride, d, e, tau, work, -1)
+					lwork = (int(work[0]) + 1) / 2
+					lwork = max(1, lwork)
+				case optimumWork:
+					work := make([]float64, 1)
+					impl.Dsytrd(uplo, n, a.Data, a.Stride, d, e, tau, work, -1)
+					lwork = int(work[0])
+				}
+				work := make([]float64, lwork)
+
+				impl.Dsytrd(uplo, n, a.Data, a.Stride, d, e, tau, work, lwork)
+
+				prefix := fmt.Sprintf("Case #%v: uplo=%v,n=%v,lda=%v,work=%v",
+					tc, uplo, n, lda, wl)
+
+				if !generalOutsideAllNaN(a) {
+					t.Errorf("%v: out-of-range write to A", prefix)
+				}
+
+				// Extract Q by doing what Dorgtr does.
+				q := cloneGeneral(a)
+				if uplo == blas.Upper {
+					for j := 0; j < n-1; j++ {
+						for i := 0; i < j; i++ {
+							q.Data[i*q.Stride+j] = q.Data[i*q.Stride+j+1]
+						}
+						q.Data[(n-1)*q.Stride+j] = 0
+					}
+					for i := 0; i < n-1; i++ {
+						q.Data[i*q.Stride+n-1] = 0
+					}
+					q.Data[(n-1)*q.Stride+n-1] = 1
+					if n > 1 {
+						work = make([]float64, n-1)
+						impl.Dorgql(n-1, n-1, n-1, q.Data, q.Stride, tau, work, len(work))
+					}
+				} else {
+					for j := n - 1; j > 0; j-- {
+						q.Data[j] = 0
+						for i := j + 1; i < n; i++ {
+							q.Data[i*q.Stride+j] = q.Data[i*q.Stride+j-1]
+						}
+					}
+					q.Data[0] = 1
+					for i := 1; i < n; i++ {
+						q.Data[i*q.Stride] = 0
+					}
+					if n > 1 {
+						work = make([]float64, n-1)
+						impl.Dorgqr(n-1, n-1, n-1, q.Data[q.Stride+1:], q.Stride, tau, work, len(work))
+					}
+				}
+				if !isOrthonormal(q) {
+					t.Errorf("%v: Q not orthogonal", prefix)
+				}
+
+				// Contruct symmetric tridiagonal T from d and e.
+				tMat := zeros(n, n, n)
+				for i := 0; i < n; i++ {
+					tMat.Data[i*tMat.Stride+i] = d[i]
+				}
+				if uplo == blas.Upper {
+					for j := 1; j < n; j++ {
+						tMat.Data[(j-1)*tMat.Stride+j] = e[j-1]
+						tMat.Data[j*tMat.Stride+j-1] = e[j-1]
+					}
+				} else {
+					for j := 0; j < n-1; j++ {
+						tMat.Data[(j+1)*tMat.Stride+j] = e[j]
+						tMat.Data[j*tMat.Stride+j+1] = e[j]
+					}
+				}
+
+				// Compute Q^T * A * Q.
+				tmp := zeros(n, n, n)
+				blas64.Gemm(blas.Trans, blas.NoTrans, 1, q, aCopy, 0, tmp)
+				got := zeros(n, n, n)
+				blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, tmp, q, 0, got)
+
+				// Compare with T.
+				if !equalApproxGeneral(got, tMat, tol) {
+					t.Errorf("%v: Q^T*A*Q != T", prefix)
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dtgsja.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dtgsja.go
new file mode 100644
index 00000000..af4cec80
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dtgsja.go
@@ -0,0 +1,165 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dtgsjaer interface {
+	Dlanger
+	Dtgsja(jobU, jobV, jobQ lapack.GSVDJob, m, p, n, k, l int, a []float64, lda int, b []float64, ldb int, tola, tolb float64, alpha, beta, u []float64, ldu int, v []float64, ldv int, q []float64, ldq int, work []float64) (cycles int, ok bool)
+}
+
+func DtgsjaTest(t *testing.T, impl Dtgsjaer) {
+	rnd := rand.New(rand.NewSource(1))
+	for cas, test := range []struct {
+		m, p, n, k, l, lda, ldb, ldu, ldv, ldq int
+
+		ok bool
+	}{
+		{m: 5, p: 5, n: 5, k: 2, l: 2, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+		{m: 5, p: 5, n: 5, k: 4, l: 1, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+		{m: 5, p: 5, n: 10, k: 2, l: 2, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+		{m: 5, p: 5, n: 10, k: 4, l: 1, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+		{m: 5, p: 5, n: 10, k: 4, l: 2, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+		{m: 10, p: 5, n: 5, k: 2, l: 2, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+		{m: 10, p: 5, n: 5, k: 4, l: 1, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+		{m: 10, p: 10, n: 10, k: 5, l: 3, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+		{m: 10, p: 10, n: 10, k: 6, l: 4, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+		{m: 5, p: 5, n: 5, k: 2, l: 2, lda: 10, ldb: 10, ldu: 10, ldv: 10, ldq: 10, ok: true},
+		{m: 5, p: 5, n: 5, k: 4, l: 1, lda: 10, ldb: 10, ldu: 10, ldv: 10, ldq: 10, ok: true},
+		{m: 5, p: 5, n: 10, k: 2, l: 2, lda: 20, ldb: 20, ldu: 10, ldv: 10, ldq: 20, ok: true},
+		{m: 5, p: 5, n: 10, k: 4, l: 1, lda: 20, ldb: 20, ldu: 10, ldv: 10, ldq: 20, ok: true},
+		{m: 5, p: 5, n: 10, k: 4, l: 2, lda: 20, ldb: 20, ldu: 10, ldv: 10, ldq: 20, ok: true},
+		{m: 10, p: 5, n: 5, k: 2, l: 2, lda: 10, ldb: 10, ldu: 20, ldv: 10, ldq: 10, ok: true},
+		{m: 10, p: 5, n: 5, k: 4, l: 1, lda: 10, ldb: 10, ldu: 20, ldv: 10, ldq: 10, ok: true},
+		{m: 10, p: 10, n: 10, k: 5, l: 3, lda: 20, ldb: 20, ldu: 20, ldv: 20, ldq: 20, ok: true},
+		{m: 10, p: 10, n: 10, k: 6, l: 4, lda: 20, ldb: 20, ldu: 20, ldv: 20, ldq: 20, ok: true},
+	} {
+		m := test.m
+		p := test.p
+		n := test.n
+		k := test.k
+		l := test.l
+		lda := test.lda
+		if lda == 0 {
+			lda = n
+		}
+		ldb := test.ldb
+		if ldb == 0 {
+			ldb = n
+		}
+		ldu := test.ldu
+		if ldu == 0 {
+			ldu = m
+		}
+		ldv := test.ldv
+		if ldv == 0 {
+			ldv = p
+		}
+		ldq := test.ldq
+		if ldq == 0 {
+			ldq = n
+		}
+
+		a := blockedUpperTriGeneral(m, n, k, l, lda, true, rnd)
+		aCopy := cloneGeneral(a)
+		b := blockedUpperTriGeneral(p, n, k, l, ldb, false, rnd)
+		bCopy := cloneGeneral(b)
+
+		tola := float64(max(m, n)) * impl.Dlange(lapack.NormFrob, m, n, a.Data, a.Stride, nil) * dlamchE
+		tolb := float64(max(p, n)) * impl.Dlange(lapack.NormFrob, p, n, b.Data, b.Stride, nil) * dlamchE
+
+		alpha := make([]float64, n)
+		beta := make([]float64, n)
+
+		work := make([]float64, 2*n)
+
+		u := nanGeneral(m, m, ldu)
+		v := nanGeneral(p, p, ldv)
+		q := nanGeneral(n, n, ldq)
+
+		_, ok := impl.Dtgsja(lapack.GSVDUnit, lapack.GSVDUnit, lapack.GSVDUnit,
+			m, p, n, k, l,
+			a.Data, a.Stride,
+			b.Data, b.Stride,
+			tola, tolb,
+			alpha, beta,
+			u.Data, u.Stride,
+			v.Data, v.Stride,
+			q.Data, q.Stride,
+			work)
+
+		if !ok {
+			if test.ok {
+				t.Errorf("test %d unexpectedly did not converge", cas)
+			}
+			continue
+		}
+
+		// Check orthogonality of U, V and Q.
+		if !isOrthonormal(u) {
+			t.Errorf("test %d: U is not orthogonal\n%+v", cas, u)
+		}
+		if !isOrthonormal(v) {
+			t.Errorf("test %d: V is not orthogonal\n%+v", cas, v)
+		}
+		if !isOrthonormal(q) {
+			t.Errorf("test %d: Q is not orthogonal\n%+v", cas, q)
+		}
+
+		// Check C^2 + S^2 = I.
+		var elements []float64
+		if m-k-l >= 0 {
+			elements = alpha[k : k+l]
+		} else {
+			elements = alpha[k:m]
+		}
+		for i := range elements {
+			i += k
+			d := alpha[i]*alpha[i] + beta[i]*beta[i]
+			if !floats.EqualWithinAbsOrRel(d, 1, 1e-14, 1e-14) {
+				t.Errorf("test %d: alpha_%d^2 + beta_%d^2 != 1: got: %v", cas, i, i, d)
+			}
+		}
+
+		zeroR, d1, d2 := constructGSVDresults(n, p, m, k, l, a, b, alpha, beta)
+
+		// Check U^T*A*Q = D1*[ 0 R ].
+		uTmp := nanGeneral(m, n, n)
+		blas64.Gemm(blas.Trans, blas.NoTrans, 1, u, aCopy, 0, uTmp)
+		uAns := nanGeneral(m, n, n)
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, uTmp, q, 0, uAns)
+
+		d10r := nanGeneral(m, n, n)
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, d1, zeroR, 0, d10r)
+
+		if !equalApproxGeneral(uAns, d10r, 1e-14) {
+			t.Errorf("test %d: U^T*A*Q != D1*[ 0 R ]\nU^T*A*Q:\n%+v\nD1*[ 0 R ]:\n%+v",
+				cas, uAns, d10r)
+		}
+
+		// Check V^T*B*Q = D2*[ 0 R ].
+		vTmp := nanGeneral(p, n, n)
+		blas64.Gemm(blas.Trans, blas.NoTrans, 1, v, bCopy, 0, vTmp)
+		vAns := nanGeneral(p, n, n)
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, vTmp, q, 0, vAns)
+
+		d20r := nanGeneral(p, n, n)
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, d2, zeroR, 0, d20r)
+
+		if !equalApproxGeneral(vAns, d20r, 1e-14) {
+			t.Errorf("test %d: V^T*B*Q != D2*[ 0 R ]\nV^T*B*Q:\n%+v\nD2*[ 0 R ]:\n%+v",
+				cas, vAns, d20r)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dtrcon.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dtrcon.go
new file mode 100644
index 00000000..1e490ca9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dtrcon.go
@@ -0,0 +1,184 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dtrconer interface {
+	Dgeconer
+	Dtrcon(norm lapack.MatrixNorm, uplo blas.Uplo, diag blas.Diag, n int, a []float64, lda int, work []float64, iwork []int) float64
+}
+
+func DtrconTest(t *testing.T, impl Dtrconer) {
+	rnd := rand.New(rand.NewSource(1))
+	// Hand crafted tests.
+	for _, test := range []struct {
+		a       []float64
+		n       int
+		uplo    blas.Uplo
+		diag    blas.Diag
+		condOne float64
+		condInf float64
+	}{
+		{
+			a: []float64{
+				8, 5, 6,
+				0, 7, 8,
+				0, 0, 6,
+			},
+			n:       3,
+			uplo:    blas.Upper,
+			diag:    blas.Unit,
+			condOne: 1.0 / 645,
+			condInf: 1.0 / 480,
+		},
+		{
+			a: []float64{
+				8, 5, 6,
+				0, 7, 8,
+				0, 0, 6,
+			},
+			n:       3,
+			uplo:    blas.Upper,
+			diag:    blas.NonUnit,
+			condOne: 0.137704918032787,
+			condInf: 0.157894736842105,
+		},
+		{
+			a: []float64{
+				8, 0, 0,
+				5, 7, 0,
+				6, 8, 6,
+			},
+			n:       3,
+			uplo:    blas.Lower,
+			diag:    blas.Unit,
+			condOne: 1.0 / 480,
+			condInf: 1.0 / 645,
+		},
+		{
+			a: []float64{
+				8, 0, 0,
+				5, 7, 0,
+				6, 8, 6,
+			},
+			n:       3,
+			uplo:    blas.Lower,
+			diag:    blas.NonUnit,
+			condOne: 0.157894736842105,
+			condInf: 0.137704918032787,
+		},
+	} {
+		lda := test.n
+		work := make([]float64, 3*test.n)
+		for i := range work {
+			work[i] = rnd.Float64()
+		}
+		iwork := make([]int, test.n)
+		for i := range iwork {
+			iwork[i] = int(rnd.Int31())
+		}
+		aCopy := make([]float64, len(test.a))
+		copy(aCopy, test.a)
+		condOne := impl.Dtrcon(lapack.MaxColumnSum, test.uplo, test.diag, test.n, test.a, lda, work, iwork)
+		if math.Abs(condOne-test.condOne) > 1e-14 {
+			t.Errorf("One norm mismatch. Want %v, got %v.", test.condOne, condOne)
+		}
+		if !floats.Equal(aCopy, test.a) {
+			t.Errorf("a modified during call")
+		}
+		condInf := impl.Dtrcon(lapack.MaxRowSum, test.uplo, test.diag, test.n, test.a, lda, work, iwork)
+		if math.Abs(condInf-test.condInf) > 1e-14 {
+			t.Errorf("Inf norm mismatch. Want %v, got %v.", test.condInf, condInf)
+		}
+		if !floats.Equal(aCopy, test.a) {
+			t.Errorf("a modified during call")
+		}
+	}
+
+	// Dtrcon does not match the Dgecon output in many cases. See
+	// https://github.com/xianyi/OpenBLAS/issues/636
+	// TODO(btracey): Uncomment this when the mismatch between Dgecon and Dtrcon
+	// is understood.
+	/*
+		// Randomized tests against Dgecon.
+		for _, uplo := range []blas.Uplo{blas.Lower, blas.Upper} {
+			for _, diag := range []blas.Diag{blas.NonUnit, blas.Unit} {
+				for _, test := range []struct {
+					n, lda int
+				}{
+					{3, 0},
+					{4, 9},
+				} {
+					for trial := 0; trial < 1; trial++ {
+						n := test.n
+						lda := test.lda
+						if lda == 0 {
+							lda = n
+						}
+						a := make([]float64, n*lda)
+						if trial == 0 {
+							for i := range a {
+								a[i] = float64(i + 2)
+							}
+						} else {
+							for i := range a {
+								a[i] = rnd.NormFloat64()
+							}
+						}
+
+						aDense := make([]float64, len(a))
+						if uplo == blas.Upper {
+							for i := 0; i < n; i++ {
+								for j := i; j < n; j++ {
+									aDense[i*lda+j] = a[i*lda+j]
+								}
+							}
+						} else {
+							for i := 0; i < n; i++ {
+								for j := 0; j <= i; j++ {
+									aDense[i*lda+j] = a[i*lda+j]
+								}
+							}
+						}
+						if diag == blas.Unit {
+							for i := 0; i < n; i++ {
+								aDense[i*lda+i] = 1
+							}
+						}
+
+						ipiv := make([]int, n)
+						work := make([]float64, 4*n)
+						denseOne := impl.Dlange(lapack.MaxColumnSum, n, n, aDense, lda, work)
+						denseInf := impl.Dlange(lapack.MaxRowSum, n, n, aDense, lda, work)
+
+						aDenseLU := make([]float64, len(aDense))
+						copy(aDenseLU, aDense)
+						impl.Dgetrf(n, n, aDenseLU, lda, ipiv)
+						iwork := make([]int, n)
+						want := impl.Dgecon(lapack.MaxColumnSum, n, aDenseLU, lda, denseOne, work, iwork)
+						got := impl.Dtrcon(lapack.MaxColumnSum, uplo, diag, n, a, lda, work, iwork)
+						if math.Abs(want-got) > 1e-14 {
+							t.Errorf("One norm mismatch. Upper = %v, unit = %v, want %v, got %v", uplo == blas.Upper, diag == blas.Unit, want, got)
+						}
+						want = impl.Dgecon(lapack.MaxRowSum, n, aDenseLU, lda, denseInf, work, iwork)
+						got = impl.Dtrcon(lapack.MaxRowSum, uplo, diag, n, a, lda, work, iwork)
+						if math.Abs(want-got) > 1e-14 {
+							t.Errorf("Inf norm mismatch. Upper = %v, unit = %v, want %v, got %v", uplo == blas.Upper, diag == blas.Unit, want, got)
+						}
+					}
+				}
+			}
+		}
+	*/
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dtrevc3.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dtrevc3.go
new file mode 100644
index 00000000..60c51241
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dtrevc3.go
@@ -0,0 +1,221 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dtrevc3er interface {
+	Dtrevc3(side lapack.EVSide, howmny lapack.HowMany, selected []bool, n int, t []float64, ldt int, vl []float64, ldvl int, vr []float64, ldvr int, mm int, work []float64, lwork int) int
+}
+
+func Dtrevc3Test(t *testing.T, impl Dtrevc3er) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, side := range []lapack.EVSide{lapack.RightEV, lapack.LeftEV, lapack.RightLeftEV} {
+		for _, howmny := range []lapack.HowMany{lapack.AllEV, lapack.AllEVMulQ, lapack.SelectedEV} {
+			for _, n := range []int{0, 1, 2, 3, 4, 5, 10, 34, 100} {
+				for _, extra := range []int{0, 11} {
+					for _, optwork := range []bool{true, false} {
+						for cas := 0; cas < 10; cas++ {
+							tmat := randomSchurCanonical(n, n+extra, rnd)
+							testDtrevc3(t, impl, side, howmny, tmat, optwork, rnd)
+						}
+					}
+				}
+			}
+		}
+	}
+}
+
+func testDtrevc3(t *testing.T, impl Dtrevc3er, side lapack.EVSide, howmny lapack.HowMany, tmat blas64.General, optwork bool, rnd *rand.Rand) {
+	const tol = 1e-14
+
+	n := tmat.Rows
+	extra := tmat.Stride - tmat.Cols
+	right := side != lapack.LeftEV
+	left := side != lapack.RightEV
+
+	var selected, selectedWant []bool
+	var mWant int // How many columns will the eigenvectors occupy.
+	if howmny == lapack.SelectedEV {
+		selected = make([]bool, n)
+		selectedWant = make([]bool, n)
+		// Dtrevc3 will compute only selected eigenvectors. Pick them
+		// randomly disregarding whether they are real or complex.
+		for i := range selected {
+			if rnd.Float64() < 0.5 {
+				selected[i] = true
+			}
+		}
+		// Dtrevc3 will modify (standardize) the slice selected based on
+		// whether the corresponding eigenvalues are real or complex. Do
+		// the same process here to fill selectedWant.
+		for i := 0; i < n; {
+			if i == n-1 || tmat.Data[(i+1)*tmat.Stride+i] == 0 {
+				// Real eigenvalue.
+				if selected[i] {
+					selectedWant[i] = true
+					mWant++ // Real eigenvectors occupy one column.
+				}
+				i++
+			} else {
+				// Complex eigenvalue.
+				if selected[i] || selected[i+1] {
+					// Dtrevc3 will modify selected so that
+					// only the first element of the pair is
+					// true.
+					selectedWant[i] = true
+					mWant += 2 // Complex eigenvectors occupy two columns.
+				}
+				i += 2
+			}
+		}
+	} else {
+		// All eigenvectors occupy n columns.
+		mWant = n
+	}
+
+	var vr blas64.General
+	if right {
+		if howmny == lapack.AllEVMulQ {
+			vr = eye(n, n+extra)
+		} else {
+			// VR will be overwritten.
+			vr = nanGeneral(n, mWant, n+extra)
+		}
+	}
+
+	var vl blas64.General
+	if left {
+		if howmny == lapack.AllEVMulQ {
+			vl = eye(n, n+extra)
+		} else {
+			// VL will be overwritten.
+			vl = nanGeneral(n, mWant, n+extra)
+		}
+	}
+
+	work := make([]float64, max(1, 3*n))
+	if optwork {
+		impl.Dtrevc3(side, howmny, nil, n, nil, 1, nil, 1, nil, 1, mWant, work, -1)
+		work = make([]float64, int(work[0]))
+	}
+
+	m := impl.Dtrevc3(side, howmny, selected, n, tmat.Data, tmat.Stride,
+		vl.Data, vl.Stride, vr.Data, vr.Stride, mWant, work, len(work))
+
+	prefix := fmt.Sprintf("Case side=%v, howmny=%v, n=%v, extra=%v, optwk=%v",
+		side, howmny, n, extra, optwork)
+
+	if !generalOutsideAllNaN(tmat) {
+		t.Errorf("%v: out-of-range write to T", prefix)
+	}
+	if !generalOutsideAllNaN(vl) {
+		t.Errorf("%v: out-of-range write to VL", prefix)
+	}
+	if !generalOutsideAllNaN(vr) {
+		t.Errorf("%v: out-of-range write to VR", prefix)
+	}
+
+	if m != mWant {
+		t.Errorf("%v: unexpected value of m. Want %v, got %v", prefix, mWant, m)
+	}
+
+	if howmny == lapack.SelectedEV {
+		for i := range selected {
+			if selected[i] != selectedWant[i] {
+				t.Errorf("%v: unexpected selected[%v]", prefix, i)
+			}
+		}
+	}
+
+	// Check that the columns of VR and VL are actually eigenvectors and
+	// that the magnitude of their largest element is 1.
+	var k int
+	for j := 0; j < n; {
+		re := tmat.Data[j*tmat.Stride+j]
+		if j == n-1 || tmat.Data[(j+1)*tmat.Stride+j] == 0 {
+			if howmny == lapack.SelectedEV && !selected[j] {
+				j++
+				continue
+			}
+			if right {
+				ev := columnOf(vr, k)
+				norm := floats.Norm(ev, math.Inf(1))
+				if math.Abs(norm-1) > tol {
+					t.Errorf("%v: magnitude of largest element of VR[:,%v] not 1", prefix, k)
+				}
+				if !isRightEigenvectorOf(tmat, ev, nil, complex(re, 0), tol) {
+					t.Errorf("%v: VR[:,%v] is not real right eigenvector", prefix, k)
+				}
+			}
+			if left {
+				ev := columnOf(vl, k)
+				norm := floats.Norm(ev, math.Inf(1))
+				if math.Abs(norm-1) > tol {
+					t.Errorf("%v: magnitude of largest element of VL[:,%v] not 1", prefix, k)
+				}
+				if !isLeftEigenvectorOf(tmat, ev, nil, complex(re, 0), tol) {
+					t.Errorf("%v: VL[:,%v] is not real left eigenvector", prefix, k)
+				}
+			}
+			k++
+			j++
+			continue
+		}
+		if howmny == lapack.SelectedEV && !selected[j] {
+			j += 2
+			continue
+		}
+		im := math.Sqrt(math.Abs(tmat.Data[(j+1)*tmat.Stride+j])) *
+			math.Sqrt(math.Abs(tmat.Data[j*tmat.Stride+j+1]))
+		if right {
+			evre := columnOf(vr, k)
+			evim := columnOf(vr, k+1)
+			var evmax float64
+			for i, v := range evre {
+				evmax = math.Max(evmax, math.Abs(v)+math.Abs(evim[i]))
+			}
+			if math.Abs(evmax-1) > tol {
+				t.Errorf("%v: magnitude of largest element of VR[:,%v] not 1", prefix, k)
+			}
+			if !isRightEigenvectorOf(tmat, evre, evim, complex(re, im), tol) {
+				t.Errorf("%v: VR[:,%v:%v] is not complex right eigenvector", prefix, k, k+1)
+			}
+			floats.Scale(-1, evim)
+			if !isRightEigenvectorOf(tmat, evre, evim, complex(re, -im), tol) {
+				t.Errorf("%v: VR[:,%v:%v] is not complex right eigenvector", prefix, k, k+1)
+			}
+		}
+		if left {
+			evre := columnOf(vl, k)
+			evim := columnOf(vl, k+1)
+			var evmax float64
+			for i, v := range evre {
+				evmax = math.Max(evmax, math.Abs(v)+math.Abs(evim[i]))
+			}
+			if math.Abs(evmax-1) > tol {
+				t.Errorf("%v: magnitude of largest element of VL[:,%v] not 1", prefix, k)
+			}
+			if !isLeftEigenvectorOf(tmat, evre, evim, complex(re, im), tol) {
+				t.Errorf("%v: VL[:,%v:%v] is not complex left eigenvector", prefix, k, k+1)
+			}
+			floats.Scale(-1, evim)
+			if !isLeftEigenvectorOf(tmat, evre, evim, complex(re, -im), tol) {
+				t.Errorf("%v: VL[:,%v:%v] is not complex left eigenvector", prefix, k, k+1)
+			}
+		}
+		k += 2
+		j += 2
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dtrexc.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dtrexc.go
new file mode 100644
index 00000000..855805fb
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dtrexc.go
@@ -0,0 +1,219 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math/cmplx"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dtrexcer interface {
+	Dtrexc(compq lapack.EVComp, n int, t []float64, ldt int, q []float64, ldq int, ifst, ilst int, work []float64) (ifstOut, ilstOut int, ok bool)
+}
+
+func DtrexcTest(t *testing.T, impl Dtrexcer) {
+	rnd := rand.New(rand.NewSource(1))
+
+	for _, compq := range []lapack.EVComp{lapack.None, lapack.UpdateSchur} {
+		for _, n := range []int{1, 2, 3, 4, 5, 6, 10, 18, 31, 53} {
+			for _, extra := range []int{0, 1, 11} {
+				for cas := 0; cas < 100; cas++ {
+					tmat := randomSchurCanonical(n, n+extra, rnd)
+					ifst := rnd.Intn(n)
+					ilst := rnd.Intn(n)
+					testDtrexc(t, impl, compq, tmat, ifst, ilst, extra, rnd)
+				}
+			}
+		}
+	}
+
+	for _, compq := range []lapack.EVComp{lapack.None, lapack.UpdateSchur} {
+		for _, extra := range []int{0, 1, 11} {
+			tmat := randomSchurCanonical(0, extra, rnd)
+			testDtrexc(t, impl, compq, tmat, 0, 0, extra, rnd)
+		}
+	}
+}
+
+func testDtrexc(t *testing.T, impl Dtrexcer, compq lapack.EVComp, tmat blas64.General, ifst, ilst, extra int, rnd *rand.Rand) {
+	const tol = 1e-13
+
+	n := tmat.Rows
+	fstSize, fstFirst := schurBlockSize(tmat, ifst)
+	lstSize, lstFirst := schurBlockSize(tmat, ilst)
+
+	tmatCopy := cloneGeneral(tmat)
+
+	var wantq bool
+	var q, qCopy blas64.General
+	if compq == lapack.UpdateSchur {
+		wantq = true
+		q = eye(n, n+extra)
+		qCopy = cloneGeneral(q)
+	}
+
+	work := nanSlice(n)
+
+	ifstGot, ilstGot, ok := impl.Dtrexc(compq, n, tmat.Data, tmat.Stride, q.Data, q.Stride, ifst, ilst, work)
+
+	prefix := fmt.Sprintf("Case compq=%v, n=%v, ifst=%v, nbf=%v, ilst=%v, nbl=%v, extra=%v",
+		compq, n, ifst, fstSize, ilst, lstSize, extra)
+
+	if !generalOutsideAllNaN(tmat) {
+		t.Errorf("%v: out-of-range write to T", prefix)
+	}
+	if wantq && !generalOutsideAllNaN(q) {
+		t.Errorf("%v: out-of-range write to Q", prefix)
+	}
+
+	if !ok {
+		t.Logf("%v: Dtrexc returned ok=false", prefix)
+	}
+
+	// Check that the index of the first block was correctly updated (if
+	// necessary).
+	ifstWant := ifst
+	if !fstFirst {
+		ifstWant = ifst - 1
+	}
+	if ifstWant != ifstGot {
+		t.Errorf("%v: unexpected ifst index. Want %v, got %v ", prefix, ifstWant, ifstGot)
+	}
+
+	// Check that the index of the last block is as expected when ok=true.
+	// When ok=false, we don't know at which block the algorithm failed, so
+	// we don't check.
+	ilstWant := ilst
+	if !lstFirst {
+		ilstWant--
+	}
+	if ok {
+		if ifstWant < ilstWant {
+			// If the blocks are swapped backwards, these
+			// adjustments are not necessary, the first row of the
+			// last block will end up at ifst.
+			switch {
+			case fstSize == 2 && lstSize == 1:
+				ilstWant--
+			case fstSize == 1 && lstSize == 2:
+				ilstWant++
+			}
+		}
+		if ilstWant != ilstGot {
+			t.Errorf("%v: unexpected ilst index. Want %v, got %v", prefix, ilstWant, ilstGot)
+		}
+	}
+
+	if n <= 1 || ifstGot == ilstGot {
+		// Too small matrix or no swapping.
+		// Check that T was not modified.
+		for i := 0; i < n; i++ {
+			for j := 0; j < n; j++ {
+				if tmat.Data[i*tmat.Stride+j] != tmatCopy.Data[i*tmatCopy.Stride+j] {
+					t.Errorf("%v: unexpected modification at T[%v,%v]", prefix, i, j)
+				}
+			}
+		}
+		if !wantq {
+			return
+		}
+		// Check that Q was not modified.
+		for i := 0; i < n; i++ {
+			for j := 0; j < n; j++ {
+				if q.Data[i*q.Stride+j] != qCopy.Data[i*qCopy.Stride+j] {
+					t.Errorf("%v: unexpected modification at Q[%v,%v]", prefix, i, j)
+				}
+			}
+		}
+		return
+	}
+
+	if !isSchurCanonicalGeneral(tmat) {
+		t.Errorf("%v: T is not in Schur canonical form", prefix)
+	}
+
+	// Check that T was not modified except above the second subdiagonal in
+	// rows and columns [modMin,modMax].
+	modMin := min(ifstGot, ilstGot)
+	modMax := max(ifstGot, ilstGot) + fstSize
+	for i := 0; i < n; i++ {
+		for j := 0; j < n; j++ {
+			if modMin <= i && i < modMax && j+1 >= i {
+				continue
+			}
+			if modMin <= j && j < modMax && j+1 >= i {
+				continue
+			}
+			diff := tmat.Data[i*tmat.Stride+j] - tmatCopy.Data[i*tmatCopy.Stride+j]
+			if diff != 0 {
+				t.Errorf("%v: unexpected modification at T[%v,%v]", prefix, i, j)
+			}
+		}
+	}
+
+	// Check that the block at ifstGot was delivered to ilstGot correctly.
+	if fstSize == 1 {
+		// 1×1 blocks are swapped exactly.
+		got := tmat.Data[ilstGot*tmat.Stride+ilstGot]
+		want := tmatCopy.Data[ifstGot*tmatCopy.Stride+ifstGot]
+		if want != got {
+			t.Errorf("%v: unexpected 1×1 block at T[%v,%v]. Want %v, got %v",
+				prefix, want, got, ilstGot, ilstGot)
+		}
+	} else {
+		// Check that the swapped 2×2 block is in Schur canonical form.
+		a, b, c, d := extract2x2Block(tmat.Data[ilstGot*tmat.Stride+ilstGot:], tmat.Stride)
+		if !isSchurCanonical(a, b, c, d) {
+			t.Errorf("%v: 2×2 block at T[%v,%v] not in Schur canonical form", prefix, ilstGot, ilstGot)
+		}
+		ev1Got, ev2Got := schurBlockEigenvalues(a, b, c, d)
+
+		// Check that the swapped 2×2 block has the same eigenvalues.
+		// The block was originally located at T[ifstGot,ifstGot].
+		a, b, c, d = extract2x2Block(tmatCopy.Data[ifstGot*tmatCopy.Stride+ifstGot:], tmatCopy.Stride)
+		ev1Want, ev2Want := schurBlockEigenvalues(a, b, c, d)
+		if cmplx.Abs(ev1Got-ev1Want) > tol {
+			t.Errorf("%v: unexpected first eigenvalue of 2×2 block at T[%v,%v]. Want %v, got %v",
+				prefix, ilstGot, ilstGot, ev1Want, ev1Got)
+		}
+		if cmplx.Abs(ev2Got-ev2Want) > tol {
+			t.Errorf("%v: unexpected second eigenvalue of 2×2 block at T[%v,%v]. Want %v, got %v",
+				prefix, ilstGot, ilstGot, ev2Want, ev2Got)
+		}
+	}
+
+	if !wantq {
+		return
+	}
+
+	if !isOrthonormal(q) {
+		t.Errorf("%v: Q is not orthogonal", prefix)
+	}
+	// Check that Q is unchanged outside of columns [modMin,modMax].
+	for i := 0; i < n; i++ {
+		for j := 0; j < n; j++ {
+			if modMin <= j && j < modMax {
+				continue
+			}
+			if q.Data[i*q.Stride+j]-qCopy.Data[i*qCopy.Stride+j] != 0 {
+				t.Errorf("%v: unexpected modification of Q[%v,%v]", prefix, i, j)
+			}
+		}
+	}
+	// Check that Q^T TOrig Q == T.
+	tq := eye(n, n)
+	blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, tmatCopy, q, 0, tq)
+	qtq := eye(n, n)
+	blas64.Gemm(blas.Trans, blas.NoTrans, 1, q, tq, 0, qtq)
+	if !equalApproxGeneral(qtq, tmat, tol) {
+		t.Errorf("%v: Q^T (initial T) Q and (final T) are not equal", prefix)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dtrti2.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dtrti2.go
new file mode 100644
index 00000000..acb8b5e9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dtrti2.go
@@ -0,0 +1,163 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+)
+
+type Dtrti2er interface {
+	Dtrti2(uplo blas.Uplo, diag blas.Diag, n int, a []float64, lda int)
+}
+
+func Dtrti2Test(t *testing.T, impl Dtrti2er) {
+	const tol = 1e-14
+	for _, test := range []struct {
+		a    []float64
+		n    int
+		uplo blas.Uplo
+		diag blas.Diag
+		ans  []float64
+	}{
+		{
+			a: []float64{
+				2, 3, 4,
+				0, 5, 6,
+				8, 0, 8},
+			n:    3,
+			uplo: blas.Upper,
+			diag: blas.NonUnit,
+			ans: []float64{
+				0.5, -0.3, -0.025,
+				0, 0.2, -0.15,
+				8, 0, 0.125,
+			},
+		},
+		{
+			a: []float64{
+				5, 3, 4,
+				0, 7, 6,
+				10, 0, 8},
+			n:    3,
+			uplo: blas.Upper,
+			diag: blas.Unit,
+			ans: []float64{
+				5, -3, 14,
+				0, 7, -6,
+				10, 0, 8,
+			},
+		},
+		{
+			a: []float64{
+				2, 0, 0,
+				3, 5, 0,
+				4, 6, 8},
+			n:    3,
+			uplo: blas.Lower,
+			diag: blas.NonUnit,
+			ans: []float64{
+				0.5, 0, 0,
+				-0.3, 0.2, 0,
+				-0.025, -0.15, 0.125,
+			},
+		},
+		{
+			a: []float64{
+				1, 0, 0,
+				3, 1, 0,
+				4, 6, 1},
+			n:    3,
+			uplo: blas.Lower,
+			diag: blas.Unit,
+			ans: []float64{
+				1, 0, 0,
+				-3, 1, 0,
+				14, -6, 1,
+			},
+		},
+	} {
+		impl.Dtrti2(test.uplo, test.diag, test.n, test.a, test.n)
+		if !floats.EqualApprox(test.ans, test.a, tol) {
+			t.Errorf("Matrix inverse mismatch. Want %v, got %v.", test.ans, test.a)
+		}
+	}
+	rnd := rand.New(rand.NewSource(1))
+	bi := blas64.Implementation()
+	for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
+		for _, diag := range []blas.Diag{blas.NonUnit, blas.Unit} {
+			for _, test := range []struct {
+				n, lda int
+			}{
+				{1, 0},
+				{2, 0},
+				{3, 0},
+				{1, 5},
+				{2, 5},
+				{3, 5},
+			} {
+				n := test.n
+				lda := test.lda
+				if lda == 0 {
+					lda = n
+				}
+				a := make([]float64, n*lda)
+				for i := range a {
+					a[i] = rnd.Float64()
+				}
+				aCopy := make([]float64, len(a))
+				copy(aCopy, a)
+				impl.Dtrti2(uplo, diag, n, a, lda)
+				if uplo == blas.Upper {
+					for i := 1; i < n; i++ {
+						for j := 0; j < i; j++ {
+							aCopy[i*lda+j] = 0
+							a[i*lda+j] = 0
+						}
+					}
+				} else {
+					for i := 0; i < n; i++ {
+						for j := i + 1; j < n; j++ {
+							aCopy[i*lda+j] = 0
+							a[i*lda+j] = 0
+						}
+					}
+				}
+				if diag == blas.Unit {
+					for i := 0; i < n; i++ {
+						a[i*lda+i] = 1
+						aCopy[i*lda+i] = 1
+					}
+				}
+				ans := make([]float64, len(a))
+				bi.Dgemm(blas.NoTrans, blas.NoTrans, n, n, n, 1, a, lda, aCopy, lda, 0, ans, lda)
+				iseye := true
+				for i := 0; i < n; i++ {
+					for j := 0; j < n; j++ {
+						if i == j {
+							if math.Abs(ans[i*lda+i]-1) > tol {
+								iseye = false
+								break
+							}
+						} else {
+							if math.Abs(ans[i*lda+j]) > tol {
+								iseye = false
+								break
+							}
+						}
+					}
+				}
+				if !iseye {
+					t.Errorf("inv(A) * A != I. Upper = %v, unit = %v, ans = %v", uplo == blas.Upper, diag == blas.Unit, ans)
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dtrtri.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dtrtri.go
new file mode 100644
index 00000000..1224b7b7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dtrtri.go
@@ -0,0 +1,95 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dtrtrier interface {
+	Dtrconer
+	Dtrtri(uplo blas.Uplo, diag blas.Diag, n int, a []float64, lda int) bool
+}
+
+func DtrtriTest(t *testing.T, impl Dtrtrier) {
+	const tol = 1e-6
+	rnd := rand.New(rand.NewSource(1))
+	bi := blas64.Implementation()
+	for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
+		for _, diag := range []blas.Diag{blas.NonUnit, blas.Unit} {
+			for _, test := range []struct {
+				n, lda int
+			}{
+				{3, 0},
+				{70, 0},
+				{200, 0},
+				{3, 5},
+				{70, 92},
+				{200, 205},
+			} {
+				n := test.n
+				lda := test.lda
+				if lda == 0 {
+					lda = n
+				}
+				a := make([]float64, n*lda)
+				for i := range a {
+					a[i] = rnd.Float64() + 1 // This keeps the matrices well conditioned.
+				}
+				aCopy := make([]float64, len(a))
+				copy(aCopy, a)
+				impl.Dtrtri(uplo, diag, n, a, lda)
+				if uplo == blas.Upper {
+					for i := 1; i < n; i++ {
+						for j := 0; j < i; j++ {
+							aCopy[i*lda+j] = 0
+							a[i*lda+j] = 0
+						}
+					}
+				} else {
+					for i := 0; i < n; i++ {
+						for j := i + 1; j < n; j++ {
+							aCopy[i*lda+j] = 0
+							a[i*lda+j] = 0
+						}
+					}
+				}
+				if diag == blas.Unit {
+					for i := 0; i < n; i++ {
+						a[i*lda+i] = 1
+						aCopy[i*lda+i] = 1
+					}
+				}
+				ans := make([]float64, len(a))
+				bi.Dgemm(blas.NoTrans, blas.NoTrans, n, n, n, 1, a, lda, aCopy, lda, 0, ans, lda)
+				iseye := true
+				for i := 0; i < n; i++ {
+					for j := 0; j < n; j++ {
+						if i == j {
+							if math.Abs(ans[i*lda+i]-1) > tol {
+								iseye = false
+								break
+							}
+						} else {
+							if math.Abs(ans[i*lda+j]) > tol {
+								iseye = false
+								break
+							}
+						}
+					}
+				}
+				if !iseye {
+					t.Errorf("inv(A) * A != I. Upper = %v, unit = %v, n = %v, lda = %v",
+						uplo == blas.Upper, diag == blas.Unit, n, lda)
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/fortran.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/fortran.go
new file mode 100644
index 00000000..45ea6d07
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/fortran.go
@@ -0,0 +1,33 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"strings"
+)
+
+// This file implements types for helping to convert to Fortran testing capabilities.
+
+// fortran64 is a float64 type that prints as a double precision constant in
+// Fortran format.
+type fortran64 float64
+
+func (f fortran64) String() string {
+	// Replace exponent with D
+	s := fmt.Sprintf("%0.16E", f)
+	s = strings.Replace(s, "E", "D", 1)
+	return s
+}
+
+// printFortranArray prints a Go slice as an array that can be copied into a
+// fortran script.
+func printFortranArray(z []float64, name string) {
+	fmt.Printf("%s(1:%d) = (/%v, &\n", name, len(z), fortran64(z[0]))
+	for i := 1; i < len(z)-1; i++ {
+		fmt.Printf("%v, &\n", fortran64(z[i]))
+	}
+	fmt.Printf("%s/)\n", fortran64(z[len(z)-1]))
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/general.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/general.go
new file mode 100644
index 00000000..f2376a7d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/general.go
@@ -0,0 +1,1516 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"fmt"
+	"math"
+	"math/cmplx"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/lapack"
+)
+
+const (
+	// dlamchE is the machine epsilon. For IEEE this is 2^{-53}.
+	dlamchE = 1.0 / (1 << 53)
+	dlamchB = 2
+	dlamchP = dlamchB * dlamchE
+	// dlamchS is the smallest normal number. For IEEE this is 2^{-1022}.
+	dlamchS = 1.0 / (1 << 256) / (1 << 256) / (1 << 256) / (1 << 254)
+)
+
+func max(a, b int) int {
+	if a > b {
+		return a
+	}
+	return b
+}
+
+func min(a, b int) int {
+	if a < b {
+		return a
+	}
+	return b
+}
+
+// worklen describes how much workspace a test should use.
+type worklen int
+
+const (
+	minimumWork worklen = iota
+	mediumWork
+	optimumWork
+)
+
+// nanSlice allocates a new slice of length n filled with NaN.
+func nanSlice(n int) []float64 {
+	s := make([]float64, n)
+	for i := range s {
+		s[i] = math.NaN()
+	}
+	return s
+}
+
+// randomSlice allocates a new slice of length n filled with random values.
+func randomSlice(n int, rnd *rand.Rand) []float64 {
+	s := make([]float64, n)
+	for i := range s {
+		s[i] = rnd.NormFloat64()
+	}
+	return s
+}
+
+// nanGeneral allocates a new r×c general matrix filled with NaN values.
+func nanGeneral(r, c, stride int) blas64.General {
+	if r < 0 || c < 0 {
+		panic("bad matrix size")
+	}
+	if r == 0 || c == 0 {
+		return blas64.General{Stride: max(1, stride)}
+	}
+	if stride < c {
+		panic("bad stride")
+	}
+	return blas64.General{
+		Rows:   r,
+		Cols:   c,
+		Stride: stride,
+		Data:   nanSlice((r-1)*stride + c),
+	}
+}
+
+// randomGeneral allocates a new r×c general matrix filled with random
+// numbers. Out-of-range elements are filled with NaN values.
+func randomGeneral(r, c, stride int, rnd *rand.Rand) blas64.General {
+	ans := nanGeneral(r, c, stride)
+	for i := 0; i < r; i++ {
+		for j := 0; j < c; j++ {
+			ans.Data[i*ans.Stride+j] = rnd.NormFloat64()
+		}
+	}
+	return ans
+}
+
+// randomHessenberg allocates a new n×n Hessenberg matrix filled with zeros
+// under the first subdiagonal and with random numbers elsewhere. Out-of-range
+// elements are filled with NaN values.
+func randomHessenberg(n, stride int, rnd *rand.Rand) blas64.General {
+	ans := nanGeneral(n, n, stride)
+	for i := 0; i < n; i++ {
+		for j := 0; j < i-1; j++ {
+			ans.Data[i*ans.Stride+j] = 0
+		}
+		for j := max(0, i-1); j < n; j++ {
+			ans.Data[i*ans.Stride+j] = rnd.NormFloat64()
+		}
+	}
+	return ans
+}
+
+// randomSchurCanonical returns a random, general matrix in Schur canonical
+// form, that is, block upper triangular with 1×1 and 2×2 diagonal blocks where
+// each 2×2 diagonal block has its diagonal elements equal and its off-diagonal
+// elements of opposite sign.
+func randomSchurCanonical(n, stride int, rnd *rand.Rand) blas64.General {
+	t := randomGeneral(n, n, stride, rnd)
+	// Zero out the lower triangle.
+	for i := 0; i < t.Rows; i++ {
+		for j := 0; j < i; j++ {
+			t.Data[i*t.Stride+j] = 0
+		}
+	}
+	// Randomly create 2×2 diagonal blocks.
+	for i := 0; i < t.Rows; {
+		if i == t.Rows-1 || rnd.Float64() < 0.5 {
+			// 1×1 block.
+			i++
+			continue
+		}
+		// 2×2 block.
+		// Diagonal elements equal.
+		t.Data[(i+1)*t.Stride+i+1] = t.Data[i*t.Stride+i]
+		// Off-diagonal elements of opposite sign.
+		c := rnd.NormFloat64()
+		if math.Signbit(c) == math.Signbit(t.Data[i*t.Stride+i+1]) {
+			c *= -1
+		}
+		t.Data[(i+1)*t.Stride+i] = c
+		i += 2
+	}
+	return t
+}
+
+// blockedUpperTriGeneral returns a normal random, general matrix in the form
+//
+//            c-k-l  k    l
+//  A =    k [  0   A12  A13 ] if r-k-l >= 0;
+//         l [  0    0   A23 ]
+//     r-k-l [  0    0    0  ]
+//
+//          c-k-l  k    l
+//  A =  k [  0   A12  A13 ] if r-k-l < 0;
+//     r-k [  0    0   A23 ]
+//
+// where the k×k matrix A12 and l×l matrix is non-singular
+// upper triangular. A23 is l×l upper triangular if r-k-l >= 0,
+// otherwise A23 is (r-k)×l upper trapezoidal.
+func blockedUpperTriGeneral(r, c, k, l, stride int, kblock bool, rnd *rand.Rand) blas64.General {
+	t := l
+	if kblock {
+		t += k
+	}
+	ans := zeros(r, c, stride)
+	for i := 0; i < min(r, t); i++ {
+		var v float64
+		for v == 0 {
+			v = rnd.NormFloat64()
+		}
+		ans.Data[i*ans.Stride+i+(c-t)] = v
+	}
+	for i := 0; i < min(r, t); i++ {
+		for j := i + (c - t) + 1; j < c; j++ {
+			ans.Data[i*ans.Stride+j] = rnd.NormFloat64()
+		}
+	}
+	return ans
+}
+
+// nanTriangular allocates a new r×c triangular matrix filled with NaN values.
+func nanTriangular(uplo blas.Uplo, n, stride int) blas64.Triangular {
+	if n < 0 {
+		panic("bad matrix size")
+	}
+	if n == 0 {
+		return blas64.Triangular{
+			Stride: max(1, stride),
+			Uplo:   uplo,
+			Diag:   blas.NonUnit,
+		}
+	}
+	if stride < n {
+		panic("bad stride")
+	}
+	return blas64.Triangular{
+		N:      n,
+		Stride: stride,
+		Data:   nanSlice((n-1)*stride + n),
+		Uplo:   uplo,
+		Diag:   blas.NonUnit,
+	}
+}
+
+// generalOutsideAllNaN returns whether all out-of-range elements have NaN
+// values.
+func generalOutsideAllNaN(a blas64.General) bool {
+	// Check after last column.
+	for i := 0; i < a.Rows-1; i++ {
+		for _, v := range a.Data[i*a.Stride+a.Cols : i*a.Stride+a.Stride] {
+			if !math.IsNaN(v) {
+				return false
+			}
+		}
+	}
+	// Check after last element.
+	last := (a.Rows-1)*a.Stride + a.Cols
+	if a.Rows == 0 || a.Cols == 0 {
+		last = 0
+	}
+	for _, v := range a.Data[last:] {
+		if !math.IsNaN(v) {
+			return false
+		}
+	}
+	return true
+}
+
+// triangularOutsideAllNaN returns whether all out-of-triangle elements have NaN
+// values.
+func triangularOutsideAllNaN(a blas64.Triangular) bool {
+	if a.Uplo == blas.Upper {
+		// Check below diagonal.
+		for i := 0; i < a.N; i++ {
+			for _, v := range a.Data[i*a.Stride : i*a.Stride+i] {
+				if !math.IsNaN(v) {
+					return false
+				}
+			}
+		}
+		// Check after last column.
+		for i := 0; i < a.N-1; i++ {
+			for _, v := range a.Data[i*a.Stride+a.N : i*a.Stride+a.Stride] {
+				if !math.IsNaN(v) {
+					return false
+				}
+			}
+		}
+	} else {
+		// Check above diagonal.
+		for i := 0; i < a.N-1; i++ {
+			for _, v := range a.Data[i*a.Stride+i+1 : i*a.Stride+a.Stride] {
+				if !math.IsNaN(v) {
+					return false
+				}
+			}
+		}
+	}
+	// Check after last element.
+	for _, v := range a.Data[max(0, a.N-1)*a.Stride+a.N:] {
+		if !math.IsNaN(v) {
+			return false
+		}
+	}
+	return true
+}
+
+// transposeGeneral returns a new general matrix that is the transpose of the
+// input. Nothing is done with data outside the {rows, cols} limit of the general.
+func transposeGeneral(a blas64.General) blas64.General {
+	ans := blas64.General{
+		Rows:   a.Cols,
+		Cols:   a.Rows,
+		Stride: a.Rows,
+		Data:   make([]float64, a.Cols*a.Rows),
+	}
+	for i := 0; i < a.Rows; i++ {
+		for j := 0; j < a.Cols; j++ {
+			ans.Data[j*ans.Stride+i] = a.Data[i*a.Stride+j]
+		}
+	}
+	return ans
+}
+
+// columnNorms returns the column norms of a.
+func columnNorms(m, n int, a []float64, lda int) []float64 {
+	bi := blas64.Implementation()
+	norms := make([]float64, n)
+	for j := 0; j < n; j++ {
+		norms[j] = bi.Dnrm2(m, a[j:], lda)
+	}
+	return norms
+}
+
+// extractVMat collects the single reflectors from a into a matrix.
+func extractVMat(m, n int, a []float64, lda int, direct lapack.Direct, store lapack.StoreV) blas64.General {
+	k := min(m, n)
+	switch {
+	default:
+		panic("not implemented")
+	case direct == lapack.Forward && store == lapack.ColumnWise:
+		v := blas64.General{
+			Rows:   m,
+			Cols:   k,
+			Stride: k,
+			Data:   make([]float64, m*k),
+		}
+		for i := 0; i < k; i++ {
+			for j := 0; j < i; j++ {
+				v.Data[j*v.Stride+i] = 0
+			}
+			v.Data[i*v.Stride+i] = 1
+			for j := i + 1; j < m; j++ {
+				v.Data[j*v.Stride+i] = a[j*lda+i]
+			}
+		}
+		return v
+	case direct == lapack.Forward && store == lapack.RowWise:
+		v := blas64.General{
+			Rows:   k,
+			Cols:   n,
+			Stride: n,
+			Data:   make([]float64, k*n),
+		}
+		for i := 0; i < k; i++ {
+			for j := 0; j < i; j++ {
+				v.Data[i*v.Stride+j] = 0
+			}
+			v.Data[i*v.Stride+i] = 1
+			for j := i + 1; j < n; j++ {
+				v.Data[i*v.Stride+j] = a[i*lda+j]
+			}
+		}
+		return v
+	}
+}
+
+// constructBidiagonal constructs a bidiagonal matrix with the given diagonal
+// and off-diagonal elements.
+func constructBidiagonal(uplo blas.Uplo, n int, d, e []float64) blas64.General {
+	bMat := blas64.General{
+		Rows:   n,
+		Cols:   n,
+		Stride: n,
+		Data:   make([]float64, n*n),
+	}
+
+	for i := 0; i < n-1; i++ {
+		bMat.Data[i*bMat.Stride+i] = d[i]
+		if uplo == blas.Upper {
+			bMat.Data[i*bMat.Stride+i+1] = e[i]
+		} else {
+			bMat.Data[(i+1)*bMat.Stride+i] = e[i]
+		}
+	}
+	bMat.Data[(n-1)*bMat.Stride+n-1] = d[n-1]
+	return bMat
+}
+
+// constructVMat transforms the v matrix based on the storage.
+func constructVMat(vMat blas64.General, store lapack.StoreV, direct lapack.Direct) blas64.General {
+	m := vMat.Rows
+	k := vMat.Cols
+	switch {
+	default:
+		panic("not implemented")
+	case store == lapack.ColumnWise && direct == lapack.Forward:
+		ldv := k
+		v := make([]float64, m*k)
+		for i := 0; i < m; i++ {
+			for j := 0; j < k; j++ {
+				if j > i {
+					v[i*ldv+j] = 0
+				} else if j == i {
+					v[i*ldv+i] = 1
+				} else {
+					v[i*ldv+j] = vMat.Data[i*vMat.Stride+j]
+				}
+			}
+		}
+		return blas64.General{
+			Rows:   m,
+			Cols:   k,
+			Stride: k,
+			Data:   v,
+		}
+	case store == lapack.RowWise && direct == lapack.Forward:
+		ldv := m
+		v := make([]float64, m*k)
+		for i := 0; i < m; i++ {
+			for j := 0; j < k; j++ {
+				if j > i {
+					v[j*ldv+i] = 0
+				} else if j == i {
+					v[j*ldv+i] = 1
+				} else {
+					v[j*ldv+i] = vMat.Data[i*vMat.Stride+j]
+				}
+			}
+		}
+		return blas64.General{
+			Rows:   k,
+			Cols:   m,
+			Stride: m,
+			Data:   v,
+		}
+	case store == lapack.ColumnWise && direct == lapack.Backward:
+		rowsv := m
+		ldv := k
+		v := make([]float64, m*k)
+		for i := 0; i < m; i++ {
+			for j := 0; j < k; j++ {
+				vrow := rowsv - i - 1
+				vcol := k - j - 1
+				if j > i {
+					v[vrow*ldv+vcol] = 0
+				} else if j == i {
+					v[vrow*ldv+vcol] = 1
+				} else {
+					v[vrow*ldv+vcol] = vMat.Data[i*vMat.Stride+j]
+				}
+			}
+		}
+		return blas64.General{
+			Rows:   rowsv,
+			Cols:   ldv,
+			Stride: ldv,
+			Data:   v,
+		}
+	case store == lapack.RowWise && direct == lapack.Backward:
+		rowsv := k
+		ldv := m
+		v := make([]float64, m*k)
+		for i := 0; i < m; i++ {
+			for j := 0; j < k; j++ {
+				vcol := ldv - i - 1
+				vrow := k - j - 1
+				if j > i {
+					v[vrow*ldv+vcol] = 0
+				} else if j == i {
+					v[vrow*ldv+vcol] = 1
+				} else {
+					v[vrow*ldv+vcol] = vMat.Data[i*vMat.Stride+j]
+				}
+			}
+		}
+		return blas64.General{
+			Rows:   rowsv,
+			Cols:   ldv,
+			Stride: ldv,
+			Data:   v,
+		}
+	}
+}
+
+func constructH(tau []float64, v blas64.General, store lapack.StoreV, direct lapack.Direct) blas64.General {
+	m := v.Rows
+	k := v.Cols
+	if store == lapack.RowWise {
+		m, k = k, m
+	}
+	h := blas64.General{
+		Rows:   m,
+		Cols:   m,
+		Stride: m,
+		Data:   make([]float64, m*m),
+	}
+	for i := 0; i < m; i++ {
+		h.Data[i*m+i] = 1
+	}
+	for i := 0; i < k; i++ {
+		vecData := make([]float64, m)
+		if store == lapack.ColumnWise {
+			for j := 0; j < m; j++ {
+				vecData[j] = v.Data[j*v.Cols+i]
+			}
+		} else {
+			for j := 0; j < m; j++ {
+				vecData[j] = v.Data[i*v.Cols+j]
+			}
+		}
+		vec := blas64.Vector{
+			Inc:  1,
+			Data: vecData,
+		}
+
+		hi := blas64.General{
+			Rows:   m,
+			Cols:   m,
+			Stride: m,
+			Data:   make([]float64, m*m),
+		}
+		for i := 0; i < m; i++ {
+			hi.Data[i*m+i] = 1
+		}
+		// hi = I - tau * v * v^T
+		blas64.Ger(-tau[i], vec, vec, hi)
+
+		hcopy := blas64.General{
+			Rows:   m,
+			Cols:   m,
+			Stride: m,
+			Data:   make([]float64, m*m),
+		}
+		copy(hcopy.Data, h.Data)
+		if direct == lapack.Forward {
+			// H = H * H_I in forward mode
+			blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, hcopy, hi, 0, h)
+		} else {
+			// H = H_I * H in backward mode
+			blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, hi, hcopy, 0, h)
+		}
+	}
+	return h
+}
+
+// constructQ constructs the Q matrix from the result of dgeqrf and dgeqr2.
+func constructQ(kind string, m, n int, a []float64, lda int, tau []float64) blas64.General {
+	k := min(m, n)
+	return constructQK(kind, m, n, k, a, lda, tau)
+}
+
+// constructQK constructs the Q matrix from the result of dgeqrf and dgeqr2 using
+// the first k reflectors.
+func constructQK(kind string, m, n, k int, a []float64, lda int, tau []float64) blas64.General {
+	var sz int
+	switch kind {
+	case "QR":
+		sz = m
+	case "LQ", "RQ":
+		sz = n
+	}
+
+	q := blas64.General{
+		Rows:   sz,
+		Cols:   sz,
+		Stride: sz,
+		Data:   make([]float64, sz*sz),
+	}
+	for i := 0; i < sz; i++ {
+		q.Data[i*sz+i] = 1
+	}
+	qCopy := blas64.General{
+		Rows:   q.Rows,
+		Cols:   q.Cols,
+		Stride: q.Stride,
+		Data:   make([]float64, len(q.Data)),
+	}
+	for i := 0; i < k; i++ {
+		h := blas64.General{
+			Rows:   sz,
+			Cols:   sz,
+			Stride: sz,
+			Data:   make([]float64, sz*sz),
+		}
+		for j := 0; j < sz; j++ {
+			h.Data[j*sz+j] = 1
+		}
+		vVec := blas64.Vector{
+			Inc:  1,
+			Data: make([]float64, sz),
+		}
+		switch kind {
+		case "QR":
+			vVec.Data[i] = 1
+			for j := i + 1; j < sz; j++ {
+				vVec.Data[j] = a[lda*j+i]
+			}
+		case "LQ":
+			vVec.Data[i] = 1
+			for j := i + 1; j < sz; j++ {
+				vVec.Data[j] = a[i*lda+j]
+			}
+		case "RQ":
+			for j := 0; j < n-k+i; j++ {
+				vVec.Data[j] = a[(m-k+i)*lda+j]
+			}
+			vVec.Data[n-k+i] = 1
+		}
+		blas64.Ger(-tau[i], vVec, vVec, h)
+		copy(qCopy.Data, q.Data)
+		// Multiply q by the new h.
+		switch kind {
+		case "QR", "RQ":
+			blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, qCopy, h, 0, q)
+		case "LQ":
+			blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, h, qCopy, 0, q)
+		}
+	}
+	return q
+}
+
+// checkBidiagonal checks the bidiagonal decomposition from dlabrd and dgebd2.
+// The input to this function is the answer returned from the routines, stored
+// in a, d, e, tauP, and tauQ. The data of original A matrix (before
+// decomposition) is input in aCopy.
+//
+// checkBidiagonal constructs the V and U matrices, and from them constructs Q
+// and P. Using these constructions, it checks that Q^T * A * P and checks that
+// the result is bidiagonal.
+func checkBidiagonal(t *testing.T, m, n, nb int, a []float64, lda int, d, e, tauP, tauQ, aCopy []float64) {
+	// Check the answer.
+	// Construct V and U.
+	qMat := constructQPBidiagonal(lapack.ApplyQ, m, n, nb, a, lda, tauQ)
+	pMat := constructQPBidiagonal(lapack.ApplyP, m, n, nb, a, lda, tauP)
+
+	// Compute Q^T * A * P.
+	aMat := blas64.General{
+		Rows:   m,
+		Cols:   n,
+		Stride: lda,
+		Data:   make([]float64, len(aCopy)),
+	}
+	copy(aMat.Data, aCopy)
+
+	tmp1 := blas64.General{
+		Rows:   m,
+		Cols:   n,
+		Stride: n,
+		Data:   make([]float64, m*n),
+	}
+	blas64.Gemm(blas.Trans, blas.NoTrans, 1, qMat, aMat, 0, tmp1)
+	tmp2 := blas64.General{
+		Rows:   m,
+		Cols:   n,
+		Stride: n,
+		Data:   make([]float64, m*n),
+	}
+	blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, tmp1, pMat, 0, tmp2)
+
+	// Check that the first nb rows and cols of tm2 are upper bidiagonal
+	// if m >= n, and lower bidiagonal otherwise.
+	correctDiag := true
+	matchD := true
+	matchE := true
+	for i := 0; i < m; i++ {
+		for j := 0; j < n; j++ {
+			if i >= nb && j >= nb {
+				continue
+			}
+			v := tmp2.Data[i*tmp2.Stride+j]
+			if i == j {
+				if math.Abs(d[i]-v) > 1e-12 {
+					matchD = false
+				}
+				continue
+			}
+			if m >= n && i == j-1 {
+				if math.Abs(e[j-1]-v) > 1e-12 {
+					matchE = false
+				}
+				continue
+			}
+			if m < n && i-1 == j {
+				if math.Abs(e[i-1]-v) > 1e-12 {
+					matchE = false
+				}
+				continue
+			}
+			if math.Abs(v) > 1e-12 {
+				correctDiag = false
+			}
+		}
+	}
+	if !correctDiag {
+		t.Errorf("Updated A not bi-diagonal")
+	}
+	if !matchD {
+		fmt.Println("d = ", d)
+		t.Errorf("D Mismatch")
+	}
+	if !matchE {
+		t.Errorf("E mismatch")
+	}
+}
+
+// constructQPBidiagonal constructs Q or P from the Bidiagonal decomposition
+// computed by dlabrd and bgebd2.
+func constructQPBidiagonal(vect lapack.DecompUpdate, m, n, nb int, a []float64, lda int, tau []float64) blas64.General {
+	sz := n
+	if vect == lapack.ApplyQ {
+		sz = m
+	}
+
+	var ldv int
+	var v blas64.General
+	if vect == lapack.ApplyQ {
+		ldv = nb
+		v = blas64.General{
+			Rows:   m,
+			Cols:   nb,
+			Stride: ldv,
+			Data:   make([]float64, m*ldv),
+		}
+	} else {
+		ldv = n
+		v = blas64.General{
+			Rows:   nb,
+			Cols:   n,
+			Stride: ldv,
+			Data:   make([]float64, m*ldv),
+		}
+	}
+
+	if vect == lapack.ApplyQ {
+		if m >= n {
+			for i := 0; i < m; i++ {
+				for j := 0; j <= min(nb-1, i); j++ {
+					if i == j {
+						v.Data[i*ldv+j] = 1
+						continue
+					}
+					v.Data[i*ldv+j] = a[i*lda+j]
+				}
+			}
+		} else {
+			for i := 1; i < m; i++ {
+				for j := 0; j <= min(nb-1, i-1); j++ {
+					if i-1 == j {
+						v.Data[i*ldv+j] = 1
+						continue
+					}
+					v.Data[i*ldv+j] = a[i*lda+j]
+				}
+			}
+		}
+	} else {
+		if m < n {
+			for i := 0; i < nb; i++ {
+				for j := i; j < n; j++ {
+					if i == j {
+						v.Data[i*ldv+j] = 1
+						continue
+					}
+					v.Data[i*ldv+j] = a[i*lda+j]
+				}
+			}
+		} else {
+			for i := 0; i < nb; i++ {
+				for j := i + 1; j < n; j++ {
+					if j-1 == i {
+						v.Data[i*ldv+j] = 1
+						continue
+					}
+					v.Data[i*ldv+j] = a[i*lda+j]
+				}
+			}
+		}
+	}
+
+	// The variable name is a computation of Q, but the algorithm is mostly the
+	// same for computing P (just with different data).
+	qMat := blas64.General{
+		Rows:   sz,
+		Cols:   sz,
+		Stride: sz,
+		Data:   make([]float64, sz*sz),
+	}
+	hMat := blas64.General{
+		Rows:   sz,
+		Cols:   sz,
+		Stride: sz,
+		Data:   make([]float64, sz*sz),
+	}
+	// set Q to I
+	for i := 0; i < sz; i++ {
+		qMat.Data[i*qMat.Stride+i] = 1
+	}
+	for i := 0; i < nb; i++ {
+		qCopy := blas64.General{Rows: qMat.Rows, Cols: qMat.Cols, Stride: qMat.Stride, Data: make([]float64, len(qMat.Data))}
+		copy(qCopy.Data, qMat.Data)
+
+		// Set g and h to I
+		for i := 0; i < sz; i++ {
+			for j := 0; j < sz; j++ {
+				if i == j {
+					hMat.Data[i*sz+j] = 1
+				} else {
+					hMat.Data[i*sz+j] = 0
+				}
+			}
+		}
+		var vi blas64.Vector
+		// H -= tauQ[i] * v[i] * v[i]^t
+		if vect == lapack.ApplyQ {
+			vi = blas64.Vector{
+				Inc:  v.Stride,
+				Data: v.Data[i:],
+			}
+		} else {
+			vi = blas64.Vector{
+				Inc:  1,
+				Data: v.Data[i*v.Stride:],
+			}
+		}
+		blas64.Ger(-tau[i], vi, vi, hMat)
+		// Q = Q * G[1]
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, qCopy, hMat, 0, qMat)
+	}
+	return qMat
+}
+
+// printRowise prints the matrix with one row per line. This is useful for debugging.
+// If beyond is true, it prints beyond the final column to lda. If false, only
+// the columns are printed.
+func printRowise(a []float64, m, n, lda int, beyond bool) {
+	for i := 0; i < m; i++ {
+		end := n
+		if beyond {
+			end = lda
+		}
+		fmt.Println(a[i*lda : i*lda+end])
+	}
+}
+
+// isOrthonormal checks that a general matrix is orthonormal.
+func isOrthonormal(q blas64.General) bool {
+	n := q.Rows
+	for i := 0; i < n; i++ {
+		for j := i; j < n; j++ {
+			dot := blas64.Dot(n,
+				blas64.Vector{Inc: 1, Data: q.Data[i*q.Stride:]},
+				blas64.Vector{Inc: 1, Data: q.Data[j*q.Stride:]},
+			)
+			if math.IsNaN(dot) {
+				return false
+			}
+			if i == j {
+				if math.Abs(dot-1) > 1e-10 {
+					return false
+				}
+			} else {
+				if math.Abs(dot) > 1e-10 {
+					return false
+				}
+			}
+		}
+	}
+	return true
+}
+
+// copyMatrix copies an m×n matrix src of stride n into an m×n matrix dst of stride ld.
+func copyMatrix(m, n int, dst []float64, ld int, src []float64) {
+	for i := 0; i < m; i++ {
+		copy(dst[i*ld:i*ld+n], src[i*n:i*n+n])
+	}
+}
+
+func copyGeneral(dst, src blas64.General) {
+	r := min(dst.Rows, src.Rows)
+	c := min(dst.Cols, src.Cols)
+	for i := 0; i < r; i++ {
+		copy(dst.Data[i*dst.Stride:i*dst.Stride+c], src.Data[i*src.Stride:i*src.Stride+c])
+	}
+}
+
+// cloneGeneral allocates and returns an exact copy of the given general matrix.
+func cloneGeneral(a blas64.General) blas64.General {
+	c := a
+	c.Data = make([]float64, len(a.Data))
+	copy(c.Data, a.Data)
+	return c
+}
+
+// equalApprox returns whether the matrices A and B of order n are approximately
+// equal within given tolerance.
+func equalApprox(m, n int, a []float64, lda int, b []float64, tol float64) bool {
+	for i := 0; i < m; i++ {
+		for j := 0; j < n; j++ {
+			diff := a[i*lda+j] - b[i*n+j]
+			if math.IsNaN(diff) || math.Abs(diff) > tol {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+// equalApproxGeneral returns whether the general matrices a and b are
+// approximately equal within given tolerance.
+func equalApproxGeneral(a, b blas64.General, tol float64) bool {
+	if a.Rows != b.Rows || a.Cols != b.Cols {
+		panic("bad input")
+	}
+	for i := 0; i < a.Rows; i++ {
+		for j := 0; j < a.Cols; j++ {
+			diff := a.Data[i*a.Stride+j] - b.Data[i*b.Stride+j]
+			if math.IsNaN(diff) || math.Abs(diff) > tol {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+// equalApproxTriangular returns whether the triangular matrices A and B of
+// order n are approximately equal within given tolerance.
+func equalApproxTriangular(upper bool, n int, a []float64, lda int, b []float64, tol float64) bool {
+	if upper {
+		for i := 0; i < n; i++ {
+			for j := i; j < n; j++ {
+				diff := a[i*lda+j] - b[i*n+j]
+				if math.IsNaN(diff) || math.Abs(diff) > tol {
+					return false
+				}
+			}
+		}
+		return true
+	}
+	for i := 0; i < n; i++ {
+		for j := 0; j <= i; j++ {
+			diff := a[i*lda+j] - b[i*n+j]
+			if math.IsNaN(diff) || math.Abs(diff) > tol {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+func equalApproxSymmetric(a, b blas64.Symmetric, tol float64) bool {
+	if a.Uplo != b.Uplo {
+		return false
+	}
+	if a.N != b.N {
+		return false
+	}
+	if a.Uplo == blas.Upper {
+		for i := 0; i < a.N; i++ {
+			for j := i; j < a.N; j++ {
+				if !floats.EqualWithinAbsOrRel(a.Data[i*a.Stride+j], b.Data[i*b.Stride+j], tol, tol) {
+					return false
+				}
+			}
+		}
+		return true
+	}
+	for i := 0; i < a.N; i++ {
+		for j := 0; j <= i; j++ {
+			if !floats.EqualWithinAbsOrRel(a.Data[i*a.Stride+j], b.Data[i*b.Stride+j], tol, tol) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+// randSymBand creates a random symmetric banded matrix, and returns both the
+// random matrix and the equivalent Symmetric matrix for testing. rnder
+// specifies the random number
+func randSymBand(ul blas.Uplo, n, ldab, kb int, rnd *rand.Rand) (blas64.Symmetric, blas64.SymmetricBand) {
+	// A matrix is positive definite if and only if it has a Cholesky
+	// decomposition. Generate a random banded lower triangular matrix
+	// to construct the random symmetric matrix.
+	a := make([]float64, n*n)
+	for i := 0; i < n; i++ {
+		for j := max(0, i-kb); j <= i; j++ {
+			a[i*n+j] = rnd.NormFloat64()
+		}
+		a[i*n+i] = math.Abs(a[i*n+i])
+		// Add an extra amound to the diagonal in order to improve the condition number.
+		a[i*n+i] += 1.5 * rnd.Float64()
+	}
+	agen := blas64.General{
+		Rows:   n,
+		Cols:   n,
+		Stride: n,
+		Data:   a,
+	}
+
+	// Construct the SymDense from a*a^T
+	c := make([]float64, n*n)
+	cgen := blas64.General{
+		Rows:   n,
+		Cols:   n,
+		Stride: n,
+		Data:   c,
+	}
+	blas64.Gemm(blas.NoTrans, blas.Trans, 1, agen, agen, 0, cgen)
+	sym := blas64.Symmetric{
+		N:      n,
+		Stride: n,
+		Data:   c,
+		Uplo:   ul,
+	}
+
+	b := symToSymBand(ul, c, n, n, kb, ldab)
+	band := blas64.SymmetricBand{
+		N:      n,
+		K:      kb,
+		Stride: ldab,
+		Data:   b,
+		Uplo:   ul,
+	}
+
+	return sym, band
+}
+
+// symToSymBand takes the data in a Symmetric matrix and returns a
+// SymmetricBanded matrix.
+func symToSymBand(ul blas.Uplo, a []float64, n, lda, kb, ldab int) []float64 {
+	if ul == blas.Upper {
+		band := make([]float64, (n-1)*ldab+kb+1)
+		for i := 0; i < n; i++ {
+			for j := i; j < min(i+kb+1, n); j++ {
+				band[i*ldab+j-i] = a[i*lda+j]
+			}
+		}
+		return band
+	}
+	band := make([]float64, (n-1)*ldab+kb+1)
+	for i := 0; i < n; i++ {
+		for j := max(0, i-kb); j <= i; j++ {
+			band[i*ldab+j-i+kb] = a[i*lda+j]
+		}
+	}
+	return band
+}
+
+// symBandToSym takes a banded symmetric matrix and returns the same data as
+// a Symmetric matrix.
+func symBandToSym(ul blas.Uplo, band []float64, n, kb, ldab int) blas64.Symmetric {
+	sym := make([]float64, n*n)
+	if ul == blas.Upper {
+		for i := 0; i < n; i++ {
+			for j := 0; j < min(kb+1+i, n)-i; j++ {
+				sym[i*n+i+j] = band[i*ldab+j]
+			}
+		}
+	} else {
+		for i := 0; i < n; i++ {
+			for j := kb - min(i, kb); j < kb+1; j++ {
+				sym[i*n+i-kb+j] = band[i*ldab+j]
+			}
+		}
+	}
+	return blas64.Symmetric{
+		N:      n,
+		Stride: n,
+		Data:   sym,
+		Uplo:   ul,
+	}
+}
+
+// eye returns an identity matrix of given order and stride.
+func eye(n, stride int) blas64.General {
+	ans := nanGeneral(n, n, stride)
+	for i := 0; i < n; i++ {
+		for j := 0; j < n; j++ {
+			ans.Data[i*ans.Stride+j] = 0
+		}
+		ans.Data[i*ans.Stride+i] = 1
+	}
+	return ans
+}
+
+// zeros returns an m×n matrix with given stride filled with zeros.
+func zeros(m, n, stride int) blas64.General {
+	a := nanGeneral(m, n, stride)
+	for i := 0; i < m; i++ {
+		for j := 0; j < n; j++ {
+			a.Data[i*a.Stride+j] = 0
+		}
+	}
+	return a
+}
+
+// extract2x2Block returns the elements of T at [0,0], [0,1], [1,0], and [1,1].
+func extract2x2Block(t []float64, ldt int) (a, b, c, d float64) {
+	return t[0], t[1], t[ldt], t[ldt+1]
+}
+
+// isSchurCanonical returns whether the 2×2 matrix [a b; c d] is in Schur
+// canonical form.
+func isSchurCanonical(a, b, c, d float64) bool {
+	return c == 0 || (a == d && math.Signbit(b) != math.Signbit(c))
+}
+
+// isSchurCanonicalGeneral returns whether T is block upper triangular with 1×1
+// and 2×2 diagonal blocks, each 2×2 block in Schur canonical form. The function
+// checks only along the diagonal and the first subdiagonal, otherwise the lower
+// triangle is not accessed.
+func isSchurCanonicalGeneral(t blas64.General) bool {
+	if t.Rows != t.Cols {
+		panic("invalid matrix")
+	}
+	for i := 0; i < t.Rows-1; {
+		if t.Data[(i+1)*t.Stride+i] == 0 {
+			// 1×1 block.
+			i++
+			continue
+		}
+		// 2×2 block.
+		a, b, c, d := extract2x2Block(t.Data[i*t.Stride+i:], t.Stride)
+		if !isSchurCanonical(a, b, c, d) {
+			return false
+		}
+		i += 2
+	}
+	return true
+}
+
+// schurBlockEigenvalues returns the two eigenvalues of the 2×2 matrix [a b; c d]
+// that must be in Schur canonical form.
+func schurBlockEigenvalues(a, b, c, d float64) (ev1, ev2 complex128) {
+	if !isSchurCanonical(a, b, c, d) {
+		panic("block not in Schur canonical form")
+	}
+	if c == 0 {
+		return complex(a, 0), complex(d, 0)
+	}
+	im := math.Sqrt(-b * c)
+	return complex(a, im), complex(a, -im)
+}
+
+// schurBlockSize returns the size of the diagonal block at i-th row in the
+// upper quasi-triangular matrix t in Schur canonical form, and whether i points
+// to the first row of the block. For zero-sized matrices the function returns 0
+// and true.
+func schurBlockSize(t blas64.General, i int) (size int, first bool) {
+	if t.Rows != t.Cols {
+		panic("matrix not square")
+	}
+	if t.Rows == 0 {
+		return 0, true
+	}
+	if i < 0 || t.Rows <= i {
+		panic("index out of range")
+	}
+
+	first = true
+	if i > 0 && t.Data[i*t.Stride+i-1] != 0 {
+		// There is a non-zero element to the left, therefore i must
+		// point to the second row in a 2×2 diagonal block.
+		first = false
+		i--
+	}
+	size = 1
+	if i+1 < t.Rows && t.Data[(i+1)*t.Stride+i] != 0 {
+		// There is a non-zero element below, this must be a 2×2
+		// diagonal block.
+		size = 2
+	}
+	return size, first
+}
+
+// containsComplex returns whether z is approximately equal to one of the complex
+// numbers in v. If z is found, its index in v will be also returned.
+func containsComplex(v []complex128, z complex128, tol float64) (found bool, index int) {
+	for i := range v {
+		if cmplx.Abs(v[i]-z) < tol {
+			return true, i
+		}
+	}
+	return false, -1
+}
+
+// isAllNaN returns whether x contains only NaN values.
+func isAllNaN(x []float64) bool {
+	for _, v := range x {
+		if !math.IsNaN(v) {
+			return false
+		}
+	}
+	return true
+}
+
+// isUpperHessenberg returns whether h contains only zeros below the
+// subdiagonal.
+func isUpperHessenberg(h blas64.General) bool {
+	if h.Rows != h.Cols {
+		panic("matrix not square")
+	}
+	n := h.Rows
+	for i := 0; i < n; i++ {
+		for j := 0; j < n; j++ {
+			if i > j+1 && h.Data[i*h.Stride+j] != 0 {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+// isUpperTriangular returns whether a contains only zeros below the diagonal.
+func isUpperTriangular(a blas64.General) bool {
+	n := a.Rows
+	for i := 1; i < n; i++ {
+		for j := 0; j < i; j++ {
+			if a.Data[i*a.Stride+j] != 0 {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+// unbalancedSparseGeneral returns an m×n dense matrix with a random sparse
+// structure consisting of nz nonzero elements. The matrix will be unbalanced by
+// multiplying each element randomly by its row or column index.
+func unbalancedSparseGeneral(m, n, stride int, nonzeros int, rnd *rand.Rand) blas64.General {
+	a := zeros(m, n, stride)
+	for k := 0; k < nonzeros; k++ {
+		i := rnd.Intn(n)
+		j := rnd.Intn(n)
+		if rnd.Float64() < 0.5 {
+			a.Data[i*stride+j] = float64(i+1) * rnd.NormFloat64()
+		} else {
+			a.Data[i*stride+j] = float64(j+1) * rnd.NormFloat64()
+		}
+	}
+	return a
+}
+
+// columnOf returns a copy of the j-th column of a.
+func columnOf(a blas64.General, j int) []float64 {
+	if j < 0 || a.Cols <= j {
+		panic("bad column index")
+	}
+	col := make([]float64, a.Rows)
+	for i := range col {
+		col[i] = a.Data[i*a.Stride+j]
+	}
+	return col
+}
+
+// isRightEigenvectorOf returns whether the vector xRe+i*xIm, where i is the
+// imaginary unit, is the right eigenvector of A corresponding to the eigenvalue
+// lambda.
+//
+// A right eigenvector corresponding to a complex eigenvalue λ is a complex
+// non-zero vector x such that
+//  A x = λ x.
+func isRightEigenvectorOf(a blas64.General, xRe, xIm []float64, lambda complex128, tol float64) bool {
+	if a.Rows != a.Cols {
+		panic("matrix not square")
+	}
+
+	if imag(lambda) != 0 && xIm == nil {
+		// Complex eigenvalue of a real matrix cannot have a real
+		// eigenvector.
+		return false
+	}
+
+	n := a.Rows
+
+	// Compute A real(x) and store the result into xReAns.
+	xReAns := make([]float64, n)
+	blas64.Gemv(blas.NoTrans, 1, a, blas64.Vector{1, xRe}, 0, blas64.Vector{1, xReAns})
+
+	if imag(lambda) == 0 && xIm == nil {
+		// Real eigenvalue and eigenvector.
+
+		// Compute λx and store the result into lambdax.
+		lambdax := make([]float64, n)
+		floats.AddScaled(lambdax, real(lambda), xRe)
+
+		// This is expressed as the inverse to catch the case
+		// xReAns_i = Inf and lambdax_i = Inf of the same sign.
+		return !(floats.Distance(xReAns, lambdax, math.Inf(1)) > tol)
+	}
+
+	// Complex eigenvector, and real or complex eigenvalue.
+
+	// Compute A imag(x) and store the result into xImAns.
+	xImAns := make([]float64, n)
+	blas64.Gemv(blas.NoTrans, 1, a, blas64.Vector{1, xIm}, 0, blas64.Vector{1, xImAns})
+
+	// Compute λx and store the result into lambdax.
+	lambdax := make([]complex128, n)
+	for i := range lambdax {
+		lambdax[i] = lambda * complex(xRe[i], xIm[i])
+	}
+
+	for i, v := range lambdax {
+		ax := complex(xReAns[i], xImAns[i])
+		if cmplx.Abs(v-ax) > tol {
+			return false
+		}
+	}
+	return true
+}
+
+// isLeftEigenvectorOf returns whether the vector yRe+i*yIm, where i is the
+// imaginary unit, is the left eigenvector of A corresponding to the eigenvalue
+// lambda.
+//
+// A left eigenvector corresponding to a complex eigenvalue λ is a complex
+// non-zero vector y such that
+//  y^H A = λ y^H,
+// which is equivalent for real A to
+//  A^T y = conj(λ) y,
+func isLeftEigenvectorOf(a blas64.General, yRe, yIm []float64, lambda complex128, tol float64) bool {
+	if a.Rows != a.Cols {
+		panic("matrix not square")
+	}
+
+	if imag(lambda) != 0 && yIm == nil {
+		// Complex eigenvalue of a real matrix cannot have a real
+		// eigenvector.
+		return false
+	}
+
+	n := a.Rows
+
+	// Compute A^T real(y) and store the result into yReAns.
+	yReAns := make([]float64, n)
+	blas64.Gemv(blas.Trans, 1, a, blas64.Vector{1, yRe}, 0, blas64.Vector{1, yReAns})
+
+	if imag(lambda) == 0 && yIm == nil {
+		// Real eigenvalue and eigenvector.
+
+		// Compute λy and store the result into lambday.
+		lambday := make([]float64, n)
+		floats.AddScaled(lambday, real(lambda), yRe)
+
+		// This is expressed as the inverse to catch the case
+		// yReAns_i = Inf and lambday_i = Inf of the same sign.
+		return !(floats.Distance(yReAns, lambday, math.Inf(1)) > tol)
+	}
+
+	// Complex eigenvector, and real or complex eigenvalue.
+
+	// Compute A^T imag(y) and store the result into yImAns.
+	yImAns := make([]float64, n)
+	blas64.Gemv(blas.Trans, 1, a, blas64.Vector{1, yIm}, 0, blas64.Vector{1, yImAns})
+
+	// Compute conj(λ)y and store the result into lambday.
+	lambda = cmplx.Conj(lambda)
+	lambday := make([]complex128, n)
+	for i := range lambday {
+		lambday[i] = lambda * complex(yRe[i], yIm[i])
+	}
+
+	for i, v := range lambday {
+		ay := complex(yReAns[i], yImAns[i])
+		if cmplx.Abs(v-ay) > tol {
+			return false
+		}
+	}
+	return true
+}
+
+// rootsOfUnity returns the n complex numbers whose n-th power is equal to 1.
+func rootsOfUnity(n int) []complex128 {
+	w := make([]complex128, n)
+	for i := 0; i < n; i++ {
+		angle := math.Pi * float64(2*i) / float64(n)
+		w[i] = complex(math.Cos(angle), math.Sin(angle))
+	}
+	return w
+}
+
+// randomOrthogonal returns an n×n random orthogonal matrix.
+func randomOrthogonal(n int, rnd *rand.Rand) blas64.General {
+	q := eye(n, n)
+	x := make([]float64, n)
+	v := make([]float64, n)
+	for j := 0; j < n-1; j++ {
+		// x represents the j-th column of a random matrix.
+		for i := 0; i < j; i++ {
+			x[i] = 0
+		}
+		for i := j; i < n; i++ {
+			x[i] = rnd.NormFloat64()
+		}
+		// Compute v that represents the elementary reflector that
+		// annihilates the subdiagonal elements of x.
+		reflector(v, x, j)
+		// Compute Q * H_j and store the result into Q.
+		applyReflector(q, q, v)
+	}
+	if !isOrthonormal(q) {
+		panic("Q not orthogonal")
+	}
+	return q
+}
+
+// reflector generates a Householder reflector v that zeros out subdiagonal
+// entries in the j-th column of a matrix.
+func reflector(v, col []float64, j int) {
+	n := len(col)
+	if len(v) != n {
+		panic("slice length mismatch")
+	}
+	if j < 0 || n <= j {
+		panic("invalid column index")
+	}
+
+	for i := range v {
+		v[i] = 0
+	}
+	if j == n-1 {
+		return
+	}
+	s := floats.Norm(col[j:], 2)
+	if s == 0 {
+		return
+	}
+	v[j] = col[j] + math.Copysign(s, col[j])
+	copy(v[j+1:], col[j+1:])
+	s = floats.Norm(v[j:], 2)
+	floats.Scale(1/s, v[j:])
+}
+
+// applyReflector computes Q*H where H is a Householder matrix represented by
+// the Householder reflector v.
+func applyReflector(qh blas64.General, q blas64.General, v []float64) {
+	n := len(v)
+	if qh.Rows != n || qh.Cols != n {
+		panic("bad size of qh")
+	}
+	if q.Rows != n || q.Cols != n {
+		panic("bad size of q")
+	}
+	qv := make([]float64, n)
+	blas64.Gemv(blas.NoTrans, 1, q, blas64.Vector{1, v}, 0, blas64.Vector{1, qv})
+	for i := 0; i < n; i++ {
+		for j := 0; j < n; j++ {
+			qh.Data[i*qh.Stride+j] = q.Data[i*q.Stride+j]
+		}
+	}
+	for i := 0; i < n; i++ {
+		for j := 0; j < n; j++ {
+			qh.Data[i*qh.Stride+j] -= 2 * qv[i] * v[j]
+		}
+	}
+	var norm2 float64
+	for _, vi := range v {
+		norm2 += vi * vi
+	}
+	norm2inv := 1 / norm2
+	for i := 0; i < n; i++ {
+		for j := 0; j < n; j++ {
+			qh.Data[i*qh.Stride+j] *= norm2inv
+		}
+	}
+}
+
+// constructGSVDresults returns the matrices [ 0 R ], D1 and D2 described
+// in the documentation of Dtgsja and Dggsvd3, and the result matrix in
+// the documentation for Dggsvp3.
+func constructGSVDresults(n, p, m, k, l int, a, b blas64.General, alpha, beta []float64) (zeroR, d1, d2 blas64.General) {
+	// [ 0 R ]
+	zeroR = zeros(k+l, n, n)
+	dst := zeroR
+	dst.Rows = min(m, k+l)
+	dst.Cols = k + l
+	dst.Data = zeroR.Data[n-k-l:]
+	src := a
+	src.Rows = min(m, k+l)
+	src.Cols = k + l
+	src.Data = a.Data[n-k-l:]
+	copyGeneral(dst, src)
+	if m < k+l {
+		// [ 0 R ]
+		dst.Rows = k + l - m
+		dst.Cols = k + l - m
+		dst.Data = zeroR.Data[m*zeroR.Stride+n-(k+l-m):]
+		src = b
+		src.Rows = k + l - m
+		src.Cols = k + l - m
+		src.Data = b.Data[(m-k)*b.Stride+n+m-k-l:]
+		copyGeneral(dst, src)
+	}
+
+	// D1
+	d1 = zeros(m, k+l, k+l)
+	for i := 0; i < k; i++ {
+		d1.Data[i*d1.Stride+i] = 1
+	}
+	for i := k; i < min(m, k+l); i++ {
+		d1.Data[i*d1.Stride+i] = alpha[i]
+	}
+
+	// D2
+	d2 = zeros(p, k+l, k+l)
+	for i := 0; i < min(l, m-k); i++ {
+		d2.Data[i*d2.Stride+i+k] = beta[k+i]
+	}
+	for i := m - k; i < l; i++ {
+		d2.Data[i*d2.Stride+i+k] = 1
+	}
+
+	return zeroR, d1, d2
+}
+
+func constructGSVPresults(n, p, m, k, l int, a, b blas64.General) (zeroA, zeroB blas64.General) {
+	zeroA = zeros(m, n, n)
+	dst := zeroA
+	dst.Rows = min(m, k+l)
+	dst.Cols = k + l
+	dst.Data = zeroA.Data[n-k-l:]
+	src := a
+	dst.Rows = min(m, k+l)
+	src.Cols = k + l
+	src.Data = a.Data[n-k-l:]
+	copyGeneral(dst, src)
+
+	zeroB = zeros(p, n, n)
+	dst = zeroB
+	dst.Rows = l
+	dst.Cols = l
+	dst.Data = zeroB.Data[n-l:]
+	src = b
+	dst.Rows = l
+	src.Cols = l
+	src.Data = b.Data[n-l:]
+	copyGeneral(dst, src)
+
+	return zeroA, zeroB
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/iladlc.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/iladlc.go
new file mode 100644
index 00000000..b8a5b2b3
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/iladlc.go
@@ -0,0 +1,83 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import "testing"
+
+type Iladlcer interface {
+	Iladlc(m, n int, a []float64, lda int) int
+}
+
+func IladlcTest(t *testing.T, impl Iladlcer) {
+	for i, test := range []struct {
+		a         []float64
+		m, n, lda int
+		ans       int
+	}{
+		{
+			a:   []float64{0, 0, 0, 0},
+			m:   1,
+			n:   1,
+			lda: 2,
+			ans: -1,
+		},
+		{
+			a:   []float64{0, 0, 0, 0},
+			m:   2,
+			n:   2,
+			lda: 2,
+			ans: -1,
+		},
+		{
+			a:   []float64{0, 0, 0, 0},
+			m:   4,
+			n:   1,
+			lda: 1,
+			ans: -1,
+		},
+		{
+			a:   []float64{0, 0, 0, 0},
+			m:   1,
+			n:   4,
+			lda: 4,
+			ans: -1,
+		},
+		{
+			a: []float64{
+				1, 2, 3, 4,
+				5, 6, 7, 8,
+			},
+			m:   2,
+			n:   4,
+			lda: 4,
+			ans: 3,
+		},
+		{
+			a: []float64{
+				1, 2, 3, 0,
+				0, 0, 0, 0,
+			},
+			m:   2,
+			n:   4,
+			lda: 4,
+			ans: 2,
+		},
+		{
+			a: []float64{
+				0, 0, 3, 4,
+				0, 0, 0, 0,
+			},
+			m:   2,
+			n:   2,
+			lda: 4,
+			ans: -1,
+		},
+	} {
+		ans := impl.Iladlc(test.m, test.n, test.a, test.lda)
+		if ans != test.ans {
+			t.Errorf("Column mismatch case %v. Want: %v, got: %v", i, test.ans, ans)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/iladlr.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/iladlr.go
new file mode 100644
index 00000000..bd74d28c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/iladlr.go
@@ -0,0 +1,83 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import "testing"
+
+type Iladlrer interface {
+	Iladlr(m, n int, a []float64, lda int) int
+}
+
+func IladlrTest(t *testing.T, impl Iladlrer) {
+	for i, test := range []struct {
+		a         []float64
+		m, n, lda int
+		ans       int
+	}{
+		{
+			a:   []float64{0, 0, 0, 0},
+			m:   1,
+			n:   1,
+			lda: 2,
+			ans: -1,
+		},
+		{
+			a:   []float64{0, 0, 0, 0},
+			m:   2,
+			n:   2,
+			lda: 2,
+			ans: -1,
+		},
+		{
+			a:   []float64{0, 0, 0, 0},
+			m:   4,
+			n:   1,
+			lda: 1,
+			ans: -1,
+		},
+		{
+			a:   []float64{0, 0, 0, 0},
+			m:   1,
+			n:   4,
+			lda: 4,
+			ans: -1,
+		},
+		{
+			a: []float64{
+				1, 2, 3, 4,
+				5, 6, 7, 8,
+			},
+			m:   2,
+			n:   4,
+			lda: 4,
+			ans: 1,
+		},
+		{
+			a: []float64{
+				1, 2, 3, 0,
+				0, 0, 0, 0,
+			},
+			m:   2,
+			n:   4,
+			lda: 4,
+			ans: 0,
+		},
+		{
+			a: []float64{
+				0, 0, 3, 4,
+				0, 0, 0, 0,
+			},
+			m:   2,
+			n:   2,
+			lda: 4,
+			ans: -1,
+		},
+	} {
+		ans := impl.Iladlr(test.m, test.n, test.a, test.lda)
+		if ans != test.ans {
+			t.Errorf("Column mismatch case %v. Want: %v, got: %v", i, test.ans, ans)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/matgen.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/matgen.go
new file mode 100644
index 00000000..b47d9270
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/matgen.go
@@ -0,0 +1,655 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dlatm1 computes the entries of dst as specified by mode, cond and rsign.
+//
+// mode describes how dst will be computed:
+//  |mode| == 1: dst[0] = 1 and dst[1:n] = 1/cond
+//  |mode| == 2: dst[:n-1] = 1/cond and dst[n-1] = 1
+//  |mode| == 3: dst[i] = cond^{-i/(n-1)}, i=0,...,n-1
+//  |mode| == 4: dst[i] = 1 - i*(1-1/cond)/(n-1)
+//  |mode| == 5: dst[i] = random number in the range (1/cond, 1) such that
+//                    their logarithms are uniformly distributed
+//  |mode| == 6: dst[i] = random number from the distribution given by dist
+// If mode is negative, the order of the elements of dst will be reversed.
+// For other values of mode Dlatm1 will panic.
+//
+// If rsign is true and mode is not ±6, each entry of dst will be multiplied by 1
+// or -1 with probability 0.5
+//
+// dist specifies the type of distribution to be used when mode == ±6:
+//  dist == 1: Uniform[0,1)
+//  dist == 2: Uniform[-1,1)
+//  dist == 3: Normal(0,1)
+// For other values of dist Dlatm1 will panic.
+//
+// rnd is used as a source of random numbers.
+func Dlatm1(dst []float64, mode int, cond float64, rsign bool, dist int, rnd *rand.Rand) {
+	amode := mode
+	if amode < 0 {
+		amode = -amode
+	}
+	if amode < 1 || 6 < amode {
+		panic("testlapack: invalid mode")
+	}
+	if cond < 1 {
+		panic("testlapack: cond < 1")
+	}
+	if amode == 6 && (dist < 1 || 3 < dist) {
+		panic("testlapack: invalid dist")
+	}
+
+	n := len(dst)
+	if n == 0 {
+		return
+	}
+
+	switch amode {
+	case 1:
+		dst[0] = 1
+		for i := 1; i < n; i++ {
+			dst[i] = 1 / cond
+		}
+	case 2:
+		for i := 0; i < n-1; i++ {
+			dst[i] = 1
+		}
+		dst[n-1] = 1 / cond
+	case 3:
+		dst[0] = 1
+		if n > 1 {
+			alpha := math.Pow(cond, -1/float64(n-1))
+			for i := 1; i < n; i++ {
+				dst[i] = math.Pow(alpha, float64(i))
+			}
+		}
+	case 4:
+		dst[0] = 1
+		if n > 1 {
+			condInv := 1 / cond
+			alpha := (1 - condInv) / float64(n-1)
+			for i := 1; i < n; i++ {
+				dst[i] = float64(n-i-1)*alpha + condInv
+			}
+		}
+	case 5:
+		alpha := math.Log(1 / cond)
+		for i := range dst {
+			dst[i] = math.Exp(alpha * rnd.Float64())
+		}
+	case 6:
+		switch dist {
+		case 1:
+			for i := range dst {
+				dst[i] = rnd.Float64()
+			}
+		case 2:
+			for i := range dst {
+				dst[i] = 2*rnd.Float64() - 1
+			}
+		case 3:
+			for i := range dst {
+				dst[i] = rnd.NormFloat64()
+			}
+		}
+	}
+
+	if rsign && amode != 6 {
+		for i, v := range dst {
+			if rnd.Float64() < 0.5 {
+				dst[i] = -v
+			}
+		}
+	}
+
+	if mode < 0 {
+		for i := 0; i < n/2; i++ {
+			dst[i], dst[n-i-1] = dst[n-i-1], dst[i]
+		}
+	}
+}
+
+// Dlagsy generates an n×n symmetric matrix A, by pre- and post- multiplying a
+// real diagonal matrix D with a random orthogonal matrix:
+//  A = U * D * U^T.
+//
+// work must have length at least 2*n, otherwise Dlagsy will panic.
+//
+// The parameter k is unused but it must satisfy
+//  0 <= k <= n-1.
+func Dlagsy(n, k int, d []float64, a []float64, lda int, rnd *rand.Rand, work []float64) {
+	checkMatrix(n, n, a, lda)
+	if k < 0 || max(0, n-1) < k {
+		panic("testlapack: invalid value of k")
+	}
+	if len(d) != n {
+		panic("testlapack: bad length of d")
+	}
+	if len(work) < 2*n {
+		panic("testlapack: insufficient work length")
+	}
+
+	// Initialize lower triangle of A to diagonal matrix.
+	for i := 1; i < n; i++ {
+		for j := 0; j < i; j++ {
+			a[i*lda+j] = 0
+		}
+	}
+	for i := 0; i < n; i++ {
+		a[i*lda+i] = d[i]
+	}
+
+	bi := blas64.Implementation()
+
+	// Generate lower triangle of symmetric matrix.
+	for i := n - 2; i >= 0; i-- {
+		for j := 0; j < n-i; j++ {
+			work[j] = rnd.NormFloat64()
+		}
+		wn := bi.Dnrm2(n-i, work[:n-i], 1)
+		wa := math.Copysign(wn, work[0])
+		var tau float64
+		if wn != 0 {
+			wb := work[0] + wa
+			bi.Dscal(n-i-1, 1/wb, work[1:n-i], 1)
+			work[0] = 1
+			tau = wb / wa
+		}
+
+		// Apply random reflection to A[i:n,i:n] from the left and the
+		// right.
+		//
+		// Compute y := tau * A * u.
+		bi.Dsymv(blas.Lower, n-i, tau, a[i*lda+i:], lda, work[:n-i], 1, 0, work[n:2*n-i], 1)
+
+		// Compute v := y - 1/2 * tau * ( y, u ) * u.
+		alpha := -0.5 * tau * bi.Ddot(n-i, work[n:2*n-i], 1, work[:n-i], 1)
+		bi.Daxpy(n-i, alpha, work[:n-i], 1, work[n:2*n-i], 1)
+
+		// Apply the transformation as a rank-2 update to A[i:n,i:n].
+		bi.Dsyr2(blas.Lower, n-i, -1, work[:n-i], 1, work[n:2*n-i], 1, a[i*lda+i:], lda)
+	}
+
+	// Store full symmetric matrix.
+	for i := 1; i < n; i++ {
+		for j := 0; j < i; j++ {
+			a[j*lda+i] = a[i*lda+j]
+		}
+	}
+}
+
+// Dlagge generates a real general m×n matrix A, by pre- and post-multiplying
+// a real diagonal matrix D with random orthogonal matrices:
+//  A = U*D*V.
+//
+// d must have length min(m,n), and work must have length m+n, otherwise Dlagge
+// will panic.
+//
+// The parameters ku and kl are unused but they must satisfy
+//  0 <= kl <= m-1,
+//  0 <= ku <= n-1.
+func Dlagge(m, n, kl, ku int, d []float64, a []float64, lda int, rnd *rand.Rand, work []float64) {
+	checkMatrix(m, n, a, lda)
+	if kl < 0 || max(0, m-1) < kl {
+		panic("testlapack: invalid value of kl")
+	}
+	if ku < 0 || max(0, n-1) < ku {
+		panic("testlapack: invalid value of ku")
+	}
+	if len(d) != min(m, n) {
+		panic("testlapack: bad length of d")
+	}
+	if len(work) < m+n {
+		panic("testlapack: insufficient work length")
+	}
+
+	// Initialize A to diagonal matrix.
+	for i := 0; i < m; i++ {
+		for j := 0; j < n; j++ {
+			a[i*lda+j] = 0
+		}
+	}
+	for i := 0; i < min(m, n); i++ {
+		a[i*lda+i] = d[i]
+	}
+
+	// Quick exit if the user wants a diagonal matrix.
+	// if kl == 0 && ku == 0 {
+	// 	return
+	// }
+
+	bi := blas64.Implementation()
+
+	// Pre- and post-multiply A by random orthogonal matrices.
+	for i := min(m, n) - 1; i >= 0; i-- {
+		if i < m-1 {
+			for j := 0; j < m-i; j++ {
+				work[j] = rnd.NormFloat64()
+			}
+			wn := bi.Dnrm2(m-i, work[:m-i], 1)
+			wa := math.Copysign(wn, work[0])
+			var tau float64
+			if wn != 0 {
+				wb := work[0] + wa
+				bi.Dscal(m-i-1, 1/wb, work[1:m-i], 1)
+				work[0] = 1
+				tau = wb / wa
+			}
+
+			// Multiply A[i:m,i:n] by random reflection from the left.
+			bi.Dgemv(blas.Trans, m-i, n-i,
+				1, a[i*lda+i:], lda, work[:m-i], 1,
+				0, work[m:m+n-i], 1)
+			bi.Dger(m-i, n-i,
+				-tau, work[:m-i], 1, work[m:m+n-i], 1,
+				a[i*lda+i:], lda)
+		}
+		if i < n-1 {
+			for j := 0; j < n-i; j++ {
+				work[j] = rnd.NormFloat64()
+			}
+			wn := bi.Dnrm2(n-i, work[:n-i], 1)
+			wa := math.Copysign(wn, work[0])
+			var tau float64
+			if wn != 0 {
+				wb := work[0] + wa
+				bi.Dscal(n-i-1, 1/wb, work[1:n-i], 1)
+				work[0] = 1
+				tau = wb / wa
+			}
+
+			// Multiply A[i:m,i:n] by random reflection from the right.
+			bi.Dgemv(blas.NoTrans, m-i, n-i,
+				1, a[i*lda+i:], lda, work[:n-i], 1,
+				0, work[n:n+m-i], 1)
+			bi.Dger(m-i, n-i,
+				-tau, work[n:n+m-i], 1, work[:n-i], 1,
+				a[i*lda+i:], lda)
+		}
+	}
+
+	// TODO(vladimir-ch): Reduce number of subdiagonals to kl and number of
+	// superdiagonals to ku.
+}
+
+// dlarnv fills dst with random numbers from a uniform or normal distribution
+// specified by dist:
+//  dist=1: uniform(0,1),
+//  dist=2: uniform(-1,1),
+//  dist=3: normal(0,1).
+// For other values of dist dlarnv will panic.
+func dlarnv(dst []float64, dist int, rnd *rand.Rand) {
+	switch dist {
+	default:
+		panic("testlapack: invalid dist")
+	case 1:
+		for i := range dst {
+			dst[i] = rnd.Float64()
+		}
+	case 2:
+		for i := range dst {
+			dst[i] = 2*rnd.Float64() - 1
+		}
+	case 3:
+		for i := range dst {
+			dst[i] = rnd.NormFloat64()
+		}
+	}
+}
+
+// dlattr generates an n×n triangular test matrix A with its properties uniquely
+// determined by imat and uplo, and returns whether A has unit diagonal. If diag
+// is blas.Unit, the diagonal elements are set so that A[k,k]=k.
+//
+// trans specifies whether the matrix A or its transpose will be used.
+//
+// If imat is greater than 10, dlattr also generates the right hand side of the
+// linear system A*x=b, or A^T*x=b. Valid values of imat are 7, and all between 11
+// and 19, inclusive.
+//
+// b mush have length n, and work must have length 3*n, and dlattr will panic
+// otherwise.
+func dlattr(imat int, uplo blas.Uplo, trans blas.Transpose, n int, a []float64, lda int, b, work []float64, rnd *rand.Rand) (diag blas.Diag) {
+	checkMatrix(n, n, a, lda)
+	if len(b) != n {
+		panic("testlapack: bad length of b")
+	}
+	if len(work) < 3*n {
+		panic("testlapack: insufficient length of work")
+	}
+	if uplo != blas.Upper && uplo != blas.Lower {
+		panic("testlapack: bad uplo")
+	}
+	if trans != blas.Trans && trans != blas.NoTrans {
+		panic("testlapack: bad trans")
+	}
+
+	if n == 0 {
+		return blas.NonUnit
+	}
+
+	ulp := dlamchE * dlamchB
+	smlnum := dlamchS
+	bignum := (1 - ulp) / smlnum
+
+	bi := blas64.Implementation()
+
+	switch imat {
+	default:
+		// TODO(vladimir-ch): Implement the remaining cases.
+		panic("testlapack: invalid or unimplemented imat")
+	case 7:
+		// Identity matrix. The diagonal is set to NaN.
+		diag = blas.Unit
+		switch uplo {
+		case blas.Upper:
+			for i := 0; i < n; i++ {
+				a[i*lda+i] = math.NaN()
+				for j := i + 1; j < n; j++ {
+					a[i*lda+j] = 0
+				}
+			}
+		case blas.Lower:
+			for i := 0; i < n; i++ {
+				for j := 0; j < i; j++ {
+					a[i*lda+j] = 0
+				}
+				a[i*lda+i] = math.NaN()
+			}
+		}
+	case 11:
+		// Generate a triangular matrix with elements between -1 and 1,
+		// give the diagonal norm 2 to make it well-conditioned, and
+		// make the right hand side large so that it requires scaling.
+		diag = blas.NonUnit
+		switch uplo {
+		case blas.Upper:
+			for i := 0; i < n-1; i++ {
+				dlarnv(a[i*lda+i:i*lda+n], 2, rnd)
+			}
+		case blas.Lower:
+			for i := 1; i < n; i++ {
+				dlarnv(a[i*lda:i*lda+i+1], 2, rnd)
+			}
+		}
+		for i := 0; i < n; i++ {
+			a[i*lda+i] = math.Copysign(2, a[i*lda+i])
+		}
+		// Set the right hand side so that the largest value is bignum.
+		dlarnv(b, 2, rnd)
+		imax := bi.Idamax(n, b, 1)
+		bscal := bignum / math.Max(1, b[imax])
+		bi.Dscal(n, bscal, b, 1)
+	case 12:
+		// Make the first diagonal element in the solve small to cause
+		// immediate overflow when dividing by T[j,j]. The off-diagonal
+		// elements are small (cnorm[j] < 1).
+		diag = blas.NonUnit
+		tscal := 1 / math.Max(1, float64(n-1))
+		switch uplo {
+		case blas.Upper:
+			for i := 0; i < n; i++ {
+				dlarnv(a[i*lda+i:i*lda+n], 2, rnd)
+				bi.Dscal(n-i-1, tscal, a[i*lda+i+1:], 1)
+				a[i*lda+i] = math.Copysign(1, a[i*lda+i])
+			}
+			a[(n-1)*lda+n-1] *= smlnum
+		case blas.Lower:
+			for i := 0; i < n; i++ {
+				dlarnv(a[i*lda:i*lda+i+1], 2, rnd)
+				bi.Dscal(i, tscal, a[i*lda:], 1)
+				a[i*lda+i] = math.Copysign(1, a[i*lda+i])
+			}
+			a[0] *= smlnum
+		}
+		dlarnv(b, 2, rnd)
+	case 13:
+		// Make the first diagonal element in the solve small to cause
+		// immediate overflow when dividing by T[j,j]. The off-diagonal
+		// elements are O(1) (cnorm[j] > 1).
+		diag = blas.NonUnit
+		switch uplo {
+		case blas.Upper:
+			for i := 0; i < n; i++ {
+				dlarnv(a[i*lda+i:i*lda+n], 2, rnd)
+				a[i*lda+i] = math.Copysign(1, a[i*lda+i])
+			}
+			a[(n-1)*lda+n-1] *= smlnum
+		case blas.Lower:
+			for i := 0; i < n; i++ {
+				dlarnv(a[i*lda:i*lda+i+1], 2, rnd)
+				a[i*lda+i] = math.Copysign(1, a[i*lda+i])
+			}
+			a[0] *= smlnum
+		}
+		dlarnv(b, 2, rnd)
+	case 14:
+		// T is diagonal with small numbers on the diagonal to
+		// make the growth factor underflow, but a small right hand side
+		// chosen so that the solution does not overflow.
+		diag = blas.NonUnit
+		switch uplo {
+		case blas.Upper:
+			for i := 0; i < n; i++ {
+				for j := i + 1; j < n; j++ {
+					a[i*lda+j] = 0
+				}
+				if (n-1-i)&0x2 == 0 {
+					a[i*lda+i] = smlnum
+				} else {
+					a[i*lda+i] = 1
+				}
+			}
+		case blas.Lower:
+			for i := 0; i < n; i++ {
+				for j := 0; j < i; j++ {
+					a[i*lda+j] = 0
+				}
+				if i&0x2 == 0 {
+					a[i*lda+i] = smlnum
+				} else {
+					a[i*lda+i] = 1
+				}
+			}
+		}
+		// Set the right hand side alternately zero and small.
+		switch uplo {
+		case blas.Upper:
+			b[0] = 0
+			for i := n - 1; i > 0; i -= 2 {
+				b[i] = 0
+				b[i-1] = smlnum
+			}
+		case blas.Lower:
+			for i := 0; i < n-1; i += 2 {
+				b[i] = 0
+				b[i+1] = smlnum
+			}
+			b[n-1] = 0
+		}
+	case 15:
+		// Make the diagonal elements small to cause gradual overflow
+		// when dividing by T[j,j]. To control the amount of scaling
+		// needed, the matrix is bidiagonal.
+		diag = blas.NonUnit
+		texp := 1 / math.Max(1, float64(n-1))
+		tscal := math.Pow(smlnum, texp)
+		switch uplo {
+		case blas.Upper:
+			for i := 0; i < n; i++ {
+				a[i*lda+i] = tscal
+				if i < n-1 {
+					a[i*lda+i+1] = -1
+				}
+				for j := i + 2; j < n; j++ {
+					a[i*lda+j] = 0
+				}
+			}
+		case blas.Lower:
+			for i := 0; i < n; i++ {
+				for j := 0; j < i-1; j++ {
+					a[i*lda+j] = 0
+				}
+				if i > 0 {
+					a[i*lda+i-1] = -1
+				}
+				a[i*lda+i] = tscal
+			}
+		}
+		dlarnv(b, 2, rnd)
+	case 16:
+		// One zero diagonal element.
+		diag = blas.NonUnit
+		switch uplo {
+		case blas.Upper:
+			for i := 0; i < n; i++ {
+				dlarnv(a[i*lda+i:i*lda+n], 2, rnd)
+				a[i*lda+i] = math.Copysign(2, a[i*lda+i])
+			}
+		case blas.Lower:
+			for i := 0; i < n; i++ {
+				dlarnv(a[i*lda:i*lda+i+1], 2, rnd)
+				a[i*lda+i] = math.Copysign(2, a[i*lda+i])
+			}
+		}
+		iy := n / 2
+		a[iy*lda+iy] = 0
+		dlarnv(b, 2, rnd)
+		bi.Dscal(n, 2, b, 1)
+	case 17:
+		// Make the offdiagonal elements large to cause overflow when
+		// adding a column of T. In the non-transposed case, the matrix
+		// is constructed to cause overflow when adding a column in
+		// every other step.
+		diag = blas.NonUnit
+		tscal := (1 - ulp) / (dlamchS / ulp)
+		texp := 1.0
+		switch uplo {
+		case blas.Upper:
+			for i := 0; i < n; i++ {
+				for j := i; j < n; j++ {
+					a[i*lda+j] = 0
+				}
+			}
+			for j := n - 1; j >= 1; j -= 2 {
+				a[j] = -tscal / float64(n+1)
+				a[j*lda+j] = 1
+				b[j] = texp * (1 - ulp)
+				a[j-1] = -tscal / float64(n+1) / float64(n+2)
+				a[(j-1)*lda+j-1] = 1
+				b[j-1] = texp * float64(n*n+n-1)
+				texp *= 2
+			}
+			b[0] = float64(n+1) / float64(n+2) * tscal
+		case blas.Lower:
+			for i := 0; i < n; i++ {
+				for j := 0; j <= i; j++ {
+					a[i*lda+j] = 0
+				}
+			}
+			for j := 0; j < n-1; j += 2 {
+				a[(n-1)*lda+j] = -tscal / float64(n+1)
+				a[j*lda+j] = 1
+				b[j] = texp * (1 - ulp)
+				a[(n-1)*lda+j+1] = -tscal / float64(n+1) / float64(n+2)
+				a[(j+1)*lda+j+1] = 1
+				b[j+1] = texp * float64(n*n+n-1)
+				texp *= 2
+			}
+			b[n-1] = float64(n+1) / float64(n+2) * tscal
+		}
+	case 18:
+		// Generate a unit triangular matrix with elements between -1
+		// and 1, and make the right hand side large so that it requires
+		// scaling. The diagonal is set to NaN.
+		diag = blas.Unit
+		switch uplo {
+		case blas.Upper:
+			for i := 0; i < n; i++ {
+				a[i*lda+i] = math.NaN()
+				dlarnv(a[i*lda+i+1:i*lda+n], 2, rnd)
+			}
+		case blas.Lower:
+			for i := 0; i < n; i++ {
+				dlarnv(a[i*lda:i*lda+i], 2, rnd)
+				a[i*lda+i] = math.NaN()
+			}
+		}
+		// Set the right hand side so that the largest value is bignum.
+		dlarnv(b, 2, rnd)
+		iy := bi.Idamax(n, b, 1)
+		bnorm := math.Abs(b[iy])
+		bscal := bignum / math.Max(1, bnorm)
+		bi.Dscal(n, bscal, b, 1)
+	case 19:
+		// Generate a triangular matrix with elements between
+		// bignum/(n-1) and bignum so that at least one of the column
+		// norms will exceed bignum.
+		// Dlatrs cannot handle this case for (typically) n>5.
+		diag = blas.NonUnit
+		tleft := bignum / math.Max(1, float64(n-1))
+		tscal := bignum * (float64(n-1) / math.Max(1, float64(n)))
+		switch uplo {
+		case blas.Upper:
+			for i := 0; i < n; i++ {
+				dlarnv(a[i*lda+i:i*lda+n], 2, rnd)
+				for j := i; j < n; j++ {
+					aij := a[i*lda+j]
+					a[i*lda+j] = math.Copysign(tleft, aij) + tscal*aij
+				}
+			}
+		case blas.Lower:
+			for i := 0; i < n; i++ {
+				dlarnv(a[i*lda:i*lda+i+1], 2, rnd)
+				for j := 0; j <= i; j++ {
+					aij := a[i*lda+j]
+					a[i*lda+j] = math.Copysign(tleft, aij) + tscal*aij
+				}
+			}
+		}
+		dlarnv(b, 2, rnd)
+		bi.Dscal(n, 2, b, 1)
+	}
+
+	// Flip the matrix if the transpose will be used.
+	if trans == blas.Trans {
+		switch uplo {
+		case blas.Upper:
+			for j := 0; j < n/2; j++ {
+				bi.Dswap(n-2*j-1, a[j*lda+j:], 1, a[(j+1)*lda+n-j-1:], -lda)
+			}
+		case blas.Lower:
+			for j := 0; j < n/2; j++ {
+				bi.Dswap(n-2*j-1, a[j*lda+j:], lda, a[(n-j-1)*lda+j+1:], -1)
+			}
+		}
+	}
+
+	return diag
+}
+
+func checkMatrix(m, n int, a []float64, lda int) {
+	if m < 0 {
+		panic("testlapack: m < 0")
+	}
+	if n < 0 {
+		panic("testlapack: n < 0")
+	}
+	if lda < max(1, n) {
+		panic("testlapack: lda < max(1, n)")
+	}
+	if len(a) < (m-1)*lda+n {
+		panic("testlapack: insufficient matrix slice length")
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/matgen_test.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/matgen_test.go
new file mode 100644
index 00000000..1bb86d3c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/matgen_test.go
@@ -0,0 +1,90 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+func TestDlagsy(t *testing.T) {
+	const tol = 1e-14
+	rnd := rand.New(rand.NewSource(1))
+	for _, n := range []int{0, 1, 2, 3, 4, 5, 10, 50} {
+		for _, lda := range []int{0, 2*n + 1} {
+			if lda == 0 {
+				lda = max(1, n)
+			}
+			d := make([]float64, n)
+			for i := range d {
+				d[i] = 1
+			}
+			a := blas64.General{
+				Rows:   n,
+				Cols:   n,
+				Stride: lda,
+				Data:   nanSlice(n * lda),
+			}
+			work := make([]float64, a.Rows+a.Cols)
+
+			Dlagsy(a.Rows, 0, d, a.Data, a.Stride, rnd, work)
+
+			isIdentity := true
+		identityLoop:
+			for i := 0; i < n; i++ {
+				for j := 0; j < n; j++ {
+					aij := a.Data[i*a.Stride+j]
+					if math.IsNaN(aij) {
+						isIdentity = false
+					}
+					if i == j && math.Abs(aij-1) > tol {
+						isIdentity = false
+					}
+					if i != j && math.Abs(aij) > tol {
+						isIdentity = false
+					}
+					if !isIdentity {
+						break identityLoop
+					}
+				}
+			}
+			if !isIdentity {
+				t.Errorf("Case n=%v,lda=%v: unexpected result", n, lda)
+			}
+		}
+	}
+}
+
+func TestDlagge(t *testing.T) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, n := range []int{0, 1, 2, 3, 4, 5, 10, 50} {
+		for _, lda := range []int{0, 2*n + 1} {
+			if lda == 0 {
+				lda = max(1, n)
+			}
+			d := make([]float64, n)
+			for i := range d {
+				d[i] = 1
+			}
+			a := blas64.General{
+				Rows:   n,
+				Cols:   n,
+				Stride: lda,
+				Data:   nanSlice(n * lda),
+			}
+			work := make([]float64, a.Rows+a.Cols)
+
+			Dlagge(a.Rows, a.Cols, 0, 0, d, a.Data, a.Stride, rnd, work)
+
+			if !isOrthonormal(a) {
+				t.Errorf("Case n=%v,lda=%v: unexpected result", n, lda)
+			}
+		}
+	}
+
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/test_matrices.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/test_matrices.go
new file mode 100644
index 00000000..6be490b2
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/test_matrices.go
@@ -0,0 +1,615 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// A123 is the non-symmetric singular matrix
+//      [ 1 2 3 ]
+//  A = [ 4 5 6 ]
+//      [ 7 8 9 ]
+// It has three distinct real eigenvalues.
+type A123 struct{}
+
+func (A123) Matrix() blas64.General {
+	return blas64.General{
+		Rows:   3,
+		Cols:   3,
+		Stride: 3,
+		Data: []float64{
+			1, 2, 3,
+			4, 5, 6,
+			7, 8, 9,
+		},
+	}
+}
+
+func (A123) Eigenvalues() []complex128 {
+	return []complex128{16.116843969807043, -1.116843969807043, 0}
+}
+
+func (A123) LeftEV() blas64.General {
+	return blas64.General{
+		Rows:   3,
+		Cols:   3,
+		Stride: 3,
+		Data: []float64{
+			-0.464547273387671, -0.570795531228578, -0.677043789069485,
+			-0.882905959653586, -0.239520420054206, 0.403865119545174,
+			0.408248290463862, -0.816496580927726, 0.408248290463863,
+		},
+	}
+}
+
+func (A123) RightEV() blas64.General {
+	return blas64.General{
+		Rows:   3,
+		Cols:   3,
+		Stride: 3,
+		Data: []float64{
+			-0.231970687246286, -0.785830238742067, 0.408248290463864,
+			-0.525322093301234, -0.086751339256628, -0.816496580927726,
+			-0.818673499356181, 0.612327560228810, 0.408248290463863,
+		},
+	}
+}
+
+// AntisymRandom is a anti-symmetric random matrix. All its eigenvalues are
+// imaginary with one zero if the order is odd.
+type AntisymRandom struct {
+	mat blas64.General
+}
+
+func NewAntisymRandom(n int, rnd *rand.Rand) AntisymRandom {
+	a := zeros(n, n, n)
+	for i := 0; i < n; i++ {
+		for j := i + 1; j < n; j++ {
+			r := rnd.NormFloat64()
+			a.Data[i*a.Stride+j] = r
+			a.Data[j*a.Stride+i] = -r
+		}
+	}
+	return AntisymRandom{a}
+}
+
+func (a AntisymRandom) Matrix() blas64.General {
+	return cloneGeneral(a.mat)
+}
+
+func (AntisymRandom) Eigenvalues() []complex128 {
+	return nil
+}
+
+// Circulant is a generally non-symmetric matrix given by
+//  A[i,j] = 1 + (j-i+n)%n.
+// For example, for n=5,
+//      [ 1 2 3 4 5 ]
+//      [ 5 1 2 3 4 ]
+//  A = [ 4 5 1 2 3 ]
+//      [ 3 4 5 1 2 ]
+//      [ 2 3 4 5 1 ]
+// It has real and complex eigenvalues, some possibly repeated.
+type Circulant int
+
+func (c Circulant) Matrix() blas64.General {
+	n := int(c)
+	a := zeros(n, n, n)
+	for i := 0; i < n; i++ {
+		for j := 0; j < n; j++ {
+			a.Data[i*a.Stride+j] = float64(1 + (j-i+n)%n)
+		}
+	}
+	return a
+}
+
+func (c Circulant) Eigenvalues() []complex128 {
+	n := int(c)
+	w := rootsOfUnity(n)
+	ev := make([]complex128, n)
+	for k := 0; k < n; k++ {
+		ev[k] = complex(float64(n), 0)
+	}
+	for i := n - 1; i > 0; i-- {
+		for k := 0; k < n; k++ {
+			ev[k] = ev[k]*w[k] + complex(float64(i), 0)
+		}
+	}
+	return ev
+}
+
+// Clement is a generally non-symmetric matrix given by
+//  A[i,j] = i+1,  if j == i+1,
+//         = n-i,  if j == i-1,
+//         = 0,    otherwise.
+// For example, for n=5,
+//      [ . 1 . . . ]
+//      [ 4 . 2 . . ]
+//  A = [ . 3 . 3 . ]
+//      [ . . 2 . 4 ]
+//      [ . . . 1 . ]
+// It has n distinct real eigenvalues.
+type Clement int
+
+func (c Clement) Matrix() blas64.General {
+	n := int(c)
+	a := zeros(n, n, n)
+	for i := 0; i < n; i++ {
+		if i < n-1 {
+			a.Data[i*a.Stride+i+1] = float64(i + 1)
+		}
+		if i > 0 {
+			a.Data[i*a.Stride+i-1] = float64(n - i)
+		}
+	}
+	return a
+}
+
+func (c Clement) Eigenvalues() []complex128 {
+	n := int(c)
+	ev := make([]complex128, n)
+	for i := range ev {
+		ev[i] = complex(float64(-n+2*i+1), 0)
+	}
+	return ev
+}
+
+// Creation is a singular non-symmetric matrix given by
+//  A[i,j] = i,  if j == i-1,
+//         = 0,  otherwise.
+// For example, for n=5,
+//      [ . . . . . ]
+//      [ 1 . . . . ]
+//  A = [ . 2 . . . ]
+//      [ . . 3 . . ]
+//      [ . . . 4 . ]
+// Zero is its only eigenvalue.
+type Creation int
+
+func (c Creation) Matrix() blas64.General {
+	n := int(c)
+	a := zeros(n, n, n)
+	for i := 1; i < n; i++ {
+		a.Data[i*a.Stride+i-1] = float64(i)
+	}
+	return a
+}
+
+func (c Creation) Eigenvalues() []complex128 {
+	return make([]complex128, int(c))
+}
+
+// Diagonal is a diagonal matrix given by
+//  A[i,j] = i+1,  if i == j,
+//         = 0,    otherwise.
+// For example, for n=5,
+//      [ 1 . . . . ]
+//      [ . 2 . . . ]
+//  A = [ . . 3 . . ]
+//      [ . . . 4 . ]
+//      [ . . . . 5 ]
+// It has n real eigenvalues {1,...,n}.
+type Diagonal int
+
+func (d Diagonal) Matrix() blas64.General {
+	n := int(d)
+	a := zeros(n, n, n)
+	for i := 0; i < n; i++ {
+		a.Data[i*a.Stride+i] = float64(i)
+	}
+	return a
+}
+
+func (d Diagonal) Eigenvalues() []complex128 {
+	n := int(d)
+	ev := make([]complex128, n)
+	for i := range ev {
+		ev[i] = complex(float64(i), 0)
+	}
+	return ev
+}
+
+// Downshift is a non-singular upper Hessenberg matrix given by
+//  A[i,j] = 1,  if (i-j+n)%n == 1,
+//         = 0,  otherwise.
+// For example, for n=5,
+//      [ . . . . 1 ]
+//      [ 1 . . . . ]
+//  A = [ . 1 . . . ]
+//      [ . . 1 . . ]
+//      [ . . . 1 . ]
+// Its eigenvalues are the complex roots of unity.
+type Downshift int
+
+func (d Downshift) Matrix() blas64.General {
+	n := int(d)
+	a := zeros(n, n, n)
+	a.Data[n-1] = 1
+	for i := 1; i < n; i++ {
+		a.Data[i*a.Stride+i-1] = 1
+	}
+	return a
+}
+
+func (d Downshift) Eigenvalues() []complex128 {
+	return rootsOfUnity(int(d))
+}
+
+// Fibonacci is an upper Hessenberg matrix with 3 distinct real eigenvalues. For
+// example, for n=5,
+//      [ . 1 . . . ]
+//      [ 1 1 . . . ]
+//  A = [ . 1 1 . . ]
+//      [ . . 1 1 . ]
+//      [ . . . 1 1 ]
+type Fibonacci int
+
+func (f Fibonacci) Matrix() blas64.General {
+	n := int(f)
+	a := zeros(n, n, n)
+	if n > 1 {
+		a.Data[1] = 1
+	}
+	for i := 1; i < n; i++ {
+		a.Data[i*a.Stride+i-1] = 1
+		a.Data[i*a.Stride+i] = 1
+	}
+	return a
+}
+
+func (f Fibonacci) Eigenvalues() []complex128 {
+	n := int(f)
+	ev := make([]complex128, n)
+	if n == 0 || n == 1 {
+		return ev
+	}
+	phi := 0.5 * (1 + math.Sqrt(5))
+	ev[0] = complex(phi, 0)
+	for i := 1; i < n-1; i++ {
+		ev[i] = 1 + 0i
+	}
+	ev[n-1] = complex(1-phi, 0)
+	return ev
+}
+
+// Gear is a singular non-symmetric matrix with real eigenvalues. For example,
+// for n=5,
+//      [ . 1 . . 1 ]
+//      [ 1 . 1 . . ]
+//  A = [ . 1 . 1 . ]
+//      [ . . 1 . 1 ]
+//      [-1 . . 1 . ]
+type Gear int
+
+func (g Gear) Matrix() blas64.General {
+	n := int(g)
+	a := zeros(n, n, n)
+	if n == 1 {
+		return a
+	}
+	for i := 0; i < n-1; i++ {
+		a.Data[i*a.Stride+i+1] = 1
+	}
+	for i := 1; i < n; i++ {
+		a.Data[i*a.Stride+i-1] = 1
+	}
+	a.Data[n-1] = 1
+	a.Data[(n-1)*a.Stride] = -1
+	return a
+}
+
+func (g Gear) Eigenvalues() []complex128 {
+	n := int(g)
+	ev := make([]complex128, n)
+	if n == 0 || n == 1 {
+		return ev
+	}
+	if n == 2 {
+		ev[0] = complex(0, 1)
+		ev[1] = complex(0, -1)
+		return ev
+	}
+	w := 0
+	ev[w] = math.Pi / 2
+	w++
+	phi := (n - 1) / 2
+	for p := 1; p <= phi; p++ {
+		ev[w] = complex(float64(2*p)*math.Pi/float64(n), 0)
+		w++
+	}
+	phi = n / 2
+	for p := 1; p <= phi; p++ {
+		ev[w] = complex(float64(2*p-1)*math.Pi/float64(n), 0)
+		w++
+	}
+	for i, v := range ev {
+		ev[i] = complex(2*math.Cos(real(v)), 0)
+	}
+	return ev
+}
+
+// Grcar is an upper Hessenberg matrix given by
+//  A[i,j] = -1  if i == j+1,
+//         = 1   if i <= j and j <= i+k,
+//         = 0   otherwise.
+// For example, for n=5 and k=2,
+//      [  1  1  1  .  . ]
+//      [ -1  1  1  1  . ]
+//  A = [  . -1  1  1  1 ]
+//      [  .  . -1  1  1 ]
+//      [  .  .  . -1  1 ]
+// The matrix has sensitive eigenvalues but they are not given explicitly.
+type Grcar struct {
+	N int
+	K int
+}
+
+func (g Grcar) Matrix() blas64.General {
+	n := g.N
+	a := zeros(n, n, n)
+	for k := 0; k <= g.K; k++ {
+		for i := 0; i < n-k; i++ {
+			a.Data[i*a.Stride+i+k] = 1
+		}
+	}
+	for i := 1; i < n; i++ {
+		a.Data[i*a.Stride+i-1] = -1
+	}
+	return a
+}
+
+func (Grcar) Eigenvalues() []complex128 {
+	return nil
+}
+
+// Hanowa is a non-symmetric non-singular matrix of even order given by
+//  A[i,j] = alpha    if i == j,
+//         = -i-1     if i < n/2 and j == i + n/2,
+//         = i+1-n/2  if i >= n/2 and j == i - n/2,
+//         = 0        otherwise.
+// The matrix has complex eigenvalues.
+type Hanowa struct {
+	N     int // Order of the matrix, must be even.
+	Alpha float64
+}
+
+func (h Hanowa) Matrix() blas64.General {
+	if h.N&0x1 != 0 {
+		panic("lapack: matrix order must be even")
+	}
+	n := h.N
+	a := zeros(n, n, n)
+	for i := 0; i < n; i++ {
+		a.Data[i*a.Stride+i] = h.Alpha
+	}
+	for i := 0; i < n/2; i++ {
+		a.Data[i*a.Stride+i+n/2] = float64(-i - 1)
+	}
+	for i := n / 2; i < n; i++ {
+		a.Data[i*a.Stride+i-n/2] = float64(i + 1 - n/2)
+	}
+	return a
+}
+
+func (h Hanowa) Eigenvalues() []complex128 {
+	if h.N&0x1 != 0 {
+		panic("lapack: matrix order must be even")
+	}
+	n := int(h.N)
+	ev := make([]complex128, n)
+	for i := 0; i < n/2; i++ {
+		ev[2*i] = complex(h.Alpha, float64(-i-1))
+		ev[2*i+1] = complex(h.Alpha, float64(i+1))
+	}
+	return ev
+}
+
+// Lesp is a tridiagonal, generally non-symmetric matrix given by
+//  A[i,j] = -2*i-5   if i == j,
+//         = 1/(i+1)  if i == j-1,
+//         = j+1      if i == j+1.
+// For example, for n=5,
+//      [  -5    2    .    .    . ]
+//      [ 1/2   -7    3    .    . ]
+//  A = [   .  1/3   -9    4    . ]
+//      [   .    .  1/4  -11    5 ]
+//      [   .    .    .  1/5  -13 ].
+// The matrix has sensitive eigenvalues but they are not given explicitly.
+type Lesp int
+
+func (l Lesp) Matrix() blas64.General {
+	n := int(l)
+	a := zeros(n, n, n)
+	for i := 0; i < n; i++ {
+		a.Data[i*a.Stride+i] = float64(-2*i - 5)
+	}
+	for i := 0; i < n-1; i++ {
+		a.Data[i*a.Stride+i+1] = float64(i + 2)
+	}
+	for i := 1; i < n; i++ {
+		a.Data[i*a.Stride+i-1] = 1 / float64(i+1)
+	}
+	return a
+}
+
+func (Lesp) Eigenvalues() []complex128 {
+	return nil
+}
+
+// Rutis is the 4×4 non-symmetric matrix
+//      [ 4 -5  0  3 ]
+//  A = [ 0  4 -3 -5 ]
+//      [ 5 -3  4  0 ]
+//      [ 3  0  5  4 ]
+// It has two distinct real eigenvalues and a pair of complex eigenvalues.
+type Rutis struct{}
+
+func (Rutis) Matrix() blas64.General {
+	return blas64.General{
+		Rows:   4,
+		Cols:   4,
+		Stride: 4,
+		Data: []float64{
+			4, -5, 0, 3,
+			0, 4, -3, -5,
+			5, -3, 4, 0,
+			3, 0, 5, 4,
+		},
+	}
+}
+
+func (Rutis) Eigenvalues() []complex128 {
+	return []complex128{12, 1 + 5i, 1 - 5i, 2}
+}
+
+// Tris is a tridiagonal matrix given by
+//  A[i,j] = x  if i == j-1,
+//         = y  if i == j,
+//         = z  if i == j+1.
+// If x*z is negative, the matrix has complex eigenvalues.
+type Tris struct {
+	N       int
+	X, Y, Z float64
+}
+
+func (t Tris) Matrix() blas64.General {
+	n := t.N
+	a := zeros(n, n, n)
+	for i := 1; i < n; i++ {
+		a.Data[i*a.Stride+i-1] = t.X
+	}
+	for i := 0; i < n; i++ {
+		a.Data[i*a.Stride+i] = t.Y
+	}
+	for i := 0; i < n-1; i++ {
+		a.Data[i*a.Stride+i+1] = t.Z
+	}
+	return a
+}
+
+func (t Tris) Eigenvalues() []complex128 {
+	n := int(t.N)
+	ev := make([]complex128, n)
+	for i := range ev {
+		angle := float64(i+1) * math.Pi / float64(n+1)
+		arg := t.X * t.Z
+		if arg >= 0 {
+			ev[i] = complex(t.Y+2*math.Sqrt(arg)*math.Cos(angle), 0)
+		} else {
+			ev[i] = complex(t.Y, 2*math.Sqrt(-arg)*math.Cos(angle))
+		}
+	}
+	return ev
+}
+
+// Wilk4 is a 4×4 lower triangular matrix with 4 distinct real eigenvalues.
+type Wilk4 struct{}
+
+func (Wilk4) Matrix() blas64.General {
+	return blas64.General{
+		Rows:   4,
+		Cols:   4,
+		Stride: 4,
+		Data: []float64{
+			0.9143e-4, 0.0, 0.0, 0.0,
+			0.8762, 0.7156e-4, 0.0, 0.0,
+			0.7943, 0.8143, 0.9504e-4, 0.0,
+			0.8017, 0.6123, 0.7165, 0.7123e-4,
+		},
+	}
+}
+
+func (Wilk4) Eigenvalues() []complex128 {
+	return []complex128{
+		0.9504e-4, 0.9143e-4, 0.7156e-4, 0.7123e-4,
+	}
+}
+
+// Wilk12 is a 12×12 lower Hessenberg matrix with 12 distinct real eigenvalues.
+type Wilk12 struct{}
+
+func (Wilk12) Matrix() blas64.General {
+	return blas64.General{
+		Rows:   12,
+		Cols:   12,
+		Stride: 12,
+		Data: []float64{
+			12, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+			11, 11, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+			10, 10, 10, 9, 0, 0, 0, 0, 0, 0, 0, 0,
+			9, 9, 9, 9, 8, 0, 0, 0, 0, 0, 0, 0,
+			8, 8, 8, 8, 8, 7, 0, 0, 0, 0, 0, 0,
+			7, 7, 7, 7, 7, 7, 6, 0, 0, 0, 0, 0,
+			6, 6, 6, 6, 6, 6, 6, 5, 0, 0, 0, 0,
+			5, 5, 5, 5, 5, 5, 5, 5, 4, 0, 0, 0,
+			4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 0, 0,
+			3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 0,
+			2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1,
+			1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+		},
+	}
+}
+
+func (Wilk12) Eigenvalues() []complex128 {
+	return []complex128{
+		32.2288915015722210,
+		20.1989886458770691,
+		12.3110774008685340,
+		6.9615330855671154,
+		3.5118559485807528,
+		1.5539887091319704,
+		0.6435053190136506,
+		0.2847497205488856,
+		0.1436465181918488,
+		0.0812276683076552,
+		0.0495074140194613,
+		0.0310280683208907,
+	}
+}
+
+// Wilk20 is a 20×20 lower Hessenberg matrix. If the parameter is 0, the matrix
+// has 20 distinct real eigenvalues. If the parameter is 1e-10, the matrix has 6
+// real eigenvalues and 7 pairs of complex eigenvalues.
+type Wilk20 float64
+
+func (w Wilk20) Matrix() blas64.General {
+	a := zeros(20, 20, 20)
+	for i := 0; i < 20; i++ {
+		a.Data[i*a.Stride+i] = float64(i + 1)
+	}
+	for i := 0; i < 19; i++ {
+		a.Data[i*a.Stride+i+1] = 20
+	}
+	a.Data[19*a.Stride] = float64(w)
+	return a
+}
+
+func (w Wilk20) Eigenvalues() []complex128 {
+	if float64(w) == 0 {
+		ev := make([]complex128, 20)
+		for i := range ev {
+			ev[i] = complex(float64(i+1), 0)
+		}
+		return ev
+	}
+	return nil
+}
+
+// Zero is a matrix with all elements equal to zero.
+type Zero int
+
+func (z Zero) Matrix() blas64.General {
+	n := int(z)
+	return zeros(n, n, n)
+}
+
+func (z Zero) Eigenvalues() []complex128 {
+	n := int(z)
+	return make([]complex128, n)
+}
diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/testdata/dlahr2data.json.gz b/vendor/gonum.org/v1/gonum/lapack/testlapack/testdata/dlahr2data.json.gz
new file mode 100644
index 0000000000000000000000000000000000000000..7652126afd729e72194c4025c7865532ac6707d1
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diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/testdata/dlaqr5data.json.gz b/vendor/gonum.org/v1/gonum/lapack/testlapack/testdata/dlaqr5data.json.gz
new file mode 100644
index 0000000000000000000000000000000000000000..9e629480b659636d23a5a70ad74133c499c21689
GIT binary patch
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diff --git a/vendor/gonum.org/v1/gonum/mat/README.md b/vendor/gonum.org/v1/gonum/mat/README.md
new file mode 100644
index 00000000..151e8a27
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/README.md
@@ -0,0 +1,3 @@
+# Gonum matrix [![GoDoc](https://godoc.org/gonum.org/v1/gonum/matrix?status.svg)](https://godoc.org/gonum.org/v1/gonum/matrix)
+
+Package matrix is a matrix package for the Go language.
diff --git a/vendor/gonum.org/v1/gonum/mat/band.go b/vendor/gonum.org/v1/gonum/mat/band.go
new file mode 100644
index 00000000..296040ea
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/band.go
@@ -0,0 +1,228 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+var (
+	bandDense *BandDense
+	_         Matrix    = bandDense
+	_         Banded    = bandDense
+	_         RawBander = bandDense
+
+	_ NonZeroDoer    = bandDense
+	_ RowNonZeroDoer = bandDense
+	_ ColNonZeroDoer = bandDense
+)
+
+// BandDense represents a band matrix in dense storage format.
+type BandDense struct {
+	mat blas64.Band
+}
+
+// Banded is a band matrix representation.
+type Banded interface {
+	Matrix
+	// Bandwidth returns the lower and upper bandwidth values for
+	// the matrix. The total bandwidth of the matrix is kl+ku+1.
+	Bandwidth() (kl, ku int)
+
+	// TBand is the equivalent of the T() method in the Matrix
+	// interface but guarantees the transpose is of banded type.
+	TBand() Banded
+}
+
+// A RawBander can return a blas64.Band representation of the receiver.
+// Changes to the blas64.Band.Data slice will be reflected in the original
+// matrix, changes to the Rows, Cols, KL, KU and Stride fields will not.
+type RawBander interface {
+	RawBand() blas64.Band
+}
+
+// A MutableBanded can set elements of a band matrix.
+type MutableBanded interface {
+	Banded
+	SetBand(i, j int, v float64)
+}
+
+var (
+	_ Matrix            = TransposeBand{}
+	_ Banded            = TransposeBand{}
+	_ UntransposeBander = TransposeBand{}
+)
+
+// TransposeBand is a type for performing an implicit transpose of a band
+// matrix. It implements the Banded interface, returning values from the
+// transpose of the matrix within.
+type TransposeBand struct {
+	Banded Banded
+}
+
+// At returns the value of the element at row i and column j of the transposed
+// matrix, that is, row j and column i of the Banded field.
+func (t TransposeBand) At(i, j int) float64 {
+	return t.Banded.At(j, i)
+}
+
+// Dims returns the dimensions of the transposed matrix.
+func (t TransposeBand) Dims() (r, c int) {
+	c, r = t.Banded.Dims()
+	return r, c
+}
+
+// T performs an implicit transpose by returning the Banded field.
+func (t TransposeBand) T() Matrix {
+	return t.Banded
+}
+
+// Bandwidth returns the lower and upper bandwidth values for
+// the transposed matrix.
+func (t TransposeBand) Bandwidth() (kl, ku int) {
+	kl, ku = t.Banded.Bandwidth()
+	return ku, kl
+}
+
+// TBand performs an implicit transpose by returning the Banded field.
+func (t TransposeBand) TBand() Banded {
+	return t.Banded
+}
+
+// Untranspose returns the Banded field.
+func (t TransposeBand) Untranspose() Matrix {
+	return t.Banded
+}
+
+// UntransposeBand returns the Banded field.
+func (t TransposeBand) UntransposeBand() Banded {
+	return t.Banded
+}
+
+// NewBandDense creates a new Band matrix with r rows and c columns. If data == nil,
+// a new slice is allocated for the backing slice. If len(data) == min(r, c+kl)*(kl+ku+1),
+// data is used as the backing slice, and changes to the elements of the returned
+// BandDense will be reflected in data. If neither of these is true, NewBandDense
+// will panic. kl must be at least zero and less r, and ku must be at least zero and
+// less than c, otherwise NewBandDense will panic.
+//
+// The data must be arranged in row-major order constructed by removing the zeros
+// from the rows outside the band and aligning the diagonals. For example, the matrix
+//    1  2  3  0  0  0
+//    4  5  6  7  0  0
+//    0  8  9 10 11  0
+//    0  0 12 13 14 15
+//    0  0  0 16 17 18
+//    0  0  0  0 19 20
+// becomes (* entries are never accessed)
+//     *  1  2  3
+//     4  5  6  7
+//     8  9 10 11
+//    12 13 14 15
+//    16 17 18  *
+//    19 20  *  *
+// which is passed to NewBandDense as []float64{*, 1, 2, 3, 4, ...} with kl=1 and ku=2.
+// Only the values in the band portion of the matrix are used.
+func NewBandDense(r, c, kl, ku int, data []float64) *BandDense {
+	if r < 0 || c < 0 || kl < 0 || ku < 0 {
+		panic("mat: negative dimension")
+	}
+	if kl+1 > r || ku+1 > c {
+		panic("mat: band out of range")
+	}
+	bc := kl + ku + 1
+	if data != nil && len(data) != min(r, c+kl)*bc {
+		panic(ErrShape)
+	}
+	if data == nil {
+		data = make([]float64, min(r, c+kl)*bc)
+	}
+	return &BandDense{
+		mat: blas64.Band{
+			Rows:   r,
+			Cols:   c,
+			KL:     kl,
+			KU:     ku,
+			Stride: bc,
+			Data:   data,
+		},
+	}
+}
+
+// NewDiagonalRect is a convenience function that returns a diagonal matrix represented by a
+// BandDense. The length of data must be min(r, c) otherwise NewDiagonalRect will panic.
+func NewDiagonalRect(r, c int, data []float64) *BandDense {
+	return NewBandDense(r, c, 0, 0, data)
+}
+
+// Dims returns the number of rows and columns in the matrix.
+func (b *BandDense) Dims() (r, c int) {
+	return b.mat.Rows, b.mat.Cols
+}
+
+// Bandwidth returns the upper and lower bandwidths of the matrix.
+func (b *BandDense) Bandwidth() (kl, ku int) {
+	return b.mat.KL, b.mat.KU
+}
+
+// T performs an implicit transpose by returning the receiver inside a Transpose.
+func (b *BandDense) T() Matrix {
+	return Transpose{b}
+}
+
+// TBand performs an implicit transpose by returning the receiver inside a TransposeBand.
+func (b *BandDense) TBand() Banded {
+	return TransposeBand{b}
+}
+
+// RawBand returns the underlying blas64.Band used by the receiver.
+// Changes to elements in the receiver following the call will be reflected
+// in returned blas64.Band.
+func (b *BandDense) RawBand() blas64.Band {
+	return b.mat
+}
+
+// DoNonZero calls the function fn for each of the non-zero elements of b. The function fn
+// takes a row/column index and the element value of b at (i, j).
+func (b *BandDense) DoNonZero(fn func(i, j int, v float64)) {
+	for i := 0; i < min(b.mat.Rows, b.mat.Cols+b.mat.KL); i++ {
+		for j := max(0, i-b.mat.KL); j < min(b.mat.Cols, i+b.mat.KU+1); j++ {
+			v := b.at(i, j)
+			if v != 0 {
+				fn(i, j, v)
+			}
+		}
+	}
+}
+
+// DoRowNonZero calls the function fn for each of the non-zero elements of row i of b. The function fn
+// takes a row/column index and the element value of b at (i, j).
+func (b *BandDense) DoRowNonZero(i int, fn func(i, j int, v float64)) {
+	if i < 0 || b.mat.Rows <= i {
+		panic(ErrRowAccess)
+	}
+	for j := max(0, i-b.mat.KL); j < min(b.mat.Cols, i+b.mat.KU+1); j++ {
+		v := b.at(i, j)
+		if v != 0 {
+			fn(i, j, v)
+		}
+	}
+}
+
+// DoColNonZero calls the function fn for each of the non-zero elements of column j of b. The function fn
+// takes a row/column index and the element value of b at (i, j).
+func (b *BandDense) DoColNonZero(j int, fn func(i, j int, v float64)) {
+	if j < 0 || b.mat.Cols <= j {
+		panic(ErrColAccess)
+	}
+	for i := 0; i < min(b.mat.Rows, b.mat.Cols+b.mat.KL); i++ {
+		if i-b.mat.KL <= j && j < i+b.mat.KU+1 {
+			v := b.at(i, j)
+			if v != 0 {
+				fn(i, j, v)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/band_test.go b/vendor/gonum.org/v1/gonum/mat/band_test.go
new file mode 100644
index 00000000..f24d7f5c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/band_test.go
@@ -0,0 +1,377 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"reflect"
+	"testing"
+
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+func TestNewBand(t *testing.T) {
+	for i, test := range []struct {
+		data   []float64
+		r, c   int
+		kl, ku int
+		mat    *BandDense
+		dense  *Dense
+	}{
+		{
+			data: []float64{
+				-1, 1, 2, 3,
+				4, 5, 6, 7,
+				8, 9, 10, 11,
+				12, 13, 14, 15,
+				16, 17, 18, -1,
+				19, 20, -1, -1,
+			},
+			r: 6, c: 6,
+			kl: 1, ku: 2,
+			mat: &BandDense{
+				mat: blas64.Band{
+					Rows:   6,
+					Cols:   6,
+					KL:     1,
+					KU:     2,
+					Stride: 4,
+					Data: []float64{
+						-1, 1, 2, 3,
+						4, 5, 6, 7,
+						8, 9, 10, 11,
+						12, 13, 14, 15,
+						16, 17, 18, -1,
+						19, 20, -1, -1,
+					},
+				},
+			},
+			dense: NewDense(6, 6, []float64{
+				1, 2, 3, 0, 0, 0,
+				4, 5, 6, 7, 0, 0,
+				0, 8, 9, 10, 11, 0,
+				0, 0, 12, 13, 14, 15,
+				0, 0, 0, 16, 17, 18,
+				0, 0, 0, 0, 19, 20,
+			}),
+		},
+		{
+			data: []float64{
+				-1, 1, 2, 3,
+				4, 5, 6, 7,
+				8, 9, 10, 11,
+				12, 13, 14, 15,
+				16, 17, 18, -1,
+				19, 20, -1, -1,
+				21, -1, -1, -1,
+			},
+			r: 10, c: 6,
+			kl: 1, ku: 2,
+			mat: &BandDense{
+				mat: blas64.Band{
+					Rows:   10,
+					Cols:   6,
+					KL:     1,
+					KU:     2,
+					Stride: 4,
+					Data: []float64{
+						-1, 1, 2, 3,
+						4, 5, 6, 7,
+						8, 9, 10, 11,
+						12, 13, 14, 15,
+						16, 17, 18, -1,
+						19, 20, -1, -1,
+						21, -1, -1, -1,
+					},
+				},
+			},
+			dense: NewDense(10, 6, []float64{
+				1, 2, 3, 0, 0, 0,
+				4, 5, 6, 7, 0, 0,
+				0, 8, 9, 10, 11, 0,
+				0, 0, 12, 13, 14, 15,
+				0, 0, 0, 16, 17, 18,
+				0, 0, 0, 0, 19, 20,
+				0, 0, 0, 0, 0, 21,
+				0, 0, 0, 0, 0, 0,
+				0, 0, 0, 0, 0, 0,
+				0, 0, 0, 0, 0, 0,
+			}),
+		},
+		{
+			data: []float64{
+				-1, 1, 2, 3,
+				4, 5, 6, 7,
+				8, 9, 10, 11,
+				12, 13, 14, 15,
+				16, 17, 18, 19,
+				20, 21, 22, 23,
+			},
+			r: 6, c: 10,
+			kl: 1, ku: 2,
+			mat: &BandDense{
+				mat: blas64.Band{
+					Rows:   6,
+					Cols:   10,
+					KL:     1,
+					KU:     2,
+					Stride: 4,
+					Data: []float64{
+						-1, 1, 2, 3,
+						4, 5, 6, 7,
+						8, 9, 10, 11,
+						12, 13, 14, 15,
+						16, 17, 18, 19,
+						20, 21, 22, 23,
+					},
+				},
+			},
+			dense: NewDense(6, 10, []float64{
+				1, 2, 3, 0, 0, 0, 0, 0, 0, 0,
+				4, 5, 6, 7, 0, 0, 0, 0, 0, 0,
+				0, 8, 9, 10, 11, 0, 0, 0, 0, 0,
+				0, 0, 12, 13, 14, 15, 0, 0, 0, 0,
+				0, 0, 0, 16, 17, 18, 19, 0, 0, 0,
+				0, 0, 0, 0, 20, 21, 22, 23, 0, 0,
+			}),
+		},
+	} {
+		band := NewBandDense(test.r, test.c, test.kl, test.ku, test.data)
+		rows, cols := band.Dims()
+
+		if rows != test.r {
+			t.Errorf("unexpected number of rows for test %d: got: %d want: %d", i, rows, test.r)
+		}
+		if cols != test.c {
+			t.Errorf("unexpected number of cols for test %d: got: %d want: %d", i, cols, test.c)
+		}
+		if !reflect.DeepEqual(band, test.mat) {
+			t.Errorf("unexpected value via reflect for test %d: got: %v want: %v", i, band, test.mat)
+		}
+		if !Equal(band, test.mat) {
+			t.Errorf("unexpected value via mat.Equal for test %d: got: %v want: %v", i, band, test.mat)
+		}
+		if !Equal(band, test.dense) {
+			t.Errorf("unexpected value via mat.Equal(band, dense) for test %d:\ngot:\n% v\nwant:\n% v", i, Formatted(band), Formatted(test.dense))
+		}
+	}
+}
+
+func TestNewDiagonalRect(t *testing.T) {
+	for i, test := range []struct {
+		data  []float64
+		r, c  int
+		mat   *BandDense
+		dense *Dense
+	}{
+		{
+			data: []float64{1, 2, 3, 4, 5, 6},
+			r:    6, c: 6,
+			mat: &BandDense{
+				mat: blas64.Band{
+					Rows:   6,
+					Cols:   6,
+					Stride: 1,
+					Data:   []float64{1, 2, 3, 4, 5, 6},
+				},
+			},
+			dense: NewDense(6, 6, []float64{
+				1, 0, 0, 0, 0, 0,
+				0, 2, 0, 0, 0, 0,
+				0, 0, 3, 0, 0, 0,
+				0, 0, 0, 4, 0, 0,
+				0, 0, 0, 0, 5, 0,
+				0, 0, 0, 0, 0, 6,
+			}),
+		},
+		{
+			data: []float64{1, 2, 3, 4, 5, 6},
+			r:    7, c: 6,
+			mat: &BandDense{
+				mat: blas64.Band{
+					Rows:   7,
+					Cols:   6,
+					Stride: 1,
+					Data:   []float64{1, 2, 3, 4, 5, 6},
+				},
+			},
+			dense: NewDense(7, 6, []float64{
+				1, 0, 0, 0, 0, 0,
+				0, 2, 0, 0, 0, 0,
+				0, 0, 3, 0, 0, 0,
+				0, 0, 0, 4, 0, 0,
+				0, 0, 0, 0, 5, 0,
+				0, 0, 0, 0, 0, 6,
+				0, 0, 0, 0, 0, 0,
+			}),
+		},
+		{
+			data: []float64{1, 2, 3, 4, 5, 6},
+			r:    6, c: 7,
+			mat: &BandDense{
+				mat: blas64.Band{
+					Rows:   6,
+					Cols:   7,
+					Stride: 1,
+					Data:   []float64{1, 2, 3, 4, 5, 6},
+				},
+			},
+			dense: NewDense(6, 7, []float64{
+				1, 0, 0, 0, 0, 0, 0,
+				0, 2, 0, 0, 0, 0, 0,
+				0, 0, 3, 0, 0, 0, 0,
+				0, 0, 0, 4, 0, 0, 0,
+				0, 0, 0, 0, 5, 0, 0,
+				0, 0, 0, 0, 0, 6, 0,
+			}),
+		},
+	} {
+		band := NewDiagonalRect(test.r, test.c, test.data)
+		rows, cols := band.Dims()
+
+		if rows != test.r {
+			t.Errorf("unexpected number of rows for test %d: got: %d want: %d", i, rows, test.r)
+		}
+		if cols != test.c {
+			t.Errorf("unexpected number of cols for test %d: got: %d want: %d", i, cols, test.c)
+		}
+		if !reflect.DeepEqual(band, test.mat) {
+			t.Errorf("unexpected value via reflect for test %d: got: %v want: %v", i, band, test.mat)
+		}
+		if !Equal(band, test.mat) {
+			t.Errorf("unexpected value via mat.Equal for test %d: got: %v want: %v", i, band, test.mat)
+		}
+		if !Equal(band, test.dense) {
+			t.Errorf("unexpected value via mat.Equal(band, dense) for test %d:\ngot:\n% v\nwant:\n% v", i, Formatted(band), Formatted(test.dense))
+		}
+	}
+}
+
+func TestBandAtSet(t *testing.T) {
+	// 2  3  4  0  0  0
+	// 5  6  7  8  0  0
+	// 0  9 10 11 12  0
+	// 0  0 13 14 15 16
+	// 0  0  0 17 18 19
+	// 0  0  0  0 21 22
+	band := NewBandDense(6, 6, 1, 2, []float64{
+		-1, 2, 3, 4,
+		5, 6, 7, 8,
+		9, 10, 11, 12,
+		13, 14, 15, 16,
+		17, 18, 19, -1,
+		21, 22, -1, -1,
+	})
+
+	rows, cols := band.Dims()
+	kl, ku := band.Bandwidth()
+
+	// Explicitly test all indexes.
+	want := bandImplicit{rows, cols, kl, ku, func(i, j int) float64 {
+		return float64(i*(kl+ku) + j + kl + 1)
+	}}
+	for i := 0; i < 6; i++ {
+		for j := 0; j < 6; j++ {
+			if band.At(i, j) != want.At(i, j) {
+				t.Errorf("unexpected value for band.At(%d, %d): got:%v want:%v", i, j, band.At(i, j), want.At(i, j))
+			}
+		}
+	}
+	// Do that same thing via a call to Equal.
+	if !Equal(band, want) {
+		t.Errorf("unexpected value via mat.Equal:\ngot:\n% v\nwant:\n% v", Formatted(band), Formatted(want))
+	}
+
+	// Check At out of bounds
+	for _, row := range []int{-1, rows, rows + 1} {
+		panicked, message := panics(func() { band.At(row, 0) })
+		if !panicked || message != ErrRowAccess.Error() {
+			t.Errorf("expected panic for invalid row access N=%d r=%d", rows, row)
+		}
+	}
+	for _, col := range []int{-1, cols, cols + 1} {
+		panicked, message := panics(func() { band.At(0, col) })
+		if !panicked || message != ErrColAccess.Error() {
+			t.Errorf("expected panic for invalid column access N=%d c=%d", cols, col)
+		}
+	}
+
+	// Check Set out of bounds
+	for _, row := range []int{-1, rows, rows + 1} {
+		panicked, message := panics(func() { band.SetBand(row, 0, 1.2) })
+		if !panicked || message != ErrRowAccess.Error() {
+			t.Errorf("expected panic for invalid row access N=%d r=%d", rows, row)
+		}
+	}
+	for _, col := range []int{-1, cols, cols + 1} {
+		panicked, message := panics(func() { band.SetBand(0, col, 1.2) })
+		if !panicked || message != ErrColAccess.Error() {
+			t.Errorf("expected panic for invalid column access N=%d c=%d", cols, col)
+		}
+	}
+
+	for _, st := range []struct {
+		row, col int
+	}{
+		{row: 0, col: 3},
+		{row: 0, col: 4},
+		{row: 0, col: 5},
+		{row: 1, col: 4},
+		{row: 1, col: 5},
+		{row: 2, col: 5},
+		{row: 2, col: 0},
+		{row: 3, col: 1},
+		{row: 4, col: 2},
+		{row: 5, col: 3},
+	} {
+		panicked, message := panics(func() { band.SetBand(st.row, st.col, 1.2) })
+		if !panicked || message != ErrBandSet.Error() {
+			t.Errorf("expected panic for %+v %s", st, message)
+		}
+	}
+
+	for _, st := range []struct {
+		row, col  int
+		orig, new float64
+	}{
+		{row: 1, col: 2, orig: 7, new: 15},
+		{row: 2, col: 3, orig: 11, new: 15},
+	} {
+		if e := band.At(st.row, st.col); e != st.orig {
+			t.Errorf("unexpected value for At(%d, %d): got: %v want: %v", st.row, st.col, e, st.orig)
+		}
+		band.SetBand(st.row, st.col, st.new)
+		if e := band.At(st.row, st.col); e != st.new {
+			t.Errorf("unexpected value for At(%d, %d) after SetBand(%[1]d, %d, %v): got: %v want: %[3]v", st.row, st.col, st.new, e)
+		}
+	}
+}
+
+// bandImplicit is an implicit band matrix returning val(i, j)
+// for the value at (i, j).
+type bandImplicit struct {
+	r, c, kl, ku int
+	val          func(i, j int) float64
+}
+
+func (b bandImplicit) Dims() (r, c int) {
+	return b.r, b.c
+}
+
+func (b bandImplicit) T() Matrix {
+	return Transpose{b}
+}
+
+func (b bandImplicit) At(i, j int) float64 {
+	if i < 0 || b.r <= i {
+		panic("row")
+	}
+	if j < 0 || b.c <= j {
+		panic("col")
+	}
+	if j < i-b.kl || i+b.ku < j {
+		return 0
+	}
+	return b.val(i, j)
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/cblas_test.go b/vendor/gonum.org/v1/gonum/mat/cblas_test.go
new file mode 100644
index 00000000..7371e8ba
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/cblas_test.go
@@ -0,0 +1,16 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build cblas
+
+package mat
+
+import (
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/netlib/blas"
+)
+
+func init() {
+	blas64.Use(blas.Implementation{})
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/cholesky.go b/vendor/gonum.org/v1/gonum/mat/cholesky.go
new file mode 100644
index 00000000..fa4e91c6
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/cholesky.go
@@ -0,0 +1,479 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack/lapack64"
+)
+
+const (
+	badTriangle = "mat: invalid triangle"
+	badCholesky = "mat: invalid Cholesky factorization"
+)
+
+// Cholesky is a type for creating and using the Cholesky factorization of a
+// symmetric positive definite matrix.
+//
+// Cholesky methods may only be called on a value that has been successfully
+// initialized by a call to Factorize that has returned true. Calls to methods
+// of an unsuccessful Cholesky factorization will panic.
+type Cholesky struct {
+	// The chol pointer must never be retained as a pointer outside the Cholesky
+	// struct, either by returning chol outside the struct or by setting it to
+	// a pointer coming from outside. The same prohibition applies to the data
+	// slice within chol.
+	chol *TriDense
+	cond float64
+}
+
+// updateCond updates the condition number of the Cholesky decomposition. If
+// norm > 0, then that norm is used as the norm of the original matrix A, otherwise
+// the norm is estimated from the decomposition.
+func (c *Cholesky) updateCond(norm float64) {
+	n := c.chol.mat.N
+	work := getFloats(3*n, false)
+	defer putFloats(work)
+	if norm < 0 {
+		// This is an approximation. By the definition of a norm,
+		//  |AB| <= |A| |B|.
+		// Since A = U^T*U, we get for the condition number κ that
+		//  κ(A) := |A| |A^-1| = |U^T*U| |A^-1| <= |U^T| |U| |A^-1|,
+		// so this will overestimate the condition number somewhat.
+		// The norm of the original factorized matrix cannot be stored
+		// because of update possibilities.
+		unorm := lapack64.Lantr(CondNorm, c.chol.mat, work)
+		lnorm := lapack64.Lantr(CondNormTrans, c.chol.mat, work)
+		norm = unorm * lnorm
+	}
+	sym := c.chol.asSymBlas()
+	iwork := getInts(n, false)
+	v := lapack64.Pocon(sym, norm, work, iwork)
+	putInts(iwork)
+	c.cond = 1 / v
+}
+
+// Cond returns the condition number of the factorized matrix.
+func (c *Cholesky) Cond() float64 {
+	return c.cond
+}
+
+// Factorize calculates the Cholesky decomposition of the matrix A and returns
+// whether the matrix is positive definite. If Factorize returns false, the
+// factorization must not be used.
+func (c *Cholesky) Factorize(a Symmetric) (ok bool) {
+	n := a.Symmetric()
+	if c.isZero() {
+		c.chol = NewTriDense(n, Upper, nil)
+	} else {
+		c.chol = NewTriDense(n, Upper, use(c.chol.mat.Data, n*n))
+	}
+	copySymIntoTriangle(c.chol, a)
+
+	sym := c.chol.asSymBlas()
+	work := getFloats(c.chol.mat.N, false)
+	norm := lapack64.Lansy(CondNorm, sym, work)
+	putFloats(work)
+	_, ok = lapack64.Potrf(sym)
+	if ok {
+		c.updateCond(norm)
+	} else {
+		c.Reset()
+	}
+	return ok
+}
+
+// Reset resets the factorization so that it can be reused as the receiver of a
+// dimensionally restricted operation.
+func (c *Cholesky) Reset() {
+	if !c.isZero() {
+		c.chol.Reset()
+	}
+	c.cond = math.Inf(1)
+}
+
+// SetFromU sets the Cholesky decomposition from the given triangular matrix.
+// SetFromU panics if t is not upper triangular. Note that t is copied into,
+// not stored inside, the receiver.
+func (c *Cholesky) SetFromU(t *TriDense) {
+	n, kind := t.Triangle()
+	if kind != Upper {
+		panic("cholesky: matrix must be upper triangular")
+	}
+	if c.isZero() {
+		c.chol = NewTriDense(n, Upper, nil)
+	} else {
+		c.chol = NewTriDense(n, Upper, use(c.chol.mat.Data, n*n))
+	}
+	c.chol.Copy(t)
+	c.updateCond(-1)
+}
+
+// Clone makes a copy of the input Cholesky into the receiver, overwriting the
+// previous value of the receiver. Clone does not place any restrictions on receiver
+// shape. Clone panics if the input Cholesky is not the result of a valid decomposition.
+func (c *Cholesky) Clone(chol *Cholesky) {
+	if !chol.valid() {
+		panic(badCholesky)
+	}
+	n := chol.Size()
+	if c.isZero() {
+		c.chol = NewTriDense(n, Upper, nil)
+	} else {
+		c.chol = NewTriDense(n, Upper, use(c.chol.mat.Data, n*n))
+	}
+	c.chol.Copy(chol.chol)
+	c.cond = chol.cond
+}
+
+// Size returns the dimension of the factorized matrix.
+func (c *Cholesky) Size() int {
+	if !c.valid() {
+		panic(badCholesky)
+	}
+	return c.chol.mat.N
+}
+
+// Det returns the determinant of the matrix that has been factorized.
+func (c *Cholesky) Det() float64 {
+	if !c.valid() {
+		panic(badCholesky)
+	}
+	return math.Exp(c.LogDet())
+}
+
+// LogDet returns the log of the determinant of the matrix that has been factorized.
+func (c *Cholesky) LogDet() float64 {
+	if !c.valid() {
+		panic(badCholesky)
+	}
+	var det float64
+	for i := 0; i < c.chol.mat.N; i++ {
+		det += 2 * math.Log(c.chol.mat.Data[i*c.chol.mat.Stride+i])
+	}
+	return det
+}
+
+// Solve finds the matrix m that solves A * m = b where A is represented
+// by the Cholesky decomposition, placing the result in m.
+func (c *Cholesky) Solve(m *Dense, b Matrix) error {
+	if !c.valid() {
+		panic(badCholesky)
+	}
+	n := c.chol.mat.N
+	bm, bn := b.Dims()
+	if n != bm {
+		panic(ErrShape)
+	}
+
+	m.reuseAs(bm, bn)
+	if b != m {
+		m.Copy(b)
+	}
+	blas64.Trsm(blas.Left, blas.Trans, 1, c.chol.mat, m.mat)
+	blas64.Trsm(blas.Left, blas.NoTrans, 1, c.chol.mat, m.mat)
+	if c.cond > ConditionTolerance {
+		return Condition(c.cond)
+	}
+	return nil
+}
+
+// SolveChol finds the matrix m that solves A * m = B where A and B are represented
+// by their Cholesky decompositions a and b, placing the result in the receiver.
+func (a *Cholesky) SolveChol(m *Dense, b *Cholesky) error {
+	if !a.valid() || !b.valid() {
+		panic(badCholesky)
+	}
+	bn := b.chol.mat.N
+	if a.chol.mat.N != bn {
+		panic(ErrShape)
+	}
+
+	m.reuseAsZeroed(bn, bn)
+	m.Copy(b.chol.T())
+	blas64.Trsm(blas.Left, blas.Trans, 1, a.chol.mat, m.mat)
+	blas64.Trsm(blas.Left, blas.NoTrans, 1, a.chol.mat, m.mat)
+	blas64.Trmm(blas.Right, blas.NoTrans, 1, b.chol.mat, m.mat)
+	if a.cond > ConditionTolerance {
+		return Condition(a.cond)
+	}
+	return nil
+}
+
+// SolveVec finds the vector v that solves A * v = b where A is represented
+// by the Cholesky decomposition, placing the result in v.
+func (c *Cholesky) SolveVec(v, b *VecDense) error {
+	if !c.valid() {
+		panic(badCholesky)
+	}
+	n := c.chol.mat.N
+	vn := b.Len()
+	if vn != n {
+		panic(ErrShape)
+	}
+	if v != b {
+		v.checkOverlap(b.mat)
+	}
+	v.reuseAs(n)
+	if v != b {
+		v.CopyVec(b)
+	}
+	blas64.Trsv(blas.Trans, c.chol.mat, v.mat)
+	blas64.Trsv(blas.NoTrans, c.chol.mat, v.mat)
+	if c.cond > ConditionTolerance {
+		return Condition(c.cond)
+	}
+	return nil
+
+}
+
+// UTo extracts the n×n upper triangular matrix U from a Cholesky
+// decomposition into dst and returns the result. If dst is nil a new
+// TriDense is allocated.
+//  A = U^T * U.
+func (c *Cholesky) UTo(dst *TriDense) *TriDense {
+	if !c.valid() {
+		panic(badCholesky)
+	}
+	n := c.chol.mat.N
+	if dst == nil {
+		dst = NewTriDense(n, Upper, make([]float64, n*n))
+	} else {
+		dst.reuseAs(n, Upper)
+	}
+	dst.Copy(c.chol)
+	return dst
+}
+
+// LTo extracts the n×n lower triangular matrix L from a Cholesky
+// decomposition into dst and returns the result. If dst is nil a new
+// TriDense is allocated.
+//  A = L * L^T.
+func (c *Cholesky) LTo(dst *TriDense) *TriDense {
+	if !c.valid() {
+		panic(badCholesky)
+	}
+	n := c.chol.mat.N
+	if dst == nil {
+		dst = NewTriDense(n, Lower, make([]float64, n*n))
+	} else {
+		dst.reuseAs(n, Lower)
+	}
+	dst.Copy(c.chol.TTri())
+	return dst
+}
+
+// To reconstructs the original positive definite matrix given its
+// Cholesky decomposition into dst and returns the result. If dst is nil
+// a new SymDense is allocated.
+func (c *Cholesky) To(dst *SymDense) *SymDense {
+	if !c.valid() {
+		panic(badCholesky)
+	}
+	n := c.chol.mat.N
+	if dst == nil {
+		dst = NewSymDense(n, make([]float64, n*n))
+	} else {
+		dst.reuseAs(n)
+	}
+	dst.SymOuterK(1, c.chol.T())
+	return dst
+}
+
+// InverseTo computes the inverse of the matrix represented by its Cholesky
+// factorization and stores the result into s. If the factorized
+// matrix is ill-conditioned, a Condition error will be returned.
+// Note that matrix inversion is numerically unstable, and should generally be
+// avoided where possible, for example by using the Solve routines.
+func (c *Cholesky) InverseTo(s *SymDense) error {
+	if !c.valid() {
+		panic(badCholesky)
+	}
+	// TODO(btracey): Replace this code with a direct call to Dpotri when it
+	// is available.
+	s.reuseAs(c.chol.mat.N)
+	// If:
+	//  chol(A) = U^T * U
+	// Then:
+	//  chol(A^-1) = S * S^T
+	// where S = U^-1
+	var t TriDense
+	err := t.InverseTri(c.chol)
+	s.SymOuterK(1, &t)
+	return err
+}
+
+// SymRankOne performs a rank-1 update of the original matrix A and refactorizes
+// its Cholesky factorization, storing the result into the receiver. That is, if
+// in the original Cholesky factorization
+//  U^T * U = A,
+// in the updated factorization
+//  U'^T * U' = A + alpha * x * x^T = A'.
+//
+// Note that when alpha is negative, the updating problem may be ill-conditioned
+// and the results may be inaccurate, or the updated matrix A' may not be
+// positive definite and not have a Cholesky factorization. SymRankOne returns
+// whether the updated matrix A' is positive definite.
+//
+// SymRankOne updates a Cholesky factorization in O(n²) time. The Cholesky
+// factorization computation from scratch is O(n³).
+func (c *Cholesky) SymRankOne(orig *Cholesky, alpha float64, x *VecDense) (ok bool) {
+	if !orig.valid() {
+		panic(badCholesky)
+	}
+	n := orig.Size()
+	if x.Len() != n {
+		panic(ErrShape)
+	}
+	if orig != c {
+		if c.isZero() {
+			c.chol = NewTriDense(n, Upper, nil)
+		} else if c.chol.mat.N != n {
+			panic(ErrShape)
+		}
+		c.chol.Copy(orig.chol)
+	}
+
+	if alpha == 0 {
+		return true
+	}
+
+	// Algorithms for updating and downdating the Cholesky factorization are
+	// described, for example, in
+	// - J. J. Dongarra, J. R. Bunch, C. B. Moler, G. W. Stewart: LINPACK
+	//   Users' Guide. SIAM (1979), pages 10.10--10.14
+	// or
+	// - P. E. Gill, G. H. Golub, W. Murray, and M. A. Saunders: Methods for
+	//   modifying matrix factorizations. Mathematics of Computation 28(126)
+	//   (1974), Method C3 on page 521
+	//
+	// The implementation is based on LINPACK code
+	// http://www.netlib.org/linpack/dchud.f
+	// http://www.netlib.org/linpack/dchdd.f
+	// and
+	// https://icl.cs.utk.edu/lapack-forum/viewtopic.php?f=2&t=2646
+	//
+	// According to http://icl.cs.utk.edu/lapack-forum/archives/lapack/msg00301.html
+	// LINPACK is released under BSD license.
+	//
+	// See also:
+	// - M. A. Saunders: Large-scale Linear Programming Using the Cholesky
+	//   Factorization. Technical Report Stanford University (1972)
+	//   http://i.stanford.edu/pub/cstr/reports/cs/tr/72/252/CS-TR-72-252.pdf
+	// - Matthias Seeger: Low rank updates for the Cholesky decomposition.
+	//   EPFL Technical Report 161468 (2004)
+	//   http://infoscience.epfl.ch/record/161468
+
+	work := getFloats(n, false)
+	defer putFloats(work)
+	blas64.Copy(n, x.RawVector(), blas64.Vector{1, work})
+
+	if alpha > 0 {
+		// Compute rank-1 update.
+		if alpha != 1 {
+			blas64.Scal(n, math.Sqrt(alpha), blas64.Vector{1, work})
+		}
+		umat := c.chol.mat
+		stride := umat.Stride
+		for i := 0; i < n; i++ {
+			// Compute parameters of the Givens matrix that zeroes
+			// the i-th element of x.
+			c, s, r, _ := blas64.Rotg(umat.Data[i*stride+i], work[i])
+			if r < 0 {
+				// Multiply by -1 to have positive diagonal
+				// elemnts.
+				r *= -1
+				c *= -1
+				s *= -1
+			}
+			umat.Data[i*stride+i] = r
+			if i < n-1 {
+				// Multiply the extended factorization matrix by
+				// the Givens matrix from the left. Only
+				// the i-th row and x are modified.
+				blas64.Rot(n-i-1,
+					blas64.Vector{1, umat.Data[i*stride+i+1 : i*stride+n]},
+					blas64.Vector{1, work[i+1 : n]},
+					c, s)
+			}
+		}
+		c.updateCond(-1)
+		return true
+	}
+
+	// Compute rank-1 downdate.
+	alpha = math.Sqrt(-alpha)
+	if alpha != 1 {
+		blas64.Scal(n, alpha, blas64.Vector{1, work})
+	}
+	// Solve U^T * p = x storing the result into work.
+	ok = lapack64.Trtrs(blas.Trans, c.chol.RawTriangular(), blas64.General{
+		Rows:   n,
+		Cols:   1,
+		Stride: 1,
+		Data:   work,
+	})
+	if !ok {
+		// The original matrix is singular. Should not happen, because
+		// the factorization is valid.
+		panic(badCholesky)
+	}
+	norm := blas64.Nrm2(n, blas64.Vector{1, work})
+	if norm >= 1 {
+		// The updated matrix is not positive definite.
+		return false
+	}
+	norm = math.Sqrt((1 + norm) * (1 - norm))
+	cos := getFloats(n, false)
+	defer putFloats(cos)
+	sin := getFloats(n, false)
+	defer putFloats(sin)
+	for i := n - 1; i >= 0; i-- {
+		// Compute parameters of Givens matrices that zero elements of p
+		// backwards.
+		cos[i], sin[i], norm, _ = blas64.Rotg(norm, work[i])
+		if norm < 0 {
+			norm *= -1
+			cos[i] *= -1
+			sin[i] *= -1
+		}
+	}
+	umat := c.chol.mat
+	stride := umat.Stride
+	for i := n - 1; i >= 0; i-- {
+		// Apply Givens matrices to U.
+		// TODO(vladimir-ch): Use workspace to avoid modifying the
+		// receiver in case an invalid factorization is created.
+		blas64.Rot(n-i, blas64.Vector{1, work[i:n]}, blas64.Vector{1, umat.Data[i*stride+i : i*stride+n]}, cos[i], sin[i])
+		if umat.Data[i*stride+i] == 0 {
+			// The matrix is singular (may rarely happen due to
+			// floating-point effects?).
+			ok = false
+		} else if umat.Data[i*stride+i] < 0 {
+			// Diagonal elements should be positive. If it happens
+			// that on the i-th row the diagonal is negative,
+			// multiply U from the left by an identity matrix that
+			// has -1 on the i-th row.
+			blas64.Scal(n-i, -1, blas64.Vector{1, umat.Data[i*stride+i : i*stride+n]})
+		}
+	}
+	if ok {
+		c.updateCond(-1)
+	} else {
+		c.Reset()
+	}
+	return ok
+}
+
+func (c *Cholesky) isZero() bool {
+	return c.chol == nil
+}
+
+func (c *Cholesky) valid() bool {
+	return !c.isZero() && !c.chol.IsZero()
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/cholesky_example_test.go b/vendor/gonum.org/v1/gonum/mat/cholesky_example_test.go
new file mode 100644
index 00000000..8f75d79b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/cholesky_example_test.go
@@ -0,0 +1,121 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat_test
+
+import (
+	"fmt"
+
+	"gonum.org/v1/gonum/mat"
+)
+
+func ExampleCholesky() {
+	// Construct a symmetric positive definite matrix.
+	tmp := mat.NewDense(4, 4, []float64{
+		2, 6, 8, -4,
+		1, 8, 7, -2,
+		2, 2, 1, 7,
+		8, -2, -2, 1,
+	})
+	var a mat.SymDense
+	a.SymOuterK(1, tmp)
+
+	fmt.Printf("a = %0.4v\n", mat.Formatted(&a, mat.Prefix("    ")))
+
+	// Compute the cholesky factorization.
+	var chol mat.Cholesky
+	if ok := chol.Factorize(&a); !ok {
+		fmt.Println("a matrix is not positive semi-definite.")
+	}
+
+	// Find the determinant.
+	fmt.Printf("\nThe determinant of a is %0.4g\n\n", chol.Det())
+
+	// Use the factorization to solve the system of equations a * x = b.
+	b := mat.NewVecDense(4, []float64{1, 2, 3, 4})
+	var x mat.VecDense
+	if err := chol.SolveVec(&x, b); err != nil {
+		fmt.Println("Matrix is near singular: ", err)
+	}
+	fmt.Println("Solve a * x = b")
+	fmt.Printf("x = %0.4v\n", mat.Formatted(&x, mat.Prefix("    ")))
+
+	// Extract the factorization and check that it equals the original matrix.
+	t := chol.LTo(nil)
+	var test mat.Dense
+	test.Mul(t, t.T())
+	fmt.Println()
+	fmt.Printf("L * L^T = %0.4v\n", mat.Formatted(&a, mat.Prefix("          ")))
+
+	// Output:
+	// a = ⎡120  114   -4  -16⎤
+	//     ⎢114  118   11  -24⎥
+	//     ⎢ -4   11   58   17⎥
+	//     ⎣-16  -24   17   73⎦
+	//
+	// The determinant of a is 1.543e+06
+	//
+	// Solve a * x = b
+	// x = ⎡  -0.239⎤
+	//     ⎢  0.2732⎥
+	//     ⎢-0.04681⎥
+	//     ⎣  0.1031⎦
+	//
+	// L * L^T = ⎡120  114   -4  -16⎤
+	//           ⎢114  118   11  -24⎥
+	//           ⎢ -4   11   58   17⎥
+	//           ⎣-16  -24   17   73⎦
+}
+
+func ExampleCholesky_SymRankOne() {
+	a := mat.NewSymDense(4, []float64{
+		1, 1, 1, 1,
+		0, 2, 3, 4,
+		0, 0, 6, 10,
+		0, 0, 0, 20,
+	})
+	fmt.Printf("A = %0.4v\n", mat.Formatted(a, mat.Prefix("    ")))
+
+	// Compute the Cholesky factorization.
+	var chol mat.Cholesky
+	if ok := chol.Factorize(a); !ok {
+		fmt.Println("matrix a is not positive definite.")
+	}
+
+	x := mat.NewVecDense(4, []float64{0, 0, 0, 1})
+	fmt.Printf("\nx = %0.4v\n", mat.Formatted(x, mat.Prefix("    ")))
+
+	// Rank-1 update the factorization.
+	chol.SymRankOne(&chol, 1, x)
+	// Rank-1 update the matrix a.
+	a.SymRankOne(a, 1, x)
+
+	au := chol.To(nil)
+
+	// Print the matrix that was updated directly.
+	fmt.Printf("\nA' =        %0.4v\n", mat.Formatted(a, mat.Prefix("            ")))
+	// Print the matrix recovered from the factorization.
+	fmt.Printf("\nU'^T * U' = %0.4v\n", mat.Formatted(au, mat.Prefix("            ")))
+
+	// Output:
+	// A = ⎡ 1   1   1   1⎤
+	//     ⎢ 1   2   3   4⎥
+	//     ⎢ 1   3   6  10⎥
+	//     ⎣ 1   4  10  20⎦
+	//
+	// x = ⎡0⎤
+	//     ⎢0⎥
+	//     ⎢0⎥
+	//     ⎣1⎦
+	//
+	// A' =        ⎡ 1   1   1   1⎤
+	//             ⎢ 1   2   3   4⎥
+	//             ⎢ 1   3   6  10⎥
+	//             ⎣ 1   4  10  21⎦
+	//
+	// U'^T * U' = ⎡ 1   1   1   1⎤
+	//             ⎢ 1   2   3   4⎥
+	//             ⎢ 1   3   6  10⎥
+	//             ⎣ 1   4  10  21⎦
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/cholesky_test.go b/vendor/gonum.org/v1/gonum/mat/cholesky_test.go
new file mode 100644
index 00000000..6a5c853d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/cholesky_test.go
@@ -0,0 +1,453 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas/testblas"
+)
+
+func TestCholesky(t *testing.T) {
+	for _, test := range []struct {
+		a *SymDense
+
+		cond   float64
+		want   *TriDense
+		posdef bool
+	}{
+		{
+			a: NewSymDense(3, []float64{
+				4, 1, 1,
+				0, 2, 3,
+				0, 0, 6,
+			}),
+			cond: 37,
+			want: NewTriDense(3, true, []float64{
+				2, 0.5, 0.5,
+				0, 1.3228756555322954, 2.0788046015507495,
+				0, 0, 1.195228609334394,
+			}),
+			posdef: true,
+		},
+	} {
+		_, n := test.a.Dims()
+		for _, chol := range []*Cholesky{
+			{},
+			{chol: NewTriDense(n-1, true, nil)},
+			{chol: NewTriDense(n, true, nil)},
+			{chol: NewTriDense(n+1, true, nil)},
+		} {
+			ok := chol.Factorize(test.a)
+			if ok != test.posdef {
+				t.Errorf("unexpected return from Cholesky factorization: got: ok=%t want: ok=%t", ok, test.posdef)
+			}
+			fc := DenseCopyOf(chol.chol)
+			if !Equal(fc, test.want) {
+				t.Error("incorrect Cholesky factorization")
+			}
+			if math.Abs(test.cond-chol.cond) > 1e-13 {
+				t.Errorf("Condition number mismatch: Want %v, got %v", test.cond, chol.cond)
+			}
+			U := chol.UTo(nil)
+			aCopy := DenseCopyOf(test.a)
+			var a Dense
+			a.Mul(U.TTri(), U)
+			if !EqualApprox(&a, aCopy, 1e-14) {
+				t.Error("unexpected Cholesky factor product")
+			}
+
+			L := chol.LTo(nil)
+			a.Mul(L, L.TTri())
+			if !EqualApprox(&a, aCopy, 1e-14) {
+				t.Error("unexpected Cholesky factor product")
+			}
+		}
+	}
+}
+
+func TestCholeskySolve(t *testing.T) {
+	for _, test := range []struct {
+		a   *SymDense
+		b   *Dense
+		ans *Dense
+	}{
+		{
+			a: NewSymDense(2, []float64{
+				1, 0,
+				0, 1,
+			}),
+			b:   NewDense(2, 1, []float64{5, 6}),
+			ans: NewDense(2, 1, []float64{5, 6}),
+		},
+		{
+			a: NewSymDense(3, []float64{
+				53, 59, 37,
+				0, 83, 71,
+				37, 71, 101,
+			}),
+			b:   NewDense(3, 1, []float64{5, 6, 7}),
+			ans: NewDense(3, 1, []float64{0.20745069393718094, -0.17421475529583694, 0.11577794010226464}),
+		},
+	} {
+		var chol Cholesky
+		ok := chol.Factorize(test.a)
+		if !ok {
+			t.Fatal("unexpected Cholesky factorization failure: not positive definite")
+		}
+
+		var x Dense
+		chol.Solve(&x, test.b)
+		if !EqualApprox(&x, test.ans, 1e-12) {
+			t.Error("incorrect Cholesky solve solution")
+		}
+
+		var ans Dense
+		ans.Mul(test.a, &x)
+		if !EqualApprox(&ans, test.b, 1e-12) {
+			t.Error("incorrect Cholesky solve solution product")
+		}
+	}
+}
+
+func TestCholeskySolveChol(t *testing.T) {
+	for _, test := range []struct {
+		a, b *SymDense
+	}{
+		{
+			a: NewSymDense(2, []float64{
+				1, 0,
+				0, 1,
+			}),
+			b: NewSymDense(2, []float64{
+				1, 0,
+				0, 1,
+			}),
+		},
+		{
+			a: NewSymDense(2, []float64{
+				1, 0,
+				0, 1,
+			}),
+			b: NewSymDense(2, []float64{
+				2, 0,
+				0, 2,
+			}),
+		},
+		{
+			a: NewSymDense(3, []float64{
+				53, 59, 37,
+				59, 83, 71,
+				37, 71, 101,
+			}),
+			b: NewSymDense(3, []float64{
+				2, -1, 0,
+				-1, 2, -1,
+				0, -1, 2,
+			}),
+		},
+	} {
+		var chola, cholb Cholesky
+		ok := chola.Factorize(test.a)
+		if !ok {
+			t.Fatal("unexpected Cholesky factorization failure for a: not positive definite")
+		}
+		ok = cholb.Factorize(test.b)
+		if !ok {
+			t.Fatal("unexpected Cholesky factorization failure for b: not positive definite")
+		}
+
+		var x Dense
+		chola.SolveChol(&x, &cholb)
+
+		var ans Dense
+		ans.Mul(test.a, &x)
+		if !EqualApprox(&ans, test.b, 1e-12) {
+			var y Dense
+			y.Solve(test.a, test.b)
+			t.Errorf("incorrect Cholesky solve solution product\ngot solution:\n%.4v\nwant solution\n%.4v",
+				Formatted(&x), Formatted(&y))
+		}
+	}
+}
+
+func TestCholeskySolveVec(t *testing.T) {
+	for _, test := range []struct {
+		a   *SymDense
+		b   *VecDense
+		ans *VecDense
+	}{
+		{
+			a: NewSymDense(2, []float64{
+				1, 0,
+				0, 1,
+			}),
+			b:   NewVecDense(2, []float64{5, 6}),
+			ans: NewVecDense(2, []float64{5, 6}),
+		},
+		{
+			a: NewSymDense(3, []float64{
+				53, 59, 37,
+				0, 83, 71,
+				0, 0, 101,
+			}),
+			b:   NewVecDense(3, []float64{5, 6, 7}),
+			ans: NewVecDense(3, []float64{0.20745069393718094, -0.17421475529583694, 0.11577794010226464}),
+		},
+	} {
+		var chol Cholesky
+		ok := chol.Factorize(test.a)
+		if !ok {
+			t.Fatal("unexpected Cholesky factorization failure: not positive definite")
+		}
+
+		var x VecDense
+		chol.SolveVec(&x, test.b)
+		if !EqualApprox(&x, test.ans, 1e-12) {
+			t.Error("incorrect Cholesky solve solution")
+		}
+
+		var ans VecDense
+		ans.MulVec(test.a, &x)
+		if !EqualApprox(&ans, test.b, 1e-12) {
+			t.Error("incorrect Cholesky solve solution product")
+		}
+	}
+}
+
+func TestCholeskyTo(t *testing.T) {
+	for _, test := range []*SymDense{
+		NewSymDense(3, []float64{
+			53, 59, 37,
+			0, 83, 71,
+			0, 0, 101,
+		}),
+	} {
+		var chol Cholesky
+		ok := chol.Factorize(test)
+		if !ok {
+			t.Fatal("unexpected Cholesky factorization failure: not positive definite")
+		}
+		s := chol.To(nil)
+
+		if !EqualApprox(s, test, 1e-12) {
+			t.Errorf("Cholesky reconstruction not equal to original matrix.\nWant:\n% v\nGot:\n% v\n", Formatted(test), Formatted(s))
+		}
+	}
+}
+
+func TestCloneCholesky(t *testing.T) {
+	for _, test := range []*SymDense{
+		NewSymDense(3, []float64{
+			53, 59, 37,
+			0, 83, 71,
+			0, 0, 101,
+		}),
+	} {
+		var chol Cholesky
+		ok := chol.Factorize(test)
+		if !ok {
+			panic("bad test")
+		}
+		var chol2 Cholesky
+		chol2.Clone(&chol)
+
+		if chol.cond != chol2.cond {
+			t.Errorf("condition number mismatch from zero")
+		}
+		if !Equal(chol.chol, chol2.chol) {
+			t.Errorf("chol mismatch from zero")
+		}
+
+		// Corrupt chol2 and try again
+		chol2.cond = math.NaN()
+		chol2.chol = NewTriDense(2, Upper, nil)
+		chol2.Clone(&chol)
+		if chol.cond != chol2.cond {
+			t.Errorf("condition number mismatch from non-zero")
+		}
+		if !Equal(chol.chol, chol2.chol) {
+			t.Errorf("chol mismatch from non-zero")
+		}
+	}
+}
+
+func TestCholeskyInverseTo(t *testing.T) {
+	for _, n := range []int{1, 3, 5, 9} {
+		data := make([]float64, n*n)
+		for i := range data {
+			data[i] = rand.NormFloat64()
+		}
+		var s SymDense
+		s.SymOuterK(1, NewDense(n, n, data))
+
+		var chol Cholesky
+		ok := chol.Factorize(&s)
+		if !ok {
+			t.Errorf("Bad test, cholesky decomposition failed")
+		}
+
+		var sInv SymDense
+		chol.InverseTo(&sInv)
+
+		var ans Dense
+		ans.Mul(&sInv, &s)
+		if !equalApprox(eye(n), &ans, 1e-8, false) {
+			var diff Dense
+			diff.Sub(eye(n), &ans)
+			t.Errorf("SymDense times Cholesky inverse not identity. Norm diff = %v", Norm(&diff, 2))
+		}
+	}
+}
+
+func TestCholeskySymRankOne(t *testing.T) {
+	rand.Seed(1)
+	for _, n := range []int{1, 2, 3, 4, 5, 7, 10, 20, 50, 100} {
+		for k := 0; k < 10; k++ {
+			data := make([]float64, n*n)
+			for i := range data {
+				data[i] = rand.NormFloat64()
+			}
+
+			var a SymDense
+			a.SymOuterK(1, NewDense(n, n, data))
+
+			xdata := make([]float64, n)
+			for i := range xdata {
+				xdata[i] = rand.NormFloat64()
+			}
+			x := NewVecDense(n, xdata)
+
+			var chol Cholesky
+			ok := chol.Factorize(&a)
+			if !ok {
+				t.Errorf("Bad random test, Cholesky factorization failed")
+				continue
+			}
+
+			alpha := rand.Float64()
+			ok = chol.SymRankOne(&chol, alpha, x)
+			if !ok {
+				t.Errorf("n=%v, alpha=%v: unexpected failure", n, alpha)
+				continue
+			}
+			a.SymRankOne(&a, alpha, x)
+
+			var achol SymDense
+			chol.To(&achol)
+			if !EqualApprox(&achol, &a, 1e-13) {
+				t.Errorf("n=%v, alpha=%v: mismatch between updated matrix and from Cholesky:\nupdated:\n%v\nfrom Cholesky:\n%v",
+					n, alpha, Formatted(&a), Formatted(&achol))
+			}
+		}
+	}
+
+	for i, test := range []struct {
+		a     *SymDense
+		alpha float64
+		x     []float64
+
+		wantOk bool
+	}{
+		{
+			// Update (to positive definite matrix).
+			a: NewSymDense(4, []float64{
+				1, 1, 1, 1,
+				0, 2, 3, 4,
+				0, 0, 6, 10,
+				0, 0, 0, 20,
+			}),
+			alpha:  1,
+			x:      []float64{0, 0, 0, 1},
+			wantOk: true,
+		},
+		{
+			// Downdate to singular matrix.
+			a: NewSymDense(4, []float64{
+				1, 1, 1, 1,
+				0, 2, 3, 4,
+				0, 0, 6, 10,
+				0, 0, 0, 20,
+			}),
+			alpha:  -1,
+			x:      []float64{0, 0, 0, 1},
+			wantOk: false,
+		},
+		{
+			// Downdate to positive definite matrix.
+			a: NewSymDense(4, []float64{
+				1, 1, 1, 1,
+				0, 2, 3, 4,
+				0, 0, 6, 10,
+				0, 0, 0, 20,
+			}),
+			alpha:  -1 / 2,
+			x:      []float64{0, 0, 0, 1},
+			wantOk: true,
+		},
+	} {
+		var chol Cholesky
+		ok := chol.Factorize(test.a)
+		if !ok {
+			t.Errorf("Case %v: bad test, Cholesky factorization failed", i)
+			continue
+		}
+
+		x := NewVecDense(len(test.x), test.x)
+		ok = chol.SymRankOne(&chol, test.alpha, x)
+		if !ok {
+			if test.wantOk {
+				t.Errorf("Case %v: unexpected failure from SymRankOne", i)
+			}
+			continue
+		}
+		if ok && !test.wantOk {
+			t.Errorf("Case %v: expected a failure from SymRankOne", i)
+		}
+
+		a := test.a
+		a.SymRankOne(a, test.alpha, x)
+
+		var achol SymDense
+		chol.To(&achol)
+		if !EqualApprox(&achol, a, 1e-13) {
+			t.Errorf("Case %v: mismatch between updated matrix and from Cholesky:\nupdated:\n%v\nfrom Cholesky:\n%v",
+				i, Formatted(a), Formatted(&achol))
+		}
+	}
+}
+
+func BenchmarkCholeskySmall(b *testing.B) {
+	benchmarkCholesky(b, 2)
+}
+
+func BenchmarkCholeskyMedium(b *testing.B) {
+	benchmarkCholesky(b, testblas.MediumMat)
+}
+
+func BenchmarkCholeskyLarge(b *testing.B) {
+	benchmarkCholesky(b, testblas.LargeMat)
+}
+
+func benchmarkCholesky(b *testing.B, n int) {
+	base := make([]float64, n*n)
+	for i := range base {
+		base[i] = rand.Float64()
+	}
+	bm := NewDense(n, n, base)
+	bm.Mul(bm.T(), bm)
+	am := NewSymDense(n, bm.mat.Data)
+
+	var chol Cholesky
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		ok := chol.Factorize(am)
+		if !ok {
+			panic("not pos def")
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/cmatrix.go b/vendor/gonum.org/v1/gonum/mat/cmatrix.go
new file mode 100644
index 00000000..a2894237
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/cmatrix.go
@@ -0,0 +1,71 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+// CMatrix is the basic matrix interface type for complex matrices.
+type CMatrix interface {
+	// Dims returns the dimensions of a Matrix.
+	Dims() (r, c int)
+
+	// At returns the value of a matrix element at row i, column j.
+	// It will panic if i or j are out of bounds for the matrix.
+	At(i, j int) complex128
+
+	// H returns the conjugate transpose of the Matrix. Whether H
+	// returns a copy of the underlying data is implementation dependent.
+	// This method may be implemented using the Conjugate type, which
+	// provides an implicit matrix conjugate transpose.
+	H() CMatrix
+}
+
+var (
+	_ CMatrix      = Conjugate{}
+	_ Unconjugator = Conjugate{}
+)
+
+// Conjugate is a type for performing an implicit matrix conjugate transpose.
+// It implements the Matrix interface, returning values from the conjugate
+// transpose of the matrix within.
+type Conjugate struct {
+	CMatrix CMatrix
+}
+
+// At returns the value of the element at row i and column j of the transposed
+// matrix, that is, row j and column i of the Matrix field.
+func (t Conjugate) At(i, j int) complex128 {
+	z := t.CMatrix.At(j, i)
+	return complex(real(z), -imag(z))
+}
+
+// Dims returns the dimensions of the transposed matrix. The number of rows returned
+// is the number of columns in the Matrix field, and the number of columns is
+// the number of rows in the Matrix field.
+func (t Conjugate) Dims() (r, c int) {
+	c, r = t.CMatrix.Dims()
+	return r, c
+}
+
+// H performs an implicit conjugate transpose by returning the Matrix field.
+func (t Conjugate) H() CMatrix {
+	return t.CMatrix
+}
+
+// Unconjugate returns the Matrix field.
+func (t Conjugate) Unconjugate() CMatrix {
+	return t.CMatrix
+}
+
+// Unconjugator is a type that can undo an implicit conjugate transpose.
+type Unconjugator interface {
+	// Note: This interface is needed to unify all of the Conjugate types. In
+	// the cmat128 methods, we need to test if the Matrix has been implicitly
+	// transposed. If this is checked by testing for the specific Conjugate type
+	// then the behavior will be different if the user uses H() or HTri() for a
+	// triangular matrix.
+
+	// Unconjugate returns the underlying Matrix stored for the implicit
+	// conjugate transpose.
+	Unconjugate() CMatrix
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/consts.go b/vendor/gonum.org/v1/gonum/mat/consts.go
new file mode 100644
index 00000000..a7025fff
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/consts.go
@@ -0,0 +1,54 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+// TriKind represents the triangularity of the matrix.
+type TriKind bool
+
+const (
+	// Upper specifies an upper triangular matrix.
+	Upper TriKind = true
+	// Lower specifies a lower triangular matrix.
+	Lower TriKind = false
+)
+
+// SVDKind specifies the treatment of singular vectors during an SVD
+// factorization.
+type SVDKind int
+
+const (
+	// SVDNone specifies that no singular vectors should be computed during
+	// the decomposition.
+	SVDNone SVDKind = iota + 1
+	// SVDThin computes the thin singular vectors, that is, it computes
+	//  A = U~ * Σ * V~^T
+	// where U~ is of size m×min(m,n), Σ is a diagonal matrix of size min(m,n)×min(m,n)
+	// and V~ is of size n×min(m,n).
+	SVDThin
+	// SVDFull computes the full singular value decomposition,
+	//  A = U * Σ * V^T
+	// where U is of size m×m, Σ is an m×n diagonal matrix, and V is an n×n matrix.
+	SVDFull
+)
+
+// GSVDKind specifies the treatment of singular vectors during a GSVD
+// factorization.
+type GSVDKind int
+
+const (
+	// GSVDU specifies that the U singular vectors should be computed during
+	// the decomposition.
+	GSVDU GSVDKind = 1 << iota
+	// GSVDV specifies that the V singular vectors should be computed during
+	// the decomposition.
+	GSVDV
+	// GSVDQ specifies that the Q singular vectors should be computed during
+	// the decomposition.
+	GSVDQ
+
+	// GSVDNone specifies that no singular vector should be computed during
+	// the decomposition.
+	GSVDNone
+)
diff --git a/vendor/gonum.org/v1/gonum/mat/dense.go b/vendor/gonum.org/v1/gonum/mat/dense.go
new file mode 100644
index 00000000..1fab99c2
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/dense.go
@@ -0,0 +1,534 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+var (
+	dense *Dense
+
+	_ Matrix  = dense
+	_ Mutable = dense
+
+	_ Cloner       = dense
+	_ RowViewer    = dense
+	_ ColViewer    = dense
+	_ RawRowViewer = dense
+	_ Grower       = dense
+
+	_ RawMatrixSetter = dense
+	_ RawMatrixer     = dense
+
+	_ Reseter = dense
+)
+
+// Dense is a dense matrix representation.
+type Dense struct {
+	mat blas64.General
+
+	capRows, capCols int
+}
+
+// NewDense creates a new Dense matrix with r rows and c columns. If data == nil,
+// a new slice is allocated for the backing slice. If len(data) == r*c, data is
+// used as the backing slice, and changes to the elements of the returned Dense
+// will be reflected in data. If neither of these is true, NewDense will panic.
+//
+// The data must be arranged in row-major order, i.e. the (i*c + j)-th
+// element in the data slice is the {i, j}-th element in the matrix.
+func NewDense(r, c int, data []float64) *Dense {
+	if data != nil && r*c != len(data) {
+		panic(ErrShape)
+	}
+	if data == nil {
+		data = make([]float64, r*c)
+	}
+	return &Dense{
+		mat: blas64.General{
+			Rows:   r,
+			Cols:   c,
+			Stride: c,
+			Data:   data,
+		},
+		capRows: r,
+		capCols: c,
+	}
+}
+
+// reuseAs resizes an empty matrix to a r×c matrix,
+// or checks that a non-empty matrix is r×c.
+//
+// reuseAs must be kept in sync with reuseAsZeroed.
+func (m *Dense) reuseAs(r, c int) {
+	if m.mat.Rows > m.capRows || m.mat.Cols > m.capCols {
+		// Panic as a string, not a mat.Error.
+		panic("mat: caps not correctly set")
+	}
+	if m.IsZero() {
+		m.mat = blas64.General{
+			Rows:   r,
+			Cols:   c,
+			Stride: c,
+			Data:   use(m.mat.Data, r*c),
+		}
+		m.capRows = r
+		m.capCols = c
+		return
+	}
+	if r != m.mat.Rows || c != m.mat.Cols {
+		panic(ErrShape)
+	}
+}
+
+// reuseAsZeroed resizes an empty matrix to a r×c matrix,
+// or checks that a non-empty matrix is r×c. It zeroes
+// all the elements of the matrix.
+//
+// reuseAsZeroed must be kept in sync with reuseAs.
+func (m *Dense) reuseAsZeroed(r, c int) {
+	if m.mat.Rows > m.capRows || m.mat.Cols > m.capCols {
+		// Panic as a string, not a mat.Error.
+		panic("mat: caps not correctly set")
+	}
+	if m.IsZero() {
+		m.mat = blas64.General{
+			Rows:   r,
+			Cols:   c,
+			Stride: c,
+			Data:   useZeroed(m.mat.Data, r*c),
+		}
+		m.capRows = r
+		m.capCols = c
+		return
+	}
+	if r != m.mat.Rows || c != m.mat.Cols {
+		panic(ErrShape)
+	}
+	for i := 0; i < r; i++ {
+		zero(m.mat.Data[i*m.mat.Stride : i*m.mat.Stride+c])
+	}
+}
+
+// untranspose untransposes a matrix if applicable. If a is an Untransposer, then
+// untranspose returns the underlying matrix and true. If it is not, then it returns
+// the input matrix and false.
+func untranspose(a Matrix) (Matrix, bool) {
+	if ut, ok := a.(Untransposer); ok {
+		return ut.Untranspose(), true
+	}
+	return a, false
+}
+
+// isolatedWorkspace returns a new dense matrix w with the size of a and
+// returns a callback to defer which performs cleanup at the return of the call.
+// This should be used when a method receiver is the same pointer as an input argument.
+func (m *Dense) isolatedWorkspace(a Matrix) (w *Dense, restore func()) {
+	r, c := a.Dims()
+	w = getWorkspace(r, c, false)
+	return w, func() {
+		m.Copy(w)
+		putWorkspace(w)
+	}
+}
+
+// Reset zeros the dimensions of the matrix so that it can be reused as the
+// receiver of a dimensionally restricted operation.
+//
+// See the Reseter interface for more information.
+func (m *Dense) Reset() {
+	// Row, Cols and Stride must be zeroed in unison.
+	m.mat.Rows, m.mat.Cols, m.mat.Stride = 0, 0, 0
+	m.capRows, m.capCols = 0, 0
+	m.mat.Data = m.mat.Data[:0]
+}
+
+// IsZero returns whether the receiver is zero-sized. Zero-sized matrices can be the
+// receiver for size-restricted operations. Dense matrices can be zeroed using Reset.
+func (m *Dense) IsZero() bool {
+	// It must be the case that m.Dims() returns
+	// zeros in this case. See comment in Reset().
+	return m.mat.Stride == 0
+}
+
+// asTriDense returns a TriDense with the given size and side. The backing data
+// of the TriDense is the same as the receiver.
+func (m *Dense) asTriDense(n int, diag blas.Diag, uplo blas.Uplo) *TriDense {
+	return &TriDense{
+		mat: blas64.Triangular{
+			N:      n,
+			Stride: m.mat.Stride,
+			Data:   m.mat.Data,
+			Uplo:   uplo,
+			Diag:   diag,
+		},
+		cap: n,
+	}
+}
+
+// DenseCopyOf returns a newly allocated copy of the elements of a.
+func DenseCopyOf(a Matrix) *Dense {
+	d := &Dense{}
+	d.Clone(a)
+	return d
+}
+
+// SetRawMatrix sets the underlying blas64.General used by the receiver.
+// Changes to elements in the receiver following the call will be reflected
+// in b.
+func (m *Dense) SetRawMatrix(b blas64.General) {
+	m.capRows, m.capCols = b.Rows, b.Cols
+	m.mat = b
+}
+
+// RawMatrix returns the underlying blas64.General used by the receiver.
+// Changes to elements in the receiver following the call will be reflected
+// in returned blas64.General.
+func (m *Dense) RawMatrix() blas64.General { return m.mat }
+
+// Dims returns the number of rows and columns in the matrix.
+func (m *Dense) Dims() (r, c int) { return m.mat.Rows, m.mat.Cols }
+
+// Caps returns the number of rows and columns in the backing matrix.
+func (m *Dense) Caps() (r, c int) { return m.capRows, m.capCols }
+
+// T performs an implicit transpose by returning the receiver inside a Transpose.
+func (m *Dense) T() Matrix {
+	return Transpose{m}
+}
+
+// ColView returns a VecDense reflecting the column j, backed by the matrix data.
+//
+// See ColViewer for more information.
+func (m *Dense) ColView(j int) *VecDense {
+	if j >= m.mat.Cols || j < 0 {
+		panic(ErrColAccess)
+	}
+	return &VecDense{
+		mat: blas64.Vector{
+			Inc:  m.mat.Stride,
+			Data: m.mat.Data[j : (m.mat.Rows-1)*m.mat.Stride+j+1],
+		},
+		n: m.mat.Rows,
+	}
+}
+
+// SetCol sets the values in the specified column of the matrix to the values
+// in src. len(src) must equal the number of rows in the receiver.
+func (m *Dense) SetCol(j int, src []float64) {
+	if j >= m.mat.Cols || j < 0 {
+		panic(ErrColAccess)
+	}
+	if len(src) != m.mat.Rows {
+		panic(ErrColLength)
+	}
+
+	blas64.Copy(m.mat.Rows,
+		blas64.Vector{Inc: 1, Data: src},
+		blas64.Vector{Inc: m.mat.Stride, Data: m.mat.Data[j:]},
+	)
+}
+
+// SetRow sets the values in the specified rows of the matrix to the values
+// in src. len(src) must equal the number of columns in the receiver.
+func (m *Dense) SetRow(i int, src []float64) {
+	if i >= m.mat.Rows || i < 0 {
+		panic(ErrRowAccess)
+	}
+	if len(src) != m.mat.Cols {
+		panic(ErrRowLength)
+	}
+
+	copy(m.rawRowView(i), src)
+}
+
+// RowView returns row i of the matrix data represented as a column vector,
+// backed by the matrix data.
+//
+// See RowViewer for more information.
+func (m *Dense) RowView(i int) *VecDense {
+	if i >= m.mat.Rows || i < 0 {
+		panic(ErrRowAccess)
+	}
+	return &VecDense{
+		mat: blas64.Vector{
+			Inc:  1,
+			Data: m.rawRowView(i),
+		},
+		n: m.mat.Cols,
+	}
+}
+
+// RawRowView returns a slice backed by the same array as backing the
+// receiver.
+func (m *Dense) RawRowView(i int) []float64 {
+	if i >= m.mat.Rows || i < 0 {
+		panic(ErrRowAccess)
+	}
+	return m.rawRowView(i)
+}
+
+func (m *Dense) rawRowView(i int) []float64 {
+	return m.mat.Data[i*m.mat.Stride : i*m.mat.Stride+m.mat.Cols]
+}
+
+// Slice returns a new Matrix that shares backing data with the receiver.
+// The returned matrix starts at {i,j} of the receiver and extends k-i rows
+// and l-j columns. The final row in the resulting matrix is k-1 and the
+// final column is l-1.
+// Slice panics with ErrIndexOutOfRange if the slice is outside the capacity
+// of the receiver.
+func (m *Dense) Slice(i, k, j, l int) Matrix {
+	mr, mc := m.Caps()
+	if i < 0 || mr <= i || j < 0 || mc <= j || k <= i || mr < k || l <= j || mc < l {
+		panic(ErrIndexOutOfRange)
+	}
+	t := *m
+	t.mat.Data = t.mat.Data[i*t.mat.Stride+j : (k-1)*t.mat.Stride+l]
+	t.mat.Rows = k - i
+	t.mat.Cols = l - j
+	t.capRows -= i
+	t.capCols -= j
+	return &t
+}
+
+// Grow returns the receiver expanded by r rows and c columns. If the dimensions
+// of the expanded matrix are outside the capacities of the receiver a new
+// allocation is made, otherwise not. Note the receiver itself is not modified
+// during the call to Grow.
+func (m *Dense) Grow(r, c int) Matrix {
+	if r < 0 || c < 0 {
+		panic(ErrIndexOutOfRange)
+	}
+	if r == 0 && c == 0 {
+		return m
+	}
+
+	r += m.mat.Rows
+	c += m.mat.Cols
+
+	var t Dense
+	switch {
+	case m.mat.Rows == 0 || m.mat.Cols == 0:
+		t.mat = blas64.General{
+			Rows:   r,
+			Cols:   c,
+			Stride: c,
+			// We zero because we don't know how the matrix will be used.
+			// In other places, the mat is immediately filled with a result;
+			// this is not the case here.
+			Data: useZeroed(m.mat.Data, r*c),
+		}
+	case r > m.capRows || c > m.capCols:
+		cr := max(r, m.capRows)
+		cc := max(c, m.capCols)
+		t.mat = blas64.General{
+			Rows:   r,
+			Cols:   c,
+			Stride: cc,
+			Data:   make([]float64, cr*cc),
+		}
+		t.capRows = cr
+		t.capCols = cc
+		// Copy the complete matrix over to the new matrix.
+		// Including elements not currently visible. Use a temporary structure
+		// to avoid modifying the receiver.
+		var tmp Dense
+		tmp.mat = blas64.General{
+			Rows:   m.mat.Rows,
+			Cols:   m.mat.Cols,
+			Stride: m.mat.Stride,
+			Data:   m.mat.Data,
+		}
+		tmp.capRows = m.capRows
+		tmp.capCols = m.capCols
+		t.Copy(&tmp)
+		return &t
+	default:
+		t.mat = blas64.General{
+			Data:   m.mat.Data[:(r-1)*m.mat.Stride+c],
+			Rows:   r,
+			Cols:   c,
+			Stride: m.mat.Stride,
+		}
+	}
+	t.capRows = r
+	t.capCols = c
+	return &t
+}
+
+// Clone makes a copy of a into the receiver, overwriting the previous value of
+// the receiver. The clone operation does not make any restriction on shape and
+// will not cause shadowing.
+//
+// See the Cloner interface for more information.
+func (m *Dense) Clone(a Matrix) {
+	r, c := a.Dims()
+	mat := blas64.General{
+		Rows:   r,
+		Cols:   c,
+		Stride: c,
+	}
+	m.capRows, m.capCols = r, c
+
+	aU, trans := untranspose(a)
+	switch aU := aU.(type) {
+	case RawMatrixer:
+		amat := aU.RawMatrix()
+		mat.Data = make([]float64, r*c)
+		if trans {
+			for i := 0; i < r; i++ {
+				blas64.Copy(c,
+					blas64.Vector{Inc: amat.Stride, Data: amat.Data[i : i+(c-1)*amat.Stride+1]},
+					blas64.Vector{Inc: 1, Data: mat.Data[i*c : (i+1)*c]})
+			}
+		} else {
+			for i := 0; i < r; i++ {
+				copy(mat.Data[i*c:(i+1)*c], amat.Data[i*amat.Stride:i*amat.Stride+c])
+			}
+		}
+	case *VecDense:
+		amat := aU.mat
+		mat.Data = make([]float64, aU.n)
+		blas64.Copy(aU.n,
+			blas64.Vector{Inc: amat.Inc, Data: amat.Data},
+			blas64.Vector{Inc: 1, Data: mat.Data})
+	default:
+		mat.Data = make([]float64, r*c)
+		w := *m
+		w.mat = mat
+		for i := 0; i < r; i++ {
+			for j := 0; j < c; j++ {
+				w.set(i, j, a.At(i, j))
+			}
+		}
+		*m = w
+		return
+	}
+	m.mat = mat
+}
+
+// Copy makes a copy of elements of a into the receiver. It is similar to the
+// built-in copy; it copies as much as the overlap between the two matrices and
+// returns the number of rows and columns it copied. If a aliases the receiver
+// and is a transposed Dense or VecDense, with a non-unitary increment, Copy will
+// panic.
+//
+// See the Copier interface for more information.
+func (m *Dense) Copy(a Matrix) (r, c int) {
+	r, c = a.Dims()
+	if a == m {
+		return r, c
+	}
+	r = min(r, m.mat.Rows)
+	c = min(c, m.mat.Cols)
+	if r == 0 || c == 0 {
+		return 0, 0
+	}
+
+	aU, trans := untranspose(a)
+	switch aU := aU.(type) {
+	case RawMatrixer:
+		amat := aU.RawMatrix()
+		if trans {
+			if amat.Stride != 1 {
+				m.checkOverlap(amat)
+			}
+			for i := 0; i < r; i++ {
+				blas64.Copy(c,
+					blas64.Vector{Inc: amat.Stride, Data: amat.Data[i : i+(c-1)*amat.Stride+1]},
+					blas64.Vector{Inc: 1, Data: m.mat.Data[i*m.mat.Stride : i*m.mat.Stride+c]})
+			}
+		} else {
+			switch o := offset(m.mat.Data, amat.Data); {
+			case o < 0:
+				for i := r - 1; i >= 0; i-- {
+					copy(m.mat.Data[i*m.mat.Stride:i*m.mat.Stride+c], amat.Data[i*amat.Stride:i*amat.Stride+c])
+				}
+			case o > 0:
+				for i := 0; i < r; i++ {
+					copy(m.mat.Data[i*m.mat.Stride:i*m.mat.Stride+c], amat.Data[i*amat.Stride:i*amat.Stride+c])
+				}
+			default:
+				// Nothing to do.
+			}
+		}
+	case *VecDense:
+		var n, stride int
+		amat := aU.mat
+		if trans {
+			if amat.Inc != 1 {
+				m.checkOverlap(aU.asGeneral())
+			}
+			n = c
+			stride = 1
+		} else {
+			n = r
+			stride = m.mat.Stride
+		}
+		if amat.Inc == 1 && stride == 1 {
+			copy(m.mat.Data, amat.Data[:n])
+			break
+		}
+		switch o := offset(m.mat.Data, amat.Data); {
+		case o < 0:
+			blas64.Copy(n,
+				blas64.Vector{Inc: -amat.Inc, Data: amat.Data},
+				blas64.Vector{Inc: -stride, Data: m.mat.Data})
+		case o > 0:
+			blas64.Copy(n,
+				blas64.Vector{Inc: amat.Inc, Data: amat.Data},
+				blas64.Vector{Inc: stride, Data: m.mat.Data})
+		default:
+			// Nothing to do.
+		}
+	default:
+		for i := 0; i < r; i++ {
+			for j := 0; j < c; j++ {
+				m.set(i, j, a.At(i, j))
+			}
+		}
+	}
+
+	return r, c
+}
+
+// Stack appends the rows of b onto the rows of a, placing the result into the
+// receiver with b placed in the greater indexed rows. Stack will panic if the
+// two input matrices do not have the same number of columns or the constructed
+// stacked matrix is not the same shape as the receiver.
+func (m *Dense) Stack(a, b Matrix) {
+	ar, ac := a.Dims()
+	br, bc := b.Dims()
+	if ac != bc || m == a || m == b {
+		panic(ErrShape)
+	}
+
+	m.reuseAs(ar+br, ac)
+
+	m.Copy(a)
+	w := m.Slice(ar, ar+br, 0, bc).(*Dense)
+	w.Copy(b)
+}
+
+// Augment creates the augmented matrix of a and b, where b is placed in the
+// greater indexed columns. Augment will panic if the two input matrices do
+// not have the same number of rows or the constructed augmented matrix is
+// not the same shape as the receiver.
+func (m *Dense) Augment(a, b Matrix) {
+	ar, ac := a.Dims()
+	br, bc := b.Dims()
+	if ar != br || m == a || m == b {
+		panic(ErrShape)
+	}
+
+	m.reuseAs(ar, ac+bc)
+
+	m.Copy(a)
+	w := m.Slice(0, br, ac, ac+bc).(*Dense)
+	w.Copy(b)
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/dense_arithmetic.go b/vendor/gonum.org/v1/gonum/mat/dense_arithmetic.go
new file mode 100644
index 00000000..db18e735
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/dense_arithmetic.go
@@ -0,0 +1,719 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack/lapack64"
+)
+
+// Add adds a and b element-wise, placing the result in the receiver. Add
+// will panic if the two matrices do not have the same shape.
+func (m *Dense) Add(a, b Matrix) {
+	ar, ac := a.Dims()
+	br, bc := b.Dims()
+	if ar != br || ac != bc {
+		panic(ErrShape)
+	}
+
+	aU, _ := untranspose(a)
+	bU, _ := untranspose(b)
+	m.reuseAs(ar, ac)
+
+	if arm, ok := a.(RawMatrixer); ok {
+		if brm, ok := b.(RawMatrixer); ok {
+			amat, bmat := arm.RawMatrix(), brm.RawMatrix()
+			if m != aU {
+				m.checkOverlap(amat)
+			}
+			if m != bU {
+				m.checkOverlap(bmat)
+			}
+			for ja, jb, jm := 0, 0, 0; ja < ar*amat.Stride; ja, jb, jm = ja+amat.Stride, jb+bmat.Stride, jm+m.mat.Stride {
+				for i, v := range amat.Data[ja : ja+ac] {
+					m.mat.Data[i+jm] = v + bmat.Data[i+jb]
+				}
+			}
+			return
+		}
+	}
+
+	var restore func()
+	if m == aU {
+		m, restore = m.isolatedWorkspace(aU)
+		defer restore()
+	} else if m == bU {
+		m, restore = m.isolatedWorkspace(bU)
+		defer restore()
+	}
+
+	for r := 0; r < ar; r++ {
+		for c := 0; c < ac; c++ {
+			m.set(r, c, a.At(r, c)+b.At(r, c))
+		}
+	}
+}
+
+// Sub subtracts the matrix b from a, placing the result in the receiver. Sub
+// will panic if the two matrices do not have the same shape.
+func (m *Dense) Sub(a, b Matrix) {
+	ar, ac := a.Dims()
+	br, bc := b.Dims()
+	if ar != br || ac != bc {
+		panic(ErrShape)
+	}
+
+	aU, _ := untranspose(a)
+	bU, _ := untranspose(b)
+	m.reuseAs(ar, ac)
+
+	if arm, ok := a.(RawMatrixer); ok {
+		if brm, ok := b.(RawMatrixer); ok {
+			amat, bmat := arm.RawMatrix(), brm.RawMatrix()
+			if m != aU {
+				m.checkOverlap(amat)
+			}
+			if m != bU {
+				m.checkOverlap(bmat)
+			}
+			for ja, jb, jm := 0, 0, 0; ja < ar*amat.Stride; ja, jb, jm = ja+amat.Stride, jb+bmat.Stride, jm+m.mat.Stride {
+				for i, v := range amat.Data[ja : ja+ac] {
+					m.mat.Data[i+jm] = v - bmat.Data[i+jb]
+				}
+			}
+			return
+		}
+	}
+
+	var restore func()
+	if m == aU {
+		m, restore = m.isolatedWorkspace(aU)
+		defer restore()
+	} else if m == bU {
+		m, restore = m.isolatedWorkspace(bU)
+		defer restore()
+	}
+
+	for r := 0; r < ar; r++ {
+		for c := 0; c < ac; c++ {
+			m.set(r, c, a.At(r, c)-b.At(r, c))
+		}
+	}
+}
+
+// MulElem performs element-wise multiplication of a and b, placing the result
+// in the receiver. MulElem will panic if the two matrices do not have the same
+// shape.
+func (m *Dense) MulElem(a, b Matrix) {
+	ar, ac := a.Dims()
+	br, bc := b.Dims()
+	if ar != br || ac != bc {
+		panic(ErrShape)
+	}
+
+	aU, _ := untranspose(a)
+	bU, _ := untranspose(b)
+	m.reuseAs(ar, ac)
+
+	if arm, ok := a.(RawMatrixer); ok {
+		if brm, ok := b.(RawMatrixer); ok {
+			amat, bmat := arm.RawMatrix(), brm.RawMatrix()
+			if m != aU {
+				m.checkOverlap(amat)
+			}
+			if m != bU {
+				m.checkOverlap(bmat)
+			}
+			for ja, jb, jm := 0, 0, 0; ja < ar*amat.Stride; ja, jb, jm = ja+amat.Stride, jb+bmat.Stride, jm+m.mat.Stride {
+				for i, v := range amat.Data[ja : ja+ac] {
+					m.mat.Data[i+jm] = v * bmat.Data[i+jb]
+				}
+			}
+			return
+		}
+	}
+
+	var restore func()
+	if m == aU {
+		m, restore = m.isolatedWorkspace(aU)
+		defer restore()
+	} else if m == bU {
+		m, restore = m.isolatedWorkspace(bU)
+		defer restore()
+	}
+
+	for r := 0; r < ar; r++ {
+		for c := 0; c < ac; c++ {
+			m.set(r, c, a.At(r, c)*b.At(r, c))
+		}
+	}
+}
+
+// DivElem performs element-wise division of a by b, placing the result
+// in the receiver. DivElem will panic if the two matrices do not have the same
+// shape.
+func (m *Dense) DivElem(a, b Matrix) {
+	ar, ac := a.Dims()
+	br, bc := b.Dims()
+	if ar != br || ac != bc {
+		panic(ErrShape)
+	}
+
+	aU, _ := untranspose(a)
+	bU, _ := untranspose(b)
+	m.reuseAs(ar, ac)
+
+	if arm, ok := a.(RawMatrixer); ok {
+		if brm, ok := b.(RawMatrixer); ok {
+			amat, bmat := arm.RawMatrix(), brm.RawMatrix()
+			if m != aU {
+				m.checkOverlap(amat)
+			}
+			if m != bU {
+				m.checkOverlap(bmat)
+			}
+			for ja, jb, jm := 0, 0, 0; ja < ar*amat.Stride; ja, jb, jm = ja+amat.Stride, jb+bmat.Stride, jm+m.mat.Stride {
+				for i, v := range amat.Data[ja : ja+ac] {
+					m.mat.Data[i+jm] = v / bmat.Data[i+jb]
+				}
+			}
+			return
+		}
+	}
+
+	var restore func()
+	if m == aU {
+		m, restore = m.isolatedWorkspace(aU)
+		defer restore()
+	} else if m == bU {
+		m, restore = m.isolatedWorkspace(bU)
+		defer restore()
+	}
+
+	for r := 0; r < ar; r++ {
+		for c := 0; c < ac; c++ {
+			m.set(r, c, a.At(r, c)/b.At(r, c))
+		}
+	}
+}
+
+// Inverse computes the inverse of the matrix a, storing the result into the
+// receiver. If a is ill-conditioned, a Condition error will be returned.
+// Note that matrix inversion is numerically unstable, and should generally
+// be avoided where possible, for example by using the Solve routines.
+func (m *Dense) Inverse(a Matrix) error {
+	// TODO(btracey): Special case for RawTriangular, etc.
+	r, c := a.Dims()
+	if r != c {
+		panic(ErrSquare)
+	}
+	m.reuseAs(a.Dims())
+	aU, aTrans := untranspose(a)
+	switch rm := aU.(type) {
+	case RawMatrixer:
+		if m != aU || aTrans {
+			if m == aU || m.checkOverlap(rm.RawMatrix()) {
+				tmp := getWorkspace(r, c, false)
+				tmp.Copy(a)
+				m.Copy(tmp)
+				putWorkspace(tmp)
+				break
+			}
+			m.Copy(a)
+		}
+	default:
+		m.Copy(a)
+	}
+	ipiv := getInts(r, false)
+	defer putInts(ipiv)
+	ok := lapack64.Getrf(m.mat, ipiv)
+	if !ok {
+		return Condition(math.Inf(1))
+	}
+	work := getFloats(4*r, false) // must be at least 4*r for cond.
+	lapack64.Getri(m.mat, ipiv, work, -1)
+	if int(work[0]) > 4*r {
+		l := int(work[0])
+		putFloats(work)
+		work = getFloats(l, false)
+	} else {
+		work = work[:4*r]
+	}
+	defer putFloats(work)
+	lapack64.Getri(m.mat, ipiv, work, len(work))
+	norm := lapack64.Lange(CondNorm, m.mat, work)
+	rcond := lapack64.Gecon(CondNorm, m.mat, norm, work, ipiv) // reuse ipiv
+	if rcond == 0 {
+		return Condition(math.Inf(1))
+	}
+	cond := 1 / rcond
+	if cond > ConditionTolerance {
+		return Condition(cond)
+	}
+	return nil
+}
+
+// Mul takes the matrix product of a and b, placing the result in the receiver.
+// If the number of columns in a does not equal the number of rows in b, Mul will panic.
+func (m *Dense) Mul(a, b Matrix) {
+	ar, ac := a.Dims()
+	br, bc := b.Dims()
+
+	if ac != br {
+		panic(ErrShape)
+	}
+
+	aU, aTrans := untranspose(a)
+	bU, bTrans := untranspose(b)
+	m.reuseAs(ar, bc)
+	var restore func()
+	if m == aU {
+		m, restore = m.isolatedWorkspace(aU)
+		defer restore()
+	} else if m == bU {
+		m, restore = m.isolatedWorkspace(bU)
+		defer restore()
+	}
+	aT := blas.NoTrans
+	if aTrans {
+		aT = blas.Trans
+	}
+	bT := blas.NoTrans
+	if bTrans {
+		bT = blas.Trans
+	}
+
+	// Some of the cases do not have a transpose option, so create
+	// temporary memory.
+	// C = A^T * B = (B^T * A)^T
+	// C^T = B^T * A.
+	if aUrm, ok := aU.(RawMatrixer); ok {
+		amat := aUrm.RawMatrix()
+		if restore == nil {
+			m.checkOverlap(amat)
+		}
+		if bUrm, ok := bU.(RawMatrixer); ok {
+			bmat := bUrm.RawMatrix()
+			if restore == nil {
+				m.checkOverlap(bmat)
+			}
+			blas64.Gemm(aT, bT, 1, amat, bmat, 0, m.mat)
+			return
+		}
+		if bU, ok := bU.(RawSymmetricer); ok {
+			bmat := bU.RawSymmetric()
+			if aTrans {
+				c := getWorkspace(ac, ar, false)
+				blas64.Symm(blas.Left, 1, bmat, amat, 0, c.mat)
+				strictCopy(m, c.T())
+				putWorkspace(c)
+				return
+			}
+			blas64.Symm(blas.Right, 1, bmat, amat, 0, m.mat)
+			return
+		}
+		if bU, ok := bU.(RawTriangular); ok {
+			// Trmm updates in place, so copy aU first.
+			bmat := bU.RawTriangular()
+			if aTrans {
+				c := getWorkspace(ac, ar, false)
+				var tmp Dense
+				tmp.SetRawMatrix(amat)
+				c.Copy(&tmp)
+				bT := blas.Trans
+				if bTrans {
+					bT = blas.NoTrans
+				}
+				blas64.Trmm(blas.Left, bT, 1, bmat, c.mat)
+				strictCopy(m, c.T())
+				putWorkspace(c)
+				return
+			}
+			m.Copy(a)
+			blas64.Trmm(blas.Right, bT, 1, bmat, m.mat)
+			return
+		}
+		if bU, ok := bU.(*VecDense); ok {
+			m.checkOverlap(bU.asGeneral())
+			bvec := bU.RawVector()
+			if bTrans {
+				// {ar,1} x {1,bc}, which is not a vector.
+				// Instead, construct B as a General.
+				bmat := blas64.General{
+					Rows:   bc,
+					Cols:   1,
+					Stride: bvec.Inc,
+					Data:   bvec.Data,
+				}
+				blas64.Gemm(aT, bT, 1, amat, bmat, 0, m.mat)
+				return
+			}
+			cvec := blas64.Vector{
+				Inc:  m.mat.Stride,
+				Data: m.mat.Data,
+			}
+			blas64.Gemv(aT, 1, amat, bvec, 0, cvec)
+			return
+		}
+	}
+	if bUrm, ok := bU.(RawMatrixer); ok {
+		bmat := bUrm.RawMatrix()
+		if restore == nil {
+			m.checkOverlap(bmat)
+		}
+		if aU, ok := aU.(RawSymmetricer); ok {
+			amat := aU.RawSymmetric()
+			if bTrans {
+				c := getWorkspace(bc, br, false)
+				blas64.Symm(blas.Right, 1, amat, bmat, 0, c.mat)
+				strictCopy(m, c.T())
+				putWorkspace(c)
+				return
+			}
+			blas64.Symm(blas.Left, 1, amat, bmat, 0, m.mat)
+			return
+		}
+		if aU, ok := aU.(RawTriangular); ok {
+			// Trmm updates in place, so copy bU first.
+			amat := aU.RawTriangular()
+			if bTrans {
+				c := getWorkspace(bc, br, false)
+				var tmp Dense
+				tmp.SetRawMatrix(bmat)
+				c.Copy(&tmp)
+				aT := blas.Trans
+				if aTrans {
+					aT = blas.NoTrans
+				}
+				blas64.Trmm(blas.Right, aT, 1, amat, c.mat)
+				strictCopy(m, c.T())
+				putWorkspace(c)
+				return
+			}
+			m.Copy(b)
+			blas64.Trmm(blas.Left, aT, 1, amat, m.mat)
+			return
+		}
+		if aU, ok := aU.(*VecDense); ok {
+			m.checkOverlap(aU.asGeneral())
+			avec := aU.RawVector()
+			if aTrans {
+				// {1,ac} x {ac, bc}
+				// Transpose B so that the vector is on the right.
+				cvec := blas64.Vector{
+					Inc:  1,
+					Data: m.mat.Data,
+				}
+				bT := blas.Trans
+				if bTrans {
+					bT = blas.NoTrans
+				}
+				blas64.Gemv(bT, 1, bmat, avec, 0, cvec)
+				return
+			}
+			// {ar,1} x {1,bc} which is not a vector result.
+			// Instead, construct A as a General.
+			amat := blas64.General{
+				Rows:   ar,
+				Cols:   1,
+				Stride: avec.Inc,
+				Data:   avec.Data,
+			}
+			blas64.Gemm(aT, bT, 1, amat, bmat, 0, m.mat)
+			return
+		}
+	}
+
+	row := getFloats(ac, false)
+	defer putFloats(row)
+	for r := 0; r < ar; r++ {
+		for i := range row {
+			row[i] = a.At(r, i)
+		}
+		for c := 0; c < bc; c++ {
+			var v float64
+			for i, e := range row {
+				v += e * b.At(i, c)
+			}
+			m.mat.Data[r*m.mat.Stride+c] = v
+		}
+	}
+}
+
+// strictCopy copies a into m panicking if the shape of a and m differ.
+func strictCopy(m *Dense, a Matrix) {
+	r, c := m.Copy(a)
+	if r != m.mat.Rows || c != m.mat.Cols {
+		// Panic with a string since this
+		// is not a user-facing panic.
+		panic(ErrShape.Error())
+	}
+}
+
+// Exp calculates the exponential of the matrix a, e^a, placing the result
+// in the receiver. Exp will panic with matrix.ErrShape if a is not square.
+//
+// Exp uses the scaling and squaring method described in section 3 of
+// http://www.cs.cornell.edu/cv/researchpdf/19ways+.pdf.
+func (m *Dense) Exp(a Matrix) {
+	r, c := a.Dims()
+	if r != c {
+		panic(ErrShape)
+	}
+
+	var w *Dense
+	if m.IsZero() {
+		m.reuseAsZeroed(r, r)
+		w = m
+	} else {
+		w = getWorkspace(r, r, true)
+	}
+	for i := 0; i < r*r; i += r + 1 {
+		w.mat.Data[i] = 1
+	}
+
+	const (
+		terms   = 10
+		scaling = 4
+	)
+
+	small := getWorkspace(r, r, false)
+	small.Scale(math.Pow(2, -scaling), a)
+	power := getWorkspace(r, r, false)
+	power.Copy(small)
+
+	var (
+		tmp   = getWorkspace(r, r, false)
+		factI = 1.
+	)
+	for i := 1.; i < terms; i++ {
+		factI *= i
+
+		// This is OK to do because power and tmp are
+		// new Dense values so all rows are contiguous.
+		// TODO(kortschak) Make this explicit in the NewDense doc comment.
+		for j, v := range power.mat.Data {
+			tmp.mat.Data[j] = v / factI
+		}
+
+		w.Add(w, tmp)
+		if i < terms-1 {
+			tmp.Mul(power, small)
+			tmp, power = power, tmp
+		}
+	}
+	putWorkspace(small)
+	putWorkspace(power)
+	for i := 0; i < scaling; i++ {
+		tmp.Mul(w, w)
+		tmp, w = w, tmp
+	}
+	putWorkspace(tmp)
+
+	if w != m {
+		m.Copy(w)
+		putWorkspace(w)
+	}
+}
+
+// Pow calculates the integral power of the matrix a to n, placing the result
+// in the receiver. Pow will panic if n is negative or if a is not square.
+func (m *Dense) Pow(a Matrix, n int) {
+	if n < 0 {
+		panic("matrix: illegal power")
+	}
+	r, c := a.Dims()
+	if r != c {
+		panic(ErrShape)
+	}
+
+	m.reuseAs(r, c)
+
+	// Take possible fast paths.
+	switch n {
+	case 0:
+		for i := 0; i < r; i++ {
+			zero(m.mat.Data[i*m.mat.Stride : i*m.mat.Stride+c])
+			m.mat.Data[i*m.mat.Stride+i] = 1
+		}
+		return
+	case 1:
+		m.Copy(a)
+		return
+	case 2:
+		m.Mul(a, a)
+		return
+	}
+
+	// Perform iterative exponentiation by squaring in work space.
+	w := getWorkspace(r, r, false)
+	w.Copy(a)
+	s := getWorkspace(r, r, false)
+	s.Copy(a)
+	x := getWorkspace(r, r, false)
+	for n--; n > 0; n >>= 1 {
+		if n&1 != 0 {
+			x.Mul(w, s)
+			w, x = x, w
+		}
+		if n != 1 {
+			x.Mul(s, s)
+			s, x = x, s
+		}
+	}
+	m.Copy(w)
+	putWorkspace(w)
+	putWorkspace(s)
+	putWorkspace(x)
+}
+
+// Scale multiplies the elements of a by f, placing the result in the receiver.
+//
+// See the Scaler interface for more information.
+func (m *Dense) Scale(f float64, a Matrix) {
+	ar, ac := a.Dims()
+
+	m.reuseAs(ar, ac)
+
+	aU, aTrans := untranspose(a)
+	if rm, ok := aU.(RawMatrixer); ok {
+		amat := rm.RawMatrix()
+		if m == aU || m.checkOverlap(amat) {
+			var restore func()
+			m, restore = m.isolatedWorkspace(a)
+			defer restore()
+		}
+		if !aTrans {
+			for ja, jm := 0, 0; ja < ar*amat.Stride; ja, jm = ja+amat.Stride, jm+m.mat.Stride {
+				for i, v := range amat.Data[ja : ja+ac] {
+					m.mat.Data[i+jm] = v * f
+				}
+			}
+		} else {
+			for ja, jm := 0, 0; ja < ac*amat.Stride; ja, jm = ja+amat.Stride, jm+1 {
+				for i, v := range amat.Data[ja : ja+ar] {
+					m.mat.Data[i*m.mat.Stride+jm] = v * f
+				}
+			}
+		}
+		return
+	}
+
+	for r := 0; r < ar; r++ {
+		for c := 0; c < ac; c++ {
+			m.set(r, c, f*a.At(r, c))
+		}
+	}
+}
+
+// Apply applies the function fn to each of the elements of a, placing the
+// resulting matrix in the receiver. The function fn takes a row/column
+// index and element value and returns some function of that tuple.
+func (m *Dense) Apply(fn func(i, j int, v float64) float64, a Matrix) {
+	ar, ac := a.Dims()
+
+	m.reuseAs(ar, ac)
+
+	aU, aTrans := untranspose(a)
+	if rm, ok := aU.(RawMatrixer); ok {
+		amat := rm.RawMatrix()
+		if m == aU || m.checkOverlap(amat) {
+			var restore func()
+			m, restore = m.isolatedWorkspace(a)
+			defer restore()
+		}
+		if !aTrans {
+			for j, ja, jm := 0, 0, 0; ja < ar*amat.Stride; j, ja, jm = j+1, ja+amat.Stride, jm+m.mat.Stride {
+				for i, v := range amat.Data[ja : ja+ac] {
+					m.mat.Data[i+jm] = fn(j, i, v)
+				}
+			}
+		} else {
+			for j, ja, jm := 0, 0, 0; ja < ac*amat.Stride; j, ja, jm = j+1, ja+amat.Stride, jm+1 {
+				for i, v := range amat.Data[ja : ja+ar] {
+					m.mat.Data[i*m.mat.Stride+jm] = fn(i, j, v)
+				}
+			}
+		}
+		return
+	}
+
+	for r := 0; r < ar; r++ {
+		for c := 0; c < ac; c++ {
+			m.set(r, c, fn(r, c, a.At(r, c)))
+		}
+	}
+}
+
+// RankOne performs a rank-one update to the matrix a and stores the result
+// in the receiver. If a is zero, see Outer.
+//  m = a + alpha * x * y'
+func (m *Dense) RankOne(a Matrix, alpha float64, x, y *VecDense) {
+	ar, ac := a.Dims()
+	if x.Len() != ar {
+		panic(ErrShape)
+	}
+	if y.Len() != ac {
+		panic(ErrShape)
+	}
+
+	m.checkOverlap(x.asGeneral())
+	m.checkOverlap(y.asGeneral())
+
+	var w Dense
+	if m == a {
+		w = *m
+	}
+	w.reuseAs(ar, ac)
+
+	// Copy over to the new memory if necessary
+	if m != a {
+		w.Copy(a)
+	}
+	blas64.Ger(alpha, x.mat, y.mat, w.mat)
+	*m = w
+}
+
+// Outer calculates the outer product of x and y, and stores the result
+// in the receiver.
+//  m = alpha * x * y'
+// In order to update an existing matrix, see RankOne.
+func (m *Dense) Outer(alpha float64, x, y *VecDense) {
+	r := x.Len()
+	c := y.Len()
+
+	// Copied from reuseAs with use replaced by useZeroed
+	// and a final zero of the matrix elements if we pass
+	// the shape checks.
+	// TODO(kortschak): Factor out into reuseZeroedAs if
+	// we find another case that needs it.
+	if m.mat.Rows > m.capRows || m.mat.Cols > m.capCols {
+		// Panic as a string, not a mat.Error.
+		panic("mat: caps not correctly set")
+	}
+	if m.IsZero() {
+		m.mat = blas64.General{
+			Rows:   r,
+			Cols:   c,
+			Stride: c,
+			Data:   useZeroed(m.mat.Data, r*c),
+		}
+		m.capRows = r
+		m.capCols = c
+	} else if r != m.mat.Rows || c != m.mat.Cols {
+		panic(ErrShape)
+	} else {
+		m.checkOverlap(x.asGeneral())
+		m.checkOverlap(y.asGeneral())
+		for i := 0; i < r; i++ {
+			zero(m.mat.Data[i*m.mat.Stride : i*m.mat.Stride+c])
+		}
+	}
+
+	blas64.Ger(alpha, x.mat, y.mat, m.mat)
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/dense_test.go b/vendor/gonum.org/v1/gonum/mat/dense_test.go
new file mode 100644
index 00000000..34b37cc3
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/dense_test.go
@@ -0,0 +1,2005 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"fmt"
+	"math"
+	"math/rand"
+	"reflect"
+	"testing"
+
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+)
+
+func asBasicMatrix(d *Dense) Matrix            { return (*basicMatrix)(d) }
+func asBasicSymmetric(s *SymDense) Matrix      { return (*basicSymmetric)(s) }
+func asBasicTriangular(t *TriDense) Triangular { return (*basicTriangular)(t) }
+
+func TestNewDense(t *testing.T) {
+	for i, test := range []struct {
+		a          []float64
+		rows, cols int
+		min, max   float64
+		fro        float64
+		mat        *Dense
+	}{
+		{
+			[]float64{
+				0, 0, 0,
+				0, 0, 0,
+				0, 0, 0,
+			},
+			3, 3,
+			0, 0,
+			0,
+			&Dense{
+				mat: blas64.General{
+					Rows: 3, Cols: 3,
+					Stride: 3,
+					Data:   []float64{0, 0, 0, 0, 0, 0, 0, 0, 0},
+				},
+				capRows: 3, capCols: 3,
+			},
+		},
+		{
+			[]float64{
+				1, 1, 1,
+				1, 1, 1,
+				1, 1, 1,
+			},
+			3, 3,
+			1, 1,
+			3,
+			&Dense{
+				mat: blas64.General{
+					Rows: 3, Cols: 3,
+					Stride: 3,
+					Data:   []float64{1, 1, 1, 1, 1, 1, 1, 1, 1},
+				},
+				capRows: 3, capCols: 3,
+			},
+		},
+		{
+			[]float64{
+				1, 0, 0,
+				0, 1, 0,
+				0, 0, 1,
+			},
+			3, 3,
+			0, 1,
+			1.7320508075688772,
+			&Dense{
+				mat: blas64.General{
+					Rows: 3, Cols: 3,
+					Stride: 3,
+					Data:   []float64{1, 0, 0, 0, 1, 0, 0, 0, 1},
+				},
+				capRows: 3, capCols: 3,
+			},
+		},
+		{
+			[]float64{
+				-1, 0, 0,
+				0, -1, 0,
+				0, 0, -1,
+			},
+			3, 3,
+			-1, 0,
+			1.7320508075688772,
+			&Dense{
+				mat: blas64.General{
+					Rows: 3, Cols: 3,
+					Stride: 3,
+					Data:   []float64{-1, 0, 0, 0, -1, 0, 0, 0, -1},
+				},
+				capRows: 3, capCols: 3,
+			},
+		},
+		{
+			[]float64{
+				1, 2, 3,
+				4, 5, 6,
+			},
+			2, 3,
+			1, 6,
+			9.539392014169458,
+			&Dense{
+				mat: blas64.General{
+					Rows: 2, Cols: 3,
+					Stride: 3,
+					Data:   []float64{1, 2, 3, 4, 5, 6},
+				},
+				capRows: 2, capCols: 3,
+			},
+		},
+		{
+			[]float64{
+				1, 2,
+				3, 4,
+				5, 6,
+			},
+			3, 2,
+			1, 6,
+			9.539392014169458,
+			&Dense{
+				mat: blas64.General{
+					Rows: 3, Cols: 2,
+					Stride: 2,
+					Data:   []float64{1, 2, 3, 4, 5, 6},
+				},
+				capRows: 3, capCols: 2,
+			},
+		},
+	} {
+		m := NewDense(test.rows, test.cols, test.a)
+		rows, cols := m.Dims()
+		if rows != test.rows {
+			t.Errorf("unexpected number of rows for test %d: got: %d want: %d", i, rows, test.rows)
+		}
+		if cols != test.cols {
+			t.Errorf("unexpected number of cols for test %d: got: %d want: %d", i, cols, test.cols)
+		}
+		if min := Min(m); min != test.min {
+			t.Errorf("unexpected min for test %d: got: %v want: %v", i, min, test.min)
+		}
+		if max := Max(m); max != test.max {
+			t.Errorf("unexpected max for test %d: got: %v want: %v", i, max, test.max)
+		}
+		if fro := Norm(m, 2); math.Abs(Norm(m, 2)-test.fro) > 1e-14 {
+			t.Errorf("unexpected Frobenius norm for test %d: got: %v want: %v", i, fro, test.fro)
+		}
+		if !reflect.DeepEqual(m, test.mat) {
+			t.Errorf("unexpected matrix for test %d", i)
+		}
+		if !Equal(m, test.mat) {
+			t.Errorf("matrix does not equal expected matrix for test %d", i)
+		}
+	}
+}
+
+func TestAtSet(t *testing.T) {
+	for test, af := range [][][]float64{
+		{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}, // even
+		{{1, 2}, {4, 5}, {7, 8}},          // wide
+		{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}, //skinny
+	} {
+		m := NewDense(flatten(af))
+		rows, cols := m.Dims()
+		for i := 0; i < rows; i++ {
+			for j := 0; j < cols; j++ {
+				if m.At(i, j) != af[i][j] {
+					t.Errorf("unexpected value for At(%d, %d) for test %d: got: %v want: %v",
+						i, j, test, m.At(i, j), af[i][j])
+				}
+
+				v := float64(i * j)
+				m.Set(i, j, v)
+				if m.At(i, j) != v {
+					t.Errorf("unexpected value for At(%d, %d) after Set(%[1]d, %d, %v) for test %d: got: %v want: %[3]v",
+						i, j, v, test, m.At(i, j))
+				}
+			}
+		}
+		// Check access out of bounds fails
+		for _, row := range []int{-1, rows, rows + 1} {
+			panicked, message := panics(func() { m.At(row, 0) })
+			if !panicked || message != ErrRowAccess.Error() {
+				t.Errorf("expected panic for invalid row access N=%d r=%d", rows, row)
+			}
+		}
+		for _, col := range []int{-1, cols, cols + 1} {
+			panicked, message := panics(func() { m.At(0, col) })
+			if !panicked || message != ErrColAccess.Error() {
+				t.Errorf("expected panic for invalid column access N=%d c=%d", cols, col)
+			}
+		}
+
+		// Check Set out of bounds
+		for _, row := range []int{-1, rows, rows + 1} {
+			panicked, message := panics(func() { m.Set(row, 0, 1.2) })
+			if !panicked || message != ErrRowAccess.Error() {
+				t.Errorf("expected panic for invalid row access N=%d r=%d", rows, row)
+			}
+		}
+		for _, col := range []int{-1, cols, cols + 1} {
+			panicked, message := panics(func() { m.Set(0, col, 1.2) })
+			if !panicked || message != ErrColAccess.Error() {
+				t.Errorf("expected panic for invalid column access N=%d c=%d", cols, col)
+			}
+		}
+	}
+}
+
+func TestSetRowColumn(t *testing.T) {
+	for _, as := range [][][]float64{
+		{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}},
+		{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}, {10, 11, 12}},
+		{{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}},
+	} {
+		for ri, row := range as {
+			a := NewDense(flatten(as))
+			m := &Dense{}
+			m.Clone(a)
+			a.SetRow(ri, make([]float64, a.mat.Cols))
+			m.Sub(m, a)
+			nt := Norm(m, 2)
+			nr := floats.Norm(row, 2)
+			if math.Abs(nt-nr) > 1e-14 {
+				t.Errorf("Row %d norm mismatch, want: %g, got: %g", ri, nr, nt)
+			}
+		}
+
+		for ci := range as[0] {
+			a := NewDense(flatten(as))
+			m := &Dense{}
+			m.Clone(a)
+			a.SetCol(ci, make([]float64, a.mat.Rows))
+			col := make([]float64, a.mat.Rows)
+			for j := range col {
+				col[j] = float64(ci + 1 + j*a.mat.Cols)
+			}
+			m.Sub(m, a)
+			nt := Norm(m, 2)
+			nc := floats.Norm(col, 2)
+			if math.Abs(nt-nc) > 1e-14 {
+				t.Errorf("Column %d norm mismatch, want: %g, got: %g", ci, nc, nt)
+			}
+		}
+	}
+}
+
+func TestRowColView(t *testing.T) {
+	for _, test := range []struct {
+		mat [][]float64
+	}{
+		{
+			mat: [][]float64{
+				{1, 2, 3, 4, 5},
+				{6, 7, 8, 9, 10},
+				{11, 12, 13, 14, 15},
+				{16, 17, 18, 19, 20},
+				{21, 22, 23, 24, 25},
+			},
+		},
+		{
+			mat: [][]float64{
+				{1, 2, 3, 4},
+				{6, 7, 8, 9},
+				{11, 12, 13, 14},
+				{16, 17, 18, 19},
+				{21, 22, 23, 24},
+			},
+		},
+		{
+			mat: [][]float64{
+				{1, 2, 3, 4, 5},
+				{6, 7, 8, 9, 10},
+				{11, 12, 13, 14, 15},
+				{16, 17, 18, 19, 20},
+			},
+		},
+	} {
+		// This over cautious approach to building a matrix data
+		// slice is to ensure that changes to flatten in the future
+		// do not mask a regression to the issue identified in
+		// gonum/matrix#110.
+		rows, cols, flat := flatten(test.mat)
+		m := NewDense(rows, cols, flat[:len(flat):len(flat)])
+
+		for _, row := range []int{-1, rows, rows + 1} {
+			panicked, message := panics(func() { m.At(row, 0) })
+			if !panicked || message != ErrRowAccess.Error() {
+				t.Errorf("expected panic for invalid row access rows=%d r=%d", rows, row)
+			}
+		}
+		for _, col := range []int{-1, cols, cols + 1} {
+			panicked, message := panics(func() { m.At(0, col) })
+			if !panicked || message != ErrColAccess.Error() {
+				t.Errorf("expected panic for invalid column access cols=%d c=%d", cols, col)
+			}
+		}
+
+		for i := 0; i < rows; i++ {
+			vr := m.RowView(i)
+			if vr.Len() != cols {
+				t.Errorf("unexpected number of columns: got: %d want: %d", vr.Len(), cols)
+			}
+			for j := 0; j < cols; j++ {
+				if got := vr.At(j, 0); got != test.mat[i][j] {
+					t.Errorf("unexpected value for row.At(%d, 0): got: %v want: %v",
+						j, got, test.mat[i][j])
+				}
+			}
+		}
+		for j := 0; j < cols; j++ {
+			vc := m.ColView(j)
+			if vc.Len() != rows {
+				t.Errorf("unexpected number of rows: got: %d want: %d", vc.Len(), rows)
+			}
+			for i := 0; i < rows; i++ {
+				if got := vc.At(i, 0); got != test.mat[i][j] {
+					t.Errorf("unexpected value for col.At(%d, 0): got: %v want: %v",
+						i, got, test.mat[i][j])
+				}
+			}
+		}
+		m = m.Slice(1, rows-1, 1, cols-1).(*Dense)
+		for i := 1; i < rows-1; i++ {
+			vr := m.RowView(i - 1)
+			if vr.Len() != cols-2 {
+				t.Errorf("unexpected number of columns: got: %d want: %d", vr.Len(), cols-2)
+			}
+			for j := 1; j < cols-1; j++ {
+				if got := vr.At(j-1, 0); got != test.mat[i][j] {
+					t.Errorf("unexpected value for row.At(%d, 0): got: %v want: %v",
+						j-1, got, test.mat[i][j])
+				}
+			}
+		}
+		for j := 1; j < cols-1; j++ {
+			vc := m.ColView(j - 1)
+			if vc.Len() != rows-2 {
+				t.Errorf("unexpected number of rows: got: %d want: %d", vc.Len(), rows-2)
+			}
+			for i := 1; i < rows-1; i++ {
+				if got := vc.At(i-1, 0); got != test.mat[i][j] {
+					t.Errorf("unexpected value for col.At(%d, 0): got: %v want: %v",
+						i-1, got, test.mat[i][j])
+				}
+			}
+		}
+	}
+}
+
+func TestGrow(t *testing.T) {
+	m := &Dense{}
+	m = m.Grow(10, 10).(*Dense)
+	rows, cols := m.Dims()
+	capRows, capCols := m.Caps()
+	if rows != 10 {
+		t.Errorf("unexpected value for rows: got: %d want: 10", rows)
+	}
+	if cols != 10 {
+		t.Errorf("unexpected value for cols: got: %d want: 10", cols)
+	}
+	if capRows != 10 {
+		t.Errorf("unexpected value for capRows: got: %d want: 10", capRows)
+	}
+	if capCols != 10 {
+		t.Errorf("unexpected value for capCols: got: %d want: 10", capCols)
+	}
+
+	// Test grow within caps is in-place.
+	m.Set(1, 1, 1)
+	v := m.Slice(1, 5, 1, 5).(*Dense)
+	if v.At(0, 0) != m.At(1, 1) {
+		t.Errorf("unexpected viewed element value: got: %v want: %v", v.At(0, 0), m.At(1, 1))
+	}
+	v = v.Grow(5, 5).(*Dense)
+	if !Equal(v, m.Slice(1, 10, 1, 10)) {
+		t.Error("unexpected view value after grow")
+	}
+
+	// Test grow bigger than caps copies.
+	v = v.Grow(5, 5).(*Dense)
+	if !Equal(v.Slice(0, 9, 0, 9), m.Slice(1, 10, 1, 10)) {
+		t.Error("unexpected mismatched common view value after grow")
+	}
+	v.Set(0, 0, 0)
+	if Equal(v.Slice(0, 9, 0, 9), m.Slice(1, 10, 1, 10)) {
+		t.Error("unexpected matching view value after grow past capacity")
+	}
+
+	// Test grow uses existing data slice when matrix is zero size.
+	v.Reset()
+	p, l := &v.mat.Data[:1][0], cap(v.mat.Data)
+	*p = 1 // This element is at position (-1, -1) relative to v and so should not be visible.
+	v = v.Grow(5, 5).(*Dense)
+	if &v.mat.Data[:1][0] != p {
+		t.Error("grow unexpectedly copied slice within cap limit")
+	}
+	if cap(v.mat.Data) != l {
+		t.Errorf("unexpected change in data slice capacity: got: %d want: %d", cap(v.mat.Data), l)
+	}
+	if v.At(0, 0) != 0 {
+		t.Errorf("unexpected value for At(0, 0): got: %v want: 0", v.At(0, 0))
+	}
+}
+
+func TestAdd(t *testing.T) {
+	for i, test := range []struct {
+		a, b, r [][]float64
+	}{
+		{
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+		},
+		{
+			[][]float64{{1, 1, 1}, {1, 1, 1}, {1, 1, 1}},
+			[][]float64{{1, 1, 1}, {1, 1, 1}, {1, 1, 1}},
+			[][]float64{{2, 2, 2}, {2, 2, 2}, {2, 2, 2}},
+		},
+		{
+			[][]float64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}},
+			[][]float64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}},
+			[][]float64{{2, 0, 0}, {0, 2, 0}, {0, 0, 2}},
+		},
+		{
+			[][]float64{{-1, 0, 0}, {0, -1, 0}, {0, 0, -1}},
+			[][]float64{{-1, 0, 0}, {0, -1, 0}, {0, 0, -1}},
+			[][]float64{{-2, 0, 0}, {0, -2, 0}, {0, 0, -2}},
+		},
+		{
+			[][]float64{{1, 2, 3}, {4, 5, 6}},
+			[][]float64{{1, 2, 3}, {4, 5, 6}},
+			[][]float64{{2, 4, 6}, {8, 10, 12}},
+		},
+	} {
+		a := NewDense(flatten(test.a))
+		b := NewDense(flatten(test.b))
+		r := NewDense(flatten(test.r))
+
+		var temp Dense
+		temp.Add(a, b)
+		if !Equal(&temp, r) {
+			t.Errorf("unexpected result from Add for test %d %v Add %v: got: %v want: %v",
+				i, test.a, test.b, unflatten(temp.mat.Rows, temp.mat.Cols, temp.mat.Data), test.r)
+		}
+
+		zero(temp.mat.Data)
+		temp.Add(a, b)
+		if !Equal(&temp, r) {
+			t.Errorf("unexpected result from Add for test %d %v Add %v: got: %v want: %v",
+				i, test.a, test.b, unflatten(temp.mat.Rows, temp.mat.Cols, temp.mat.Data), test.r)
+		}
+
+		// These probably warrant a better check and failure. They should never happen in the wild though.
+		temp.mat.Data = nil
+		panicked, message := panics(func() { temp.Add(a, b) })
+		if !panicked || message != "runtime error: index out of range" {
+			t.Error("exected runtime panic for nil data slice")
+		}
+
+		a.Add(a, b)
+		if !Equal(a, r) {
+			t.Errorf("unexpected result from Add for test %d %v Add %v: got: %v want: %v",
+				i, test.a, test.b, unflatten(a.mat.Rows, a.mat.Cols, a.mat.Data), test.r)
+		}
+	}
+
+	panicked, message := panics(func() {
+		m := NewDense(10, 10, nil)
+		a := NewDense(5, 5, nil)
+		m.Slice(1, 6, 1, 6).(*Dense).Add(a, m.Slice(2, 7, 2, 7))
+	})
+	if !panicked {
+		t.Error("expected panic for overlapping matrices")
+	}
+	if message != regionOverlap {
+		t.Errorf("unexpected panic message: got: %q want: %q", message, regionOverlap)
+	}
+
+	method := func(receiver, a, b Matrix) {
+		type Adder interface {
+			Add(a, b Matrix)
+		}
+		rd := receiver.(Adder)
+		rd.Add(a, b)
+	}
+	denseComparison := func(receiver, a, b *Dense) {
+		receiver.Add(a, b)
+	}
+	testTwoInput(t, "Add", &Dense{}, method, denseComparison, legalTypesAll, legalSizeSameRectangular, 1e-14)
+}
+
+func TestSub(t *testing.T) {
+	for i, test := range []struct {
+		a, b, r [][]float64
+	}{
+		{
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+		},
+		{
+			[][]float64{{1, 1, 1}, {1, 1, 1}, {1, 1, 1}},
+			[][]float64{{1, 1, 1}, {1, 1, 1}, {1, 1, 1}},
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+		},
+		{
+			[][]float64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}},
+			[][]float64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}},
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+		},
+		{
+			[][]float64{{-1, 0, 0}, {0, -1, 0}, {0, 0, -1}},
+			[][]float64{{-1, 0, 0}, {0, -1, 0}, {0, 0, -1}},
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+		},
+		{
+			[][]float64{{1, 2, 3}, {4, 5, 6}},
+			[][]float64{{1, 2, 3}, {4, 5, 6}},
+			[][]float64{{0, 0, 0}, {0, 0, 0}},
+		},
+	} {
+		a := NewDense(flatten(test.a))
+		b := NewDense(flatten(test.b))
+		r := NewDense(flatten(test.r))
+
+		var temp Dense
+		temp.Sub(a, b)
+		if !Equal(&temp, r) {
+			t.Errorf("unexpected result from Sub for test %d %v Sub %v: got: %v want: %v",
+				i, test.a, test.b, unflatten(temp.mat.Rows, temp.mat.Cols, temp.mat.Data), test.r)
+		}
+
+		zero(temp.mat.Data)
+		temp.Sub(a, b)
+		if !Equal(&temp, r) {
+			t.Errorf("unexpected result from Sub for test %d %v Sub %v: got: %v want: %v",
+				i, test.a, test.b, unflatten(temp.mat.Rows, temp.mat.Cols, temp.mat.Data), test.r)
+		}
+
+		// These probably warrant a better check and failure. They should never happen in the wild though.
+		temp.mat.Data = nil
+		panicked, message := panics(func() { temp.Sub(a, b) })
+		if !panicked || message != "runtime error: index out of range" {
+			t.Error("exected runtime panic for nil data slice")
+		}
+
+		a.Sub(a, b)
+		if !Equal(a, r) {
+			t.Errorf("unexpected result from Sub for test %d %v Sub %v: got: %v want: %v",
+				i, test.a, test.b, unflatten(a.mat.Rows, a.mat.Cols, a.mat.Data), test.r)
+		}
+	}
+
+	panicked, message := panics(func() {
+		m := NewDense(10, 10, nil)
+		a := NewDense(5, 5, nil)
+		m.Slice(1, 6, 1, 6).(*Dense).Sub(a, m.Slice(2, 7, 2, 7))
+	})
+	if !panicked {
+		t.Error("expected panic for overlapping matrices")
+	}
+	if message != regionOverlap {
+		t.Errorf("unexpected panic message: got: %q want: %q", message, regionOverlap)
+	}
+
+	method := func(receiver, a, b Matrix) {
+		type Suber interface {
+			Sub(a, b Matrix)
+		}
+		rd := receiver.(Suber)
+		rd.Sub(a, b)
+	}
+	denseComparison := func(receiver, a, b *Dense) {
+		receiver.Sub(a, b)
+	}
+	testTwoInput(t, "Sub", &Dense{}, method, denseComparison, legalTypesAll, legalSizeSameRectangular, 1e-14)
+}
+
+func TestMulElem(t *testing.T) {
+	for i, test := range []struct {
+		a, b, r [][]float64
+	}{
+		{
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+		},
+		{
+			[][]float64{{1, 1, 1}, {1, 1, 1}, {1, 1, 1}},
+			[][]float64{{1, 1, 1}, {1, 1, 1}, {1, 1, 1}},
+			[][]float64{{1, 1, 1}, {1, 1, 1}, {1, 1, 1}},
+		},
+		{
+			[][]float64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}},
+			[][]float64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}},
+			[][]float64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}},
+		},
+		{
+			[][]float64{{-1, 0, 0}, {0, -1, 0}, {0, 0, -1}},
+			[][]float64{{-1, 0, 0}, {0, -1, 0}, {0, 0, -1}},
+			[][]float64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}},
+		},
+		{
+			[][]float64{{1, 2, 3}, {4, 5, 6}},
+			[][]float64{{1, 2, 3}, {4, 5, 6}},
+			[][]float64{{1, 4, 9}, {16, 25, 36}},
+		},
+	} {
+		a := NewDense(flatten(test.a))
+		b := NewDense(flatten(test.b))
+		r := NewDense(flatten(test.r))
+
+		var temp Dense
+		temp.MulElem(a, b)
+		if !Equal(&temp, r) {
+			t.Errorf("unexpected result from MulElem for test %d %v MulElem %v: got: %v want: %v",
+				i, test.a, test.b, unflatten(temp.mat.Rows, temp.mat.Cols, temp.mat.Data), test.r)
+		}
+
+		zero(temp.mat.Data)
+		temp.MulElem(a, b)
+		if !Equal(&temp, r) {
+			t.Errorf("unexpected result from MulElem for test %d %v MulElem %v: got: %v want: %v",
+				i, test.a, test.b, unflatten(temp.mat.Rows, temp.mat.Cols, temp.mat.Data), test.r)
+		}
+
+		// These probably warrant a better check and failure. They should never happen in the wild though.
+		temp.mat.Data = nil
+		panicked, message := panics(func() { temp.MulElem(a, b) })
+		if !panicked || message != "runtime error: index out of range" {
+			t.Error("exected runtime panic for nil data slice")
+		}
+
+		a.MulElem(a, b)
+		if !Equal(a, r) {
+			t.Errorf("unexpected result from MulElem for test %d %v MulElem %v: got: %v want: %v",
+				i, test.a, test.b, unflatten(a.mat.Rows, a.mat.Cols, a.mat.Data), test.r)
+		}
+	}
+
+	panicked, message := panics(func() {
+		m := NewDense(10, 10, nil)
+		a := NewDense(5, 5, nil)
+		m.Slice(1, 6, 1, 6).(*Dense).MulElem(a, m.Slice(2, 7, 2, 7))
+	})
+	if !panicked {
+		t.Error("expected panic for overlapping matrices")
+	}
+	if message != regionOverlap {
+		t.Errorf("unexpected panic message: got: %q want: %q", message, regionOverlap)
+	}
+
+	method := func(receiver, a, b Matrix) {
+		type ElemMuler interface {
+			MulElem(a, b Matrix)
+		}
+		rd := receiver.(ElemMuler)
+		rd.MulElem(a, b)
+	}
+	denseComparison := func(receiver, a, b *Dense) {
+		receiver.MulElem(a, b)
+	}
+	testTwoInput(t, "MulElem", &Dense{}, method, denseComparison, legalTypesAll, legalSizeSameRectangular, 1e-14)
+}
+
+// A comparison that treats NaNs as equal, for testing.
+func (m *Dense) same(b Matrix) bool {
+	br, bc := b.Dims()
+	if br != m.mat.Rows || bc != m.mat.Cols {
+		return false
+	}
+	for r := 0; r < br; r++ {
+		for c := 0; c < bc; c++ {
+			if av, bv := m.At(r, c), b.At(r, c); av != bv && !(math.IsNaN(av) && math.IsNaN(bv)) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+func TestDivElem(t *testing.T) {
+	for i, test := range []struct {
+		a, b, r [][]float64
+	}{
+		{
+			[][]float64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}},
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+			[][]float64{{math.Inf(1), math.NaN(), math.NaN()}, {math.NaN(), math.Inf(1), math.NaN()}, {math.NaN(), math.NaN(), math.Inf(1)}},
+		},
+		{
+			[][]float64{{1, 1, 1}, {1, 1, 1}, {1, 1, 1}},
+			[][]float64{{1, 1, 1}, {1, 1, 1}, {1, 1, 1}},
+			[][]float64{{1, 1, 1}, {1, 1, 1}, {1, 1, 1}},
+		},
+		{
+			[][]float64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}},
+			[][]float64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}},
+			[][]float64{{1, math.NaN(), math.NaN()}, {math.NaN(), 1, math.NaN()}, {math.NaN(), math.NaN(), 1}},
+		},
+		{
+			[][]float64{{-1, 0, 0}, {0, -1, 0}, {0, 0, -1}},
+			[][]float64{{-1, 0, 0}, {0, -1, 0}, {0, 0, -1}},
+			[][]float64{{1, math.NaN(), math.NaN()}, {math.NaN(), 1, math.NaN()}, {math.NaN(), math.NaN(), 1}},
+		},
+		{
+			[][]float64{{1, 2, 3}, {4, 5, 6}},
+			[][]float64{{1, 2, 3}, {4, 5, 6}},
+			[][]float64{{1, 1, 1}, {1, 1, 1}},
+		},
+	} {
+		a := NewDense(flatten(test.a))
+		b := NewDense(flatten(test.b))
+		r := NewDense(flatten(test.r))
+
+		var temp Dense
+		temp.DivElem(a, b)
+		if !temp.same(r) {
+			t.Errorf("unexpected result from DivElem for test %d %v DivElem %v: got: %v want: %v",
+				i, test.a, test.b, unflatten(temp.mat.Rows, temp.mat.Cols, temp.mat.Data), test.r)
+		}
+
+		zero(temp.mat.Data)
+		temp.DivElem(a, b)
+		if !temp.same(r) {
+			t.Errorf("unexpected result from DivElem for test %d %v DivElem %v: got: %v want: %v",
+				i, test.a, test.b, unflatten(temp.mat.Rows, temp.mat.Cols, temp.mat.Data), test.r)
+		}
+
+		// These probably warrant a better check and failure. They should never happen in the wild though.
+		temp.mat.Data = nil
+		panicked, message := panics(func() { temp.DivElem(a, b) })
+		if !panicked || message != "runtime error: index out of range" {
+			t.Error("exected runtime panic for nil data slice")
+		}
+
+		a.DivElem(a, b)
+		if !a.same(r) {
+			t.Errorf("unexpected result from DivElem for test %d %v DivElem %v: got: %v want: %v",
+				i, test.a, test.b, unflatten(a.mat.Rows, a.mat.Cols, a.mat.Data), test.r)
+		}
+	}
+
+	panicked, message := panics(func() {
+		m := NewDense(10, 10, nil)
+		a := NewDense(5, 5, nil)
+		m.Slice(1, 6, 1, 6).(*Dense).DivElem(a, m.Slice(2, 7, 2, 7))
+	})
+	if !panicked {
+		t.Error("expected panic for overlapping matrices")
+	}
+	if message != regionOverlap {
+		t.Errorf("unexpected panic message: got: %q want: %q", message, regionOverlap)
+	}
+
+	method := func(receiver, a, b Matrix) {
+		type ElemDiver interface {
+			DivElem(a, b Matrix)
+		}
+		rd := receiver.(ElemDiver)
+		rd.DivElem(a, b)
+	}
+	denseComparison := func(receiver, a, b *Dense) {
+		receiver.DivElem(a, b)
+	}
+	testTwoInput(t, "DivElem", &Dense{}, method, denseComparison, legalTypesAll, legalSizeSameRectangular, 1e-14)
+}
+
+func TestMul(t *testing.T) {
+	for i, test := range []struct {
+		a, b, r [][]float64
+	}{
+		{
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+		},
+		{
+			[][]float64{{1, 1, 1}, {1, 1, 1}, {1, 1, 1}},
+			[][]float64{{1, 1, 1}, {1, 1, 1}, {1, 1, 1}},
+			[][]float64{{3, 3, 3}, {3, 3, 3}, {3, 3, 3}},
+		},
+		{
+			[][]float64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}},
+			[][]float64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}},
+			[][]float64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}},
+		},
+		{
+			[][]float64{{-1, 0, 0}, {0, -1, 0}, {0, 0, -1}},
+			[][]float64{{-1, 0, 0}, {0, -1, 0}, {0, 0, -1}},
+			[][]float64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}},
+		},
+		{
+			[][]float64{{1, 2, 3}, {4, 5, 6}},
+			[][]float64{{1, 2}, {3, 4}, {5, 6}},
+			[][]float64{{22, 28}, {49, 64}},
+		},
+		{
+			[][]float64{{0, 1, 1}, {0, 1, 1}, {0, 1, 1}},
+			[][]float64{{0, 1, 1}, {0, 1, 1}, {0, 1, 1}},
+			[][]float64{{0, 2, 2}, {0, 2, 2}, {0, 2, 2}},
+		},
+	} {
+		a := NewDense(flatten(test.a))
+		b := NewDense(flatten(test.b))
+		r := NewDense(flatten(test.r))
+
+		var temp Dense
+		temp.Mul(a, b)
+		if !Equal(&temp, r) {
+			t.Errorf("unexpected result from Mul for test %d %v Mul %v: got: %v want: %v",
+				i, test.a, test.b, unflatten(temp.mat.Rows, temp.mat.Cols, temp.mat.Data), test.r)
+		}
+
+		zero(temp.mat.Data)
+		temp.Mul(a, b)
+		if !Equal(&temp, r) {
+			t.Errorf("unexpected result from Mul for test %d %v Mul %v: got: %v want: %v",
+				i, test.a, test.b, unflatten(temp.mat.Rows, temp.mat.Cols, temp.mat.Data), test.r)
+		}
+
+		// These probably warrant a better check and failure. They should never happen in the wild though.
+		temp.mat.Data = nil
+		panicked, message := panics(func() { temp.Mul(a, b) })
+		if !panicked || message != "blas: index of c out of range" {
+			if message != "" {
+				t.Errorf("expected runtime panic for nil data slice: got %q", message)
+			} else {
+				t.Error("expected runtime panic for nil data slice")
+			}
+		}
+	}
+
+	panicked, message := panics(func() {
+		m := NewDense(10, 10, nil)
+		a := NewDense(5, 5, nil)
+		m.Slice(1, 6, 1, 6).(*Dense).Mul(a, m.Slice(2, 7, 2, 7))
+	})
+	if !panicked {
+		t.Error("expected panic for overlapping matrices")
+	}
+	if message != regionOverlap {
+		t.Errorf("unexpected panic message: got: %q want: %q", message, regionOverlap)
+	}
+
+	method := func(receiver, a, b Matrix) {
+		type Muler interface {
+			Mul(a, b Matrix)
+		}
+		rd := receiver.(Muler)
+		rd.Mul(a, b)
+	}
+	denseComparison := func(receiver, a, b *Dense) {
+		receiver.Mul(a, b)
+	}
+	legalSizeMul := func(ar, ac, br, bc int) bool {
+		return ac == br
+	}
+	testTwoInput(t, "Mul", &Dense{}, method, denseComparison, legalTypesAll, legalSizeMul, 1e-14)
+}
+
+func randDense(size int, rho float64, rnd func() float64) (*Dense, error) {
+	if size == 0 {
+		return nil, ErrZeroLength
+	}
+	d := &Dense{
+		mat: blas64.General{
+			Rows: size, Cols: size, Stride: size,
+			Data: make([]float64, size*size),
+		},
+		capRows: size, capCols: size,
+	}
+	for i := 0; i < size; i++ {
+		for j := 0; j < size; j++ {
+			if rand.Float64() < rho {
+				d.Set(i, j, rnd())
+			}
+		}
+	}
+	return d, nil
+}
+
+func TestExp(t *testing.T) {
+	for i, test := range []struct {
+		a    [][]float64
+		want [][]float64
+		mod  func(*Dense)
+	}{
+		{
+			a:    [][]float64{{-49, 24}, {-64, 31}},
+			want: [][]float64{{-0.7357587581474017, 0.5518190996594223}, {-1.4715175990917921, 1.103638240717339}},
+		},
+		{
+			a:    [][]float64{{-49, 24}, {-64, 31}},
+			want: [][]float64{{-0.7357587581474017, 0.5518190996594223}, {-1.4715175990917921, 1.103638240717339}},
+			mod: func(a *Dense) {
+				d := make([]float64, 100)
+				for i := range d {
+					d[i] = math.NaN()
+				}
+				*a = *NewDense(10, 10, d).Slice(1, 3, 1, 3).(*Dense)
+			},
+		},
+		{
+			a:    [][]float64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}},
+			want: [][]float64{{2.71828182845905, 0, 0}, {0, 2.71828182845905, 0}, {0, 0, 2.71828182845905}},
+		},
+	} {
+		var got Dense
+		if test.mod != nil {
+			test.mod(&got)
+		}
+		got.Exp(NewDense(flatten(test.a)))
+		if !EqualApprox(&got, NewDense(flatten(test.want)), 1e-12) {
+			t.Errorf("unexpected result for Exp test %d", i)
+		}
+	}
+}
+
+func TestPow(t *testing.T) {
+	for i, test := range []struct {
+		a    [][]float64
+		n    int
+		mod  func(*Dense)
+		want [][]float64
+	}{
+		{
+			a:    [][]float64{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}},
+			n:    0,
+			want: [][]float64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}},
+		},
+		{
+			a:    [][]float64{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}},
+			n:    0,
+			want: [][]float64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}},
+			mod: func(a *Dense) {
+				d := make([]float64, 100)
+				for i := range d {
+					d[i] = math.NaN()
+				}
+				*a = *NewDense(10, 10, d).Slice(1, 4, 1, 4).(*Dense)
+			},
+		},
+		{
+			a:    [][]float64{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}},
+			n:    1,
+			want: [][]float64{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}},
+		},
+		{
+			a:    [][]float64{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}},
+			n:    1,
+			want: [][]float64{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}},
+			mod: func(a *Dense) {
+				d := make([]float64, 100)
+				for i := range d {
+					d[i] = math.NaN()
+				}
+				*a = *NewDense(10, 10, d).Slice(1, 4, 1, 4).(*Dense)
+			},
+		},
+		{
+			a:    [][]float64{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}},
+			n:    2,
+			want: [][]float64{{30, 36, 42}, {66, 81, 96}, {102, 126, 150}},
+		},
+		{
+			a:    [][]float64{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}},
+			n:    2,
+			want: [][]float64{{30, 36, 42}, {66, 81, 96}, {102, 126, 150}},
+			mod: func(a *Dense) {
+				d := make([]float64, 100)
+				for i := range d {
+					d[i] = math.NaN()
+				}
+				*a = *NewDense(10, 10, d).Slice(1, 4, 1, 4).(*Dense)
+			},
+		},
+		{
+			a:    [][]float64{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}},
+			n:    3,
+			want: [][]float64{{468, 576, 684}, {1062, 1305, 1548}, {1656, 2034, 2412}},
+		},
+		{
+			a:    [][]float64{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}},
+			n:    3,
+			want: [][]float64{{468, 576, 684}, {1062, 1305, 1548}, {1656, 2034, 2412}},
+			mod: func(a *Dense) {
+				d := make([]float64, 100)
+				for i := range d {
+					d[i] = math.NaN()
+				}
+				*a = *NewDense(10, 10, d).Slice(1, 4, 1, 4).(*Dense)
+			},
+		},
+	} {
+		var got Dense
+		if test.mod != nil {
+			test.mod(&got)
+		}
+		got.Pow(NewDense(flatten(test.a)), test.n)
+		if !EqualApprox(&got, NewDense(flatten(test.want)), 1e-12) {
+			t.Errorf("unexpected result for Pow test %d", i)
+		}
+	}
+}
+
+func TestScale(t *testing.T) {
+	for _, f := range []float64{0.5, 1, 3} {
+		method := func(receiver, a Matrix) {
+			type Scaler interface {
+				Scale(f float64, a Matrix)
+			}
+			rd := receiver.(Scaler)
+			rd.Scale(f, a)
+		}
+		denseComparison := func(receiver, a *Dense) {
+			receiver.Scale(f, a)
+		}
+		testOneInput(t, "Scale", &Dense{}, method, denseComparison, isAnyType, isAnySize, 1e-14)
+	}
+}
+
+func TestPowN(t *testing.T) {
+	for i, test := range []struct {
+		a   [][]float64
+		mod func(*Dense)
+	}{
+		{
+			a: [][]float64{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}},
+		},
+		{
+			a: [][]float64{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}},
+			mod: func(a *Dense) {
+				d := make([]float64, 100)
+				for i := range d {
+					d[i] = math.NaN()
+				}
+				*a = *NewDense(10, 10, d).Slice(1, 4, 1, 4).(*Dense)
+			},
+		},
+	} {
+		for n := 1; n <= 14; n++ {
+			var got, want Dense
+			if test.mod != nil {
+				test.mod(&got)
+			}
+			got.Pow(NewDense(flatten(test.a)), n)
+			want.iterativePow(NewDense(flatten(test.a)), n)
+			if !Equal(&got, &want) {
+				t.Errorf("unexpected result for iterative Pow test %d", i)
+			}
+		}
+	}
+}
+
+func (m *Dense) iterativePow(a Matrix, n int) {
+	m.Clone(a)
+	for i := 1; i < n; i++ {
+		m.Mul(m, a)
+	}
+}
+
+func TestCloneT(t *testing.T) {
+	for i, test := range []struct {
+		a, want [][]float64
+	}{
+		{
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+		},
+		{
+			[][]float64{{1, 1, 1}, {1, 1, 1}, {1, 1, 1}},
+			[][]float64{{1, 1, 1}, {1, 1, 1}, {1, 1, 1}},
+		},
+		{
+			[][]float64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}},
+			[][]float64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}},
+		},
+		{
+			[][]float64{{-1, 0, 0}, {0, -1, 0}, {0, 0, -1}},
+			[][]float64{{-1, 0, 0}, {0, -1, 0}, {0, 0, -1}},
+		},
+		{
+			[][]float64{{1, 2, 3}, {4, 5, 6}},
+			[][]float64{{1, 4}, {2, 5}, {3, 6}},
+		},
+	} {
+		a := NewDense(flatten(test.a))
+		want := NewDense(flatten(test.want))
+
+		var got, gotT Dense
+
+		for j := 0; j < 2; j++ {
+			got.Clone(a.T())
+			if !Equal(&got, want) {
+				t.Errorf("expected transpose for test %d iteration %d: %v transpose = %v",
+					i, j, test.a, test.want)
+			}
+			gotT.Clone(got.T())
+			if !Equal(&gotT, a) {
+				t.Errorf("expected transpose for test %d iteration %d: %v transpose = %v",
+					i, j, test.a, test.want)
+			}
+
+			zero(got.mat.Data)
+		}
+	}
+}
+
+func TestCopyT(t *testing.T) {
+	for i, test := range []struct {
+		a, want [][]float64
+	}{
+		{
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+		},
+		{
+			[][]float64{{1, 1, 1}, {1, 1, 1}, {1, 1, 1}},
+			[][]float64{{1, 1, 1}, {1, 1, 1}, {1, 1, 1}},
+		},
+		{
+			[][]float64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}},
+			[][]float64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}},
+		},
+		{
+			[][]float64{{-1, 0, 0}, {0, -1, 0}, {0, 0, -1}},
+			[][]float64{{-1, 0, 0}, {0, -1, 0}, {0, 0, -1}},
+		},
+		{
+			[][]float64{{1, 2, 3}, {4, 5, 6}},
+			[][]float64{{1, 4}, {2, 5}, {3, 6}},
+		},
+	} {
+		a := NewDense(flatten(test.a))
+		want := NewDense(flatten(test.want))
+
+		ar, ac := a.Dims()
+		got := NewDense(ac, ar, nil)
+		rr := NewDense(ar, ac, nil)
+
+		for j := 0; j < 2; j++ {
+			got.Copy(a.T())
+			if !Equal(got, want) {
+				t.Errorf("expected transpose for test %d iteration %d: %v transpose = %v",
+					i, j, test.a, test.want)
+			}
+			rr.Copy(got.T())
+			if !Equal(rr, a) {
+				t.Errorf("expected transpose for test %d iteration %d: %v transpose = %v",
+					i, j, test.a, test.want)
+			}
+
+			zero(got.mat.Data)
+		}
+	}
+}
+
+func TestCopyDenseAlias(t *testing.T) {
+	for _, trans := range []bool{false, true} {
+		for di := 0; di < 2; di++ {
+			for dj := 0; dj < 2; dj++ {
+				for si := 0; si < 2; si++ {
+					for sj := 0; sj < 2; sj++ {
+						a := NewDense(3, 3, []float64{
+							1, 2, 3,
+							4, 5, 6,
+							7, 8, 9,
+						})
+						src := a.Slice(si, si+2, sj, sj+2)
+						want := DenseCopyOf(src)
+						got := a.Slice(di, di+2, dj, dj+2).(*Dense)
+
+						if trans {
+							panicked, _ := panics(func() { got.Copy(src.T()) })
+							if !panicked {
+								t.Errorf("expected panic for transpose aliased copy with offsets dst(%d,%d) src(%d,%d):\ngot:\n%v\nwant:\n%v",
+									di, dj, si, sj, Formatted(got), Formatted(want),
+								)
+							}
+							continue
+						}
+
+						got.Copy(src)
+						if !Equal(got, want) {
+							t.Errorf("unexpected aliased copy result with offsets dst(%d,%d) src(%d,%d):\ngot:\n%v\nwant:\n%v",
+								di, dj, si, sj, Formatted(got), Formatted(want),
+							)
+						}
+					}
+				}
+			}
+		}
+	}
+}
+
+func TestCopyVecDenseAlias(t *testing.T) {
+	for _, horiz := range []bool{false, true} {
+		for do := 0; do < 2; do++ {
+			for di := 0; di < 3; di++ {
+				for si := 0; si < 3; si++ {
+					a := NewDense(3, 3, []float64{
+						1, 2, 3,
+						4, 5, 6,
+						7, 8, 9,
+					})
+					var src *VecDense
+					var want *Dense
+					if horiz {
+						src = a.RowView(si)
+						want = DenseCopyOf(a.Slice(si, si+1, 0, 2))
+					} else {
+						src = a.ColView(si)
+						want = DenseCopyOf(a.Slice(0, 2, si, si+1))
+					}
+
+					var got *Dense
+					if horiz {
+						got = a.Slice(di, di+1, do, do+2).(*Dense)
+						got.Copy(src.T())
+					} else {
+						got = a.Slice(do, do+2, di, di+1).(*Dense)
+						got.Copy(src)
+					}
+
+					if !Equal(got, want) {
+						t.Errorf("unexpected aliased copy result with offsets dst(%d) src(%d):\ngot:\n%v\nwant:\n%v",
+							di, si, Formatted(got), Formatted(want),
+						)
+					}
+				}
+			}
+		}
+	}
+}
+
+func identity(r, c int, v float64) float64 { return v }
+
+func TestApply(t *testing.T) {
+	for i, test := range []struct {
+		a, want [][]float64
+		fn      func(r, c int, v float64) float64
+	}{
+		{
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+			identity,
+		},
+		{
+			[][]float64{{1, 1, 1}, {1, 1, 1}, {1, 1, 1}},
+			[][]float64{{1, 1, 1}, {1, 1, 1}, {1, 1, 1}},
+			identity,
+		},
+		{
+			[][]float64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}},
+			[][]float64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}},
+			identity,
+		},
+		{
+			[][]float64{{-1, 0, 0}, {0, -1, 0}, {0, 0, -1}},
+			[][]float64{{-1, 0, 0}, {0, -1, 0}, {0, 0, -1}},
+			identity,
+		},
+		{
+			[][]float64{{1, 2, 3}, {4, 5, 6}},
+			[][]float64{{1, 2, 3}, {4, 5, 6}},
+			identity,
+		},
+		{
+			[][]float64{{1, 2, 3}, {4, 5, 6}},
+			[][]float64{{2, 4, 6}, {8, 10, 12}},
+			func(r, c int, v float64) float64 { return v * 2 },
+		},
+		{
+			[][]float64{{1, 2, 3}, {4, 5, 6}},
+			[][]float64{{0, 2, 0}, {0, 5, 0}},
+			func(r, c int, v float64) float64 {
+				if c == 1 {
+					return v
+				}
+				return 0
+			},
+		},
+		{
+			[][]float64{{1, 2, 3}, {4, 5, 6}},
+			[][]float64{{0, 0, 0}, {4, 5, 6}},
+			func(r, c int, v float64) float64 {
+				if r == 1 {
+					return v
+				}
+				return 0
+			},
+		},
+	} {
+		a := NewDense(flatten(test.a))
+		want := NewDense(flatten(test.want))
+
+		var got Dense
+
+		for j := 0; j < 2; j++ {
+			got.Apply(test.fn, a)
+			if !Equal(&got, want) {
+				t.Errorf("unexpected result for test %d iteration %d: got: %v want: %v", i, j, got.mat.Data, want.mat.Data)
+			}
+		}
+	}
+
+	for _, fn := range []func(r, c int, v float64) float64{
+		identity,
+		func(r, c int, v float64) float64 {
+			if r < c {
+				return v
+			}
+			return -v
+		},
+		func(r, c int, v float64) float64 {
+			if r%2 == 0 && c%2 == 0 {
+				return v
+			}
+			return -v
+		},
+		func(_, _ int, v float64) float64 { return v * v },
+		func(_, _ int, v float64) float64 { return -v },
+	} {
+		method := func(receiver, x Matrix) {
+			type Applier interface {
+				Apply(func(r, c int, v float64) float64, Matrix)
+			}
+			rd := receiver.(Applier)
+			rd.Apply(fn, x)
+		}
+		denseComparison := func(receiver, x *Dense) {
+			receiver.Apply(fn, x)
+		}
+		testOneInput(t, "Apply", &Dense{}, method, denseComparison, isAnyType, isAnySize, 0)
+	}
+}
+
+func TestClone(t *testing.T) {
+	for i, test := range []struct {
+		a    [][]float64
+		i, j int
+		v    float64
+	}{
+		{
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+			1, 1,
+			1,
+		},
+		{
+			[][]float64{{1, 1, 1}, {1, 1, 1}, {1, 1, 1}},
+			0, 0,
+			0,
+		},
+	} {
+		a := NewDense(flatten(test.a))
+		b := *a
+		a.Clone(a)
+		a.Set(test.i, test.j, test.v)
+
+		if Equal(&b, a) {
+			t.Errorf("unexpected mirror of write to cloned matrix for test %d: %v cloned and altered = %v",
+				i, a, &b)
+		}
+	}
+}
+
+// TODO(kortschak) Roll this into testOneInput when it exists.
+func TestCopyPanic(t *testing.T) {
+	for _, a := range []*Dense{
+		{},
+		{mat: blas64.General{Rows: 1}},
+		{mat: blas64.General{Cols: 1}},
+	} {
+		var rows, cols int
+		m := NewDense(1, 1, nil)
+		panicked, message := panics(func() { rows, cols = m.Copy(a) })
+		if panicked {
+			t.Errorf("unexpected panic: %v", message)
+		}
+		if rows != 0 {
+			t.Errorf("unexpected rows: got: %d want: 0", rows)
+		}
+		if cols != 0 {
+			t.Errorf("unexpected cols: got: %d want: 0", cols)
+		}
+	}
+}
+
+func TestStack(t *testing.T) {
+	for i, test := range []struct {
+		a, b, e [][]float64
+	}{
+		{
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}, {0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+		},
+		{
+			[][]float64{{1, 1, 1}, {1, 1, 1}, {1, 1, 1}},
+			[][]float64{{1, 1, 1}, {1, 1, 1}, {1, 1, 1}},
+			[][]float64{{1, 1, 1}, {1, 1, 1}, {1, 1, 1}, {1, 1, 1}, {1, 1, 1}, {1, 1, 1}},
+		},
+		{
+			[][]float64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}},
+			[][]float64{{0, 1, 0}, {0, 0, 1}, {1, 0, 0}},
+			[][]float64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}, {0, 1, 0}, {0, 0, 1}, {1, 0, 0}},
+		},
+	} {
+		a := NewDense(flatten(test.a))
+		b := NewDense(flatten(test.b))
+
+		var s Dense
+		s.Stack(a, b)
+
+		if !Equal(&s, NewDense(flatten(test.e))) {
+			t.Errorf("unexpected result for Stack test %d: %v stack %v = %v", i, a, b, s)
+		}
+	}
+
+	method := func(receiver, a, b Matrix) {
+		type Stacker interface {
+			Stack(a, b Matrix)
+		}
+		rd := receiver.(Stacker)
+		rd.Stack(a, b)
+	}
+	denseComparison := func(receiver, a, b *Dense) {
+		receiver.Stack(a, b)
+	}
+	testTwoInput(t, "Stack", &Dense{}, method, denseComparison, legalTypesAll, legalSizeSameWidth, 0)
+}
+
+func TestAugment(t *testing.T) {
+	for i, test := range []struct {
+		a, b, e [][]float64
+	}{
+		{
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+			[][]float64{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}},
+			[][]float64{{0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}},
+		},
+		{
+			[][]float64{{1, 1, 1}, {1, 1, 1}, {1, 1, 1}},
+			[][]float64{{1, 1, 1}, {1, 1, 1}, {1, 1, 1}},
+			[][]float64{{1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1}},
+		},
+		{
+			[][]float64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}},
+			[][]float64{{0, 1, 0}, {0, 0, 1}, {1, 0, 0}},
+			[][]float64{{1, 0, 0, 0, 1, 0}, {0, 1, 0, 0, 0, 1}, {0, 0, 1, 1, 0, 0}},
+		},
+	} {
+		a := NewDense(flatten(test.a))
+		b := NewDense(flatten(test.b))
+
+		var s Dense
+		s.Augment(a, b)
+
+		if !Equal(&s, NewDense(flatten(test.e))) {
+			t.Errorf("unexpected result for Augment test %d: %v augment %v = %v", i, a, b, s)
+		}
+	}
+
+	method := func(receiver, a, b Matrix) {
+		type Augmenter interface {
+			Augment(a, b Matrix)
+		}
+		rd := receiver.(Augmenter)
+		rd.Augment(a, b)
+	}
+	denseComparison := func(receiver, a, b *Dense) {
+		receiver.Augment(a, b)
+	}
+	testTwoInput(t, "Augment", &Dense{}, method, denseComparison, legalTypesAll, legalSizeSameHeight, 0)
+}
+
+func TestRankOne(t *testing.T) {
+	for i, test := range []struct {
+		x     []float64
+		y     []float64
+		m     [][]float64
+		alpha float64
+	}{
+		{
+			x:     []float64{5},
+			y:     []float64{10},
+			m:     [][]float64{{2}},
+			alpha: -3,
+		},
+		{
+			x:     []float64{5, 6, 1},
+			y:     []float64{10},
+			m:     [][]float64{{2}, {-3}, {5}},
+			alpha: -3,
+		},
+
+		{
+			x:     []float64{5},
+			y:     []float64{10, 15, 8},
+			m:     [][]float64{{2, -3, 5}},
+			alpha: -3,
+		},
+		{
+			x: []float64{1, 5},
+			y: []float64{10, 15},
+			m: [][]float64{
+				{2, -3},
+				{4, -1},
+			},
+			alpha: -3,
+		},
+		{
+			x: []float64{2, 3, 9},
+			y: []float64{8, 9},
+			m: [][]float64{
+				{2, 3},
+				{4, 5},
+				{6, 7},
+			},
+			alpha: -3,
+		},
+		{
+			x: []float64{2, 3},
+			y: []float64{8, 9, 9},
+			m: [][]float64{
+				{2, 3, 6},
+				{4, 5, 7},
+			},
+			alpha: -3,
+		},
+	} {
+		want := &Dense{}
+		xm := NewDense(len(test.x), 1, test.x)
+		ym := NewDense(1, len(test.y), test.y)
+
+		want.Mul(xm, ym)
+		want.Scale(test.alpha, want)
+		want.Add(want, NewDense(flatten(test.m)))
+
+		a := NewDense(flatten(test.m))
+		m := &Dense{}
+		// Check with a new matrix
+		m.RankOne(a, test.alpha, NewVecDense(len(test.x), test.x), NewVecDense(len(test.y), test.y))
+		if !Equal(m, want) {
+			t.Errorf("unexpected result for RankOne test %d iteration 0: got: %+v want: %+v", i, m, want)
+		}
+		// Check with the same matrix
+		a.RankOne(a, test.alpha, NewVecDense(len(test.x), test.x), NewVecDense(len(test.y), test.y))
+		if !Equal(a, want) {
+			t.Errorf("unexpected result for Outer test %d iteration 1: got: %+v want: %+v", i, m, want)
+		}
+	}
+}
+
+func TestOuter(t *testing.T) {
+	for i, test := range []struct {
+		x []float64
+		y []float64
+	}{
+		{
+			x: []float64{5},
+			y: []float64{10},
+		},
+		{
+			x: []float64{5, 6, 1},
+			y: []float64{10},
+		},
+
+		{
+			x: []float64{5},
+			y: []float64{10, 15, 8},
+		},
+		{
+			x: []float64{1, 5},
+			y: []float64{10, 15},
+		},
+		{
+			x: []float64{2, 3, 9},
+			y: []float64{8, 9},
+		},
+		{
+			x: []float64{2, 3},
+			y: []float64{8, 9, 9},
+		},
+	} {
+		for _, f := range []float64{0.5, 1, 3} {
+			want := &Dense{}
+			xm := NewDense(len(test.x), 1, test.x)
+			ym := NewDense(1, len(test.y), test.y)
+
+			want.Mul(xm, ym)
+			want.Scale(f, want)
+
+			var m Dense
+			for j := 0; j < 2; j++ {
+				// Check with a new matrix - and then again.
+				m.Outer(f, NewVecDense(len(test.x), test.x), NewVecDense(len(test.y), test.y))
+				if !Equal(&m, want) {
+					t.Errorf("unexpected result for Outer test %d iteration %d scale %v: got: %+v want: %+v", i, j, f, m, want)
+				}
+			}
+		}
+	}
+}
+
+func TestInverse(t *testing.T) {
+	for i, test := range []struct {
+		a    Matrix
+		want Matrix // nil indicates that a is singular.
+		tol  float64
+	}{
+		{
+			a: NewDense(3, 3, []float64{
+				8, 1, 6,
+				3, 5, 7,
+				4, 9, 2,
+			}),
+			want: NewDense(3, 3, []float64{
+				0.147222222222222, -0.144444444444444, 0.063888888888889,
+				-0.061111111111111, 0.022222222222222, 0.105555555555556,
+				-0.019444444444444, 0.188888888888889, -0.102777777777778,
+			}),
+			tol: 1e-14,
+		},
+		{
+			a: NewDense(3, 3, []float64{
+				8, 1, 6,
+				3, 5, 7,
+				4, 9, 2,
+			}).T(),
+			want: NewDense(3, 3, []float64{
+				0.147222222222222, -0.144444444444444, 0.063888888888889,
+				-0.061111111111111, 0.022222222222222, 0.105555555555556,
+				-0.019444444444444, 0.188888888888889, -0.102777777777778,
+			}).T(),
+			tol: 1e-14,
+		},
+
+		// This case does not fail, but we do not guarantee that. The success
+		// is because the receiver and the input are aligned in the call to
+		// inverse. If there was a misalignment, the result would likely be
+		// incorrect and no shadowing panic would occur.
+		{
+			a: asBasicMatrix(NewDense(3, 3, []float64{
+				8, 1, 6,
+				3, 5, 7,
+				4, 9, 2,
+			})),
+			want: NewDense(3, 3, []float64{
+				0.147222222222222, -0.144444444444444, 0.063888888888889,
+				-0.061111111111111, 0.022222222222222, 0.105555555555556,
+				-0.019444444444444, 0.188888888888889, -0.102777777777778,
+			}),
+			tol: 1e-14,
+		},
+
+		// The following case fails as it does not follow the shadowing rules.
+		// Specifically, the test extracts the underlying *Dense, and uses
+		// it as a receiver with the basicMatrix as input. The basicMatrix type
+		// allows shadowing of the input data without providing the Raw method
+		// required for detection of shadowing.
+		//
+		// We specifically state we do not check this case.
+		//
+		// {
+		// 	a: asBasicMatrix(NewDense(3, 3, []float64{
+		// 		8, 1, 6,
+		// 		3, 5, 7,
+		// 		4, 9, 2,
+		// 	})).T(),
+		// 	want: NewDense(3, 3, []float64{
+		// 		0.147222222222222, -0.144444444444444, 0.063888888888889,
+		// 		-0.061111111111111, 0.022222222222222, 0.105555555555556,
+		// 		-0.019444444444444, 0.188888888888889, -0.102777777777778,
+		// 	}).T(),
+		// 	tol: 1e-14,
+		// },
+
+		{
+			a: NewDense(4, 4, []float64{
+				5, 2, 8, 7,
+				4, 5, 8, 2,
+				8, 5, 3, 2,
+				8, 7, 7, 5,
+			}),
+			want: NewDense(4, 4, []float64{
+				0.100548446069470, 0.021937842778793, 0.334552102376599, -0.283363802559415,
+				-0.226691042047532, -0.067641681901280, -0.281535648994515, 0.457038391224863,
+				0.080438756855576, 0.217550274223035, 0.067641681901280, -0.226691042047532,
+				0.043875685557587, -0.244972577696527, -0.235831809872029, 0.330895795246801,
+			}),
+			tol: 1e-14,
+		},
+
+		// Tests with singular matrix.
+		{
+			a: NewDense(1, 1, []float64{
+				0,
+			}),
+		},
+		{
+			a: NewDense(2, 2, []float64{
+				0, 0,
+				0, 0,
+			}),
+		},
+		{
+			a: NewDense(2, 2, []float64{
+				0, 0,
+				0, 1,
+			}),
+		},
+		{
+			a: NewDense(3, 3, []float64{
+				0, 0, 0,
+				0, 0, 0,
+				0, 0, 0,
+			}),
+		},
+		{
+			a: NewDense(4, 4, []float64{
+				0, 0, 0, 0,
+				0, 0, 0, 0,
+				0, 0, 0, 0,
+				0, 0, 0, 0,
+			}),
+		},
+		{
+			a: NewDense(4, 4, []float64{
+				0, 0, 0, 0,
+				0, 0, 0, 0,
+				0, 0, 20, 20,
+				0, 0, 20, 20,
+			}),
+		},
+		{
+			a: NewDense(4, 4, []float64{
+				0, 1, 0, 0,
+				0, 0, 1, 0,
+				0, 0, 0, 1,
+				0, 0, 0, 0,
+			}),
+		},
+		{
+			a: NewDense(4, 4, []float64{
+				1, 1, 1, 1,
+				1, 1, 1, 1,
+				1, 1, 1, 1,
+				1, 1, 1, 1,
+			}),
+		},
+		{
+			a: NewDense(5, 5, []float64{
+				0, 1, 0, 0, 0,
+				4, 0, 2, 0, 0,
+				0, 3, 0, 3, 0,
+				0, 0, 2, 0, 4,
+				0, 0, 0, 1, 0,
+			}),
+		},
+		{
+			a: NewDense(5, 5, []float64{
+				4, -1, -1, -1, -1,
+				-1, 4, -1, -1, -1,
+				-1, -1, 4, -1, -1,
+				-1, -1, -1, 4, -1,
+				-1, -1, -1, -1, 4,
+			}),
+		},
+		{
+			a: NewDense(5, 5, []float64{
+				2, -1, 0, 0, -1,
+				-1, 2, -1, 0, 0,
+				0, -1, 2, -1, 0,
+				0, 0, -1, 2, -1,
+				-1, 0, 0, -1, 2,
+			}),
+		},
+		{
+			a: NewDense(5, 5, []float64{
+				1, 2, 3, 5, 8,
+				2, 3, 5, 8, 13,
+				3, 5, 8, 13, 21,
+				5, 8, 13, 21, 34,
+				8, 13, 21, 34, 55,
+			}),
+		},
+		{
+			a: NewDense(8, 8, []float64{
+				611, 196, -192, 407, -8, -52, -49, 29,
+				196, 899, 113, -192, -71, -43, -8, -44,
+				-192, 113, 899, 196, 61, 49, 8, 52,
+				407, -192, 196, 611, 8, 44, 59, -23,
+				-8, -71, 61, 8, 411, -599, 208, 208,
+				-52, -43, 49, 44, -599, 411, 208, 208,
+				-49, -8, 8, 59, 208, 208, 99, -911,
+				29, -44, 52, -23, 208, 208, -911, 99,
+			}),
+		},
+	} {
+		var got Dense
+		err := got.Inverse(test.a)
+		if test.want == nil {
+			if err == nil {
+				t.Errorf("Case %d: expected error for singular matrix", i)
+			}
+			continue
+		}
+		if err != nil {
+			t.Errorf("Case %d: unexpected error: %v", i, err)
+			continue
+		}
+		if !equalApprox(&got, test.want, test.tol, false) {
+			t.Errorf("Case %d, inverse mismatch.", i)
+		}
+		var m Dense
+		m.Mul(&got, test.a)
+		r, _ := test.a.Dims()
+		d := make([]float64, r*r)
+		for i := 0; i < r*r; i += r + 1 {
+			d[i] = 1
+		}
+		eye := NewDense(r, r, d)
+		if !equalApprox(eye, &m, 1e-14, false) {
+			t.Errorf("Case %d, A^-1 * A != I", i)
+		}
+
+		var tmp Dense
+		tmp.Clone(test.a)
+		aU, transposed := untranspose(test.a)
+		if transposed {
+			switch aU := aU.(type) {
+			case *Dense:
+				err = aU.Inverse(test.a)
+			case *basicMatrix:
+				err = (*Dense)(aU).Inverse(test.a)
+			default:
+				continue
+			}
+			m.Mul(aU, &tmp)
+		} else {
+			switch a := test.a.(type) {
+			case *Dense:
+				err = a.Inverse(test.a)
+				m.Mul(a, &tmp)
+			case *basicMatrix:
+				err = (*Dense)(a).Inverse(test.a)
+				m.Mul(a, &tmp)
+			default:
+				continue
+			}
+		}
+		if err != nil {
+			t.Errorf("Error computing inverse: %v", err)
+		}
+		if !equalApprox(eye, &m, 1e-14, false) {
+			t.Errorf("Case %d, A^-1 * A != I", i)
+			fmt.Println(Formatted(&m))
+		}
+	}
+}
+
+var (
+	wd *Dense
+)
+
+func BenchmarkMulDense100Half(b *testing.B)        { denseMulBench(b, 100, 0.5) }
+func BenchmarkMulDense100Tenth(b *testing.B)       { denseMulBench(b, 100, 0.1) }
+func BenchmarkMulDense1000Half(b *testing.B)       { denseMulBench(b, 1000, 0.5) }
+func BenchmarkMulDense1000Tenth(b *testing.B)      { denseMulBench(b, 1000, 0.1) }
+func BenchmarkMulDense1000Hundredth(b *testing.B)  { denseMulBench(b, 1000, 0.01) }
+func BenchmarkMulDense1000Thousandth(b *testing.B) { denseMulBench(b, 1000, 0.001) }
+func denseMulBench(b *testing.B, size int, rho float64) {
+	b.StopTimer()
+	a, _ := randDense(size, rho, rand.NormFloat64)
+	d, _ := randDense(size, rho, rand.NormFloat64)
+	b.StartTimer()
+	for i := 0; i < b.N; i++ {
+		var n Dense
+		n.Mul(a, d)
+		wd = &n
+	}
+}
+
+func BenchmarkPreMulDense100Half(b *testing.B)        { densePreMulBench(b, 100, 0.5) }
+func BenchmarkPreMulDense100Tenth(b *testing.B)       { densePreMulBench(b, 100, 0.1) }
+func BenchmarkPreMulDense1000Half(b *testing.B)       { densePreMulBench(b, 1000, 0.5) }
+func BenchmarkPreMulDense1000Tenth(b *testing.B)      { densePreMulBench(b, 1000, 0.1) }
+func BenchmarkPreMulDense1000Hundredth(b *testing.B)  { densePreMulBench(b, 1000, 0.01) }
+func BenchmarkPreMulDense1000Thousandth(b *testing.B) { densePreMulBench(b, 1000, 0.001) }
+func densePreMulBench(b *testing.B, size int, rho float64) {
+	b.StopTimer()
+	a, _ := randDense(size, rho, rand.NormFloat64)
+	d, _ := randDense(size, rho, rand.NormFloat64)
+	wd = NewDense(size, size, nil)
+	b.StartTimer()
+	for i := 0; i < b.N; i++ {
+		wd.Mul(a, d)
+	}
+}
+
+func BenchmarkRow10(b *testing.B)   { rowBench(b, 10) }
+func BenchmarkRow100(b *testing.B)  { rowBench(b, 100) }
+func BenchmarkRow1000(b *testing.B) { rowBench(b, 1000) }
+
+func rowBench(b *testing.B, size int) {
+	a, _ := randDense(size, 1, rand.NormFloat64)
+	_, c := a.Dims()
+	dst := make([]float64, c)
+
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		Row(dst, 0, a)
+	}
+}
+
+func BenchmarkExp10(b *testing.B)   { expBench(b, 10) }
+func BenchmarkExp100(b *testing.B)  { expBench(b, 100) }
+func BenchmarkExp1000(b *testing.B) { expBench(b, 1000) }
+
+func expBench(b *testing.B, size int) {
+	a, _ := randDense(size, 1, rand.NormFloat64)
+
+	b.ResetTimer()
+	var m Dense
+	for i := 0; i < b.N; i++ {
+		m.Exp(a)
+	}
+}
+
+func BenchmarkPow10_3(b *testing.B)   { powBench(b, 10, 3) }
+func BenchmarkPow100_3(b *testing.B)  { powBench(b, 100, 3) }
+func BenchmarkPow1000_3(b *testing.B) { powBench(b, 1000, 3) }
+func BenchmarkPow10_4(b *testing.B)   { powBench(b, 10, 4) }
+func BenchmarkPow100_4(b *testing.B)  { powBench(b, 100, 4) }
+func BenchmarkPow1000_4(b *testing.B) { powBench(b, 1000, 4) }
+func BenchmarkPow10_5(b *testing.B)   { powBench(b, 10, 5) }
+func BenchmarkPow100_5(b *testing.B)  { powBench(b, 100, 5) }
+func BenchmarkPow1000_5(b *testing.B) { powBench(b, 1000, 5) }
+func BenchmarkPow10_6(b *testing.B)   { powBench(b, 10, 6) }
+func BenchmarkPow100_6(b *testing.B)  { powBench(b, 100, 6) }
+func BenchmarkPow1000_6(b *testing.B) { powBench(b, 1000, 6) }
+func BenchmarkPow10_7(b *testing.B)   { powBench(b, 10, 7) }
+func BenchmarkPow100_7(b *testing.B)  { powBench(b, 100, 7) }
+func BenchmarkPow1000_7(b *testing.B) { powBench(b, 1000, 7) }
+func BenchmarkPow10_8(b *testing.B)   { powBench(b, 10, 8) }
+func BenchmarkPow100_8(b *testing.B)  { powBench(b, 100, 8) }
+func BenchmarkPow1000_8(b *testing.B) { powBench(b, 1000, 8) }
+func BenchmarkPow10_9(b *testing.B)   { powBench(b, 10, 9) }
+func BenchmarkPow100_9(b *testing.B)  { powBench(b, 100, 9) }
+func BenchmarkPow1000_9(b *testing.B) { powBench(b, 1000, 9) }
+
+func powBench(b *testing.B, size, n int) {
+	a, _ := randDense(size, 1, rand.NormFloat64)
+
+	b.ResetTimer()
+	var m Dense
+	for i := 0; i < b.N; i++ {
+		m.Pow(a, n)
+	}
+}
+
+func BenchmarkMulTransDense100Half(b *testing.B)        { denseMulTransBench(b, 100, 0.5) }
+func BenchmarkMulTransDense100Tenth(b *testing.B)       { denseMulTransBench(b, 100, 0.1) }
+func BenchmarkMulTransDense1000Half(b *testing.B)       { denseMulTransBench(b, 1000, 0.5) }
+func BenchmarkMulTransDense1000Tenth(b *testing.B)      { denseMulTransBench(b, 1000, 0.1) }
+func BenchmarkMulTransDense1000Hundredth(b *testing.B)  { denseMulTransBench(b, 1000, 0.01) }
+func BenchmarkMulTransDense1000Thousandth(b *testing.B) { denseMulTransBench(b, 1000, 0.001) }
+func denseMulTransBench(b *testing.B, size int, rho float64) {
+	b.StopTimer()
+	a, _ := randDense(size, rho, rand.NormFloat64)
+	d, _ := randDense(size, rho, rand.NormFloat64)
+	b.StartTimer()
+	for i := 0; i < b.N; i++ {
+		var n Dense
+		n.Mul(a, d.T())
+		wd = &n
+	}
+}
+
+func BenchmarkMulTransDenseSym100Half(b *testing.B)        { denseMulTransSymBench(b, 100, 0.5) }
+func BenchmarkMulTransDenseSym100Tenth(b *testing.B)       { denseMulTransSymBench(b, 100, 0.1) }
+func BenchmarkMulTransDenseSym1000Half(b *testing.B)       { denseMulTransSymBench(b, 1000, 0.5) }
+func BenchmarkMulTransDenseSym1000Tenth(b *testing.B)      { denseMulTransSymBench(b, 1000, 0.1) }
+func BenchmarkMulTransDenseSym1000Hundredth(b *testing.B)  { denseMulTransSymBench(b, 1000, 0.01) }
+func BenchmarkMulTransDenseSym1000Thousandth(b *testing.B) { denseMulTransSymBench(b, 1000, 0.001) }
+func denseMulTransSymBench(b *testing.B, size int, rho float64) {
+	b.StopTimer()
+	a, _ := randDense(size, rho, rand.NormFloat64)
+	b.StartTimer()
+	for i := 0; i < b.N; i++ {
+		var n Dense
+		n.Mul(a, a.T())
+		wd = &n
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/doc.go b/vendor/gonum.org/v1/gonum/mat/doc.go
new file mode 100644
index 00000000..eecb742c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/doc.go
@@ -0,0 +1,173 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package mat provides implementations of float64 and complex128 matrix
+// structures and linear algebra operations on them.
+//
+// Overview
+//
+// This section provides a quick overview of the mat package. The following
+// sections provide more in depth commentary.
+//
+// mat provides:
+//  - Interfaces for Matrix classes (Matrix, Symmetric, Triangular)
+//  - Concrete implementations (Dense, SymDense, TriDense)
+//  - Methods and functions for using matrix data (Add, Trace, SymRankOne)
+//  - Types for constructing and using matrix factorizations (QR, LU)
+//  - The complementary types for complex matrices, CMatrix, CSymDense, etc.
+//
+// A matrix may be constructed through the corresponding New function. If no
+// backing array is provided the matrix will be initialized to all zeros.
+//  // Allocate a zeroed real matrix of size 3×5
+//  zero := mat.NewDense(3, 5, nil)
+// If a backing data slice is provided, the matrix will have those elements.
+// Matrices are all stored in row-major format.
+//  // Generate a 6×6 matrix of random values.
+//  data := make([]float64, 36)
+//  for i := range data {
+//  	data[i] = rand.NormFloat64()
+//  }
+//  a := mat.NewDense(6, 6, data)
+// Operations involving matrix data are implemented as functions when the values
+// of the matrix remain unchanged
+//  tr := mat.Trace(a)
+// and are implemented as methods when the operation modifies the receiver.
+//  zero.Copy(a)
+//
+// Receivers must be the correct size for the matrix operations, otherwise the
+// operation will panic. As a special case for convenience, a zero-value matrix
+// will be modified to have the correct size, allocating data if necessary.
+//  var c mat.Dense // construct a new zero-sized matrix
+//  c.Mul(a, a)     // c is automatically adjusted to be 6×6
+//
+// Zero-value of a matrix
+//
+// A zero-value matrix is either the Go language definition of a zero-value or
+// is a zero-sized matrix with zero-length stride. Matrix implementations may have
+// a Reset method to revert the receiver into a zero-valued matrix and an IsZero
+// method that returns whether the matrix is zero-valued.
+// So the following will all result in a zero-value matrix.
+//  - var a mat.Dense
+//  - a := NewDense(0, 0, make([]float64, 0, 100))
+//  - a.Reset()
+// A zero-value matrix can not be sliced even if it does have an adequately sized
+// backing data slice, but can be expanded using its Grow method if it exists.
+//
+// The Matrix Interfaces
+//
+// The Matrix interface is the common link between the concrete types of real
+// matrices, The Matrix interface is defined by three functions: Dims, which
+// returns the dimensions of the Matrix, At, which returns the element in the
+// specified location, and T for returning a Transpose (discussed later). All of
+// the concrete types can perform these behaviors and so implement the interface.
+// Methods and functions are designed to use this interface, so in particular the method
+//  func (m *Dense) Mul(a, b Matrix)
+// constructs a *Dense from the result of a multiplication with any Matrix types,
+// not just *Dense. Where more restrictive requirements must be met, there are also the
+// Symmetric and Triangular interfaces. For example, in
+//  func (s *SymDense) AddSym(a, b Symmetric)
+// the Symmetric interface guarantees a symmetric result.
+//
+// The CMatrix interface plays the same role for complex matrices. The difference
+// is that the CMatrix type has the H method instead T, for returning the conjugate
+// transpose.
+//
+// (Conjugate) Transposes
+//
+// The T method is used for transposition on real matrices, and H is used for
+// conjugate transposition on complex matrices. For example, c.Mul(a.T(), b) computes
+// c = a^T * b. The mat types implement this method implicitly —
+// see the Transpose and Conjugate types for more details. Note that some
+// operations have a transpose as part of their definition, as in *SymDense.SymOuterK.
+//
+// Matrix Factorization
+//
+// Matrix factorizations, such as the LU decomposition, typically have their own
+// specific data storage, and so are each implemented as a specific type. The
+// factorization can be computed through a call to Factorize
+//  var lu mat.LU
+//  lu.Factorize(a)
+// The elements of the factorization can be extracted through methods on the
+// factorized type, i.e. *LU.UTo. The factorization types can also be used directly,
+// as in *Dense.SolveCholesky. Some factorizations can be updated directly,
+// without needing to update the original matrix and refactorize,
+// as in *LU.RankOne.
+//
+// BLAS and LAPACK
+//
+// BLAS and LAPACK are the standard APIs for linear algebra routines. Many
+// operations in mat are implemented using calls to the wrapper functions
+// in gonum/blas/blas64 and gonum/lapack/lapack64 and their complex equivalents.
+// By default, blas64 and lapack64 call the native Go implementations of the
+// routines. Alternatively, it is possible to use C-based implementations of the
+// APIs through the respective cgo packages and "Use" functions. The Go
+// implementation of LAPACK (used by default) makes calls
+// through blas64, so if a cgo BLAS implementation is registered, the lapack64
+// calls will be partially executed in Go and partially executed in C.
+//
+// Type Switching
+//
+// The Matrix abstraction enables efficiency as well as interoperability. Go's
+// type reflection capabilities are used to choose the most efficient routine
+// given the specific concrete types. For example, in
+//  c.Mul(a, b)
+// if a and b both implement RawMatrixer, that is, they can be represented as a
+// blas64.General, blas64.Gemm (general matrix multiplication) is called, while
+// instead if b is a RawSymmetricer blas64.Symm is used (general-symmetric
+// multiplication), and if b is a *VecDense blas64.Gemv is used.
+//
+// There are many possible type combinations and special cases. No specific guarantees
+// are made about the performance of any method, and in particular, note that an
+// abstract matrix type may be copied into a concrete type of the corresponding
+// value. If there are specific special cases that are needed, please submit a
+// pull-request or file an issue.
+//
+// Invariants
+//
+// Matrix input arguments to functions are never directly modified. If an operation
+// changes Matrix data, the mutated matrix will be the receiver of a function.
+//
+// For convenience, a matrix may be used as both a receiver and as an input, e.g.
+//  a.Pow(a, 6)
+//  v.SolveVec(a.T(), v)
+// though in many cases this will cause an allocation (see Element Aliasing).
+// An exception to this rule is Copy, which does not allow a.Copy(a.T()).
+//
+// Element Aliasing
+//
+// Most methods in mat modify receiver data. It is forbidden for the modified
+// data region of the receiver to overlap the used data area of the input
+// arguments. The exception to this rule is when the method receiver is equal to one
+// of the input arguments, as in the a.Pow(a, 6) call above, or its implicit transpose.
+//
+// This prohibition is to help avoid subtle mistakes when the method needs to read
+// from and write to the same data region. There are ways to make mistakes using the
+// mat API, and mat functions will detect and complain about those.
+// There are many ways to make mistakes by excursion from the mat API via
+// interaction with raw matrix values.
+//
+// If you need to read the rest of this section to understand the behavior of
+// your program, you are being clever. Don't be clever. If you must be clever,
+// blas64 and lapack64 may be used to call the behavior directly.
+//
+// mat will use the following rules to detect overlap between the receiver and one
+// of the inputs:
+//  - the input implements one of the Raw methods, and
+//  - the Raw type matches that of the receiver or
+//    one is a RawMatrixer and the other is a RawVectorer, and
+//  - the address ranges of the backing data slices overlap, and
+//  - the strides differ or there is an overlap in the used data elements.
+// If such an overlap is detected, the method will panic.
+//
+// The following cases will not panic:
+//  - the data slices do not overlap,
+//  - there is pointer identity between the receiver and input values after
+//    the value has been untransposed if necessary.
+//
+// mat will not attempt to detect element overlap if the input does not implement a
+// Raw method, or if the Raw method differs from that of the receiver except when a
+// conversion has occurred through a mat API function. Method behavior is undefined
+// if there is undetected overlap.
+//
+package mat // import "gonum.org/v1/gonum/mat"
diff --git a/vendor/gonum.org/v1/gonum/mat/eigen.go b/vendor/gonum.org/v1/gonum/mat/eigen.go
new file mode 100644
index 00000000..0c677a8a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/eigen.go
@@ -0,0 +1,260 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"gonum.org/v1/gonum/lapack"
+	"gonum.org/v1/gonum/lapack/lapack64"
+)
+
+const (
+	badFact   = "mat: use without successful factorization"
+	badNoVect = "mat: eigenvectors not computed"
+)
+
+// EigenSym is a type for creating and manipulating the Eigen decomposition of
+// symmetric matrices.
+type EigenSym struct {
+	vectorsComputed bool
+
+	values  []float64
+	vectors *Dense
+}
+
+// Factorize computes the eigenvalue decomposition of the symmetric matrix a.
+// The Eigen decomposition is defined as
+//  A = P * D * P^-1
+// where D is a diagonal matrix containing the eigenvalues of the matrix, and
+// P is a matrix of the eigenvectors of A. If the vectors input argument is
+// false, the eigenvectors are not computed.
+//
+// Factorize returns whether the decomposition succeeded. If the decomposition
+// failed, methods that require a successful factorization will panic.
+func (e *EigenSym) Factorize(a Symmetric, vectors bool) (ok bool) {
+	n := a.Symmetric()
+	sd := NewSymDense(n, nil)
+	sd.CopySym(a)
+
+	jobz := lapack.EVJob(lapack.None)
+	if vectors {
+		jobz = lapack.ComputeEV
+	}
+	w := make([]float64, n)
+	work := []float64{0}
+	lapack64.Syev(jobz, sd.mat, w, work, -1)
+
+	work = getFloats(int(work[0]), false)
+	ok = lapack64.Syev(jobz, sd.mat, w, work, len(work))
+	putFloats(work)
+	if !ok {
+		e.vectorsComputed = false
+		e.values = nil
+		e.vectors = nil
+		return false
+	}
+	e.vectorsComputed = vectors
+	e.values = w
+	e.vectors = NewDense(n, n, sd.mat.Data)
+	return true
+}
+
+// succFact returns whether the receiver contains a successful factorization.
+func (e *EigenSym) succFact() bool {
+	return len(e.values) != 0
+}
+
+// Values extracts the eigenvalues of the factorized matrix. If dst is
+// non-nil, the values are stored in-place into dst. In this case
+// dst must have length n, otherwise Values will panic. If dst is
+// nil, then a new slice will be allocated of the proper length and filled
+// with the eigenvalues.
+//
+// Values panics if the Eigen decomposition was not successful.
+func (e *EigenSym) Values(dst []float64) []float64 {
+	if !e.succFact() {
+		panic(badFact)
+	}
+	if dst == nil {
+		dst = make([]float64, len(e.values))
+	}
+	if len(dst) != len(e.values) {
+		panic(ErrSliceLengthMismatch)
+	}
+	copy(dst, e.values)
+	return dst
+}
+
+// EigenvectorsSym extracts the eigenvectors of the factorized matrix and stores
+// them in the receiver. Each eigenvector is a column corresponding to the
+// respective eigenvalue returned by e.Values.
+//
+// EigenvectorsSym panics if the factorization was not successful or if the
+// decomposition did not compute the eigenvectors.
+func (m *Dense) EigenvectorsSym(e *EigenSym) {
+	if !e.succFact() {
+		panic(badFact)
+	}
+	if !e.vectorsComputed {
+		panic(badNoVect)
+	}
+	m.reuseAs(len(e.values), len(e.values))
+	m.Copy(e.vectors)
+}
+
+// Eigen is a type for creating and using the eigenvalue decomposition of a dense matrix.
+type Eigen struct {
+	n int // The size of the factorized matrix.
+
+	right bool // have the right eigenvectors been computed
+	left  bool // have the left eigenvectors been computed
+
+	values   []complex128
+	rVectors *Dense
+	lVectors *Dense
+}
+
+// succFact returns whether the receiver contains a successful factorization.
+func (e *Eigen) succFact() bool {
+	return len(e.values) != 0
+}
+
+// Factorize computes the eigenvalues of the square matrix a, and optionally
+// the eigenvectors.
+//
+// A right eigenvalue/eigenvector combination is defined by
+//  A * x_r = λ * x_r
+// where x_r is the column vector called an eigenvector, and λ is the corresponding
+// eigenvector.
+//
+// Similarly, a left eigenvalue/eigenvector combination is defined by
+//  x_l * A = λ * x_l
+// The eigenvalues, but not the eigenvectors, are the same for both decompositions.
+//
+// Typically eigenvectors refer to right eigenvectors.
+//
+// In all cases, Eigen computes the eigenvalues of the matrix. If right and left
+// are true, then the right and left eigenvectors will be computed, respectively.
+// Eigen panics if the input matrix is not square.
+//
+// Factorize returns whether the decomposition succeeded. If the decomposition
+// failed, methods that require a successful factorization will panic.
+func (e *Eigen) Factorize(a Matrix, left, right bool) (ok bool) {
+	// TODO(btracey): Change implementation to store VecDenses as a *CMat when
+	// #308 is resolved.
+
+	// Copy a because it is modified during the Lapack call.
+	r, c := a.Dims()
+	if r != c {
+		panic(ErrShape)
+	}
+	var sd Dense
+	sd.Clone(a)
+
+	var vl, vr Dense
+	var jobvl lapack.LeftEVJob = lapack.None
+	var jobvr lapack.RightEVJob = lapack.None
+	if left {
+		vl = *NewDense(r, r, nil)
+		jobvl = lapack.ComputeLeftEV
+	}
+	if right {
+		vr = *NewDense(c, c, nil)
+		jobvr = lapack.ComputeRightEV
+	}
+
+	wr := getFloats(c, false)
+	defer putFloats(wr)
+	wi := getFloats(c, false)
+	defer putFloats(wi)
+
+	work := []float64{0}
+	lapack64.Geev(jobvl, jobvr, sd.mat, wr, wi, vl.mat, vr.mat, work, -1)
+	work = getFloats(int(work[0]), false)
+	first := lapack64.Geev(jobvl, jobvr, sd.mat, wr, wi, vl.mat, vr.mat, work, len(work))
+	putFloats(work)
+
+	if first != 0 {
+		e.values = nil
+		return false
+	}
+	e.n = r
+	e.right = right
+	e.left = left
+	e.lVectors = &vl
+	e.rVectors = &vr
+	values := make([]complex128, r)
+	for i, v := range wr {
+		values[i] = complex(v, wi[i])
+	}
+	e.values = values
+	return true
+}
+
+// Values extracts the eigenvalues of the factorized matrix. If dst is
+// non-nil, the values are stored in-place into dst. In this case
+// dst must have length n, otherwise Values will panic. If dst is
+// nil, then a new slice will be allocated of the proper length and
+// filed with the eigenvalues.
+//
+// Values panics if the Eigen decomposition was not successful.
+func (e *Eigen) Values(dst []complex128) []complex128 {
+	if !e.succFact() {
+		panic(badFact)
+	}
+	if dst == nil {
+		dst = make([]complex128, e.n)
+	}
+	if len(dst) != e.n {
+		panic(ErrSliceLengthMismatch)
+	}
+	copy(dst, e.values)
+	return dst
+}
+
+// Vectors returns the right eigenvectors of the decomposition. Vectors
+// will panic if the right eigenvectors were not computed during the factorization,
+// or if the factorization was not successful.
+//
+// The returned matrix will contain the right eigenvectors of the decomposition
+// in the columns of the n×n matrix in the same order as their eigenvalues.
+// If the j-th eigenvalue is real, then
+//  u_j = VL[:,j],
+//  v_j = VR[:,j],
+// and if it is not real, then j and j+1 form a complex conjugate pair and the
+// eigenvectors can be recovered as
+//  u_j     = VL[:,j] + i*VL[:,j+1],
+//  u_{j+1} = VL[:,j] - i*VL[:,j+1],
+//  v_j     = VR[:,j] + i*VR[:,j+1],
+//  v_{j+1} = VR[:,j] - i*VR[:,j+1],
+// where i is the imaginary unit. The computed eigenvectors are normalized to
+// have Euclidean norm equal to 1 and largest component real.
+//
+// BUG: This signature and behavior will change when issue #308 is resolved.
+func (e *Eigen) Vectors() *Dense {
+	if !e.succFact() {
+		panic(badFact)
+	}
+	if !e.right {
+		panic(badNoVect)
+	}
+	return DenseCopyOf(e.rVectors)
+}
+
+// LeftVectors returns the left eigenvectors of the decomposition. LeftVectors
+// will panic if the left eigenvectors were not computed during the factorization.
+// or if the factorization was not successful.
+//
+// See the documentation in lapack64.Geev for the format of the vectors.
+//
+// BUG: This signature and behavior will change when issue #308 is resolved.
+func (e *Eigen) LeftVectors() *Dense {
+	if !e.succFact() {
+		panic(badFact)
+	}
+	if !e.left {
+		panic(badNoVect)
+	}
+	return DenseCopyOf(e.lVectors)
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/eigen_test.go b/vendor/gonum.org/v1/gonum/mat/eigen_test.go
new file mode 100644
index 00000000..1980fbe4
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/eigen_test.go
@@ -0,0 +1,164 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+func TestEigen(t *testing.T) {
+	for i, test := range []struct {
+		a *Dense
+
+		values []complex128
+		left   *Dense
+		right  *Dense
+	}{
+		{
+			a: NewDense(3, 3, []float64{
+				1, 0, 0,
+				0, 1, 0,
+				0, 0, 1,
+			}),
+			values: []complex128{1, 1, 1},
+			left: NewDense(3, 3, []float64{
+				1, 0, 0,
+				0, 1, 0,
+				0, 0, 1,
+			}),
+			right: NewDense(3, 3, []float64{
+				1, 0, 0,
+				0, 1, 0,
+				0, 0, 1,
+			}),
+		},
+	} {
+		var e1, e2, e3, e4 Eigen
+		ok := e1.Factorize(test.a, true, true)
+		if !ok {
+			panic("bad factorization")
+		}
+		e2.Factorize(test.a, false, true)
+		e3.Factorize(test.a, true, false)
+		e4.Factorize(test.a, false, false)
+
+		v1 := e1.Values(nil)
+		if !cmplxEqual(v1, test.values) {
+			t.Errorf("eigenvector mismatch. Case %v", i)
+		}
+		if !Equal(e1.LeftVectors(), test.left) {
+			t.Errorf("left eigenvector mismatch. Case %v", i)
+		}
+		if !Equal(e1.Vectors(), test.right) {
+			t.Errorf("right eigenvector mismatch. Case %v", i)
+		}
+
+		// Check that the eigenvectors and values are the same in all combinations.
+		if !cmplxEqual(v1, e2.Values(nil)) {
+			t.Errorf("eigenvector mismatch. Case %v", i)
+		}
+		if !cmplxEqual(v1, e3.Values(nil)) {
+			t.Errorf("eigenvector mismatch. Case %v", i)
+		}
+		if !cmplxEqual(v1, e4.Values(nil)) {
+			t.Errorf("eigenvector mismatch. Case %v", i)
+		}
+		if !Equal(e1.Vectors(), e2.Vectors()) {
+			t.Errorf("right eigenvector mismatch. Case %v", i)
+		}
+		if !Equal(e1.LeftVectors(), e3.LeftVectors()) {
+			t.Errorf("right eigenvector mismatch. Case %v", i)
+		}
+
+		// TODO(btracey): Also add in a test for correctness when #308 is
+		// resolved and we have a CMat.Mul().
+	}
+}
+
+func cmplxEqual(v1, v2 []complex128) bool {
+	for i, v := range v1 {
+		if v != v2[i] {
+			return false
+		}
+	}
+	return true
+}
+
+func TestSymEigen(t *testing.T) {
+	// Hand coded tests with results from lapack.
+	for _, test := range []struct {
+		mat *SymDense
+
+		values  []float64
+		vectors *Dense
+	}{
+		{
+			mat:    NewSymDense(3, []float64{8, 2, 4, 2, 6, 10, 4, 10, 5}),
+			values: []float64{-4.707679201365891, 6.294580208480216, 17.413098992885672},
+			vectors: NewDense(3, 3, []float64{
+				-0.127343483135656, -0.902414161226903, -0.411621572466779,
+				-0.664177720955769, 0.385801900032553, -0.640331827193739,
+				0.736648893495999, 0.191847792659746, -0.648492738712395,
+			}),
+		},
+	} {
+		var es EigenSym
+		ok := es.Factorize(test.mat, true)
+		if !ok {
+			t.Errorf("bad factorization")
+		}
+		if !floats.EqualApprox(test.values, es.values, 1e-14) {
+			t.Errorf("Eigenvalue mismatch")
+		}
+		if !EqualApprox(test.vectors, es.vectors, 1e-14) {
+			t.Errorf("Eigenvector mismatch")
+		}
+
+		var es2 EigenSym
+		es2.Factorize(test.mat, false)
+		if !floats.EqualApprox(es2.values, es.values, 1e-14) {
+			t.Errorf("Eigenvalue mismatch when no vectors computed")
+		}
+	}
+
+	// Randomized tests
+	rnd := rand.New(rand.NewSource(1))
+	for _, n := range []int{3, 5, 10, 70} {
+		for cas := 0; cas < 10; cas++ {
+			a := make([]float64, n*n)
+			for i := range a {
+				a[i] = rnd.NormFloat64()
+			}
+			s := NewSymDense(n, a)
+			var es EigenSym
+			ok := es.Factorize(s, true)
+			if !ok {
+				t.Errorf("Bad test")
+			}
+
+			// Check that the eigenvectors are orthonormal.
+			if !isOrthonormal(es.vectors, 1e-8) {
+				t.Errorf("Eigenvectors not orthonormal")
+			}
+
+			// Check that the eigenvalues are actually eigenvalues.
+			for i := 0; i < n; i++ {
+				v := NewVecDense(n, Col(nil, i, es.vectors))
+				var m VecDense
+				m.MulVec(s, v)
+
+				var scal VecDense
+				scal.ScaleVec(es.values[i], v)
+
+				if !EqualApprox(&m, &scal, 1e-8) {
+					t.Errorf("Eigenvalue does not match")
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/errors.go b/vendor/gonum.org/v1/gonum/mat/errors.go
new file mode 100644
index 00000000..38bd7d5a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/errors.go
@@ -0,0 +1,148 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"fmt"
+	"runtime"
+
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Condition is the condition number of a matrix. The condition
+// number is defined as |A| * |A^-1|.
+//
+// One important use of Condition is during linear solve routines (finding x such
+// that A * x = b). The condition number of A indicates the accuracy of
+// the computed solution. A Condition error will be returned if the condition
+// number of A is sufficiently large. If A is exactly singular to working precision,
+// Condition == ∞, and the solve algorithm may have completed early. If Condition
+// is large and finite the solve algorithm will be performed, but the computed
+// solution may be innacurate. Due to the nature of finite precision arithmetic,
+// the value of Condition is only an approximate test of singularity.
+type Condition float64
+
+func (c Condition) Error() string {
+	return fmt.Sprintf("matrix singular or near-singular with condition number %.4e", c)
+}
+
+// ConditionTolerance is the tolerance limit of the condition number. If the
+// condition number is above this value, the matrix is considered singular.
+const ConditionTolerance = 1e16
+
+const (
+	// CondNorm is the matrix norm used for computing the condition number by routines
+	// in the matrix packages.
+	CondNorm = lapack.MaxRowSum
+
+	// CondNormTrans is the norm used to compute on A^T to get the same result as
+	// computing CondNorm on A.
+	CondNormTrans = lapack.MaxColumnSum
+)
+
+const stackTraceBufferSize = 1 << 20
+
+// Maybe will recover a panic with a type mat.Error from fn, and return this error
+// as the Err field of an ErrorStack. The stack trace for the panicking function will be
+// recovered and placed in the StackTrace field. Any other error is re-panicked.
+func Maybe(fn func()) (err error) {
+	defer func() {
+		if r := recover(); r != nil {
+			if e, ok := r.(Error); ok {
+				if e.string == "" {
+					panic("mat: invalid error")
+				}
+				buf := make([]byte, stackTraceBufferSize)
+				n := runtime.Stack(buf, false)
+				err = ErrorStack{Err: e, StackTrace: string(buf[:n])}
+				return
+			}
+			panic(r)
+		}
+	}()
+	fn()
+	return
+}
+
+// MaybeFloat will recover a panic with a type mat.Error from fn, and return this error
+// as the Err field of an ErrorStack. The stack trace for the panicking function will be
+// recovered and placed in the StackTrace field. Any other error is re-panicked.
+func MaybeFloat(fn func() float64) (f float64, err error) {
+	defer func() {
+		if r := recover(); r != nil {
+			if e, ok := r.(Error); ok {
+				if e.string == "" {
+					panic("mat: invalid error")
+				}
+				buf := make([]byte, stackTraceBufferSize)
+				n := runtime.Stack(buf, false)
+				err = ErrorStack{Err: e, StackTrace: string(buf[:n])}
+				return
+			}
+			panic(r)
+		}
+	}()
+	return fn(), nil
+}
+
+// MaybeComplex will recover a panic with a type mat.Error from fn, and return this error
+// as the Err field of an ErrorStack. The stack trace for the panicking function will be
+// recovered and placed in the StackTrace field. Any other error is re-panicked.
+func MaybeComplex(fn func() complex128) (f complex128, err error) {
+	defer func() {
+		if r := recover(); r != nil {
+			if e, ok := r.(Error); ok {
+				if e.string == "" {
+					panic("mat: invalid error")
+				}
+				buf := make([]byte, stackTraceBufferSize)
+				n := runtime.Stack(buf, false)
+				err = ErrorStack{Err: e, StackTrace: string(buf[:n])}
+				return
+			}
+			panic(r)
+		}
+	}()
+	return fn(), nil
+}
+
+// Error represents matrix handling errors. These errors can be recovered by Maybe wrappers.
+type Error struct{ string }
+
+func (err Error) Error() string { return err.string }
+
+var (
+	ErrIndexOutOfRange     = Error{"matrix: index out of range"}
+	ErrRowAccess           = Error{"matrix: row index out of range"}
+	ErrColAccess           = Error{"matrix: column index out of range"}
+	ErrVectorAccess        = Error{"matrix: vector index out of range"}
+	ErrZeroLength          = Error{"matrix: zero length in matrix definition"}
+	ErrRowLength           = Error{"matrix: row length mismatch"}
+	ErrColLength           = Error{"matrix: col length mismatch"}
+	ErrSquare              = Error{"matrix: expect square matrix"}
+	ErrNormOrder           = Error{"matrix: invalid norm order for matrix"}
+	ErrSingular            = Error{"matrix: matrix is singular"}
+	ErrShape               = Error{"matrix: dimension mismatch"}
+	ErrIllegalStride       = Error{"matrix: illegal stride"}
+	ErrPivot               = Error{"matrix: malformed pivot list"}
+	ErrTriangle            = Error{"matrix: triangular storage mismatch"}
+	ErrTriangleSet         = Error{"matrix: triangular set out of bounds"}
+	ErrBandSet             = Error{"matrix: band set out of bounds"}
+	ErrSliceLengthMismatch = Error{"matrix: input slice length mismatch"}
+	ErrNotPSD              = Error{"matrix: input not positive symmetric definite"}
+	ErrFailedEigen         = Error{"matrix: eigendecomposition not successful"}
+)
+
+// ErrorStack represents matrix handling errors that have been recovered by Maybe wrappers.
+type ErrorStack struct {
+	Err error
+
+	// StackTrace is the stack trace
+	// recovered by Maybe, MaybeFloat
+	// or MaybeComplex.
+	StackTrace string
+}
+
+func (err ErrorStack) Error() string { return err.Err.Error() }
diff --git a/vendor/gonum.org/v1/gonum/mat/errors_test.go b/vendor/gonum.org/v1/gonum/mat/errors_test.go
new file mode 100644
index 00000000..7a1a7dd7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/errors_test.go
@@ -0,0 +1,56 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import "testing"
+
+func leaksPanic(fn func()) (panicked bool) {
+	defer func() {
+		r := recover()
+		panicked = r != nil
+	}()
+	Maybe(fn)
+	return
+}
+
+func TestMaybe(t *testing.T) {
+	for i, test := range []struct {
+		fn     func()
+		panics bool
+		errors bool
+	}{
+		{
+			fn:     func() {},
+			panics: false,
+			errors: false,
+		},
+		{
+			fn:     func() { panic("panic") },
+			panics: true,
+			errors: false,
+		},
+		{
+			fn:     func() { panic(Error{"panic"}) },
+			panics: false,
+			errors: true,
+		},
+	} {
+		panicked := leaksPanic(test.fn)
+		if panicked != test.panics {
+			t.Errorf("unexpected panic state for test %d: got: panicked=%t want: panicked=%t",
+				i, panicked, test.panics)
+		}
+		if test.errors {
+			err := Maybe(test.fn)
+			stack, ok := err.(ErrorStack)
+			if !ok {
+				t.Errorf("unexpected error type: got:%T want:%T", stack, ErrorStack{})
+			}
+			if stack.StackTrace == "" {
+				t.Error("expected non-empty stack trace")
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/fao_data_test.go b/vendor/gonum.org/v1/gonum/mat/fao_data_test.go
new file mode 100644
index 00000000..e32e1676
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/fao_data_test.go
@@ -0,0 +1,122 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat_test
+
+import "gonum.org/v1/gonum/mat"
+
+// FAO is a dataset extracted from Food and Agriculture Organization of the
+// United Nations "FAO Statistical Pocketbook: World Food and Agriculture 2015".
+// pp49-52.
+var FAO = struct {
+	Africa                *mat.Dense
+	Asia                  *mat.Dense
+	LatinAmericaCaribbean *mat.Dense
+	Oceania               *mat.Dense
+}{
+	Africa: mat.NewDense(21, 3, []float64{
+		// 1990, 2000, 2014
+		35.3, 38, 30.7, // Employment in agriculture (%)
+		9.2, 20.3, 25.2, // Employment in agriculture, female (%)
+		3163, 14718, 20667, // Energy consump, power irrigation (mln kWh)
+
+		2597, 2717, 2903, // Dietary energy supply (kcal/pc/day)
+		113, 116, 123, // Average dietary energy supply adequacy (%)
+		58, 55, 52, // Dietary en supp, cereals/roots/tubers (%)
+		18.6, 15, 10.8, // Prevalence of undernourishment (%)
+		8832, 10241, 13915, // GDP per capita (US$, PPP)
+		-0.4, -0.2, 50.7, // Cereal import dependency ratio (%)
+		78.5, 83, 88.7, // Improved water source (% pop)
+
+		// Production indices (2004-06=100)
+		73, 90, 121, // Net food
+		72, 89, 123, // Net crops
+		82, 92, 123, // Cereals
+		51, 77, 141, // Vegetable oils
+		74, 94, 119, // Roots and tubers
+		58, 86, 127, // Fruit and vegetables
+		86, 93, 132, // Sugar
+		76, 92, 115, // Livestock
+		83, 89, 114, // Milk
+		74, 91, 118, // Meat
+		72, 92, 119, // Fish
+	}),
+
+	Asia: mat.NewDense(21, 3, []float64{
+		// 1990, 2000, 2014
+		30.9, 24.5, 27.6, // Employment in agriculture (%)
+		40.9, 29.4, 31.1, // Employment in agriculture, female (%)
+		7614, 38316, 82411, // Energy consump, power irrigation (mln kWh)
+
+		2320, 2402, 2581, // Dietary energy supply (kcal/pc/day)
+		107, 110, 117, // Average dietary energy supply adequacy (%)
+		66, 65, 63, // Dietary en supp, cereals/roots/tubers (%)
+		27.6, 25.7, 19.8, // Prevalence of undernourishment (%)
+		3315, 3421, 4575, // GDP per capita (US$, PPP)
+		25.9, 28.1, 42, // Cereal import dependency ratio (%)
+		55.5, 61.1, 68.7, // Improved water source (% pop)
+
+		// Production indices (2004-06=100)
+		60, 82, 129, // Net food
+		59, 82, 127, // Net crops
+		66, 79, 131, // Cereals
+		58, 79, 128, // Vegetable oils
+		50, 80, 133, // Roots and tubers
+		58, 82, 124, // Fruit and vegetables
+		76, 94, 114, // Sugar
+		65, 84, 126, // Livestock
+		59, 77, 125, // Milk
+		67, 87, 127, // Meat
+		65, 90, 119, // Fish
+	}),
+
+	LatinAmericaCaribbean: mat.NewDense(14, 3, []float64{
+		// 1990, 2000, 2014
+		19.5, 14.2, 15.8, // Employment in agriculture (%)
+		13.7, 6.2, 7.6, // Employment in agriculture, female (%)
+
+		2669, 2787, 3069, // Dietary energy supply (kcal/pc/day)
+		117, 120, 129, // Average dietary energy supply adequacy (%)
+		42, 41, 40, // Dietary en supp, cereals/roots/tubers (%)
+		14.7, 12.1, 5.5, // Prevalence of undernourishment (%)
+		9837, 10976, 13915, // GDP per capita (US$, PPP)
+		13, 12, 49.7, // Cereal import dependency ratio (%)
+		85.1, 89.8, 94, // Improved water source (% pop)
+
+		// Production indices (2004-06=100)
+		60, 83, 129, // Net food
+		64, 83, 131, // Net crops
+		62, 88, 139, // Cereals
+		58, 84, 123, // Livestock
+		82, 107, 71, // Fish
+	}),
+
+	Oceania: mat.NewDense(21, 3, []float64{
+		// 1990, 2000, 2014
+		6.2, 17.1, 3.8, // Employment in agriculture (%)
+		4.5, 3.9, 4.4, // Employment in agriculture, female (%)
+		415, 1028, 8667, // Energy consump, power irrigation (mln kWh)
+
+		2454, 2436, 2542, // Dietary energy supply (kcal/pc/day)
+		113, 112, 114, // Average dietary energy supply adequacy (%)
+		49, 50, 48, // Dietary en supp, cereals/roots/tubers (%)
+		15.7, 16.1, 14.2, // Prevalence of undernourishment (%)
+		2269, 2536, 3110, // GDP per capita (US$, PPP)
+		95.2, 95.9, 95.4, // Cereal import dependency ratio (%)
+		49.7, 53.2, 55.5, // Improved water source (% pop)
+
+		// Production indices (2004-06=100)
+		72, 99, 116, // Net food
+		69, 105, 126, // Net crops
+		77, 113, 117, // Cereals
+		41, 122, 215, // Vegetable oils
+		80, 90, 110, // Roots and tubers
+		66, 88, 104, // Fruit and vegetables
+		70, 104, 71, // Sugar
+		79, 97, 107, // Livestock
+		56, 92, 113, // Milk
+		79, 96, 105, // Meat
+		51, 78, 85, // Fish
+	}),
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/format.go b/vendor/gonum.org/v1/gonum/mat/format.go
new file mode 100644
index 00000000..8ab70ed3
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/format.go
@@ -0,0 +1,238 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"fmt"
+	"strconv"
+)
+
+// Formatted returns a fmt.Formatter for the matrix m using the given options.
+func Formatted(m Matrix, options ...FormatOption) fmt.Formatter {
+	f := formatter{
+		matrix: m,
+		dot:    '.',
+	}
+	for _, o := range options {
+		o(&f)
+	}
+	return f
+}
+
+type formatter struct {
+	matrix  Matrix
+	prefix  string
+	margin  int
+	dot     byte
+	squeeze bool
+}
+
+// FormatOption is a functional option for matrix formatting.
+type FormatOption func(*formatter)
+
+// Prefix sets the formatted prefix to the string p. Prefix is a string that is prepended to
+// each line of output.
+func Prefix(p string) FormatOption {
+	return func(f *formatter) { f.prefix = p }
+}
+
+// Excerpt sets the maximum number of rows and columns to print at the margins of the matrix
+// to m. If m is zero or less all elements are printed.
+func Excerpt(m int) FormatOption {
+	return func(f *formatter) { f.margin = m }
+}
+
+// DotByte sets the dot character to b. The dot character is used to replace zero elements
+// if the result is printed with the fmt ' ' verb flag. Without a DotByte option, the default
+// dot character is '.'.
+func DotByte(b byte) FormatOption {
+	return func(f *formatter) { f.dot = b }
+}
+
+// Squeeze sets the printing behaviour to minimise column width for each individual column.
+func Squeeze() FormatOption {
+	return func(f *formatter) { f.squeeze = true }
+}
+
+// Format satisfies the fmt.Formatter interface.
+func (f formatter) Format(fs fmt.State, c rune) {
+	if c == 'v' && fs.Flag('#') {
+		fmt.Fprintf(fs, "%#v", f.matrix)
+		return
+	}
+	format(f.matrix, f.prefix, f.margin, f.dot, f.squeeze, fs, c)
+}
+
+// format prints a pretty representation of m to the fs io.Writer. The format character c
+// specifies the numerical representation of of elements; valid values are those for float64
+// specified in the fmt package, with their associated flags. In addition to this, a space
+// preceding a verb indicates that zero values should be represented by the dot character.
+// The printed range of the matrix can be limited by specifying a positive value for margin;
+// If margin is greater than zero, only the first and last margin rows/columns of the matrix
+// are output. If squeeze is true, column widths are determined on a per-column basis.
+//
+// format will not provide Go syntax output.
+func format(m Matrix, prefix string, margin int, dot byte, squeeze bool, fs fmt.State, c rune) {
+	rows, cols := m.Dims()
+
+	var printed int
+	if margin <= 0 {
+		printed = rows
+		if cols > printed {
+			printed = cols
+		}
+	} else {
+		printed = margin
+	}
+
+	prec, pOk := fs.Precision()
+	if !pOk {
+		prec = -1
+	}
+
+	var (
+		maxWidth int
+		widths   widther
+		buf, pad []byte
+	)
+	if squeeze {
+		widths = make(columnWidth, cols)
+	} else {
+		widths = new(uniformWidth)
+	}
+	switch c {
+	case 'v', 'e', 'E', 'f', 'F', 'g', 'G':
+		if c == 'v' {
+			buf, maxWidth = maxCellWidth(m, 'g', printed, prec, widths)
+		} else {
+			buf, maxWidth = maxCellWidth(m, c, printed, prec, widths)
+		}
+	default:
+		fmt.Fprintf(fs, "%%!%c(%T=Dims(%d, %d))", c, m, rows, cols)
+		return
+	}
+	width, _ := fs.Width()
+	width = max(width, maxWidth)
+	pad = make([]byte, max(width, 2))
+	for i := range pad {
+		pad[i] = ' '
+	}
+
+	first := true
+	if rows > 2*printed || cols > 2*printed {
+		first = false
+		fmt.Fprintf(fs, "Dims(%d, %d)\n", rows, cols)
+	}
+
+	skipZero := fs.Flag(' ')
+	for i := 0; i < rows; i++ {
+		if !first {
+			fmt.Fprint(fs, prefix)
+		}
+		first = false
+		var el string
+		switch {
+		case rows == 1:
+			fmt.Fprint(fs, "[")
+			el = "]"
+		case i == 0:
+			fmt.Fprint(fs, "⎡")
+			el = "⎤\n"
+		case i < rows-1:
+			fmt.Fprint(fs, "⎢")
+			el = "⎥\n"
+		default:
+			fmt.Fprint(fs, "⎣")
+			el = "⎦"
+		}
+
+		for j := 0; j < cols; j++ {
+			if j >= printed && j < cols-printed {
+				j = cols - printed - 1
+				if i == 0 || i == rows-1 {
+					fmt.Fprint(fs, "...  ...  ")
+				} else {
+					fmt.Fprint(fs, "          ")
+				}
+				continue
+			}
+
+			v := m.At(i, j)
+			if v == 0 && skipZero {
+				buf = buf[:1]
+				buf[0] = dot
+			} else {
+				if c == 'v' {
+					buf = strconv.AppendFloat(buf[:0], v, 'g', prec, 64)
+				} else {
+					buf = strconv.AppendFloat(buf[:0], v, byte(c), prec, 64)
+				}
+			}
+			if fs.Flag('-') {
+				fs.Write(buf)
+				fs.Write(pad[:widths.width(j)-len(buf)])
+			} else {
+				fs.Write(pad[:widths.width(j)-len(buf)])
+				fs.Write(buf)
+			}
+
+			if j < cols-1 {
+				fs.Write(pad[:2])
+			}
+		}
+
+		fmt.Fprint(fs, el)
+
+		if i >= printed-1 && i < rows-printed && 2*printed < rows {
+			i = rows - printed - 1
+			fmt.Fprintf(fs, "%s .\n%[1]s .\n%[1]s .\n", prefix)
+			continue
+		}
+	}
+}
+
+func maxCellWidth(m Matrix, c rune, printed, prec int, w widther) ([]byte, int) {
+	var (
+		buf        = make([]byte, 0, 64)
+		rows, cols = m.Dims()
+		max        int
+	)
+	for i := 0; i < rows; i++ {
+		if i >= printed-1 && i < rows-printed && 2*printed < rows {
+			i = rows - printed - 1
+			continue
+		}
+		for j := 0; j < cols; j++ {
+			if j >= printed && j < cols-printed {
+				continue
+			}
+
+			buf = strconv.AppendFloat(buf, m.At(i, j), byte(c), prec, 64)
+			if len(buf) > max {
+				max = len(buf)
+			}
+			if len(buf) > w.width(j) {
+				w.setWidth(j, len(buf))
+			}
+			buf = buf[:0]
+		}
+	}
+	return buf, max
+}
+
+type widther interface {
+	width(i int) int
+	setWidth(i, w int)
+}
+
+type uniformWidth int
+
+func (u *uniformWidth) width(_ int) int   { return int(*u) }
+func (u *uniformWidth) setWidth(_, w int) { *u = uniformWidth(w) }
+
+type columnWidth []int
+
+func (c columnWidth) width(i int) int   { return c[i] }
+func (c columnWidth) setWidth(i, w int) { c[i] = w }
diff --git a/vendor/gonum.org/v1/gonum/mat/format_example_test.go b/vendor/gonum.org/v1/gonum/mat/format_example_test.go
new file mode 100644
index 00000000..59f26c70
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/format_example_test.go
@@ -0,0 +1,112 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat_test
+
+import (
+	"fmt"
+
+	"gonum.org/v1/gonum/mat"
+)
+
+func ExampleFormatted() {
+	a := mat.NewDense(3, 3, []float64{1, 2, 3, 0, 4, 5, 0, 0, 6})
+
+	// Create a matrix formatting value with a prefix and calculating each column
+	// width individually...
+	fa := mat.Formatted(a, mat.Prefix("    "), mat.Squeeze())
+
+	// and then print with and without zero value elements.
+	fmt.Printf("with all values:\na = %v\n\n", fa)
+	fmt.Printf("with only non-zero values:\na = % v\n\n", fa)
+
+	// Modify the matrix...
+	a.Set(0, 2, 0)
+
+	// and print it without zero value elements.
+	fmt.Printf("after modification with only non-zero values:\na = % v\n\n", fa)
+
+	// Modify the matrix again...
+	a.Set(0, 2, 123.456)
+
+	// and print it using scientific notation for large exponents.
+	fmt.Printf("after modification with scientific notation:\na = %.2g\n\n", fa)
+	// See golang.org/pkg/fmt/ floating-point verbs for a comprehensive list.
+
+	// Output:
+	// with all values:
+	// a = ⎡1  2  3⎤
+	//     ⎢0  4  5⎥
+	//     ⎣0  0  6⎦
+	//
+	// with only non-zero values:
+	// a = ⎡1  2  3⎤
+	//     ⎢.  4  5⎥
+	//     ⎣.  .  6⎦
+	//
+	// after modification with only non-zero values:
+	// a = ⎡1  2  .⎤
+	//     ⎢.  4  5⎥
+	//     ⎣.  .  6⎦
+	//
+	// after modification with scientific notation:
+	// a = ⎡1  2  1.2e+02⎤
+	//     ⎢0  4        5⎥
+	//     ⎣0  0        6⎦
+}
+
+func ExampleExcerpt() {
+	// Excerpt allows diagnostic display of very large
+	// matrices and vectors.
+
+	// The big matrix is too large to properly print...
+	big := mat.NewDense(100, 100, nil)
+	for i := 0; i < 100; i++ {
+		big.Set(i, i, 1)
+	}
+
+	// so only print corner excerpts of the matrix.
+	fmt.Printf("excerpt big identity matrix: %v\n\n",
+		mat.Formatted(big, mat.Prefix(" "), mat.Excerpt(3)))
+
+	// The long vector is also too large, ...
+	long := mat.NewVecDense(100, nil)
+	for i := 0; i < 100; i++ {
+		long.SetVec(i, float64(i))
+	}
+
+	// ... so print end excerpts of the vector,
+	fmt.Printf("excerpt long column vector: %v\n\n",
+		mat.Formatted(long, mat.Prefix(" "), mat.Excerpt(3)))
+	// or its transpose.
+	fmt.Printf("excerpt long row vector: %v\n",
+		mat.Formatted(long.T(), mat.Prefix(" "), mat.Excerpt(3)))
+
+	// Output:
+	// excerpt big identity matrix: Dims(100, 100)
+	//  ⎡1  0  0  ...  ...  0  0  0⎤
+	//  ⎢0  1  0            0  0  0⎥
+	//  ⎢0  0  1            0  0  0⎥
+	//   .
+	//   .
+	//   .
+	//  ⎢0  0  0            1  0  0⎥
+	//  ⎢0  0  0            0  1  0⎥
+	//  ⎣0  0  0  ...  ...  0  0  1⎦
+	//
+	// excerpt long column vector: Dims(100, 1)
+	//  ⎡ 0⎤
+	//  ⎢ 1⎥
+	//  ⎢ 2⎥
+	//   .
+	//   .
+	//   .
+	//  ⎢97⎥
+	//  ⎢98⎥
+	//  ⎣99⎦
+	//
+	// excerpt long row vector: Dims(1, 100)
+	//  [ 0   1   2  ...  ...  97  98  99]
+
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/format_test.go b/vendor/gonum.org/v1/gonum/mat/format_test.go
new file mode 100644
index 00000000..2b725571
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/format_test.go
@@ -0,0 +1,150 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"fmt"
+	"math"
+	"testing"
+)
+
+func TestFormat(t *testing.T) {
+	type rp struct {
+		format string
+		output string
+	}
+	sqrt := func(_, _ int, v float64) float64 { return math.Sqrt(v) }
+	for i, test := range []struct {
+		m   fmt.Formatter
+		rep []rp
+	}{
+		// Dense matrix representation
+		{
+			Formatted(NewDense(3, 3, []float64{0, 0, 0, 0, 0, 0, 0, 0, 0})),
+			[]rp{
+				{"%v", "⎡0  0  0⎤\n⎢0  0  0⎥\n⎣0  0  0⎦"},
+				{"% f", "⎡.  .  .⎤\n⎢.  .  .⎥\n⎣.  .  .⎦"},
+				{"%#v", "&mat.Dense{mat:blas64.General{Rows:3, Cols:3, Stride:3, Data:[]float64{0, 0, 0, 0, 0, 0, 0, 0, 0}}, capRows:3, capCols:3}"},
+				{"%s", "%!s(*mat.Dense=Dims(3, 3))"},
+			},
+		},
+		{
+			Formatted(NewDense(3, 3, []float64{1, 1, 1, 1, 1, 1, 1, 1, 1})),
+			[]rp{
+				{"%v", "⎡1  1  1⎤\n⎢1  1  1⎥\n⎣1  1  1⎦"},
+				{"% f", "⎡1  1  1⎤\n⎢1  1  1⎥\n⎣1  1  1⎦"},
+				{"%#v", "&mat.Dense{mat:blas64.General{Rows:3, Cols:3, Stride:3, Data:[]float64{1, 1, 1, 1, 1, 1, 1, 1, 1}}, capRows:3, capCols:3}"},
+			},
+		},
+		{
+			Formatted(NewDense(3, 3, []float64{1, 1, 1, 1, 1, 1, 1, 1, 1}), Prefix("\t")),
+			[]rp{
+				{"%v", "⎡1  1  1⎤\n\t⎢1  1  1⎥\n\t⎣1  1  1⎦"},
+				{"% f", "⎡1  1  1⎤\n\t⎢1  1  1⎥\n\t⎣1  1  1⎦"},
+				{"%#v", "&mat.Dense{mat:blas64.General{Rows:3, Cols:3, Stride:3, Data:[]float64{1, 1, 1, 1, 1, 1, 1, 1, 1}}, capRows:3, capCols:3}"},
+			},
+		},
+		{
+			Formatted(NewDense(3, 3, []float64{1, 0, 0, 0, 1, 0, 0, 0, 1})),
+			[]rp{
+				{"%v", "⎡1  0  0⎤\n⎢0  1  0⎥\n⎣0  0  1⎦"},
+				{"% f", "⎡1  .  .⎤\n⎢.  1  .⎥\n⎣.  .  1⎦"},
+				{"%#v", "&mat.Dense{mat:blas64.General{Rows:3, Cols:3, Stride:3, Data:[]float64{1, 0, 0, 0, 1, 0, 0, 0, 1}}, capRows:3, capCols:3}"},
+			},
+		},
+		{
+			Formatted(NewDense(2, 3, []float64{1, 2, 3, 4, 5, 6})),
+			[]rp{
+				{"%v", "⎡1  2  3⎤\n⎣4  5  6⎦"},
+				{"% f", "⎡1  2  3⎤\n⎣4  5  6⎦"},
+				{"%#v", "&mat.Dense{mat:blas64.General{Rows:2, Cols:3, Stride:3, Data:[]float64{1, 2, 3, 4, 5, 6}}, capRows:2, capCols:3}"},
+			},
+		},
+		{
+			Formatted(NewDense(3, 2, []float64{1, 2, 3, 4, 5, 6})),
+			[]rp{
+				{"%v", "⎡1  2⎤\n⎢3  4⎥\n⎣5  6⎦"},
+				{"% f", "⎡1  2⎤\n⎢3  4⎥\n⎣5  6⎦"},
+				{"%#v", "&mat.Dense{mat:blas64.General{Rows:3, Cols:2, Stride:2, Data:[]float64{1, 2, 3, 4, 5, 6}}, capRows:3, capCols:2}"},
+			},
+		},
+		{
+			func() fmt.Formatter {
+				m := NewDense(2, 3, []float64{0, 1, 2, 3, 4, 5})
+				m.Apply(sqrt, m)
+				return Formatted(m)
+			}(),
+			[]rp{
+				{"%v", "⎡                 0                   1  1.4142135623730951⎤\n⎣1.7320508075688772                   2    2.23606797749979⎦"},
+				{"%.2f", "⎡0.00  1.00  1.41⎤\n⎣1.73  2.00  2.24⎦"},
+				{"% f", "⎡                 .                   1  1.4142135623730951⎤\n⎣1.7320508075688772                   2    2.23606797749979⎦"},
+				{"%#v", "&mat.Dense{mat:blas64.General{Rows:2, Cols:3, Stride:3, Data:[]float64{0, 1, 1.4142135623730951, 1.7320508075688772, 2, 2.23606797749979}}, capRows:2, capCols:3}"},
+			},
+		},
+		{
+			func() fmt.Formatter {
+				m := NewDense(3, 2, []float64{0, 1, 2, 3, 4, 5})
+				m.Apply(sqrt, m)
+				return Formatted(m)
+			}(),
+			[]rp{
+				{"%v", "⎡                 0                   1⎤\n⎢1.4142135623730951  1.7320508075688772⎥\n⎣                 2    2.23606797749979⎦"},
+				{"%.2f", "⎡0.00  1.00⎤\n⎢1.41  1.73⎥\n⎣2.00  2.24⎦"},
+				{"% f", "⎡                 .                   1⎤\n⎢1.4142135623730951  1.7320508075688772⎥\n⎣                 2    2.23606797749979⎦"},
+				{"%#v", "&mat.Dense{mat:blas64.General{Rows:3, Cols:2, Stride:2, Data:[]float64{0, 1, 1.4142135623730951, 1.7320508075688772, 2, 2.23606797749979}}, capRows:3, capCols:2}"},
+			},
+		},
+		{
+			func() fmt.Formatter {
+				m := NewDense(2, 3, []float64{0, 1, 2, 3, 4, 5})
+				m.Apply(sqrt, m)
+				return Formatted(m, Squeeze())
+			}(),
+			[]rp{
+				{"%v", "⎡                 0  1  1.4142135623730951⎤\n⎣1.7320508075688772  2    2.23606797749979⎦"},
+				{"%.2f", "⎡0.00  1.00  1.41⎤\n⎣1.73  2.00  2.24⎦"},
+				{"% f", "⎡                 .  1  1.4142135623730951⎤\n⎣1.7320508075688772  2    2.23606797749979⎦"},
+				{"%#v", "&mat.Dense{mat:blas64.General{Rows:2, Cols:3, Stride:3, Data:[]float64{0, 1, 1.4142135623730951, 1.7320508075688772, 2, 2.23606797749979}}, capRows:2, capCols:3}"},
+			},
+		},
+		{
+			func() fmt.Formatter {
+				m := NewDense(1, 10, []float64{1, 2, 3, 4, 5, 6, 7, 8, 9, 10})
+				return Formatted(m, Excerpt(3))
+			}(),
+			[]rp{
+				{"%v", "Dims(1, 10)\n[ 1   2   3  ...  ...   8   9  10]"},
+			},
+		},
+		{
+			func() fmt.Formatter {
+				m := NewDense(10, 1, []float64{1, 2, 3, 4, 5, 6, 7, 8, 9, 10})
+				return Formatted(m, Excerpt(3))
+			}(),
+			[]rp{
+				{"%v", "Dims(10, 1)\n⎡ 1⎤\n⎢ 2⎥\n⎢ 3⎥\n .\n .\n .\n⎢ 8⎥\n⎢ 9⎥\n⎣10⎦"},
+			},
+		},
+		{
+			func() fmt.Formatter {
+				m := NewDense(10, 10, nil)
+				for i := 0; i < 10; i++ {
+					m.Set(i, i, 1)
+				}
+				return Formatted(m, Excerpt(3))
+			}(),
+			[]rp{
+				{"%v", "Dims(10, 10)\n⎡1  0  0  ...  ...  0  0  0⎤\n⎢0  1  0            0  0  0⎥\n⎢0  0  1            0  0  0⎥\n .\n .\n .\n⎢0  0  0            1  0  0⎥\n⎢0  0  0            0  1  0⎥\n⎣0  0  0  ...  ...  0  0  1⎦"},
+			},
+		},
+	} {
+		for j, rp := range test.rep {
+			got := fmt.Sprintf(rp.format, test.m)
+			if got != rp.output {
+				t.Errorf("unexpected format result test %d part %d:\ngot:\n%s\nwant:\n%s", i, j, got, rp.output)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/gsvd.go b/vendor/gonum.org/v1/gonum/mat/gsvd.go
new file mode 100644
index 00000000..663a0729
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/gsvd.go
@@ -0,0 +1,371 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/lapack"
+	"gonum.org/v1/gonum/lapack/lapack64"
+)
+
+// GSVD is a type for creating and using the Generalized Singular Value Decomposition
+// (GSVD) of a matrix.
+//
+// The factorization is a linear transformation of the data sets from the given
+// variable×sample spaces to reduced and diagonalized "eigenvariable"×"eigensample"
+// spaces.
+type GSVD struct {
+	kind GSVDKind
+
+	r, p, c, k, l int
+	s1, s2        []float64
+	a, b, u, v, q blas64.General
+
+	work  []float64
+	iwork []int
+}
+
+// Factorize computes the generalized singular value decomposition (GSVD) of the input
+// the r×c matrix A and the p×c matrix B. The singular values of A and B are computed
+// in all cases, while the singular vectors are optionally computed depending on the
+// input kind.
+//
+// The full singular value decomposition (kind == GSVDU|GSVDV|GSVDQ) deconstructs A and B as
+//  A = U * Σ₁ * [ 0 R ] * Q^T
+//
+//  B = V * Σ₂ * [ 0 R ] * Q^T
+// where Σ₁ and Σ₂ are r×(k+l) and p×(k+l) diagonal matrices of singular values, and
+// U, V and Q are r×r, p×p and c×c orthogonal matrices of singular vectors. k+l is the
+// effective numerical rank of the matrix [ A^T B^T ]^T.
+//
+// It is frequently not necessary to compute the full GSVD. Computation time and
+// storage costs can be reduced using the appropriate kind. Either only the singular
+// values can be computed (kind == SVDNone), or in conjunction with specific singular
+// vectors (kind bit set according to matrix.GSVDU, matrix.GSVDV and matrix.GSVDQ).
+//
+// Factorize returns whether the decomposition succeeded. If the decomposition
+// failed, routines that require a successful factorization will panic.
+func (gsvd *GSVD) Factorize(a, b Matrix, kind GSVDKind) (ok bool) {
+	r, c := a.Dims()
+	gsvd.r, gsvd.c = r, c
+	p, c := b.Dims()
+	gsvd.p = p
+	if gsvd.c != c {
+		panic(ErrShape)
+	}
+	var jobU, jobV, jobQ lapack.GSVDJob
+	switch {
+	default:
+		panic("gsvd: bad input kind")
+	case kind == GSVDNone:
+		jobU = lapack.GSVDNone
+		jobV = lapack.GSVDNone
+		jobQ = lapack.GSVDNone
+	case (GSVDU|GSVDV|GSVDQ)&kind != 0:
+		if GSVDU&kind != 0 {
+			jobU = lapack.GSVDU
+			gsvd.u = blas64.General{
+				Rows:   r,
+				Cols:   r,
+				Stride: r,
+				Data:   use(gsvd.u.Data, r*r),
+			}
+		}
+		if GSVDV&kind != 0 {
+			jobV = lapack.GSVDV
+			gsvd.v = blas64.General{
+				Rows:   p,
+				Cols:   p,
+				Stride: p,
+				Data:   use(gsvd.v.Data, p*p),
+			}
+		}
+		if GSVDQ&kind != 0 {
+			jobQ = lapack.GSVDQ
+			gsvd.q = blas64.General{
+				Rows:   c,
+				Cols:   c,
+				Stride: c,
+				Data:   use(gsvd.q.Data, c*c),
+			}
+		}
+	}
+
+	// A and B are destroyed on call, so copy the matrices.
+	aCopy := DenseCopyOf(a)
+	bCopy := DenseCopyOf(b)
+
+	gsvd.s1 = use(gsvd.s1, c)
+	gsvd.s2 = use(gsvd.s2, c)
+
+	gsvd.iwork = useInt(gsvd.iwork, c)
+
+	gsvd.work = use(gsvd.work, 1)
+	lapack64.Ggsvd3(jobU, jobV, jobQ, aCopy.mat, bCopy.mat, gsvd.s1, gsvd.s2, gsvd.u, gsvd.v, gsvd.q, gsvd.work, -1, gsvd.iwork)
+	gsvd.work = use(gsvd.work, int(gsvd.work[0]))
+	gsvd.k, gsvd.l, ok = lapack64.Ggsvd3(jobU, jobV, jobQ, aCopy.mat, bCopy.mat, gsvd.s1, gsvd.s2, gsvd.u, gsvd.v, gsvd.q, gsvd.work, len(gsvd.work), gsvd.iwork)
+	if ok {
+		gsvd.a = aCopy.mat
+		gsvd.b = bCopy.mat
+		gsvd.kind = kind
+	}
+	return ok
+}
+
+// Kind returns the matrix.GSVDKind of the decomposition. If no decomposition has been
+// computed, Kind returns 0.
+func (gsvd *GSVD) Kind() GSVDKind {
+	return gsvd.kind
+}
+
+// Rank returns the k and l terms of the rank of [ A^T B^T ]^T.
+func (gsvd *GSVD) Rank() (k, l int) {
+	return gsvd.k, gsvd.l
+}
+
+// GeneralizedValues returns the generalized singular values of the factorized matrices.
+// If the input slice is non-nil, the values will be stored in-place into the slice.
+// In this case, the slice must have length min(r,c)-k, and GeneralizedValues will
+// panic with matrix.ErrSliceLengthMismatch otherwise. If the input slice is nil,
+// a new slice of the appropriate length will be allocated and returned.
+//
+// GeneralizedValues will panic if the receiver does not contain a successful factorization.
+func (gsvd *GSVD) GeneralizedValues(v []float64) []float64 {
+	if gsvd.kind == 0 {
+		panic("gsvd: no decomposition computed")
+	}
+	r := gsvd.r
+	c := gsvd.c
+	k := gsvd.k
+	d := min(r, c)
+	if v == nil {
+		v = make([]float64, d-k)
+	}
+	if len(v) != d-k {
+		panic(ErrSliceLengthMismatch)
+	}
+	floats.DivTo(v, gsvd.s1[k:d], gsvd.s2[k:d])
+	return v
+}
+
+// ValuesA returns the singular values of the factorized A matrix.
+// If the input slice is non-nil, the values will be stored in-place into the slice.
+// In this case, the slice must have length min(r,c)-k, and ValuesA will panic with
+// matrix.ErrSliceLengthMismatch otherwise. If the input slice is nil,
+// a new slice of the appropriate length will be allocated and returned.
+//
+// ValuesA will panic if the receiver does not contain a successful factorization.
+func (gsvd *GSVD) ValuesA(s []float64) []float64 {
+	if gsvd.kind == 0 {
+		panic("gsvd: no decomposition computed")
+	}
+	r := gsvd.r
+	c := gsvd.c
+	k := gsvd.k
+	d := min(r, c)
+	if s == nil {
+		s = make([]float64, d-k)
+	}
+	if len(s) != d-k {
+		panic(ErrSliceLengthMismatch)
+	}
+	copy(s, gsvd.s1[k:min(r, c)])
+	return s
+}
+
+// ValuesB returns the singular values of the factorized B matrix.
+// If the input slice is non-nil, the values will be stored in-place into the slice.
+// In this case, the slice must have length min(r,c)-k, and ValuesB will panic with
+// matrix.ErrSliceLengthMismatch otherwise. If the input slice is nil,
+// a new slice of the appropriate length will be allocated and returned.
+//
+// ValuesB will panic if the receiver does not contain a successful factorization.
+func (gsvd *GSVD) ValuesB(s []float64) []float64 {
+	if gsvd.kind == 0 {
+		panic("gsvd: no decomposition computed")
+	}
+	r := gsvd.r
+	c := gsvd.c
+	k := gsvd.k
+	d := min(r, c)
+	if s == nil {
+		s = make([]float64, d-k)
+	}
+	if len(s) != d-k {
+		panic(ErrSliceLengthMismatch)
+	}
+	copy(s, gsvd.s2[k:d])
+	return s
+}
+
+// ZeroRTo extracts the matrix [ 0 R ] from the singular value decomposition, storing
+// the result in-place into dst. [ 0 R ] is size (k+l)×c.
+// If dst is nil, a new matrix is allocated. The resulting ZeroR matrix is returned.
+//
+// ZeroRTo will panic if the receiver does not contain a successful factorization.
+func (gsvd *GSVD) ZeroRTo(dst *Dense) *Dense {
+	if gsvd.kind == 0 {
+		panic("gsvd: no decomposition computed")
+	}
+	r := gsvd.r
+	c := gsvd.c
+	k := gsvd.k
+	l := gsvd.l
+	h := min(k+l, r)
+	if dst == nil {
+		dst = NewDense(k+l, c, nil)
+	} else {
+		dst.reuseAsZeroed(k+l, c)
+	}
+	a := Dense{
+		mat:     gsvd.a,
+		capRows: r,
+		capCols: c,
+	}
+	dst.Slice(0, h, c-k-l, c).(*Dense).
+		Copy(a.Slice(0, h, c-k-l, c))
+	if r < k+l {
+		b := Dense{
+			mat:     gsvd.b,
+			capRows: gsvd.p,
+			capCols: c,
+		}
+		dst.Slice(r, k+l, c+r-k-l, c).(*Dense).
+			Copy(b.Slice(r-k, l, c+r-k-l, c))
+	}
+	return dst
+}
+
+// SigmaATo extracts the matrix Σ₁ from the singular value decomposition, storing
+// the result in-place into dst. Σ₁ is size r×(k+l).
+// If dst is nil, a new matrix is allocated. The resulting SigmaA matrix is returned.
+//
+// SigmaATo will panic if the receiver does not contain a successful factorization.
+func (gsvd *GSVD) SigmaATo(dst *Dense) *Dense {
+	if gsvd.kind == 0 {
+		panic("gsvd: no decomposition computed")
+	}
+	r := gsvd.r
+	k := gsvd.k
+	l := gsvd.l
+	if dst == nil {
+		dst = NewDense(r, k+l, nil)
+	} else {
+		dst.reuseAsZeroed(r, k+l)
+	}
+	for i := 0; i < k; i++ {
+		dst.set(i, i, 1)
+	}
+	for i := k; i < min(r, k+l); i++ {
+		dst.set(i, i, gsvd.s1[i])
+	}
+	return dst
+}
+
+// SigmaBTo extracts the matrix Σ₂ from the singular value decomposition, storing
+// the result in-place into dst. Σ₂ is size p×(k+l).
+// If dst is nil, a new matrix is allocated. The resulting SigmaB matrix is returned.
+//
+// SigmaBTo will panic if the receiver does not contain a successful factorization.
+func (gsvd *GSVD) SigmaBTo(dst *Dense) *Dense {
+	if gsvd.kind == 0 {
+		panic("gsvd: no decomposition computed")
+	}
+	r := gsvd.r
+	p := gsvd.p
+	k := gsvd.k
+	l := gsvd.l
+	if dst == nil {
+		dst = NewDense(p, k+l, nil)
+	} else {
+		dst.reuseAsZeroed(p, k+l)
+	}
+	for i := 0; i < min(l, r-k); i++ {
+		dst.set(i, i+k, gsvd.s2[k+i])
+	}
+	for i := r - k; i < l; i++ {
+		dst.set(i, i+k, 1)
+	}
+	return dst
+}
+
+// UTo extracts the matrix U from the singular value decomposition, storing
+// the result in-place into dst. U is size r×r.
+// If dst is nil, a new matrix is allocated. The resulting U matrix is returned.
+//
+// UTo will panic if the receiver does not contain a successful factorization.
+func (gsvd *GSVD) UTo(dst *Dense) *Dense {
+	if gsvd.kind&GSVDU == 0 {
+		panic("mat: improper GSVD kind")
+	}
+	r := gsvd.u.Rows
+	c := gsvd.u.Cols
+	if dst == nil {
+		dst = NewDense(r, c, nil)
+	} else {
+		dst.reuseAs(r, c)
+	}
+
+	tmp := &Dense{
+		mat:     gsvd.u,
+		capRows: r,
+		capCols: c,
+	}
+	dst.Copy(tmp)
+	return dst
+}
+
+// VTo extracts the matrix V from the singular value decomposition, storing
+// the result in-place into dst. V is size p×p.
+// If dst is nil, a new matrix is allocated. The resulting V matrix is returned.
+//
+// VTo will panic if the receiver does not contain a successful factorization.
+func (gsvd *GSVD) VTo(dst *Dense) *Dense {
+	if gsvd.kind&GSVDV == 0 {
+		panic("mat: improper GSVD kind")
+	}
+	r := gsvd.v.Rows
+	c := gsvd.v.Cols
+	if dst == nil {
+		dst = NewDense(r, c, nil)
+	} else {
+		dst.reuseAs(r, c)
+	}
+
+	tmp := &Dense{
+		mat:     gsvd.v,
+		capRows: r,
+		capCols: c,
+	}
+	dst.Copy(tmp)
+	return dst
+}
+
+// QTo extracts the matrix Q from the singular value decomposition, storing
+// the result in-place into dst. Q is size c×c.
+// If dst is nil, a new matrix is allocated. The resulting Q matrix is returned.
+//
+// QTo will panic if the receiver does not contain a successful factorization.
+func (gsvd *GSVD) QTo(dst *Dense) *Dense {
+	if gsvd.kind&GSVDQ == 0 {
+		panic("mat: improper GSVD kind")
+	}
+	r := gsvd.q.Rows
+	c := gsvd.q.Cols
+	if dst == nil {
+		dst = NewDense(r, c, nil)
+	} else {
+		dst.reuseAs(r, c)
+	}
+
+	tmp := &Dense{
+		mat:     gsvd.q,
+		capRows: r,
+		capCols: c,
+	}
+	dst.Copy(tmp)
+	return dst
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/gsvd_example_test.go b/vendor/gonum.org/v1/gonum/mat/gsvd_example_test.go
new file mode 100644
index 00000000..48898ccc
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/gsvd_example_test.go
@@ -0,0 +1,85 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat_test
+
+import (
+	"fmt"
+	"log"
+	"math"
+
+	"gonum.org/v1/gonum/mat"
+)
+
+func ExampleGSVD() {
+	// Perform a GSVD factorization on food production/consumption data for the
+	// three years 1990, 2000 and 2014, for Africa and Latin America/Caribbean.
+	//
+	// See Lee et al. doi:10.1371/journal.pone.0030098 and
+	// Alter at al. doi:10.1073/pnas.0530258100 for more details.
+	var gsvd mat.GSVD
+	ok := gsvd.Factorize(FAO.Africa, FAO.LatinAmericaCaribbean, mat.GSVDU|mat.GSVDV|mat.GSVDQ)
+	if !ok {
+		log.Fatal("GSVD factorization failed")
+	}
+
+	u := gsvd.UTo(nil)
+	v := gsvd.VTo(nil)
+
+	s1 := gsvd.ValuesA(nil)
+	s2 := gsvd.ValuesB(nil)
+
+	fmt.Printf("Africa\n\ts1 = %.4f\n\n\tU = %.4f\n\n",
+		s1, mat.Formatted(u, mat.Prefix("\t    "), mat.Excerpt(2)))
+	fmt.Printf("Latin America/Caribbean\n\ts2 = %.4f\n\n\tV = %.4f\n",
+		s2, mat.Formatted(v, mat.Prefix("\t    "), mat.Excerpt(2)))
+
+	var q mat.Dense
+	q.Mul(gsvd.ZeroRTo(nil), gsvd.QTo(nil))
+	fmt.Printf("\nCommon basis vectors\n\n\tQ^T = %.4f\n",
+		mat.Formatted(q.T(), mat.Prefix("\t      ")))
+
+	// Calculate the antisymmetric angular distances for each eigenvariable.
+	fmt.Println("\nSignificance:")
+	for i := 0; i < 3; i++ {
+		fmt.Printf("\teigenvar_%d: %+.4f\n", i, math.Atan(s1[i]/s2[i])-math.Pi/4)
+	}
+
+	// Output:
+	//
+	// Africa
+	// 	s1 = [1.0000 0.9344 0.5118]
+	//
+	// 	U = Dims(21, 21)
+	// 	    ⎡-0.0005   0.0142  ...  ...  -0.0060  -0.0055⎤
+	// 	    ⎢-0.0010   0.0019             0.0071   0.0075⎥
+	// 	     .
+	// 	     .
+	// 	     .
+	// 	    ⎢-0.0007  -0.0024             0.9999  -0.0001⎥
+	// 	    ⎣-0.0010  -0.0016  ...  ...  -0.0001   0.9999⎦
+	//
+	// Latin America/Caribbean
+	// 	s2 = [0.0047 0.3563 0.8591]
+	//
+	// 	V = Dims(14, 14)
+	// 	    ⎡ 0.1362   0.0008  ...  ...   0.0700   0.2636⎤
+	// 	    ⎢ 0.1830  -0.0040             0.2908   0.7834⎥
+	// 	     .
+	// 	     .
+	// 	     .
+	// 	    ⎢-0.2598  -0.0324             0.9339  -0.2170⎥
+	// 	    ⎣-0.8386   0.1494  ...  ...  -0.1639   0.4121⎦
+	//
+	// Common basis vectors
+	//
+	// 	Q^T = ⎡ -8172.4084   -4524.2933    4813.9616⎤
+	// 	      ⎢ 22581.8020   12397.1070  -16364.8933⎥
+	// 	      ⎣ -8910.8462  -10902.1488   15762.8719⎦
+	//
+	// Significance:
+	// 	eigenvar_0: +0.7807
+	// 	eigenvar_1: +0.4211
+	// 	eigenvar_2: -0.2482
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/gsvd_test.go b/vendor/gonum.org/v1/gonum/mat/gsvd_test.go
new file mode 100644
index 00000000..6e8ef0f5
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/gsvd_test.go
@@ -0,0 +1,117 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+func TestGSVD(t *testing.T) {
+	const tol = 1e-10
+	rnd := rand.New(rand.NewSource(1))
+	for _, test := range []struct {
+		m, p, n int
+	}{
+		{5, 3, 5},
+		{5, 3, 3},
+		{3, 3, 5},
+		{5, 5, 5},
+		{5, 5, 3},
+		{3, 5, 5},
+		{150, 150, 150},
+		{200, 150, 150},
+		{150, 150, 200},
+		{150, 200, 150},
+		{200, 200, 150},
+		{150, 200, 200},
+	} {
+		m := test.m
+		p := test.p
+		n := test.n
+		for trial := 0; trial < 10; trial++ {
+			a := NewDense(m, n, nil)
+			for i := range a.mat.Data {
+				a.mat.Data[i] = rnd.NormFloat64()
+			}
+			aCopy := DenseCopyOf(a)
+
+			b := NewDense(p, n, nil)
+			for i := range b.mat.Data {
+				b.mat.Data[i] = rnd.NormFloat64()
+			}
+			bCopy := DenseCopyOf(b)
+
+			// Test Full decomposition.
+			var gsvd GSVD
+			ok := gsvd.Factorize(a, b, GSVDU|GSVDV|GSVDQ)
+			if !ok {
+				t.Errorf("GSVD factorization failed")
+			}
+			if !Equal(a, aCopy) {
+				t.Errorf("A changed during call to GSVD.Factorize with GSVDU|GSVDV|GSVDQ")
+			}
+			if !Equal(b, bCopy) {
+				t.Errorf("B changed during call to GSVD.Factorize with GSVDU|GSVDV|GSVDQ")
+			}
+			c, s, sigma1, sigma2, zeroR, u, v, q := extractGSVD(&gsvd)
+			var ansU, ansV, d1R, d2R Dense
+			ansU.Product(u.T(), a, q)
+			ansV.Product(v.T(), b, q)
+			d1R.Mul(sigma1, zeroR)
+			d2R.Mul(sigma2, zeroR)
+			if !EqualApprox(&ansU, &d1R, tol) {
+				t.Errorf("Answer mismatch with GSVDU|GSVDV|GSVDQ\nU^T * A * Q:\n% 0.2f\nΣ₁ * [ 0 R ]:\n% 0.2f",
+					Formatted(&ansU), Formatted(&d1R))
+			}
+			if !EqualApprox(&ansV, &d2R, tol) {
+				t.Errorf("Answer mismatch with GSVDU|GSVDV|GSVDQ\nV^T * B  *Q:\n% 0.2f\nΣ₂ * [ 0 R ]:\n% 0.2f",
+					Formatted(&d2R), Formatted(&ansV))
+			}
+
+			// Check C^2 + S^2 = I.
+			for i := range c {
+				d := c[i]*c[i] + s[i]*s[i]
+				if !floats.EqualWithinAbsOrRel(d, 1, 1e-14, 1e-14) {
+					t.Errorf("c_%d^2 + s_%d^2 != 1: got: %v", i, i, d)
+				}
+			}
+
+			// Test None decomposition.
+			ok = gsvd.Factorize(a, b, GSVDNone)
+			if !ok {
+				t.Errorf("GSVD factorization failed")
+			}
+			if !Equal(a, aCopy) {
+				t.Errorf("A changed during call to GSVD with GSVDNone")
+			}
+			if !Equal(b, bCopy) {
+				t.Errorf("B changed during call to GSVD with GSVDNone")
+			}
+			cNone := gsvd.ValuesA(nil)
+			if !floats.EqualApprox(c, cNone, tol) {
+				t.Errorf("Singular value mismatch between GSVDU|GSVDV|GSVDQ and GSVDNone decomposition")
+			}
+			sNone := gsvd.ValuesB(nil)
+			if !floats.EqualApprox(s, sNone, tol) {
+				t.Errorf("Singular value mismatch between GSVDU|GSVDV|GSVDQ and GSVDNone decomposition")
+			}
+		}
+	}
+}
+
+func extractGSVD(gsvd *GSVD) (c, s []float64, s1, s2, zR, u, v, q *Dense) {
+	s1 = gsvd.SigmaATo(nil)
+	s2 = gsvd.SigmaBTo(nil)
+	zR = gsvd.ZeroRTo(nil)
+	u = gsvd.UTo(nil)
+	v = gsvd.VTo(nil)
+	q = gsvd.QTo(nil)
+	c = gsvd.ValuesA(nil)
+	s = gsvd.ValuesB(nil)
+	return c, s, s1, s2, zR, u, v, q
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/hogsvd.go b/vendor/gonum.org/v1/gonum/mat/hogsvd.go
new file mode 100644
index 00000000..2d3c0403
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/hogsvd.go
@@ -0,0 +1,213 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"errors"
+
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// HOGSVD is a type for creating and using the Higher Order Generalized Singular Value
+// Decomposition (HOGSVD) of a set of matrices.
+//
+// The factorization is a linear transformation of the data sets from the given
+// variable×sample spaces to reduced and diagonalized "eigenvariable"×"eigensample"
+// spaces.
+type HOGSVD struct {
+	n int
+	v *Dense
+	b []Dense
+
+	err error
+}
+
+// Factorize computes the higher order generalized singular value decomposition (HOGSVD)
+// of the n input r_i×c column tall matrices in m. HOGSV extends the GSVD case from 2 to n
+// input matrices.
+//
+//  M_0 = U_0 * Σ_0 * V^T
+//  M_1 = U_1 * Σ_1 * V^T
+//  .
+//  .
+//  .
+//  M_{n-1} = U_{n-1} * Σ_{n-1} * V^T
+//
+// where U_i are r_i×c matrices of singular vectors, Σ are c×c matrices singular values, and V
+// is a c×c matrix of singular vectors.
+//
+// Factorize returns whether the decomposition succeeded. If the decomposition
+// failed, routines that require a successful factorization will panic.
+func (gsvd *HOGSVD) Factorize(m ...Matrix) (ok bool) {
+	// Factorize performs the HOGSVD factorisation
+	// essentially as described by Ponnapalli et al.
+	// https://doi.org/10.1371/journal.pone.0028072
+
+	if len(m) < 2 {
+		panic("hogsvd: too few matrices")
+	}
+	gsvd.n = 0
+
+	r, c := m[0].Dims()
+	a := make([]Cholesky, len(m))
+	var ts SymDense
+	for i, d := range m {
+		rd, cd := d.Dims()
+		if rd < cd {
+			gsvd.err = ErrShape
+			return false
+		}
+		if rd > r {
+			r = rd
+		}
+		if cd != c {
+			panic(ErrShape)
+		}
+		ts.Reset()
+		ts.SymOuterK(1, d.T())
+		ok = a[i].Factorize(&ts)
+		if !ok {
+			gsvd.err = errors.New("hogsvd: cholesky decomposition failed")
+			return false
+		}
+	}
+
+	s := getWorkspace(c, c, true)
+	defer putWorkspace(s)
+	sij := getWorkspace(c, c, false)
+	defer putWorkspace(sij)
+	for i, ai := range a {
+		for _, aj := range a[i+1:] {
+			gsvd.err = ai.SolveChol(sij, &aj)
+			if gsvd.err != nil {
+				return false
+			}
+			s.Add(s, sij)
+
+			gsvd.err = aj.SolveChol(sij, &ai)
+			if gsvd.err != nil {
+				return false
+			}
+			s.Add(s, sij)
+		}
+	}
+	s.Scale(1/float64(len(m)*(len(m)-1)), s)
+
+	var eig Eigen
+	ok = eig.Factorize(s.T(), false, true)
+	if !ok {
+		gsvd.err = errors.New("hogsvd: eigen decomposition failed")
+		return false
+	}
+	v := eig.Vectors()
+	for j := 0; j < c; j++ {
+		cv := v.ColView(j)
+		cv.ScaleVec(1/blas64.Nrm2(c, cv.mat), cv)
+	}
+
+	b := make([]Dense, len(m))
+	biT := getWorkspace(c, r, false)
+	defer putWorkspace(biT)
+	for i, d := range m {
+		// All calls to reset will leave a zeroed
+		// matrix with capacity to store the result
+		// without additional allocation.
+		biT.Reset()
+		gsvd.err = biT.Solve(v, d.T())
+		if gsvd.err != nil {
+			return false
+		}
+		b[i].Clone(biT.T())
+	}
+
+	gsvd.n = len(m)
+	gsvd.v = v
+	gsvd.b = b
+	return true
+}
+
+// Err returns the reason for a factorization failure.
+func (gsvd *HOGSVD) Err() error {
+	return gsvd.err
+}
+
+// Len returns the number of matrices that have been factorized. If Len returns
+// zero, the factorization was not successful.
+func (gsvd *HOGSVD) Len() int {
+	return gsvd.n
+}
+
+// UTo extracts the matrix U_n from the singular value decomposition, storing
+// the result in-place into dst. U_n is size r×c.
+// If dst is nil, a new matrix is allocated. The resulting U matrix is returned.
+//
+// UTo will panic if the receiver does not contain a successful factorization.
+func (gsvd *HOGSVD) UTo(dst *Dense, n int) *Dense {
+	if gsvd.n == 0 {
+		panic("hogsvd: unsuccessful factorization")
+	}
+	if n < 0 || gsvd.n <= n {
+		panic("hogsvd: invalid index")
+	}
+
+	if dst == nil {
+		r, c := gsvd.b[n].Dims()
+		dst = NewDense(r, c, nil)
+	} else {
+		dst.reuseAs(gsvd.b[n].Dims())
+	}
+	dst.Copy(&gsvd.b[n])
+	for j, f := range gsvd.Values(nil, n) {
+		v := dst.ColView(j)
+		v.ScaleVec(1/f, v)
+	}
+	return dst
+}
+
+// Values returns the nth set of singular values of the factorized system.
+// If the input slice is non-nil, the values will be stored in-place into the slice.
+// In this case, the slice must have length c, and Values will panic with
+// matrix.ErrSliceLengthMismatch otherwise. If the input slice is nil,
+// a new slice of the appropriate length will be allocated and returned.
+//
+// Values will panic if the receiver does not contain a successful factorization.
+func (gsvd *HOGSVD) Values(s []float64, n int) []float64 {
+	if gsvd.n == 0 {
+		panic("hogsvd: unsuccessful factorization")
+	}
+	if n < 0 || gsvd.n <= n {
+		panic("hogsvd: invalid index")
+	}
+
+	r, c := gsvd.b[n].Dims()
+	if s == nil {
+		s = make([]float64, c)
+	} else if len(s) != c {
+		panic(ErrSliceLengthMismatch)
+	}
+	for j := 0; j < c; j++ {
+		s[j] = blas64.Nrm2(r, gsvd.b[n].ColView(j).mat)
+	}
+	return s
+}
+
+// VTo extracts the matrix V from the singular value decomposition, storing
+// the result in-place into dst. V is size c×c.
+// If dst is nil, a new matrix is allocated. The resulting V matrix is returned.
+//
+// VTo will panic if the receiver does not contain a successful factorization.
+func (gsvd *HOGSVD) VTo(dst *Dense) *Dense {
+	if gsvd.n == 0 {
+		panic("hogsvd: unsuccessful factorization")
+	}
+	if dst == nil {
+		r, c := gsvd.v.Dims()
+		dst = NewDense(r, c, nil)
+	} else {
+		dst.reuseAs(gsvd.v.Dims())
+	}
+	dst.Copy(gsvd.v)
+	return dst
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/hogsvd_example_test.go b/vendor/gonum.org/v1/gonum/mat/hogsvd_example_test.go
new file mode 100644
index 00000000..a1651448
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/hogsvd_example_test.go
@@ -0,0 +1,134 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat_test
+
+import (
+	"fmt"
+	"log"
+
+	"gonum.org/v1/gonum/mat"
+)
+
+func ExampleHOGSVD() {
+	// Perform an HOGSVD factorization on food production/consumption data for the
+	// three years 1990, 2000 and 2014.
+	//
+	// See Ponnapalli et al. doi:10.1371/journal.pone.0028072 and
+	// Alter at al. doi:10.1073/pnas.0530258100 for more details.
+	var gsvd mat.HOGSVD
+	ok := gsvd.Factorize(FAO.Africa, FAO.Asia, FAO.LatinAmericaCaribbean, FAO.Oceania)
+	if !ok {
+		log.Fatalf("HOGSVD factorization failed: %v", gsvd.Err())
+	}
+
+	for i, n := range []string{"Africa", "Asia", "Latin America/Caribbean", "Oceania"} {
+		u := gsvd.UTo(nil, i)
+		s := gsvd.Values(nil, i)
+		fmt.Printf("%s\n\ts_%d = %.4f\n\n\tU_%[2]d = %.4[4]f\n",
+			n, i, s, mat.Formatted(u, mat.Prefix("\t      ")))
+	}
+
+	v := gsvd.VTo(nil)
+	fmt.Printf("\nCommon basis vectors\n\n\tV^T = %.4f",
+		mat.Formatted(v.T(), mat.Prefix("\t      ")))
+
+	// Output:
+	//
+	// Africa
+	// 	s_0 = [45507.3278 18541.9293 21503.0778]
+	//
+	// 	U_0 = ⎡-0.0005  -0.0039  -0.0019⎤
+	// 	      ⎢-0.0010  -0.0007  -0.0012⎥
+	// 	      ⎢-1.0000  -0.0507  -0.9964⎥
+	// 	      ⎢-0.0022  -0.2906  -0.0415⎥
+	// 	      ⎢ 0.0001  -0.0127  -0.0016⎥
+	// 	      ⎢ 0.0003  -0.0067  -0.0010⎥
+	// 	      ⎢ 0.0003  -0.0022  -0.0003⎥
+	// 	      ⎢-0.0086  -0.9550   0.0734⎥
+	// 	      ⎢ 0.0017   0.0002   0.0059⎥
+	// 	      ⎢-0.0002  -0.0088  -0.0014⎥
+	// 	      ⎢-0.0006  -0.0078  -0.0001⎥
+	// 	      ⎢-0.0005  -0.0076   0.0003⎥
+	// 	      ⎢ 0.0001  -0.0090   0.0008⎥
+	// 	      ⎢-0.0005  -0.0050   0.0029⎥
+	// 	      ⎢-0.0011  -0.0078  -0.0012⎥
+	// 	      ⎢-0.0014  -0.0058  -0.0002⎥
+	// 	      ⎢ 0.0007  -0.0095   0.0020⎥
+	// 	      ⎢-0.0008  -0.0081  -0.0009⎥
+	// 	      ⎢ 0.0004  -0.0092   0.0006⎥
+	// 	      ⎢-0.0007  -0.0079  -0.0006⎥
+	// 	      ⎣-0.0011  -0.0076  -0.0010⎦
+	// Asia
+	// 	s_1 = [77228.2804 8413.7024 14711.1879]
+	//
+	// 	U_1 = ⎡ 0.0005  -0.0080   0.0011⎤
+	// 	      ⎢ 0.0008  -0.0108   0.0016⎥
+	// 	      ⎢-0.9998   0.0612   0.9949⎥
+	// 	      ⎢ 0.0007  -0.5734  -0.0468⎥
+	// 	      ⎢ 0.0001  -0.0265  -0.0022⎥
+	// 	      ⎢ 0.0001  -0.0165  -0.0019⎥
+	// 	      ⎢ 0.0000  -0.0070  -0.0013⎥
+	// 	      ⎢ 0.0196  -0.8148   0.0893⎥
+	// 	      ⎢ 0.0002  -0.0063   0.0012⎥
+	// 	      ⎢-0.0001  -0.0135  -0.0013⎥
+	// 	      ⎢-0.0004  -0.0135   0.0019⎥
+	// 	      ⎢-0.0005  -0.0132   0.0014⎥
+	// 	      ⎢ 0.0003  -0.0155   0.0045⎥
+	// 	      ⎢-0.0003  -0.0130   0.0025⎥
+	// 	      ⎢-0.0007  -0.0105   0.0016⎥
+	// 	      ⎢-0.0006  -0.0129   0.0007⎥
+	// 	      ⎢-0.0006  -0.0178  -0.0023⎥
+	// 	      ⎢-0.0003  -0.0149   0.0016⎥
+	// 	      ⎢-0.0001  -0.0134   0.0030⎥
+	// 	      ⎢-0.0004  -0.0154   0.0010⎥
+	// 	      ⎣-0.0009  -0.0147  -0.0019⎦
+	// Latin America/Caribbean
+	// 	s_2 = [274.1364 20736.3116 729.6947]
+	//
+	// 	U_2 = ⎡ 0.1060  -0.0021   0.0174⎤
+	// 	      ⎢ 0.1415  -0.0016   0.0289⎥
+	// 	      ⎢ 0.2350  -0.2669  -0.9212⎥
+	// 	      ⎢ 0.0290  -0.0118  -0.0429⎥
+	// 	      ⎢ 0.0226  -0.0043  -0.0213⎥
+	// 	      ⎢ 0.0117  -0.0016  -0.0197⎥
+	// 	      ⎢-0.6263  -0.9635   0.2234⎥
+	// 	      ⎢ 0.2334  -0.0013   0.1275⎥
+	// 	      ⎢-0.0358  -0.0085  -0.0498⎥
+	// 	      ⎢-0.1238  -0.0054   0.0313⎥
+	// 	      ⎢-0.0421  -0.0059   0.0528⎥
+	// 	      ⎢-0.1471  -0.0056   0.0350⎥
+	// 	      ⎢-0.2158  -0.0052  -0.0044⎥
+	// 	      ⎣-0.6154  -0.0078  -0.2717⎦
+	// Oceania
+	// 	s_3 = [8954.1914 6942.6316 17233.0561]
+	//
+	// 	U_3 = ⎡-0.0080  -0.0012  -0.0040⎤
+	// 	      ⎢ 0.0004  -0.0014   0.0001⎥
+	// 	      ⎢ 0.9973  -0.0315   0.9991⎥
+	// 	      ⎢ 0.0473  -0.7426  -0.0359⎥
+	// 	      ⎢ 0.0018  -0.0342  -0.0020⎥
+	// 	      ⎢-0.0005  -0.0148  -0.0016⎥
+	// 	      ⎢-0.0004  -0.0047  -0.0007⎥
+	// 	      ⎢-0.0246  -0.6642  -0.0138⎥
+	// 	      ⎢ 0.0003  -0.0287  -0.0023⎥
+	// 	      ⎢-0.0011  -0.0148  -0.0014⎥
+	// 	      ⎢-0.0108  -0.0198  -0.0039⎥
+	// 	      ⎢-0.0149  -0.0183  -0.0048⎥
+	// 	      ⎢-0.0178  -0.0208  -0.0075⎥
+	// 	      ⎢-0.0266  -0.0063  -0.0016⎥
+	// 	      ⎢-0.0012  -0.0234  -0.0006⎥
+	// 	      ⎢-0.0084  -0.0184  -0.0030⎥
+	// 	      ⎢-0.0232  -0.0191  -0.0124⎥
+	// 	      ⎢-0.0072  -0.0226  -0.0035⎥
+	// 	      ⎢-0.0150  -0.0144  -0.0045⎥
+	// 	      ⎢-0.0068  -0.0227  -0.0034⎥
+	// 	      ⎣-0.0127  -0.0136  -0.0049⎦
+	//
+	// Common basis vectors
+	//
+	// 	V^T = ⎡-0.0897  -0.4460  -0.8905⎤
+	// 	      ⎢-0.4911  -0.5432  -0.6810⎥
+	// 	      ⎣ 0.0644   0.2841   0.9566⎦
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/hogsvd_test.go b/vendor/gonum.org/v1/gonum/mat/hogsvd_test.go
new file mode 100644
index 00000000..5838b61b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/hogsvd_test.go
@@ -0,0 +1,87 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"math/rand"
+	"testing"
+)
+
+func TestHOGSVD(t *testing.T) {
+	const tol = 1e-10
+	rnd := rand.New(rand.NewSource(1))
+	for cas, test := range []struct {
+		r, c int
+	}{
+		{5, 3},
+		{5, 5},
+		{150, 150},
+		{200, 150},
+
+		// Calculating A_i*A_j^T and A_j*A_i^T fails for wide matrices.
+		{3, 5},
+	} {
+		r := test.r
+		c := test.c
+		for n := 3; n < 6; n++ {
+			data := make([]Matrix, n)
+			dataCopy := make([]*Dense, n)
+			for trial := 0; trial < 10; trial++ {
+				for i := range data {
+					d := NewDense(r, c, nil)
+					for j := range d.mat.Data {
+						d.mat.Data[j] = rnd.Float64()
+					}
+					data[i] = d
+					dataCopy[i] = DenseCopyOf(d)
+				}
+
+				var gsvd HOGSVD
+				ok := gsvd.Factorize(data...)
+				if r >= c {
+					if !ok {
+						t.Errorf("HOGSVD factorization failed for %d %d×%d matrices: %v", n, r, c, gsvd.Err())
+						continue
+					}
+				} else {
+					if ok {
+						t.Errorf("HOGSVD factorization unexpectedly succeeded for for %d %d×%d matrices", n, r, c)
+					}
+					continue
+				}
+				for i := range data {
+					if !Equal(data[i], dataCopy[i]) {
+						t.Errorf("A changed during call to HOGSVD.Factorize")
+					}
+				}
+				u, s, v := extractHOGSVD(&gsvd)
+				for i, want := range data {
+					var got Dense
+					sigma := NewDense(c, c, nil)
+					for j := 0; j < c; j++ {
+						sigma.Set(j, j, s[i][j])
+					}
+
+					got.Product(u[i], sigma, v.T())
+					if !EqualApprox(&got, want, tol) {
+						t.Errorf("test %d n=%d trial %d: unexpected answer\nU_%[4]d * S_%[4]d * V^T:\n% 0.2f\nD_%d:\n% 0.2f",
+							cas, n, trial, i, Formatted(&got, Excerpt(5)), i, Formatted(want, Excerpt(5)))
+					}
+				}
+			}
+		}
+	}
+}
+
+func extractHOGSVD(gsvd *HOGSVD) (u []*Dense, s [][]float64, v *Dense) {
+	u = make([]*Dense, gsvd.Len())
+	s = make([][]float64, gsvd.Len())
+	for i := 0; i < gsvd.Len(); i++ {
+		u[i] = gsvd.UTo(nil, i)
+		s[i] = gsvd.Values(nil, i)
+	}
+	v = gsvd.VTo(nil)
+	return u, s, v
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/index_bound_checks.go b/vendor/gonum.org/v1/gonum/mat/index_bound_checks.go
new file mode 100644
index 00000000..9633b21b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/index_bound_checks.go
@@ -0,0 +1,227 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// This file must be kept in sync with index_no_bound_checks.go.
+
+//+build bounds
+
+package mat
+
+// At returns the element at row i, column j.
+func (m *Dense) At(i, j int) float64 {
+	return m.at(i, j)
+}
+
+func (m *Dense) at(i, j int) float64 {
+	if uint(i) >= uint(m.mat.Rows) {
+		panic(ErrRowAccess)
+	}
+	if uint(j) >= uint(m.mat.Cols) {
+		panic(ErrColAccess)
+	}
+	return m.mat.Data[i*m.mat.Stride+j]
+}
+
+// Set sets the element at row i, column j to the value v.
+func (m *Dense) Set(i, j int, v float64) {
+	m.set(i, j, v)
+}
+
+func (m *Dense) set(i, j int, v float64) {
+	if uint(i) >= uint(m.mat.Rows) {
+		panic(ErrRowAccess)
+	}
+	if uint(j) >= uint(m.mat.Cols) {
+		panic(ErrColAccess)
+	}
+	m.mat.Data[i*m.mat.Stride+j] = v
+}
+
+// At returns the element at row i.
+// It panics if i is out of bounds or if j is not zero.
+func (v *VecDense) At(i, j int) float64 {
+	if j != 0 {
+		panic(ErrColAccess)
+	}
+	return v.at(i)
+}
+
+func (v *VecDense) at(i int) float64 {
+	if uint(i) >= uint(v.n) {
+		panic(ErrRowAccess)
+	}
+	return v.mat.Data[i*v.mat.Inc]
+}
+
+// SetVec sets the element at row i to the value val.
+// It panics if i is out of bounds.
+func (v *VecDense) SetVec(i int, val float64) {
+	v.setVec(i, val)
+}
+
+func (v *VecDense) setVec(i int, val float64) {
+	if uint(i) >= uint(v.n) {
+		panic(ErrVectorAccess)
+	}
+	v.mat.Data[i*v.mat.Inc] = val
+}
+
+// At returns the element at row i and column j.
+func (t *SymDense) At(i, j int) float64 {
+	return t.at(i, j)
+}
+
+func (t *SymDense) at(i, j int) float64 {
+	if uint(i) >= uint(t.mat.N) {
+		panic(ErrRowAccess)
+	}
+	if uint(j) >= uint(t.mat.N) {
+		panic(ErrColAccess)
+	}
+	if i > j {
+		i, j = j, i
+	}
+	return t.mat.Data[i*t.mat.Stride+j]
+}
+
+// SetSym sets the elements at (i,j) and (j,i) to the value v.
+func (t *SymDense) SetSym(i, j int, v float64) {
+	t.set(i, j, v)
+}
+
+func (t *SymDense) set(i, j int, v float64) {
+	if uint(i) >= uint(t.mat.N) {
+		panic(ErrRowAccess)
+	}
+	if uint(j) >= uint(t.mat.N) {
+		panic(ErrColAccess)
+	}
+	if i > j {
+		i, j = j, i
+	}
+	t.mat.Data[i*t.mat.Stride+j] = v
+}
+
+// At returns the element at row i, column j.
+func (t *TriDense) At(i, j int) float64 {
+	return t.at(i, j)
+}
+
+func (t *TriDense) at(i, j int) float64 {
+	if uint(i) >= uint(t.mat.N) {
+		panic(ErrRowAccess)
+	}
+	if uint(j) >= uint(t.mat.N) {
+		panic(ErrColAccess)
+	}
+	isUpper := t.isUpper()
+	if (isUpper && i > j) || (!isUpper && i < j) {
+		return 0
+	}
+	return t.mat.Data[i*t.mat.Stride+j]
+}
+
+// SetTri sets the element of the triangular matrix at row i, column j to the value v.
+// It panics if the location is outside the appropriate half of the matrix.
+func (t *TriDense) SetTri(i, j int, v float64) {
+	t.set(i, j, v)
+}
+
+func (t *TriDense) set(i, j int, v float64) {
+	if uint(i) >= uint(t.mat.N) {
+		panic(ErrRowAccess)
+	}
+	if uint(j) >= uint(t.mat.N) {
+		panic(ErrColAccess)
+	}
+	isUpper := t.isUpper()
+	if (isUpper && i > j) || (!isUpper && i < j) {
+		panic(ErrTriangleSet)
+	}
+	t.mat.Data[i*t.mat.Stride+j] = v
+}
+
+// At returns the element at row i, column j.
+func (b *BandDense) At(i, j int) float64 {
+	return b.at(i, j)
+}
+
+func (b *BandDense) at(i, j int) float64 {
+	if uint(i) >= uint(b.mat.Rows) {
+		panic(ErrRowAccess)
+	}
+	if uint(j) >= uint(b.mat.Cols) {
+		panic(ErrColAccess)
+	}
+	pj := j + b.mat.KL - i
+	if pj < 0 || b.mat.KL+b.mat.KU+1 <= pj {
+		return 0
+	}
+	return b.mat.Data[i*b.mat.Stride+pj]
+}
+
+// SetBand sets the element at row i, column j to the value v.
+// It panics if the location is outside the appropriate region of the matrix.
+func (b *BandDense) SetBand(i, j int, v float64) {
+	b.set(i, j, v)
+}
+
+func (b *BandDense) set(i, j int, v float64) {
+	if uint(i) >= uint(b.mat.Rows) {
+		panic(ErrRowAccess)
+	}
+	if uint(j) >= uint(b.mat.Cols) {
+		panic(ErrColAccess)
+	}
+	pj := j + b.mat.KL - i
+	if pj < 0 || b.mat.KL+b.mat.KU+1 <= pj {
+		panic(ErrBandSet)
+	}
+	b.mat.Data[i*b.mat.Stride+pj] = v
+}
+
+// At returns the element at row i, column j.
+func (s *SymBandDense) At(i, j int) float64 {
+	return s.at(i, j)
+}
+
+func (s *SymBandDense) at(i, j int) float64 {
+	if uint(i) >= uint(s.mat.N) {
+		panic(ErrRowAccess)
+	}
+	if uint(j) >= uint(s.mat.N) {
+		panic(ErrColAccess)
+	}
+	if i > j {
+		i, j = j, i
+	}
+	pj := j - i
+	if s.mat.K+1 <= pj {
+		return 0
+	}
+	return s.mat.Data[i*s.mat.Stride+pj]
+}
+
+// SetSymBand sets the element at row i, column j to the value v.
+// It panics if the location is outside the appropriate region of the matrix.
+func (s *SymBandDense) SetSymBand(i, j int, v float64) {
+	s.set(i, j, v)
+}
+
+func (s *SymBandDense) set(i, j int, v float64) {
+	if uint(i) >= uint(s.mat.N) {
+		panic(ErrRowAccess)
+	}
+	if uint(j) >= uint(s.mat.N) {
+		panic(ErrColAccess)
+	}
+	if i > j {
+		i, j = j, i
+	}
+	pj := j - i
+	if s.mat.K+1 <= pj {
+		panic(ErrBandSet)
+	}
+	s.mat.Data[i*s.mat.Stride+pj] = v
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/index_no_bound_checks.go b/vendor/gonum.org/v1/gonum/mat/index_no_bound_checks.go
new file mode 100644
index 00000000..2aa378cb
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/index_no_bound_checks.go
@@ -0,0 +1,228 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// This file must be kept in sync with index_bound_checks.go.
+
+//+build !bounds
+
+package mat
+
+// At returns the element at row i, column j.
+func (m *Dense) At(i, j int) float64 {
+	if uint(i) >= uint(m.mat.Rows) {
+		panic(ErrRowAccess)
+	}
+	if uint(j) >= uint(m.mat.Cols) {
+		panic(ErrColAccess)
+	}
+	return m.at(i, j)
+}
+
+func (m *Dense) at(i, j int) float64 {
+	return m.mat.Data[i*m.mat.Stride+j]
+}
+
+// Set sets the element at row i, column j to the value v.
+func (m *Dense) Set(i, j int, v float64) {
+	if uint(i) >= uint(m.mat.Rows) {
+		panic(ErrRowAccess)
+	}
+	if uint(j) >= uint(m.mat.Cols) {
+		panic(ErrColAccess)
+	}
+	m.set(i, j, v)
+}
+
+func (m *Dense) set(i, j int, v float64) {
+	m.mat.Data[i*m.mat.Stride+j] = v
+}
+
+// At returns the element at row i.
+// It panics if i is out of bounds or if j is not zero.
+func (v *VecDense) At(i, j int) float64 {
+	if uint(i) >= uint(v.n) {
+		panic(ErrRowAccess)
+	}
+	if j != 0 {
+		panic(ErrColAccess)
+	}
+	return v.at(i)
+}
+
+func (v *VecDense) at(i int) float64 {
+	return v.mat.Data[i*v.mat.Inc]
+}
+
+// SetVec sets the element at row i to the value val.
+// It panics if i is out of bounds.
+func (v *VecDense) SetVec(i int, val float64) {
+	if uint(i) >= uint(v.n) {
+		panic(ErrVectorAccess)
+	}
+	v.setVec(i, val)
+}
+
+func (v *VecDense) setVec(i int, val float64) {
+	v.mat.Data[i*v.mat.Inc] = val
+}
+
+// At returns the element at row i and column j.
+func (s *SymDense) At(i, j int) float64 {
+	if uint(i) >= uint(s.mat.N) {
+		panic(ErrRowAccess)
+	}
+	if uint(j) >= uint(s.mat.N) {
+		panic(ErrColAccess)
+	}
+	return s.at(i, j)
+}
+
+func (s *SymDense) at(i, j int) float64 {
+	if i > j {
+		i, j = j, i
+	}
+	return s.mat.Data[i*s.mat.Stride+j]
+}
+
+// SetSym sets the elements at (i,j) and (j,i) to the value v.
+func (s *SymDense) SetSym(i, j int, v float64) {
+	if uint(i) >= uint(s.mat.N) {
+		panic(ErrRowAccess)
+	}
+	if uint(j) >= uint(s.mat.N) {
+		panic(ErrColAccess)
+	}
+	s.set(i, j, v)
+}
+
+func (s *SymDense) set(i, j int, v float64) {
+	if i > j {
+		i, j = j, i
+	}
+	s.mat.Data[i*s.mat.Stride+j] = v
+}
+
+// At returns the element at row i, column j.
+func (t *TriDense) At(i, j int) float64 {
+	if uint(i) >= uint(t.mat.N) {
+		panic(ErrRowAccess)
+	}
+	if uint(j) >= uint(t.mat.N) {
+		panic(ErrColAccess)
+	}
+	return t.at(i, j)
+}
+
+func (t *TriDense) at(i, j int) float64 {
+	isUpper := t.triKind()
+	if (isUpper && i > j) || (!isUpper && i < j) {
+		return 0
+	}
+	return t.mat.Data[i*t.mat.Stride+j]
+}
+
+// SetTri sets the element at row i, column j to the value v.
+// It panics if the location is outside the appropriate half of the matrix.
+func (t *TriDense) SetTri(i, j int, v float64) {
+	if uint(i) >= uint(t.mat.N) {
+		panic(ErrRowAccess)
+	}
+	if uint(j) >= uint(t.mat.N) {
+		panic(ErrColAccess)
+	}
+	isUpper := t.isUpper()
+	if (isUpper && i > j) || (!isUpper && i < j) {
+		panic(ErrTriangleSet)
+	}
+	t.set(i, j, v)
+}
+
+func (t *TriDense) set(i, j int, v float64) {
+	t.mat.Data[i*t.mat.Stride+j] = v
+}
+
+// At returns the element at row i, column j.
+func (b *BandDense) At(i, j int) float64 {
+	if uint(i) >= uint(b.mat.Rows) {
+		panic(ErrRowAccess)
+	}
+	if uint(j) >= uint(b.mat.Cols) {
+		panic(ErrColAccess)
+	}
+	return b.at(i, j)
+}
+
+func (b *BandDense) at(i, j int) float64 {
+	pj := j + b.mat.KL - i
+	if pj < 0 || b.mat.KL+b.mat.KU+1 <= pj {
+		return 0
+	}
+	return b.mat.Data[i*b.mat.Stride+pj]
+}
+
+// SetBand sets the element at row i, column j to the value v.
+// It panics if the location is outside the appropriate region of the matrix.
+func (b *BandDense) SetBand(i, j int, v float64) {
+	if uint(i) >= uint(b.mat.Rows) {
+		panic(ErrRowAccess)
+	}
+	if uint(j) >= uint(b.mat.Cols) {
+		panic(ErrColAccess)
+	}
+	pj := j + b.mat.KL - i
+	if pj < 0 || b.mat.KL+b.mat.KU+1 <= pj {
+		panic(ErrBandSet)
+	}
+	b.set(i, j, v)
+}
+
+func (b *BandDense) set(i, j int, v float64) {
+	pj := j + b.mat.KL - i
+	b.mat.Data[i*b.mat.Stride+pj] = v
+}
+
+// At returns the element at row i, column j.
+func (s *SymBandDense) At(i, j int) float64 {
+	if uint(i) >= uint(s.mat.N) {
+		panic(ErrRowAccess)
+	}
+	if uint(j) >= uint(s.mat.N) {
+		panic(ErrColAccess)
+	}
+	return s.at(i, j)
+}
+
+func (s *SymBandDense) at(i, j int) float64 {
+	if i > j {
+		i, j = j, i
+	}
+	pj := j - i
+	if s.mat.K+1 <= pj {
+		return 0
+	}
+	return s.mat.Data[i*s.mat.Stride+pj]
+}
+
+// SetSymBand sets the element at row i, column j to the value v.
+// It panics if the location is outside the appropriate region of the matrix.
+func (s *SymBandDense) SetSymBand(i, j int, v float64) {
+	if uint(i) >= uint(s.mat.N) {
+		panic(ErrRowAccess)
+	}
+	if uint(j) >= uint(s.mat.N) {
+		panic(ErrColAccess)
+	}
+	s.set(i, j, v)
+}
+
+func (s *SymBandDense) set(i, j int, v float64) {
+	if i > j {
+		i, j = j, i
+	}
+	pj := j - i
+	if s.mat.K+1 <= pj {
+		panic(ErrBandSet)
+	}
+	s.mat.Data[i*s.mat.Stride+pj] = v
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/inner.go b/vendor/gonum.org/v1/gonum/mat/inner.go
new file mode 100644
index 00000000..1acc615e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/inner.go
@@ -0,0 +1,102 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/internal/asm/f64"
+)
+
+// Inner computes the generalized inner product
+//   x^T A y
+// between vectors x and y with matrix A. This is only a true inner product if
+// A is symmetric positive definite, though the operation works for any matrix A.
+//
+// Inner panics if x.Len != m or y.Len != n when A is an m x n matrix.
+func Inner(x *VecDense, A Matrix, y *VecDense) float64 {
+	m, n := A.Dims()
+	if x.Len() != m {
+		panic(ErrShape)
+	}
+	if y.Len() != n {
+		panic(ErrShape)
+	}
+	if m == 0 || n == 0 {
+		return 0
+	}
+
+	var sum float64
+
+	switch b := A.(type) {
+	case RawSymmetricer:
+		bmat := b.RawSymmetric()
+		if bmat.Uplo != blas.Upper {
+			// Panic as a string not a mat.Error.
+			panic(badSymTriangle)
+		}
+		for i := 0; i < x.Len(); i++ {
+			xi := x.at(i)
+			if xi != 0 {
+				if y.mat.Inc == 1 {
+					sum += xi * f64.DotUnitary(
+						bmat.Data[i*bmat.Stride+i:i*bmat.Stride+n],
+						y.mat.Data[i:],
+					)
+				} else {
+					sum += xi * f64.DotInc(
+						bmat.Data[i*bmat.Stride+i:i*bmat.Stride+n],
+						y.mat.Data[i*y.mat.Inc:], uintptr(n-i),
+						1, uintptr(y.mat.Inc),
+						0, 0,
+					)
+				}
+			}
+			yi := y.at(i)
+			if i != n-1 && yi != 0 {
+				if x.mat.Inc == 1 {
+					sum += yi * f64.DotUnitary(
+						bmat.Data[i*bmat.Stride+i+1:i*bmat.Stride+n],
+						x.mat.Data[i+1:],
+					)
+				} else {
+					sum += yi * f64.DotInc(
+						bmat.Data[i*bmat.Stride+i+1:i*bmat.Stride+n],
+						x.mat.Data[(i+1)*x.mat.Inc:], uintptr(n-i-1),
+						1, uintptr(x.mat.Inc),
+						0, 0,
+					)
+				}
+			}
+		}
+	case RawMatrixer:
+		bmat := b.RawMatrix()
+		for i := 0; i < x.Len(); i++ {
+			xi := x.at(i)
+			if xi != 0 {
+				if y.mat.Inc == 1 {
+					sum += xi * f64.DotUnitary(
+						bmat.Data[i*bmat.Stride:i*bmat.Stride+n],
+						y.mat.Data,
+					)
+				} else {
+					sum += xi * f64.DotInc(
+						bmat.Data[i*bmat.Stride:i*bmat.Stride+n],
+						y.mat.Data, uintptr(n),
+						1, uintptr(y.mat.Inc),
+						0, 0,
+					)
+				}
+			}
+		}
+	default:
+		for i := 0; i < x.Len(); i++ {
+			xi := x.at(i)
+			for j := 0; j < y.Len(); j++ {
+				sum += xi * A.At(i, j) * y.at(j)
+			}
+		}
+	}
+	return sum
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/inner_test.go b/vendor/gonum.org/v1/gonum/mat/inner_test.go
new file mode 100644
index 00000000..05a76b72
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/inner_test.go
@@ -0,0 +1,181 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"math"
+	"testing"
+
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/blas/testblas"
+)
+
+func TestInner(t *testing.T) {
+	for i, test := range []struct {
+		x []float64
+		y []float64
+		m [][]float64
+	}{
+		{
+			x: []float64{5},
+			y: []float64{10},
+			m: [][]float64{{2}},
+		},
+		{
+			x: []float64{5, 6, 1},
+			y: []float64{10},
+			m: [][]float64{{2}, {-3}, {5}},
+		},
+		{
+			x: []float64{5},
+			y: []float64{10, 15},
+			m: [][]float64{{2, -3}},
+		},
+		{
+			x: []float64{1, 5},
+			y: []float64{10, 15},
+			m: [][]float64{
+				{2, -3},
+				{4, -1},
+			},
+		},
+		{
+			x: []float64{2, 3, 9},
+			y: []float64{8, 9},
+			m: [][]float64{
+				{2, 3},
+				{4, 5},
+				{6, 7},
+			},
+		},
+		{
+			x: []float64{2, 3},
+			y: []float64{8, 9, 9},
+			m: [][]float64{
+				{2, 3, 6},
+				{4, 5, 7},
+			},
+		},
+	} {
+		for _, inc := range []struct{ x, y int }{
+			{1, 1},
+			{1, 2},
+			{2, 1},
+			{2, 2},
+		} {
+			x := NewDense(1, len(test.x), test.x)
+			m := NewDense(flatten(test.m))
+			mWant := NewDense(flatten(test.m))
+			y := NewDense(len(test.y), 1, test.y)
+
+			var tmp, cell Dense
+			tmp.Mul(mWant, y)
+			cell.Mul(x, &tmp)
+
+			rm, cm := cell.Dims()
+			if rm != 1 {
+				t.Errorf("Test %d result doesn't have 1 row", i)
+			}
+			if cm != 1 {
+				t.Errorf("Test %d result doesn't have 1 column", i)
+			}
+
+			want := cell.At(0, 0)
+			got := Inner(makeVecDenseInc(inc.x, test.x), m, makeVecDenseInc(inc.y, test.y))
+			if got != want {
+				t.Errorf("Test %v: want %v, got %v", i, want, got)
+			}
+		}
+	}
+}
+
+func TestInnerSym(t *testing.T) {
+	for _, inc := range []struct{ x, y int }{
+		{1, 1},
+		{1, 2},
+		{2, 1},
+		{2, 2},
+	} {
+		n := 10
+		xData := make([]float64, n)
+		yData := make([]float64, n)
+		data := make([]float64, n*n)
+		for i := 0; i < n; i++ {
+			xData[i] = float64(i)
+			yData[i] = float64(i)
+			for j := i; j < n; j++ {
+				data[i*n+j] = float64(i*n + j)
+				data[j*n+i] = data[i*n+j]
+			}
+		}
+		x := makeVecDenseInc(inc.x, xData)
+		y := makeVecDenseInc(inc.y, yData)
+		m := NewDense(n, n, data)
+		ans := Inner(x, m, y)
+		sym := NewSymDense(n, data)
+		// Poison the lower half of data to ensure it is not used.
+		for i := 1; i < n; i++ {
+			for j := 0; j < i; j++ {
+				data[i*n+j] = math.NaN()
+			}
+		}
+
+		if math.Abs(Inner(x, sym, y)-ans) > 1e-14 {
+			t.Error("inner different symmetric and dense")
+		}
+	}
+}
+
+func makeVecDenseInc(inc int, f []float64) *VecDense {
+	v := &VecDense{
+		n: len(f),
+		mat: blas64.Vector{
+			Inc:  inc,
+			Data: make([]float64, (len(f)-1)*inc+1),
+		},
+	}
+
+	// Contaminate backing data in all positions...
+	const base = 100
+	for i := range v.mat.Data {
+		v.mat.Data[i] = float64(i + base)
+	}
+
+	// then write real elements.
+	for i := range f {
+		v.mat.Data[i*inc] = f[i]
+	}
+	return v
+}
+
+func benchmarkInner(b *testing.B, m, n int) {
+	x := NewVecDense(m, nil)
+	randomSlice(x.mat.Data)
+	y := NewVecDense(n, nil)
+	randomSlice(y.mat.Data)
+	data := make([]float64, m*n)
+	randomSlice(data)
+	mat := &Dense{mat: blas64.General{Rows: m, Cols: n, Stride: n, Data: data}, capRows: m, capCols: n}
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		Inner(x, mat, y)
+	}
+}
+
+func BenchmarkInnerSmSm(b *testing.B) {
+	benchmarkInner(b, testblas.SmallMat, testblas.SmallMat)
+}
+
+func BenchmarkInnerMedMed(b *testing.B) {
+	benchmarkInner(b, testblas.MediumMat, testblas.MediumMat)
+}
+
+func BenchmarkInnerLgLg(b *testing.B) {
+	benchmarkInner(b, testblas.LargeMat, testblas.LargeMat)
+}
+
+func BenchmarkInnerLgSm(b *testing.B) {
+	benchmarkInner(b, testblas.LargeMat, testblas.SmallMat)
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/io.go b/vendor/gonum.org/v1/gonum/mat/io.go
new file mode 100644
index 00000000..db429bfa
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/io.go
@@ -0,0 +1,360 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"encoding/binary"
+	"errors"
+	"io"
+	"math"
+)
+
+const (
+	// maxLen is the biggest slice/array len one can create on a 32/64b platform.
+	maxLen = int64(int(^uint(0) >> 1))
+)
+
+var (
+	sizeInt64   = binary.Size(int64(0))
+	sizeFloat64 = binary.Size(float64(0))
+
+	errTooBig    = errors.New("mat: resulting data slice too big")
+	errTooSmall  = errors.New("mat: input slice too small")
+	errBadBuffer = errors.New("mat: data buffer size mismatch")
+	errBadSize   = errors.New("mat: invalid dimension")
+)
+
+// MarshalBinary encodes the receiver into a binary form and returns the result.
+//
+// Dense is little-endian encoded as follows:
+//   0 -  7  number of rows    (int64)
+//   8 - 15  number of columns (int64)
+//  16 - ..  matrix data elements (float64)
+//           [0,0] [0,1] ... [0,ncols-1]
+//           [1,0] [1,1] ... [1,ncols-1]
+//           ...
+//           [nrows-1,0] ... [nrows-1,ncols-1]
+func (m Dense) MarshalBinary() ([]byte, error) {
+	bufLen := int64(m.mat.Rows)*int64(m.mat.Cols)*int64(sizeFloat64) + 2*int64(sizeInt64)
+	if bufLen <= 0 {
+		// bufLen is too big and has wrapped around.
+		return nil, errTooBig
+	}
+
+	p := 0
+	buf := make([]byte, bufLen)
+	binary.LittleEndian.PutUint64(buf[p:p+sizeInt64], uint64(m.mat.Rows))
+	p += sizeInt64
+	binary.LittleEndian.PutUint64(buf[p:p+sizeInt64], uint64(m.mat.Cols))
+	p += sizeInt64
+
+	r, c := m.Dims()
+	for i := 0; i < r; i++ {
+		for j := 0; j < c; j++ {
+			binary.LittleEndian.PutUint64(buf[p:p+sizeFloat64], math.Float64bits(m.at(i, j)))
+			p += sizeFloat64
+		}
+	}
+
+	return buf, nil
+}
+
+// MarshalBinaryTo encodes the receiver into a binary form and writes it into w.
+// MarshalBinaryTo returns the number of bytes written into w and an error, if any.
+//
+// See MarshalBinary for the on-disk layout.
+func (m Dense) MarshalBinaryTo(w io.Writer) (int, error) {
+	var n int
+	var buf [8]byte
+	binary.LittleEndian.PutUint64(buf[:], uint64(m.mat.Rows))
+	nn, err := w.Write(buf[:])
+	n += nn
+	if err != nil {
+		return n, err
+	}
+	binary.LittleEndian.PutUint64(buf[:], uint64(m.mat.Cols))
+	nn, err = w.Write(buf[:])
+	n += nn
+	if err != nil {
+		return n, err
+	}
+
+	r, c := m.Dims()
+	for i := 0; i < r; i++ {
+		for j := 0; j < c; j++ {
+			binary.LittleEndian.PutUint64(buf[:], math.Float64bits(m.at(i, j)))
+			nn, err = w.Write(buf[:])
+			n += nn
+			if err != nil {
+				return n, err
+			}
+		}
+	}
+
+	return n, nil
+}
+
+// UnmarshalBinary decodes the binary form into the receiver.
+// It panics if the receiver is a non-zero Dense matrix.
+//
+// See MarshalBinary for the on-disk layout.
+//
+// Limited checks on the validity of the binary input are performed:
+//  - matrix.ErrShape is returned if the number of rows or columns is negative,
+//  - an error is returned if the resulting Dense matrix is too
+//  big for the current architecture (e.g. a 16GB matrix written by a
+//  64b application and read back from a 32b application.)
+// UnmarshalBinary does not limit the size of the unmarshaled matrix, and so
+// it should not be used on untrusted data.
+func (m *Dense) UnmarshalBinary(data []byte) error {
+	if !m.IsZero() {
+		panic("mat: unmarshal into non-zero matrix")
+	}
+
+	if len(data) < 2*sizeInt64 {
+		return errTooSmall
+	}
+
+	p := 0
+	rows := int64(binary.LittleEndian.Uint64(data[p : p+sizeInt64]))
+	p += sizeInt64
+	cols := int64(binary.LittleEndian.Uint64(data[p : p+sizeInt64]))
+	p += sizeInt64
+	if rows < 0 || cols < 0 {
+		return errBadSize
+	}
+
+	size := rows * cols
+	if int(size) < 0 || size > maxLen {
+		return errTooBig
+	}
+
+	if len(data) != int(size)*sizeFloat64+2*sizeInt64 {
+		return errBadBuffer
+	}
+
+	m.reuseAs(int(rows), int(cols))
+	for i := range m.mat.Data {
+		m.mat.Data[i] = math.Float64frombits(binary.LittleEndian.Uint64(data[p : p+sizeFloat64]))
+		p += sizeFloat64
+	}
+
+	return nil
+}
+
+// UnmarshalBinaryFrom decodes the binary form into the receiver and returns
+// the number of bytes read and an error if any.
+// It panics if the receiver is a non-zero Dense matrix.
+//
+// See MarshalBinary for the on-disk layout.
+//
+// Limited checks on the validity of the binary input are performed:
+//  - matrix.ErrShape is returned if the number of rows or columns is negative,
+//  - an error is returned if the resulting Dense matrix is too
+//  big for the current architecture (e.g. a 16GB matrix written by a
+//  64b application and read back from a 32b application.)
+// UnmarshalBinary does not limit the size of the unmarshaled matrix, and so
+// it should not be used on untrusted data.
+func (m *Dense) UnmarshalBinaryFrom(r io.Reader) (int, error) {
+	if !m.IsZero() {
+		panic("mat: unmarshal into non-zero matrix")
+	}
+
+	var (
+		n   int
+		buf [8]byte
+	)
+	nn, err := readFull(r, buf[:])
+	n += nn
+	if err != nil {
+		return n, err
+	}
+	rows := int64(binary.LittleEndian.Uint64(buf[:]))
+
+	nn, err = readFull(r, buf[:])
+	n += nn
+	if err != nil {
+		return n, err
+	}
+	cols := int64(binary.LittleEndian.Uint64(buf[:]))
+	if rows < 0 || cols < 0 {
+		return n, errBadSize
+	}
+
+	size := rows * cols
+	if int(size) < 0 || size > maxLen {
+		return n, errTooBig
+	}
+
+	m.reuseAs(int(rows), int(cols))
+	for i := range m.mat.Data {
+		nn, err = readFull(r, buf[:])
+		n += nn
+		if err != nil {
+			return n, err
+		}
+		m.mat.Data[i] = math.Float64frombits(binary.LittleEndian.Uint64(buf[:]))
+	}
+
+	return n, nil
+}
+
+// MarshalBinary encodes the receiver into a binary form and returns the result.
+//
+// VecDense is little-endian encoded as follows:
+//   0 -  7  number of elements     (int64)
+//   8 - ..  vector's data elements (float64)
+func (v VecDense) MarshalBinary() ([]byte, error) {
+	bufLen := int64(sizeInt64) + int64(v.n)*int64(sizeFloat64)
+	if bufLen <= 0 {
+		// bufLen is too big and has wrapped around.
+		return nil, errTooBig
+	}
+
+	p := 0
+	buf := make([]byte, bufLen)
+	binary.LittleEndian.PutUint64(buf[p:p+sizeInt64], uint64(v.n))
+	p += sizeInt64
+
+	for i := 0; i < v.n; i++ {
+		binary.LittleEndian.PutUint64(buf[p:p+sizeFloat64], math.Float64bits(v.at(i)))
+		p += sizeFloat64
+	}
+
+	return buf, nil
+}
+
+// MarshalBinaryTo encodes the receiver into a binary form, writes it to w and
+// returns the number of bytes written and an error if any.
+//
+// See MarshalBainry for the on-disk format.
+func (v VecDense) MarshalBinaryTo(w io.Writer) (int, error) {
+	var (
+		n   int
+		buf [8]byte
+	)
+
+	binary.LittleEndian.PutUint64(buf[:], uint64(v.n))
+	nn, err := w.Write(buf[:])
+	n += nn
+	if err != nil {
+		return n, err
+	}
+
+	for i := 0; i < v.n; i++ {
+		binary.LittleEndian.PutUint64(buf[:], math.Float64bits(v.at(i)))
+		nn, err = w.Write(buf[:])
+		n += nn
+		if err != nil {
+			return n, err
+		}
+	}
+
+	return n, nil
+}
+
+// UnmarshalBinary decodes the binary form into the receiver.
+// It panics if the receiver is a non-zero VecDense.
+//
+// See MarshalBinary for the on-disk layout.
+//
+// Limited checks on the validity of the binary input are performed:
+//  - matrix.ErrShape is returned if the number of rows is negative,
+//  - an error is returned if the resulting VecDense is too
+//  big for the current architecture (e.g. a 16GB vector written by a
+//  64b application and read back from a 32b application.)
+// UnmarshalBinary does not limit the size of the unmarshaled vector, and so
+// it should not be used on untrusted data.
+func (v *VecDense) UnmarshalBinary(data []byte) error {
+	if !v.IsZero() {
+		panic("mat: unmarshal into non-zero vector")
+	}
+
+	p := 0
+	n := int64(binary.LittleEndian.Uint64(data[p : p+sizeInt64]))
+	p += sizeInt64
+	if n < 0 {
+		return errBadSize
+	}
+	if n > maxLen {
+		return errTooBig
+	}
+	if len(data) != int(n)*sizeFloat64+sizeInt64 {
+		return errBadBuffer
+	}
+
+	v.reuseAs(int(n))
+	for i := range v.mat.Data {
+		v.mat.Data[i] = math.Float64frombits(binary.LittleEndian.Uint64(data[p : p+sizeFloat64]))
+		p += sizeFloat64
+	}
+
+	return nil
+}
+
+// UnmarshalBinaryFrom decodes the binary form into the receiver, from the
+// io.Reader and returns the number of bytes read and an error if any.
+// It panics if the receiver is a non-zero VecDense.
+//
+// See MarshalBinary for the on-disk layout.
+// See UnmarshalBinary for the list of sanity checks performed on the input.
+func (v *VecDense) UnmarshalBinaryFrom(r io.Reader) (int, error) {
+	if !v.IsZero() {
+		panic("mat: unmarshal into non-zero vector")
+	}
+
+	var (
+		n   int
+		buf [8]byte
+	)
+	nn, err := readFull(r, buf[:])
+	n += nn
+	if err != nil {
+		return n, err
+	}
+	sz := int64(binary.LittleEndian.Uint64(buf[:]))
+	if sz < 0 {
+		return n, errBadSize
+	}
+	if sz > maxLen {
+		return n, errTooBig
+	}
+
+	v.reuseAs(int(sz))
+	for i := range v.mat.Data {
+		nn, err = readFull(r, buf[:])
+		n += nn
+		if err != nil {
+			return n, err
+		}
+		v.mat.Data[i] = math.Float64frombits(binary.LittleEndian.Uint64(buf[:]))
+	}
+
+	if n != sizeInt64+int(sz)*sizeFloat64 {
+		return n, io.ErrUnexpectedEOF
+	}
+
+	return n, nil
+}
+
+// readFull reads from r into buf until it has read len(buf).
+// It returns the number of bytes copied and an error if fewer bytes were read.
+// If an EOF happens after reading fewer than len(buf) bytes, io.ErrUnexpectedEOF is returned.
+func readFull(r io.Reader, buf []byte) (int, error) {
+	var n int
+	var err error
+	for n < len(buf) && err == nil {
+		var nn int
+		nn, err = r.Read(buf[n:])
+		n += nn
+	}
+	if n == len(buf) {
+		return n, nil
+	}
+	if err == io.EOF {
+		return n, io.ErrUnexpectedEOF
+	}
+	return n, err
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/io_test.go b/vendor/gonum.org/v1/gonum/mat/io_test.go
new file mode 100644
index 00000000..e2dd639d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/io_test.go
@@ -0,0 +1,731 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"bytes"
+	"encoding"
+	"io"
+	"io/ioutil"
+	"math"
+	"testing"
+
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+var (
+	_ encoding.BinaryMarshaler   = (*Dense)(nil)
+	_ encoding.BinaryUnmarshaler = (*Dense)(nil)
+	_ encoding.BinaryMarshaler   = (*VecDense)(nil)
+	_ encoding.BinaryUnmarshaler = (*VecDense)(nil)
+)
+
+var denseData = []struct {
+	raw  []byte
+	want *Dense
+	eq   func(got, want Matrix) bool
+}{
+	{
+		raw:  []byte("\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00"),
+		want: NewDense(0, 0, []float64{}),
+		eq:   Equal,
+	},
+	{
+		raw:  []byte("\x02\x00\x00\x00\x00\x00\x00\x00\x02\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xf0?\x00\x00\x00\x00\x00\x00\x00@\x00\x00\x00\x00\x00\x00\b@\x00\x00\x00\x00\x00\x00\x10@"),
+		want: NewDense(2, 2, []float64{1, 2, 3, 4}),
+		eq:   Equal,
+	},
+	{
+		raw:  []byte("\x02\x00\x00\x00\x00\x00\x00\x00\x03\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xf0?\x00\x00\x00\x00\x00\x00\x00@\x00\x00\x00\x00\x00\x00\b@\x00\x00\x00\x00\x00\x00\x10@\x00\x00\x00\x00\x00\x00\x14@\x00\x00\x00\x00\x00\x00\x18@"),
+		want: NewDense(2, 3, []float64{1, 2, 3, 4, 5, 6}),
+		eq:   Equal,
+	},
+	{
+		raw:  []byte("\x03\x00\x00\x00\x00\x00\x00\x00\x02\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xf0?\x00\x00\x00\x00\x00\x00\x00@\x00\x00\x00\x00\x00\x00\b@\x00\x00\x00\x00\x00\x00\x10@\x00\x00\x00\x00\x00\x00\x14@\x00\x00\x00\x00\x00\x00\x18@"),
+		want: NewDense(3, 2, []float64{1, 2, 3, 4, 5, 6}),
+		eq:   Equal,
+	},
+	{
+		raw:  []byte("\x03\x00\x00\x00\x00\x00\x00\x00\x03\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xf0?\x00\x00\x00\x00\x00\x00\x00@\x00\x00\x00\x00\x00\x00\b@\x00\x00\x00\x00\x00\x00\x10@\x00\x00\x00\x00\x00\x00\x14@\x00\x00\x00\x00\x00\x00\x18@\x00\x00\x00\x00\x00\x00\x1c@\x00\x00\x00\x00\x00\x00 @\x00\x00\x00\x00\x00\x00\"@"),
+		want: NewDense(3, 3, []float64{1, 2, 3, 4, 5, 6, 7, 8, 9}),
+		eq:   Equal,
+	},
+	{
+		raw:  []byte("\x02\x00\x00\x00\x00\x00\x00\x00\x02\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xf0?\x00\x00\x00\x00\x00\x00\x00@\x00\x00\x00\x00\x00\x00\x10@\x00\x00\x00\x00\x00\x00\x14@"),
+		want: NewDense(3, 3, []float64{1, 2, 3, 4, 5, 6, 7, 8, 9}).Slice(0, 2, 0, 2).(*Dense),
+		eq:   Equal,
+	},
+	{
+		raw:  []byte("\x02\x00\x00\x00\x00\x00\x00\x00\x02\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x14@\x00\x00\x00\x00\x00\x00\x18@\x00\x00\x00\x00\x00\x00 @\x00\x00\x00\x00\x00\x00\"@"),
+		want: NewDense(3, 3, []float64{1, 2, 3, 4, 5, 6, 7, 8, 9}).Slice(1, 3, 1, 3).(*Dense),
+		eq:   Equal,
+	},
+	{
+		raw:  []byte("\x03\x00\x00\x00\x00\x00\x00\x00\x02\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00@\x00\x00\x00\x00\x00\x00\b@\x00\x00\x00\x00\x00\x00\x14@\x00\x00\x00\x00\x00\x00\x18@\x00\x00\x00\x00\x00\x00 @\x00\x00\x00\x00\x00\x00\"@"),
+		want: NewDense(3, 3, []float64{1, 2, 3, 4, 5, 6, 7, 8, 9}).Slice(0, 3, 1, 3).(*Dense),
+		eq:   Equal,
+	},
+	{
+		raw:  []byte("\x01\x00\x00\x00\x00\x00\x00\x00\x04\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xf0\xff\x00\x00\x00\x00\x00\x00\xf0\u007f\x01\x00\x00\x00\x00\x00\xf8\u007f"),
+		want: NewDense(1, 4, []float64{0, math.Inf(-1), math.Inf(+1), math.NaN()}),
+		eq: func(got, want Matrix) bool {
+			for _, v := range []bool{
+				got.At(0, 0) == 0,
+				math.IsInf(got.At(0, 1), -1),
+				math.IsInf(got.At(0, 2), +1),
+				math.IsNaN(got.At(0, 3)),
+			} {
+				if !v {
+					return false
+				}
+			}
+			return true
+		},
+	},
+}
+
+func TestDenseMarshal(t *testing.T) {
+	for i, test := range denseData {
+		buf, err := test.want.MarshalBinary()
+		if err != nil {
+			t.Errorf("error encoding test-%d: %v\n", i, err)
+			continue
+		}
+
+		nrows, ncols := test.want.Dims()
+		sz := nrows*ncols*sizeFloat64 + 2*sizeInt64
+		if len(buf) != sz {
+			t.Errorf("encoded size test-%d: want=%d got=%d\n", i, sz, len(buf))
+		}
+
+		if !bytes.Equal(buf, test.raw) {
+			t.Errorf("error encoding test-%d: bytes mismatch.\n got=%q\nwant=%q\n",
+				i,
+				string(buf),
+				string(test.raw),
+			)
+			continue
+		}
+	}
+}
+
+func TestDenseMarshalTo(t *testing.T) {
+	for i, test := range denseData {
+		buf := new(bytes.Buffer)
+		n, err := test.want.MarshalBinaryTo(buf)
+		if err != nil {
+			t.Errorf("error encoding test-%d: %v\n", i, err)
+			continue
+		}
+
+		nrows, ncols := test.want.Dims()
+		sz := nrows*ncols*sizeFloat64 + 2*sizeInt64
+		if n != sz {
+			t.Errorf("encoded size test-%d: want=%d got=%d\n", i, sz, n)
+		}
+
+		if !bytes.Equal(buf.Bytes(), test.raw) {
+			t.Errorf("error encoding test-%d: bytes mismatch.\n got=%q\nwant=%q\n",
+				i,
+				string(buf.Bytes()),
+				string(test.raw),
+			)
+			continue
+		}
+	}
+}
+
+func TestDenseUnmarshal(t *testing.T) {
+	for i, test := range denseData {
+		var v Dense
+		err := v.UnmarshalBinary(test.raw)
+		if err != nil {
+			t.Errorf("error decoding test-%d: %v\n", i, err)
+			continue
+		}
+		if !test.eq(&v, test.want) {
+			t.Errorf("error decoding test-%d: values differ.\n got=%v\nwant=%v\n",
+				i,
+				&v,
+				test.want,
+			)
+		}
+	}
+}
+
+func TestDenseUnmarshalFrom(t *testing.T) {
+	for i, test := range denseData {
+		var v Dense
+		buf := bytes.NewReader(test.raw)
+		n, err := v.UnmarshalBinaryFrom(buf)
+		if err != nil {
+			t.Errorf("error decoding test-%d: %v\n", i, err)
+			continue
+		}
+		if n != len(test.raw) {
+			t.Errorf("error decoding test-%d: lengths differ.\n got=%d\nwant=%d\n",
+				i, n, len(test.raw),
+			)
+		}
+		if !test.eq(&v, test.want) {
+			t.Errorf("error decoding test-%d: values differ.\n got=%v\nwant=%v\n",
+				i,
+				&v,
+				test.want,
+			)
+		}
+	}
+}
+
+func TestDenseUnmarshalFromError(t *testing.T) {
+	test := denseData[1]
+	for i, tt := range []struct {
+		beg int
+		end int
+	}{
+		{
+			beg: 0,
+			end: len(test.raw) - 1,
+		},
+		{
+			beg: 0,
+			end: len(test.raw) - sizeFloat64,
+		},
+		{
+			beg: 0,
+			end: 0,
+		},
+		{
+			beg: 0,
+			end: 1,
+		},
+		{
+			beg: 0,
+			end: sizeInt64,
+		},
+		{
+			beg: 0,
+			end: sizeInt64 - 1,
+		},
+		{
+			beg: 0,
+			end: sizeInt64 + 1,
+		},
+		{
+			beg: 0,
+			end: 2*sizeInt64 - 1,
+		},
+		{
+			beg: 0,
+			end: 2 * sizeInt64,
+		},
+		{
+			beg: 0,
+			end: 2*sizeInt64 + 1,
+		},
+		{
+			beg: 0,
+			end: 2*sizeInt64 + sizeFloat64 - 1,
+		},
+		{
+			beg: 0,
+			end: 2*sizeInt64 + sizeFloat64,
+		},
+		{
+			beg: 0,
+			end: 2*sizeInt64 + sizeFloat64 + 1,
+		},
+	} {
+		buf := bytes.NewReader(test.raw[tt.beg:tt.end])
+		var m Dense
+		_, err := m.UnmarshalBinaryFrom(buf)
+		if err != io.ErrUnexpectedEOF {
+			t.Errorf("test #%d: error decoding. got=%v. want=%v\n", i, err, io.ErrUnexpectedEOF)
+		}
+	}
+}
+
+func TestDenseIORoundTrip(t *testing.T) {
+	for i, test := range denseData {
+		buf, err := test.want.MarshalBinary()
+		if err != nil {
+			t.Errorf("error encoding test #%d: %v\n", i, err)
+		}
+
+		var got Dense
+		err = got.UnmarshalBinary(buf)
+		if err != nil {
+			t.Errorf("error decoding test #%d: %v\n", i, err)
+		}
+
+		if !test.eq(&got, test.want) {
+			t.Errorf("r/w test #%d failed\n got=%#v\nwant=%#v\n", i, &got, test.want)
+		}
+
+		wbuf := new(bytes.Buffer)
+		_, err = test.want.MarshalBinaryTo(wbuf)
+		if err != nil {
+			t.Errorf("error encoding test #%d: %v\n", i, err)
+		}
+
+		if !bytes.Equal(buf, wbuf.Bytes()) {
+			t.Errorf("r/w test #%d encoding via MarshalBinary and MarshalBinaryTo differ:\nwith-stream: %q\n  no-stream: %q\n",
+				i, wbuf.Bytes(), buf,
+			)
+		}
+
+		var wgot Dense
+		_, err = wgot.UnmarshalBinaryFrom(wbuf)
+		if err != nil {
+			t.Errorf("error decoding test #%d: %v\n", i, err)
+		}
+
+		if !test.eq(&wgot, test.want) {
+			t.Errorf("r/w test #%d failed\n got=%#v\nwant=%#v\n", i, &wgot, test.want)
+		}
+	}
+}
+
+var vectorData = []struct {
+	raw  []byte
+	want *VecDense
+	eq   func(got, want Matrix) bool
+}{
+	{
+		raw:  []byte("\x00\x00\x00\x00\x00\x00\x00\x00"),
+		want: NewVecDense(0, []float64{}),
+		eq:   Equal,
+	},
+	{
+		raw:  []byte("\x04\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xf0?\x00\x00\x00\x00\x00\x00\x00@\x00\x00\x00\x00\x00\x00\b@\x00\x00\x00\x00\x00\x00\x10@"),
+		want: NewVecDense(4, []float64{1, 2, 3, 4}),
+		eq:   Equal,
+	},
+	{
+		raw:  []byte("\x06\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xf0?\x00\x00\x00\x00\x00\x00\x00@\x00\x00\x00\x00\x00\x00\b@\x00\x00\x00\x00\x00\x00\x10@\x00\x00\x00\x00\x00\x00\x14@\x00\x00\x00\x00\x00\x00\x18@"),
+		want: NewVecDense(6, []float64{1, 2, 3, 4, 5, 6}),
+		eq:   Equal,
+	},
+	{
+		raw:  []byte("\t\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xf0?\x00\x00\x00\x00\x00\x00\x00@\x00\x00\x00\x00\x00\x00\b@\x00\x00\x00\x00\x00\x00\x10@\x00\x00\x00\x00\x00\x00\x14@\x00\x00\x00\x00\x00\x00\x18@\x00\x00\x00\x00\x00\x00\x1c@\x00\x00\x00\x00\x00\x00 @\x00\x00\x00\x00\x00\x00\"@"),
+		want: NewVecDense(9, []float64{1, 2, 3, 4, 5, 6, 7, 8, 9}),
+		eq:   Equal,
+	},
+	{
+		raw:  []byte("\x03\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xf0?\x00\x00\x00\x00\x00\x00\x00@\x00\x00\x00\x00\x00\x00\b@"),
+		want: NewVecDense(9, []float64{1, 2, 3, 4, 5, 6, 7, 8, 9}).SliceVec(0, 3),
+		eq:   Equal,
+	},
+	{
+		raw:  []byte("\x03\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00@\x00\x00\x00\x00\x00\x00\b@\x00\x00\x00\x00\x00\x00\x10@"),
+		want: NewVecDense(9, []float64{1, 2, 3, 4, 5, 6, 7, 8, 9}).SliceVec(1, 4),
+		eq:   Equal,
+	},
+	{
+		raw:  []byte("\b\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xf0?\x00\x00\x00\x00\x00\x00\x00@\x00\x00\x00\x00\x00\x00\b@\x00\x00\x00\x00\x00\x00\x10@\x00\x00\x00\x00\x00\x00\x14@\x00\x00\x00\x00\x00\x00\x18@\x00\x00\x00\x00\x00\x00\x1c@\x00\x00\x00\x00\x00\x00 @"),
+		want: NewVecDense(9, []float64{1, 2, 3, 4, 5, 6, 7, 8, 9}).SliceVec(0, 8),
+		eq:   Equal,
+	},
+	{
+		raw: []byte("\x03\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\b@\x00\x00\x00\x00\x00\x00\x18@"),
+		want: &VecDense{
+			mat: blas64.Vector{
+				Data: []float64{0, 1, 2, 3, 4, 5, 6},
+				Inc:  3,
+			},
+			n: 3,
+		},
+		eq: Equal,
+	},
+	{
+		raw:  []byte("\x04\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xf0\xff\x00\x00\x00\x00\x00\x00\xf0\u007f\x01\x00\x00\x00\x00\x00\xf8\u007f"),
+		want: NewVecDense(4, []float64{0, math.Inf(-1), math.Inf(+1), math.NaN()}),
+		eq: func(got, want Matrix) bool {
+			for _, v := range []bool{
+				got.At(0, 0) == 0,
+				math.IsInf(got.At(1, 0), -1),
+				math.IsInf(got.At(2, 0), +1),
+				math.IsNaN(got.At(3, 0)),
+			} {
+				if !v {
+					return false
+				}
+			}
+			return true
+		},
+	},
+}
+
+func TestVecDenseMarshal(t *testing.T) {
+	for i, test := range vectorData {
+		buf, err := test.want.MarshalBinary()
+		if err != nil {
+			t.Errorf("error encoding test-%d: %v\n", i, err)
+			continue
+		}
+
+		nrows, ncols := test.want.Dims()
+		sz := nrows*ncols*sizeFloat64 + sizeInt64
+		if len(buf) != sz {
+			t.Errorf("encoded size test-%d: want=%d got=%d\n", i, sz, len(buf))
+		}
+
+		if !bytes.Equal(buf, test.raw) {
+			t.Errorf("error encoding test-%d: bytes mismatch.\n got=%q\nwant=%q\n",
+				i,
+				string(buf),
+				string(test.raw),
+			)
+			continue
+		}
+	}
+}
+
+func TestVecDenseMarshalTo(t *testing.T) {
+	for i, test := range vectorData {
+		buf := new(bytes.Buffer)
+		n, err := test.want.MarshalBinaryTo(buf)
+		if err != nil {
+			t.Errorf("error encoding test-%d: %v\n", i, err)
+			continue
+		}
+
+		nrows, ncols := test.want.Dims()
+		sz := nrows*ncols*sizeFloat64 + sizeInt64
+		if n != sz {
+			t.Errorf("encoded size test-%d: want=%d got=%d\n", i, sz, n)
+		}
+
+		if !bytes.Equal(buf.Bytes(), test.raw) {
+			t.Errorf("error encoding test-%d: bytes mismatch.\n got=%q\nwant=%q\n",
+				i,
+				string(buf.Bytes()),
+				string(test.raw),
+			)
+			continue
+		}
+	}
+}
+
+func TestVecDenseUnmarshal(t *testing.T) {
+	for i, test := range vectorData {
+		var v VecDense
+		err := v.UnmarshalBinary(test.raw)
+		if err != nil {
+			t.Errorf("error decoding test-%d: %v\n", i, err)
+			continue
+		}
+		if !test.eq(&v, test.want) {
+			t.Errorf("error decoding test-%d: values differ.\n got=%v\nwant=%v\n",
+				i,
+				&v,
+				test.want,
+			)
+		}
+	}
+}
+
+func TestVecDenseUnmarshalFrom(t *testing.T) {
+	for i, test := range vectorData {
+		var v VecDense
+		buf := bytes.NewReader(test.raw)
+		n, err := v.UnmarshalBinaryFrom(buf)
+		if err != nil {
+			t.Errorf("error decoding test-%d: %v\n", i, err)
+			continue
+		}
+		if n != len(test.raw) {
+			t.Errorf("error decoding test-%d: lengths differ.\n got=%d\nwant=%d\n",
+				i,
+				n,
+				len(test.raw),
+			)
+		}
+		if !test.eq(&v, test.want) {
+			t.Errorf("error decoding test-%d: values differ.\n got=%v\nwant=%v\n",
+				i,
+				&v,
+				test.want,
+			)
+		}
+	}
+}
+
+func TestVecDenseUnmarshalFromError(t *testing.T) {
+	test := vectorData[1]
+	for i, tt := range []struct {
+		beg int
+		end int
+	}{
+		{
+			beg: 0,
+			end: len(test.raw) - 1,
+		},
+		{
+			beg: 0,
+			end: len(test.raw) - sizeFloat64,
+		},
+		{
+			beg: 0,
+			end: 0,
+		},
+		{
+			beg: 0,
+			end: 1,
+		},
+		{
+			beg: 0,
+			end: sizeInt64,
+		},
+		{
+			beg: 0,
+			end: sizeInt64 - 1,
+		},
+		{
+			beg: 0,
+			end: sizeInt64 + 1,
+		},
+		{
+			beg: 0,
+			end: sizeInt64 + sizeFloat64 - 1,
+		},
+		{
+			beg: 0,
+			end: sizeInt64 + sizeFloat64,
+		},
+		{
+			beg: 0,
+			end: sizeInt64 + sizeFloat64 + 1,
+		},
+	} {
+		buf := bytes.NewReader(test.raw[tt.beg:tt.end])
+		var v VecDense
+		_, err := v.UnmarshalBinaryFrom(buf)
+		if err != io.ErrUnexpectedEOF {
+			t.Errorf("test #%d: error decoding. got=%v. want=%v\n", i, err, io.ErrUnexpectedEOF)
+		}
+	}
+}
+
+func TestVecDenseIORoundTrip(t *testing.T) {
+	for i, test := range vectorData {
+		buf, err := test.want.MarshalBinary()
+		if err != nil {
+			t.Errorf("error encoding test #%d: %v\n", i, err)
+		}
+
+		var got VecDense
+		err = got.UnmarshalBinary(buf)
+		if err != nil {
+			t.Errorf("error decoding test #%d: %v\n", i, err)
+		}
+		if !test.eq(&got, test.want) {
+			t.Errorf("r/w test #%d failed\n got=%#v\nwant=%#v\n", i, &got, test.want)
+		}
+
+		wbuf := new(bytes.Buffer)
+		_, err = test.want.MarshalBinaryTo(wbuf)
+		if err != nil {
+			t.Errorf("error encoding test #%d: %v\n", i, err)
+		}
+
+		if !bytes.Equal(buf, wbuf.Bytes()) {
+			t.Errorf("test #%d encoding via MarshalBinary and MarshalBinaryTo differ:\nwith-stream: %q\n  no-stream: %q\n",
+				i, wbuf.Bytes(), buf,
+			)
+		}
+
+		var wgot VecDense
+		_, err = wgot.UnmarshalBinaryFrom(wbuf)
+		if err != nil {
+			t.Errorf("error decoding test #%d: %v\n", i, err)
+		}
+
+		if !test.eq(&wgot, test.want) {
+			t.Errorf("r/w test #%d failed\n got=%#v\nwant=%#v\n", i, &wgot, test.want)
+		}
+	}
+}
+
+func BenchmarkMarshalDense10(b *testing.B)    { marshalBinaryBenchDense(b, 10) }
+func BenchmarkMarshalDense100(b *testing.B)   { marshalBinaryBenchDense(b, 100) }
+func BenchmarkMarshalDense1000(b *testing.B)  { marshalBinaryBenchDense(b, 1000) }
+func BenchmarkMarshalDense10000(b *testing.B) { marshalBinaryBenchDense(b, 10000) }
+
+func marshalBinaryBenchDense(b *testing.B, size int) {
+	data := make([]float64, size)
+	for i := range data {
+		data[i] = float64(i)
+	}
+	m := NewDense(1, size, data)
+	b.ResetTimer()
+
+	for n := 0; n < b.N; n++ {
+		m.MarshalBinary()
+	}
+}
+
+func BenchmarkUnmarshalDense10(b *testing.B)    { unmarshalBinaryBenchDense(b, 10) }
+func BenchmarkUnmarshalDense100(b *testing.B)   { unmarshalBinaryBenchDense(b, 100) }
+func BenchmarkUnmarshalDense1000(b *testing.B)  { unmarshalBinaryBenchDense(b, 1000) }
+func BenchmarkUnmarshalDense10000(b *testing.B) { unmarshalBinaryBenchDense(b, 10000) }
+
+func unmarshalBinaryBenchDense(b *testing.B, size int) {
+	data := make([]float64, size)
+	for i := range data {
+		data[i] = float64(i)
+	}
+	buf, err := NewDense(1, size, data).MarshalBinary()
+	if err != nil {
+		b.Fatalf("error creating binary buffer (size=%d): %v\n", size, err)
+	}
+	b.ResetTimer()
+
+	for n := 0; n < b.N; n++ {
+		var m Dense
+		m.UnmarshalBinary(buf)
+	}
+}
+
+func BenchmarkMarshalToDense10(b *testing.B)    { marshalBinaryToBenchDense(b, 10) }
+func BenchmarkMarshalToDense100(b *testing.B)   { marshalBinaryToBenchDense(b, 100) }
+func BenchmarkMarshalToDense1000(b *testing.B)  { marshalBinaryToBenchDense(b, 1000) }
+func BenchmarkMarshalToDense10000(b *testing.B) { marshalBinaryToBenchDense(b, 10000) }
+
+func marshalBinaryToBenchDense(b *testing.B, size int) {
+	data := make([]float64, size)
+	for i := range data {
+		data[i] = float64(i)
+	}
+	m := NewDense(1, size, data)
+	w := ioutil.Discard
+	b.ResetTimer()
+
+	for n := 0; n < b.N; n++ {
+		m.MarshalBinaryTo(w)
+	}
+}
+
+type readerTest struct {
+	buf []byte
+	pos int
+}
+
+func (r *readerTest) Read(data []byte) (int, error) {
+	n := copy(data, r.buf[r.pos:r.pos+len(data)])
+	r.pos += n
+	return n, nil
+}
+
+func (r *readerTest) reset() {
+	r.pos = 0
+}
+
+func BenchmarkUnmarshalFromDense10(b *testing.B)    { unmarshalBinaryFromBenchDense(b, 10) }
+func BenchmarkUnmarshalFromDense100(b *testing.B)   { unmarshalBinaryFromBenchDense(b, 100) }
+func BenchmarkUnmarshalFromDense1000(b *testing.B)  { unmarshalBinaryFromBenchDense(b, 1000) }
+func BenchmarkUnmarshalFromDense10000(b *testing.B) { unmarshalBinaryFromBenchDense(b, 10000) }
+
+func unmarshalBinaryFromBenchDense(b *testing.B, size int) {
+	data := make([]float64, size)
+	for i := range data {
+		data[i] = float64(i)
+	}
+	buf, err := NewDense(1, size, data).MarshalBinary()
+	if err != nil {
+		b.Fatalf("error creating binary buffer (size=%d): %v\n", size, err)
+	}
+	r := &readerTest{buf: buf}
+	b.ResetTimer()
+
+	for n := 0; n < b.N; n++ {
+		var m Dense
+		m.UnmarshalBinaryFrom(r)
+		r.reset()
+	}
+}
+
+func BenchmarkMarshalVecDense10(b *testing.B)    { marshalBinaryBenchVecDense(b, 10) }
+func BenchmarkMarshalVecDense100(b *testing.B)   { marshalBinaryBenchVecDense(b, 100) }
+func BenchmarkMarshalVecDense1000(b *testing.B)  { marshalBinaryBenchVecDense(b, 1000) }
+func BenchmarkMarshalVecDense10000(b *testing.B) { marshalBinaryBenchVecDense(b, 10000) }
+
+func marshalBinaryBenchVecDense(b *testing.B, size int) {
+	data := make([]float64, size)
+	for i := range data {
+		data[i] = float64(i)
+	}
+	vec := NewVecDense(size, data)
+	b.ResetTimer()
+
+	for n := 0; n < b.N; n++ {
+		vec.MarshalBinary()
+	}
+}
+
+func BenchmarkUnmarshalVecDense10(b *testing.B)    { unmarshalBinaryBenchVecDense(b, 10) }
+func BenchmarkUnmarshalVecDense100(b *testing.B)   { unmarshalBinaryBenchVecDense(b, 100) }
+func BenchmarkUnmarshalVecDense1000(b *testing.B)  { unmarshalBinaryBenchVecDense(b, 1000) }
+func BenchmarkUnmarshalVecDense10000(b *testing.B) { unmarshalBinaryBenchVecDense(b, 10000) }
+
+func unmarshalBinaryBenchVecDense(b *testing.B, size int) {
+	data := make([]float64, size)
+	for i := range data {
+		data[i] = float64(i)
+	}
+	buf, err := NewVecDense(size, data).MarshalBinary()
+	if err != nil {
+		b.Fatalf("error creating binary buffer (size=%d): %v\n", size, err)
+	}
+	b.ResetTimer()
+
+	for n := 0; n < b.N; n++ {
+		var vec VecDense
+		vec.UnmarshalBinary(buf)
+	}
+}
+
+func BenchmarkMarshalToVecDense10(b *testing.B)    { marshalBinaryToBenchVecDense(b, 10) }
+func BenchmarkMarshalToVecDense100(b *testing.B)   { marshalBinaryToBenchVecDense(b, 100) }
+func BenchmarkMarshalToVecDense1000(b *testing.B)  { marshalBinaryToBenchVecDense(b, 1000) }
+func BenchmarkMarshalToVecDense10000(b *testing.B) { marshalBinaryToBenchVecDense(b, 10000) }
+
+func marshalBinaryToBenchVecDense(b *testing.B, size int) {
+	data := make([]float64, size)
+	for i := range data {
+		data[i] = float64(i)
+	}
+	vec := NewVecDense(size, data)
+	w := ioutil.Discard
+	b.ResetTimer()
+
+	for n := 0; n < b.N; n++ {
+		vec.MarshalBinaryTo(w)
+	}
+}
+
+func BenchmarkUnmarshalFromVecDense10(b *testing.B)    { unmarshalBinaryFromBenchVecDense(b, 10) }
+func BenchmarkUnmarshalFromVecDense100(b *testing.B)   { unmarshalBinaryFromBenchVecDense(b, 100) }
+func BenchmarkUnmarshalFromVecDense1000(b *testing.B)  { unmarshalBinaryFromBenchVecDense(b, 1000) }
+func BenchmarkUnmarshalFromVecDense10000(b *testing.B) { unmarshalBinaryFromBenchVecDense(b, 10000) }
+
+func unmarshalBinaryFromBenchVecDense(b *testing.B, size int) {
+	data := make([]float64, size)
+	for i := range data {
+		data[i] = float64(i)
+	}
+	buf, err := NewVecDense(size, data).MarshalBinary()
+	if err != nil {
+		b.Fatalf("error creating binary buffer (size=%d): %v\n", size, err)
+	}
+	r := &readerTest{buf: buf}
+	b.ResetTimer()
+
+	for n := 0; n < b.N; n++ {
+		var vec VecDense
+		vec.UnmarshalBinaryFrom(r)
+		r.reset()
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/list_test.go b/vendor/gonum.org/v1/gonum/mat/list_test.go
new file mode 100644
index 00000000..5f0cdafa
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/list_test.go
@@ -0,0 +1,1151 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"fmt"
+	"math"
+	"math/rand"
+	"reflect"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+)
+
+// legalSizeSameRectangular returns whether the two matrices have the same rectangular shape.
+func legalSizeSameRectangular(ar, ac, br, bc int) bool {
+	if ar != br {
+		return false
+	}
+	if ac != bc {
+		return false
+	}
+	return true
+}
+
+// legalSizeSameSquare returns whether the two matrices have the same square shape.
+func legalSizeSameSquare(ar, ac, br, bc int) bool {
+	if ar != br {
+		return false
+	}
+	if ac != bc {
+		return false
+	}
+	if ar != ac {
+		return false
+	}
+	return true
+}
+
+// legalSizeSameHeight returns whether the two matrices have the same number of rows.
+func legalSizeSameHeight(ar, _, br, _ int) bool {
+	return ar == br
+}
+
+// legalSizeSameWidth returns whether the two matrices have the same number of columns.
+func legalSizeSameWidth(_, ac, _, bc int) bool {
+	return ac == bc
+}
+
+// legalSizeSolve returns whether the two matrices can be used in a linear solve.
+func legalSizeSolve(ar, ac, br, bc int) bool {
+	return ar == br
+}
+
+// legalSizeSameVec returns whether the two matrices are column vectors of the
+// same dimension.
+func legalSizeSameVec(ar, ac, br, bc int) bool {
+	return ac == 1 && bc == 1 && ar == br
+}
+
+// isAnySize returns true for all matrix sizes.
+func isAnySize(ar, ac int) bool {
+	return true
+}
+
+// isAnySize2 returns true for all matrix sizes.
+func isAnySize2(ar, ac, br, bc int) bool {
+	return true
+}
+
+// isAnyVecDense returns true for any column vector sizes.
+func isAnyVecDense(ar, ac int) bool {
+	return ac == 1
+}
+
+// isSquare returns whether the input matrix is square.
+func isSquare(r, c int) bool {
+	return r == c
+}
+
+// sameAnswerFloat returns whether the two inputs are both NaN or are equal.
+func sameAnswerFloat(a, b interface{}) bool {
+	if math.IsNaN(a.(float64)) {
+		return math.IsNaN(b.(float64))
+	}
+	return a.(float64) == b.(float64)
+}
+
+// sameAnswerFloatApproxTol returns a function that determines whether its two
+// inputs are both NaN or within tol of each other.
+func sameAnswerFloatApproxTol(tol float64) func(a, b interface{}) bool {
+	return func(a, b interface{}) bool {
+		if math.IsNaN(a.(float64)) {
+			return math.IsNaN(b.(float64))
+		}
+		return floats.EqualWithinAbsOrRel(a.(float64), b.(float64), tol, tol)
+	}
+}
+
+func sameAnswerF64SliceOfSlice(a, b interface{}) bool {
+	for i, v := range a.([][]float64) {
+		if same := floats.Same(v, b.([][]float64)[i]); !same {
+			return false
+		}
+	}
+	return true
+}
+
+// sameAnswerBool returns whether the two inputs have the same value.
+func sameAnswerBool(a, b interface{}) bool {
+	return a.(bool) == b.(bool)
+}
+
+// isAnyType returns true for all Matrix types.
+func isAnyType(Matrix) bool {
+	return true
+}
+
+// legalTypesAll returns true for all Matrix types.
+func legalTypesAll(a, b Matrix) bool {
+	return true
+}
+
+// legalTypeSym returns whether a is a Symmetric.
+func legalTypeSym(a Matrix) bool {
+	_, ok := a.(Symmetric)
+	return ok
+}
+
+// legalTypesSym returns whether both input arguments are Symmetric.
+func legalTypesSym(a, b Matrix) bool {
+	if _, ok := a.(Symmetric); !ok {
+		return false
+	}
+	if _, ok := b.(Symmetric); !ok {
+		return false
+	}
+	return true
+}
+
+// legalTypeVec returns whether v is a *VecDense.
+func legalTypeVec(v Matrix) bool {
+	_, ok := v.(*VecDense)
+	return ok
+}
+
+// legalTypesVecVec returns whether both inputs are *VecDense.
+func legalTypesVecVec(a, b Matrix) bool {
+	if _, ok := a.(*VecDense); !ok {
+		return false
+	}
+	if _, ok := b.(*VecDense); !ok {
+		return false
+	}
+	return true
+}
+
+// legalTypesNotVecVec returns whether the first input is an arbitrary Matrix
+// and the second input is a *VecDense.
+func legalTypesNotVecVec(a, b Matrix) bool {
+	_, ok := b.(*VecDense)
+	return ok
+}
+
+// legalDims returns whether {m,n} is a valid dimension of the given matrix type.
+func legalDims(a Matrix, m, n int) bool {
+	switch t := a.(type) {
+	default:
+		panic("legal dims type not coded")
+	case Untransposer:
+		return legalDims(t.Untranspose(), n, m)
+	case *Dense, *basicMatrix:
+		if m < 0 || n < 0 {
+			return false
+		}
+		return true
+	case *SymDense, *TriDense, *basicSymmetric, *basicTriangular:
+		if m < 0 || n < 0 || m != n {
+			return false
+		}
+		return true
+	case *VecDense:
+		if m < 0 || n < 0 {
+			return false
+		}
+		return n == 1
+	}
+}
+
+// returnAs returns the matrix a with the type of t. Used for making a concrete
+// type and changing to the basic form.
+func returnAs(a, t Matrix) Matrix {
+	switch mat := a.(type) {
+	default:
+		panic("unknown type for a")
+	case *Dense:
+		switch t.(type) {
+		default:
+			panic("bad type")
+		case *Dense:
+			return mat
+		case *basicMatrix:
+			return asBasicMatrix(mat)
+		}
+	case *SymDense:
+		switch t.(type) {
+		default:
+			panic("bad type")
+		case *SymDense:
+			return mat
+		case *basicSymmetric:
+			return asBasicSymmetric(mat)
+		}
+	case *TriDense:
+		switch t.(type) {
+		default:
+			panic("bad type")
+		case *TriDense:
+			return mat
+		case *basicTriangular:
+			return asBasicTriangular(mat)
+		}
+	}
+}
+
+// retranspose returns the matrix m inside an Untransposer of the type
+// of a.
+func retranspose(a, m Matrix) Matrix {
+	switch a.(type) {
+	case TransposeTri:
+		return TransposeTri{m.(Triangular)}
+	case Transpose:
+		return Transpose{m}
+	case Untransposer:
+		panic("unknown transposer type")
+	default:
+		panic("a is not an untransposer")
+	}
+}
+
+// makeRandOf returns a new randomly filled m×n matrix of the underlying matrix type.
+func makeRandOf(a Matrix, m, n int) Matrix {
+	var rMatrix Matrix
+	switch t := a.(type) {
+	default:
+		panic("unknown type for make rand of")
+	case Untransposer:
+		rMatrix = retranspose(a, makeRandOf(t.Untranspose(), n, m))
+	case *Dense, *basicMatrix:
+		mat := NewDense(m, n, nil)
+		for i := 0; i < m; i++ {
+			for j := 0; j < n; j++ {
+				mat.Set(i, j, rand.NormFloat64())
+			}
+		}
+		rMatrix = returnAs(mat, t)
+	case *VecDense:
+		if m == 0 && n == 0 {
+			return &VecDense{}
+		}
+		if n != 1 {
+			panic(fmt.Sprintf("bad vector size: m = %v, n = %v", m, n))
+		}
+		length := m
+		inc := 1
+		if t.mat.Inc != 0 {
+			inc = t.mat.Inc
+		}
+		mat := &VecDense{
+			mat: blas64.Vector{
+				Inc:  inc,
+				Data: make([]float64, inc*(length-1)+1),
+			},
+			n: length,
+		}
+		for i := 0; i < length; i++ {
+			mat.SetVec(i, rand.NormFloat64())
+		}
+		return mat
+	case *SymDense, *basicSymmetric:
+		if m != n {
+			panic("bad size")
+		}
+		mat := NewSymDense(n, nil)
+		for i := 0; i < m; i++ {
+			for j := i; j < n; j++ {
+				mat.SetSym(i, j, rand.NormFloat64())
+			}
+		}
+		rMatrix = returnAs(mat, t)
+	case *TriDense, *basicTriangular:
+		if m != n {
+			panic("bad size")
+		}
+
+		// This is necessary because we are making
+		// a triangle from the zero value, which
+		// always returns upper as true.
+		var triKind TriKind
+		switch t := t.(type) {
+		case *TriDense:
+			triKind = t.triKind()
+		case *basicTriangular:
+			triKind = (*TriDense)(t).triKind()
+		}
+
+		mat := NewTriDense(n, triKind, nil)
+		if triKind == Upper {
+			for i := 0; i < m; i++ {
+				for j := i; j < n; j++ {
+					mat.SetTri(i, j, rand.NormFloat64())
+				}
+			}
+		} else {
+			for i := 0; i < m; i++ {
+				for j := 0; j <= i; j++ {
+					mat.SetTri(i, j, rand.NormFloat64())
+				}
+			}
+		}
+		rMatrix = returnAs(mat, t)
+	}
+	if mr, mc := rMatrix.Dims(); mr != m || mc != n {
+		panic(fmt.Sprintf("makeRandOf for %T returns wrong size: %d×%d != %d×%d", a, m, n, mr, mc))
+	}
+	return rMatrix
+}
+
+// makeCopyOf returns a copy of the matrix.
+func makeCopyOf(a Matrix) Matrix {
+	switch t := a.(type) {
+	default:
+		panic("unknown type in makeCopyOf")
+	case Untransposer:
+		return retranspose(a, makeCopyOf(t.Untranspose()))
+	case *Dense, *basicMatrix:
+		var m Dense
+		m.Clone(a)
+		return returnAs(&m, t)
+	case *SymDense, *basicSymmetric:
+		n := t.(Symmetric).Symmetric()
+		m := NewSymDense(n, nil)
+		m.CopySym(t.(Symmetric))
+		return returnAs(m, t)
+	case *TriDense, *basicTriangular:
+		n, upper := t.(Triangular).Triangle()
+		m := NewTriDense(n, upper, nil)
+		if upper {
+			for i := 0; i < n; i++ {
+				for j := i; j < n; j++ {
+					m.SetTri(i, j, t.At(i, j))
+				}
+			}
+		} else {
+			for i := 0; i < n; i++ {
+				for j := 0; j <= i; j++ {
+					m.SetTri(i, j, t.At(i, j))
+				}
+			}
+		}
+		return returnAs(m, t)
+	case *VecDense:
+		m := &VecDense{
+			mat: blas64.Vector{
+				Inc:  t.mat.Inc,
+				Data: make([]float64, t.mat.Inc*(t.n-1)+1),
+			},
+			n: t.n,
+		}
+		copy(m.mat.Data, t.mat.Data)
+		return m
+	}
+}
+
+// sameType returns true if a and b have the same underlying type.
+func sameType(a, b Matrix) bool {
+	return reflect.ValueOf(a).Type() == reflect.ValueOf(b).Type()
+}
+
+// maybeSame returns true if the two matrices could be represented by the same
+// pointer.
+func maybeSame(receiver, a Matrix) bool {
+	rr, rc := receiver.Dims()
+	u, trans := a.(Untransposer)
+	if trans {
+		a = u.Untranspose()
+	}
+	if !sameType(receiver, a) {
+		return false
+	}
+	ar, ac := a.Dims()
+	if rr != ar || rc != ac {
+		return false
+	}
+	if _, ok := a.(Triangular); ok {
+		// They are both triangular types. The TriType needs to match
+		_, aKind := a.(Triangular).Triangle()
+		_, rKind := receiver.(Triangular).Triangle()
+		if aKind != rKind {
+			return false
+		}
+	}
+	return true
+}
+
+// equalApprox returns whether the elements of a and b are the same to within
+// the tolerance. If ignoreNaN is true the test is relaxed such that NaN == NaN.
+func equalApprox(a, b Matrix, tol float64, ignoreNaN bool) bool {
+	ar, ac := a.Dims()
+	br, bc := b.Dims()
+	if ar != br {
+		return false
+	}
+	if ac != bc {
+		return false
+	}
+	for i := 0; i < ar; i++ {
+		for j := 0; j < ac; j++ {
+			if !floats.EqualWithinAbsOrRel(a.At(i, j), b.At(i, j), tol, tol) {
+				if ignoreNaN && math.IsNaN(a.At(i, j)) && math.IsNaN(b.At(i, j)) {
+					continue
+				}
+				return false
+			}
+		}
+	}
+	return true
+}
+
+// equal returns true if the matrices have equal entries.
+func equal(a, b Matrix) bool {
+	ar, ac := a.Dims()
+	br, bc := b.Dims()
+	if ar != br {
+		return false
+	}
+	if ac != bc {
+		return false
+	}
+	for i := 0; i < ar; i++ {
+		for j := 0; j < ac; j++ {
+			if a.At(i, j) != b.At(i, j) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+// isDiagonal returns whether a is a diagonal matrix.
+func isDiagonal(a Matrix) bool {
+	r, c := a.Dims()
+	for i := 0; i < r; i++ {
+		for j := 0; j < c; j++ {
+			if a.At(i, j) != 0 && i != j {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+// equalDiagonal returns whether a and b are equal on the diagonal.
+func equalDiagonal(a, b Matrix) bool {
+	ar, ac := a.Dims()
+	br, bc := a.Dims()
+	if min(ar, ac) != min(br, bc) {
+		return false
+	}
+	for i := 0; i < min(ar, ac); i++ {
+		if a.At(i, i) != b.At(i, i) {
+			return false
+		}
+	}
+	return true
+}
+
+// underlyingData extracts the underlying data of the matrix a.
+func underlyingData(a Matrix) []float64 {
+	switch t := a.(type) {
+	default:
+		panic("matrix type not implemented for extracting underlying data")
+	case Untransposer:
+		return underlyingData(t.Untranspose())
+	case *Dense:
+		return t.mat.Data
+	case *SymDense:
+		return t.mat.Data
+	case *TriDense:
+		return t.mat.Data
+	case *VecDense:
+		return t.mat.Data
+	}
+}
+
+// testMatrices is a list of matrix types to test.
+// The TriDense types have actual sizes because the return from Triangular is
+// only valid when n == 0.
+var testMatrices = []Matrix{
+	&Dense{},
+	&SymDense{},
+	NewTriDense(3, true, nil),
+	NewTriDense(3, false, nil),
+	NewVecDense(0, nil),
+	&VecDense{mat: blas64.Vector{Inc: 10}},
+	&basicMatrix{},
+	&basicSymmetric{},
+	&basicTriangular{cap: 3, mat: blas64.Triangular{N: 3, Stride: 3, Uplo: blas.Upper}},
+	&basicTriangular{cap: 3, mat: blas64.Triangular{N: 3, Stride: 3, Uplo: blas.Lower}},
+
+	Transpose{&Dense{}},
+	Transpose{NewTriDense(3, true, nil)},
+	TransposeTri{NewTriDense(3, true, nil)},
+	Transpose{NewTriDense(3, false, nil)},
+	TransposeTri{NewTriDense(3, false, nil)},
+	Transpose{NewVecDense(0, nil)},
+	Transpose{&VecDense{mat: blas64.Vector{Inc: 10}}},
+	Transpose{&basicMatrix{}},
+	Transpose{&basicSymmetric{}},
+	Transpose{&basicTriangular{cap: 3, mat: blas64.Triangular{N: 3, Stride: 3, Uplo: blas.Upper}}},
+	Transpose{&basicTriangular{cap: 3, mat: blas64.Triangular{N: 3, Stride: 3, Uplo: blas.Lower}}},
+}
+
+var sizes = []struct {
+	ar, ac int
+}{
+	{1, 1},
+	{1, 3},
+	{3, 1},
+
+	{6, 6},
+	{6, 11},
+	{11, 6},
+}
+
+func testOneInputFunc(t *testing.T,
+	// name is the name of the function being tested.
+	name string,
+
+	// f is the function being tested.
+	f func(a Matrix) interface{},
+
+	// denseComparison performs the same operation, but using Dense matrices for
+	// comparison.
+	denseComparison func(a *Dense) interface{},
+
+	// sameAnswer compares the result from two different evaluations of the function
+	// and returns true if they are the same. The specific function being tested
+	// determines the definition of "same". It may mean identical or it may mean
+	// approximately equal.
+	sameAnswer func(a, b interface{}) bool,
+
+	// legalType returns true if the type of the input is a legal type for the
+	// input of the function.
+	legalType func(a Matrix) bool,
+
+	// legalSize returns true if the size is valid for the function.
+	legalSize func(r, c int) bool,
+) {
+	for _, aMat := range testMatrices {
+		for _, test := range sizes {
+			// Skip the test if the argument would not be assignable to the
+			// method's corresponding input parameter or it is not possible
+			// to construct an argument of the requested size.
+			if !legalType(aMat) {
+				continue
+			}
+			if !legalDims(aMat, test.ar, test.ac) {
+				continue
+			}
+			a := makeRandOf(aMat, test.ar, test.ac)
+
+			// Compute the true answer if the sizes are legal.
+			dimsOK := legalSize(test.ar, test.ac)
+			var want interface{}
+			if dimsOK {
+				var aDense Dense
+				aDense.Clone(a)
+				want = denseComparison(&aDense)
+			}
+			aCopy := makeCopyOf(a)
+			// Test the method for a zero-value of the receiver.
+			aType, aTrans := untranspose(a)
+			errStr := fmt.Sprintf("%v(%T), size: %#v, atrans %t", name, aType, test, aTrans)
+			var got interface{}
+			panicked, err := panics(func() { got = f(a) })
+			if !dimsOK && !panicked {
+				t.Errorf("Did not panic with illegal size: %s", errStr)
+				continue
+			}
+			if dimsOK && panicked {
+				t.Errorf("Panicked with legal size: %s: %v", errStr, err)
+				continue
+			}
+			if !equal(a, aCopy) {
+				t.Errorf("First input argument changed in call: %s", errStr)
+			}
+			if !dimsOK {
+				continue
+			}
+			if !sameAnswer(want, got) {
+				t.Errorf("Answer mismatch: %s", errStr)
+			}
+		}
+	}
+}
+
+var sizePairs = []struct {
+	ar, ac, br, bc int
+}{
+	{1, 1, 1, 1},
+	{6, 6, 6, 6},
+	{7, 7, 7, 7},
+
+	{1, 1, 1, 5},
+	{1, 1, 5, 1},
+	{1, 5, 1, 1},
+	{5, 1, 1, 1},
+
+	{5, 5, 5, 1},
+	{5, 5, 1, 5},
+	{5, 1, 5, 5},
+	{1, 5, 5, 5},
+
+	{6, 6, 6, 11},
+	{6, 6, 11, 6},
+	{6, 11, 6, 6},
+	{11, 6, 6, 6},
+	{11, 11, 11, 6},
+	{11, 11, 6, 11},
+	{11, 6, 11, 11},
+	{6, 11, 11, 11},
+
+	{1, 1, 5, 5},
+	{1, 5, 1, 5},
+	{1, 5, 5, 1},
+	{5, 1, 1, 5},
+	{5, 1, 5, 1},
+	{5, 5, 1, 1},
+	{6, 6, 11, 11},
+	{6, 11, 6, 11},
+	{6, 11, 11, 6},
+	{11, 6, 6, 11},
+	{11, 6, 11, 6},
+	{11, 11, 6, 6},
+
+	{1, 1, 17, 11},
+	{1, 1, 11, 17},
+	{1, 11, 1, 17},
+	{1, 17, 1, 11},
+	{1, 11, 17, 1},
+	{1, 17, 11, 1},
+	{11, 1, 1, 17},
+	{17, 1, 1, 11},
+	{11, 1, 17, 1},
+	{17, 1, 11, 1},
+	{11, 17, 1, 1},
+	{17, 11, 1, 1},
+
+	{6, 6, 1, 11},
+	{6, 6, 11, 1},
+	{6, 11, 6, 1},
+	{6, 1, 6, 11},
+	{6, 11, 1, 6},
+	{6, 1, 11, 6},
+	{11, 6, 6, 1},
+	{1, 6, 6, 11},
+	{11, 6, 1, 6},
+	{1, 6, 11, 6},
+	{11, 1, 6, 6},
+	{1, 11, 6, 6},
+
+	{6, 6, 17, 1},
+	{6, 6, 1, 17},
+	{6, 1, 6, 17},
+	{6, 17, 6, 1},
+	{6, 1, 17, 6},
+	{6, 17, 1, 6},
+	{1, 6, 6, 17},
+	{17, 6, 6, 1},
+	{1, 6, 17, 6},
+	{17, 6, 1, 6},
+	{1, 17, 6, 6},
+	{17, 1, 6, 6},
+
+	{6, 6, 17, 11},
+	{6, 6, 11, 17},
+	{6, 11, 6, 17},
+	{6, 17, 6, 11},
+	{6, 11, 17, 6},
+	{6, 17, 11, 6},
+	{11, 6, 6, 17},
+	{17, 6, 6, 11},
+	{11, 6, 17, 6},
+	{17, 6, 11, 6},
+	{11, 17, 6, 6},
+	{17, 11, 6, 6},
+}
+
+func testTwoInputFunc(t *testing.T,
+	// name is the name of the function being tested.
+	name string,
+
+	// f is the function being tested.
+	f func(a, b Matrix) interface{},
+
+	// denseComparison performs the same operation, but using Dense matrices for
+	// comparison.
+	denseComparison func(a, b *Dense) interface{},
+
+	// sameAnswer compares the result from two different evaluations of the function
+	// and returns true if they are the same. The specific function being tested
+	// determines the definition of "same". It may mean identical or it may mean
+	// approximately equal.
+	sameAnswer func(a, b interface{}) bool,
+
+	// legalType returns true if the types of the inputs are legal for the
+	// input of the function.
+	legalType func(a, b Matrix) bool,
+
+	// legalSize returns true if the sizes are valid for the function.
+	legalSize func(ar, ac, br, bc int) bool,
+) {
+	for _, aMat := range testMatrices {
+		for _, bMat := range testMatrices {
+			// Loop over all of the size combinations (bigger, smaller, etc.).
+			for _, test := range sizePairs {
+				// Skip the test if the argument would not be assignable to the
+				// method's corresponding input parameter or it is not possible
+				// to construct an argument of the requested size.
+				if !legalType(aMat, bMat) {
+					continue
+				}
+				if !legalDims(aMat, test.ar, test.ac) {
+					continue
+				}
+				if !legalDims(bMat, test.br, test.bc) {
+					continue
+				}
+				a := makeRandOf(aMat, test.ar, test.ac)
+				b := makeRandOf(bMat, test.br, test.bc)
+
+				// Compute the true answer if the sizes are legal.
+				dimsOK := legalSize(test.ar, test.ac, test.br, test.bc)
+				var want interface{}
+				if dimsOK {
+					var aDense, bDense Dense
+					aDense.Clone(a)
+					bDense.Clone(b)
+					want = denseComparison(&aDense, &bDense)
+				}
+				aCopy := makeCopyOf(a)
+				bCopy := makeCopyOf(b)
+				// Test the method for a zero-value of the receiver.
+				aType, aTrans := untranspose(a)
+				bType, bTrans := untranspose(b)
+				errStr := fmt.Sprintf("%v(%T, %T), size: %#v, atrans %t, btrans %t", name, aType, bType, test, aTrans, bTrans)
+				var got interface{}
+				panicked, err := panics(func() { got = f(a, b) })
+				if !dimsOK && !panicked {
+					t.Errorf("Did not panic with illegal size: %s", errStr)
+					continue
+				}
+				if dimsOK && panicked {
+					t.Errorf("Panicked with legal size: %s: %v", errStr, err)
+					continue
+				}
+				if !equal(a, aCopy) {
+					t.Errorf("First input argument changed in call: %s", errStr)
+				}
+				if !equal(b, bCopy) {
+					t.Errorf("First input argument changed in call: %s", errStr)
+				}
+				if !dimsOK {
+					continue
+				}
+				if !sameAnswer(want, got) {
+					t.Errorf("Answer mismatch: %s", errStr)
+				}
+			}
+		}
+	}
+}
+
+// testOneInput tests a method that has one matrix input argument
+func testOneInput(t *testing.T,
+	// name is the name of the method being tested.
+	name string,
+
+	// receiver is a value of the receiver type.
+	receiver Matrix,
+
+	// method is the generalized receiver.Method(a).
+	method func(receiver, a Matrix),
+
+	// denseComparison performs the same operation as method, but with dense
+	// matrices for comparison with the result.
+	denseComparison func(receiver, a *Dense),
+
+	// legalTypes returns whether the concrete types in Matrix are valid for
+	// the method.
+	legalType func(a Matrix) bool,
+
+	// legalSize returns whether the matrix sizes are valid for the method.
+	legalSize func(ar, ac int) bool,
+
+	// tol is the tolerance for equality when comparing method results.
+	tol float64,
+) {
+	for _, aMat := range testMatrices {
+		for _, test := range sizes {
+			// Skip the test if the argument would not be assignable to the
+			// method's corresponding input parameter or it is not possible
+			// to construct an argument of the requested size.
+			if !legalType(aMat) {
+				continue
+			}
+			if !legalDims(aMat, test.ar, test.ac) {
+				continue
+			}
+			a := makeRandOf(aMat, test.ar, test.ac)
+
+			// Compute the true answer if the sizes are legal.
+			dimsOK := legalSize(test.ar, test.ac)
+			var want Dense
+			if dimsOK {
+				var aDense Dense
+				aDense.Clone(a)
+				denseComparison(&want, &aDense)
+			}
+			aCopy := makeCopyOf(a)
+
+			// Test the method for a zero-value of the receiver.
+			aType, aTrans := untranspose(a)
+			errStr := fmt.Sprintf("%T.%s(%T), size: %#v, atrans %v", receiver, name, aType, test, aTrans)
+			zero := makeRandOf(receiver, 0, 0)
+			panicked, err := panics(func() { method(zero, a) })
+			if !dimsOK && !panicked {
+				t.Errorf("Did not panic with illegal size: %s", errStr)
+				continue
+			}
+			if dimsOK && panicked {
+				t.Errorf("Panicked with legal size: %s: %v", errStr, err)
+				continue
+			}
+			if !equal(a, aCopy) {
+				t.Errorf("First input argument changed in call: %s", errStr)
+			}
+			if !dimsOK {
+				continue
+			}
+			if !equalApprox(zero, &want, tol, false) {
+				t.Errorf("Answer mismatch with zero receiver: %s.\nGot:\n% v\nWant:\n% v\n", errStr, Formatted(zero), Formatted(&want))
+				continue
+			}
+
+			// Test the method with a non-zero-value of the receiver.
+			// The receiver has been overwritten in place so use its size
+			// to construct a new random matrix.
+			rr, rc := zero.Dims()
+			neverZero := makeRandOf(receiver, rr, rc)
+			panicked, _ = panics(func() { method(neverZero, a) })
+			if panicked {
+				t.Errorf("Panicked with non-zero receiver: %s", errStr)
+			}
+			if !equalApprox(neverZero, &want, tol, false) {
+				t.Errorf("Answer mismatch non-zero receiver: %s", errStr)
+			}
+
+			// Test with an incorrectly sized matrix.
+			switch receiver.(type) {
+			default:
+				panic("matrix type not coded for incorrect receiver size")
+			case *Dense:
+				wrongSize := makeRandOf(receiver, rr+1, rc)
+				panicked, _ = panics(func() { method(wrongSize, a) })
+				if !panicked {
+					t.Errorf("Did not panic with wrong number of rows: %s", errStr)
+				}
+				wrongSize = makeRandOf(receiver, rr, rc+1)
+				panicked, _ = panics(func() { method(wrongSize, a) })
+				if !panicked {
+					t.Errorf("Did not panic with wrong number of columns: %s", errStr)
+				}
+			case *TriDense, *SymDense:
+				// Add to the square size.
+				wrongSize := makeRandOf(receiver, rr+1, rc+1)
+				panicked, _ = panics(func() { method(wrongSize, a) })
+				if !panicked {
+					t.Errorf("Did not panic with wrong size: %s", errStr)
+				}
+			case *VecDense:
+				// Add to the column length.
+				wrongSize := makeRandOf(receiver, rr+1, rc)
+				panicked, _ = panics(func() { method(wrongSize, a) })
+				if !panicked {
+					t.Errorf("Did not panic with wrong number of rows: %s", errStr)
+				}
+			}
+
+			// The receiver and the input may share a matrix pointer
+			// if the type and size of the receiver and one of the
+			// arguments match. Test the method works properly
+			// when this is the case.
+			aMaybeSame := maybeSame(neverZero, a)
+			if aMaybeSame {
+				aSame := makeCopyOf(a)
+				receiver = aSame
+				u, ok := aSame.(Untransposer)
+				if ok {
+					receiver = u.Untranspose()
+				}
+				preData := underlyingData(receiver)
+				panicked, err = panics(func() { method(receiver, aSame) })
+				if panicked {
+					t.Errorf("Panics when a maybeSame: %s: %v", errStr, err)
+				} else {
+					if !equalApprox(receiver, &want, tol, false) {
+						t.Errorf("Wrong answer when a maybeSame: %s", errStr)
+					}
+					postData := underlyingData(receiver)
+					if !floats.Equal(preData, postData) {
+						t.Errorf("Original data slice not modified when a maybeSame: %s", errStr)
+					}
+				}
+			}
+		}
+	}
+}
+
+// testTwoInput tests a method that has two input arguments.
+func testTwoInput(t *testing.T,
+	// name is the name of the method being tested.
+	name string,
+
+	// receiver is a value of the receiver type.
+	receiver Matrix,
+
+	// method is the generalized receiver.Method(a, b).
+	method func(receiver, a, b Matrix),
+
+	// denseComparison performs the same operation as method, but with dense
+	// matrices for comparison with the result.
+	denseComparison func(receiver, a, b *Dense),
+
+	// legalTypes returns whether the concrete types in Matrix are valid for
+	// the method.
+	legalTypes func(a, b Matrix) bool,
+
+	// legalSize returns whether the matrix sizes are valid for the method.
+	legalSize func(ar, ac, br, bc int) bool,
+
+	// tol is the tolerance for equality when comparing method results.
+	tol float64,
+) {
+	for _, aMat := range testMatrices {
+		for _, bMat := range testMatrices {
+			// Loop over all of the size combinations (bigger, smaller, etc.).
+			for _, test := range sizePairs {
+				// Skip the test if any argument would not be assignable to the
+				// method's corresponding input parameter or it is not possible
+				// to construct an argument of the requested size.
+				if !legalTypes(aMat, bMat) {
+					continue
+				}
+				if !legalDims(aMat, test.ar, test.ac) {
+					continue
+				}
+				if !legalDims(bMat, test.br, test.bc) {
+					continue
+				}
+				a := makeRandOf(aMat, test.ar, test.ac)
+				b := makeRandOf(bMat, test.br, test.bc)
+
+				// Compute the true answer if the sizes are legal.
+				dimsOK := legalSize(test.ar, test.ac, test.br, test.bc)
+				var want Dense
+				if dimsOK {
+					var aDense, bDense Dense
+					aDense.Clone(a)
+					bDense.Clone(b)
+					denseComparison(&want, &aDense, &bDense)
+				}
+				aCopy := makeCopyOf(a)
+				bCopy := makeCopyOf(b)
+
+				// Test the method for a zero-value of the receiver.
+				aType, aTrans := untranspose(a)
+				bType, bTrans := untranspose(b)
+				errStr := fmt.Sprintf("%T.%s(%T, %T), sizes: %#v, atrans %v, btrans %v", receiver, name, aType, bType, test, aTrans, bTrans)
+				zero := makeRandOf(receiver, 0, 0)
+				panicked, err := panics(func() { method(zero, a, b) })
+				if !dimsOK && !panicked {
+					t.Errorf("Did not panic with illegal size: %s", errStr)
+					continue
+				}
+				if dimsOK && panicked {
+					t.Errorf("Panicked with legal size: %s: %v", errStr, err)
+					continue
+				}
+				if !equal(a, aCopy) {
+					t.Errorf("First input argument changed in call: %s", errStr)
+				}
+				if !equal(b, bCopy) {
+					t.Errorf("Second input argument changed in call: %s", errStr)
+				}
+				if !dimsOK {
+					continue
+				}
+				wasZero, zero := zero, nil // Nil-out zero so we detect illegal use.
+				// NaN equality is allowed because of 0/0 in DivElem test.
+				if !equalApprox(wasZero, &want, tol, true) {
+					t.Errorf("Answer mismatch with zero receiver: %s", errStr)
+					continue
+				}
+
+				// Test the method with a non-zero-value of the receiver.
+				// The receiver has been overwritten in place so use its size
+				// to construct a new random matrix.
+				rr, rc := wasZero.Dims()
+				neverZero := makeRandOf(receiver, rr, rc)
+				panicked, message := panics(func() { method(neverZero, a, b) })
+				if panicked {
+					t.Errorf("Panicked with non-zero receiver: %s: %s", errStr, message)
+				}
+				// NaN equality is allowed because of 0/0 in DivElem test.
+				if !equalApprox(neverZero, &want, tol, true) {
+					t.Errorf("Answer mismatch non-zero receiver: %s", errStr)
+				}
+
+				// Test with an incorrectly sized matrix.
+				switch receiver.(type) {
+				default:
+					panic("matrix type not coded for incorrect receiver size")
+				case *Dense:
+					wrongSize := makeRandOf(receiver, rr+1, rc)
+					panicked, _ = panics(func() { method(wrongSize, a, b) })
+					if !panicked {
+						t.Errorf("Did not panic with wrong number of rows: %s", errStr)
+					}
+					wrongSize = makeRandOf(receiver, rr, rc+1)
+					panicked, _ = panics(func() { method(wrongSize, a, b) })
+					if !panicked {
+						t.Errorf("Did not panic with wrong number of columns: %s", errStr)
+					}
+				case *TriDense, *SymDense:
+					// Add to the square size.
+					wrongSize := makeRandOf(receiver, rr+1, rc+1)
+					panicked, _ = panics(func() { method(wrongSize, a, b) })
+					if !panicked {
+						t.Errorf("Did not panic with wrong size: %s", errStr)
+					}
+				case *VecDense:
+					// Add to the column length.
+					wrongSize := makeRandOf(receiver, rr+1, rc)
+					panicked, _ = panics(func() { method(wrongSize, a, b) })
+					if !panicked {
+						t.Errorf("Did not panic with wrong number of rows: %s", errStr)
+					}
+				}
+
+				// The receiver and an input may share a matrix pointer
+				// if the type and size of the receiver and one of the
+				// arguments match. Test the method works properly
+				// when this is the case.
+				aMaybeSame := maybeSame(neverZero, a)
+				bMaybeSame := maybeSame(neverZero, b)
+				if aMaybeSame {
+					aSame := makeCopyOf(a)
+					receiver = aSame
+					u, ok := aSame.(Untransposer)
+					if ok {
+						receiver = u.Untranspose()
+					}
+					preData := underlyingData(receiver)
+					panicked, err = panics(func() { method(receiver, aSame, b) })
+					if panicked {
+						t.Errorf("Panics when a maybeSame: %s: %v", errStr, err)
+					} else {
+						if !equalApprox(receiver, &want, tol, false) {
+							t.Errorf("Wrong answer when a maybeSame: %s", errStr)
+						}
+						postData := underlyingData(receiver)
+						if !floats.Equal(preData, postData) {
+							t.Errorf("Original data slice not modified when a maybeSame: %s", errStr)
+						}
+					}
+				}
+				if bMaybeSame {
+					bSame := makeCopyOf(b)
+					receiver = bSame
+					u, ok := bSame.(Untransposer)
+					if ok {
+						receiver = u.Untranspose()
+					}
+					preData := underlyingData(receiver)
+					panicked, err = panics(func() { method(receiver, a, bSame) })
+					if panicked {
+						t.Errorf("Panics when b maybeSame: %s: %v", errStr, err)
+					} else {
+						if !equalApprox(receiver, &want, tol, false) {
+							t.Errorf("Wrong answer when b maybeSame: %s", errStr)
+						}
+						postData := underlyingData(receiver)
+						if !floats.Equal(preData, postData) {
+							t.Errorf("Original data slice not modified when b maybeSame: %s", errStr)
+						}
+					}
+				}
+				if aMaybeSame && bMaybeSame {
+					aSame := makeCopyOf(a)
+					receiver = aSame
+					u, ok := aSame.(Untransposer)
+					if ok {
+						receiver = u.Untranspose()
+					}
+					// Ensure that b is the correct transpose type if applicable.
+					// The receiver is always a concrete type so use it.
+					bSame := receiver
+					u, ok = b.(Untransposer)
+					if ok {
+						bSame = retranspose(b, receiver)
+					}
+					// Compute the real answer for this case. It is different
+					// from the initial answer since now a and b have the
+					// same data.
+					zero = makeRandOf(wasZero, 0, 0)
+					method(zero, aSame, bSame)
+					wasZero, zero = zero, nil // Nil-out zero so we detect illegal use.
+					preData := underlyingData(receiver)
+					panicked, err = panics(func() { method(receiver, aSame, bSame) })
+					if panicked {
+						t.Errorf("Panics when both maybeSame: %s: %v", errStr, err)
+					} else {
+						if !equalApprox(receiver, wasZero, tol, false) {
+							t.Errorf("Wrong answer when both maybeSame: %s", errStr)
+						}
+						postData := underlyingData(receiver)
+						if !floats.Equal(preData, postData) {
+							t.Errorf("Original data slice not modified when both maybeSame: %s", errStr)
+						}
+					}
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/lq.go b/vendor/gonum.org/v1/gonum/mat/lq.go
new file mode 100644
index 00000000..54c49336
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/lq.go
@@ -0,0 +1,225 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+	"gonum.org/v1/gonum/lapack/lapack64"
+)
+
+// LQ is a type for creating and using the LQ factorization of a matrix.
+type LQ struct {
+	lq   *Dense
+	tau  []float64
+	cond float64
+}
+
+func (lq *LQ) updateCond(norm lapack.MatrixNorm) {
+	// Since A = L*Q, and Q is orthogonal, we get for the condition number κ
+	//  κ(A) := |A| |A^-1| = |L*Q| |(L*Q)^-1| = |L| |Q^T * L^-1|
+	//        = |L| |L^-1| = κ(L),
+	// where we used that fact that Q^-1 = Q^T. However, this assumes that
+	// the matrix norm is invariant under orthogonal transformations which
+	// is not the case for CondNorm. Hopefully the error is negligible: κ
+	// is only a qualitative measure anyway.
+	m := lq.lq.mat.Rows
+	work := getFloats(3*m, false)
+	iwork := getInts(m, false)
+	l := lq.lq.asTriDense(m, blas.NonUnit, blas.Lower)
+	v := lapack64.Trcon(norm, l.mat, work, iwork)
+	lq.cond = 1 / v
+	putFloats(work)
+	putInts(iwork)
+}
+
+// Factorize computes the LQ factorization of an m×n matrix a where n <= m. The LQ
+// factorization always exists even if A is singular.
+//
+// The LQ decomposition is a factorization of the matrix A such that A = L * Q.
+// The matrix Q is an orthonormal n×n matrix, and L is an m×n upper triangular matrix.
+// L and Q can be extracted from the LTo and QTo methods.
+func (lq *LQ) Factorize(a Matrix) {
+	lq.factorize(a, CondNorm)
+}
+
+func (lq *LQ) factorize(a Matrix, norm lapack.MatrixNorm) {
+	m, n := a.Dims()
+	if m > n {
+		panic(ErrShape)
+	}
+	k := min(m, n)
+	if lq.lq == nil {
+		lq.lq = &Dense{}
+	}
+	lq.lq.Clone(a)
+	work := []float64{0}
+	lq.tau = make([]float64, k)
+	lapack64.Gelqf(lq.lq.mat, lq.tau, work, -1)
+	work = getFloats(int(work[0]), false)
+	lapack64.Gelqf(lq.lq.mat, lq.tau, work, len(work))
+	putFloats(work)
+	lq.updateCond(norm)
+}
+
+// Cond returns the condition number for the factorized matrix.
+// Cond will panic if the receiver does not contain a successful factorization.
+func (lq *LQ) Cond() float64 {
+	if lq.lq == nil || lq.lq.IsZero() {
+		panic("lq: no decomposition computed")
+	}
+	return lq.cond
+}
+
+// TODO(btracey): Add in the "Reduced" forms for extracting the m×m orthogonal
+// and upper triangular matrices.
+
+// LTo extracts the m×n lower trapezoidal matrix from a LQ decomposition.
+// If dst is nil, a new matrix is allocated. The resulting L matrix is returned.
+func (lq *LQ) LTo(dst *Dense) *Dense {
+	r, c := lq.lq.Dims()
+	if dst == nil {
+		dst = NewDense(r, c, nil)
+	} else {
+		dst.reuseAs(r, c)
+	}
+
+	// Disguise the LQ as a lower triangular.
+	t := &TriDense{
+		mat: blas64.Triangular{
+			N:      r,
+			Stride: lq.lq.mat.Stride,
+			Data:   lq.lq.mat.Data,
+			Uplo:   blas.Lower,
+			Diag:   blas.NonUnit,
+		},
+		cap: lq.lq.capCols,
+	}
+	dst.Copy(t)
+
+	if r == c {
+		return dst
+	}
+	// Zero right of the triangular.
+	for i := 0; i < r; i++ {
+		zero(dst.mat.Data[i*dst.mat.Stride+r : i*dst.mat.Stride+c])
+	}
+
+	return dst
+}
+
+// QTo extracts the n×n orthonormal matrix Q from an LQ decomposition.
+// If dst is nil, a new matrix is allocated. The resulting Q matrix is returned.
+func (lq *LQ) QTo(dst *Dense) *Dense {
+	_, c := lq.lq.Dims()
+	if dst == nil {
+		dst = NewDense(c, c, nil)
+	} else {
+		dst.reuseAsZeroed(c, c)
+	}
+	q := dst.mat
+
+	// Set Q = I.
+	ldq := q.Stride
+	for i := 0; i < c; i++ {
+		q.Data[i*ldq+i] = 1
+	}
+
+	// Construct Q from the elementary reflectors.
+	work := []float64{0}
+	lapack64.Ormlq(blas.Left, blas.NoTrans, lq.lq.mat, lq.tau, q, work, -1)
+	work = getFloats(int(work[0]), false)
+	lapack64.Ormlq(blas.Left, blas.NoTrans, lq.lq.mat, lq.tau, q, work, len(work))
+	putFloats(work)
+
+	return dst
+}
+
+// Solve finds a minimum-norm solution to a system of linear equations defined
+// by the matrices A and b, where A is an m×n matrix represented in its LQ factorized
+// form. If A is singular or near-singular a Condition error is returned. Please
+// see the documentation for Condition for more information.
+//
+// The minimization problem solved depends on the input parameters.
+//  If trans == false, find the minimum norm solution of A * X = b.
+//  If trans == true, find X such that ||A*X - b||_2 is minimized.
+// The solution matrix, X, is stored in place into m.
+func (lq *LQ) Solve(m *Dense, trans bool, b Matrix) error {
+	r, c := lq.lq.Dims()
+	br, bc := b.Dims()
+
+	// The LQ solve algorithm stores the result in-place into the right hand side.
+	// The storage for the answer must be large enough to hold both b and x.
+	// However, this method's receiver must be the size of x. Copy b, and then
+	// copy the result into m at the end.
+	if trans {
+		if c != br {
+			panic(ErrShape)
+		}
+		m.reuseAs(r, bc)
+	} else {
+		if r != br {
+			panic(ErrShape)
+		}
+		m.reuseAs(c, bc)
+	}
+	// Do not need to worry about overlap between m and b because x has its own
+	// independent storage.
+	x := getWorkspace(max(r, c), bc, false)
+	x.Copy(b)
+	t := lq.lq.asTriDense(lq.lq.mat.Rows, blas.NonUnit, blas.Lower).mat
+	if trans {
+		work := []float64{0}
+		lapack64.Ormlq(blas.Left, blas.NoTrans, lq.lq.mat, lq.tau, x.mat, work, -1)
+		work = getFloats(int(work[0]), false)
+		lapack64.Ormlq(blas.Left, blas.NoTrans, lq.lq.mat, lq.tau, x.mat, work, len(work))
+		putFloats(work)
+
+		ok := lapack64.Trtrs(blas.Trans, t, x.mat)
+		if !ok {
+			return Condition(math.Inf(1))
+		}
+	} else {
+		ok := lapack64.Trtrs(blas.NoTrans, t, x.mat)
+		if !ok {
+			return Condition(math.Inf(1))
+		}
+		for i := r; i < c; i++ {
+			zero(x.mat.Data[i*x.mat.Stride : i*x.mat.Stride+bc])
+		}
+		work := []float64{0}
+		lapack64.Ormlq(blas.Left, blas.Trans, lq.lq.mat, lq.tau, x.mat, work, -1)
+		work = getFloats(int(work[0]), false)
+		lapack64.Ormlq(blas.Left, blas.Trans, lq.lq.mat, lq.tau, x.mat, work, len(work))
+		putFloats(work)
+	}
+	// M was set above to be the correct size for the result.
+	m.Copy(x)
+	putWorkspace(x)
+	if lq.cond > ConditionTolerance {
+		return Condition(lq.cond)
+	}
+	return nil
+}
+
+// SolveVec finds a minimum-norm solution to a system of linear equations.
+// Please see LQ.Solve for the full documentation.
+func (lq *LQ) SolveVec(v *VecDense, trans bool, b *VecDense) error {
+	if v != b {
+		v.checkOverlap(b.mat)
+	}
+	r, c := lq.lq.Dims()
+	// The Solve implementation is non-trivial, so rather than duplicate the code,
+	// instead recast the VecDenses as Dense and call the matrix code.
+	if trans {
+		v.reuseAs(r)
+	} else {
+		v.reuseAs(c)
+	}
+	return lq.Solve(v.asDense(), trans, b.asDense())
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/lq_test.go b/vendor/gonum.org/v1/gonum/mat/lq_test.go
new file mode 100644
index 00000000..9902b62a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/lq_test.go
@@ -0,0 +1,179 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"math/rand"
+	"testing"
+)
+
+func TestLQ(t *testing.T) {
+	for _, test := range []struct {
+		m, n int
+	}{
+		{5, 5},
+		{5, 10},
+	} {
+		m := test.m
+		n := test.n
+		a := NewDense(m, n, nil)
+		for i := 0; i < m; i++ {
+			for j := 0; j < n; j++ {
+				a.Set(i, j, rand.NormFloat64())
+			}
+		}
+		var want Dense
+		want.Clone(a)
+
+		var lq LQ
+		lq.Factorize(a)
+		q := lq.QTo(nil)
+
+		if !isOrthonormal(q, 1e-10) {
+			t.Errorf("Q is not orthonormal: m = %v, n = %v", m, n)
+		}
+
+		l := lq.LTo(nil)
+
+		var got Dense
+		got.Mul(l, q)
+		if !EqualApprox(&got, &want, 1e-12) {
+			t.Errorf("LQ does not equal original matrix. \nWant: %v\nGot: %v", want, got)
+		}
+	}
+}
+
+func TestSolveLQ(t *testing.T) {
+	for _, trans := range []bool{false, true} {
+		for _, test := range []struct {
+			m, n, bc int
+		}{
+			{5, 5, 1},
+			{5, 10, 1},
+			{5, 5, 3},
+			{5, 10, 3},
+		} {
+			m := test.m
+			n := test.n
+			bc := test.bc
+			a := NewDense(m, n, nil)
+			for i := 0; i < m; i++ {
+				for j := 0; j < n; j++ {
+					a.Set(i, j, rand.Float64())
+				}
+			}
+			br := m
+			if trans {
+				br = n
+			}
+			b := NewDense(br, bc, nil)
+			for i := 0; i < br; i++ {
+				for j := 0; j < bc; j++ {
+					b.Set(i, j, rand.Float64())
+				}
+			}
+			var x Dense
+			lq := &LQ{}
+			lq.Factorize(a)
+			lq.Solve(&x, trans, b)
+
+			// Test that the normal equations hold.
+			// A^T * A * x = A^T * b if !trans
+			// A * A^T * x = A * b if trans
+			var lhs Dense
+			var rhs Dense
+			if trans {
+				var tmp Dense
+				tmp.Mul(a, a.T())
+				lhs.Mul(&tmp, &x)
+				rhs.Mul(a, b)
+			} else {
+				var tmp Dense
+				tmp.Mul(a.T(), a)
+				lhs.Mul(&tmp, &x)
+				rhs.Mul(a.T(), b)
+			}
+			if !EqualApprox(&lhs, &rhs, 1e-10) {
+				t.Errorf("Normal equations do not hold.\nLHS: %v\n, RHS: %v\n", lhs, rhs)
+			}
+		}
+	}
+	// TODO(btracey): Add in testOneInput when it exists.
+}
+
+func TestSolveLQVec(t *testing.T) {
+	for _, trans := range []bool{false, true} {
+		for _, test := range []struct {
+			m, n int
+		}{
+			{5, 5},
+			{5, 10},
+		} {
+			m := test.m
+			n := test.n
+			a := NewDense(m, n, nil)
+			for i := 0; i < m; i++ {
+				for j := 0; j < n; j++ {
+					a.Set(i, j, rand.Float64())
+				}
+			}
+			br := m
+			if trans {
+				br = n
+			}
+			b := NewVecDense(br, nil)
+			for i := 0; i < br; i++ {
+				b.SetVec(i, rand.Float64())
+			}
+			var x VecDense
+			lq := &LQ{}
+			lq.Factorize(a)
+			lq.SolveVec(&x, trans, b)
+
+			// Test that the normal equations hold.
+			// A^T * A * x = A^T * b if !trans
+			// A * A^T * x = A * b if trans
+			var lhs Dense
+			var rhs Dense
+			if trans {
+				var tmp Dense
+				tmp.Mul(a, a.T())
+				lhs.Mul(&tmp, &x)
+				rhs.Mul(a, b)
+			} else {
+				var tmp Dense
+				tmp.Mul(a.T(), a)
+				lhs.Mul(&tmp, &x)
+				rhs.Mul(a.T(), b)
+			}
+			if !EqualApprox(&lhs, &rhs, 1e-10) {
+				t.Errorf("Normal equations do not hold.\nLHS: %v\n, RHS: %v\n", lhs, rhs)
+			}
+		}
+	}
+	// TODO(btracey): Add in testOneInput when it exists.
+}
+
+func TestSolveLQCond(t *testing.T) {
+	for _, test := range []*Dense{
+		NewDense(2, 2, []float64{1, 0, 0, 1e-20}),
+		NewDense(2, 3, []float64{1, 0, 0, 0, 1e-20, 0}),
+	} {
+		m, _ := test.Dims()
+		var lq LQ
+		lq.Factorize(test)
+		b := NewDense(m, 2, nil)
+		var x Dense
+		if err := lq.Solve(&x, false, b); err == nil {
+			t.Error("No error for near-singular matrix in matrix solve.")
+		}
+
+		bvec := NewVecDense(m, nil)
+		var xvec VecDense
+		if err := lq.SolveVec(&xvec, false, bvec); err == nil {
+			t.Error("No error for near-singular matrix in matrix solve.")
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/lu.go b/vendor/gonum.org/v1/gonum/mat/lu.go
new file mode 100644
index 00000000..ff0df0cf
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/lu.go
@@ -0,0 +1,373 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/lapack"
+	"gonum.org/v1/gonum/lapack/lapack64"
+)
+
+const badSliceLength = "mat: improper slice length"
+
+// LU is a type for creating and using the LU factorization of a matrix.
+type LU struct {
+	lu    *Dense
+	pivot []int
+	cond  float64
+}
+
+// updateCond updates the stored condition number of the matrix. anorm is the
+// norm of the original matrix. If anorm is negative it will be estimated.
+func (lu *LU) updateCond(anorm float64, norm lapack.MatrixNorm) {
+	n := lu.lu.mat.Cols
+	work := getFloats(4*n, false)
+	defer putFloats(work)
+	iwork := getInts(n, false)
+	defer putInts(iwork)
+	if anorm < 0 {
+		// This is an approximation. By the definition of a norm,
+		//  |AB| <= |A| |B|.
+		// Since A = L*U, we get for the condition number κ that
+		//  κ(A) := |A| |A^-1| = |L*U| |A^-1| <= |L| |U| |A^-1|,
+		// so this will overestimate the condition number somewhat.
+		// The norm of the original factorized matrix cannot be stored
+		// because of update possibilities.
+		u := lu.lu.asTriDense(n, blas.NonUnit, blas.Upper)
+		l := lu.lu.asTriDense(n, blas.Unit, blas.Lower)
+		unorm := lapack64.Lantr(norm, u.mat, work)
+		lnorm := lapack64.Lantr(norm, l.mat, work)
+		anorm = unorm * lnorm
+	}
+	v := lapack64.Gecon(norm, lu.lu.mat, anorm, work, iwork)
+	lu.cond = 1 / v
+}
+
+// Factorize computes the LU factorization of the square matrix a and stores the
+// result. The LU decomposition will complete regardless of the singularity of a.
+//
+// The LU factorization is computed with pivoting, and so really the decomposition
+// is a PLU decomposition where P is a permutation matrix. The individual matrix
+// factors can be extracted from the factorization using the Permutation method
+// on Dense, and the LU LTo and UTo methods.
+func (lu *LU) Factorize(a Matrix) {
+	lu.factorize(a, CondNorm)
+}
+
+func (lu *LU) factorize(a Matrix, norm lapack.MatrixNorm) {
+	r, c := a.Dims()
+	if r != c {
+		panic(ErrSquare)
+	}
+	if lu.lu == nil {
+		lu.lu = NewDense(r, r, nil)
+	} else {
+		lu.lu.Reset()
+		lu.lu.reuseAs(r, r)
+	}
+	lu.lu.Copy(a)
+	if cap(lu.pivot) < r {
+		lu.pivot = make([]int, r)
+	}
+	lu.pivot = lu.pivot[:r]
+	work := getFloats(r, false)
+	anorm := lapack64.Lange(norm, lu.lu.mat, work)
+	putFloats(work)
+	lapack64.Getrf(lu.lu.mat, lu.pivot)
+	lu.updateCond(anorm, norm)
+}
+
+// Cond returns the condition number for the factorized matrix.
+// Cond will panic if the receiver does not contain a successful factorization.
+func (lu *LU) Cond() float64 {
+	if lu.lu == nil || lu.lu.IsZero() {
+		panic("lu: no decomposition computed")
+	}
+	return lu.cond
+}
+
+// Reset resets the factorization so that it can be reused as the receiver of a
+// dimensionally restricted operation.
+func (lu *LU) Reset() {
+	if lu.lu != nil {
+		lu.lu.Reset()
+	}
+	lu.pivot = lu.pivot[:0]
+}
+
+func (lu *LU) isZero() bool {
+	return len(lu.pivot) == 0
+}
+
+// Det returns the determinant of the matrix that has been factorized. In many
+// expressions, using LogDet will be more numerically stable.
+func (lu *LU) Det() float64 {
+	det, sign := lu.LogDet()
+	return math.Exp(det) * sign
+}
+
+// LogDet returns the log of the determinant and the sign of the determinant
+// for the matrix that has been factorized. Numerical stability in product and
+// division expressions is generally improved by working in log space.
+func (lu *LU) LogDet() (det float64, sign float64) {
+	_, n := lu.lu.Dims()
+	logDiag := getFloats(n, false)
+	defer putFloats(logDiag)
+	sign = 1.0
+	for i := 0; i < n; i++ {
+		v := lu.lu.at(i, i)
+		if v < 0 {
+			sign *= -1
+		}
+		if lu.pivot[i] != i {
+			sign *= -1
+		}
+		logDiag[i] = math.Log(math.Abs(v))
+	}
+	return floats.Sum(logDiag), sign
+}
+
+// Pivot returns pivot indices that enable the construction of the permutation
+// matrix P (see Dense.Permutation). If swaps == nil, then new memory will be
+// allocated, otherwise the length of the input must be equal to the size of the
+// factorized matrix.
+func (lu *LU) Pivot(swaps []int) []int {
+	_, n := lu.lu.Dims()
+	if swaps == nil {
+		swaps = make([]int, n)
+	}
+	if len(swaps) != n {
+		panic(badSliceLength)
+	}
+	// Perform the inverse of the row swaps in order to find the final
+	// row swap position.
+	for i := range swaps {
+		swaps[i] = i
+	}
+	for i := n - 1; i >= 0; i-- {
+		v := lu.pivot[i]
+		swaps[i], swaps[v] = swaps[v], swaps[i]
+	}
+	return swaps
+}
+
+// RankOne updates an LU factorization as if a rank-one update had been applied to
+// the original matrix A, storing the result into the receiver. That is, if in
+// the original LU decomposition P * L * U = A, in the updated decomposition
+// P * L * U = A + alpha * x * y^T.
+func (lu *LU) RankOne(orig *LU, alpha float64, x, y *VecDense) {
+	// RankOne uses algorithm a1 on page 28 of "Multiple-Rank Updates to Matrix
+	// Factorizations for Nonlinear Analysis and Circuit Design" by Linzhong Deng.
+	// http://web.stanford.edu/group/SOL/dissertations/Linzhong-Deng-thesis.pdf
+	_, n := orig.lu.Dims()
+	if x.Len() != n {
+		panic(ErrShape)
+	}
+	if y.Len() != n {
+		panic(ErrShape)
+	}
+	if orig != lu {
+		if lu.isZero() {
+			if cap(lu.pivot) < n {
+				lu.pivot = make([]int, n)
+			}
+			lu.pivot = lu.pivot[:n]
+			if lu.lu == nil {
+				lu.lu = NewDense(n, n, nil)
+			} else {
+				lu.lu.reuseAs(n, n)
+			}
+		} else if len(lu.pivot) != n {
+			panic(ErrShape)
+		}
+		copy(lu.pivot, orig.pivot)
+		lu.lu.Copy(orig.lu)
+	}
+
+	xs := getFloats(n, false)
+	defer putFloats(xs)
+	ys := getFloats(n, false)
+	defer putFloats(ys)
+	for i := 0; i < n; i++ {
+		xs[i] = x.at(i)
+		ys[i] = y.at(i)
+	}
+
+	// Adjust for the pivoting in the LU factorization
+	for i, v := range lu.pivot {
+		xs[i], xs[v] = xs[v], xs[i]
+	}
+
+	lum := lu.lu.mat
+	omega := alpha
+	for j := 0; j < n; j++ {
+		ujj := lum.Data[j*lum.Stride+j]
+		ys[j] /= ujj
+		theta := 1 + xs[j]*ys[j]*omega
+		beta := omega * ys[j] / theta
+		gamma := omega * xs[j]
+		omega -= beta * gamma
+		lum.Data[j*lum.Stride+j] *= theta
+		for i := j + 1; i < n; i++ {
+			xs[i] -= lum.Data[i*lum.Stride+j] * xs[j]
+			tmp := ys[i]
+			ys[i] -= lum.Data[j*lum.Stride+i] * ys[j]
+			lum.Data[i*lum.Stride+j] += beta * xs[i]
+			lum.Data[j*lum.Stride+i] += gamma * tmp
+		}
+	}
+	lu.updateCond(-1, CondNorm)
+}
+
+// LTo extracts the lower triangular matrix from an LU factorization.
+// If dst is nil, a new matrix is allocated. The resulting L matrix is returned.
+func (lu *LU) LTo(dst *TriDense) *TriDense {
+	_, n := lu.lu.Dims()
+	if dst == nil {
+		dst = NewTriDense(n, Lower, nil)
+	} else {
+		dst.reuseAs(n, Lower)
+	}
+	// Extract the lower triangular elements.
+	for i := 0; i < n; i++ {
+		for j := 0; j < i; j++ {
+			dst.mat.Data[i*dst.mat.Stride+j] = lu.lu.mat.Data[i*lu.lu.mat.Stride+j]
+		}
+	}
+	// Set ones on the diagonal.
+	for i := 0; i < n; i++ {
+		dst.mat.Data[i*dst.mat.Stride+i] = 1
+	}
+	return dst
+}
+
+// UTo extracts the upper triangular matrix from an LU factorization.
+// If dst is nil, a new matrix is allocated. The resulting U matrix is returned.
+func (lu *LU) UTo(dst *TriDense) *TriDense {
+	_, n := lu.lu.Dims()
+	if dst == nil {
+		dst = NewTriDense(n, Upper, nil)
+	} else {
+		dst.reuseAs(n, Upper)
+	}
+	// Extract the upper triangular elements.
+	for i := 0; i < n; i++ {
+		for j := i; j < n; j++ {
+			dst.mat.Data[i*dst.mat.Stride+j] = lu.lu.mat.Data[i*lu.lu.mat.Stride+j]
+		}
+	}
+	return dst
+}
+
+// Permutation constructs an r×r permutation matrix with the given row swaps.
+// A permutation matrix has exactly one element equal to one in each row and column
+// and all other elements equal to zero. swaps[i] specifies the row with which
+// i will be swapped, which is equivalent to the non-zero column of row i.
+func (m *Dense) Permutation(r int, swaps []int) {
+	m.reuseAs(r, r)
+	for i := 0; i < r; i++ {
+		zero(m.mat.Data[i*m.mat.Stride : i*m.mat.Stride+r])
+		v := swaps[i]
+		if v < 0 || v >= r {
+			panic(ErrRowAccess)
+		}
+		m.mat.Data[i*m.mat.Stride+v] = 1
+	}
+}
+
+// Solve solves a system of linear equations using the LU decomposition of a matrix.
+// It computes
+//  A * x = b if trans == false
+//  A^T * x = b if trans == true
+// In both cases, A is represented in LU factorized form, and the matrix x is
+// stored into m.
+//
+// If A is singular or near-singular a Condition error is returned. Please see
+// the documentation for Condition for more information.
+func (lu *LU) Solve(m *Dense, trans bool, b Matrix) error {
+	_, n := lu.lu.Dims()
+	br, bc := b.Dims()
+	if br != n {
+		panic(ErrShape)
+	}
+	// TODO(btracey): Should test the condition number instead of testing that
+	// the determinant is exactly zero.
+	if lu.Det() == 0 {
+		return Condition(math.Inf(1))
+	}
+
+	m.reuseAs(n, bc)
+	bU, _ := untranspose(b)
+	var restore func()
+	if m == bU {
+		m, restore = m.isolatedWorkspace(bU)
+		defer restore()
+	} else if rm, ok := bU.(RawMatrixer); ok {
+		m.checkOverlap(rm.RawMatrix())
+	}
+
+	m.Copy(b)
+	t := blas.NoTrans
+	if trans {
+		t = blas.Trans
+	}
+	lapack64.Getrs(t, lu.lu.mat, m.mat, lu.pivot)
+	if lu.cond > ConditionTolerance {
+		return Condition(lu.cond)
+	}
+	return nil
+}
+
+// SolveVec solves a system of linear equations using the LU decomposition of a matrix.
+// It computes
+//  A * x = b if trans == false
+//  A^T * x = b if trans == true
+// In both cases, A is represented in LU factorized form, and the matrix x is
+// stored into v.
+//
+// If A is singular or near-singular a Condition error is returned. Please see
+// the documentation for Condition for more information.
+func (lu *LU) SolveVec(v *VecDense, trans bool, b *VecDense) error {
+	_, n := lu.lu.Dims()
+	bn := b.Len()
+	if bn != n {
+		panic(ErrShape)
+	}
+	if v != b {
+		v.checkOverlap(b.mat)
+	}
+	// TODO(btracey): Should test the condition number instead of testing that
+	// the determinant is exactly zero.
+	if lu.Det() == 0 {
+		return Condition(math.Inf(1))
+	}
+
+	v.reuseAs(n)
+	var restore func()
+	if v == b {
+		v, restore = v.isolatedWorkspace(b)
+		defer restore()
+	}
+	v.CopyVec(b)
+	vMat := blas64.General{
+		Rows:   n,
+		Cols:   1,
+		Stride: v.mat.Inc,
+		Data:   v.mat.Data,
+	}
+	t := blas.NoTrans
+	if trans {
+		t = blas.Trans
+	}
+	lapack64.Getrs(t, lu.lu.mat, vMat, lu.pivot)
+	if lu.cond > ConditionTolerance {
+		return Condition(lu.cond)
+	}
+	return nil
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/lu_test.go b/vendor/gonum.org/v1/gonum/mat/lu_test.go
new file mode 100644
index 00000000..c210670f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/lu_test.go
@@ -0,0 +1,189 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"math/rand"
+	"testing"
+)
+
+func TestLUD(t *testing.T) {
+	for _, n := range []int{1, 5, 10, 11, 50} {
+		a := NewDense(n, n, nil)
+		for i := 0; i < n; i++ {
+			for j := 0; j < n; j++ {
+				a.Set(i, j, rand.NormFloat64())
+			}
+		}
+		var want Dense
+		want.Clone(a)
+
+		var lu LU
+		lu.Factorize(a)
+
+		l := lu.LTo(nil)
+		u := lu.UTo(nil)
+		var p Dense
+		pivot := lu.Pivot(nil)
+		p.Permutation(n, pivot)
+		var got Dense
+		got.Product(&p, l, u)
+		if !EqualApprox(&got, &want, 1e-12) {
+			t.Errorf("PLU does not equal original matrix.\nWant: %v\n Got: %v", want, got)
+		}
+	}
+}
+
+func TestLURankOne(t *testing.T) {
+	for _, pivoting := range []bool{true} {
+		for _, n := range []int{3, 10, 50} {
+			// Construct a random LU factorization
+			lu := &LU{}
+			lu.lu = NewDense(n, n, nil)
+			for i := 0; i < n; i++ {
+				for j := 0; j < n; j++ {
+					lu.lu.Set(i, j, rand.Float64())
+				}
+			}
+			lu.pivot = make([]int, n)
+			for i := range lu.pivot {
+				lu.pivot[i] = i
+			}
+			if pivoting {
+				// For each row, randomly swap with itself or a row after (like is done)
+				// in the actual LU factorization.
+				for i := range lu.pivot {
+					idx := i + rand.Intn(n-i)
+					lu.pivot[i], lu.pivot[idx] = lu.pivot[idx], lu.pivot[i]
+				}
+			}
+			// Apply a rank one update. Ensure the update magnitude is larger than
+			// the equal tolerance.
+			alpha := rand.Float64() + 1
+			x := NewVecDense(n, nil)
+			y := NewVecDense(n, nil)
+			for i := 0; i < n; i++ {
+				x.setVec(i, rand.Float64()+1)
+				y.setVec(i, rand.Float64()+1)
+			}
+			a := luReconstruct(lu)
+			a.RankOne(a, alpha, x, y)
+
+			var luNew LU
+			luNew.RankOne(lu, alpha, x, y)
+			lu.RankOne(lu, alpha, x, y)
+
+			aR1New := luReconstruct(&luNew)
+			aR1 := luReconstruct(lu)
+
+			if !Equal(aR1, aR1New) {
+				t.Error("Different answer when new receiver")
+			}
+			if !EqualApprox(aR1, a, 1e-10) {
+				t.Errorf("Rank one mismatch, pivot %v.\nWant: %v\nGot:%v\n", pivoting, a, aR1)
+			}
+		}
+	}
+}
+
+// luReconstruct reconstructs the original A matrix from an LU decomposition.
+func luReconstruct(lu *LU) *Dense {
+	var L, U TriDense
+	lu.LTo(&L)
+	lu.UTo(&U)
+	var P Dense
+	pivot := lu.Pivot(nil)
+	P.Permutation(len(pivot), pivot)
+
+	var a Dense
+	a.Mul(&L, &U)
+	a.Mul(&P, &a)
+	return &a
+}
+
+func TestSolveLU(t *testing.T) {
+	for _, test := range []struct {
+		n, bc int
+	}{
+		{5, 5},
+		{5, 10},
+		{10, 5},
+	} {
+		n := test.n
+		bc := test.bc
+		a := NewDense(n, n, nil)
+		for i := 0; i < n; i++ {
+			for j := 0; j < n; j++ {
+				a.Set(i, j, rand.NormFloat64())
+			}
+		}
+		b := NewDense(n, bc, nil)
+		for i := 0; i < n; i++ {
+			for j := 0; j < bc; j++ {
+				b.Set(i, j, rand.NormFloat64())
+			}
+		}
+		var lu LU
+		lu.Factorize(a)
+		var x Dense
+		if err := lu.Solve(&x, false, b); err != nil {
+			continue
+		}
+		var got Dense
+		got.Mul(a, &x)
+		if !EqualApprox(&got, b, 1e-12) {
+			t.Errorf("Solve mismatch for non-singular matrix. n = %v, bc = %v.\nWant: %v\nGot: %v", n, bc, b, got)
+		}
+	}
+	// TODO(btracey): Add testOneInput test when such a function exists.
+}
+
+func TestSolveLUCond(t *testing.T) {
+	for _, test := range []*Dense{
+		NewDense(2, 2, []float64{1, 0, 0, 1e-20}),
+	} {
+		m, _ := test.Dims()
+		var lu LU
+		lu.Factorize(test)
+		b := NewDense(m, 2, nil)
+		var x Dense
+		if err := lu.Solve(&x, false, b); err == nil {
+			t.Error("No error for near-singular matrix in matrix solve.")
+		}
+
+		bvec := NewVecDense(m, nil)
+		var xvec VecDense
+		if err := lu.SolveVec(&xvec, false, bvec); err == nil {
+			t.Error("No error for near-singular matrix in matrix solve.")
+		}
+	}
+}
+
+func TestSolveLUVec(t *testing.T) {
+	for _, n := range []int{5, 10} {
+		a := NewDense(n, n, nil)
+		for i := 0; i < n; i++ {
+			for j := 0; j < n; j++ {
+				a.Set(i, j, rand.NormFloat64())
+			}
+		}
+		b := NewVecDense(n, nil)
+		for i := 0; i < n; i++ {
+			b.SetVec(i, rand.NormFloat64())
+		}
+		var lu LU
+		lu.Factorize(a)
+		var x VecDense
+		if err := lu.SolveVec(&x, false, b); err != nil {
+			continue
+		}
+		var got VecDense
+		got.MulVec(a, &x)
+		if !EqualApprox(&got, b, 1e-12) {
+			t.Errorf("Solve mismatch n = %v.\nWant: %v\nGot: %v", n, b, got)
+		}
+	}
+	// TODO(btracey): Add testOneInput test when such a function exists.
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/matrix.go b/vendor/gonum.org/v1/gonum/mat/matrix.go
new file mode 100644
index 00000000..6ba51eaf
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/matrix.go
@@ -0,0 +1,881 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/lapack"
+	"gonum.org/v1/gonum/lapack/lapack64"
+)
+
+// Matrix is the basic matrix interface type.
+type Matrix interface {
+	// Dims returns the dimensions of a Matrix.
+	Dims() (r, c int)
+
+	// At returns the value of a matrix element at row i, column j.
+	// It will panic if i or j are out of bounds for the matrix.
+	At(i, j int) float64
+
+	// T returns the transpose of the Matrix. Whether T returns a copy of the
+	// underlying data is implementation dependent.
+	// This method may be implemented using the Transpose type, which
+	// provides an implicit matrix transpose.
+	T() Matrix
+}
+
+var (
+	_ Matrix       = Transpose{}
+	_ Untransposer = Transpose{}
+)
+
+// Transpose is a type for performing an implicit matrix transpose. It implements
+// the Matrix interface, returning values from the transpose of the matrix within.
+type Transpose struct {
+	Matrix Matrix
+}
+
+// At returns the value of the element at row i and column j of the transposed
+// matrix, that is, row j and column i of the Matrix field.
+func (t Transpose) At(i, j int) float64 {
+	return t.Matrix.At(j, i)
+}
+
+// Dims returns the dimensions of the transposed matrix. The number of rows returned
+// is the number of columns in the Matrix field, and the number of columns is
+// the number of rows in the Matrix field.
+func (t Transpose) Dims() (r, c int) {
+	c, r = t.Matrix.Dims()
+	return r, c
+}
+
+// T performs an implicit transpose by returning the Matrix field.
+func (t Transpose) T() Matrix {
+	return t.Matrix
+}
+
+// Untranspose returns the Matrix field.
+func (t Transpose) Untranspose() Matrix {
+	return t.Matrix
+}
+
+// Untransposer is a type that can undo an implicit transpose.
+type Untransposer interface {
+	// Note: This interface is needed to unify all of the Transpose types. In
+	// the mat methods, we need to test if the Matrix has been implicitly
+	// transposed. If this is checked by testing for the specific Transpose type
+	// then the behavior will be different if the user uses T() or TTri() for a
+	// triangular matrix.
+
+	// Untranspose returns the underlying Matrix stored for the implicit transpose.
+	Untranspose() Matrix
+}
+
+// UntransposeBander is a type that can undo an implicit band transpose.
+type UntransposeBander interface {
+	// Untranspose returns the underlying Banded stored for the implicit transpose.
+	UntransposeBand() Banded
+}
+
+// UntransposeTrier is a type that can undo an implicit triangular transpose.
+type UntransposeTrier interface {
+	// Untranspose returns the underlying Triangular stored for the implicit transpose.
+	UntransposeTri() Triangular
+}
+
+// Mutable is a matrix interface type that allows elements to be altered.
+type Mutable interface {
+	// Set alters the matrix element at row i, column j to v.
+	// It will panic if i or j are out of bounds for the matrix.
+	Set(i, j int, v float64)
+
+	Matrix
+}
+
+// A RowViewer can return a VecDense reflecting a row that is backed by the matrix
+// data. The VecDense returned will have length equal to the number of columns.
+type RowViewer interface {
+	RowView(i int) *VecDense
+}
+
+// A RawRowViewer can return a slice of float64 reflecting a row that is backed by the matrix
+// data.
+type RawRowViewer interface {
+	RawRowView(i int) []float64
+}
+
+// A ColViewer can return a VecDense reflecting a column that is backed by the matrix
+// data. The VecDense returned will have length equal to the number of rows.
+type ColViewer interface {
+	ColView(j int) *VecDense
+}
+
+// A RawColViewer can return a slice of float64 reflecting a column that is backed by the matrix
+// data.
+type RawColViewer interface {
+	RawColView(j int) []float64
+}
+
+// A Cloner can make a copy of a into the receiver, overwriting the previous value of the
+// receiver. The clone operation does not make any restriction on shape and will not cause
+// shadowing.
+type Cloner interface {
+	Clone(a Matrix)
+}
+
+// A Reseter can reset the matrix so that it can be reused as the receiver of a dimensionally
+// restricted operation. This is commonly used when the matrix is being used as a workspace
+// or temporary matrix.
+//
+// If the matrix is a view, using the reset matrix may result in data corruption in elements
+// outside the view.
+type Reseter interface {
+	Reset()
+}
+
+// A Copier can make a copy of elements of a into the receiver. The submatrix copied
+// starts at row and column 0 and has dimensions equal to the minimum dimensions of
+// the two matrices. The number of row and columns copied is returned.
+// Copy will copy from a source that aliases the receiver unless the source is transposed;
+// an aliasing transpose copy will panic with the exception for a special case when
+// the source data has a unitary increment or stride.
+type Copier interface {
+	Copy(a Matrix) (r, c int)
+}
+
+// A Grower can grow the size of the represented matrix by the given number of rows and columns.
+// Growing beyond the size given by the Caps method will result in the allocation of a new
+// matrix and copying of the elements. If Grow is called with negative increments it will
+// panic with ErrIndexOutOfRange.
+type Grower interface {
+	Caps() (r, c int)
+	Grow(r, c int) Matrix
+}
+
+// A BandWidther represents a banded matrix and can return the left and right half-bandwidths, k1 and
+// k2.
+type BandWidther interface {
+	BandWidth() (k1, k2 int)
+}
+
+// A RawMatrixSetter can set the underlying blas64.General used by the receiver. There is no restriction
+// on the shape of the receiver. Changes to the receiver's elements will be reflected in the blas64.General.Data.
+type RawMatrixSetter interface {
+	SetRawMatrix(a blas64.General)
+}
+
+// A RawMatrixer can return a blas64.General representation of the receiver. Changes to the blas64.General.Data
+// slice will be reflected in the original matrix, changes to the Rows, Cols and Stride fields will not.
+type RawMatrixer interface {
+	RawMatrix() blas64.General
+}
+
+// A RawVectorer can return a blas64.Vector representation of the receiver. Changes to the blas64.Vector.Data
+// slice will be reflected in the original matrix, changes to the Inc field will not.
+type RawVectorer interface {
+	RawVector() blas64.Vector
+}
+
+// A NonZeroDoer can call a function for each non-zero element of the receiver.
+// The parameters of the function are the element indices and its value.
+type NonZeroDoer interface {
+	DoNonZero(func(i, j int, v float64))
+}
+
+// A RowNonZeroDoer can call a function for each non-zero element of a row of the receiver.
+// The parameters of the function are the element indices and its value.
+type RowNonZeroDoer interface {
+	DoRowNonZero(i int, fn func(i, j int, v float64))
+}
+
+// A ColNonZeroDoer can call a function for each non-zero element of a column of the receiver.
+// The parameters of the function are the element indices and its value.
+type ColNonZeroDoer interface {
+	DoColNonZero(j int, fn func(i, j int, v float64))
+}
+
+// TODO(btracey): Consider adding CopyCol/CopyRow if the behavior seems useful.
+// TODO(btracey): Add in fast paths to Row/Col for the other concrete types
+// (TriDense, etc.) as well as relevant interfaces (RowColer, RawRowViewer, etc.)
+
+// Col copies the elements in the jth column of the matrix into the slice dst.
+// The length of the provided slice must equal the number of rows, unless the
+// slice is nil in which case a new slice is first allocated.
+func Col(dst []float64, j int, a Matrix) []float64 {
+	r, c := a.Dims()
+	if j < 0 || j >= c {
+		panic(ErrColAccess)
+	}
+	if dst == nil {
+		dst = make([]float64, r)
+	} else {
+		if len(dst) != r {
+			panic(ErrColLength)
+		}
+	}
+	aU, aTrans := untranspose(a)
+	if rm, ok := aU.(RawMatrixer); ok {
+		m := rm.RawMatrix()
+		if aTrans {
+			copy(dst, m.Data[j*m.Stride:j*m.Stride+m.Cols])
+			return dst
+		}
+		blas64.Copy(r,
+			blas64.Vector{Inc: m.Stride, Data: m.Data[j:]},
+			blas64.Vector{Inc: 1, Data: dst},
+		)
+		return dst
+	}
+	for i := 0; i < r; i++ {
+		dst[i] = a.At(i, j)
+	}
+	return dst
+}
+
+// Row copies the elements in the jth column of the matrix into the slice dst.
+// The length of the provided slice must equal the number of columns, unless the
+// slice is nil in which case a new slice is first allocated.
+func Row(dst []float64, i int, a Matrix) []float64 {
+	r, c := a.Dims()
+	if i < 0 || i >= r {
+		panic(ErrColAccess)
+	}
+	if dst == nil {
+		dst = make([]float64, c)
+	} else {
+		if len(dst) != c {
+			panic(ErrRowLength)
+		}
+	}
+	aU, aTrans := untranspose(a)
+	if rm, ok := aU.(RawMatrixer); ok {
+		m := rm.RawMatrix()
+		if aTrans {
+			blas64.Copy(c,
+				blas64.Vector{Inc: m.Stride, Data: m.Data[i:]},
+				blas64.Vector{Inc: 1, Data: dst},
+			)
+			return dst
+		}
+		copy(dst, m.Data[i*m.Stride:i*m.Stride+m.Cols])
+		return dst
+	}
+	for j := 0; j < c; j++ {
+		dst[j] = a.At(i, j)
+	}
+	return dst
+}
+
+// Cond returns the condition number of the given matrix under the given norm.
+// The condition number must be based on the 1-norm, 2-norm or ∞-norm.
+// Cond will panic with matrix.ErrShape if the matrix has zero size.
+//
+// BUG(btracey): The computation of the 1-norm and ∞-norm for non-square matrices
+// is innacurate, although is typically the right order of magnitude. See
+// https://github.com/xianyi/OpenBLAS/issues/636. While the value returned will
+// change with the resolution of this bug, the result from Cond will match the
+// condition number used internally.
+func Cond(a Matrix, norm float64) float64 {
+	m, n := a.Dims()
+	if m == 0 || n == 0 {
+		panic(ErrShape)
+	}
+	var lnorm lapack.MatrixNorm
+	switch norm {
+	default:
+		panic("mat: bad norm value")
+	case 1:
+		lnorm = lapack.MaxColumnSum
+	case 2:
+		var svd SVD
+		ok := svd.Factorize(a, SVDNone)
+		if !ok {
+			return math.Inf(1)
+		}
+		return svd.Cond()
+	case math.Inf(1):
+		lnorm = lapack.MaxRowSum
+	}
+
+	if m == n {
+		// Use the LU decomposition to compute the condition number.
+		var lu LU
+		lu.factorize(a, lnorm)
+		return lu.Cond()
+	}
+	if m > n {
+		// Use the QR factorization to compute the condition number.
+		var qr QR
+		qr.factorize(a, lnorm)
+		return qr.Cond()
+	}
+	// Use the LQ factorization to compute the condition number.
+	var lq LQ
+	lq.factorize(a, lnorm)
+	return lq.Cond()
+}
+
+// Det returns the determinant of the matrix a. In many expressions using LogDet
+// will be more numerically stable.
+func Det(a Matrix) float64 {
+	det, sign := LogDet(a)
+	return math.Exp(det) * sign
+}
+
+// Dot returns the sum of the element-wise product of a and b.
+// Dot panics if the matrix sizes are unequal.
+func Dot(a, b *VecDense) float64 {
+	la := a.Len()
+	lb := b.Len()
+	if la != lb {
+		panic(ErrShape)
+	}
+	return blas64.Dot(la, a.mat, b.mat)
+}
+
+// Equal returns whether the matrices a and b have the same size
+// and are element-wise equal.
+func Equal(a, b Matrix) bool {
+	ar, ac := a.Dims()
+	br, bc := b.Dims()
+	if ar != br || ac != bc {
+		return false
+	}
+	aU, aTrans := untranspose(a)
+	bU, bTrans := untranspose(b)
+	if rma, ok := aU.(RawMatrixer); ok {
+		if rmb, ok := bU.(RawMatrixer); ok {
+			ra := rma.RawMatrix()
+			rb := rmb.RawMatrix()
+			if aTrans == bTrans {
+				for i := 0; i < ra.Rows; i++ {
+					for j := 0; j < ra.Cols; j++ {
+						if ra.Data[i*ra.Stride+j] != rb.Data[i*rb.Stride+j] {
+							return false
+						}
+					}
+				}
+				return true
+			}
+			for i := 0; i < ra.Rows; i++ {
+				for j := 0; j < ra.Cols; j++ {
+					if ra.Data[i*ra.Stride+j] != rb.Data[j*rb.Stride+i] {
+						return false
+					}
+				}
+			}
+			return true
+		}
+	}
+	if rma, ok := aU.(RawSymmetricer); ok {
+		if rmb, ok := bU.(RawSymmetricer); ok {
+			ra := rma.RawSymmetric()
+			rb := rmb.RawSymmetric()
+			// Symmetric matrices are always upper and equal to their transpose.
+			for i := 0; i < ra.N; i++ {
+				for j := i; j < ra.N; j++ {
+					if ra.Data[i*ra.Stride+j] != rb.Data[i*rb.Stride+j] {
+						return false
+					}
+				}
+			}
+			return true
+		}
+	}
+	if ra, ok := aU.(*VecDense); ok {
+		if rb, ok := bU.(*VecDense); ok {
+			// If the raw vectors are the same length they must either both be
+			// transposed or both not transposed (or have length 1).
+			for i := 0; i < ra.n; i++ {
+				if ra.mat.Data[i*ra.mat.Inc] != rb.mat.Data[i*rb.mat.Inc] {
+					return false
+				}
+			}
+			return true
+		}
+	}
+	for i := 0; i < ar; i++ {
+		for j := 0; j < ac; j++ {
+			if a.At(i, j) != b.At(i, j) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+// EqualApprox returns whether the matrices a and b have the same size and contain all equal
+// elements with tolerance for element-wise equality specified by epsilon. Matrices
+// with non-equal shapes are not equal.
+func EqualApprox(a, b Matrix, epsilon float64) bool {
+	ar, ac := a.Dims()
+	br, bc := b.Dims()
+	if ar != br || ac != bc {
+		return false
+	}
+	aU, aTrans := untranspose(a)
+	bU, bTrans := untranspose(b)
+	if rma, ok := aU.(RawMatrixer); ok {
+		if rmb, ok := bU.(RawMatrixer); ok {
+			ra := rma.RawMatrix()
+			rb := rmb.RawMatrix()
+			if aTrans == bTrans {
+				for i := 0; i < ra.Rows; i++ {
+					for j := 0; j < ra.Cols; j++ {
+						if !floats.EqualWithinAbsOrRel(ra.Data[i*ra.Stride+j], rb.Data[i*rb.Stride+j], epsilon, epsilon) {
+							return false
+						}
+					}
+				}
+				return true
+			}
+			for i := 0; i < ra.Rows; i++ {
+				for j := 0; j < ra.Cols; j++ {
+					if !floats.EqualWithinAbsOrRel(ra.Data[i*ra.Stride+j], rb.Data[j*rb.Stride+i], epsilon, epsilon) {
+						return false
+					}
+				}
+			}
+			return true
+		}
+	}
+	if rma, ok := aU.(RawSymmetricer); ok {
+		if rmb, ok := bU.(RawSymmetricer); ok {
+			ra := rma.RawSymmetric()
+			rb := rmb.RawSymmetric()
+			// Symmetric matrices are always upper and equal to their transpose.
+			for i := 0; i < ra.N; i++ {
+				for j := i; j < ra.N; j++ {
+					if !floats.EqualWithinAbsOrRel(ra.Data[i*ra.Stride+j], rb.Data[i*rb.Stride+j], epsilon, epsilon) {
+						return false
+					}
+				}
+			}
+			return true
+		}
+	}
+	if ra, ok := aU.(*VecDense); ok {
+		if rb, ok := bU.(*VecDense); ok {
+			// If the raw vectors are the same length they must either both be
+			// transposed or both not transposed (or have length 1).
+			for i := 0; i < ra.n; i++ {
+				if !floats.EqualWithinAbsOrRel(ra.mat.Data[i*ra.mat.Inc], rb.mat.Data[i*rb.mat.Inc], epsilon, epsilon) {
+					return false
+				}
+			}
+			return true
+		}
+	}
+	for i := 0; i < ar; i++ {
+		for j := 0; j < ac; j++ {
+			if !floats.EqualWithinAbsOrRel(a.At(i, j), b.At(i, j), epsilon, epsilon) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+// LogDet returns the log of the determinant and the sign of the determinant
+// for the matrix that has been factorized. Numerical stability in product and
+// division expressions is generally improved by working in log space.
+func LogDet(a Matrix) (det float64, sign float64) {
+	// TODO(btracey): Add specialized routines for TriDense, etc.
+	var lu LU
+	lu.Factorize(a)
+	return lu.LogDet()
+}
+
+// Max returns the largest element value of the matrix A.
+// Max will panic with matrix.ErrShape if the matrix has zero size.
+func Max(a Matrix) float64 {
+	r, c := a.Dims()
+	if r == 0 || c == 0 {
+		panic(ErrShape)
+	}
+	// Max(A) = Max(A^T)
+	aU, _ := untranspose(a)
+	switch m := aU.(type) {
+	case RawMatrixer:
+		rm := m.RawMatrix()
+		max := math.Inf(-1)
+		for i := 0; i < rm.Rows; i++ {
+			for _, v := range rm.Data[i*rm.Stride : i*rm.Stride+rm.Cols] {
+				if v > max {
+					max = v
+				}
+			}
+		}
+		return max
+	case RawTriangular:
+		rm := m.RawTriangular()
+		// The max of a triangular is at least 0 unless the size is 1.
+		if rm.N == 1 {
+			return rm.Data[0]
+		}
+		max := 0.0
+		if rm.Uplo == blas.Upper {
+			for i := 0; i < rm.N; i++ {
+				for _, v := range rm.Data[i*rm.Stride+i : i*rm.Stride+rm.N] {
+					if v > max {
+						max = v
+					}
+				}
+			}
+			return max
+		}
+		for i := 0; i < rm.N; i++ {
+			for _, v := range rm.Data[i*rm.Stride : i*rm.Stride+i+1] {
+				if v > max {
+					max = v
+				}
+			}
+		}
+		return max
+	case RawSymmetricer:
+		rm := m.RawSymmetric()
+		if rm.Uplo != blas.Upper {
+			panic(badSymTriangle)
+		}
+		max := math.Inf(-1)
+		for i := 0; i < rm.N; i++ {
+			for _, v := range rm.Data[i*rm.Stride+i : i*rm.Stride+rm.N] {
+				if v > max {
+					max = v
+				}
+			}
+		}
+		return max
+	default:
+		r, c := aU.Dims()
+		max := math.Inf(-1)
+		for i := 0; i < r; i++ {
+			for j := 0; j < c; j++ {
+				v := aU.At(i, j)
+				if v > max {
+					max = v
+				}
+			}
+		}
+		return max
+	}
+}
+
+// Min returns the smallest element value of the matrix A.
+// Min will panic with matrix.ErrShape if the matrix has zero size.
+func Min(a Matrix) float64 {
+	r, c := a.Dims()
+	if r == 0 || c == 0 {
+		panic(ErrShape)
+	}
+	// Min(A) = Min(A^T)
+	aU, _ := untranspose(a)
+	switch m := aU.(type) {
+	case RawMatrixer:
+		rm := m.RawMatrix()
+		min := math.Inf(1)
+		for i := 0; i < rm.Rows; i++ {
+			for _, v := range rm.Data[i*rm.Stride : i*rm.Stride+rm.Cols] {
+				if v < min {
+					min = v
+				}
+			}
+		}
+		return min
+	case RawTriangular:
+		rm := m.RawTriangular()
+		// The min of a triangular is at most 0 unless the size is 1.
+		if rm.N == 1 {
+			return rm.Data[0]
+		}
+		min := 0.0
+		if rm.Uplo == blas.Upper {
+			for i := 0; i < rm.N; i++ {
+				for _, v := range rm.Data[i*rm.Stride+i : i*rm.Stride+rm.N] {
+					if v < min {
+						min = v
+					}
+				}
+			}
+			return min
+		}
+		for i := 0; i < rm.N; i++ {
+			for _, v := range rm.Data[i*rm.Stride : i*rm.Stride+i+1] {
+				if v < min {
+					min = v
+				}
+			}
+		}
+		return min
+	case RawSymmetricer:
+		rm := m.RawSymmetric()
+		if rm.Uplo != blas.Upper {
+			panic(badSymTriangle)
+		}
+		min := math.Inf(1)
+		for i := 0; i < rm.N; i++ {
+			for _, v := range rm.Data[i*rm.Stride+i : i*rm.Stride+rm.N] {
+				if v < min {
+					min = v
+				}
+			}
+		}
+		return min
+	default:
+		r, c := aU.Dims()
+		min := math.Inf(1)
+		for i := 0; i < r; i++ {
+			for j := 0; j < c; j++ {
+				v := aU.At(i, j)
+				if v < min {
+					min = v
+				}
+			}
+		}
+		return min
+	}
+}
+
+// Norm returns the specified (induced) norm of the matrix a. See
+// https://en.wikipedia.org/wiki/Matrix_norm for the definition of an induced norm.
+//
+// Valid norms are:
+//    1 - The maximum absolute column sum
+//    2 - Frobenius norm, the square root of the sum of the squares of the elements.
+//  Inf - The maximum absolute row sum.
+// Norm will panic with ErrNormOrder if an illegal norm order is specified and
+// with matrix.ErrShape if the matrix has zero size.
+func Norm(a Matrix, norm float64) float64 {
+	r, c := a.Dims()
+	if r == 0 || c == 0 {
+		panic(ErrShape)
+	}
+	aU, aTrans := untranspose(a)
+	var work []float64
+	switch rma := aU.(type) {
+	case RawMatrixer:
+		rm := rma.RawMatrix()
+		n := normLapack(norm, aTrans)
+		if n == lapack.MaxColumnSum {
+			work = getFloats(rm.Cols, false)
+			defer putFloats(work)
+		}
+		return lapack64.Lange(n, rm, work)
+	case RawTriangular:
+		rm := rma.RawTriangular()
+		n := normLapack(norm, aTrans)
+		if n == lapack.MaxRowSum || n == lapack.MaxColumnSum {
+			work = getFloats(rm.N, false)
+			defer putFloats(work)
+		}
+		return lapack64.Lantr(n, rm, work)
+	case RawSymmetricer:
+		rm := rma.RawSymmetric()
+		n := normLapack(norm, aTrans)
+		if n == lapack.MaxRowSum || n == lapack.MaxColumnSum {
+			work = getFloats(rm.N, false)
+			defer putFloats(work)
+		}
+		return lapack64.Lansy(n, rm, work)
+	case *VecDense:
+		rv := rma.RawVector()
+		switch norm {
+		default:
+			panic("unreachable")
+		case 1:
+			if aTrans {
+				imax := blas64.Iamax(rma.n, rv)
+				return math.Abs(rma.At(imax, 0))
+			}
+			return blas64.Asum(rma.n, rv)
+		case 2:
+			return blas64.Nrm2(rma.n, rv)
+		case math.Inf(1):
+			if aTrans {
+				return blas64.Asum(rma.n, rv)
+			}
+			imax := blas64.Iamax(rma.n, rv)
+			return math.Abs(rma.At(imax, 0))
+		}
+	}
+	switch norm {
+	default:
+		panic("unreachable")
+	case 1:
+		var max float64
+		for j := 0; j < c; j++ {
+			var sum float64
+			for i := 0; i < r; i++ {
+				sum += math.Abs(a.At(i, j))
+			}
+			if sum > max {
+				max = sum
+			}
+		}
+		return max
+	case 2:
+		var sum float64
+		for i := 0; i < r; i++ {
+			for j := 0; j < c; j++ {
+				v := a.At(i, j)
+				sum += v * v
+			}
+		}
+		return math.Sqrt(sum)
+	case math.Inf(1):
+		var max float64
+		for i := 0; i < r; i++ {
+			var sum float64
+			for j := 0; j < c; j++ {
+				sum += math.Abs(a.At(i, j))
+			}
+			if sum > max {
+				max = sum
+			}
+		}
+		return max
+	}
+}
+
+// normLapack converts the float64 norm input in Norm to a lapack.MatrixNorm.
+func normLapack(norm float64, aTrans bool) lapack.MatrixNorm {
+	switch norm {
+	case 1:
+		n := lapack.MaxColumnSum
+		if aTrans {
+			n = lapack.MaxRowSum
+		}
+		return n
+	case 2:
+		return lapack.NormFrob
+	case math.Inf(1):
+		n := lapack.MaxRowSum
+		if aTrans {
+			n = lapack.MaxColumnSum
+		}
+		return n
+	default:
+		panic(ErrNormOrder)
+	}
+}
+
+// Sum returns the sum of the elements of the matrix.
+func Sum(a Matrix) float64 {
+	// TODO(btracey): Add a fast path for the other supported matrix types.
+
+	r, c := a.Dims()
+	var sum float64
+	aU, _ := untranspose(a)
+	if rma, ok := aU.(RawMatrixer); ok {
+		rm := rma.RawMatrix()
+		for i := 0; i < rm.Rows; i++ {
+			for _, v := range rm.Data[i*rm.Stride : i*rm.Stride+rm.Cols] {
+				sum += v
+			}
+		}
+		return sum
+	}
+	for i := 0; i < r; i++ {
+		for j := 0; j < c; j++ {
+			sum += a.At(i, j)
+		}
+	}
+	return sum
+}
+
+// Trace returns the trace of the matrix. Trace will panic if the
+// matrix is not square.
+func Trace(a Matrix) float64 {
+	r, c := a.Dims()
+	if r != c {
+		panic(ErrSquare)
+	}
+
+	aU, _ := untranspose(a)
+	switch m := aU.(type) {
+	case RawMatrixer:
+		rm := m.RawMatrix()
+		var t float64
+		for i := 0; i < r; i++ {
+			t += rm.Data[i*rm.Stride+i]
+		}
+		return t
+	case RawTriangular:
+		rm := m.RawTriangular()
+		var t float64
+		for i := 0; i < r; i++ {
+			t += rm.Data[i*rm.Stride+i]
+		}
+		return t
+	case RawSymmetricer:
+		rm := m.RawSymmetric()
+		var t float64
+		for i := 0; i < r; i++ {
+			t += rm.Data[i*rm.Stride+i]
+		}
+		return t
+	default:
+		var t float64
+		for i := 0; i < r; i++ {
+			t += a.At(i, i)
+		}
+		return t
+	}
+}
+
+func min(a, b int) int {
+	if a < b {
+		return a
+	}
+	return b
+}
+
+func max(a, b int) int {
+	if a > b {
+		return a
+	}
+	return b
+}
+
+// use returns a float64 slice with l elements, using f if it
+// has the necessary capacity, otherwise creating a new slice.
+func use(f []float64, l int) []float64 {
+	if l <= cap(f) {
+		return f[:l]
+	}
+	return make([]float64, l)
+}
+
+// useZeroed returns a float64 slice with l elements, using f if it
+// has the necessary capacity, otherwise creating a new slice. The
+// elements of the returned slice are guaranteed to be zero.
+func useZeroed(f []float64, l int) []float64 {
+	if l <= cap(f) {
+		f = f[:l]
+		zero(f)
+		return f
+	}
+	return make([]float64, l)
+}
+
+// zero zeros the given slice's elements.
+func zero(f []float64) {
+	for i := range f {
+		f[i] = 0
+	}
+}
+
+// useInt returns an int slice with l elements, using i if it
+// has the necessary capacity, otherwise creating a new slice.
+func useInt(i []int, l int) []int {
+	if l <= cap(i) {
+		return i[:l]
+	}
+	return make([]int, l)
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/matrix_test.go b/vendor/gonum.org/v1/gonum/mat/matrix_test.go
new file mode 100644
index 00000000..7a576529
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/matrix_test.go
@@ -0,0 +1,624 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"fmt"
+	"math"
+	"reflect"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+)
+
+func panics(fn func()) (panicked bool, message string) {
+	defer func() {
+		r := recover()
+		panicked = r != nil
+		message = fmt.Sprint(r)
+	}()
+	fn()
+	return
+}
+
+func flatten(f [][]float64) (r, c int, d []float64) {
+	r = len(f)
+	if r == 0 {
+		panic("bad test: no row")
+	}
+	c = len(f[0])
+	d = make([]float64, 0, r*c)
+	for _, row := range f {
+		if len(row) != c {
+			panic("bad test: ragged input")
+		}
+		d = append(d, row...)
+	}
+	return r, c, d
+}
+
+func unflatten(r, c int, d []float64) [][]float64 {
+	m := make([][]float64, r)
+	for i := 0; i < r; i++ {
+		m[i] = d[i*c : (i+1)*c]
+	}
+	return m
+}
+
+// eye returns a new identity matrix of size n×n.
+func eye(n int) *Dense {
+	d := make([]float64, n*n)
+	for i := 0; i < n*n; i += n + 1 {
+		d[i] = 1
+	}
+	return NewDense(n, n, d)
+}
+
+func TestCol(t *testing.T) {
+	for id, af := range [][][]float64{
+		{
+			{1, 2, 3},
+			{4, 5, 6},
+			{7, 8, 9},
+		},
+		{
+			{1, 2, 3},
+			{4, 5, 6},
+			{7, 8, 9},
+			{10, 11, 12},
+		},
+		{
+			{1, 2, 3, 4},
+			{5, 6, 7, 8},
+			{9, 10, 11, 12},
+		},
+	} {
+		a := NewDense(flatten(af))
+		col := make([]float64, a.mat.Rows)
+		for j := range af[0] {
+			for i := range col {
+				col[i] = float64(i*a.mat.Cols + j + 1)
+			}
+
+			if got := Col(nil, j, a); !reflect.DeepEqual(got, col) {
+				t.Errorf("test %d: unexpected values returned for dense col %d: got: %v want: %v",
+					id, j, got, col)
+			}
+
+			got := make([]float64, a.mat.Rows)
+			if Col(got, j, a); !reflect.DeepEqual(got, col) {
+				t.Errorf("test %d: unexpected values filled for dense col %d: got: %v want: %v",
+					id, j, got, col)
+			}
+		}
+	}
+
+	denseComparison := func(a *Dense) interface{} {
+		r, c := a.Dims()
+		ans := make([][]float64, c)
+		for j := range ans {
+			ans[j] = make([]float64, r)
+			for i := range ans[j] {
+				ans[j][i] = a.At(i, j)
+			}
+		}
+		return ans
+	}
+
+	f := func(a Matrix) interface{} {
+		_, c := a.Dims()
+		ans := make([][]float64, c)
+		for j := range ans {
+			ans[j] = Col(nil, j, a)
+		}
+		return ans
+	}
+	testOneInputFunc(t, "Col", f, denseComparison, sameAnswerF64SliceOfSlice, isAnyType, isAnySize)
+
+	f = func(a Matrix) interface{} {
+		r, c := a.Dims()
+		ans := make([][]float64, c)
+		for j := range ans {
+			ans[j] = make([]float64, r)
+			Col(ans[j], j, a)
+		}
+		return ans
+	}
+	testOneInputFunc(t, "Col", f, denseComparison, sameAnswerF64SliceOfSlice, isAnyType, isAnySize)
+}
+
+func TestRow(t *testing.T) {
+	for id, af := range [][][]float64{
+		{
+			{1, 2, 3},
+			{4, 5, 6},
+			{7, 8, 9},
+		},
+		{
+			{1, 2, 3},
+			{4, 5, 6},
+			{7, 8, 9},
+			{10, 11, 12},
+		},
+		{
+			{1, 2, 3, 4},
+			{5, 6, 7, 8},
+			{9, 10, 11, 12},
+		},
+	} {
+		a := NewDense(flatten(af))
+		for i, row := range af {
+			if got := Row(nil, i, a); !reflect.DeepEqual(got, row) {
+				t.Errorf("test %d: unexpected values returned for dense row %d: got: %v want: %v",
+					id, i, got, row)
+			}
+
+			got := make([]float64, len(row))
+			if Row(got, i, a); !reflect.DeepEqual(got, row) {
+				t.Errorf("test %d: unexpected values filled for dense row %d: got: %v want: %v",
+					id, i, got, row)
+			}
+		}
+	}
+
+	denseComparison := func(a *Dense) interface{} {
+		r, c := a.Dims()
+		ans := make([][]float64, r)
+		for i := range ans {
+			ans[i] = make([]float64, c)
+			for j := range ans[i] {
+				ans[i][j] = a.At(i, j)
+			}
+		}
+		return ans
+	}
+
+	f := func(a Matrix) interface{} {
+		r, _ := a.Dims()
+		ans := make([][]float64, r)
+		for i := range ans {
+			ans[i] = Row(nil, i, a)
+		}
+		return ans
+	}
+	testOneInputFunc(t, "Row", f, denseComparison, sameAnswerF64SliceOfSlice, isAnyType, isAnySize)
+
+	f = func(a Matrix) interface{} {
+		r, c := a.Dims()
+		ans := make([][]float64, r)
+		for i := range ans {
+			ans[i] = make([]float64, c)
+			Row(ans[i], i, a)
+		}
+		return ans
+	}
+	testOneInputFunc(t, "Row", f, denseComparison, sameAnswerF64SliceOfSlice, isAnyType, isAnySize)
+}
+
+func TestCond(t *testing.T) {
+	for i, test := range []struct {
+		a       *Dense
+		condOne float64
+		condTwo float64
+		condInf float64
+	}{
+		{
+			a: NewDense(3, 3, []float64{
+				8, 1, 6,
+				3, 5, 7,
+				4, 9, 2,
+			}),
+			condOne: 16.0 / 3.0,
+			condTwo: 4.330127018922192,
+			condInf: 16.0 / 3.0,
+		},
+		{
+			a: NewDense(4, 4, []float64{
+				2, 9, 3, 2,
+				10, 9, 9, 3,
+				1, 1, 5, 2,
+				8, 4, 10, 2,
+			}),
+			condOne: 1 / 0.024740155174938,
+			condTwo: 34.521576567075087,
+			condInf: 1 / 0.012034465570035,
+		},
+		{
+			a: NewDense(3, 3, []float64{
+				5, 6, 7,
+				8, -2, 1,
+				7, 7, 7}),
+			condOne: 30.769230769230749,
+			condTwo: 21.662689498448440,
+			condInf: 31.153846153846136,
+		},
+	} {
+		orig := DenseCopyOf(test.a)
+		condOne := Cond(test.a, 1)
+		if !floats.EqualWithinAbsOrRel(test.condOne, condOne, 1e-13, 1e-13) {
+			t.Errorf("Case %d: one norm mismatch. Want %v, got %v", i, test.condOne, condOne)
+		}
+		if !Equal(test.a, orig) {
+			t.Errorf("Case %d: unexpected mutation of input matrix for one norm. Want %v, got %v", i, orig, test.a)
+		}
+		condTwo := Cond(test.a, 2)
+		if !floats.EqualWithinAbsOrRel(test.condTwo, condTwo, 1e-13, 1e-13) {
+			t.Errorf("Case %d: two norm mismatch. Want %v, got %v", i, test.condTwo, condTwo)
+		}
+		if !Equal(test.a, orig) {
+			t.Errorf("Case %d: unexpected mutation of input matrix for two norm. Want %v, got %v", i, orig, test.a)
+		}
+		condInf := Cond(test.a, math.Inf(1))
+		if !floats.EqualWithinAbsOrRel(test.condInf, condInf, 1e-13, 1e-13) {
+			t.Errorf("Case %d: inf norm mismatch. Want %v, got %v", i, test.condInf, condInf)
+		}
+		if !Equal(test.a, orig) {
+			t.Errorf("Case %d: unexpected mutation of input matrix for inf norm. Want %v, got %v", i, orig, test.a)
+		}
+	}
+
+	for _, test := range []struct {
+		name string
+		norm float64
+	}{
+		{
+			name: "CondOne",
+			norm: 1,
+		},
+		{
+			name: "CondTwo",
+			norm: 2,
+		},
+		{
+			name: "CondInf",
+			norm: math.Inf(1),
+		},
+	} {
+		f := func(a Matrix) interface{} {
+			return Cond(a, test.norm)
+		}
+		denseComparison := func(a *Dense) interface{} {
+			return Cond(a, test.norm)
+		}
+		testOneInputFunc(t, test.name, f, denseComparison, sameAnswerFloatApproxTol(1e-12), isAnyType, isAnySize)
+	}
+}
+
+func TestDet(t *testing.T) {
+	for c, test := range []struct {
+		a   *Dense
+		ans float64
+	}{
+		{
+			a:   NewDense(2, 2, []float64{1, 0, 0, 1}),
+			ans: 1,
+		},
+		{
+			a:   NewDense(2, 2, []float64{1, 0, 0, -1}),
+			ans: -1,
+		},
+		{
+			a: NewDense(3, 3, []float64{
+				1, 2, 0,
+				0, 1, 2,
+				0, 2, 1,
+			}),
+			ans: -3,
+		},
+		{
+			a: NewDense(3, 3, []float64{
+				1, 2, 3,
+				5, 7, 9,
+				6, 9, 12,
+			}),
+			ans: 0,
+		},
+	} {
+		a := DenseCopyOf(test.a)
+		det := Det(a)
+		if !Equal(a, test.a) {
+			t.Errorf("Input matrix changed during Det. Case %d.", c)
+		}
+		if !floats.EqualWithinAbsOrRel(det, test.ans, 1e-14, 1e-14) {
+			t.Errorf("Det mismatch case %d. Got %v, want %v", c, det, test.ans)
+		}
+	}
+	// Perform the normal list test to ensure it works for all types.
+	f := func(a Matrix) interface{} {
+		return Det(a)
+	}
+	denseComparison := func(a *Dense) interface{} {
+		return Det(a)
+	}
+	testOneInputFunc(t, "Det", f, denseComparison, sameAnswerFloatApproxTol(1e-12), isAnyType, isSquare)
+
+	// Check that it gives approximately the same answer as Cholesky
+	// Ensure the input matrices are wider than tall so they are full rank
+	isWide := func(ar, ac int) bool {
+		return ar <= ac
+	}
+	f = func(a Matrix) interface{} {
+		ar, ac := a.Dims()
+		if !isWide(ar, ac) {
+			panic(ErrShape)
+		}
+		var tmp Dense
+		tmp.Mul(a, a.T())
+		return Det(&tmp)
+	}
+	denseComparison = func(a *Dense) interface{} {
+		ar, ac := a.Dims()
+		if !isWide(ar, ac) {
+			panic(ErrShape)
+		}
+		var tmp SymDense
+		tmp.SymOuterK(1, a)
+		var chol Cholesky
+		ok := chol.Factorize(&tmp)
+		if !ok {
+			panic("bad chol test")
+		}
+		return chol.Det()
+	}
+	testOneInputFunc(t, "DetVsChol", f, denseComparison, sameAnswerFloatApproxTol(1e-10), isAnyType, isWide)
+}
+
+func TestDot(t *testing.T) {
+	f := func(a, b Matrix) interface{} {
+		return Dot(a.(*VecDense), b.(*VecDense))
+	}
+	denseComparison := func(a, b *Dense) interface{} {
+		ra, ca := a.Dims()
+		rb, cb := b.Dims()
+		if ra != rb || ca != cb {
+			panic(ErrShape)
+		}
+		var sum float64
+		for i := 0; i < ra; i++ {
+			for j := 0; j < ca; j++ {
+				sum += a.At(i, j) * b.At(i, j)
+			}
+		}
+		return sum
+	}
+	testTwoInputFunc(t, "Dot", f, denseComparison, sameAnswerFloatApproxTol(1e-12), legalTypesVecVec, legalSizeSameVec)
+}
+
+func TestEqual(t *testing.T) {
+	f := func(a, b Matrix) interface{} {
+		return Equal(a, b)
+	}
+	denseComparison := func(a, b *Dense) interface{} {
+		return Equal(a, b)
+	}
+	testTwoInputFunc(t, "Equal", f, denseComparison, sameAnswerBool, legalTypesAll, isAnySize2)
+}
+
+func TestMax(t *testing.T) {
+	// A direct test of Max with *Dense arguments is in TestNewDense.
+	f := func(a Matrix) interface{} {
+		return Max(a)
+	}
+	denseComparison := func(a *Dense) interface{} {
+		return Max(a)
+	}
+	testOneInputFunc(t, "Max", f, denseComparison, sameAnswerFloat, isAnyType, isAnySize)
+}
+
+func TestMin(t *testing.T) {
+	// A direct test of Min with *Dense arguments is in TestNewDense.
+	f := func(a Matrix) interface{} {
+		return Min(a)
+	}
+	denseComparison := func(a *Dense) interface{} {
+		return Min(a)
+	}
+	testOneInputFunc(t, "Min", f, denseComparison, sameAnswerFloat, isAnyType, isAnySize)
+}
+
+func TestNorm(t *testing.T) {
+	for i, test := range []struct {
+		a    [][]float64
+		ord  float64
+		norm float64
+	}{
+		{
+			a:    [][]float64{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}, {10, 11, 12}},
+			ord:  1,
+			norm: 30,
+		},
+		{
+			a:    [][]float64{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}, {10, 11, 12}},
+			ord:  2,
+			norm: 25.495097567963924,
+		},
+		{
+			a:    [][]float64{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}, {10, 11, 12}},
+			ord:  math.Inf(1),
+			norm: 33,
+		},
+		{
+			a:    [][]float64{{1, -2, -2}, {-4, 5, 6}},
+			ord:  1,
+			norm: 8,
+		},
+		{
+			a:    [][]float64{{1, -2, -2}, {-4, 5, 6}},
+			ord:  math.Inf(1),
+			norm: 15,
+		},
+	} {
+		a := NewDense(flatten(test.a))
+		if math.Abs(Norm(a, test.ord)-test.norm) > 1e-14 {
+			t.Errorf("Mismatch test %d: %v norm = %f", i, test.a, test.norm)
+		}
+	}
+
+	for _, test := range []struct {
+		name string
+		norm float64
+	}{
+		{"NormOne", 1},
+		{"NormTwo", 2},
+		{"NormInf", math.Inf(1)},
+	} {
+		f := func(a Matrix) interface{} {
+			return Norm(a, test.norm)
+		}
+		denseComparison := func(a *Dense) interface{} {
+			return Norm(a, test.norm)
+		}
+		testOneInputFunc(t, test.name, f, denseComparison, sameAnswerFloatApproxTol(1e-12), isAnyType, isAnySize)
+	}
+}
+
+func TestNormZero(t *testing.T) {
+	for _, a := range []Matrix{
+		&Dense{},
+		&SymDense{},
+		&SymDense{mat: blas64.Symmetric{Uplo: blas.Upper}},
+		&TriDense{},
+		&TriDense{mat: blas64.Triangular{Uplo: blas.Upper, Diag: blas.NonUnit}},
+		&VecDense{},
+	} {
+		for _, norm := range []float64{1, 2, math.Inf(1)} {
+			panicked, message := panics(func() { Norm(a, norm) })
+			if !panicked {
+				t.Errorf("expected panic for Norm(&%T{}, %v)", a, norm)
+			}
+			if message != ErrShape.Error() {
+				t.Errorf("unexpected panic string for Norm(&%T{}, %v): got:%s want:%s",
+					a, norm, message, ErrShape.Error())
+			}
+		}
+	}
+}
+
+func TestSum(t *testing.T) {
+	f := func(a Matrix) interface{} {
+		return Sum(a)
+	}
+	denseComparison := func(a *Dense) interface{} {
+		return Sum(a)
+	}
+	testOneInputFunc(t, "Sum", f, denseComparison, sameAnswerFloatApproxTol(1e-12), isAnyType, isAnySize)
+}
+
+func TestTrace(t *testing.T) {
+	for _, test := range []struct {
+		a     *Dense
+		trace float64
+	}{
+		{
+			a:     NewDense(3, 3, []float64{1, 2, 3, 4, 5, 6, 7, 8, 9}),
+			trace: 15,
+		},
+	} {
+		trace := Trace(test.a)
+		if trace != test.trace {
+			t.Errorf("Trace mismatch. Want %v, got %v", test.trace, trace)
+		}
+	}
+	f := func(a Matrix) interface{} {
+		return Trace(a)
+	}
+	denseComparison := func(a *Dense) interface{} {
+		return Trace(a)
+	}
+	testOneInputFunc(t, "Trace", f, denseComparison, sameAnswerFloat, isAnyType, isSquare)
+}
+
+func TestDoer(t *testing.T) {
+	type MatrixDoer interface {
+		Matrix
+		NonZeroDoer
+		RowNonZeroDoer
+		ColNonZeroDoer
+	}
+	ones := func(n int) []float64 {
+		data := make([]float64, n)
+		for i := range data {
+			data[i] = 1
+		}
+		return data
+	}
+	for i, m := range []MatrixDoer{
+		NewTriDense(3, Lower, ones(3*3)),
+		NewTriDense(3, Upper, ones(3*3)),
+		NewBandDense(6, 6, 1, 1, ones(3*6)),
+		NewBandDense(6, 10, 1, 1, ones(3*6)),
+		NewBandDense(10, 6, 1, 1, ones(7*3)),
+		NewSymBandDense(3, 0, ones(3)),
+		NewSymBandDense(3, 1, ones(3*(1+1))),
+		NewSymBandDense(6, 1, ones(6*(1+1))),
+		NewSymBandDense(6, 2, ones(6*(2+1))),
+	} {
+		r, c := m.Dims()
+
+		want := Sum(m)
+
+		// got and fn sum the accessed elements in
+		// the Doer that is being operated on.
+		// fn also tests that the accessed elements
+		// are within the writable areas of the
+		// matrix to check that only valid elements
+		// are operated on.
+		var got float64
+		fn := func(i, j int, v float64) {
+			got += v
+			switch m := m.(type) {
+			case MutableTriangular:
+				m.SetTri(i, j, v)
+			case MutableBanded:
+				m.SetBand(i, j, v)
+			case MutableSymBanded:
+				m.SetSymBand(i, j, v)
+			default:
+				panic("bad test: need mutable type")
+			}
+		}
+
+		panicked, message := panics(func() { m.DoNonZero(fn) })
+		if panicked {
+			t.Errorf("unexpected panic for Doer test %d: %q", i, message)
+			continue
+		}
+		if got != want {
+			t.Errorf("unexpected Doer sum: got:%f want:%f", got, want)
+		}
+
+		// Reset got for testing with DoRowNonZero.
+		got = 0
+		panicked, message = panics(func() {
+			for i := 0; i < r; i++ {
+				m.DoRowNonZero(i, fn)
+			}
+		})
+		if panicked {
+			t.Errorf("unexpected panic for RowDoer test %d: %q", i, message)
+			continue
+		}
+		if got != want {
+			t.Errorf("unexpected RowDoer sum: got:%f want:%f", got, want)
+		}
+
+		// Reset got for testing with DoColNonZero.
+		got = 0
+		panicked, message = panics(func() {
+			for j := 0; j < c; j++ {
+				m.DoColNonZero(j, fn)
+			}
+		})
+		if panicked {
+			t.Errorf("unexpected panic for ColDoer test %d: %q", i, message)
+			continue
+		}
+		if got != want {
+			t.Errorf("unexpected ColDoer sum: got:%f want:%f", got, want)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/mul_test.go b/vendor/gonum.org/v1/gonum/mat/mul_test.go
new file mode 100644
index 00000000..57ec17f2
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/mul_test.go
@@ -0,0 +1,283 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+)
+
+// TODO: Need to add tests where one is overwritten.
+func TestMulTypes(t *testing.T) {
+	for _, test := range []struct {
+		ar     int
+		ac     int
+		br     int
+		bc     int
+		Panics bool
+	}{
+		{
+			ar:     5,
+			ac:     5,
+			br:     5,
+			bc:     5,
+			Panics: false,
+		},
+		{
+			ar:     10,
+			ac:     5,
+			br:     5,
+			bc:     3,
+			Panics: false,
+		},
+		{
+			ar:     10,
+			ac:     5,
+			br:     5,
+			bc:     8,
+			Panics: false,
+		},
+		{
+			ar:     8,
+			ac:     10,
+			br:     10,
+			bc:     3,
+			Panics: false,
+		},
+		{
+			ar:     8,
+			ac:     3,
+			br:     3,
+			bc:     10,
+			Panics: false,
+		},
+		{
+			ar:     5,
+			ac:     8,
+			br:     8,
+			bc:     10,
+			Panics: false,
+		},
+		{
+			ar:     5,
+			ac:     12,
+			br:     12,
+			bc:     8,
+			Panics: false,
+		},
+		{
+			ar:     5,
+			ac:     7,
+			br:     8,
+			bc:     10,
+			Panics: true,
+		},
+	} {
+		ar := test.ar
+		ac := test.ac
+		br := test.br
+		bc := test.bc
+
+		// Generate random matrices
+		avec := make([]float64, ar*ac)
+		randomSlice(avec)
+		a := NewDense(ar, ac, avec)
+
+		bvec := make([]float64, br*bc)
+		randomSlice(bvec)
+
+		b := NewDense(br, bc, bvec)
+
+		// Check that it panics if it is supposed to
+		if test.Panics {
+			c := NewDense(0, 0, nil)
+			fn := func() {
+				c.Mul(a, b)
+			}
+			pan, _ := panics(fn)
+			if !pan {
+				t.Errorf("Mul did not panic with dimension mismatch")
+			}
+			continue
+		}
+
+		cvec := make([]float64, ar*bc)
+
+		// Get correct matrix multiply answer from blas64.Gemm
+		blas64.Gemm(blas.NoTrans, blas.NoTrans,
+			1, a.mat, b.mat,
+			0, blas64.General{Rows: ar, Cols: bc, Stride: bc, Data: cvec},
+		)
+
+		avecCopy := append([]float64{}, avec...)
+		bvecCopy := append([]float64{}, bvec...)
+		cvecCopy := append([]float64{}, cvec...)
+
+		acomp := matComp{r: ar, c: ac, data: avecCopy}
+		bcomp := matComp{r: br, c: bc, data: bvecCopy}
+		ccomp := matComp{r: ar, c: bc, data: cvecCopy}
+
+		// Do normal multiply with empty dense
+		d := NewDense(0, 0, nil)
+
+		testMul(t, a, b, d, acomp, bcomp, ccomp, false, "zero receiver")
+
+		// Normal multiply with existing receiver
+		c := NewDense(ar, bc, cvec)
+		randomSlice(cvec)
+		testMul(t, a, b, c, acomp, bcomp, ccomp, false, "existing receiver")
+
+		// Cast a as a basic matrix
+		am := (*basicMatrix)(a)
+		bm := (*basicMatrix)(b)
+		d.Reset()
+		testMul(t, am, b, d, acomp, bcomp, ccomp, true, "a is basic, receiver is zero")
+		d.Reset()
+		testMul(t, a, bm, d, acomp, bcomp, ccomp, true, "b is basic, receiver is zero")
+		d.Reset()
+		testMul(t, am, bm, d, acomp, bcomp, ccomp, true, "both basic, receiver is zero")
+		randomSlice(cvec)
+		testMul(t, am, b, d, acomp, bcomp, ccomp, true, "a is basic, receiver is full")
+		randomSlice(cvec)
+		testMul(t, a, bm, d, acomp, bcomp, ccomp, true, "b is basic, receiver is full")
+		randomSlice(cvec)
+		testMul(t, am, bm, d, acomp, bcomp, ccomp, true, "both basic, receiver is full")
+	}
+}
+
+func randomSlice(s []float64) {
+	for i := range s {
+		s[i] = rand.NormFloat64()
+	}
+}
+
+type matComp struct {
+	r, c int
+	data []float64
+}
+
+func testMul(t *testing.T, a, b Matrix, c *Dense, acomp, bcomp, ccomp matComp, cvecApprox bool, name string) {
+	c.Mul(a, b)
+	var aDense *Dense
+	switch t := a.(type) {
+	case *Dense:
+		aDense = t
+	case *basicMatrix:
+		aDense = (*Dense)(t)
+	}
+
+	var bDense *Dense
+	switch t := b.(type) {
+	case *Dense:
+		bDense = t
+	case *basicMatrix:
+		bDense = (*Dense)(t)
+	}
+
+	if !denseEqual(aDense, acomp) {
+		t.Errorf("a changed unexpectedly for %v", name)
+	}
+	if !denseEqual(bDense, bcomp) {
+		t.Errorf("b changed unexpectedly for %v", name)
+	}
+	if cvecApprox {
+		if !denseEqualApprox(c, ccomp, 1e-14) {
+			t.Errorf("mul answer not within tol for %v", name)
+		}
+		return
+	}
+
+	if !denseEqual(c, ccomp) {
+		t.Errorf("mul answer not equal for %v", name)
+	}
+}
+
+type basicMatrix Dense
+
+func (m *basicMatrix) At(r, c int) float64 {
+	return (*Dense)(m).At(r, c)
+}
+
+func (m *basicMatrix) Dims() (r, c int) {
+	return (*Dense)(m).Dims()
+}
+
+func (m *basicMatrix) T() Matrix {
+	return Transpose{m}
+}
+
+type basicSymmetric SymDense
+
+var _ Symmetric = &basicSymmetric{}
+
+func (m *basicSymmetric) At(r, c int) float64 {
+	return (*SymDense)(m).At(r, c)
+}
+
+func (m *basicSymmetric) Dims() (r, c int) {
+	return (*SymDense)(m).Dims()
+}
+
+func (m *basicSymmetric) T() Matrix {
+	return m
+}
+
+func (m *basicSymmetric) Symmetric() int {
+	return (*SymDense)(m).Symmetric()
+}
+
+type basicTriangular TriDense
+
+func (m *basicTriangular) At(r, c int) float64 {
+	return (*TriDense)(m).At(r, c)
+}
+
+func (m *basicTriangular) Dims() (r, c int) {
+	return (*TriDense)(m).Dims()
+}
+
+func (m *basicTriangular) T() Matrix {
+	return Transpose{m}
+}
+
+func (m *basicTriangular) Triangle() (int, TriKind) {
+	return (*TriDense)(m).Triangle()
+}
+
+func (m *basicTriangular) TTri() Triangular {
+	return TransposeTri{m}
+}
+
+func denseEqual(a *Dense, acomp matComp) bool {
+	ar2, ac2 := a.Dims()
+	if ar2 != acomp.r {
+		return false
+	}
+	if ac2 != acomp.c {
+		return false
+	}
+	if !floats.Equal(a.mat.Data, acomp.data) {
+		return false
+	}
+	return true
+}
+
+func denseEqualApprox(a *Dense, acomp matComp, tol float64) bool {
+	ar2, ac2 := a.Dims()
+	if ar2 != acomp.r {
+		return false
+	}
+	if ac2 != acomp.c {
+		return false
+	}
+	if !floats.EqualApprox(a.mat.Data, acomp.data, tol) {
+		return false
+	}
+	return true
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/offset.go b/vendor/gonum.org/v1/gonum/mat/offset.go
new file mode 100644
index 00000000..01e7d34f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/offset.go
@@ -0,0 +1,20 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build !appengine
+
+package mat
+
+import "unsafe"
+
+// offset returns the number of float64 values b[0] is after a[0].
+func offset(a, b []float64) int {
+	if &a[0] == &b[0] {
+		return 0
+	}
+	// This expression must be atomic with respect to GC moves.
+	// At this stage this is true, because the GC does not
+	// move. See https://golang.org/issue/12445.
+	return int(uintptr(unsafe.Pointer(&b[0]))-uintptr(unsafe.Pointer(&a[0]))) / int(unsafe.Sizeof(float64(0)))
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/offset_appengine.go b/vendor/gonum.org/v1/gonum/mat/offset_appengine.go
new file mode 100644
index 00000000..a4e7b27a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/offset_appengine.go
@@ -0,0 +1,24 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//+build appengine
+
+package mat
+
+import "reflect"
+
+var sizeOfFloat64 = int(reflect.TypeOf(float64(0)).Size())
+
+// offset returns the number of float64 values b[0] is after a[0].
+func offset(a, b []float64) int {
+	va0 := reflect.ValueOf(a).Index(0)
+	vb0 := reflect.ValueOf(b).Index(0)
+	if va0.Addr() == vb0.Addr() {
+		return 0
+	}
+	// This expression must be atomic with respect to GC moves.
+	// At this stage this is true, because the GC does not
+	// move. See https://golang.org/issue/12445.
+	return int(vb0.UnsafeAddr()-va0.UnsafeAddr()) / sizeOfFloat64
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/pool.go b/vendor/gonum.org/v1/gonum/mat/pool.go
new file mode 100644
index 00000000..7adb3275
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/pool.go
@@ -0,0 +1,236 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"sync"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+var tab64 = [64]byte{
+	0x3f, 0x00, 0x3a, 0x01, 0x3b, 0x2f, 0x35, 0x02,
+	0x3c, 0x27, 0x30, 0x1b, 0x36, 0x21, 0x2a, 0x03,
+	0x3d, 0x33, 0x25, 0x28, 0x31, 0x12, 0x1c, 0x14,
+	0x37, 0x1e, 0x22, 0x0b, 0x2b, 0x0e, 0x16, 0x04,
+	0x3e, 0x39, 0x2e, 0x34, 0x26, 0x1a, 0x20, 0x29,
+	0x32, 0x24, 0x11, 0x13, 0x1d, 0x0a, 0x0d, 0x15,
+	0x38, 0x2d, 0x19, 0x1f, 0x23, 0x10, 0x09, 0x0c,
+	0x2c, 0x18, 0x0f, 0x08, 0x17, 0x07, 0x06, 0x05,
+}
+
+// bits returns the ceiling of base 2 log of v.
+// Approach based on http://stackoverflow.com/a/11398748.
+func bits(v uint64) byte {
+	if v == 0 {
+		return 0
+	}
+	v <<= 2
+	v--
+	v |= v >> 1
+	v |= v >> 2
+	v |= v >> 4
+	v |= v >> 8
+	v |= v >> 16
+	v |= v >> 32
+	return tab64[((v-(v>>1))*0x07EDD5E59A4E28C2)>>58] - 1
+}
+
+var (
+	// pool contains size stratified workspace Dense pools.
+	// Each pool element i returns sized matrices with a data
+	// slice capped at 1<<i.
+	pool [63]sync.Pool
+
+	// poolSym is the SymDense equivalent of pool.
+	poolSym [63]sync.Pool
+
+	// poolTri is the TriDense equivalent of pool.
+	poolTri [63]sync.Pool
+
+	// poolVec is the VecDense equivalent of pool.
+	poolVec [63]sync.Pool
+
+	// poolFloats is the []float64 equivalent of pool.
+	poolFloats [63]sync.Pool
+
+	// poolInts is the []int equivalent of pool.
+	poolInts [63]sync.Pool
+)
+
+func init() {
+	for i := range pool {
+		l := 1 << uint(i)
+		pool[i].New = func() interface{} {
+			return &Dense{mat: blas64.General{
+				Data: make([]float64, l),
+			}}
+		}
+		poolSym[i].New = func() interface{} {
+			return &SymDense{mat: blas64.Symmetric{
+				Uplo: blas.Upper,
+				Data: make([]float64, l),
+			}}
+		}
+		poolTri[i].New = func() interface{} {
+			return &TriDense{mat: blas64.Triangular{
+				Data: make([]float64, l),
+			}}
+		}
+		poolVec[i].New = func() interface{} {
+			return &VecDense{mat: blas64.Vector{
+				Inc:  1,
+				Data: make([]float64, l),
+			}}
+		}
+		poolFloats[i].New = func() interface{} {
+			return make([]float64, l)
+		}
+		poolInts[i].New = func() interface{} {
+			return make([]int, l)
+		}
+	}
+}
+
+// getWorkspace returns a *Dense of size r×c and a data slice
+// with a cap that is less than 2*r*c. If clear is true, the
+// data slice visible through the Matrix interface is zeroed.
+func getWorkspace(r, c int, clear bool) *Dense {
+	l := uint64(r * c)
+	w := pool[bits(l)].Get().(*Dense)
+	w.mat.Data = w.mat.Data[:l]
+	if clear {
+		zero(w.mat.Data)
+	}
+	w.mat.Rows = r
+	w.mat.Cols = c
+	w.mat.Stride = c
+	w.capRows = r
+	w.capCols = c
+	return w
+}
+
+// putWorkspace replaces a used *Dense into the appropriate size
+// workspace pool. putWorkspace must not be called with a matrix
+// where references to the underlying data slice have been kept.
+func putWorkspace(w *Dense) {
+	pool[bits(uint64(cap(w.mat.Data)))].Put(w)
+}
+
+// getWorkspaceSym returns a *SymDense of size n and a cap that
+// is less than 2*n. If clear is true, the data slice visible
+// through the Matrix interface is zeroed.
+func getWorkspaceSym(n int, clear bool) *SymDense {
+	l := uint64(n)
+	l *= l
+	s := poolSym[bits(l)].Get().(*SymDense)
+	s.mat.Data = s.mat.Data[:l]
+	if clear {
+		zero(s.mat.Data)
+	}
+	s.mat.N = n
+	s.mat.Stride = n
+	s.cap = n
+	return s
+}
+
+// putWorkspaceSym replaces a used *SymDense into the appropriate size
+// workspace pool. putWorkspaceSym must not be called with a matrix
+// where references to the underlying data slice have been kept.
+func putWorkspaceSym(s *SymDense) {
+	poolSym[bits(uint64(cap(s.mat.Data)))].Put(s)
+}
+
+// getWorkspaceTri returns a *TriDense of size n and a cap that
+// is less than 2*n. If clear is true, the data slice visible
+// through the Matrix interface is zeroed.
+func getWorkspaceTri(n int, kind TriKind, clear bool) *TriDense {
+	l := uint64(n)
+	l *= l
+	t := poolTri[bits(l)].Get().(*TriDense)
+	t.mat.Data = t.mat.Data[:l]
+	if clear {
+		zero(t.mat.Data)
+	}
+	t.mat.N = n
+	t.mat.Stride = n
+	if kind == Upper {
+		t.mat.Uplo = blas.Upper
+	} else if kind == Lower {
+		t.mat.Uplo = blas.Lower
+	} else {
+		panic(ErrTriangle)
+	}
+	t.mat.Diag = blas.NonUnit
+	t.cap = n
+	return t
+}
+
+// putWorkspaceTri replaces a used *TriDense into the appropriate size
+// workspace pool. putWorkspaceTri must not be called with a matrix
+// where references to the underlying data slice have been kept.
+func putWorkspaceTri(t *TriDense) {
+	poolTri[bits(uint64(cap(t.mat.Data)))].Put(t)
+}
+
+// getWorkspaceVec returns a *VecDense of length n and a cap that
+// is less than 2*n. If clear is true, the data slice visible
+// through the Matrix interface is zeroed.
+func getWorkspaceVec(n int, clear bool) *VecDense {
+	l := uint64(n)
+	v := poolVec[bits(l)].Get().(*VecDense)
+	v.mat.Data = v.mat.Data[:l]
+	if clear {
+		zero(v.mat.Data)
+	}
+	v.n = n
+	return v
+}
+
+// putWorkspaceVec replaces a used *VecDense into the appropriate size
+// workspace pool. putWorkspaceVec must not be called with a matrix
+// where references to the underlying data slice have been kept.
+func putWorkspaceVec(v *VecDense) {
+	poolVec[bits(uint64(cap(v.mat.Data)))].Put(v)
+}
+
+// getFloats returns a []float64 of length l and a cap that is
+// less than 2*l. If clear is true, the slice visible is zeroed.
+func getFloats(l int, clear bool) []float64 {
+	w := poolFloats[bits(uint64(l))].Get().([]float64)
+	w = w[:l]
+	if clear {
+		zero(w)
+	}
+	return w
+}
+
+// putFloats replaces a used []float64 into the appropriate size
+// workspace pool. putFloats must not be called with a slice
+// where references to the underlying data have been kept.
+func putFloats(w []float64) {
+	poolFloats[bits(uint64(cap(w)))].Put(w)
+}
+
+// getInts returns a []ints of length l and a cap that is
+// less than 2*l. If clear is true, the slice visible is zeroed.
+func getInts(l int, clear bool) []int {
+	w := poolInts[bits(uint64(l))].Get().([]int)
+	w = w[:l]
+	if clear {
+		for i := range w {
+			w[i] = 0
+		}
+	}
+	return w
+}
+
+// putInts replaces a used []int into the appropriate size
+// workspace pool. putInts must not be called with a slice
+// where references to the underlying data have been kept.
+func putInts(w []int) {
+	poolInts[bits(uint64(cap(w)))].Put(w)
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/pool_test.go b/vendor/gonum.org/v1/gonum/mat/pool_test.go
new file mode 100644
index 00000000..fcf831ad
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/pool_test.go
@@ -0,0 +1,81 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"math"
+	"math/rand"
+	"reflect"
+	"testing"
+)
+
+func TestPool(t *testing.T) {
+	for i := 1; i < 10; i++ {
+		for j := 1; j < 10; j++ {
+			m := NewDense(i, j, nil)
+			for k := 0; k < 5; k++ {
+				work := make([]*Dense, rand.Intn(10)+1)
+				for l := range work {
+					w := getWorkspace(i, j, true)
+					if !reflect.DeepEqual(w.mat, m.mat) {
+						t.Error("unexpected non-zeroed matrix returned by getWorkspace")
+					}
+					if w.capRows != m.capRows {
+						t.Error("unexpected capacity matrix returned by getWorkspace")
+					}
+					if w.capCols != m.capCols {
+						t.Error("unexpected capacity matrix returned by getWorkspace")
+					}
+					if cap(w.mat.Data) >= 2*len(w.mat.Data) {
+						t.Errorf("r: %d c: %d -> len: %d cap: %d", i, j, len(w.mat.Data), cap(w.mat.Data))
+					}
+					w.Set(0, 0, math.NaN())
+					work[l] = w
+				}
+				for _, w := range work {
+					putWorkspace(w)
+				}
+			}
+		}
+	}
+}
+
+var benchmat *Dense
+
+func poolBenchmark(n, r, c int, clear bool) {
+	for i := 0; i < n; i++ {
+		benchmat = getWorkspace(r, c, clear)
+		putWorkspace(benchmat)
+	}
+}
+
+func newBenchmark(n, r, c int) {
+	for i := 0; i < n; i++ {
+		benchmat = NewDense(r, c, nil)
+	}
+}
+
+func BenchmarkPool10by10Uncleared(b *testing.B)   { poolBenchmark(b.N, 10, 10, false) }
+func BenchmarkPool10by10Cleared(b *testing.B)     { poolBenchmark(b.N, 10, 10, true) }
+func BenchmarkNew10by10(b *testing.B)             { newBenchmark(b.N, 10, 10) }
+func BenchmarkPool100by100Uncleared(b *testing.B) { poolBenchmark(b.N, 100, 100, false) }
+func BenchmarkPool100by100Cleared(b *testing.B)   { poolBenchmark(b.N, 100, 100, true) }
+func BenchmarkNew100by100(b *testing.B)           { newBenchmark(b.N, 100, 100) }
+
+func BenchmarkMulWorkspaceDense100Half(b *testing.B)        { denseMulWorkspaceBench(b, 100, 0.5) }
+func BenchmarkMulWorkspaceDense100Tenth(b *testing.B)       { denseMulWorkspaceBench(b, 100, 0.1) }
+func BenchmarkMulWorkspaceDense1000Half(b *testing.B)       { denseMulWorkspaceBench(b, 1000, 0.5) }
+func BenchmarkMulWorkspaceDense1000Tenth(b *testing.B)      { denseMulWorkspaceBench(b, 1000, 0.1) }
+func BenchmarkMulWorkspaceDense1000Hundredth(b *testing.B)  { denseMulWorkspaceBench(b, 1000, 0.01) }
+func BenchmarkMulWorkspaceDense1000Thousandth(b *testing.B) { denseMulWorkspaceBench(b, 1000, 0.001) }
+func denseMulWorkspaceBench(b *testing.B, size int, rho float64) {
+	b.StopTimer()
+	a, _ := randDense(size, rho, rand.NormFloat64)
+	d, _ := randDense(size, rho, rand.NormFloat64)
+	b.StartTimer()
+	for i := 0; i < b.N; i++ {
+		a.Mul(a, d)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/product.go b/vendor/gonum.org/v1/gonum/mat/product.go
new file mode 100644
index 00000000..5a0343b7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/product.go
@@ -0,0 +1,193 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import "fmt"
+
+// Product calculates the product of the given factors and places the result in
+// the receiver. The order of multiplication operations is optimized to minimize
+// the number of floating point operations on the basis that all matrix
+// multiplications are general.
+func (m *Dense) Product(factors ...Matrix) {
+	// The operation order optimisation is the naive O(n^3) dynamic
+	// programming approach and does not take into consideration
+	// finer-grained optimisations that might be available.
+	//
+	// TODO(kortschak) Consider using the O(nlogn) or O(mlogn)
+	// algorithms that are available. e.g.
+	//
+	// e.g. http://www.jofcis.com/publishedpapers/2014_10_10_4299_4306.pdf
+	//
+	// In the case that this is replaced, retain this code in
+	// tests to compare against.
+
+	r, c := m.Dims()
+	switch len(factors) {
+	case 0:
+		if r != 0 || c != 0 {
+			panic(ErrShape)
+		}
+		return
+	case 1:
+		m.reuseAs(factors[0].Dims())
+		m.Copy(factors[0])
+		return
+	case 2:
+		// Don't do work that we know the answer to.
+		m.Mul(factors[0], factors[1])
+		return
+	}
+
+	p := newMultiplier(m, factors)
+	p.optimize()
+	result := p.multiply()
+	m.reuseAs(result.Dims())
+	m.Copy(result)
+	putWorkspace(result)
+}
+
+// debugProductWalk enables debugging output for Product.
+const debugProductWalk = false
+
+// multiplier performs operation order optimisation and tree traversal.
+type multiplier struct {
+	// factors is the ordered set of
+	// factors to multiply.
+	factors []Matrix
+	// dims is the chain of factor
+	// dimensions.
+	dims []int
+
+	// table contains the dynamic
+	// programming costs and subchain
+	// division indices.
+	table table
+}
+
+func newMultiplier(m *Dense, factors []Matrix) *multiplier {
+	// Check size early, but don't yet
+	// allocate data for m.
+	r, c := m.Dims()
+	fr, fc := factors[0].Dims() // newMultiplier is only called with len(factors) > 2.
+	if !m.IsZero() {
+		if fr != r {
+			panic(ErrShape)
+		}
+		if _, lc := factors[len(factors)-1].Dims(); lc != c {
+			panic(ErrShape)
+		}
+	}
+
+	dims := make([]int, len(factors)+1)
+	dims[0] = r
+	dims[len(dims)-1] = c
+	pc := fc
+	for i, f := range factors[1:] {
+		cr, cc := f.Dims()
+		dims[i+1] = cr
+		if pc != cr {
+			panic(ErrShape)
+		}
+		pc = cc
+	}
+
+	return &multiplier{
+		factors: factors,
+		dims:    dims,
+		table:   newTable(len(factors)),
+	}
+}
+
+// optimize determines an optimal matrix multiply operation order.
+func (p *multiplier) optimize() {
+	if debugProductWalk {
+		fmt.Printf("chain dims: %v\n", p.dims)
+	}
+	const maxInt = int(^uint(0) >> 1)
+	for f := 1; f < len(p.factors); f++ {
+		for i := 0; i < len(p.factors)-f; i++ {
+			j := i + f
+			p.table.set(i, j, entry{cost: maxInt})
+			for k := i; k < j; k++ {
+				cost := p.table.at(i, k).cost + p.table.at(k+1, j).cost + p.dims[i]*p.dims[k+1]*p.dims[j+1]
+				if cost < p.table.at(i, j).cost {
+					p.table.set(i, j, entry{cost: cost, k: k})
+				}
+			}
+		}
+	}
+}
+
+// multiply walks the optimal operation tree found by optimize,
+// leaving the final result in the stack. It returns the
+// product, which may be copied but should be returned to
+// the workspace pool.
+func (p *multiplier) multiply() *Dense {
+	result, _ := p.multiplySubchain(0, len(p.factors)-1)
+	if debugProductWalk {
+		r, c := result.Dims()
+		fmt.Printf("\tpop result (%d×%d) cost=%d\n", r, c, p.table.at(0, len(p.factors)-1).cost)
+	}
+	return result.(*Dense)
+}
+
+func (p *multiplier) multiplySubchain(i, j int) (m Matrix, intermediate bool) {
+	if i == j {
+		return p.factors[i], false
+	}
+
+	a, aTmp := p.multiplySubchain(i, p.table.at(i, j).k)
+	b, bTmp := p.multiplySubchain(p.table.at(i, j).k+1, j)
+
+	ar, ac := a.Dims()
+	br, bc := b.Dims()
+	if ac != br {
+		// Panic with a string since this
+		// is not a user-facing panic.
+		panic(ErrShape.Error())
+	}
+
+	if debugProductWalk {
+		fmt.Printf("\tpush f[%d] (%d×%d)%s * f[%d] (%d×%d)%s\n",
+			i, ar, ac, result(aTmp), j, br, bc, result(bTmp))
+	}
+
+	r := getWorkspace(ar, bc, false)
+	r.Mul(a, b)
+	if aTmp {
+		putWorkspace(a.(*Dense))
+	}
+	if bTmp {
+		putWorkspace(b.(*Dense))
+	}
+	return r, true
+}
+
+type entry struct {
+	k    int // is the chain subdivision index.
+	cost int // cost is the cost of the operation.
+}
+
+// table is a row major n×n dynamic programming table.
+type table struct {
+	n       int
+	entries []entry
+}
+
+func newTable(n int) table {
+	return table{n: n, entries: make([]entry, n*n)}
+}
+
+func (t table) at(i, j int) entry     { return t.entries[i*t.n+j] }
+func (t table) set(i, j int, e entry) { t.entries[i*t.n+j] = e }
+
+type result bool
+
+func (r result) String() string {
+	if r {
+		return " (popped result)"
+	}
+	return ""
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/product_test.go b/vendor/gonum.org/v1/gonum/mat/product_test.go
new file mode 100644
index 00000000..2ce0e575
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/product_test.go
@@ -0,0 +1,251 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"fmt"
+	"math/rand"
+	"testing"
+)
+
+type dims struct{ r, c int }
+
+var productTests = []struct {
+	n       int
+	factors []dims
+	product dims
+	panics  bool
+}{
+	{
+		n:       1,
+		factors: []dims{{3, 4}},
+		product: dims{3, 4},
+		panics:  false,
+	},
+	{
+		n:       1,
+		factors: []dims{{2, 4}},
+		product: dims{3, 4},
+		panics:  true,
+	},
+	{
+		n:       3,
+		factors: []dims{{10, 30}, {30, 5}, {5, 60}},
+		product: dims{10, 60},
+		panics:  false,
+	},
+	{
+		n:       3,
+		factors: []dims{{100, 30}, {30, 5}, {5, 60}},
+		product: dims{10, 60},
+		panics:  true,
+	},
+	{
+		n:       7,
+		factors: []dims{{60, 5}, {5, 5}, {5, 4}, {4, 10}, {10, 22}, {22, 45}, {45, 10}},
+		product: dims{60, 10},
+		panics:  false,
+	},
+	{
+		n:       7,
+		factors: []dims{{60, 5}, {5, 5}, {5, 400}, {4, 10}, {10, 22}, {22, 45}, {45, 10}},
+		product: dims{60, 10},
+		panics:  true,
+	},
+	{
+		n:       3,
+		factors: []dims{{1, 1000}, {1000, 2}, {2, 2}},
+		product: dims{1, 2},
+		panics:  false,
+	},
+
+	// Random chains.
+	{
+		n:       0,
+		product: dims{0, 0},
+		panics:  false,
+	},
+	{
+		n:       2,
+		product: dims{60, 10},
+		panics:  false,
+	},
+	{
+		n:       3,
+		product: dims{60, 10},
+		panics:  false,
+	},
+	{
+		n:       4,
+		product: dims{60, 10},
+		panics:  false,
+	},
+	{
+		n:       10,
+		product: dims{60, 10},
+		panics:  false,
+	},
+}
+
+func TestProduct(t *testing.T) {
+	for _, test := range productTests {
+		dimensions := test.factors
+		if dimensions == nil && test.n > 0 {
+			dimensions = make([]dims, test.n)
+			for i := range dimensions {
+				if i != 0 {
+					dimensions[i].r = dimensions[i-1].c
+				}
+				dimensions[i].c = rand.Intn(50) + 1
+			}
+			dimensions[0].r = test.product.r
+			dimensions[test.n-1].c = test.product.c
+		}
+		factors := make([]Matrix, test.n)
+		for i, d := range dimensions {
+			data := make([]float64, d.r*d.c)
+			for i := range data {
+				data[i] = rand.Float64()
+			}
+			factors[i] = NewDense(d.r, d.c, data)
+		}
+
+		want := &Dense{}
+		if !test.panics {
+			a := &Dense{}
+			for i, b := range factors {
+				if i == 0 {
+					want.Clone(b)
+					continue
+				}
+				a, want = want, &Dense{}
+				want.Mul(a, b)
+			}
+		}
+
+		got := NewDense(test.product.r, test.product.c, nil)
+		panicked, message := panics(func() {
+			got.Product(factors...)
+		})
+		if test.panics {
+			if !panicked {
+				t.Errorf("fail to panic with product chain dimensions: %+v result dimension: %+v",
+					dimensions, test.product)
+			}
+			continue
+		} else if panicked {
+			t.Errorf("unexpected panic %q with product chain dimensions: %+v result dimension: %+v",
+				message, dimensions, test.product)
+			continue
+		}
+
+		if len(factors) > 0 {
+			p := newMultiplier(NewDense(test.product.r, test.product.c, nil), factors)
+			p.optimize()
+			gotCost := p.table.at(0, len(factors)-1).cost
+			expr, wantCost, ok := bestExpressionFor(dimensions)
+			if !ok {
+				t.Fatal("unexpected number of expressions in brute force expression search")
+			}
+			if gotCost != wantCost {
+				t.Errorf("unexpected cost for chain dimensions: %+v got: %v want: %v\n%s",
+					dimensions, got, want, expr)
+			}
+		}
+
+		if !EqualApprox(got, want, 1e-14) {
+			t.Errorf("unexpected result from product chain dimensions: %+v", dimensions)
+		}
+	}
+}
+
+// node is a subexpression node.
+type node struct {
+	dims
+	left, right *node
+}
+
+func (n *node) String() string {
+	if n.left == nil || n.right == nil {
+		rows, cols := n.shape()
+		return fmt.Sprintf("[%d×%d]", rows, cols)
+	}
+	rows, cols := n.shape()
+	return fmt.Sprintf("(%s * %s):[%d×%d]", n.left, n.right, rows, cols)
+}
+
+// shape returns the dimensions of the result of the subexpression.
+func (n *node) shape() (rows, cols int) {
+	if n.left == nil || n.right == nil {
+		return n.r, n.c
+	}
+	rows, _ = n.left.shape()
+	_, cols = n.right.shape()
+	return rows, cols
+}
+
+// cost returns the cost to evaluate the subexpression.
+func (n *node) cost() int {
+	if n.left == nil || n.right == nil {
+		return 0
+	}
+	lr, lc := n.left.shape()
+	_, rc := n.right.shape()
+	return lr*lc*rc + n.left.cost() + n.right.cost()
+}
+
+// expressionsFor returns a channel that can be used to iterate over all
+// expressions of the given factor dimensions.
+func expressionsFor(factors []dims) chan *node {
+	if len(factors) == 1 {
+		c := make(chan *node, 1)
+		c <- &node{dims: factors[0]}
+		close(c)
+		return c
+	}
+	c := make(chan *node)
+	go func() {
+		for i := 1; i < len(factors); i++ {
+			for left := range expressionsFor(factors[:i]) {
+				for right := range expressionsFor(factors[i:]) {
+					c <- &node{left: left, right: right}
+				}
+			}
+		}
+		close(c)
+	}()
+	return c
+}
+
+// catalan returns the nth 0-based Catalan number.
+func catalan(n int) int {
+	p := 1
+	for k := n + 1; k < 2*n+1; k++ {
+		p *= k
+	}
+	for k := 2; k < n+2; k++ {
+		p /= k
+	}
+	return p
+}
+
+// bestExpressonFor returns the lowest cost expression for the given expression
+// factor dimensions, the cost of the expression and whether the number of
+// expressions searched matches the Catalan number for the number of factors.
+func bestExpressionFor(factors []dims) (exp *node, cost int, ok bool) {
+	const maxInt = int(^uint(0) >> 1)
+	min := maxInt
+	var best *node
+	var n int
+	for exp := range expressionsFor(factors) {
+		n++
+		cost := exp.cost()
+		if cost < min {
+			min = cost
+			best = exp
+		}
+	}
+	return best, min, n == catalan(len(factors)-1)
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/qr.go b/vendor/gonum.org/v1/gonum/mat/qr.go
new file mode 100644
index 00000000..b89f8fb7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/qr.go
@@ -0,0 +1,221 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+	"gonum.org/v1/gonum/lapack/lapack64"
+)
+
+// QR is a type for creating and using the QR factorization of a matrix.
+type QR struct {
+	qr   *Dense
+	tau  []float64
+	cond float64
+}
+
+func (qr *QR) updateCond(norm lapack.MatrixNorm) {
+	// Since A = Q*R, and Q is orthogonal, we get for the condition number κ
+	//  κ(A) := |A| |A^-1| = |Q*R| |(Q*R)^-1| = |R| |R^-1 * Q^T|
+	//        = |R| |R^-1| = κ(R),
+	// where we used that fact that Q^-1 = Q^T. However, this assumes that
+	// the matrix norm is invariant under orthogonal transformations which
+	// is not the case for CondNorm. Hopefully the error is negligible: κ
+	// is only a qualitative measure anyway.
+	n := qr.qr.mat.Cols
+	work := getFloats(3*n, false)
+	iwork := getInts(n, false)
+	r := qr.qr.asTriDense(n, blas.NonUnit, blas.Upper)
+	v := lapack64.Trcon(norm, r.mat, work, iwork)
+	putFloats(work)
+	putInts(iwork)
+	qr.cond = 1 / v
+}
+
+// Factorize computes the QR factorization of an m×n matrix a where m >= n. The QR
+// factorization always exists even if A is singular.
+//
+// The QR decomposition is a factorization of the matrix A such that A = Q * R.
+// The matrix Q is an orthonormal m×m matrix, and R is an m×n upper triangular matrix.
+// Q and R can be extracted using the QTo and RTo methods.
+func (qr *QR) Factorize(a Matrix) {
+	qr.factorize(a, CondNorm)
+}
+
+func (qr *QR) factorize(a Matrix, norm lapack.MatrixNorm) {
+	m, n := a.Dims()
+	if m < n {
+		panic(ErrShape)
+	}
+	k := min(m, n)
+	if qr.qr == nil {
+		qr.qr = &Dense{}
+	}
+	qr.qr.Clone(a)
+	work := []float64{0}
+	qr.tau = make([]float64, k)
+	lapack64.Geqrf(qr.qr.mat, qr.tau, work, -1)
+
+	work = getFloats(int(work[0]), false)
+	lapack64.Geqrf(qr.qr.mat, qr.tau, work, len(work))
+	putFloats(work)
+	qr.updateCond(norm)
+}
+
+// Cond returns the condition number for the factorized matrix.
+// Cond will panic if the receiver does not contain a successful factorization.
+func (qr *QR) Cond() float64 {
+	if qr.qr == nil || qr.qr.IsZero() {
+		panic("qr: no decomposition computed")
+	}
+	return qr.cond
+}
+
+// TODO(btracey): Add in the "Reduced" forms for extracting the n×n orthogonal
+// and upper triangular matrices.
+
+// RTo extracts the m×n upper trapezoidal matrix from a QR decomposition.
+// If dst is nil, a new matrix is allocated. The resulting dst matrix is returned.
+func (qr *QR) RTo(dst *Dense) *Dense {
+	r, c := qr.qr.Dims()
+	if dst == nil {
+		dst = NewDense(r, c, nil)
+	} else {
+		dst.reuseAs(r, c)
+	}
+
+	// Disguise the QR as an upper triangular
+	t := &TriDense{
+		mat: blas64.Triangular{
+			N:      c,
+			Stride: qr.qr.mat.Stride,
+			Data:   qr.qr.mat.Data,
+			Uplo:   blas.Upper,
+			Diag:   blas.NonUnit,
+		},
+		cap: qr.qr.capCols,
+	}
+	dst.Copy(t)
+
+	// Zero below the triangular.
+	for i := r; i < c; i++ {
+		zero(dst.mat.Data[i*dst.mat.Stride : i*dst.mat.Stride+c])
+	}
+
+	return dst
+}
+
+// QTo extracts the m×m orthonormal matrix Q from a QR decomposition.
+// If dst is nil, a new matrix is allocated. The resulting Q matrix is returned.
+func (qr *QR) QTo(dst *Dense) *Dense {
+	r, _ := qr.qr.Dims()
+	if dst == nil {
+		dst = NewDense(r, r, nil)
+	} else {
+		dst.reuseAsZeroed(r, r)
+	}
+
+	// Set Q = I.
+	for i := 0; i < r*r; i += r + 1 {
+		dst.mat.Data[i] = 1
+	}
+
+	// Construct Q from the elementary reflectors.
+	work := []float64{0}
+	lapack64.Ormqr(blas.Left, blas.NoTrans, qr.qr.mat, qr.tau, dst.mat, work, -1)
+	work = getFloats(int(work[0]), false)
+	lapack64.Ormqr(blas.Left, blas.NoTrans, qr.qr.mat, qr.tau, dst.mat, work, len(work))
+	putFloats(work)
+
+	return dst
+}
+
+// Solve finds a minimum-norm solution to a system of linear equations defined
+// by the matrices A and b, where A is an m×n matrix represented in its QR factorized
+// form. If A is singular or near-singular a Condition error is returned. Please
+// see the documentation for Condition for more information.
+//
+// The minimization problem solved depends on the input parameters.
+//  If trans == false, find X such that ||A*X - b||_2 is minimized.
+//  If trans == true, find the minimum norm solution of A^T * X = b.
+// The solution matrix, X, is stored in place into m.
+func (qr *QR) Solve(m *Dense, trans bool, b Matrix) error {
+	r, c := qr.qr.Dims()
+	br, bc := b.Dims()
+
+	// The QR solve algorithm stores the result in-place into the right hand side.
+	// The storage for the answer must be large enough to hold both b and x.
+	// However, this method's receiver must be the size of x. Copy b, and then
+	// copy the result into m at the end.
+	if trans {
+		if c != br {
+			panic(ErrShape)
+		}
+		m.reuseAs(r, bc)
+	} else {
+		if r != br {
+			panic(ErrShape)
+		}
+		m.reuseAs(c, bc)
+	}
+	// Do not need to worry about overlap between m and b because x has its own
+	// independent storage.
+	x := getWorkspace(max(r, c), bc, false)
+	x.Copy(b)
+	t := qr.qr.asTriDense(qr.qr.mat.Cols, blas.NonUnit, blas.Upper).mat
+	if trans {
+		ok := lapack64.Trtrs(blas.Trans, t, x.mat)
+		if !ok {
+			return Condition(math.Inf(1))
+		}
+		for i := c; i < r; i++ {
+			zero(x.mat.Data[i*x.mat.Stride : i*x.mat.Stride+bc])
+		}
+		work := []float64{0}
+		lapack64.Ormqr(blas.Left, blas.NoTrans, qr.qr.mat, qr.tau, x.mat, work, -1)
+		work = getFloats(int(work[0]), false)
+		lapack64.Ormqr(blas.Left, blas.NoTrans, qr.qr.mat, qr.tau, x.mat, work, len(work))
+		putFloats(work)
+	} else {
+		work := []float64{0}
+		lapack64.Ormqr(blas.Left, blas.Trans, qr.qr.mat, qr.tau, x.mat, work, -1)
+		work = getFloats(int(work[0]), false)
+		lapack64.Ormqr(blas.Left, blas.Trans, qr.qr.mat, qr.tau, x.mat, work, len(work))
+		putFloats(work)
+
+		ok := lapack64.Trtrs(blas.NoTrans, t, x.mat)
+		if !ok {
+			return Condition(math.Inf(1))
+		}
+	}
+	// M was set above to be the correct size for the result.
+	m.Copy(x)
+	putWorkspace(x)
+	if qr.cond > ConditionTolerance {
+		return Condition(qr.cond)
+	}
+	return nil
+}
+
+// SolveVec finds a minimum-norm solution to a system of linear equations.
+// Please see QR.Solve for the full documentation.
+func (qr *QR) SolveVec(v *VecDense, trans bool, b *VecDense) error {
+	if v != b {
+		v.checkOverlap(b.mat)
+	}
+	r, c := qr.qr.Dims()
+	// The Solve implementation is non-trivial, so rather than duplicate the code,
+	// instead recast the VecDenses as Dense and call the matrix code.
+	if trans {
+		v.reuseAs(r)
+	} else {
+		v.reuseAs(c)
+	}
+	return qr.Solve(v.asDense(), trans, b.asDense())
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/qr_test.go b/vendor/gonum.org/v1/gonum/mat/qr_test.go
new file mode 100644
index 00000000..71a2d6e6
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/qr_test.go
@@ -0,0 +1,205 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+func TestQR(t *testing.T) {
+	for _, test := range []struct {
+		m, n int
+	}{
+		{5, 5},
+		{10, 5},
+	} {
+		m := test.m
+		n := test.n
+		a := NewDense(m, n, nil)
+		for i := 0; i < m; i++ {
+			for j := 0; j < n; j++ {
+				a.Set(i, j, rand.NormFloat64())
+			}
+		}
+		var want Dense
+		want.Clone(a)
+
+		var qr QR
+		qr.Factorize(a)
+		q := qr.QTo(nil)
+
+		if !isOrthonormal(q, 1e-10) {
+			t.Errorf("Q is not orthonormal: m = %v, n = %v", m, n)
+		}
+
+		r := qr.RTo(nil)
+
+		var got Dense
+		got.Mul(q, r)
+		if !EqualApprox(&got, &want, 1e-12) {
+			t.Errorf("QR does not equal original matrix. \nWant: %v\nGot: %v", want, got)
+		}
+	}
+}
+
+func isOrthonormal(q *Dense, tol float64) bool {
+	m, n := q.Dims()
+	if m != n {
+		return false
+	}
+	for i := 0; i < m; i++ {
+		for j := i; j < m; j++ {
+			dot := blas64.Dot(m,
+				blas64.Vector{Inc: 1, Data: q.mat.Data[i*q.mat.Stride:]},
+				blas64.Vector{Inc: 1, Data: q.mat.Data[j*q.mat.Stride:]},
+			)
+			// Dot product should be 1 if i == j and 0 otherwise.
+			if i == j && math.Abs(dot-1) > tol {
+				return false
+			}
+			if i != j && math.Abs(dot) > tol {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+func TestSolveQR(t *testing.T) {
+	for _, trans := range []bool{false, true} {
+		for _, test := range []struct {
+			m, n, bc int
+		}{
+			{5, 5, 1},
+			{10, 5, 1},
+			{5, 5, 3},
+			{10, 5, 3},
+		} {
+			m := test.m
+			n := test.n
+			bc := test.bc
+			a := NewDense(m, n, nil)
+			for i := 0; i < m; i++ {
+				for j := 0; j < n; j++ {
+					a.Set(i, j, rand.Float64())
+				}
+			}
+			br := m
+			if trans {
+				br = n
+			}
+			b := NewDense(br, bc, nil)
+			for i := 0; i < br; i++ {
+				for j := 0; j < bc; j++ {
+					b.Set(i, j, rand.Float64())
+				}
+			}
+			var x Dense
+			var qr QR
+			qr.Factorize(a)
+			qr.Solve(&x, trans, b)
+
+			// Test that the normal equations hold.
+			// A^T * A * x = A^T * b if !trans
+			// A * A^T * x = A * b if trans
+			var lhs Dense
+			var rhs Dense
+			if trans {
+				var tmp Dense
+				tmp.Mul(a, a.T())
+				lhs.Mul(&tmp, &x)
+				rhs.Mul(a, b)
+			} else {
+				var tmp Dense
+				tmp.Mul(a.T(), a)
+				lhs.Mul(&tmp, &x)
+				rhs.Mul(a.T(), b)
+			}
+			if !EqualApprox(&lhs, &rhs, 1e-10) {
+				t.Errorf("Normal equations do not hold.\nLHS: %v\n, RHS: %v\n", lhs, rhs)
+			}
+		}
+	}
+	// TODO(btracey): Add in testOneInput when it exists.
+}
+
+func TestSolveQRVec(t *testing.T) {
+	for _, trans := range []bool{false, true} {
+		for _, test := range []struct {
+			m, n int
+		}{
+			{5, 5},
+			{10, 5},
+		} {
+			m := test.m
+			n := test.n
+			a := NewDense(m, n, nil)
+			for i := 0; i < m; i++ {
+				for j := 0; j < n; j++ {
+					a.Set(i, j, rand.Float64())
+				}
+			}
+			br := m
+			if trans {
+				br = n
+			}
+			b := NewVecDense(br, nil)
+			for i := 0; i < br; i++ {
+				b.SetVec(i, rand.Float64())
+			}
+			var x VecDense
+			var qr QR
+			qr.Factorize(a)
+			qr.SolveVec(&x, trans, b)
+
+			// Test that the normal equations hold.
+			// A^T * A * x = A^T * b if !trans
+			// A * A^T * x = A * b if trans
+			var lhs Dense
+			var rhs Dense
+			if trans {
+				var tmp Dense
+				tmp.Mul(a, a.T())
+				lhs.Mul(&tmp, &x)
+				rhs.Mul(a, b)
+			} else {
+				var tmp Dense
+				tmp.Mul(a.T(), a)
+				lhs.Mul(&tmp, &x)
+				rhs.Mul(a.T(), b)
+			}
+			if !EqualApprox(&lhs, &rhs, 1e-10) {
+				t.Errorf("Normal equations do not hold.\nLHS: %v\n, RHS: %v\n", lhs, rhs)
+			}
+		}
+	}
+	// TODO(btracey): Add in testOneInput when it exists.
+}
+
+func TestSolveQRCond(t *testing.T) {
+	for _, test := range []*Dense{
+		NewDense(2, 2, []float64{1, 0, 0, 1e-20}),
+		NewDense(3, 2, []float64{1, 0, 0, 1e-20, 0, 0}),
+	} {
+		m, _ := test.Dims()
+		var qr QR
+		qr.Factorize(test)
+		b := NewDense(m, 2, nil)
+		var x Dense
+		if err := qr.Solve(&x, false, b); err == nil {
+			t.Error("No error for near-singular matrix in matrix solve.")
+		}
+
+		bvec := NewVecDense(m, nil)
+		var xvec VecDense
+		if err := qr.SolveVec(&xvec, false, bvec); err == nil {
+			t.Error("No error for near-singular matrix in matrix solve.")
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/shadow.go b/vendor/gonum.org/v1/gonum/mat/shadow.go
new file mode 100644
index 00000000..91ed21f9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/shadow.go
@@ -0,0 +1,280 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+const (
+	// regionOverlap is the panic string used for the general case
+	// of a matrix region overlap between a source and destination.
+	regionOverlap = "mat: bad region: overlap"
+
+	// regionIdentity is the panic string used for the specific
+	// case of complete agreement between a source and a destination.
+	regionIdentity = "mat: bad region: identical"
+
+	// mismatchedStrides is the panic string used for overlapping
+	// data slices with differing strides.
+	mismatchedStrides = "mat: bad region: different strides"
+)
+
+// checkOverlap returns false if the receiver does not overlap data elements
+// referenced by the parameter and panics otherwise.
+//
+// checkOverlap methods return a boolean to allow the check call to be added to a
+// boolean expression, making use of short-circuit operators.
+
+func (m *Dense) checkOverlap(a blas64.General) bool {
+	mat := m.RawMatrix()
+	if cap(mat.Data) == 0 || cap(a.Data) == 0 {
+		return false
+	}
+
+	off := offset(mat.Data[:1], a.Data[:1])
+
+	if off == 0 {
+		// At least one element overlaps.
+		if mat.Cols == a.Cols && mat.Rows == a.Rows && mat.Stride == a.Stride {
+			panic(regionIdentity)
+		}
+		panic(regionOverlap)
+	}
+
+	if off > 0 && len(mat.Data) <= off {
+		// We know m is completely before a.
+		return false
+	}
+	if off < 0 && len(a.Data) <= -off {
+		// We know m is completely after a.
+		return false
+	}
+
+	if mat.Stride != a.Stride {
+		// Too hard, so assume the worst.
+		panic(mismatchedStrides)
+	}
+
+	if off < 0 {
+		off = -off
+		mat.Cols, a.Cols = a.Cols, mat.Cols
+	}
+	if rectanglesOverlap(off, mat.Cols, a.Cols, mat.Stride) {
+		panic(regionOverlap)
+	}
+	return false
+}
+
+func (s *SymDense) checkOverlap(a blas64.Symmetric) bool {
+	mat := s.RawSymmetric()
+	if cap(mat.Data) == 0 || cap(a.Data) == 0 {
+		return false
+	}
+
+	off := offset(mat.Data[:1], a.Data[:1])
+
+	if off == 0 {
+		// At least one element overlaps.
+		if mat.N == a.N && mat.Stride == a.Stride {
+			panic(regionIdentity)
+		}
+		panic(regionOverlap)
+	}
+
+	if off > 0 && len(mat.Data) <= off {
+		// We know s is completely before a.
+		return false
+	}
+	if off < 0 && len(a.Data) <= -off {
+		// We know s is completely after a.
+		return false
+	}
+
+	if mat.Stride != a.Stride {
+		// Too hard, so assume the worst.
+		panic(mismatchedStrides)
+	}
+
+	if off < 0 {
+		off = -off
+		mat.N, a.N = a.N, mat.N
+		// If we created the matrix it will always
+		// be in the upper triangle, but don't trust
+		// that this is the case.
+		mat.Uplo, a.Uplo = a.Uplo, mat.Uplo
+	}
+	if trianglesOverlap(off, mat.N, a.N, mat.Stride, mat.Uplo == blas.Upper, a.Uplo == blas.Upper) {
+		panic(regionOverlap)
+	}
+	return false
+}
+
+func (t *TriDense) checkOverlap(a blas64.Triangular) bool {
+	mat := t.RawTriangular()
+	if cap(mat.Data) == 0 || cap(a.Data) == 0 {
+		return false
+	}
+
+	off := offset(mat.Data[:1], a.Data[:1])
+
+	if off == 0 {
+		// At least one element overlaps.
+		if mat.N == a.N && mat.Stride == a.Stride {
+			panic(regionIdentity)
+		}
+		panic(regionOverlap)
+	}
+
+	if off > 0 && len(mat.Data) <= off {
+		// We know t is completely before a.
+		return false
+	}
+	if off < 0 && len(a.Data) <= -off {
+		// We know t is completely after a.
+		return false
+	}
+
+	if mat.Stride != a.Stride {
+		// Too hard, so assume the worst.
+		panic(mismatchedStrides)
+	}
+
+	if off < 0 {
+		off = -off
+		mat.N, a.N = a.N, mat.N
+		mat.Uplo, a.Uplo = a.Uplo, mat.Uplo
+	}
+	if trianglesOverlap(off, mat.N, a.N, mat.Stride, mat.Uplo == blas.Upper, a.Uplo == blas.Upper) {
+		panic(regionOverlap)
+	}
+	return false
+}
+
+func (v *VecDense) checkOverlap(a blas64.Vector) bool {
+	mat := v.mat
+	if cap(mat.Data) == 0 || cap(a.Data) == 0 {
+		return false
+	}
+
+	off := offset(mat.Data[:1], a.Data[:1])
+
+	if off == 0 {
+		// At least one element overlaps.
+		if mat.Inc == a.Inc && len(mat.Data) == len(a.Data) {
+			panic(regionIdentity)
+		}
+		panic(regionOverlap)
+	}
+
+	if off > 0 && len(mat.Data) <= off {
+		// We know v is completely before a.
+		return false
+	}
+	if off < 0 && len(a.Data) <= -off {
+		// We know v is completely after a.
+		return false
+	}
+
+	if mat.Inc != a.Inc {
+		// Too hard, so assume the worst.
+		panic(mismatchedStrides)
+	}
+
+	if mat.Inc == 1 || off&mat.Inc == 0 {
+		panic(regionOverlap)
+	}
+	return false
+}
+
+// rectanglesOverlap returns whether the strided rectangles a and b overlap
+// when b is offset by off elements after a but has at least one element before
+// the end of a. off must be positive. a and b have aCols and bCols respectively.
+//
+// rectanglesOverlap works by shifting both matrices left such that the left
+// column of a is at 0. The column indexes are flattened by obtaining the shifted
+// relative left and right column positions modulo the common stride. This allows
+// direct comparison of the column offsets when the matrix backing data slices
+// are known to overlap.
+func rectanglesOverlap(off, aCols, bCols, stride int) bool {
+	if stride == 1 {
+		// Unit stride means overlapping data
+		// slices must overlap as matrices.
+		return true
+	}
+
+	// Flatten the shifted matrix column positions
+	// so a starts at 0, modulo the common stride.
+	aTo := aCols
+	// The mod stride operations here make the from
+	// and to indexes comparable between a and b when
+	// the data slices of a and b overlap.
+	bFrom := off % stride
+	bTo := (bFrom + bCols) % stride
+
+	if bTo == 0 || bFrom < bTo {
+		// b matrix is not wrapped: compare for
+		// simple overlap.
+		return bFrom < aTo
+	}
+
+	// b strictly wraps and so must overlap with a.
+	return true
+}
+
+// trianglesOverlap returns whether the strided triangles a and b overlap
+// when b is offset by off elements after a but has at least one element before
+// the end of a. off must be positive. a and b are aSize×aSize and bSize×bSize
+// respectively.
+func trianglesOverlap(off, aSize, bSize, stride int, aUpper, bUpper bool) bool {
+	if !rectanglesOverlap(off, aSize, bSize, stride) {
+		// Fast return if bounding rectangles do not overlap.
+		return false
+	}
+
+	// Find location of b relative to a.
+	rowOffset := off / stride
+	colOffset := off % stride
+	if (off+bSize)%stride < colOffset {
+		// We have wrapped, so readjust offsets.
+		rowOffset++
+		colOffset -= stride
+	}
+
+	if aUpper {
+		// Check whether the upper left of b
+		// is in the triangle of a
+		if rowOffset >= 0 && rowOffset <= colOffset {
+			return true
+		}
+		// Check whether the upper right of b
+		// is in the triangle of a.
+		return bUpper && rowOffset < colOffset+bSize
+	}
+
+	// Check whether the upper left of b
+	// is in the triangle of a
+	if colOffset >= 0 && rowOffset >= colOffset {
+		return true
+	}
+	if bUpper {
+		// Check whether the upper right corner of b
+		// is in a or the upper row of b spans a row
+		// of a.
+		return rowOffset > colOffset+bSize || colOffset < 0
+	}
+	if colOffset < 0 {
+		// Check whether the lower left of a
+		// is in the triangle of b or below
+		// the diagonal of a. This requires a
+		// swap of reference origin.
+		return -rowOffset+aSize > -colOffset
+	}
+	// Check whether the lower left of b
+	// is in the triangle of a or below
+	// the diagonal of a.
+	return rowOffset+bSize > colOffset
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/shadow_test.go b/vendor/gonum.org/v1/gonum/mat/shadow_test.go
new file mode 100644
index 00000000..564d9e66
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/shadow_test.go
@@ -0,0 +1,274 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+func TestDenseOverlaps(t *testing.T) {
+	type view struct {
+		i, j, r, c int
+		*Dense
+	}
+
+	rnd := rand.New(rand.NewSource(1))
+
+	for r := 1; r < 20; r++ {
+		for c := 1; c < 20; c++ {
+			m := NewDense(r, c, nil)
+			panicked, message := panics(func() { m.checkOverlap(m.RawMatrix()) })
+			if !panicked {
+				t.Error("expected matrix overlap with self")
+			}
+			if message != regionIdentity {
+				t.Errorf("unexpected panic message for self overlap: got: %q want: %q", message, regionIdentity)
+			}
+
+			for i := 0; i < 1000; i++ {
+				var views [2]view
+				for k := range views {
+					if r > 1 {
+						views[k].i = rnd.Intn(r - 1)
+						views[k].r = rnd.Intn(r-views[k].i-1) + 1
+					} else {
+						views[k].r = 1
+					}
+					if c > 1 {
+						views[k].j = rnd.Intn(c - 1)
+						views[k].c = rnd.Intn(c-views[k].j-1) + 1
+					} else {
+						views[k].c = 1
+					}
+					views[k].Dense = m.Slice(views[k].i, views[k].i+views[k].r, views[k].j, views[k].j+views[k].c).(*Dense)
+
+					panicked, _ = panics(func() { m.checkOverlap(views[k].RawMatrix()) })
+					if !panicked {
+						t.Errorf("expected matrix (%d×%d) overlap with view {rows=%d:%d, cols=%d:%d}",
+							r, c, views[k].i, views[k].i+views[k].r, views[k].j, views[k].j+views[k].c)
+					}
+					panicked, _ = panics(func() { views[k].checkOverlap(m.RawMatrix()) })
+					if !panicked {
+						t.Errorf("expected view {rows=%d:%d, cols=%d:%d} overlap with parent (%d×%d)",
+							views[k].i, views[k].i+views[k].r, views[k].j, views[k].j+views[k].c, r, c)
+					}
+				}
+
+				overlapRows := intervalsOverlap(
+					interval{views[0].i, views[0].i + views[0].r},
+					interval{views[1].i, views[1].i + views[1].r},
+				)
+				overlapCols := intervalsOverlap(
+					interval{views[0].j, views[0].j + views[0].c},
+					interval{views[1].j, views[1].j + views[1].c},
+				)
+				want := overlapRows && overlapCols
+
+				for k, v := range views {
+					w := views[1-k]
+					got, _ := panics(func() { v.checkOverlap(w.RawMatrix()) })
+					if got != want {
+						t.Errorf("unexpected result for overlap test for {rows=%d:%d, cols=%d:%d} with {rows=%d:%d, cols=%d:%d}: got: %t want: %t",
+							v.i, v.i+v.r, v.j, v.j+v.c,
+							w.i, w.i+w.r, w.j, w.j+w.c,
+							got, want)
+					}
+				}
+			}
+		}
+	}
+}
+
+func TestTriDenseOverlaps(t *testing.T) {
+	type view struct {
+		i, j, n int
+		*TriDense
+	}
+
+	rnd := rand.New(rand.NewSource(1))
+
+	for _, parentKind := range []TriKind{Upper, Lower} {
+		for n := 1; n < 20; n++ {
+			data := make([]float64, n*n)
+			for i := range data {
+				data[i] = float64(i + 1)
+			}
+			m := NewDense(n, n, data)
+			mt := denseAsTriDense(m, parentKind)
+			panicked, message := panics(func() { mt.checkOverlap(mt.RawTriangular()) })
+			if !panicked {
+				t.Error("expected matrix overlap with self")
+			}
+			if message != regionIdentity {
+				t.Errorf("unexpected panic message for self overlap: got: %q want: %q", message, regionIdentity)
+			}
+
+			for i := 0; i < 1000; i++ {
+				var views [2]view
+				for k := range views {
+					if n > 1 {
+						views[k].i = rnd.Intn(n - 1)
+						views[k].j = rnd.Intn(n - 1)
+						views[k].n = rnd.Intn(n-max(views[k].i, views[k].j)-1) + 1
+					} else {
+						views[k].n = 1
+					}
+					viewKind := []TriKind{Upper, Lower}[rnd.Intn(2)]
+					views[k].TriDense = denseAsTriDense(
+						m.Slice(views[k].i, views[k].i+views[k].n, views[k].j, views[k].j+views[k].n).(*Dense),
+						viewKind)
+
+					wantPanick := overlapsParentTriangle(views[k].i, views[k].j, views[k].n, parentKind, viewKind)
+
+					panicked, _ = panics(func() { mt.checkOverlap(views[k].RawTriangular()) })
+					if panicked != wantPanick {
+						t.Errorf("unexpected (%d×%d)%s overlap with view {rows=%d:%d, cols=%d:%d}%s got:%t want:%t\n% v\n\n% v\n",
+							n, n, kindString(parentKind),
+							views[k].i, views[k].i+views[k].n, views[k].j, views[k].j+views[k].n, kindString(viewKind),
+							panicked, wantPanick,
+							Formatted(mt), Formatted(views[k].TriDense))
+					}
+					panicked, _ = panics(func() { views[k].checkOverlap(mt.RawTriangular()) })
+					if panicked != wantPanick {
+						t.Errorf("unexpected {rows=%d:%d, cols=%d:%d}%s overlap with parent (%d×%d)%s got:%t want:%t\n% v\n\n% v\n",
+							views[k].i, views[k].i+views[k].n, views[k].j, views[k].j+views[k].n, kindString(viewKind),
+							n, n, kindString(parentKind),
+							panicked, wantPanick,
+							Formatted(views[k].TriDense), Formatted(mt))
+					}
+				}
+
+				want := overlapSiblingTriangles(
+					views[0].i, views[0].j, views[0].n, views[0].mat.Uplo == blas.Upper,
+					views[1].i, views[1].j, views[1].n, views[1].mat.Uplo == blas.Upper,
+				)
+
+				for k, v := range views {
+					w := views[1-k]
+					got, _ := panics(func() { v.checkOverlap(w.RawTriangular()) })
+					if got != want {
+						t.Errorf("unexpected result for overlap test for {rows=%d:%d, cols=%d:%d}%s with {rows=%d:%d, cols=%d:%d}%s: got:%t want:%t\n% v\n\n% v\n",
+							v.i, v.i+v.n, v.j, v.j+v.n, kindString(v.mat.Uplo == blas.Upper),
+							w.i, w.i+w.n, w.j, w.j+w.n, kindString(w.mat.Uplo == blas.Upper),
+							got, want,
+							Formatted(v.TriDense), Formatted(w.TriDense))
+					}
+				}
+			}
+		}
+	}
+}
+
+type interval struct{ from, to int }
+
+func intervalsOverlap(a, b interval) bool {
+	return a.to > b.from && b.to > a.from
+}
+
+func overlapsParentTriangle(i, j, n int, parent, view TriKind) bool {
+	switch parent {
+	case Upper:
+		if i <= j {
+			return true
+		}
+		if view == Upper {
+			return i < j+n
+		}
+
+	case Lower:
+		if i >= j {
+			return true
+		}
+		if view == Lower {
+			return i+n > j
+		}
+	}
+
+	return false
+}
+
+func overlapSiblingTriangles(ai, aj, an int, aKind TriKind, bi, bj, bn int, bKind TriKind) bool {
+	for i := max(ai, bi); i < min(ai+an, bi+bn); i++ {
+		var a, b interval
+
+		if aKind == Upper {
+			a = interval{from: aj - ai + i, to: aj + an}
+		} else {
+			a = interval{from: aj, to: aj - ai + i + 1}
+		}
+
+		if bKind == Upper {
+			b = interval{from: bj - bi + i, to: bj + bn}
+		} else {
+			b = interval{from: bj, to: bj - bi + i + 1}
+		}
+
+		if intervalsOverlap(a, b) {
+			return true
+		}
+	}
+	return false
+}
+
+func kindString(k TriKind) string {
+	if k == Upper {
+		return "U"
+	}
+	return "L"
+}
+
+// See https://github.com/gonum/matrix/issues/359 for details.
+func TestIssue359(t *testing.T) {
+	for xi := 0; xi < 2; xi++ {
+		for xj := 0; xj < 2; xj++ {
+			for yi := 0; yi < 2; yi++ {
+				for yj := 0; yj < 2; yj++ {
+					a := NewDense(3, 3, []float64{
+						1, 2, 3,
+						4, 5, 6,
+						7, 8, 9,
+					})
+					x := a.Slice(xi, xi+2, xj, xj+2).(*Dense)
+					y := a.Slice(yi, yi+2, yj, yj+2).(*Dense)
+
+					panicked, _ := panics(func() { x.checkOverlap(y.mat) })
+					if !panicked {
+						t.Errorf("expected panic for aliased with offsets x(%d,%d) y(%d,%d):\nx:\n%v\ny:\n%v",
+							xi, xj, yi, yj, Formatted(x), Formatted(y),
+						)
+					}
+				}
+			}
+		}
+	}
+}
+
+// denseAsTriDense returns a triangular matrix derived from the
+// square matrix m, with the orientation specified by kind.
+func denseAsTriDense(m *Dense, kind TriKind) *TriDense {
+	r, c := m.Dims()
+	if r != c {
+		panic(ErrShape)
+	}
+	n := r
+	uplo := blas.Lower
+	if kind == Upper {
+		uplo = blas.Upper
+	}
+	return &TriDense{
+		mat: blas64.Triangular{
+			N:      n,
+			Stride: m.mat.Stride,
+			Data:   m.mat.Data,
+			Uplo:   uplo,
+			Diag:   blas.NonUnit,
+		},
+		cap: n,
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/solve.go b/vendor/gonum.org/v1/gonum/mat/solve.go
new file mode 100644
index 00000000..ef3d00ef
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/solve.go
@@ -0,0 +1,127 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack/lapack64"
+)
+
+// Solve finds a minimum-norm solution to a system of linear equations defined
+// by the matrices a and b. If A is singular or near-singular, a Condition error
+// is returned. Please see the documentation for Condition for more information.
+//
+// The minimization problem solved depends on the input parameters:
+//  - if m >= n, find X such that ||A*X - B||_2 is minimized,
+//  - if m < n, find the minimum norm solution of A * X = B.
+// The solution matrix, X, is stored in-place into the receiver.
+func (m *Dense) Solve(a, b Matrix) error {
+	ar, ac := a.Dims()
+	br, bc := b.Dims()
+	if ar != br {
+		panic(ErrShape)
+	}
+	m.reuseAs(ac, bc)
+
+	// TODO(btracey): Add special cases for SymDense, etc.
+	aU, aTrans := untranspose(a)
+	bU, bTrans := untranspose(b)
+	switch rma := aU.(type) {
+	case RawTriangular:
+		side := blas.Left
+		tA := blas.NoTrans
+		if aTrans {
+			tA = blas.Trans
+		}
+
+		switch rm := bU.(type) {
+		case RawMatrixer:
+			if m != bU || bTrans {
+				if m == bU || m.checkOverlap(rm.RawMatrix()) {
+					tmp := getWorkspace(br, bc, false)
+					tmp.Copy(b)
+					m.Copy(tmp)
+					putWorkspace(tmp)
+					break
+				}
+				m.Copy(b)
+			}
+		default:
+			if m != bU {
+				m.Copy(b)
+			} else if bTrans {
+				// m and b share data so Copy cannot be used directly.
+				tmp := getWorkspace(br, bc, false)
+				tmp.Copy(b)
+				m.Copy(tmp)
+				putWorkspace(tmp)
+			}
+		}
+
+		rm := rma.RawTriangular()
+		blas64.Trsm(side, tA, 1, rm, m.mat)
+		work := getFloats(3*rm.N, false)
+		iwork := getInts(rm.N, false)
+		cond := lapack64.Trcon(CondNorm, rm, work, iwork)
+		putFloats(work)
+		putInts(iwork)
+		if cond > ConditionTolerance {
+			return Condition(cond)
+		}
+		return nil
+	}
+
+	switch {
+	case ar == ac:
+		if a == b {
+			// x = I.
+			if ar == 1 {
+				m.mat.Data[0] = 1
+				return nil
+			}
+			for i := 0; i < ar; i++ {
+				v := m.mat.Data[i*m.mat.Stride : i*m.mat.Stride+ac]
+				zero(v)
+				v[i] = 1
+			}
+			return nil
+		}
+		var lu LU
+		lu.Factorize(a)
+		return lu.Solve(m, false, b)
+	case ar > ac:
+		var qr QR
+		qr.Factorize(a)
+		return qr.Solve(m, false, b)
+	default:
+		var lq LQ
+		lq.Factorize(a)
+		return lq.Solve(m, false, b)
+	}
+}
+
+// SolveVec finds a minimum-norm solution to a system of linear equations defined
+// by the matrix a and the right-hand side vector b. If A is singular or
+// near-singular, a Condition error is returned. Please see the documentation for
+// Dense.Solve for more information.
+func (v *VecDense) SolveVec(a Matrix, b *VecDense) error {
+	if v != b {
+		v.checkOverlap(b.mat)
+	}
+	_, c := a.Dims()
+	// The Solve implementation is non-trivial, so rather than duplicate the code,
+	// instead recast the VecDenses as Dense and call the matrix code.
+	v.reuseAs(c)
+	m := v.asDense()
+	// We conditionally create bm as m when b and v are identical
+	// to prevent the overlap detection code from identifying m
+	// and bm as overlapping but not identical.
+	bm := m
+	if v != b {
+		bm = b.asDense()
+	}
+	return m.Solve(a, bm)
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/solve_test.go b/vendor/gonum.org/v1/gonum/mat/solve_test.go
new file mode 100644
index 00000000..08ed5839
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/solve_test.go
@@ -0,0 +1,296 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"math/rand"
+	"testing"
+)
+
+func TestSolve(t *testing.T) {
+	// Hand-coded cases.
+	for _, test := range []struct {
+		a         [][]float64
+		b         [][]float64
+		ans       [][]float64
+		shouldErr bool
+	}{
+		{
+			a:         [][]float64{{6}},
+			b:         [][]float64{{3}},
+			ans:       [][]float64{{0.5}},
+			shouldErr: false,
+		},
+		{
+			a: [][]float64{
+				{1, 0, 0},
+				{0, 1, 0},
+				{0, 0, 1},
+			},
+			b: [][]float64{
+				{3},
+				{2},
+				{1},
+			},
+			ans: [][]float64{
+				{3},
+				{2},
+				{1},
+			},
+			shouldErr: false,
+		},
+		{
+			a: [][]float64{
+				{0.8147, 0.9134, 0.5528},
+				{0.9058, 0.6324, 0.8723},
+				{0.1270, 0.0975, 0.7612},
+			},
+			b: [][]float64{
+				{0.278},
+				{0.547},
+				{0.958},
+			},
+			ans: [][]float64{
+				{-0.932687281002860},
+				{0.303963920182067},
+				{1.375216503507109},
+			},
+			shouldErr: false,
+		},
+		{
+			a: [][]float64{
+				{0.8147, 0.9134, 0.5528},
+				{0.9058, 0.6324, 0.8723},
+			},
+			b: [][]float64{
+				{0.278},
+				{0.547},
+			},
+			ans: [][]float64{
+				{0.25919787248965376},
+				{-0.25560256266441034},
+				{0.5432324059702451},
+			},
+			shouldErr: false,
+		},
+		{
+			a: [][]float64{
+				{0.8147, 0.9134, 0.9},
+				{0.9058, 0.6324, 0.9},
+				{0.1270, 0.0975, 0.1},
+				{1.6, 2.8, -3.5},
+			},
+			b: [][]float64{
+				{0.278},
+				{0.547},
+				{-0.958},
+				{1.452},
+			},
+			ans: [][]float64{
+				{0.820970340787782},
+				{-0.218604626527306},
+				{-0.212938815234215},
+			},
+			shouldErr: false,
+		},
+		{
+			a: [][]float64{
+				{0.8147, 0.9134, 0.231, -1.65},
+				{0.9058, 0.6324, 0.9, 0.72},
+				{0.1270, 0.0975, 0.1, 1.723},
+				{1.6, 2.8, -3.5, 0.987},
+				{7.231, 9.154, 1.823, 0.9},
+			},
+			b: [][]float64{
+				{0.278, 8.635},
+				{0.547, 9.125},
+				{-0.958, -0.762},
+				{1.452, 1.444},
+				{1.999, -7.234},
+			},
+			ans: [][]float64{
+				{1.863006789511373, 44.467887791812750},
+				{-1.127270935407224, -34.073794226035126},
+				{-0.527926457947330, -8.032133759788573},
+				{-0.248621916204897, -2.366366415805275},
+			},
+			shouldErr: false,
+		},
+		{
+			a: [][]float64{
+				{0, 0},
+				{0, 0},
+			},
+			b: [][]float64{
+				{3},
+				{2},
+			},
+			ans:       nil,
+			shouldErr: true,
+		},
+		{
+			a: [][]float64{
+				{0, 0},
+				{0, 0},
+				{0, 0},
+			},
+			b: [][]float64{
+				{3},
+				{2},
+				{1},
+			},
+			ans:       nil,
+			shouldErr: true,
+		},
+		{
+			a: [][]float64{
+				{0, 0, 0},
+				{0, 0, 0},
+			},
+			b: [][]float64{
+				{3},
+				{2},
+			},
+			ans:       nil,
+			shouldErr: true,
+		},
+	} {
+		a := NewDense(flatten(test.a))
+		b := NewDense(flatten(test.b))
+
+		var ans *Dense
+		if test.ans != nil {
+			ans = NewDense(flatten(test.ans))
+		}
+
+		var x Dense
+		err := x.Solve(a, b)
+		if err != nil {
+			if !test.shouldErr {
+				t.Errorf("Unexpected solve error: %s", err)
+			}
+			continue
+		}
+		if err == nil && test.shouldErr {
+			t.Errorf("Did not error during solve.")
+			continue
+		}
+		if !EqualApprox(&x, ans, 1e-12) {
+			t.Errorf("Solve answer mismatch. Want %v, got %v", ans, x)
+		}
+	}
+
+	// Random Cases.
+	for _, test := range []struct {
+		m, n, bc int
+	}{
+		{5, 5, 1},
+		{5, 10, 1},
+		{10, 5, 1},
+		{5, 5, 7},
+		{5, 10, 7},
+		{10, 5, 7},
+		{5, 5, 12},
+		{5, 10, 12},
+		{10, 5, 12},
+	} {
+		m := test.m
+		n := test.n
+		bc := test.bc
+		a := NewDense(m, n, nil)
+		for i := 0; i < m; i++ {
+			for j := 0; j < n; j++ {
+				a.Set(i, j, rand.Float64())
+			}
+		}
+		br := m
+		b := NewDense(br, bc, nil)
+		for i := 0; i < br; i++ {
+			for j := 0; j < bc; j++ {
+				b.Set(i, j, rand.Float64())
+			}
+		}
+		var x Dense
+		x.Solve(a, b)
+
+		// Test that the normal equations hold.
+		// A^T * A * x = A^T * b
+		var tmp, lhs, rhs Dense
+		tmp.Mul(a.T(), a)
+		lhs.Mul(&tmp, &x)
+		rhs.Mul(a.T(), b)
+		if !EqualApprox(&lhs, &rhs, 1e-10) {
+			t.Errorf("Normal equations do not hold.\nLHS: %v\n, RHS: %v\n", lhs, rhs)
+		}
+	}
+
+	// Use testTwoInput.
+	method := func(receiver, a, b Matrix) {
+		type Solver interface {
+			Solve(a, b Matrix) error
+		}
+		rd := receiver.(Solver)
+		rd.Solve(a, b)
+	}
+	denseComparison := func(receiver, a, b *Dense) {
+		receiver.Solve(a, b)
+	}
+	testTwoInput(t, "Solve", &Dense{}, method, denseComparison, legalTypesAll, legalSizeSolve, 1e-7)
+}
+
+func TestSolveVec(t *testing.T) {
+	for _, test := range []struct {
+		m, n int
+	}{
+		{5, 5},
+		{5, 10},
+		{10, 5},
+		{5, 5},
+		{5, 10},
+		{10, 5},
+		{5, 5},
+		{5, 10},
+		{10, 5},
+	} {
+		m := test.m
+		n := test.n
+		a := NewDense(m, n, nil)
+		for i := 0; i < m; i++ {
+			for j := 0; j < n; j++ {
+				a.Set(i, j, rand.Float64())
+			}
+		}
+		br := m
+		b := NewVecDense(br, nil)
+		for i := 0; i < br; i++ {
+			b.SetVec(i, rand.Float64())
+		}
+		var x VecDense
+		x.SolveVec(a, b)
+
+		// Test that the normal equations hold.
+		// A^T * A * x = A^T * b
+		var tmp, lhs, rhs Dense
+		tmp.Mul(a.T(), a)
+		lhs.Mul(&tmp, &x)
+		rhs.Mul(a.T(), b)
+		if !EqualApprox(&lhs, &rhs, 1e-10) {
+			t.Errorf("Normal equations do not hold.\nLHS: %v\n, RHS: %v\n", lhs, rhs)
+		}
+	}
+
+	// Use testTwoInput
+	method := func(receiver, a, b Matrix) {
+		type SolveVecer interface {
+			SolveVec(a Matrix, b *VecDense) error
+		}
+		rd := receiver.(SolveVecer)
+		rd.SolveVec(a, b.(*VecDense))
+	}
+	denseComparison := func(receiver, a, b *Dense) {
+		receiver.Solve(a, b)
+	}
+	testTwoInput(t, "SolveVec", &VecDense{}, method, denseComparison, legalTypesNotVecVec, legalSizeSolve, 1e-12)
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/svd.go b/vendor/gonum.org/v1/gonum/mat/svd.go
new file mode 100644
index 00000000..9d386d81
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/svd.go
@@ -0,0 +1,190 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack"
+	"gonum.org/v1/gonum/lapack/lapack64"
+)
+
+// SVD is a type for creating and using the Singular Value Decomposition (SVD)
+// of a matrix.
+type SVD struct {
+	kind SVDKind
+
+	s  []float64
+	u  blas64.General
+	vt blas64.General
+}
+
+// Factorize computes the singular value decomposition (SVD) of the input matrix
+// A. The singular values of A are computed in all cases, while the singular
+// vectors are optionally computed depending on the input kind.
+//
+// The full singular value decomposition (kind == SVDFull) deconstructs A as
+//  A = U * Σ * V^T
+// where Σ is an m×n diagonal matrix of singular vectors, U is an m×m unitary
+// matrix of left singular vectors, and V is an n×n matrix of right singular vectors.
+//
+// It is frequently not necessary to compute the full SVD. Computation time and
+// storage costs can be reduced using the appropriate kind. Only the singular
+// values can be computed (kind == SVDNone), or a "thin" representation of the
+// singular vectors (kind = SVDThin). The thin representation can save a significant
+// amount of memory if m >> n. See the documentation for the lapack.SVDKind values
+// for more information.
+//
+// Factorize returns whether the decomposition succeeded. If the decomposition
+// failed, routines that require a successful factorization will panic.
+func (svd *SVD) Factorize(a Matrix, kind SVDKind) (ok bool) {
+	m, n := a.Dims()
+	var jobU, jobVT lapack.SVDJob
+	switch kind {
+	default:
+		panic("svd: bad input kind")
+	case SVDNone:
+		jobU = lapack.SVDNone
+		jobVT = lapack.SVDNone
+	case SVDFull:
+		// TODO(btracey): This code should be modified to have the smaller
+		// matrix written in-place into aCopy when the lapack/native/dgesvd
+		// implementation is complete.
+		svd.u = blas64.General{
+			Rows:   m,
+			Cols:   m,
+			Stride: m,
+			Data:   use(svd.u.Data, m*m),
+		}
+		svd.vt = blas64.General{
+			Rows:   n,
+			Cols:   n,
+			Stride: n,
+			Data:   use(svd.vt.Data, n*n),
+		}
+		jobU = lapack.SVDAll
+		jobVT = lapack.SVDAll
+	case SVDThin:
+		// TODO(btracey): This code should be modified to have the larger
+		// matrix written in-place into aCopy when the lapack/native/dgesvd
+		// implementation is complete.
+		svd.u = blas64.General{
+			Rows:   m,
+			Cols:   min(m, n),
+			Stride: min(m, n),
+			Data:   use(svd.u.Data, m*min(m, n)),
+		}
+		svd.vt = blas64.General{
+			Rows:   min(m, n),
+			Cols:   n,
+			Stride: n,
+			Data:   use(svd.vt.Data, min(m, n)*n),
+		}
+		jobU = lapack.SVDInPlace
+		jobVT = lapack.SVDInPlace
+	}
+
+	// A is destroyed on call, so copy the matrix.
+	aCopy := DenseCopyOf(a)
+	svd.kind = kind
+	svd.s = use(svd.s, min(m, n))
+
+	work := []float64{0}
+	lapack64.Gesvd(jobU, jobVT, aCopy.mat, svd.u, svd.vt, svd.s, work, -1)
+	work = getFloats(int(work[0]), false)
+	ok = lapack64.Gesvd(jobU, jobVT, aCopy.mat, svd.u, svd.vt, svd.s, work, len(work))
+	putFloats(work)
+	if !ok {
+		svd.kind = 0
+	}
+	return ok
+}
+
+// Kind returns the matrix.SVDKind of the decomposition. If no decomposition has been
+// computed, Kind returns 0.
+func (svd *SVD) Kind() SVDKind {
+	return svd.kind
+}
+
+// Cond returns the 2-norm condition number for the factorized matrix. Cond will
+// panic if the receiver does not contain a successful factorization.
+func (svd *SVD) Cond() float64 {
+	if svd.kind == 0 {
+		panic("svd: no decomposition computed")
+	}
+	return svd.s[0] / svd.s[len(svd.s)-1]
+}
+
+// Values returns the singular values of the factorized matrix in decreasing order.
+// If the input slice is non-nil, the values will be stored in-place into the slice.
+// In this case, the slice must have length min(m,n), and Values will panic with
+// matrix.ErrSliceLengthMismatch otherwise. If the input slice is nil,
+// a new slice of the appropriate length will be allocated and returned.
+//
+// Values will panic if the receiver does not contain a successful factorization.
+func (svd *SVD) Values(s []float64) []float64 {
+	if svd.kind == 0 {
+		panic("svd: no decomposition computed")
+	}
+	if s == nil {
+		s = make([]float64, len(svd.s))
+	}
+	if len(s) != len(svd.s) {
+		panic(ErrSliceLengthMismatch)
+	}
+	copy(s, svd.s)
+	return s
+}
+
+// UTo extracts the matrix U from the singular value decomposition, storing
+// the result in-place into dst. U is size m×m if svd.Kind() == SVDFull,
+// of size m×min(m,n) if svd.Kind() == SVDThin, and UTo panics otherwise.
+func (svd *SVD) UTo(dst *Dense) *Dense {
+	kind := svd.kind
+	if kind != SVDFull && kind != SVDThin {
+		panic("mat: improper SVD kind")
+	}
+	r := svd.u.Rows
+	c := svd.u.Cols
+	if dst == nil {
+		dst = NewDense(r, c, nil)
+	} else {
+		dst.reuseAs(r, c)
+	}
+
+	tmp := &Dense{
+		mat:     svd.u,
+		capRows: r,
+		capCols: c,
+	}
+	dst.Copy(tmp)
+
+	return dst
+}
+
+// VTo extracts the matrix V from the singular value decomposition, storing
+// the result in-place into dst. V is size n×n if svd.Kind() == SVDFull,
+// of size n×min(m,n) if svd.Kind() == SVDThin, and VTo panics otherwise.
+func (svd *SVD) VTo(dst *Dense) *Dense {
+	kind := svd.kind
+	if kind != SVDFull && kind != SVDThin {
+		panic("mat: improper SVD kind")
+	}
+	r := svd.vt.Rows
+	c := svd.vt.Cols
+	if dst == nil {
+		dst = NewDense(c, r, nil)
+	} else {
+		dst.reuseAs(c, r)
+	}
+
+	tmp := &Dense{
+		mat:     svd.vt,
+		capRows: r,
+		capCols: c,
+	}
+	dst.Copy(tmp.T())
+
+	return dst
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/svd_test.go b/vendor/gonum.org/v1/gonum/mat/svd_test.go
new file mode 100644
index 00000000..54815c85
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/svd_test.go
@@ -0,0 +1,172 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+func TestSVD(t *testing.T) {
+	// Hand coded tests
+	for _, test := range []struct {
+		a *Dense
+		u *Dense
+		v *Dense
+		s []float64
+	}{
+		{
+			a: NewDense(4, 2, []float64{2, 4, 1, 3, 0, 0, 0, 0}),
+			u: NewDense(4, 2, []float64{
+				-0.8174155604703632, -0.5760484367663209,
+				-0.5760484367663209, 0.8174155604703633,
+				0, 0,
+				0, 0,
+			}),
+			v: NewDense(2, 2, []float64{
+				-0.4045535848337571, -0.9145142956773044,
+				-0.9145142956773044, 0.4045535848337571,
+			}),
+			s: []float64{5.464985704219041, 0.365966190626258},
+		},
+		{
+			// Issue #5.
+			a: NewDense(3, 11, []float64{
+				1, 1, 0, 1, 0, 0, 0, 0, 0, 11, 1,
+				1, 0, 0, 0, 0, 0, 1, 0, 0, 12, 2,
+				1, 1, 0, 0, 0, 0, 0, 0, 1, 13, 3,
+			}),
+			u: NewDense(3, 3, []float64{
+				-0.5224167862273765, 0.7864430360363114, 0.3295270133658976,
+				-0.5739526766688285, -0.03852203026050301, -0.8179818935216693,
+				-0.6306021141833781, -0.6164603833618163, 0.4715056408282468,
+			}),
+			v: NewDense(11, 3, []float64{
+				-0.08123293141915189, 0.08528085505260324, -0.013165501690885152,
+				-0.05423546426886932, 0.1102707844980355, 0.622210623111631,
+				0, 0, 0,
+				-0.0245733326078166, 0.510179651760153, 0.25596360803140994,
+				0, 0, 0,
+				0, 0, 0,
+				-0.026997467150282436, -0.024989929445430496, -0.6353761248025164,
+				0, 0, 0,
+				-0.029662131661052707, -0.3999088672621176, 0.3662470150802212,
+				-0.9798839760830571, 0.11328174160898856, -0.047702613241813366,
+				-0.16755466189153964, -0.7395268089170608, 0.08395240366704032,
+			}),
+			s: []float64{21.259500881097434, 1.5415021616856566, 1.2873979074613628},
+		},
+	} {
+		var svd SVD
+		ok := svd.Factorize(test.a, SVDThin)
+		if !ok {
+			t.Errorf("SVD failed")
+		}
+		s, u, v := extractSVD(&svd)
+		if !floats.EqualApprox(s, test.s, 1e-10) {
+			t.Errorf("Singular value mismatch. Got %v, want %v.", s, test.s)
+		}
+		if !EqualApprox(u, test.u, 1e-10) {
+			t.Errorf("U mismatch.\nGot:\n%v\nWant:\n%v", Formatted(u), Formatted(test.u))
+		}
+		if !EqualApprox(v, test.v, 1e-10) {
+			t.Errorf("V mismatch.\nGot:\n%v\nWant:\n%v", Formatted(v), Formatted(test.v))
+		}
+		m, n := test.a.Dims()
+		sigma := NewDense(min(m, n), min(m, n), nil)
+		for i := 0; i < min(m, n); i++ {
+			sigma.Set(i, i, s[i])
+		}
+
+		var ans Dense
+		ans.Product(u, sigma, v.T())
+		if !EqualApprox(test.a, &ans, 1e-10) {
+			t.Errorf("A reconstruction mismatch.\nGot:\n%v\nWant:\n%v\n", Formatted(&ans), Formatted(test.a))
+		}
+	}
+
+	for _, test := range []struct {
+		m, n int
+	}{
+		{5, 5},
+		{5, 3},
+		{3, 5},
+		{150, 150},
+		{200, 150},
+		{150, 200},
+	} {
+		m := test.m
+		n := test.n
+		for trial := 0; trial < 10; trial++ {
+			a := NewDense(m, n, nil)
+			for i := range a.mat.Data {
+				a.mat.Data[i] = rand.NormFloat64()
+			}
+			aCopy := DenseCopyOf(a)
+
+			// Test Full decomposition.
+			var svd SVD
+			ok := svd.Factorize(a, SVDFull)
+			if !ok {
+				t.Errorf("SVD factorization failed")
+			}
+			if !Equal(a, aCopy) {
+				t.Errorf("A changed during call to SVD with full")
+			}
+			s, u, v := extractSVD(&svd)
+			sigma := NewDense(m, n, nil)
+			for i := 0; i < min(m, n); i++ {
+				sigma.Set(i, i, s[i])
+			}
+			var ansFull Dense
+			ansFull.Product(u, sigma, v.T())
+			if !EqualApprox(&ansFull, a, 1e-8) {
+				t.Errorf("Answer mismatch when SVDFull")
+			}
+
+			// Test Thin decomposition.
+			ok = svd.Factorize(a, SVDThin)
+			if !ok {
+				t.Errorf("SVD factorization failed")
+			}
+			if !Equal(a, aCopy) {
+				t.Errorf("A changed during call to SVD with Thin")
+			}
+			sThin, u, v := extractSVD(&svd)
+			if !floats.EqualApprox(s, sThin, 1e-8) {
+				t.Errorf("Singular value mismatch between Full and Thin decomposition")
+			}
+			sigma = NewDense(min(m, n), min(m, n), nil)
+			for i := 0; i < min(m, n); i++ {
+				sigma.Set(i, i, sThin[i])
+			}
+			ansFull.Reset()
+			ansFull.Product(u, sigma, v.T())
+			if !EqualApprox(&ansFull, a, 1e-8) {
+				t.Errorf("Answer mismatch when SVDFull")
+			}
+
+			// Test None decomposition.
+			ok = svd.Factorize(a, SVDNone)
+			if !ok {
+				t.Errorf("SVD factorization failed")
+			}
+			if !Equal(a, aCopy) {
+				t.Errorf("A changed during call to SVD with none")
+			}
+			sNone := make([]float64, min(m, n))
+			svd.Values(sNone)
+			if !floats.EqualApprox(s, sNone, 1e-8) {
+				t.Errorf("Singular value mismatch between Full and None decomposition")
+			}
+		}
+	}
+}
+
+func extractSVD(svd *SVD) (s []float64, u, v *Dense) {
+	return svd.Values(nil), svd.UTo(nil), svd.VTo(nil)
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/symband.go b/vendor/gonum.org/v1/gonum/mat/symband.go
new file mode 100644
index 00000000..986a3335
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/symband.go
@@ -0,0 +1,175 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+var (
+	symBandDense *SymBandDense
+	_            Matrix           = symBandDense
+	_            Symmetric        = symBandDense
+	_            Banded           = symBandDense
+	_            RawSymBander     = symBandDense
+	_            MutableSymBanded = symBandDense
+
+	_ NonZeroDoer    = symBandDense
+	_ RowNonZeroDoer = symBandDense
+	_ ColNonZeroDoer = symBandDense
+)
+
+// SymBandDense represents a symmetric band matrix in dense storage format.
+type SymBandDense struct {
+	mat blas64.SymmetricBand
+}
+
+// MutableSymBanded is a symmetric band matrix interface type that allows elements
+// to be altered.
+type MutableSymBanded interface {
+	Symmetric
+	Bandwidth() (kl, ku int)
+	SetSymBand(i, j int, v float64)
+}
+
+// A RawSymBander can return a blas64.SymmetricBand representation of the receiver.
+// Changes to the blas64.SymmetricBand.Data slice will be reflected in the original
+// matrix, changes to the N, K, Stride and Uplo fields will not.
+type RawSymBander interface {
+	RawSymBand() blas64.SymmetricBand
+}
+
+// NewSymBandDense creates a new SymBand matrix with n rows and columns. If data == nil,
+// a new slice is allocated for the backing slice. If len(data) == n*(k+1),
+// data is used as the backing slice, and changes to the elements of the returned
+// SymBandDense will be reflected in data. If neither of these is true, NewSymBandDense
+// will panic. k must be at least zero and less than n, otherwise NewBandDense will panic.
+//
+// The data must be arranged in row-major order constructed by removing the zeros
+// from the rows outside the band and aligning the diagonals. SymBandDense matrices
+// are stored in the upper triangle. For example, the matrix
+//    1  2  3  0  0  0
+//    2  4  5  6  0  0
+//    3  5  7  8  9  0
+//    0  6  8 10 11 12
+//    0  0  9 11 13 14
+//    0  0  0 12 14 15
+// becomes (* entries are never accessed)
+//     1  2  3
+//     4  5  6
+//     7  8  9
+//    10 11 12
+//    13 14  *
+//    15  *  *
+// which is passed to NewBandDense as []float64{1, 2, 3, 4, ...} with k=2.
+// Only the values in the band portion of the matrix are used.
+func NewSymBandDense(n, k int, data []float64) *SymBandDense {
+	if n < 0 || k < 0 {
+		panic("mat: negative dimension")
+	}
+	if k+1 > n {
+		panic("mat: band out of range")
+	}
+	bc := k + 1
+	if data != nil && len(data) != n*bc {
+		panic(ErrShape)
+	}
+	if data == nil {
+		data = make([]float64, n*bc)
+	}
+	return &SymBandDense{
+		mat: blas64.SymmetricBand{
+			N:      n,
+			K:      k,
+			Stride: bc,
+			Uplo:   blas.Upper,
+			Data:   data,
+		},
+	}
+}
+
+// NewDiagonal is a convenience function that returns a diagonal matrix represented by a
+// SymBandDense. The length of data must be n or data must be nil, otherwise NewDiagonal
+// will panic.
+func NewDiagonal(n int, data []float64) *SymBandDense {
+	return NewSymBandDense(n, 0, data)
+}
+
+// Dims returns the number of rows and columns in the matrix.
+func (s *SymBandDense) Dims() (r, c int) {
+	return s.mat.N, s.mat.N
+}
+
+// Symmetric returns the size of the receiver.
+func (s *SymBandDense) Symmetric() int {
+	return s.mat.N
+}
+
+// Bandwidth returns the bandwidths of the matrix.
+func (s *SymBandDense) Bandwidth() (kl, ku int) {
+	return s.mat.K, s.mat.K
+}
+
+// T implements the Matrix interface. Symmetric matrices, by definition, are
+// equal to their transpose, and this is a no-op.
+func (s *SymBandDense) T() Matrix {
+	return s
+}
+
+// TBand implements the Banded interface.
+func (s *SymBandDense) TBand() Banded {
+	return s
+}
+
+// RawSymBand returns the underlying blas64.SymBand used by the receiver.
+// Changes to elements in the receiver following the call will be reflected
+// in returned blas64.SymBand.
+func (s *SymBandDense) RawSymBand() blas64.SymmetricBand {
+	return s.mat
+}
+
+// DoNonZero calls the function fn for each of the non-zero elements of s. The function fn
+// takes a row/column index and the element value of s at (i, j).
+func (s *SymBandDense) DoNonZero(fn func(i, j int, v float64)) {
+	for i := 0; i < s.mat.N; i++ {
+		for j := max(0, i-s.mat.K); j < min(s.mat.N, i+s.mat.K+1); j++ {
+			v := s.at(i, j)
+			if v != 0 {
+				fn(i, j, v)
+			}
+		}
+	}
+}
+
+// DoRowNonZero calls the function fn for each of the non-zero elements of row i of s. The function fn
+// takes a row/column index and the element value of s at (i, j).
+func (s *SymBandDense) DoRowNonZero(i int, fn func(i, j int, v float64)) {
+	if i < 0 || s.mat.N <= i {
+		panic(ErrRowAccess)
+	}
+	for j := max(0, i-s.mat.K); j < min(s.mat.N, i+s.mat.K+1); j++ {
+		v := s.at(i, j)
+		if v != 0 {
+			fn(i, j, v)
+		}
+	}
+}
+
+// DoColNonZero calls the function fn for each of the non-zero elements of column j of s. The function fn
+// takes a row/column index and the element value of s at (i, j).
+func (s *SymBandDense) DoColNonZero(j int, fn func(i, j int, v float64)) {
+	if j < 0 || s.mat.N <= j {
+		panic(ErrColAccess)
+	}
+	for i := 0; i < s.mat.N; i++ {
+		if i-s.mat.K <= j && j < i+s.mat.K+1 {
+			v := s.at(i, j)
+			if v != 0 {
+				fn(i, j, v)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/symband_test.go b/vendor/gonum.org/v1/gonum/mat/symband_test.go
new file mode 100644
index 00000000..cf3e6808
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/symband_test.go
@@ -0,0 +1,230 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"reflect"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+func TestNewSymBand(t *testing.T) {
+	for i, test := range []struct {
+		data  []float64
+		n     int
+		k     int
+		mat   *SymBandDense
+		dense *Dense
+	}{
+		{
+			data: []float64{
+				1, 2, 3,
+				4, 5, 6,
+				7, 8, 9,
+				10, 11, 12,
+				13, 14, -1,
+				15, -1, -1,
+			},
+			n: 6,
+			k: 2,
+			mat: &SymBandDense{
+				mat: blas64.SymmetricBand{
+					N:      6,
+					K:      2,
+					Stride: 3,
+					Uplo:   blas.Upper,
+					Data: []float64{
+						1, 2, 3,
+						4, 5, 6,
+						7, 8, 9,
+						10, 11, 12,
+						13, 14, -1,
+						15, -1, -1,
+					},
+				},
+			},
+			dense: NewDense(6, 6, []float64{
+				1, 2, 3, 0, 0, 0,
+				2, 4, 5, 6, 0, 0,
+				3, 5, 7, 8, 9, 0,
+				0, 6, 8, 10, 11, 12,
+				0, 0, 9, 11, 13, 14,
+				0, 0, 0, 12, 14, 15,
+			}),
+		},
+	} {
+		band := NewSymBandDense(test.n, test.k, test.data)
+		rows, cols := band.Dims()
+
+		if rows != test.n {
+			t.Errorf("unexpected number of rows for test %d: got: %d want: %d", i, rows, test.n)
+		}
+		if cols != test.n {
+			t.Errorf("unexpected number of cols for test %d: got: %d want: %d", i, cols, test.n)
+		}
+		if !reflect.DeepEqual(band, test.mat) {
+			t.Errorf("unexpected value via reflect for test %d: got: %v want: %v", i, band, test.mat)
+		}
+		if !Equal(band, test.mat) {
+			t.Errorf("unexpected value via mat.Equal for test %d: got: %v want: %v", i, band, test.mat)
+		}
+		if !Equal(band, test.dense) {
+			t.Errorf("unexpected value via mat.Equal(band, dense) for test %d:\ngot:\n% v\nwant:\n% v", i, Formatted(band), Formatted(test.dense))
+		}
+	}
+}
+
+func TestNewDiagonal(t *testing.T) {
+	for i, test := range []struct {
+		data  []float64
+		n     int
+		mat   *SymBandDense
+		dense *Dense
+	}{
+		{
+			data: []float64{1, 2, 3, 4, 5, 6},
+			n:    6,
+			mat: &SymBandDense{
+				mat: blas64.SymmetricBand{
+					N:      6,
+					Stride: 1,
+					Uplo:   blas.Upper,
+					Data:   []float64{1, 2, 3, 4, 5, 6},
+				},
+			},
+			dense: NewDense(6, 6, []float64{
+				1, 0, 0, 0, 0, 0,
+				0, 2, 0, 0, 0, 0,
+				0, 0, 3, 0, 0, 0,
+				0, 0, 0, 4, 0, 0,
+				0, 0, 0, 0, 5, 0,
+				0, 0, 0, 0, 0, 6,
+			}),
+		},
+	} {
+		band := NewDiagonal(test.n, test.data)
+		rows, cols := band.Dims()
+
+		if rows != test.n {
+			t.Errorf("unexpected number of rows for test %d: got: %d want: %d", i, rows, test.n)
+		}
+		if cols != test.n {
+			t.Errorf("unexpected number of cols for test %d: got: %d want: %d", i, cols, test.n)
+		}
+		if !reflect.DeepEqual(band, test.mat) {
+			t.Errorf("unexpected value via reflect for test %d: got: %v want: %v", i, band, test.mat)
+		}
+		if !Equal(band, test.mat) {
+			t.Errorf("unexpected value via mat.Equal for test %d: got: %v want: %v", i, band, test.mat)
+		}
+		if !Equal(band, test.dense) {
+			t.Errorf("unexpected value via mat.Equal(band, dense) for test %d:\ngot:\n% v\nwant:\n% v", i, Formatted(band), Formatted(test.dense))
+		}
+	}
+}
+
+func TestSymBandAtSet(t *testing.T) {
+	// 1  2  3  0  0  0
+	// 2  4  5  6  0  0
+	// 3  5  7  8  9  0
+	// 0  6  8 10 11 12
+	// 0  0  9 11 13 14
+	// 0  0  0 12 14 16
+	band := NewSymBandDense(6, 2, []float64{
+		1, 2, 3,
+		4, 5, 6,
+		7, 8, 9,
+		10, 11, 12,
+		13, 14, -1,
+		16, -1, -1,
+	})
+
+	rows, cols := band.Dims()
+	kl, ku := band.Bandwidth()
+
+	// Explicitly test all indexes.
+	want := bandImplicit{rows, cols, kl, ku, func(i, j int) float64 {
+		if i > j {
+			i, j = j, i
+		}
+		return float64(i*ku + j + 1)
+	}}
+	for i := 0; i < 6; i++ {
+		for j := 0; j < 6; j++ {
+			if band.At(i, j) != want.At(i, j) {
+				t.Errorf("unexpected value for band.At(%d, %d): got:%v want:%v", i, j, band.At(i, j), want.At(i, j))
+			}
+		}
+	}
+	// Do that same thing via a call to Equal.
+	if !Equal(band, want) {
+		t.Errorf("unexpected value via mat.Equal:\ngot:\n% v\nwant:\n% v", Formatted(band), Formatted(want))
+	}
+
+	// Check At out of bounds
+	for _, row := range []int{-1, rows, rows + 1} {
+		panicked, message := panics(func() { band.At(row, 0) })
+		if !panicked || message != ErrRowAccess.Error() {
+			t.Errorf("expected panic for invalid row access N=%d r=%d", rows, row)
+		}
+	}
+	for _, col := range []int{-1, cols, cols + 1} {
+		panicked, message := panics(func() { band.At(0, col) })
+		if !panicked || message != ErrColAccess.Error() {
+			t.Errorf("expected panic for invalid column access N=%d c=%d", cols, col)
+		}
+	}
+
+	// Check Set out of bounds
+	for _, row := range []int{-1, rows, rows + 1} {
+		panicked, message := panics(func() { band.SetSymBand(row, 0, 1.2) })
+		if !panicked || message != ErrRowAccess.Error() {
+			t.Errorf("expected panic for invalid row access N=%d r=%d", rows, row)
+		}
+	}
+	for _, col := range []int{-1, cols, cols + 1} {
+		panicked, message := panics(func() { band.SetSymBand(0, col, 1.2) })
+		if !panicked || message != ErrColAccess.Error() {
+			t.Errorf("expected panic for invalid column access N=%d c=%d", cols, col)
+		}
+	}
+
+	for _, st := range []struct {
+		row, col int
+	}{
+		{row: 0, col: 3},
+		{row: 0, col: 4},
+		{row: 0, col: 5},
+		{row: 1, col: 4},
+		{row: 1, col: 5},
+		{row: 2, col: 5},
+		{row: 3, col: 0},
+		{row: 4, col: 1},
+		{row: 5, col: 2},
+	} {
+		panicked, message := panics(func() { band.SetSymBand(st.row, st.col, 1.2) })
+		if !panicked || message != ErrBandSet.Error() {
+			t.Errorf("expected panic for %+v %s", st, message)
+		}
+	}
+
+	for _, st := range []struct {
+		row, col  int
+		orig, new float64
+	}{
+		{row: 1, col: 2, orig: 5, new: 15},
+		{row: 2, col: 3, orig: 8, new: 15},
+	} {
+		if e := band.At(st.row, st.col); e != st.orig {
+			t.Errorf("unexpected value for At(%d, %d): got: %v want: %v", st.row, st.col, e, st.orig)
+		}
+		band.SetSymBand(st.row, st.col, st.new)
+		if e := band.At(st.row, st.col); e != st.new {
+			t.Errorf("unexpected value for At(%d, %d) after SetSymBand(%[1]d, %d, %v): got: %v want: %[3]v", st.row, st.col, st.new, e)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/symmetric.go b/vendor/gonum.org/v1/gonum/mat/symmetric.go
new file mode 100644
index 00000000..98802d94
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/symmetric.go
@@ -0,0 +1,502 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+var (
+	symDense *SymDense
+
+	_ Matrix           = symDense
+	_ Symmetric        = symDense
+	_ RawSymmetricer   = symDense
+	_ MutableSymmetric = symDense
+)
+
+const (
+	badSymTriangle = "mat: blas64.Symmetric not upper"
+	badSymCap      = "mat: bad capacity for SymDense"
+)
+
+// SymDense is a symmetric matrix that uses dense storage. SymDense
+// matrices are stored in the upper triangle.
+type SymDense struct {
+	mat blas64.Symmetric
+	cap int
+}
+
+// Symmetric represents a symmetric matrix (where the element at {i, j} equals
+// the element at {j, i}). Symmetric matrices are always square.
+type Symmetric interface {
+	Matrix
+	// Symmetric returns the number of rows/columns in the matrix.
+	Symmetric() int
+}
+
+// A RawSymmetricer can return a view of itself as a BLAS Symmetric matrix.
+type RawSymmetricer interface {
+	RawSymmetric() blas64.Symmetric
+}
+
+// A MutableSymmetric can set elements of a symmetric matrix.
+type MutableSymmetric interface {
+	Symmetric
+	SetSym(i, j int, v float64)
+}
+
+// NewSymDense creates a new Symmetric matrix with n rows and columns. If data == nil,
+// a new slice is allocated for the backing slice. If len(data) == n*n, data is
+// used as the backing slice, and changes to the elements of the returned SymDense
+// will be reflected in data. If neither of these is true, NewSymDense will panic.
+//
+// The data must be arranged in row-major order, i.e. the (i*c + j)-th
+// element in the data slice is the {i, j}-th element in the matrix.
+// Only the values in the upper triangular portion of the matrix are used.
+func NewSymDense(n int, data []float64) *SymDense {
+	if n < 0 {
+		panic("mat: negative dimension")
+	}
+	if data != nil && n*n != len(data) {
+		panic(ErrShape)
+	}
+	if data == nil {
+		data = make([]float64, n*n)
+	}
+	return &SymDense{
+		mat: blas64.Symmetric{
+			N:      n,
+			Stride: n,
+			Data:   data,
+			Uplo:   blas.Upper,
+		},
+		cap: n,
+	}
+}
+
+// Dims returns the number of rows and columns in the matrix.
+func (s *SymDense) Dims() (r, c int) {
+	return s.mat.N, s.mat.N
+}
+
+// Caps returns the number of rows and columns in the backing matrix.
+func (s *SymDense) Caps() (r, c int) {
+	return s.cap, s.cap
+}
+
+// T implements the Matrix interface. Symmetric matrices, by definition, are
+// equal to their transpose, and this is a no-op.
+func (s *SymDense) T() Matrix {
+	return s
+}
+
+func (s *SymDense) Symmetric() int {
+	return s.mat.N
+}
+
+// RawSymmetric returns the matrix as a blas64.Symmetric. The returned
+// value must be stored in upper triangular format.
+func (s *SymDense) RawSymmetric() blas64.Symmetric {
+	return s.mat
+}
+
+// SetRawSymmetric sets the underlying blas64.Symmetric used by the receiver.
+// Changes to elements in the receiver following the call will be reflected
+// in b. SetRawSymmetric will panic if b is not an upper-encoded symmetric
+// matrix.
+func (s *SymDense) SetRawSymmetric(b blas64.Symmetric) {
+	if b.Uplo != blas.Upper {
+		panic(badSymTriangle)
+	}
+	s.mat = b
+}
+
+// Reset zeros the dimensions of the matrix so that it can be reused as the
+// receiver of a dimensionally restricted operation.
+//
+// See the Reseter interface for more information.
+func (s *SymDense) Reset() {
+	// N and Stride must be zeroed in unison.
+	s.mat.N, s.mat.Stride = 0, 0
+	s.mat.Data = s.mat.Data[:0]
+}
+
+// IsZero returns whether the receiver is zero-sized. Zero-sized matrices can be the
+// receiver for size-restricted operations. SymDense matrices can be zeroed using Reset.
+func (s *SymDense) IsZero() bool {
+	// It must be the case that m.Dims() returns
+	// zeros in this case. See comment in Reset().
+	return s.mat.N == 0
+}
+
+// reuseAs resizes an empty matrix to a n×n matrix,
+// or checks that a non-empty matrix is n×n.
+func (s *SymDense) reuseAs(n int) {
+	if s.mat.N > s.cap {
+		panic(badSymCap)
+	}
+	if s.IsZero() {
+		s.mat = blas64.Symmetric{
+			N:      n,
+			Stride: n,
+			Data:   use(s.mat.Data, n*n),
+			Uplo:   blas.Upper,
+		}
+		s.cap = n
+		return
+	}
+	if s.mat.Uplo != blas.Upper {
+		panic(badSymTriangle)
+	}
+	if s.mat.N != n {
+		panic(ErrShape)
+	}
+}
+
+func (s *SymDense) isolatedWorkspace(a Symmetric) (w *SymDense, restore func()) {
+	n := a.Symmetric()
+	w = getWorkspaceSym(n, false)
+	return w, func() {
+		s.CopySym(w)
+		putWorkspaceSym(w)
+	}
+}
+
+func (s *SymDense) AddSym(a, b Symmetric) {
+	n := a.Symmetric()
+	if n != b.Symmetric() {
+		panic(ErrShape)
+	}
+	s.reuseAs(n)
+
+	if a, ok := a.(RawSymmetricer); ok {
+		if b, ok := b.(RawSymmetricer); ok {
+			amat, bmat := a.RawSymmetric(), b.RawSymmetric()
+			if s != a {
+				s.checkOverlap(amat)
+			}
+			if s != b {
+				s.checkOverlap(bmat)
+			}
+			for i := 0; i < n; i++ {
+				btmp := bmat.Data[i*bmat.Stride+i : i*bmat.Stride+n]
+				stmp := s.mat.Data[i*s.mat.Stride+i : i*s.mat.Stride+n]
+				for j, v := range amat.Data[i*amat.Stride+i : i*amat.Stride+n] {
+					stmp[j] = v + btmp[j]
+				}
+			}
+			return
+		}
+	}
+
+	for i := 0; i < n; i++ {
+		stmp := s.mat.Data[i*s.mat.Stride : i*s.mat.Stride+n]
+		for j := i; j < n; j++ {
+			stmp[j] = a.At(i, j) + b.At(i, j)
+		}
+	}
+}
+
+func (s *SymDense) CopySym(a Symmetric) int {
+	n := a.Symmetric()
+	n = min(n, s.mat.N)
+	if n == 0 {
+		return 0
+	}
+	switch a := a.(type) {
+	case RawSymmetricer:
+		amat := a.RawSymmetric()
+		if amat.Uplo != blas.Upper {
+			panic(badSymTriangle)
+		}
+		for i := 0; i < n; i++ {
+			copy(s.mat.Data[i*s.mat.Stride+i:i*s.mat.Stride+n], amat.Data[i*amat.Stride+i:i*amat.Stride+n])
+		}
+	default:
+		for i := 0; i < n; i++ {
+			stmp := s.mat.Data[i*s.mat.Stride : i*s.mat.Stride+n]
+			for j := i; j < n; j++ {
+				stmp[j] = a.At(i, j)
+			}
+		}
+	}
+	return n
+}
+
+// SymRankOne performs a symetric rank-one update to the matrix a and stores
+// the result in the receiver
+//  s = a + alpha * x * x'
+func (s *SymDense) SymRankOne(a Symmetric, alpha float64, x *VecDense) {
+	n := x.Len()
+	if a.Symmetric() != n {
+		panic(ErrShape)
+	}
+	s.reuseAs(n)
+	if s != a {
+		if rs, ok := a.(RawSymmetricer); ok {
+			s.checkOverlap(rs.RawSymmetric())
+		}
+		s.CopySym(a)
+	}
+	blas64.Syr(alpha, x.mat, s.mat)
+}
+
+// SymRankK performs a symmetric rank-k update to the matrix a and stores the
+// result into the receiver. If a is zero, see SymOuterK.
+//  s = a + alpha * x * x'
+func (s *SymDense) SymRankK(a Symmetric, alpha float64, x Matrix) {
+	n := a.Symmetric()
+	r, _ := x.Dims()
+	if r != n {
+		panic(ErrShape)
+	}
+	xMat, aTrans := untranspose(x)
+	var g blas64.General
+	if rm, ok := xMat.(RawMatrixer); ok {
+		g = rm.RawMatrix()
+	} else {
+		g = DenseCopyOf(x).mat
+		aTrans = false
+	}
+	if a != s {
+		if rs, ok := a.(RawSymmetricer); ok {
+			s.checkOverlap(rs.RawSymmetric())
+		}
+		s.reuseAs(n)
+		s.CopySym(a)
+	}
+	t := blas.NoTrans
+	if aTrans {
+		t = blas.Trans
+	}
+	blas64.Syrk(t, alpha, g, 1, s.mat)
+}
+
+// SymOuterK calculates the outer product of x with itself and stores
+// the result into the receiver. It is equivalent to the matrix
+// multiplication
+//  s = alpha * x * x'.
+// In order to update an existing matrix, see SymRankOne.
+func (s *SymDense) SymOuterK(alpha float64, x Matrix) {
+	n, _ := x.Dims()
+	switch {
+	case s.IsZero():
+		s.mat = blas64.Symmetric{
+			N:      n,
+			Stride: n,
+			Data:   useZeroed(s.mat.Data, n*n),
+			Uplo:   blas.Upper,
+		}
+		s.cap = n
+		s.SymRankK(s, alpha, x)
+	case s.mat.Uplo != blas.Upper:
+		panic(badSymTriangle)
+	case s.mat.N == n:
+		if s == x {
+			w := getWorkspaceSym(n, true)
+			w.SymRankK(w, alpha, x)
+			s.CopySym(w)
+			putWorkspaceSym(w)
+		} else {
+			if rs, ok := x.(RawSymmetricer); ok {
+				s.checkOverlap(rs.RawSymmetric())
+			}
+			// Only zero the upper triangle.
+			for i := 0; i < n; i++ {
+				ri := i * s.mat.Stride
+				zero(s.mat.Data[ri+i : ri+n])
+			}
+			s.SymRankK(s, alpha, x)
+		}
+	default:
+		panic(ErrShape)
+	}
+}
+
+// RankTwo performs a symmmetric rank-two update to the matrix a and stores
+// the result in the receiver
+//  m = a + alpha * (x * y' + y * x')
+func (s *SymDense) RankTwo(a Symmetric, alpha float64, x, y *VecDense) {
+	n := s.mat.N
+	if x.Len() != n {
+		panic(ErrShape)
+	}
+	if y.Len() != n {
+		panic(ErrShape)
+	}
+	var w SymDense
+	if s == a {
+		w = *s
+	}
+	w.reuseAs(n)
+	if s != a {
+		if rs, ok := a.(RawSymmetricer); ok {
+			s.checkOverlap(rs.RawSymmetric())
+		}
+		w.CopySym(a)
+	}
+	blas64.Syr2(alpha, x.mat, y.mat, w.mat)
+	*s = w
+}
+
+// ScaleSym multiplies the elements of a by f, placing the result in the receiver.
+func (s *SymDense) ScaleSym(f float64, a Symmetric) {
+	n := a.Symmetric()
+	s.reuseAs(n)
+	if a, ok := a.(RawSymmetricer); ok {
+		amat := a.RawSymmetric()
+		if s != a {
+			s.checkOverlap(amat)
+		}
+		for i := 0; i < n; i++ {
+			for j := i; j < n; j++ {
+				s.mat.Data[i*s.mat.Stride+j] = f * amat.Data[i*amat.Stride+j]
+			}
+		}
+		return
+	}
+	for i := 0; i < n; i++ {
+		for j := i; j < n; j++ {
+			s.mat.Data[i*s.mat.Stride+j] = f * a.At(i, j)
+		}
+	}
+}
+
+// SubsetSym extracts a subset of the rows and columns of the matrix a and stores
+// the result in-place into the receiver. The resulting matrix size is
+// len(set)×len(set). Specifically, at the conclusion of SubsetSym,
+// s.At(i, j) equals a.At(set[i], set[j]). Note that the supplied set does not
+// have to be a strict subset, dimension repeats are allowed.
+func (s *SymDense) SubsetSym(a Symmetric, set []int) {
+	n := len(set)
+	na := a.Symmetric()
+	s.reuseAs(n)
+	var restore func()
+	if a == s {
+		s, restore = s.isolatedWorkspace(a)
+		defer restore()
+	}
+
+	if a, ok := a.(RawSymmetricer); ok {
+		raw := a.RawSymmetric()
+		if s != a {
+			s.checkOverlap(raw)
+		}
+		for i := 0; i < n; i++ {
+			ssub := s.mat.Data[i*s.mat.Stride : i*s.mat.Stride+n]
+			r := set[i]
+			rsub := raw.Data[r*raw.Stride : r*raw.Stride+na]
+			for j := i; j < n; j++ {
+				c := set[j]
+				if r <= c {
+					ssub[j] = rsub[c]
+				} else {
+					ssub[j] = raw.Data[c*raw.Stride+r]
+				}
+			}
+		}
+		return
+	}
+	for i := 0; i < n; i++ {
+		for j := i; j < n; j++ {
+			s.mat.Data[i*s.mat.Stride+j] = a.At(set[i], set[j])
+		}
+	}
+}
+
+// SliceSquare returns a new Matrix that shares backing data with the receiver.
+// The returned matrix starts at {i,i} of the receiver and extends k-i rows
+// and columns. The final row and column in the resulting matrix is k-1.
+// SliceSquare panics with ErrIndexOutOfRange if the slice is outside the capacity
+// of the receiver.
+func (s *SymDense) SliceSquare(i, k int) Matrix {
+	sz := s.cap
+	if i < 0 || sz < i || k < i || sz < k {
+		panic(ErrIndexOutOfRange)
+	}
+	v := *s
+	v.mat.Data = s.mat.Data[i*s.mat.Stride+i : (k-1)*s.mat.Stride+k]
+	v.mat.N = k - i
+	v.cap = s.cap - i
+	return &v
+}
+
+// GrowSquare returns the receiver expanded by n rows and n columns. If the
+// dimensions of the expanded matrix are outside the capacity of the receiver
+// a new allocation is made, otherwise not. Note that the receiver itself is
+// not modified during the call to GrowSquare.
+func (s *SymDense) GrowSquare(n int) Matrix {
+	if n < 0 {
+		panic(ErrIndexOutOfRange)
+	}
+	if n == 0 {
+		return s
+	}
+	var v SymDense
+	n += s.mat.N
+	if n > s.cap {
+		v.mat = blas64.Symmetric{
+			N:      n,
+			Stride: n,
+			Uplo:   blas.Upper,
+			Data:   make([]float64, n*n),
+		}
+		v.cap = n
+		// Copy elements, including those not currently visible. Use a temporary
+		// structure to avoid modifying the receiver.
+		var tmp SymDense
+		tmp.mat = blas64.Symmetric{
+			N:      s.cap,
+			Stride: s.mat.Stride,
+			Data:   s.mat.Data,
+			Uplo:   s.mat.Uplo,
+		}
+		tmp.cap = s.cap
+		v.CopySym(&tmp)
+		return &v
+	}
+	v.mat = blas64.Symmetric{
+		N:      n,
+		Stride: s.mat.Stride,
+		Uplo:   blas.Upper,
+		Data:   s.mat.Data[:(n-1)*s.mat.Stride+n],
+	}
+	v.cap = s.cap
+	return &v
+}
+
+// PowPSD computes a^pow where a is a positive symmetric definite matrix.
+//
+// PowPSD returns an error if the matrix is not  not positive symmetric definite
+// or the Eigendecomposition is not successful.
+func (s *SymDense) PowPSD(a Symmetric, pow float64) error {
+	dim := a.Symmetric()
+	s.reuseAs(dim)
+
+	var eigen EigenSym
+	ok := eigen.Factorize(a, true)
+	if !ok {
+		return ErrFailedEigen
+	}
+	values := eigen.Values(nil)
+	for i, v := range values {
+		if v <= 0 {
+			return ErrNotPSD
+		}
+		values[i] = math.Pow(v, pow)
+	}
+	var u Dense
+	u.EigenvectorsSym(&eigen)
+
+	s.SymOuterK(values[0], u.ColView(0))
+	for i := 1; i < dim; i++ {
+		s.SymRankOne(s, values[i], u.ColView(i))
+	}
+	return nil
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/symmetric_example_test.go b/vendor/gonum.org/v1/gonum/mat/symmetric_example_test.go
new file mode 100644
index 00000000..2616d6f4
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/symmetric_example_test.go
@@ -0,0 +1,54 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat_test
+
+import (
+	"fmt"
+
+	"gonum.org/v1/gonum/mat"
+)
+
+func ExampleSymDense_SubsetSym() {
+	n := 5
+	s := mat.NewSymDense(5, nil)
+	count := 1.0
+	for i := 0; i < n; i++ {
+		for j := i; j < n; j++ {
+			s.SetSym(i, j, count)
+			count++
+		}
+	}
+	fmt.Println("Original matrix:")
+	fmt.Printf("%0.4v\n\n", mat.Formatted(s))
+
+	// Take the subset {0, 2, 4}
+	var sub mat.SymDense
+	sub.SubsetSym(s, []int{0, 2, 4})
+	fmt.Println("Subset {0, 2, 4}")
+	fmt.Printf("%0.4v\n\n", mat.Formatted(&sub))
+
+	// Take the subset {0, 0, 4}
+	sub.SubsetSym(s, []int{0, 0, 4})
+	fmt.Println("Subset {0, 0, 4}")
+	fmt.Printf("%0.4v\n\n", mat.Formatted(&sub))
+
+	// Output:
+	// Original matrix:
+	// ⎡ 1   2   3   4   5⎤
+	// ⎢ 2   6   7   8   9⎥
+	// ⎢ 3   7  10  11  12⎥
+	// ⎢ 4   8  11  13  14⎥
+	// ⎣ 5   9  12  14  15⎦
+	//
+	// Subset {0, 2, 4}
+	// ⎡ 1   3   5⎤
+	// ⎢ 3  10  12⎥
+	// ⎣ 5  12  15⎦
+	//
+	// Subset {0, 0, 4}
+	// ⎡ 1   1   5⎤
+	// ⎢ 1   1   5⎥
+	// ⎣ 5   5  15⎦
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/symmetric_test.go b/vendor/gonum.org/v1/gonum/mat/symmetric_test.go
new file mode 100644
index 00000000..48210aa4
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/symmetric_test.go
@@ -0,0 +1,694 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"fmt"
+	"math/rand"
+	"os"
+	"reflect"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/floats"
+)
+
+func TestNewSymmetric(t *testing.T) {
+	for i, test := range []struct {
+		data []float64
+		n    int
+		mat  *SymDense
+	}{
+		{
+			data: []float64{
+				1, 2, 3,
+				4, 5, 6,
+				7, 8, 9,
+			},
+			n: 3,
+			mat: &SymDense{
+				mat: blas64.Symmetric{
+					N:      3,
+					Stride: 3,
+					Uplo:   blas.Upper,
+					Data:   []float64{1, 2, 3, 4, 5, 6, 7, 8, 9},
+				},
+				cap: 3,
+			},
+		},
+	} {
+		sym := NewSymDense(test.n, test.data)
+		rows, cols := sym.Dims()
+
+		if rows != test.n {
+			t.Errorf("unexpected number of rows for test %d: got: %d want: %d", i, rows, test.n)
+		}
+		if cols != test.n {
+			t.Errorf("unexpected number of cols for test %d: got: %d want: %d", i, cols, test.n)
+		}
+		if !reflect.DeepEqual(sym, test.mat) {
+			t.Errorf("unexpected data slice for test %d: got: %v want: %v", i, sym, test.mat)
+		}
+
+		m := NewDense(test.n, test.n, test.data)
+		if !reflect.DeepEqual(sym.mat.Data, m.mat.Data) {
+			t.Errorf("unexpected data slice mismatch for test %d: got: %v want: %v", i, sym.mat.Data, m.mat.Data)
+		}
+	}
+
+	panicked, message := panics(func() { NewSymDense(3, []float64{1, 2}) })
+	if !panicked || message != ErrShape.Error() {
+		t.Error("expected panic for invalid data slice length")
+	}
+}
+
+func TestSymAtSet(t *testing.T) {
+	sym := &SymDense{
+		mat: blas64.Symmetric{
+			N:      3,
+			Stride: 3,
+			Uplo:   blas.Upper,
+			Data:   []float64{1, 2, 3, 4, 5, 6, 7, 8, 9},
+		},
+		cap: 3,
+	}
+	rows, cols := sym.Dims()
+
+	// Check At out of bounds
+	for _, row := range []int{-1, rows, rows + 1} {
+		panicked, message := panics(func() { sym.At(row, 0) })
+		if !panicked || message != ErrRowAccess.Error() {
+			t.Errorf("expected panic for invalid row access N=%d r=%d", rows, row)
+		}
+	}
+	for _, col := range []int{-1, cols, cols + 1} {
+		panicked, message := panics(func() { sym.At(0, col) })
+		if !panicked || message != ErrColAccess.Error() {
+			t.Errorf("expected panic for invalid column access N=%d c=%d", cols, col)
+		}
+	}
+
+	// Check Set out of bounds
+	for _, row := range []int{-1, rows, rows + 1} {
+		panicked, message := panics(func() { sym.SetSym(row, 0, 1.2) })
+		if !panicked || message != ErrRowAccess.Error() {
+			t.Errorf("expected panic for invalid row access N=%d r=%d", rows, row)
+		}
+	}
+	for _, col := range []int{-1, cols, cols + 1} {
+		panicked, message := panics(func() { sym.SetSym(0, col, 1.2) })
+		if !panicked || message != ErrColAccess.Error() {
+			t.Errorf("expected panic for invalid column access N=%d c=%d", cols, col)
+		}
+	}
+
+	for _, st := range []struct {
+		row, col  int
+		orig, new float64
+	}{
+		{row: 1, col: 2, orig: 6, new: 15},
+		{row: 2, col: 1, orig: 15, new: 12},
+	} {
+		if e := sym.At(st.row, st.col); e != st.orig {
+			t.Errorf("unexpected value for At(%d, %d): got: %v want: %v", st.row, st.col, e, st.orig)
+		}
+		if e := sym.At(st.col, st.row); e != st.orig {
+			t.Errorf("unexpected value for At(%d, %d): got: %v want: %v", st.col, st.row, e, st.orig)
+		}
+		sym.SetSym(st.row, st.col, st.new)
+		if e := sym.At(st.row, st.col); e != st.new {
+			t.Errorf("unexpected value for At(%d, %d) after SetSym(%[1]d, %[2]d, %[4]v): got: %[3]v want: %v", st.row, st.col, e, st.new)
+		}
+		if e := sym.At(st.col, st.row); e != st.new {
+			t.Errorf("unexpected value for At(%d, %d) after SetSym(%[2]d, %[1]d, %[4]v): got: %[3]v want: %v", st.col, st.row, e, st.new)
+		}
+	}
+}
+
+func TestSymAdd(t *testing.T) {
+	for _, test := range []struct {
+		n int
+	}{
+		{n: 1},
+		{n: 2},
+		{n: 3},
+		{n: 4},
+		{n: 5},
+		{n: 10},
+	} {
+		n := test.n
+		a := NewSymDense(n, nil)
+		for i := range a.mat.Data {
+			a.mat.Data[i] = rand.Float64()
+		}
+		b := NewSymDense(n, nil)
+		for i := range a.mat.Data {
+			b.mat.Data[i] = rand.Float64()
+		}
+		var m Dense
+		m.Add(a, b)
+
+		// Check with new receiver
+		var s SymDense
+		s.AddSym(a, b)
+		for i := 0; i < n; i++ {
+			for j := i; j < n; j++ {
+				want := m.At(i, j)
+				if got := s.At(i, j); got != want {
+					t.Errorf("unexpected value for At(%d, %d): got: %v want: %v", i, j, got, want)
+				}
+			}
+		}
+
+		// Check with equal receiver
+		s.CopySym(a)
+		s.AddSym(&s, b)
+		for i := 0; i < n; i++ {
+			for j := i; j < n; j++ {
+				want := m.At(i, j)
+				if got := s.At(i, j); got != want {
+					t.Errorf("unexpected value for At(%d, %d): got: %v want: %v", i, j, got, want)
+				}
+			}
+		}
+	}
+
+	method := func(receiver, a, b Matrix) {
+		type addSymer interface {
+			AddSym(a, b Symmetric)
+		}
+		rd := receiver.(addSymer)
+		rd.AddSym(a.(Symmetric), b.(Symmetric))
+	}
+	denseComparison := func(receiver, a, b *Dense) {
+		receiver.Add(a, b)
+	}
+	testTwoInput(t, "AddSym", &SymDense{}, method, denseComparison, legalTypesSym, legalSizeSameSquare, 1e-14)
+}
+
+func TestCopy(t *testing.T) {
+	for _, test := range []struct {
+		n int
+	}{
+		{n: 1},
+		{n: 2},
+		{n: 3},
+		{n: 4},
+		{n: 5},
+		{n: 10},
+	} {
+		n := test.n
+		a := NewSymDense(n, nil)
+		for i := range a.mat.Data {
+			a.mat.Data[i] = rand.Float64()
+		}
+		s := NewSymDense(n, nil)
+		s.CopySym(a)
+		for i := 0; i < n; i++ {
+			for j := i; j < n; j++ {
+				want := a.At(i, j)
+				if got := s.At(i, j); got != want {
+					t.Errorf("unexpected value for At(%d, %d): got: %v want: %v", i, j, got, want)
+				}
+			}
+		}
+	}
+}
+
+// TODO(kortschak) Roll this into testOneInput when it exists.
+// https://github.com/gonum/matrix/issues/171
+func TestSymCopyPanic(t *testing.T) {
+	var (
+		a SymDense
+		n int
+	)
+	m := NewSymDense(1, nil)
+	panicked, message := panics(func() { n = m.CopySym(&a) })
+	if panicked {
+		t.Errorf("unexpected panic: %v", message)
+	}
+	if n != 0 {
+		t.Errorf("unexpected n: got: %d want: 0", n)
+	}
+}
+
+func TestSymRankOne(t *testing.T) {
+	for _, test := range []struct {
+		n int
+	}{
+		{n: 1},
+		{n: 2},
+		{n: 3},
+		{n: 4},
+		{n: 5},
+		{n: 10},
+	} {
+		n := test.n
+		alpha := 2.0
+		a := NewSymDense(n, nil)
+		for i := range a.mat.Data {
+			a.mat.Data[i] = rand.Float64()
+		}
+		x := make([]float64, n)
+		for i := range x {
+			x[i] = rand.Float64()
+		}
+
+		xMat := NewDense(n, 1, x)
+		var m Dense
+		m.Mul(xMat, xMat.T())
+		m.Scale(alpha, &m)
+		m.Add(&m, a)
+
+		// Check with new receiver
+		s := NewSymDense(n, nil)
+		s.SymRankOne(a, alpha, NewVecDense(len(x), x))
+		for i := 0; i < n; i++ {
+			for j := i; j < n; j++ {
+				want := m.At(i, j)
+				if got := s.At(i, j); got != want {
+					t.Errorf("unexpected value for At(%d, %d): got: %v want: %v", i, j, got, want)
+				}
+			}
+		}
+
+		// Check with reused receiver
+		copy(s.mat.Data, a.mat.Data)
+		s.SymRankOne(s, alpha, NewVecDense(len(x), x))
+		for i := 0; i < n; i++ {
+			for j := i; j < n; j++ {
+				want := m.At(i, j)
+				if got := s.At(i, j); got != want {
+					t.Errorf("unexpected value for At(%d, %d): got: %v want: %v", i, j, got, want)
+				}
+			}
+		}
+	}
+
+	alpha := 3.0
+	method := func(receiver, a, b Matrix) {
+		type SymRankOner interface {
+			SymRankOne(a Symmetric, alpha float64, x *VecDense)
+		}
+		rd := receiver.(SymRankOner)
+		rd.SymRankOne(a.(Symmetric), alpha, b.(*VecDense))
+	}
+	denseComparison := func(receiver, a, b *Dense) {
+		var tmp Dense
+		tmp.Mul(b, b.T())
+		tmp.Scale(alpha, &tmp)
+		receiver.Add(a, &tmp)
+	}
+	legalTypes := func(a, b Matrix) bool {
+		_, ok := a.(Symmetric)
+		if !ok {
+			return false
+		}
+		_, ok = b.(*VecDense)
+		return ok
+	}
+	legalSize := func(ar, ac, br, bc int) bool {
+		if ar != ac {
+			return false
+		}
+		return br == ar
+	}
+	testTwoInput(t, "SymRankOne", &SymDense{}, method, denseComparison, legalTypes, legalSize, 1e-14)
+}
+
+func TestIssue250SymRankOne(t *testing.T) {
+	x := NewVecDense(5, []float64{1, 2, 3, 4, 5})
+	var s1, s2 SymDense
+	s1.SymRankOne(NewSymDense(5, nil), 1, x)
+	s2.SymRankOne(NewSymDense(5, nil), 1, x)
+	s2.SymRankOne(NewSymDense(5, nil), 1, x)
+	if !Equal(&s1, &s2) {
+		t.Error("unexpected result from repeat")
+	}
+}
+
+func TestRankTwo(t *testing.T) {
+	for _, test := range []struct {
+		n int
+	}{
+		{n: 1},
+		{n: 2},
+		{n: 3},
+		{n: 4},
+		{n: 5},
+		{n: 10},
+	} {
+		n := test.n
+		alpha := 2.0
+		a := NewSymDense(n, nil)
+		for i := range a.mat.Data {
+			a.mat.Data[i] = rand.Float64()
+		}
+		x := make([]float64, n)
+		y := make([]float64, n)
+		for i := range x {
+			x[i] = rand.Float64()
+			y[i] = rand.Float64()
+		}
+
+		xMat := NewDense(n, 1, x)
+		yMat := NewDense(n, 1, y)
+		var m Dense
+		m.Mul(xMat, yMat.T())
+		var tmp Dense
+		tmp.Mul(yMat, xMat.T())
+		m.Add(&m, &tmp)
+		m.Scale(alpha, &m)
+		m.Add(&m, a)
+
+		// Check with new receiver
+		s := NewSymDense(n, nil)
+		s.RankTwo(a, alpha, NewVecDense(len(x), x), NewVecDense(len(y), y))
+		for i := 0; i < n; i++ {
+			for j := i; j < n; j++ {
+				if !floats.EqualWithinAbsOrRel(s.At(i, j), m.At(i, j), 1e-14, 1e-14) {
+					t.Errorf("unexpected element value at (%d,%d): got: %f want: %f", i, j, m.At(i, j), s.At(i, j))
+				}
+			}
+		}
+
+		// Check with reused receiver
+		copy(s.mat.Data, a.mat.Data)
+		s.RankTwo(s, alpha, NewVecDense(len(x), x), NewVecDense(len(y), y))
+		for i := 0; i < n; i++ {
+			for j := i; j < n; j++ {
+				if !floats.EqualWithinAbsOrRel(s.At(i, j), m.At(i, j), 1e-14, 1e-14) {
+					t.Errorf("unexpected element value at (%d,%d): got: %f want: %f", i, j, m.At(i, j), s.At(i, j))
+				}
+			}
+		}
+	}
+}
+
+func TestSymRankK(t *testing.T) {
+	alpha := 3.0
+	method := func(receiver, a, b Matrix) {
+		type SymRankKer interface {
+			SymRankK(a Symmetric, alpha float64, x Matrix)
+		}
+		rd := receiver.(SymRankKer)
+		rd.SymRankK(a.(Symmetric), alpha, b)
+	}
+	denseComparison := func(receiver, a, b *Dense) {
+		var tmp Dense
+		tmp.Mul(b, b.T())
+		tmp.Scale(alpha, &tmp)
+		receiver.Add(a, &tmp)
+	}
+	legalTypes := func(a, b Matrix) bool {
+		_, ok := a.(Symmetric)
+		return ok
+	}
+	legalSize := func(ar, ac, br, bc int) bool {
+		if ar != ac {
+			return false
+		}
+		return br == ar
+	}
+	testTwoInput(t, "SymRankK", &SymDense{}, method, denseComparison, legalTypes, legalSize, 1e-14)
+}
+
+func TestSymOuterK(t *testing.T) {
+	for _, f := range []float64{0.5, 1, 3} {
+		method := func(receiver, x Matrix) {
+			type SymOuterKer interface {
+				SymOuterK(alpha float64, x Matrix)
+			}
+			rd := receiver.(SymOuterKer)
+			rd.SymOuterK(f, x)
+		}
+		denseComparison := func(receiver, x *Dense) {
+			receiver.Mul(x, x.T())
+			receiver.Scale(f, receiver)
+		}
+		testOneInput(t, "SymOuterK", &SymDense{}, method, denseComparison, isAnyType, isAnySize, 1e-14)
+	}
+}
+
+func TestIssue250SymOuterK(t *testing.T) {
+	x := NewVecDense(5, []float64{1, 2, 3, 4, 5})
+	var s1, s2 SymDense
+	s1.SymOuterK(1, x)
+	s2.SymOuterK(1, x)
+	s2.SymOuterK(1, x)
+	if !Equal(&s1, &s2) {
+		t.Error("unexpected result from repeat")
+	}
+}
+
+func TestScaleSym(t *testing.T) {
+	for _, f := range []float64{0.5, 1, 3} {
+		method := func(receiver, a Matrix) {
+			type ScaleSymer interface {
+				ScaleSym(f float64, a Symmetric)
+			}
+			rd := receiver.(ScaleSymer)
+			rd.ScaleSym(f, a.(Symmetric))
+		}
+		denseComparison := func(receiver, a *Dense) {
+			receiver.Scale(f, a)
+		}
+		testOneInput(t, "ScaleSym", &SymDense{}, method, denseComparison, legalTypeSym, isSquare, 1e-14)
+	}
+}
+
+func TestSubsetSym(t *testing.T) {
+	for _, test := range []struct {
+		a    *SymDense
+		dims []int
+		ans  *SymDense
+	}{
+		{
+			a: NewSymDense(3, []float64{
+				1, 2, 3,
+				0, 4, 5,
+				0, 0, 6,
+			}),
+			dims: []int{0, 2},
+			ans: NewSymDense(2, []float64{
+				1, 3,
+				0, 6,
+			}),
+		},
+		{
+			a: NewSymDense(3, []float64{
+				1, 2, 3,
+				0, 4, 5,
+				0, 0, 6,
+			}),
+			dims: []int{2, 0},
+			ans: NewSymDense(2, []float64{
+				6, 3,
+				0, 1,
+			}),
+		},
+		{
+			a: NewSymDense(3, []float64{
+				1, 2, 3,
+				0, 4, 5,
+				0, 0, 6,
+			}),
+			dims: []int{1, 1, 1},
+			ans: NewSymDense(3, []float64{
+				4, 4, 4,
+				0, 4, 4,
+				0, 0, 4,
+			}),
+		},
+	} {
+		var s SymDense
+		s.SubsetSym(test.a, test.dims)
+		if !Equal(&s, test.ans) {
+			t.Errorf("SubsetSym mismatch dims %v\nGot:\n% v\nWant:\n% v\n", test.dims, s, test.ans)
+		}
+	}
+
+	dims := []int{0, 2}
+	maxDim := dims[0]
+	for _, v := range dims {
+		if maxDim < v {
+			maxDim = v
+		}
+	}
+	method := func(receiver, a Matrix) {
+		type SubsetSymer interface {
+			SubsetSym(a Symmetric, set []int)
+		}
+		rd := receiver.(SubsetSymer)
+		rd.SubsetSym(a.(Symmetric), dims)
+	}
+	denseComparison := func(receiver, a *Dense) {
+		*receiver = *NewDense(len(dims), len(dims), nil)
+		sz := len(dims)
+		for i := 0; i < sz; i++ {
+			for j := 0; j < sz; j++ {
+				receiver.Set(i, j, a.At(dims[i], dims[j]))
+			}
+		}
+	}
+	legalSize := func(ar, ac int) bool {
+		return ar == ac && ar > maxDim
+	}
+
+	testOneInput(t, "SubsetSym", &SymDense{}, method, denseComparison, legalTypeSym, legalSize, 0)
+}
+
+func TestViewGrowSquare(t *testing.T) {
+	// n is the size of the original SymDense.
+	// The first view uses start1, span1. The second view uses start2, span2 on
+	// the first view.
+	for _, test := range []struct {
+		n, start1, span1, start2, span2 int
+	}{
+		{10, 0, 10, 0, 10},
+		{10, 0, 8, 0, 8},
+		{10, 2, 8, 0, 6},
+		{10, 2, 7, 4, 2},
+		{10, 2, 6, 0, 5},
+	} {
+		n := test.n
+		s := NewSymDense(n, nil)
+		for i := 0; i < n; i++ {
+			for j := i; j < n; j++ {
+				s.SetSym(i, j, float64((i+1)*n+j+1))
+			}
+		}
+
+		// Take a subset and check the view matches.
+		start1 := test.start1
+		span1 := test.span1
+		v := s.SliceSquare(start1, start1+span1).(*SymDense)
+		for i := 0; i < span1; i++ {
+			for j := i; j < span1; j++ {
+				if v.At(i, j) != s.At(start1+i, start1+j) {
+					t.Errorf("View mismatch")
+				}
+			}
+		}
+
+		start2 := test.start2
+		span2 := test.span2
+		v2 := v.SliceSquare(start2, start2+span2).(*SymDense)
+
+		for i := 0; i < span2; i++ {
+			for j := i; j < span2; j++ {
+				if v2.At(i, j) != s.At(start1+start2+i, start1+start2+j) {
+					t.Errorf("Second view mismatch")
+				}
+			}
+		}
+
+		// Check that a write to the view is reflected in the original.
+		v2.SetSym(0, 0, 1.2)
+		if s.At(start1+start2, start1+start2) != 1.2 {
+			t.Errorf("Write to view not reflected in original")
+		}
+
+		// Grow the matrix back to the original view
+		gn := n - start1 - start2
+		g := v2.GrowSquare(gn - v2.Symmetric()).(*SymDense)
+		g.SetSym(1, 1, 2.2)
+
+		for i := 0; i < gn; i++ {
+			for j := 0; j < gn; j++ {
+				if g.At(i, j) != s.At(start1+start2+i, start1+start2+j) {
+					t.Errorf("Grow mismatch")
+
+					fmt.Printf("g=\n% v\n", Formatted(g))
+					fmt.Printf("s=\n% v\n", Formatted(s))
+					os.Exit(1)
+				}
+			}
+		}
+
+		// View g, then grow it and make sure all the elements were copied.
+		gv := g.SliceSquare(0, gn-1).(*SymDense)
+
+		gg := gv.GrowSquare(2)
+		for i := 0; i < gn; i++ {
+			for j := 0; j < gn; j++ {
+				if g.At(i, j) != gg.At(i, j) {
+					t.Errorf("Expand mismatch")
+				}
+			}
+		}
+	}
+}
+
+func TestPowPSD(t *testing.T) {
+	for cas, test := range []struct {
+		a   *SymDense
+		pow float64
+		ans *SymDense
+	}{
+		// Comparison with Matlab.
+		{
+			a:   NewSymDense(2, []float64{10, 5, 5, 12}),
+			pow: 0.5,
+			ans: NewSymDense(2, []float64{3.065533767740645, 0.776210486171016, 0.776210486171016, 3.376017962209052}),
+		},
+		{
+			a:   NewSymDense(2, []float64{11, -1, -1, 8}),
+			pow: 0.5,
+			ans: NewSymDense(2, []float64{3.312618742210524, -0.162963396980939, -0.162963396980939, 2.823728551267709}),
+		},
+		{
+			a:   NewSymDense(2, []float64{10, 5, 5, 12}),
+			pow: -0.5,
+			ans: NewSymDense(2, []float64{0.346372134547712, -0.079637515547296, -0.079637515547296, 0.314517128328794}),
+		},
+		{
+			a:   NewSymDense(3, []float64{15, -1, -3, -1, 8, 6, -3, 6, 14}),
+			pow: 0.6,
+			ans: NewSymDense(3, []float64{
+				5.051214323034288, -0.163162161893975, -0.612153996497505,
+				-0.163162161893976, 3.283474884617009, 1.432842761381493,
+				-0.612153996497505, 1.432842761381494, 4.695873060862573,
+			}),
+		},
+	} {
+		var s SymDense
+		err := s.PowPSD(test.a, test.pow)
+		if err != nil {
+			panic("bad test")
+		}
+		if !EqualApprox(&s, test.ans, 1e-10) {
+			t.Errorf("Case %d, pow mismatch", cas)
+			fmt.Println(Formatted(&s))
+			fmt.Println(Formatted(test.ans))
+		}
+	}
+
+	// Compare with Dense.Pow
+	rnd := rand.New(rand.NewSource(1))
+	for dim := 2; dim < 10; dim++ {
+		for pow := 2; pow < 6; pow++ {
+			a := NewDense(dim, dim, nil)
+			for i := 0; i < dim; i++ {
+				for j := 0; j < dim; j++ {
+					a.Set(i, j, rnd.Float64())
+				}
+			}
+			var mat SymDense
+			mat.SymOuterK(1, a)
+
+			var sym SymDense
+			sym.PowPSD(&mat, float64(pow))
+
+			var dense Dense
+			dense.Pow(&mat, pow)
+
+			if !EqualApprox(&sym, &dense, 1e-10) {
+				t.Errorf("Dim %d: pow mismatch", dim)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/triangular.go b/vendor/gonum.org/v1/gonum/mat/triangular.go
new file mode 100644
index 00000000..19b15bba
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/triangular.go
@@ -0,0 +1,540 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/lapack/lapack64"
+)
+
+var (
+	triDense *TriDense
+	_        Matrix            = triDense
+	_        Triangular        = triDense
+	_        RawTriangular     = triDense
+	_        MutableTriangular = triDense
+
+	_ NonZeroDoer    = triDense
+	_ RowNonZeroDoer = triDense
+	_ ColNonZeroDoer = triDense
+)
+
+const badTriCap = "mat: bad capacity for TriDense"
+
+// TriDense represents an upper or lower triangular matrix in dense storage
+// format.
+type TriDense struct {
+	mat blas64.Triangular
+	cap int
+}
+
+// Triangular represents a triangular matrix. Triangular matrices are always square.
+type Triangular interface {
+	Matrix
+	// Triangular returns the number of rows/columns in the matrix and its
+	// orientation.
+	Triangle() (n int, kind TriKind)
+
+	// TTri is the equivalent of the T() method in the Matrix interface but
+	// guarantees the transpose is of triangular type.
+	TTri() Triangular
+}
+
+// A RawTriangular can return a view of itself as a BLAS Triangular matrix.
+type RawTriangular interface {
+	RawTriangular() blas64.Triangular
+}
+
+// A MutableTriangular can set elements of a triangular matrix.
+type MutableTriangular interface {
+	Triangular
+	SetTri(i, j int, v float64)
+}
+
+var (
+	_ Matrix           = TransposeTri{}
+	_ Triangular       = TransposeTri{}
+	_ UntransposeTrier = TransposeTri{}
+)
+
+// TransposeTri is a type for performing an implicit transpose of a Triangular
+// matrix. It implements the Triangular interface, returning values from the
+// transpose of the matrix within.
+type TransposeTri struct {
+	Triangular Triangular
+}
+
+// At returns the value of the element at row i and column j of the transposed
+// matrix, that is, row j and column i of the Triangular field.
+func (t TransposeTri) At(i, j int) float64 {
+	return t.Triangular.At(j, i)
+}
+
+// Dims returns the dimensions of the transposed matrix. Triangular matrices are
+// square and thus this is the same size as the original Triangular.
+func (t TransposeTri) Dims() (r, c int) {
+	c, r = t.Triangular.Dims()
+	return r, c
+}
+
+// T performs an implicit transpose by returning the Triangular field.
+func (t TransposeTri) T() Matrix {
+	return t.Triangular
+}
+
+// Triangle returns the number of rows/columns in the matrix and its orientation.
+func (t TransposeTri) Triangle() (int, TriKind) {
+	n, upper := t.Triangular.Triangle()
+	return n, !upper
+}
+
+// TTri performs an implicit transpose by returning the Triangular field.
+func (t TransposeTri) TTri() Triangular {
+	return t.Triangular
+}
+
+// Untranspose returns the Triangular field.
+func (t TransposeTri) Untranspose() Matrix {
+	return t.Triangular
+}
+
+func (t TransposeTri) UntransposeTri() Triangular {
+	return t.Triangular
+}
+
+// NewTriDense creates a new Triangular matrix with n rows and columns. If data == nil,
+// a new slice is allocated for the backing slice. If len(data) == n*n, data is
+// used as the backing slice, and changes to the elements of the returned TriDense
+// will be reflected in data. If neither of these is true, NewTriDense will panic.
+//
+// The data must be arranged in row-major order, i.e. the (i*c + j)-th
+// element in the data slice is the {i, j}-th element in the matrix.
+// Only the values in the triangular portion corresponding to kind are used.
+func NewTriDense(n int, kind TriKind, data []float64) *TriDense {
+	if n < 0 {
+		panic("mat: negative dimension")
+	}
+	if data != nil && len(data) != n*n {
+		panic(ErrShape)
+	}
+	if data == nil {
+		data = make([]float64, n*n)
+	}
+	uplo := blas.Lower
+	if kind == Upper {
+		uplo = blas.Upper
+	}
+	return &TriDense{
+		mat: blas64.Triangular{
+			N:      n,
+			Stride: n,
+			Data:   data,
+			Uplo:   uplo,
+			Diag:   blas.NonUnit,
+		},
+		cap: n,
+	}
+}
+
+func (t *TriDense) Dims() (r, c int) {
+	return t.mat.N, t.mat.N
+}
+
+// Triangle returns the dimension of t and its orientation. The returned
+// orientation is only valid when n is not zero.
+func (t *TriDense) Triangle() (n int, kind TriKind) {
+	return t.mat.N, TriKind(!t.IsZero()) && t.triKind()
+}
+
+func (t *TriDense) isUpper() bool {
+	return isUpperUplo(t.mat.Uplo)
+}
+
+func (t *TriDense) triKind() TriKind {
+	return TriKind(isUpperUplo(t.mat.Uplo))
+}
+
+func isUpperUplo(u blas.Uplo) bool {
+	switch u {
+	case blas.Upper:
+		return true
+	case blas.Lower:
+		return false
+	default:
+		panic(badTriangle)
+	}
+}
+
+// asSymBlas returns the receiver restructured as a blas64.Symmetric with the
+// same backing memory. Panics if the receiver is unit.
+// This returns a blas64.Symmetric and not a *SymDense because SymDense can only
+// be upper triangular.
+func (t *TriDense) asSymBlas() blas64.Symmetric {
+	if t.mat.Diag == blas.Unit {
+		panic("mat: cannot convert unit TriDense into blas64.Symmetric")
+	}
+	return blas64.Symmetric{
+		N:      t.mat.N,
+		Stride: t.mat.Stride,
+		Data:   t.mat.Data,
+		Uplo:   t.mat.Uplo,
+	}
+}
+
+// T performs an implicit transpose by returning the receiver inside a Transpose.
+func (t *TriDense) T() Matrix {
+	return Transpose{t}
+}
+
+// TTri performs an implicit transpose by returning the receiver inside a TransposeTri.
+func (t *TriDense) TTri() Triangular {
+	return TransposeTri{t}
+}
+
+func (t *TriDense) RawTriangular() blas64.Triangular {
+	return t.mat
+}
+
+// Reset zeros the dimensions of the matrix so that it can be reused as the
+// receiver of a dimensionally restricted operation.
+//
+// See the Reseter interface for more information.
+func (t *TriDense) Reset() {
+	// N and Stride must be zeroed in unison.
+	t.mat.N, t.mat.Stride = 0, 0
+	// Defensively zero Uplo to ensure
+	// it is set correctly later.
+	t.mat.Uplo = 0
+	t.mat.Data = t.mat.Data[:0]
+}
+
+// IsZero returns whether the receiver is zero-sized. Zero-sized matrices can be the
+// receiver for size-restricted operations. TriDense matrices can be zeroed using Reset.
+func (t *TriDense) IsZero() bool {
+	// It must be the case that t.Dims() returns
+	// zeros in this case. See comment in Reset().
+	return t.mat.Stride == 0
+}
+
+// untranspose untransposes a matrix if applicable. If a is an Untransposer, then
+// untranspose returns the underlying matrix and true. If it is not, then it returns
+// the input matrix and false.
+func untransposeTri(a Triangular) (Triangular, bool) {
+	if ut, ok := a.(UntransposeTrier); ok {
+		return ut.UntransposeTri(), true
+	}
+	return a, false
+}
+
+// reuseAs resizes a zero receiver to an n×n triangular matrix with the given
+// orientation. If the receiver is non-zero, reuseAs checks that the receiver
+// is the correct size and orientation.
+func (t *TriDense) reuseAs(n int, kind TriKind) {
+	ul := blas.Lower
+	if kind == Upper {
+		ul = blas.Upper
+	}
+	if t.mat.N > t.cap {
+		panic(badTriCap)
+	}
+	if t.IsZero() {
+		t.mat = blas64.Triangular{
+			N:      n,
+			Stride: n,
+			Diag:   blas.NonUnit,
+			Data:   use(t.mat.Data, n*n),
+			Uplo:   ul,
+		}
+		t.cap = n
+		return
+	}
+	if t.mat.N != n {
+		panic(ErrShape)
+	}
+	if t.mat.Uplo != ul {
+		panic(ErrTriangle)
+	}
+}
+
+// isolatedWorkspace returns a new TriDense matrix w with the size of a and
+// returns a callback to defer which performs cleanup at the return of the call.
+// This should be used when a method receiver is the same pointer as an input argument.
+func (t *TriDense) isolatedWorkspace(a Triangular) (w *TriDense, restore func()) {
+	n, kind := a.Triangle()
+	if n == 0 {
+		panic("zero size")
+	}
+	w = getWorkspaceTri(n, kind, false)
+	return w, func() {
+		t.Copy(w)
+		putWorkspaceTri(w)
+	}
+}
+
+// Copy makes a copy of elements of a into the receiver. It is similar to the
+// built-in copy; it copies as much as the overlap between the two matrices and
+// returns the number of rows and columns it copied. Only elements within the
+// receiver's non-zero triangle are set.
+//
+// See the Copier interface for more information.
+func (t *TriDense) Copy(a Matrix) (r, c int) {
+	r, c = a.Dims()
+	r = min(r, t.mat.N)
+	c = min(c, t.mat.N)
+	if r == 0 || c == 0 {
+		return 0, 0
+	}
+
+	switch a := a.(type) {
+	case RawMatrixer:
+		amat := a.RawMatrix()
+		if t.isUpper() {
+			for i := 0; i < r; i++ {
+				copy(t.mat.Data[i*t.mat.Stride+i:i*t.mat.Stride+c], amat.Data[i*amat.Stride+i:i*amat.Stride+c])
+			}
+		} else {
+			for i := 0; i < r; i++ {
+				copy(t.mat.Data[i*t.mat.Stride:i*t.mat.Stride+i+1], amat.Data[i*amat.Stride:i*amat.Stride+i+1])
+			}
+		}
+	case RawTriangular:
+		amat := a.RawTriangular()
+		aIsUpper := isUpperUplo(amat.Uplo)
+		tIsUpper := t.isUpper()
+		switch {
+		case tIsUpper && aIsUpper:
+			for i := 0; i < r; i++ {
+				copy(t.mat.Data[i*t.mat.Stride+i:i*t.mat.Stride+c], amat.Data[i*amat.Stride+i:i*amat.Stride+c])
+			}
+		case !tIsUpper && !aIsUpper:
+			for i := 0; i < r; i++ {
+				copy(t.mat.Data[i*t.mat.Stride:i*t.mat.Stride+i+1], amat.Data[i*amat.Stride:i*amat.Stride+i+1])
+			}
+		default:
+			for i := 0; i < r; i++ {
+				t.set(i, i, amat.Data[i*amat.Stride+i])
+			}
+		}
+	default:
+		isUpper := t.isUpper()
+		for i := 0; i < r; i++ {
+			if isUpper {
+				for j := i; j < c; j++ {
+					t.set(i, j, a.At(i, j))
+				}
+			} else {
+				for j := 0; j <= i; j++ {
+					t.set(i, j, a.At(i, j))
+				}
+			}
+		}
+	}
+
+	return r, c
+}
+
+// InverseTri computes the inverse of the triangular matrix a, storing the result
+// into the receiver. If a is ill-conditioned, a Condition error will be returned.
+// Note that matrix inversion is numerically unstable, and should generally be
+// avoided where possible, for example by using the Solve routines.
+func (t *TriDense) InverseTri(a Triangular) error {
+	if rt, ok := a.(RawTriangular); ok {
+		t.checkOverlap(rt.RawTriangular())
+	}
+	n, _ := a.Triangle()
+	t.reuseAs(a.Triangle())
+	t.Copy(a)
+	work := getFloats(3*n, false)
+	iwork := getInts(n, false)
+	cond := lapack64.Trcon(CondNorm, t.mat, work, iwork)
+	putFloats(work)
+	putInts(iwork)
+	if math.IsInf(cond, 1) {
+		return Condition(cond)
+	}
+	ok := lapack64.Trtri(t.mat)
+	if !ok {
+		return Condition(math.Inf(1))
+	}
+	if cond > ConditionTolerance {
+		return Condition(cond)
+	}
+	return nil
+}
+
+// MulTri takes the product of triangular matrices a and b and places the result
+// in the receiver. The size of a and b must match, and they both must have the
+// same TriKind, or Mul will panic.
+func (t *TriDense) MulTri(a, b Triangular) {
+	n, kind := a.Triangle()
+	nb, kindb := b.Triangle()
+	if n != nb {
+		panic(ErrShape)
+	}
+	if kind != kindb {
+		panic(ErrTriangle)
+	}
+
+	aU, _ := untransposeTri(a)
+	bU, _ := untransposeTri(b)
+	t.reuseAs(n, kind)
+	var restore func()
+	if t == aU {
+		t, restore = t.isolatedWorkspace(aU)
+		defer restore()
+	} else if t == bU {
+		t, restore = t.isolatedWorkspace(bU)
+		defer restore()
+	}
+
+	// TODO(btracey): Improve the set of fast-paths.
+	if kind == Upper {
+		for i := 0; i < n; i++ {
+			for j := i; j < n; j++ {
+				var v float64
+				for k := i; k <= j; k++ {
+					v += a.At(i, k) * b.At(k, j)
+				}
+				t.SetTri(i, j, v)
+			}
+		}
+		return
+	}
+	for i := 0; i < n; i++ {
+		for j := 0; j <= i; j++ {
+			var v float64
+			for k := j; k <= i; k++ {
+				v += a.At(i, k) * b.At(k, j)
+			}
+			t.SetTri(i, j, v)
+		}
+	}
+}
+
+// copySymIntoTriangle copies a symmetric matrix into a TriDense
+func copySymIntoTriangle(t *TriDense, s Symmetric) {
+	n, upper := t.Triangle()
+	ns := s.Symmetric()
+	if n != ns {
+		panic("mat: triangle size mismatch")
+	}
+	ts := t.mat.Stride
+	if rs, ok := s.(RawSymmetricer); ok {
+		sd := rs.RawSymmetric()
+		ss := sd.Stride
+		if upper {
+			if sd.Uplo == blas.Upper {
+				for i := 0; i < n; i++ {
+					copy(t.mat.Data[i*ts+i:i*ts+n], sd.Data[i*ss+i:i*ss+n])
+				}
+				return
+			}
+			for i := 0; i < n; i++ {
+				for j := i; j < n; j++ {
+					t.mat.Data[i*ts+j] = sd.Data[j*ss+i]
+				}
+			}
+			return
+		}
+		if sd.Uplo == blas.Upper {
+			for i := 0; i < n; i++ {
+				for j := 0; j <= i; j++ {
+					t.mat.Data[i*ts+j] = sd.Data[j*ss+i]
+				}
+			}
+			return
+		}
+		for i := 0; i < n; i++ {
+			copy(t.mat.Data[i*ts:i*ts+i+1], sd.Data[i*ss:i*ss+i+1])
+		}
+		return
+	}
+	if upper {
+		for i := 0; i < n; i++ {
+			for j := i; j < n; j++ {
+				t.mat.Data[i*ts+j] = s.At(i, j)
+			}
+		}
+		return
+	}
+	for i := 0; i < n; i++ {
+		for j := 0; j <= i; j++ {
+			t.mat.Data[i*ts+j] = s.At(i, j)
+		}
+	}
+}
+
+// DoNonZero calls the function fn for each of the non-zero elements of t. The function fn
+// takes a row/column index and the element value of t at (i, j).
+func (t *TriDense) DoNonZero(fn func(i, j int, v float64)) {
+	if t.isUpper() {
+		for i := 0; i < t.mat.N; i++ {
+			for j := i; j < t.mat.N; j++ {
+				v := t.at(i, j)
+				if v != 0 {
+					fn(i, j, v)
+				}
+			}
+		}
+		return
+	}
+	for i := 0; i < t.mat.N; i++ {
+		for j := 0; j <= i; j++ {
+			v := t.at(i, j)
+			if v != 0 {
+				fn(i, j, v)
+			}
+		}
+	}
+}
+
+// DoRowNonZero calls the function fn for each of the non-zero elements of row i of t. The function fn
+// takes a row/column index and the element value of t at (i, j).
+func (t *TriDense) DoRowNonZero(i int, fn func(i, j int, v float64)) {
+	if i < 0 || t.mat.N <= i {
+		panic(ErrRowAccess)
+	}
+	if t.isUpper() {
+		for j := i; j < t.mat.N; j++ {
+			v := t.at(i, j)
+			if v != 0 {
+				fn(i, j, v)
+			}
+		}
+		return
+	}
+	for j := 0; j <= i; j++ {
+		v := t.at(i, j)
+		if v != 0 {
+			fn(i, j, v)
+		}
+	}
+}
+
+// DoColNonZero calls the function fn for each of the non-zero elements of column j of t. The function fn
+// takes a row/column index and the element value of t at (i, j).
+func (t *TriDense) DoColNonZero(j int, fn func(i, j int, v float64)) {
+	if j < 0 || t.mat.N <= j {
+		panic(ErrColAccess)
+	}
+	if t.isUpper() {
+		for i := 0; i <= j; i++ {
+			v := t.at(i, j)
+			if v != 0 {
+				fn(i, j, v)
+			}
+		}
+		return
+	}
+	for i := j; i < t.mat.N; i++ {
+		v := t.at(i, j)
+		if v != 0 {
+			fn(i, j, v)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/triangular_test.go b/vendor/gonum.org/v1/gonum/mat/triangular_test.go
new file mode 100644
index 00000000..883322d7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/triangular_test.go
@@ -0,0 +1,438 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"math"
+	"math/rand"
+	"reflect"
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+func TestNewTriangular(t *testing.T) {
+	for i, test := range []struct {
+		data []float64
+		n    int
+		kind TriKind
+		mat  *TriDense
+	}{
+		{
+			data: []float64{
+				1, 2, 3,
+				4, 5, 6,
+				7, 8, 9,
+			},
+			n:    3,
+			kind: Upper,
+			mat: &TriDense{
+				mat: blas64.Triangular{
+					N:      3,
+					Stride: 3,
+					Uplo:   blas.Upper,
+					Data:   []float64{1, 2, 3, 4, 5, 6, 7, 8, 9},
+					Diag:   blas.NonUnit,
+				},
+				cap: 3,
+			},
+		},
+	} {
+		tri := NewTriDense(test.n, test.kind, test.data)
+		rows, cols := tri.Dims()
+
+		if rows != test.n {
+			t.Errorf("unexpected number of rows for test %d: got: %d want: %d", i, rows, test.n)
+		}
+		if cols != test.n {
+			t.Errorf("unexpected number of cols for test %d: got: %d want: %d", i, cols, test.n)
+		}
+		if !reflect.DeepEqual(tri, test.mat) {
+			t.Errorf("unexpected data slice for test %d: got: %v want: %v", i, tri, test.mat)
+		}
+	}
+
+	for _, kind := range []TriKind{Lower, Upper} {
+		panicked, message := panics(func() { NewTriDense(3, kind, []float64{1, 2}) })
+		if !panicked || message != ErrShape.Error() {
+			t.Errorf("expected panic for invalid data slice length for upper=%t", kind)
+		}
+	}
+}
+
+func TestTriAtSet(t *testing.T) {
+	tri := &TriDense{
+		mat: blas64.Triangular{
+			N:      3,
+			Stride: 3,
+			Uplo:   blas.Upper,
+			Data:   []float64{1, 2, 3, 4, 5, 6, 7, 8, 9},
+			Diag:   blas.NonUnit,
+		},
+		cap: 3,
+	}
+
+	rows, cols := tri.Dims()
+
+	// Check At out of bounds
+	for _, row := range []int{-1, rows, rows + 1} {
+		panicked, message := panics(func() { tri.At(row, 0) })
+		if !panicked || message != ErrRowAccess.Error() {
+			t.Errorf("expected panic for invalid row access N=%d r=%d", rows, row)
+		}
+	}
+	for _, col := range []int{-1, cols, cols + 1} {
+		panicked, message := panics(func() { tri.At(0, col) })
+		if !panicked || message != ErrColAccess.Error() {
+			t.Errorf("expected panic for invalid column access N=%d c=%d", cols, col)
+		}
+	}
+
+	// Check Set out of bounds
+	for _, row := range []int{-1, rows, rows + 1} {
+		panicked, message := panics(func() { tri.SetTri(row, 0, 1.2) })
+		if !panicked || message != ErrRowAccess.Error() {
+			t.Errorf("expected panic for invalid row access N=%d r=%d", rows, row)
+		}
+	}
+	for _, col := range []int{-1, cols, cols + 1} {
+		panicked, message := panics(func() { tri.SetTri(0, col, 1.2) })
+		if !panicked || message != ErrColAccess.Error() {
+			t.Errorf("expected panic for invalid column access N=%d c=%d", cols, col)
+		}
+	}
+
+	for _, st := range []struct {
+		row, col int
+		uplo     blas.Uplo
+	}{
+		{row: 2, col: 1, uplo: blas.Upper},
+		{row: 1, col: 2, uplo: blas.Lower},
+	} {
+		tri.mat.Uplo = st.uplo
+		panicked, message := panics(func() { tri.SetTri(st.row, st.col, 1.2) })
+		if !panicked || message != ErrTriangleSet.Error() {
+			t.Errorf("expected panic for %+v", st)
+		}
+	}
+
+	for _, st := range []struct {
+		row, col  int
+		uplo      blas.Uplo
+		orig, new float64
+	}{
+		{row: 2, col: 1, uplo: blas.Lower, orig: 8, new: 15},
+		{row: 1, col: 2, uplo: blas.Upper, orig: 6, new: 15},
+	} {
+		tri.mat.Uplo = st.uplo
+		if e := tri.At(st.row, st.col); e != st.orig {
+			t.Errorf("unexpected value for At(%d, %d): got: %v want: %v", st.row, st.col, e, st.orig)
+		}
+		tri.SetTri(st.row, st.col, st.new)
+		if e := tri.At(st.row, st.col); e != st.new {
+			t.Errorf("unexpected value for At(%d, %d) after SetTri(%[1]d, %d, %v): got: %v want: %[3]v", st.row, st.col, st.new, e)
+		}
+	}
+}
+
+func TestTriDenseCopy(t *testing.T) {
+	for i := 0; i < 100; i++ {
+		size := rand.Intn(100)
+		r, err := randDense(size, 0.9, rand.NormFloat64)
+		if size == 0 {
+			if err != ErrZeroLength {
+				t.Fatalf("expected error %v: got: %v", ErrZeroLength, err)
+			}
+			continue
+		}
+		if err != nil {
+			t.Fatalf("unexpected error: %v", err)
+		}
+
+		u := NewTriDense(size, true, nil)
+		l := NewTriDense(size, false, nil)
+
+		for _, typ := range []Matrix{r, (*basicMatrix)(r)} {
+			for j := range u.mat.Data {
+				u.mat.Data[j] = math.NaN()
+				l.mat.Data[j] = math.NaN()
+			}
+			u.Copy(typ)
+			l.Copy(typ)
+			for m := 0; m < size; m++ {
+				for n := 0; n < size; n++ {
+					want := typ.At(m, n)
+					switch {
+					case m < n: // Upper triangular matrix.
+						if got := u.At(m, n); got != want {
+							t.Errorf("unexpected upper value for At(%d, %d) for test %d: got: %v want: %v", m, n, i, got, want)
+						}
+					case m == n: // Diagonal matrix.
+						if got := u.At(m, n); got != want {
+							t.Errorf("unexpected upper value for At(%d, %d) for test %d: got: %v want: %v", m, n, i, got, want)
+						}
+						if got := l.At(m, n); got != want {
+							t.Errorf("unexpected diagonal value for At(%d, %d) for test %d: got: %v want: %v", m, n, i, got, want)
+						}
+					case m < n: // Lower triangular matrix.
+						if got := l.At(m, n); got != want {
+							t.Errorf("unexpected lower value for At(%d, %d) for test %d: got: %v want: %v", m, n, i, got, want)
+						}
+					}
+				}
+			}
+		}
+	}
+}
+
+func TestTriTriDenseCopy(t *testing.T) {
+	for i := 0; i < 100; i++ {
+		size := rand.Intn(100)
+		r, err := randDense(size, 1, rand.NormFloat64)
+		if size == 0 {
+			if err != ErrZeroLength {
+				t.Fatalf("expected error %v: got: %v", ErrZeroLength, err)
+			}
+			continue
+		}
+		if err != nil {
+			t.Fatalf("unexpected error: %v", err)
+		}
+
+		ur := NewTriDense(size, true, nil)
+		lr := NewTriDense(size, false, nil)
+
+		ur.Copy(r)
+		lr.Copy(r)
+
+		u := NewTriDense(size, true, nil)
+		u.Copy(ur)
+		if !equal(u, ur) {
+			t.Fatal("unexpected result for U triangle copy of U triangle: not equal")
+		}
+
+		l := NewTriDense(size, false, nil)
+		l.Copy(lr)
+		if !equal(l, lr) {
+			t.Fatal("unexpected result for L triangle copy of L triangle: not equal")
+		}
+
+		zero(u.mat.Data)
+		u.Copy(lr)
+		if !isDiagonal(u) {
+			t.Fatal("unexpected result for U triangle copy of L triangle: off diagonal non-zero element")
+		}
+		if !equalDiagonal(u, lr) {
+			t.Fatal("unexpected result for U triangle copy of L triangle: diagonal not equal")
+		}
+
+		zero(l.mat.Data)
+		l.Copy(ur)
+		if !isDiagonal(l) {
+			t.Fatal("unexpected result for L triangle copy of U triangle: off diagonal non-zero element")
+		}
+		if !equalDiagonal(l, ur) {
+			t.Fatal("unexpected result for L triangle copy of U triangle: diagonal not equal")
+		}
+	}
+}
+
+func TestTriInverse(t *testing.T) {
+	for _, kind := range []TriKind{Upper, Lower} {
+		for _, n := range []int{1, 3, 5, 9} {
+			data := make([]float64, n*n)
+			for i := range data {
+				data[i] = rand.NormFloat64()
+			}
+			a := NewTriDense(n, kind, data)
+			var tr TriDense
+			err := tr.InverseTri(a)
+			if err != nil {
+				t.Errorf("Bad test: %s", err)
+			}
+			var d Dense
+			d.Mul(a, &tr)
+			if !equalApprox(eye(n), &d, 1e-8, false) {
+				var diff Dense
+				diff.Sub(eye(n), &d)
+				t.Errorf("Tri times inverse is not identity. Norm of difference: %v", Norm(&diff, 2))
+			}
+		}
+	}
+}
+
+func TestTriMul(t *testing.T) {
+	method := func(receiver, a, b Matrix) {
+		type MulTrier interface {
+			MulTri(a, b Triangular)
+		}
+		receiver.(MulTrier).MulTri(a.(Triangular), b.(Triangular))
+	}
+	denseComparison := func(receiver, a, b *Dense) {
+		receiver.Mul(a, b)
+	}
+	legalSizeTriMul := func(ar, ac, br, bc int) bool {
+		// Need both to be square and the sizes to be the same
+		return ar == ac && br == bc && ar == br
+	}
+
+	// The legal types are triangles with the same TriKind.
+	// legalTypesTri returns whether both input arguments are Triangular.
+	legalTypes := func(a, b Matrix) bool {
+		at, ok := a.(Triangular)
+		if !ok {
+			return false
+		}
+		bt, ok := b.(Triangular)
+		if !ok {
+			return false
+		}
+		_, ak := at.Triangle()
+		_, bk := bt.Triangle()
+		return ak == bk
+	}
+	legalTypesLower := func(a, b Matrix) bool {
+		legal := legalTypes(a, b)
+		if !legal {
+			return false
+		}
+		_, kind := a.(Triangular).Triangle()
+		r := kind == Lower
+		return r
+	}
+	receiver := NewTriDense(3, Lower, nil)
+	testTwoInput(t, "TriMul", receiver, method, denseComparison, legalTypesLower, legalSizeTriMul, 1e-14)
+
+	legalTypesUpper := func(a, b Matrix) bool {
+		legal := legalTypes(a, b)
+		if !legal {
+			return false
+		}
+		_, kind := a.(Triangular).Triangle()
+		r := kind == Upper
+		return r
+	}
+	receiver = NewTriDense(3, Upper, nil)
+	testTwoInput(t, "TriMul", receiver, method, denseComparison, legalTypesUpper, legalSizeTriMul, 1e-14)
+}
+
+func TestCopySymIntoTriangle(t *testing.T) {
+	nan := math.NaN()
+	for tc, test := range []struct {
+		n     int
+		sUplo blas.Uplo
+		s     []float64
+
+		tUplo TriKind
+		want  []float64
+	}{
+		{
+			n:     3,
+			sUplo: blas.Upper,
+			s: []float64{
+				1, 2, 3,
+				nan, 4, 5,
+				nan, nan, 6,
+			},
+			tUplo: Upper,
+			want: []float64{
+				1, 2, 3,
+				0, 4, 5,
+				0, 0, 6,
+			},
+		},
+		{
+			n:     3,
+			sUplo: blas.Lower,
+			s: []float64{
+				1, nan, nan,
+				2, 3, nan,
+				4, 5, 6,
+			},
+			tUplo: Upper,
+			want: []float64{
+				1, 2, 4,
+				0, 3, 5,
+				0, 0, 6,
+			},
+		},
+		{
+			n:     3,
+			sUplo: blas.Upper,
+			s: []float64{
+				1, 2, 3,
+				nan, 4, 5,
+				nan, nan, 6,
+			},
+			tUplo: Lower,
+			want: []float64{
+				1, 0, 0,
+				2, 4, 0,
+				3, 5, 6,
+			},
+		},
+		{
+			n:     3,
+			sUplo: blas.Lower,
+			s: []float64{
+				1, nan, nan,
+				2, 3, nan,
+				4, 5, 6,
+			},
+			tUplo: Lower,
+			want: []float64{
+				1, 0, 0,
+				2, 3, 0,
+				4, 5, 6,
+			},
+		},
+	} {
+		n := test.n
+		s := NewSymDense(n, test.s)
+		// For the purpose of the test, break the assumption that
+		// symmetric is stored in the upper triangle (only when S is
+		// RawSymmetricer).
+		s.mat.Uplo = test.sUplo
+
+		t1 := NewTriDense(n, test.tUplo, nil)
+		copySymIntoTriangle(t1, s)
+
+		equal := true
+	loop1:
+		for i := 0; i < n; i++ {
+			for j := 0; j < n; j++ {
+				if t1.At(i, j) != test.want[i*n+j] {
+					equal = false
+					break loop1
+				}
+			}
+		}
+		if !equal {
+			t.Errorf("Case %v: unexpected T when S is RawSymmetricer", tc)
+		}
+
+		if test.sUplo == blas.Lower {
+			continue
+		}
+
+		sb := (basicSymmetric)(*s)
+		t2 := NewTriDense(n, test.tUplo, nil)
+		copySymIntoTriangle(t2, &sb)
+		equal = true
+	loop2:
+		for i := 0; i < n; i++ {
+			for j := 0; j < n; j++ {
+				if t1.At(i, j) != test.want[i*n+j] {
+					equal = false
+					break loop2
+				}
+			}
+		}
+		if !equal {
+			t.Errorf("Case %v: unexpected T when S is not RawSymmetricer", tc)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/vector.go b/vendor/gonum.org/v1/gonum/mat/vector.go
new file mode 100644
index 00000000..110581ad
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/vector.go
@@ -0,0 +1,484 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+	"gonum.org/v1/gonum/internal/asm/f64"
+)
+
+var (
+	vector *VecDense
+
+	_ Matrix  = vector
+	_ Vector  = vector
+	_ Reseter = vector
+)
+
+// Vector is a column vector.
+type Vector interface {
+	Matrix
+	Len() int
+}
+
+// VecDense represents a column vector.
+type VecDense struct {
+	mat blas64.Vector
+	n   int
+	// A BLAS vector can have a negative increment, but allowing this
+	// in the mat type complicates a lot of code, and doesn't gain anything.
+	// VecDense must have positive increment in this package.
+}
+
+// NewVecDense creates a new VecDense of length n. If data == nil,
+// a new slice is allocated for the backing slice. If len(data) == n, data is
+// used as the backing slice, and changes to the elements of the returned VecDense
+// will be reflected in data. If neither of these is true, NewVecDense will panic.
+func NewVecDense(n int, data []float64) *VecDense {
+	if len(data) != n && data != nil {
+		panic(ErrShape)
+	}
+	if data == nil {
+		data = make([]float64, n)
+	}
+	return &VecDense{
+		mat: blas64.Vector{
+			Inc:  1,
+			Data: data,
+		},
+		n: n,
+	}
+}
+
+// SliceVec returns a new VecDense that shares backing data with the receiver.
+// The returned matrix starts at i of the receiver and extends k-i elements.
+// SliceVec panics with ErrIndexOutOfRange if the slice is outside the capacity
+// of the receiver.
+func (v *VecDense) SliceVec(i, k int) *VecDense {
+	if i < 0 || k <= i || v.Cap() < k {
+		panic(ErrIndexOutOfRange)
+	}
+	return &VecDense{
+		n: k - i,
+		mat: blas64.Vector{
+			Inc:  v.mat.Inc,
+			Data: v.mat.Data[i*v.mat.Inc : (k-1)*v.mat.Inc+1],
+		},
+	}
+}
+
+// Dims returns the number of rows and columns in the matrix. Columns is always 1
+// for a non-Reset vector.
+func (v *VecDense) Dims() (r, c int) {
+	if v.IsZero() {
+		return 0, 0
+	}
+	return v.n, 1
+}
+
+// Caps returns the number of rows and columns in the backing matrix. Columns is always 1
+// for a non-Reset vector.
+func (v *VecDense) Caps() (r, c int) {
+	if v.IsZero() {
+		return 0, 0
+	}
+	return v.Cap(), 1
+}
+
+// Len returns the length of the vector.
+func (v *VecDense) Len() int {
+	return v.n
+}
+
+// Cap returns the capacity of the vector.
+func (v *VecDense) Cap() int {
+	if v.IsZero() {
+		return 0
+	}
+	return (cap(v.mat.Data)-1)/v.mat.Inc + 1
+}
+
+// T performs an implicit transpose by returning the receiver inside a Transpose.
+func (v *VecDense) T() Matrix {
+	return Transpose{v}
+}
+
+// Reset zeros the length of the vector so that it can be reused as the
+// receiver of a dimensionally restricted operation.
+//
+// See the Reseter interface for more information.
+func (v *VecDense) Reset() {
+	// No change of Inc or n to 0 may be
+	// made unless both are set to 0.
+	v.mat.Inc = 0
+	v.n = 0
+	v.mat.Data = v.mat.Data[:0]
+}
+
+// CloneVec makes a copy of a into the receiver, overwriting the previous value
+// of the receiver.
+func (v *VecDense) CloneVec(a *VecDense) {
+	if v == a {
+		return
+	}
+	v.n = a.n
+	v.mat = blas64.Vector{
+		Inc:  1,
+		Data: use(v.mat.Data, v.n),
+	}
+	blas64.Copy(v.n, a.mat, v.mat)
+}
+
+func (v *VecDense) RawVector() blas64.Vector {
+	return v.mat
+}
+
+// CopyVec makes a copy of elements of a into the receiver. It is similar to the
+// built-in copy; it copies as much as the overlap between the two vectors and
+// returns the number of elements it copied.
+func (v *VecDense) CopyVec(a *VecDense) int {
+	n := min(v.Len(), a.Len())
+	if v != a {
+		blas64.Copy(n, a.mat, v.mat)
+	}
+	return n
+}
+
+// ScaleVec scales the vector a by alpha, placing the result in the receiver.
+func (v *VecDense) ScaleVec(alpha float64, a *VecDense) {
+	n := a.Len()
+	if v != a {
+		v.reuseAs(n)
+		if v.mat.Inc == 1 && a.mat.Inc == 1 {
+			f64.ScalUnitaryTo(v.mat.Data, alpha, a.mat.Data)
+			return
+		}
+		f64.ScalIncTo(v.mat.Data, uintptr(v.mat.Inc),
+			alpha, a.mat.Data, uintptr(n), uintptr(a.mat.Inc))
+		return
+	}
+	if v.mat.Inc == 1 {
+		f64.ScalUnitary(alpha, v.mat.Data)
+		return
+	}
+	f64.ScalInc(alpha, v.mat.Data, uintptr(n), uintptr(v.mat.Inc))
+}
+
+// AddScaledVec adds the vectors a and alpha*b, placing the result in the receiver.
+func (v *VecDense) AddScaledVec(a *VecDense, alpha float64, b *VecDense) {
+	if alpha == 1 {
+		v.AddVec(a, b)
+		return
+	}
+	if alpha == -1 {
+		v.SubVec(a, b)
+		return
+	}
+
+	ar := a.Len()
+	br := b.Len()
+
+	if ar != br {
+		panic(ErrShape)
+	}
+
+	if v != a {
+		v.checkOverlap(a.mat)
+	}
+	if v != b {
+		v.checkOverlap(b.mat)
+	}
+
+	v.reuseAs(ar)
+
+	switch {
+	case alpha == 0: // v <- a
+		v.CopyVec(a)
+	case v == a && v == b: // v <- v + alpha * v = (alpha + 1) * v
+		blas64.Scal(ar, alpha+1, v.mat)
+	case v == a && v != b: // v <- v + alpha * b
+		if v.mat.Inc == 1 && b.mat.Inc == 1 {
+			// Fast path for a common case.
+			f64.AxpyUnitaryTo(v.mat.Data, alpha, b.mat.Data, a.mat.Data)
+		} else {
+			f64.AxpyInc(alpha, b.mat.Data, v.mat.Data,
+				uintptr(ar), uintptr(b.mat.Inc), uintptr(v.mat.Inc), 0, 0)
+		}
+	default: // v <- a + alpha * b or v <- a + alpha * v
+		if v.mat.Inc == 1 && a.mat.Inc == 1 && b.mat.Inc == 1 {
+			// Fast path for a common case.
+			f64.AxpyUnitaryTo(v.mat.Data, alpha, b.mat.Data, a.mat.Data)
+		} else {
+			f64.AxpyIncTo(v.mat.Data, uintptr(v.mat.Inc), 0,
+				alpha, b.mat.Data, a.mat.Data,
+				uintptr(ar), uintptr(b.mat.Inc), uintptr(a.mat.Inc), 0, 0)
+		}
+	}
+}
+
+// AddVec adds the vectors a and b, placing the result in the receiver.
+func (v *VecDense) AddVec(a, b *VecDense) {
+	ar := a.Len()
+	br := b.Len()
+
+	if ar != br {
+		panic(ErrShape)
+	}
+
+	if v != a {
+		v.checkOverlap(a.mat)
+	}
+	if v != b {
+		v.checkOverlap(b.mat)
+	}
+
+	v.reuseAs(ar)
+
+	if v.mat.Inc == 1 && a.mat.Inc == 1 && b.mat.Inc == 1 {
+		// Fast path for a common case.
+		f64.AxpyUnitaryTo(v.mat.Data, 1, b.mat.Data, a.mat.Data)
+		return
+	}
+	f64.AxpyIncTo(v.mat.Data, uintptr(v.mat.Inc), 0,
+		1, b.mat.Data, a.mat.Data,
+		uintptr(ar), uintptr(b.mat.Inc), uintptr(a.mat.Inc), 0, 0)
+}
+
+// SubVec subtracts the vector b from a, placing the result in the receiver.
+func (v *VecDense) SubVec(a, b *VecDense) {
+	ar := a.Len()
+	br := b.Len()
+
+	if ar != br {
+		panic(ErrShape)
+	}
+
+	if v != a {
+		v.checkOverlap(a.mat)
+	}
+	if v != b {
+		v.checkOverlap(b.mat)
+	}
+
+	v.reuseAs(ar)
+
+	if v.mat.Inc == 1 && a.mat.Inc == 1 && b.mat.Inc == 1 {
+		// Fast path for a common case.
+		f64.AxpyUnitaryTo(v.mat.Data, -1, b.mat.Data, a.mat.Data)
+		return
+	}
+	f64.AxpyIncTo(v.mat.Data, uintptr(v.mat.Inc), 0,
+		-1, b.mat.Data, a.mat.Data,
+		uintptr(ar), uintptr(b.mat.Inc), uintptr(a.mat.Inc), 0, 0)
+}
+
+// MulElemVec performs element-wise multiplication of a and b, placing the result
+// in the receiver.
+func (v *VecDense) MulElemVec(a, b *VecDense) {
+	ar := a.Len()
+	br := b.Len()
+
+	if ar != br {
+		panic(ErrShape)
+	}
+
+	if v != a {
+		v.checkOverlap(a.mat)
+	}
+	if v != b {
+		v.checkOverlap(b.mat)
+	}
+
+	v.reuseAs(ar)
+
+	amat, bmat := a.RawVector(), b.RawVector()
+	for i := 0; i < v.n; i++ {
+		v.mat.Data[i*v.mat.Inc] = amat.Data[i*amat.Inc] * bmat.Data[i*bmat.Inc]
+	}
+}
+
+// DivElemVec performs element-wise division of a by b, placing the result
+// in the receiver.
+func (v *VecDense) DivElemVec(a, b *VecDense) {
+	ar := a.Len()
+	br := b.Len()
+
+	if ar != br {
+		panic(ErrShape)
+	}
+
+	if v != a {
+		v.checkOverlap(a.mat)
+	}
+	if v != b {
+		v.checkOverlap(b.mat)
+	}
+
+	v.reuseAs(ar)
+
+	amat, bmat := a.RawVector(), b.RawVector()
+	for i := 0; i < v.n; i++ {
+		v.mat.Data[i*v.mat.Inc] = amat.Data[i*amat.Inc] / bmat.Data[i*bmat.Inc]
+	}
+}
+
+// MulVec computes a * b. The result is stored into the receiver.
+// MulVec panics if the number of columns in a does not equal the number of rows in b.
+func (v *VecDense) MulVec(a Matrix, b *VecDense) {
+	r, c := a.Dims()
+	br := b.Len()
+	if c != br {
+		panic(ErrShape)
+	}
+
+	if v != b {
+		v.checkOverlap(b.mat)
+	}
+
+	a, trans := untranspose(a)
+	ar, ac := a.Dims()
+	v.reuseAs(r)
+	var restore func()
+	if v == a {
+		v, restore = v.isolatedWorkspace(a.(*VecDense))
+		defer restore()
+	} else if v == b {
+		v, restore = v.isolatedWorkspace(b)
+		defer restore()
+	}
+
+	switch a := a.(type) {
+	case *VecDense:
+		if v != a {
+			v.checkOverlap(a.mat)
+		}
+
+		if a.Len() == 1 {
+			// {1,1} x {1,n}
+			av := a.At(0, 0)
+			for i := 0; i < b.Len(); i++ {
+				v.mat.Data[i*v.mat.Inc] = av * b.mat.Data[i*b.mat.Inc]
+			}
+			return
+		}
+		if b.Len() == 1 {
+			// {1,n} x {1,1}
+			bv := b.At(0, 0)
+			for i := 0; i < a.Len(); i++ {
+				v.mat.Data[i*v.mat.Inc] = bv * a.mat.Data[i*a.mat.Inc]
+			}
+			return
+		}
+		// {n,1} x {1,n}
+		var sum float64
+		for i := 0; i < c; i++ {
+			sum += a.At(i, 0) * b.At(i, 0)
+		}
+		v.SetVec(0, sum)
+		return
+	case RawSymmetricer:
+		amat := a.RawSymmetric()
+		blas64.Symv(1, amat, b.mat, 0, v.mat)
+	case RawTriangular:
+		v.CopyVec(b)
+		amat := a.RawTriangular()
+		ta := blas.NoTrans
+		if trans {
+			ta = blas.Trans
+		}
+		blas64.Trmv(ta, amat, v.mat)
+	case RawMatrixer:
+		amat := a.RawMatrix()
+		// We don't know that a is a *Dense, so make
+		// a temporary Dense to check overlap.
+		(&Dense{mat: amat}).checkOverlap(v.asGeneral())
+		t := blas.NoTrans
+		if trans {
+			t = blas.Trans
+		}
+		blas64.Gemv(t, 1, amat, b.mat, 0, v.mat)
+	default:
+		if trans {
+			col := make([]float64, ar)
+			for c := 0; c < ac; c++ {
+				for i := range col {
+					col[i] = a.At(i, c)
+				}
+				var f float64
+				for i, e := range col {
+					f += e * b.mat.Data[i*b.mat.Inc]
+				}
+				v.mat.Data[c*v.mat.Inc] = f
+			}
+		} else {
+			row := make([]float64, ac)
+			for r := 0; r < ar; r++ {
+				for i := range row {
+					row[i] = a.At(r, i)
+				}
+				var f float64
+				for i, e := range row {
+					f += e * b.mat.Data[i*b.mat.Inc]
+				}
+				v.mat.Data[r*v.mat.Inc] = f
+			}
+		}
+	}
+}
+
+// reuseAs resizes an empty vector to a r×1 vector,
+// or checks that a non-empty matrix is r×1.
+func (v *VecDense) reuseAs(r int) {
+	if v.IsZero() {
+		v.mat = blas64.Vector{
+			Inc:  1,
+			Data: use(v.mat.Data, r),
+		}
+		v.n = r
+		return
+	}
+	if r != v.n {
+		panic(ErrShape)
+	}
+}
+
+// IsZero returns whether the receiver is zero-sized. Zero-sized vectors can be the
+// receiver for size-restricted operations. VecDenses can be zeroed using Reset.
+func (v *VecDense) IsZero() bool {
+	// It must be the case that v.Dims() returns
+	// zeros in this case. See comment in Reset().
+	return v.mat.Inc == 0
+}
+
+func (v *VecDense) isolatedWorkspace(a *VecDense) (n *VecDense, restore func()) {
+	l := a.Len()
+	n = getWorkspaceVec(l, false)
+	return n, func() {
+		v.CopyVec(n)
+		putWorkspaceVec(n)
+	}
+}
+
+// asDense returns a Dense representation of the receiver with the same
+// underlying data.
+func (v *VecDense) asDense() *Dense {
+	return &Dense{
+		mat:     v.asGeneral(),
+		capRows: v.n,
+		capCols: 1,
+	}
+}
+
+// asGeneral returns a blas64.General representation of the receiver with the
+// same underlying data.
+func (v *VecDense) asGeneral() blas64.General {
+	return blas64.General{
+		Rows:   v.n,
+		Cols:   1,
+		Stride: v.mat.Inc,
+		Data:   v.mat.Data,
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mat/vector_test.go b/vendor/gonum.org/v1/gonum/mat/vector_test.go
new file mode 100644
index 00000000..4f39f71f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mat/vector_test.go
@@ -0,0 +1,530 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+	"math/rand"
+	"reflect"
+	"testing"
+
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+func TestNewVecDense(t *testing.T) {
+	for i, test := range []struct {
+		n      int
+		data   []float64
+		vector *VecDense
+	}{
+		{
+			n:    3,
+			data: []float64{4, 5, 6},
+			vector: &VecDense{
+				mat: blas64.Vector{
+					Data: []float64{4, 5, 6},
+					Inc:  1,
+				},
+				n: 3,
+			},
+		},
+		{
+			n:    3,
+			data: nil,
+			vector: &VecDense{
+				mat: blas64.Vector{
+					Data: []float64{0, 0, 0},
+					Inc:  1,
+				},
+				n: 3,
+			},
+		},
+	} {
+		v := NewVecDense(test.n, test.data)
+		rows, cols := v.Dims()
+		if rows != test.n {
+			t.Errorf("unexpected number of rows for test %d: got: %d want: %d", i, rows, test.n)
+		}
+		if cols != 1 {
+			t.Errorf("unexpected number of cols for test %d: got: %d want: 1", i, cols)
+		}
+		if !reflect.DeepEqual(v, test.vector) {
+			t.Errorf("unexpected data slice for test %d: got: %v want: %v", i, v, test.vector)
+		}
+	}
+}
+
+func TestCap(t *testing.T) {
+	for i, test := range []struct {
+		vector *VecDense
+		want   int
+	}{
+		{vector: NewVecDense(3, nil), want: 3},
+		{
+			vector: &VecDense{
+				mat: blas64.Vector{
+					Data: make([]float64, 7, 10),
+					Inc:  3,
+				},
+				n: 3,
+			},
+			want: 4,
+		},
+		{
+			vector: &VecDense{
+				mat: blas64.Vector{
+					Data: make([]float64, 10),
+					Inc:  3,
+				},
+				n: 4,
+			},
+			want: 4,
+		},
+		{
+			vector: &VecDense{
+				mat: blas64.Vector{
+					Data: make([]float64, 11),
+					Inc:  3,
+				},
+				n: 4,
+			},
+			want: 4,
+		},
+		{
+			vector: &VecDense{
+				mat: blas64.Vector{
+					Data: make([]float64, 12),
+					Inc:  3,
+				},
+				n: 4,
+			},
+			want: 4,
+		},
+		{
+			vector: &VecDense{
+				mat: blas64.Vector{
+					Data: make([]float64, 13),
+					Inc:  3,
+				},
+				n: 4,
+			},
+			want: 5,
+		},
+	} {
+		got := test.vector.Cap()
+		if got != test.want {
+			t.Errorf("unexpected capacty for test %d: got: %d want: %d", i, got, test.want)
+		}
+	}
+}
+
+func TestVecDenseAtSet(t *testing.T) {
+	for i, test := range []struct {
+		vector *VecDense
+	}{
+		{
+			vector: &VecDense{
+				mat: blas64.Vector{
+					Data: []float64{0, 1, 2},
+					Inc:  1,
+				},
+				n: 3,
+			},
+		},
+		{
+			vector: &VecDense{
+				mat: blas64.Vector{
+					Data: []float64{0, 10, 10, 1, 10, 10, 2},
+					Inc:  3,
+				},
+				n: 3,
+			},
+		},
+	} {
+		v := test.vector
+		n := test.vector.n
+
+		for _, row := range []int{-1, n} {
+			panicked, message := panics(func() { v.At(row, 0) })
+			if !panicked || message != ErrRowAccess.Error() {
+				t.Errorf("expected panic for invalid row access for test %d n=%d r=%d", i, n, row)
+			}
+		}
+		for _, col := range []int{-1, 1} {
+			panicked, message := panics(func() { v.At(0, col) })
+			if !panicked || message != ErrColAccess.Error() {
+				t.Errorf("expected panic for invalid column access for test %d n=%d c=%d", i, n, col)
+			}
+		}
+
+		for _, row := range []int{0, 1, n - 1} {
+			if e := v.At(row, 0); e != float64(row) {
+				t.Errorf("unexpected value for At(%d, 0) for test %d : got: %v want: %v", row, i, e, float64(row))
+			}
+		}
+
+		for _, row := range []int{-1, n} {
+			panicked, message := panics(func() { v.SetVec(row, 100) })
+			if !panicked || message != ErrVectorAccess.Error() {
+				t.Errorf("expected panic for invalid row access for test %d n=%d r=%d", i, n, row)
+			}
+		}
+
+		for inc, row := range []int{0, 2} {
+			v.SetVec(row, 100+float64(inc))
+			if e := v.At(row, 0); e != 100+float64(inc) {
+				t.Errorf("unexpected value for At(%d, 0) after SetVec(%[1]d, %v) for test %d: got: %v want: %[2]v", row, 100+float64(inc), i, e)
+			}
+		}
+	}
+}
+
+func TestVecDenseMul(t *testing.T) {
+	method := func(receiver, a, b Matrix) {
+		type mulVecer interface {
+			MulVec(a Matrix, b *VecDense)
+		}
+		rd := receiver.(mulVecer)
+		rd.MulVec(a, b.(*VecDense))
+	}
+	denseComparison := func(receiver, a, b *Dense) {
+		receiver.Mul(a, b)
+	}
+	legalSizeMulVec := func(ar, ac, br, bc int) bool {
+		var legal bool
+		if bc != 1 {
+			legal = false
+		} else {
+			legal = ac == br
+		}
+		return legal
+	}
+	testTwoInput(t, "MulVec", &VecDense{}, method, denseComparison, legalTypesNotVecVec, legalSizeMulVec, 1e-14)
+}
+
+func TestVecDenseScale(t *testing.T) {
+	for i, test := range []struct {
+		a     *VecDense
+		alpha float64
+		want  *VecDense
+	}{
+		{
+			a:     NewVecDense(3, []float64{0, 1, 2}),
+			alpha: 0,
+			want:  NewVecDense(3, []float64{0, 0, 0}),
+		},
+		{
+			a:     NewVecDense(3, []float64{0, 1, 2}),
+			alpha: 1,
+			want:  NewVecDense(3, []float64{0, 1, 2}),
+		},
+		{
+			a:     NewVecDense(3, []float64{0, 1, 2}),
+			alpha: -2,
+			want:  NewVecDense(3, []float64{0, -2, -4}),
+		},
+		{
+			a:     NewDense(3, 1, []float64{0, 1, 2}).ColView(0),
+			alpha: 0,
+			want:  NewVecDense(3, []float64{0, 0, 0}),
+		},
+		{
+			a:     NewDense(3, 1, []float64{0, 1, 2}).ColView(0),
+			alpha: 1,
+			want:  NewVecDense(3, []float64{0, 1, 2}),
+		},
+		{
+			a:     NewDense(3, 1, []float64{0, 1, 2}).ColView(0),
+			alpha: -2,
+			want:  NewVecDense(3, []float64{0, -2, -4}),
+		},
+		{
+			a: NewDense(3, 3, []float64{
+				0, 1, 2,
+				3, 4, 5,
+				6, 7, 8,
+			}).ColView(1),
+			alpha: -2,
+			want:  NewVecDense(3, []float64{-2, -8, -14}),
+		},
+	} {
+		var v VecDense
+		v.ScaleVec(test.alpha, test.a)
+		if !reflect.DeepEqual(v.RawVector(), test.want.RawVector()) {
+			t.Errorf("test %d: unexpected result for v = alpha * a: got: %v want: %v", i, v.RawVector(), test.want.RawVector())
+		}
+
+		v.CopyVec(test.a)
+		v.ScaleVec(test.alpha, &v)
+		if !reflect.DeepEqual(v.RawVector(), test.want.RawVector()) {
+			t.Errorf("test %d: unexpected result for v = alpha * v: got: %v want: %v", i, v.RawVector(), test.want.RawVector())
+		}
+	}
+
+	for _, alpha := range []float64{0, 1, -1, 2.3, -2.3} {
+		method := func(receiver, a Matrix) {
+			type scaleVecer interface {
+				ScaleVec(float64, *VecDense)
+			}
+			v := receiver.(scaleVecer)
+			v.ScaleVec(alpha, a.(*VecDense))
+		}
+		denseComparison := func(receiver, a *Dense) {
+			receiver.Scale(alpha, a)
+		}
+		testOneInput(t, "ScaleVec", &VecDense{}, method, denseComparison, legalTypeVec, isAnyVecDense, 0)
+	}
+}
+
+func TestVecDenseAddScaled(t *testing.T) {
+	for _, alpha := range []float64{0, 1, -1, 2.3, -2.3} {
+		method := func(receiver, a, b Matrix) {
+			type addScaledVecer interface {
+				AddScaledVec(*VecDense, float64, *VecDense)
+			}
+			v := receiver.(addScaledVecer)
+			v.AddScaledVec(a.(*VecDense), alpha, b.(*VecDense))
+		}
+		denseComparison := func(receiver, a, b *Dense) {
+			var sb Dense
+			sb.Scale(alpha, b)
+			receiver.Add(a, &sb)
+		}
+		testTwoInput(t, "AddScaledVec", &VecDense{}, method, denseComparison, legalTypesVecVec, legalSizeSameVec, 1e-14)
+	}
+}
+
+func TestVecDenseAdd(t *testing.T) {
+	for i, test := range []struct {
+		a, b *VecDense
+		want *VecDense
+	}{
+		{
+			a:    NewVecDense(3, []float64{0, 1, 2}),
+			b:    NewVecDense(3, []float64{0, 2, 3}),
+			want: NewVecDense(3, []float64{0, 3, 5}),
+		},
+		{
+			a:    NewVecDense(3, []float64{0, 1, 2}),
+			b:    NewDense(3, 1, []float64{0, 2, 3}).ColView(0),
+			want: NewVecDense(3, []float64{0, 3, 5}),
+		},
+		{
+			a:    NewDense(3, 1, []float64{0, 1, 2}).ColView(0),
+			b:    NewDense(3, 1, []float64{0, 2, 3}).ColView(0),
+			want: NewVecDense(3, []float64{0, 3, 5}),
+		},
+	} {
+		var v VecDense
+		v.AddVec(test.a, test.b)
+		if !reflect.DeepEqual(v.RawVector(), test.want.RawVector()) {
+			t.Errorf("unexpected result for test %d: got: %v want: %v", i, v.RawVector(), test.want.RawVector())
+		}
+	}
+}
+
+func TestVecDenseSub(t *testing.T) {
+	for i, test := range []struct {
+		a, b *VecDense
+		want *VecDense
+	}{
+		{
+			a:    NewVecDense(3, []float64{0, 1, 2}),
+			b:    NewVecDense(3, []float64{0, 0.5, 1}),
+			want: NewVecDense(3, []float64{0, 0.5, 1}),
+		},
+		{
+			a:    NewVecDense(3, []float64{0, 1, 2}),
+			b:    NewDense(3, 1, []float64{0, 0.5, 1}).ColView(0),
+			want: NewVecDense(3, []float64{0, 0.5, 1}),
+		},
+		{
+			a:    NewDense(3, 1, []float64{0, 1, 2}).ColView(0),
+			b:    NewDense(3, 1, []float64{0, 0.5, 1}).ColView(0),
+			want: NewVecDense(3, []float64{0, 0.5, 1}),
+		},
+	} {
+		var v VecDense
+		v.SubVec(test.a, test.b)
+		if !reflect.DeepEqual(v.RawVector(), test.want.RawVector()) {
+			t.Errorf("unexpected result for test %d: got: %v want: %v", i, v.RawVector(), test.want.RawVector())
+		}
+	}
+}
+
+func TestVecDenseMulElem(t *testing.T) {
+	for i, test := range []struct {
+		a, b *VecDense
+		want *VecDense
+	}{
+		{
+			a:    NewVecDense(3, []float64{0, 1, 2}),
+			b:    NewVecDense(3, []float64{0, 2, 3}),
+			want: NewVecDense(3, []float64{0, 2, 6}),
+		},
+		{
+			a:    NewVecDense(3, []float64{0, 1, 2}),
+			b:    NewDense(3, 1, []float64{0, 2, 3}).ColView(0),
+			want: NewVecDense(3, []float64{0, 2, 6}),
+		},
+		{
+			a:    NewDense(3, 1, []float64{0, 1, 2}).ColView(0),
+			b:    NewDense(3, 1, []float64{0, 2, 3}).ColView(0),
+			want: NewVecDense(3, []float64{0, 2, 6}),
+		},
+	} {
+		var v VecDense
+		v.MulElemVec(test.a, test.b)
+		if !reflect.DeepEqual(v.RawVector(), test.want.RawVector()) {
+			t.Errorf("unexpected result for test %d: got: %v want: %v", i, v.RawVector(), test.want.RawVector())
+		}
+	}
+}
+
+func TestVecDenseDivElem(t *testing.T) {
+	for i, test := range []struct {
+		a, b *VecDense
+		want *VecDense
+	}{
+		{
+			a:    NewVecDense(3, []float64{0.5, 1, 2}),
+			b:    NewVecDense(3, []float64{0.5, 0.5, 1}),
+			want: NewVecDense(3, []float64{1, 2, 2}),
+		},
+		{
+			a:    NewVecDense(3, []float64{0.5, 1, 2}),
+			b:    NewDense(3, 1, []float64{0.5, 0.5, 1}).ColView(0),
+			want: NewVecDense(3, []float64{1, 2, 2}),
+		},
+		{
+			a:    NewDense(3, 1, []float64{0.5, 1, 2}).ColView(0),
+			b:    NewDense(3, 1, []float64{0.5, 0.5, 1}).ColView(0),
+			want: NewVecDense(3, []float64{1, 2, 2}),
+		},
+	} {
+		var v VecDense
+		v.DivElemVec(test.a, test.b)
+		if !reflect.DeepEqual(v.RawVector(), test.want.RawVector()) {
+			t.Errorf("unexpected result for test %d: got: %v want: %v", i, v.RawVector(), test.want.RawVector())
+		}
+	}
+}
+
+func BenchmarkAddScaledVec10Inc1(b *testing.B)      { addScaledVecBench(b, 10, 1) }
+func BenchmarkAddScaledVec100Inc1(b *testing.B)     { addScaledVecBench(b, 100, 1) }
+func BenchmarkAddScaledVec1000Inc1(b *testing.B)    { addScaledVecBench(b, 1000, 1) }
+func BenchmarkAddScaledVec10000Inc1(b *testing.B)   { addScaledVecBench(b, 10000, 1) }
+func BenchmarkAddScaledVec100000Inc1(b *testing.B)  { addScaledVecBench(b, 100000, 1) }
+func BenchmarkAddScaledVec10Inc2(b *testing.B)      { addScaledVecBench(b, 10, 2) }
+func BenchmarkAddScaledVec100Inc2(b *testing.B)     { addScaledVecBench(b, 100, 2) }
+func BenchmarkAddScaledVec1000Inc2(b *testing.B)    { addScaledVecBench(b, 1000, 2) }
+func BenchmarkAddScaledVec10000Inc2(b *testing.B)   { addScaledVecBench(b, 10000, 2) }
+func BenchmarkAddScaledVec100000Inc2(b *testing.B)  { addScaledVecBench(b, 100000, 2) }
+func BenchmarkAddScaledVec10Inc20(b *testing.B)     { addScaledVecBench(b, 10, 20) }
+func BenchmarkAddScaledVec100Inc20(b *testing.B)    { addScaledVecBench(b, 100, 20) }
+func BenchmarkAddScaledVec1000Inc20(b *testing.B)   { addScaledVecBench(b, 1000, 20) }
+func BenchmarkAddScaledVec10000Inc20(b *testing.B)  { addScaledVecBench(b, 10000, 20) }
+func BenchmarkAddScaledVec100000Inc20(b *testing.B) { addScaledVecBench(b, 100000, 20) }
+func addScaledVecBench(b *testing.B, size, inc int) {
+	x := randVecDense(size, inc, 1, rand.NormFloat64)
+	y := randVecDense(size, inc, 1, rand.NormFloat64)
+	b.ResetTimer()
+	var v VecDense
+	for i := 0; i < b.N; i++ {
+		v.AddScaledVec(y, 2, x)
+	}
+}
+
+func BenchmarkScaleVec10Inc1(b *testing.B)      { scaleVecBench(b, 10, 1) }
+func BenchmarkScaleVec100Inc1(b *testing.B)     { scaleVecBench(b, 100, 1) }
+func BenchmarkScaleVec1000Inc1(b *testing.B)    { scaleVecBench(b, 1000, 1) }
+func BenchmarkScaleVec10000Inc1(b *testing.B)   { scaleVecBench(b, 10000, 1) }
+func BenchmarkScaleVec100000Inc1(b *testing.B)  { scaleVecBench(b, 100000, 1) }
+func BenchmarkScaleVec10Inc2(b *testing.B)      { scaleVecBench(b, 10, 2) }
+func BenchmarkScaleVec100Inc2(b *testing.B)     { scaleVecBench(b, 100, 2) }
+func BenchmarkScaleVec1000Inc2(b *testing.B)    { scaleVecBench(b, 1000, 2) }
+func BenchmarkScaleVec10000Inc2(b *testing.B)   { scaleVecBench(b, 10000, 2) }
+func BenchmarkScaleVec100000Inc2(b *testing.B)  { scaleVecBench(b, 100000, 2) }
+func BenchmarkScaleVec10Inc20(b *testing.B)     { scaleVecBench(b, 10, 20) }
+func BenchmarkScaleVec100Inc20(b *testing.B)    { scaleVecBench(b, 100, 20) }
+func BenchmarkScaleVec1000Inc20(b *testing.B)   { scaleVecBench(b, 1000, 20) }
+func BenchmarkScaleVec10000Inc20(b *testing.B)  { scaleVecBench(b, 10000, 20) }
+func BenchmarkScaleVec100000Inc20(b *testing.B) { scaleVecBench(b, 100000, 20) }
+func scaleVecBench(b *testing.B, size, inc int) {
+	x := randVecDense(size, inc, 1, rand.NormFloat64)
+	b.ResetTimer()
+	var v VecDense
+	for i := 0; i < b.N; i++ {
+		v.ScaleVec(2, x)
+	}
+}
+
+func BenchmarkAddVec10Inc1(b *testing.B)      { addVecBench(b, 10, 1) }
+func BenchmarkAddVec100Inc1(b *testing.B)     { addVecBench(b, 100, 1) }
+func BenchmarkAddVec1000Inc1(b *testing.B)    { addVecBench(b, 1000, 1) }
+func BenchmarkAddVec10000Inc1(b *testing.B)   { addVecBench(b, 10000, 1) }
+func BenchmarkAddVec100000Inc1(b *testing.B)  { addVecBench(b, 100000, 1) }
+func BenchmarkAddVec10Inc2(b *testing.B)      { addVecBench(b, 10, 2) }
+func BenchmarkAddVec100Inc2(b *testing.B)     { addVecBench(b, 100, 2) }
+func BenchmarkAddVec1000Inc2(b *testing.B)    { addVecBench(b, 1000, 2) }
+func BenchmarkAddVec10000Inc2(b *testing.B)   { addVecBench(b, 10000, 2) }
+func BenchmarkAddVec100000Inc2(b *testing.B)  { addVecBench(b, 100000, 2) }
+func BenchmarkAddVec10Inc20(b *testing.B)     { addVecBench(b, 10, 20) }
+func BenchmarkAddVec100Inc20(b *testing.B)    { addVecBench(b, 100, 20) }
+func BenchmarkAddVec1000Inc20(b *testing.B)   { addVecBench(b, 1000, 20) }
+func BenchmarkAddVec10000Inc20(b *testing.B)  { addVecBench(b, 10000, 20) }
+func BenchmarkAddVec100000Inc20(b *testing.B) { addVecBench(b, 100000, 20) }
+func addVecBench(b *testing.B, size, inc int) {
+	x := randVecDense(size, inc, 1, rand.NormFloat64)
+	y := randVecDense(size, inc, 1, rand.NormFloat64)
+	b.ResetTimer()
+	var v VecDense
+	for i := 0; i < b.N; i++ {
+		v.AddVec(x, y)
+	}
+}
+
+func BenchmarkSubVec10Inc1(b *testing.B)      { subVecBench(b, 10, 1) }
+func BenchmarkSubVec100Inc1(b *testing.B)     { subVecBench(b, 100, 1) }
+func BenchmarkSubVec1000Inc1(b *testing.B)    { subVecBench(b, 1000, 1) }
+func BenchmarkSubVec10000Inc1(b *testing.B)   { subVecBench(b, 10000, 1) }
+func BenchmarkSubVec100000Inc1(b *testing.B)  { subVecBench(b, 100000, 1) }
+func BenchmarkSubVec10Inc2(b *testing.B)      { subVecBench(b, 10, 2) }
+func BenchmarkSubVec100Inc2(b *testing.B)     { subVecBench(b, 100, 2) }
+func BenchmarkSubVec1000Inc2(b *testing.B)    { subVecBench(b, 1000, 2) }
+func BenchmarkSubVec10000Inc2(b *testing.B)   { subVecBench(b, 10000, 2) }
+func BenchmarkSubVec100000Inc2(b *testing.B)  { subVecBench(b, 100000, 2) }
+func BenchmarkSubVec10Inc20(b *testing.B)     { subVecBench(b, 10, 20) }
+func BenchmarkSubVec100Inc20(b *testing.B)    { subVecBench(b, 100, 20) }
+func BenchmarkSubVec1000Inc20(b *testing.B)   { subVecBench(b, 1000, 20) }
+func BenchmarkSubVec10000Inc20(b *testing.B)  { subVecBench(b, 10000, 20) }
+func BenchmarkSubVec100000Inc20(b *testing.B) { subVecBench(b, 100000, 20) }
+func subVecBench(b *testing.B, size, inc int) {
+	x := randVecDense(size, inc, 1, rand.NormFloat64)
+	y := randVecDense(size, inc, 1, rand.NormFloat64)
+	b.ResetTimer()
+	var v VecDense
+	for i := 0; i < b.N; i++ {
+		v.SubVec(x, y)
+	}
+}
+
+func randVecDense(size, inc int, rho float64, rnd func() float64) *VecDense {
+	if size <= 0 {
+		panic("bad vector size")
+	}
+	data := make([]float64, size*inc)
+	for i := range data {
+		if rand.Float64() < rho {
+			data[i] = rnd()
+		}
+	}
+	return &VecDense{
+		mat: blas64.Vector{
+			Inc:  inc,
+			Data: data,
+		},
+		n: size,
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/README.md b/vendor/gonum.org/v1/gonum/mathext/README.md
new file mode 100644
index 00000000..b3bc6442
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/README.md
@@ -0,0 +1,3 @@
+# mathext [![GoDoc](https://godoc.org/gonum.org/v1/gonum/mathext?status.svg)](https://godoc.org/gonum.org/v1/gonum/mathext)
+
+Package mathext implements basic elementary functions not included in the Go standard library.
diff --git a/vendor/gonum.org/v1/gonum/mathext/airy.go b/vendor/gonum.org/v1/gonum/mathext/airy.go
new file mode 100644
index 00000000..1022e938
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/airy.go
@@ -0,0 +1,37 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mathext
+
+import "gonum.org/v1/gonum/mathext/internal/amos"
+
+// AiryAi returns the value of the Airy function at z. The Airy function here,
+// Ai(z), is one of the two linearly independent solutions to
+//  y'' - y*z = 0.
+// See http://mathworld.wolfram.com/AiryFunctions.html for more detailed information.
+func AiryAi(z complex128) complex128 {
+	// id specifies the order of the derivative to compute,
+	// 0 for the function itself and 1 for the derivative.
+	// kode specifies the scaling option. See the function
+	// documentation for the exact behavior.
+	id := 0
+	kode := 1
+	air, aii, _ := amos.Zairy(real(z), imag(z), id, kode)
+	return complex(air, aii)
+}
+
+// AiryAiDeriv returns the value of the derivative of the Airy function at z. The
+// Airy function here, Ai(z), is one of the two linearly independent solutions to
+//  y'' - y*z = 0.
+// See http://mathworld.wolfram.com/AiryFunctions.html for more detailed information.
+func AiryAiDeriv(z complex128) complex128 {
+	// id specifies the order of the derivative to compute,
+	// 0 for the function itself and 1 for the derivative.
+	// kode specifies the scaling option. See the function
+	// documentation for the exact behavior.
+	id := 1
+	kode := 1
+	air, aii, _ := amos.Zairy(real(z), imag(z), id, kode)
+	return complex(air, aii)
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/airy_test.go b/vendor/gonum.org/v1/gonum/mathext/airy_test.go
new file mode 100644
index 00000000..4359abd5
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/airy_test.go
@@ -0,0 +1,28 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mathext
+
+import (
+	"math"
+	"testing"
+)
+
+func TestAiry(t *testing.T) {
+	for _, test := range []struct {
+		z, ans complex128
+	}{
+		// Results computed using Octave.
+		{5, 1.08344428136074e-04},
+		{5i, 29.9014823980070 + 21.6778315987835i},
+	} {
+		ans := AiryAi(test.z)
+		if math.Abs(real(ans)-real(test.ans)) > 1e-10 {
+			t.Errorf("Real part mismatch. Got %v, want %v", real(ans), real(test.ans))
+		}
+		if math.Abs(imag(ans)-imag(test.ans)) > 1e-10 {
+			t.Errorf("Imaginary part mismatch. Got %v, want %v", imag(ans), imag(test.ans))
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/beta.go b/vendor/gonum.org/v1/gonum/mathext/beta.go
new file mode 100644
index 00000000..03f53f09
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/beta.go
@@ -0,0 +1,34 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mathext
+
+import "gonum.org/v1/gonum/mathext/internal/gonum"
+
+// Beta returns the value of the complete beta function B(a, b). It is defined as
+//  Γ(a)Γ(b) / Γ(a+b)
+// Special cases are:
+//  B(a,b) returns NaN if a or b is Inf
+//  B(a,b) returns NaN if a and b are 0
+//  B(a,b) returns NaN if a or b is NaN
+//  B(a,b) returns NaN if a or b is < 0
+//  B(a,b) returns +Inf if a xor b is 0.
+//
+// See http://mathworld.wolfram.com/BetaFunction.html for more detailed informations.
+func Beta(a, b float64) float64 {
+	return gonum.Beta(a, b)
+}
+
+// Lbeta returns the natural logarithm of the complete beta function B(a,b).
+// Lbeta is defined as:
+//  Ln(Γ(a)Γ(b)/Γ(a+b))
+// Special cases are:
+//  Lbeta(a,b) returns NaN if a or b is Inf
+//  Lbeta(a,b) returns NaN if a and b are 0
+//  Lbeta(a,b) returns NaN if a or b is NaN
+//  Lbeta(a,b) returns NaN if a or b is < 0
+//  Lbeta(a,b) returns +Inf if a xor b is 0.
+func Lbeta(a, b float64) float64 {
+	return gonum.Lbeta(a, b)
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/beta_test.go b/vendor/gonum.org/v1/gonum/mathext/beta_test.go
new file mode 100644
index 00000000..7e0cd4c8
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/beta_test.go
@@ -0,0 +1,177 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mathext_test
+
+import (
+	"math"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mathext"
+)
+
+var betaTests = []struct {
+	p, q float64
+	want float64
+}{
+	{
+		p:    1,
+		q:    2,
+		want: 0.5, // obtained from scipy.special.beta(1,2) (version=0.18.0)
+	},
+	{
+		p:    10,
+		q:    20,
+		want: 4.9925087406346778e-09, // obtained from scipy.special.beta(10,20) (version=0.18.0)
+	},
+	{
+		p:    +0,
+		q:    10,
+		want: math.Inf(+1),
+	},
+	{
+		p:    -0,
+		q:    10,
+		want: math.Inf(+1),
+	},
+	{
+		p:    0,
+		q:    0,
+		want: math.NaN(),
+	},
+	{
+		p:    0,
+		q:    math.Inf(-1),
+		want: math.NaN(),
+	},
+	{
+		p:    10,
+		q:    math.Inf(-1),
+		want: math.NaN(),
+	},
+	{
+		p:    0,
+		q:    math.Inf(+1),
+		want: math.NaN(),
+	},
+	{
+		p:    10,
+		q:    math.Inf(+1),
+		want: math.NaN(),
+	},
+	{
+		p:    math.NaN(),
+		q:    10,
+		want: math.NaN(),
+	},
+	{
+		p:    math.NaN(),
+		q:    0,
+		want: math.NaN(),
+	},
+	{
+		p:    -1,
+		q:    0,
+		want: math.NaN(),
+	},
+	{
+		p:    -1,
+		q:    +1,
+		want: math.NaN(),
+	},
+}
+
+func TestBeta(t *testing.T) {
+	for i, test := range betaTests {
+		v := mathext.Beta(test.p, test.q)
+		testOK := func(x float64) bool {
+			return floats.EqualWithinAbsOrRel(x, test.want, 1e-15, 1e-15) || (math.IsNaN(test.want) && math.IsNaN(x))
+		}
+		if !testOK(v) {
+			t.Errorf("test #%d: Beta(%v, %v)=%v. want=%v\n",
+				i, test.p, test.q, v, test.want,
+			)
+		}
+
+		u := mathext.Beta(test.q, test.p)
+		if !testOK(u) {
+			t.Errorf("test #%[1]d: Beta(%[2]v, %[3]v)=%[4]v != Beta(%[3]v, %[2]v)=%[5]v)\n",
+				i, test.p, test.q, v, u,
+			)
+		}
+
+		if math.IsInf(v, +1) || math.IsNaN(v) {
+			continue
+		}
+
+		vv := mathext.Beta(test.p, test.q+1)
+		uu := mathext.Beta(test.p+1, test.q)
+		if !floats.EqualWithinAbsOrRel(v, vv+uu, 1e-15, 1e-15) {
+			t.Errorf(
+				"test #%[1]d: Beta(%[2]v, %[3]v)=%[4]v != Beta(%[2]v+1, %[3]v) + Beta(%[2]v, %[3]v+1) (=%[5]v + %[6]v = %[7]v)\n",
+				i, test.p, test.q, v, uu, vv, uu+vv,
+			)
+		}
+
+		vbeta2 := beta2(test.p, test.q)
+		if !floats.EqualWithinAbsOrRel(v, vbeta2, 1e-15, 1e-15) {
+			t.Errorf(
+				"test #%[1]d: Beta(%[2]v, %[3]v) != Γ(p)Γ(q) / Γ(p+q) (v=%[4]v u=%[5]v)\n",
+				i, test.p, test.q, v, vbeta2,
+			)
+		}
+	}
+}
+
+func beta2(x, y float64) float64 {
+	return math.Gamma(x) * math.Gamma(y) / math.Gamma(x+y)
+}
+
+func BenchmarkBeta(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		_ = mathext.Beta(10, 20)
+	}
+}
+
+func BenchmarkBeta2(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		_ = math.Gamma(10) * math.Gamma(20) / math.Gamma(10+20)
+	}
+}
+
+func TestLbeta(t *testing.T) {
+	for i, test := range betaTests {
+		want := math.Log(test.want)
+		v := mathext.Lbeta(test.p, test.q)
+
+		testOK := func(x float64) bool {
+			return floats.EqualWithinAbsOrRel(x, want, 1e-15, 1e-15) || (math.IsNaN(want) && math.IsNaN(x))
+		}
+		if !testOK(v) {
+			t.Errorf("test #%d: Lbeta(%v, %v)=%v. want=%v\n",
+				i, test.p, test.q, v, want,
+			)
+		}
+
+		u := mathext.Lbeta(test.q, test.p)
+		if !testOK(u) {
+			t.Errorf("test #%[1]d: Lbeta(%[2]v, %[3]v)=%[4]v != Lbeta(%[3]v, %[2]v)=%[5]v)\n",
+				i, test.p, test.q, v, u,
+			)
+		}
+
+		if math.IsInf(v, +1) || math.IsNaN(v) {
+			continue
+		}
+
+		vbeta2 := math.Log(beta2(test.p, test.q))
+		if !floats.EqualWithinAbsOrRel(v, vbeta2, 1e-15, 1e-15) {
+			t.Errorf(
+				"test #%[1]d: Lbeta(%[2]v, %[3]v) != Log(Γ(p)Γ(q) / Γ(p+q)) (v=%[4]v u=%[5]v)\n",
+				i, test.p, test.q, v, vbeta2,
+			)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/betainc.go b/vendor/gonum.org/v1/gonum/mathext/betainc.go
new file mode 100644
index 00000000..77791ce9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/betainc.go
@@ -0,0 +1,29 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mathext
+
+import "gonum.org/v1/gonum/mathext/internal/cephes"
+
+// RegIncBeta returns the value of the regularized incomplete beta function
+// I(x;a,b). It is defined as
+//  I(x;a,b) = B(x;a,b) / B(a,b)
+//           = Γ(a+b) / (Γ(a)*Γ(b)) * int_0^x u^(a-1) * (1-u)^(b-1) du.
+// The domain of definition is 0 <= x <= 1, and the parameters a and b must be positive.
+// For other values of x, a, and b RegIncBeta will panic.
+func RegIncBeta(a, b float64, x float64) float64 {
+	return cephes.Incbet(a, b, x)
+}
+
+// InvRegIncBeta computes the inverse of the regularized incomplete beta function.
+// It returns the x for which
+//  y = I(x;a,b)
+// The domain of definition is 0 <= y <= 1, and the parameters a and b must be
+// positive. For other values of x, a, and b InvRegIncBeta will panic.
+func InvRegIncBeta(a, b float64, y float64) float64 {
+	if y < 0 || y > 1 {
+		panic("mathext: parameter out of range")
+	}
+	return cephes.Incbi(a, b, y)
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/betainc_test.go b/vendor/gonum.org/v1/gonum/mathext/betainc_test.go
new file mode 100644
index 00000000..f1e0c950
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/betainc_test.go
@@ -0,0 +1,75 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mathext
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+func TestIncBeta(t *testing.T) {
+	tol := 1e-14
+	tol2 := 1e-10
+	// Test against values from scipy
+	for i, test := range []struct {
+		a, b, x, ans float64
+	}{
+		{1, 1, 0.8, 0.8},
+		{1, 5, 0.8, 0.99968000000000001},
+		{10, 10, 0.8, 0.99842087945083291},
+		{10, 10, 0.1, 3.929882327128003e-06},
+		{10, 2, 0.4, 0.00073400320000000028},
+		{0.1, 0.2, 0.6, 0.69285678232066683},
+		{1, 10, 0.7489, 0.99999900352334858},
+	} {
+		y := RegIncBeta(test.a, test.b, test.x)
+		if !floats.EqualWithinAbsOrRel(y, test.ans, tol, tol) {
+			t.Errorf("Incomplete beta mismatch. Case %v: Got %v, want %v", i, y, test.ans)
+		}
+
+		yc := 1 - RegIncBeta(test.b, test.a, 1-test.x)
+		if !floats.EqualWithinAbsOrRel(y, yc, tol, tol) {
+			t.Errorf("Incomplete beta complementary mismatch. Case %v: Got %v, want %v", i, y, yc)
+		}
+
+		x := InvRegIncBeta(test.a, test.b, y)
+		if !floats.EqualWithinAbsOrRel(x, test.x, tol2, tol2) {
+			t.Errorf("Inverse incomplete beta mismatch. Case %v: Got %v, want %v", i, x, test.x)
+		}
+	}
+
+	// Confirm that Invincbeta and Incbeta agree. Sweep over a variety of
+	// a, b, and y values.
+	tol = 1e-6
+	steps := 201
+	ints := make([]float64, steps)
+	floats.Span(ints, 0, 1)
+
+	sz := 51
+	min := 1e-2
+	max := 1e2
+	as := make([]float64, sz)
+	floats.LogSpan(as, min, max)
+	bs := make([]float64, sz)
+	floats.LogSpan(bs, min, max)
+
+	for _, a := range as {
+		for _, b := range bs {
+			for _, yr := range ints {
+				x := InvRegIncBeta(a, b, yr)
+				if x > 1-1e-6 {
+					// Numerical error too large
+					continue
+				}
+				y := RegIncBeta(a, b, x)
+				if !floats.EqualWithinAbsOrRel(yr, y, tol, tol) {
+					t.Errorf("Mismatch between inv inc beta and inc beta. a = %v, b = %v, x = %v, got %v, want %v.", a, b, x, y, yr)
+					break
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/digamma.go b/vendor/gonum.org/v1/gonum/mathext/digamma.go
new file mode 100644
index 00000000..81132dd1
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/digamma.go
@@ -0,0 +1,28 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mathext
+
+import (
+	"math"
+)
+
+// Digamma returns the logorithmic derivative of the gamma function at x.
+//  ψ(x) = d/dx (Ln (Γ(x)).
+// Note that if x is a negative integer in [-7, 0] this function will return
+// negative Inf.
+func Digamma(x float64) float64 {
+	// This is adapted from
+	// http://web.science.mq.edu.au/~mjohnson/code/digamma.c
+	var result float64
+	for ; x < 7.0; x++ {
+		result -= 1 / x
+	}
+	x -= 1.0 / 2.0
+	xx := 1.0 / x
+	xx2 := xx * xx
+	xx4 := xx2 * xx2
+	result += math.Log(x) + (1./24.)*xx2 - (7.0/960.0)*xx4 + (31.0/8064.0)*xx4*xx2 - (127.0/30720.0)*xx4*xx4
+	return result
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/digamma_test.go b/vendor/gonum.org/v1/gonum/mathext/digamma_test.go
new file mode 100644
index 00000000..0e113ed1
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/digamma_test.go
@@ -0,0 +1,27 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mathext
+
+import (
+	"math"
+	"testing"
+)
+
+func TestDigamma(t *testing.T) {
+	for i, test := range []struct {
+		x, want float64
+	}{
+		// Results computed using WolframAlpha.
+		{-100.5, 4.615124601338064117341315601525112558522917517910505881343},
+		{.5, -1.96351002602142347944097633299875556719315960466043},
+		{10, 2.251752589066721107647456163885851537211808918028330369448},
+		{math.Pow10(20), 46.05170185988091368035482909368728415202202143924212618733},
+	} {
+
+		if got := Digamma(test.x); math.Abs(got-test.want) > 1e-10 {
+			t.Errorf("test %d Digamma(%g) failed: got %g want %g", i, test.x, got, test.want)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/doc.go b/vendor/gonum.org/v1/gonum/mathext/doc.go
new file mode 100644
index 00000000..b1c350ee
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/doc.go
@@ -0,0 +1,7 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package mathext implements special math functions not implemented by the
+// Go standard library.
+package mathext // import "gonum.org/v1/gonum/mathext"
diff --git a/vendor/gonum.org/v1/gonum/mathext/ell_carlson.go b/vendor/gonum.org/v1/gonum/mathext/ell_carlson.go
new file mode 100644
index 00000000..159f0a9e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/ell_carlson.go
@@ -0,0 +1,156 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mathext
+
+import (
+	"math"
+)
+
+// EllipticRF computes the symmetric elliptic integral R_F(x,y,z):
+//  R_F(x,y,z) = (1/2)\int_{0}^{\infty}{1/s(t)} dt,
+//  s(t) = \sqrt{(t+x)(t+y)(t+z)}.
+//
+// The arguments x, y, z must satisfy the following conditions, otherwise the function returns math.NaN():
+//  0 ≤ x,y,z ≤ upper,
+//  lower ≤ x+y,y+z,z+x,
+// where:
+//  lower = 5/(2^1022) = 1.112536929253601e-307,
+//  upper = (2^1022)/5 = 8.988465674311580e+306.
+//
+// The definition of the symmetric elliptic integral R_F can be found in NIST
+// Digital Library of Mathematical Functions (http://dlmf.nist.gov/19.16.E1).
+func EllipticRF(x, y, z float64) float64 {
+	// The original Fortran code was published as Algorithm 577 in ACM TOMS (http://doi.org/10.1145/355958.355970).
+	// This code is also available as a part of SLATEC Common Mathematical Library (http://netlib.org/slatec/index.html). Later, Carlson described
+	// an improved version in http://dx.doi.org/10.1007/BF02198293 (also available at https://arxiv.org/abs/math/9409227).
+	const (
+		lower = 5.0 / (1 << 256) / (1 << 256) / (1 << 256) / (1 << 254) // 5*2^-1022
+		upper = 1 / lower
+		tol   = 1.2674918778210762260320167734407048051023273568443e-02 // (3ε)^(1/8)
+	)
+	if x < 0 || y < 0 || z < 0 || math.IsNaN(x) || math.IsNaN(y) || math.IsNaN(z) {
+		return math.NaN()
+	}
+	if upper < x || upper < y || upper < z {
+		return math.NaN()
+	}
+	if x+y < lower || y+z < lower || z+x < lower {
+		return math.NaN()
+	}
+
+	A0 := (x + y + z) / 3
+	An := A0
+	Q := math.Max(math.Max(math.Abs(A0-x), math.Abs(A0-y)), math.Abs(A0-z)) / tol
+	xn, yn, zn := x, y, z
+	mul := 1.0
+
+	for Q >= mul*math.Abs(An) {
+		xnsqrt, ynsqrt, znsqrt := math.Sqrt(xn), math.Sqrt(yn), math.Sqrt(zn)
+		lambda := xnsqrt*ynsqrt + ynsqrt*znsqrt + znsqrt*xnsqrt
+		An = (An + lambda) * 0.25
+		xn = (xn + lambda) * 0.25
+		yn = (yn + lambda) * 0.25
+		zn = (zn + lambda) * 0.25
+		mul *= 4
+	}
+
+	X := (A0 - x) / (mul * An)
+	Y := (A0 - y) / (mul * An)
+	Z := -(X + Y)
+	E2 := X*Y - Z*Z
+	E3 := X * Y * Z
+
+	// http://dlmf.nist.gov/19.36.E1
+	return (1 - 1/10.0*E2 + 1/14.0*E3 + 1/24.0*E2*E2 - 3/44.0*E2*E3 - 5/208.0*E2*E2*E2 + 3/104.0*E3*E3 + 1/16.0*E2*E2*E3) / math.Sqrt(An)
+}
+
+// EllipticRD computes the symmetric elliptic integral R_D(x,y,z):
+//  R_D(x,y,z) = (1/2)\int_{0}^{\infty}{1/(s(t)(t+z))} dt,
+//  s(t) = \sqrt{(t+x)(t+y)(t+z)}.
+//
+// The arguments x, y, z must satisfy the following conditions, otherwise the function returns math.NaN():
+//  0 ≤ x,y ≤ upper,
+//  lower ≤ z ≤ upper,
+//  lower ≤ x+y,
+// where:
+//  lower = (5/(2^1022))^(1/3) = 4.809554074311679e-103,
+//  upper = ((2^1022)/5)^(1/3) = 2.079194837087086e+102.
+//
+// The definition of the symmetric elliptic integral R_D can be found in NIST
+// Digital Library of Mathematical Functions (http://dlmf.nist.gov/19.16.E5).
+func EllipticRD(x, y, z float64) float64 {
+	// The original Fortran code was published as Algorithm 577 in ACM TOMS (http://doi.org/10.1145/355958.355970).
+	// This code is also available as a part of SLATEC Common Mathematical Library (http://netlib.org/slatec/index.html). Later, Carlson described
+	// an improved version in http://dx.doi.org/10.1007/BF02198293 (also available at https://arxiv.org/abs/math/9409227).
+	const (
+		lower = 4.8095540743116787026618007863123676393525016818363e-103 // (5*2^-1022)^(1/3)
+		upper = 1 / lower
+		tol   = 9.0351169339315770474760122547068324993857488849382e-03 // (ε/5)^(1/8)
+	)
+	if x < 0 || y < 0 || math.IsNaN(x) || math.IsNaN(y) || math.IsNaN(z) {
+		return math.NaN()
+	}
+	if upper < x || upper < y || upper < z {
+		return math.NaN()
+	}
+	if x+y < lower || z < lower {
+		return math.NaN()
+	}
+
+	A0 := (x + y + 3*z) / 5
+	An := A0
+	Q := math.Max(math.Max(math.Abs(A0-x), math.Abs(A0-y)), math.Abs(A0-z)) / tol
+	xn, yn, zn := x, y, z
+	mul, s := 1.0, 0.0
+
+	for Q >= mul*math.Abs(An) {
+		xnsqrt, ynsqrt, znsqrt := math.Sqrt(xn), math.Sqrt(yn), math.Sqrt(zn)
+		lambda := xnsqrt*ynsqrt + ynsqrt*znsqrt + znsqrt*xnsqrt
+		s += 1 / (mul * znsqrt * (zn + lambda))
+		An = (An + lambda) * 0.25
+		xn = (xn + lambda) * 0.25
+		yn = (yn + lambda) * 0.25
+		zn = (zn + lambda) * 0.25
+		mul *= 4
+	}
+
+	X := (A0 - x) / (mul * An)
+	Y := (A0 - y) / (mul * An)
+	Z := -(X + Y) / 3
+	E2 := X*Y - 6*Z*Z
+	E3 := (3*X*Y - 8*Z*Z) * Z
+	E4 := 3 * (X*Y - Z*Z) * Z * Z
+	E5 := X * Y * Z * Z * Z
+
+	// http://dlmf.nist.gov/19.36.E2
+	return (1-3/14.0*E2+1/6.0*E3+9/88.0*E2*E2-3/22.0*E4-9/52.0*E2*E3+3/26.0*E5-1/16.0*E2*E2*E2+3/40.0*E3*E3+3/20.0*E2*E4+45/272.0*E2*E2*E3-9/68.0*(E3*E4+E2*E5))/(mul*An*math.Sqrt(An)) + 3*s
+}
+
+// EllipticF computes the Legendre's elliptic integral of the 1st kind F(phi,m), 0≤m<1:
+//  F(\phi,m) = \int_{0}^{\phi} 1 / \sqrt{1-m\sin^2(\theta)} d\theta
+//
+// Legendre's elliptic integrals can be expressed as symmetric elliptic integrals, in this case:
+//  F(\phi,m) = \sin\phi R_F(\cos^2\phi,1-m\sin^2\phi,1)
+//
+// The definition of F(phi,k) where k=sqrt(m) can be found in NIST Digital Library of Mathematical
+// Functions (http://dlmf.nist.gov/19.2.E4).
+func EllipticF(phi, m float64) float64 {
+	s, c := math.Sincos(phi)
+	return s * EllipticRF(c*c, 1-m*s*s, 1)
+}
+
+// EllipticE computes the Legendre's elliptic integral of the 2nd kind E(phi,m), 0≤m<1:
+//  E(\phi,m) = \int_{0}^{\phi} \sqrt{1-m\sin^2(\theta)} d\theta
+//
+// Legendre's elliptic integrals can be expressed as symmetric elliptic integrals, in this case:
+//  E(\phi,m) = \sin\phi R_F(\cos^2\phi,1-m\sin^2\phi,1)-(m/3)\sin^3\phi R_D(\cos^2\phi,1-m\sin^2\phi,1)
+//
+// The definition of E(phi,k) where k=sqrt(m) can be found in NIST Digital Library of Mathematical
+// Functions (http://dlmf.nist.gov/19.2.E5).
+func EllipticE(phi, m float64) float64 {
+	s, c := math.Sincos(phi)
+	x, y := c*c, 1-m*s*s
+	return s * (EllipticRF(x, y, 1) - (m/3)*s*s*EllipticRD(x, y, 1))
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/ell_carlson_test.go b/vendor/gonum.org/v1/gonum/mathext/ell_carlson_test.go
new file mode 100644
index 00000000..4018bc1c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/ell_carlson_test.go
@@ -0,0 +1,103 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mathext
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+)
+
+// Testing EllipticF (and EllipticRF) using the addition theorems from http://dlmf.nist.gov/19.11.i
+func TestEllipticF(t *testing.T) {
+	const tol = 1.0e-14
+	rnd := rand.New(rand.NewSource(1))
+
+	// The following EllipticF(pi/3,m), m=0.1(0.1)0.9 was computed in Maxima 5.38.0 using Bigfloat arithmetic.
+	vF := [...]float64{
+		1.0631390181954904767742338285104637431858016483079,
+		1.0803778062523490005579242592072579594037132891908,
+		1.0991352230920430074586978843452269008747645822123,
+		1.1196949183404746257742176145632376703505764745654,
+		1.1424290580457772555013955266260457822322036529624,
+		1.1678400583161860445148860686430780757517286094732,
+		1.1966306515644649360767197589467723191317720122309,
+		1.2298294422249382706933871574135731278765534034979,
+		1.2690359140762658660446752406901433173504503955036,
+	}
+	phi := math.Pi / 3
+	for m := 1; m <= 9; m++ {
+		mf := float64(m) / 10
+		delta := math.Abs(EllipticF(phi, mf) - vF[m-1])
+		if delta > tol {
+			t.Fatalf("EllipticF(pi/3,m) test fail for m=%v", mf)
+		}
+	}
+
+	for test := 0; test < 100; test++ {
+		alpha := rnd.Float64() * math.Pi / 4
+		beta := rnd.Float64() * math.Pi / 4
+		for mi := 0; mi < 9999; mi++ {
+			m := float64(mi) / 10000
+			Fa := EllipticF(alpha, m)
+			Fb := EllipticF(beta, m)
+			sina, cosa := math.Sincos(alpha)
+			sinb, cosb := math.Sincos(beta)
+			tan := (sina*math.Sqrt(1-m*sinb*sinb) + sinb*math.Sqrt(1-m*sina*sina)) / (cosa + cosb)
+			gamma := 2 * math.Atan(tan)
+			Fg := EllipticF(gamma, m)
+			delta := math.Abs(Fa + Fb - Fg)
+			if delta > tol {
+				t.Fatalf("EllipticF test fail for m=%v, alpha=%v, beta=%v", m, alpha, beta)
+			}
+		}
+	}
+}
+
+// Testing EllipticE (and EllipticRF, EllipticRD) using the addition theorems from http://dlmf.nist.gov/19.11.i
+func TestEllipticE(t *testing.T) {
+	const tol = 1.0e-14
+	rnd := rand.New(rand.NewSource(1))
+
+	// The following EllipticE(pi/3,m), m=0.1(0.1)0.9 was computed in Maxima 5.38.0 using Bigfloat arithmetic.
+	vE := [...]float64{
+		1.0316510822817691068014397636905610074934300946730,
+		1.0156973658341766636288643556414001451527597364432,
+		9.9929636467826398814855428365155224243586391115108e-1,
+		9.8240033979859736941287149003648737502960015189033e-1,
+		9.6495145764299257550956863602992167490195750321518e-1,
+		9.4687829659158090935158610908054896203271861698355e-1,
+		9.2809053417715769009517654522979827392794124845027e-1,
+		9.0847044378047233264777277954768245721857017157916e-1,
+		8.8785835036531301307661603341327881634688308777383e-1,
+	}
+	phi := math.Pi / 3
+	for m := 1; m <= 9; m++ {
+		mf := float64(m) / 10
+		delta := math.Abs(EllipticE(phi, mf) - vE[m-1])
+		if delta > tol {
+			t.Fatalf("EllipticE(pi/3,m) test fail for m=%v", mf)
+		}
+	}
+
+	for test := 0; test < 100; test++ {
+		alpha := rnd.Float64() * math.Pi / 4
+		beta := rnd.Float64() * math.Pi / 4
+		for mi := 0; mi < 9999; mi++ {
+			m := float64(mi) / 10000
+			Ea := EllipticE(alpha, m)
+			Eb := EllipticE(beta, m)
+			sina, cosa := math.Sincos(alpha)
+			sinb, cosb := math.Sincos(beta)
+			tan := (sina*math.Sqrt(1-m*sinb*sinb) + sinb*math.Sqrt(1-m*sina*sina)) / (cosa + cosb)
+			gamma := 2 * math.Atan(tan)
+			Eg := EllipticE(gamma, m)
+			delta := math.Abs(Ea + Eb - Eg - m*sina*sinb*math.Sin(gamma))
+			if delta > tol {
+				t.Fatalf("EllipticE test fail for m=%v, alpha=%v, beta=%v", m, alpha, beta)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/ell_complete.go b/vendor/gonum.org/v1/gonum/mathext/ell_complete.go
new file mode 100644
index 00000000..08586ec0
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/ell_complete.go
@@ -0,0 +1,157 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mathext
+
+import (
+	"math"
+)
+
+// CompleteK computes the complete elliptic integral of the 1st kind, 0≤m≤1.
+// It returns math.NaN() if m is not in [0,1].
+//
+//	K(m) = \int_{0}^{\pi/2} 1 / {\sqrt{1-m{\sin^2\theta}}} d\theta
+//
+// See: http://dx.doi.org/10.1016/j.cam.2014.12.038 for the computation method.
+func CompleteK(m float64) float64 {
+	if m < 0 || 1 < m || math.IsNaN(m) {
+		return math.NaN()
+	}
+
+	mc := 1 - m
+
+	if mc > 0.592990 {
+		t := 2.45694208987494165*mc - 1.45694208987494165
+		p := 3703.75266375099019 + t*(5462.47093231923466+t*(2744.82029097576810+t*(543.839017382099411+t*(36.2381612593459565+t*0.393188651542789784))))
+		q := 2077.94377067058435 + t*(3398.00069767755460+t*(1959.05960044399275+t*(472.794455487539279+t*(43.5464368440078942+t))))
+		return p / q
+	}
+	if mc > 0.350756 {
+		t := 4.12823963605439369*mc - 1.44800482178389491
+		p := 4264.28203103974630 + t*(6341.90978213264024+t*(3214.59187442783167+t*(642.790566685354573+t*(43.2589626155454993+t*0.475223892294445943))))
+		q := 2125.06914237062279 + t*(3479.95663350926514+t*(2006.03187933518870+t*(482.900172581418890+t*(44.1848041560412224+t))))
+		return p / q
+	}
+	if mc > 0.206924 {
+		t := 6.95255575949719117*mc - 1.43865064797819679
+		p := 4870.25402224986382 + t*(7307.18826377416591+t*(3738.29369283392307+t*(754.928587580583704+t*(51.3609902253065926+t*0.571948962277566451))))
+		q := 2172.51745704102287 + t*(3565.04737778032566+t*(2056.13612019430497+t*(493.962405117599400+t*(44.9026847057686146+t))))
+		return p / q
+	}
+	if mc > 0.121734 {
+		t := 11.7384669562155183*mc - 1.42897053644793990
+		p := 5514.8512729127464 + t*(8350.4595896779631+t*(4313.60788246750934+t*(880.27903031894216+t*(60.598720224393536+t*0.68504458747933773))))
+		q := 2218.41682813309737 + t*(3650.41829123846319+t*(2107.97379949034285+t*(505.74295207655096+t*(45.6911096775045314+t))))
+		return p / q
+	}
+	if mc > 0.071412 {
+		t := 19.8720241643813839*mc - 1.41910098962680339
+		p := 6188.8743957372448 + t*(9459.3331440432847+t*(4935.41351498551527+t*(1018.21910476032105+t*(70.981049144472361+t*0.81599895108245948))))
+		q := 2260.73112539748448 + t*(3732.66955095581621+t*(2159.68721749761492+t*(517.86964191812384+t*(46.5298955058476510+t))))
+		return p / q
+	}
+	if mc > 0.041770 {
+		t := 33.7359152553808785*mc - 1.40914918021725929
+		p := 6879.5170681289562 + t*(10615.0836403687221+t*(5594.8381504799829+t*(1167.26108955935542+t*(82.452856129147838+t*0.96592719058503951))))
+		q := 2296.88303450660439 + t*(3807.37745652028212+t*(2208.74949754945558+t*(529.79651353072921+t*(47.3844470709989137+t))))
+		return p / q
+	}
+	if mc > 0.024360 {
+		t := 57.4382538770821367*mc - 1.39919586444572085
+		p := 7570.6827538712100 + t*(11792.9392624454532+t*(6279.2661370014890+t*(1325.01058966228180+t*(94.886883830605940+t*1.13537029594409690))))
+		q := 2324.04824540459984 + t*(3869.56755306385732+t*(2252.22250562615338+t*(540.85752251676412+t*(48.2089280211559345+t))))
+		return p / q
+	}
+	if mc > 0.014165 {
+		t := 98.0872976949485042*mc - 1.38940657184894556
+		p := 8247.2601660137746 + t*(12967.7060124572914+t*(6974.7495213178613+t*(1488.54008220335966+t*(108.098282908839979+t*1.32411616748380686))))
+		q := 2340.47337508405427 + t*(3915.63324533769906+t*(2287.70677154700516+t*(550.45072377717361+t*(48.9575432570382154+t))))
+		return p / q
+	}
+	if mc > 0.008213 {
+		t := 168.010752688172043*mc - 1.37987231182795699
+		p := 8894.2961573611293 + t*(14113.7038749808951+t*(7666.5611739483371+t*(1654.60731579994159+t*(121.863474964652041+t*1.53112170837206117))))
+		q := 2344.88618943372377 + t*(3942.81065054556536+t*(2313.28396270968662+t*(558.07615380622169+t*(49.5906602613891184+t))))
+		return p / q
+	}
+	if mc > 0 {
+		t := 1.0 - 121.758188238159016*mc
+		p := -math.Log(mc*0.0625) * (34813.4518336350547 + t*(235.767716637974271+t*0.199792723884069485)) / (69483.5736412906324 + t*(614.265044703187382+t))
+		q := -mc * (9382.53386835986099 + t*(51.6478985993381223+t*0.00410754154682816898)) / (37327.7262507318317 + t*(408.017247271148538+t))
+		return p + q
+	}
+
+	return math.Inf(1)
+}
+
+// CompleteE computes the complete elliptic integral of the 2nd kind, 0≤m≤1.
+// It returns math.NaN() if m is not in [0,1].
+//
+//	E(m) = \int_{0}^{\pi/2} {\sqrt{1-m{\sin^2\theta}}} d\theta
+//
+// See: http://dx.doi.org/10.1016/j.cam.2014.12.038 for the computation method.
+func CompleteE(m float64) float64 {
+	if m < 0 || 1 < m || math.IsNaN(m) {
+		return math.NaN()
+	}
+
+	mc := 1 - m
+
+	if mc > 0.566638 {
+		t := 2.30753965506897236*mc - 1.30753965506897236
+		p := 19702.2363352671642 + t*(31904.1559574281609+t*(18177.1879313824040+t*(4362.94760768571862+t*(409.975559128654710+t*10.3244775335024885))))
+		q := 14241.2135819448616 + t*(20909.9899599927367+t*(10266.4884503526076+t*(1934.86289070792954+t*(117.162100771599098+t))))
+		return p / q
+	}
+	if mc > 0.315153 {
+		t := 3.97638030101198879*mc - 1.25316818100483130
+		p := 16317.0721393008221 + t*(26627.8852140835023+t*(15129.4009798463159+t*(3574.15857605556033+t*(326.113727011739428+t*7.93163724081373477))))
+		q := 13047.1505096551210 + t*(19753.5762165922376+t*(9964.25173735060361+t*(1918.72232033637537+t*(117.670514069579649+t))))
+		return p / q
+	}
+	if mc > 0.171355 {
+		t := 6.95419964116329852*mc - 1.19163687951153702
+		p := 13577.3850240991520 + t*(22545.4744699553993+t*(12871.9137872656293+t*(3000.74575264868572+t*(263.964361648520708+t*6.08522443139677663))))
+		q := 11717.3306408059832 + t*(18431.1264424290258+t*(9619.40382323874064+t*(1904.06010727307491+t*(118.690522739531267+t))))
+		return p / q
+	}
+	if mc > 0.090670 {
+		t := 12.3938774245522712*mc - 1.12375286608415443
+		p := 11307.9485341543712 + t*(19328.6173704569489+t*(11208.6068472959372+t*(2596.54874477084334+t*(219.253495956962613+t*4.66931143174036616))))
+		q := 10307.6837501971393 + t*(16982.2450249024383+t*(9241.7604666150102+t*(1893.41905403040679+t*(120.498555754227847+t))))
+		return p / q
+	}
+	if mc > 0.046453 {
+		t := 22.6157360291290680*mc - 1.05056878576113260
+		p := 9383.1490856819874 + t*(16718.9730458676860+t*(9977.2498973537718+t*(2323.49987246555537+t*(188.618148076418837+t*3.59313532204509922))))
+		q := 8877.1964704758383 + t*(15450.0537230364062+t*(8840.2771293410661+t*(1889.13672102820913+t*(123.422125687316355+t))))
+		return p / q
+	}
+	if mc > 0.022912 {
+		t := 42.4790790535661187*mc - 0.973280659275306911
+		p := 7719.1171817802054 + t*(14521.7363804934985+t*(9045.3996063894006+t*(2149.92068078627829+t*(169.386557799782496+t*2.78515570453129137))))
+		q := 7479.7539074698012 + t*(13874.4978011497847+t*(8420.3848818926324+t*(1892.69753150329759+t*(127.802109608726363+t))))
+		return p / q
+	}
+	if mc > 0.010809 {
+		t := 82.6241427745187144*mc - 0.893084359249772784
+		p := 6261.6095608987273 + t*(12593.0874916293982+t*(8304.3265605809870+t*(2048.68391263416822+t*(159.371262600702237+t*2.18867046462858104))))
+		q := 6156.4532048239501 + t*(12283.8373999680518+t*(7979.7435857665227+t*(1903.60556312663537+t*(133.911640385965187+t))))
+		return p / q
+	}
+	if mc > 0.004841 {
+		t := 167.560321715817694*mc - 0.811159517426273458
+		p := 4978.06146583586728 + t*(10831.7178150656694+t*(7664.6703673290453+t*(1995.66437151562090+t*(156.689647694892782+t*1.75859085945198570))))
+		q := 4935.56743322938333 + t*(10694.5510113880077+t*(7506.8028283118051+t*(1918.38517009740321+t*(141.854303920116856+t))))
+		return p / q
+	}
+	if mc > 0 {
+		t := 1.0 - 206.568890725056806*mc
+		p := -mc * math.Log(mc*0.0625) * (41566.6612602868736 + t*(154.034981522913482+t*0.0618072471798575991)) / (165964.442527585615 + t*(917.589668642251803+t))
+		q := (132232.803956682877 + t*(353.375480007017643-t*1.40105837312528026)) / (132393.665743088043 + t*(192.112635228732532-t))
+		return p + q
+	}
+
+	return 1
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/ell_complete_test.go b/vendor/gonum.org/v1/gonum/mathext/ell_complete_test.go
new file mode 100644
index 00000000..54840c58
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/ell_complete_test.go
@@ -0,0 +1,27 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mathext
+
+import (
+	"math"
+	"testing"
+)
+
+// TestCompleteKE checks if the Legendre's relation for m=0.0001(0.0001)0.9999
+// is satisfied with accuracy 1e-14.
+func TestCompleteKE(t *testing.T) {
+	const tol = 1.0e-14
+
+	for m := 1; m <= 9999; m++ {
+		mf := float64(m) / 10000
+		mp := 1 - mf
+		K, Kp := CompleteK(mf), CompleteK(mp)
+		E, Ep := CompleteE(mf), CompleteE(mp)
+		legendre := math.Abs(E*Kp + Ep*K - K*Kp - math.Pi/2)
+		if legendre > tol {
+			t.Fatalf("legendre > tol: m=%v, legendre=%v, tol=%v", mf, legendre, tol)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/erf.go b/vendor/gonum.org/v1/gonum/mathext/erf.go
new file mode 100644
index 00000000..cee4dbc2
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/erf.go
@@ -0,0 +1,91 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mathext
+
+import "math"
+
+/*
+Copyright (c) 2012 The Probab Authors. All rights reserved.
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+* Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+* Redistributions in binary form must reproduce the above
+copyright notice, this list of conditions and the following disclaimer
+in the documentation and/or other materials provided with the
+distribution.
+* Neither the name of Google Inc. nor the names of its
+contributors may be used to endorse or promote products derived from
+this software without specific prior written permission.
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*/
+
+// NormalQuantile computes the quantile function (inverse CDF) of the standard
+// normal. NormalQuantile panics if the input p is less than 0 or greater than 1.
+func NormalQuantile(p float64) float64 {
+	switch {
+	case p < 0 || 1 < p:
+		panic("mathext: quantile out of bounds")
+	case p == 1:
+		return math.Inf(1)
+	case p == 0:
+		return math.Inf(-1)
+	}
+	// Compute rational approximation based on the value of p.
+
+	dp := p - 0.5
+	if math.Abs(dp) <= 0.425 {
+		z := 0.180625 - dp*dp
+		z1 := ((((((zQSA[0]*z+zQSA[1])*z+zQSA[2])*z+zQSA[3])*z+zQSA[4])*z+zQSA[5])*z+zQSA[6])*z + zQSA[7]
+		z2 := ((((((zQSB[0]*z+zQSB[1])*z+zQSB[2])*z+zQSB[3])*z+zQSB[4])*z+zQSB[5])*z+zQSB[6])*z + zQSB[7]
+		return dp * z1 / z2
+	}
+
+	if p < 0.5 {
+		r := math.Sqrt(-math.Log(p))
+		if r <= 5.0 {
+			z := r - 1.6
+			z1 := ((((((zQIA[0]*z+zQIA[1])*z+zQIA[2])*z+zQIA[3])*z+zQIA[4])*z+zQIA[5])*z+zQIA[6])*z + zQIA[7]
+			z2 := ((((((zQIB[0]*z+zQIB[1])*z+zQIB[2])*z+zQIB[3])*z+zQIB[4])*z+zQIB[5])*z+zQIB[6])*z + zQIB[7]
+			return -z1 / z2
+		}
+		z := r - 5
+		z1 := ((((((zQTA[0]*z+zQTA[1])*z+zQTA[2])*z+zQTA[3])*z+zQTA[4])*z+zQTA[5])*z+zQTA[6])*z + zQTA[7]
+		z2 := ((((((zQTB[0]*z+zQTB[1])*z+zQTB[2])*z+zQTB[3])*z+zQTB[4])*z+zQTB[5])*z+zQTB[6])*z + zQTB[7]
+		return -z1 / z2
+	}
+	r := math.Sqrt(-math.Log(1 - p))
+	if r <= 5.0 {
+		z := r - 1.6
+		z1 := ((((((zQIA[0]*z+zQIA[1])*z+zQIA[2])*z+zQIA[3])*z+zQIA[4])*z+zQIA[5])*z+zQIA[6])*z + zQIA[7]
+		z2 := ((((((zQIB[0]*z+zQIB[1])*z+zQIB[2])*z+zQIB[3])*z+zQIB[4])*z+zQIB[5])*z+zQIB[6])*z + zQIB[7]
+		return z1 / z2
+	}
+
+	z := r - 5
+	z1 := ((((((zQTA[0]*z+zQTA[1])*z+zQTA[2])*z+zQTA[3])*z+zQTA[4])*z+zQTA[5])*z+zQTA[6])*z + zQTA[7]
+	z2 := ((((((zQTB[0]*z+zQTB[1])*z+zQTB[2])*z+zQTB[3])*z+zQTB[4])*z+zQTB[5])*z+zQTB[6])*z + zQTB[7]
+	return z1 / z2
+}
+
+var (
+	zQSA = [...]float64{2509.0809287301226727, 33430.575583588128105, 67265.770927008700853, 45921.953931549871457, 13731.693765509461125, 1971.5909503065514427, 133.14166789178437745, 3.387132872796366608}
+	zQSB = [...]float64{5226.495278852854561, 28729.085735721942674, 39307.89580009271061, 21213.794301586595867, 5394.1960214247511077, 687.1870074920579083, 42.313330701600911252, 1.0}
+	zQIA = [...]float64{7.7454501427834140764e-4, 0.0227238449892691845833, 0.24178072517745061177, 1.27045825245236838258, 3.64784832476320460504, 5.7694972214606914055, 4.6303378461565452959, 1.42343711074968357734}
+	zQIB = [...]float64{1.05075007164441684324e-9, 5.475938084995344946e-4, 0.0151986665636164571966, 0.14810397642748007459, 0.68976733498510000455, 1.6763848301838038494, 2.05319162663775882187, 1.0}
+	zQTA = [...]float64{2.01033439929228813265e-7, 2.71155556874348757815e-5, 0.0012426609473880784386, 0.026532189526576123093, 0.29656057182850489123, 1.7848265399172913358, 5.4637849111641143699, 6.6579046435011037772}
+	zQTB = [...]float64{2.04426310338993978564e-15, 1.4215117583164458887e-7, 1.8463183175100546818e-5, 7.868691311456132591e-4, 0.0148753612908506148525, 0.13692988092273580531, 0.59983220655588793769, 1.0}
+)
diff --git a/vendor/gonum.org/v1/gonum/mathext/erf_test.go b/vendor/gonum.org/v1/gonum/mathext/erf_test.go
new file mode 100644
index 00000000..f698e51e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/erf_test.go
@@ -0,0 +1,69 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mathext
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+func TestNormalQuantile(t *testing.T) {
+	// Values from https://www.johndcook.com/blog/normal_cdf_inverse/
+	p := []float64{
+		0.0000001,
+		0.00001,
+		0.001,
+		0.05,
+		0.15,
+		0.25,
+		0.35,
+		0.45,
+		0.55,
+		0.65,
+		0.75,
+		0.85,
+		0.95,
+		0.999,
+		0.99999,
+		0.9999999,
+	}
+	ans := []float64{
+		-5.199337582187471,
+		-4.264890793922602,
+		-3.090232306167813,
+		-1.6448536269514729,
+		-1.0364333894937896,
+		-0.6744897501960817,
+		-0.38532046640756773,
+		-0.12566134685507402,
+		0.12566134685507402,
+		0.38532046640756773,
+		0.6744897501960817,
+		1.0364333894937896,
+		1.6448536269514729,
+		3.090232306167813,
+		4.264890793922602,
+		5.199337582187471,
+	}
+	for i, v := range p {
+		got := NormalQuantile(v)
+		if !floats.EqualWithinAbsOrRel(got, ans[i], 1e-10, 1e-10) {
+			t.Errorf("Quantile mismatch. Case %d, want: %v, got: %v", i, ans[i], got)
+		}
+	}
+}
+
+var nqtmp float64
+
+func BenchmarkNormalQuantile(b *testing.B) {
+	ps := make([]float64, 1000) // ensure there are small values
+	floats.Span(ps, 0, 1)
+	for i := 0; i < b.N; i++ {
+		for _, v := range ps {
+			nqtmp = NormalQuantile(v)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/gamma_inc.go b/vendor/gonum.org/v1/gonum/mathext/gamma_inc.go
new file mode 100644
index 00000000..db16dad9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/gamma_inc.go
@@ -0,0 +1,50 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mathext
+
+import (
+	"gonum.org/v1/gonum/mathext/internal/cephes"
+)
+
+// GammaInc computes the incomplete Gamma integral.
+//  GammaInc(a,x) = (1/ Γ(a)) \int_0^x e^{-t} t^{a-1} dt
+// The input argument a must be positive and x must be non-negative or GammaInc
+// will panic.
+//
+// See http://mathworld.wolfram.com/IncompleteGammaFunction.html
+// or https://en.wikipedia.org/wiki/Incomplete_gamma_function for more detailed
+// information.
+func GammaInc(a, x float64) float64 {
+	return cephes.Igam(a, x)
+}
+
+// GammaIncComp computes the complemented incomplete Gamma integral.
+//  GammaIncComp(a,x) = 1 - GammaInc(a,x)
+//                    = (1/ Γ(a)) \int_0^\infty e^{-t} t^{a-1} dt
+// The input argument a must be positive and x must be non-negative or
+// GammaIncComp will panic.
+func GammaIncComp(a, x float64) float64 {
+	return cephes.IgamC(a, x)
+}
+
+// GammaIncInv computes the inverse of the incomplete Gamma integral. That is,
+// it returns the x such that:
+//  GammaInc(a, x) = y
+// The input argument a must be positive and y must be between 0 and 1
+// inclusive or GammaIncInv will panic. GammaIncInv should return a positive
+// number, but can return NaN if there is a failure to converge.
+func GammaIncInv(a, y float64) float64 {
+	return gammaIncInv(a, y)
+}
+
+// GammaIncCompInv computes the inverse of the complemented incomplete Gamma
+// integral. That is, it returns the x such that:
+//  GammaIncComp(a, x) = y
+// The input argument a must be positive and y must be between 0 and 1
+// inclusive or GammaIncCompInv will panic. GammaIncCompInv should return a
+// positive number, but can return 0 even with non-zero y due to underflow.
+func GammaIncCompInv(a, y float64) float64 {
+	return cephes.IgamI(a, y)
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/gamma_inc_inv.go b/vendor/gonum.org/v1/gonum/mathext/gamma_inc_inv.go
new file mode 100644
index 00000000..650717b0
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/gamma_inc_inv.go
@@ -0,0 +1,56 @@
+// Derived from SciPy's special/c_misc/gammaincinv.c
+// https://github.com/scipy/scipy/blob/master/scipy/special/c_misc/gammaincinv.c
+
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mathext
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/mathext/internal/cephes"
+)
+
+const (
+	allowedATol = 1e-306
+	allowedRTol = 1e-6
+)
+
+func gammaInc(x float64, params []float64) float64 {
+	return cephes.Igam(params[0], x) - params[1]
+}
+
+// gammaIncInv is the inverse of the incomplete Gamma integral. That is, it
+// returns x such that:
+//  Igam(a, x) = y
+// The input argument a must be positive and y must be between 0 and 1
+// inclusive or gammaIncInv will panic. gammaIncInv should return a
+// positive number, but can return NaN if there is a failure to converge.
+func gammaIncInv(a, y float64) float64 {
+	// For y not small, we just use
+	//  IgamI(a, 1-y)
+	// (inverse of the complemented incomplete Gamma integral). For y small,
+	// however, 1-y is about 1, and we lose digits.
+	if a <= 0 || y <= 0 || y >= 0.25 {
+		return cephes.IgamI(a, 1-y)
+	}
+
+	lo := 0.0
+	flo := -y
+	hi := cephes.IgamI(a, 0.75)
+	fhi := 0.25 - y
+
+	params := []float64{a, y}
+
+	// Also, after we generate a small interval by bisection above, false
+	// position will do a large step from an interval of width ~1e-4 to ~1e-14
+	// in one step (a=10, x=0.05, but similar for other values).
+	result, bestX, _, errEst := falsePosition(lo, hi, flo, fhi, 2*machEp, 2*machEp, 1e-2*a, gammaInc, params)
+	if result == fSolveMaxIterations && errEst > allowedATol+allowedRTol*math.Abs(bestX) {
+		bestX = math.NaN()
+	}
+
+	return bestX
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/gamma_inc_test.go b/vendor/gonum.org/v1/gonum/mathext/gamma_inc_test.go
new file mode 100644
index 00000000..03d5f014
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/gamma_inc_test.go
@@ -0,0 +1,138 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mathext
+
+import (
+	"math"
+	"testing"
+)
+
+func TestGammaInc(t *testing.T) {
+	for i, test := range []struct {
+		a, x, want float64
+	}{
+		// Results computed using scipy.special.gamminc
+		{0, 0, 0},
+		{0.0001, 1, 0.99997805936186279},
+		{0.001, 0.005, 0.99528424172333985},
+		{0.01, 10, 0.99999995718295021},
+		{0.1, 10, 0.99999944520142825},
+		{0.25, 0.75, 0.89993651328449831},
+		{0.5, 0.5, 0.68268949213708596},
+		{0.5, 2, 0.95449973610364147},
+		{0.75, 2.5, 0.95053039734695643},
+		{1, 0.5, 0.39346934028736652},
+		{1, 1, 0.63212055882855778},
+		{1.5, 0.75, 0.31772966966378746},
+		{2.5, 1, 0.15085496391539038},
+		{3, 0.05, 2.0067493624397931e-05},
+		{3, 20, 0.99999954448504946},
+		{5, 50, 1},
+		{7, 10, 0.86985857911751696},
+		{10, 0.9, 4.2519575433351128e-08},
+		{10, 5, 0.031828057306204811},
+		{25, 10, 4.6949381426799868e-05},
+	} {
+		if got := GammaInc(test.a, test.x); math.Abs(got-test.want) > 1e-10 {
+			t.Errorf("test %d GammaInc(%g, %g) failed: got %g want %g", i, test.a, test.x, got, test.want)
+		}
+	}
+}
+
+func TestGammaIncComp(t *testing.T) {
+	for i, test := range []struct {
+		a, x, want float64
+	}{
+		// Results computed using scipy.special.gammincc
+		{0.00001, 0.075, 2.0866541002417804e-05},
+		{0.0001, 1, 2.1940638138146658e-05},
+		{0.001, 0.005, 0.0047157582766601536},
+		{0.01, 0.9, 0.0026263432520514662},
+		{0.25, 0.75, 0.10006348671550169},
+		{0.5, 0.5, 0.31731050786291404},
+		{0.75, 0.25, 0.65343980284081038},
+		{0.9, 0.01, 0.98359881081593148},
+		{1, 0, 1},
+		{1, 0.075, 0.92774348632855297},
+		{1, 1, 0.36787944117144233},
+		{1, 10, 4.5399929762484861e-05},
+		{1, math.Inf(1), 0},
+		{3, 20, 4.5551495055892125e-07},
+		{5, 10, 0.029252688076961127},
+		{10, 3, 0.99889751186988451},
+		{50, 25, 0.99999304669475242},
+		{100, 10, 1},
+		{500, 500, 0.49405285382921321},
+		{500, 550, 0.014614408126291296},
+	} {
+		if got := GammaIncComp(test.a, test.x); math.Abs(got-test.want) > 1e-10 {
+			t.Errorf("test %d GammaIncComp(%g, %g) failed: got %g want %g", i, test.a, test.x, got, test.want)
+		}
+	}
+}
+
+func TestGammaIncInv(t *testing.T) {
+	for i, test := range []struct {
+		a, x, want float64
+	}{
+		// Results computed using scipy.special.gammincinv
+		{0.001, 0.99, 2.4259428385570885e-05},
+		{0.01, 0.99, 0.26505255025157959},
+		{0.1, 0.5, 0.00059339110446022798},
+		{0.2, 0.8, 0.26354363204872067},
+		{0.25, 0.5, 0.043673802352873381},
+		{0.5, 0.25, 0.050765522133810789},
+		{0.5, 0.5, 0.22746821155978625},
+		{0.75, 0.25, 0.15340752707472377},
+		{1, 0, 0},
+		{1, 0.075, 0.077961541469711862},
+		{1, 1, math.Inf(1)},
+		{2.5, 0.99, 7.5431362346944937},
+		{10, 0.5, 9.6687146147141299},
+		{25, 0.01, 14.853341349420646},
+		{25, 0.99, 38.076945624506337},
+		{50, 0.75, 54.570620535040511},
+		{100, 0.25, 93.08583383712174},
+		{1000, 0.01, 927.90815979664251},
+		{1000, 0.99, 1075.0328320864389},
+		{10000, 0.5, 9999.6666686420485},
+	} {
+		if got := GammaIncInv(test.a, test.x); math.Abs(got-test.want) > 1e-10 {
+			t.Errorf("test %d GammaIncInv(%g, %g) failed: got %g want %g", i, test.a, test.x, got, test.want)
+		}
+	}
+}
+
+func TestGammaIncCompInv(t *testing.T) {
+	for i, test := range []struct {
+		a, x, want float64
+	}{
+		// Results computed using scipy.special.gamminccinv
+		{0.001, 0.01, 2.4259428385570885e-05},
+		{0.01, 0.01, 0.26505255025158292},
+		{0.03, 0.4, 2.316980536227699e-08},
+		{0.1, 0.5, 0.00059339110446022798},
+		{0.1, 0.75, 5.7917132949696076e-07},
+		{0.25, 0.25, 0.26062600197823282},
+		{0.5, 0.1, 1.3527717270477047},
+		{0.5, 0.5, 0.22746821155978625},
+		{0.75, 0.25, 1.0340914067758025},
+		{1, 0, math.Inf(1)},
+		{1, 0.5, 0.69314718055994529},
+		{1, 1, 0},
+		{3, 0.75, 1.727299417860519},
+		{25, 0.4, 25.945791937289371},
+		{25, 0.7, 22.156653488661991},
+		{10, 0.5, 9.6687146147141299},
+		{100, 0.25, 106.5510925269767},
+		{1000, 0.01, 1075.0328320864389},
+		{1000, 0.99, 927.90815979664251},
+		{10000, 0.5, 9999.6666686420485},
+	} {
+		if got := GammaIncCompInv(test.a, test.x); math.Abs(got-test.want) > 1e-10 {
+			t.Errorf("test %d GammaIncCompInv(%g, %g) failed: got %g want %g", i, test.a, test.x, got, test.want)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amos.go b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amos.go
new file mode 100644
index 00000000..2bd74d43
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amos.go
@@ -0,0 +1,2154 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package amos
+
+import (
+	"math"
+	"math/cmplx"
+)
+
+/*
+The AMOS functions are included in SLATEC, and the SLATEC guide (http://www.netlib.org/slatec/guide) explicitly states:
+"The Library is in the public domain and distributed by the Energy
+Science and Technology Software Center."
+Mention of AMOS's inclusion in SLATEC goes back at least to this 1985 technical report from Sandia National Labs: http://infoserve.sandia.gov/sand_doc/1985/851018.pdf
+*/
+
+// math.NaN() are for padding to keep indexing easy.
+var imach = []int{-0, 5, 6, 0, 0, 32, 4, 2, 31, 2147483647, 2, 24, -125, 127, 53, -1021, 1023}
+
+var dmach = []float64{math.NaN(), 2.23E-308, 1.79E-308, 1.11E-16, 2.22E-16, 0.30103000998497009}
+
+func abs(a int) int {
+	if a >= 0 {
+		return a
+	}
+	return -a
+}
+
+func min(a, b int) int {
+	if a < b {
+		return a
+	}
+	return b
+}
+
+func max(a, b int) int {
+	if a > b {
+		return a
+	}
+	return b
+}
+
+func Zairy(ZR, ZI float64, ID, KODE int) (AIR, AII float64, NZ int) {
+	// zairy is adapted from the original Netlib code by Donald Amos.
+	// http://www.netlib.no/netlib/amos/zairy.f
+
+	// Original comment:
+	/*
+		C***BEGIN PROLOGUE  ZAIRY
+		C***DATE WRITTEN   830501   (YYMMDD)
+		C***REVISION DATE  890801   (YYMMDD)
+		C***CATEGORY NO.  B5K
+		C***KEYWORDS  AIRY FUNCTION,BESSEL FUNCTIONS OF ORDER ONE THIRD
+		C***AUTHOR  AMOS, DONALD E., SANDIA NATIONAL LABORATORIES
+		C***PURPOSE  TO COMPUTE AIRY FUNCTIONS AI(Z) AND DAI(Z) FOR COMPLEX Z
+		C***DESCRIPTION
+		C
+		C                      ***A DOUBLE PRECISION ROUTINE***
+		C         ON KODE=1, ZAIRY COMPUTES THE COMPLEX AIRY FUNCTION AI(Z) OR
+		C         ITS DERIVATIVE DAI(Z)/DZ ON ID=0 OR ID=1 RESPECTIVELY. ON
+		C         KODE=2, A SCALING OPTION CEXP(ZTA)*AI(Z) OR CEXP(ZTA)*
+		C         DAI(Z)/DZ IS PROVIDED TO REMOVE THE EXPONENTIAL DECAY IN
+		C         -PI/3<ARG(Z)<PI/3 AND THE EXPONENTIAL GROWTH IN
+		C         PI/3<ABS(ARG(Z))<PI WHERE ZTA=(2/3)*Z*CSQRT(Z).
+		C
+		C         WHILE THE AIRY FUNCTIONS AI(Z) AND DAI(Z)/DZ ARE ANALYTIC IN
+		C         THE WHOLE Z PLANE, THE CORRESPONDING SCALED FUNCTIONS DEFINED
+		C         FOR KODE=2 HAVE A CUT ALONG THE NEGATIVE REAL AXIS.
+		C         DEFINTIONS AND NOTATION ARE FOUND IN THE NBS HANDBOOK OF
+		C         MATHEMATICAL FUNCTIONS (REF. 1).
+		C
+		C         INPUT      ZR,ZI ARE DOUBLE PRECISION
+		C           ZR,ZI  - Z=CMPLX(ZR,ZI)
+		C           ID     - ORDER OF DERIVATIVE, ID=0 OR ID=1
+		C           KODE   - A PARAMETER TO INDICATE THE SCALING OPTION
+		C                    KODE= 1  returnS
+		C                             AI=AI(Z)                ON ID=0 OR
+		C                             AI=DAI(Z)/DZ            ON ID=1
+		C                        = 2  returnS
+		C                             AI=CEXP(ZTA)*AI(Z)       ON ID=0 OR
+		C                             AI=CEXP(ZTA)*DAI(Z)/DZ   ON ID=1 WHERE
+		C                             ZTA=(2/3)*Z*CSQRT(Z)
+		C
+		C         OUTPUT     AIR,AII ARE DOUBLE PRECISION
+		C           AIR,AII- COMPLEX ANSWER DEPENDING ON THE CHOICES FOR ID AND
+		C                    KODE
+		C           NZ     - UNDERFLOW INDICATOR
+		C                    NZ= 0   , NORMAL return
+		C                    NZ= 1   , AI=CMPLX(0.0E0,0.0E0) DUE TO UNDERFLOW IN
+		C                              -PI/3<ARG(Z)<PI/3 ON KODE=1
+		C           IERR   - ERROR FLAG
+		C                    IERR=0, NORMAL return - COMPUTATION COMPLETED
+		C                    IERR=1, INPUT ERROR   - NO COMPUTATION
+		C                    IERR=2, OVERFLOW      - NO COMPUTATION, REAL(ZTA)
+		C                            TOO LARGE ON KODE=1
+		C                    IERR=3, CABS(Z) LARGE      - COMPUTATION COMPLETED
+		C                            LOSSES OF SIGNIFCANCE BY ARGUMENT REDUCTION
+		C                            PRODUCE LESS THAN HALF OF MACHINE ACCURACY
+		C                    IERR=4, CABS(Z) TOO LARGE  - NO COMPUTATION
+		C                            COMPLETE LOSS OF ACCURACY BY ARGUMENT
+		C                            REDUCTION
+		C                    IERR=5, ERROR              - NO COMPUTATION,
+		C                            ALGORITHM TERMINATION CONDITION NOT MET
+		C
+		C***LONG DESCRIPTION
+		C
+		C         AI AND DAI ARE COMPUTED FOR CABS(Z)>1.0 FROM THE K BESSEL
+		C         FUNCTIONS BY
+		C
+		C            AI(Z)=C*SQRT(Z)*K(1/3,ZTA) , DAI(Z)=-C*Z*K(2/3,ZTA)
+		C                           C=1.0/(PI*SQRT(3.0))
+		C                            ZTA=(2/3)*Z**(3/2)
+		C
+		C         WITH THE POWER SERIES FOR CABS(Z)<=1.0.
+		C
+		C         IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE-
+		C         MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z IS LARGE, LOSSES
+		C         OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR. CONSEQUENTLY, IF
+		C         THE MAGNITUDE OF ZETA=(2/3)*Z**1.5 EXCEEDS U1=SQRT(0.5/UR),
+		C         THEN LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR
+		C         FLAG IERR=3 IS TRIGGERED WHERE UR=math.Max(dmach[4),1.0D-18) IS
+		C         DOUBLE PRECISION UNIT ROUNDOFF LIMITED TO 18 DIGITS PRECISION.
+		C         ALSO, if THE MAGNITUDE OF ZETA IS LARGER THAN U2=0.5/UR, THEN
+		C         ALL SIGNIFICANCE IS LOST AND IERR=4. IN ORDER TO USE THE INT
+		C         FUNCTION, ZETA MUST BE FURTHER RESTRICTED NOT TO EXCEED THE
+		C         LARGEST INTEGER, U3=I1MACH(9). THUS, THE MAGNITUDE OF ZETA
+		C         MUST BE RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2,
+		C         AND U3 ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE
+		C         PRECISION ARITHMETIC AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE
+		C         PRECISION ARITHMETIC RESPECTIVELY. THIS MAKES U2 AND U3 LIMIT-
+		C         ING IN THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT THE MAG-
+		C         NITUDE OF Z CANNOT EXCEED 3.1E+4 IN SINGLE AND 2.1E+6 IN
+		C         DOUBLE PRECISION ARITHMETIC. THIS ALSO MEANS THAT ONE CAN
+		C         EXPECT TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES,
+		C         NO DIGITS IN SINGLE PRECISION AND ONLY 7 DIGITS IN DOUBLE
+		C         PRECISION ARITHMETIC. SIMILAR CONSIDERATIONS HOLD FOR OTHER
+		C         MACHINES.
+		C
+		C         THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX
+		C         BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT
+		C         ROUNDOFF,1.0E-18) IS THE NOMINAL PRECISION AND 10**S REPRE-
+		C         SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE
+		C         ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))),
+		C         ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF
+		C         CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY
+		C         HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN
+		C         ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY
+		C         SEVERAL ORDERS OF MAGNITUDE. if ONE COMPONENT IS 10**K LARGER
+		C         THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K,
+		C         0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS
+		C         THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER
+		C         COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY
+		C         BECAUSE, IN COMPLEX ARITHMETIC WITH PRECISION P, THE SMALLER
+		C         COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE
+		C         MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES,
+		C         THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P,
+		C         OR -PI/2+P.
+		C
+		C***REFERENCES  HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ
+		C                 AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF
+		C                 COMMERCE, 1955.
+		C
+		C               COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+		C                 AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983
+		C
+		C               A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+		C                 ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85-
+		C                 1018, MAY, 1985
+		C
+		C               A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+		C                 ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS.
+		C                 MATH. SOFTWARE, 1986
+	*/
+	var AI, CONE, CSQ, CY, S1, S2, TRM1, TRM2, Z, ZTA, Z3 complex128
+	var AA, AD, AK, ALIM, ATRM, AZ, AZ3, BK,
+		CC, CK, COEF, CONEI, CONER, CSQI, CSQR, C1, C2, DIG,
+		DK, D1, D2, ELIM, FID, FNU, PTR, RL, R1M5, SFAC, STI, STR,
+		S1I, S1R, S2I, S2R, TOL, TRM1I, TRM1R, TRM2I, TRM2R, TTH, ZEROI,
+		ZEROR, ZTAI, ZTAR, Z3I, Z3R, ALAZ, BB float64
+	var IERR, IFLAG, K, K1, K2, MR, NN int
+	var tmp complex128
+
+	// Extra element for padding.
+	CYR := []float64{math.NaN(), 0}
+	CYI := []float64{math.NaN(), 0}
+
+	_ = AI
+	_ = CONE
+	_ = CSQ
+	_ = CY
+	_ = S1
+	_ = S2
+	_ = TRM1
+	_ = TRM2
+	_ = Z
+	_ = ZTA
+	_ = Z3
+
+	TTH = 6.66666666666666667E-01
+	C1 = 3.55028053887817240E-01
+	C2 = 2.58819403792806799E-01
+	COEF = 1.83776298473930683E-01
+	ZEROR = 0
+	ZEROI = 0
+	CONER = 1
+	CONEI = 0
+
+	NZ = 0
+	if ID < 0 || ID > 1 {
+		IERR = 1
+	}
+	if KODE < 1 || KODE > 2 {
+		IERR = 1
+	}
+	if IERR != 0 {
+		return
+	}
+	AZ = cmplx.Abs(complex(ZR, ZI))
+	TOL = math.Max(dmach[4], 1.0E-18)
+	FID = float64(ID)
+	if AZ > 1.0E0 {
+		goto Seventy
+	}
+
+	// POWER SERIES FOR CABS(Z)<=1.
+	S1R = CONER
+	S1I = CONEI
+	S2R = CONER
+	S2I = CONEI
+	if AZ < TOL {
+		goto OneSeventy
+	}
+	AA = AZ * AZ
+	if AA < TOL/AZ {
+		goto Forty
+	}
+	TRM1R = CONER
+	TRM1I = CONEI
+	TRM2R = CONER
+	TRM2I = CONEI
+	ATRM = 1.0E0
+	STR = ZR*ZR - ZI*ZI
+	STI = ZR*ZI + ZI*ZR
+	Z3R = STR*ZR - STI*ZI
+	Z3I = STR*ZI + STI*ZR
+	AZ3 = AZ * AA
+	AK = 2.0E0 + FID
+	BK = 3.0E0 - FID - FID
+	CK = 4.0E0 - FID
+	DK = 3.0E0 + FID + FID
+	D1 = AK * DK
+	D2 = BK * CK
+	AD = math.Min(D1, D2)
+	AK = 24.0E0 + 9.0E0*FID
+	BK = 30.0E0 - 9.0E0*FID
+	for K = 1; K <= 25; K++ {
+		STR = (TRM1R*Z3R - TRM1I*Z3I) / D1
+		TRM1I = (TRM1R*Z3I + TRM1I*Z3R) / D1
+		TRM1R = STR
+		S1R = S1R + TRM1R
+		S1I = S1I + TRM1I
+		STR = (TRM2R*Z3R - TRM2I*Z3I) / D2
+		TRM2I = (TRM2R*Z3I + TRM2I*Z3R) / D2
+		TRM2R = STR
+		S2R = S2R + TRM2R
+		S2I = S2I + TRM2I
+		ATRM = ATRM * AZ3 / AD
+		D1 = D1 + AK
+		D2 = D2 + BK
+		AD = math.Min(D1, D2)
+		if ATRM < TOL*AD {
+			goto Forty
+		}
+		AK = AK + 18.0E0
+		BK = BK + 18.0E0
+	}
+Forty:
+	if ID == 1 {
+		goto Fifty
+	}
+	AIR = S1R*C1 - C2*(ZR*S2R-ZI*S2I)
+	AII = S1I*C1 - C2*(ZR*S2I+ZI*S2R)
+	if KODE == 1 {
+		return
+	}
+	tmp = cmplx.Sqrt(complex(ZR, ZI))
+	STR = real(tmp)
+	STI = imag(tmp)
+	ZTAR = TTH * (ZR*STR - ZI*STI)
+	ZTAI = TTH * (ZR*STI + ZI*STR)
+	tmp = cmplx.Exp(complex(ZTAR, ZTAI))
+	STR = real(tmp)
+	STI = imag(tmp)
+	PTR = AIR*STR - AII*STI
+	AII = AIR*STI + AII*STR
+	AIR = PTR
+	return
+
+Fifty:
+	AIR = -S2R * C2
+	AII = -S2I * C2
+	if AZ <= TOL {
+		goto Sixty
+	}
+	STR = ZR*S1R - ZI*S1I
+	STI = ZR*S1I + ZI*S1R
+	CC = C1 / (1.0E0 + FID)
+	AIR = AIR + CC*(STR*ZR-STI*ZI)
+	AII = AII + CC*(STR*ZI+STI*ZR)
+
+Sixty:
+	if KODE == 1 {
+		return
+	}
+	tmp = cmplx.Sqrt(complex(ZR, ZI))
+	STR = real(tmp)
+	STI = imag(tmp)
+	ZTAR = TTH * (ZR*STR - ZI*STI)
+	ZTAI = TTH * (ZR*STI + ZI*STR)
+	tmp = cmplx.Exp(complex(ZTAR, ZTAI))
+	STR = real(tmp)
+	STI = imag(tmp)
+	PTR = STR*AIR - STI*AII
+	AII = STR*AII + STI*AIR
+	AIR = PTR
+	return
+
+	// CASE FOR CABS(Z)>1.0.
+Seventy:
+	FNU = (1.0E0 + FID) / 3.0E0
+
+	/*
+	   SET PARAMETERS RELATED TO MACHINE CONSTANTS.
+	   TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0D-18.
+	   ELIM IS THE APPROXIMATE EXPONENTIAL OVER-&&UNDERFLOW LIMIT.
+	   EXP(-ELIM)<EXP(-ALIM)=EXP(-ELIM)/TOL    AND
+	   EXP(ELIM)>EXP(ALIM)=EXP(ELIM)*TOL       ARE INTERVALS NEAR
+	   UNDERFLOW&&OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE.
+	   RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR LA>=Z.
+	   DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG).
+	*/
+	K1 = imach[15]
+	K2 = imach[16]
+	R1M5 = dmach[5]
+
+	K = min(abs(K1), abs(K2))
+	ELIM = 2.303E0 * (float64(K)*R1M5 - 3.0E0)
+	K1 = imach[14] - 1
+	AA = R1M5 * float64(K1)
+	DIG = math.Min(AA, 18.0E0)
+	AA = AA * 2.303E0
+	ALIM = ELIM + math.Max(-AA, -41.45E0)
+	RL = 1.2E0*DIG + 3.0E0
+	ALAZ = math.Log(AZ)
+
+	// TEST FOR PROPER RANGE.
+	AA = 0.5E0 / TOL
+	BB = float64(float32(imach[9])) * 0.5E0
+	AA = math.Min(AA, BB)
+	AA = math.Pow(AA, TTH)
+	if AZ > AA {
+		goto TwoSixty
+	}
+	AA = math.Sqrt(AA)
+	if AZ > AA {
+		IERR = 3
+	}
+	tmp = cmplx.Sqrt(complex(ZR, ZI))
+	CSQR = real(tmp)
+	CSQI = imag(tmp)
+	ZTAR = TTH * (ZR*CSQR - ZI*CSQI)
+	ZTAI = TTH * (ZR*CSQI + ZI*CSQR)
+
+	//  RE(ZTA)<=0 WHEN RE(Z)<0, ESPECIALLY WHEN IM(Z) IS SMALL.
+	IFLAG = 0
+	SFAC = 1.0E0
+	AK = ZTAI
+	if ZR >= 0.0E0 {
+		goto Eighty
+	}
+	BK = ZTAR
+	CK = -math.Abs(BK)
+	ZTAR = CK
+	ZTAI = AK
+
+Eighty:
+	if ZI != 0.0E0 {
+		goto Ninety
+	}
+	if ZR > 0.0E0 {
+		goto Ninety
+	}
+	ZTAR = 0.0E0
+	ZTAI = AK
+Ninety:
+	AA = ZTAR
+	if AA >= 0.0E0 && ZR > 0.0E0 {
+		goto OneTen
+	}
+	if KODE == 2 {
+		goto OneHundred
+	}
+
+	// OVERFLOW TEST.
+	if AA > (-ALIM) {
+		goto OneHundred
+	}
+	AA = -AA + 0.25E0*ALAZ
+	IFLAG = 1
+	SFAC = TOL
+	if AA > ELIM {
+		goto TwoSeventy
+	}
+
+OneHundred:
+	// CBKNU AND CACON return EXP(ZTA)*K(FNU,ZTA) ON KODE=2.
+	MR = 1
+	if ZI < 0.0E0 {
+		MR = -1
+	}
+	ZTAR, ZTAI, FNU, KODE, MR, _, CYR, CYI, NN, RL, TOL, ELIM, ALIM = Zacai(ZTAR, ZTAI, FNU, KODE, MR, 1, CYR, CYI, NN, RL, TOL, ELIM, ALIM)
+	if NN < 0 {
+		goto TwoEighty
+	}
+	NZ = NZ + NN
+	goto OneThirty
+
+OneTen:
+	if KODE == 2 {
+		goto OneTwenty
+	}
+
+	// UNDERFLOW TEST.
+	if AA < ALIM {
+		goto OneTwenty
+	}
+	AA = -AA - 0.25E0*ALAZ
+	IFLAG = 2
+	SFAC = 1.0E0 / TOL
+	if AA < (-ELIM) {
+		goto TwoTen
+	}
+OneTwenty:
+	ZTAR, ZTAI, FNU, KODE, _, CYR, CYI, NZ, TOL, ELIM, ALIM = Zbknu(ZTAR, ZTAI, FNU, KODE, 1, CYR, CYI, NZ, TOL, ELIM, ALIM)
+
+OneThirty:
+	S1R = CYR[1] * COEF
+	S1I = CYI[1] * COEF
+	if IFLAG != 0 {
+		goto OneFifty
+	}
+	if ID == 1 {
+		goto OneFourty
+	}
+	AIR = CSQR*S1R - CSQI*S1I
+	AII = CSQR*S1I + CSQI*S1R
+	return
+OneFourty:
+	AIR = -(ZR*S1R - ZI*S1I)
+	AII = -(ZR*S1I + ZI*S1R)
+	return
+OneFifty:
+	S1R = S1R * SFAC
+	S1I = S1I * SFAC
+	if ID == 1 {
+		goto OneSixty
+	}
+	STR = S1R*CSQR - S1I*CSQI
+	S1I = S1R*CSQI + S1I*CSQR
+	S1R = STR
+	AIR = S1R / SFAC
+	AII = S1I / SFAC
+	return
+OneSixty:
+	STR = -(S1R*ZR - S1I*ZI)
+	S1I = -(S1R*ZI + S1I*ZR)
+	S1R = STR
+	AIR = S1R / SFAC
+	AII = S1I / SFAC
+	return
+OneSeventy:
+	AA = 1.0E+3 * dmach[1]
+	S1R = ZEROR
+	S1I = ZEROI
+	if ID == 1 {
+		goto OneNinety
+	}
+	if AZ <= AA {
+		goto OneEighty
+	}
+	S1R = C2 * ZR
+	S1I = C2 * ZI
+OneEighty:
+	AIR = C1 - S1R
+	AII = -S1I
+	return
+OneNinety:
+	AIR = -C2
+	AII = 0.0E0
+	AA = math.Sqrt(AA)
+	if AZ <= AA {
+		goto TwoHundred
+	}
+	S1R = 0.5E0 * (ZR*ZR - ZI*ZI)
+	S1I = ZR * ZI
+TwoHundred:
+	AIR = AIR + C1*S1R
+	AII = AII + C1*S1I
+	return
+TwoTen:
+	NZ = 1
+	AIR = ZEROR
+	AII = ZEROI
+	return
+TwoSeventy:
+	NZ = 0
+	IERR = 2
+	return
+TwoEighty:
+	if NN == (-1) {
+		goto TwoSeventy
+	}
+	NZ = 0
+	IERR = 5
+	return
+TwoSixty:
+	IERR = 4
+	NZ = 0
+	return
+}
+
+// sbknu computes the k bessel function in the right half z plane.
+func Zbknu(ZR, ZI, FNU float64, KODE, N int, YR, YI []float64, NZ int, TOL, ELIM, ALIM float64) (ZRout, ZIout, FNUout float64, KODEout, Nout int, YRout, YIout []float64, NZout int, TOLout, ELIMout, ALIMout float64) {
+	/* Old dimension comment.
+		DIMENSION YR(N), YI(N), CC(8), CSSR(3), CSRR(3), BRY(3), CYR(2),
+	     * CYI(2)
+	*/
+
+	// TODO(btracey): Find which of these are inputs/outputs/both and clean up
+	// the function call.
+	// YR and YI have length n (but n+1 with better indexing)
+	var AA, AK, ASCLE, A1, A2, BB, BK, CAZ,
+		CBI, CBR, CCHI, CCHR, CKI, CKR, COEFI, COEFR, CONEI, CONER,
+		CRSCR, CSCLR, CSHI, CSHR, CSI, CSR, CTWOR,
+		CZEROI, CZEROR, CZI, CZR, DNU, DNU2, DPI, ETEST, FC, FHS,
+		FI, FK, FKS, FMUI, FMUR, FPI, FR, G1, G2, HPI, PI, PR, PTI,
+		PTR, P1I, P1R, P2I, P2M, P2R, QI, QR, RAK, RCAZ, RTHPI, RZI,
+		RZR, R1, S, SMUI, SMUR, SPI, STI, STR, S1I, S1R, S2I, S2R, TM,
+		TTH, T1, T2, ELM, CELMR, ZDR, ZDI, AS, ALAS, HELIM float64
+
+	var I, IFLAG, INU, K, KFLAG, KK, KMAX, KODED, IDUM, J, IC, INUB, NW int
+
+	var sinh, cosh complex128
+	//var sin, cos float64
+
+	var tmp, p complex128
+	var CSSR, CSRR, BRY [4]float64
+	var CYR, CYI [3]float64
+
+	KMAX = 30
+	CZEROR = 0
+	CZEROI = 0
+	CONER = 1
+	CONEI = 0
+	CTWOR = 2
+	R1 = 2
+
+	DPI = 3.14159265358979324E0
+	RTHPI = 1.25331413731550025E0
+	SPI = 1.90985931710274403E0
+	HPI = 1.57079632679489662E0
+	FPI = 1.89769999331517738E0
+	TTH = 6.66666666666666666E-01
+
+	CC := [9]float64{math.NaN(), 5.77215664901532861E-01, -4.20026350340952355E-02,
+		-4.21977345555443367E-02, 7.21894324666309954E-03,
+		-2.15241674114950973E-04, -2.01348547807882387E-05,
+		1.13302723198169588E-06, 6.11609510448141582E-09}
+
+	CAZ = cmplx.Abs(complex(ZR, ZI))
+	CSCLR = 1.0E0 / TOL
+	CRSCR = TOL
+	CSSR[1] = CSCLR
+	CSSR[2] = 1.0E0
+	CSSR[3] = CRSCR
+	CSRR[1] = CRSCR
+	CSRR[2] = 1.0E0
+	CSRR[3] = CSCLR
+	BRY[1] = 1.0E+3 * dmach[1] / TOL
+	BRY[2] = 1.0E0 / BRY[1]
+	BRY[3] = dmach[2]
+	NZ = 0
+	IFLAG = 0
+	KODED = KODE
+	RCAZ = 1.0E0 / CAZ
+	STR = ZR * RCAZ
+	STI = -ZI * RCAZ
+	RZR = (STR + STR) * RCAZ
+	RZI = (STI + STI) * RCAZ
+	INU = int(float32(FNU + 0.5))
+	DNU = FNU - float64(INU)
+	if math.Abs(DNU) == 0.5E0 {
+		goto OneTen
+	}
+	DNU2 = 0.0E0
+	if math.Abs(DNU) > TOL {
+		DNU2 = DNU * DNU
+	}
+	if CAZ > R1 {
+		goto OneTen
+	}
+
+	// SERIES FOR CABS(Z)<=R1.
+	FC = 1.0E0
+	tmp = cmplx.Log(complex(RZR, RZI))
+	SMUR = real(tmp)
+	SMUI = imag(tmp)
+	FMUR = SMUR * DNU
+	FMUI = SMUI * DNU
+	tmp = complex(FMUR, FMUI)
+	sinh = cmplx.Sinh(tmp)
+	cosh = cmplx.Cosh(tmp)
+	CSHR = real(sinh)
+	CSHI = imag(sinh)
+	CCHR = real(cosh)
+	CCHI = imag(cosh)
+	if DNU == 0.0E0 {
+		goto Ten
+	}
+	FC = DNU * DPI
+	FC = FC / math.Sin(FC)
+	SMUR = CSHR / DNU
+	SMUI = CSHI / DNU
+Ten:
+	A2 = 1.0E0 + DNU
+
+	// GAM(1-Z)*GAM(1+Z)=PI*Z/SIN(PI*Z), T1=1/GAM(1-DNU), T2=1/GAM(1+DNU).
+	T2 = math.Exp(-dgamln(A2, IDUM))
+	T1 = 1.0E0 / (T2 * FC)
+	if math.Abs(DNU) > 0.1E0 {
+		goto Forty
+	}
+
+	// SERIES FOR F0 TO RESOLVE INDETERMINACY FOR SMALL ABS(DNU).
+	AK = 1.0E0
+	S = CC[1]
+	for K = 2; K <= 8; K++ {
+		AK = AK * DNU2
+		TM = CC[K] * AK
+		S = S + TM
+		if math.Abs(TM) < TOL {
+			goto Thirty
+		}
+	}
+Thirty:
+	G1 = -S
+	goto Fifty
+Forty:
+	G1 = (T1 - T2) / (DNU + DNU)
+Fifty:
+	G2 = (T1 + T2) * 0.5E0
+	FR = FC * (CCHR*G1 + SMUR*G2)
+	FI = FC * (CCHI*G1 + SMUI*G2)
+	tmp = cmplx.Exp(complex(FMUR, FMUI))
+	STR = real(tmp)
+	STI = imag(tmp)
+	PR = 0.5E0 * STR / T2
+	PI = 0.5E0 * STI / T2
+	tmp = complex(0.5, 0) / complex(STR, STI)
+	PTR = real(tmp)
+	PTI = imag(tmp)
+	QR = PTR / T1
+	QI = PTI / T1
+	S1R = FR
+	S1I = FI
+	S2R = PR
+	S2I = PI
+	AK = 1.0E0
+	A1 = 1.0E0
+	CKR = CONER
+	CKI = CONEI
+	BK = 1.0E0 - DNU2
+	if INU > 0 || N > 1 {
+		goto Eighty
+	}
+
+	// GENERATE K(FNU,Z), 0.0E0 <= FNU < 0.5E0 AND N=1.
+	if CAZ < TOL {
+		goto Seventy
+	}
+	tmp = complex(ZR, ZI) * complex(ZR, ZI)
+	CZR = real(tmp)
+	CZI = imag(tmp)
+	CZR = 0.25E0 * CZR
+	CZI = 0.25E0 * CZI
+	T1 = 0.25E0 * CAZ * CAZ
+Sixty:
+	FR = (FR*AK + PR + QR) / BK
+	FI = (FI*AK + PI + QI) / BK
+	STR = 1.0E0 / (AK - DNU)
+	PR = PR * STR
+	PI = PI * STR
+	STR = 1.0E0 / (AK + DNU)
+	QR = QR * STR
+	QI = QI * STR
+	STR = CKR*CZR - CKI*CZI
+	RAK = 1.0E0 / AK
+	CKI = (CKR*CZI + CKI*CZR) * RAK
+	CKR = STR * RAK
+	S1R = CKR*FR - CKI*FI + S1R
+	S1I = CKR*FI + CKI*FR + S1I
+	A1 = A1 * T1 * RAK
+	BK = BK + AK + AK + 1.0E0
+	AK = AK + 1.0E0
+	if A1 > TOL {
+		goto Sixty
+	}
+Seventy:
+	YR[1] = S1R
+	YI[1] = S1I
+	if KODED == 1 {
+		return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+	}
+	tmp = cmplx.Exp(complex(ZR, ZI))
+	STR = real(tmp)
+	STI = imag(tmp)
+	tmp = complex(S1R, S1I) * complex(STR, STI)
+	YR[1] = real(tmp)
+	YI[1] = imag(tmp)
+	return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+
+	// GENERATE K(DNU,Z) AND K(DNU+1,Z) FOR FORWARD RECURRENCE.
+Eighty:
+	if CAZ < TOL {
+		goto OneHundred
+	}
+	tmp = complex(ZR, ZI) * complex(ZR, ZI)
+	CZR = real(tmp)
+	CZI = imag(tmp)
+	CZR = 0.25E0 * CZR
+	CZI = 0.25E0 * CZI
+	T1 = 0.25E0 * CAZ * CAZ
+Ninety:
+	FR = (FR*AK + PR + QR) / BK
+	FI = (FI*AK + PI + QI) / BK
+	STR = 1.0E0 / (AK - DNU)
+	PR = PR * STR
+	PI = PI * STR
+	STR = 1.0E0 / (AK + DNU)
+	QR = QR * STR
+	QI = QI * STR
+	STR = CKR*CZR - CKI*CZI
+	RAK = 1.0E0 / AK
+	CKI = (CKR*CZI + CKI*CZR) * RAK
+	CKR = STR * RAK
+	S1R = CKR*FR - CKI*FI + S1R
+	S1I = CKR*FI + CKI*FR + S1I
+	STR = PR - FR*AK
+	STI = PI - FI*AK
+	S2R = CKR*STR - CKI*STI + S2R
+	S2I = CKR*STI + CKI*STR + S2I
+	A1 = A1 * T1 * RAK
+	BK = BK + AK + AK + 1.0E0
+	AK = AK + 1.0E0
+	if A1 > TOL {
+		goto Ninety
+	}
+OneHundred:
+	KFLAG = 2
+	A1 = FNU + 1.0E0
+	AK = A1 * math.Abs(SMUR)
+	if AK > ALIM {
+		KFLAG = 3
+	}
+	STR = CSSR[KFLAG]
+	P2R = S2R * STR
+	P2I = S2I * STR
+	tmp = complex(P2R, P2I) * complex(RZR, RZI)
+	S2R = real(tmp)
+	S2I = imag(tmp)
+	S1R = S1R * STR
+	S1I = S1I * STR
+	if KODED == 1 {
+		goto TwoTen
+	}
+	tmp = cmplx.Exp(complex(ZR, ZI))
+	FR = real(tmp)
+	FI = imag(tmp)
+	tmp = complex(S1R, S1I) * complex(FR, FI)
+	S1R = real(tmp)
+	S1I = imag(tmp)
+	tmp = complex(S2R, S2I) * complex(FR, FI)
+	S2R = real(tmp)
+	S2I = imag(tmp)
+	goto TwoTen
+
+	// IFLAG=0 MEANS NO UNDERFLOW OCCURRED
+	// IFLAG=1 MEANS AN UNDERFLOW OCCURRED- COMPUTATION PROCEEDS WITH
+	// KODED=2 AND A TEST FOR ON SCALE VALUES IS MADE DURING FORWARD RECURSION
+OneTen:
+	tmp = cmplx.Sqrt(complex(ZR, ZI))
+	STR = real(tmp)
+	STI = imag(tmp)
+	tmp = complex(RTHPI, CZEROI) / complex(STR, STI)
+	COEFR = real(tmp)
+	COEFI = imag(tmp)
+	KFLAG = 2
+	if KODED == 2 {
+		goto OneTwenty
+	}
+	if ZR > ALIM {
+		goto TwoNinety
+	}
+
+	STR = math.Exp(-ZR) * CSSR[KFLAG]
+	//sin, cos = math.Sincos(ZI)
+	STI = -STR * math.Sin(ZI)
+	STR = STR * math.Cos(ZI)
+	tmp = complex(COEFR, COEFI) * complex(STR, STI)
+	COEFR = real(tmp)
+	COEFI = imag(tmp)
+OneTwenty:
+	if math.Abs(DNU) == 0.5E0 {
+		goto ThreeHundred
+	}
+	// MILLER ALGORITHM FOR CABS(Z)>R1.
+	AK = math.Cos(DPI * DNU)
+	AK = math.Abs(AK)
+	if AK == CZEROR {
+		goto ThreeHundred
+	}
+	FHS = math.Abs(0.25E0 - DNU2)
+	if FHS == CZEROR {
+		goto ThreeHundred
+	}
+
+	// COMPUTE R2=F(E). if CABS(Z)>=R2, USE FORWARD RECURRENCE TO
+	// DETERMINE THE BACKWARD INDEX K. R2=F(E) IS A STRAIGHT LINE ON
+	// 12<=E<=60. E IS COMPUTED FROM 2**(-E)=B**(1-I1MACH(14))=
+	// TOL WHERE B IS THE BASE OF THE ARITHMETIC.
+	T1 = float64(imach[14] - 1)
+	T1 = T1 * dmach[5] * 3.321928094E0
+	T1 = math.Max(T1, 12.0E0)
+	T1 = math.Min(T1, 60.0E0)
+	T2 = TTH*T1 - 6.0E0
+	if ZR != 0.0E0 {
+		goto OneThirty
+	}
+	T1 = HPI
+	goto OneFourty
+OneThirty:
+	T1 = math.Atan(ZI / ZR)
+	T1 = math.Abs(T1)
+OneFourty:
+	if T2 > CAZ {
+		goto OneSeventy
+	}
+	// FORWARD RECURRENCE LOOP WHEN CABS(Z)>=R2.
+	ETEST = AK / (DPI * CAZ * TOL)
+	FK = CONER
+	if ETEST < CONER {
+		goto OneEighty
+	}
+	FKS = CTWOR
+	CKR = CAZ + CAZ + CTWOR
+	P1R = CZEROR
+	P2R = CONER
+	for I = 1; I <= KMAX; I++ {
+		AK = FHS / FKS
+		CBR = CKR / (FK + CONER)
+		PTR = P2R
+		P2R = CBR*P2R - P1R*AK
+		P1R = PTR
+		CKR = CKR + CTWOR
+		FKS = FKS + FK + FK + CTWOR
+		FHS = FHS + FK + FK
+		FK = FK + CONER
+		STR = math.Abs(P2R) * FK
+		if ETEST < STR {
+			goto OneSixty
+		}
+	}
+	goto ThreeTen
+OneSixty:
+	FK = FK + SPI*T1*math.Sqrt(T2/CAZ)
+	FHS = math.Abs(0.25 - DNU2)
+	goto OneEighty
+OneSeventy:
+	// COMPUTE BACKWARD INDEX K FOR CABS(Z)<R2.
+	A2 = math.Sqrt(CAZ)
+	AK = FPI * AK / (TOL * math.Sqrt(A2))
+	AA = 3.0E0 * T1 / (1.0E0 + CAZ)
+	BB = 14.7E0 * T1 / (28.0E0 + CAZ)
+	AK = (math.Log(AK) + CAZ*math.Cos(AA)/(1.0E0+0.008E0*CAZ)) / math.Cos(BB)
+	FK = 0.12125E0*AK*AK/CAZ + 1.5E0
+OneEighty:
+	// BACKWARD RECURRENCE LOOP FOR MILLER ALGORITHM.
+	K = int(float32(FK))
+	FK = float64(K)
+	FKS = FK * FK
+	P1R = CZEROR
+	P1I = CZEROI
+	P2R = TOL
+	P2I = CZEROI
+	CSR = P2R
+	CSI = P2I
+	for I = 1; I <= K; I++ {
+		A1 = FKS - FK
+		AK = (FKS + FK) / (A1 + FHS)
+		RAK = 2.0E0 / (FK + CONER)
+		CBR = (FK + ZR) * RAK
+		CBI = ZI * RAK
+		PTR = P2R
+		PTI = P2I
+		P2R = (PTR*CBR - PTI*CBI - P1R) * AK
+		P2I = (PTI*CBR + PTR*CBI - P1I) * AK
+		P1R = PTR
+		P1I = PTI
+		CSR = CSR + P2R
+		CSI = CSI + P2I
+		FKS = A1 - FK + CONER
+		FK = FK - CONER
+	}
+	// COMPUTE (P2/CS)=(P2/CABS(CS))*(CONJG(CS)/CABS(CS)) FOR BETTER SCALING.
+	TM = cmplx.Abs(complex(CSR, CSI))
+	PTR = 1.0E0 / TM
+	S1R = P2R * PTR
+	S1I = P2I * PTR
+	CSR = CSR * PTR
+	CSI = -CSI * PTR
+	tmp = complex(COEFR, COEFI) * complex(S1R, S1I)
+	STR = real(tmp)
+	STI = imag(tmp)
+	tmp = complex(STR, STI) * complex(CSR, CSI)
+	S1R = real(tmp)
+	S1I = imag(tmp)
+	if INU > 0 || N > 1 {
+		goto TwoHundred
+	}
+	ZDR = ZR
+	ZDI = ZI
+	if IFLAG == 1 {
+		goto TwoSeventy
+	}
+	goto TwoFourty
+TwoHundred:
+	// COMPUTE P1/P2=(P1/CABS(P2)*CONJG(P2)/CABS(P2) FOR SCALING.
+	TM = cmplx.Abs(complex(P2R, P2I))
+	PTR = 1.0E0 / TM
+	P1R = P1R * PTR
+	P1I = P1I * PTR
+	P2R = P2R * PTR
+	P2I = -P2I * PTR
+	tmp = complex(P1R, P1I) * complex(P2R, P2I)
+	PTR = real(tmp)
+	PTI = imag(tmp)
+	STR = DNU + 0.5E0 - PTR
+	STI = -PTI
+	tmp = complex(STR, STI) / complex(ZR, ZI)
+	STR = real(tmp)
+	STI = imag(tmp)
+	STR = STR + 1.0E0
+	tmp = complex(STR, STI) * complex(S1R, S1I)
+	S2R = real(tmp)
+	S2I = imag(tmp)
+
+	// FORWARD RECURSION ON THE THREE TERM RECURSION WITH RELATION WITH
+	// SCALING NEAR EXPONENT EXTREMES ON KFLAG=1 OR KFLAG=3
+TwoTen:
+	STR = DNU + 1.0E0
+	CKR = STR * RZR
+	CKI = STR * RZI
+	if N == 1 {
+		INU = INU - 1
+	}
+	if INU > 0 {
+		goto TwoTwenty
+	}
+	if N > 1 {
+		goto TwoFifteen
+	}
+	S1R = S2R
+	S1I = S2I
+TwoFifteen:
+	ZDR = ZR
+	ZDI = ZI
+	if IFLAG == 1 {
+		goto TwoSeventy
+	}
+	goto TwoFourty
+TwoTwenty:
+	INUB = 1
+	if IFLAG == 1 {
+		goto TwoSixtyOne
+	}
+TwoTwentyFive:
+	P1R = CSRR[KFLAG]
+	ASCLE = BRY[KFLAG]
+	for I = INUB; I <= INU; I++ {
+		STR = S2R
+		STI = S2I
+		S2R = CKR*STR - CKI*STI + S1R
+		S2I = CKR*STI + CKI*STR + S1I
+		S1R = STR
+		S1I = STI
+		CKR = CKR + RZR
+		CKI = CKI + RZI
+		if KFLAG >= 3 {
+			continue
+		}
+		P2R = S2R * P1R
+		P2I = S2I * P1R
+		STR = math.Abs(P2R)
+		STI = math.Abs(P2I)
+		P2M = math.Max(STR, STI)
+		if P2M <= ASCLE {
+			continue
+		}
+		KFLAG = KFLAG + 1
+		ASCLE = BRY[KFLAG]
+		S1R = S1R * P1R
+		S1I = S1I * P1R
+		S2R = P2R
+		S2I = P2I
+		STR = CSSR[KFLAG]
+		S1R = S1R * STR
+		S1I = S1I * STR
+		S2R = S2R * STR
+		S2I = S2I * STR
+		P1R = CSRR[KFLAG]
+	}
+	if N != 1 {
+		goto TwoFourty
+	}
+	S1R = S2R
+	S1I = S2I
+TwoFourty:
+	STR = CSRR[KFLAG]
+	YR[1] = S1R * STR
+	YI[1] = S1I * STR
+	if N == 1 {
+		return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+	}
+	YR[2] = S2R * STR
+	YI[2] = S2I * STR
+	if N == 2 {
+		return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+	}
+	KK = 2
+TwoFifty:
+	KK = KK + 1
+	if KK > N {
+		return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+	}
+	P1R = CSRR[KFLAG]
+	ASCLE = BRY[KFLAG]
+	for I = KK; I <= N; I++ {
+		P2R = S2R
+		P2I = S2I
+		S2R = CKR*P2R - CKI*P2I + S1R
+		S2I = CKI*P2R + CKR*P2I + S1I
+		S1R = P2R
+		S1I = P2I
+		CKR = CKR + RZR
+		CKI = CKI + RZI
+		P2R = S2R * P1R
+		P2I = S2I * P1R
+		YR[I] = P2R
+		YI[I] = P2I
+		if KFLAG >= 3 {
+			continue
+		}
+		STR = math.Abs(P2R)
+		STI = math.Abs(P2I)
+		P2M = math.Max(STR, STI)
+		if P2M <= ASCLE {
+			continue
+		}
+		KFLAG = KFLAG + 1
+		ASCLE = BRY[KFLAG]
+		S1R = S1R * P1R
+		S1I = S1I * P1R
+		S2R = P2R
+		S2I = P2I
+		STR = CSSR[KFLAG]
+		S1R = S1R * STR
+		S1I = S1I * STR
+		S2R = S2R * STR
+		S2I = S2I * STR
+		P1R = CSRR[KFLAG]
+	}
+	return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+
+	// IFLAG=1 CASES, FORWARD RECURRENCE ON SCALED VALUES ON UNDERFLOW.
+TwoSixtyOne:
+	HELIM = 0.5E0 * ELIM
+	ELM = math.Exp(-ELIM)
+	CELMR = ELM
+	ASCLE = BRY[1]
+	ZDR = ZR
+	ZDI = ZI
+	IC = -1
+	J = 2
+	for I = 1; I <= INU; I++ {
+		STR = S2R
+		STI = S2I
+		S2R = STR*CKR - STI*CKI + S1R
+		S2I = STI*CKR + STR*CKI + S1I
+		S1R = STR
+		S1I = STI
+		CKR = CKR + RZR
+		CKI = CKI + RZI
+		AS = cmplx.Abs(complex(S2R, S2I))
+		ALAS = math.Log(AS)
+		P2R = -ZDR + ALAS
+		if P2R < (-ELIM) {
+			goto TwoSixtyThree
+		}
+		tmp = cmplx.Log(complex(S2R, S2I))
+		STR = real(tmp)
+		STI = imag(tmp)
+		P2R = -ZDR + STR
+		P2I = -ZDI + STI
+		P2M = math.Exp(P2R) / TOL
+		// sin, cos = math.Sincos(P2I)
+		P1R = P2M * math.Cos(P2I)
+		P1I = P2M * math.Sin(P2I)
+		p = complex(P1R, P1I)
+		NW = Zuchk(p, ASCLE, TOL)
+		if NW != 0 {
+			goto TwoSixtyThree
+		}
+		J = 3 - J
+		CYR[J] = P1R
+		CYI[J] = P1I
+		if IC == (I - 1) {
+			goto TwoSixtyFour
+		}
+		IC = I
+		continue
+	TwoSixtyThree:
+		if ALAS < HELIM {
+			continue
+		}
+		ZDR = ZDR - ELIM
+		S1R = S1R * CELMR
+		S1I = S1I * CELMR
+		S2R = S2R * CELMR
+		S2I = S2I * CELMR
+	}
+	if N != 1 {
+		goto TwoSeventy
+	}
+	S1R = S2R
+	S1I = S2I
+	goto TwoSeventy
+TwoSixtyFour:
+	KFLAG = 1
+	INUB = I + 1
+	S2R = CYR[J]
+	S2I = CYI[J]
+	J = 3 - J
+	S1R = CYR[J]
+	S1I = CYI[J]
+	if INUB <= INU {
+		goto TwoTwentyFive
+	}
+	if N != 1 {
+		goto TwoFourty
+	}
+	S1R = S2R
+	S1I = S2I
+	goto TwoFourty
+TwoSeventy:
+	YR[1] = S1R
+	YI[1] = S1I
+	if N == 1 {
+		goto TwoEighty
+	}
+	YR[2] = S2R
+	YI[2] = S2I
+TwoEighty:
+	ASCLE = BRY[1]
+	ZDR, ZDI, FNU, N, YR, YI, NZ, RZR, RZI, ASCLE, TOL, ELIM = Zkscl(ZDR, ZDI, FNU, N, YR, YI, NZ, RZR, RZI, ASCLE, TOL, ELIM)
+	INU = N - NZ
+	if INU <= 0 {
+		return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+	}
+	KK = NZ + 1
+	S1R = YR[KK]
+	S1I = YI[KK]
+	YR[KK] = S1R * CSRR[1]
+	YI[KK] = S1I * CSRR[1]
+	if INU == 1 {
+		return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+	}
+	KK = NZ + 2
+	S2R = YR[KK]
+	S2I = YI[KK]
+	YR[KK] = S2R * CSRR[1]
+	YI[KK] = S2I * CSRR[1]
+	if INU == 2 {
+		return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+	}
+	T2 = FNU + float64(float32(KK-1))
+	CKR = T2 * RZR
+	CKI = T2 * RZI
+	KFLAG = 1
+	goto TwoFifty
+TwoNinety:
+
+	// SCALE BY math.Exp(Z), IFLAG = 1 CASES.
+
+	KODED = 2
+	IFLAG = 1
+	KFLAG = 2
+	goto OneTwenty
+
+	// FNU=HALF ODD INTEGER CASE, DNU=-0.5
+ThreeHundred:
+	S1R = COEFR
+	S1I = COEFI
+	S2R = COEFR
+	S2I = COEFI
+	goto TwoTen
+
+ThreeTen:
+	NZ = -2
+	return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+}
+
+// SET K FUNCTIONS TO ZERO ON UNDERFLOW, CONTINUE RECURRENCE
+// ON SCALED FUNCTIONS UNTIL TWO MEMBERS COME ON SCALE, THEN
+// return WITH MIN(NZ+2,N) VALUES SCALED BY 1/TOL.
+func Zkscl(ZRR, ZRI, FNU float64, N int, YR, YI []float64, NZ int, RZR, RZI, ASCLE, TOL, ELIM float64) (
+	ZRRout, ZRIout, FNUout float64, Nout int, YRout, YIout []float64, NZout int, RZRout, RZIout, ASCLEout, TOLout, ELIMout float64) {
+	var ACS, AS, CKI, CKR, CSI, CSR, FN, STR, S1I, S1R, S2I,
+		S2R, ZEROI, ZEROR, ZDR, ZDI, CELMR, ELM, HELIM, ALAS float64
+
+	var I, IC, KK, NN, NW int
+	var tmp, c complex128
+	var CYR, CYI [3]float64
+	var sin, cos float64
+
+	// DIMENSION YR(N), YI(N), CYR(2), CYI(2)
+	ZEROR = 0
+	ZEROI = 0
+	NZ = 0
+	IC = 0
+	NN = min(2, N)
+	for I = 1; I <= NN; I++ {
+		S1R = YR[I]
+		S1I = YI[I]
+		CYR[I] = S1R
+		CYI[I] = S1I
+		AS = cmplx.Abs(complex(S1R, S1I))
+		ACS = -ZRR + math.Log(AS)
+		NZ = NZ + 1
+		YR[I] = ZEROR
+		YI[I] = ZEROI
+		if ACS < (-ELIM) {
+			continue
+		}
+
+		tmp = cmplx.Log(complex(S1R, S1I))
+		CSR = real(tmp)
+		CSI = imag(tmp)
+		CSR = CSR - ZRR
+		CSI = CSI - ZRI
+		STR = math.Exp(CSR) / TOL
+		// sin, cos = math.Sincos(CSI)
+		CSR = STR * math.Cos(CSI)
+		CSI = STR * math.Sin(CSI)
+		c = complex(CSR, CSI)
+		NW = Zuchk(c, ASCLE, TOL)
+		if NW != 0 {
+			continue
+		}
+		YR[I] = CSR
+		YI[I] = CSI
+		IC = I
+		NZ = NZ - 1
+	}
+	if N == 1 {
+		return ZRR, ZRI, FNU, N, YR, YI, NZ, RZR, RZI, ASCLE, TOL, ELIM
+	}
+	if IC > 1 {
+		goto Twenty
+	}
+	YR[1] = ZEROR
+	YI[1] = ZEROI
+	NZ = 2
+Twenty:
+	if N == 2 {
+		return ZRR, ZRI, FNU, N, YR, YI, NZ, RZR, RZI, ASCLE, TOL, ELIM
+	}
+	if NZ == 0 {
+		return ZRR, ZRI, FNU, N, YR, YI, NZ, RZR, RZI, ASCLE, TOL, ELIM
+	}
+	FN = FNU + 1.0E0
+	CKR = FN * RZR
+	CKI = FN * RZI
+	S1R = CYR[1]
+	S1I = CYI[1]
+	S2R = CYR[2]
+	S2I = CYI[2]
+	HELIM = 0.5E0 * ELIM
+	ELM = math.Exp(-ELIM)
+	CELMR = ELM
+	ZDR = ZRR
+	ZDI = ZRI
+
+	// FIND TWO CONSECUTIVE Y VALUES ON SCALE. SCALE RECURRENCE IF
+	// S2 GETS LARGER THAN EXP(ELIM/2)
+	for I = 3; I <= N; I++ {
+		KK = I
+		CSR = S2R
+		CSI = S2I
+		S2R = CKR*CSR - CKI*CSI + S1R
+		S2I = CKI*CSR + CKR*CSI + S1I
+		S1R = CSR
+		S1I = CSI
+		CKR = CKR + RZR
+		CKI = CKI + RZI
+		AS = cmplx.Abs(complex(S2R, S2I))
+		ALAS = math.Log(AS)
+		ACS = -ZDR + ALAS
+		NZ = NZ + 1
+		YR[I] = ZEROR
+		YI[I] = ZEROI
+		if ACS < (-ELIM) {
+			goto TwentyFive
+		}
+		tmp = cmplx.Log(complex(S2R, S2I))
+		CSR = real(tmp)
+		CSI = imag(tmp)
+		CSR = CSR - ZDR
+		CSI = CSI - ZDI
+		STR = math.Exp(CSR) / TOL
+		sin, cos = math.Sincos(CSI)
+		CSR = STR * cos
+		CSI = STR * sin
+		c = complex(CSR, CSI)
+		NW = Zuchk(c, ASCLE, TOL)
+		if NW != 0 {
+			goto TwentyFive
+		}
+		YR[I] = CSR
+		YI[I] = CSI
+		NZ = NZ - 1
+		if IC == KK-1 {
+			goto Forty
+		}
+		IC = KK
+		continue
+	TwentyFive:
+		if ALAS < HELIM {
+			continue
+		}
+		ZDR = ZDR - ELIM
+		S1R = S1R * CELMR
+		S1I = S1I * CELMR
+		S2R = S2R * CELMR
+		S2I = S2I * CELMR
+	}
+	NZ = N
+	if IC == N {
+		NZ = N - 1
+	}
+	goto FourtyFive
+Forty:
+	NZ = KK - 2
+FourtyFive:
+	for I = 1; I <= NZ; I++ {
+		YR[I] = ZEROR
+		YI[I] = ZEROI
+	}
+	return ZRR, ZRI, FNU, N, YR, YI, NZ, RZR, RZI, ASCLE, TOL, ELIM
+}
+
+// Zuchk tests whether the magnitude of the real or imaginary part would
+// underflow when y is scaled by tol.
+//
+// y enters as a scaled quantity whose magnitude is greater than
+//  1e3 + 3*dmach(1)/tol
+// y is accepted if the underflow is at least one precision below the magnitude
+// of the largest component. Otherwise an underflow is assumed as the phase angle
+// does not have sufficient accuracy.
+func Zuchk(y complex128, scale, tol float64) int {
+	absR := math.Abs(real(y))
+	absI := math.Abs(imag(y))
+	minAbs := math.Min(absR, absI)
+	if minAbs > scale {
+		return 0
+	}
+	maxAbs := math.Max(absR, absI)
+	minAbs /= tol
+	if maxAbs < minAbs {
+		return 1
+	}
+	return 0
+}
+
+// ZACAI APPLIES THE ANALYTIC CONTINUATION FORMULA
+//
+//  K(FNU,ZN*EXP(MP))=K(FNU,ZN)*EXP(-MP*FNU) - MP*I(FNU,ZN)
+//        MP=PI*MR*CMPLX(0.0,1.0)
+//
+// TO CONTINUE THE K FUNCTION FROM THE RIGHT HALF TO THE LEFT
+// HALF Z PLANE FOR USE WITH ZAIRY WHERE FNU=1/3 OR 2/3 AND N=1.
+// ZACAI IS THE SAME AS ZACON WITH THE PARTS FOR LARGER ORDERS AND
+// RECURRENCE REMOVED. A RECURSIVE CALL TO ZACON CAN RESULT if ZACON
+// IS CALLED FROM ZAIRY.
+func Zacai(ZR, ZI, FNU float64, KODE, MR, N int, YR, YI []float64, NZ int, RL, TOL, ELIM, ALIM float64) (
+	ZRout, ZIout, FNUout float64, KODEout, MRout, Nout int, YRout, YIout []float64, NZout int, RLout, TOLout, ELIMout, ALIMout float64) {
+	var ARG, ASCLE, AZ, CSGNR, CSGNI, CSPNR,
+		CSPNI, C1R, C1I, C2R, C2I, DFNU, FMR, PI,
+		SGN, YY, ZNR, ZNI float64
+	var INU, IUF, NN, NW int
+	var zn, c1, c2, z complex128
+	var y []complex128
+	//var sin, cos float64
+
+	CYR := []float64{math.NaN(), 0, 0}
+	CYI := []float64{math.NaN(), 0, 0}
+
+	PI = math.Pi
+	NZ = 0
+	ZNR = -ZR
+	ZNI = -ZI
+	AZ = cmplx.Abs(complex(ZR, ZI))
+	NN = N
+	DFNU = FNU + float64(float32(N-1))
+	if AZ <= 2.0E0 {
+		goto Ten
+	}
+	if AZ*AZ*0.25 > DFNU+1.0E0 {
+		goto Twenty
+	}
+Ten:
+	// POWER SERIES FOR THE I FUNCTION.
+	z = complex(ZNR, ZNI)
+	y = make([]complex128, len(YR))
+	for i, v := range YR {
+		y[i] = complex(v, YI[i])
+	}
+	NW = Zseri(z, FNU, KODE, NN, y[1:], TOL, ELIM, ALIM)
+	for i, v := range y {
+		YR[i] = real(v)
+		YI[i] = imag(v)
+	}
+	goto Forty
+Twenty:
+	if AZ < RL {
+		goto Thirty
+	}
+	// ASYMPTOTIC EXPANSION FOR LARGE Z FOR THE I FUNCTION.
+	ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, RL, TOL, ELIM, ALIM = Zasyi(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, RL, TOL, ELIM, ALIM)
+	if NW < 0 {
+		goto Eighty
+	}
+	goto Forty
+Thirty:
+	// MILLER ALGORITHM NORMALIZED BY THE SERIES FOR THE I FUNCTION
+	ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, TOL = Zmlri(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, TOL)
+	if NW < 0 {
+		goto Eighty
+	}
+Forty:
+	// ANALYTIC CONTINUATION TO THE LEFT HALF PLANE FOR THE K FUNCTION.
+	ZNR, ZNI, FNU, KODE, _, CYR, CYI, NW, TOL, ELIM, ALIM = Zbknu(ZNR, ZNI, FNU, KODE, 1, CYR, CYI, NW, TOL, ELIM, ALIM)
+	if NW != 0 {
+		goto Eighty
+	}
+	FMR = float64(float32(MR))
+	SGN = -math.Copysign(PI, FMR)
+	CSGNR = 0.0E0
+	CSGNI = SGN
+	if KODE == 1 {
+		goto Fifty
+	}
+	YY = -ZNI
+	//sin, cos = math.Sincos(YY)
+	CSGNR = -CSGNI * math.Sin(YY)
+	CSGNI = CSGNI * math.Cos(YY)
+Fifty:
+	// CALCULATE CSPN=EXP(FNU*PI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE
+	// WHEN FNU IS LARGE
+	INU = int(float32(FNU))
+	ARG = (FNU - float64(float32(INU))) * SGN
+	//sin, cos = math.Sincos(ARG)
+	CSPNR = math.Cos(ARG)
+	CSPNI = math.Sin(ARG)
+	if INU%2 == 0 {
+		goto Sixty
+	}
+	CSPNR = -CSPNR
+	CSPNI = -CSPNI
+Sixty:
+	C1R = CYR[1]
+	C1I = CYI[1]
+	C2R = YR[1]
+	C2I = YI[1]
+	if KODE == 1 {
+		goto Seventy
+	}
+	IUF = 0
+	ASCLE = 1.0E+3 * dmach[1] / TOL
+	zn = complex(ZNR, ZNI)
+	c1 = complex(C1R, C1I)
+	c2 = complex(C2R, C2I)
+	c1, c2, NW, IUF = Zs1s2(zn, c1, c2, ASCLE, ALIM, IUF)
+	C1R = real(c1)
+	C1I = imag(c1)
+	C2R = real(c2)
+	C2I = imag(c2)
+	NZ = NZ + NW
+Seventy:
+	YR[1] = CSPNR*C1R - CSPNI*C1I + CSGNR*C2R - CSGNI*C2I
+	YI[1] = CSPNR*C1I + CSPNI*C1R + CSGNR*C2I + CSGNI*C2R
+	return ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, RL, TOL, ELIM, ALIM
+Eighty:
+	NZ = -1
+	if NW == -2 {
+		NZ = -2
+	}
+	return ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, RL, TOL, ELIM, ALIM
+}
+
+// ZASYI COMPUTES THE I BESSEL FUNCTION FOR REAL(Z)>=0.0 BY
+// MEANS OF THE ASYMPTOTIC EXPANSION FOR LARGE CABS(Z) IN THE
+// REGION CABS(Z)>MAX(RL,FNU*FNU/2). NZ=0 IS A NORMAL return.
+// NZ<0 INDICATES AN OVERFLOW ON KODE=1.
+func Zasyi(ZR, ZI, FNU float64, KODE, N int, YR, YI []float64, NZ int, RL, TOL, ELIM, ALIM float64) (
+	ZRout, ZIout, FNUout float64, KODEout, Nout int, YRout, YIout []float64, NZout int, RLout, TOLout, ELIMout, ALIMout float64) {
+	var AA, AEZ, AK, AK1I, AK1R, ARG, ARM, ATOL,
+		AZ, BB, BK, CKI, CKR, CONEI, CONER, CS1I, CS1R, CS2I, CS2R, CZI,
+		CZR, DFNU, DKI, DKR, DNU2, EZI, EZR, FDN, PI, P1I,
+		P1R, RAZ, RTPI, RTR1, RZI, RZR, S, SGN, SQK, STI, STR, S2I,
+		S2R, TZI, TZR, ZEROI, ZEROR float64
+
+	var I, IB, IL, INU, J, JL, K, KODED, M, NN int
+	var tmp complex128
+	// var sin, cos float64
+
+	PI = math.Pi
+	RTPI = 0.159154943091895336E0
+	ZEROR = 0
+	ZEROI = 0
+	CONER = 1
+	CONEI = 0
+
+	NZ = 0
+	AZ = cmplx.Abs(complex(ZR, ZI))
+	ARM = 1.0E3 * dmach[1]
+	RTR1 = math.Sqrt(ARM)
+	IL = min(2, N)
+	DFNU = FNU + float64(float32(N-IL))
+
+	// OVERFLOW TEST
+	RAZ = 1.0E0 / AZ
+	STR = ZR * RAZ
+	STI = -ZI * RAZ
+	AK1R = RTPI * STR * RAZ
+	AK1I = RTPI * STI * RAZ
+	tmp = cmplx.Sqrt(complex(AK1R, AK1I))
+	AK1R = real(tmp)
+	AK1I = imag(tmp)
+	CZR = ZR
+	CZI = ZI
+	if KODE != 2 {
+		goto Ten
+	}
+	CZR = ZEROR
+	CZI = ZI
+Ten:
+	if math.Abs(CZR) > ELIM {
+		goto OneHundred
+	}
+	DNU2 = DFNU + DFNU
+	KODED = 1
+	if (math.Abs(CZR) > ALIM) && (N > 2) {
+		goto Twenty
+	}
+	KODED = 0
+	tmp = cmplx.Exp(complex(CZR, CZI))
+	STR = real(tmp)
+	STI = imag(tmp)
+	tmp = complex(AK1R, AK1I) * complex(STR, STI)
+	AK1R = real(tmp)
+	AK1I = imag(tmp)
+Twenty:
+	FDN = 0.0E0
+	if DNU2 > RTR1 {
+		FDN = DNU2 * DNU2
+	}
+	EZR = ZR * 8.0E0
+	EZI = ZI * 8.0E0
+
+	// WHEN Z IS IMAGINARY, THE ERROR TEST MUST BE MADE RELATIVE TO THE
+	// FIRST RECIPROCAL POWER SINCE THIS IS THE LEADING TERM OF THE
+	// EXPANSION FOR THE IMAGINARY PART.
+	AEZ = 8.0E0 * AZ
+	S = TOL / AEZ
+	JL = int(float32(RL+RL)) + 2
+	P1R = ZEROR
+	P1I = ZEROI
+	if ZI == 0.0E0 {
+		goto Thirty
+	}
+
+	// CALCULATE EXP(PI*(0.5+FNU+N-IL)*I) TO MINIMIZE LOSSES OF
+	// SIGNIFICANCE WHEN FNU OR N IS LARGE
+	INU = int(float32(FNU))
+	ARG = (FNU - float64(float32(INU))) * PI
+	INU = INU + N - IL
+	//sin, cos = math.Sincos(ARG)
+	AK = -math.Sin(ARG)
+	BK = math.Cos(ARG)
+	if ZI < 0.0E0 {
+		BK = -BK
+	}
+	P1R = AK
+	P1I = BK
+	if INU%2 == 0 {
+		goto Thirty
+	}
+	P1R = -P1R
+	P1I = -P1I
+Thirty:
+	for K = 1; K <= IL; K++ {
+		SQK = FDN - 1.0E0
+		ATOL = S * math.Abs(SQK)
+		SGN = 1.0E0
+		CS1R = CONER
+		CS1I = CONEI
+		CS2R = CONER
+		CS2I = CONEI
+		CKR = CONER
+		CKI = CONEI
+		AK = 0.0E0
+		AA = 1.0E0
+		BB = AEZ
+		DKR = EZR
+		DKI = EZI
+		// TODO(btracey): This loop is executed tens of thousands of times. Why?
+		// is that really necessary?
+		for J = 1; J <= JL; J++ {
+			tmp = complex(CKR, CKI) / complex(DKR, DKI)
+			STR = real(tmp)
+			STI = imag(tmp)
+			CKR = STR * SQK
+			CKI = STI * SQK
+			CS2R = CS2R + CKR
+			CS2I = CS2I + CKI
+			SGN = -SGN
+			CS1R = CS1R + CKR*SGN
+			CS1I = CS1I + CKI*SGN
+			DKR = DKR + EZR
+			DKI = DKI + EZI
+			AA = AA * math.Abs(SQK) / BB
+			BB = BB + AEZ
+			AK = AK + 8.0E0
+			SQK = SQK - AK
+			if AA <= ATOL {
+				goto Fifty
+			}
+		}
+		goto OneTen
+	Fifty:
+		S2R = CS1R
+		S2I = CS1I
+		if ZR+ZR >= ELIM {
+			goto Sixty
+		}
+		TZR = ZR + ZR
+		TZI = ZI + ZI
+		tmp = cmplx.Exp(complex(-TZR, -TZI))
+		STR = real(tmp)
+		STI = imag(tmp)
+		tmp = complex(STR, STI) * complex(P1R, P1I)
+		STR = real(tmp)
+		STI = imag(tmp)
+		tmp = complex(STR, STI) * complex(CS2R, CS2I)
+		STR = real(tmp)
+		STI = imag(tmp)
+		S2R = S2R + STR
+		S2I = S2I + STI
+	Sixty:
+		FDN = FDN + 8.0E0*DFNU + 4.0E0
+		P1R = -P1R
+		P1I = -P1I
+		M = N - IL + K
+		YR[M] = S2R*AK1R - S2I*AK1I
+		YI[M] = S2R*AK1I + S2I*AK1R
+	}
+	if N <= 2 {
+		return ZR, ZI, FNU, KODE, N, YR, YI, NZ, RL, TOL, ELIM, ALIM
+	}
+	NN = N
+	K = NN - 2
+	AK = float64(float32(K))
+	STR = ZR * RAZ
+	STI = -ZI * RAZ
+	RZR = (STR + STR) * RAZ
+	RZI = (STI + STI) * RAZ
+	IB = 3
+	for I = IB; I <= NN; I++ {
+		YR[K] = (AK+FNU)*(RZR*YR[K+1]-RZI*YI[K+1]) + YR[K+2]
+		YI[K] = (AK+FNU)*(RZR*YI[K+1]+RZI*YR[K+1]) + YI[K+2]
+		AK = AK - 1.0E0
+		K = K - 1
+	}
+	if KODED == 0 {
+		return ZR, ZI, FNU, KODE, N, YR, YI, NZ, RL, TOL, ELIM, ALIM
+	}
+	tmp = cmplx.Exp(complex(CZR, CZI))
+	CKR = real(tmp)
+	CKI = imag(tmp)
+	for I = 1; I <= NN; I++ {
+		STR = YR[I]*CKR - YI[I]*CKI
+		YI[I] = YR[I]*CKI + YI[I]*CKR
+		YR[I] = STR
+	}
+	return ZR, ZI, FNU, KODE, N, YR, YI, NZ, RL, TOL, ELIM, ALIM
+OneHundred:
+	NZ = -1
+	return ZR, ZI, FNU, KODE, N, YR, YI, NZ, RL, TOL, ELIM, ALIM
+OneTen:
+	NZ = -2
+	return ZR, ZI, FNU, KODE, N, YR, YI, NZ, RL, TOL, ELIM, ALIM
+}
+
+// ZMLRI COMPUTES THE I BESSEL FUNCTION FOR RE(Z)>=0.0 BY THE
+// MILLER ALGORITHM NORMALIZED BY A NEUMANN SERIES.
+func Zmlri(ZR, ZI, FNU float64, KODE, N int, YR, YI []float64, NZ int, TOL float64) (
+	ZRout, ZIout, FNUout float64, KODEout, Nout int, YRout, YIout []float64, NZout int, TOLout float64) {
+	var ACK, AK, AP, AT, AZ, BK, CKI, CKR, CNORMI,
+		CNORMR, CONEI, CONER, FKAP, FKK, FLAM, FNF, PTI, PTR, P1I,
+		P1R, P2I, P2R, RAZ, RHO, RHO2, RZI, RZR, SCLE, STI, STR, SUMI,
+		SUMR, TFNF, TST, ZEROI, ZEROR float64
+	var I, IAZ, IDUM, IFNU, INU, ITIME, K, KK, KM, M int
+	var tmp complex128
+	ZEROR = 0
+	ZEROI = 0
+	CONER = 1
+	CONEI = 0
+
+	SCLE = dmach[1] / TOL
+	NZ = 0
+	AZ = cmplx.Abs(complex(ZR, ZI))
+	IAZ = int(float32(AZ))
+	IFNU = int(float32(FNU))
+	INU = IFNU + N - 1
+	AT = float64(float32(IAZ)) + 1.0E0
+	RAZ = 1.0E0 / AZ
+	STR = ZR * RAZ
+	STI = -ZI * RAZ
+	CKR = STR * AT * RAZ
+	CKI = STI * AT * RAZ
+	RZR = (STR + STR) * RAZ
+	RZI = (STI + STI) * RAZ
+	P1R = ZEROR
+	P1I = ZEROI
+	P2R = CONER
+	P2I = CONEI
+	ACK = (AT + 1.0E0) * RAZ
+	RHO = ACK + math.Sqrt(ACK*ACK-1.0E0)
+	RHO2 = RHO * RHO
+	TST = (RHO2 + RHO2) / ((RHO2 - 1.0E0) * (RHO - 1.0E0))
+	TST = TST / TOL
+
+	// COMPUTE RELATIVE TRUNCATION ERROR INDEX FOR SERIES.
+	//fmt.Println("before loop", P2R, P2I, CKR, CKI, RZR, RZI, TST, AK)
+	AK = AT
+	for I = 1; I <= 80; I++ {
+		PTR = P2R
+		PTI = P2I
+		P2R = P1R - (CKR*PTR - CKI*PTI)
+		P2I = P1I - (CKI*PTR + CKR*PTI)
+		P1R = PTR
+		P1I = PTI
+		CKR = CKR + RZR
+		CKI = CKI + RZI
+		AP = cmplx.Abs(complex(P2R, P2I))
+		if AP > TST*AK*AK {
+			goto Twenty
+		}
+		AK = AK + 1.0E0
+	}
+	goto OneTen
+Twenty:
+	I = I + 1
+	K = 0
+	if INU < IAZ {
+		goto Forty
+	}
+	// COMPUTE RELATIVE TRUNCATION ERROR FOR RATIOS.
+	P1R = ZEROR
+	P1I = ZEROI
+	P2R = CONER
+	P2I = CONEI
+	AT = float64(float32(INU)) + 1.0E0
+	STR = ZR * RAZ
+	STI = -ZI * RAZ
+	CKR = STR * AT * RAZ
+	CKI = STI * AT * RAZ
+	ACK = AT * RAZ
+	TST = math.Sqrt(ACK / TOL)
+	ITIME = 1
+	for K = 1; K <= 80; K++ {
+		PTR = P2R
+		PTI = P2I
+		P2R = P1R - (CKR*PTR - CKI*PTI)
+		P2I = P1I - (CKR*PTI + CKI*PTR)
+		P1R = PTR
+		P1I = PTI
+		CKR = CKR + RZR
+		CKI = CKI + RZI
+		AP = cmplx.Abs(complex(P2R, P2I))
+		if AP < TST {
+			continue
+		}
+		if ITIME == 2 {
+			goto Forty
+		}
+		ACK = cmplx.Abs(complex(CKR, CKI))
+		FLAM = ACK + math.Sqrt(ACK*ACK-1.0E0)
+		FKAP = AP / cmplx.Abs(complex(P1R, P1I))
+		RHO = math.Min(FLAM, FKAP)
+		TST = TST * math.Sqrt(RHO/(RHO*RHO-1.0E0))
+		ITIME = 2
+	}
+	goto OneTen
+Forty:
+	// BACKWARD RECURRENCE AND SUM NORMALIZING RELATION.
+	K = K + 1
+	KK = max(I+IAZ, K+INU)
+	FKK = float64(float32(KK))
+	P1R = ZEROR
+	P1I = ZEROI
+
+	// SCALE P2 AND SUM BY SCLE.
+	P2R = SCLE
+	P2I = ZEROI
+	FNF = FNU - float64(float32(IFNU))
+	TFNF = FNF + FNF
+	BK = dgamln(FKK+TFNF+1.0E0, IDUM) - dgamln(FKK+1.0E0, IDUM) - dgamln(TFNF+1.0E0, IDUM)
+	BK = math.Exp(BK)
+	SUMR = ZEROR
+	SUMI = ZEROI
+	KM = KK - INU
+	for I = 1; I <= KM; I++ {
+		PTR = P2R
+		PTI = P2I
+		P2R = P1R + (FKK+FNF)*(RZR*PTR-RZI*PTI)
+		P2I = P1I + (FKK+FNF)*(RZI*PTR+RZR*PTI)
+		P1R = PTR
+		P1I = PTI
+		AK = 1.0E0 - TFNF/(FKK+TFNF)
+		ACK = BK * AK
+		SUMR = SUMR + (ACK+BK)*P1R
+		SUMI = SUMI + (ACK+BK)*P1I
+		BK = ACK
+		FKK = FKK - 1.0E0
+	}
+	YR[N] = P2R
+	YI[N] = P2I
+	if N == 1 {
+		goto Seventy
+	}
+	for I = 2; I <= N; I++ {
+		PTR = P2R
+		PTI = P2I
+		P2R = P1R + (FKK+FNF)*(RZR*PTR-RZI*PTI)
+		P2I = P1I + (FKK+FNF)*(RZI*PTR+RZR*PTI)
+		P1R = PTR
+		P1I = PTI
+		AK = 1.0E0 - TFNF/(FKK+TFNF)
+		ACK = BK * AK
+		SUMR = SUMR + (ACK+BK)*P1R
+		SUMI = SUMI + (ACK+BK)*P1I
+		BK = ACK
+		FKK = FKK - 1.0E0
+		M = N - I + 1
+		YR[M] = P2R
+		YI[M] = P2I
+	}
+Seventy:
+	if IFNU <= 0 {
+		goto Ninety
+	}
+	for I = 1; I <= IFNU; I++ {
+		PTR = P2R
+		PTI = P2I
+		P2R = P1R + (FKK+FNF)*(RZR*PTR-RZI*PTI)
+		P2I = P1I + (FKK+FNF)*(RZR*PTI+RZI*PTR)
+		P1R = PTR
+		P1I = PTI
+		AK = 1.0E0 - TFNF/(FKK+TFNF)
+		ACK = BK * AK
+		SUMR = SUMR + (ACK+BK)*P1R
+		SUMI = SUMI + (ACK+BK)*P1I
+		BK = ACK
+		FKK = FKK - 1.0E0
+	}
+Ninety:
+	PTR = ZR
+	PTI = ZI
+	if KODE == 2 {
+		PTR = ZEROR
+	}
+	tmp = cmplx.Log(complex(RZR, RZI))
+	STR = real(tmp)
+	STI = imag(tmp)
+	P1R = -FNF*STR + PTR
+	P1I = -FNF*STI + PTI
+	AP = dgamln(1.0E0+FNF, IDUM)
+	PTR = P1R - AP
+	PTI = P1I
+
+	// THE DIVISION CEXP(PT)/(SUM+P2) IS ALTERED TO AVOID OVERFLOW
+	// IN THE DENOMINATOR BY SQUARING LARGE QUANTITIES.
+	P2R = P2R + SUMR
+	P2I = P2I + SUMI
+	AP = cmplx.Abs(complex(P2R, P2I))
+	P1R = 1.0E0 / AP
+	tmp = cmplx.Exp(complex(PTR, PTI))
+	STR = real(tmp)
+	STI = imag(tmp)
+	CKR = STR * P1R
+	CKI = STI * P1R
+	PTR = P2R * P1R
+	PTI = -P2I * P1R
+	tmp = complex(CKR, CKI) * complex(PTR, PTI)
+	CNORMR = real(tmp)
+	CNORMI = imag(tmp)
+	for I = 1; I <= N; I++ {
+		STR = YR[I]*CNORMR - YI[I]*CNORMI
+		YI[I] = YR[I]*CNORMI + YI[I]*CNORMR
+		YR[I] = STR
+	}
+	return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL
+OneTen:
+	NZ = -2
+	return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL
+}
+
+// Zseri computes the I bessel function for real(z) >= 0 by means of the power
+// series for large |z| in the region |z| <= 2*sqrt(fnu+1).
+//
+// nz = 0 is a normal return. nz > 0 means that the last nz components were set
+// to zero due to underflow. nz < 0 means that underflow occurred, but the
+// condition |z| <= 2*sqrt(fnu+1) was violated and the computation must be
+// completed in another routine with n -= abs(nz).
+func Zseri(z complex128, fnu float64, kode, n int, y []complex128, tol, elim, alim float64) (nz int) {
+	// TODO(btracey): The original fortran line is "ARM = 1.0D+3*D1MACH(1)". Evidently, in Fortran
+	// this is interpreted as one to the power of +3*D1MACH(1). While it is possible
+	// this was intentional, it seems unlikely.
+	arm := 1000 * dmach[1]
+	az := cmplx.Abs(z)
+	if az < arm {
+		for i := 0; i < n; i++ {
+			y[i] = 0
+		}
+		if fnu == 0 {
+			y[0] = 1
+			n--
+		}
+		if az == 0 {
+			return 0
+		}
+		return n
+	}
+	hz := 0.5 * z
+	var cz complex128
+	var acz float64
+	if az > math.Sqrt(arm) {
+		cz = hz * hz
+		acz = cmplx.Abs(cz)
+	}
+	NN := n
+	ck := cmplx.Log(hz)
+	var ak1 complex128
+	for {
+		dfnu := fnu + float64(NN-1)
+		// Underflow test.
+		ak1 = ck * complex(dfnu, 0)
+		ak := dgamln(dfnu+1, 0)
+		ak1 -= complex(ak, 0)
+		if kode == 2 {
+			ak1 -= complex(real(z), 0)
+		}
+		if real(ak1) > -elim {
+			break
+		}
+		nz++
+		y[NN-1] = 0
+		if acz > dfnu {
+			// Return with nz < 0 if abs(Z*Z/4)>fnu+u-nz-1 complete the calculation
+			// in cbinu with n = n - abs(nz).
+			nz *= -1
+			return nz
+		}
+		NN--
+		if NN == 0 {
+			return nz
+		}
+	}
+	crscr := 1.0
+	var flag int
+	var scale float64
+	aa := real(ak1)
+	if aa <= -alim {
+		flag = 1
+		crscr = tol
+		scale = arm / tol
+		aa -= math.Log(tol)
+	}
+	var w [2]complex128
+	for {
+		coef := cmplx.Exp(complex(aa, imag(ak1)))
+		atol := tol * acz / (fnu + float64(NN))
+		for i := 0; i < min(2, NN); i++ {
+			FNUP := fnu + float64(NN-i)
+			s1 := 1 + 0i
+			if acz >= tol*FNUP {
+				ak2 := 1 + 0i
+				ak := FNUP + 2
+				S := FNUP
+				scl := 2.0
+				first := true
+				for first || scl > atol {
+					ak2 = ak2 * cz * complex(1/S, 0)
+					scl *= acz / S
+					s1 += ak2
+					S += ak
+					ak += 2
+					first = false
+				}
+			}
+			s2 := s1 * coef
+			w[i] = s2
+			if flag == 1 {
+				if Zuchk(s2, scale, tol) != 0 {
+					var full bool
+					var dfnu float64
+					// This code is similar to the code that exists above. The
+					// code copying is here because the original Fortran used
+					// a goto to solve the loop-and-a-half problem. Removing the
+					// goto makes the behavior of the function and variable scoping
+					// much clearer, but requires copying this code due to Go's
+					// goto rules.
+					for {
+						if full {
+							dfnu = fnu + float64(NN-1)
+							// Underflow test.
+							ak1 = ck * complex(dfnu, 0)
+							ak1 -= complex(dgamln(dfnu+1, 0), 0)
+							if kode == 2 {
+								ak1 -= complex(real(z), 0)
+							}
+							if real(ak1) > -elim {
+								break
+							}
+						} else {
+							full = true
+						}
+						nz++
+						y[NN-1] = 0
+						if acz > dfnu {
+							// Return with nz < 0 if abs(Z*Z/4)>fnu+u-nz-1 complete the calculation
+							// in cbinu with n = n - abs(nz).
+							nz *= -1
+							return nz
+						}
+						NN--
+						if NN == 0 {
+							return nz
+						}
+					}
+					continue
+				}
+			}
+			y[NN-i-1] = s2 * complex(crscr, 0)
+			coef /= hz
+			coef *= complex(FNUP-1, 0)
+		}
+		break
+	}
+	if NN <= 2 {
+		return nz
+	}
+	rz := complex(2*real(z)/(az*az), -2*imag(z)/(az*az))
+	if flag == 0 {
+		for i := NN - 3; i >= 0; i-- {
+			y[i] = complex(float64(i+1)+fnu, 0)*rz*y[i+1] + y[i+2]
+		}
+		return nz
+	}
+
+	// exp(-alim)=exp(-elim)/tol=approximately one digit of precision above the
+	// underflow limit, which equals scale = dmach[1)*SS*1e3.
+	s1 := w[0]
+	s2 := w[1]
+	for K := NN - 3; K >= 0; K-- {
+		s1, s2 = s2, s1+complex(float64(K+1)+fnu, 0)*(rz*s2)
+		ck := s2 * complex(crscr, 0)
+		y[K] = ck
+		if cmplx.Abs(ck) > scale {
+			for ; K >= 0; K-- {
+				y[K] = complex(float64(K+1)+fnu, 0)*rz*y[K+1] + y[K+2]
+			}
+			return nz
+		}
+	}
+	return nz
+}
+
+// Zs1s2 tests for a possible underflow resulting from the addition of the I and
+// K functions in the analytic continuation formula where s1 == K function and
+// s2 == I function.
+//
+// When kode == 1, the I and K functions are different orders of magnitude.
+//
+// When kode == 2, they may both be of the same order of magnitude, but the maximum
+// must be at least one precision above the underflow limit.
+func Zs1s2(zr, s1, s2 complex128, scale, lim float64, iuf int) (s1o, s2o complex128, nz, iufo int) {
+	if s1 == 0 || math.Log(cmplx.Abs(s1))-2*real(zr) < -lim {
+		if cmplx.Abs(s2) > scale {
+			return 0, s2, 0, iuf
+		}
+		return 0, 0, 1, 0
+	}
+	// TODO(btracey): Written like this for numerical rounding reasons.
+	// Fix once we're sure other changes are correct.
+	s1 = cmplx.Exp(cmplx.Log(s1) - zr - zr)
+	if math.Max(cmplx.Abs(s1), cmplx.Abs(s2)) > scale {
+		return s1, s2, 0, iuf + 1
+	}
+	return 0, 0, 1, 0
+}
+
+func dgamln(z float64, ierr int) float64 {
+	//return amoslib.DgamlnFort(z)
+	// Go implementation.
+	if z < 0 {
+		return 0
+	}
+	a2, _ := math.Lgamma(z)
+	return a2
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amos_test.go b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amos_test.go
new file mode 100644
index 00000000..59cdfa4f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amos_test.go
@@ -0,0 +1,521 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package amos
+
+import (
+	"math"
+	"math/rand"
+	"strconv"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+type input struct {
+	x    []float64
+	is   []int
+	kode int
+	id   int
+	yr   []float64
+	yi   []float64
+	n    int
+	tol  float64
+}
+
+func randnum(rnd *rand.Rand) float64 {
+	r := 2e2 // Fortran has infinite loop if this is set higher than 2e3
+	if rnd.Float64() > 0.99 {
+		return 0
+	}
+	return rnd.Float64()*r - r/2
+}
+
+func randInput(rnd *rand.Rand) input {
+	x := make([]float64, 8)
+	for j := range x {
+		x[j] = randnum(rnd)
+	}
+	is := make([]int, 3)
+	for j := range is {
+		is[j] = rand.Intn(1000)
+	}
+	kode := rand.Intn(2) + 1
+	id := rand.Intn(2)
+	n := rand.Intn(5) + 1
+	yr := make([]float64, n+1)
+	yi := make([]float64, n+1)
+	for j := range yr {
+		yr[j] = randnum(rnd)
+		yi[j] = randnum(rnd)
+	}
+	tol := 1e-14
+
+	return input{
+		x, is, kode, id, yr, yi, n, tol,
+	}
+}
+
+const nInputs = 100000
+
+func TestAiry(t *testing.T) {
+	rnd := rand.New(rand.NewSource(1))
+	for i := 0; i < nInputs; i++ {
+		in := randInput(rnd)
+		zairytest(t, in.x, in.kode, in.id)
+	}
+}
+
+func TestZacai(t *testing.T) {
+	rnd := rand.New(rand.NewSource(1))
+	for i := 0; i < nInputs; i++ {
+		in := randInput(rnd)
+		zacaitest(t, in.x, in.is, in.tol, in.n, in.yr, in.yi, in.kode)
+	}
+}
+
+func TestZbknu(t *testing.T) {
+	rnd := rand.New(rand.NewSource(1))
+	for i := 0; i < nInputs; i++ {
+		in := randInput(rnd)
+		zbknutest(t, in.x, in.is, in.tol, in.n, in.yr, in.yi, in.kode)
+	}
+}
+
+func TestZasyi(t *testing.T) {
+	rnd := rand.New(rand.NewSource(1))
+	for i := 0; i < nInputs; i++ {
+		in := randInput(rnd)
+		zasyitest(t, in.x, in.is, in.tol, in.n, in.yr, in.yi, in.kode)
+	}
+}
+
+func TestZseri(t *testing.T) {
+	rnd := rand.New(rand.NewSource(1))
+	for i := 0; i < nInputs; i++ {
+		in := randInput(rnd)
+		zseritest(t, in.x, in.is, in.tol, in.n, in.yr, in.yi, in.kode)
+	}
+}
+
+func TestZmlri(t *testing.T) {
+	rnd := rand.New(rand.NewSource(1))
+	for i := 0; i < nInputs; i++ {
+		in := randInput(rnd)
+		zmlritest(t, in.x, in.is, in.tol, in.n, in.yr, in.yi, in.kode)
+	}
+}
+
+func TestZkscl(t *testing.T) {
+	rnd := rand.New(rand.NewSource(1))
+	for i := 0; i < nInputs; i++ {
+		in := randInput(rnd)
+		zkscltest(t, in.x, in.is, in.tol, in.n, in.yr, in.yi)
+	}
+}
+
+func TestZuchk(t *testing.T) {
+	rnd := rand.New(rand.NewSource(1))
+	for i := 0; i < nInputs; i++ {
+		in := randInput(rnd)
+		zuchktest(t, in.x, in.is, in.tol)
+	}
+}
+
+func TestZs1s2(t *testing.T) {
+	rnd := rand.New(rand.NewSource(1))
+	for i := 0; i < nInputs; i++ {
+		in := randInput(rnd)
+		zs1s2test(t, in.x, in.is)
+	}
+}
+
+func zs1s2test(t *testing.T, x []float64, is []int) {
+
+	type data struct {
+		ZRR, ZRI, S1R, S1I, S2R, S2I float64
+		NZ                           int
+		ASCLE, ALIM                  float64
+		IUF                          int
+	}
+
+	input := data{
+		x[0], x[1], x[2], x[3], x[4], x[5],
+		is[0],
+		x[6], x[7],
+		is[1],
+	}
+
+	zr := complex(input.ZRR, input.ZRI)
+	s1 := complex(input.S1R, input.S1I)
+	s2 := complex(input.S2R, input.S2I)
+	impl := func(input data) data {
+		s1, s2, nz, iuf := Zs1s2(zr, s1, s2, input.ASCLE, input.ALIM, input.IUF)
+		zrr := real(zr)
+		zri := imag(zr)
+		s1r := real(s1)
+		s1i := imag(s1)
+		s2r := real(s2)
+		s2i := imag(s2)
+		alim := input.ALIM
+		ascle := input.ASCLE
+		return data{zrr, zri, s1r, s1i, s2r, s2i, nz, ascle, alim, iuf}
+	}
+
+	comp := func(input data) data {
+		zrr, zri, s1r, s1i, s2r, s2i, nz, ascle, alim, iuf :=
+			zs1s2Orig(input.ZRR, input.ZRI, input.S1R, input.S1I, input.S2R, input.S2I, input.NZ, input.ASCLE, input.ALIM, input.IUF)
+		return data{zrr, zri, s1r, s1i, s2r, s2i, nz, ascle, alim, iuf}
+	}
+
+	oi := impl(input)
+	oc := comp(input)
+
+	sameF64(t, "zs1s2 zrr", oc.ZRR, oi.ZRR)
+	sameF64(t, "zs1s2 zri", oc.ZRI, oi.ZRI)
+	sameF64(t, "zs1s2 s1r", oc.S1R, oi.S1R)
+	sameF64(t, "zs1s2 s1i", oc.S1I, oi.S1I)
+	sameF64(t, "zs1s2 s2r", oc.S2R, oi.S2R)
+	sameF64(t, "zs1s2 s2i", oc.S2I, oi.S2I)
+	sameF64(t, "zs1s2 ascle", oc.ASCLE, oi.ASCLE)
+	sameF64(t, "zs1s2 alim", oc.ALIM, oi.ALIM)
+	sameInt(t, "iuf", oc.IUF, oi.IUF)
+	sameInt(t, "nz", oc.NZ, oi.NZ)
+}
+
+func zuchktest(t *testing.T, x []float64, is []int, tol float64) {
+	YR := x[0]
+	YI := x[1]
+	NZ := is[0]
+	ASCLE := x[2]
+	TOL := tol
+
+	YRfort, YIfort, NZfort, ASCLEfort, TOLfort := zuchkOrig(YR, YI, NZ, ASCLE, TOL)
+	y := complex(YR, YI)
+	NZamos := Zuchk(y, ASCLE, TOL)
+	YRamos := real(y)
+	YIamos := imag(y)
+	ASCLEamos := ASCLE
+	TOLamos := TOL
+
+	sameF64(t, "zuchk yr", YRfort, YRamos)
+	sameF64(t, "zuchk yi", YIfort, YIamos)
+	sameInt(t, "zuchk nz", NZfort, NZamos)
+	sameF64(t, "zuchk ascle", ASCLEfort, ASCLEamos)
+	sameF64(t, "zuchk tol", TOLfort, TOLamos)
+}
+
+func zkscltest(t *testing.T, x []float64, is []int, tol float64, n int, yr, yi []float64) {
+	ZRR := x[0]
+	ZRI := x[1]
+	FNU := x[2]
+	NZ := is[1]
+	ELIM := x[3]
+	ASCLE := x[4]
+	RZR := x[6]
+	RZI := x[7]
+
+	yrfort := make([]float64, len(yr))
+	copy(yrfort, yr)
+	yifort := make([]float64, len(yi))
+	copy(yifort, yi)
+	ZRRfort, ZRIfort, FNUfort, Nfort, YRfort, YIfort, NZfort, RZRfort, RZIfort, ASCLEfort, TOLfort, ELIMfort :=
+		zksclOrig(ZRR, ZRI, FNU, n, yrfort, yifort, NZ, RZR, RZI, ASCLE, tol, ELIM)
+
+	yramos := make([]float64, len(yr))
+	copy(yramos, yr)
+	yiamos := make([]float64, len(yi))
+	copy(yiamos, yi)
+	ZRRamos, ZRIamos, FNUamos, Namos, YRamos, YIamos, NZamos, RZRamos, RZIamos, ASCLEamos, TOLamos, ELIMamos :=
+		Zkscl(ZRR, ZRI, FNU, n, yramos, yiamos, NZ, RZR, RZI, ASCLE, tol, ELIM)
+
+	sameF64(t, "zkscl zrr", ZRRfort, ZRRamos)
+	sameF64(t, "zkscl zri", ZRIfort, ZRIamos)
+	sameF64(t, "zkscl fnu", FNUfort, FNUamos)
+	sameInt(t, "zkscl n", Nfort, Namos)
+	sameInt(t, "zkscl nz", NZfort, NZamos)
+	sameF64(t, "zkscl rzr", RZRfort, RZRamos)
+	sameF64(t, "zkscl rzi", RZIfort, RZIamos)
+	sameF64(t, "zkscl ascle", ASCLEfort, ASCLEamos)
+	sameF64(t, "zkscl tol", TOLfort, TOLamos)
+	sameF64(t, "zkscl elim", ELIMfort, ELIMamos)
+
+	sameF64SApprox(t, "zkscl yr", YRfort, YRamos, 1e-14)
+	sameF64SApprox(t, "zkscl yi", YIfort, YIamos, 1e-14)
+}
+
+func zmlritest(t *testing.T, x []float64, is []int, tol float64, n int, yr, yi []float64, kode int) {
+	ZR := x[0]
+	ZI := x[1]
+	FNU := x[2]
+	KODE := kode
+	NZ := is[1]
+
+	yrfort := make([]float64, len(yr))
+	copy(yrfort, yr)
+	yifort := make([]float64, len(yi))
+	copy(yifort, yi)
+	ZRfort, ZIfort, FNUfort, KODEfort, Nfort, YRfort, YIfort, NZfort, TOLfort :=
+		zmlriOrig(ZR, ZI, FNU, KODE, n, yrfort, yifort, NZ, tol)
+
+	yramos := make([]float64, len(yr))
+	copy(yramos, yr)
+	yiamos := make([]float64, len(yi))
+	copy(yiamos, yi)
+	ZRamos, ZIamos, FNUamos, KODEamos, Namos, YRamos, YIamos, NZamos, TOLamos :=
+		Zmlri(ZR, ZI, FNU, KODE, n, yramos, yiamos, NZ, tol)
+
+	sameF64(t, "zmlri zr", ZRfort, ZRamos)
+	sameF64(t, "zmlri zi", ZIfort, ZIamos)
+	sameF64(t, "zmlri fnu", FNUfort, FNUamos)
+	sameInt(t, "zmlri kode", KODEfort, KODEamos)
+	sameInt(t, "zmlri n", Nfort, Namos)
+	sameInt(t, "zmlri nz", NZfort, NZamos)
+	sameF64(t, "zmlri tol", TOLfort, TOLamos)
+
+	sameF64S(t, "zmlri yr", YRfort, YRamos)
+	sameF64S(t, "zmlri yi", YIfort, YIamos)
+}
+
+func zseritest(t *testing.T, x []float64, is []int, tol float64, n int, yr, yi []float64, kode int) {
+	ZR := x[0]
+	ZI := x[1]
+	FNU := x[2]
+	KODE := kode
+	NZ := is[1]
+	ELIM := x[3]
+	ALIM := x[4]
+
+	yrfort := make([]float64, len(yr))
+	copy(yrfort, yr)
+	yifort := make([]float64, len(yi))
+	copy(yifort, yi)
+	ZRfort, ZIfort, FNUfort, KODEfort, Nfort, YRfort, YIfort, NZfort, TOLfort, ELIMfort, ALIMfort :=
+		zseriOrig(ZR, ZI, FNU, KODE, n, yrfort, yifort, NZ, tol, ELIM, ALIM)
+
+	yramos := make([]float64, len(yr))
+	copy(yramos, yr)
+	yiamos := make([]float64, len(yi))
+	copy(yiamos, yi)
+	y := make([]complex128, len(yramos))
+	for i, v := range yramos {
+		y[i] = complex(v, yiamos[i])
+	}
+	z := complex(ZR, ZI)
+
+	NZamos := Zseri(z, FNU, KODE, n, y[1:], tol, ELIM, ALIM)
+
+	ZRamos := real(z)
+	ZIamos := imag(z)
+	FNUamos := FNU
+	KODEamos := KODE
+	Namos := n
+	TOLamos := tol
+	ELIMamos := ELIM
+	ALIMamos := ALIM
+	YRamos := make([]float64, len(y))
+	YIamos := make([]float64, len(y))
+	for i, v := range y {
+		YRamos[i] = real(v)
+		YIamos[i] = imag(v)
+	}
+
+	sameF64(t, "zseri zr", ZRfort, ZRamos)
+	sameF64(t, "zseri zi", ZIfort, ZIamos)
+	sameF64(t, "zseri fnu", FNUfort, FNUamos)
+	sameInt(t, "zseri kode", KODEfort, KODEamos)
+	sameInt(t, "zseri n", Nfort, Namos)
+	sameInt(t, "zseri nz", NZfort, NZamos)
+	sameF64(t, "zseri tol", TOLfort, TOLamos)
+	sameF64(t, "zseri elim", ELIMfort, ELIMamos)
+	sameF64(t, "zseri elim", ALIMfort, ALIMamos)
+
+	sameF64SApprox(t, "zseri yr", YRfort, YRamos, 1e-10)
+	sameF64SApprox(t, "zseri yi", YIfort, YIamos, 1e-10)
+}
+
+func zasyitest(t *testing.T, x []float64, is []int, tol float64, n int, yr, yi []float64, kode int) {
+	ZR := x[0]
+	ZI := x[1]
+	FNU := x[2]
+	KODE := kode
+	NZ := is[1]
+	ELIM := x[3]
+	ALIM := x[4]
+	RL := x[5]
+
+	yrfort := make([]float64, len(yr))
+	copy(yrfort, yr)
+	yifort := make([]float64, len(yi))
+	copy(yifort, yi)
+	ZRfort, ZIfort, FNUfort, KODEfort, Nfort, YRfort, YIfort, NZfort, RLfort, TOLfort, ELIMfort, ALIMfort :=
+		zasyiOrig(ZR, ZI, FNU, KODE, n, yrfort, yifort, NZ, RL, tol, ELIM, ALIM)
+
+	yramos := make([]float64, len(yr))
+	copy(yramos, yr)
+	yiamos := make([]float64, len(yi))
+	copy(yiamos, yi)
+	ZRamos, ZIamos, FNUamos, KODEamos, Namos, YRamos, YIamos, NZamos, RLamos, TOLamos, ELIMamos, ALIMamos :=
+		Zasyi(ZR, ZI, FNU, KODE, n, yramos, yiamos, NZ, RL, tol, ELIM, ALIM)
+
+	sameF64(t, "zasyi zr", ZRfort, ZRamos)
+	sameF64(t, "zasyi zr", ZIfort, ZIamos)
+	sameF64(t, "zasyi fnu", FNUfort, FNUamos)
+	sameInt(t, "zasyi kode", KODEfort, KODEamos)
+	sameInt(t, "zasyi n", Nfort, Namos)
+	sameInt(t, "zasyi nz", NZfort, NZamos)
+	sameF64(t, "zasyi rl", RLfort, RLamos)
+	sameF64(t, "zasyi tol", TOLfort, TOLamos)
+	sameF64(t, "zasyi elim", ELIMfort, ELIMamos)
+	sameF64(t, "zasyi alim", ALIMfort, ALIMamos)
+
+	sameF64SApprox(t, "zasyi yr", YRfort, YRamos, 1e-12)
+	sameF64SApprox(t, "zasyi yi", YIfort, YIamos, 1e-12)
+}
+
+func zbknutest(t *testing.T, x []float64, is []int, tol float64, n int, yr, yi []float64, kode int) {
+	ZR := x[0]
+	ZI := x[1]
+	FNU := x[2]
+	KODE := kode
+	NZ := is[1]
+	ELIM := x[3]
+	ALIM := x[4]
+
+	yrfort := make([]float64, len(yr))
+	copy(yrfort, yr)
+	yifort := make([]float64, len(yi))
+	copy(yifort, yi)
+	ZRfort, ZIfort, FNUfort, KODEfort, Nfort, YRfort, YIfort, NZfort, TOLfort, ELIMfort, ALIMfort :=
+		zbknuOrig(ZR, ZI, FNU, KODE, n, yrfort, yifort, NZ, tol, ELIM, ALIM)
+
+	yramos := make([]float64, len(yr))
+	copy(yramos, yr)
+	yiamos := make([]float64, len(yi))
+	copy(yiamos, yi)
+	ZRamos, ZIamos, FNUamos, KODEamos, Namos, YRamos, YIamos, NZamos, TOLamos, ELIMamos, ALIMamos :=
+		Zbknu(ZR, ZI, FNU, KODE, n, yramos, yiamos, NZ, tol, ELIM, ALIM)
+
+	sameF64(t, "zbknu zr", ZRfort, ZRamos)
+	sameF64(t, "zbknu zr", ZIfort, ZIamos)
+	sameF64(t, "zbknu fnu", FNUfort, FNUamos)
+	sameInt(t, "zbknu kode", KODEfort, KODEamos)
+	sameInt(t, "zbknu n", Nfort, Namos)
+	sameInt(t, "zbknu nz", NZfort, NZamos)
+	sameF64(t, "zbknu tol", TOLfort, TOLamos)
+	sameF64(t, "zbknu elim", ELIMfort, ELIMamos)
+	sameF64(t, "zbknu alim", ALIMfort, ALIMamos)
+
+	sameF64SApprox(t, "zbknu yr", YRfort, YRamos, 1e-12)
+	sameF64SApprox(t, "zbknu yi", YIfort, YIamos, 1e-12)
+}
+
+func zairytest(t *testing.T, x []float64, kode, id int) {
+	ZR := x[0]
+	ZI := x[1]
+	KODE := kode
+	ID := id
+
+	AIRfort, AIIfort, NZfort := zairyOrig(ZR, ZI, ID, KODE)
+	AIRamos, AIIamos, NZamos := Zairy(ZR, ZI, ID, KODE)
+
+	sameF64Approx(t, "zairy air", AIRfort, AIRamos, 1e-12)
+	sameF64Approx(t, "zairy aii", AIIfort, AIIamos, 1e-12)
+	sameInt(t, "zairy nz", NZfort, NZamos)
+}
+
+func zacaitest(t *testing.T, x []float64, is []int, tol float64, n int, yr, yi []float64, kode int) {
+	ZR := x[0]
+	ZI := x[1]
+	FNU := x[2]
+	KODE := kode
+	NZ := is[1]
+	MR := is[2]
+	ELIM := x[3]
+	ALIM := x[4]
+	RL := x[5]
+
+	yrfort := make([]float64, len(yr))
+	copy(yrfort, yr)
+	yifort := make([]float64, len(yi))
+	copy(yifort, yi)
+	ZRfort, ZIfort, FNUfort, KODEfort, MRfort, Nfort, YRfort, YIfort, NZfort, RLfort, TOLfort, ELIMfort, ALIMfort :=
+		zacaiOrig(ZR, ZI, FNU, KODE, MR, n, yrfort, yifort, NZ, RL, tol, ELIM, ALIM)
+
+	yramos := make([]float64, len(yr))
+	copy(yramos, yr)
+	yiamos := make([]float64, len(yi))
+	copy(yiamos, yi)
+	ZRamos, ZIamos, FNUamos, KODEamos, MRamos, Namos, YRamos, YIamos, NZamos, RLamos, TOLamos, ELIMamos, ALIMamos :=
+		Zacai(ZR, ZI, FNU, KODE, MR, n, yramos, yiamos, NZ, RL, tol, ELIM, ALIM)
+
+	sameF64(t, "zacai zr", ZRfort, ZRamos)
+	sameF64(t, "zacai zi", ZIfort, ZIamos)
+	sameF64(t, "zacai fnu", FNUfort, FNUamos)
+	sameInt(t, "zacai kode", KODEfort, KODEamos)
+	sameInt(t, "zacai mr", MRfort, MRamos)
+	sameInt(t, "zacai n", Nfort, Namos)
+	sameInt(t, "zacai nz", NZfort, NZamos)
+	sameF64(t, "zacai rl", RLfort, RLamos)
+	sameF64(t, "zacai tol", TOLfort, TOLamos)
+	sameF64(t, "zacai elim", ELIMfort, ELIMamos)
+	sameF64(t, "zacai elim", ALIMfort, ALIMamos)
+
+	sameF64SApprox(t, "zacai yr", YRfort, YRamos, 1e-12)
+	sameF64SApprox(t, "zacai yi", YIfort, YIamos, 1e-12)
+}
+
+func sameF64(t *testing.T, str string, c, native float64) {
+	if math.IsNaN(c) && math.IsNaN(native) {
+		return
+	}
+	if c == native {
+		return
+	}
+	cb := math.Float64bits(c)
+	nb := math.Float64bits(native)
+	t.Errorf("Case %s: Float64 mismatch. c = %v, native = %v\n cb: %v, nb: %v\n", str, c, native, cb, nb)
+}
+
+func sameF64Approx(t *testing.T, str string, c, native, tol float64) {
+	if math.IsNaN(c) && math.IsNaN(native) {
+		return
+	}
+	if floats.EqualWithinAbsOrRel(c, native, tol, tol) {
+		return
+	}
+	// Have a much looser tolerance for correctness when the values are large.
+	// Floating point noise makes the relative tolerance difference greater for
+	// higher values.
+	if c > 1e200 && floats.EqualWithinAbsOrRel(c, native, 10, 10) {
+		return
+	}
+	cb := math.Float64bits(c)
+	nb := math.Float64bits(native)
+	t.Errorf("Case %s: Float64 mismatch. c = %v, native = %v\n cb: %v, nb: %v\n", str, c, native, cb, nb)
+}
+
+func sameInt(t *testing.T, str string, c, native int) {
+	if c != native {
+		t.Errorf("Case %s: Int mismatch. c = %v, native = %v.", str, c, native)
+	}
+}
+
+func sameF64S(t *testing.T, str string, c, native []float64) {
+	if len(c) != len(native) {
+		panic(str)
+	}
+	for i, v := range c {
+		sameF64(t, str+"_idx_"+strconv.Itoa(i), v, native[i])
+	}
+}
+
+func sameF64SApprox(t *testing.T, str string, c, native []float64, tol float64) {
+	if len(c) != len(native) {
+		panic(str)
+	}
+	for i, v := range c {
+		sameF64Approx(t, str+"_idx_"+strconv.Itoa(i), v, native[i], tol)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/Make.files b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/Make.files
new file mode 100644
index 00000000..81c7c715
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/Make.files
@@ -0,0 +1,5 @@
+$(CUR_SRCS) +=  d1mach.f zabs.f   zasyi.f  zbesk.f  zbknu.f  zexp.f   zmlt.f   zshch.f  zuni1.f  zunk2.f \
+	dgamln.f zacai.f  zbesh.f  zbesy.f  zbuni.f  zkscl.f  zrati.f  zsqrt.f  zuni2.f  zuoik.f \
+	i1mach.f zacon.f  zbesi.f  zbinu.f  zbunk.f  zlog.f   zs1s2.f  zuchk.f  zunik.f  zwrsk.f \
+	xerror.f zairy.f  zbesj.f  zbiry.f  zdiv.f   zmlri.f  zseri.f  zunhj.f  zunk1.f
+
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/d1mach.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/d1mach.f
new file mode 100644
index 00000000..0d344def
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/d1mach.f
@@ -0,0 +1,97 @@
+*DECK D1MACH
+      DOUBLE PRECISION FUNCTION D1MACH(I)
+C***BEGIN PROLOGUE  D1MACH
+C***DATE WRITTEN   750101   (YYMMDD)
+C***REVISION DATE  890213   (YYMMDD)
+C***CATEGORY NO.  R1
+C***KEYWORDS  LIBRARY=SLATEC,TYPE=DOUBLE PRECISION(R1MACH-S D1MACH-D),
+C             MACHINE CONSTANTS
+C***AUTHOR  FOX, P. A., (BELL LABS)
+C           HALL, A. D., (BELL LABS)
+C           SCHRYER, N. L., (BELL LABS)
+C***PURPOSE  Returns double precision machine dependent constants
+C***DESCRIPTION
+C
+C   D1MACH can be used to obtain machine-dependent parameters
+C   for the local machine environment.  It is a function
+C   subprogram with one (input) argument, and can be called
+C   as follows, for example
+C
+C        D = D1MACH(I)
+C
+C   where I=1,...,5.  The (output) value of D above is
+C   determined by the (input) value of I.  The results for
+C   various values of I are discussed below.
+C
+C   D1MACH( 1) = B**(EMIN-1), the smallest positive magnitude.
+C   D1MACH( 2) = B**EMAX*(1 - B**(-T)), the largest magnitude.
+C   D1MACH( 3) = B**(-T), the smallest relative spacing.
+C   D1MACH( 4) = B**(1-T), the largest relative spacing.
+C   D1MACH( 5) = LOG10(B)
+C
+C   Assume double precision numbers are represented in the T-digit,
+C   base-B form
+C
+C              sign (B**E)*( (X(1)/B) + ... + (X(T)/B**T) )
+C
+C   where 0 .LE. X(I) .LT. B for I=1,...,T, 0 .LT. X(1), and
+C   EMIN .LE. E .LE. EMAX.
+C
+C   The values of B, T, EMIN and EMAX are provided in I1MACH as
+C   follows:
+C   I1MACH(10) = B, the base.
+C   I1MACH(14) = T, the number of base-B digits.
+C   I1MACH(15) = EMIN, the smallest exponent E.
+C   I1MACH(16) = EMAX, the largest exponent E.
+C
+C   To alter this function for a particular environment,
+C   the desired set of DATA statements should be activated by
+C   removing the C from column 1.  Also, the values of
+C   D1MACH(1) - D1MACH(4) should be checked for consistency
+C   with the local operating system.
+C
+C***REFERENCES  FOX P.A., HALL A.D., SCHRYER N.L.,*FRAMEWORK FOR A
+C                 PORTABLE LIBRARY*, ACM TRANSACTIONS ON MATHEMATICAL
+C                 SOFTWARE, VOL. 4, NO. 2, JUNE 1978, PP. 177-188.
+C***ROUTINES CALLED  XERROR
+C***END PROLOGUE  D1MACH
+C
+      INTEGER SMALL(4)
+      INTEGER LARGE(4)
+      INTEGER RIGHT(4)
+      INTEGER DIVER(4)
+      INTEGER LOG10(4)
+C
+      DOUBLE PRECISION DMACH(5)
+      SAVE DMACH
+C
+C      EQUIVALENCE (DMACH(1),SMALL(1))
+C      EQUIVALENCE (DMACH(2),LARGE(1))
+C      EQUIVALENCE (DMACH(3),RIGHT(1))
+C      EQUIVALENCE (DMACH(4),DIVER(1))
+C      EQUIVALENCE (DMACH(5),LOG10(1))
+C
+C     MACHINE CONSTANTS FOR THE IBM PC
+C     ASSUMES THAT ALL ARITHMETIC IS DONE IN DOUBLE PRECISION
+C     ON 8088, I.E., NOT IN 80 BIT FORM FOR THE 8087.
+C
+      DATA DMACH(1) / 2.23D-308 /
+C      DATA SMALL(1),SMALL(2) /  2002288515,    1050897 /
+      DATA DMACH(2) / 1.79D-308 /
+C      DATA LARGE(1),LARGE(2) /  1487780761, 2146426097 /
+      DATA DMACH(3) / 1.11D-16 /
+C      DATA RIGHT(1),RIGHT(2) / -1209488034, 1017118298 /
+      DATA DMACH(4) / 2.22D-16 /
+C      DATA DIVER(1),DIVER(2) / -1209488034, 1018166874 /
+      DATA DMACH(5) / 0.3010299956639812 /
+C      DATA LOG10(1),LOG10(2) /  1352628735, 1070810131 /
+C
+C
+C***FIRST EXECUTABLE STATEMENT  D1MACH
+      IF (I .LT. 1  .OR.  I .GT. 5)
+     1   CALL XERROR ('D1MACH -- I OUT OF BOUNDS', 25, 1, 2)
+C
+      D1MACH = DMACH(I)
+      RETURN
+C
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/dgamln.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/dgamln.f
new file mode 100644
index 00000000..792014be
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/dgamln.f
@@ -0,0 +1,189 @@
+      DOUBLE PRECISION FUNCTION DGAMLN(Z,IERR)
+C***BEGIN PROLOGUE  DGAMLN
+C***DATE WRITTEN   830501   (YYMMDD)
+C***REVISION DATE  830501   (YYMMDD)
+C***CATEGORY NO.  B5F
+C***KEYWORDS  GAMMA FUNCTION,LOGARITHM OF GAMMA FUNCTION
+C***AUTHOR  AMOS, DONALD E., SANDIA NATIONAL LABORATORIES
+C***PURPOSE  TO COMPUTE THE LOGARITHM OF THE GAMMA FUNCTION
+C***DESCRIPTION
+C
+C               **** A DOUBLE PRECISION ROUTINE ****
+C         DGAMLN COMPUTES THE NATURAL LOG OF THE GAMMA FUNCTION FOR
+C         Z.GT.0.  THE ASYMPTOTIC EXPANSION IS USED TO GENERATE VALUES
+C         GREATER THAN ZMIN WHICH ARE ADJUSTED BY THE RECURSION
+C         G(Z+1)=Z*G(Z) FOR Z.LE.ZMIN.  THE FUNCTION WAS MADE AS
+C         PORTABLE AS POSSIBLE BY COMPUTIMG ZMIN FROM THE NUMBER OF BASE
+C         10 DIGITS IN A WORD, RLN=AMAX1(-ALOG10(R1MACH(4)),0.5E-18)
+C         LIMITED TO 18 DIGITS OF (RELATIVE) ACCURACY.
+C
+C         SINCE INTEGER ARGUMENTS ARE COMMON, A TABLE LOOK UP ON 100
+C         VALUES IS USED FOR SPEED OF EXECUTION.
+C
+C     DESCRIPTION OF ARGUMENTS
+C
+C         INPUT      Z IS D0UBLE PRECISION
+C           Z      - ARGUMENT, Z.GT.0.0D0
+C
+C         OUTPUT      DGAMLN IS DOUBLE PRECISION
+C           DGAMLN  - NATURAL LOG OF THE GAMMA FUNCTION AT Z.NE.0.0D0
+C           IERR    - ERROR FLAG
+C                     IERR=0, NORMAL RETURN, COMPUTATION COMPLETED
+C                     IERR=1, Z.LE.0.0D0,    NO COMPUTATION
+C
+C
+C***REFERENCES  COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+C                 BY D. E. AMOS, SAND83-0083, MAY, 1983.
+C***ROUTINES CALLED  I1MACH,D1MACH
+C***END PROLOGUE  DGAMLN
+      DOUBLE PRECISION CF, CON, FLN, FZ, GLN, RLN, S, TLG, TRM, TST,
+     * T1, WDTOL, Z, ZDMY, ZINC, ZM, ZMIN, ZP, ZSQ, D1MACH
+      INTEGER I, IERR, I1M, K, MZ, NZ, I1MACH
+      DIMENSION CF(22), GLN(100)
+C           LNGAMMA(N), N=1,100
+      DATA GLN(1), GLN(2), GLN(3), GLN(4), GLN(5), GLN(6), GLN(7),
+     1     GLN(8), GLN(9), GLN(10), GLN(11), GLN(12), GLN(13), GLN(14),
+     2     GLN(15), GLN(16), GLN(17), GLN(18), GLN(19), GLN(20),
+     3     GLN(21), GLN(22)/
+     4     0.00000000000000000D+00,     0.00000000000000000D+00,
+     5     6.93147180559945309D-01,     1.79175946922805500D+00,
+     6     3.17805383034794562D+00,     4.78749174278204599D+00,
+     7     6.57925121201010100D+00,     8.52516136106541430D+00,
+     8     1.06046029027452502D+01,     1.28018274800814696D+01,
+     9     1.51044125730755153D+01,     1.75023078458738858D+01,
+     A     1.99872144956618861D+01,     2.25521638531234229D+01,
+     B     2.51912211827386815D+01,     2.78992713838408916D+01,
+     C     3.06718601060806728D+01,     3.35050734501368889D+01,
+     D     3.63954452080330536D+01,     3.93398841871994940D+01,
+     E     4.23356164607534850D+01,     4.53801388984769080D+01/
+      DATA GLN(23), GLN(24), GLN(25), GLN(26), GLN(27), GLN(28),
+     1     GLN(29), GLN(30), GLN(31), GLN(32), GLN(33), GLN(34),
+     2     GLN(35), GLN(36), GLN(37), GLN(38), GLN(39), GLN(40),
+     3     GLN(41), GLN(42), GLN(43), GLN(44)/
+     4     4.84711813518352239D+01,     5.16066755677643736D+01,
+     5     5.47847293981123192D+01,     5.80036052229805199D+01,
+     6     6.12617017610020020D+01,     6.45575386270063311D+01,
+     7     6.78897431371815350D+01,     7.12570389671680090D+01,
+     8     7.46582363488301644D+01,     7.80922235533153106D+01,
+     9     8.15579594561150372D+01,     8.50544670175815174D+01,
+     A     8.85808275421976788D+01,     9.21361756036870925D+01,
+     B     9.57196945421432025D+01,     9.93306124547874269D+01,
+     C     1.02968198614513813D+02,     1.06631760260643459D+02,
+     D     1.10320639714757395D+02,     1.14034211781461703D+02,
+     E     1.17771881399745072D+02,     1.21533081515438634D+02/
+      DATA GLN(45), GLN(46), GLN(47), GLN(48), GLN(49), GLN(50),
+     1     GLN(51), GLN(52), GLN(53), GLN(54), GLN(55), GLN(56),
+     2     GLN(57), GLN(58), GLN(59), GLN(60), GLN(61), GLN(62),
+     3     GLN(63), GLN(64), GLN(65), GLN(66)/
+     4     1.25317271149356895D+02,     1.29123933639127215D+02,
+     5     1.32952575035616310D+02,     1.36802722637326368D+02,
+     6     1.40673923648234259D+02,     1.44565743946344886D+02,
+     7     1.48477766951773032D+02,     1.52409592584497358D+02,
+     8     1.56360836303078785D+02,     1.60331128216630907D+02,
+     9     1.64320112263195181D+02,     1.68327445448427652D+02,
+     A     1.72352797139162802D+02,     1.76395848406997352D+02,
+     B     1.80456291417543771D+02,     1.84533828861449491D+02,
+     C     1.88628173423671591D+02,     1.92739047287844902D+02,
+     D     1.96866181672889994D+02,     2.01009316399281527D+02,
+     E     2.05168199482641199D+02,     2.09342586752536836D+02/
+      DATA GLN(67), GLN(68), GLN(69), GLN(70), GLN(71), GLN(72),
+     1     GLN(73), GLN(74), GLN(75), GLN(76), GLN(77), GLN(78),
+     2     GLN(79), GLN(80), GLN(81), GLN(82), GLN(83), GLN(84),
+     3     GLN(85), GLN(86), GLN(87), GLN(88)/
+     4     2.13532241494563261D+02,     2.17736934113954227D+02,
+     5     2.21956441819130334D+02,     2.26190548323727593D+02,
+     6     2.30439043565776952D+02,     2.34701723442818268D+02,
+     7     2.38978389561834323D+02,     2.43268849002982714D+02,
+     8     2.47572914096186884D+02,     2.51890402209723194D+02,
+     9     2.56221135550009525D+02,     2.60564940971863209D+02,
+     A     2.64921649798552801D+02,     2.69291097651019823D+02,
+     B     2.73673124285693704D+02,     2.78067573440366143D+02,
+     C     2.82474292687630396D+02,     2.86893133295426994D+02,
+     D     2.91323950094270308D+02,     2.95766601350760624D+02,
+     E     3.00220948647014132D+02,     3.04686856765668715D+02/
+      DATA GLN(89), GLN(90), GLN(91), GLN(92), GLN(93), GLN(94),
+     1     GLN(95), GLN(96), GLN(97), GLN(98), GLN(99), GLN(100)/
+     2     3.09164193580146922D+02,     3.13652829949879062D+02,
+     3     3.18152639620209327D+02,     3.22663499126726177D+02,
+     4     3.27185287703775217D+02,     3.31717887196928473D+02,
+     5     3.36261181979198477D+02,     3.40815058870799018D+02,
+     6     3.45379407062266854D+02,     3.49954118040770237D+02,
+     7     3.54539085519440809D+02,     3.59134205369575399D+02/
+C             COEFFICIENTS OF ASYMPTOTIC EXPANSION
+      DATA CF(1), CF(2), CF(3), CF(4), CF(5), CF(6), CF(7), CF(8),
+     1     CF(9), CF(10), CF(11), CF(12), CF(13), CF(14), CF(15),
+     2     CF(16), CF(17), CF(18), CF(19), CF(20), CF(21), CF(22)/
+     3     8.33333333333333333D-02,    -2.77777777777777778D-03,
+     4     7.93650793650793651D-04,    -5.95238095238095238D-04,
+     5     8.41750841750841751D-04,    -1.91752691752691753D-03,
+     6     6.41025641025641026D-03,    -2.95506535947712418D-02,
+     7     1.79644372368830573D-01,    -1.39243221690590112D+00,
+     8     1.34028640441683920D+01,    -1.56848284626002017D+02,
+     9     2.19310333333333333D+03,    -3.61087712537249894D+04,
+     A     6.91472268851313067D+05,    -1.52382215394074162D+07,
+     B     3.82900751391414141D+08,    -1.08822660357843911D+10,
+     C     3.47320283765002252D+11,    -1.23696021422692745D+13,
+     D     4.88788064793079335D+14,    -2.13203339609193739D+16/
+C
+C             LN(2*PI)
+      DATA CON                    /     1.83787706640934548D+00/
+C
+C***FIRST EXECUTABLE STATEMENT  DGAMLN
+      IERR=0
+      IF (Z.LE.0.0D0) GO TO 70
+      IF (Z.GT.101.0D0) GO TO 10
+      NZ = INT(SNGL(Z))
+      FZ = Z - FLOAT(NZ)
+      IF (FZ.GT.0.0D0) GO TO 10
+      IF (NZ.GT.100) GO TO 10
+      DGAMLN = GLN(NZ)
+      RETURN
+   10 CONTINUE
+      WDTOL = D1MACH(4)
+      WDTOL = DMAX1(WDTOL,0.5D-18)
+      I1M = I1MACH(14)
+      RLN = D1MACH(5)*FLOAT(I1M)
+      FLN = DMIN1(RLN,20.0D0)
+      FLN = DMAX1(FLN,3.0D0)
+      FLN = FLN - 3.0D0
+      ZM = 1.8000D0 + 0.3875D0*FLN
+      MZ = INT(SNGL(ZM)) + 1
+      ZMIN = FLOAT(MZ)
+      ZDMY = Z
+      ZINC = 0.0D0
+      IF (Z.GE.ZMIN) GO TO 20
+      ZINC = ZMIN - FLOAT(NZ)
+      ZDMY = Z + ZINC
+   20 CONTINUE
+      ZP = 1.0D0/ZDMY
+      T1 = CF(1)*ZP
+      S = T1
+      IF (ZP.LT.WDTOL) GO TO 40
+      ZSQ = ZP*ZP
+      TST = T1*WDTOL
+      DO 30 K=2,22
+        ZP = ZP*ZSQ
+        TRM = CF(K)*ZP
+        IF (DABS(TRM).LT.TST) GO TO 40
+        S = S + TRM
+   30 CONTINUE
+   40 CONTINUE
+      IF (ZINC.NE.0.0D0) GO TO 50
+      TLG = DLOG(Z)
+      DGAMLN = Z*(TLG-1.0D0) + 0.5D0*(CON-TLG) + S
+      RETURN
+   50 CONTINUE
+      ZP = 1.0D0
+      NZ = INT(SNGL(ZINC))
+      DO 60 I=1,NZ
+        ZP = ZP*(Z+FLOAT(I-1))
+   60 CONTINUE
+      TLG = DLOG(ZDMY)
+      DGAMLN = ZDMY*(TLG-1.0D0) - DLOG(ZP) + 0.5D0*(CON-TLG) + S
+      RETURN
+C
+C
+   70 CONTINUE
+      IERR=1
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/fortran.go b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/fortran.go
new file mode 100644
index 00000000..52e17e1f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/fortran.go
@@ -0,0 +1,366 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build fortran
+// TODO(jonlawlor): remove fortran build tag when gonum only supports go 1.7+.
+
+package amoslib
+
+/*
+double mzabs_(double * ar, double * ai);
+void zs1s2_(double * ZRR, double * ZRI, double * S1R, double * S1I, double * S2R, double * S2I, int* NZ, double *ASCLE, double * ALIM, int * IUF);
+void zacai_(double * ZR, double * ZI, double * FNU, int * KODE, int * N, int * MR, double * YR, double * YI, int * NZ, double * RL, double * tol, double * elim, double * alim);
+void zseri_(double * ZR, double * ZI, double * FNU, int * KODE, int * N, double * YR, double * YI, int * NZ, double * tol, double * elim, double * alim);
+void zmlri_(double * ZR, double * ZI, double * FNU, int * KODE, int * N, double * YR, double * YI, int * NZ, double * tol);
+void zbknu_(double * ZR, double * ZI, double * FNU, int * KODE, int * N, double * YR, double * YI, int * NZ, double * tol, double * elim, double * alim);
+void zasyi_(double * ZR, double * ZI, double * FNU, int * KODE, int * N, double * YR, double * YI, int * NZ,double * RL, double * tol, double * elim, double * alim);
+void zkscl_(double * ZRR, double * ZRI, double * FNU, int * N, double * YR, double * YI, int * NZ, double * RZR, double * RZI, double * ASCLE, double * tol, double * elim);
+void zuchk_(double * YR, double * YI, int * NZ, double * ASCLE, double * TOL);
+void zairy_(double * ZR, double * ZI, int * ID, int * KODE, double * AIR, double * AII, int * NZ, int * IERR);
+void zlog_(double * ar, double * ai, double * br, double * bi, int * ierr);
+void zexp_(double * ar, double * ai, double * br, double * bi);
+void zsqrt_(double * ar, double * ai, double * br, double * bi);
+void zdiv_(double * ar, double * ai, double * br, double * bi, double * cr, double * ci);
+void zmlt_(double * ar, double * ai, double * br, double * bi, double * cr, double * ci);
+double dgamln_(double *z, int * ierr);
+void zshch_(double * zr, double * zi, double * cshr, double * cshi, double * cchr, double * cchi);
+double mysqrt_(double * A);
+double myexp_(double * A);
+double mycos_(double * A);
+double mysin_(double * A);
+double mylog_(double * A);
+double mytan_(double * A);
+double myatan_(double * A);
+double myabs_(double * A);
+double mymin_(double * A, double * B);
+double mymax_(double * A, double * B);
+*/
+import "C"
+import "unsafe"
+
+func MinFort(a, b float64) float64 {
+	ans := C.mymin_((*C.double)(&a), (*C.double)(&b))
+	return float64(ans)
+}
+
+func MaxFort(a, b float64) float64 {
+	ans := C.mymax_((*C.double)(&a), (*C.double)(&b))
+	return float64(ans)
+}
+
+func AbsFort(a float64) float64 {
+	ans := C.myabs_((*C.double)(&a))
+	return float64(ans)
+}
+
+func AtanFort(a float64) float64 {
+	ans := C.myatan_((*C.double)(&a))
+	return float64(ans)
+}
+
+func TanFort(a float64) float64 {
+	ans := C.mytan_((*C.double)(&a))
+	return float64(ans)
+}
+
+func LogFort(a float64) float64 {
+	ans := C.mylog_((*C.double)(&a))
+	return float64(ans)
+}
+
+func SinFort(a float64) float64 {
+	ans := C.mysin_((*C.double)(&a))
+	return float64(ans)
+}
+
+func CosFort(a float64) float64 {
+	ans := C.mycos_((*C.double)(&a))
+	return float64(ans)
+}
+
+func ExpFort(a float64) float64 {
+	ans := C.myexp_((*C.double)(&a))
+	return float64(ans)
+}
+
+func SqrtFort(a float64) float64 {
+	ans := C.mysqrt_((*C.double)(&a))
+	return float64(ans)
+}
+
+func DgamlnFort(a float64) float64 {
+	var ierr int
+	pierr := (*C.int)(unsafe.Pointer(&ierr))
+	pa := (*C.double)(&a)
+	ans := C.dgamln_(pa, pierr)
+	return (float64)(ans)
+}
+
+func ZmltFort(a, b complex128) complex128 {
+	ar := real(a)
+	ai := imag(a)
+	br := real(b)
+	bi := imag(b)
+	var cr, ci float64
+	C.zmlt_(
+		(*C.double)(&ar), (*C.double)(&ai),
+		(*C.double)(&br), (*C.double)(&bi),
+		(*C.double)(&cr), (*C.double)(&ci),
+	)
+	return complex(cr, ci)
+}
+
+func ZdivFort(a, b complex128) complex128 {
+	ar := real(a)
+	ai := imag(a)
+	br := real(b)
+	bi := imag(b)
+	var cr, ci float64
+	C.zdiv_(
+		(*C.double)(&ar), (*C.double)(&ai),
+		(*C.double)(&br), (*C.double)(&bi),
+		(*C.double)(&cr), (*C.double)(&ci),
+	)
+	return complex(cr, ci)
+}
+
+func ZabsFort(a complex128) float64 {
+	ar := real(a)
+	ai := imag(a)
+	return float64(C.mzabs_((*C.double)(&ar), (*C.double)(&ai)))
+}
+
+func ZsqrtFort(a complex128) (b complex128) {
+	ar := real(a)
+	ai := imag(a)
+
+	var br, bi float64
+
+	par := (*C.double)(&ar)
+	pai := (*C.double)(&ai)
+	pbr := (*C.double)(&br)
+	pbi := (*C.double)(&bi)
+
+	C.zsqrt_(par, pai, pbr, pbi)
+	return complex(br, bi)
+}
+
+func ZexpFort(a complex128) (b complex128) {
+	ar := real(a)
+	ai := imag(a)
+
+	var br, bi float64
+
+	par := (*C.double)(&ar)
+	pai := (*C.double)(&ai)
+	pbr := (*C.double)(&br)
+	pbi := (*C.double)(&bi)
+
+	C.zexp_(par, pai, pbr, pbi)
+	return complex(br, bi)
+}
+
+func ZlogFort(a complex128) (b complex128) {
+	ar := real(a)
+	ai := imag(a)
+	var ierr int
+	var br, bi float64
+
+	par := (*C.double)(&ar)
+	pai := (*C.double)(&ai)
+	pbr := (*C.double)(&br)
+	pbi := (*C.double)(&bi)
+	pierr := (*C.int)(unsafe.Pointer(&ierr))
+	C.zlog_(par, pai, pbr, pbi, pierr)
+	return complex(br, bi)
+}
+
+func Zshch(ZR, ZI, CSHR, CSHI, CCHR, CCHI float64) (ZRout, ZIout, CSHRout, CSHIout, CCHRout, CCHIout float64) {
+	pzr := (*C.double)(&ZR)
+	pzi := (*C.double)(&ZI)
+	pcshr := (*C.double)(&CSHR)
+	pcshi := (*C.double)(&CSHI)
+	pcchr := (*C.double)(&CCHR)
+	pcchi := (*C.double)(&CCHI)
+
+	C.zshch_(pzr, pzi, pcshr, pcshi, pcchr, pcchi)
+	return ZR, ZI, CSHR, CSHI, CCHR, CCHI
+}
+
+func ZairyFort(ZR, ZI float64, ID, KODE int) (AIR, AII float64, NZ int) {
+	var IERR int
+	pzr := (*C.double)(&ZR)
+	pzi := (*C.double)(&ZI)
+	pid := (*C.int)(unsafe.Pointer(&ID))
+	pkode := (*C.int)(unsafe.Pointer(&KODE))
+
+	pair := (*C.double)(&AIR)
+	paii := (*C.double)(&AII)
+	pnz := (*C.int)(unsafe.Pointer(&NZ))
+	pierr := (*C.int)(unsafe.Pointer(&IERR))
+	C.zairy_(pzr, pzi, pid, pkode, pair, paii, pnz, pierr)
+
+	NZ = int(*pnz)
+	return AIR, AII, NZ
+}
+
+func ZksclFort(ZRR, ZRI, FNU float64, N int, YR, YI []float64, NZ int, RZR, RZI, ASCLE, TOL, ELIM float64) (
+	ZRout, ZIout, FNUout float64, Nout int, YRout, YIout []float64, NZout int, RZRout, RZIout, ASCLEout, TOLout, ELIMout float64) {
+
+	pzrr := (*C.double)(&ZRR)
+	pzri := (*C.double)(&ZRI)
+	pfnu := (*C.double)(&FNU)
+	pn := (*C.int)(unsafe.Pointer(&N))
+	pyr := (*C.double)(&YR[0])
+	pyi := (*C.double)(&YI[0])
+	pnz := (*C.int)(unsafe.Pointer(&NZ))
+	przr := (*C.double)(&RZR)
+	przi := (*C.double)(&RZI)
+	pascle := (*C.double)(&ASCLE)
+	ptol := (*C.double)(&TOL)
+	pelim := (*C.double)(&ELIM)
+
+	C.zkscl_(pzrr, pzri, pfnu, pn, pyr, pyi, pnz, przr, przi, pascle, ptol, pelim)
+	N = int(*pn)
+	NZ = int(*pnz)
+	return ZRR, ZRI, FNU, N, YR, YI, NZ, RZR, RZI, ASCLE, TOL, ELIM
+}
+
+func ZbknuFort(ZR, ZI, FNU float64, KODE, N int, YR, YI []float64, NZ int, TOL, ELIM, ALIM float64) (
+	ZRout, ZIout, FNUout float64, KODEout, Nout int, YRout, YIout []float64, NZout int, TOLout, ELIMout, ALIMout float64) {
+
+	pzr := (*C.double)(&ZR)
+	pzi := (*C.double)(&ZI)
+	pfnu := (*C.double)(&FNU)
+	pkode := (*C.int)(unsafe.Pointer(&KODE))
+	pn := (*C.int)(unsafe.Pointer(&N))
+	pyr := (*C.double)(&YR[0])
+	pyi := (*C.double)(&YI[0])
+	pnz := (*C.int)(unsafe.Pointer(&NZ))
+	ptol := (*C.double)(&TOL)
+	pelim := (*C.double)(&ELIM)
+	palim := (*C.double)(&ALIM)
+
+	C.zbknu_(pzr, pzi, pfnu, pkode, pn, pyr, pyi, pnz, ptol, pelim, palim)
+	KODE = int(*pkode)
+	N = int(*pn)
+	NZ = int(*pnz)
+	return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+}
+
+func ZasyiFort(ZR, ZI, FNU float64, KODE, N int, YR, YI []float64, NZ int, RL, TOL, ELIM, ALIM float64) (
+	ZRout, ZIout, FNUout float64, KODEout, Nout int, YRout, YIout []float64, NZout int, RLout, TOLout, ELIMout, ALIMout float64) {
+
+	pzr := (*C.double)(&ZR)
+	pzi := (*C.double)(&ZI)
+	pfnu := (*C.double)(&FNU)
+	pkode := (*C.int)(unsafe.Pointer(&KODE))
+	pn := (*C.int)(unsafe.Pointer(&N))
+	pyr := (*C.double)(&YR[0])
+	pyi := (*C.double)(&YI[0])
+	pnz := (*C.int)(unsafe.Pointer(&NZ))
+	prl := (*C.double)(&RL)
+	ptol := (*C.double)(&TOL)
+	pelim := (*C.double)(&ELIM)
+	palim := (*C.double)(&ALIM)
+
+	C.zasyi_(pzr, pzi, pfnu, pkode, pn, pyr, pyi, pnz, prl, ptol, pelim, palim)
+	KODE = int(*pkode)
+	N = int(*pn)
+	NZ = int(*pnz)
+	return ZR, ZI, FNU, KODE, N, YR, YI, NZ, RL, TOL, ELIM, ALIM
+}
+
+func ZuchkFort(YR, YI float64, NZ int, ASCLE, TOL float64) (YRout, YIout float64, NZout int, ASCLEout, TOLout float64) {
+	pyr := (*C.double)(&YR)
+	pyi := (*C.double)(&YI)
+	pnz := (*C.int)(unsafe.Pointer(&NZ))
+	pascle := (*C.double)(&ASCLE)
+	ptol := (*C.double)(&TOL)
+
+	C.zuchk_(pyr, pyi, pnz, pascle, ptol)
+	return YR, YI, NZ, ASCLE, TOL
+}
+
+func Zs1s2Fort(ZRR, ZRI, S1R, S1I, S2R, S2I float64, NZ int, ASCLE, ALIM float64, IUF int) (
+	ZRRout, ZRIout, S1Rout, S1Iout, S2Rout, S2Iout float64, NZout int, ASCLEout, ALIMout float64, IUFout int) {
+
+	pzrr := (*C.double)(&ZRR)
+	pzri := (*C.double)(&ZRI)
+	ps1r := (*C.double)(&S1R)
+	ps1i := (*C.double)(&S1I)
+	ps2r := (*C.double)(&S2R)
+	ps2i := (*C.double)(&S2I)
+	pnz := (*C.int)(unsafe.Pointer(&NZ))
+	pascle := (*C.double)(&ASCLE)
+	palim := (*C.double)(&ALIM)
+	piuf := (*C.int)(unsafe.Pointer(&IUF))
+
+	C.zs1s2_(pzrr, pzri, ps1r, ps1i, ps2r, ps2i, pnz, pascle, palim, piuf)
+	return ZRR, ZRI, S1R, S1I, S2R, S2I, NZ, ASCLE, ALIM, IUF
+}
+
+func ZacaiFort(ZR, ZI, FNU float64, KODE, MR, N int, YR, YI []float64, NZ int, RL, TOL, ELIM, ALIM float64) (
+	ZRout, ZIout, FNUout float64, KODEout, MRout, Nout int, YRout, YIout []float64, NZout int, RLout, TOLout, ELIMout, ALIMout float64) {
+	pzr := (*C.double)(&ZR)
+	pzi := (*C.double)(&ZI)
+	pfnu := (*C.double)(&FNU)
+	pkode := (*C.int)(unsafe.Pointer(&KODE))
+	pmr := (*C.int)(unsafe.Pointer(&MR))
+	pn := (*C.int)(unsafe.Pointer(&N))
+	pyr := (*C.double)(&YR[0])
+	pyi := (*C.double)(&YI[0])
+	pnz := (*C.int)(unsafe.Pointer(&NZ))
+	prl := (*C.double)(&RL)
+	ptol := (*C.double)(&TOL)
+	pelim := (*C.double)(&ELIM)
+	palim := (*C.double)(&ALIM)
+
+	C.zacai_(pzr, pzi, pfnu, pkode, pmr, pn, pyr, pyi, pnz, prl, ptol, pelim, palim)
+	KODE = int(*pkode)
+	MR = int(*pmr)
+	N = int(*pn)
+	NZ = int(*pnz)
+	return ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, RL, TOL, ELIM, ALIM
+}
+
+func ZseriFort(ZR, ZI, FNU float64, KODE, N int, YR, YI []float64, NZ int, TOL, ELIM, ALIM float64) (
+	ZRout, ZIout, FNUout float64, KODEout, Nout int, YRout, YIout []float64, NZout int, TOLout, ELIMout, ALIMout float64) {
+	pzr := (*C.double)(&ZR)
+	pzi := (*C.double)(&ZI)
+	pfnu := (*C.double)(&FNU)
+	pkode := (*C.int)(unsafe.Pointer(&KODE))
+	pn := (*C.int)(unsafe.Pointer(&N))
+	pyr := (*C.double)(&YR[0])
+	pyi := (*C.double)(&YI[0])
+	pnz := (*C.int)(unsafe.Pointer(&NZ))
+	ptol := (*C.double)(&TOL)
+	pelim := (*C.double)(&ELIM)
+	palim := (*C.double)(&ALIM)
+
+	C.zseri_(pzr, pzi, pfnu, pkode, pn, pyr, pyi, pnz, ptol, pelim, palim)
+	KODE = int(*pkode)
+	N = int(*pn)
+	NZ = int(*pnz)
+	return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+}
+
+func ZmlriFort(ZR, ZI, FNU float64, KODE, N int, YR, YI []float64, NZ int, TOL float64) (
+	ZRout, ZIout, FNUout float64, KODEout, Nout int, YRout, YIout []float64, NZout int, TOLout float64) {
+	pzr := (*C.double)(&ZR)
+	pzi := (*C.double)(&ZI)
+	pfnu := (*C.double)(&FNU)
+	pkode := (*C.int)(unsafe.Pointer(&KODE))
+	pn := (*C.int)(unsafe.Pointer(&N))
+	pyr := (*C.double)(&YR[0])
+	pyi := (*C.double)(&YI[0])
+	pnz := (*C.int)(unsafe.Pointer(&NZ))
+	ptol := (*C.double)(&TOL)
+
+	C.zmlri_(pzr, pzi, pfnu, pkode, pn, pyr, pyi, pnz, ptol)
+	KODE = int(*pkode)
+	N = int(*pn)
+	NZ = int(*pnz)
+	return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/i1mach.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/i1mach.f
new file mode 100644
index 00000000..b9683336
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/i1mach.f
@@ -0,0 +1,113 @@
+*DECK I1MACH
+      INTEGER FUNCTION I1MACH(I)
+C***BEGIN PROLOGUE  I1MACH
+C***DATE WRITTEN   750101   (YYMMDD)
+C***REVISION DATE  890213   (YYMMDD)
+C***CATEGORY NO.  R1
+C***KEYWORDS  LIBRARY=SLATEC,TYPE=INTEGER(I1MACH-I),MACHINE CONSTANTS
+C***AUTHOR  FOX, P. A., (BELL LABS)
+C           HALL, A. D., (BELL LABS)
+C           SCHRYER, N. L., (BELL LABS)
+C***PURPOSE  Returns integer machine dependent constants
+C***DESCRIPTION
+C
+C     I1MACH can be used to obtain machine-dependent parameters
+C     for the local machine environment.  It is a function
+C     subroutine with one (input) argument, and can be called
+C     as follows, for example
+C
+C          K = I1MACH(I)
+C
+C     where I=1,...,16.  The (output) value of K above is
+C     determined by the (input) value of I.  The results for
+C     various values of I are discussed below.
+C
+C  I/O unit numbers.
+C    I1MACH( 1) = the standard input unit.
+C    I1MACH( 2) = the standard output unit.
+C    I1MACH( 3) = the standard punch unit.
+C    I1MACH( 4) = the standard error message unit.
+C
+C  Words.
+C    I1MACH( 5) = the number of bits per integer storage unit.
+C    I1MACH( 6) = the number of characters per integer storage unit.
+C
+C  Integers.
+C    assume integers are represented in the S-digit, base-A form
+C
+C               sign ( X(S-1)*A**(S-1) + ... + X(1)*A + X(0) )
+C
+C               where 0 .LE. X(I) .LT. A for I=0,...,S-1.
+C    I1MACH( 7) = A, the base.
+C    I1MACH( 8) = S, the number of base-A digits.
+C    I1MACH( 9) = A**S - 1, the largest magnitude.
+C
+C  Floating-Point Numbers.
+C    Assume floating-point numbers are represented in the T-digit,
+C    base-B form
+C               sign (B**E)*( (X(1)/B) + ... + (X(T)/B**T) )
+C
+C               where 0 .LE. X(I) .LT. B for I=1,...,T,
+C               0 .LT. X(1), and EMIN .LE. E .LE. EMAX.
+C    I1MACH(10) = B, the base.
+C
+C  Single-Precision
+C    I1MACH(11) = T, the number of base-B digits.
+C    I1MACH(12) = EMIN, the smallest exponent E.
+C    I1MACH(13) = EMAX, the largest exponent E.
+C
+C  Double-Precision
+C    I1MACH(14) = T, the number of base-B digits.
+C    I1MACH(15) = EMIN, the smallest exponent E.
+C    I1MACH(16) = EMAX, the largest exponent E.
+C
+C  To alter this function for a particular environment,
+C  the desired set of DATA statements should be activated by
+C  removing the C from column 1.  Also, the values of
+C  I1MACH(1) - I1MACH(4) should be checked for consistency
+C  with the local operating system.
+C
+C***REFERENCES  FOX P.A., HALL A.D., SCHRYER N.L.,*FRAMEWORK FOR A
+C                 PORTABLE LIBRARY*, ACM TRANSACTIONS ON MATHEMATICAL
+C                 SOFTWARE, VOL. 4, NO. 2, JUNE 1978, PP. 177-188.
+C***ROUTINES CALLED  (NONE)
+C***END PROLOGUE  I1MACH
+C
+      INTEGER IMACH(16),OUTPUT
+      SAVE IMACH
+      EQUIVALENCE (IMACH(4),OUTPUT)
+C
+C     MACHINE CONSTANTS FOR THE IBM PC
+C
+      DATA IMACH( 1) /     5 /
+      DATA IMACH( 2) /     6 /
+      DATA IMACH( 3) /     0 /
+      DATA IMACH( 4) /     0 /
+      DATA IMACH( 5) /    32 /
+      DATA IMACH( 6) /     4 /
+      DATA IMACH( 7) /     2 /
+      DATA IMACH( 8) /    31 /
+      DATA IMACH( 9) / 2147483647 /
+      DATA IMACH(10) /     2 /
+      DATA IMACH(11) /    24 /
+      DATA IMACH(12) /  -125 /
+      DATA IMACH(13) /   127 /
+      DATA IMACH(14) /    53 /
+      DATA IMACH(15) / -1021 /
+      DATA IMACH(16) /  1023 /
+C
+C***FIRST EXECUTABLE STATEMENT  I1MACH
+      IF (I .LT. 1  .OR.  I .GT. 16) GO TO 10
+C
+      I1MACH = IMACH(I)
+      RETURN
+C
+   10 CONTINUE
+      WRITE (UNIT = OUTPUT, FMT = 9000)
+ 9000 FORMAT ('1ERROR    1 IN I1MACH - I OUT OF BOUNDS')
+C
+C     CALL FDUMP
+C
+C
+      STOP
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/myabs.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/myabs.f
new file mode 100644
index 00000000..5060195c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/myabs.f
@@ -0,0 +1,5 @@
+      DOUBLE PRECISION FUNCTION MYABS(A)
+      DOUBLE PRECISION A
+      MYABS = DABS(A)
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/myatan.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/myatan.f
new file mode 100644
index 00000000..0887fdae
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/myatan.f
@@ -0,0 +1,5 @@
+      DOUBLE PRECISION FUNCTION MYATAN(A)
+      DOUBLE PRECISION A
+      MYATAN = DATAN(A)
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/mycos.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/mycos.f
new file mode 100644
index 00000000..c39e46df
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/mycos.f
@@ -0,0 +1,5 @@
+      DOUBLE PRECISION FUNCTION MYCOS(A)
+      DOUBLE PRECISION A
+      MYCOS = DCOS(A)
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/myexp.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/myexp.f
new file mode 100644
index 00000000..44a2a80b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/myexp.f
@@ -0,0 +1,5 @@
+      DOUBLE PRECISION FUNCTION MYEXP(A)
+      DOUBLE PRECISION A
+      MYEXP = DEXP(A)
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/mylog.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/mylog.f
new file mode 100644
index 00000000..ac7e3a34
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/mylog.f
@@ -0,0 +1,5 @@
+      DOUBLE PRECISION FUNCTION MYLOG(A)
+      DOUBLE PRECISION A
+      MYLOG = DLOG(A)
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/mymax.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/mymax.f
new file mode 100644
index 00000000..0438eb46
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/mymax.f
@@ -0,0 +1,5 @@
+      DOUBLE PRECISION FUNCTION MYMAX(A, B)
+      DOUBLE PRECISION A, B
+      MYMAX = DMAX1(A,B)
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/mymin.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/mymin.f
new file mode 100644
index 00000000..950606c6
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/mymin.f
@@ -0,0 +1,5 @@
+      DOUBLE PRECISION FUNCTION MYMIN(A, B)
+      DOUBLE PRECISION A, B
+      MYMIN = DMIN1(A,B)
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/mysin.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/mysin.f
new file mode 100644
index 00000000..1663ed56
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/mysin.f
@@ -0,0 +1,5 @@
+      DOUBLE PRECISION FUNCTION MYSIN(A)
+      DOUBLE PRECISION A
+      MYSIN = DSIN(A)
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/mysqrt.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/mysqrt.f
new file mode 100644
index 00000000..a3998389
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/mysqrt.f
@@ -0,0 +1,5 @@
+      DOUBLE PRECISION FUNCTION MYSQRT(A)
+      DOUBLE PRECISION A
+      MYSQRT = SQRT(A)
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/mytan.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/mytan.f
new file mode 100644
index 00000000..239aa682
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/mytan.f
@@ -0,0 +1,5 @@
+      DOUBLE PRECISION FUNCTION MYTAN(A)
+      DOUBLE PRECISION A
+      MYTAN = DTAN(A)
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/xerror.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/xerror.f
new file mode 100644
index 00000000..baa55067
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/xerror.f
@@ -0,0 +1,22 @@
+      SUBROUTINE XERROR(MESS,NMESS,L1,L2)
+C
+C     THIS IS A DUMMY XERROR ROUTINE TO PRINT ERROR MESSAGES WITH NMESS
+C     CHARACTERS. L1 AND L2 ARE DUMMY PARAMETERS TO MAKE THIS CALL
+C     COMPATIBLE WITH THE SLATEC XERROR ROUTINE. THIS IS A FORTRAN 77
+C     ROUTINE.
+C
+      CHARACTER*(*) MESS
+      NN=NMESS/70
+      NR=NMESS-70*NN
+      IF(NR.NE.0) NN=NN+1
+      K=1
+      PRINT 900
+  900 FORMAT(/)
+      DO 10 I=1,NN
+        KMIN=MIN0(K+69,NMESS)
+        PRINT *, MESS(K:KMIN)
+        K=K+70
+   10 CONTINUE
+      PRINT 900
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zabs.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zabs.f
new file mode 100644
index 00000000..23e00a64
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zabs.f
@@ -0,0 +1,34 @@
+      DOUBLE PRECISION FUNCTION MZABS(ZR, ZI)
+C***BEGIN PROLOGUE  ZABS
+C***REFER TO  ZBESH,ZBESI,ZBESJ,ZBESK,ZBESY,ZAIRY,ZBIRY
+C
+C     ZABS COMPUTES THE ABSOLUTE VALUE OR MAGNITUDE OF A DOUBLE
+C     PRECISION COMPLEX VARIABLE CMPLX(ZR,ZI)
+C
+C***ROUTINES CALLED  (NONE)
+C***END PROLOGUE  ZABS
+      DOUBLE PRECISION ZR, ZI, U, V, Q, S
+
+      MZABS = ZABS(CMPLX(ZR,ZI,kind=KIND(1.0D0)))
+      RETURN
+      END
+
+c      U = DABS(ZR)
+c      V = DABS(ZI)
+c      S = U + V
+C-----------------------------------------------------------------------
+C     S*1.0D0 MAKES AN UNNORMALIZED UNDERFLOW ON CDC MACHINES INTO A
+C     TRUE FLOATING ZERO
+C-----------------------------------------------------------------------
+c      S = S*1.0D+0
+c      IF (S.EQ.0.0D+0) GO TO 20
+c      IF (U.GT.V) GO TO 10
+c      Q = U/V
+c      ZABS = V*DSQRT(1.D+0+Q*Q)
+c      RETURN
+c   10 Q = V/U
+c      ZABS = U*DSQRT(1.D+0+Q*Q)
+c      RETURN
+c   20 ZABS = 0.0D+0
+c      RETURN
+c      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zacai.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zacai.f
new file mode 100644
index 00000000..aa05a5c7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zacai.f
@@ -0,0 +1,99 @@
+      SUBROUTINE ZACAI(ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, RL, TOL,
+     * ELIM, ALIM)
+C***BEGIN PROLOGUE  ZACAI
+C***REFER TO  ZAIRY
+C
+C     ZACAI APPLIES THE ANALYTIC CONTINUATION FORMULA
+C
+C         K(FNU,ZN*EXP(MP))=K(FNU,ZN)*EXP(-MP*FNU) - MP*I(FNU,ZN)
+C                 MP=PI*MR*CMPLX(0.0,1.0)
+C
+C     TO CONTINUE THE K FUNCTION FROM THE RIGHT HALF TO THE LEFT
+C     HALF Z PLANE FOR USE WITH ZAIRY WHERE FNU=1/3 OR 2/3 AND N=1.
+C     ZACAI IS THE SAME AS ZACON WITH THE PARTS FOR LARGER ORDERS AND
+C     RECURRENCE REMOVED. A RECURSIVE CALL TO ZACON CAN RESULT IF ZACON
+C     IS CALLED FROM ZAIRY.
+C
+C***ROUTINES CALLED  ZASYI,ZBKNU,ZMLRI,ZSERI,ZS1S2,D1MACH,ZABS
+C***END PROLOGUE  ZACAI
+C     COMPLEX CSGN,CSPN,C1,C2,Y,Z,ZN,CY
+      DOUBLE PRECISION ALIM, ARG, ASCLE, AZ, CSGNR, CSGNI, CSPNR,
+     * CSPNI, C1R, C1I, C2R, C2I, CYR, CYI, DFNU, ELIM, FMR, FNU, PI,
+     * RL, SGN, TOL, YY, YR, YI, ZR, ZI, ZNR, ZNI, D1MACH, ZABS
+      INTEGER INU, IUF, KODE, MR, N, NN, NW, NZ
+      DIMENSION YR(N), YI(N), CYR(2), CYI(2)
+      DATA PI / 3.14159265358979324D0 /
+      NZ = 0
+      ZNR = -ZR
+      ZNI = -ZI
+      AZ = ZABS(CMPLX(ZR,ZI,kind=KIND(1.0D0)))
+      NN = N
+      DFNU = FNU + DBLE(FLOAT(N-1))
+      IF (AZ.LE.2.0D0) GO TO 10
+      IF (AZ*AZ*0.25D0.GT.DFNU+1.0D0) GO TO 20
+   10 CONTINUE
+C-----------------------------------------------------------------------
+C     POWER SERIES FOR THE I FUNCTION
+C-----------------------------------------------------------------------
+      CALL ZSERI(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, TOL, ELIM, ALIM)
+      GO TO 40
+   20 CONTINUE
+      IF (AZ.LT.RL) GO TO 30
+C-----------------------------------------------------------------------
+C     ASYMPTOTIC EXPANSION FOR LARGE Z FOR THE I FUNCTION
+C-----------------------------------------------------------------------
+      CALL ZASYI(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, RL, TOL, ELIM,
+     * ALIM)
+      IF (NW.LT.0) GO TO 80
+      GO TO 40
+   30 CONTINUE
+C-----------------------------------------------------------------------
+C     MILLER ALGORITHM NORMALIZED BY THE SERIES FOR THE I FUNCTION
+C-----------------------------------------------------------------------
+      CALL ZMLRI(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, TOL)
+      IF(NW.LT.0) GO TO 80
+   40 CONTINUE
+C-----------------------------------------------------------------------
+C     ANALYTIC CONTINUATION TO THE LEFT HALF PLANE FOR THE K FUNCTION
+C-----------------------------------------------------------------------
+      CALL ZBKNU(ZNR, ZNI, FNU, KODE, 1, CYR, CYI, NW, TOL, ELIM, ALIM)
+      IF (NW.NE.0) GO TO 80
+      FMR = DBLE(FLOAT(MR))
+      SGN = -DSIGN(PI,FMR)
+      CSGNR = 0.0D0
+      CSGNI = SGN
+      IF (KODE.EQ.1) GO TO 50
+      YY = -ZNI
+      CSGNR = -CSGNI*DSIN(YY)
+      CSGNI = CSGNI*DCOS(YY)
+   50 CONTINUE
+C-----------------------------------------------------------------------
+C     CALCULATE CSPN=EXP(FNU*PI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE
+C     WHEN FNU IS LARGE
+C-----------------------------------------------------------------------
+      INU = INT(SNGL(FNU))
+      ARG = (FNU-DBLE(FLOAT(INU)))*SGN
+      CSPNR = DCOS(ARG)
+      CSPNI = DSIN(ARG)
+      IF (MOD(INU,2).EQ.0) GO TO 60
+      CSPNR = -CSPNR
+      CSPNI = -CSPNI
+   60 CONTINUE
+      C1R = CYR(1)
+      C1I = CYI(1)
+      C2R = YR(1)
+      C2I = YI(1)
+      IF (KODE.EQ.1) GO TO 70
+      IUF = 0
+      ASCLE = 1.0D+3*D1MACH(1)/TOL
+      CALL ZS1S2(ZNR, ZNI, C1R, C1I, C2R, C2I, NW, ASCLE, ALIM, IUF)
+      NZ = NZ + NW
+   70 CONTINUE
+      YR(1) = CSPNR*C1R - CSPNI*C1I + CSGNR*C2R - CSGNI*C2I
+      YI(1) = CSPNR*C1I + CSPNI*C1R + CSGNR*C2I + CSGNI*C2R
+      RETURN
+   80 CONTINUE
+      NZ = -1
+      IF(NW.EQ.(-2)) NZ=-2
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zacon.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zacon.f
new file mode 100644
index 00000000..ba593590
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zacon.f
@@ -0,0 +1,203 @@
+      SUBROUTINE ZACON(ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, RL, FNUL,
+     * TOL, ELIM, ALIM)
+C***BEGIN PROLOGUE  ZACON
+C***REFER TO  ZBESK,ZBESH
+C
+C     ZACON APPLIES THE ANALYTIC CONTINUATION FORMULA
+C
+C         K(FNU,ZN*EXP(MP))=K(FNU,ZN)*EXP(-MP*FNU) - MP*I(FNU,ZN)
+C                 MP=PI*MR*CMPLX(0.0,1.0)
+C
+C     TO CONTINUE THE K FUNCTION FROM THE RIGHT HALF TO THE LEFT
+C     HALF Z PLANE
+C
+C***ROUTINES CALLED  ZBINU,ZBKNU,ZS1S2,D1MACH,ZABS,ZMLT
+C***END PROLOGUE  ZACON
+C     COMPLEX CK,CONE,CSCL,CSCR,CSGN,CSPN,CY,CZERO,C1,C2,RZ,SC1,SC2,ST,
+C    *S1,S2,Y,Z,ZN
+      DOUBLE PRECISION ALIM, ARG, ASCLE, AS2, AZN, BRY, BSCLE, CKI,
+     * CKR, CONER, CPN, CSCL, CSCR, CSGNI, CSGNR, CSPNI, CSPNR,
+     * CSR, CSRR, CSSR, CYI, CYR, C1I, C1M, C1R, C2I, C2R, ELIM, FMR,
+     * FN, FNU, FNUL, PI, PTI, PTR, RAZN, RL, RZI, RZR, SC1I, SC1R,
+     * SC2I, SC2R, SGN, SPN, STI, STR, S1I, S1R, S2I, S2R, TOL, YI, YR,
+     * YY, ZEROR, ZI, ZNI, ZNR, ZR, D1MACH, ZABS
+      INTEGER I, INU, IUF, KFLAG, KODE, MR, N, NN, NW, NZ
+      DIMENSION YR(N), YI(N), CYR(2), CYI(2), CSSR(3), CSRR(3), BRY(3)
+      DATA PI / 3.14159265358979324D0 /
+      DATA ZEROR,CONER / 0.0D0,1.0D0 /
+      NZ = 0
+      ZNR = -ZR
+      ZNI = -ZI
+      NN = N
+      CALL ZBINU(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, RL, FNUL, TOL,
+     * ELIM, ALIM)
+      IF (NW.LT.0) GO TO 90
+C-----------------------------------------------------------------------
+C     ANALYTIC CONTINUATION TO THE LEFT HALF PLANE FOR THE K FUNCTION
+C-----------------------------------------------------------------------
+      NN = MIN0(2,N)
+      CALL ZBKNU(ZNR, ZNI, FNU, KODE, NN, CYR, CYI, NW, TOL, ELIM, ALIM)
+      IF (NW.NE.0) GO TO 90
+      S1R = CYR(1)
+      S1I = CYI(1)
+      FMR = DBLE(FLOAT(MR))
+      SGN = -DSIGN(PI,FMR)
+      CSGNR = ZEROR
+      CSGNI = SGN
+      IF (KODE.EQ.1) GO TO 10
+      YY = -ZNI
+      CPN = DCOS(YY)
+      SPN = DSIN(YY)
+      CALL ZMLT(CSGNR, CSGNI, CPN, SPN, CSGNR, CSGNI)
+   10 CONTINUE
+C-----------------------------------------------------------------------
+C     CALCULATE CSPN=EXP(FNU*PI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE
+C     WHEN FNU IS LARGE
+C-----------------------------------------------------------------------
+      INU = INT(SNGL(FNU))
+      ARG = (FNU-DBLE(FLOAT(INU)))*SGN
+      CPN = DCOS(ARG)
+      SPN = DSIN(ARG)
+      CSPNR = CPN
+      CSPNI = SPN
+      IF (MOD(INU,2).EQ.0) GO TO 20
+      CSPNR = -CSPNR
+      CSPNI = -CSPNI
+   20 CONTINUE
+      IUF = 0
+      C1R = S1R
+      C1I = S1I
+      C2R = YR(1)
+      C2I = YI(1)
+      ASCLE = 1.0D+3*D1MACH(1)/TOL
+      IF (KODE.EQ.1) GO TO 30
+      CALL ZS1S2(ZNR, ZNI, C1R, C1I, C2R, C2I, NW, ASCLE, ALIM, IUF)
+      NZ = NZ + NW
+      SC1R = C1R
+      SC1I = C1I
+   30 CONTINUE
+      CALL ZMLT(CSPNR, CSPNI, C1R, C1I, STR, STI)
+      CALL ZMLT(CSGNR, CSGNI, C2R, C2I, PTR, PTI)
+      YR(1) = STR + PTR
+      YI(1) = STI + PTI
+      IF (N.EQ.1) RETURN
+      CSPNR = -CSPNR
+      CSPNI = -CSPNI
+      S2R = CYR(2)
+      S2I = CYI(2)
+      C1R = S2R
+      C1I = S2I
+      C2R = YR(2)
+      C2I = YI(2)
+      IF (KODE.EQ.1) GO TO 40
+      CALL ZS1S2(ZNR, ZNI, C1R, C1I, C2R, C2I, NW, ASCLE, ALIM, IUF)
+      NZ = NZ + NW
+      SC2R = C1R
+      SC2I = C1I
+   40 CONTINUE
+      CALL ZMLT(CSPNR, CSPNI, C1R, C1I, STR, STI)
+      CALL ZMLT(CSGNR, CSGNI, C2R, C2I, PTR, PTI)
+      YR(2) = STR + PTR
+      YI(2) = STI + PTI
+      IF (N.EQ.2) RETURN
+      CSPNR = -CSPNR
+      CSPNI = -CSPNI
+      AZN = ZABS(CMPLX(ZNR,ZNI,kind=KIND(1.0D0)))
+      RAZN = 1.0D0/AZN
+      STR = ZNR*RAZN
+      STI = -ZNI*RAZN
+      RZR = (STR+STR)*RAZN
+      RZI = (STI+STI)*RAZN
+      FN = FNU + 1.0D0
+      CKR = FN*RZR
+      CKI = FN*RZI
+C-----------------------------------------------------------------------
+C     SCALE NEAR EXPONENT EXTREMES DURING RECURRENCE ON K FUNCTIONS
+C-----------------------------------------------------------------------
+      CSCL = 1.0D0/TOL
+      CSCR = TOL
+      CSSR(1) = CSCL
+      CSSR(2) = CONER
+      CSSR(3) = CSCR
+      CSRR(1) = CSCR
+      CSRR(2) = CONER
+      CSRR(3) = CSCL
+      BRY(1) = ASCLE
+      BRY(2) = 1.0D0/ASCLE
+      BRY(3) = D1MACH(2)
+      AS2 = ZABS(CMPLX(S2R,S2I,kind=KIND(1.0D0)))
+      KFLAG = 2
+      IF (AS2.GT.BRY(1)) GO TO 50
+      KFLAG = 1
+      GO TO 60
+   50 CONTINUE
+      IF (AS2.LT.BRY(2)) GO TO 60
+      KFLAG = 3
+   60 CONTINUE
+      BSCLE = BRY(KFLAG)
+      S1R = S1R*CSSR(KFLAG)
+      S1I = S1I*CSSR(KFLAG)
+      S2R = S2R*CSSR(KFLAG)
+      S2I = S2I*CSSR(KFLAG)
+      CSR = CSRR(KFLAG)
+      DO 80 I=3,N
+        STR = S2R
+        STI = S2I
+        S2R = CKR*STR - CKI*STI + S1R
+        S2I = CKR*STI + CKI*STR + S1I
+        S1R = STR
+        S1I = STI
+        C1R = S2R*CSR
+        C1I = S2I*CSR
+        STR = C1R
+        STI = C1I
+        C2R = YR(I)
+        C2I = YI(I)
+        IF (KODE.EQ.1) GO TO 70
+        IF (IUF.LT.0) GO TO 70
+        CALL ZS1S2(ZNR, ZNI, C1R, C1I, C2R, C2I, NW, ASCLE, ALIM, IUF)
+        NZ = NZ + NW
+        SC1R = SC2R
+        SC1I = SC2I
+        SC2R = C1R
+        SC2I = C1I
+        IF (IUF.NE.3) GO TO 70
+        IUF = -4
+        S1R = SC1R*CSSR(KFLAG)
+        S1I = SC1I*CSSR(KFLAG)
+        S2R = SC2R*CSSR(KFLAG)
+        S2I = SC2I*CSSR(KFLAG)
+        STR = SC2R
+        STI = SC2I
+   70   CONTINUE
+        PTR = CSPNR*C1R - CSPNI*C1I
+        PTI = CSPNR*C1I + CSPNI*C1R
+        YR(I) = PTR + CSGNR*C2R - CSGNI*C2I
+        YI(I) = PTI + CSGNR*C2I + CSGNI*C2R
+        CKR = CKR + RZR
+        CKI = CKI + RZI
+        CSPNR = -CSPNR
+        CSPNI = -CSPNI
+        IF (KFLAG.GE.3) GO TO 80
+        PTR = DABS(C1R)
+        PTI = DABS(C1I)
+        C1M = DMAX1(PTR,PTI)
+        IF (C1M.LE.BSCLE) GO TO 80
+        KFLAG = KFLAG + 1
+        BSCLE = BRY(KFLAG)
+        S1R = S1R*CSR
+        S1I = S1I*CSR
+        S2R = STR
+        S2I = STI
+        S1R = S1R*CSSR(KFLAG)
+        S1I = S1I*CSSR(KFLAG)
+        S2R = S2R*CSSR(KFLAG)
+        S2I = S2I*CSSR(KFLAG)
+        CSR = CSRR(KFLAG)
+   80 CONTINUE
+      RETURN
+   90 CONTINUE
+      NZ = -1
+      IF(NW.EQ.(-2)) NZ=-2
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zairy.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zairy.f
new file mode 100644
index 00000000..6adab8f5
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zairy.f
@@ -0,0 +1,395 @@
+      SUBROUTINE ZAIRY(ZR, ZI, ID, KODE, AIR, AII, NZ, IERR)
+C***BEGIN PROLOGUE  ZAIRY
+C***DATE WRITTEN   830501   (YYMMDD)
+C***REVISION DATE  890801   (YYMMDD)
+C***CATEGORY NO.  B5K
+C***KEYWORDS  AIRY FUNCTION,BESSEL FUNCTIONS OF ORDER ONE THIRD
+C***AUTHOR  AMOS, DONALD E., SANDIA NATIONAL LABORATORIES
+C***PURPOSE  TO COMPUTE AIRY FUNCTIONS AI(Z) AND DAI(Z) FOR COMPLEX Z
+C***DESCRIPTION
+C
+C                      ***A DOUBLE PRECISION ROUTINE***
+C         ON KODE=1, ZAIRY COMPUTES THE COMPLEX AIRY FUNCTION AI(Z) OR
+C         ITS DERIVATIVE DAI(Z)/DZ ON ID=0 OR ID=1 RESPECTIVELY. ON
+C         KODE=2, A SCALING OPTION CEXP(ZTA)*AI(Z) OR CEXP(ZTA)*
+C         DAI(Z)/DZ IS PROVIDED TO REMOVE THE EXPONENTIAL DECAY IN
+C         -PI/3.LT.ARG(Z).LT.PI/3 AND THE EXPONENTIAL GROWTH IN
+C         PI/3.LT.ABS(ARG(Z)).LT.PI WHERE ZTA=(2/3)*Z*CSQRT(Z).
+C
+C         WHILE THE AIRY FUNCTIONS AI(Z) AND DAI(Z)/DZ ARE ANALYTIC IN
+C         THE WHOLE Z PLANE, THE CORRESPONDING SCALED FUNCTIONS DEFINED
+C         FOR KODE=2 HAVE A CUT ALONG THE NEGATIVE REAL AXIS.
+C         DEFINTIONS AND NOTATION ARE FOUND IN THE NBS HANDBOOK OF
+C         MATHEMATICAL FUNCTIONS (REF. 1).
+C
+C         INPUT      ZR,ZI ARE DOUBLE PRECISION
+C           ZR,ZI  - Z=CMPLX(ZR,ZI)
+C           ID     - ORDER OF DERIVATIVE, ID=0 OR ID=1
+C           KODE   - A PARAMETER TO INDICATE THE SCALING OPTION
+C                    KODE= 1  RETURNS
+C                             AI=AI(Z)                ON ID=0 OR
+C                             AI=DAI(Z)/DZ            ON ID=1
+C                        = 2  RETURNS
+C                             AI=CEXP(ZTA)*AI(Z)       ON ID=0 OR
+C                             AI=CEXP(ZTA)*DAI(Z)/DZ   ON ID=1 WHERE
+C                             ZTA=(2/3)*Z*CSQRT(Z)
+C
+C         OUTPUT     AIR,AII ARE DOUBLE PRECISION
+C           AIR,AII- COMPLEX ANSWER DEPENDING ON THE CHOICES FOR ID AND
+C                    KODE
+C           NZ     - UNDERFLOW INDICATOR
+C                    NZ= 0   , NORMAL RETURN
+C                    NZ= 1   , AI=CMPLX(0.0D0,0.0D0) DUE TO UNDERFLOW IN
+C                              -PI/3.LT.ARG(Z).LT.PI/3 ON KODE=1
+C           IERR   - ERROR FLAG
+C                    IERR=0, NORMAL RETURN - COMPUTATION COMPLETED
+C                    IERR=1, INPUT ERROR   - NO COMPUTATION
+C                    IERR=2, OVERFLOW      - NO COMPUTATION, REAL(ZTA)
+C                            TOO LARGE ON KODE=1
+C                    IERR=3, CABS(Z) LARGE      - COMPUTATION COMPLETED
+C                            LOSSES OF SIGNIFCANCE BY ARGUMENT REDUCTION
+C                            PRODUCE LESS THAN HALF OF MACHINE ACCURACY
+C                    IERR=4, CABS(Z) TOO LARGE  - NO COMPUTATION
+C                            COMPLETE LOSS OF ACCURACY BY ARGUMENT
+C                            REDUCTION
+C                    IERR=5, ERROR              - NO COMPUTATION,
+C                            ALGORITHM TERMINATION CONDITION NOT MET
+C
+C***LONG DESCRIPTION
+C
+C         AI AND DAI ARE COMPUTED FOR CABS(Z).GT.1.0 FROM THE K BESSEL
+C         FUNCTIONS BY
+C
+C            AI(Z)=C*SQRT(Z)*K(1/3,ZTA) , DAI(Z)=-C*Z*K(2/3,ZTA)
+C                           C=1.0/(PI*SQRT(3.0))
+C                            ZTA=(2/3)*Z**(3/2)
+C
+C         WITH THE POWER SERIES FOR CABS(Z).LE.1.0.
+C
+C         IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE-
+C         MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z IS LARGE, LOSSES
+C         OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR. CONSEQUENTLY, IF
+C         THE MAGNITUDE OF ZETA=(2/3)*Z**1.5 EXCEEDS U1=SQRT(0.5/UR),
+C         THEN LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR
+C         FLAG IERR=3 IS TRIGGERED WHERE UR=DMAX1(D1MACH(4),1.0D-18) IS
+C         DOUBLE PRECISION UNIT ROUNDOFF LIMITED TO 18 DIGITS PRECISION.
+C         ALSO, IF THE MAGNITUDE OF ZETA IS LARGER THAN U2=0.5/UR, THEN
+C         ALL SIGNIFICANCE IS LOST AND IERR=4. IN ORDER TO USE THE INT
+C         FUNCTION, ZETA MUST BE FURTHER RESTRICTED NOT TO EXCEED THE
+C         LARGEST INTEGER, U3=I1MACH(9). THUS, THE MAGNITUDE OF ZETA
+C         MUST BE RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2,
+C         AND U3 ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE
+C         PRECISION ARITHMETIC AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE
+C         PRECISION ARITHMETIC RESPECTIVELY. THIS MAKES U2 AND U3 LIMIT-
+C         ING IN THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT THE MAG-
+C         NITUDE OF Z CANNOT EXCEED 3.1E+4 IN SINGLE AND 2.1E+6 IN
+C         DOUBLE PRECISION ARITHMETIC. THIS ALSO MEANS THAT ONE CAN
+C         EXPECT TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES,
+C         NO DIGITS IN SINGLE PRECISION AND ONLY 7 DIGITS IN DOUBLE
+C         PRECISION ARITHMETIC. SIMILAR CONSIDERATIONS HOLD FOR OTHER
+C         MACHINES.
+C
+C         THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX
+C         BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT
+C         ROUNDOFF,1.0E-18) IS THE NOMINAL PRECISION AND 10**S REPRE-
+C         SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE
+C         ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))),
+C         ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF
+C         CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY
+C         HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN
+C         ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY
+C         SEVERAL ORDERS OF MAGNITUDE. IF ONE COMPONENT IS 10**K LARGER
+C         THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K,
+C         0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS
+C         THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER
+C         COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY
+C         BECAUSE, IN COMPLEX ARITHMETIC WITH PRECISION P, THE SMALLER
+C         COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE
+C         MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES,
+C         THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P,
+C         OR -PI/2+P.
+C
+C***REFERENCES  HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ
+C                 AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF
+C                 COMMERCE, 1955.
+C
+C               COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+C                 AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983
+C
+C               A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+C                 ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85-
+C                 1018, MAY, 1985
+C
+C               A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+C                 ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS.
+C                 MATH. SOFTWARE, 1986
+C
+C***ROUTINES CALLED  ZACAI,ZBKNU,ZEXP,ZSQRT,I1MACH,D1MACH
+C***END PROLOGUE  ZAIRY
+C     COMPLEX AI,CONE,CSQ,CY,S1,S2,TRM1,TRM2,Z,ZTA,Z3
+      DOUBLE PRECISION AA, AD, AII, AIR, AK, ALIM, ATRM, AZ, AZ3, BK,
+     * CC, CK, COEF, CONEI, CONER, CSQI, CSQR, CYI, CYR, C1, C2, DIG,
+     * DK, D1, D2, ELIM, FID, FNU, PTR, RL, R1M5, SFAC, STI, STR,
+     * S1I, S1R, S2I, S2R, TOL, TRM1I, TRM1R, TRM2I, TRM2R, TTH, ZEROI,
+     * ZEROR, ZI, ZR, ZTAI, ZTAR, Z3I, Z3R, D1MACH, ZABS, ALAZ, BB
+      INTEGER ID, IERR, IFLAG, K, KODE, K1, K2, MR, NN, NZ, I1MACH
+      DIMENSION CYR(1), CYI(1)
+      DATA TTH, C1, C2, COEF /6.66666666666666667D-01,
+     * 3.55028053887817240D-01,2.58819403792806799D-01,
+     * 1.83776298473930683D-01/
+      DATA ZEROR, ZEROI, CONER, CONEI /0.0D0,0.0D0,1.0D0,0.0D0/
+C***FIRST EXECUTABLE STATEMENT  ZAIRY
+      IERR = 0
+      NZ=0
+      IF (ID.LT.0 .OR. ID.GT.1) IERR=1
+      IF (KODE.LT.1 .OR. KODE.GT.2) IERR=1
+      IF (IERR.NE.0) RETURN
+      AZ = ZABS(CMPLX(ZR,ZI,kind=KIND(1.0D0)))
+      TOL = DMAX1(D1MACH(4),1.0D-18)
+      FID = DBLE(FLOAT(ID))
+      IF (AZ.GT.1.0D0) GO TO 70
+C-----------------------------------------------------------------------
+C     POWER SERIES FOR CABS(Z).LE.1.
+C-----------------------------------------------------------------------
+      S1R = CONER
+      S1I = CONEI
+      S2R = CONER
+      S2I = CONEI
+      IF (AZ.LT.TOL) GO TO 170
+      AA = AZ*AZ
+      IF (AA.LT.TOL/AZ) GO TO 40
+      TRM1R = CONER
+      TRM1I = CONEI
+      TRM2R = CONER
+      TRM2I = CONEI
+      ATRM = 1.0D0
+      STR = ZR*ZR - ZI*ZI
+      STI = ZR*ZI + ZI*ZR
+      Z3R = STR*ZR - STI*ZI
+      Z3I = STR*ZI + STI*ZR
+      AZ3 = AZ*AA
+      AK = 2.0D0 + FID
+      BK = 3.0D0 - FID - FID
+      CK = 4.0D0 - FID
+      DK = 3.0D0 + FID + FID
+      D1 = AK*DK
+      D2 = BK*CK
+      AD = DMIN1(D1,D2)
+      AK = 24.0D0 + 9.0D0*FID
+      BK = 30.0D0 - 9.0D0*FID
+      DO 30 K=1,25
+        STR = (TRM1R*Z3R-TRM1I*Z3I)/D1
+        TRM1I = (TRM1R*Z3I+TRM1I*Z3R)/D1
+        TRM1R = STR
+        S1R = S1R + TRM1R
+        S1I = S1I + TRM1I
+        STR = (TRM2R*Z3R-TRM2I*Z3I)/D2
+        TRM2I = (TRM2R*Z3I+TRM2I*Z3R)/D2
+        TRM2R = STR
+        S2R = S2R + TRM2R
+        S2I = S2I + TRM2I
+        ATRM = ATRM*AZ3/AD
+        D1 = D1 + AK
+        D2 = D2 + BK
+        AD = DMIN1(D1,D2)
+        IF (ATRM.LT.TOL*AD) GO TO 40
+        AK = AK + 18.0D0
+        BK = BK + 18.0D0
+   30 CONTINUE
+   40 CONTINUE
+      IF (ID.EQ.1) THEN
+        GO TO 50
+      END IF
+      AIR = S1R*C1 - C2*(ZR*S2R-ZI*S2I)
+      AII = S1I*C1 - C2*(ZR*S2I+ZI*S2R)
+      IF (KODE.EQ.1) RETURN
+      CALL ZSQRT(ZR, ZI, STR, STI)
+      ZTAR = TTH*(ZR*STR-ZI*STI)
+      ZTAI = TTH*(ZR*STI+ZI*STR)
+      CALL ZEXP(ZTAR, ZTAI, STR, STI)
+      PTR = AIR*STR - AII*STI
+      AII = AIR*STI + AII*STR
+      AIR = PTR
+      RETURN
+   50 CONTINUE
+      AIR = -S2R*C2
+      AII = -S2I*C2
+      IF (AZ.LE.TOL) GO TO 60
+      STR = ZR*S1R - ZI*S1I
+      STI = ZR*S1I + ZI*S1R
+      CC = C1/(1.0D0+FID)
+      AIR = AIR + CC*(STR*ZR-STI*ZI)
+      AII = AII + CC*(STR*ZI+STI*ZR)
+   60 CONTINUE
+      IF (KODE.EQ.1) RETURN
+      CALL ZSQRT(ZR, ZI, STR, STI)
+      ZTAR = TTH*(ZR*STR-ZI*STI)
+      ZTAI = TTH*(ZR*STI+ZI*STR)
+      CALL ZEXP(ZTAR, ZTAI, STR, STI)
+      PTR = STR*AIR - STI*AII
+      AII = STR*AII + STI*AIR
+      AIR = PTR
+      RETURN
+C-----------------------------------------------------------------------
+C     CASE FOR CABS(Z).GT.1.0
+C-----------------------------------------------------------------------
+   70 CONTINUE
+      FNU = (1.0D0+FID)/3.0D0
+C-----------------------------------------------------------------------
+C     SET PARAMETERS RELATED TO MACHINE CONSTANTS.
+C     TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0D-18.
+C     ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW LIMIT.
+C     EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL    AND
+C     EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL       ARE INTERVALS NEAR
+C     UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE.
+C     RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR LARGE Z.
+C     DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG).
+C-----------------------------------------------------------------------
+      K1 = I1MACH(15)
+      K2 = I1MACH(16)
+      R1M5 = D1MACH(5)
+      K = MIN0(IABS(K1),IABS(K2))
+      ELIM = 2.303D0*(DBLE(FLOAT(K))*R1M5-3.0D0)
+      K1 = I1MACH(14) - 1
+      AA = R1M5*DBLE(FLOAT(K1))
+      DIG = DMIN1(AA,18.0D0)
+      AA = AA*2.303D0
+      ALIM = ELIM + DMAX1(-AA,-41.45D0)
+      RL = 1.2D0*DIG + 3.0D0
+      ALAZ = DLOG(AZ)
+C--------------------------------------------------------------------------
+C     TEST FOR PROPER RANGE
+C-----------------------------------------------------------------------
+      AA=0.5D0/TOL
+      BB=DBLE(FLOAT(I1MACH(9)))*0.5D0
+      AA=DMIN1(AA,BB)
+      AA=AA**TTH
+      IF (AZ.GT.AA) GO TO 260
+      AA=DSQRT(AA)
+      IF (AZ.GT.AA) IERR=3
+      CALL ZSQRT(ZR, ZI, CSQR, CSQI)
+      ZTAR = TTH*(ZR*CSQR-ZI*CSQI)
+      ZTAI = TTH*(ZR*CSQI+ZI*CSQR)
+C-----------------------------------------------------------------------
+C     RE(ZTA).LE.0 WHEN RE(Z).LT.0, ESPECIALLY WHEN IM(Z) IS SMALL
+C-----------------------------------------------------------------------
+      IFLAG = 0
+      SFAC = 1.0D0
+      AK = ZTAI
+      IF (ZR.GE.0.0D0) GO TO 80
+      BK = ZTAR
+      CK = -DABS(BK)
+      ZTAR = CK
+      ZTAI = AK
+   80 CONTINUE
+      IF (ZI.NE.0.0D0) GO TO 90
+      IF (ZR.GT.0.0D0) GO TO 90
+      ZTAR = 0.0D0
+      ZTAI = AK
+   90 CONTINUE
+      AA = ZTAR
+      IF (AA.GE.0.0D0 .AND. ZR.GT.0.0D0) GO TO 110
+      IF (KODE.EQ.2) GO TO 100
+C-----------------------------------------------------------------------
+C     OVERFLOW TEST
+C-----------------------------------------------------------------------
+      IF (AA.GT.(-ALIM)) GO TO 100
+      AA = -AA + 0.25D0*ALAZ
+      IFLAG = 1
+      SFAC = TOL
+      IF (AA.GT.ELIM) GO TO 270
+  100 CONTINUE
+C-----------------------------------------------------------------------
+C     CBKNU AND CACON RETURN EXP(ZTA)*K(FNU,ZTA) ON KODE=2
+C-----------------------------------------------------------------------
+      MR = 1
+      IF (ZI.LT.0.0D0) MR = -1
+      CALL ZACAI(ZTAR, ZTAI, FNU, KODE, MR, 1, CYR, CYI, NN, RL, TOL,
+     * ELIM, ALIM)
+      IF (NN.LT.0) GO TO 280
+      NZ = NZ + NN
+      GO TO 130
+  110 CONTINUE
+      IF (KODE.EQ.2) GO TO 120
+C-----------------------------------------------------------------------
+C     UNDERFLOW TEST
+C-----------------------------------------------------------------------
+      IF (AA.LT.ALIM) GO TO 120
+      AA = -AA - 0.25D0*ALAZ
+      IFLAG = 2
+      SFAC = 1.0D0/TOL
+      IF (AA.LT.(-ELIM)) GO TO 210
+  120 CONTINUE
+      CALL ZBKNU(ZTAR, ZTAI, FNU, KODE, 1, CYR, CYI, NZ, TOL, ELIM,
+     * ALIM)
+  130 CONTINUE
+      S1R = CYR(1)*COEF
+      S1I = CYI(1)*COEF
+      IF (IFLAG.NE.0) GO TO 150
+      IF (ID.EQ.1) GO TO 140
+      AIR = CSQR*S1R - CSQI*S1I
+      AII = CSQR*S1I + CSQI*S1R
+      RETURN
+  140 CONTINUE
+      AIR = -(ZR*S1R-ZI*S1I)
+      AII = -(ZR*S1I+ZI*S1R)
+      RETURN
+  150 CONTINUE
+      S1R = S1R*SFAC
+      S1I = S1I*SFAC
+      IF (ID.EQ.1) GO TO 160
+      STR = S1R*CSQR - S1I*CSQI
+      S1I = S1R*CSQI + S1I*CSQR
+      S1R = STR
+      AIR = S1R/SFAC
+      AII = S1I/SFAC
+      RETURN
+  160 CONTINUE
+      STR = -(S1R*ZR-S1I*ZI)
+      S1I = -(S1R*ZI+S1I*ZR)
+      S1R = STR
+      AIR = S1R/SFAC
+      AII = S1I/SFAC
+      RETURN
+  170 CONTINUE
+      AA = 1.0D+3*D1MACH(1)
+      S1R = ZEROR
+      S1I = ZEROI
+      IF (ID.EQ.1) GO TO 190
+      IF (AZ.LE.AA) GO TO 180
+      S1R = C2*ZR
+      S1I = C2*ZI
+  180 CONTINUE
+      AIR = C1 - S1R
+      AII = -S1I
+      RETURN
+  190 CONTINUE
+      AIR = -C2
+      AII = 0.0D0
+      AA = DSQRT(AA)
+      IF (AZ.LE.AA) GO TO 200
+      S1R = 0.5D0*(ZR*ZR-ZI*ZI)
+      S1I = ZR*ZI
+  200 CONTINUE
+      AIR = AIR + C1*S1R
+      AII = AII + C1*S1I
+      RETURN
+  210 CONTINUE
+      NZ = 1
+      AIR = ZEROR
+      AII = ZEROI
+      RETURN
+  270 CONTINUE
+      NZ = 0
+      IERR=2
+      RETURN
+  280 CONTINUE
+      IF(NN.EQ.(-1)) GO TO 270
+      NZ=0
+      IERR=5
+      RETURN
+  260 CONTINUE
+      IERR=4
+      NZ=0
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zasyi.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zasyi.f
new file mode 100644
index 00000000..139d7390
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zasyi.f
@@ -0,0 +1,169 @@
+      SUBROUTINE ZASYI(ZR, ZI, FNU, KODE, N, YR, YI, NZ, RL, TOL, ELIM,
+     * ALIM)
+C***BEGIN PROLOGUE  ZASYI
+C***REFER TO  ZBESI,ZBESK
+C
+C     ZASYI COMPUTES THE I BESSEL FUNCTION FOR REAL(Z).GE.0.0 BY
+C     MEANS OF THE ASYMPTOTIC EXPANSION FOR LARGE CABS(Z) IN THE
+C     REGION CABS(Z).GT.MAX(RL,FNU*FNU/2). NZ=0 IS A NORMAL RETURN.
+C     NZ.LT.0 INDICATES AN OVERFLOW ON KODE=1.
+C
+C***ROUTINES CALLED  D1MACH,ZABS,ZDIV,ZEXP,ZMLT,ZSQRT
+C***END PROLOGUE  ZASYI
+C     COMPLEX AK1,CK,CONE,CS1,CS2,CZ,CZERO,DK,EZ,P1,RZ,S2,Y,Z
+      DOUBLE PRECISION AA, AEZ, AK, AK1I, AK1R, ALIM, ARG, ARM, ATOL,
+     * AZ, BB, BK, CKI, CKR, CONEI, CONER, CS1I, CS1R, CS2I, CS2R, CZI,
+     * CZR, DFNU, DKI, DKR, DNU2, ELIM, EZI, EZR, FDN, FNU, PI, P1I,
+     * P1R, RAZ, RL, RTPI, RTR1, RZI, RZR, S, SGN, SQK, STI, STR, S2I,
+     * S2R, TOL, TZI, TZR, YI, YR, ZEROI, ZEROR, ZI, ZR, D1MACH, ZABS
+      INTEGER I, IB, IL, INU, J, JL, K, KODE, KODED, M, N, NN, NZ
+      DIMENSION YR(N), YI(N)
+      DATA PI, RTPI  /3.14159265358979324D0 , 0.159154943091895336D0 /
+      DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 /
+C
+      NZ = 0
+      AZ = ZABS(CMPLX(ZR,ZI,kind=KIND(1.0D0)))
+      ARM = 1.0D+3*D1MACH(1)
+      RTR1 = DSQRT(ARM)
+      IL = MIN0(2,N)
+      DFNU = FNU + DBLE(FLOAT(N-IL))
+C-----------------------------------------------------------------------
+C     OVERFLOW TEST
+C-----------------------------------------------------------------------
+      RAZ = 1.0D0/AZ
+      STR = ZR*RAZ
+      STI = -ZI*RAZ
+      AK1R = RTPI*STR*RAZ
+      AK1I = RTPI*STI*RAZ
+      CALL ZSQRT(AK1R, AK1I, AK1R, AK1I)
+      CZR = ZR
+      CZI = ZI
+      IF (KODE.NE.2) GO TO 10
+      CZR = ZEROR
+      CZI = ZI
+   10 CONTINUE
+      IF (DABS(CZR).GT.ELIM) GO TO 100
+      DNU2 = DFNU + DFNU
+      KODED = 1
+      IF ((DABS(CZR).GT.ALIM) .AND. (N.GT.2)) GO TO 20
+      KODED = 0
+      CALL ZEXP(CZR, CZI, STR, STI)
+      CALL ZMLT(AK1R, AK1I, STR, STI, AK1R, AK1I)
+   20 CONTINUE
+      FDN = 0.0D0
+      IF (DNU2.GT.RTR1) THEN
+        FDN = DNU2*DNU2
+      END IF
+      EZR = ZR*8.0D0
+      EZI = ZI*8.0D0
+C-----------------------------------------------------------------------
+C     WHEN Z IS IMAGINARY, THE ERROR TEST MUST BE MADE RELATIVE TO THE
+C     FIRST RECIPROCAL POWER SINCE THIS IS THE LEADING TERM OF THE
+C     EXPANSION FOR THE IMAGINARY PART.
+C-----------------------------------------------------------------------
+      AEZ = 8.0D0*AZ
+      S = TOL/AEZ
+      JL = INT(SNGL(RL+RL)) + 2
+      P1R = ZEROR
+      P1I = ZEROI
+      IF (ZI.EQ.0.0D0) GO TO 30
+C-----------------------------------------------------------------------
+C     CALCULATE EXP(PI*(0.5+FNU+N-IL)*I) TO MINIMIZE LOSSES OF
+C     SIGNIFICANCE WHEN FNU OR N IS LARGE
+C-----------------------------------------------------------------------
+      INU = INT(SNGL(FNU))
+      ARG = (FNU-DBLE(FLOAT(INU)))*PI
+      INU = INU + N - IL
+      AK = -DSIN(ARG)
+      BK = DCOS(ARG)
+      IF (ZI.LT.0.0D0) BK = -BK
+      P1R = AK
+      P1I = BK
+      IF (MOD(INU,2).EQ.0) GO TO 30
+      P1R = -P1R
+      P1I = -P1I
+   30 CONTINUE
+      DO 70 K=1,IL
+        SQK = FDN - 1.0D0
+        ATOL = S*DABS(SQK)
+        SGN = 1.0D0
+        CS1R = CONER
+        CS1I = CONEI
+        CS2R = CONER
+        CS2I = CONEI
+        CKR = CONER
+        CKI = CONEI
+        AK = 0.0D0
+        AA = 1.0D0
+        BB = AEZ
+        DKR = EZR
+        DKI = EZI
+        DO 40 J=1,JL
+          CALL ZDIV(CKR, CKI, DKR, DKI, STR, STI)
+          CKR = STR*SQK
+          CKI = STI*SQK
+          CS2R = CS2R + CKR
+          CS2I = CS2I + CKI
+          SGN = -SGN
+          CS1R = CS1R + CKR*SGN
+          CS1I = CS1I + CKI*SGN
+          DKR = DKR + EZR
+          DKI = DKI + EZI
+          AA = AA*DABS(SQK)/BB
+          BB = BB + AEZ
+          AK = AK + 8.0D0
+          SQK = SQK - AK
+          IF (AA.LE.ATOL) THEN
+            GO TO 50
+          END IF
+   40   CONTINUE
+        GO TO 110
+   50   CONTINUE
+        S2R = CS1R
+        S2I = CS1I
+        IF (ZR+ZR.GE.ELIM) GO TO 60
+        TZR = ZR + ZR
+        TZI = ZI + ZI
+        CALL ZEXP(-TZR, -TZI, STR, STI)
+        CALL ZMLT(STR, STI, P1R, P1I, STR, STI)
+        CALL ZMLT(STR, STI, CS2R, CS2I, STR, STI)
+        S2R = S2R + STR
+        S2I = S2I + STI
+   60   CONTINUE
+        FDN = FDN + 8.0D0*DFNU + 4.0D0
+        P1R = -P1R
+        P1I = -P1I
+        M = N - IL + K
+        YR(M) = S2R*AK1R - S2I*AK1I
+        YI(M) = S2R*AK1I + S2I*AK1R
+   70 CONTINUE
+      IF (N.LE.2) RETURN
+      NN = N
+      K = NN - 2
+      AK = DBLE(FLOAT(K))
+      STR = ZR*RAZ
+      STI = -ZI*RAZ
+      RZR = (STR+STR)*RAZ
+      RZI = (STI+STI)*RAZ
+      IB = 3
+      DO 80 I=IB,NN
+        YR(K) = (AK+FNU)*(RZR*YR(K+1)-RZI*YI(K+1)) + YR(K+2)
+        YI(K) = (AK+FNU)*(RZR*YI(K+1)+RZI*YR(K+1)) + YI(K+2)
+        AK = AK - 1.0D0
+        K = K - 1
+   80 CONTINUE
+      IF (KODED.EQ.0) RETURN
+      CALL ZEXP(CZR, CZI, CKR, CKI)
+      DO 90 I=1,NN
+        STR = YR(I)*CKR - YI(I)*CKI
+        YI(I) = YR(I)*CKI + YI(I)*CKR
+        YR(I) = STR
+   90 CONTINUE
+      RETURN
+  100 CONTINUE
+      NZ = -1
+      RETURN
+  110 CONTINUE
+      NZ=-2
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbesh.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbesh.f
new file mode 100644
index 00000000..a055ae46
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbesh.f
@@ -0,0 +1,348 @@
+      SUBROUTINE ZBESH(ZR, ZI, FNU, KODE, M, N, CYR, CYI, NZ, IERR)
+C***BEGIN PROLOGUE  ZBESH
+C***DATE WRITTEN   830501   (YYMMDD)
+C***REVISION DATE  890801   (YYMMDD)
+C***CATEGORY NO.  B5K
+C***KEYWORDS  H-BESSEL FUNCTIONS,BESSEL FUNCTIONS OF COMPLEX ARGUMENT,
+C             BESSEL FUNCTIONS OF THIRD KIND,HANKEL FUNCTIONS
+C***AUTHOR  AMOS, DONALD E., SANDIA NATIONAL LABORATORIES
+C***PURPOSE  TO COMPUTE THE H-BESSEL FUNCTIONS OF A COMPLEX ARGUMENT
+C***DESCRIPTION
+C
+C                      ***A DOUBLE PRECISION ROUTINE***
+C         ON KODE=1, ZBESH COMPUTES AN N MEMBER SEQUENCE OF COMPLEX
+C         HANKEL (BESSEL) FUNCTIONS CY(J)=H(M,FNU+J-1,Z) FOR KINDS M=1
+C         OR 2, REAL, NONNEGATIVE ORDERS FNU+J-1, J=1,...,N, AND COMPLEX
+C         Z.NE.CMPLX(0.0,0.0) IN THE CUT PLANE -PI.LT.ARG(Z).LE.PI.
+C         ON KODE=2, ZBESH RETURNS THE SCALED HANKEL FUNCTIONS
+C
+C         CY(I)=EXP(-MM*Z*I)*H(M,FNU+J-1,Z)       MM=3-2*M,   I**2=-1.
+C
+C         WHICH REMOVES THE EXPONENTIAL BEHAVIOR IN BOTH THE UPPER AND
+C         LOWER HALF PLANES. DEFINITIONS AND NOTATION ARE FOUND IN THE
+C         NBS HANDBOOK OF MATHEMATICAL FUNCTIONS (REF. 1).
+C
+C         INPUT      ZR,ZI,FNU ARE DOUBLE PRECISION
+C           ZR,ZI  - Z=CMPLX(ZR,ZI), Z.NE.CMPLX(0.0D0,0.0D0),
+C                    -PT.LT.ARG(Z).LE.PI
+C           FNU    - ORDER OF INITIAL H FUNCTION, FNU.GE.0.0D0
+C           KODE   - A PARAMETER TO INDICATE THE SCALING OPTION
+C                    KODE= 1  RETURNS
+C                             CY(J)=H(M,FNU+J-1,Z),   J=1,...,N
+C                        = 2  RETURNS
+C                             CY(J)=H(M,FNU+J-1,Z)*EXP(-I*Z*(3-2M))
+C                                  J=1,...,N  ,  I**2=-1
+C           M      - KIND OF HANKEL FUNCTION, M=1 OR 2
+C           N      - NUMBER OF MEMBERS IN THE SEQUENCE, N.GE.1
+C
+C         OUTPUT     CYR,CYI ARE DOUBLE PRECISION
+C           CYR,CYI- DOUBLE PRECISION VECTORS WHOSE FIRST N COMPONENTS
+C                    CONTAIN REAL AND IMAGINARY PARTS FOR THE SEQUENCE
+C                    CY(J)=H(M,FNU+J-1,Z)  OR
+C                    CY(J)=H(M,FNU+J-1,Z)*EXP(-I*Z*(3-2M))  J=1,...,N
+C                    DEPENDING ON KODE, I**2=-1.
+C           NZ     - NUMBER OF COMPONENTS SET TO ZERO DUE TO UNDERFLOW,
+C                    NZ= 0   , NORMAL RETURN
+C                    NZ.GT.0 , FIRST NZ COMPONENTS OF CY SET TO ZERO DUE
+C                              TO UNDERFLOW, CY(J)=CMPLX(0.0D0,0.0D0)
+C                              J=1,...,NZ WHEN Y.GT.0.0 AND M=1 OR
+C                              Y.LT.0.0 AND M=2. FOR THE COMPLMENTARY
+C                              HALF PLANES, NZ STATES ONLY THE NUMBER
+C                              OF UNDERFLOWS.
+C           IERR   - ERROR FLAG
+C                    IERR=0, NORMAL RETURN - COMPUTATION COMPLETED
+C                    IERR=1, INPUT ERROR   - NO COMPUTATION
+C                    IERR=2, OVERFLOW      - NO COMPUTATION, FNU TOO
+C                            LARGE OR CABS(Z) TOO SMALL OR BOTH
+C                    IERR=3, CABS(Z) OR FNU+N-1 LARGE - COMPUTATION DONE
+C                            BUT LOSSES OF SIGNIFCANCE BY ARGUMENT
+C                            REDUCTION PRODUCE LESS THAN HALF OF MACHINE
+C                            ACCURACY
+C                    IERR=4, CABS(Z) OR FNU+N-1 TOO LARGE - NO COMPUTA-
+C                            TION BECAUSE OF COMPLETE LOSSES OF SIGNIFI-
+C                            CANCE BY ARGUMENT REDUCTION
+C                    IERR=5, ERROR              - NO COMPUTATION,
+C                            ALGORITHM TERMINATION CONDITION NOT MET
+C
+C***LONG DESCRIPTION
+C
+C         THE COMPUTATION IS CARRIED OUT BY THE RELATION
+C
+C         H(M,FNU,Z)=(1/MP)*EXP(-MP*FNU)*K(FNU,Z*EXP(-MP))
+C             MP=MM*HPI*I,  MM=3-2*M,  HPI=PI/2,  I**2=-1
+C
+C         FOR M=1 OR 2 WHERE THE K BESSEL FUNCTION IS COMPUTED FOR THE
+C         RIGHT HALF PLANE RE(Z).GE.0.0. THE K FUNCTION IS CONTINUED
+C         TO THE LEFT HALF PLANE BY THE RELATION
+C
+C         K(FNU,Z*EXP(MP)) = EXP(-MP*FNU)*K(FNU,Z)-MP*I(FNU,Z)
+C         MP=MR*PI*I, MR=+1 OR -1, RE(Z).GT.0, I**2=-1
+C
+C         WHERE I(FNU,Z) IS THE I BESSEL FUNCTION.
+C
+C         EXPONENTIAL DECAY OF H(M,FNU,Z) OCCURS IN THE UPPER HALF Z
+C         PLANE FOR M=1 AND THE LOWER HALF Z PLANE FOR M=2.  EXPONENTIAL
+C         GROWTH OCCURS IN THE COMPLEMENTARY HALF PLANES.  SCALING
+C         BY EXP(-MM*Z*I) REMOVES THE EXPONENTIAL BEHAVIOR IN THE
+C         WHOLE Z PLANE FOR Z TO INFINITY.
+C
+C         FOR NEGATIVE ORDERS,THE FORMULAE
+C
+C               H(1,-FNU,Z) = H(1,FNU,Z)*CEXP( PI*FNU*I)
+C               H(2,-FNU,Z) = H(2,FNU,Z)*CEXP(-PI*FNU*I)
+C                         I**2=-1
+C
+C         CAN BE USED.
+C
+C         IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE-
+C         MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z OR FNU+N-1 IS
+C         LARGE, LOSSES OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR.
+C         CONSEQUENTLY, IF EITHER ONE EXCEEDS U1=SQRT(0.5/UR), THEN
+C         LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR FLAG
+C         IERR=3 IS TRIGGERED WHERE UR=DMAX1(D1MACH(4),1.0D-18) IS
+C         DOUBLE PRECISION UNIT ROUNDOFF LIMITED TO 18 DIGITS PRECISION.
+C         IF EITHER IS LARGER THAN U2=0.5/UR, THEN ALL SIGNIFICANCE IS
+C         LOST AND IERR=4. IN ORDER TO USE THE INT FUNCTION, ARGUMENTS
+C         MUST BE FURTHER RESTRICTED NOT TO EXCEED THE LARGEST MACHINE
+C         INTEGER, U3=I1MACH(9). THUS, THE MAGNITUDE OF Z AND FNU+N-1 IS
+C         RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2, AND U3
+C         ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE PRECISION
+C         ARITHMETIC AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE PRECISION
+C         ARITHMETIC RESPECTIVELY. THIS MAKES U2 AND U3 LIMITING IN
+C         THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT ONE CAN EXPECT
+C         TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES, NO DIGITS
+C         IN SINGLE AND ONLY 7 DIGITS IN DOUBLE PRECISION ARITHMETIC.
+C         SIMILAR CONSIDERATIONS HOLD FOR OTHER MACHINES.
+C
+C         THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX
+C         BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT
+C         ROUNDOFF,1.0D-18) IS THE NOMINAL PRECISION AND 10**S REPRE-
+C         SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE
+C         ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))),
+C         ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF
+C         CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY
+C         HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN
+C         ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY
+C         SEVERAL ORDERS OF MAGNITUDE. IF ONE COMPONENT IS 10**K LARGER
+C         THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K,
+C         0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS
+C         THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER
+C         COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY
+C         BECAUSE, IN COMPLEX ARITHMETIC WITH PRECISION P, THE SMALLER
+C         COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE
+C         MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES,
+C         THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P,
+C         OR -PI/2+P.
+C
+C***REFERENCES  HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ
+C                 AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF
+C                 COMMERCE, 1955.
+C
+C               COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+C                 BY D. E. AMOS, SAND83-0083, MAY, 1983.
+C
+C               COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+C                 AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983
+C
+C               A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+C                 ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85-
+C                 1018, MAY, 1985
+C
+C               A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+C                 ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS.
+C                 MATH. SOFTWARE, 1986
+C
+C***ROUTINES CALLED  ZACON,ZBKNU,ZBUNK,ZUOIK,ZABS,I1MACH,D1MACH
+C***END PROLOGUE  ZBESH
+C
+C     COMPLEX CY,Z,ZN,ZT,CSGN
+      DOUBLE PRECISION AA, ALIM, ALN, ARG, AZ, CYI, CYR, DIG, ELIM,
+     * FMM, FN, FNU, FNUL, HPI, RHPI, RL, R1M5, SGN, STR, TOL, UFL, ZI,
+     * ZNI, ZNR, ZR, ZTI, D1MACH, ZABS, BB, ASCLE, RTOL, ATOL, STI,
+     * CSGNR, CSGNI
+      INTEGER I, IERR, INU, INUH, IR, K, KODE, K1, K2, M,
+     * MM, MR, N, NN, NUF, NW, NZ, I1MACH
+      DIMENSION CYR(N), CYI(N)
+C
+      DATA HPI /1.57079632679489662D0/
+C
+C***FIRST EXECUTABLE STATEMENT  ZBESH
+      IERR = 0
+      NZ=0
+      IF (ZR.EQ.0.0D0 .AND. ZI.EQ.0.0D0) IERR=1
+      IF (FNU.LT.0.0D0) IERR=1
+      IF (M.LT.1 .OR. M.GT.2) IERR=1
+      IF (KODE.LT.1 .OR. KODE.GT.2) IERR=1
+      IF (N.LT.1) IERR=1
+      IF (IERR.NE.0) RETURN
+      NN = N
+C-----------------------------------------------------------------------
+C     SET PARAMETERS RELATED TO MACHINE CONSTANTS.
+C     TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0E-18.
+C     ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW LIMIT.
+C     EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL    AND
+C     EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL       ARE INTERVALS NEAR
+C     UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE.
+C     RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR LARGE Z.
+C     DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG).
+C     FNUL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC SERIES FOR LARGE FNU
+C-----------------------------------------------------------------------
+      TOL = DMAX1(D1MACH(4),1.0D-18)
+      K1 = I1MACH(15)
+      K2 = I1MACH(16)
+      R1M5 = D1MACH(5)
+      K = MIN0(IABS(K1),IABS(K2))
+      ELIM = 2.303D0*(DBLE(FLOAT(K))*R1M5-3.0D0)
+      K1 = I1MACH(14) - 1
+      AA = R1M5*DBLE(FLOAT(K1))
+      DIG = DMIN1(AA,18.0D0)
+      AA = AA*2.303D0
+      ALIM = ELIM + DMAX1(-AA,-41.45D0)
+      FNUL = 10.0D0 + 6.0D0*(DIG-3.0D0)
+      RL = 1.2D0*DIG + 3.0D0
+      FN = FNU + DBLE(FLOAT(NN-1))
+      MM = 3 - M - M
+      FMM = DBLE(FLOAT(MM))
+      ZNR = FMM*ZI
+      ZNI = -FMM*ZR
+C-----------------------------------------------------------------------
+C     TEST FOR PROPER RANGE
+C-----------------------------------------------------------------------
+      AZ = ZABS(CMPLX(ZR,ZI,kind=KIND(1.0D0)))
+      AA = 0.5D0/TOL
+      BB=DBLE(FLOAT(I1MACH(9)))*0.5D0
+      AA = DMIN1(AA,BB)
+      IF (AZ.GT.AA) GO TO 260
+      IF (FN.GT.AA) GO TO 260
+      AA = DSQRT(AA)
+      IF (AZ.GT.AA) IERR=3
+      IF (FN.GT.AA) IERR=3
+C-----------------------------------------------------------------------
+C     OVERFLOW TEST ON THE LAST MEMBER OF THE SEQUENCE
+C-----------------------------------------------------------------------
+      UFL = D1MACH(1)*1.0D+3
+      IF (AZ.LT.UFL) GO TO 230
+      IF (FNU.GT.FNUL) GO TO 90
+      IF (FN.LE.1.0D0) GO TO 70
+      IF (FN.GT.2.0D0) GO TO 60
+      IF (AZ.GT.TOL) GO TO 70
+      ARG = 0.5D0*AZ
+      ALN = -FN*DLOG(ARG)
+      IF (ALN.GT.ELIM) GO TO 230
+      GO TO 70
+   60 CONTINUE
+      CALL ZUOIK(ZNR, ZNI, FNU, KODE, 2, NN, CYR, CYI, NUF, TOL, ELIM,
+     * ALIM)
+      IF (NUF.LT.0) GO TO 230
+      NZ = NZ + NUF
+      NN = NN - NUF
+C-----------------------------------------------------------------------
+C     HERE NN=N OR NN=0 SINCE NUF=0,NN, OR -1 ON RETURN FROM CUOIK
+C     IF NUF=NN, THEN CY(I)=CZERO FOR ALL I
+C-----------------------------------------------------------------------
+      IF (NN.EQ.0) GO TO 140
+   70 CONTINUE
+      IF ((ZNR.LT.0.0D0) .OR. (ZNR.EQ.0.0D0 .AND. ZNI.LT.0.0D0 .AND.
+     * M.EQ.2)) GO TO 80
+C-----------------------------------------------------------------------
+C     RIGHT HALF PLANE COMPUTATION, XN.GE.0. .AND. (XN.NE.0. .OR.
+C     YN.GE.0. .OR. M=1)
+C-----------------------------------------------------------------------
+      CALL ZBKNU(ZNR, ZNI, FNU, KODE, NN, CYR, CYI, NZ, TOL, ELIM, ALIM)
+      GO TO 110
+C-----------------------------------------------------------------------
+C     LEFT HALF PLANE COMPUTATION
+C-----------------------------------------------------------------------
+   80 CONTINUE
+      MR = -MM
+      CALL ZACON(ZNR, ZNI, FNU, KODE, MR, NN, CYR, CYI, NW, RL, FNUL,
+     * TOL, ELIM, ALIM)
+      IF (NW.LT.0) GO TO 240
+      NZ=NW
+      GO TO 110
+   90 CONTINUE
+C-----------------------------------------------------------------------
+C     UNIFORM ASYMPTOTIC EXPANSIONS FOR FNU.GT.FNUL
+C-----------------------------------------------------------------------
+      MR = 0
+      IF ((ZNR.GE.0.0D0) .AND. (ZNR.NE.0.0D0 .OR. ZNI.GE.0.0D0 .OR.
+     * M.NE.2)) GO TO 100
+      MR = -MM
+      IF (ZNR.NE.0.0D0 .OR. ZNI.GE.0.0D0) GO TO 100
+      ZNR = -ZNR
+      ZNI = -ZNI
+  100 CONTINUE
+      CALL ZBUNK(ZNR, ZNI, FNU, KODE, MR, NN, CYR, CYI, NW, TOL, ELIM,
+     * ALIM)
+      IF (NW.LT.0) GO TO 240
+      NZ = NZ + NW
+  110 CONTINUE
+C-----------------------------------------------------------------------
+C     H(M,FNU,Z) = -FMM*(I/HPI)*(ZT**FNU)*K(FNU,-Z*ZT)
+C
+C     ZT=EXP(-FMM*HPI*I) = CMPLX(0.0,-FMM), FMM=3-2*M, M=1,2
+C-----------------------------------------------------------------------
+      SGN = DSIGN(HPI,-FMM)
+C-----------------------------------------------------------------------
+C     CALCULATE EXP(FNU*HPI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE
+C     WHEN FNU IS LARGE
+C-----------------------------------------------------------------------
+      INU = INT(SNGL(FNU))
+      INUH = INU/2
+      IR = INU - 2*INUH
+      ARG = (FNU-DBLE(FLOAT(INU-IR)))*SGN
+      RHPI = 1.0D0/SGN
+C     ZNI = RHPI*DCOS(ARG)
+C     ZNR = -RHPI*DSIN(ARG)
+      CSGNI = RHPI*DCOS(ARG)
+      CSGNR = -RHPI*DSIN(ARG)
+      IF (MOD(INUH,2).EQ.0) GO TO 120
+C     ZNR = -ZNR
+C     ZNI = -ZNI
+      CSGNR = -CSGNR
+      CSGNI = -CSGNI
+  120 CONTINUE
+      ZTI = -FMM
+      RTOL = 1.0D0/TOL
+      ASCLE = UFL*RTOL
+      DO 130 I=1,NN
+C       STR = CYR(I)*ZNR - CYI(I)*ZNI
+C       CYI(I) = CYR(I)*ZNI + CYI(I)*ZNR
+C       CYR(I) = STR
+C       STR = -ZNI*ZTI
+C       ZNI = ZNR*ZTI
+C       ZNR = STR
+        AA = CYR(I)
+        BB = CYI(I)
+        ATOL = 1.0D0
+        IF (DMAX1(DABS(AA),DABS(BB)).GT.ASCLE) GO TO 135
+          AA = AA*RTOL
+          BB = BB*RTOL
+          ATOL = TOL
+  135 CONTINUE
+      STR = AA*CSGNR - BB*CSGNI
+      STI = AA*CSGNI + BB*CSGNR
+      CYR(I) = STR*ATOL
+      CYI(I) = STI*ATOL
+      STR = -CSGNI*ZTI
+      CSGNI = CSGNR*ZTI
+      CSGNR = STR
+  130 CONTINUE
+      RETURN
+  140 CONTINUE
+      IF (ZNR.LT.0.0D0) GO TO 230
+      RETURN
+  230 CONTINUE
+      NZ=0
+      IERR=2
+      RETURN
+  240 CONTINUE
+      IF(NW.EQ.(-1)) GO TO 230
+      NZ=0
+      IERR=5
+      RETURN
+  260 CONTINUE
+      NZ=0
+      IERR=4
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbesi.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbesi.f
new file mode 100644
index 00000000..5f7c1407
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbesi.f
@@ -0,0 +1,269 @@
+      SUBROUTINE ZBESI(ZR, ZI, FNU, KODE, N, CYR, CYI, NZ, IERR)
+C***BEGIN PROLOGUE  ZBESI
+C***DATE WRITTEN   830501   (YYMMDD)
+C***REVISION DATE  890801   (YYMMDD)
+C***CATEGORY NO.  B5K
+C***KEYWORDS  I-BESSEL FUNCTION,COMPLEX BESSEL FUNCTION,
+C             MODIFIED BESSEL FUNCTION OF THE FIRST KIND
+C***AUTHOR  AMOS, DONALD E., SANDIA NATIONAL LABORATORIES
+C***PURPOSE  TO COMPUTE I-BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+C***DESCRIPTION
+C
+C                    ***A DOUBLE PRECISION ROUTINE***
+C         ON KODE=1, ZBESI COMPUTES AN N MEMBER SEQUENCE OF COMPLEX
+C         BESSEL FUNCTIONS CY(J)=I(FNU+J-1,Z) FOR REAL, NONNEGATIVE
+C         ORDERS FNU+J-1, J=1,...,N AND COMPLEX Z IN THE CUT PLANE
+C         -PI.LT.ARG(Z).LE.PI. ON KODE=2, ZBESI RETURNS THE SCALED
+C         FUNCTIONS
+C
+C         CY(J)=EXP(-ABS(X))*I(FNU+J-1,Z)   J = 1,...,N , X=REAL(Z)
+C
+C         WITH THE EXPONENTIAL GROWTH REMOVED IN BOTH THE LEFT AND
+C         RIGHT HALF PLANES FOR Z TO INFINITY. DEFINITIONS AND NOTATION
+C         ARE FOUND IN THE NBS HANDBOOK OF MATHEMATICAL FUNCTIONS
+C         (REF. 1).
+C
+C         INPUT      ZR,ZI,FNU ARE DOUBLE PRECISION
+C           ZR,ZI  - Z=CMPLX(ZR,ZI),  -PI.LT.ARG(Z).LE.PI
+C           FNU    - ORDER OF INITIAL I FUNCTION, FNU.GE.0.0D0
+C           KODE   - A PARAMETER TO INDICATE THE SCALING OPTION
+C                    KODE= 1  RETURNS
+C                             CY(J)=I(FNU+J-1,Z), J=1,...,N
+C                        = 2  RETURNS
+C                             CY(J)=I(FNU+J-1,Z)*EXP(-ABS(X)), J=1,...,N
+C           N      - NUMBER OF MEMBERS OF THE SEQUENCE, N.GE.1
+C
+C         OUTPUT     CYR,CYI ARE DOUBLE PRECISION
+C           CYR,CYI- DOUBLE PRECISION VECTORS WHOSE FIRST N COMPONENTS
+C                    CONTAIN REAL AND IMAGINARY PARTS FOR THE SEQUENCE
+C                    CY(J)=I(FNU+J-1,Z)  OR
+C                    CY(J)=I(FNU+J-1,Z)*EXP(-ABS(X))  J=1,...,N
+C                    DEPENDING ON KODE, X=REAL(Z)
+C           NZ     - NUMBER OF COMPONENTS SET TO ZERO DUE TO UNDERFLOW,
+C                    NZ= 0   , NORMAL RETURN
+C                    NZ.GT.0 , LAST NZ COMPONENTS OF CY SET TO ZERO
+C                              TO UNDERFLOW, CY(J)=CMPLX(0.0D0,0.0D0)
+C                              J = N-NZ+1,...,N
+C           IERR   - ERROR FLAG
+C                    IERR=0, NORMAL RETURN - COMPUTATION COMPLETED
+C                    IERR=1, INPUT ERROR   - NO COMPUTATION
+C                    IERR=2, OVERFLOW      - NO COMPUTATION, REAL(Z) TOO
+C                            LARGE ON KODE=1
+C                    IERR=3, CABS(Z) OR FNU+N-1 LARGE - COMPUTATION DONE
+C                            BUT LOSSES OF SIGNIFCANCE BY ARGUMENT
+C                            REDUCTION PRODUCE LESS THAN HALF OF MACHINE
+C                            ACCURACY
+C                    IERR=4, CABS(Z) OR FNU+N-1 TOO LARGE - NO COMPUTA-
+C                            TION BECAUSE OF COMPLETE LOSSES OF SIGNIFI-
+C                            CANCE BY ARGUMENT REDUCTION
+C                    IERR=5, ERROR              - NO COMPUTATION,
+C                            ALGORITHM TERMINATION CONDITION NOT MET
+C
+C***LONG DESCRIPTION
+C
+C         THE COMPUTATION IS CARRIED OUT BY THE POWER SERIES FOR
+C         SMALL CABS(Z), THE ASYMPTOTIC EXPANSION FOR LARGE CABS(Z),
+C         THE MILLER ALGORITHM NORMALIZED BY THE WRONSKIAN AND A
+C         NEUMANN SERIES FOR IMTERMEDIATE MAGNITUDES, AND THE
+C         UNIFORM ASYMPTOTIC EXPANSIONS FOR I(FNU,Z) AND J(FNU,Z)
+C         FOR LARGE ORDERS. BACKWARD RECURRENCE IS USED TO GENERATE
+C         SEQUENCES OR REDUCE ORDERS WHEN NECESSARY.
+C
+C         THE CALCULATIONS ABOVE ARE DONE IN THE RIGHT HALF PLANE AND
+C         CONTINUED INTO THE LEFT HALF PLANE BY THE FORMULA
+C
+C         I(FNU,Z*EXP(M*PI)) = EXP(M*PI*FNU)*I(FNU,Z)  REAL(Z).GT.0.0
+C                       M = +I OR -I,  I**2=-1
+C
+C         FOR NEGATIVE ORDERS,THE FORMULA
+C
+C              I(-FNU,Z) = I(FNU,Z) + (2/PI)*SIN(PI*FNU)*K(FNU,Z)
+C
+C         CAN BE USED. HOWEVER,FOR LARGE ORDERS CLOSE TO INTEGERS, THE
+C         THE FUNCTION CHANGES RADICALLY. WHEN FNU IS A LARGE POSITIVE
+C         INTEGER,THE MAGNITUDE OF I(-FNU,Z)=I(FNU,Z) IS A LARGE
+C         NEGATIVE POWER OF TEN. BUT WHEN FNU IS NOT AN INTEGER,
+C         K(FNU,Z) DOMINATES IN MAGNITUDE WITH A LARGE POSITIVE POWER OF
+C         TEN AND THE MOST THAT THE SECOND TERM CAN BE REDUCED IS BY
+C         UNIT ROUNDOFF FROM THE COEFFICIENT. THUS, WIDE CHANGES CAN
+C         OCCUR WITHIN UNIT ROUNDOFF OF A LARGE INTEGER FOR FNU. HERE,
+C         LARGE MEANS FNU.GT.CABS(Z).
+C
+C         IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE-
+C         MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z OR FNU+N-1 IS
+C         LARGE, LOSSES OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR.
+C         CONSEQUENTLY, IF EITHER ONE EXCEEDS U1=SQRT(0.5/UR), THEN
+C         LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR FLAG
+C         IERR=3 IS TRIGGERED WHERE UR=DMAX1(D1MACH(4),1.0D-18) IS
+C         DOUBLE PRECISION UNIT ROUNDOFF LIMITED TO 18 DIGITS PRECISION.
+C         IF EITHER IS LARGER THAN U2=0.5/UR, THEN ALL SIGNIFICANCE IS
+C         LOST AND IERR=4. IN ORDER TO USE THE INT FUNCTION, ARGUMENTS
+C         MUST BE FURTHER RESTRICTED NOT TO EXCEED THE LARGEST MACHINE
+C         INTEGER, U3=I1MACH(9). THUS, THE MAGNITUDE OF Z AND FNU+N-1 IS
+C         RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2, AND U3
+C         ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE PRECISION
+C         ARITHMETIC AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE PRECISION
+C         ARITHMETIC RESPECTIVELY. THIS MAKES U2 AND U3 LIMITING IN
+C         THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT ONE CAN EXPECT
+C         TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES, NO DIGITS
+C         IN SINGLE AND ONLY 7 DIGITS IN DOUBLE PRECISION ARITHMETIC.
+C         SIMILAR CONSIDERATIONS HOLD FOR OTHER MACHINES.
+C
+C         THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX
+C         BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT
+C         ROUNDOFF,1.0E-18) IS THE NOMINAL PRECISION AND 10**S REPRE-
+C         SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE
+C         ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))),
+C         ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF
+C         CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY
+C         HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN
+C         ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY
+C         SEVERAL ORDERS OF MAGNITUDE. IF ONE COMPONENT IS 10**K LARGER
+C         THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K,
+C         0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS
+C         THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER
+C         COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY
+C         BECAUSE, IN COMPLEX ARITHMETIC WITH PRECISION P, THE SMALLER
+C         COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE
+C         MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES,
+C         THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P,
+C         OR -PI/2+P.
+C
+C***REFERENCES  HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ
+C                 AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF
+C                 COMMERCE, 1955.
+C
+C               COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+C                 BY D. E. AMOS, SAND83-0083, MAY, 1983.
+C
+C               COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+C                 AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983
+C
+C               A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+C                 ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85-
+C                 1018, MAY, 1985
+C
+C               A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+C                 ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS.
+C                 MATH. SOFTWARE, 1986
+C
+C***ROUTINES CALLED  ZBINU,I1MACH,D1MACH
+C***END PROLOGUE  ZBESI
+C     COMPLEX CONE,CSGN,CW,CY,CZERO,Z,ZN
+      DOUBLE PRECISION AA, ALIM, ARG, CONEI, CONER, CSGNI, CSGNR, CYI,
+     * CYR, DIG, ELIM, FNU, FNUL, PI, RL, R1M5, STR, TOL, ZI, ZNI, ZNR,
+     * ZR, D1MACH, AZ, BB, FN, ZABS, ASCLE, RTOL, ATOL, STI
+      INTEGER I, IERR, INU, K, KODE, K1,K2,N,NZ,NN, I1MACH
+      DIMENSION CYR(N), CYI(N)
+      DATA PI /3.14159265358979324D0/
+      DATA CONER, CONEI /1.0D0,0.0D0/
+C
+C***FIRST EXECUTABLE STATEMENT  ZBESI
+      IERR = 0
+      NZ=0
+      IF (FNU.LT.0.0D0) IERR=1
+      IF (KODE.LT.1 .OR. KODE.GT.2) IERR=1
+      IF (N.LT.1) IERR=1
+      IF (IERR.NE.0) RETURN
+C-----------------------------------------------------------------------
+C     SET PARAMETERS RELATED TO MACHINE CONSTANTS.
+C     TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0E-18.
+C     ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW LIMIT.
+C     EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL    AND
+C     EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL       ARE INTERVALS NEAR
+C     UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE.
+C     RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR LARGE Z.
+C     DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG).
+C     FNUL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC SERIES FOR LARGE FNU.
+C-----------------------------------------------------------------------
+      TOL = DMAX1(D1MACH(4),1.0D-18)
+      K1 = I1MACH(15)
+      K2 = I1MACH(16)
+      R1M5 = D1MACH(5)
+      K = MIN0(IABS(K1),IABS(K2))
+      ELIM = 2.303D0*(DBLE(FLOAT(K))*R1M5-3.0D0)
+      K1 = I1MACH(14) - 1
+      AA = R1M5*DBLE(FLOAT(K1))
+      DIG = DMIN1(AA,18.0D0)
+      AA = AA*2.303D0
+      ALIM = ELIM + DMAX1(-AA,-41.45D0)
+      RL = 1.2D0*DIG + 3.0D0
+      FNUL = 10.0D0 + 6.0D0*(DIG-3.0D0)
+C-----------------------------------------------------------------------------
+C     TEST FOR PROPER RANGE
+C-----------------------------------------------------------------------
+      AZ = ZABS(CMPLX(ZR,ZI,kind=KIND(1.0D0)))
+      FN = FNU+DBLE(FLOAT(N-1))
+      AA = 0.5D0/TOL
+      BB=DBLE(FLOAT(I1MACH(9)))*0.5D0
+      AA = DMIN1(AA,BB)
+      IF (AZ.GT.AA) GO TO 260
+      IF (FN.GT.AA) GO TO 260
+      AA = DSQRT(AA)
+      IF (AZ.GT.AA) IERR=3
+      IF (FN.GT.AA) IERR=3
+      ZNR = ZR
+      ZNI = ZI
+      CSGNR = CONER
+      CSGNI = CONEI
+      IF (ZR.GE.0.0D0) GO TO 40
+      ZNR = -ZR
+      ZNI = -ZI
+C-----------------------------------------------------------------------
+C     CALCULATE CSGN=EXP(FNU*PI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE
+C     WHEN FNU IS LARGE
+C-----------------------------------------------------------------------
+      INU = INT(SNGL(FNU))
+      ARG = (FNU-DBLE(FLOAT(INU)))*PI
+      IF (ZI.LT.0.0D0) ARG = -ARG
+      CSGNR = DCOS(ARG)
+      CSGNI = DSIN(ARG)
+      IF (MOD(INU,2).EQ.0) GO TO 40
+      CSGNR = -CSGNR
+      CSGNI = -CSGNI
+   40 CONTINUE
+      CALL ZBINU(ZNR, ZNI, FNU, KODE, N, CYR, CYI, NZ, RL, FNUL, TOL,
+     * ELIM, ALIM)
+      IF (NZ.LT.0) GO TO 120
+      IF (ZR.GE.0.0D0) RETURN
+C-----------------------------------------------------------------------
+C     ANALYTIC CONTINUATION TO THE LEFT HALF PLANE
+C-----------------------------------------------------------------------
+      NN = N - NZ
+      IF (NN.EQ.0) RETURN
+      RTOL = 1.0D0/TOL
+      ASCLE = D1MACH(1)*RTOL*1.0D+3
+      DO 50 I=1,NN
+C       STR = CYR(I)*CSGNR - CYI(I)*CSGNI
+C       CYI(I) = CYR(I)*CSGNI + CYI(I)*CSGNR
+C       CYR(I) = STR
+        AA = CYR(I)
+        BB = CYI(I)
+        ATOL = 1.0D0
+        IF (DMAX1(DABS(AA),DABS(BB)).GT.ASCLE) GO TO 55
+          AA = AA*RTOL
+          BB = BB*RTOL
+          ATOL = TOL
+   55   CONTINUE
+        STR = AA*CSGNR - BB*CSGNI
+        STI = AA*CSGNI + BB*CSGNR
+        CYR(I) = STR*ATOL
+        CYI(I) = STI*ATOL
+        CSGNR = -CSGNR
+        CSGNI = -CSGNI
+   50 CONTINUE
+      RETURN
+  120 CONTINUE
+      IF(NZ.EQ.(-2)) GO TO 130
+      NZ = 0
+      IERR=2
+      RETURN
+  130 CONTINUE
+      NZ=0
+      IERR=5
+      RETURN
+  260 CONTINUE
+      NZ=0
+      IERR=4
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbesj.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbesj.f
new file mode 100644
index 00000000..1fb217f4
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbesj.f
@@ -0,0 +1,266 @@
+      SUBROUTINE ZBESJ(ZR, ZI, FNU, KODE, N, CYR, CYI, NZ, IERR)
+C***BEGIN PROLOGUE  ZBESJ
+C***DATE WRITTEN   830501   (YYMMDD)
+C***REVISION DATE  890801   (YYMMDD)
+C***CATEGORY NO.  B5K
+C***KEYWORDS  J-BESSEL FUNCTION,BESSEL FUNCTION OF COMPLEX ARGUMENT,
+C             BESSEL FUNCTION OF FIRST KIND
+C***AUTHOR  AMOS, DONALD E., SANDIA NATIONAL LABORATORIES
+C***PURPOSE  TO COMPUTE THE J-BESSEL FUNCTION OF A COMPLEX ARGUMENT
+C***DESCRIPTION
+C
+C                      ***A DOUBLE PRECISION ROUTINE***
+C         ON KODE=1, CBESJ COMPUTES AN N MEMBER  SEQUENCE OF COMPLEX
+C         BESSEL FUNCTIONS CY(I)=J(FNU+I-1,Z) FOR REAL, NONNEGATIVE
+C         ORDERS FNU+I-1, I=1,...,N AND COMPLEX Z IN THE CUT PLANE
+C         -PI.LT.ARG(Z).LE.PI. ON KODE=2, CBESJ RETURNS THE SCALED
+C         FUNCTIONS
+C
+C         CY(I)=EXP(-ABS(Y))*J(FNU+I-1,Z)   I = 1,...,N , Y=AIMAG(Z)
+C
+C         WHICH REMOVE THE EXPONENTIAL GROWTH IN BOTH THE UPPER AND
+C         LOWER HALF PLANES FOR Z TO INFINITY. DEFINITIONS AND NOTATION
+C         ARE FOUND IN THE NBS HANDBOOK OF MATHEMATICAL FUNCTIONS
+C         (REF. 1).
+C
+C         INPUT      ZR,ZI,FNU ARE DOUBLE PRECISION
+C           ZR,ZI  - Z=CMPLX(ZR,ZI),  -PI.LT.ARG(Z).LE.PI
+C           FNU    - ORDER OF INITIAL J FUNCTION, FNU.GE.0.0D0
+C           KODE   - A PARAMETER TO INDICATE THE SCALING OPTION
+C                    KODE= 1  RETURNS
+C                             CY(I)=J(FNU+I-1,Z), I=1,...,N
+C                        = 2  RETURNS
+C                             CY(I)=J(FNU+I-1,Z)EXP(-ABS(Y)), I=1,...,N
+C           N      - NUMBER OF MEMBERS OF THE SEQUENCE, N.GE.1
+C
+C         OUTPUT     CYR,CYI ARE DOUBLE PRECISION
+C           CYR,CYI- DOUBLE PRECISION VECTORS WHOSE FIRST N COMPONENTS
+C                    CONTAIN REAL AND IMAGINARY PARTS FOR THE SEQUENCE
+C                    CY(I)=J(FNU+I-1,Z)  OR
+C                    CY(I)=J(FNU+I-1,Z)EXP(-ABS(Y))  I=1,...,N
+C                    DEPENDING ON KODE, Y=AIMAG(Z).
+C           NZ     - NUMBER OF COMPONENTS SET TO ZERO DUE TO UNDERFLOW,
+C                    NZ= 0   , NORMAL RETURN
+C                    NZ.GT.0 , LAST NZ COMPONENTS OF CY SET  ZERO DUE
+C                              TO UNDERFLOW, CY(I)=CMPLX(0.0D0,0.0D0),
+C                              I = N-NZ+1,...,N
+C           IERR   - ERROR FLAG
+C                    IERR=0, NORMAL RETURN - COMPUTATION COMPLETED
+C                    IERR=1, INPUT ERROR   - NO COMPUTATION
+C                    IERR=2, OVERFLOW      - NO COMPUTATION, AIMAG(Z)
+C                            TOO LARGE ON KODE=1
+C                    IERR=3, CABS(Z) OR FNU+N-1 LARGE - COMPUTATION DONE
+C                            BUT LOSSES OF SIGNIFCANCE BY ARGUMENT
+C                            REDUCTION PRODUCE LESS THAN HALF OF MACHINE
+C                            ACCURACY
+C                    IERR=4, CABS(Z) OR FNU+N-1 TOO LARGE - NO COMPUTA-
+C                            TION BECAUSE OF COMPLETE LOSSES OF SIGNIFI-
+C                            CANCE BY ARGUMENT REDUCTION
+C                    IERR=5, ERROR              - NO COMPUTATION,
+C                            ALGORITHM TERMINATION CONDITION NOT MET
+C
+C***LONG DESCRIPTION
+C
+C         THE COMPUTATION IS CARRIED OUT BY THE FORMULA
+C
+C         J(FNU,Z)=EXP( FNU*PI*I/2)*I(FNU,-I*Z)    AIMAG(Z).GE.0.0
+C
+C         J(FNU,Z)=EXP(-FNU*PI*I/2)*I(FNU, I*Z)    AIMAG(Z).LT.0.0
+C
+C         WHERE I**2 = -1 AND I(FNU,Z) IS THE I BESSEL FUNCTION.
+C
+C         FOR NEGATIVE ORDERS,THE FORMULA
+C
+C              J(-FNU,Z) = J(FNU,Z)*COS(PI*FNU) - Y(FNU,Z)*SIN(PI*FNU)
+C
+C         CAN BE USED. HOWEVER,FOR LARGE ORDERS CLOSE TO INTEGERS, THE
+C         THE FUNCTION CHANGES RADICALLY. WHEN FNU IS A LARGE POSITIVE
+C         INTEGER,THE MAGNITUDE OF J(-FNU,Z)=J(FNU,Z)*COS(PI*FNU) IS A
+C         LARGE NEGATIVE POWER OF TEN. BUT WHEN FNU IS NOT AN INTEGER,
+C         Y(FNU,Z) DOMINATES IN MAGNITUDE WITH A LARGE POSITIVE POWER OF
+C         TEN AND THE MOST THAT THE SECOND TERM CAN BE REDUCED IS BY
+C         UNIT ROUNDOFF FROM THE COEFFICIENT. THUS, WIDE CHANGES CAN
+C         OCCUR WITHIN UNIT ROUNDOFF OF A LARGE INTEGER FOR FNU. HERE,
+C         LARGE MEANS FNU.GT.CABS(Z).
+C
+C         IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE-
+C         MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z OR FNU+N-1 IS
+C         LARGE, LOSSES OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR.
+C         CONSEQUENTLY, IF EITHER ONE EXCEEDS U1=SQRT(0.5/UR), THEN
+C         LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR FLAG
+C         IERR=3 IS TRIGGERED WHERE UR=DMAX1(D1MACH(4),1.0D-18) IS
+C         DOUBLE PRECISION UNIT ROUNDOFF LIMITED TO 18 DIGITS PRECISION.
+C         IF EITHER IS LARGER THAN U2=0.5/UR, THEN ALL SIGNIFICANCE IS
+C         LOST AND IERR=4. IN ORDER TO USE THE INT FUNCTION, ARGUMENTS
+C         MUST BE FURTHER RESTRICTED NOT TO EXCEED THE LARGEST MACHINE
+C         INTEGER, U3=I1MACH(9). THUS, THE MAGNITUDE OF Z AND FNU+N-1 IS
+C         RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2, AND U3
+C         ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE PRECISION
+C         ARITHMETIC AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE PRECISION
+C         ARITHMETIC RESPECTIVELY. THIS MAKES U2 AND U3 LIMITING IN
+C         THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT ONE CAN EXPECT
+C         TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES, NO DIGITS
+C         IN SINGLE AND ONLY 7 DIGITS IN DOUBLE PRECISION ARITHMETIC.
+C         SIMILAR CONSIDERATIONS HOLD FOR OTHER MACHINES.
+C
+C         THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX
+C         BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT
+C         ROUNDOFF,1.0E-18) IS THE NOMINAL PRECISION AND 10**S REPRE-
+C         SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE
+C         ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))),
+C         ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF
+C         CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY
+C         HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN
+C         ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY
+C         SEVERAL ORDERS OF MAGNITUDE. IF ONE COMPONENT IS 10**K LARGER
+C         THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K,
+C         0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS
+C         THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER
+C         COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY
+C         BECAUSE, IN COMPLEX ARITHMETIC WITH PRECISION P, THE SMALLER
+C         COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE
+C         MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES,
+C         THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P,
+C         OR -PI/2+P.
+C
+C***REFERENCES  HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ
+C                 AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF
+C                 COMMERCE, 1955.
+C
+C               COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+C                 BY D. E. AMOS, SAND83-0083, MAY, 1983.
+C
+C               COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+C                 AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983
+C
+C               A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+C                 ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85-
+C                 1018, MAY, 1985
+C
+C               A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+C                 ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS.
+C                 MATH. SOFTWARE, 1986
+C
+C***ROUTINES CALLED  ZBINU,I1MACH,D1MACH
+C***END PROLOGUE  ZBESJ
+C
+C     COMPLEX CI,CSGN,CY,Z,ZN
+      DOUBLE PRECISION AA, ALIM, ARG, CII, CSGNI, CSGNR, CYI, CYR, DIG,
+     * ELIM, FNU, FNUL, HPI, RL, R1M5, STR, TOL, ZI, ZNI, ZNR, ZR,
+     * D1MACH, BB, FN, AZ, ZABS, ASCLE, RTOL, ATOL, STI
+      INTEGER I, IERR, INU, INUH, IR, K, KODE, K1, K2, N, NL, NZ, I1MACH
+      DIMENSION CYR(N), CYI(N)
+      DATA HPI /1.57079632679489662D0/
+C
+C***FIRST EXECUTABLE STATEMENT  ZBESJ
+      IERR = 0
+      NZ=0
+      IF (FNU.LT.0.0D0) IERR=1
+      IF (KODE.LT.1 .OR. KODE.GT.2) IERR=1
+      IF (N.LT.1) IERR=1
+      IF (IERR.NE.0) RETURN
+C-----------------------------------------------------------------------
+C     SET PARAMETERS RELATED TO MACHINE CONSTANTS.
+C     TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0E-18.
+C     ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW LIMIT.
+C     EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL    AND
+C     EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL       ARE INTERVALS NEAR
+C     UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE.
+C     RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR LARGE Z.
+C     DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG).
+C     FNUL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC SERIES FOR LARGE FNU.
+C-----------------------------------------------------------------------
+      TOL = DMAX1(D1MACH(4),1.0D-18)
+      K1 = I1MACH(15)
+      K2 = I1MACH(16)
+      R1M5 = D1MACH(5)
+      K = MIN0(IABS(K1),IABS(K2))
+      ELIM = 2.303D0*(DBLE(FLOAT(K))*R1M5-3.0D0)
+      K1 = I1MACH(14) - 1
+      AA = R1M5*DBLE(FLOAT(K1))
+      DIG = DMIN1(AA,18.0D0)
+      AA = AA*2.303D0
+      ALIM = ELIM + DMAX1(-AA,-41.45D0)
+      RL = 1.2D0*DIG + 3.0D0
+      FNUL = 10.0D0 + 6.0D0*(DIG-3.0D0)
+C-----------------------------------------------------------------------
+C     TEST FOR PROPER RANGE
+C-----------------------------------------------------------------------
+      AZ = ZABS(CMPLX(ZR,ZI,kind=KIND(1.0D0)))
+      FN = FNU+DBLE(FLOAT(N-1))
+      AA = 0.5D0/TOL
+      BB=DBLE(FLOAT(I1MACH(9)))*0.5D0
+      AA = DMIN1(AA,BB)
+      IF (AZ.GT.AA) GO TO 260
+      IF (FN.GT.AA) GO TO 260
+      AA = DSQRT(AA)
+      IF (AZ.GT.AA) IERR=3
+      IF (FN.GT.AA) IERR=3
+C-----------------------------------------------------------------------
+C     CALCULATE CSGN=EXP(FNU*HPI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE
+C     WHEN FNU IS LARGE
+C-----------------------------------------------------------------------
+      CII = 1.0D0
+      INU = INT(SNGL(FNU))
+      INUH = INU/2
+      IR = INU - 2*INUH
+      ARG = (FNU-DBLE(FLOAT(INU-IR)))*HPI
+      CSGNR = DCOS(ARG)
+      CSGNI = DSIN(ARG)
+      IF (MOD(INUH,2).EQ.0) GO TO 40
+      CSGNR = -CSGNR
+      CSGNI = -CSGNI
+   40 CONTINUE
+C-----------------------------------------------------------------------
+C     ZN IS IN THE RIGHT HALF PLANE
+C-----------------------------------------------------------------------
+      ZNR = ZI
+      ZNI = -ZR
+      IF (ZI.GE.0.0D0) GO TO 50
+      ZNR = -ZNR
+      ZNI = -ZNI
+      CSGNI = -CSGNI
+      CII = -CII
+   50 CONTINUE
+      CALL ZBINU(ZNR, ZNI, FNU, KODE, N, CYR, CYI, NZ, RL, FNUL, TOL,
+     * ELIM, ALIM)
+      IF (NZ.LT.0) GO TO 130
+      NL = N - NZ
+      IF (NL.EQ.0) RETURN
+      RTOL = 1.0D0/TOL
+      ASCLE = D1MACH(1)*RTOL*1.0D+3
+      DO 60 I=1,NL
+C       STR = CYR(I)*CSGNR - CYI(I)*CSGNI
+C       CYI(I) = CYR(I)*CSGNI + CYI(I)*CSGNR
+C       CYR(I) = STR
+        AA = CYR(I)
+        BB = CYI(I)
+        ATOL = 1.0D0
+        IF (DMAX1(DABS(AA),DABS(BB)).GT.ASCLE) GO TO 55
+          AA = AA*RTOL
+          BB = BB*RTOL
+          ATOL = TOL
+   55   CONTINUE
+        STR = AA*CSGNR - BB*CSGNI
+        STI = AA*CSGNI + BB*CSGNR
+        CYR(I) = STR*ATOL
+        CYI(I) = STI*ATOL
+        STR = -CSGNI*CII
+        CSGNI = CSGNR*CII
+        CSGNR = STR
+   60 CONTINUE
+      RETURN
+  130 CONTINUE
+      IF(NZ.EQ.(-2)) GO TO 140
+      NZ = 0
+      IERR = 2
+      RETURN
+  140 CONTINUE
+      NZ=0
+      IERR=5
+      RETURN
+  260 CONTINUE
+      NZ=0
+      IERR=4
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbesk.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbesk.f
new file mode 100644
index 00000000..c2228288
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbesk.f
@@ -0,0 +1,281 @@
+      SUBROUTINE ZBESK(ZR, ZI, FNU, KODE, N, CYR, CYI, NZ, IERR)
+C***BEGIN PROLOGUE  ZBESK
+C***DATE WRITTEN   830501   (YYMMDD)
+C***REVISION DATE  890801   (YYMMDD)
+C***CATEGORY NO.  B5K
+C***KEYWORDS  K-BESSEL FUNCTION,COMPLEX BESSEL FUNCTION,
+C             MODIFIED BESSEL FUNCTION OF THE SECOND KIND,
+C             BESSEL FUNCTION OF THE THIRD KIND
+C***AUTHOR  AMOS, DONALD E., SANDIA NATIONAL LABORATORIES
+C***PURPOSE  TO COMPUTE K-BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+C***DESCRIPTION
+C
+C                      ***A DOUBLE PRECISION ROUTINE***
+C
+C         ON KODE=1, CBESK COMPUTES AN N MEMBER SEQUENCE OF COMPLEX
+C         BESSEL FUNCTIONS CY(J)=K(FNU+J-1,Z) FOR REAL, NONNEGATIVE
+C         ORDERS FNU+J-1, J=1,...,N AND COMPLEX Z.NE.CMPLX(0.0,0.0)
+C         IN THE CUT PLANE -PI.LT.ARG(Z).LE.PI. ON KODE=2, CBESK
+C         RETURNS THE SCALED K FUNCTIONS,
+C
+C         CY(J)=EXP(Z)*K(FNU+J-1,Z) , J=1,...,N,
+C
+C         WHICH REMOVE THE EXPONENTIAL BEHAVIOR IN BOTH THE LEFT AND
+C         RIGHT HALF PLANES FOR Z TO INFINITY. DEFINITIONS AND
+C         NOTATION ARE FOUND IN THE NBS HANDBOOK OF MATHEMATICAL
+C         FUNCTIONS (REF. 1).
+C
+C         INPUT      ZR,ZI,FNU ARE DOUBLE PRECISION
+C           ZR,ZI  - Z=CMPLX(ZR,ZI), Z.NE.CMPLX(0.0D0,0.0D0),
+C                    -PI.LT.ARG(Z).LE.PI
+C           FNU    - ORDER OF INITIAL K FUNCTION, FNU.GE.0.0D0
+C           N      - NUMBER OF MEMBERS OF THE SEQUENCE, N.GE.1
+C           KODE   - A PARAMETER TO INDICATE THE SCALING OPTION
+C                    KODE= 1  RETURNS
+C                             CY(I)=K(FNU+I-1,Z), I=1,...,N
+C                        = 2  RETURNS
+C                             CY(I)=K(FNU+I-1,Z)*EXP(Z), I=1,...,N
+C
+C         OUTPUT     CYR,CYI ARE DOUBLE PRECISION
+C           CYR,CYI- DOUBLE PRECISION VECTORS WHOSE FIRST N COMPONENTS
+C                    CONTAIN REAL AND IMAGINARY PARTS FOR THE SEQUENCE
+C                    CY(I)=K(FNU+I-1,Z), I=1,...,N OR
+C                    CY(I)=K(FNU+I-1,Z)*EXP(Z), I=1,...,N
+C                    DEPENDING ON KODE
+C           NZ     - NUMBER OF COMPONENTS SET TO ZERO DUE TO UNDERFLOW.
+C                    NZ= 0   , NORMAL RETURN
+C                    NZ.GT.0 , FIRST NZ COMPONENTS OF CY SET TO ZERO DUE
+C                              TO UNDERFLOW, CY(I)=CMPLX(0.0D0,0.0D0),
+C                              I=1,...,N WHEN X.GE.0.0. WHEN X.LT.0.0
+C                              NZ STATES ONLY THE NUMBER OF UNDERFLOWS
+C                              IN THE SEQUENCE.
+C
+C           IERR   - ERROR FLAG
+C                    IERR=0, NORMAL RETURN - COMPUTATION COMPLETED
+C                    IERR=1, INPUT ERROR   - NO COMPUTATION
+C                    IERR=2, OVERFLOW      - NO COMPUTATION, FNU IS
+C                            TOO LARGE OR CABS(Z) IS TOO SMALL OR BOTH
+C                    IERR=3, CABS(Z) OR FNU+N-1 LARGE - COMPUTATION DONE
+C                            BUT LOSSES OF SIGNIFCANCE BY ARGUMENT
+C                            REDUCTION PRODUCE LESS THAN HALF OF MACHINE
+C                            ACCURACY
+C                    IERR=4, CABS(Z) OR FNU+N-1 TOO LARGE - NO COMPUTA-
+C                            TION BECAUSE OF COMPLETE LOSSES OF SIGNIFI-
+C                            CANCE BY ARGUMENT REDUCTION
+C                    IERR=5, ERROR              - NO COMPUTATION,
+C                            ALGORITHM TERMINATION CONDITION NOT MET
+C
+C***LONG DESCRIPTION
+C
+C         EQUATIONS OF THE REFERENCE ARE IMPLEMENTED FOR SMALL ORDERS
+C         DNU AND DNU+1.0 IN THE RIGHT HALF PLANE X.GE.0.0. FORWARD
+C         RECURRENCE GENERATES HIGHER ORDERS. K IS CONTINUED TO THE LEFT
+C         HALF PLANE BY THE RELATION
+C
+C         K(FNU,Z*EXP(MP)) = EXP(-MP*FNU)*K(FNU,Z)-MP*I(FNU,Z)
+C         MP=MR*PI*I, MR=+1 OR -1, RE(Z).GT.0, I**2=-1
+C
+C         WHERE I(FNU,Z) IS THE I BESSEL FUNCTION.
+C
+C         FOR LARGE ORDERS, FNU.GT.FNUL, THE K FUNCTION IS COMPUTED
+C         BY MEANS OF ITS UNIFORM ASYMPTOTIC EXPANSIONS.
+C
+C         FOR NEGATIVE ORDERS, THE FORMULA
+C
+C                       K(-FNU,Z) = K(FNU,Z)
+C
+C         CAN BE USED.
+C
+C         CBESK ASSUMES THAT A SIGNIFICANT DIGIT SINH(X) FUNCTION IS
+C         AVAILABLE.
+C
+C         IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE-
+C         MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z OR FNU+N-1 IS
+C         LARGE, LOSSES OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR.
+C         CONSEQUENTLY, IF EITHER ONE EXCEEDS U1=SQRT(0.5/UR), THEN
+C         LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR FLAG
+C         IERR=3 IS TRIGGERED WHERE UR=DMAX1(D1MACH(4),1.0D-18) IS
+C         DOUBLE PRECISION UNIT ROUNDOFF LIMITED TO 18 DIGITS PRECISION.
+C         IF EITHER IS LARGER THAN U2=0.5/UR, THEN ALL SIGNIFICANCE IS
+C         LOST AND IERR=4. IN ORDER TO USE THE INT FUNCTION, ARGUMENTS
+C         MUST BE FURTHER RESTRICTED NOT TO EXCEED THE LARGEST MACHINE
+C         INTEGER, U3=I1MACH(9). THUS, THE MAGNITUDE OF Z AND FNU+N-1 IS
+C         RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2, AND U3
+C         ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE PRECISION
+C         ARITHMETIC AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE PRECISION
+C         ARITHMETIC RESPECTIVELY. THIS MAKES U2 AND U3 LIMITING IN
+C         THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT ONE CAN EXPECT
+C         TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES, NO DIGITS
+C         IN SINGLE AND ONLY 7 DIGITS IN DOUBLE PRECISION ARITHMETIC.
+C         SIMILAR CONSIDERATIONS HOLD FOR OTHER MACHINES.
+C
+C         THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX
+C         BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT
+C         ROUNDOFF,1.0E-18) IS THE NOMINAL PRECISION AND 10**S REPRE-
+C         SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE
+C         ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))),
+C         ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF
+C         CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY
+C         HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN
+C         ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY
+C         SEVERAL ORDERS OF MAGNITUDE. IF ONE COMPONENT IS 10**K LARGER
+C         THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K,
+C         0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS
+C         THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER
+C         COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY
+C         BECAUSE, IN COMPLEX ARITHMETIC WITH PRECISION P, THE SMALLER
+C         COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE
+C         MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES,
+C         THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P,
+C         OR -PI/2+P.
+C
+C***REFERENCES  HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ
+C                 AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF
+C                 COMMERCE, 1955.
+C
+C               COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+C                 BY D. E. AMOS, SAND83-0083, MAY, 1983.
+C
+C               COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+C                 AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983.
+C
+C               A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+C                 ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85-
+C                 1018, MAY, 1985
+C
+C               A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+C                 ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS.
+C                 MATH. SOFTWARE, 1986
+C
+C***ROUTINES CALLED  ZACON,ZBKNU,ZBUNK,ZUOIK,ZABS,I1MACH,D1MACH
+C***END PROLOGUE  ZBESK
+C
+C     COMPLEX CY,Z
+      DOUBLE PRECISION AA, ALIM, ALN, ARG, AZ, CYI, CYR, DIG, ELIM, FN,
+     * FNU, FNUL, RL, R1M5, TOL, UFL, ZI, ZR, D1MACH, ZABS, BB
+      INTEGER IERR, K, KODE, K1, K2, MR, N, NN, NUF, NW, NZ, I1MACH
+      DIMENSION CYR(N), CYI(N)
+C***FIRST EXECUTABLE STATEMENT  ZBESK
+      IERR = 0
+      NZ=0
+      IF (ZI.EQ.0.0E0 .AND. ZR.EQ.0.0E0) IERR=1
+      IF (FNU.LT.0.0D0) IERR=1
+      IF (KODE.LT.1 .OR. KODE.GT.2) IERR=1
+      IF (N.LT.1) IERR=1
+      IF (IERR.NE.0) RETURN
+      NN = N
+C-----------------------------------------------------------------------
+C     SET PARAMETERS RELATED TO MACHINE CONSTANTS.
+C     TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0E-18.
+C     ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW LIMIT.
+C     EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL    AND
+C     EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL       ARE INTERVALS NEAR
+C     UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE.
+C     RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR LARGE Z.
+C     DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG).
+C     FNUL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC SERIES FOR LARGE FNU
+C-----------------------------------------------------------------------
+      TOL = DMAX1(D1MACH(4),1.0D-18)
+      K1 = I1MACH(15)
+      K2 = I1MACH(16)
+      R1M5 = D1MACH(5)
+      K = MIN0(IABS(K1),IABS(K2))
+      ELIM = 2.303D0*(DBLE(FLOAT(K))*R1M5-3.0D0)
+      K1 = I1MACH(14) - 1
+      AA = R1M5*DBLE(FLOAT(K1))
+      DIG = DMIN1(AA,18.0D0)
+      AA = AA*2.303D0
+      ALIM = ELIM + DMAX1(-AA,-41.45D0)
+      FNUL = 10.0D0 + 6.0D0*(DIG-3.0D0)
+      RL = 1.2D0*DIG + 3.0D0
+C-----------------------------------------------------------------------------
+C     TEST FOR PROPER RANGE
+C-----------------------------------------------------------------------
+      AZ = ZABS(CMPLX(ZR,ZI,kind=KIND(1.0D0)))
+      FN = FNU + DBLE(FLOAT(NN-1))
+      AA = 0.5D0/TOL
+      BB=DBLE(FLOAT(I1MACH(9)))*0.5D0
+      AA = DMIN1(AA,BB)
+      IF (AZ.GT.AA) GO TO 260
+      IF (FN.GT.AA) GO TO 260
+      AA = DSQRT(AA)
+      IF (AZ.GT.AA) IERR=3
+      IF (FN.GT.AA) IERR=3
+C-----------------------------------------------------------------------
+C     OVERFLOW TEST ON THE LAST MEMBER OF THE SEQUENCE
+C-----------------------------------------------------------------------
+C     UFL = DEXP(-ELIM)
+      UFL = D1MACH(1)*1.0D+3
+      IF (AZ.LT.UFL) GO TO 180
+      IF (FNU.GT.FNUL) GO TO 80
+      IF (FN.LE.1.0D0) GO TO 60
+      IF (FN.GT.2.0D0) GO TO 50
+      IF (AZ.GT.TOL) GO TO 60
+      ARG = 0.5D0*AZ
+      ALN = -FN*DLOG(ARG)
+      IF (ALN.GT.ELIM) GO TO 180
+      GO TO 60
+   50 CONTINUE
+      CALL ZUOIK(ZR, ZI, FNU, KODE, 2, NN, CYR, CYI, NUF, TOL, ELIM,
+     * ALIM)
+      IF (NUF.LT.0) GO TO 180
+      NZ = NZ + NUF
+      NN = NN - NUF
+C-----------------------------------------------------------------------
+C     HERE NN=N OR NN=0 SINCE NUF=0,NN, OR -1 ON RETURN FROM CUOIK
+C     IF NUF=NN, THEN CY(I)=CZERO FOR ALL I
+C-----------------------------------------------------------------------
+      IF (NN.EQ.0) GO TO 100
+   60 CONTINUE
+      IF (ZR.LT.0.0D0) GO TO 70
+C-----------------------------------------------------------------------
+C     RIGHT HALF PLANE COMPUTATION, REAL(Z).GE.0.
+C-----------------------------------------------------------------------
+      CALL ZBKNU(ZR, ZI, FNU, KODE, NN, CYR, CYI, NW, TOL, ELIM, ALIM)
+      IF (NW.LT.0) GO TO 200
+      NZ=NW
+      RETURN
+C-----------------------------------------------------------------------
+C     LEFT HALF PLANE COMPUTATION
+C     PI/2.LT.ARG(Z).LE.PI AND -PI.LT.ARG(Z).LT.-PI/2.
+C-----------------------------------------------------------------------
+   70 CONTINUE
+      IF (NZ.NE.0) GO TO 180
+      MR = 1
+      IF (ZI.LT.0.0D0) MR = -1
+      CALL ZACON(ZR, ZI, FNU, KODE, MR, NN, CYR, CYI, NW, RL, FNUL,
+     * TOL, ELIM, ALIM)
+      IF (NW.LT.0) GO TO 200
+      NZ=NW
+      RETURN
+C-----------------------------------------------------------------------
+C     UNIFORM ASYMPTOTIC EXPANSIONS FOR FNU.GT.FNUL
+C-----------------------------------------------------------------------
+   80 CONTINUE
+      MR = 0
+      IF (ZR.GE.0.0D0) GO TO 90
+      MR = 1
+      IF (ZI.LT.0.0D0) MR = -1
+   90 CONTINUE
+      CALL ZBUNK(ZR, ZI, FNU, KODE, MR, NN, CYR, CYI, NW, TOL, ELIM,
+     * ALIM)
+      IF (NW.LT.0) GO TO 200
+      NZ = NZ + NW
+      RETURN
+  100 CONTINUE
+      IF (ZR.LT.0.0D0) GO TO 180
+      RETURN
+  180 CONTINUE
+      NZ = 0
+      IERR=2
+      RETURN
+  200 CONTINUE
+      IF(NW.EQ.(-1)) GO TO 180
+      NZ=0
+      IERR=5
+      RETURN
+  260 CONTINUE
+      NZ=0
+      IERR=4
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbesy.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbesy.f
new file mode 100644
index 00000000..05ec40be
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbesy.f
@@ -0,0 +1,244 @@
+      SUBROUTINE ZBESY(ZR, ZI, FNU, KODE, N, CYR, CYI, NZ, CWRKR, CWRKI,
+     *                 IERR)
+C***BEGIN PROLOGUE  ZBESY
+C***DATE WRITTEN   830501   (YYMMDD)
+C***REVISION DATE  890801   (YYMMDD)
+C***CATEGORY NO.  B5K
+C***KEYWORDS  Y-BESSEL FUNCTION,BESSEL FUNCTION OF COMPLEX ARGUMENT,
+C             BESSEL FUNCTION OF SECOND KIND
+C***AUTHOR  AMOS, DONALD E., SANDIA NATIONAL LABORATORIES
+C***PURPOSE  TO COMPUTE THE Y-BESSEL FUNCTION OF A COMPLEX ARGUMENT
+C***DESCRIPTION
+C
+C                      ***A DOUBLE PRECISION ROUTINE***
+C
+C         ON KODE=1, CBESY COMPUTES AN N MEMBER SEQUENCE OF COMPLEX
+C         BESSEL FUNCTIONS CY(I)=Y(FNU+I-1,Z) FOR REAL, NONNEGATIVE
+C         ORDERS FNU+I-1, I=1,...,N AND COMPLEX Z IN THE CUT PLANE
+C         -PI.LT.ARG(Z).LE.PI. ON KODE=2, CBESY RETURNS THE SCALED
+C         FUNCTIONS
+C
+C         CY(I)=EXP(-ABS(Y))*Y(FNU+I-1,Z)   I = 1,...,N , Y=AIMAG(Z)
+C
+C         WHICH REMOVE THE EXPONENTIAL GROWTH IN BOTH THE UPPER AND
+C         LOWER HALF PLANES FOR Z TO INFINITY. DEFINITIONS AND NOTATION
+C         ARE FOUND IN THE NBS HANDBOOK OF MATHEMATICAL FUNCTIONS
+C         (REF. 1).
+C
+C         INPUT      ZR,ZI,FNU ARE DOUBLE PRECISION
+C           ZR,ZI  - Z=CMPLX(ZR,ZI), Z.NE.CMPLX(0.0D0,0.0D0),
+C                    -PI.LT.ARG(Z).LE.PI
+C           FNU    - ORDER OF INITIAL Y FUNCTION, FNU.GE.0.0D0
+C           KODE   - A PARAMETER TO INDICATE THE SCALING OPTION
+C                    KODE= 1  RETURNS
+C                             CY(I)=Y(FNU+I-1,Z), I=1,...,N
+C                        = 2  RETURNS
+C                             CY(I)=Y(FNU+I-1,Z)*EXP(-ABS(Y)), I=1,...,N
+C                             WHERE Y=AIMAG(Z)
+C           N      - NUMBER OF MEMBERS OF THE SEQUENCE, N.GE.1
+C           CWRKR, - DOUBLE PRECISION WORK VECTORS OF DIMENSION AT
+C           CWRKI    AT LEAST N
+C
+C         OUTPUT     CYR,CYI ARE DOUBLE PRECISION
+C           CYR,CYI- DOUBLE PRECISION VECTORS WHOSE FIRST N COMPONENTS
+C                    CONTAIN REAL AND IMAGINARY PARTS FOR THE SEQUENCE
+C                    CY(I)=Y(FNU+I-1,Z)  OR
+C                    CY(I)=Y(FNU+I-1,Z)*EXP(-ABS(Y))  I=1,...,N
+C                    DEPENDING ON KODE.
+C           NZ     - NZ=0 , A NORMAL RETURN
+C                    NZ.GT.0 , NZ COMPONENTS OF CY SET TO ZERO DUE TO
+C                    UNDERFLOW (GENERALLY ON KODE=2)
+C           IERR   - ERROR FLAG
+C                    IERR=0, NORMAL RETURN - COMPUTATION COMPLETED
+C                    IERR=1, INPUT ERROR   - NO COMPUTATION
+C                    IERR=2, OVERFLOW      - NO COMPUTATION, FNU IS
+C                            TOO LARGE OR CABS(Z) IS TOO SMALL OR BOTH
+C                    IERR=3, CABS(Z) OR FNU+N-1 LARGE - COMPUTATION DONE
+C                            BUT LOSSES OF SIGNIFCANCE BY ARGUMENT
+C                            REDUCTION PRODUCE LESS THAN HALF OF MACHINE
+C                            ACCURACY
+C                    IERR=4, CABS(Z) OR FNU+N-1 TOO LARGE - NO COMPUTA-
+C                            TION BECAUSE OF COMPLETE LOSSES OF SIGNIFI-
+C                            CANCE BY ARGUMENT REDUCTION
+C                    IERR=5, ERROR              - NO COMPUTATION,
+C                            ALGORITHM TERMINATION CONDITION NOT MET
+C
+C***LONG DESCRIPTION
+C
+C         THE COMPUTATION IS CARRIED OUT BY THE FORMULA
+C
+C         Y(FNU,Z)=0.5*(H(1,FNU,Z)-H(2,FNU,Z))/I
+C
+C         WHERE I**2 = -1 AND THE HANKEL BESSEL FUNCTIONS H(1,FNU,Z)
+C         AND H(2,FNU,Z) ARE CALCULATED IN CBESH.
+C
+C         FOR NEGATIVE ORDERS,THE FORMULA
+C
+C              Y(-FNU,Z) = Y(FNU,Z)*COS(PI*FNU) + J(FNU,Z)*SIN(PI*FNU)
+C
+C         CAN BE USED. HOWEVER,FOR LARGE ORDERS CLOSE TO HALF ODD
+C         INTEGERS THE FUNCTION CHANGES RADICALLY. WHEN FNU IS A LARGE
+C         POSITIVE HALF ODD INTEGER,THE MAGNITUDE OF Y(-FNU,Z)=J(FNU,Z)*
+C         SIN(PI*FNU) IS A LARGE NEGATIVE POWER OF TEN. BUT WHEN FNU IS
+C         NOT A HALF ODD INTEGER, Y(FNU,Z) DOMINATES IN MAGNITUDE WITH A
+C         LARGE POSITIVE POWER OF TEN AND THE MOST THAT THE SECOND TERM
+C         CAN BE REDUCED IS BY UNIT ROUNDOFF FROM THE COEFFICIENT. THUS,
+C         WIDE CHANGES CAN OCCUR WITHIN UNIT ROUNDOFF OF A LARGE HALF
+C         ODD INTEGER. HERE, LARGE MEANS FNU.GT.CABS(Z).
+C
+C         IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE-
+C         MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z OR FNU+N-1 IS
+C         LARGE, LOSSES OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR.
+C         CONSEQUENTLY, IF EITHER ONE EXCEEDS U1=SQRT(0.5/UR), THEN
+C         LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR FLAG
+C         IERR=3 IS TRIGGERED WHERE UR=DMAX1(D1MACH(4),1.0D-18) IS
+C         DOUBLE PRECISION UNIT ROUNDOFF LIMITED TO 18 DIGITS PRECISION.
+C         IF EITHER IS LARGER THAN U2=0.5/UR, THEN ALL SIGNIFICANCE IS
+C         LOST AND IERR=4. IN ORDER TO USE THE INT FUNCTION, ARGUMENTS
+C         MUST BE FURTHER RESTRICTED NOT TO EXCEED THE LARGEST MACHINE
+C         INTEGER, U3=I1MACH(9). THUS, THE MAGNITUDE OF Z AND FNU+N-1 IS
+C         RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2, AND U3
+C         ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE PRECISION
+C         ARITHMETIC AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE PRECISION
+C         ARITHMETIC RESPECTIVELY. THIS MAKES U2 AND U3 LIMITING IN
+C         THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT ONE CAN EXPECT
+C         TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES, NO DIGITS
+C         IN SINGLE AND ONLY 7 DIGITS IN DOUBLE PRECISION ARITHMETIC.
+C         SIMILAR CONSIDERATIONS HOLD FOR OTHER MACHINES.
+C
+C         THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX
+C         BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT
+C         ROUNDOFF,1.0E-18) IS THE NOMINAL PRECISION AND 10**S REPRE-
+C         SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE
+C         ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))),
+C         ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF
+C         CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY
+C         HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN
+C         ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY
+C         SEVERAL ORDERS OF MAGNITUDE. IF ONE COMPONENT IS 10**K LARGER
+C         THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K,
+C         0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS
+C         THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER
+C         COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY
+C         BECAUSE, IN COMPLEX ARITHMETIC WITH PRECISION P, THE SMALLER
+C         COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE
+C         MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES,
+C         THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P,
+C         OR -PI/2+P.
+C
+C***REFERENCES  HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ
+C                 AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF
+C                 COMMERCE, 1955.
+C
+C               COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+C                 BY D. E. AMOS, SAND83-0083, MAY, 1983.
+C
+C               COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+C                 AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983
+C
+C               A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+C                 ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85-
+C                 1018, MAY, 1985
+C
+C               A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+C                 ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS.
+C                 MATH. SOFTWARE, 1986
+C
+C***ROUTINES CALLED  ZBESH,I1MACH,D1MACH
+C***END PROLOGUE  ZBESY
+C
+C     COMPLEX CWRK,CY,C1,C2,EX,HCI,Z,ZU,ZV
+      DOUBLE PRECISION CWRKI, CWRKR, CYI, CYR, C1I, C1R, C2I, C2R,
+     * ELIM, EXI, EXR, EY, FNU, HCII, STI, STR, TAY, ZI, ZR, DEXP,
+     * D1MACH, ASCLE, RTOL, ATOL, AA, BB, TOL
+      INTEGER I, IERR, K, KODE, K1, K2, N, NZ, NZ1, NZ2, I1MACH
+      DIMENSION CYR(N), CYI(N), CWRKR(N), CWRKI(N)
+C***FIRST EXECUTABLE STATEMENT  ZBESY
+      IERR = 0
+      NZ=0
+      IF (ZR.EQ.0.0D0 .AND. ZI.EQ.0.0D0) IERR=1
+      IF (FNU.LT.0.0D0) IERR=1
+      IF (KODE.LT.1 .OR. KODE.GT.2) IERR=1
+      IF (N.LT.1) IERR=1
+      IF (IERR.NE.0) RETURN
+      HCII = 0.5D0
+      CALL ZBESH(ZR, ZI, FNU, KODE, 1, N, CYR, CYI, NZ1, IERR)
+      IF (IERR.NE.0.AND.IERR.NE.3) GO TO 170
+      CALL ZBESH(ZR, ZI, FNU, KODE, 2, N, CWRKR, CWRKI, NZ2, IERR)
+      IF (IERR.NE.0.AND.IERR.NE.3) GO TO 170
+      NZ = MIN0(NZ1,NZ2)
+      IF (KODE.EQ.2) GO TO 60
+      DO 50 I=1,N
+        STR = CWRKR(I) - CYR(I)
+        STI = CWRKI(I) - CYI(I)
+        CYR(I) = -STI*HCII
+        CYI(I) = STR*HCII
+   50 CONTINUE
+      RETURN
+   60 CONTINUE
+      TOL = DMAX1(D1MACH(4),1.0D-18)
+      K1 = I1MACH(15)
+      K2 = I1MACH(16)
+      K = MIN0(IABS(K1),IABS(K2))
+      R1M5 = D1MACH(5)
+C-----------------------------------------------------------------------
+C     ELIM IS THE APPROXIMATE EXPONENTIAL UNDER- AND OVERFLOW LIMIT
+C-----------------------------------------------------------------------
+      ELIM = 2.303D0*(DBLE(FLOAT(K))*R1M5-3.0D0)
+      EXR = DCOS(ZR)
+      EXI = DSIN(ZR)
+      EY = 0.0D0
+      TAY = DABS(ZI+ZI)
+      IF (TAY.LT.ELIM) EY = DEXP(-TAY)
+      IF (ZI.LT.0.0D0) GO TO 90
+      C1R = EXR*EY
+      C1I = EXI*EY
+      C2R = EXR
+      C2I = -EXI
+   70 CONTINUE
+      NZ = 0
+      RTOL = 1.0D0/TOL
+      ASCLE = D1MACH(1)*RTOL*1.0D+3
+      DO 80 I=1,N
+C       STR = C1R*CYR(I) - C1I*CYI(I)
+C       STI = C1R*CYI(I) + C1I*CYR(I)
+C       STR = -STR + C2R*CWRKR(I) - C2I*CWRKI(I)
+C       STI = -STI + C2R*CWRKI(I) + C2I*CWRKR(I)
+C       CYR(I) = -STI*HCII
+C       CYI(I) = STR*HCII
+        AA = CWRKR(I)
+        BB = CWRKI(I)
+        ATOL = 1.0D0
+        IF (DMAX1(DABS(AA),DABS(BB)).GT.ASCLE) GO TO 75
+          AA = AA*RTOL
+          BB = BB*RTOL
+          ATOL = TOL
+   75   CONTINUE
+        STR = (AA*C2R - BB*C2I)*ATOL
+        STI = (AA*C2I + BB*C2R)*ATOL
+        AA = CYR(I)
+        BB = CYI(I)
+        ATOL = 1.0D0
+        IF (DMAX1(DABS(AA),DABS(BB)).GT.ASCLE) GO TO 85
+          AA = AA*RTOL
+          BB = BB*RTOL
+          ATOL = TOL
+   85   CONTINUE
+        STR = STR - (AA*C1R - BB*C1I)*ATOL
+        STI = STI - (AA*C1I + BB*C1R)*ATOL
+        CYR(I) = -STI*HCII
+        CYI(I) =  STR*HCII
+        IF (STR.EQ.0.0D0 .AND. STI.EQ.0.0D0 .AND. EY.EQ.0.0D0) NZ = NZ
+     *   + 1
+   80 CONTINUE
+      RETURN
+   90 CONTINUE
+      C1R = EXR
+      C1I = EXI
+      C2R = EXR*EY
+      C2I = -EXI*EY
+      GO TO 70
+  170 CONTINUE
+      NZ = 0
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbinu.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbinu.f
new file mode 100644
index 00000000..b740e707
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbinu.f
@@ -0,0 +1,110 @@
+      SUBROUTINE ZBINU(ZR, ZI, FNU, KODE, N, CYR, CYI, NZ, RL, FNUL,
+     * TOL, ELIM, ALIM)
+C***BEGIN PROLOGUE  ZBINU
+C***REFER TO  ZBESH,ZBESI,ZBESJ,ZBESK,ZAIRY,ZBIRY
+C
+C     ZBINU COMPUTES THE I FUNCTION IN THE RIGHT HALF Z PLANE
+C
+C***ROUTINES CALLED  ZABS,ZASYI,ZBUNI,ZMLRI,ZSERI,ZUOIK,ZWRSK
+C***END PROLOGUE  ZBINU
+      DOUBLE PRECISION ALIM, AZ, CWI, CWR, CYI, CYR, DFNU, ELIM, FNU,
+     * FNUL, RL, TOL, ZEROI, ZEROR, ZI, ZR, ZABS
+      INTEGER I, INW, KODE, N, NLAST, NN, NUI, NW, NZ
+      DIMENSION CYR(N), CYI(N), CWR(2), CWI(2)
+      DATA ZEROR,ZEROI / 0.0D0, 0.0D0 /
+C
+      NZ = 0
+      AZ = ZABS(CMPLX(ZR,ZI,kind=KIND(1.0D0)))
+      NN = N
+      DFNU = FNU + DBLE(FLOAT(N-1))
+      IF (AZ.LE.2.0D0) GO TO 10
+      IF (AZ*AZ*0.25D0.GT.DFNU+1.0D0) GO TO 20
+   10 CONTINUE
+C-----------------------------------------------------------------------
+C     POWER SERIES
+C-----------------------------------------------------------------------
+      CALL ZSERI(ZR, ZI, FNU, KODE, NN, CYR, CYI, NW, TOL, ELIM, ALIM)
+      INW = IABS(NW)
+      NZ = NZ + INW
+      NN = NN - INW
+      IF (NN.EQ.0) RETURN
+      IF (NW.GE.0) GO TO 120
+      DFNU = FNU + DBLE(FLOAT(NN-1))
+   20 CONTINUE
+      IF (AZ.LT.RL) GO TO 40
+      IF (DFNU.LE.1.0D0) GO TO 30
+      IF (AZ+AZ.LT.DFNU*DFNU) GO TO 50
+C-----------------------------------------------------------------------
+C     ASYMPTOTIC EXPANSION FOR LARGE Z
+C-----------------------------------------------------------------------
+   30 CONTINUE
+      CALL ZASYI(ZR, ZI, FNU, KODE, NN, CYR, CYI, NW, RL, TOL, ELIM,
+     * ALIM)
+      IF (NW.LT.0) GO TO 130
+      GO TO 120
+   40 CONTINUE
+      IF (DFNU.LE.1.0D0) GO TO 70
+   50 CONTINUE
+C-----------------------------------------------------------------------
+C     OVERFLOW AND UNDERFLOW TEST ON I SEQUENCE FOR MILLER ALGORITHM
+C-----------------------------------------------------------------------
+      CALL ZUOIK(ZR, ZI, FNU, KODE, 1, NN, CYR, CYI, NW, TOL, ELIM,
+     * ALIM)
+      IF (NW.LT.0) GO TO 130
+      NZ = NZ + NW
+      NN = NN - NW
+      IF (NN.EQ.0) RETURN
+      DFNU = FNU+DBLE(FLOAT(NN-1))
+      IF (DFNU.GT.FNUL) GO TO 110
+      IF (AZ.GT.FNUL) GO TO 110
+   60 CONTINUE
+      IF (AZ.GT.RL) GO TO 80
+   70 CONTINUE
+C-----------------------------------------------------------------------
+C     MILLER ALGORITHM NORMALIZED BY THE SERIES
+C-----------------------------------------------------------------------
+      CALL ZMLRI(ZR, ZI, FNU, KODE, NN, CYR, CYI, NW, TOL)
+      IF(NW.LT.0) GO TO 130
+      GO TO 120
+   80 CONTINUE
+C-----------------------------------------------------------------------
+C     MILLER ALGORITHM NORMALIZED BY THE WRONSKIAN
+C-----------------------------------------------------------------------
+C-----------------------------------------------------------------------
+C     OVERFLOW TEST ON K FUNCTIONS USED IN WRONSKIAN
+C-----------------------------------------------------------------------
+      CALL ZUOIK(ZR, ZI, FNU, KODE, 2, 2, CWR, CWI, NW, TOL, ELIM,
+     * ALIM)
+      IF (NW.GE.0) GO TO 100
+      NZ = NN
+      DO 90 I=1,NN
+        CYR(I) = ZEROR
+        CYI(I) = ZEROI
+   90 CONTINUE
+      RETURN
+  100 CONTINUE
+      IF (NW.GT.0) GO TO 130
+      CALL ZWRSK(ZR, ZI, FNU, KODE, NN, CYR, CYI, NW, CWR, CWI, TOL,
+     * ELIM, ALIM)
+      IF (NW.LT.0) GO TO 130
+      GO TO 120
+  110 CONTINUE
+C-----------------------------------------------------------------------
+C     INCREMENT FNU+NN-1 UP TO FNUL, COMPUTE AND RECUR BACKWARD
+C-----------------------------------------------------------------------
+      NUI = INT(SNGL(FNUL-DFNU)) + 1
+      NUI = MAX0(NUI,0)
+      CALL ZBUNI(ZR, ZI, FNU, KODE, NN, CYR, CYI, NW, NUI, NLAST, FNUL,
+     * TOL, ELIM, ALIM)
+      IF (NW.LT.0) GO TO 130
+      NZ = NZ + NW
+      IF (NLAST.EQ.0) GO TO 120
+      NN = NLAST
+      GO TO 60
+  120 CONTINUE
+      RETURN
+  130 CONTINUE
+      NZ = -1
+      IF(NW.EQ.(-2)) NZ=-2
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbiry.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbiry.f
new file mode 100644
index 00000000..f042d824
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbiry.f
@@ -0,0 +1,364 @@
+      SUBROUTINE ZBIRY(ZR, ZI, ID, KODE, BIR, BII, IERR)
+C***BEGIN PROLOGUE  ZBIRY
+C***DATE WRITTEN   830501   (YYMMDD)
+C***REVISION DATE  890801   (YYMMDD)
+C***CATEGORY NO.  B5K
+C***KEYWORDS  AIRY FUNCTION,BESSEL FUNCTIONS OF ORDER ONE THIRD
+C***AUTHOR  AMOS, DONALD E., SANDIA NATIONAL LABORATORIES
+C***PURPOSE  TO COMPUTE AIRY FUNCTIONS BI(Z) AND DBI(Z) FOR COMPLEX Z
+C***DESCRIPTION
+C
+C                      ***A DOUBLE PRECISION ROUTINE***
+C         ON KODE=1, CBIRY COMPUTES THE COMPLEX AIRY FUNCTION BI(Z) OR
+C         ITS DERIVATIVE DBI(Z)/DZ ON ID=0 OR ID=1 RESPECTIVELY. ON
+C         KODE=2, A SCALING OPTION CEXP(-AXZTA)*BI(Z) OR CEXP(-AXZTA)*
+C         DBI(Z)/DZ IS PROVIDED TO REMOVE THE EXPONENTIAL BEHAVIOR IN
+C         BOTH THE LEFT AND RIGHT HALF PLANES WHERE
+C         ZTA=(2/3)*Z*CSQRT(Z)=CMPLX(XZTA,YZTA) AND AXZTA=ABS(XZTA).
+C         DEFINTIONS AND NOTATION ARE FOUND IN THE NBS HANDBOOK OF
+C         MATHEMATICAL FUNCTIONS (REF. 1).
+C
+C         INPUT      ZR,ZI ARE DOUBLE PRECISION
+C           ZR,ZI  - Z=CMPLX(ZR,ZI)
+C           ID     - ORDER OF DERIVATIVE, ID=0 OR ID=1
+C           KODE   - A PARAMETER TO INDICATE THE SCALING OPTION
+C                    KODE= 1  RETURNS
+C                             BI=BI(Z)                 ON ID=0 OR
+C                             BI=DBI(Z)/DZ             ON ID=1
+C                        = 2  RETURNS
+C                             BI=CEXP(-AXZTA)*BI(Z)     ON ID=0 OR
+C                             BI=CEXP(-AXZTA)*DBI(Z)/DZ ON ID=1 WHERE
+C                             ZTA=(2/3)*Z*CSQRT(Z)=CMPLX(XZTA,YZTA)
+C                             AND AXZTA=ABS(XZTA)
+C
+C         OUTPUT     BIR,BII ARE DOUBLE PRECISION
+C           BIR,BII- COMPLEX ANSWER DEPENDING ON THE CHOICES FOR ID AND
+C                    KODE
+C           IERR   - ERROR FLAG
+C                    IERR=0, NORMAL RETURN - COMPUTATION COMPLETED
+C                    IERR=1, INPUT ERROR   - NO COMPUTATION
+C                    IERR=2, OVERFLOW      - NO COMPUTATION, REAL(Z)
+C                            TOO LARGE ON KODE=1
+C                    IERR=3, CABS(Z) LARGE      - COMPUTATION COMPLETED
+C                            LOSSES OF SIGNIFCANCE BY ARGUMENT REDUCTION
+C                            PRODUCE LESS THAN HALF OF MACHINE ACCURACY
+C                    IERR=4, CABS(Z) TOO LARGE  - NO COMPUTATION
+C                            COMPLETE LOSS OF ACCURACY BY ARGUMENT
+C                            REDUCTION
+C                    IERR=5, ERROR              - NO COMPUTATION,
+C                            ALGORITHM TERMINATION CONDITION NOT MET
+C
+C***LONG DESCRIPTION
+C
+C         BI AND DBI ARE COMPUTED FOR CABS(Z).GT.1.0 FROM THE I BESSEL
+C         FUNCTIONS BY
+C
+C                BI(Z)=C*SQRT(Z)*( I(-1/3,ZTA) + I(1/3,ZTA) )
+C               DBI(Z)=C *  Z  * ( I(-2/3,ZTA) + I(2/3,ZTA) )
+C                               C=1.0/SQRT(3.0)
+C                             ZTA=(2/3)*Z**(3/2)
+C
+C         WITH THE POWER SERIES FOR CABS(Z).LE.1.0.
+C
+C         IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE-
+C         MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z IS LARGE, LOSSES
+C         OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR. CONSEQUENTLY, IF
+C         THE MAGNITUDE OF ZETA=(2/3)*Z**1.5 EXCEEDS U1=SQRT(0.5/UR),
+C         THEN LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR
+C         FLAG IERR=3 IS TRIGGERED WHERE UR=DMAX1(D1MACH(4),1.0D-18) IS
+C         DOUBLE PRECISION UNIT ROUNDOFF LIMITED TO 18 DIGITS PRECISION.
+C         ALSO, IF THE MAGNITUDE OF ZETA IS LARGER THAN U2=0.5/UR, THEN
+C         ALL SIGNIFICANCE IS LOST AND IERR=4. IN ORDER TO USE THE INT
+C         FUNCTION, ZETA MUST BE FURTHER RESTRICTED NOT TO EXCEED THE
+C         LARGEST INTEGER, U3=I1MACH(9). THUS, THE MAGNITUDE OF ZETA
+C         MUST BE RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2,
+C         AND U3 ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE
+C         PRECISION ARITHMETIC AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE
+C         PRECISION ARITHMETIC RESPECTIVELY. THIS MAKES U2 AND U3 LIMIT-
+C         ING IN THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT THE MAG-
+C         NITUDE OF Z CANNOT EXCEED 3.1E+4 IN SINGLE AND 2.1E+6 IN
+C         DOUBLE PRECISION ARITHMETIC. THIS ALSO MEANS THAT ONE CAN
+C         EXPECT TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES,
+C         NO DIGITS IN SINGLE PRECISION AND ONLY 7 DIGITS IN DOUBLE
+C         PRECISION ARITHMETIC. SIMILAR CONSIDERATIONS HOLD FOR OTHER
+C         MACHINES.
+C
+C         THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX
+C         BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT
+C         ROUNDOFF,1.0E-18) IS THE NOMINAL PRECISION AND 10**S REPRE-
+C         SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE
+C         ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))),
+C         ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF
+C         CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY
+C         HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN
+C         ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY
+C         SEVERAL ORDERS OF MAGNITUDE. IF ONE COMPONENT IS 10**K LARGER
+C         THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K,
+C         0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS
+C         THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER
+C         COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY
+C         BECAUSE, IN COMPLEX ARITHMETIC WITH PRECISION P, THE SMALLER
+C         COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE
+C         MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES,
+C         THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P,
+C         OR -PI/2+P.
+C
+C***REFERENCES  HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ
+C                 AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF
+C                 COMMERCE, 1955.
+C
+C               COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+C                 AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983
+C
+C               A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+C                 ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85-
+C                 1018, MAY, 1985
+C
+C               A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+C                 ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS.
+C                 MATH. SOFTWARE, 1986
+C
+C***ROUTINES CALLED  ZBINU,ZABS,ZDIV,ZSQRT,D1MACH,I1MACH
+C***END PROLOGUE  ZBIRY
+C     COMPLEX BI,CONE,CSQ,CY,S1,S2,TRM1,TRM2,Z,ZTA,Z3
+      DOUBLE PRECISION AA, AD, AK, ALIM, ATRM, AZ, AZ3, BB, BII, BIR,
+     * BK, CC, CK, COEF, CONEI, CONER, CSQI, CSQR, CYI, CYR, C1, C2,
+     * DIG, DK, D1, D2, EAA, ELIM, FID, FMR, FNU, FNUL, PI, RL, R1M5,
+     * SFAC, STI, STR, S1I, S1R, S2I, S2R, TOL, TRM1I, TRM1R, TRM2I,
+     * TRM2R, TTH, ZI, ZR, ZTAI, ZTAR, Z3I, Z3R, D1MACH, ZABS
+      INTEGER ID, IERR, K, KODE, K1, K2, NZ, I1MACH
+      DIMENSION CYR(2), CYI(2)
+      DATA TTH, C1, C2, COEF, PI /6.66666666666666667D-01,
+     * 6.14926627446000736D-01,4.48288357353826359D-01,
+     * 5.77350269189625765D-01,3.14159265358979324D+00/
+      DATA CONER, CONEI /1.0D0,0.0D0/
+C***FIRST EXECUTABLE STATEMENT  ZBIRY
+      IERR = 0
+      NZ=0
+      IF (ID.LT.0 .OR. ID.GT.1) IERR=1
+      IF (KODE.LT.1 .OR. KODE.GT.2) IERR=1
+      IF (IERR.NE.0) RETURN
+      AZ = ZABS(CMPLX(ZR,ZI,kind=KIND(1.0D0)))
+      TOL = DMAX1(D1MACH(4),1.0D-18)
+      FID = DBLE(FLOAT(ID))
+      IF (AZ.GT.1.0E0) GO TO 70
+C-----------------------------------------------------------------------
+C     POWER SERIES FOR CABS(Z).LE.1.
+C-----------------------------------------------------------------------
+      S1R = CONER
+      S1I = CONEI
+      S2R = CONER
+      S2I = CONEI
+      IF (AZ.LT.TOL) GO TO 130
+      AA = AZ*AZ
+      IF (AA.LT.TOL/AZ) GO TO 40
+      TRM1R = CONER
+      TRM1I = CONEI
+      TRM2R = CONER
+      TRM2I = CONEI
+      ATRM = 1.0D0
+      STR = ZR*ZR - ZI*ZI
+      STI = ZR*ZI + ZI*ZR
+      Z3R = STR*ZR - STI*ZI
+      Z3I = STR*ZI + STI*ZR
+      AZ3 = AZ*AA
+      AK = 2.0D0 + FID
+      BK = 3.0D0 - FID - FID
+      CK = 4.0D0 - FID
+      DK = 3.0D0 + FID + FID
+      D1 = AK*DK
+      D2 = BK*CK
+      AD = DMIN1(D1,D2)
+      AK = 24.0D0 + 9.0D0*FID
+      BK = 30.0D0 - 9.0D0*FID
+      DO 30 K=1,25
+        STR = (TRM1R*Z3R-TRM1I*Z3I)/D1
+        TRM1I = (TRM1R*Z3I+TRM1I*Z3R)/D1
+        TRM1R = STR
+        S1R = S1R + TRM1R
+        S1I = S1I + TRM1I
+        STR = (TRM2R*Z3R-TRM2I*Z3I)/D2
+        TRM2I = (TRM2R*Z3I+TRM2I*Z3R)/D2
+        TRM2R = STR
+        S2R = S2R + TRM2R
+        S2I = S2I + TRM2I
+        ATRM = ATRM*AZ3/AD
+        D1 = D1 + AK
+        D2 = D2 + BK
+        AD = DMIN1(D1,D2)
+        IF (ATRM.LT.TOL*AD) GO TO 40
+        AK = AK + 18.0D0
+        BK = BK + 18.0D0
+   30 CONTINUE
+   40 CONTINUE
+      IF (ID.EQ.1) GO TO 50
+      BIR = C1*S1R + C2*(ZR*S2R-ZI*S2I)
+      BII = C1*S1I + C2*(ZR*S2I+ZI*S2R)
+      IF (KODE.EQ.1) RETURN
+      CALL ZSQRT(ZR, ZI, STR, STI)
+      ZTAR = TTH*(ZR*STR-ZI*STI)
+      ZTAI = TTH*(ZR*STI+ZI*STR)
+      AA = ZTAR
+      AA = -DABS(AA)
+      EAA = DEXP(AA)
+      BIR = BIR*EAA
+      BII = BII*EAA
+      RETURN
+   50 CONTINUE
+      BIR = S2R*C2
+      BII = S2I*C2
+      IF (AZ.LE.TOL) GO TO 60
+      CC = C1/(1.0D0+FID)
+      STR = S1R*ZR - S1I*ZI
+      STI = S1R*ZI + S1I*ZR
+      BIR = BIR + CC*(STR*ZR-STI*ZI)
+      BII = BII + CC*(STR*ZI+STI*ZR)
+   60 CONTINUE
+      IF (KODE.EQ.1) RETURN
+      CALL ZSQRT(ZR, ZI, STR, STI)
+      ZTAR = TTH*(ZR*STR-ZI*STI)
+      ZTAI = TTH*(ZR*STI+ZI*STR)
+      AA = ZTAR
+      AA = -DABS(AA)
+      EAA = DEXP(AA)
+      BIR = BIR*EAA
+      BII = BII*EAA
+      RETURN
+C-----------------------------------------------------------------------
+C     CASE FOR CABS(Z).GT.1.0
+C-----------------------------------------------------------------------
+   70 CONTINUE
+      FNU = (1.0D0+FID)/3.0D0
+C-----------------------------------------------------------------------
+C     SET PARAMETERS RELATED TO MACHINE CONSTANTS.
+C     TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0E-18.
+C     ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW LIMIT.
+C     EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL    AND
+C     EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL       ARE INTERVALS NEAR
+C     UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE.
+C     RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR LARGE Z.
+C     DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG).
+C     FNUL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC SERIES FOR LARGE FNU.
+C-----------------------------------------------------------------------
+      K1 = I1MACH(15)
+      K2 = I1MACH(16)
+      R1M5 = D1MACH(5)
+      K = MIN0(IABS(K1),IABS(K2))
+      ELIM = 2.303D0*(DBLE(FLOAT(K))*R1M5-3.0D0)
+      K1 = I1MACH(14) - 1
+      AA = R1M5*DBLE(FLOAT(K1))
+      DIG = DMIN1(AA,18.0D0)
+      AA = AA*2.303D0
+      ALIM = ELIM + DMAX1(-AA,-41.45D0)
+      RL = 1.2D0*DIG + 3.0D0
+      FNUL = 10.0D0 + 6.0D0*(DIG-3.0D0)
+C-----------------------------------------------------------------------
+C     TEST FOR RANGE
+C-----------------------------------------------------------------------
+      AA=0.5D0/TOL
+      BB=DBLE(FLOAT(I1MACH(9)))*0.5D0
+      AA=DMIN1(AA,BB)
+      AA=AA**TTH
+      IF (AZ.GT.AA) GO TO 260
+      AA=DSQRT(AA)
+      IF (AZ.GT.AA) IERR=3
+      CALL ZSQRT(ZR, ZI, CSQR, CSQI)
+      ZTAR = TTH*(ZR*CSQR-ZI*CSQI)
+      ZTAI = TTH*(ZR*CSQI+ZI*CSQR)
+C-----------------------------------------------------------------------
+C     RE(ZTA).LE.0 WHEN RE(Z).LT.0, ESPECIALLY WHEN IM(Z) IS SMALL
+C-----------------------------------------------------------------------
+      SFAC = 1.0D0
+      AK = ZTAI
+      IF (ZR.GE.0.0D0) GO TO 80
+      BK = ZTAR
+      CK = -DABS(BK)
+      ZTAR = CK
+      ZTAI = AK
+   80 CONTINUE
+      IF (ZI.NE.0.0D0 .OR. ZR.GT.0.0D0) GO TO 90
+      ZTAR = 0.0D0
+      ZTAI = AK
+   90 CONTINUE
+      AA = ZTAR
+      IF (KODE.EQ.2) GO TO 100
+C-----------------------------------------------------------------------
+C     OVERFLOW TEST
+C-----------------------------------------------------------------------
+      BB = DABS(AA)
+      IF (BB.LT.ALIM) GO TO 100
+      BB = BB + 0.25D0*DLOG(AZ)
+      SFAC = TOL
+      IF (BB.GT.ELIM) GO TO 190
+  100 CONTINUE
+      FMR = 0.0D0
+      IF (AA.GE.0.0D0 .AND. ZR.GT.0.0D0) GO TO 110
+      FMR = PI
+      IF (ZI.LT.0.0D0) FMR = -PI
+      ZTAR = -ZTAR
+      ZTAI = -ZTAI
+  110 CONTINUE
+C-----------------------------------------------------------------------
+C     AA=FACTOR FOR ANALYTIC CONTINUATION OF I(FNU,ZTA)
+C     KODE=2 RETURNS EXP(-ABS(XZTA))*I(FNU,ZTA) FROM CBESI
+C-----------------------------------------------------------------------
+      CALL ZBINU(ZTAR, ZTAI, FNU, KODE, 1, CYR, CYI, NZ, RL, FNUL, TOL,
+     * ELIM, ALIM)
+      IF (NZ.LT.0) GO TO 200
+      AA = FMR*FNU
+      Z3R = SFAC
+      STR = DCOS(AA)
+      STI = DSIN(AA)
+      S1R = (STR*CYR(1)-STI*CYI(1))*Z3R
+      S1I = (STR*CYI(1)+STI*CYR(1))*Z3R
+      FNU = (2.0D0-FID)/3.0D0
+      CALL ZBINU(ZTAR, ZTAI, FNU, KODE, 2, CYR, CYI, NZ, RL, FNUL, TOL,
+     * ELIM, ALIM)
+      CYR(1) = CYR(1)*Z3R
+      CYI(1) = CYI(1)*Z3R
+      CYR(2) = CYR(2)*Z3R
+      CYI(2) = CYI(2)*Z3R
+C-----------------------------------------------------------------------
+C     BACKWARD RECUR ONE STEP FOR ORDERS -1/3 OR -2/3
+C-----------------------------------------------------------------------
+      CALL ZDIV(CYR(1), CYI(1), ZTAR, ZTAI, STR, STI)
+      S2R = (FNU+FNU)*STR + CYR(2)
+      S2I = (FNU+FNU)*STI + CYI(2)
+      AA = FMR*(FNU-1.0D0)
+      STR = DCOS(AA)
+      STI = DSIN(AA)
+      S1R = COEF*(S1R+S2R*STR-S2I*STI)
+      S1I = COEF*(S1I+S2R*STI+S2I*STR)
+      IF (ID.EQ.1) GO TO 120
+      STR = CSQR*S1R - CSQI*S1I
+      S1I = CSQR*S1I + CSQI*S1R
+      S1R = STR
+      BIR = S1R/SFAC
+      BII = S1I/SFAC
+      RETURN
+  120 CONTINUE
+      STR = ZR*S1R - ZI*S1I
+      S1I = ZR*S1I + ZI*S1R
+      S1R = STR
+      BIR = S1R/SFAC
+      BII = S1I/SFAC
+      RETURN
+  130 CONTINUE
+      AA = C1*(1.0D0-FID) + FID*C2
+      BIR = AA
+      BII = 0.0D0
+      RETURN
+  190 CONTINUE
+      IERR=2
+      NZ=0
+      RETURN
+  200 CONTINUE
+      IF(NZ.EQ.(-1)) GO TO 190
+      NZ=0
+      IERR=5
+      RETURN
+  260 CONTINUE
+      IERR=4
+      NZ=0
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbknu.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbknu.f
new file mode 100644
index 00000000..ef932d40
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbknu.f
@@ -0,0 +1,568 @@
+      SUBROUTINE ZBKNU(ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM,
+     * ALIM)
+C***BEGIN PROLOGUE  ZBKNU
+C***REFER TO  ZBESI,ZBESK,ZAIRY,ZBESH
+C
+C     ZBKNU COMPUTES THE K BESSEL FUNCTION IN THE RIGHT HALF Z PLANE.
+C
+C***ROUTINES CALLED  DGAMLN,I1MACH,D1MACH,ZKSCL,ZSHCH,ZUCHK,ZABS,ZDIV,
+C                    ZEXP,ZLOG,ZMLT,ZSQRT
+C***END PROLOGUE  ZBKNU
+C
+      DOUBLE PRECISION AA, AK, ALIM, ASCLE, A1, A2, BB, BK, BRY, CAZ,
+     * CBI, CBR, CC, CCHI, CCHR, CKI, CKR, COEFI, COEFR, CONEI, CONER,
+     * CRSCR, CSCLR, CSHI, CSHR, CSI, CSR, CSRR, CSSR, CTWOR,
+     * CZEROI, CZEROR, CZI, CZR, DNU, DNU2, DPI, ELIM, ETEST, FC, FHS,
+     * FI, FK, FKS, FMUI, FMUR, FNU, FPI, FR, G1, G2, HPI, PI, PR, PTI,
+     * PTR, P1I, P1R, P2I, P2M, P2R, QI, QR, RAK, RCAZ, RTHPI, RZI,
+     * RZR, R1, S, SMUI, SMUR, SPI, STI, STR, S1I, S1R, S2I, S2R, TM,
+     * TOL, TTH, T1, T2, YI, YR, ZI, ZR, DGAMLN, D1MACH, ZABS, ELM,
+     * CELMR, ZDR, ZDI, AS, ALAS, HELIM, CYR, CYI
+      INTEGER I, IFLAG, INU, K, KFLAG, KK, KMAX, KODE, KODED, N, NZ,
+     * IDUM, I1MACH, J, IC, INUB, NW
+      DIMENSION YR(N), YI(N), CC(8), CSSR(3), CSRR(3), BRY(3), CYR(2),
+     * CYI(2)
+C     COMPLEX Z,Y,A,B,RZ,SMU,FU,FMU,F,FLRZ,CZ,S1,S2,CSH,CCH
+C     COMPLEX CK,P,Q,COEF,P1,P2,CBK,PT,CZERO,CONE,CTWO,ST,EZ,CS,DK
+C
+      DATA KMAX / 30 /
+      DATA CZEROR,CZEROI,CONER,CONEI,CTWOR,R1/
+     1  0.0D0 , 0.0D0 , 1.0D0 , 0.0D0 , 2.0D0 , 2.0D0 /
+      DATA DPI, RTHPI, SPI ,HPI, FPI, TTH /
+     1     3.14159265358979324D0,       1.25331413731550025D0,
+     2     1.90985931710274403D0,       1.57079632679489662D0,
+     3     1.89769999331517738D0,       6.66666666666666666D-01/
+      DATA CC(1), CC(2), CC(3), CC(4), CC(5), CC(6), CC(7), CC(8)/
+     1     5.77215664901532861D-01,    -4.20026350340952355D-02,
+     2    -4.21977345555443367D-02,     7.21894324666309954D-03,
+     3    -2.15241674114950973D-04,    -2.01348547807882387D-05,
+     4     1.13302723198169588D-06,     6.11609510448141582D-09/
+C
+      CAZ = ZABS(CMPLX(ZR,ZI,kind=KIND(1.0D0)))
+      CSCLR = 1.0D0/TOL
+      CRSCR = TOL
+      CSSR(1) = CSCLR
+      CSSR(2) = 1.0D0
+      CSSR(3) = CRSCR
+      CSRR(1) = CRSCR
+      CSRR(2) = 1.0D0
+      CSRR(3) = CSCLR
+      BRY(1) = 1.0D+3*D1MACH(1)/TOL
+      BRY(2) = 1.0D0/BRY(1)
+      BRY(3) = D1MACH(2)
+      NZ = 0
+      IFLAG = 0
+      KODED = KODE
+      RCAZ = 1.0D0/CAZ
+      STR = ZR*RCAZ
+      STI = -ZI*RCAZ
+      RZR = (STR+STR)*RCAZ
+      RZI = (STI+STI)*RCAZ
+      INU = INT(SNGL(FNU+0.5D0))
+      DNU = FNU - DBLE(FLOAT(INU))
+      IF (DABS(DNU).EQ.0.5D0) GO TO 110
+      DNU2 = 0.0D0
+      IF (DABS(DNU).GT.TOL) DNU2 = DNU*DNU
+      IF (CAZ.GT.R1) GO TO 110
+C-----------------------------------------------------------------------
+C     SERIES FOR CABS(Z).LE.R1
+C-----------------------------------------------------------------------
+      FC = 1.0D0
+      CALL ZLOG(RZR, RZI, SMUR, SMUI, IDUM)
+      FMUR = SMUR*DNU
+      FMUI = SMUI*DNU
+      CALL ZSHCH(FMUR, FMUI, CSHR, CSHI, CCHR, CCHI)
+      IF (DNU.EQ.0.0D0) GO TO 10
+      FC = DNU*DPI
+      FC = FC/DSIN(FC)
+      SMUR = CSHR/DNU
+      SMUI = CSHI/DNU
+   10 CONTINUE
+      A2 = 1.0D0 + DNU
+C-----------------------------------------------------------------------
+C     GAM(1-Z)*GAM(1+Z)=PI*Z/SIN(PI*Z), T1=1/GAM(1-DNU), T2=1/GAM(1+DNU)
+C-----------------------------------------------------------------------
+      T2 = DEXP(-DGAMLN(A2,IDUM))
+      T1 = 1.0D0/(T2*FC)
+      IF (DABS(DNU).GT.0.1D0) GO TO 40
+C-----------------------------------------------------------------------
+C     SERIES FOR F0 TO RESOLVE INDETERMINACY FOR SMALL ABS(DNU)
+C-----------------------------------------------------------------------
+      AK = 1.0D0
+      S = CC(1)
+      DO 20 K=2,8
+        AK = AK*DNU2
+        TM = CC(K)*AK
+        S = S + TM
+        IF (DABS(TM).LT.TOL) GO TO 30
+   20 CONTINUE
+   30 G1 = -S
+      GO TO 50
+   40 CONTINUE
+      G1 = (T1-T2)/(DNU+DNU)
+   50 CONTINUE
+      G2 = (T1+T2)*0.5D0
+      FR = FC*(CCHR*G1+SMUR*G2)
+      FI = FC*(CCHI*G1+SMUI*G2)
+      CALL ZEXP(FMUR, FMUI, STR, STI)
+      PR = 0.5D0*STR/T2
+      PI = 0.5D0*STI/T2
+      CALL ZDIV(0.5D0, 0.0D0, STR, STI, PTR, PTI)
+      QR = PTR/T1
+      QI = PTI/T1
+      S1R = FR
+      S1I = FI
+      S2R = PR
+      S2I = PI
+      AK = 1.0D0
+      A1 = 1.0D0
+      CKR = CONER
+      CKI = CONEI
+      BK = 1.0D0 - DNU2
+      IF (INU.GT.0 .OR. N.GT.1) GO TO 80
+C-----------------------------------------------------------------------
+C     GENERATE K(FNU,Z), 0.0D0 .LE. FNU .LT. 0.5D0 AND N=1
+C-----------------------------------------------------------------------
+      IF (CAZ.LT.TOL) GO TO 70
+      CALL ZMLT(ZR, ZI, ZR, ZI, CZR, CZI)
+      CZR = 0.25D0*CZR
+      CZI = 0.25D0*CZI
+      T1 = 0.25D0*CAZ*CAZ
+   60 CONTINUE
+      FR = (FR*AK+PR+QR)/BK
+      FI = (FI*AK+PI+QI)/BK
+      STR = 1.0D0/(AK-DNU)
+      PR = PR*STR
+      PI = PI*STR
+      STR = 1.0D0/(AK+DNU)
+      QR = QR*STR
+      QI = QI*STR
+      STR = CKR*CZR - CKI*CZI
+      RAK = 1.0D0/AK
+      CKI = (CKR*CZI+CKI*CZR)*RAK
+      CKR = STR*RAK
+      S1R = CKR*FR - CKI*FI + S1R
+      S1I = CKR*FI + CKI*FR + S1I
+      A1 = A1*T1*RAK
+      BK = BK + AK + AK + 1.0D0
+      AK = AK + 1.0D0
+      IF (A1.GT.TOL) GO TO 60
+   70 CONTINUE
+      YR(1) = S1R
+      YI(1) = S1I
+      IF (KODED.EQ.1) RETURN
+      CALL ZEXP(ZR, ZI, STR, STI)
+      CALL ZMLT(S1R, S1I, STR, STI, YR(1), YI(1))
+      RETURN
+C-----------------------------------------------------------------------
+C     GENERATE K(DNU,Z) AND K(DNU+1,Z) FOR FORWARD RECURRENCE
+C-----------------------------------------------------------------------
+   80 CONTINUE
+      IF (CAZ.LT.TOL) GO TO 100
+      CALL ZMLT(ZR, ZI, ZR, ZI, CZR, CZI)
+      CZR = 0.25D0*CZR
+      CZI = 0.25D0*CZI
+      T1 = 0.25D0*CAZ*CAZ
+   90 CONTINUE
+      FR = (FR*AK+PR+QR)/BK
+      FI = (FI*AK+PI+QI)/BK
+      STR = 1.0D0/(AK-DNU)
+      PR = PR*STR
+      PI = PI*STR
+      STR = 1.0D0/(AK+DNU)
+      QR = QR*STR
+      QI = QI*STR
+      STR = CKR*CZR - CKI*CZI
+      RAK = 1.0D0/AK
+      CKI = (CKR*CZI+CKI*CZR)*RAK
+      CKR = STR*RAK
+      S1R = CKR*FR - CKI*FI + S1R
+      S1I = CKR*FI + CKI*FR + S1I
+      STR = PR - FR*AK
+      STI = PI - FI*AK
+      S2R = CKR*STR - CKI*STI + S2R
+      S2I = CKR*STI + CKI*STR + S2I
+      A1 = A1*T1*RAK
+      BK = BK + AK + AK + 1.0D0
+      AK = AK + 1.0D0
+      IF (A1.GT.TOL) GO TO 90
+  100 CONTINUE
+      KFLAG = 2
+      A1 = FNU + 1.0D0
+      AK = A1*DABS(SMUR)
+      IF (AK.GT.ALIM) KFLAG = 3
+      STR = CSSR(KFLAG)
+      P2R = S2R*STR
+      P2I = S2I*STR
+      CALL ZMLT(P2R, P2I, RZR, RZI, S2R, S2I)
+      S1R = S1R*STR
+      S1I = S1I*STR
+      IF (KODED.EQ.1) GO TO 210
+      CALL ZEXP(ZR, ZI, FR, FI)
+      CALL ZMLT(S1R, S1I, FR, FI, S1R, S1I)
+      CALL ZMLT(S2R, S2I, FR, FI, S2R, S2I)
+      GO TO 210
+C-----------------------------------------------------------------------
+C     IFLAG=0 MEANS NO UNDERFLOW OCCURRED
+C     IFLAG=1 MEANS AN UNDERFLOW OCCURRED- COMPUTATION PROCEEDS WITH
+C     KODED=2 AND A TEST FOR ON SCALE VALUES IS MADE DURING FORWARD
+C     RECURSION
+C-----------------------------------------------------------------------
+  110 CONTINUE
+      CALL ZSQRT(ZR, ZI, STR, STI)
+      CALL ZDIV(RTHPI, CZEROI, STR, STI, COEFR, COEFI)
+      KFLAG = 2
+      IF (KODED.EQ.2) GO TO 120
+      IF (ZR.GT.ALIM) GO TO 290
+C     BLANK LINE
+      STR = DEXP(-ZR)*CSSR(KFLAG)
+      STI = -STR*DSIN(ZI)
+      STR = STR*DCOS(ZI)
+      CALL ZMLT(COEFR, COEFI, STR, STI, COEFR, COEFI)
+  120 CONTINUE
+      IF (DABS(DNU).EQ.0.5D0) GO TO 300
+C-----------------------------------------------------------------------
+C     MILLER ALGORITHM FOR CABS(Z).GT.R1
+C-----------------------------------------------------------------------
+      AK = DCOS(DPI*DNU)
+      AK = DABS(AK)
+      IF (AK.EQ.CZEROR) GO TO 300
+      FHS = DABS(0.25D0-DNU2)
+      IF (FHS.EQ.CZEROR) GO TO 300
+C-----------------------------------------------------------------------
+C     COMPUTE R2=F(E). IF CABS(Z).GE.R2, USE FORWARD RECURRENCE TO
+C     DETERMINE THE BACKWARD INDEX K. R2=F(E) IS A STRAIGHT LINE ON
+C     12.LE.E.LE.60. E IS COMPUTED FROM 2**(-E)=B**(1-I1MACH(14))=
+C     TOL WHERE B IS THE BASE OF THE ARITHMETIC.
+C-----------------------------------------------------------------------
+      T1 = DBLE(FLOAT(I1MACH(14)-1))
+      T1 = T1*D1MACH(5)*3.321928094D0
+      T1 = DMAX1(T1,12.0D0)
+      T1 = DMIN1(T1,60.0D0)
+      T2 = TTH*T1 - 6.0D0
+      IF (ZR.NE.0.0D0) GO TO 130
+      T1 = HPI
+      GO TO 140
+  130 CONTINUE
+      T1 = DATAN(ZI/ZR)
+      T1 = DABS(T1)
+  140 CONTINUE
+      IF (T2.GT.CAZ) GO TO 170
+C-----------------------------------------------------------------------
+C     FORWARD RECURRENCE LOOP WHEN CABS(Z).GE.R2
+C-----------------------------------------------------------------------
+      ETEST = AK/(DPI*CAZ*TOL)
+      FK = CONER
+      IF (ETEST.LT.CONER) GO TO 180
+      FKS = CTWOR
+      CKR = CAZ + CAZ + CTWOR
+      P1R = CZEROR
+      P2R = CONER
+      DO 150 I=1,KMAX
+        AK = FHS/FKS
+        CBR = CKR/(FK+CONER)
+        PTR = P2R
+        P2R = CBR*P2R - P1R*AK
+        P1R = PTR
+        CKR = CKR + CTWOR
+        FKS = FKS + FK + FK + CTWOR
+        FHS = FHS + FK + FK
+        FK = FK + CONER
+        STR = DABS(P2R)*FK
+        IF (ETEST.LT.STR) GO TO 160
+  150 CONTINUE
+      GO TO 310
+  160 CONTINUE
+      FK = FK + SPI*T1*DSQRT(T2/CAZ)
+      FHS = DABS(0.25D0-DNU2)
+      GO TO 180
+  170 CONTINUE
+C-----------------------------------------------------------------------
+C     COMPUTE BACKWARD INDEX K FOR CABS(Z).LT.R2
+C-----------------------------------------------------------------------
+      A2 = DSQRT(CAZ)
+      AK = FPI*AK/(TOL*DSQRT(A2))
+      AA = 3.0D0*T1/(1.0D0+CAZ)
+      BB = 14.7D0*T1/(28.0D0+CAZ)
+      AK = (DLOG(AK)+CAZ*DCOS(AA)/(1.0D0+0.008D0*CAZ))/DCOS(BB)
+      FK = 0.12125D0*AK*AK/CAZ + 1.5D0
+  180 CONTINUE
+C-----------------------------------------------------------------------
+C     BACKWARD RECURRENCE LOOP FOR MILLER ALGORITHM
+C-----------------------------------------------------------------------
+      K = INT(SNGL(FK))
+      FK = DBLE(FLOAT(K))
+      FKS = FK*FK
+      P1R = CZEROR
+      P1I = CZEROI
+      P2R = TOL
+      P2I = CZEROI
+      CSR = P2R
+      CSI = P2I
+      DO 190 I=1,K
+        A1 = FKS - FK
+        AK = (FKS+FK)/(A1+FHS)
+        RAK = 2.0D0/(FK+CONER)
+        CBR = (FK+ZR)*RAK
+        CBI = ZI*RAK
+        PTR = P2R
+        PTI = P2I
+        P2R = (PTR*CBR-PTI*CBI-P1R)*AK
+        P2I = (PTI*CBR+PTR*CBI-P1I)*AK
+        P1R = PTR
+        P1I = PTI
+        CSR = CSR + P2R
+        CSI = CSI + P2I
+        FKS = A1 - FK + CONER
+        FK = FK - CONER
+  190 CONTINUE
+C-----------------------------------------------------------------------
+C     COMPUTE (P2/CS)=(P2/CABS(CS))*(CONJG(CS)/CABS(CS)) FOR BETTER
+C     SCALING
+C-----------------------------------------------------------------------
+      TM = ZABS(CMPLX(CSR,CSI,kind=KIND(1.0D0)))
+      PTR = 1.0D0/TM
+      S1R = P2R*PTR
+      S1I = P2I*PTR
+      CSR = CSR*PTR
+      CSI = -CSI*PTR
+      CALL ZMLT(COEFR, COEFI, S1R, S1I, STR, STI)
+      CALL ZMLT(STR, STI, CSR, CSI, S1R, S1I)
+      IF (INU.GT.0 .OR. N.GT.1) GO TO 200
+      ZDR = ZR
+      ZDI = ZI
+      IF(IFLAG.EQ.1) GO TO 270
+      GO TO 240
+  200 CONTINUE
+C-----------------------------------------------------------------------
+C     COMPUTE P1/P2=(P1/CABS(P2)*CONJG(P2)/CABS(P2) FOR SCALING
+C-----------------------------------------------------------------------
+      TM = ZABS(CMPLX(P2R,P2I,kind=KIND(1.0D0)))
+      PTR = 1.0D0/TM
+      P1R = P1R*PTR
+      P1I = P1I*PTR
+      P2R = P2R*PTR
+      P2I = -P2I*PTR
+      CALL ZMLT(P1R, P1I, P2R, P2I, PTR, PTI)
+      STR = DNU + 0.5D0 - PTR
+      STI = -PTI
+      CALL ZDIV(STR, STI, ZR, ZI, STR, STI)
+      STR = STR + 1.0D0
+      CALL ZMLT(STR, STI, S1R, S1I, S2R, S2I)
+C-----------------------------------------------------------------------
+C     FORWARD RECURSION ON THE THREE TERM RECURSION WITH RELATION WITH
+C     SCALING NEAR EXPONENT EXTREMES ON KFLAG=1 OR KFLAG=3
+C-----------------------------------------------------------------------
+  210 CONTINUE
+      STR = DNU + 1.0D0
+      CKR = STR*RZR
+      CKI = STR*RZI
+      IF (N.EQ.1) INU = INU - 1
+      IF (INU.GT.0) GO TO 220
+      IF (N.GT.1) GO TO 215
+      S1R = S2R
+      S1I = S2I
+  215 CONTINUE
+      ZDR = ZR
+      ZDI = ZI
+      IF(IFLAG.EQ.1) GO TO 270
+      GO TO 240
+  220 CONTINUE
+      INUB = 1
+      IF(IFLAG.EQ.1) GO TO 261
+  225 CONTINUE
+      P1R = CSRR(KFLAG)
+      ASCLE = BRY(KFLAG)
+      DO 230 I=INUB,INU
+        STR = S2R
+        STI = S2I
+        S2R = CKR*STR - CKI*STI + S1R
+        S2I = CKR*STI + CKI*STR + S1I
+        S1R = STR
+        S1I = STI
+        CKR = CKR + RZR
+        CKI = CKI + RZI
+        IF (KFLAG.GE.3) GO TO 230
+        P2R = S2R*P1R
+        P2I = S2I*P1R
+        STR = DABS(P2R)
+        STI = DABS(P2I)
+        P2M = DMAX1(STR,STI)
+        IF (P2M.LE.ASCLE) GO TO 230
+        KFLAG = KFLAG + 1
+        ASCLE = BRY(KFLAG)
+        S1R = S1R*P1R
+        S1I = S1I*P1R
+        S2R = P2R
+        S2I = P2I
+        STR = CSSR(KFLAG)
+        S1R = S1R*STR
+        S1I = S1I*STR
+        S2R = S2R*STR
+        S2I = S2I*STR
+        P1R = CSRR(KFLAG)
+  230 CONTINUE
+      IF (N.NE.1) GO TO 240
+      S1R = S2R
+      S1I = S2I
+  240 CONTINUE
+      STR = CSRR(KFLAG)
+      YR(1) = S1R*STR
+      YI(1) = S1I*STR
+      IF (N.EQ.1) RETURN
+      YR(2) = S2R*STR
+      YI(2) = S2I*STR
+      IF (N.EQ.2) RETURN
+      KK = 2
+  250 CONTINUE
+      KK = KK + 1
+      IF (KK.GT.N) RETURN
+      P1R = CSRR(KFLAG)
+      ASCLE = BRY(KFLAG)
+      DO 260 I=KK,N
+        P2R = S2R
+        P2I = S2I
+        S2R = CKR*P2R - CKI*P2I + S1R
+        S2I = CKI*P2R + CKR*P2I + S1I
+        S1R = P2R
+        S1I = P2I
+        CKR = CKR + RZR
+        CKI = CKI + RZI
+        P2R = S2R*P1R
+        P2I = S2I*P1R
+        YR(I) = P2R
+        YI(I) = P2I
+        IF (KFLAG.GE.3) GO TO 260
+        STR = DABS(P2R)
+        STI = DABS(P2I)
+        P2M = DMAX1(STR,STI)
+        IF (P2M.LE.ASCLE) GO TO 260
+        KFLAG = KFLAG + 1
+        ASCLE = BRY(KFLAG)
+        S1R = S1R*P1R
+        S1I = S1I*P1R
+        S2R = P2R
+        S2I = P2I
+        STR = CSSR(KFLAG)
+        S1R = S1R*STR
+        S1I = S1I*STR
+        S2R = S2R*STR
+        S2I = S2I*STR
+        P1R = CSRR(KFLAG)
+  260 CONTINUE
+      RETURN
+C-----------------------------------------------------------------------
+C     IFLAG=1 CASES, FORWARD RECURRENCE ON SCALED VALUES ON UNDERFLOW
+C-----------------------------------------------------------------------
+  261 CONTINUE
+      HELIM = 0.5D0*ELIM
+      ELM = DEXP(-ELIM)
+      CELMR = ELM
+      ASCLE = BRY(1)
+      ZDR = ZR
+      ZDI = ZI
+      IC = -1
+      J = 2
+      DO 262 I=1,INU
+        STR = S2R
+        STI = S2I
+        S2R = STR*CKR-STI*CKI+S1R
+        S2I = STI*CKR+STR*CKI+S1I
+        S1R = STR
+        S1I = STI
+        CKR = CKR+RZR
+        CKI = CKI+RZI
+        AS = ZABS(CMPLX(S2R,S2I,kind=KIND(1.0D0)))
+        ALAS = DLOG(AS)
+        P2R = -ZDR+ALAS
+        IF(P2R.LT.(-ELIM)) GO TO 263
+        CALL ZLOG(S2R,S2I,STR,STI,IDUM)
+        P2R = -ZDR+STR
+        P2I = -ZDI+STI
+        P2M = DEXP(P2R)/TOL
+        P1R = P2M*DCOS(P2I)
+        P1I = P2M*DSIN(P2I)
+        CALL ZUCHK(P1R,P1I,NW,ASCLE,TOL)
+        IF(NW.NE.0) GO TO 263
+        J = 3 - J
+        CYR(J) = P1R
+        CYI(J) = P1I
+        IF(IC.EQ.(I-1)) GO TO 264
+        IC = I
+        GO TO 262
+  263   CONTINUE
+        IF(ALAS.LT.HELIM) GO TO 262
+        ZDR = ZDR-ELIM
+        S1R = S1R*CELMR
+        S1I = S1I*CELMR
+        S2R = S2R*CELMR
+        S2I = S2I*CELMR
+  262 CONTINUE
+      IF(N.NE.1) GO TO 270
+      S1R = S2R
+      S1I = S2I
+      GO TO 270
+  264 CONTINUE
+      KFLAG = 1
+      INUB = I+1
+      S2R = CYR(J)
+      S2I = CYI(J)
+      J = 3 - J
+      S1R = CYR(J)
+      S1I = CYI(J)
+      IF(INUB.LE.INU) GO TO 225
+      IF(N.NE.1) GO TO 240
+      S1R = S2R
+      S1I = S2I
+      GO TO 240
+  270 CONTINUE
+      YR(1) = S1R
+      YI(1) = S1I
+      IF(N.EQ.1) GO TO 280
+      YR(2) = S2R
+      YI(2) = S2I
+  280 CONTINUE
+      ASCLE = BRY(1)
+      CALL ZKSCL(ZDR,ZDI,FNU,N,YR,YI,NZ,RZR,RZI,ASCLE,TOL,ELIM)
+      INU = N - NZ
+      IF (INU.LE.0) RETURN
+      KK = NZ + 1
+      S1R = YR(KK)
+      S1I = YI(KK)
+      YR(KK) = S1R*CSRR(1)
+      YI(KK) = S1I*CSRR(1)
+      IF (INU.EQ.1) RETURN
+      KK = NZ + 2
+      S2R = YR(KK)
+      S2I = YI(KK)
+      YR(KK) = S2R*CSRR(1)
+      YI(KK) = S2I*CSRR(1)
+      IF (INU.EQ.2) RETURN
+      T2 = FNU + DBLE(FLOAT(KK-1))
+      CKR = T2*RZR
+      CKI = T2*RZI
+      KFLAG = 1
+      GO TO 250
+  290 CONTINUE
+C-----------------------------------------------------------------------
+C     SCALE BY DEXP(Z), IFLAG = 1 CASES
+C-----------------------------------------------------------------------
+      KODED = 2
+      IFLAG = 1
+      KFLAG = 2
+      GO TO 120
+C-----------------------------------------------------------------------
+C     FNU=HALF ODD INTEGER CASE, DNU=-0.5
+C-----------------------------------------------------------------------
+  300 CONTINUE
+      S1R = COEFR
+      S1I = COEFI
+      S2R = COEFR
+      S2I = COEFI
+      GO TO 210
+C
+C
+  310 CONTINUE
+      NZ=-2
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbuni.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbuni.f
new file mode 100644
index 00000000..3811b89a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbuni.f
@@ -0,0 +1,174 @@
+      SUBROUTINE ZBUNI(ZR, ZI, FNU, KODE, N, YR, YI, NZ, NUI, NLAST,
+     * FNUL, TOL, ELIM, ALIM)
+C***BEGIN PROLOGUE  ZBUNI
+C***REFER TO  ZBESI,ZBESK
+C
+C     ZBUNI COMPUTES THE I BESSEL FUNCTION FOR LARGE CABS(Z).GT.
+C     FNUL AND FNU+N-1.LT.FNUL. THE ORDER IS INCREASED FROM
+C     FNU+N-1 GREATER THAN FNUL BY ADDING NUI AND COMPUTING
+C     ACCORDING TO THE UNIFORM ASYMPTOTIC EXPANSION FOR I(FNU,Z)
+C     ON IFORM=1 AND THE EXPANSION FOR J(FNU,Z) ON IFORM=2
+C
+C***ROUTINES CALLED  ZUNI1,ZUNI2,ZABS,D1MACH
+C***END PROLOGUE  ZBUNI
+C     COMPLEX CSCL,CSCR,CY,RZ,ST,S1,S2,Y,Z
+      DOUBLE PRECISION ALIM, AX, AY, CSCLR, CSCRR, CYI, CYR, DFNU,
+     * ELIM, FNU, FNUI, FNUL, GNU, RAZ, RZI, RZR, STI, STR, S1I, S1R,
+     * S2I, S2R, TOL, YI, YR, ZI, ZR, ZABS, ASCLE, BRY, C1R, C1I, C1M,
+     * D1MACH
+      INTEGER I, IFLAG, IFORM, K, KODE, N, NL, NLAST, NUI, NW, NZ
+      DIMENSION YR(N), YI(N), CYR(2), CYI(2), BRY(3)
+      NZ = 0
+      AX = DABS(ZR)*1.7321D0
+      AY = DABS(ZI)
+      IFORM = 1
+      IF (AY.GT.AX) IFORM = 2
+      IF (NUI.EQ.0) GO TO 60
+      FNUI = DBLE(FLOAT(NUI))
+      DFNU = FNU + DBLE(FLOAT(N-1))
+      GNU = DFNU + FNUI
+      IF (IFORM.EQ.2) GO TO 10
+C-----------------------------------------------------------------------
+C     ASYMPTOTIC EXPANSION FOR I(FNU,Z) FOR LARGE FNU APPLIED IN
+C     -PI/3.LE.ARG(Z).LE.PI/3
+C-----------------------------------------------------------------------
+      CALL ZUNI1(ZR, ZI, GNU, KODE, 2, CYR, CYI, NW, NLAST, FNUL, TOL,
+     * ELIM, ALIM)
+      GO TO 20
+   10 CONTINUE
+C-----------------------------------------------------------------------
+C     ASYMPTOTIC EXPANSION FOR J(FNU,Z*EXP(M*HPI)) FOR LARGE FNU
+C     APPLIED IN PI/3.LT.ABS(ARG(Z)).LE.PI/2 WHERE M=+I OR -I
+C     AND HPI=PI/2
+C-----------------------------------------------------------------------
+      CALL ZUNI2(ZR, ZI, GNU, KODE, 2, CYR, CYI, NW, NLAST, FNUL, TOL,
+     * ELIM, ALIM)
+   20 CONTINUE
+      IF (NW.LT.0) GO TO 50
+      IF (NW.NE.0) GO TO 90
+      STR = ZABS(CMPLX(CYR(1),CYI(1),kind=KIND(1.0D0)))
+C----------------------------------------------------------------------
+C     SCALE BACKWARD RECURRENCE, BRY(3) IS DEFINED BUT NEVER USED
+C----------------------------------------------------------------------
+      BRY(1)=1.0D+3*D1MACH(1)/TOL
+      BRY(2) = 1.0D0/BRY(1)
+      BRY(3) = BRY(2)
+      IFLAG = 2
+      ASCLE = BRY(2)
+      CSCLR = 1.0D0
+      IF (STR.GT.BRY(1)) GO TO 21
+      IFLAG = 1
+      ASCLE = BRY(1)
+      CSCLR = 1.0D0/TOL
+      GO TO 25
+   21 CONTINUE
+      IF (STR.LT.BRY(2)) GO TO 25
+      IFLAG = 3
+      ASCLE=BRY(3)
+      CSCLR = TOL
+   25 CONTINUE
+      CSCRR = 1.0D0/CSCLR
+      S1R = CYR(2)*CSCLR
+      S1I = CYI(2)*CSCLR
+      S2R = CYR(1)*CSCLR
+      S2I = CYI(1)*CSCLR
+      RAZ = 1.0D0/ZABS(CMPLX(ZR,ZI,kind=KIND(1.0D0)))
+      STR = ZR*RAZ
+      STI = -ZI*RAZ
+      RZR = (STR+STR)*RAZ
+      RZI = (STI+STI)*RAZ
+      DO 30 I=1,NUI
+        STR = S2R
+        STI = S2I
+        S2R = (DFNU+FNUI)*(RZR*STR-RZI*STI) + S1R
+        S2I = (DFNU+FNUI)*(RZR*STI+RZI*STR) + S1I
+        S1R = STR
+        S1I = STI
+        FNUI = FNUI - 1.0D0
+        IF (IFLAG.GE.3) GO TO 30
+        STR = S2R*CSCRR
+        STI = S2I*CSCRR
+        C1R = DABS(STR)
+        C1I = DABS(STI)
+        C1M = DMAX1(C1R,C1I)
+        IF (C1M.LE.ASCLE) GO TO 30
+        IFLAG = IFLAG+1
+        ASCLE = BRY(IFLAG)
+        S1R = S1R*CSCRR
+        S1I = S1I*CSCRR
+        S2R = STR
+        S2I = STI
+        CSCLR = CSCLR*TOL
+        CSCRR = 1.0D0/CSCLR
+        S1R = S1R*CSCLR
+        S1I = S1I*CSCLR
+        S2R = S2R*CSCLR
+        S2I = S2I*CSCLR
+   30 CONTINUE
+      YR(N) = S2R*CSCRR
+      YI(N) = S2I*CSCRR
+      IF (N.EQ.1) RETURN
+      NL = N - 1
+      FNUI = DBLE(FLOAT(NL))
+      K = NL
+      DO 40 I=1,NL
+        STR = S2R
+        STI = S2I
+        S2R = (FNU+FNUI)*(RZR*STR-RZI*STI) + S1R
+        S2I = (FNU+FNUI)*(RZR*STI+RZI*STR) + S1I
+        S1R = STR
+        S1I = STI
+        STR = S2R*CSCRR
+        STI = S2I*CSCRR
+        YR(K) = STR
+        YI(K) = STI
+        FNUI = FNUI - 1.0D0
+        K = K - 1
+        IF (IFLAG.GE.3) GO TO 40
+        C1R = DABS(STR)
+        C1I = DABS(STI)
+        C1M = DMAX1(C1R,C1I)
+        IF (C1M.LE.ASCLE) GO TO 40
+        IFLAG = IFLAG+1
+        ASCLE = BRY(IFLAG)
+        S1R = S1R*CSCRR
+        S1I = S1I*CSCRR
+        S2R = STR
+        S2I = STI
+        CSCLR = CSCLR*TOL
+        CSCRR = 1.0D0/CSCLR
+        S1R = S1R*CSCLR
+        S1I = S1I*CSCLR
+        S2R = S2R*CSCLR
+        S2I = S2I*CSCLR
+   40 CONTINUE
+      RETURN
+   50 CONTINUE
+      NZ = -1
+      IF(NW.EQ.(-2)) NZ=-2
+      RETURN
+   60 CONTINUE
+      IF (IFORM.EQ.2) GO TO 70
+C-----------------------------------------------------------------------
+C     ASYMPTOTIC EXPANSION FOR I(FNU,Z) FOR LARGE FNU APPLIED IN
+C     -PI/3.LE.ARG(Z).LE.PI/3
+C-----------------------------------------------------------------------
+      CALL ZUNI1(ZR, ZI, FNU, KODE, N, YR, YI, NW, NLAST, FNUL, TOL,
+     * ELIM, ALIM)
+      GO TO 80
+   70 CONTINUE
+C-----------------------------------------------------------------------
+C     ASYMPTOTIC EXPANSION FOR J(FNU,Z*EXP(M*HPI)) FOR LARGE FNU
+C     APPLIED IN PI/3.LT.ABS(ARG(Z)).LE.PI/2 WHERE M=+I OR -I
+C     AND HPI=PI/2
+C-----------------------------------------------------------------------
+      CALL ZUNI2(ZR, ZI, FNU, KODE, N, YR, YI, NW, NLAST, FNUL, TOL,
+     * ELIM, ALIM)
+   80 CONTINUE
+      IF (NW.LT.0) GO TO 50
+      NZ = NW
+      RETURN
+   90 CONTINUE
+      NLAST = N
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbunk.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbunk.f
new file mode 100644
index 00000000..b20b79f3
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zbunk.f
@@ -0,0 +1,35 @@
+      SUBROUTINE ZBUNK(ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, TOL, ELIM,
+     * ALIM)
+C***BEGIN PROLOGUE  ZBUNK
+C***REFER TO  ZBESK,ZBESH
+C
+C     ZBUNK COMPUTES THE K BESSEL FUNCTION FOR FNU.GT.FNUL.
+C     ACCORDING TO THE UNIFORM ASYMPTOTIC EXPANSION FOR K(FNU,Z)
+C     IN ZUNK1 AND THE EXPANSION FOR H(2,FNU,Z) IN ZUNK2
+C
+C***ROUTINES CALLED  ZUNK1,ZUNK2
+C***END PROLOGUE  ZBUNK
+C     COMPLEX Y,Z
+      DOUBLE PRECISION ALIM, AX, AY, ELIM, FNU, TOL, YI, YR, ZI, ZR
+      INTEGER KODE, MR, N, NZ
+      DIMENSION YR(N), YI(N)
+      NZ = 0
+      AX = DABS(ZR)*1.7321D0
+      AY = DABS(ZI)
+      IF (AY.GT.AX) GO TO 10
+C-----------------------------------------------------------------------
+C     ASYMPTOTIC EXPANSION FOR K(FNU,Z) FOR LARGE FNU APPLIED IN
+C     -PI/3.LE.ARG(Z).LE.PI/3
+C-----------------------------------------------------------------------
+      CALL ZUNK1(ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, TOL, ELIM, ALIM)
+      GO TO 20
+   10 CONTINUE
+C-----------------------------------------------------------------------
+C     ASYMPTOTIC EXPANSION FOR H(2,FNU,Z*EXP(M*HPI)) FOR LARGE FNU
+C     APPLIED IN PI/3.LT.ABS(ARG(Z)).LE.PI/2 WHERE M=+I OR -I
+C     AND HPI=PI/2
+C-----------------------------------------------------------------------
+      CALL ZUNK2(ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, TOL, ELIM, ALIM)
+   20 CONTINUE
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zdiv.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zdiv.f
new file mode 100644
index 00000000..ac73b86d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zdiv.f
@@ -0,0 +1,19 @@
+      SUBROUTINE ZDIV(AR, AI, BR, BI, CR, CI)
+C***BEGIN PROLOGUE  ZDIV
+C***REFER TO  ZBESH,ZBESI,ZBESJ,ZBESK,ZBESY,ZAIRY,ZBIRY
+C
+C     DOUBLE PRECISION COMPLEX DIVIDE C=A/B.
+C
+C***ROUTINES CALLED  ZABS
+C***END PROLOGUE  ZDIV
+      DOUBLE PRECISION AR, AI, BR, BI, CR, CI, BM, CA, CB, CC, CD
+      DOUBLE PRECISION ZABS
+      BM = 1.0D0/ZABS(CMPLX(BR,BI,kind=KIND(1.0D0)))
+      CC = BR*BM
+      CD = BI*BM
+      CA = (AR*CC+AI*CD)*BM
+      CB = (AI*CC-AR*CD)*BM
+      CR = CA
+      CI = CB
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zexp.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zexp.f
new file mode 100644
index 00000000..fcb553c1
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zexp.f
@@ -0,0 +1,16 @@
+      SUBROUTINE ZEXP(AR, AI, BR, BI)
+C***BEGIN PROLOGUE  ZEXP
+C***REFER TO  ZBESH,ZBESI,ZBESJ,ZBESK,ZBESY,ZAIRY,ZBIRY
+C
+C     DOUBLE PRECISION COMPLEX EXPONENTIAL FUNCTION B=EXP(A)
+C
+C***ROUTINES CALLED  (NONE)
+C***END PROLOGUE  ZEXP
+      DOUBLE PRECISION AR, AI, BR, BI, ZM, CA, CB
+      ZM = DEXP(AR)
+      CA = ZM*DCOS(AI)
+      CB = ZM*DSIN(AI)
+      BR = CA
+      BI = CB
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zkscl.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zkscl.f
new file mode 100644
index 00000000..eeda4715
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zkscl.f
@@ -0,0 +1,121 @@
+      SUBROUTINE ZKSCL(ZRR,ZRI,FNU,N,YR,YI,NZ,RZR,RZI,ASCLE,TOL,ELIM)
+C***BEGIN PROLOGUE  ZKSCL
+C***REFER TO  ZBESK
+C
+C     SET K FUNCTIONS TO ZERO ON UNDERFLOW, CONTINUE RECURRENCE
+C     ON SCALED FUNCTIONS UNTIL TWO MEMBERS COME ON SCALE, THEN
+C     RETURN WITH MIN(NZ+2,N) VALUES SCALED BY 1/TOL.
+C
+C***ROUTINES CALLED  ZUCHK,ZABS,ZLOG
+C***END PROLOGUE  ZKSCL
+C     COMPLEX CK,CS,CY,CZERO,RZ,S1,S2,Y,ZR,ZD,CELM
+      DOUBLE PRECISION ACS, AS, ASCLE, CKI, CKR, CSI, CSR, CYI,
+     * CYR, ELIM, FN, FNU, RZI, RZR, STR, S1I, S1R, S2I,
+     * S2R, TOL, YI, YR, ZEROI, ZEROR, ZRI, ZRR, ZABS,
+     * ZDR, ZDI, CELMR, ELM, HELIM, ALAS
+      INTEGER I, IC, IDUM, KK, N, NN, NW, NZ
+      DIMENSION YR(N), YI(N), CYR(2), CYI(2)
+      DATA ZEROR,ZEROI / 0.0D0 , 0.0D0 /
+C
+      NZ = 0
+      IC = 0
+      NN = MIN0(2,N)
+      DO 10 I=1,NN
+        S1R = YR(I)
+        S1I = YI(I)
+        CYR(I) = S1R
+        CYI(I) = S1I
+        AS = ZABS(CMPLX(S1R,S1I,kind=KIND(1.0D0)))
+        ACS = -ZRR + DLOG(AS)
+        NZ = NZ + 1
+        YR(I) = ZEROR
+        YI(I) = ZEROI
+        IF (ACS.LT.(-ELIM)) GO TO 10
+        CALL ZLOG(S1R, S1I, CSR, CSI, IDUM)
+        CSR = CSR - ZRR
+        CSI = CSI - ZRI
+        STR = DEXP(CSR)/TOL
+        CSR = STR*DCOS(CSI)
+        CSI = STR*DSIN(CSI)
+        CALL ZUCHK(CSR, CSI, NW, ASCLE, TOL)
+        IF (NW.NE.0) GO TO 10
+        YR(I) = CSR
+        YI(I) = CSI
+        IC = I
+        NZ = NZ - 1
+   10 CONTINUE
+      IF (N.EQ.1) RETURN
+      IF (IC.GT.1) GO TO 20
+      YR(1) = ZEROR
+      YI(1) = ZEROI
+      NZ = 2
+   20 CONTINUE
+      IF (N.EQ.2) RETURN
+      IF (NZ.EQ.0) RETURN
+      FN = FNU + 1.0D0
+      CKR = FN*RZR
+      CKI = FN*RZI
+      S1R = CYR(1)
+      S1I = CYI(1)
+      S2R = CYR(2)
+      S2I = CYI(2)
+      HELIM = 0.5D0*ELIM
+      ELM = DEXP(-ELIM)
+      CELMR = ELM
+      ZDR = ZRR
+      ZDI = ZRI
+C
+C     FIND TWO CONSECUTIVE Y VALUES ON SCALE. SCALE RECURRENCE IF
+C     S2 GETS LARGER THAN EXP(ELIM/2)
+C
+      DO 30 I=3,N
+        KK = I
+        CSR = S2R
+        CSI = S2I
+        S2R = CKR*CSR - CKI*CSI + S1R
+        S2I = CKI*CSR + CKR*CSI + S1I
+        S1R = CSR
+        S1I = CSI
+        CKR = CKR + RZR
+        CKI = CKI + RZI
+        AS = ZABS(CMPLX(S2R,S2I,kind=KIND(1.0D0)))
+        ALAS = DLOG(AS)
+        ACS = -ZDR + ALAS
+        NZ = NZ + 1
+        YR(I) = ZEROR
+        YI(I) = ZEROI
+        IF (ACS.LT.(-ELIM)) GO TO 25
+        CALL ZLOG(S2R, S2I, CSR, CSI, IDUM)
+        CSR = CSR - ZDR
+        CSI = CSI - ZDI
+        STR = DEXP(CSR)/TOL
+        CSR = STR*DCOS(CSI)
+        CSI = STR*DSIN(CSI)
+        CALL ZUCHK(CSR, CSI, NW, ASCLE, TOL)
+        IF (NW.NE.0) GO TO 25
+        YR(I) = CSR
+        YI(I) = CSI
+        NZ = NZ - 1
+        IF (IC.EQ.KK-1) GO TO 40
+        IC = KK
+        GO TO 30
+   25   CONTINUE
+        IF(ALAS.LT.HELIM) GO TO 30
+        ZDR = ZDR - ELIM
+        S1R = S1R*CELMR
+        S1I = S1I*CELMR
+        S2R = S2R*CELMR
+        S2I = S2I*CELMR
+   30 CONTINUE
+      NZ = N
+      IF(IC.EQ.N) NZ=N-1
+      GO TO 45
+   40 CONTINUE
+      NZ = KK - 2
+   45 CONTINUE
+      DO 50 I=1,NZ
+        YR(I) = ZEROR
+        YI(I) = ZEROI
+   50 CONTINUE
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zlog.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zlog.f
new file mode 100644
index 00000000..bb22cd01
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zlog.f
@@ -0,0 +1,41 @@
+      SUBROUTINE ZLOG(AR, AI, BR, BI, IERR)
+C***BEGIN PROLOGUE  ZLOG
+C***REFER TO  ZBESH,ZBESI,ZBESJ,ZBESK,ZBESY,ZAIRY,ZBIRY
+C
+C     DOUBLE PRECISION COMPLEX LOGARITHM B=CLOG(A)
+C     IERR=0,NORMAL RETURN      IERR=1, Z=CMPLX(0.0,0.0)
+C***ROUTINES CALLED  ZABS
+C***END PROLOGUE  ZLOG
+      DOUBLE PRECISION AR, AI, BR, BI, ZM, DTHETA, DPI, DHPI
+      DOUBLE PRECISION ZABS
+      DATA DPI , DHPI  / 3.141592653589793238462643383D+0,
+     1                   1.570796326794896619231321696D+0/
+C
+      IERR=0
+      IF (AR.EQ.0.0D+0) GO TO 10
+      IF (AI.EQ.0.0D+0) GO TO 20
+      DTHETA = DATAN(AI/AR)
+      IF (DTHETA.LE.0.0D+0) GO TO 40
+      IF (AR.LT.0.0D+0) DTHETA = DTHETA - DPI
+      GO TO 50
+   10 IF (AI.EQ.0.0D+0) GO TO 60
+      BI = DHPI
+      BR = DLOG(DABS(AI))
+      IF (AI.LT.0.0D+0) BI = -BI
+      RETURN
+   20 IF (AR.GT.0.0D+0) GO TO 30
+      BR = DLOG(DABS(AR))
+      BI = DPI
+      RETURN
+   30 BR = DLOG(AR)
+      BI = 0.0D+0
+      RETURN
+   40 IF (AR.LT.0.0D+0) DTHETA = DTHETA + DPI
+   50 ZM = ZABS(CMPLX(AR,AI,kind=KIND(1.0D0)))
+      BR = DLOG(ZM)
+      BI = DTHETA
+      RETURN
+   60 CONTINUE
+      IERR=1
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zmlri.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zmlri.f
new file mode 100644
index 00000000..c112f79d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zmlri.f
@@ -0,0 +1,206 @@
+      SUBROUTINE ZMLRI(ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL)
+C***BEGIN PROLOGUE  ZMLRI
+C***REFER TO  ZBESI,ZBESK
+C
+C     ZMLRI COMPUTES THE I BESSEL FUNCTION FOR RE(Z).GE.0.0 BY THE
+C     MILLER ALGORITHM NORMALIZED BY A NEUMANN SERIES.
+C
+C***ROUTINES CALLED  DGAMLN,D1MACH,ZABS,ZEXP,ZLOG,ZMLT
+C***END PROLOGUE  ZMLRI
+C     COMPLEX CK,CNORM,CONE,CTWO,CZERO,PT,P1,P2,RZ,SUM,Y,Z
+      DOUBLE PRECISION ACK, AK, AP, AT, AZ, BK, CKI, CKR, CNORMI,
+     * CNORMR, CONEI, CONER, FKAP, FKK, FLAM, FNF, FNU, PTI, PTR, P1I,
+     * P1R, P2I, P2R, RAZ, RHO, RHO2, RZI, RZR, SCLE, STI, STR, SUMI,
+     * SUMR, TFNF, TOL, TST, YI, YR, ZEROI, ZEROR, ZI, ZR, DGAMLN,
+     * D1MACH, ZABS
+      INTEGER I, IAZ, IDUM, IFNU, INU, ITIME, K, KK, KM, KODE, M, N, NZ
+      DIMENSION YR(N), YI(N)
+      DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 /
+      SCLE = D1MACH(1)/TOL
+      NZ=0
+      AZ = ZABS(CMPLX(ZR,ZI,kind=KIND(1.0D0)))
+      IAZ = INT(SNGL(AZ))
+      IFNU = INT(SNGL(FNU))
+      INU = IFNU + N - 1
+      AT = DBLE(FLOAT(IAZ)) + 1.0D0
+      RAZ = 1.0D0/AZ
+      STR = ZR*RAZ
+      STI = -ZI*RAZ
+      CKR = STR*AT*RAZ
+      CKI = STI*AT*RAZ
+      RZR = (STR+STR)*RAZ
+      RZI = (STI+STI)*RAZ
+      P1R = ZEROR
+      P1I = ZEROI
+      P2R = CONER
+      P2I = CONEI
+      ACK = (AT+1.0D0)*RAZ
+      RHO = ACK + DSQRT(ACK*ACK-1.0D0)
+      RHO2 = RHO*RHO
+      TST = (RHO2+RHO2)/((RHO2-1.0D0)*(RHO-1.0D0))
+      TST = TST/TOL
+C-----------------------------------------------------------------------
+C     COMPUTE RELATIVE TRUNCATION ERROR INDEX FOR SERIES
+C-----------------------------------------------------------------------
+      AK = AT
+      DO 10 I=1,80
+        PTR = P2R
+        PTI = P2I
+        P2R = P1R - (CKR*PTR-CKI*PTI)
+        P2I = P1I - (CKI*PTR+CKR*PTI)
+        P1R = PTR
+        P1I = PTI
+        CKR = CKR + RZR
+        CKI = CKI + RZI
+        AP = ZABS(CMPLX(P2R,P2I,kind=KIND(1.0D0)))
+        IF (AP.GT.TST*AK*AK) THEN
+          GO TO 20
+        END IF
+        AK = AK + 1.0D0
+   10 CONTINUE
+      GO TO 110
+   20 CONTINUE
+      I = I + 1
+      K = 0
+      IF (INU.LT.IAZ) GO TO 40
+C-----------------------------------------------------------------------
+C     COMPUTE RELATIVE TRUNCATION ERROR FOR RATIOS
+C-----------------------------------------------------------------------
+      P1R = ZEROR
+      P1I = ZEROI
+      P2R = CONER
+      P2I = CONEI
+      AT = DBLE(FLOAT(INU)) + 1.0D0
+      STR = ZR*RAZ
+      STI = -ZI*RAZ
+      CKR = STR*AT*RAZ
+      CKI = STI*AT*RAZ
+      ACK = AT*RAZ
+      TST = DSQRT(ACK/TOL)
+      ITIME = 1
+      DO 30 K=1,80
+        PTR = P2R
+        PTI = P2I
+        P2R = P1R - (CKR*PTR-CKI*PTI)
+        P2I = P1I - (CKR*PTI+CKI*PTR)
+        P1R = PTR
+        P1I = PTI
+        CKR = CKR + RZR
+        CKI = CKI + RZI
+        AP = ZABS(CMPLX(P2R,P2I,kind=KIND(1.0D0)))
+        IF (AP.LT.TST) GO TO 30
+        IF (ITIME.EQ.2) GO TO 40
+        ACK = ZABS(CMPLX(CKR,CKI,kind=KIND(1.0D0)))
+        FLAM = ACK + DSQRT(ACK*ACK-1.0D0)
+        FKAP = AP/ZABS(CMPLX(P1R,P1I,kind=KIND(1.0D0)))
+        RHO = DMIN1(FLAM,FKAP)
+        TST = TST*DSQRT(RHO/(RHO*RHO-1.0D0))
+        ITIME = 2
+   30 CONTINUE
+      GO TO 110
+   40 CONTINUE
+C-----------------------------------------------------------------------
+C     BACKWARD RECURRENCE AND SUM NORMALIZING RELATION
+C-----------------------------------------------------------------------
+      K = K + 1
+      KK = MAX0(I+IAZ,K+INU)
+      FKK = DBLE(FLOAT(KK))
+      P1R = ZEROR
+      P1I = ZEROI
+C-----------------------------------------------------------------------
+C     SCALE P2 AND SUM BY SCLE
+C-----------------------------------------------------------------------
+      P2R = SCLE
+      P2I = ZEROI
+      FNF = FNU - DBLE(FLOAT(IFNU))
+      TFNF = FNF + FNF
+      BK = DGAMLN(FKK+TFNF+1.0D0,IDUM) - DGAMLN(FKK+1.0D0,IDUM) -
+     * DGAMLN(TFNF+1.0D0,IDUM)
+      BK = DEXP(BK)
+      SUMR = ZEROR
+      SUMI = ZEROI
+      KM = KK - INU
+      DO 50 I=1,KM
+        PTR = P2R
+        PTI = P2I
+        P2R = P1R + (FKK+FNF)*(RZR*PTR-RZI*PTI)
+        P2I = P1I + (FKK+FNF)*(RZI*PTR+RZR*PTI)
+        P1R = PTR
+        P1I = PTI
+        AK = 1.0D0 - TFNF/(FKK+TFNF)
+        ACK = BK*AK
+        SUMR = SUMR + (ACK+BK)*P1R
+        SUMI = SUMI + (ACK+BK)*P1I
+        BK = ACK
+        FKK = FKK - 1.0D0
+   50 CONTINUE
+      YR(N) = P2R
+      YI(N) = P2I
+      IF (N.EQ.1) GO TO 70
+      DO 60 I=2,N
+        PTR = P2R
+        PTI = P2I
+        P2R = P1R + (FKK+FNF)*(RZR*PTR-RZI*PTI)
+        P2I = P1I + (FKK+FNF)*(RZI*PTR+RZR*PTI)
+        P1R = PTR
+        P1I = PTI
+        AK = 1.0D0 - TFNF/(FKK+TFNF)
+        ACK = BK*AK
+        SUMR = SUMR + (ACK+BK)*P1R
+        SUMI = SUMI + (ACK+BK)*P1I
+        BK = ACK
+        FKK = FKK - 1.0D0
+        M = N - I + 1
+        YR(M) = P2R
+        YI(M) = P2I
+   60 CONTINUE
+   70 CONTINUE
+      IF (IFNU.LE.0) GO TO 90
+      DO 80 I=1,IFNU
+        PTR = P2R
+        PTI = P2I
+        P2R = P1R + (FKK+FNF)*(RZR*PTR-RZI*PTI)
+        P2I = P1I + (FKK+FNF)*(RZR*PTI+RZI*PTR)
+        P1R = PTR
+        P1I = PTI
+        AK = 1.0D0 - TFNF/(FKK+TFNF)
+        ACK = BK*AK
+        SUMR = SUMR + (ACK+BK)*P1R
+        SUMI = SUMI + (ACK+BK)*P1I
+        BK = ACK
+        FKK = FKK - 1.0D0
+   80 CONTINUE
+   90 CONTINUE
+      PTR = ZR
+      PTI = ZI
+      IF (KODE.EQ.2) PTR = ZEROR
+      CALL ZLOG(RZR, RZI, STR, STI, IDUM)
+      P1R = -FNF*STR + PTR
+      P1I = -FNF*STI + PTI
+      AP = DGAMLN(1.0D0+FNF,IDUM)
+      PTR = P1R - AP
+      PTI = P1I
+C-----------------------------------------------------------------------
+C     THE DIVISION CEXP(PT)/(SUM+P2) IS ALTERED TO AVOID OVERFLOW
+C     IN THE DENOMINATOR BY SQUARING LARGE QUANTITIES
+C-----------------------------------------------------------------------
+      P2R = P2R + SUMR
+      P2I = P2I + SUMI
+      AP = ZABS(CMPLX(P2R,P2I,kind=KIND(1.0D0)))
+      P1R = 1.0D0/AP
+      CALL ZEXP(PTR, PTI, STR, STI)
+      CKR = STR*P1R
+      CKI = STI*P1R
+      PTR = P2R*P1R
+      PTI = -P2I*P1R
+      CALL ZMLT(CKR, CKI, PTR, PTI, CNORMR, CNORMI)
+      DO 100 I=1,N
+        STR = YR(I)*CNORMR - YI(I)*CNORMI
+        YI(I) = YR(I)*CNORMI + YI(I)*CNORMR
+        YR(I) = STR
+  100 CONTINUE
+      RETURN
+  110 CONTINUE
+      NZ=-2
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zmlt.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zmlt.f
new file mode 100644
index 00000000..3bde7d34
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zmlt.f
@@ -0,0 +1,15 @@
+      SUBROUTINE ZMLT(AR, AI, BR, BI, CR, CI)
+C***BEGIN PROLOGUE  ZMLT
+C***REFER TO  ZBESH,ZBESI,ZBESJ,ZBESK,ZBESY,ZAIRY,ZBIRY
+C
+C     DOUBLE PRECISION COMPLEX MULTIPLY, C=A*B.
+C
+C***ROUTINES CALLED  (NONE)
+C***END PROLOGUE  ZMLT
+      DOUBLE PRECISION AR, AI, BR, BI, CR, CI, CA, CB
+      CA = AR*BR - AI*BI
+      CB = AR*BI + AI*BR
+      CR = CA
+      CI = CB
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zrati.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zrati.f
new file mode 100644
index 00000000..b66bd201
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zrati.f
@@ -0,0 +1,132 @@
+      SUBROUTINE ZRATI(ZR, ZI, FNU, N, CYR, CYI, TOL)
+C***BEGIN PROLOGUE  ZRATI
+C***REFER TO  ZBESI,ZBESK,ZBESH
+C
+C     ZRATI COMPUTES RATIOS OF I BESSEL FUNCTIONS BY BACKWARD
+C     RECURRENCE.  THE STARTING INDEX IS DETERMINED BY FORWARD
+C     RECURRENCE AS DESCRIBED IN J. RES. OF NAT. BUR. OF STANDARDS-B,
+C     MATHEMATICAL SCIENCES, VOL 77B, P111-114, SEPTEMBER, 1973,
+C     BESSEL FUNCTIONS I AND J OF COMPLEX ARGUMENT AND INTEGER ORDER,
+C     BY D. J. SOOKNE.
+C
+C***ROUTINES CALLED  ZABS,ZDIV
+C***END PROLOGUE  ZRATI
+C     COMPLEX Z,CY(1),CONE,CZERO,P1,P2,T1,RZ,PT,CDFNU
+      DOUBLE PRECISION AK, AMAGZ, AP1, AP2, ARG, AZ, CDFNUI, CDFNUR,
+     * CONEI, CONER, CYI, CYR, CZEROI, CZEROR, DFNU, FDNU, FLAM, FNU,
+     * FNUP, PTI, PTR, P1I, P1R, P2I, P2R, RAK, RAP1, RHO, RT2, RZI,
+     * RZR, TEST, TEST1, TOL, TTI, TTR, T1I, T1R, ZI, ZR, ZABS
+      INTEGER I, ID, IDNU, INU, ITIME, K, KK, MAGZ, N
+      DIMENSION CYR(N), CYI(N)
+      DATA CZEROR,CZEROI,CONER,CONEI,RT2/
+     1 0.0D0, 0.0D0, 1.0D0, 0.0D0, 1.41421356237309505D0 /
+      AZ = ZABS(CMPLX(ZR,ZI,kind=KIND(1.0D0)))
+      INU = INT(SNGL(FNU))
+      IDNU = INU + N - 1
+      MAGZ = INT(SNGL(AZ))
+      AMAGZ = DBLE(FLOAT(MAGZ+1))
+      FDNU = DBLE(FLOAT(IDNU))
+      FNUP = DMAX1(AMAGZ,FDNU)
+      ID = IDNU - MAGZ - 1
+      ITIME = 1
+      K = 1
+      PTR = 1.0D0/AZ
+      RZR = PTR*(ZR+ZR)*PTR
+      RZI = -PTR*(ZI+ZI)*PTR
+      T1R = RZR*FNUP
+      T1I = RZI*FNUP
+      P2R = -T1R
+      P2I = -T1I
+      P1R = CONER
+      P1I = CONEI
+      T1R = T1R + RZR
+      T1I = T1I + RZI
+      IF (ID.GT.0) ID = 0
+      AP2 = ZABS(CMPLX(P2R,P2I,kind=KIND(1.0D0)))
+      AP1 = ZABS(CMPLX(P1R,P1I,kind=KIND(1.0D0)))
+C-----------------------------------------------------------------------
+C     THE OVERFLOW TEST ON K(FNU+I-1,Z) BEFORE THE CALL TO CBKNU
+C     GUARANTEES THAT P2 IS ON SCALE. SCALE TEST1 AND ALL SUBSEQUENT
+C     P2 VALUES BY AP1 TO ENSURE THAT AN OVERFLOW DOES NOT OCCUR
+C     PREMATURELY.
+C-----------------------------------------------------------------------
+      ARG = (AP2+AP2)/(AP1*TOL)
+      TEST1 = DSQRT(ARG)
+      TEST = TEST1
+      RAP1 = 1.0D0/AP1
+      P1R = P1R*RAP1
+      P1I = P1I*RAP1
+      P2R = P2R*RAP1
+      P2I = P2I*RAP1
+      AP2 = AP2*RAP1
+   10 CONTINUE
+      K = K + 1
+      AP1 = AP2
+      PTR = P2R
+      PTI = P2I
+      P2R = P1R - (T1R*PTR-T1I*PTI)
+      P2I = P1I - (T1R*PTI+T1I*PTR)
+      P1R = PTR
+      P1I = PTI
+      T1R = T1R + RZR
+      T1I = T1I + RZI
+      AP2 = ZABS(CMPLX(P2R,P2I,kind=KIND(1.0D0)))
+      IF (AP1.LE.TEST) GO TO 10
+      IF (ITIME.EQ.2) GO TO 20
+      AK = ZABS(CMPLX(T1R,T1I,kind=KIND(1.0D0))*0.5D0)
+      FLAM = AK + DSQRT(AK*AK-1.0D0)
+      RHO = DMIN1(AP2/AP1,FLAM)
+      TEST = TEST1*DSQRT(RHO/(RHO*RHO-1.0D0))
+      ITIME = 2
+      GO TO 10
+   20 CONTINUE
+      KK = K + 1 - ID
+      AK = DBLE(FLOAT(KK))
+      T1R = AK
+      T1I = CZEROI
+      DFNU = FNU + DBLE(FLOAT(N-1))
+      P1R = 1.0D0/AP2
+      P1I = CZEROI
+      P2R = CZEROR
+      P2I = CZEROI
+      DO 30 I=1,KK
+        PTR = P1R
+        PTI = P1I
+        RAP1 = DFNU + T1R
+        TTR = RZR*RAP1
+        TTI = RZI*RAP1
+        P1R = (PTR*TTR-PTI*TTI) + P2R
+        P1I = (PTR*TTI+PTI*TTR) + P2I
+        P2R = PTR
+        P2I = PTI
+        T1R = T1R - CONER
+   30 CONTINUE
+      IF (P1R.NE.CZEROR .OR. P1I.NE.CZEROI) GO TO 40
+      P1R = TOL
+      P1I = TOL
+   40 CONTINUE
+      CALL ZDIV(P2R, P2I, P1R, P1I, CYR(N), CYI(N))
+      IF (N.EQ.1) RETURN
+      K = N - 1
+      AK = DBLE(FLOAT(K))
+      T1R = AK
+      T1I = CZEROI
+      CDFNUR = FNU*RZR
+      CDFNUI = FNU*RZI
+      DO 60 I=2,N
+        PTR = CDFNUR + (T1R*RZR-T1I*RZI) + CYR(K+1)
+        PTI = CDFNUI + (T1R*RZI+T1I*RZR) + CYI(K+1)
+        AK = ZABS(CMPLX(PTR,PTI,kind=KIND(1.0D0)))
+        IF (AK.NE.CZEROR) GO TO 50
+        PTR = TOL
+        PTI = TOL
+        AK = TOL*RT2
+   50   CONTINUE
+        RAK = CONER/AK
+        CYR(K) = RAK*PTR*RAK
+        CYI(K) = -RAK*PTI*RAK
+        T1R = T1R - CONER
+        K = K - 1
+   60 CONTINUE
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zs1s2.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zs1s2.f
new file mode 100644
index 00000000..0a6da311
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zs1s2.f
@@ -0,0 +1,51 @@
+      SUBROUTINE ZS1S2(ZRR, ZRI, S1R, S1I, S2R, S2I, NZ, ASCLE, ALIM,
+     * IUF)
+C***BEGIN PROLOGUE  ZS1S2
+C***REFER TO  ZBESK,ZAIRY
+C
+C     ZS1S2 TESTS FOR A POSSIBLE UNDERFLOW RESULTING FROM THE
+C     ADDITION OF THE I AND K FUNCTIONS IN THE ANALYTIC CON-
+C     TINUATION FORMULA WHERE S1=K FUNCTION AND S2=I FUNCTION.
+C     ON KODE=1 THE I AND K FUNCTIONS ARE DIFFERENT ORDERS OF
+C     MAGNITUDE, BUT FOR KODE=2 THEY CAN BE OF THE SAME ORDER
+C     OF MAGNITUDE AND THE MAXIMUM MUST BE AT LEAST ONE
+C     PRECISION ABOVE THE UNDERFLOW LIMIT.
+C
+C***ROUTINES CALLED  ZABS,ZEXP,ZLOG
+C***END PROLOGUE  ZS1S2
+C     COMPLEX CZERO,C1,S1,S1D,S2,ZR
+      DOUBLE PRECISION AA, ALIM, ALN, ASCLE, AS1, AS2, C1I, C1R, S1DI,
+     * S1DR, S1I, S1R, S2I, S2R, ZEROI, ZEROR, ZRI, ZRR, ZABS
+      INTEGER IUF, IDUM, NZ
+      DATA ZEROR,ZEROI  / 0.0D0 , 0.0D0 /
+      NZ = 0
+      AS1 = ZABS(CMPLX(S1R,S1I,kind=KIND(1.0D0)))
+      AS2 = ZABS(CMPLX(S2R,S2I,kind=KIND(1.0D0)))
+      IF (S1R.EQ.0.0D0 .AND. S1I.EQ.0.0D0) GO TO 10
+      IF (AS1.EQ.0.0D0) GO TO 10
+      ALN = -ZRR - ZRR + DLOG(AS1)
+      S1DR = S1R
+      S1DI = S1I
+      S1R = ZEROR
+      S1I = ZEROI
+      AS1 = ZEROR
+      IF (ALN.LT.(-ALIM)) GO TO 10
+      CALL ZLOG(S1DR, S1DI, C1R, C1I, IDUM)
+      C1R = C1R - ZRR - ZRR
+      C1I = C1I - ZRI - ZRI
+      CALL ZEXP(C1R, C1I, S1R, S1I)
+      AS1 = ZABS(CMPLX(S1R,S1I,kind=KIND(1.0D0)))
+      IUF = IUF + 1
+   10 CONTINUE
+      AA = DMAX1(AS1,AS2)
+      IF (AA.GT.ASCLE) THEN
+        RETURN
+      END IF
+      S1R = ZEROR
+      S1I = ZEROI
+      S2R = ZEROR
+      S2I = ZEROI
+      NZ = 1
+      IUF = 0
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zseri.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zseri.f
new file mode 100644
index 00000000..862fbf61
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zseri.f
@@ -0,0 +1,195 @@
+      SUBROUTINE ZSERI(ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM,
+     * ALIM)
+C***BEGIN PROLOGUE  ZSERI
+C***REFER TO  ZBESI,ZBESK
+C
+C     ZSERI COMPUTES THE I BESSEL FUNCTION FOR REAL(Z).GE.0.0 BY
+C     MEANS OF THE POWER SERIES FOR LARGE CABS(Z) IN THE
+C     REGION CABS(Z).LE.2*SQRT(FNU+1). NZ=0 IS A NORMAL RETURN.
+C     NZ.GT.0 MEANS THAT THE LAST NZ COMPONENTS WERE SET TO ZERO
+C     DUE TO UNDERFLOW. NZ.LT.0 MEANS UNDERFLOW OCCURRED, BUT THE
+C     CONDITION CABS(Z).LE.2*SQRT(FNU+1) WAS VIOLATED AND THE
+C     COMPUTATION MUST BE COMPLETED IN ANOTHER ROUTINE WITH N=N-ABS(NZ).
+C
+C***ROUTINES CALLED  DGAMLN,D1MACH,ZUCHK,ZABS,ZDIV,ZLOG,ZMLT
+C***END PROLOGUE  ZSERI
+C     COMPLEX AK1,CK,COEF,CONE,CRSC,CSCL,CZ,CZERO,HZ,RZ,S1,S2,Y,Z
+      DOUBLE PRECISION AA, ACZ, AK, AK1I, AK1R, ALIM, ARM, ASCLE, ATOL,
+     * AZ, CKI, CKR, COEFI, COEFR, CONEI, CONER, CRSCR, CZI, CZR, DFNU,
+     * ELIM, FNU, FNUP, HZI, HZR, RAZ, RS, RTR1, RZI, RZR, S, SS, STI,
+     * STR, S1I, S1R, S2I, S2R, TOL, YI, YR, WI, WR, ZEROI, ZEROR, ZI,
+     * ZR, DGAMLN, D1MACH, ZABS
+      INTEGER I, IB, IDUM, IFLAG, IL, K, KODE, L, M, N, NN, NZ, NW
+      DIMENSION YR(N), YI(N), WR(2), WI(2)
+      DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 /
+C
+
+      NZ = 0
+      AZ = ZABS(CMPLX(ZR,ZI,kind=KIND(1.0D0)))
+      IF (AZ.EQ.0.0D0) GO TO 160
+      ARM = 1.0D+3*D1MACH(1)
+      RTR1 = DSQRT(ARM)
+      CRSCR = 1.0D0
+      IFLAG = 0
+      IF (AZ.LT.ARM) THEN
+        GO TO 150
+      END IF
+      HZR = 0.5D0*ZR
+      HZI = 0.5D0*ZI
+      CZR = ZEROR
+      CZI = ZEROI
+      IF (AZ.LE.RTR1) GO TO 10
+      CALL ZMLT(HZR, HZI, HZR, HZI, CZR, CZI)
+   10 CONTINUE
+      ACZ = ZABS(CMPLX(CZR,CZI,kind=KIND(1.0D0)))
+      NN = N
+      CALL ZLOG(HZR, HZI, CKR, CKI, IDUM)
+   20 CONTINUE
+      DFNU = FNU + DBLE(FLOAT(NN-1))
+      FNUP = DFNU + 1.0D0
+C-----------------------------------------------------------------------
+C     UNDERFLOW TEST
+C-----------------------------------------------------------------------
+      AK1R = CKR*DFNU
+      AK1I = CKI*DFNU
+      AK = DGAMLN(FNUP,IDUM)
+      AK1R = AK1R - AK
+      IF (KODE.EQ.2) AK1R = AK1R - ZR
+      IF (AK1R.GT.(-ELIM)) GO TO 40
+   30 CONTINUE
+      NZ = NZ + 1
+      YR(NN) = ZEROR
+      YI(NN) = ZEROI
+      IF (ACZ.GT.DFNU) GO TO 190
+      NN = NN - 1
+      IF (NN.EQ.0) RETURN
+      GO TO 20
+   40 CONTINUE
+      IF (AK1R.GT.(-ALIM)) GO TO 50
+      IFLAG = 1
+      SS = 1.0D0/TOL
+      CRSCR = TOL
+      ASCLE = ARM*SS
+   50 CONTINUE
+      AA = DEXP(AK1R)
+      IF (IFLAG.EQ.1) AA = AA*SS
+      COEFR = AA*DCOS(AK1I)
+      COEFI = AA*DSIN(AK1I)
+      ATOL = TOL*ACZ/FNUP
+      IL = MIN0(2,NN)
+      DO 90 I=1,IL
+        DFNU = FNU + DBLE(FLOAT(NN-I))
+        FNUP = DFNU + 1.0D0
+        S1R = CONER
+        S1I = CONEI
+        IF (ACZ.LT.TOL*FNUP) GO TO 70
+        AK1R = CONER
+        AK1I = CONEI
+        AK = FNUP + 2.0D0
+        S = FNUP
+        AA = 2.0D0
+   60   CONTINUE
+        RS = 1.0D0/S
+        STR = AK1R*CZR - AK1I*CZI
+        STI = AK1R*CZI + AK1I*CZR
+        AK1R = STR*RS
+        AK1I = STI*RS
+        S1R = S1R + AK1R
+        S1I = S1I + AK1I
+        S = S + AK
+        AK = AK + 2.0D0
+        AA = AA*ACZ*RS
+        IF (AA.GT.ATOL) GO TO 60
+   70   CONTINUE
+        S2R = S1R*COEFR - S1I*COEFI
+        S2I = S1R*COEFI + S1I*COEFR
+        WR(I) = S2R
+        WI(I) = S2I
+        IF (IFLAG.EQ.0) GO TO 80
+        CALL ZUCHK(S2R, S2I, NW, ASCLE, TOL)
+        IF (NW.NE.0) GO TO 30
+   80   CONTINUE
+        M = NN - I + 1
+        YR(M) = S2R*CRSCR
+        YI(M) = S2I*CRSCR
+        IF (I.EQ.IL) GO TO 90
+        CALL ZDIV(COEFR, COEFI, HZR, HZI, STR, STI)
+        COEFR = STR*DFNU
+        COEFI = STI*DFNU
+   90 CONTINUE
+      IF (NN.LE.2) THEN
+        RETURN
+      END IF
+      K = NN - 2
+      AK = DBLE(FLOAT(K))
+      RAZ = 1.0D0/AZ
+      STR = ZR*RAZ
+      STI = -ZI*RAZ
+      RZR = (STR+STR)*RAZ
+      RZI = (STI+STI)*RAZ
+      IF (IFLAG.EQ.1) GO TO 120
+      IB = 3
+  100 CONTINUE
+      DO 110 I=IB,NN
+        YR(K) = (AK+FNU)*(RZR*YR(K+1)-RZI*YI(K+1)) + YR(K+2)
+        YI(K) = (AK+FNU)*(RZR*YI(K+1)+RZI*YR(K+1)) + YI(K+2)
+        AK = AK - 1.0D0
+        K = K - 1
+  110 CONTINUE
+      RETURN
+C-----------------------------------------------------------------------
+C     RECUR BACKWARD WITH SCALED VALUES
+C-----------------------------------------------------------------------
+  120 CONTINUE
+C-----------------------------------------------------------------------
+C     EXP(-ALIM)=EXP(-ELIM)/TOL=APPROX. ONE PRECISION ABOVE THE
+C     UNDERFLOW LIMIT = ASCLE = D1MACH(1)*SS*1.0D+3
+C-----------------------------------------------------------------------
+      S1R = WR(1)
+      S1I = WI(1)
+      S2R = WR(2)
+      S2I = WI(2)
+      DO 130 L=3,NN
+        CKR = S2R
+        CKI = S2I
+        S2R = S1R + (AK+FNU)*(RZR*CKR-RZI*CKI)
+        S2I = S1I + (AK+FNU)*(RZR*CKI+RZI*CKR)
+        S1R = CKR
+        S1I = CKI
+        CKR = S2R*CRSCR
+        CKI = S2I*CRSCR
+        YR(K) = CKR
+        YI(K) = CKI
+        AK = AK - 1.0D0
+        K = K - 1
+        IF (ZABS(CMPLX(CKR,CKI,kind=KIND(1.0D0))).GT.ASCLE) GO TO 140
+  130 CONTINUE
+      RETURN
+  140 CONTINUE
+      IB = L + 1
+      IF (IB.GT.NN) RETURN
+      GO TO 100
+  150 CONTINUE
+      NZ = N
+      IF (FNU.EQ.0.0D0) NZ = NZ - 1
+  160 CONTINUE
+      YR(1) = ZEROR
+      YI(1) = ZEROI
+      IF (FNU.NE.0.0D0) GO TO 170
+      YR(1) = CONER
+      YI(1) = CONEI
+  170 CONTINUE
+      IF (N.EQ.1) RETURN
+      DO 180 I=2,N
+        YR(I) = ZEROR
+        YI(I) = ZEROI
+  180 CONTINUE
+      RETURN
+C-----------------------------------------------------------------------
+C     RETURN WITH NZ.LT.0 IF CABS(Z*Z/4).GT.FNU+N-NZ-1 COMPLETE
+C     THE CALCULATION IN CBINU WITH N=N-IABS(NZ)
+C-----------------------------------------------------------------------
+  190 CONTINUE
+      NZ = -NZ
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zshch.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zshch.f
new file mode 100644
index 00000000..168e62e5
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zshch.f
@@ -0,0 +1,22 @@
+      SUBROUTINE ZSHCH(ZR, ZI, CSHR, CSHI, CCHR, CCHI)
+C***BEGIN PROLOGUE  ZSHCH
+C***REFER TO  ZBESK,ZBESH
+C
+C     ZSHCH COMPUTES THE COMPLEX HYPERBOLIC FUNCTIONS CSH=SINH(X+I*Y)
+C     AND CCH=COSH(X+I*Y), WHERE I**2=-1.
+C
+C***ROUTINES CALLED  (NONE)
+C***END PROLOGUE  ZSHCH
+C
+      DOUBLE PRECISION CCHI, CCHR, CH, CN, CSHI, CSHR, SH, SN, ZI, ZR,
+     * DCOSH, DSINH
+      SH = DSINH(ZR)
+      CH = DCOSH(ZR)
+      SN = DSIN(ZI)
+      CN = DCOS(ZI)
+      CSHR = SH*CN
+      CSHI = CH*SN
+      CCHR = CH*CN
+      CCHI = SH*SN
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zsqrt.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zsqrt.f
new file mode 100644
index 00000000..289545cd
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zsqrt.f
@@ -0,0 +1,45 @@
+      SUBROUTINE ZSQRT(AR, AI, BR, BI)
+C***BEGIN PROLOGUE  ZSQRT
+C***REFER TO  ZBESH,ZBESI,ZBESJ,ZBESK,ZBESY,ZAIRY,ZBIRY
+C
+C     DOUBLE PRECISION COMPLEX SQUARE ROOT, B=CSQRT(A)
+C
+C***ROUTINES CALLED  ZABS
+C***END PROLOGUE  ZSQRT
+      DOUBLE PRECISION AR, AI, BR, BI, ZM, DTHETA, DPI, DRT
+      DOUBLE PRECISION ZABS
+
+      DATA DRT , DPI / 7.071067811865475244008443621D-1,
+     1                 3.141592653589793238462643383D+0/
+      ZM = ZABS(CMPLX(AR,AI,kind=KIND(1.0D0)))
+      ZM = DSQRT(ZM)
+      IF (AR.EQ.0.0D+0) GO TO 10
+      IF (AI.EQ.0.0D+0) GO TO 20
+      DTHETA = DATAN(AI/AR)
+      IF (DTHETA.LE.0.0D+0) GO TO 40
+      IF (AR.LT.0.0D+0) DTHETA = DTHETA - DPI
+      GO TO 50
+   10 IF (AI.GT.0.0D+0) GO TO 60
+      IF (AI.LT.0.0D+0) GO TO 70
+      BR = 0.0D+0
+      BI = 0.0D+0
+      RETURN
+   20 IF (AR.GT.0.0D+0) GO TO 30
+      BR = 0.0D+0
+      BI = DSQRT(DABS(AR))
+      RETURN
+   30 BR = DSQRT(AR)
+      BI = 0.0D+0
+      RETURN
+   40 IF (AR.LT.0.0D+0) DTHETA = DTHETA + DPI
+   50 DTHETA = DTHETA*0.5D+0
+      BR = ZM*DCOS(DTHETA)
+      BI = ZM*DSIN(DTHETA)
+      RETURN
+   60 BR = ZM*DRT
+      BI = ZM*DRT
+      RETURN
+   70 BR = ZM*DRT
+      BI = -ZM*DRT
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zuchk.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zuchk.f
new file mode 100644
index 00000000..d15dc841
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zuchk.f
@@ -0,0 +1,28 @@
+      SUBROUTINE ZUCHK(YR, YI, NZ, ASCLE, TOL)
+C***BEGIN PROLOGUE  ZUCHK
+C***REFER TO ZSERI,ZUOIK,ZUNK1,ZUNK2,ZUNI1,ZUNI2,ZKSCL
+C
+C      Y ENTERS AS A SCALED QUANTITY WHOSE MAGNITUDE IS GREATER THAN
+C      EXP(-ALIM)=ASCLE=1.0E+3*D1MACH(1)/TOL. THE TEST IS MADE TO SEE
+C      IF THE MAGNITUDE OF THE REAL OR IMAGINARY PART WOULD UNDERFLOW
+C      WHEN Y IS SCALED (BY TOL) TO ITS PROPER VALUE. Y IS ACCEPTED
+C      IF THE UNDERFLOW IS AT LEAST ONE PRECISION BELOW THE MAGNITUDE
+C      OF THE LARGEST COMPONENT; OTHERWISE THE PHASE ANGLE DOES NOT HAVE
+C      ABSOLUTE ACCURACY AND AN UNDERFLOW IS ASSUMED.
+C
+C***ROUTINES CALLED  (NONE)
+C***END PROLOGUE  ZUCHK
+C
+C     COMPLEX Y
+      DOUBLE PRECISION ASCLE, SS, ST, TOL, WR, WI, YR, YI
+      INTEGER NZ
+      NZ = 0
+      WR = DABS(YR)
+      WI = DABS(YI)
+      ST = DMIN1(WR,WI)
+      IF (ST.GT.ASCLE) RETURN
+      SS = DMAX1(WR,WI)
+      ST = ST/TOL
+      IF (SS.LT.ST) NZ = 1
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zunhj.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zunhj.f
new file mode 100644
index 00000000..9b4df7a1
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zunhj.f
@@ -0,0 +1,714 @@
+      SUBROUTINE ZUNHJ(ZR, ZI, FNU, IPMTR, TOL, PHIR, PHII, ARGR, ARGI,
+     * ZETA1R, ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI)
+C***BEGIN PROLOGUE  ZUNHJ
+C***REFER TO  ZBESI,ZBESK
+C
+C     REFERENCES
+C         HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ AND I.A.
+C         STEGUN, AMS55, NATIONAL BUREAU OF STANDARDS, 1965, CHAPTER 9.
+C
+C         ASYMPTOTICS AND SPECIAL FUNCTIONS BY F.W.J. OLVER, ACADEMIC
+C         PRESS, N.Y., 1974, PAGE 420
+C
+C     ABSTRACT
+C         ZUNHJ COMPUTES PARAMETERS FOR BESSEL FUNCTIONS C(FNU,Z) =
+C         J(FNU,Z), Y(FNU,Z) OR H(I,FNU,Z) I=1,2 FOR LARGE ORDERS FNU
+C         BY MEANS OF THE UNIFORM ASYMPTOTIC EXPANSION
+C
+C         C(FNU,Z)=C1*PHI*( ASUM*AIRY(ARG) + C2*BSUM*DAIRY(ARG) )
+C
+C         FOR PROPER CHOICES OF C1, C2, AIRY AND DAIRY WHERE AIRY IS
+C         AN AIRY FUNCTION AND DAIRY IS ITS DERIVATIVE.
+C
+C               (2/3)*FNU*ZETA**1.5 = ZETA1-ZETA2,
+C
+C         ZETA1=0.5*FNU*CLOG((1+W)/(1-W)), ZETA2=FNU*W FOR SCALING
+C         PURPOSES IN AIRY FUNCTIONS FROM CAIRY OR CBIRY.
+C
+C         MCONJ=SIGN OF AIMAG(Z), BUT IS AMBIGUOUS WHEN Z IS REAL AND
+C         MUST BE SPECIFIED. IPMTR=0 RETURNS ALL PARAMETERS. IPMTR=
+C         1 COMPUTES ALL EXCEPT ASUM AND BSUM.
+C
+C***ROUTINES CALLED  ZABS,ZDIV,ZLOG,ZSQRT,D1MACH
+C***END PROLOGUE  ZUNHJ
+C     COMPLEX ARG,ASUM,BSUM,CFNU,CONE,CR,CZERO,DR,P,PHI,PRZTH,PTFN,
+C    *RFN13,RTZTA,RZTH,SUMA,SUMB,TFN,T2,UP,W,W2,Z,ZA,ZB,ZC,ZETA,ZETA1,
+C    *ZETA2,ZTH
+      DOUBLE PRECISION ALFA, ANG, AP, AR, ARGI, ARGR, ASUMI, ASUMR,
+     * ATOL, AW2, AZTH, BETA, BR, BSUMI, BSUMR, BTOL, C, CONEI, CONER,
+     * CRI, CRR, DRI, DRR, EX1, EX2, FNU, FN13, FN23, GAMA, GPI, HPI,
+     * PHII, PHIR, PI, PP, PR, PRZTHI, PRZTHR, PTFNI, PTFNR, RAW, RAW2,
+     * RAZTH, RFNU, RFNU2, RFN13, RTZTI, RTZTR, RZTHI, RZTHR, STI, STR,
+     * SUMAI, SUMAR, SUMBI, SUMBR, TEST, TFNI, TFNR, THPI, TOL, TZAI,
+     * TZAR, T2I, T2R, UPI, UPR, WI, WR, W2I, W2R, ZAI, ZAR, ZBI, ZBR,
+     * ZCI, ZCR, ZEROI, ZEROR, ZETAI, ZETAR, ZETA1I, ZETA1R, ZETA2I,
+     * ZETA2R, ZI, ZR, ZTHI, ZTHR, ZABS, AC, D1MACH
+      INTEGER IAS, IBS, IPMTR, IS, J, JR, JU, K, KMAX, KP1, KS, L, LR,
+     * LRP1, L1, L2, M, IDUM
+      DIMENSION AR(14), BR(14), C(105), ALFA(180), BETA(210), GAMA(30),
+     * AP(30), PR(30), PI(30), UPR(14), UPI(14), CRR(14), CRI(14),
+     * DRR(14), DRI(14)
+      DATA AR(1), AR(2), AR(3), AR(4), AR(5), AR(6), AR(7), AR(8),
+     1     AR(9), AR(10), AR(11), AR(12), AR(13), AR(14)/
+     2     1.00000000000000000D+00,     1.04166666666666667D-01,
+     3     8.35503472222222222D-02,     1.28226574556327160D-01,
+     4     2.91849026464140464D-01,     8.81627267443757652D-01,
+     5     3.32140828186276754D+00,     1.49957629868625547D+01,
+     6     7.89230130115865181D+01,     4.74451538868264323D+02,
+     7     3.20749009089066193D+03,     2.40865496408740049D+04,
+     8     1.98923119169509794D+05,     1.79190200777534383D+06/
+      DATA BR(1), BR(2), BR(3), BR(4), BR(5), BR(6), BR(7), BR(8),
+     1     BR(9), BR(10), BR(11), BR(12), BR(13), BR(14)/
+     2     1.00000000000000000D+00,    -1.45833333333333333D-01,
+     3    -9.87413194444444444D-02,    -1.43312053915895062D-01,
+     4    -3.17227202678413548D-01,    -9.42429147957120249D-01,
+     5    -3.51120304082635426D+00,    -1.57272636203680451D+01,
+     6    -8.22814390971859444D+01,    -4.92355370523670524D+02,
+     7    -3.31621856854797251D+03,    -2.48276742452085896D+04,
+     8    -2.04526587315129788D+05,    -1.83844491706820990D+06/
+      DATA C(1), C(2), C(3), C(4), C(5), C(6), C(7), C(8), C(9), C(10),
+     1     C(11), C(12), C(13), C(14), C(15), C(16), C(17), C(18),
+     2     C(19), C(20), C(21), C(22), C(23), C(24)/
+     3     1.00000000000000000D+00,    -2.08333333333333333D-01,
+     4     1.25000000000000000D-01,     3.34201388888888889D-01,
+     5    -4.01041666666666667D-01,     7.03125000000000000D-02,
+     6    -1.02581259645061728D+00,     1.84646267361111111D+00,
+     7    -8.91210937500000000D-01,     7.32421875000000000D-02,
+     8     4.66958442342624743D+00,    -1.12070026162229938D+01,
+     9     8.78912353515625000D+00,    -2.36408691406250000D+00,
+     A     1.12152099609375000D-01,    -2.82120725582002449D+01,
+     B     8.46362176746007346D+01,    -9.18182415432400174D+01,
+     C     4.25349987453884549D+01,    -7.36879435947963170D+00,
+     D     2.27108001708984375D-01,     2.12570130039217123D+02,
+     E    -7.65252468141181642D+02,     1.05999045252799988D+03/
+      DATA C(25), C(26), C(27), C(28), C(29), C(30), C(31), C(32),
+     1     C(33), C(34), C(35), C(36), C(37), C(38), C(39), C(40),
+     2     C(41), C(42), C(43), C(44), C(45), C(46), C(47), C(48)/
+     3    -6.99579627376132541D+02,     2.18190511744211590D+02,
+     4    -2.64914304869515555D+01,     5.72501420974731445D-01,
+     5    -1.91945766231840700D+03,     8.06172218173730938D+03,
+     6    -1.35865500064341374D+04,     1.16553933368645332D+04,
+     7    -5.30564697861340311D+03,     1.20090291321635246D+03,
+     8    -1.08090919788394656D+02,     1.72772750258445740D+00,
+     9     2.02042913309661486D+04,    -9.69805983886375135D+04,
+     A     1.92547001232531532D+05,    -2.03400177280415534D+05,
+     B     1.22200464983017460D+05,    -4.11926549688975513D+04,
+     C     7.10951430248936372D+03,    -4.93915304773088012D+02,
+     D     6.07404200127348304D+00,    -2.42919187900551333D+05,
+     E     1.31176361466297720D+06,    -2.99801591853810675D+06/
+      DATA C(49), C(50), C(51), C(52), C(53), C(54), C(55), C(56),
+     1     C(57), C(58), C(59), C(60), C(61), C(62), C(63), C(64),
+     2     C(65), C(66), C(67), C(68), C(69), C(70), C(71), C(72)/
+     3     3.76327129765640400D+06,    -2.81356322658653411D+06,
+     4     1.26836527332162478D+06,    -3.31645172484563578D+05,
+     5     4.52187689813627263D+04,    -2.49983048181120962D+03,
+     6     2.43805296995560639D+01,     3.28446985307203782D+06,
+     7    -1.97068191184322269D+07,     5.09526024926646422D+07,
+     8    -7.41051482115326577D+07,     6.63445122747290267D+07,
+     9    -3.75671766607633513D+07,     1.32887671664218183D+07,
+     A    -2.78561812808645469D+06,     3.08186404612662398D+05,
+     B    -1.38860897537170405D+04,     1.10017140269246738D+02,
+     C    -4.93292536645099620D+07,     3.25573074185765749D+08,
+     D    -9.39462359681578403D+08,     1.55359689957058006D+09,
+     E    -1.62108055210833708D+09,     1.10684281682301447D+09/
+      DATA C(73), C(74), C(75), C(76), C(77), C(78), C(79), C(80),
+     1     C(81), C(82), C(83), C(84), C(85), C(86), C(87), C(88),
+     2     C(89), C(90), C(91), C(92), C(93), C(94), C(95), C(96)/
+     3    -4.95889784275030309D+08,     1.42062907797533095D+08,
+     4    -2.44740627257387285D+07,     2.24376817792244943D+06,
+     5    -8.40054336030240853D+04,     5.51335896122020586D+02,
+     6     8.14789096118312115D+08,    -5.86648149205184723D+09,
+     7     1.86882075092958249D+10,    -3.46320433881587779D+10,
+     8     4.12801855797539740D+10,    -3.30265997498007231D+10,
+     9     1.79542137311556001D+10,    -6.56329379261928433D+09,
+     A     1.55927986487925751D+09,    -2.25105661889415278D+08,
+     B     1.73951075539781645D+07,    -5.49842327572288687D+05,
+     C     3.03809051092238427D+03,    -1.46792612476956167D+10,
+     D     1.14498237732025810D+11,    -3.99096175224466498D+11,
+     E     8.19218669548577329D+11,    -1.09837515608122331D+12/
+      DATA C(97), C(98), C(99), C(100), C(101), C(102), C(103), C(104),
+     1     C(105)/
+     2     1.00815810686538209D+12,    -6.45364869245376503D+11,
+     3     2.87900649906150589D+11,    -8.78670721780232657D+10,
+     4     1.76347306068349694D+10,    -2.16716498322379509D+09,
+     5     1.43157876718888981D+08,    -3.87183344257261262D+06,
+     6     1.82577554742931747D+04/
+      DATA ALFA(1), ALFA(2), ALFA(3), ALFA(4), ALFA(5), ALFA(6),
+     1     ALFA(7), ALFA(8), ALFA(9), ALFA(10), ALFA(11), ALFA(12),
+     2     ALFA(13), ALFA(14), ALFA(15), ALFA(16), ALFA(17), ALFA(18),
+     3     ALFA(19), ALFA(20), ALFA(21), ALFA(22)/
+     4    -4.44444444444444444D-03,    -9.22077922077922078D-04,
+     5    -8.84892884892884893D-05,     1.65927687832449737D-04,
+     6     2.46691372741792910D-04,     2.65995589346254780D-04,
+     7     2.61824297061500945D-04,     2.48730437344655609D-04,
+     8     2.32721040083232098D-04,     2.16362485712365082D-04,
+     9     2.00738858762752355D-04,     1.86267636637545172D-04,
+     A     1.73060775917876493D-04,     1.61091705929015752D-04,
+     B     1.50274774160908134D-04,     1.40503497391269794D-04,
+     C     1.31668816545922806D-04,     1.23667445598253261D-04,
+     D     1.16405271474737902D-04,     1.09798298372713369D-04,
+     E     1.03772410422992823D-04,     9.82626078369363448D-05/
+      DATA ALFA(23), ALFA(24), ALFA(25), ALFA(26), ALFA(27), ALFA(28),
+     1     ALFA(29), ALFA(30), ALFA(31), ALFA(32), ALFA(33), ALFA(34),
+     2     ALFA(35), ALFA(36), ALFA(37), ALFA(38), ALFA(39), ALFA(40),
+     3     ALFA(41), ALFA(42), ALFA(43), ALFA(44)/
+     4     9.32120517249503256D-05,     8.85710852478711718D-05,
+     5     8.42963105715700223D-05,     8.03497548407791151D-05,
+     6     7.66981345359207388D-05,     7.33122157481777809D-05,
+     7     7.01662625163141333D-05,     6.72375633790160292D-05,
+     8     6.93735541354588974D-04,     2.32241745182921654D-04,
+     9    -1.41986273556691197D-05,    -1.16444931672048640D-04,
+     A    -1.50803558053048762D-04,    -1.55121924918096223D-04,
+     B    -1.46809756646465549D-04,    -1.33815503867491367D-04,
+     C    -1.19744975684254051D-04,    -1.06184319207974020D-04,
+     D    -9.37699549891194492D-05,    -8.26923045588193274D-05,
+     E    -7.29374348155221211D-05,    -6.44042357721016283D-05/
+      DATA ALFA(45), ALFA(46), ALFA(47), ALFA(48), ALFA(49), ALFA(50),
+     1     ALFA(51), ALFA(52), ALFA(53), ALFA(54), ALFA(55), ALFA(56),
+     2     ALFA(57), ALFA(58), ALFA(59), ALFA(60), ALFA(61), ALFA(62),
+     3     ALFA(63), ALFA(64), ALFA(65), ALFA(66)/
+     4    -5.69611566009369048D-05,    -5.04731044303561628D-05,
+     5    -4.48134868008882786D-05,    -3.98688727717598864D-05,
+     6    -3.55400532972042498D-05,    -3.17414256609022480D-05,
+     7    -2.83996793904174811D-05,    -2.54522720634870566D-05,
+     8    -2.28459297164724555D-05,    -2.05352753106480604D-05,
+     9    -1.84816217627666085D-05,    -1.66519330021393806D-05,
+     A    -1.50179412980119482D-05,    -1.35554031379040526D-05,
+     B    -1.22434746473858131D-05,    -1.10641884811308169D-05,
+     C    -3.54211971457743841D-04,    -1.56161263945159416D-04,
+     D     3.04465503594936410D-05,     1.30198655773242693D-04,
+     E     1.67471106699712269D-04,     1.70222587683592569D-04/
+      DATA ALFA(67), ALFA(68), ALFA(69), ALFA(70), ALFA(71), ALFA(72),
+     1     ALFA(73), ALFA(74), ALFA(75), ALFA(76), ALFA(77), ALFA(78),
+     2     ALFA(79), ALFA(80), ALFA(81), ALFA(82), ALFA(83), ALFA(84),
+     3     ALFA(85), ALFA(86), ALFA(87), ALFA(88)/
+     4     1.56501427608594704D-04,     1.36339170977445120D-04,
+     5     1.14886692029825128D-04,     9.45869093034688111D-05,
+     6     7.64498419250898258D-05,     6.07570334965197354D-05,
+     7     4.74394299290508799D-05,     3.62757512005344297D-05,
+     8     2.69939714979224901D-05,     1.93210938247939253D-05,
+     9     1.30056674793963203D-05,     7.82620866744496661D-06,
+     A     3.59257485819351583D-06,     1.44040049814251817D-07,
+     B    -2.65396769697939116D-06,    -4.91346867098485910D-06,
+     C    -6.72739296091248287D-06,    -8.17269379678657923D-06,
+     D    -9.31304715093561232D-06,    -1.02011418798016441D-05,
+     E    -1.08805962510592880D-05,    -1.13875481509603555D-05/
+      DATA ALFA(89), ALFA(90), ALFA(91), ALFA(92), ALFA(93), ALFA(94),
+     1     ALFA(95), ALFA(96), ALFA(97), ALFA(98), ALFA(99), ALFA(100),
+     2     ALFA(101), ALFA(102), ALFA(103), ALFA(104), ALFA(105),
+     3     ALFA(106), ALFA(107), ALFA(108), ALFA(109), ALFA(110)/
+     4    -1.17519675674556414D-05,    -1.19987364870944141D-05,
+     5     3.78194199201772914D-04,     2.02471952761816167D-04,
+     6    -6.37938506318862408D-05,    -2.38598230603005903D-04,
+     7    -3.10916256027361568D-04,    -3.13680115247576316D-04,
+     8    -2.78950273791323387D-04,    -2.28564082619141374D-04,
+     9    -1.75245280340846749D-04,    -1.25544063060690348D-04,
+     A    -8.22982872820208365D-05,    -4.62860730588116458D-05,
+     B    -1.72334302366962267D-05,     5.60690482304602267D-06,
+     C     2.31395443148286800D-05,     3.62642745856793957D-05,
+     D     4.58006124490188752D-05,     5.24595294959114050D-05,
+     E     5.68396208545815266D-05,     5.94349820393104052D-05/
+      DATA ALFA(111), ALFA(112), ALFA(113), ALFA(114), ALFA(115),
+     1     ALFA(116), ALFA(117), ALFA(118), ALFA(119), ALFA(120),
+     2     ALFA(121), ALFA(122), ALFA(123), ALFA(124), ALFA(125),
+     3     ALFA(126), ALFA(127), ALFA(128), ALFA(129), ALFA(130)/
+     4     6.06478527578421742D-05,     6.08023907788436497D-05,
+     5     6.01577894539460388D-05,     5.89199657344698500D-05,
+     6     5.72515823777593053D-05,     5.52804375585852577D-05,
+     7     5.31063773802880170D-05,     5.08069302012325706D-05,
+     8     4.84418647620094842D-05,     4.60568581607475370D-05,
+     9    -6.91141397288294174D-04,    -4.29976633058871912D-04,
+     A     1.83067735980039018D-04,     6.60088147542014144D-04,
+     B     8.75964969951185931D-04,     8.77335235958235514D-04,
+     C     7.49369585378990637D-04,     5.63832329756980918D-04,
+     D     3.68059319971443156D-04,     1.88464535514455599D-04/
+      DATA ALFA(131), ALFA(132), ALFA(133), ALFA(134), ALFA(135),
+     1     ALFA(136), ALFA(137), ALFA(138), ALFA(139), ALFA(140),
+     2     ALFA(141), ALFA(142), ALFA(143), ALFA(144), ALFA(145),
+     3     ALFA(146), ALFA(147), ALFA(148), ALFA(149), ALFA(150)/
+     4     3.70663057664904149D-05,    -8.28520220232137023D-05,
+     5    -1.72751952869172998D-04,    -2.36314873605872983D-04,
+     6    -2.77966150694906658D-04,    -3.02079514155456919D-04,
+     7    -3.12594712643820127D-04,    -3.12872558758067163D-04,
+     8    -3.05678038466324377D-04,    -2.93226470614557331D-04,
+     9    -2.77255655582934777D-04,    -2.59103928467031709D-04,
+     A    -2.39784014396480342D-04,    -2.20048260045422848D-04,
+     B    -2.00443911094971498D-04,    -1.81358692210970687D-04,
+     C    -1.63057674478657464D-04,    -1.45712672175205844D-04,
+     D    -1.29425421983924587D-04,    -1.14245691942445952D-04/
+      DATA ALFA(151), ALFA(152), ALFA(153), ALFA(154), ALFA(155),
+     1     ALFA(156), ALFA(157), ALFA(158), ALFA(159), ALFA(160),
+     2     ALFA(161), ALFA(162), ALFA(163), ALFA(164), ALFA(165),
+     3     ALFA(166), ALFA(167), ALFA(168), ALFA(169), ALFA(170)/
+     4     1.92821964248775885D-03,     1.35592576302022234D-03,
+     5    -7.17858090421302995D-04,    -2.58084802575270346D-03,
+     6    -3.49271130826168475D-03,    -3.46986299340960628D-03,
+     7    -2.82285233351310182D-03,    -1.88103076404891354D-03,
+     8    -8.89531718383947600D-04,     3.87912102631035228D-06,
+     9     7.28688540119691412D-04,     1.26566373053457758D-03,
+     A     1.62518158372674427D-03,     1.83203153216373172D-03,
+     B     1.91588388990527909D-03,     1.90588846755546138D-03,
+     C     1.82798982421825727D-03,     1.70389506421121530D-03,
+     D     1.55097127171097686D-03,     1.38261421852276159D-03/
+      DATA ALFA(171), ALFA(172), ALFA(173), ALFA(174), ALFA(175),
+     1     ALFA(176), ALFA(177), ALFA(178), ALFA(179), ALFA(180)/
+     2     1.20881424230064774D-03,     1.03676532638344962D-03,
+     3     8.71437918068619115D-04,     7.16080155297701002D-04,
+     4     5.72637002558129372D-04,     4.42089819465802277D-04,
+     5     3.24724948503090564D-04,     2.20342042730246599D-04,
+     6     1.28412898401353882D-04,     4.82005924552095464D-05/
+      DATA BETA(1), BETA(2), BETA(3), BETA(4), BETA(5), BETA(6),
+     1     BETA(7), BETA(8), BETA(9), BETA(10), BETA(11), BETA(12),
+     2     BETA(13), BETA(14), BETA(15), BETA(16), BETA(17), BETA(18),
+     3     BETA(19), BETA(20), BETA(21), BETA(22)/
+     4     1.79988721413553309D-02,     5.59964911064388073D-03,
+     5     2.88501402231132779D-03,     1.80096606761053941D-03,
+     6     1.24753110589199202D-03,     9.22878876572938311D-04,
+     7     7.14430421727287357D-04,     5.71787281789704872D-04,
+     8     4.69431007606481533D-04,     3.93232835462916638D-04,
+     9     3.34818889318297664D-04,     2.88952148495751517D-04,
+     A     2.52211615549573284D-04,     2.22280580798883327D-04,
+     B     1.97541838033062524D-04,     1.76836855019718004D-04,
+     C     1.59316899661821081D-04,     1.44347930197333986D-04,
+     D     1.31448068119965379D-04,     1.20245444949302884D-04,
+     E     1.10449144504599392D-04,     1.01828770740567258D-04/
+      DATA BETA(23), BETA(24), BETA(25), BETA(26), BETA(27), BETA(28),
+     1     BETA(29), BETA(30), BETA(31), BETA(32), BETA(33), BETA(34),
+     2     BETA(35), BETA(36), BETA(37), BETA(38), BETA(39), BETA(40),
+     3     BETA(41), BETA(42), BETA(43), BETA(44)/
+     4     9.41998224204237509D-05,     8.74130545753834437D-05,
+     5     8.13466262162801467D-05,     7.59002269646219339D-05,
+     6     7.09906300634153481D-05,     6.65482874842468183D-05,
+     7     6.25146958969275078D-05,     5.88403394426251749D-05,
+     8    -1.49282953213429172D-03,    -8.78204709546389328D-04,
+     9    -5.02916549572034614D-04,    -2.94822138512746025D-04,
+     A    -1.75463996970782828D-04,    -1.04008550460816434D-04,
+     B    -5.96141953046457895D-05,    -3.12038929076098340D-05,
+     C    -1.26089735980230047D-05,    -2.42892608575730389D-07,
+     D     8.05996165414273571D-06,     1.36507009262147391D-05,
+     E     1.73964125472926261D-05,     1.98672978842133780D-05/
+      DATA BETA(45), BETA(46), BETA(47), BETA(48), BETA(49), BETA(50),
+     1     BETA(51), BETA(52), BETA(53), BETA(54), BETA(55), BETA(56),
+     2     BETA(57), BETA(58), BETA(59), BETA(60), BETA(61), BETA(62),
+     3     BETA(63), BETA(64), BETA(65), BETA(66)/
+     4     2.14463263790822639D-05,     2.23954659232456514D-05,
+     5     2.28967783814712629D-05,     2.30785389811177817D-05,
+     6     2.30321976080909144D-05,     2.28236073720348722D-05,
+     7     2.25005881105292418D-05,     2.20981015361991429D-05,
+     8     2.16418427448103905D-05,     2.11507649256220843D-05,
+     9     2.06388749782170737D-05,     2.01165241997081666D-05,
+     A     1.95913450141179244D-05,     1.90689367910436740D-05,
+     B     1.85533719641636667D-05,     1.80475722259674218D-05,
+     C     5.52213076721292790D-04,     4.47932581552384646D-04,
+     D     2.79520653992020589D-04,     1.52468156198446602D-04,
+     E     6.93271105657043598D-05,     1.76258683069991397D-05/
+      DATA BETA(67), BETA(68), BETA(69), BETA(70), BETA(71), BETA(72),
+     1     BETA(73), BETA(74), BETA(75), BETA(76), BETA(77), BETA(78),
+     2     BETA(79), BETA(80), BETA(81), BETA(82), BETA(83), BETA(84),
+     3     BETA(85), BETA(86), BETA(87), BETA(88)/
+     4    -1.35744996343269136D-05,    -3.17972413350427135D-05,
+     5    -4.18861861696693365D-05,    -4.69004889379141029D-05,
+     6    -4.87665447413787352D-05,    -4.87010031186735069D-05,
+     7    -4.74755620890086638D-05,    -4.55813058138628452D-05,
+     8    -4.33309644511266036D-05,    -4.09230193157750364D-05,
+     9    -3.84822638603221274D-05,    -3.60857167535410501D-05,
+     A    -3.37793306123367417D-05,    -3.15888560772109621D-05,
+     B    -2.95269561750807315D-05,    -2.75978914828335759D-05,
+     C    -2.58006174666883713D-05,    -2.41308356761280200D-05,
+     D    -2.25823509518346033D-05,    -2.11479656768912971D-05,
+     E    -1.98200638885294927D-05,    -1.85909870801065077D-05/
+      DATA BETA(89), BETA(90), BETA(91), BETA(92), BETA(93), BETA(94),
+     1     BETA(95), BETA(96), BETA(97), BETA(98), BETA(99), BETA(100),
+     2     BETA(101), BETA(102), BETA(103), BETA(104), BETA(105),
+     3     BETA(106), BETA(107), BETA(108), BETA(109), BETA(110)/
+     4    -1.74532699844210224D-05,    -1.63997823854497997D-05,
+     5    -4.74617796559959808D-04,    -4.77864567147321487D-04,
+     6    -3.20390228067037603D-04,    -1.61105016119962282D-04,
+     7    -4.25778101285435204D-05,     3.44571294294967503D-05,
+     8     7.97092684075674924D-05,     1.03138236708272200D-04,
+     9     1.12466775262204158D-04,     1.13103642108481389D-04,
+     A     1.08651634848774268D-04,     1.01437951597661973D-04,
+     B     9.29298396593363896D-05,     8.40293133016089978D-05,
+     C     7.52727991349134062D-05,     6.69632521975730872D-05,
+     D     5.92564547323194704D-05,     5.22169308826975567D-05,
+     E     4.58539485165360646D-05,     4.01445513891486808D-05/
+      DATA BETA(111), BETA(112), BETA(113), BETA(114), BETA(115),
+     1     BETA(116), BETA(117), BETA(118), BETA(119), BETA(120),
+     2     BETA(121), BETA(122), BETA(123), BETA(124), BETA(125),
+     3     BETA(126), BETA(127), BETA(128), BETA(129), BETA(130)/
+     4     3.50481730031328081D-05,     3.05157995034346659D-05,
+     5     2.64956119950516039D-05,     2.29363633690998152D-05,
+     6     1.97893056664021636D-05,     1.70091984636412623D-05,
+     7     1.45547428261524004D-05,     1.23886640995878413D-05,
+     8     1.04775876076583236D-05,     8.79179954978479373D-06,
+     9     7.36465810572578444D-04,     8.72790805146193976D-04,
+     A     6.22614862573135066D-04,     2.85998154194304147D-04,
+     B     3.84737672879366102D-06,    -1.87906003636971558D-04,
+     C    -2.97603646594554535D-04,    -3.45998126832656348D-04,
+     D    -3.53382470916037712D-04,    -3.35715635775048757D-04/
+      DATA BETA(131), BETA(132), BETA(133), BETA(134), BETA(135),
+     1     BETA(136), BETA(137), BETA(138), BETA(139), BETA(140),
+     2     BETA(141), BETA(142), BETA(143), BETA(144), BETA(145),
+     3     BETA(146), BETA(147), BETA(148), BETA(149), BETA(150)/
+     4    -3.04321124789039809D-04,    -2.66722723047612821D-04,
+     5    -2.27654214122819527D-04,    -1.89922611854562356D-04,
+     6    -1.55058918599093870D-04,    -1.23778240761873630D-04,
+     7    -9.62926147717644187D-05,    -7.25178327714425337D-05,
+     8    -5.22070028895633801D-05,    -3.50347750511900522D-05,
+     9    -2.06489761035551757D-05,    -8.70106096849767054D-06,
+     A     1.13698686675100290D-06,     9.16426474122778849D-06,
+     B     1.56477785428872620D-05,     2.08223629482466847D-05,
+     C     2.48923381004595156D-05,     2.80340509574146325D-05,
+     D     3.03987774629861915D-05,     3.21156731406700616D-05/
+      DATA BETA(151), BETA(152), BETA(153), BETA(154), BETA(155),
+     1     BETA(156), BETA(157), BETA(158), BETA(159), BETA(160),
+     2     BETA(161), BETA(162), BETA(163), BETA(164), BETA(165),
+     3     BETA(166), BETA(167), BETA(168), BETA(169), BETA(170)/
+     4    -1.80182191963885708D-03,    -2.43402962938042533D-03,
+     5    -1.83422663549856802D-03,    -7.62204596354009765D-04,
+     6     2.39079475256927218D-04,     9.49266117176881141D-04,
+     7     1.34467449701540359D-03,     1.48457495259449178D-03,
+     8     1.44732339830617591D-03,     1.30268261285657186D-03,
+     9     1.10351597375642682D-03,     8.86047440419791759D-04,
+     A     6.73073208165665473D-04,     4.77603872856582378D-04,
+     B     3.05991926358789362D-04,     1.60315694594721630D-04,
+     C     4.00749555270613286D-05,    -5.66607461635251611D-05,
+     D    -1.32506186772982638D-04,    -1.90296187989614057D-04/
+      DATA BETA(171), BETA(172), BETA(173), BETA(174), BETA(175),
+     1     BETA(176), BETA(177), BETA(178), BETA(179), BETA(180),
+     2     BETA(181), BETA(182), BETA(183), BETA(184), BETA(185),
+     3     BETA(186), BETA(187), BETA(188), BETA(189), BETA(190)/
+     4    -2.32811450376937408D-04,    -2.62628811464668841D-04,
+     5    -2.82050469867598672D-04,    -2.93081563192861167D-04,
+     6    -2.97435962176316616D-04,    -2.96557334239348078D-04,
+     7    -2.91647363312090861D-04,    -2.83696203837734166D-04,
+     8    -2.73512317095673346D-04,    -2.61750155806768580D-04,
+     9     6.38585891212050914D-03,     9.62374215806377941D-03,
+     A     7.61878061207001043D-03,     2.83219055545628054D-03,
+     B    -2.09841352012720090D-03,    -5.73826764216626498D-03,
+     C    -7.70804244495414620D-03,    -8.21011692264844401D-03,
+     D    -7.65824520346905413D-03,    -6.47209729391045177D-03/
+      DATA BETA(191), BETA(192), BETA(193), BETA(194), BETA(195),
+     1     BETA(196), BETA(197), BETA(198), BETA(199), BETA(200),
+     2     BETA(201), BETA(202), BETA(203), BETA(204), BETA(205),
+     3     BETA(206), BETA(207), BETA(208), BETA(209), BETA(210)/
+     4    -4.99132412004966473D-03,    -3.45612289713133280D-03,
+     5    -2.01785580014170775D-03,    -7.59430686781961401D-04,
+     6     2.84173631523859138D-04,     1.10891667586337403D-03,
+     7     1.72901493872728771D-03,     2.16812590802684701D-03,
+     8     2.45357710494539735D-03,     2.61281821058334862D-03,
+     9     2.67141039656276912D-03,     2.65203073395980430D-03,
+     A     2.57411652877287315D-03,     2.45389126236094427D-03,
+     B     2.30460058071795494D-03,     2.13684837686712662D-03,
+     C     1.95896528478870911D-03,     1.77737008679454412D-03,
+     D     1.59690280765839059D-03,     1.42111975664438546D-03/
+      DATA GAMA(1), GAMA(2), GAMA(3), GAMA(4), GAMA(5), GAMA(6),
+     1     GAMA(7), GAMA(8), GAMA(9), GAMA(10), GAMA(11), GAMA(12),
+     2     GAMA(13), GAMA(14), GAMA(15), GAMA(16), GAMA(17), GAMA(18),
+     3     GAMA(19), GAMA(20), GAMA(21), GAMA(22)/
+     4     6.29960524947436582D-01,     2.51984209978974633D-01,
+     5     1.54790300415655846D-01,     1.10713062416159013D-01,
+     6     8.57309395527394825D-02,     6.97161316958684292D-02,
+     7     5.86085671893713576D-02,     5.04698873536310685D-02,
+     8     4.42600580689154809D-02,     3.93720661543509966D-02,
+     9     3.54283195924455368D-02,     3.21818857502098231D-02,
+     A     2.94646240791157679D-02,     2.71581677112934479D-02,
+     B     2.51768272973861779D-02,     2.34570755306078891D-02,
+     C     2.19508390134907203D-02,     2.06210828235646240D-02,
+     D     1.94388240897880846D-02,     1.83810633800683158D-02,
+     E     1.74293213231963172D-02,     1.65685837786612353D-02/
+      DATA GAMA(23), GAMA(24), GAMA(25), GAMA(26), GAMA(27), GAMA(28),
+     1     GAMA(29), GAMA(30)/
+     2     1.57865285987918445D-02,     1.50729501494095594D-02,
+     3     1.44193250839954639D-02,     1.38184805735341786D-02,
+     4     1.32643378994276568D-02,     1.27517121970498651D-02,
+     5     1.22761545318762767D-02,     1.18338262398482403D-02/
+      DATA EX1, EX2, HPI, GPI, THPI /
+     1     3.33333333333333333D-01,     6.66666666666666667D-01,
+     2     1.57079632679489662D+00,     3.14159265358979324D+00,
+     3     4.71238898038468986D+00/
+      DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 /
+C
+      RFNU = 1.0D0/FNU
+C-----------------------------------------------------------------------
+C     OVERFLOW TEST (Z/FNU TOO SMALL)
+C-----------------------------------------------------------------------
+      TEST = D1MACH(1)*1.0D+3
+      AC = FNU*TEST
+      IF (DABS(ZR).GT.AC .OR. DABS(ZI).GT.AC) GO TO 15
+      ZETA1R = 2.0D0*DABS(DLOG(TEST))+FNU
+      ZETA1I = 0.0D0
+      ZETA2R = FNU
+      ZETA2I = 0.0D0
+      PHIR = 1.0D0
+      PHII = 0.0D0
+      ARGR = 1.0D0
+      ARGI = 0.0D0
+      RETURN
+   15 CONTINUE
+      ZBR = ZR*RFNU
+      ZBI = ZI*RFNU
+      RFNU2 = RFNU*RFNU
+C-----------------------------------------------------------------------
+C     COMPUTE IN THE FOURTH QUADRANT
+C-----------------------------------------------------------------------
+      FN13 = FNU**EX1
+      FN23 = FN13*FN13
+      RFN13 = 1.0D0/FN13
+      W2R = CONER - ZBR*ZBR + ZBI*ZBI
+      W2I = CONEI - ZBR*ZBI - ZBR*ZBI
+      AW2 = ZABS(CMPLX(W2R,W2I,kind=KIND(1.0D0)))
+      IF (AW2.GT.0.25D0) GO TO 130
+C-----------------------------------------------------------------------
+C     POWER SERIES FOR CABS(W2).LE.0.25D0
+C-----------------------------------------------------------------------
+      K = 1
+      PR(1) = CONER
+      PI(1) = CONEI
+      SUMAR = GAMA(1)
+      SUMAI = ZEROI
+      AP(1) = 1.0D0
+      IF (AW2.LT.TOL) GO TO 20
+      DO 10 K=2,30
+        PR(K) = PR(K-1)*W2R - PI(K-1)*W2I
+        PI(K) = PR(K-1)*W2I + PI(K-1)*W2R
+        SUMAR = SUMAR + PR(K)*GAMA(K)
+        SUMAI = SUMAI + PI(K)*GAMA(K)
+        AP(K) = AP(K-1)*AW2
+        IF (AP(K).LT.TOL) GO TO 20
+   10 CONTINUE
+      K = 30
+   20 CONTINUE
+      KMAX = K
+      ZETAR = W2R*SUMAR - W2I*SUMAI
+      ZETAI = W2R*SUMAI + W2I*SUMAR
+      ARGR = ZETAR*FN23
+      ARGI = ZETAI*FN23
+      CALL ZSQRT(SUMAR, SUMAI, ZAR, ZAI)
+      CALL ZSQRT(W2R, W2I, STR, STI)
+      ZETA2R = STR*FNU
+      ZETA2I = STI*FNU
+      STR = CONER + EX2*(ZETAR*ZAR-ZETAI*ZAI)
+      STI = CONEI + EX2*(ZETAR*ZAI+ZETAI*ZAR)
+      ZETA1R = STR*ZETA2R - STI*ZETA2I
+      ZETA1I = STR*ZETA2I + STI*ZETA2R
+      ZAR = ZAR + ZAR
+      ZAI = ZAI + ZAI
+      CALL ZSQRT(ZAR, ZAI, STR, STI)
+      PHIR = STR*RFN13
+      PHII = STI*RFN13
+      IF (IPMTR.EQ.1) GO TO 120
+C-----------------------------------------------------------------------
+C     SUM SERIES FOR ASUM AND BSUM
+C-----------------------------------------------------------------------
+      SUMBR = ZEROR
+      SUMBI = ZEROI
+      DO 30 K=1,KMAX
+        SUMBR = SUMBR + PR(K)*BETA(K)
+        SUMBI = SUMBI + PI(K)*BETA(K)
+   30 CONTINUE
+      ASUMR = ZEROR
+      ASUMI = ZEROI
+      BSUMR = SUMBR
+      BSUMI = SUMBI
+      L1 = 0
+      L2 = 30
+      BTOL = TOL*(DABS(BSUMR)+DABS(BSUMI))
+      ATOL = TOL
+      PP = 1.0D0
+      IAS = 0
+      IBS = 0
+      IF (RFNU2.LT.TOL) GO TO 110
+      DO 100 IS=2,7
+        ATOL = ATOL/RFNU2
+        PP = PP*RFNU2
+        IF (IAS.EQ.1) GO TO 60
+        SUMAR = ZEROR
+        SUMAI = ZEROI
+        DO 40 K=1,KMAX
+          M = L1 + K
+          SUMAR = SUMAR + PR(K)*ALFA(M)
+          SUMAI = SUMAI + PI(K)*ALFA(M)
+          IF (AP(K).LT.ATOL) GO TO 50
+   40   CONTINUE
+   50   CONTINUE
+        ASUMR = ASUMR + SUMAR*PP
+        ASUMI = ASUMI + SUMAI*PP
+        IF (PP.LT.TOL) IAS = 1
+   60   CONTINUE
+        IF (IBS.EQ.1) GO TO 90
+        SUMBR = ZEROR
+        SUMBI = ZEROI
+        DO 70 K=1,KMAX
+          M = L2 + K
+          SUMBR = SUMBR + PR(K)*BETA(M)
+          SUMBI = SUMBI + PI(K)*BETA(M)
+          IF (AP(K).LT.ATOL) GO TO 80
+   70   CONTINUE
+   80   CONTINUE
+        BSUMR = BSUMR + SUMBR*PP
+        BSUMI = BSUMI + SUMBI*PP
+        IF (PP.LT.BTOL) IBS = 1
+   90   CONTINUE
+        IF (IAS.EQ.1 .AND. IBS.EQ.1) GO TO 110
+        L1 = L1 + 30
+        L2 = L2 + 30
+  100 CONTINUE
+  110 CONTINUE
+      ASUMR = ASUMR + CONER
+      PP = RFNU*RFN13
+      BSUMR = BSUMR*PP
+      BSUMI = BSUMI*PP
+  120 CONTINUE
+      RETURN
+C-----------------------------------------------------------------------
+C     CABS(W2).GT.0.25D0
+C-----------------------------------------------------------------------
+  130 CONTINUE
+      CALL ZSQRT(W2R, W2I, WR, WI)
+      IF (WR.LT.0.0D0) WR = 0.0D0
+      IF (WI.LT.0.0D0) WI = 0.0D0
+      STR = CONER + WR
+      STI = WI
+      CALL ZDIV(STR, STI, ZBR, ZBI, ZAR, ZAI)
+      CALL ZLOG(ZAR, ZAI, ZCR, ZCI, IDUM)
+      IF (ZCI.LT.0.0D0) ZCI = 0.0D0
+      IF (ZCI.GT.HPI) ZCI = HPI
+      IF (ZCR.LT.0.0D0) ZCR = 0.0D0
+      ZTHR = (ZCR-WR)*1.5D0
+      ZTHI = (ZCI-WI)*1.5D0
+      ZETA1R = ZCR*FNU
+      ZETA1I = ZCI*FNU
+      ZETA2R = WR*FNU
+      ZETA2I = WI*FNU
+      AZTH = ZABS(CMPLX(ZTHR,ZTHI,kind=KIND(1.0D0)))
+      ANG = THPI
+      IF (ZTHR.GE.0.0D0 .AND. ZTHI.LT.0.0D0) GO TO 140
+      ANG = HPI
+      IF (ZTHR.EQ.0.0D0) GO TO 140
+      ANG = DATAN(ZTHI/ZTHR)
+      IF (ZTHR.LT.0.0D0) ANG = ANG + GPI
+  140 CONTINUE
+      PP = AZTH**EX2
+      ANG = ANG*EX2
+      ZETAR = PP*DCOS(ANG)
+      ZETAI = PP*DSIN(ANG)
+      IF (ZETAI.LT.0.0D0) ZETAI = 0.0D0
+      ARGR = ZETAR*FN23
+      ARGI = ZETAI*FN23
+      CALL ZDIV(ZTHR, ZTHI, ZETAR, ZETAI, RTZTR, RTZTI)
+      CALL ZDIV(RTZTR, RTZTI, WR, WI, ZAR, ZAI)
+      TZAR = ZAR + ZAR
+      TZAI = ZAI + ZAI
+      CALL ZSQRT(TZAR, TZAI, STR, STI)
+      PHIR = STR*RFN13
+      PHII = STI*RFN13
+      IF (IPMTR.EQ.1) GO TO 120
+      RAW = 1.0D0/DSQRT(AW2)
+      STR = WR*RAW
+      STI = -WI*RAW
+      TFNR = STR*RFNU*RAW
+      TFNI = STI*RFNU*RAW
+      RAZTH = 1.0D0/AZTH
+      STR = ZTHR*RAZTH
+      STI = -ZTHI*RAZTH
+      RZTHR = STR*RAZTH*RFNU
+      RZTHI = STI*RAZTH*RFNU
+      ZCR = RZTHR*AR(2)
+      ZCI = RZTHI*AR(2)
+      RAW2 = 1.0D0/AW2
+      STR = W2R*RAW2
+      STI = -W2I*RAW2
+      T2R = STR*RAW2
+      T2I = STI*RAW2
+      STR = T2R*C(2) + C(3)
+      STI = T2I*C(2)
+      UPR(2) = STR*TFNR - STI*TFNI
+      UPI(2) = STR*TFNI + STI*TFNR
+      BSUMR = UPR(2) + ZCR
+      BSUMI = UPI(2) + ZCI
+      ASUMR = ZEROR
+      ASUMI = ZEROI
+      IF (RFNU.LT.TOL) GO TO 220
+      PRZTHR = RZTHR
+      PRZTHI = RZTHI
+      PTFNR = TFNR
+      PTFNI = TFNI
+      UPR(1) = CONER
+      UPI(1) = CONEI
+      PP = 1.0D0
+      BTOL = TOL*(DABS(BSUMR)+DABS(BSUMI))
+      KS = 0
+      KP1 = 2
+      L = 3
+      IAS = 0
+      IBS = 0
+      DO 210 LR=2,12,2
+        LRP1 = LR + 1
+C-----------------------------------------------------------------------
+C     COMPUTE TWO ADDITIONAL CR, DR, AND UP FOR TWO MORE TERMS IN
+C     NEXT SUMA AND SUMB
+C-----------------------------------------------------------------------
+        DO 160 K=LR,LRP1
+          KS = KS + 1
+          KP1 = KP1 + 1
+          L = L + 1
+          ZAR = C(L)
+          ZAI = ZEROI
+          DO 150 J=2,KP1
+            L = L + 1
+            STR = ZAR*T2R - T2I*ZAI + C(L)
+            ZAI = ZAR*T2I + ZAI*T2R
+            ZAR = STR
+  150     CONTINUE
+          STR = PTFNR*TFNR - PTFNI*TFNI
+          PTFNI = PTFNR*TFNI + PTFNI*TFNR
+          PTFNR = STR
+          UPR(KP1) = PTFNR*ZAR - PTFNI*ZAI
+          UPI(KP1) = PTFNI*ZAR + PTFNR*ZAI
+          CRR(KS) = PRZTHR*BR(KS+1)
+          CRI(KS) = PRZTHI*BR(KS+1)
+          STR = PRZTHR*RZTHR - PRZTHI*RZTHI
+          PRZTHI = PRZTHR*RZTHI + PRZTHI*RZTHR
+          PRZTHR = STR
+          DRR(KS) = PRZTHR*AR(KS+2)
+          DRI(KS) = PRZTHI*AR(KS+2)
+  160   CONTINUE
+        PP = PP*RFNU2
+        IF (IAS.EQ.1) GO TO 180
+        SUMAR = UPR(LRP1)
+        SUMAI = UPI(LRP1)
+        JU = LRP1
+        DO 170 JR=1,LR
+          JU = JU - 1
+          SUMAR = SUMAR + CRR(JR)*UPR(JU) - CRI(JR)*UPI(JU)
+          SUMAI = SUMAI + CRR(JR)*UPI(JU) + CRI(JR)*UPR(JU)
+  170   CONTINUE
+        ASUMR = ASUMR + SUMAR
+        ASUMI = ASUMI + SUMAI
+        TEST = DABS(SUMAR) + DABS(SUMAI)
+        IF (PP.LT.TOL .AND. TEST.LT.TOL) IAS = 1
+  180   CONTINUE
+        IF (IBS.EQ.1) GO TO 200
+        SUMBR = UPR(LR+2) + UPR(LRP1)*ZCR - UPI(LRP1)*ZCI
+        SUMBI = UPI(LR+2) + UPR(LRP1)*ZCI + UPI(LRP1)*ZCR
+        JU = LRP1
+        DO 190 JR=1,LR
+          JU = JU - 1
+          SUMBR = SUMBR + DRR(JR)*UPR(JU) - DRI(JR)*UPI(JU)
+          SUMBI = SUMBI + DRR(JR)*UPI(JU) + DRI(JR)*UPR(JU)
+  190   CONTINUE
+        BSUMR = BSUMR + SUMBR
+        BSUMI = BSUMI + SUMBI
+        TEST = DABS(SUMBR) + DABS(SUMBI)
+        IF (PP.LT.BTOL .AND. TEST.LT.BTOL) IBS = 1
+  200   CONTINUE
+        IF (IAS.EQ.1 .AND. IBS.EQ.1) GO TO 220
+  210 CONTINUE
+  220 CONTINUE
+      ASUMR = ASUMR + CONER
+      STR = -BSUMR*RFN13
+      STI = -BSUMI*RFN13
+      CALL ZDIV(STR, STI, RTZTR, RTZTI, BSUMR, BSUMI)
+      GO TO 120
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zuni1.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zuni1.f
new file mode 100644
index 00000000..f3a0f246
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zuni1.f
@@ -0,0 +1,204 @@
+      SUBROUTINE ZUNI1(ZR, ZI, FNU, KODE, N, YR, YI, NZ, NLAST, FNUL,
+     * TOL, ELIM, ALIM)
+C***BEGIN PROLOGUE  ZUNI1
+C***REFER TO  ZBESI,ZBESK
+C
+C     ZUNI1 COMPUTES I(FNU,Z)  BY MEANS OF THE UNIFORM ASYMPTOTIC
+C     EXPANSION FOR I(FNU,Z) IN -PI/3.LE.ARG Z.LE.PI/3.
+C
+C     FNUL IS THE SMALLEST ORDER PERMITTED FOR THE ASYMPTOTIC
+C     EXPANSION. NLAST=0 MEANS ALL OF THE Y VALUES WERE SET.
+C     NLAST.NE.0 IS THE NUMBER LEFT TO BE COMPUTED BY ANOTHER
+C     FORMULA FOR ORDERS FNU TO FNU+NLAST-1 BECAUSE FNU+NLAST-1.LT.FNUL.
+C     Y(I)=CZERO FOR I=NLAST+1,N
+C
+C***ROUTINES CALLED  ZUCHK,ZUNIK,ZUOIK,D1MACH,ZABS
+C***END PROLOGUE  ZUNI1
+C     COMPLEX CFN,CONE,CRSC,CSCL,CSR,CSS,CWRK,CZERO,C1,C2,PHI,RZ,SUM,S1,
+C    *S2,Y,Z,ZETA1,ZETA2
+      DOUBLE PRECISION ALIM, APHI, ASCLE, BRY, CONER, CRSC,
+     * CSCL, CSRR, CSSR, CWRKI, CWRKR, C1R, C2I, C2M, C2R, ELIM, FN,
+     * FNU, FNUL, PHII, PHIR, RAST, RS1, RZI, RZR, STI, STR, SUMI,
+     * SUMR, S1I, S1R, S2I, S2R, TOL, YI, YR, ZEROI, ZEROR, ZETA1I,
+     * ZETA1R, ZETA2I, ZETA2R, ZI, ZR, CYR, CYI, D1MACH, ZABS
+      INTEGER I, IFLAG, INIT, K, KODE, M, N, ND, NLAST, NN, NUF, NW, NZ
+      DIMENSION BRY(3), YR(N), YI(N), CWRKR(16), CWRKI(16), CSSR(3),
+     * CSRR(3), CYR(2), CYI(2)
+      DATA ZEROR,ZEROI,CONER / 0.0D0, 0.0D0, 1.0D0 /
+C
+      NZ = 0
+      ND = N
+      NLAST = 0
+C-----------------------------------------------------------------------
+C     COMPUTED VALUES WITH EXPONENTS BETWEEN ALIM AND ELIM IN MAG-
+C     NITUDE ARE SCALED TO KEEP INTERMEDIATE ARITHMETIC ON SCALE,
+C     EXP(ALIM)=EXP(ELIM)*TOL
+C-----------------------------------------------------------------------
+      CSCL = 1.0D0/TOL
+      CRSC = TOL
+      CSSR(1) = CSCL
+      CSSR(2) = CONER
+      CSSR(3) = CRSC
+      CSRR(1) = CRSC
+      CSRR(2) = CONER
+      CSRR(3) = CSCL
+      BRY(1) = 1.0D+3*D1MACH(1)/TOL
+C-----------------------------------------------------------------------
+C     CHECK FOR UNDERFLOW AND OVERFLOW ON FIRST MEMBER
+C-----------------------------------------------------------------------
+      FN = DMAX1(FNU,1.0D0)
+      INIT = 0
+      CALL ZUNIK(ZR, ZI, FN, 1, 1, TOL, INIT, PHIR, PHII, ZETA1R,
+     * ZETA1I, ZETA2R, ZETA2I, SUMR, SUMI, CWRKR, CWRKI)
+      IF (KODE.EQ.1) GO TO 10
+      STR = ZR + ZETA2R
+      STI = ZI + ZETA2I
+      RAST = FN/ZABS(CMPLX(STR,STI,kind=KIND(1.0D0)))
+      STR = STR*RAST*RAST
+      STI = -STI*RAST*RAST
+      S1R = -ZETA1R + STR
+      S1I = -ZETA1I + STI
+      GO TO 20
+   10 CONTINUE
+      S1R = -ZETA1R + ZETA2R
+      S1I = -ZETA1I + ZETA2I
+   20 CONTINUE
+      RS1 = S1R
+      IF (DABS(RS1).GT.ELIM) GO TO 130
+   30 CONTINUE
+      NN = MIN0(2,ND)
+      DO 80 I=1,NN
+        FN = FNU + DBLE(FLOAT(ND-I))
+        INIT = 0
+        CALL ZUNIK(ZR, ZI, FN, 1, 0, TOL, INIT, PHIR, PHII, ZETA1R,
+     *   ZETA1I, ZETA2R, ZETA2I, SUMR, SUMI, CWRKR, CWRKI)
+        IF (KODE.EQ.1) GO TO 40
+        STR = ZR + ZETA2R
+        STI = ZI + ZETA2I
+        RAST = FN/ZABS(CMPLX(STR,STI,kind=KIND(1.0D0)))
+        STR = STR*RAST*RAST
+        STI = -STI*RAST*RAST
+        S1R = -ZETA1R + STR
+        S1I = -ZETA1I + STI + ZI
+        GO TO 50
+   40   CONTINUE
+        S1R = -ZETA1R + ZETA2R
+        S1I = -ZETA1I + ZETA2I
+   50   CONTINUE
+C-----------------------------------------------------------------------
+C     TEST FOR UNDERFLOW AND OVERFLOW
+C-----------------------------------------------------------------------
+        RS1 = S1R
+        IF (DABS(RS1).GT.ELIM) GO TO 110
+        IF (I.EQ.1) IFLAG = 2
+        IF (DABS(RS1).LT.ALIM) GO TO 60
+C-----------------------------------------------------------------------
+C     REFINE  TEST AND SCALE
+C-----------------------------------------------------------------------
+        APHI = ZABS(CMPLX(PHIR,PHII,kind=KIND(1.0D0)))
+        RS1 = RS1 + DLOG(APHI)
+        IF (DABS(RS1).GT.ELIM) GO TO 110
+        IF (I.EQ.1) IFLAG = 1
+        IF (RS1.LT.0.0D0) GO TO 60
+        IF (I.EQ.1) IFLAG = 3
+   60   CONTINUE
+C-----------------------------------------------------------------------
+C     SCALE S1 IF CABS(S1).LT.ASCLE
+C-----------------------------------------------------------------------
+        S2R = PHIR*SUMR - PHII*SUMI
+        S2I = PHIR*SUMI + PHII*SUMR
+        STR = DEXP(S1R)*CSSR(IFLAG)
+        S1R = STR*DCOS(S1I)
+        S1I = STR*DSIN(S1I)
+        STR = S2R*S1R - S2I*S1I
+        S2I = S2R*S1I + S2I*S1R
+        S2R = STR
+        IF (IFLAG.NE.1) GO TO 70
+        CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL)
+        IF (NW.NE.0) GO TO 110
+   70   CONTINUE
+        CYR(I) = S2R
+        CYI(I) = S2I
+        M = ND - I + 1
+        YR(M) = S2R*CSRR(IFLAG)
+        YI(M) = S2I*CSRR(IFLAG)
+   80 CONTINUE
+      IF (ND.LE.2) GO TO 100
+      RAST = 1.0D0/ZABS(CMPLX(ZR,ZI,kind=KIND(1.0D0)))
+      STR = ZR*RAST
+      STI = -ZI*RAST
+      RZR = (STR+STR)*RAST
+      RZI = (STI+STI)*RAST
+      BRY(2) = 1.0D0/BRY(1)
+      BRY(3) = D1MACH(2)
+      S1R = CYR(1)
+      S1I = CYI(1)
+      S2R = CYR(2)
+      S2I = CYI(2)
+      C1R = CSRR(IFLAG)
+      ASCLE = BRY(IFLAG)
+      K = ND - 2
+      FN = DBLE(FLOAT(K))
+      DO 90 I=3,ND
+        C2R = S2R
+        C2I = S2I
+        S2R = S1R + (FNU+FN)*(RZR*C2R-RZI*C2I)
+        S2I = S1I + (FNU+FN)*(RZR*C2I+RZI*C2R)
+        S1R = C2R
+        S1I = C2I
+        C2R = S2R*C1R
+        C2I = S2I*C1R
+        YR(K) = C2R
+        YI(K) = C2I
+        K = K - 1
+        FN = FN - 1.0D0
+        IF (IFLAG.GE.3) GO TO 90
+        STR = DABS(C2R)
+        STI = DABS(C2I)
+        C2M = DMAX1(STR,STI)
+        IF (C2M.LE.ASCLE) GO TO 90
+        IFLAG = IFLAG + 1
+        ASCLE = BRY(IFLAG)
+        S1R = S1R*C1R
+        S1I = S1I*C1R
+        S2R = C2R
+        S2I = C2I
+        S1R = S1R*CSSR(IFLAG)
+        S1I = S1I*CSSR(IFLAG)
+        S2R = S2R*CSSR(IFLAG)
+        S2I = S2I*CSSR(IFLAG)
+        C1R = CSRR(IFLAG)
+   90 CONTINUE
+  100 CONTINUE
+      RETURN
+C-----------------------------------------------------------------------
+C     SET UNDERFLOW AND UPDATE PARAMETERS
+C-----------------------------------------------------------------------
+  110 CONTINUE
+      IF (RS1.GT.0.0D0) GO TO 120
+      YR(ND) = ZEROR
+      YI(ND) = ZEROI
+      NZ = NZ + 1
+      ND = ND - 1
+      IF (ND.EQ.0) GO TO 100
+      CALL ZUOIK(ZR, ZI, FNU, KODE, 1, ND, YR, YI, NUF, TOL, ELIM, ALIM)
+      IF (NUF.LT.0) GO TO 120
+      ND = ND - NUF
+      NZ = NZ + NUF
+      IF (ND.EQ.0) GO TO 100
+      FN = FNU + DBLE(FLOAT(ND-1))
+      IF (FN.GE.FNUL) GO TO 30
+      NLAST = ND
+      RETURN
+  120 CONTINUE
+      NZ = -1
+      RETURN
+  130 CONTINUE
+      IF (RS1.GT.0.0D0) GO TO 120
+      NZ = N
+      DO 140 I=1,N
+        YR(I) = ZEROR
+        YI(I) = ZEROI
+  140 CONTINUE
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zuni2.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zuni2.f
new file mode 100644
index 00000000..9e5cfcdd
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zuni2.f
@@ -0,0 +1,267 @@
+      SUBROUTINE ZUNI2(ZR, ZI, FNU, KODE, N, YR, YI, NZ, NLAST, FNUL,
+     * TOL, ELIM, ALIM)
+C***BEGIN PROLOGUE  ZUNI2
+C***REFER TO  ZBESI,ZBESK
+C
+C     ZUNI2 COMPUTES I(FNU,Z) IN THE RIGHT HALF PLANE BY MEANS OF
+C     UNIFORM ASYMPTOTIC EXPANSION FOR J(FNU,ZN) WHERE ZN IS Z*I
+C     OR -Z*I AND ZN IS IN THE RIGHT HALF PLANE ALSO.
+C
+C     FNUL IS THE SMALLEST ORDER PERMITTED FOR THE ASYMPTOTIC
+C     EXPANSION. NLAST=0 MEANS ALL OF THE Y VALUES WERE SET.
+C     NLAST.NE.0 IS THE NUMBER LEFT TO BE COMPUTED BY ANOTHER
+C     FORMULA FOR ORDERS FNU TO FNU+NLAST-1 BECAUSE FNU+NLAST-1.LT.FNUL.
+C     Y(I)=CZERO FOR I=NLAST+1,N
+C
+C***ROUTINES CALLED  ZAIRY,ZUCHK,ZUNHJ,ZUOIK,D1MACH,ZABS
+C***END PROLOGUE  ZUNI2
+C     COMPLEX AI,ARG,ASUM,BSUM,CFN,CI,CID,CIP,CONE,CRSC,CSCL,CSR,CSS,
+C    *CZERO,C1,C2,DAI,PHI,RZ,S1,S2,Y,Z,ZB,ZETA1,ZETA2,ZN
+      DOUBLE PRECISION AARG, AIC, AII, AIR, ALIM, ANG, APHI, ARGI,
+     * ARGR, ASCLE, ASUMI, ASUMR, BRY, BSUMI, BSUMR, CIDI, CIPI, CIPR,
+     * CONER, CRSC, CSCL, CSRR, CSSR, C1R, C2I, C2M, C2R, DAII,
+     * DAIR, ELIM, FN, FNU, FNUL, HPI, PHII, PHIR, RAST, RAZ, RS1, RZI,
+     * RZR, STI, STR, S1I, S1R, S2I, S2R, TOL, YI, YR, ZBI, ZBR, ZEROI,
+     * ZEROR, ZETA1I, ZETA1R, ZETA2I, ZETA2R, ZI, ZNI, ZNR, ZR, CYR,
+     * CYI, D1MACH, ZABS, CAR, SAR
+      INTEGER I, IFLAG, IN, INU, J, K, KODE, N, NAI, ND, NDAI, NLAST,
+     * NN, NUF, NW, NZ, IDUM
+      DIMENSION BRY(3), YR(N), YI(N), CIPR(4), CIPI(4), CSSR(3),
+     * CSRR(3), CYR(2), CYI(2)
+      DATA ZEROR,ZEROI,CONER / 0.0D0, 0.0D0, 1.0D0 /
+      DATA CIPR(1),CIPI(1),CIPR(2),CIPI(2),CIPR(3),CIPI(3),CIPR(4),
+     * CIPI(4)/ 1.0D0,0.0D0, 0.0D0,1.0D0, -1.0D0,0.0D0, 0.0D0,-1.0D0/
+      DATA HPI, AIC  /
+     1      1.57079632679489662D+00,     1.265512123484645396D+00/
+C
+      NZ = 0
+      ND = N
+      NLAST = 0
+C-----------------------------------------------------------------------
+C     COMPUTED VALUES WITH EXPONENTS BETWEEN ALIM AND ELIM IN MAG-
+C     NITUDE ARE SCALED TO KEEP INTERMEDIATE ARITHMETIC ON SCALE,
+C     EXP(ALIM)=EXP(ELIM)*TOL
+C-----------------------------------------------------------------------
+      CSCL = 1.0D0/TOL
+      CRSC = TOL
+      CSSR(1) = CSCL
+      CSSR(2) = CONER
+      CSSR(3) = CRSC
+      CSRR(1) = CRSC
+      CSRR(2) = CONER
+      CSRR(3) = CSCL
+      BRY(1) = 1.0D+3*D1MACH(1)/TOL
+C-----------------------------------------------------------------------
+C     ZN IS IN THE RIGHT HALF PLANE AFTER ROTATION BY CI OR -CI
+C-----------------------------------------------------------------------
+      ZNR = ZI
+      ZNI = -ZR
+      ZBR = ZR
+      ZBI = ZI
+      CIDI = -CONER
+      INU = INT(SNGL(FNU))
+      ANG = HPI*(FNU-DBLE(FLOAT(INU)))
+      C2R = DCOS(ANG)
+      C2I = DSIN(ANG)
+      CAR = C2R
+      SAR = C2I
+      IN = INU + N - 1
+      IN = MOD(IN,4) + 1
+      STR = C2R*CIPR(IN) - C2I*CIPI(IN)
+      C2I = C2R*CIPI(IN) + C2I*CIPR(IN)
+      C2R = STR
+      IF (ZI.GT.0.0D0) GO TO 10
+      ZNR = -ZNR
+      ZBI = -ZBI
+      CIDI = -CIDI
+      C2I = -C2I
+   10 CONTINUE
+C-----------------------------------------------------------------------
+C     CHECK FOR UNDERFLOW AND OVERFLOW ON FIRST MEMBER
+C-----------------------------------------------------------------------
+      FN = DMAX1(FNU,1.0D0)
+      CALL ZUNHJ(ZNR, ZNI, FN, 1, TOL, PHIR, PHII, ARGR, ARGI, ZETA1R,
+     * ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI)
+      IF (KODE.EQ.1) GO TO 20
+      STR = ZBR + ZETA2R
+      STI = ZBI + ZETA2I
+      RAST = FN/ZABS(CMPLX(STR,STI,kind=KIND(1.0D0)))
+      STR = STR*RAST*RAST
+      STI = -STI*RAST*RAST
+      S1R = -ZETA1R + STR
+      S1I = -ZETA1I + STI
+      GO TO 30
+   20 CONTINUE
+      S1R = -ZETA1R + ZETA2R
+      S1I = -ZETA1I + ZETA2I
+   30 CONTINUE
+      RS1 = S1R
+      IF (DABS(RS1).GT.ELIM) GO TO 150
+   40 CONTINUE
+      NN = MIN0(2,ND)
+      DO 90 I=1,NN
+        FN = FNU + DBLE(FLOAT(ND-I))
+        CALL ZUNHJ(ZNR, ZNI, FN, 0, TOL, PHIR, PHII, ARGR, ARGI,
+     *   ZETA1R, ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI)
+        IF (KODE.EQ.1) GO TO 50
+        STR = ZBR + ZETA2R
+        STI = ZBI + ZETA2I
+        RAST = FN/ZABS(CMPLX(STR,STI,kind=KIND(1.0D0)))
+        STR = STR*RAST*RAST
+        STI = -STI*RAST*RAST
+        S1R = -ZETA1R + STR
+        S1I = -ZETA1I + STI + DABS(ZI)
+        GO TO 60
+   50   CONTINUE
+        S1R = -ZETA1R + ZETA2R
+        S1I = -ZETA1I + ZETA2I
+   60   CONTINUE
+C-----------------------------------------------------------------------
+C     TEST FOR UNDERFLOW AND OVERFLOW
+C-----------------------------------------------------------------------
+        RS1 = S1R
+        IF (DABS(RS1).GT.ELIM) GO TO 120
+        IF (I.EQ.1) IFLAG = 2
+        IF (DABS(RS1).LT.ALIM) GO TO 70
+C-----------------------------------------------------------------------
+C     REFINE  TEST AND SCALE
+C-----------------------------------------------------------------------
+C-----------------------------------------------------------------------
+        APHI = ZABS(CMPLX(PHIR,PHII,kind=KIND(1.0D0)))
+        AARG = ZABS(CMPLX(ARGR,ARGI,kind=KIND(1.0D0)))
+        RS1 = RS1 + DLOG(APHI) - 0.25D0*DLOG(AARG) - AIC
+        IF (DABS(RS1).GT.ELIM) GO TO 120
+        IF (I.EQ.1) IFLAG = 1
+        IF (RS1.LT.0.0D0) GO TO 70
+        IF (I.EQ.1) IFLAG = 3
+   70   CONTINUE
+C-----------------------------------------------------------------------
+C     SCALE S1 TO KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR
+C     EXPONENT EXTREMES
+C-----------------------------------------------------------------------
+        CALL ZAIRY(ARGR, ARGI, 0, 2, AIR, AII, NAI, IDUM)
+        CALL ZAIRY(ARGR, ARGI, 1, 2, DAIR, DAII, NDAI, IDUM)
+        STR = DAIR*BSUMR - DAII*BSUMI
+        STI = DAIR*BSUMI + DAII*BSUMR
+        STR = STR + (AIR*ASUMR-AII*ASUMI)
+        STI = STI + (AIR*ASUMI+AII*ASUMR)
+        S2R = PHIR*STR - PHII*STI
+        S2I = PHIR*STI + PHII*STR
+        STR = DEXP(S1R)*CSSR(IFLAG)
+        S1R = STR*DCOS(S1I)
+        S1I = STR*DSIN(S1I)
+        STR = S2R*S1R - S2I*S1I
+        S2I = S2R*S1I + S2I*S1R
+        S2R = STR
+        IF (IFLAG.NE.1) GO TO 80
+        CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL)
+        IF (NW.NE.0) GO TO 120
+   80   CONTINUE
+        IF (ZI.LE.0.0D0) S2I = -S2I
+        STR = S2R*C2R - S2I*C2I
+        S2I = S2R*C2I + S2I*C2R
+        S2R = STR
+        CYR(I) = S2R
+        CYI(I) = S2I
+        J = ND - I + 1
+        YR(J) = S2R*CSRR(IFLAG)
+        YI(J) = S2I*CSRR(IFLAG)
+        STR = -C2I*CIDI
+        C2I = C2R*CIDI
+        C2R = STR
+   90 CONTINUE
+      IF (ND.LE.2) GO TO 110
+      RAZ = 1.0D0/ZABS(CMPLX(ZR,ZI,kind=KIND(1.0D0)))
+      STR = ZR*RAZ
+      STI = -ZI*RAZ
+      RZR = (STR+STR)*RAZ
+      RZI = (STI+STI)*RAZ
+      BRY(2) = 1.0D0/BRY(1)
+      BRY(3) = D1MACH(2)
+      S1R = CYR(1)
+      S1I = CYI(1)
+      S2R = CYR(2)
+      S2I = CYI(2)
+      C1R = CSRR(IFLAG)
+      ASCLE = BRY(IFLAG)
+      K = ND - 2
+      FN = DBLE(FLOAT(K))
+      DO 100 I=3,ND
+        C2R = S2R
+        C2I = S2I
+        S2R = S1R + (FNU+FN)*(RZR*C2R-RZI*C2I)
+        S2I = S1I + (FNU+FN)*(RZR*C2I+RZI*C2R)
+        S1R = C2R
+        S1I = C2I
+        C2R = S2R*C1R
+        C2I = S2I*C1R
+        YR(K) = C2R
+        YI(K) = C2I
+        K = K - 1
+        FN = FN - 1.0D0
+        IF (IFLAG.GE.3) GO TO 100
+        STR = DABS(C2R)
+        STI = DABS(C2I)
+        C2M = DMAX1(STR,STI)
+        IF (C2M.LE.ASCLE) GO TO 100
+        IFLAG = IFLAG + 1
+        ASCLE = BRY(IFLAG)
+        S1R = S1R*C1R
+        S1I = S1I*C1R
+        S2R = C2R
+        S2I = C2I
+        S1R = S1R*CSSR(IFLAG)
+        S1I = S1I*CSSR(IFLAG)
+        S2R = S2R*CSSR(IFLAG)
+        S2I = S2I*CSSR(IFLAG)
+        C1R = CSRR(IFLAG)
+  100 CONTINUE
+  110 CONTINUE
+      RETURN
+  120 CONTINUE
+      IF (RS1.GT.0.0D0) GO TO 140
+C-----------------------------------------------------------------------
+C     SET UNDERFLOW AND UPDATE PARAMETERS
+C-----------------------------------------------------------------------
+      YR(ND) = ZEROR
+      YI(ND) = ZEROI
+      NZ = NZ + 1
+      ND = ND - 1
+      IF (ND.EQ.0) GO TO 110
+      CALL ZUOIK(ZR, ZI, FNU, KODE, 1, ND, YR, YI, NUF, TOL, ELIM, ALIM)
+      IF (NUF.LT.0) GO TO 140
+      ND = ND - NUF
+      NZ = NZ + NUF
+      IF (ND.EQ.0) GO TO 110
+      FN = FNU + DBLE(FLOAT(ND-1))
+      IF (FN.LT.FNUL) GO TO 130
+C      FN = CIDI
+C      J = NUF + 1
+C      K = MOD(J,4) + 1
+C      S1R = CIPR(K)
+C      S1I = CIPI(K)
+C      IF (FN.LT.0.0D0) S1I = -S1I
+C      STR = C2R*S1R - C2I*S1I
+C      C2I = C2R*S1I + C2I*S1R
+C      C2R = STR
+      IN = INU + ND - 1
+      IN = MOD(IN,4) + 1
+      C2R = CAR*CIPR(IN) - SAR*CIPI(IN)
+      C2I = CAR*CIPI(IN) + SAR*CIPR(IN)
+      IF (ZI.LE.0.0D0) C2I = -C2I
+      GO TO 40
+  130 CONTINUE
+      NLAST = ND
+      RETURN
+  140 CONTINUE
+      NZ = -1
+      RETURN
+  150 CONTINUE
+      IF (RS1.GT.0.0D0) GO TO 140
+      NZ = N
+      DO 160 I=1,N
+        YR(I) = ZEROR
+        YI(I) = ZEROI
+  160 CONTINUE
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zunik.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zunik.f
new file mode 100644
index 00000000..3e8293e3
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zunik.f
@@ -0,0 +1,211 @@
+      SUBROUTINE ZUNIK(ZRR, ZRI, FNU, IKFLG, IPMTR, TOL, INIT, PHIR,
+     * PHII, ZETA1R, ZETA1I, ZETA2R, ZETA2I, SUMR, SUMI, CWRKR, CWRKI)
+C***BEGIN PROLOGUE  ZUNIK
+C***REFER TO  ZBESI,ZBESK
+C
+C        ZUNIK COMPUTES PARAMETERS FOR THE UNIFORM ASYMPTOTIC
+C        EXPANSIONS OF THE I AND K FUNCTIONS ON IKFLG= 1 OR 2
+C        RESPECTIVELY BY
+C
+C        W(FNU,ZR) = PHI*EXP(ZETA)*SUM
+C
+C        WHERE       ZETA=-ZETA1 + ZETA2       OR
+C                          ZETA1 - ZETA2
+C
+C        THE FIRST CALL MUST HAVE INIT=0. SUBSEQUENT CALLS WITH THE
+C        SAME ZR AND FNU WILL RETURN THE I OR K FUNCTION ON IKFLG=
+C        1 OR 2 WITH NO CHANGE IN INIT. CWRK IS A COMPLEX WORK
+C        ARRAY. IPMTR=0 COMPUTES ALL PARAMETERS. IPMTR=1 COMPUTES PHI,
+C        ZETA1,ZETA2.
+C
+C***ROUTINES CALLED  ZDIV,ZLOG,ZSQRT,D1MACH
+C***END PROLOGUE  ZUNIK
+C     COMPLEX CFN,CON,CONE,CRFN,CWRK,CZERO,PHI,S,SR,SUM,T,T2,ZETA1,
+C    *ZETA2,ZN,ZR
+      DOUBLE PRECISION AC, C, CON, CONEI, CONER, CRFNI, CRFNR, CWRKI,
+     * CWRKR, FNU, PHII, PHIR, RFN, SI, SR, SRI, SRR, STI, STR, SUMI,
+     * SUMR, TEST, TI, TOL, TR, T2I, T2R, ZEROI, ZEROR, ZETA1I, ZETA1R,
+     * ZETA2I, ZETA2R, ZNI, ZNR, ZRI, ZRR, D1MACH
+      INTEGER I, IDUM, IKFLG, INIT, IPMTR, J, K, L
+      DIMENSION C(120), CWRKR(16), CWRKI(16), CON(2)
+      DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 /
+      DATA CON(1), CON(2)  /
+     1 3.98942280401432678D-01,  1.25331413731550025D+00 /
+      DATA C(1), C(2), C(3), C(4), C(5), C(6), C(7), C(8), C(9), C(10),
+     1     C(11), C(12), C(13), C(14), C(15), C(16), C(17), C(18),
+     2     C(19), C(20), C(21), C(22), C(23), C(24)/
+     3     1.00000000000000000D+00,    -2.08333333333333333D-01,
+     4     1.25000000000000000D-01,     3.34201388888888889D-01,
+     5    -4.01041666666666667D-01,     7.03125000000000000D-02,
+     6    -1.02581259645061728D+00,     1.84646267361111111D+00,
+     7    -8.91210937500000000D-01,     7.32421875000000000D-02,
+     8     4.66958442342624743D+00,    -1.12070026162229938D+01,
+     9     8.78912353515625000D+00,    -2.36408691406250000D+00,
+     A     1.12152099609375000D-01,    -2.82120725582002449D+01,
+     B     8.46362176746007346D+01,    -9.18182415432400174D+01,
+     C     4.25349987453884549D+01,    -7.36879435947963170D+00,
+     D     2.27108001708984375D-01,     2.12570130039217123D+02,
+     E    -7.65252468141181642D+02,     1.05999045252799988D+03/
+      DATA C(25), C(26), C(27), C(28), C(29), C(30), C(31), C(32),
+     1     C(33), C(34), C(35), C(36), C(37), C(38), C(39), C(40),
+     2     C(41), C(42), C(43), C(44), C(45), C(46), C(47), C(48)/
+     3    -6.99579627376132541D+02,     2.18190511744211590D+02,
+     4    -2.64914304869515555D+01,     5.72501420974731445D-01,
+     5    -1.91945766231840700D+03,     8.06172218173730938D+03,
+     6    -1.35865500064341374D+04,     1.16553933368645332D+04,
+     7    -5.30564697861340311D+03,     1.20090291321635246D+03,
+     8    -1.08090919788394656D+02,     1.72772750258445740D+00,
+     9     2.02042913309661486D+04,    -9.69805983886375135D+04,
+     A     1.92547001232531532D+05,    -2.03400177280415534D+05,
+     B     1.22200464983017460D+05,    -4.11926549688975513D+04,
+     C     7.10951430248936372D+03,    -4.93915304773088012D+02,
+     D     6.07404200127348304D+00,    -2.42919187900551333D+05,
+     E     1.31176361466297720D+06,    -2.99801591853810675D+06/
+      DATA C(49), C(50), C(51), C(52), C(53), C(54), C(55), C(56),
+     1     C(57), C(58), C(59), C(60), C(61), C(62), C(63), C(64),
+     2     C(65), C(66), C(67), C(68), C(69), C(70), C(71), C(72)/
+     3     3.76327129765640400D+06,    -2.81356322658653411D+06,
+     4     1.26836527332162478D+06,    -3.31645172484563578D+05,
+     5     4.52187689813627263D+04,    -2.49983048181120962D+03,
+     6     2.43805296995560639D+01,     3.28446985307203782D+06,
+     7    -1.97068191184322269D+07,     5.09526024926646422D+07,
+     8    -7.41051482115326577D+07,     6.63445122747290267D+07,
+     9    -3.75671766607633513D+07,     1.32887671664218183D+07,
+     A    -2.78561812808645469D+06,     3.08186404612662398D+05,
+     B    -1.38860897537170405D+04,     1.10017140269246738D+02,
+     C    -4.93292536645099620D+07,     3.25573074185765749D+08,
+     D    -9.39462359681578403D+08,     1.55359689957058006D+09,
+     E    -1.62108055210833708D+09,     1.10684281682301447D+09/
+      DATA C(73), C(74), C(75), C(76), C(77), C(78), C(79), C(80),
+     1     C(81), C(82), C(83), C(84), C(85), C(86), C(87), C(88),
+     2     C(89), C(90), C(91), C(92), C(93), C(94), C(95), C(96)/
+     3    -4.95889784275030309D+08,     1.42062907797533095D+08,
+     4    -2.44740627257387285D+07,     2.24376817792244943D+06,
+     5    -8.40054336030240853D+04,     5.51335896122020586D+02,
+     6     8.14789096118312115D+08,    -5.86648149205184723D+09,
+     7     1.86882075092958249D+10,    -3.46320433881587779D+10,
+     8     4.12801855797539740D+10,    -3.30265997498007231D+10,
+     9     1.79542137311556001D+10,    -6.56329379261928433D+09,
+     A     1.55927986487925751D+09,    -2.25105661889415278D+08,
+     B     1.73951075539781645D+07,    -5.49842327572288687D+05,
+     C     3.03809051092238427D+03,    -1.46792612476956167D+10,
+     D     1.14498237732025810D+11,    -3.99096175224466498D+11,
+     E     8.19218669548577329D+11,    -1.09837515608122331D+12/
+      DATA C(97), C(98), C(99), C(100), C(101), C(102), C(103), C(104),
+     1     C(105), C(106), C(107), C(108), C(109), C(110), C(111),
+     2     C(112), C(113), C(114), C(115), C(116), C(117), C(118)/
+     3     1.00815810686538209D+12,    -6.45364869245376503D+11,
+     4     2.87900649906150589D+11,    -8.78670721780232657D+10,
+     5     1.76347306068349694D+10,    -2.16716498322379509D+09,
+     6     1.43157876718888981D+08,    -3.87183344257261262D+06,
+     7     1.82577554742931747D+04,     2.86464035717679043D+11,
+     8    -2.40629790002850396D+12,     9.10934118523989896D+12,
+     9    -2.05168994109344374D+13,     3.05651255199353206D+13,
+     A    -3.16670885847851584D+13,     2.33483640445818409D+13,
+     B    -1.23204913055982872D+13,     4.61272578084913197D+12,
+     C    -1.19655288019618160D+12,     2.05914503232410016D+11,
+     D    -2.18229277575292237D+10,     1.24700929351271032D+09/
+      DATA C(119), C(120)/
+     1    -2.91883881222208134D+07,     1.18838426256783253D+05/
+C
+      IF (INIT.NE.0) GO TO 40
+C-----------------------------------------------------------------------
+C     INITIALIZE ALL VARIABLES
+C-----------------------------------------------------------------------
+      RFN = 1.0D0/FNU
+C-----------------------------------------------------------------------
+C     OVERFLOW TEST (ZR/FNU TOO SMALL)
+C-----------------------------------------------------------------------
+      TEST = D1MACH(1)*1.0D+3
+      AC = FNU*TEST
+      IF (DABS(ZRR).GT.AC .OR. DABS(ZRI).GT.AC) GO TO 15
+      ZETA1R = 2.0D0*DABS(DLOG(TEST))+FNU
+      ZETA1I = 0.0D0
+      ZETA2R = FNU
+      ZETA2I = 0.0D0
+      PHIR = 1.0D0
+      PHII = 0.0D0
+      RETURN
+   15 CONTINUE
+      TR = ZRR*RFN
+      TI = ZRI*RFN
+      SR = CONER + (TR*TR-TI*TI)
+      SI = CONEI + (TR*TI+TI*TR)
+      CALL ZSQRT(SR, SI, SRR, SRI)
+      STR = CONER + SRR
+      STI = CONEI + SRI
+      CALL ZDIV(STR, STI, TR, TI, ZNR, ZNI)
+      CALL ZLOG(ZNR, ZNI, STR, STI, IDUM)
+      ZETA1R = FNU*STR
+      ZETA1I = FNU*STI
+      ZETA2R = FNU*SRR
+      ZETA2I = FNU*SRI
+      CALL ZDIV(CONER, CONEI, SRR, SRI, TR, TI)
+      SRR = TR*RFN
+      SRI = TI*RFN
+      CALL ZSQRT(SRR, SRI, CWRKR(16), CWRKI(16))
+      PHIR = CWRKR(16)*CON(IKFLG)
+      PHII = CWRKI(16)*CON(IKFLG)
+      IF (IPMTR.NE.0) RETURN
+      CALL ZDIV(CONER, CONEI, SR, SI, T2R, T2I)
+      CWRKR(1) = CONER
+      CWRKI(1) = CONEI
+      CRFNR = CONER
+      CRFNI = CONEI
+      AC = 1.0D0
+      L = 1
+      DO 20 K=2,15
+        SR = ZEROR
+        SI = ZEROI
+        DO 10 J=1,K
+          L = L + 1
+          STR = SR*T2R - SI*T2I + C(L)
+          SI = SR*T2I + SI*T2R
+          SR = STR
+   10   CONTINUE
+        STR = CRFNR*SRR - CRFNI*SRI
+        CRFNI = CRFNR*SRI + CRFNI*SRR
+        CRFNR = STR
+        CWRKR(K) = CRFNR*SR - CRFNI*SI
+        CWRKI(K) = CRFNR*SI + CRFNI*SR
+        AC = AC*RFN
+        TEST = DABS(CWRKR(K)) + DABS(CWRKI(K))
+        IF (AC.LT.TOL .AND. TEST.LT.TOL) GO TO 30
+   20 CONTINUE
+      K = 15
+   30 CONTINUE
+      INIT = K
+   40 CONTINUE
+      IF (IKFLG.EQ.2) GO TO 60
+C-----------------------------------------------------------------------
+C     COMPUTE SUM FOR THE I FUNCTION
+C-----------------------------------------------------------------------
+      SR = ZEROR
+      SI = ZEROI
+      DO 50 I=1,INIT
+        SR = SR + CWRKR(I)
+        SI = SI + CWRKI(I)
+   50 CONTINUE
+      SUMR = SR
+      SUMI = SI
+      PHIR = CWRKR(16)*CON(1)
+      PHII = CWRKI(16)*CON(1)
+      RETURN
+   60 CONTINUE
+C-----------------------------------------------------------------------
+C     COMPUTE SUM FOR THE K FUNCTION
+C-----------------------------------------------------------------------
+      SR = ZEROR
+      SI = ZEROI
+      TR = CONER
+      DO 70 I=1,INIT
+        SR = SR + TR*CWRKR(I)
+        SI = SI + TR*CWRKI(I)
+        TR = -TR
+   70 CONTINUE
+      SUMR = SR
+      SUMI = SI
+      PHIR = CWRKR(16)*CON(2)
+      PHII = CWRKI(16)*CON(2)
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zunk1.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zunk1.f
new file mode 100644
index 00000000..6b2418dd
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zunk1.f
@@ -0,0 +1,426 @@
+      SUBROUTINE ZUNK1(ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, TOL, ELIM,
+     * ALIM)
+C***BEGIN PROLOGUE  ZUNK1
+C***REFER TO  ZBESK
+C
+C     ZUNK1 COMPUTES K(FNU,Z) AND ITS ANALYTIC CONTINUATION FROM THE
+C     RIGHT HALF PLANE TO THE LEFT HALF PLANE BY MEANS OF THE
+C     UNIFORM ASYMPTOTIC EXPANSION.
+C     MR INDICATES THE DIRECTION OF ROTATION FOR ANALYTIC CONTINUATION.
+C     NZ=-1 MEANS AN OVERFLOW WILL OCCUR
+C
+C***ROUTINES CALLED  ZKSCL,ZS1S2,ZUCHK,ZUNIK,D1MACH,ZABS
+C***END PROLOGUE  ZUNK1
+C     COMPLEX CFN,CK,CONE,CRSC,CS,CSCL,CSGN,CSPN,CSR,CSS,CWRK,CY,CZERO,
+C    *C1,C2,PHI,PHID,RZ,SUM,SUMD,S1,S2,Y,Z,ZETA1,ZETA1D,ZETA2,ZETA2D,ZR
+      DOUBLE PRECISION ALIM, ANG, APHI, ASC, ASCLE, BRY, CKI, CKR,
+     * CONER, CRSC, CSCL, CSGNI, CSPNI, CSPNR, CSR, CSRR, CSSR,
+     * CWRKI, CWRKR, CYI, CYR, C1I, C1R, C2I, C2M, C2R, ELIM, FMR, FN,
+     * FNF, FNU, PHIDI, PHIDR, PHII, PHIR, PI, RAST, RAZR, RS1, RZI,
+     * RZR, SGN, STI, STR, SUMDI, SUMDR, SUMI, SUMR, S1I, S1R, S2I,
+     * S2R, TOL, YI, YR, ZEROI, ZEROR, ZETA1I, ZETA1R, ZETA2I, ZETA2R,
+     * ZET1DI, ZET1DR, ZET2DI, ZET2DR, ZI, ZR, ZRI, ZRR, D1MACH, ZABS
+      INTEGER I, IB, IFLAG, IFN, IL, INIT, INU, IUF, K, KDFLG, KFLAG,
+     * KK, KODE, MR, N, NW, NZ, INITD, IC, IPARD, J
+      DIMENSION BRY(3), INIT(2), YR(N), YI(N), SUMR(2), SUMI(2),
+     * ZETA1R(2), ZETA1I(2), ZETA2R(2), ZETA2I(2), CYR(2), CYI(2),
+     * CWRKR(16,3), CWRKI(16,3), CSSR(3), CSRR(3), PHIR(2), PHII(2)
+      DATA ZEROR,ZEROI,CONER / 0.0D0, 0.0D0, 1.0D0 /
+      DATA PI / 3.14159265358979324D0 /
+C
+      KDFLG = 1
+      NZ = 0
+C-----------------------------------------------------------------------
+C     EXP(-ALIM)=EXP(-ELIM)/TOL=APPROX. ONE PRECISION GREATER THAN
+C     THE UNDERFLOW LIMIT
+C-----------------------------------------------------------------------
+      CSCL = 1.0D0/TOL
+      CRSC = TOL
+      CSSR(1) = CSCL
+      CSSR(2) = CONER
+      CSSR(3) = CRSC
+      CSRR(1) = CRSC
+      CSRR(2) = CONER
+      CSRR(3) = CSCL
+      BRY(1) = 1.0D+3*D1MACH(1)/TOL
+      BRY(2) = 1.0D0/BRY(1)
+      BRY(3) = D1MACH(2)
+      ZRR = ZR
+      ZRI = ZI
+      IF (ZR.GE.0.0D0) GO TO 10
+      ZRR = -ZR
+      ZRI = -ZI
+   10 CONTINUE
+      J = 2
+      DO 70 I=1,N
+C-----------------------------------------------------------------------
+C     J FLIP FLOPS BETWEEN 1 AND 2 IN J = 3 - J
+C-----------------------------------------------------------------------
+        J = 3 - J
+        FN = FNU + DBLE(FLOAT(I-1))
+        INIT(J) = 0
+        CALL ZUNIK(ZRR, ZRI, FN, 2, 0, TOL, INIT(J), PHIR(J), PHII(J),
+     *   ZETA1R(J), ZETA1I(J), ZETA2R(J), ZETA2I(J), SUMR(J), SUMI(J),
+     *   CWRKR(1,J), CWRKI(1,J))
+        IF (KODE.EQ.1) GO TO 20
+        STR = ZRR + ZETA2R(J)
+        STI = ZRI + ZETA2I(J)
+        RAST = FN/ZABS(CMPLX(STR,STI,kind=KIND(1.0D0)))
+        STR = STR*RAST*RAST
+        STI = -STI*RAST*RAST
+        S1R = ZETA1R(J) - STR
+        S1I = ZETA1I(J) - STI
+        GO TO 30
+   20   CONTINUE
+        S1R = ZETA1R(J) - ZETA2R(J)
+        S1I = ZETA1I(J) - ZETA2I(J)
+   30   CONTINUE
+        RS1 = S1R
+C-----------------------------------------------------------------------
+C     TEST FOR UNDERFLOW AND OVERFLOW
+C-----------------------------------------------------------------------
+        IF (DABS(RS1).GT.ELIM) GO TO 60
+        IF (KDFLG.EQ.1) KFLAG = 2
+        IF (DABS(RS1).LT.ALIM) GO TO 40
+C-----------------------------------------------------------------------
+C     REFINE  TEST AND SCALE
+C-----------------------------------------------------------------------
+        APHI = ZABS(CMPLX(PHIR(J),PHII(J),kind=KIND(1.0D0)))
+        RS1 = RS1 + DLOG(APHI)
+        IF (DABS(RS1).GT.ELIM) GO TO 60
+        IF (KDFLG.EQ.1) KFLAG = 1
+        IF (RS1.LT.0.0D0) GO TO 40
+        IF (KDFLG.EQ.1) KFLAG = 3
+   40   CONTINUE
+C-----------------------------------------------------------------------
+C     SCALE S1 TO KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR
+C     EXPONENT EXTREMES
+C-----------------------------------------------------------------------
+        S2R = PHIR(J)*SUMR(J) - PHII(J)*SUMI(J)
+        S2I = PHIR(J)*SUMI(J) + PHII(J)*SUMR(J)
+        STR = DEXP(S1R)*CSSR(KFLAG)
+        S1R = STR*DCOS(S1I)
+        S1I = STR*DSIN(S1I)
+        STR = S2R*S1R - S2I*S1I
+        S2I = S1R*S2I + S2R*S1I
+        S2R = STR
+        IF (KFLAG.NE.1) GO TO 50
+        CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL)
+        IF (NW.NE.0) GO TO 60
+   50   CONTINUE
+        CYR(KDFLG) = S2R
+        CYI(KDFLG) = S2I
+        YR(I) = S2R*CSRR(KFLAG)
+        YI(I) = S2I*CSRR(KFLAG)
+        IF (KDFLG.EQ.2) GO TO 75
+        KDFLG = 2
+        GO TO 70
+   60   CONTINUE
+        IF (RS1.GT.0.0D0) GO TO 300
+C-----------------------------------------------------------------------
+C     FOR ZR.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW
+C-----------------------------------------------------------------------
+        IF (ZR.LT.0.0D0) GO TO 300
+        KDFLG = 1
+        YR(I)=ZEROR
+        YI(I)=ZEROI
+        NZ=NZ+1
+        IF (I.EQ.1) GO TO 70
+        IF ((YR(I-1).EQ.ZEROR).AND.(YI(I-1).EQ.ZEROI)) GO TO 70
+        YR(I-1)=ZEROR
+        YI(I-1)=ZEROI
+        NZ=NZ+1
+   70 CONTINUE
+      I = N
+   75 CONTINUE
+      RAZR = 1.0D0/ZABS(CMPLX(ZRR,ZRI,kind=KIND(1.0D0)))
+      STR = ZRR*RAZR
+      STI = -ZRI*RAZR
+      RZR = (STR+STR)*RAZR
+      RZI = (STI+STI)*RAZR
+      CKR = FN*RZR
+      CKI = FN*RZI
+      IB = I + 1
+      IF (N.LT.IB) GO TO 160
+C-----------------------------------------------------------------------
+C     TEST LAST MEMBER FOR UNDERFLOW AND OVERFLOW. SET SEQUENCE TO ZERO
+C     ON UNDERFLOW.
+C-----------------------------------------------------------------------
+      FN = FNU + DBLE(FLOAT(N-1))
+      IPARD = 1
+      IF (MR.NE.0) IPARD = 0
+      INITD = 0
+      CALL ZUNIK(ZRR, ZRI, FN, 2, IPARD, TOL, INITD, PHIDR, PHIDI,
+     * ZET1DR, ZET1DI, ZET2DR, ZET2DI, SUMDR, SUMDI, CWRKR(1,3),
+     * CWRKI(1,3))
+      IF (KODE.EQ.1) GO TO 80
+      STR = ZRR + ZET2DR
+      STI = ZRI + ZET2DI
+      RAST = FN/ZABS(CMPLX(STR,STI,kind=KIND(1.0D0)))
+      STR = STR*RAST*RAST
+      STI = -STI*RAST*RAST
+      S1R = ZET1DR - STR
+      S1I = ZET1DI - STI
+      GO TO 90
+   80 CONTINUE
+      S1R = ZET1DR - ZET2DR
+      S1I = ZET1DI - ZET2DI
+   90 CONTINUE
+      RS1 = S1R
+      IF (DABS(RS1).GT.ELIM) GO TO 95
+      IF (DABS(RS1).LT.ALIM) GO TO 100
+C----------------------------------------------------------------------------
+C     REFINE ESTIMATE AND TEST
+C-------------------------------------------------------------------------
+      APHI = ZABS(CMPLX(PHIDR,PHIDI,kind=KIND(1.0D0)))
+      RS1 = RS1+DLOG(APHI)
+      IF (DABS(RS1).LT.ELIM) GO TO 100
+   95 CONTINUE
+      IF (DABS(RS1).GT.0.0D0) GO TO 300
+C-----------------------------------------------------------------------
+C     FOR ZR.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW
+C-----------------------------------------------------------------------
+      IF (ZR.LT.0.0D0) GO TO 300
+      NZ = N
+      DO 96 I=1,N
+        YR(I) = ZEROR
+        YI(I) = ZEROI
+   96 CONTINUE
+      RETURN
+C---------------------------------------------------------------------------
+C     FORWARD RECUR FOR REMAINDER OF THE SEQUENCE
+C----------------------------------------------------------------------------
+  100 CONTINUE
+      S1R = CYR(1)
+      S1I = CYI(1)
+      S2R = CYR(2)
+      S2I = CYI(2)
+      C1R = CSRR(KFLAG)
+      ASCLE = BRY(KFLAG)
+      DO 120 I=IB,N
+        C2R = S2R
+        C2I = S2I
+        S2R = CKR*C2R - CKI*C2I + S1R
+        S2I = CKR*C2I + CKI*C2R + S1I
+        S1R = C2R
+        S1I = C2I
+        CKR = CKR + RZR
+        CKI = CKI + RZI
+        C2R = S2R*C1R
+        C2I = S2I*C1R
+        YR(I) = C2R
+        YI(I) = C2I
+        IF (KFLAG.GE.3) GO TO 120
+        STR = DABS(C2R)
+        STI = DABS(C2I)
+        C2M = DMAX1(STR,STI)
+        IF (C2M.LE.ASCLE) GO TO 120
+        KFLAG = KFLAG + 1
+        ASCLE = BRY(KFLAG)
+        S1R = S1R*C1R
+        S1I = S1I*C1R
+        S2R = C2R
+        S2I = C2I
+        S1R = S1R*CSSR(KFLAG)
+        S1I = S1I*CSSR(KFLAG)
+        S2R = S2R*CSSR(KFLAG)
+        S2I = S2I*CSSR(KFLAG)
+        C1R = CSRR(KFLAG)
+  120 CONTINUE
+  160 CONTINUE
+      IF (MR.EQ.0) RETURN
+C-----------------------------------------------------------------------
+C     ANALYTIC CONTINUATION FOR RE(Z).LT.0.0D0
+C-----------------------------------------------------------------------
+      NZ = 0
+      FMR = DBLE(FLOAT(MR))
+      SGN = -DSIGN(PI,FMR)
+C-----------------------------------------------------------------------
+C     CSPN AND CSGN ARE COEFF OF K AND I FUNCTIONS RESP.
+C-----------------------------------------------------------------------
+      CSGNI = SGN
+      INU = INT(SNGL(FNU))
+      FNF = FNU - DBLE(FLOAT(INU))
+      IFN = INU + N - 1
+      ANG = FNF*SGN
+      CSPNR = DCOS(ANG)
+      CSPNI = DSIN(ANG)
+      IF (MOD(IFN,2).EQ.0) GO TO 170
+      CSPNR = -CSPNR
+      CSPNI = -CSPNI
+  170 CONTINUE
+      ASC = BRY(1)
+      IUF = 0
+      KK = N
+      KDFLG = 1
+      IB = IB - 1
+      IC = IB - 1
+      DO 270 K=1,N
+        FN = FNU + DBLE(FLOAT(KK-1))
+C-----------------------------------------------------------------------
+C     LOGIC TO SORT OUT CASES WHOSE PARAMETERS WERE SET FOR THE K
+C     FUNCTION ABOVE
+C-----------------------------------------------------------------------
+        M=3
+        IF (N.GT.2) GO TO 175
+  172   CONTINUE
+        INITD = INIT(J)
+        PHIDR = PHIR(J)
+        PHIDI = PHII(J)
+        ZET1DR = ZETA1R(J)
+        ZET1DI = ZETA1I(J)
+        ZET2DR = ZETA2R(J)
+        ZET2DI = ZETA2I(J)
+        SUMDR = SUMR(J)
+        SUMDI = SUMI(J)
+        M = J
+        J = 3 - J
+        GO TO 180
+  175   CONTINUE
+        IF ((KK.EQ.N).AND.(IB.LT.N)) GO TO 180
+        IF ((KK.EQ.IB).OR.(KK.EQ.IC)) GO TO 172
+        INITD = 0
+  180   CONTINUE
+        CALL ZUNIK(ZRR, ZRI, FN, 1, 0, TOL, INITD, PHIDR, PHIDI,
+     *   ZET1DR, ZET1DI, ZET2DR, ZET2DI, SUMDR, SUMDI,
+     *   CWRKR(1,M), CWRKI(1,M))
+        IF (KODE.EQ.1) GO TO 200
+        STR = ZRR + ZET2DR
+        STI = ZRI + ZET2DI
+        RAST = FN/ZABS(CMPLX(STR,STI,kind=KIND(1.0D0)))
+        STR = STR*RAST*RAST
+        STI = -STI*RAST*RAST
+        S1R = -ZET1DR + STR
+        S1I = -ZET1DI + STI
+        GO TO 210
+  200   CONTINUE
+        S1R = -ZET1DR + ZET2DR
+        S1I = -ZET1DI + ZET2DI
+  210   CONTINUE
+C-----------------------------------------------------------------------
+C     TEST FOR UNDERFLOW AND OVERFLOW
+C-----------------------------------------------------------------------
+        RS1 = S1R
+        IF (DABS(RS1).GT.ELIM) GO TO 260
+        IF (KDFLG.EQ.1) IFLAG = 2
+        IF (DABS(RS1).LT.ALIM) GO TO 220
+C-----------------------------------------------------------------------
+C     REFINE  TEST AND SCALE
+C-----------------------------------------------------------------------
+        APHI = ZABS(CMPLX(PHIDR,PHIDI,kind=KIND(1.0D0)))
+        RS1 = RS1 + DLOG(APHI)
+        IF (DABS(RS1).GT.ELIM) GO TO 260
+        IF (KDFLG.EQ.1) IFLAG = 1
+        IF (RS1.LT.0.0D0) GO TO 220
+        IF (KDFLG.EQ.1) IFLAG = 3
+  220   CONTINUE
+        STR = PHIDR*SUMDR - PHIDI*SUMDI
+        STI = PHIDR*SUMDI + PHIDI*SUMDR
+        S2R = -CSGNI*STI
+        S2I = CSGNI*STR
+        STR = DEXP(S1R)*CSSR(IFLAG)
+        S1R = STR*DCOS(S1I)
+        S1I = STR*DSIN(S1I)
+        STR = S2R*S1R - S2I*S1I
+        S2I = S2R*S1I + S2I*S1R
+        S2R = STR
+        IF (IFLAG.NE.1) GO TO 230
+        CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL)
+        IF (NW.EQ.0) GO TO 230
+        S2R = ZEROR
+        S2I = ZEROI
+  230   CONTINUE
+        CYR(KDFLG) = S2R
+        CYI(KDFLG) = S2I
+        C2R = S2R
+        C2I = S2I
+        S2R = S2R*CSRR(IFLAG)
+        S2I = S2I*CSRR(IFLAG)
+C-----------------------------------------------------------------------
+C     ADD I AND K FUNCTIONS, K SEQUENCE IN Y(I), I=1,N
+C-----------------------------------------------------------------------
+        S1R = YR(KK)
+        S1I = YI(KK)
+        IF (KODE.EQ.1) GO TO 250
+        CALL ZS1S2(ZRR, ZRI, S1R, S1I, S2R, S2I, NW, ASC, ALIM, IUF)
+        NZ = NZ + NW
+  250   CONTINUE
+        YR(KK) = S1R*CSPNR - S1I*CSPNI + S2R
+        YI(KK) = CSPNR*S1I + CSPNI*S1R + S2I
+        KK = KK - 1
+        CSPNR = -CSPNR
+        CSPNI = -CSPNI
+        IF (C2R.NE.0.0D0 .OR. C2I.NE.0.0D0) GO TO 255
+        KDFLG = 1
+        GO TO 270
+  255   CONTINUE
+        IF (KDFLG.EQ.2) GO TO 275
+        KDFLG = 2
+        GO TO 270
+  260   CONTINUE
+        IF (RS1.GT.0.0D0) GO TO 300
+        S2R = ZEROR
+        S2I = ZEROI
+        GO TO 230
+  270 CONTINUE
+      K = N
+  275 CONTINUE
+      IL = N - K
+      IF (IL.EQ.0) RETURN
+C-----------------------------------------------------------------------
+C     RECUR BACKWARD FOR REMAINDER OF I SEQUENCE AND ADD IN THE
+C     K FUNCTIONS, SCALING THE I SEQUENCE DURING RECURRENCE TO KEEP
+C     INTERMEDIATE ARITHMETIC ON SCALE NEAR EXPONENT EXTREMES.
+C-----------------------------------------------------------------------
+      S1R = CYR(1)
+      S1I = CYI(1)
+      S2R = CYR(2)
+      S2I = CYI(2)
+      CSR = CSRR(IFLAG)
+      ASCLE = BRY(IFLAG)
+      FN = DBLE(FLOAT(INU+IL))
+      DO 290 I=1,IL
+        C2R = S2R
+        C2I = S2I
+        S2R = S1R + (FN+FNF)*(RZR*C2R-RZI*C2I)
+        S2I = S1I + (FN+FNF)*(RZR*C2I+RZI*C2R)
+        S1R = C2R
+        S1I = C2I
+        FN = FN - 1.0D0
+        C2R = S2R*CSR
+        C2I = S2I*CSR
+        CKR = C2R
+        CKI = C2I
+        C1R = YR(KK)
+        C1I = YI(KK)
+        IF (KODE.EQ.1) GO TO 280
+        CALL ZS1S2(ZRR, ZRI, C1R, C1I, C2R, C2I, NW, ASC, ALIM, IUF)
+        NZ = NZ + NW
+  280   CONTINUE
+        YR(KK) = C1R*CSPNR - C1I*CSPNI + C2R
+        YI(KK) = C1R*CSPNI + C1I*CSPNR + C2I
+        KK = KK - 1
+        CSPNR = -CSPNR
+        CSPNI = -CSPNI
+        IF (IFLAG.GE.3) GO TO 290
+        C2R = DABS(CKR)
+        C2I = DABS(CKI)
+        C2M = DMAX1(C2R,C2I)
+        IF (C2M.LE.ASCLE) GO TO 290
+        IFLAG = IFLAG + 1
+        ASCLE = BRY(IFLAG)
+        S1R = S1R*CSR
+        S1I = S1I*CSR
+        S2R = CKR
+        S2I = CKI
+        S1R = S1R*CSSR(IFLAG)
+        S1I = S1I*CSSR(IFLAG)
+        S2R = S2R*CSSR(IFLAG)
+        S2I = S2I*CSSR(IFLAG)
+        CSR = CSRR(IFLAG)
+  290 CONTINUE
+      RETURN
+  300 CONTINUE
+      NZ = -1
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zunk2.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zunk2.f
new file mode 100644
index 00000000..6859f5ec
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zunk2.f
@@ -0,0 +1,505 @@
+      SUBROUTINE ZUNK2(ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, TOL, ELIM,
+     * ALIM)
+C***BEGIN PROLOGUE  ZUNK2
+C***REFER TO  ZBESK
+C
+C     ZUNK2 COMPUTES K(FNU,Z) AND ITS ANALYTIC CONTINUATION FROM THE
+C     RIGHT HALF PLANE TO THE LEFT HALF PLANE BY MEANS OF THE
+C     UNIFORM ASYMPTOTIC EXPANSIONS FOR H(KIND,FNU,ZN) AND J(FNU,ZN)
+C     WHERE ZN IS IN THE RIGHT HALF PLANE, KIND=(3-MR)/2, MR=+1 OR
+C     -1. HERE ZN=ZR*I OR -ZR*I WHERE ZR=Z IF Z IS IN THE RIGHT
+C     HALF PLANE OR ZR=-Z IF Z IS IN THE LEFT HALF PLANE. MR INDIC-
+C     ATES THE DIRECTION OF ROTATION FOR ANALYTIC CONTINUATION.
+C     NZ=-1 MEANS AN OVERFLOW WILL OCCUR
+C
+C***ROUTINES CALLED  ZAIRY,ZKSCL,ZS1S2,ZUCHK,ZUNHJ,D1MACH,ZABS
+C***END PROLOGUE  ZUNK2
+C     COMPLEX AI,ARG,ARGD,ASUM,ASUMD,BSUM,BSUMD,CFN,CI,CIP,CK,CONE,CRSC,
+C    *CR1,CR2,CS,CSCL,CSGN,CSPN,CSR,CSS,CY,CZERO,C1,C2,DAI,PHI,PHID,RZ,
+C    *S1,S2,Y,Z,ZB,ZETA1,ZETA1D,ZETA2,ZETA2D,ZN,ZR
+      DOUBLE PRECISION AARG, AIC, AII, AIR, ALIM, ANG, APHI, ARGDI,
+     * ARGDR, ARGI, ARGR, ASC, ASCLE, ASUMDI, ASUMDR, ASUMI, ASUMR,
+     * BRY, BSUMDI, BSUMDR, BSUMI, BSUMR, CAR, CIPI, CIPR, CKI, CKR,
+     * CONER, CRSC, CR1I, CR1R, CR2I, CR2R, CSCL, CSGNI, CSI,
+     * CSPNI, CSPNR, CSR, CSRR, CSSR, CYI, CYR, C1I, C1R, C2I, C2M,
+     * C2R, DAII, DAIR, ELIM, FMR, FN, FNF, FNU, HPI, PHIDI, PHIDR,
+     * PHII, PHIR, PI, PTI, PTR, RAST, RAZR, RS1, RZI, RZR, SAR, SGN,
+     * STI, STR, S1I, S1R, S2I, S2R, TOL, YI, YR, YY, ZBI, ZBR, ZEROI,
+     * ZEROR, ZETA1I, ZETA1R, ZETA2I, ZETA2R, ZET1DI, ZET1DR, ZET2DI,
+     * ZET2DR, ZI, ZNI, ZNR, ZR, ZRI, ZRR, D1MACH, ZABS
+      INTEGER I, IB, IFLAG, IFN, IL, IN, INU, IUF, K, KDFLG, KFLAG, KK,
+     * KODE, MR, N, NAI, NDAI, NW, NZ, IDUM, J, IPARD, IC
+      DIMENSION BRY(3), YR(N), YI(N), ASUMR(2), ASUMI(2), BSUMR(2),
+     * BSUMI(2), PHIR(2), PHII(2), ARGR(2), ARGI(2), ZETA1R(2),
+     * ZETA1I(2), ZETA2R(2), ZETA2I(2), CYR(2), CYI(2), CIPR(4),
+     * CIPI(4), CSSR(3), CSRR(3)
+      DATA ZEROR,ZEROI,CONER,CR1R,CR1I,CR2R,CR2I /
+     1         0.0D0, 0.0D0, 1.0D0,
+     1 1.0D0,1.73205080756887729D0 , -0.5D0,-8.66025403784438647D-01 /
+      DATA HPI, PI, AIC /
+     1     1.57079632679489662D+00,     3.14159265358979324D+00,
+     1     1.26551212348464539D+00/
+      DATA CIPR(1),CIPI(1),CIPR(2),CIPI(2),CIPR(3),CIPI(3),CIPR(4),
+     * CIPI(4) /
+     1  1.0D0,0.0D0 ,  0.0D0,-1.0D0 ,  -1.0D0,0.0D0 ,  0.0D0,1.0D0 /
+C
+      KDFLG = 1
+      NZ = 0
+C-----------------------------------------------------------------------
+C     EXP(-ALIM)=EXP(-ELIM)/TOL=APPROX. ONE PRECISION GREATER THAN
+C     THE UNDERFLOW LIMIT
+C-----------------------------------------------------------------------
+      CSCL = 1.0D0/TOL
+      CRSC = TOL
+      CSSR(1) = CSCL
+      CSSR(2) = CONER
+      CSSR(3) = CRSC
+      CSRR(1) = CRSC
+      CSRR(2) = CONER
+      CSRR(3) = CSCL
+      BRY(1) = 1.0D+3*D1MACH(1)/TOL
+      BRY(2) = 1.0D0/BRY(1)
+      BRY(3) = D1MACH(2)
+      ZRR = ZR
+      ZRI = ZI
+      IF (ZR.GE.0.0D0) GO TO 10
+      ZRR = -ZR
+      ZRI = -ZI
+   10 CONTINUE
+      YY = ZRI
+      ZNR = ZRI
+      ZNI = -ZRR
+      ZBR = ZRR
+      ZBI = ZRI
+      INU = INT(SNGL(FNU))
+      FNF = FNU - DBLE(FLOAT(INU))
+      ANG = -HPI*FNF
+      CAR = DCOS(ANG)
+      SAR = DSIN(ANG)
+      C2R = HPI*SAR
+      C2I = -HPI*CAR
+      KK = MOD(INU,4) + 1
+      STR = C2R*CIPR(KK) - C2I*CIPI(KK)
+      STI = C2R*CIPI(KK) + C2I*CIPR(KK)
+      CSR = CR1R*STR - CR1I*STI
+      CSI = CR1R*STI + CR1I*STR
+      IF (YY.GT.0.0D0) GO TO 20
+      ZNR = -ZNR
+      ZBI = -ZBI
+   20 CONTINUE
+C-----------------------------------------------------------------------
+C     K(FNU,Z) IS COMPUTED FROM H(2,FNU,-I*Z) WHERE Z IS IN THE FIRST
+C     QUADRANT. FOURTH QUADRANT VALUES (YY.LE.0.0E0) ARE COMPUTED BY
+C     CONJUGATION SINCE THE K FUNCTION IS REAL ON THE POSITIVE REAL AXIS
+C-----------------------------------------------------------------------
+      J = 2
+      DO 80 I=1,N
+C-----------------------------------------------------------------------
+C     J FLIP FLOPS BETWEEN 1 AND 2 IN J = 3 - J
+C-----------------------------------------------------------------------
+        J = 3 - J
+        FN = FNU + DBLE(FLOAT(I-1))
+        CALL ZUNHJ(ZNR, ZNI, FN, 0, TOL, PHIR(J), PHII(J), ARGR(J),
+     *   ARGI(J), ZETA1R(J), ZETA1I(J), ZETA2R(J), ZETA2I(J), ASUMR(J),
+     *   ASUMI(J), BSUMR(J), BSUMI(J))
+        IF (KODE.EQ.1) GO TO 30
+        STR = ZBR + ZETA2R(J)
+        STI = ZBI + ZETA2I(J)
+        RAST = FN/ZABS(CMPLX(STR,STI,kind=KIND(1.0D0)))
+        STR = STR*RAST*RAST
+        STI = -STI*RAST*RAST
+        S1R = ZETA1R(J) - STR
+        S1I = ZETA1I(J) - STI
+        GO TO 40
+   30   CONTINUE
+        S1R = ZETA1R(J) - ZETA2R(J)
+        S1I = ZETA1I(J) - ZETA2I(J)
+   40   CONTINUE
+C-----------------------------------------------------------------------
+C     TEST FOR UNDERFLOW AND OVERFLOW
+C-----------------------------------------------------------------------
+        RS1 = S1R
+        IF (DABS(RS1).GT.ELIM) GO TO 70
+        IF (KDFLG.EQ.1) KFLAG = 2
+        IF (DABS(RS1).LT.ALIM) GO TO 50
+C-----------------------------------------------------------------------
+C     REFINE  TEST AND SCALE
+C-----------------------------------------------------------------------
+        APHI = ZABS(CMPLX(PHIR(J),PHII(J),kind=KIND(1.0D0)))
+        AARG = ZABS(CMPLX(ARGR(J),ARGI(J),kind=KIND(1.0D0)))
+        RS1 = RS1 + DLOG(APHI) - 0.25D0*DLOG(AARG) - AIC
+        IF (DABS(RS1).GT.ELIM) GO TO 70
+        IF (KDFLG.EQ.1) KFLAG = 1
+        IF (RS1.LT.0.0D0) GO TO 50
+        IF (KDFLG.EQ.1) KFLAG = 3
+   50   CONTINUE
+C-----------------------------------------------------------------------
+C     SCALE S1 TO KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR
+C     EXPONENT EXTREMES
+C-----------------------------------------------------------------------
+        C2R = ARGR(J)*CR2R - ARGI(J)*CR2I
+        C2I = ARGR(J)*CR2I + ARGI(J)*CR2R
+        CALL ZAIRY(C2R, C2I, 0, 2, AIR, AII, NAI, IDUM)
+        CALL ZAIRY(C2R, C2I, 1, 2, DAIR, DAII, NDAI, IDUM)
+        STR = DAIR*BSUMR(J) - DAII*BSUMI(J)
+        STI = DAIR*BSUMI(J) + DAII*BSUMR(J)
+        PTR = STR*CR2R - STI*CR2I
+        PTI = STR*CR2I + STI*CR2R
+        STR = PTR + (AIR*ASUMR(J)-AII*ASUMI(J))
+        STI = PTI + (AIR*ASUMI(J)+AII*ASUMR(J))
+        PTR = STR*PHIR(J) - STI*PHII(J)
+        PTI = STR*PHII(J) + STI*PHIR(J)
+        S2R = PTR*CSR - PTI*CSI
+        S2I = PTR*CSI + PTI*CSR
+        STR = DEXP(S1R)*CSSR(KFLAG)
+        S1R = STR*DCOS(S1I)
+        S1I = STR*DSIN(S1I)
+        STR = S2R*S1R - S2I*S1I
+        S2I = S1R*S2I + S2R*S1I
+        S2R = STR
+        IF (KFLAG.NE.1) GO TO 60
+        CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL)
+        IF (NW.NE.0) GO TO 70
+   60   CONTINUE
+        IF (YY.LE.0.0D0) S2I = -S2I
+        CYR(KDFLG) = S2R
+        CYI(KDFLG) = S2I
+        YR(I) = S2R*CSRR(KFLAG)
+        YI(I) = S2I*CSRR(KFLAG)
+        STR = CSI
+        CSI = -CSR
+        CSR = STR
+        IF (KDFLG.EQ.2) GO TO 85
+        KDFLG = 2
+        GO TO 80
+   70   CONTINUE
+        IF (RS1.GT.0.0D0) GO TO 320
+C-----------------------------------------------------------------------
+C     FOR ZR.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW
+C-----------------------------------------------------------------------
+        IF (ZR.LT.0.0D0) GO TO 320
+        KDFLG = 1
+        YR(I)=ZEROR
+        YI(I)=ZEROI
+        NZ=NZ+1
+        STR = CSI
+        CSI =-CSR
+        CSR = STR
+        IF (I.EQ.1) GO TO 80
+        IF ((YR(I-1).EQ.ZEROR).AND.(YI(I-1).EQ.ZEROI)) GO TO 80
+        YR(I-1)=ZEROR
+        YI(I-1)=ZEROI
+        NZ=NZ+1
+   80 CONTINUE
+      I = N
+   85 CONTINUE
+      RAZR = 1.0D0/ZABS(CMPLX(ZRR,ZRI,kind=KIND(1.0D0)))
+      STR = ZRR*RAZR
+      STI = -ZRI*RAZR
+      RZR = (STR+STR)*RAZR
+      RZI = (STI+STI)*RAZR
+      CKR = FN*RZR
+      CKI = FN*RZI
+      IB = I + 1
+      IF (N.LT.IB) GO TO 180
+C-----------------------------------------------------------------------
+C     TEST LAST MEMBER FOR UNDERFLOW AND OVERFLOW. SET SEQUENCE TO ZERO
+C     ON UNDERFLOW.
+C-----------------------------------------------------------------------
+      FN = FNU + DBLE(FLOAT(N-1))
+      IPARD = 1
+      IF (MR.NE.0) IPARD = 0
+      CALL ZUNHJ(ZNR, ZNI, FN, IPARD, TOL, PHIDR, PHIDI, ARGDR, ARGDI,
+     * ZET1DR, ZET1DI, ZET2DR, ZET2DI, ASUMDR, ASUMDI, BSUMDR, BSUMDI)
+      IF (KODE.EQ.1) GO TO 90
+      STR = ZBR + ZET2DR
+      STI = ZBI + ZET2DI
+      RAST = FN/ZABS(CMPLX(STR,STI,kind=KIND(1.0D0)))
+      STR = STR*RAST*RAST
+      STI = -STI*RAST*RAST
+      S1R = ZET1DR - STR
+      S1I = ZET1DI - STI
+      GO TO 100
+   90 CONTINUE
+      S1R = ZET1DR - ZET2DR
+      S1I = ZET1DI - ZET2DI
+  100 CONTINUE
+      RS1 = S1R
+      IF (DABS(RS1).GT.ELIM) GO TO 105
+      IF (DABS(RS1).LT.ALIM) GO TO 120
+C----------------------------------------------------------------------------
+C     REFINE ESTIMATE AND TEST
+C-------------------------------------------------------------------------
+      APHI = ZABS(CMPLX(PHIDR,PHIDI,kind=KIND(1.0D0)))
+      RS1 = RS1+DLOG(APHI)
+      IF (DABS(RS1).LT.ELIM) GO TO 120
+  105 CONTINUE
+      IF (RS1.GT.0.0D0) GO TO 320
+C-----------------------------------------------------------------------
+C     FOR ZR.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW
+C-----------------------------------------------------------------------
+      IF (ZR.LT.0.0D0) GO TO 320
+      NZ = N
+      DO 106 I=1,N
+        YR(I) = ZEROR
+        YI(I) = ZEROI
+  106 CONTINUE
+      RETURN
+  120 CONTINUE
+      S1R = CYR(1)
+      S1I = CYI(1)
+      S2R = CYR(2)
+      S2I = CYI(2)
+      C1R = CSRR(KFLAG)
+      ASCLE = BRY(KFLAG)
+      DO 130 I=IB,N
+        C2R = S2R
+        C2I = S2I
+        S2R = CKR*C2R - CKI*C2I + S1R
+        S2I = CKR*C2I + CKI*C2R + S1I
+        S1R = C2R
+        S1I = C2I
+        CKR = CKR + RZR
+        CKI = CKI + RZI
+        C2R = S2R*C1R
+        C2I = S2I*C1R
+        YR(I) = C2R
+        YI(I) = C2I
+        IF (KFLAG.GE.3) GO TO 130
+        STR = DABS(C2R)
+        STI = DABS(C2I)
+        C2M = DMAX1(STR,STI)
+        IF (C2M.LE.ASCLE) GO TO 130
+        KFLAG = KFLAG + 1
+        ASCLE = BRY(KFLAG)
+        S1R = S1R*C1R
+        S1I = S1I*C1R
+        S2R = C2R
+        S2I = C2I
+        S1R = S1R*CSSR(KFLAG)
+        S1I = S1I*CSSR(KFLAG)
+        S2R = S2R*CSSR(KFLAG)
+        S2I = S2I*CSSR(KFLAG)
+        C1R = CSRR(KFLAG)
+  130 CONTINUE
+  180 CONTINUE
+      IF (MR.EQ.0) RETURN
+C-----------------------------------------------------------------------
+C     ANALYTIC CONTINUATION FOR RE(Z).LT.0.0D0
+C-----------------------------------------------------------------------
+      NZ = 0
+      FMR = DBLE(FLOAT(MR))
+      SGN = -DSIGN(PI,FMR)
+C-----------------------------------------------------------------------
+C     CSPN AND CSGN ARE COEFF OF K AND I FUNCIONS RESP.
+C-----------------------------------------------------------------------
+      CSGNI = SGN
+      IF (YY.LE.0.0D0) CSGNI = -CSGNI
+      IFN = INU + N - 1
+      ANG = FNF*SGN
+      CSPNR = DCOS(ANG)
+      CSPNI = DSIN(ANG)
+      IF (MOD(IFN,2).EQ.0) GO TO 190
+      CSPNR = -CSPNR
+      CSPNI = -CSPNI
+  190 CONTINUE
+C-----------------------------------------------------------------------
+C     CS=COEFF OF THE J FUNCTION TO GET THE I FUNCTION. I(FNU,Z) IS
+C     COMPUTED FROM EXP(I*FNU*HPI)*J(FNU,-I*Z) WHERE Z IS IN THE FIRST
+C     QUADRANT. FOURTH QUADRANT VALUES (YY.LE.0.0E0) ARE COMPUTED BY
+C     CONJUGATION SINCE THE I FUNCTION IS REAL ON THE POSITIVE REAL AXIS
+C-----------------------------------------------------------------------
+      CSR = SAR*CSGNI
+      CSI = CAR*CSGNI
+      IN = MOD(IFN,4) + 1
+      C2R = CIPR(IN)
+      C2I = CIPI(IN)
+      STR = CSR*C2R + CSI*C2I
+      CSI = -CSR*C2I + CSI*C2R
+      CSR = STR
+      ASC = BRY(1)
+      IUF = 0
+      KK = N
+      KDFLG = 1
+      IB = IB - 1
+      IC = IB - 1
+      DO 290 K=1,N
+        FN = FNU + DBLE(FLOAT(KK-1))
+C-----------------------------------------------------------------------
+C     LOGIC TO SORT OUT CASES WHOSE PARAMETERS WERE SET FOR THE K
+C     FUNCTION ABOVE
+C-----------------------------------------------------------------------
+        IF (N.GT.2) GO TO 175
+  172   CONTINUE
+        PHIDR = PHIR(J)
+        PHIDI = PHII(J)
+        ARGDR = ARGR(J)
+        ARGDI = ARGI(J)
+        ZET1DR = ZETA1R(J)
+        ZET1DI = ZETA1I(J)
+        ZET2DR = ZETA2R(J)
+        ZET2DI = ZETA2I(J)
+        ASUMDR = ASUMR(J)
+        ASUMDI = ASUMI(J)
+        BSUMDR = BSUMR(J)
+        BSUMDI = BSUMI(J)
+        J = 3 - J
+        GO TO 210
+  175   CONTINUE
+        IF ((KK.EQ.N).AND.(IB.LT.N)) GO TO 210
+        IF ((KK.EQ.IB).OR.(KK.EQ.IC)) GO TO 172
+        CALL ZUNHJ(ZNR, ZNI, FN, 0, TOL, PHIDR, PHIDI, ARGDR,
+     *   ARGDI, ZET1DR, ZET1DI, ZET2DR, ZET2DI, ASUMDR,
+     *   ASUMDI, BSUMDR, BSUMDI)
+  210   CONTINUE
+        IF (KODE.EQ.1) GO TO 220
+        STR = ZBR + ZET2DR
+        STI = ZBI + ZET2DI
+        RAST = FN/ZABS(CMPLX(STR,STI,kind=KIND(1.0D0)))
+        STR = STR*RAST*RAST
+        STI = -STI*RAST*RAST
+        S1R = -ZET1DR + STR
+        S1I = -ZET1DI + STI
+        GO TO 230
+  220   CONTINUE
+        S1R = -ZET1DR + ZET2DR
+        S1I = -ZET1DI + ZET2DI
+  230   CONTINUE
+C-----------------------------------------------------------------------
+C     TEST FOR UNDERFLOW AND OVERFLOW
+C-----------------------------------------------------------------------
+        RS1 = S1R
+        IF (DABS(RS1).GT.ELIM) GO TO 280
+        IF (KDFLG.EQ.1) IFLAG = 2
+        IF (DABS(RS1).LT.ALIM) GO TO 240
+C-----------------------------------------------------------------------
+C     REFINE  TEST AND SCALE
+C-----------------------------------------------------------------------
+        APHI = ZABS(CMPLX(PHIDR,PHIDI,kind=KIND(1.0D0)))
+        AARG = ZABS(CMPLX(ARGDR,ARGDI,kind=KIND(1.0D0)))
+        RS1 = RS1 + DLOG(APHI) - 0.25D0*DLOG(AARG) - AIC
+        IF (DABS(RS1).GT.ELIM) GO TO 280
+        IF (KDFLG.EQ.1) IFLAG = 1
+        IF (RS1.LT.0.0D0) GO TO 240
+        IF (KDFLG.EQ.1) IFLAG = 3
+  240   CONTINUE
+        CALL ZAIRY(ARGDR, ARGDI, 0, 2, AIR, AII, NAI, IDUM)
+        CALL ZAIRY(ARGDR, ARGDI, 1, 2, DAIR, DAII, NDAI, IDUM)
+        STR = DAIR*BSUMDR - DAII*BSUMDI
+        STI = DAIR*BSUMDI + DAII*BSUMDR
+        STR = STR + (AIR*ASUMDR-AII*ASUMDI)
+        STI = STI + (AIR*ASUMDI+AII*ASUMDR)
+        PTR = STR*PHIDR - STI*PHIDI
+        PTI = STR*PHIDI + STI*PHIDR
+        S2R = PTR*CSR - PTI*CSI
+        S2I = PTR*CSI + PTI*CSR
+        STR = DEXP(S1R)*CSSR(IFLAG)
+        S1R = STR*DCOS(S1I)
+        S1I = STR*DSIN(S1I)
+        STR = S2R*S1R - S2I*S1I
+        S2I = S2R*S1I + S2I*S1R
+        S2R = STR
+        IF (IFLAG.NE.1) GO TO 250
+        CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL)
+        IF (NW.EQ.0) GO TO 250
+        S2R = ZEROR
+        S2I = ZEROI
+  250   CONTINUE
+        IF (YY.LE.0.0D0) S2I = -S2I
+        CYR(KDFLG) = S2R
+        CYI(KDFLG) = S2I
+        C2R = S2R
+        C2I = S2I
+        S2R = S2R*CSRR(IFLAG)
+        S2I = S2I*CSRR(IFLAG)
+C-----------------------------------------------------------------------
+C     ADD I AND K FUNCTIONS, K SEQUENCE IN Y(I), I=1,N
+C-----------------------------------------------------------------------
+        S1R = YR(KK)
+        S1I = YI(KK)
+        IF (KODE.EQ.1) GO TO 270
+        CALL ZS1S2(ZRR, ZRI, S1R, S1I, S2R, S2I, NW, ASC, ALIM, IUF)
+        NZ = NZ + NW
+  270   CONTINUE
+        YR(KK) = S1R*CSPNR - S1I*CSPNI + S2R
+        YI(KK) = S1R*CSPNI + S1I*CSPNR + S2I
+        KK = KK - 1
+        CSPNR = -CSPNR
+        CSPNI = -CSPNI
+        STR = CSI
+        CSI = -CSR
+        CSR = STR
+        IF (C2R.NE.0.0D0 .OR. C2I.NE.0.0D0) GO TO 255
+        KDFLG = 1
+        GO TO 290
+  255   CONTINUE
+        IF (KDFLG.EQ.2) GO TO 295
+        KDFLG = 2
+        GO TO 290
+  280   CONTINUE
+        IF (RS1.GT.0.0D0) GO TO 320
+        S2R = ZEROR
+        S2I = ZEROI
+        GO TO 250
+  290 CONTINUE
+      K = N
+  295 CONTINUE
+      IL = N - K
+      IF (IL.EQ.0) RETURN
+C-----------------------------------------------------------------------
+C     RECUR BACKWARD FOR REMAINDER OF I SEQUENCE AND ADD IN THE
+C     K FUNCTIONS, SCALING THE I SEQUENCE DURING RECURRENCE TO KEEP
+C     INTERMEDIATE ARITHMETIC ON SCALE NEAR EXPONENT EXTREMES.
+C-----------------------------------------------------------------------
+      S1R = CYR(1)
+      S1I = CYI(1)
+      S2R = CYR(2)
+      S2I = CYI(2)
+      CSR = CSRR(IFLAG)
+      ASCLE = BRY(IFLAG)
+      FN = DBLE(FLOAT(INU+IL))
+      DO 310 I=1,IL
+        C2R = S2R
+        C2I = S2I
+        S2R = S1R + (FN+FNF)*(RZR*C2R-RZI*C2I)
+        S2I = S1I + (FN+FNF)*(RZR*C2I+RZI*C2R)
+        S1R = C2R
+        S1I = C2I
+        FN = FN - 1.0D0
+        C2R = S2R*CSR
+        C2I = S2I*CSR
+        CKR = C2R
+        CKI = C2I
+        C1R = YR(KK)
+        C1I = YI(KK)
+        IF (KODE.EQ.1) GO TO 300
+        CALL ZS1S2(ZRR, ZRI, C1R, C1I, C2R, C2I, NW, ASC, ALIM, IUF)
+        NZ = NZ + NW
+  300   CONTINUE
+        YR(KK) = C1R*CSPNR - C1I*CSPNI + C2R
+        YI(KK) = C1R*CSPNI + C1I*CSPNR + C2I
+        KK = KK - 1
+        CSPNR = -CSPNR
+        CSPNI = -CSPNI
+        IF (IFLAG.GE.3) GO TO 310
+        C2R = DABS(CKR)
+        C2I = DABS(CKI)
+        C2M = DMAX1(C2R,C2I)
+        IF (C2M.LE.ASCLE) GO TO 310
+        IFLAG = IFLAG + 1
+        ASCLE = BRY(IFLAG)
+        S1R = S1R*CSR
+        S1I = S1I*CSR
+        S2R = CKR
+        S2I = CKI
+        S1R = S1R*CSSR(IFLAG)
+        S1I = S1I*CSSR(IFLAG)
+        S2R = S2R*CSSR(IFLAG)
+        S2I = S2I*CSSR(IFLAG)
+        CSR = CSRR(IFLAG)
+  310 CONTINUE
+      RETURN
+  320 CONTINUE
+      NZ = -1
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zuoik.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zuoik.f
new file mode 100644
index 00000000..3715d6d4
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zuoik.f
@@ -0,0 +1,194 @@
+      SUBROUTINE ZUOIK(ZR, ZI, FNU, KODE, IKFLG, N, YR, YI, NUF, TOL,
+     * ELIM, ALIM)
+C***BEGIN PROLOGUE  ZUOIK
+C***REFER TO  ZBESI,ZBESK,ZBESH
+C
+C     ZUOIK COMPUTES THE LEADING TERMS OF THE UNIFORM ASYMPTOTIC
+C     EXPANSIONS FOR THE I AND K FUNCTIONS AND COMPARES THEM
+C     (IN LOGARITHMIC FORM) TO ALIM AND ELIM FOR OVER AND UNDERFLOW
+C     WHERE ALIM.LT.ELIM. IF THE MAGNITUDE, BASED ON THE LEADING
+C     EXPONENTIAL, IS LESS THAN ALIM OR GREATER THAN -ALIM, THEN
+C     THE RESULT IS ON SCALE. IF NOT, THEN A REFINED TEST USING OTHER
+C     MULTIPLIERS (IN LOGARITHMIC FORM) IS MADE BASED ON ELIM. HERE
+C     EXP(-ELIM)=SMALLEST MACHINE NUMBER*1.0E+3 AND EXP(-ALIM)=
+C     EXP(-ELIM)/TOL
+C
+C     IKFLG=1 MEANS THE I SEQUENCE IS TESTED
+C          =2 MEANS THE K SEQUENCE IS TESTED
+C     NUF = 0 MEANS THE LAST MEMBER OF THE SEQUENCE IS ON SCALE
+C         =-1 MEANS AN OVERFLOW WOULD OCCUR
+C     IKFLG=1 AND NUF.GT.0 MEANS THE LAST NUF Y VALUES WERE SET TO ZERO
+C             THE FIRST N-NUF VALUES MUST BE SET BY ANOTHER ROUTINE
+C     IKFLG=2 AND NUF.EQ.N MEANS ALL Y VALUES WERE SET TO ZERO
+C     IKFLG=2 AND 0.LT.NUF.LT.N NOT CONSIDERED. Y MUST BE SET BY
+C             ANOTHER ROUTINE
+C
+C***ROUTINES CALLED  ZUCHK,ZUNHJ,ZUNIK,D1MACH,ZABS,ZLOG
+C***END PROLOGUE  ZUOIK
+C     COMPLEX ARG,ASUM,BSUM,CWRK,CZ,CZERO,PHI,SUM,Y,Z,ZB,ZETA1,ZETA2,ZN,
+C    *ZR
+      DOUBLE PRECISION AARG, AIC, ALIM, APHI, ARGI, ARGR, ASUMI, ASUMR,
+     * ASCLE, AX, AY, BSUMI, BSUMR, CWRKI, CWRKR, CZI, CZR, ELIM, FNN,
+     * FNU, GNN, GNU, PHII, PHIR, RCZ, STR, STI, SUMI, SUMR, TOL, YI,
+     * YR, ZBI, ZBR, ZEROI, ZEROR, ZETA1I, ZETA1R, ZETA2I, ZETA2R, ZI,
+     * ZNI, ZNR, ZR, ZRI, ZRR, D1MACH, ZABS
+      INTEGER I, IDUM, IFORM, IKFLG, INIT, KODE, N, NN, NUF, NW
+      DIMENSION YR(N), YI(N), CWRKR(16), CWRKI(16)
+      DATA ZEROR,ZEROI / 0.0D0, 0.0D0 /
+      DATA AIC / 1.265512123484645396D+00 /
+      NUF = 0
+      NN = N
+      ZRR = ZR
+      ZRI = ZI
+      IF (ZR.GE.0.0D0) GO TO 10
+      ZRR = -ZR
+      ZRI = -ZI
+   10 CONTINUE
+      ZBR = ZRR
+      ZBI = ZRI
+      AX = DABS(ZR)*1.7321D0
+      AY = DABS(ZI)
+      IFORM = 1
+      IF (AY.GT.AX) IFORM = 2
+      GNU = DMAX1(FNU,1.0D0)
+      IF (IKFLG.EQ.1) GO TO 20
+      FNN = DBLE(FLOAT(NN))
+      GNN = FNU + FNN - 1.0D0
+      GNU = DMAX1(GNN,FNN)
+   20 CONTINUE
+C-----------------------------------------------------------------------
+C     ONLY THE MAGNITUDE OF ARG AND PHI ARE NEEDED ALONG WITH THE
+C     REAL PARTS OF ZETA1, ZETA2 AND ZB. NO ATTEMPT IS MADE TO GET
+C     THE SIGN OF THE IMAGINARY PART CORRECT.
+C-----------------------------------------------------------------------
+      IF (IFORM.EQ.2) GO TO 30
+      INIT = 0
+      CALL ZUNIK(ZRR, ZRI, GNU, IKFLG, 1, TOL, INIT, PHIR, PHII,
+     * ZETA1R, ZETA1I, ZETA2R, ZETA2I, SUMR, SUMI, CWRKR, CWRKI)
+      CZR = -ZETA1R + ZETA2R
+      CZI = -ZETA1I + ZETA2I
+      GO TO 50
+   30 CONTINUE
+      ZNR = ZRI
+      ZNI = -ZRR
+      IF (ZI.GT.0.0D0) GO TO 40
+      ZNR = -ZNR
+   40 CONTINUE
+      CALL ZUNHJ(ZNR, ZNI, GNU, 1, TOL, PHIR, PHII, ARGR, ARGI, ZETA1R,
+     * ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI)
+      CZR = -ZETA1R + ZETA2R
+      CZI = -ZETA1I + ZETA2I
+      AARG = ZABS(CMPLX(ARGR,ARGI,kind=KIND(1.0D0)))
+   50 CONTINUE
+      IF (KODE.EQ.1) GO TO 60
+      CZR = CZR - ZBR
+      CZI = CZI - ZBI
+   60 CONTINUE
+      IF (IKFLG.EQ.1) GO TO 70
+      CZR = -CZR
+      CZI = -CZI
+   70 CONTINUE
+      APHI = ZABS(CMPLX(PHIR,PHII,kind=KIND(1.0D0)))
+      RCZ = CZR
+C-----------------------------------------------------------------------
+C     OVERFLOW TEST
+C-----------------------------------------------------------------------
+      IF (RCZ.GT.ELIM) GO TO 210
+      IF (RCZ.LT.ALIM) GO TO 80
+      RCZ = RCZ + DLOG(APHI)
+      IF (IFORM.EQ.2) RCZ = RCZ - 0.25D0*DLOG(AARG) - AIC
+      IF (RCZ.GT.ELIM) GO TO 210
+      GO TO 130
+   80 CONTINUE
+C-----------------------------------------------------------------------
+C     UNDERFLOW TEST
+C-----------------------------------------------------------------------
+      IF (RCZ.LT.(-ELIM)) GO TO 90
+      IF (RCZ.GT.(-ALIM)) GO TO 130
+      RCZ = RCZ + DLOG(APHI)
+      IF (IFORM.EQ.2) RCZ = RCZ - 0.25D0*DLOG(AARG) - AIC
+      IF (RCZ.GT.(-ELIM)) GO TO 110
+   90 CONTINUE
+      DO 100 I=1,NN
+        YR(I) = ZEROR
+        YI(I) = ZEROI
+  100 CONTINUE
+      NUF = NN
+      RETURN
+  110 CONTINUE
+      ASCLE = 1.0D+3*D1MACH(1)/TOL
+      CALL ZLOG(PHIR, PHII, STR, STI, IDUM)
+      CZR = CZR + STR
+      CZI = CZI + STI
+      IF (IFORM.EQ.1) GO TO 120
+      CALL ZLOG(ARGR, ARGI, STR, STI, IDUM)
+      CZR = CZR - 0.25D0*STR - AIC
+      CZI = CZI - 0.25D0*STI
+  120 CONTINUE
+      AX = DEXP(RCZ)/TOL
+      AY = CZI
+      CZR = AX*DCOS(AY)
+      CZI = AX*DSIN(AY)
+      CALL ZUCHK(CZR, CZI, NW, ASCLE, TOL)
+      IF (NW.NE.0) GO TO 90
+  130 CONTINUE
+      IF (IKFLG.EQ.2) RETURN
+      IF (N.EQ.1) RETURN
+C-----------------------------------------------------------------------
+C     SET UNDERFLOWS ON I SEQUENCE
+C-----------------------------------------------------------------------
+  140 CONTINUE
+      GNU = FNU + DBLE(FLOAT(NN-1))
+      IF (IFORM.EQ.2) GO TO 150
+      INIT = 0
+      CALL ZUNIK(ZRR, ZRI, GNU, IKFLG, 1, TOL, INIT, PHIR, PHII,
+     * ZETA1R, ZETA1I, ZETA2R, ZETA2I, SUMR, SUMI, CWRKR, CWRKI)
+      CZR = -ZETA1R + ZETA2R
+      CZI = -ZETA1I + ZETA2I
+      GO TO 160
+  150 CONTINUE
+      CALL ZUNHJ(ZNR, ZNI, GNU, 1, TOL, PHIR, PHII, ARGR, ARGI, ZETA1R,
+     * ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI)
+      CZR = -ZETA1R + ZETA2R
+      CZI = -ZETA1I + ZETA2I
+      AARG = ZABS(CMPLX(ARGR,ARGI,kind=KIND(1.0D0)))
+  160 CONTINUE
+      IF (KODE.EQ.1) GO TO 170
+      CZR = CZR - ZBR
+      CZI = CZI - ZBI
+  170 CONTINUE
+      APHI = ZABS(CMPLX(PHIR,PHII,kind=KIND(1.0D0)))
+      RCZ = CZR
+      IF (RCZ.LT.(-ELIM)) GO TO 180
+      IF (RCZ.GT.(-ALIM)) RETURN
+      RCZ = RCZ + DLOG(APHI)
+      IF (IFORM.EQ.2) RCZ = RCZ - 0.25D0*DLOG(AARG) - AIC
+      IF (RCZ.GT.(-ELIM)) GO TO 190
+  180 CONTINUE
+      YR(NN) = ZEROR
+      YI(NN) = ZEROI
+      NN = NN - 1
+      NUF = NUF + 1
+      IF (NN.EQ.0) RETURN
+      GO TO 140
+  190 CONTINUE
+      ASCLE = 1.0D+3*D1MACH(1)/TOL
+      CALL ZLOG(PHIR, PHII, STR, STI, IDUM)
+      CZR = CZR + STR
+      CZI = CZI + STI
+      IF (IFORM.EQ.1) GO TO 200
+      CALL ZLOG(ARGR, ARGI, STR, STI, IDUM)
+      CZR = CZR - 0.25D0*STR - AIC
+      CZI = CZI - 0.25D0*STI
+  200 CONTINUE
+      AX = DEXP(RCZ)/TOL
+      AY = CZI
+      CZR = AX*DCOS(AY)
+      CZI = AX*DSIN(AY)
+      CALL ZUCHK(CZR, CZI, NW, ASCLE, TOL)
+      IF (NW.NE.0) GO TO 180
+      RETURN
+  210 CONTINUE
+      NUF = -1
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zwrsk.f b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zwrsk.f
new file mode 100644
index 00000000..37cb8d8c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/amoslib/zwrsk.f
@@ -0,0 +1,94 @@
+      SUBROUTINE ZWRSK(ZRR, ZRI, FNU, KODE, N, YR, YI, NZ, CWR, CWI,
+     * TOL, ELIM, ALIM)
+C***BEGIN PROLOGUE  ZWRSK
+C***REFER TO  ZBESI,ZBESK
+C
+C     ZWRSK COMPUTES THE I BESSEL FUNCTION FOR RE(Z).GE.0.0 BY
+C     NORMALIZING THE I FUNCTION RATIOS FROM ZRATI BY THE WRONSKIAN
+C
+C***ROUTINES CALLED  D1MACH,ZBKNU,ZRATI,ZABS
+C***END PROLOGUE  ZWRSK
+C     COMPLEX CINU,CSCL,CT,CW,C1,C2,RCT,ST,Y,ZR
+      DOUBLE PRECISION ACT, ACW, ALIM, ASCLE, CINUI, CINUR, CSCLR, CTI,
+     * CTR, CWI, CWR, C1I, C1R, C2I, C2R, ELIM, FNU, PTI, PTR, RACT,
+     * STI, STR, TOL, YI, YR, ZRI, ZRR, ZABS, D1MACH
+      INTEGER I, KODE, N, NW, NZ
+      DIMENSION YR(N), YI(N), CWR(2), CWI(2)
+C-----------------------------------------------------------------------
+C     I(FNU+I-1,Z) BY BACKWARD RECURRENCE FOR RATIOS
+C     Y(I)=I(FNU+I,Z)/I(FNU+I-1,Z) FROM CRATI NORMALIZED BY THE
+C     WRONSKIAN WITH K(FNU,Z) AND K(FNU+1,Z) FROM CBKNU.
+C-----------------------------------------------------------------------
+      NZ = 0
+      CALL ZBKNU(ZRR, ZRI, FNU, KODE, 2, CWR, CWI, NW, TOL, ELIM, ALIM)
+      IF (NW.NE.0) GO TO 50
+      CALL ZRATI(ZRR, ZRI, FNU, N, YR, YI, TOL)
+C-----------------------------------------------------------------------
+C     RECUR FORWARD ON I(FNU+1,Z) = R(FNU,Z)*I(FNU,Z),
+C     R(FNU+J-1,Z)=Y(J),  J=1,...,N
+C-----------------------------------------------------------------------
+      CINUR = 1.0D0
+      CINUI = 0.0D0
+      IF (KODE.EQ.1) GO TO 10
+      CINUR = DCOS(ZRI)
+      CINUI = DSIN(ZRI)
+   10 CONTINUE
+C-----------------------------------------------------------------------
+C     ON LOW EXPONENT MACHINES THE K FUNCTIONS CAN BE CLOSE TO BOTH
+C     THE UNDER AND OVERFLOW LIMITS AND THE NORMALIZATION MUST BE
+C     SCALED TO PREVENT OVER OR UNDERFLOW. CUOIK HAS DETERMINED THAT
+C     THE RESULT IS ON SCALE.
+C-----------------------------------------------------------------------
+      ACW = ZABS(CMPLX(CWR(2),CWI(2),kind=KIND(1.0D0)))
+      ASCLE = 1.0D+3*D1MACH(1)/TOL
+      CSCLR = 1.0D0
+      IF (ACW.GT.ASCLE) GO TO 20
+      CSCLR = 1.0D0/TOL
+      GO TO 30
+   20 CONTINUE
+      ASCLE = 1.0D0/ASCLE
+      IF (ACW.LT.ASCLE) GO TO 30
+      CSCLR = TOL
+   30 CONTINUE
+      C1R = CWR(1)*CSCLR
+      C1I = CWI(1)*CSCLR
+      C2R = CWR(2)*CSCLR
+      C2I = CWI(2)*CSCLR
+      STR = YR(1)
+      STI = YI(1)
+C-----------------------------------------------------------------------
+C     CINU=CINU*(CONJG(CT)/CABS(CT))*(1.0D0/CABS(CT) PREVENTS
+C     UNDER- OR OVERFLOW PREMATURELY BY SQUARING CABS(CT)
+C-----------------------------------------------------------------------
+      PTR = STR*C1R - STI*C1I
+      PTI = STR*C1I + STI*C1R
+      PTR = PTR + C2R
+      PTI = PTI + C2I
+      CTR = ZRR*PTR - ZRI*PTI
+      CTI = ZRR*PTI + ZRI*PTR
+      ACT = ZABS(CMPLX(CTR,CTI,kind=KIND(1.0D0)))
+      RACT = 1.0D0/ACT
+      CTR = CTR*RACT
+      CTI = -CTI*RACT
+      PTR = CINUR*RACT
+      PTI = CINUI*RACT
+      CINUR = PTR*CTR - PTI*CTI
+      CINUI = PTR*CTI + PTI*CTR
+      YR(1) = CINUR*CSCLR
+      YI(1) = CINUI*CSCLR
+      IF (N.EQ.1) RETURN
+      DO 40 I=2,N
+        PTR = STR*CINUR - STI*CINUI
+        CINUI = STR*CINUI + STI*CINUR
+        CINUR = PTR
+        STR = YR(I)
+        STI = YI(I)
+        YR(I) = CINUR*CSCLR
+        YI(I) = CINUI*CSCLR
+   40 CONTINUE
+      RETURN
+   50 CONTINUE
+      NZ = -1
+      IF(NW.EQ.(-2)) NZ=-2
+      RETURN
+      END
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/doc.go b/vendor/gonum.org/v1/gonum/mathext/internal/amos/doc.go
new file mode 100644
index 00000000..45182541
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// package amos implements functions originally in the Netlab code by Donald Amos.
+package amos // import "gonum.org/v1/gonum/mathext/internal/amos"
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/amos/origcode_test.go b/vendor/gonum.org/v1/gonum/mathext/internal/amos/origcode_test.go
new file mode 100644
index 00000000..a7d8be8f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/amos/origcode_test.go
@@ -0,0 +1,2276 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package amos
+
+import (
+	"math"
+	"math/cmplx"
+)
+
+// These routines are the versions directly modified from the Fortran code.
+// They are used to ensure that code style improvements do not change the
+// code output.
+
+func iabs(a int) int {
+	if a >= 0 {
+		return a
+	}
+	return -a
+}
+
+func min0(a, b int) int {
+	if a < b {
+		return a
+	}
+	return b
+}
+
+func max0(a, b int) int {
+	if a > b {
+		return a
+	}
+	return b
+}
+
+func zairyOrig(ZR, ZI float64, ID, KODE int) (AIR, AII float64, NZ int) {
+	// zairy is adapted from the original Netlib code by Donald Amos.
+	// http://www.netlib.no/netlib/amos/zairy.f
+
+	// Original comment:
+	/*
+		C***BEGIN PROLOGUE  ZAIRY
+		C***DATE WRITTEN   830501   (YYMMDD)
+		C***REVISION DATE  890801   (YYMMDD)
+		C***CATEGORY NO.  B5K
+		C***KEYWORDS  AIRY FUNCTION,BESSEL FUNCTIONS OF ORDER ONE THIRD
+		C***AUTHOR  AMOS, DONALD E., SANDIA NATIONAL LABORATORIES
+		C***PURPOSE  TO COMPUTE AIRY FUNCTIONS AI(Z) AND DAI(Z) FOR COMPLEX Z
+		C***DESCRIPTION
+		C
+		C                      ***A DOUBLE PRECISION ROUTINE***
+		C         ON KODE=1, ZAIRY COMPUTES THE COMPLEX AIRY FUNCTION AI(Z) OR
+		C         ITS DERIVATIVE DAI(Z)/DZ ON ID=0 OR ID=1 RESPECTIVELY. ON
+		C         KODE=2, A SCALING OPTION CEXP(ZTA)*AI(Z) OR CEXP(ZTA)*
+		C         DAI(Z)/DZ IS PROVIDED TO REMOVE THE EXPONENTIAL DECAY IN
+		C         -PI/3<ARG(Z)<PI/3 AND THE EXPONENTIAL GROWTH IN
+		C         PI/3<ABS(ARG(Z))<PI WHERE ZTA=(2/3)*Z*CSQRT(Z).
+		C
+		C         WHILE THE AIRY FUNCTIONS AI(Z) AND DAI(Z)/DZ ARE ANALYTIC IN
+		C         THE WHOLE Z PLANE, THE CORRESPONDING SCALED FUNCTIONS DEFINED
+		C         FOR KODE=2 HAVE A CUT ALONG THE NEGATIVE REAL AXIS.
+		C         DEFINTIONS AND NOTATION ARE FOUND IN THE NBS HANDBOOK OF
+		C         MATHEMATICAL FUNCTIONS (REF. 1).
+		C
+		C         INPUT      ZR,ZI ARE DOUBLE PRECISION
+		C           ZR,ZI  - Z=CMPLX(ZR,ZI)
+		C           ID     - ORDER OF DERIVATIVE, ID=0 OR ID=1
+		C           KODE   - A PARAMETER TO INDICATE THE SCALING OPTION
+		C                    KODE= 1  returnS
+		C                             AI=AI(Z)                ON ID=0 OR
+		C                             AI=DAI(Z)/DZ            ON ID=1
+		C                        = 2  returnS
+		C                             AI=CEXP(ZTA)*AI(Z)       ON ID=0 OR
+		C                             AI=CEXP(ZTA)*DAI(Z)/DZ   ON ID=1 WHERE
+		C                             ZTA=(2/3)*Z*CSQRT(Z)
+		C
+		C         OUTPUT     AIR,AII ARE DOUBLE PRECISION
+		C           AIR,AII- COMPLEX ANSWER DEPENDING ON THE CHOICES FOR ID AND
+		C                    KODE
+		C           NZ     - UNDERFLOW INDICATOR
+		C                    NZ= 0   , NORMAL return
+		C                    NZ= 1   , AI=CMPLX(0.0E0,0.0E0) DUE TO UNDERFLOW IN
+		C                              -PI/3<ARG(Z)<PI/3 ON KODE=1
+		C           IERR   - ERROR FLAG
+		C                    IERR=0, NORMAL return - COMPUTATION COMPLETED
+		C                    IERR=1, INPUT ERROR   - NO COMPUTATION
+		C                    IERR=2, OVERFLOW      - NO COMPUTATION, REAL(ZTA)
+		C                            TOO LARGE ON KODE=1
+		C                    IERR=3, CABS(Z) LARGE      - COMPUTATION COMPLETED
+		C                            LOSSES OF SIGNIFCANCE BY ARGUMENT REDUCTION
+		C                            PRODUCE LESS THAN HALF OF MACHINE ACCURACY
+		C                    IERR=4, CABS(Z) TOO LARGE  - NO COMPUTATION
+		C                            COMPLETE LOSS OF ACCURACY BY ARGUMENT
+		C                            REDUCTION
+		C                    IERR=5, ERROR              - NO COMPUTATION,
+		C                            ALGORITHM TERMINATION CONDITION NOT MET
+		C
+		C***LONG DESCRIPTION
+		C
+		C         AI AND DAI ARE COMPUTED FOR CABS(Z)>1.0 FROM THE K BESSEL
+		C         FUNCTIONS BY
+		C
+		C            AI(Z)=C*SQRT(Z)*K(1/3,ZTA) , DAI(Z)=-C*Z*K(2/3,ZTA)
+		C                           C=1.0/(PI*SQRT(3.0))
+		C                            ZTA=(2/3)*Z**(3/2)
+		C
+		C         WITH THE POWER SERIES FOR CABS(Z)<=1.0.
+		C
+		C         IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE-
+		C         MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z IS LARGE, LOSSES
+		C         OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR. CONSEQUENTLY, IF
+		C         THE MAGNITUDE OF ZETA=(2/3)*Z**1.5 EXCEEDS U1=SQRT(0.5/UR),
+		C         THEN LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR
+		C         FLAG IERR=3 IS TRIGGERED WHERE UR=dmax(dmach[4),1.0D-18) IS
+		C         DOUBLE PRECISION UNIT ROUNDOFF LIMITED TO 18 DIGITS PRECISION.
+		C         ALSO, if THE MAGNITUDE OF ZETA IS LARGER THAN U2=0.5/UR, THEN
+		C         ALL SIGNIFICANCE IS LOST AND IERR=4. IN ORDER TO USE THE INT
+		C         FUNCTION, ZETA MUST BE FURTHER RESTRICTED NOT TO EXCEED THE
+		C         LARGEST INTEGER, U3=I1MACH(9). THUS, THE MAGNITUDE OF ZETA
+		C         MUST BE RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2,
+		C         AND U3 ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE
+		C         PRECISION ARITHMETIC AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE
+		C         PRECISION ARITHMETIC RESPECTIVELY. THIS MAKES U2 AND U3 LIMIT-
+		C         ING IN THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT THE MAG-
+		C         NITUDE OF Z CANNOT EXCEED 3.1E+4 IN SINGLE AND 2.1E+6 IN
+		C         DOUBLE PRECISION ARITHMETIC. THIS ALSO MEANS THAT ONE CAN
+		C         EXPECT TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES,
+		C         NO DIGITS IN SINGLE PRECISION AND ONLY 7 DIGITS IN DOUBLE
+		C         PRECISION ARITHMETIC. SIMILAR CONSIDERATIONS HOLD FOR OTHER
+		C         MACHINES.
+		C
+		C         THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX
+		C         BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT
+		C         ROUNDOFF,1.0E-18) IS THE NOMINAL PRECISION AND 10**S REPRE-
+		C         SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE
+		C         ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))),
+		C         ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF
+		C         CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY
+		C         HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN
+		C         ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY
+		C         SEVERAL ORDERS OF MAGNITUDE. if ONE COMPONENT IS 10**K LARGER
+		C         THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K,
+		C         0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS
+		C         THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER
+		C         COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY
+		C         BECAUSE, IN COMPLEX ARITHMETIC WITH PRECISION P, THE SMALLER
+		C         COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE
+		C         MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES,
+		C         THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P,
+		C         OR -PI/2+P.
+		C
+		C***REFERENCES  HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ
+		C                 AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF
+		C                 COMMERCE, 1955.
+		C
+		C               COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+		C                 AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983
+		C
+		C               A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+		C                 ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85-
+		C                 1018, MAY, 1985
+		C
+		C               A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+		C                 ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS.
+		C                 MATH. SOFTWARE, 1986
+	*/
+	var AI, CONE, CSQ, CY, S1, S2, TRM1, TRM2, Z, ZTA, Z3 complex128
+	var AA, AD, AK, ALIM, ATRM, AZ, AZ3, BK,
+		CC, CK, COEF, CONEI, CONER, CSQI, CSQR, C1, C2, DIG,
+		DK, D1, D2, ELIM, FID, FNU, PTR, RL, R1M5, SFAC, STI, STR,
+		S1I, S1R, S2I, S2R, TOL, TRM1I, TRM1R, TRM2I, TRM2R, TTH, ZEROI,
+		ZEROR, ZTAI, ZTAR, Z3I, Z3R, ALAZ, BB float64
+	var IERR, IFLAG, K, K1, K2, MR, NN int
+	var tmp complex128
+
+	// Extra element for padding.
+	CYR := []float64{math.NaN(), 0}
+	CYI := []float64{math.NaN(), 0}
+
+	_ = AI
+	_ = CONE
+	_ = CSQ
+	_ = CY
+	_ = S1
+	_ = S2
+	_ = TRM1
+	_ = TRM2
+	_ = Z
+	_ = ZTA
+	_ = Z3
+
+	TTH = 6.66666666666666667E-01
+	C1 = 3.55028053887817240E-01
+	C2 = 2.58819403792806799E-01
+	COEF = 1.83776298473930683E-01
+	ZEROR = 0
+	ZEROI = 0
+	CONER = 1
+	CONEI = 0
+
+	NZ = 0
+	if ID < 0 || ID > 1 {
+		IERR = 1
+	}
+	if KODE < 1 || KODE > 2 {
+		IERR = 1
+	}
+	if IERR != 0 {
+		return
+	}
+	AZ = zabs(complex(ZR, ZI))
+	TOL = dmax(dmach[4], 1.0E-18)
+	FID = float64(ID)
+	if AZ > 1.0E0 {
+		goto Seventy
+	}
+
+	// POWER SERIES FOR CABS(Z)<=1.
+	S1R = CONER
+	S1I = CONEI
+	S2R = CONER
+	S2I = CONEI
+	if AZ < TOL {
+		goto OneSeventy
+	}
+	AA = AZ * AZ
+	if AA < TOL/AZ {
+		goto Forty
+	}
+	TRM1R = CONER
+	TRM1I = CONEI
+	TRM2R = CONER
+	TRM2I = CONEI
+	ATRM = 1.0E0
+	STR = ZR*ZR - ZI*ZI
+	STI = ZR*ZI + ZI*ZR
+	Z3R = STR*ZR - STI*ZI
+	Z3I = STR*ZI + STI*ZR
+	AZ3 = AZ * AA
+	AK = 2.0E0 + FID
+	BK = 3.0E0 - FID - FID
+	CK = 4.0E0 - FID
+	DK = 3.0E0 + FID + FID
+	D1 = AK * DK
+	D2 = BK * CK
+	AD = dmin(D1, D2)
+	AK = 24.0E0 + 9.0E0*FID
+	BK = 30.0E0 - 9.0E0*FID
+	for K = 1; K <= 25; K++ {
+		STR = (TRM1R*Z3R - TRM1I*Z3I) / D1
+		TRM1I = (TRM1R*Z3I + TRM1I*Z3R) / D1
+		TRM1R = STR
+		S1R = S1R + TRM1R
+		S1I = S1I + TRM1I
+		STR = (TRM2R*Z3R - TRM2I*Z3I) / D2
+		TRM2I = (TRM2R*Z3I + TRM2I*Z3R) / D2
+		TRM2R = STR
+		S2R = S2R + TRM2R
+		S2I = S2I + TRM2I
+		ATRM = ATRM * AZ3 / AD
+		D1 = D1 + AK
+		D2 = D2 + BK
+		AD = dmin(D1, D2)
+		if ATRM < TOL*AD {
+			goto Forty
+		}
+		AK = AK + 18.0E0
+		BK = BK + 18.0E0
+	}
+Forty:
+	if ID == 1 {
+		goto Fifty
+	}
+	AIR = S1R*C1 - C2*(ZR*S2R-ZI*S2I)
+	AII = S1I*C1 - C2*(ZR*S2I+ZI*S2R)
+	if KODE == 1 {
+		return
+	}
+	tmp = zsqrt(complex(ZR, ZI))
+	STR = real(tmp)
+	STI = imag(tmp)
+	ZTAR = TTH * (ZR*STR - ZI*STI)
+	ZTAI = TTH * (ZR*STI + ZI*STR)
+	tmp = zexp(complex(ZTAR, ZTAI))
+	STR = real(tmp)
+	STI = imag(tmp)
+	PTR = AIR*STR - AII*STI
+	AII = AIR*STI + AII*STR
+	AIR = PTR
+	return
+
+Fifty:
+	AIR = -S2R * C2
+	AII = -S2I * C2
+	if AZ <= TOL {
+		goto Sixty
+	}
+	STR = ZR*S1R - ZI*S1I
+	STI = ZR*S1I + ZI*S1R
+	CC = C1 / (1.0E0 + FID)
+	AIR = AIR + CC*(STR*ZR-STI*ZI)
+	AII = AII + CC*(STR*ZI+STI*ZR)
+
+Sixty:
+	if KODE == 1 {
+		return
+	}
+	tmp = zsqrt(complex(ZR, ZI))
+	STR = real(tmp)
+	STI = imag(tmp)
+	ZTAR = TTH * (ZR*STR - ZI*STI)
+	ZTAI = TTH * (ZR*STI + ZI*STR)
+	tmp = zexp(complex(ZTAR, ZTAI))
+	STR = real(tmp)
+	STI = imag(tmp)
+	PTR = STR*AIR - STI*AII
+	AII = STR*AII + STI*AIR
+	AIR = PTR
+	return
+
+	// CASE FOR CABS(Z)>1.0.
+Seventy:
+	FNU = (1.0E0 + FID) / 3.0E0
+
+	/*
+	   SET PARAMETERS RELATED TO MACHINE CONSTANTS.
+	   TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0D-18.
+	   ELIM IS THE APPROXIMATE EXPONENTIAL OVER-&&UNDERFLOW LIMIT.
+	   EXP(-ELIM)<EXP(-ALIM)=EXP(-ELIM)/TOL    AND
+	   EXP(ELIM)>EXP(ALIM)=EXP(ELIM)*TOL       ARE INTERVALS NEAR
+	   UNDERFLOW&&OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE.
+	   RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR LA>=Z.
+	   DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG).
+	*/
+	K1 = imach[15]
+	K2 = imach[16]
+	R1M5 = dmach[5]
+
+	K = min0(iabs(K1), iabs(K2))
+	ELIM = 2.303E0 * (float64(K)*R1M5 - 3.0E0)
+	K1 = imach[14] - 1
+	AA = R1M5 * float64(K1)
+	DIG = dmin(AA, 18.0E0)
+	AA = AA * 2.303E0
+	ALIM = ELIM + dmax(-AA, -41.45E0)
+	RL = 1.2E0*DIG + 3.0E0
+	ALAZ = dlog(AZ)
+
+	// TEST FOR PROPER RANGE.
+	AA = 0.5E0 / TOL
+	BB = float64(float32(imach[9])) * 0.5E0
+	AA = dmin(AA, BB)
+	AA = math.Pow(AA, TTH)
+	if AZ > AA {
+		goto TwoSixty
+	}
+	AA = dsqrt(AA)
+	if AZ > AA {
+		IERR = 3
+	}
+	tmp = zsqrt(complex(ZR, ZI))
+	CSQR = real(tmp)
+	CSQI = imag(tmp)
+	ZTAR = TTH * (ZR*CSQR - ZI*CSQI)
+	ZTAI = TTH * (ZR*CSQI + ZI*CSQR)
+
+	//  RE(ZTA)<=0 WHEN RE(Z)<0, ESPECIALLY WHEN IM(Z) IS SMALL.
+	IFLAG = 0
+	SFAC = 1.0E0
+	AK = ZTAI
+	if ZR >= 0.0E0 {
+		goto Eighty
+	}
+	BK = ZTAR
+	CK = -dabs(BK)
+	ZTAR = CK
+	ZTAI = AK
+
+Eighty:
+	if ZI != 0.0E0 {
+		goto Ninety
+	}
+	if ZR > 0.0E0 {
+		goto Ninety
+	}
+	ZTAR = 0.0E0
+	ZTAI = AK
+Ninety:
+	AA = ZTAR
+	if AA >= 0.0E0 && ZR > 0.0E0 {
+		goto OneTen
+	}
+	if KODE == 2 {
+		goto OneHundred
+	}
+
+	// OVERFLOW TEST.
+	if AA > (-ALIM) {
+		goto OneHundred
+	}
+	AA = -AA + 0.25E0*ALAZ
+	IFLAG = 1
+	SFAC = TOL
+	if AA > ELIM {
+		goto TwoSeventy
+	}
+
+OneHundred:
+	// CBKNU AND CACON return EXP(ZTA)*K(FNU,ZTA) ON KODE=2.
+	MR = 1
+	if ZI < 0.0E0 {
+		MR = -1
+	}
+	ZTAR, ZTAI, FNU, KODE, MR, _, CYR, CYI, NN, RL, TOL, ELIM, ALIM = zacaiOrig(ZTAR, ZTAI, FNU, KODE, MR, 1, CYR, CYI, NN, RL, TOL, ELIM, ALIM)
+	if NN < 0 {
+		goto TwoEighty
+	}
+	NZ = NZ + NN
+	goto OneThirty
+
+OneTen:
+	if KODE == 2 {
+		goto OneTwenty
+	}
+
+	// UNDERFLOW TEST.
+	if AA < ALIM {
+		goto OneTwenty
+	}
+	AA = -AA - 0.25E0*ALAZ
+	IFLAG = 2
+	SFAC = 1.0E0 / TOL
+	if AA < (-ELIM) {
+		goto TwoTen
+	}
+OneTwenty:
+	ZTAR, ZTAI, FNU, KODE, _, CYR, CYI, NZ, TOL, ELIM, ALIM = zbknuOrig(ZTAR, ZTAI, FNU, KODE, 1, CYR, CYI, NZ, TOL, ELIM, ALIM)
+
+OneThirty:
+	S1R = CYR[1] * COEF
+	S1I = CYI[1] * COEF
+	if IFLAG != 0 {
+		goto OneFifty
+	}
+	if ID == 1 {
+		goto OneFourty
+	}
+	AIR = CSQR*S1R - CSQI*S1I
+	AII = CSQR*S1I + CSQI*S1R
+	return
+OneFourty:
+	AIR = -(ZR*S1R - ZI*S1I)
+	AII = -(ZR*S1I + ZI*S1R)
+	return
+OneFifty:
+	S1R = S1R * SFAC
+	S1I = S1I * SFAC
+	if ID == 1 {
+		goto OneSixty
+	}
+	STR = S1R*CSQR - S1I*CSQI
+	S1I = S1R*CSQI + S1I*CSQR
+	S1R = STR
+	AIR = S1R / SFAC
+	AII = S1I / SFAC
+	return
+OneSixty:
+	STR = -(S1R*ZR - S1I*ZI)
+	S1I = -(S1R*ZI + S1I*ZR)
+	S1R = STR
+	AIR = S1R / SFAC
+	AII = S1I / SFAC
+	return
+OneSeventy:
+	AA = 1.0E+3 * dmach[1]
+	S1R = ZEROR
+	S1I = ZEROI
+	if ID == 1 {
+		goto OneNinety
+	}
+	if AZ <= AA {
+		goto OneEighty
+	}
+	S1R = C2 * ZR
+	S1I = C2 * ZI
+OneEighty:
+	AIR = C1 - S1R
+	AII = -S1I
+	return
+OneNinety:
+	AIR = -C2
+	AII = 0.0E0
+	AA = dsqrt(AA)
+	if AZ <= AA {
+		goto TwoHundred
+	}
+	S1R = 0.5E0 * (ZR*ZR - ZI*ZI)
+	S1I = ZR * ZI
+TwoHundred:
+	AIR = AIR + C1*S1R
+	AII = AII + C1*S1I
+	return
+TwoTen:
+	NZ = 1
+	AIR = ZEROR
+	AII = ZEROI
+	return
+TwoSeventy:
+	NZ = 0
+	IERR = 2
+	return
+TwoEighty:
+	if NN == (-1) {
+		goto TwoSeventy
+	}
+	NZ = 0
+	IERR = 5
+	return
+TwoSixty:
+	IERR = 4
+	NZ = 0
+	return
+}
+
+// sbknu computes the k bessel function in the right half z plane.
+func zbknuOrig(ZR, ZI, FNU float64, KODE, N int, YR, YI []float64, NZ int, TOL, ELIM, ALIM float64) (ZRout, ZIout, FNUout float64, KODEout, Nout int, YRout, YIout []float64, NZout int, TOLout, ELIMout, ALIMout float64) {
+	/* Old dimension comment.
+		DIMENSION YR(N), YI(N), CC(8), CSSR(3), CSRR(3), BRY(3), CYR(2),
+	     * CYI(2)
+	*/
+
+	// TODO(btracey): Find which of these are inputs/outputs/both and clean up
+	// the function call.
+	// YR and YI have length n (but n+1 with better indexing)
+	var AA, AK, ASCLE, A1, A2, BB, BK, CAZ,
+		CBI, CBR, CCHI, CCHR, CKI, CKR, COEFI, COEFR, CONEI, CONER,
+		CRSCR, CSCLR, CSHI, CSHR, CSI, CSR, CTWOR,
+		CZEROI, CZEROR, CZI, CZR, DNU, DNU2, DPI, ETEST, FC, FHS,
+		FI, FK, FKS, FMUI, FMUR, FPI, FR, G1, G2, HPI, PI, PR, PTI,
+		PTR, P1I, P1R, P2I, P2M, P2R, QI, QR, RAK, RCAZ, RTHPI, RZI,
+		RZR, R1, S, SMUI, SMUR, SPI, STI, STR, S1I, S1R, S2I, S2R, TM,
+		TTH, T1, T2, ELM, CELMR, ZDR, ZDI, AS, ALAS, HELIM float64
+
+	var I, IFLAG, INU, K, KFLAG, KK, KMAX, KODED, IDUM, J, IC, INUB, NW int
+
+	var tmp complex128
+	var CSSR, CSRR, BRY [4]float64
+	var CYR, CYI [3]float64
+
+	KMAX = 30
+	CZEROR = 0
+	CZEROI = 0
+	CONER = 1
+	CONEI = 0
+	CTWOR = 2
+	R1 = 2
+
+	DPI = 3.14159265358979324E0
+	RTHPI = 1.25331413731550025E0
+	SPI = 1.90985931710274403E0
+	HPI = 1.57079632679489662E0
+	FPI = 1.89769999331517738E0
+	TTH = 6.66666666666666666E-01
+
+	CC := [9]float64{math.NaN(), 5.77215664901532861E-01, -4.20026350340952355E-02,
+		-4.21977345555443367E-02, 7.21894324666309954E-03,
+		-2.15241674114950973E-04, -2.01348547807882387E-05,
+		1.13302723198169588E-06, 6.11609510448141582E-09}
+
+	CAZ = zabs(complex(ZR, ZI))
+	CSCLR = 1.0E0 / TOL
+	CRSCR = TOL
+	CSSR[1] = CSCLR
+	CSSR[2] = 1.0E0
+	CSSR[3] = CRSCR
+	CSRR[1] = CRSCR
+	CSRR[2] = 1.0E0
+	CSRR[3] = CSCLR
+	BRY[1] = 1.0E+3 * dmach[1] / TOL
+	BRY[2] = 1.0E0 / BRY[1]
+	BRY[3] = dmach[2]
+	NZ = 0
+	IFLAG = 0
+	KODED = KODE
+	RCAZ = 1.0E0 / CAZ
+	STR = ZR * RCAZ
+	STI = -ZI * RCAZ
+	RZR = (STR + STR) * RCAZ
+	RZI = (STI + STI) * RCAZ
+	INU = int(float32(FNU + 0.5))
+	DNU = FNU - float64(INU)
+	if dabs(DNU) == 0.5E0 {
+		goto OneTen
+	}
+	DNU2 = 0.0E0
+	if dabs(DNU) > TOL {
+		DNU2 = DNU * DNU
+	}
+	if CAZ > R1 {
+		goto OneTen
+	}
+
+	// SERIES FOR CABS(Z)<=R1.
+	FC = 1.0E0
+	tmp = zlog(complex(RZR, RZI))
+	SMUR = real(tmp)
+	SMUI = imag(tmp)
+	FMUR = SMUR * DNU
+	FMUI = SMUI * DNU
+	FMUR, FMUI, CSHR, CSHI, CCHR, CCHI = zshchOrig(FMUR, FMUI, CSHR, CSHI, CCHR, CCHI)
+	if DNU == 0.0E0 {
+		goto Ten
+	}
+	FC = DNU * DPI
+	FC = FC / dsin(FC)
+	SMUR = CSHR / DNU
+	SMUI = CSHI / DNU
+Ten:
+	A2 = 1.0E0 + DNU
+
+	// GAM(1-Z)*GAM(1+Z)=PI*Z/SIN(PI*Z), T1=1/GAM(1-DNU), T2=1/GAM(1+DNU).
+	T2 = dexp(-dgamln(A2, IDUM))
+	T1 = 1.0E0 / (T2 * FC)
+	if dabs(DNU) > 0.1E0 {
+		goto Forty
+	}
+
+	// SERIES FOR F0 TO RESOLVE INDETERMINACY FOR SMALL ABS(DNU).
+	AK = 1.0E0
+	S = CC[1]
+	for K = 2; K <= 8; K++ {
+		AK = AK * DNU2
+		TM = CC[K] * AK
+		S = S + TM
+		if dabs(TM) < TOL {
+			goto Thirty
+		}
+	}
+Thirty:
+	G1 = -S
+	goto Fifty
+Forty:
+	G1 = (T1 - T2) / (DNU + DNU)
+Fifty:
+	G2 = (T1 + T2) * 0.5E0
+	FR = FC * (CCHR*G1 + SMUR*G2)
+	FI = FC * (CCHI*G1 + SMUI*G2)
+	tmp = zexp(complex(FMUR, FMUI))
+	STR = real(tmp)
+	STI = imag(tmp)
+	PR = 0.5E0 * STR / T2
+	PI = 0.5E0 * STI / T2
+	tmp = zdiv(complex(0.5, 0), complex(STR, STI))
+	PTR = real(tmp)
+	PTI = imag(tmp)
+	QR = PTR / T1
+	QI = PTI / T1
+	S1R = FR
+	S1I = FI
+	S2R = PR
+	S2I = PI
+	AK = 1.0E0
+	A1 = 1.0E0
+	CKR = CONER
+	CKI = CONEI
+	BK = 1.0E0 - DNU2
+	if INU > 0 || N > 1 {
+		goto Eighty
+	}
+
+	// GENERATE K(FNU,Z), 0.0E0 <= FNU < 0.5E0 AND N=1.
+	if CAZ < TOL {
+		goto Seventy
+	}
+	tmp = zmlt(complex(ZR, ZI), complex(ZR, ZI))
+	CZR = real(tmp)
+	CZI = imag(tmp)
+	CZR = 0.25E0 * CZR
+	CZI = 0.25E0 * CZI
+	T1 = 0.25E0 * CAZ * CAZ
+Sixty:
+	FR = (FR*AK + PR + QR) / BK
+	FI = (FI*AK + PI + QI) / BK
+	STR = 1.0E0 / (AK - DNU)
+	PR = PR * STR
+	PI = PI * STR
+	STR = 1.0E0 / (AK + DNU)
+	QR = QR * STR
+	QI = QI * STR
+	STR = CKR*CZR - CKI*CZI
+	RAK = 1.0E0 / AK
+	CKI = (CKR*CZI + CKI*CZR) * RAK
+	CKR = STR * RAK
+	S1R = CKR*FR - CKI*FI + S1R
+	S1I = CKR*FI + CKI*FR + S1I
+	A1 = A1 * T1 * RAK
+	BK = BK + AK + AK + 1.0E0
+	AK = AK + 1.0E0
+	if A1 > TOL {
+		goto Sixty
+	}
+Seventy:
+	YR[1] = S1R
+	YI[1] = S1I
+	if KODED == 1 {
+		return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+	}
+	tmp = zexp(complex(ZR, ZI))
+	STR = real(tmp)
+	STI = imag(tmp)
+	tmp = zmlt(complex(S1R, S1I), complex(STR, STI))
+	YR[1] = real(tmp)
+	YI[1] = imag(tmp)
+	return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+
+	// GENERATE K(DNU,Z) AND K(DNU+1,Z) FOR FORWARD RECURRENCE.
+Eighty:
+	if CAZ < TOL {
+		goto OneHundred
+	}
+	tmp = zmlt(complex(ZR, ZI), complex(ZR, ZI))
+	CZR = real(tmp)
+	CZI = imag(tmp)
+	CZR = 0.25E0 * CZR
+	CZI = 0.25E0 * CZI
+	T1 = 0.25E0 * CAZ * CAZ
+Ninety:
+	FR = (FR*AK + PR + QR) / BK
+	FI = (FI*AK + PI + QI) / BK
+	STR = 1.0E0 / (AK - DNU)
+	PR = PR * STR
+	PI = PI * STR
+	STR = 1.0E0 / (AK + DNU)
+	QR = QR * STR
+	QI = QI * STR
+	STR = CKR*CZR - CKI*CZI
+	RAK = 1.0E0 / AK
+	CKI = (CKR*CZI + CKI*CZR) * RAK
+	CKR = STR * RAK
+	S1R = CKR*FR - CKI*FI + S1R
+	S1I = CKR*FI + CKI*FR + S1I
+	STR = PR - FR*AK
+	STI = PI - FI*AK
+	S2R = CKR*STR - CKI*STI + S2R
+	S2I = CKR*STI + CKI*STR + S2I
+	A1 = A1 * T1 * RAK
+	BK = BK + AK + AK + 1.0E0
+	AK = AK + 1.0E0
+	if A1 > TOL {
+		goto Ninety
+	}
+OneHundred:
+	KFLAG = 2
+	A1 = FNU + 1.0E0
+	AK = A1 * dabs(SMUR)
+	if AK > ALIM {
+		KFLAG = 3
+	}
+	STR = CSSR[KFLAG]
+	P2R = S2R * STR
+	P2I = S2I * STR
+	tmp = zmlt(complex(P2R, P2I), complex(RZR, RZI))
+	S2R = real(tmp)
+	S2I = imag(tmp)
+	S1R = S1R * STR
+	S1I = S1I * STR
+	if KODED == 1 {
+		goto TwoTen
+	}
+	tmp = zexp(complex(ZR, ZI))
+	FR = real(tmp)
+	FI = imag(tmp)
+	tmp = zmlt(complex(S1R, S1I), complex(FR, FI))
+	S1R = real(tmp)
+	S1I = imag(tmp)
+	tmp = zmlt(complex(S2R, S2I), complex(FR, FI))
+	S2R = real(tmp)
+	S2I = imag(tmp)
+	goto TwoTen
+
+	// IFLAG=0 MEANS NO UNDERFLOW OCCURRED
+	// IFLAG=1 MEANS AN UNDERFLOW OCCURRED- COMPUTATION PROCEEDS WITH
+	// KODED=2 AND A TEST FOR ON SCALE VALUES IS MADE DURING FORWARD RECURSION
+OneTen:
+	tmp = zsqrt(complex(ZR, ZI))
+	STR = real(tmp)
+	STI = imag(tmp)
+	tmp = zdiv(complex(RTHPI, CZEROI), complex(STR, STI))
+	COEFR = real(tmp)
+	COEFI = imag(tmp)
+	KFLAG = 2
+	if KODED == 2 {
+		goto OneTwenty
+	}
+	if ZR > ALIM {
+		goto TwoNinety
+	}
+
+	STR = dexp(-ZR) * CSSR[KFLAG]
+	STI = -STR * dsin(ZI)
+	STR = STR * dcos(ZI)
+	tmp = zmlt(complex(COEFR, COEFI), complex(STR, STI))
+	COEFR = real(tmp)
+	COEFI = imag(tmp)
+OneTwenty:
+	if dabs(DNU) == 0.5E0 {
+		goto ThreeHundred
+	}
+	// MILLER ALGORITHM FOR CABS(Z)>R1.
+	AK = dcos(DPI * DNU)
+	AK = dabs(AK)
+	if AK == CZEROR {
+		goto ThreeHundred
+	}
+	FHS = dabs(0.25E0 - DNU2)
+	if FHS == CZEROR {
+		goto ThreeHundred
+	}
+
+	// COMPUTE R2=F(E). if CABS(Z)>=R2, USE FORWARD RECURRENCE TO
+	// DETERMINE THE BACKWARD INDEX K. R2=F(E) IS A STRAIGHT LINE ON
+	// 12<=E<=60. E IS COMPUTED FROM 2**(-E)=B**(1-I1MACH(14))=
+	// TOL WHERE B IS THE BASE OF THE ARITHMETIC.
+	T1 = float64(imach[14] - 1)
+	T1 = T1 * dmach[5] * 3.321928094E0
+	T1 = dmax(T1, 12.0E0)
+	T1 = dmin(T1, 60.0E0)
+	T2 = TTH*T1 - 6.0E0
+	if ZR != 0.0E0 {
+		goto OneThirty
+	}
+	T1 = HPI
+	goto OneFourty
+OneThirty:
+	T1 = datan(ZI / ZR)
+	T1 = dabs(T1)
+OneFourty:
+	if T2 > CAZ {
+		goto OneSeventy
+	}
+	// FORWARD RECURRENCE LOOP WHEN CABS(Z)>=R2.
+	ETEST = AK / (DPI * CAZ * TOL)
+	FK = CONER
+	if ETEST < CONER {
+		goto OneEighty
+	}
+	FKS = CTWOR
+	CKR = CAZ + CAZ + CTWOR
+	P1R = CZEROR
+	P2R = CONER
+	for I = 1; I <= KMAX; I++ {
+		AK = FHS / FKS
+		CBR = CKR / (FK + CONER)
+		PTR = P2R
+		P2R = CBR*P2R - P1R*AK
+		P1R = PTR
+		CKR = CKR + CTWOR
+		FKS = FKS + FK + FK + CTWOR
+		FHS = FHS + FK + FK
+		FK = FK + CONER
+		STR = dabs(P2R) * FK
+		if ETEST < STR {
+			goto OneSixty
+		}
+	}
+	goto ThreeTen
+OneSixty:
+	FK = FK + SPI*T1*dsqrt(T2/CAZ)
+	FHS = dabs(0.25 - DNU2)
+	goto OneEighty
+OneSeventy:
+	// COMPUTE BACKWARD INDEX K FOR CABS(Z)<R2.
+	A2 = dsqrt(CAZ)
+	AK = FPI * AK / (TOL * dsqrt(A2))
+	AA = 3.0E0 * T1 / (1.0E0 + CAZ)
+	BB = 14.7E0 * T1 / (28.0E0 + CAZ)
+	AK = (dlog(AK) + CAZ*dcos(AA)/(1.0E0+0.008E0*CAZ)) / dcos(BB)
+	FK = 0.12125E0*AK*AK/CAZ + 1.5E0
+OneEighty:
+	// BACKWARD RECURRENCE LOOP FOR MILLER ALGORITHM.
+	K = int(float32(FK))
+	FK = float64(K)
+	FKS = FK * FK
+	P1R = CZEROR
+	P1I = CZEROI
+	P2R = TOL
+	P2I = CZEROI
+	CSR = P2R
+	CSI = P2I
+	for I = 1; I <= K; I++ {
+		A1 = FKS - FK
+		AK = (FKS + FK) / (A1 + FHS)
+		RAK = 2.0E0 / (FK + CONER)
+		CBR = (FK + ZR) * RAK
+		CBI = ZI * RAK
+		PTR = P2R
+		PTI = P2I
+		P2R = (PTR*CBR - PTI*CBI - P1R) * AK
+		P2I = (PTI*CBR + PTR*CBI - P1I) * AK
+		P1R = PTR
+		P1I = PTI
+		CSR = CSR + P2R
+		CSI = CSI + P2I
+		FKS = A1 - FK + CONER
+		FK = FK - CONER
+	}
+	// COMPUTE (P2/CS)=(P2/CABS(CS))*(CONJG(CS)/CABS(CS)) FOR BETTER SCALING.
+	TM = zabs(complex(CSR, CSI))
+	PTR = 1.0E0 / TM
+	S1R = P2R * PTR
+	S1I = P2I * PTR
+	CSR = CSR * PTR
+	CSI = -CSI * PTR
+	tmp = zmlt(complex(COEFR, COEFI), complex(S1R, S1I))
+	STR = real(tmp)
+	STI = imag(tmp)
+	tmp = zmlt(complex(STR, STI), complex(CSR, CSI))
+	S1R = real(tmp)
+	S1I = imag(tmp)
+	if INU > 0 || N > 1 {
+		goto TwoHundred
+	}
+	ZDR = ZR
+	ZDI = ZI
+	if IFLAG == 1 {
+		goto TwoSeventy
+	}
+	goto TwoFourty
+TwoHundred:
+	// COMPUTE P1/P2=(P1/CABS(P2)*CONJG(P2)/CABS(P2) FOR SCALING.
+	TM = zabs(complex(P2R, P2I))
+	PTR = 1.0E0 / TM
+	P1R = P1R * PTR
+	P1I = P1I * PTR
+	P2R = P2R * PTR
+	P2I = -P2I * PTR
+	tmp = zmlt(complex(P1R, P1I), complex(P2R, P2I))
+	PTR = real(tmp)
+	PTI = imag(tmp)
+	STR = DNU + 0.5E0 - PTR
+	STI = -PTI
+	tmp = zdiv(complex(STR, STI), complex(ZR, ZI))
+	STR = real(tmp)
+	STI = imag(tmp)
+	STR = STR + 1.0E0
+	tmp = zmlt(complex(STR, STI), complex(S1R, S1I))
+	S2R = real(tmp)
+	S2I = imag(tmp)
+
+	// FORWARD RECURSION ON THE THREE TERM RECURSION WITH RELATION WITH
+	// SCALING NEAR EXPONENT EXTREMES ON KFLAG=1 OR KFLAG=3
+TwoTen:
+	STR = DNU + 1.0E0
+	CKR = STR * RZR
+	CKI = STR * RZI
+	if N == 1 {
+		INU = INU - 1
+	}
+	if INU > 0 {
+		goto TwoTwenty
+	}
+	if N > 1 {
+		goto TwoFifteen
+	}
+	S1R = S2R
+	S1I = S2I
+TwoFifteen:
+	ZDR = ZR
+	ZDI = ZI
+	if IFLAG == 1 {
+		goto TwoSeventy
+	}
+	goto TwoFourty
+TwoTwenty:
+	INUB = 1
+	if IFLAG == 1 {
+		goto TwoSixtyOne
+	}
+TwoTwentyFive:
+	P1R = CSRR[KFLAG]
+	ASCLE = BRY[KFLAG]
+	for I = INUB; I <= INU; I++ {
+		STR = S2R
+		STI = S2I
+		S2R = CKR*STR - CKI*STI + S1R
+		S2I = CKR*STI + CKI*STR + S1I
+		S1R = STR
+		S1I = STI
+		CKR = CKR + RZR
+		CKI = CKI + RZI
+		if KFLAG >= 3 {
+			continue
+		}
+		P2R = S2R * P1R
+		P2I = S2I * P1R
+		STR = dabs(P2R)
+		STI = dabs(P2I)
+		P2M = dmax(STR, STI)
+		if P2M <= ASCLE {
+			continue
+		}
+		KFLAG = KFLAG + 1
+		ASCLE = BRY[KFLAG]
+		S1R = S1R * P1R
+		S1I = S1I * P1R
+		S2R = P2R
+		S2I = P2I
+		STR = CSSR[KFLAG]
+		S1R = S1R * STR
+		S1I = S1I * STR
+		S2R = S2R * STR
+		S2I = S2I * STR
+		P1R = CSRR[KFLAG]
+	}
+	if N != 1 {
+		goto TwoFourty
+	}
+	S1R = S2R
+	S1I = S2I
+TwoFourty:
+	STR = CSRR[KFLAG]
+	YR[1] = S1R * STR
+	YI[1] = S1I * STR
+	if N == 1 {
+		return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+	}
+	YR[2] = S2R * STR
+	YI[2] = S2I * STR
+	if N == 2 {
+		return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+	}
+	KK = 2
+TwoFifty:
+	KK = KK + 1
+	if KK > N {
+		return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+	}
+	P1R = CSRR[KFLAG]
+	ASCLE = BRY[KFLAG]
+	for I = KK; I <= N; I++ {
+		P2R = S2R
+		P2I = S2I
+		S2R = CKR*P2R - CKI*P2I + S1R
+		S2I = CKI*P2R + CKR*P2I + S1I
+		S1R = P2R
+		S1I = P2I
+		CKR = CKR + RZR
+		CKI = CKI + RZI
+		P2R = S2R * P1R
+		P2I = S2I * P1R
+		YR[I] = P2R
+		YI[I] = P2I
+		if KFLAG >= 3 {
+			continue
+		}
+		STR = dabs(P2R)
+		STI = dabs(P2I)
+		P2M = dmax(STR, STI)
+		if P2M <= ASCLE {
+			continue
+		}
+		KFLAG = KFLAG + 1
+		ASCLE = BRY[KFLAG]
+		S1R = S1R * P1R
+		S1I = S1I * P1R
+		S2R = P2R
+		S2I = P2I
+		STR = CSSR[KFLAG]
+		S1R = S1R * STR
+		S1I = S1I * STR
+		S2R = S2R * STR
+		S2I = S2I * STR
+		P1R = CSRR[KFLAG]
+	}
+	return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+
+	// IFLAG=1 CASES, FORWARD RECURRENCE ON SCALED VALUES ON UNDERFLOW.
+TwoSixtyOne:
+	HELIM = 0.5E0 * ELIM
+	ELM = dexp(-ELIM)
+	CELMR = ELM
+	ASCLE = BRY[1]
+	ZDR = ZR
+	ZDI = ZI
+	IC = -1
+	J = 2
+	for I = 1; I <= INU; I++ {
+		STR = S2R
+		STI = S2I
+		S2R = STR*CKR - STI*CKI + S1R
+		S2I = STI*CKR + STR*CKI + S1I
+		S1R = STR
+		S1I = STI
+		CKR = CKR + RZR
+		CKI = CKI + RZI
+		AS = zabs(complex(S2R, S2I))
+		ALAS = dlog(AS)
+		P2R = -ZDR + ALAS
+		if P2R < (-ELIM) {
+			goto TwoSixtyThree
+		}
+		tmp = zlog(complex(S2R, S2I))
+		STR = real(tmp)
+		STI = imag(tmp)
+		P2R = -ZDR + STR
+		P2I = -ZDI + STI
+		P2M = dexp(P2R) / TOL
+		P1R = P2M * dcos(P2I)
+		P1I = P2M * dsin(P2I)
+		P1R, P1I, NW, ASCLE, TOL = zuchkOrig(P1R, P1I, NW, ASCLE, TOL)
+		if NW != 0 {
+			goto TwoSixtyThree
+		}
+		J = 3 - J
+		CYR[J] = P1R
+		CYI[J] = P1I
+		if IC == (I - 1) {
+			goto TwoSixtyFour
+		}
+		IC = I
+		continue
+	TwoSixtyThree:
+		if ALAS < HELIM {
+			continue
+		}
+		ZDR = ZDR - ELIM
+		S1R = S1R * CELMR
+		S1I = S1I * CELMR
+		S2R = S2R * CELMR
+		S2I = S2I * CELMR
+	}
+	if N != 1 {
+		goto TwoSeventy
+	}
+	S1R = S2R
+	S1I = S2I
+	goto TwoSeventy
+TwoSixtyFour:
+	KFLAG = 1
+	INUB = I + 1
+	S2R = CYR[J]
+	S2I = CYI[J]
+	J = 3 - J
+	S1R = CYR[J]
+	S1I = CYI[J]
+	if INUB <= INU {
+		goto TwoTwentyFive
+	}
+	if N != 1 {
+		goto TwoFourty
+	}
+	S1R = S2R
+	S1I = S2I
+	goto TwoFourty
+TwoSeventy:
+	YR[1] = S1R
+	YI[1] = S1I
+	if N == 1 {
+		goto TwoEighty
+	}
+	YR[2] = S2R
+	YI[2] = S2I
+TwoEighty:
+	ASCLE = BRY[1]
+	ZDR, ZDI, FNU, N, YR, YI, NZ, RZR, RZI, ASCLE, TOL, ELIM = zksclOrig(ZDR, ZDI, FNU, N, YR, YI, NZ, RZR, RZI, ASCLE, TOL, ELIM)
+	INU = N - NZ
+	if INU <= 0 {
+		return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+	}
+	KK = NZ + 1
+	S1R = YR[KK]
+	S1I = YI[KK]
+	YR[KK] = S1R * CSRR[1]
+	YI[KK] = S1I * CSRR[1]
+	if INU == 1 {
+		return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+	}
+	KK = NZ + 2
+	S2R = YR[KK]
+	S2I = YI[KK]
+	YR[KK] = S2R * CSRR[1]
+	YI[KK] = S2I * CSRR[1]
+	if INU == 2 {
+		return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+	}
+	T2 = FNU + float64(float32(KK-1))
+	CKR = T2 * RZR
+	CKI = T2 * RZI
+	KFLAG = 1
+	goto TwoFifty
+TwoNinety:
+
+	// SCALE BY dexp(Z), IFLAG = 1 CASES.
+
+	KODED = 2
+	IFLAG = 1
+	KFLAG = 2
+	goto OneTwenty
+
+	// FNU=HALF ODD INTEGER CASE, DNU=-0.5
+ThreeHundred:
+	S1R = COEFR
+	S1I = COEFI
+	S2R = COEFR
+	S2I = COEFI
+	goto TwoTen
+
+ThreeTen:
+	NZ = -2
+	return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+}
+
+// SET K FUNCTIONS TO ZERO ON UNDERFLOW, CONTINUE RECURRENCE
+// ON SCALED FUNCTIONS UNTIL TWO MEMBERS COME ON SCALE, THEN
+// return WITH MIN(NZ+2,N) VALUES SCALED BY 1/TOL.
+func zksclOrig(ZRR, ZRI, FNU float64, N int, YR, YI []float64, NZ int, RZR, RZI, ASCLE, TOL, ELIM float64) (
+	ZRRout, ZRIout, FNUout float64, Nout int, YRout, YIout []float64, NZout int, RZRout, RZIout, ASCLEout, TOLout, ELIMout float64) {
+	var ACS, AS, CKI, CKR, CSI, CSR, FN, STR, S1I, S1R, S2I,
+		S2R, ZEROI, ZEROR, ZDR, ZDI, CELMR, ELM, HELIM, ALAS float64
+
+	var I, IC, KK, NN, NW int
+	var tmp complex128
+	var CYR, CYI [3]float64
+	// DIMENSION YR(N), YI(N), CYR(2), CYI(2)
+	ZEROR = 0
+	ZEROI = 0
+	NZ = 0
+	IC = 0
+	NN = min0(2, N)
+	for I = 1; I <= NN; I++ {
+		S1R = YR[I]
+		S1I = YI[I]
+		CYR[I] = S1R
+		CYI[I] = S1I
+		AS = zabs(complex(S1R, S1I))
+		ACS = -ZRR + dlog(AS)
+		NZ = NZ + 1
+		YR[I] = ZEROR
+		YI[I] = ZEROI
+		if ACS < (-ELIM) {
+			continue
+		}
+
+		tmp = zlog(complex(S1R, S1I))
+		CSR = real(tmp)
+		CSI = imag(tmp)
+		CSR = CSR - ZRR
+		CSI = CSI - ZRI
+		STR = dexp(CSR) / TOL
+		CSR = STR * dcos(CSI)
+		CSI = STR * dsin(CSI)
+		CSR, CSI, NW, ASCLE, TOL = zuchkOrig(CSR, CSI, NW, ASCLE, TOL)
+		if NW != 0 {
+			continue
+		}
+		YR[I] = CSR
+		YI[I] = CSI
+		IC = I
+		NZ = NZ - 1
+	}
+	if N == 1 {
+		return ZRR, ZRI, FNU, N, YR, YI, NZ, RZR, RZI, ASCLE, TOL, ELIM
+	}
+	if IC > 1 {
+		goto Twenty
+	}
+	YR[1] = ZEROR
+	YI[1] = ZEROI
+	NZ = 2
+Twenty:
+	if N == 2 {
+		return ZRR, ZRI, FNU, N, YR, YI, NZ, RZR, RZI, ASCLE, TOL, ELIM
+	}
+	if NZ == 0 {
+		return ZRR, ZRI, FNU, N, YR, YI, NZ, RZR, RZI, ASCLE, TOL, ELIM
+	}
+	FN = FNU + 1.0E0
+	CKR = FN * RZR
+	CKI = FN * RZI
+	S1R = CYR[1]
+	S1I = CYI[1]
+	S2R = CYR[2]
+	S2I = CYI[2]
+	HELIM = 0.5E0 * ELIM
+	ELM = dexp(-ELIM)
+	CELMR = ELM
+	ZDR = ZRR
+	ZDI = ZRI
+
+	// FIND TWO CONSECUTIVE Y VALUES ON SCALE. SCALE RECURRENCE IF
+	// S2 GETS LARGER THAN EXP(ELIM/2)
+	for I = 3; I <= N; I++ {
+		KK = I
+		CSR = S2R
+		CSI = S2I
+		S2R = CKR*CSR - CKI*CSI + S1R
+		S2I = CKI*CSR + CKR*CSI + S1I
+		S1R = CSR
+		S1I = CSI
+		CKR = CKR + RZR
+		CKI = CKI + RZI
+		AS = zabs(complex(S2R, S2I))
+		ALAS = dlog(AS)
+		ACS = -ZDR + ALAS
+		NZ = NZ + 1
+		YR[I] = ZEROR
+		YI[I] = ZEROI
+		if ACS < (-ELIM) {
+			goto TwentyFive
+		}
+		tmp = zlog(complex(S2R, S2I))
+		CSR = real(tmp)
+		CSI = imag(tmp)
+		CSR = CSR - ZDR
+		CSI = CSI - ZDI
+		STR = dexp(CSR) / TOL
+		CSR = STR * dcos(CSI)
+		CSI = STR * dsin(CSI)
+		CSR, CSI, NW, ASCLE, TOL = zuchkOrig(CSR, CSI, NW, ASCLE, TOL)
+		if NW != 0 {
+			goto TwentyFive
+		}
+		YR[I] = CSR
+		YI[I] = CSI
+		NZ = NZ - 1
+		if IC == KK-1 {
+			goto Forty
+		}
+		IC = KK
+		continue
+	TwentyFive:
+		if ALAS < HELIM {
+			continue
+		}
+		ZDR = ZDR - ELIM
+		S1R = S1R * CELMR
+		S1I = S1I * CELMR
+		S2R = S2R * CELMR
+		S2I = S2I * CELMR
+	}
+	NZ = N
+	if IC == N {
+		NZ = N - 1
+	}
+	goto FourtyFive
+Forty:
+	NZ = KK - 2
+FourtyFive:
+	for I = 1; I <= NZ; I++ {
+		YR[I] = ZEROR
+		YI[I] = ZEROI
+	}
+	return ZRR, ZRI, FNU, N, YR, YI, NZ, RZR, RZI, ASCLE, TOL, ELIM
+}
+
+// Y ENTERS AS A SCALED QUANTITY WHOSE MAGNITUDE IS GREATER THAN
+// EXP(-ALIM)=ASCLE=1.0E+3*dmach[1)/TOL. THE TEST IS MADE TO SEE
+// if THE MAGNITUDE OF THE REAL OR IMAGINARY PART WOULD UNDERFLOW
+// WHEN Y IS SCALED (BY TOL) TO ITS PROPER VALUE. Y IS ACCEPTED
+// if THE UNDERFLOW IS AT LEAST ONE PRECISION BELOW THE MAGNITUDE
+// OF THE LARGEST COMPONENT; OTHERWISE THE PHASE ANGLE DOES NOT HAVE
+// ABSOLUTE ACCURACY AND AN UNDERFLOW IS ASSUMED.
+func zuchkOrig(YR, YI float64, NZ int, ASCLE, TOL float64) (YRout, YIout float64, NZout int, ASCLEout, TOLout float64) {
+	var SS, ST, WR, WI float64
+	NZ = 0
+	WR = dabs(YR)
+	WI = dabs(YI)
+	ST = dmin(WR, WI)
+	if ST > ASCLE {
+		return YR, YI, NZ, ASCLE, TOL
+	}
+	SS = dmax(WR, WI)
+	ST = ST / TOL
+	if SS < ST {
+		NZ = 1
+	}
+	return YR, YI, NZ, ASCLE, TOL
+}
+
+// ZACAI APPLIES THE ANALYTIC CONTINUATION FORMULA
+//
+//  K(FNU,ZN*EXP(MP))=K(FNU,ZN)*EXP(-MP*FNU) - MP*I(FNU,ZN)
+//        MP=PI*MR*CMPLX(0.0,1.0)
+//
+// TO CONTINUE THE K FUNCTION FROM THE RIGHT HALF TO THE LEFT
+// HALF Z PLANE FOR USE WITH ZAIRY WHERE FNU=1/3 OR 2/3 AND N=1.
+// ZACAI IS THE SAME AS ZACON WITH THE PARTS FOR LARGER ORDERS AND
+// RECURRENCE REMOVED. A RECURSIVE CALL TO ZACON CAN RESULT if ZACON
+// IS CALLED FROM ZAIRY.
+func zacaiOrig(ZR, ZI, FNU float64, KODE, MR, N int, YR, YI []float64, NZ int, RL, TOL, ELIM, ALIM float64) (
+	ZRout, ZIout, FNUout float64, KODEout, MRout, Nout int, YRout, YIout []float64, NZout int, RLout, TOLout, ELIMout, ALIMout float64) {
+	var ARG, ASCLE, AZ, CSGNR, CSGNI, CSPNR,
+		CSPNI, C1R, C1I, C2R, C2I, DFNU, FMR, PI,
+		SGN, YY, ZNR, ZNI float64
+	var INU, IUF, NN, NW int
+	CYR := []float64{math.NaN(), 0, 0}
+	CYI := []float64{math.NaN(), 0, 0}
+
+	PI = math.Pi
+	NZ = 0
+	ZNR = -ZR
+	ZNI = -ZI
+	AZ = zabs(complex(ZR, ZI))
+	NN = N
+	DFNU = FNU + float64(float32(N-1))
+	if AZ <= 2.0E0 {
+		goto Ten
+	}
+	if AZ*AZ*0.25 > DFNU+1.0E0 {
+		goto Twenty
+	}
+Ten:
+	// POWER SERIES FOR THE I FUNCTION.
+	ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, TOL, ELIM, ALIM = zseriOrig(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, TOL, ELIM, ALIM)
+	goto Forty
+Twenty:
+	if AZ < RL {
+		goto Thirty
+	}
+	// ASYMPTOTIC EXPANSION FOR LARGE Z FOR THE I FUNCTION.
+	ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, RL, TOL, ELIM, ALIM = zasyiOrig(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, RL, TOL, ELIM, ALIM)
+	if NW < 0 {
+		goto Eighty
+	}
+	goto Forty
+Thirty:
+	// MILLER ALGORITHM NORMALIZED BY THE SERIES FOR THE I FUNCTION
+	ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, TOL = zmlriOrig(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, TOL)
+	if NW < 0 {
+		goto Eighty
+	}
+Forty:
+	// ANALYTIC CONTINUATION TO THE LEFT HALF PLANE FOR THE K FUNCTION.
+	ZNR, ZNI, FNU, KODE, _, CYR, CYI, NW, TOL, ELIM, ALIM = zbknuOrig(ZNR, ZNI, FNU, KODE, 1, CYR, CYI, NW, TOL, ELIM, ALIM)
+	if NW != 0 {
+		goto Eighty
+	}
+	FMR = float64(float32(MR))
+	SGN = -math.Copysign(PI, FMR)
+	CSGNR = 0.0E0
+	CSGNI = SGN
+	if KODE == 1 {
+		goto Fifty
+	}
+	YY = -ZNI
+	CSGNR = -CSGNI * dsin(YY)
+	CSGNI = CSGNI * dcos(YY)
+Fifty:
+	// CALCULATE CSPN=EXP(FNU*PI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE
+	// WHEN FNU IS LARGE
+	INU = int(float32(FNU))
+	ARG = (FNU - float64(float32(INU))) * SGN
+	CSPNR = dcos(ARG)
+	CSPNI = dsin(ARG)
+	if INU%2 == 0 {
+		goto Sixty
+	}
+	CSPNR = -CSPNR
+	CSPNI = -CSPNI
+Sixty:
+	C1R = CYR[1]
+	C1I = CYI[1]
+	C2R = YR[1]
+	C2I = YI[1]
+	if KODE == 1 {
+		goto Seventy
+	}
+	IUF = 0
+	ASCLE = 1.0E+3 * dmach[1] / TOL
+	ZNR, ZNI, C1R, C1I, C2R, C2I, NW, ASCLE, ALIM, IUF = zs1s2Orig(ZNR, ZNI, C1R, C1I, C2R, C2I, NW, ASCLE, ALIM, IUF)
+	NZ = NZ + NW
+Seventy:
+	YR[1] = CSPNR*C1R - CSPNI*C1I + CSGNR*C2R - CSGNI*C2I
+	YI[1] = CSPNR*C1I + CSPNI*C1R + CSGNR*C2I + CSGNI*C2R
+	return ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, RL, TOL, ELIM, ALIM
+Eighty:
+	NZ = -1
+	if NW == -2 {
+		NZ = -2
+	}
+	return ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, RL, TOL, ELIM, ALIM
+}
+
+// ZASYI COMPUTES THE I BESSEL FUNCTION FOR REAL(Z)>=0.0 BY
+// MEANS OF THE ASYMPTOTIC EXPANSION FOR LARGE CABS(Z) IN THE
+// REGION CABS(Z)>MAX(RL,FNU*FNU/2). NZ=0 IS A NORMAL return.
+// NZ<0 INDICATES AN OVERFLOW ON KODE=1.
+func zasyiOrig(ZR, ZI, FNU float64, KODE, N int, YR, YI []float64, NZ int, RL, TOL, ELIM, ALIM float64) (
+	ZRout, ZIout, FNUout float64, KODEout, Nout int, YRout, YIout []float64, NZout int, RLout, TOLout, ELIMout, ALIMout float64) {
+	var AA, AEZ, AK, AK1I, AK1R, ARG, ARM, ATOL,
+		AZ, BB, BK, CKI, CKR, CONEI, CONER, CS1I, CS1R, CS2I, CS2R, CZI,
+		CZR, DFNU, DKI, DKR, DNU2, EZI, EZR, FDN, PI, P1I,
+		P1R, RAZ, RTPI, RTR1, RZI, RZR, S, SGN, SQK, STI, STR, S2I,
+		S2R, TZI, TZR, ZEROI, ZEROR float64
+
+	var I, IB, IL, INU, J, JL, K, KODED, M, NN int
+	var tmp complex128
+
+	PI = math.Pi
+	RTPI = 0.159154943091895336E0
+	ZEROR = 0
+	ZEROI = 0
+	CONER = 1
+	CONEI = 0
+
+	NZ = 0
+	AZ = zabs(complex(ZR, ZI))
+	ARM = 1.0E3 * dmach[1]
+	RTR1 = dsqrt(ARM)
+	IL = min0(2, N)
+	DFNU = FNU + float64(float32(N-IL))
+
+	// OVERFLOW TEST
+	RAZ = 1.0E0 / AZ
+	STR = ZR * RAZ
+	STI = -ZI * RAZ
+	AK1R = RTPI * STR * RAZ
+	AK1I = RTPI * STI * RAZ
+	tmp = zsqrt(complex(AK1R, AK1I))
+	AK1R = real(tmp)
+	AK1I = imag(tmp)
+	CZR = ZR
+	CZI = ZI
+	if KODE != 2 {
+		goto Ten
+	}
+	CZR = ZEROR
+	CZI = ZI
+Ten:
+	if dabs(CZR) > ELIM {
+		goto OneHundred
+	}
+	DNU2 = DFNU + DFNU
+	KODED = 1
+	if (dabs(CZR) > ALIM) && (N > 2) {
+		goto Twenty
+	}
+	KODED = 0
+	tmp = zexp(complex(CZR, CZI))
+	STR = real(tmp)
+	STI = imag(tmp)
+	tmp = zmlt(complex(AK1R, AK1I), complex(STR, STI))
+	AK1R = real(tmp)
+	AK1I = imag(tmp)
+Twenty:
+	FDN = 0.0E0
+	if DNU2 > RTR1 {
+		FDN = DNU2 * DNU2
+	}
+	EZR = ZR * 8.0E0
+	EZI = ZI * 8.0E0
+
+	// WHEN Z IS IMAGINARY, THE ERROR TEST MUST BE MADE RELATIVE TO THE
+	// FIRST RECIPROCAL POWER SINCE THIS IS THE LEADING TERM OF THE
+	// EXPANSION FOR THE IMAGINARY PART.
+	AEZ = 8.0E0 * AZ
+	S = TOL / AEZ
+	JL = int(float32(RL+RL)) + 2
+	P1R = ZEROR
+	P1I = ZEROI
+	if ZI == 0.0E0 {
+		goto Thirty
+	}
+
+	// CALCULATE EXP(PI*(0.5+FNU+N-IL)*I) TO MINIMIZE LOSSES OF
+	// SIGNIFICANCE WHEN FNU OR N IS LARGE
+	INU = int(float32(FNU))
+	ARG = (FNU - float64(float32(INU))) * PI
+	INU = INU + N - IL
+	AK = -dsin(ARG)
+	BK = dcos(ARG)
+	if ZI < 0.0E0 {
+		BK = -BK
+	}
+	P1R = AK
+	P1I = BK
+	if INU%2 == 0 {
+		goto Thirty
+	}
+	P1R = -P1R
+	P1I = -P1I
+Thirty:
+	for K = 1; K <= IL; K++ {
+		SQK = FDN - 1.0E0
+		ATOL = S * dabs(SQK)
+		SGN = 1.0E0
+		CS1R = CONER
+		CS1I = CONEI
+		CS2R = CONER
+		CS2I = CONEI
+		CKR = CONER
+		CKI = CONEI
+		AK = 0.0E0
+		AA = 1.0E0
+		BB = AEZ
+		DKR = EZR
+		DKI = EZI
+		// TODO(btracey): This loop is executed tens of thousands of times. Why?
+		// is that really necessary?
+		for J = 1; J <= JL; J++ {
+			tmp = zdiv(complex(CKR, CKI), complex(DKR, DKI))
+			STR = real(tmp)
+			STI = imag(tmp)
+			CKR = STR * SQK
+			CKI = STI * SQK
+			CS2R = CS2R + CKR
+			CS2I = CS2I + CKI
+			SGN = -SGN
+			CS1R = CS1R + CKR*SGN
+			CS1I = CS1I + CKI*SGN
+			DKR = DKR + EZR
+			DKI = DKI + EZI
+			AA = AA * dabs(SQK) / BB
+			BB = BB + AEZ
+			AK = AK + 8.0E0
+			SQK = SQK - AK
+			if AA <= ATOL {
+				goto Fifty
+			}
+		}
+		goto OneTen
+	Fifty:
+		S2R = CS1R
+		S2I = CS1I
+		if ZR+ZR >= ELIM {
+			goto Sixty
+		}
+		TZR = ZR + ZR
+		TZI = ZI + ZI
+		tmp = zexp(complex(-TZR, -TZI))
+		STR = real(tmp)
+		STI = imag(tmp)
+		tmp = zmlt(complex(STR, STI), complex(P1R, P1I))
+		STR = real(tmp)
+		STI = imag(tmp)
+		tmp = zmlt(complex(STR, STI), complex(CS2R, CS2I))
+		STR = real(tmp)
+		STI = imag(tmp)
+		S2R = S2R + STR
+		S2I = S2I + STI
+	Sixty:
+		FDN = FDN + 8.0E0*DFNU + 4.0E0
+		P1R = -P1R
+		P1I = -P1I
+		M = N - IL + K
+		YR[M] = S2R*AK1R - S2I*AK1I
+		YI[M] = S2R*AK1I + S2I*AK1R
+	}
+	if N <= 2 {
+		return ZR, ZI, FNU, KODE, N, YR, YI, NZ, RL, TOL, ELIM, ALIM
+	}
+	NN = N
+	K = NN - 2
+	AK = float64(float32(K))
+	STR = ZR * RAZ
+	STI = -ZI * RAZ
+	RZR = (STR + STR) * RAZ
+	RZI = (STI + STI) * RAZ
+	IB = 3
+	for I = IB; I <= NN; I++ {
+		YR[K] = (AK+FNU)*(RZR*YR[K+1]-RZI*YI[K+1]) + YR[K+2]
+		YI[K] = (AK+FNU)*(RZR*YI[K+1]+RZI*YR[K+1]) + YI[K+2]
+		AK = AK - 1.0E0
+		K = K - 1
+	}
+	if KODED == 0 {
+		return ZR, ZI, FNU, KODE, N, YR, YI, NZ, RL, TOL, ELIM, ALIM
+	}
+	tmp = zexp(complex(CZR, CZI))
+	CKR = real(tmp)
+	CKI = imag(tmp)
+	for I = 1; I <= NN; I++ {
+		STR = YR[I]*CKR - YI[I]*CKI
+		YI[I] = YR[I]*CKI + YI[I]*CKR
+		YR[I] = STR
+	}
+	return ZR, ZI, FNU, KODE, N, YR, YI, NZ, RL, TOL, ELIM, ALIM
+OneHundred:
+	NZ = -1
+	return ZR, ZI, FNU, KODE, N, YR, YI, NZ, RL, TOL, ELIM, ALIM
+OneTen:
+	NZ = -2
+	return ZR, ZI, FNU, KODE, N, YR, YI, NZ, RL, TOL, ELIM, ALIM
+}
+
+// ZMLRI COMPUTES THE I BESSEL FUNCTION FOR RE(Z)>=0.0 BY THE
+// MILLER ALGORITHM NORMALIZED BY A NEUMANN SERIES.
+func zmlriOrig(ZR, ZI, FNU float64, KODE, N int, YR, YI []float64, NZ int, TOL float64) (
+	ZRout, ZIout, FNUout float64, KODEout, Nout int, YRout, YIout []float64, NZout int, TOLout float64) {
+	var ACK, AK, AP, AT, AZ, BK, CKI, CKR, CNORMI,
+		CNORMR, CONEI, CONER, FKAP, FKK, FLAM, FNF, PTI, PTR, P1I,
+		P1R, P2I, P2R, RAZ, RHO, RHO2, RZI, RZR, SCLE, STI, STR, SUMI,
+		SUMR, TFNF, TST, ZEROI, ZEROR float64
+	var I, IAZ, IDUM, IFNU, INU, ITIME, K, KK, KM, M int
+	var tmp complex128
+	ZEROR = 0
+	ZEROI = 0
+	CONER = 1
+	CONEI = 0
+
+	SCLE = dmach[1] / TOL
+	NZ = 0
+	AZ = zabs(complex(ZR, ZI))
+	IAZ = int(float32(AZ))
+	IFNU = int(float32(FNU))
+	INU = IFNU + N - 1
+	AT = float64(float32(IAZ)) + 1.0E0
+	RAZ = 1.0E0 / AZ
+	STR = ZR * RAZ
+	STI = -ZI * RAZ
+	CKR = STR * AT * RAZ
+	CKI = STI * AT * RAZ
+	RZR = (STR + STR) * RAZ
+	RZI = (STI + STI) * RAZ
+	P1R = ZEROR
+	P1I = ZEROI
+	P2R = CONER
+	P2I = CONEI
+	ACK = (AT + 1.0E0) * RAZ
+	RHO = ACK + dsqrt(ACK*ACK-1.0E0)
+	RHO2 = RHO * RHO
+	TST = (RHO2 + RHO2) / ((RHO2 - 1.0E0) * (RHO - 1.0E0))
+	TST = TST / TOL
+
+	// COMPUTE RELATIVE TRUNCATION ERROR INDEX FOR SERIES.
+	//fmt.Println("before loop", P2R, P2I, CKR, CKI, RZR, RZI, TST, AK)
+	AK = AT
+	for I = 1; I <= 80; I++ {
+		PTR = P2R
+		PTI = P2I
+		P2R = P1R - (CKR*PTR - CKI*PTI)
+		P2I = P1I - (CKI*PTR + CKR*PTI)
+		P1R = PTR
+		P1I = PTI
+		CKR = CKR + RZR
+		CKI = CKI + RZI
+		AP = zabs(complex(P2R, P2I))
+		if AP > TST*AK*AK {
+			goto Twenty
+		}
+		AK = AK + 1.0E0
+	}
+	goto OneTen
+Twenty:
+	I = I + 1
+	K = 0
+	if INU < IAZ {
+		goto Forty
+	}
+	// COMPUTE RELATIVE TRUNCATION ERROR FOR RATIOS.
+	P1R = ZEROR
+	P1I = ZEROI
+	P2R = CONER
+	P2I = CONEI
+	AT = float64(float32(INU)) + 1.0E0
+	STR = ZR * RAZ
+	STI = -ZI * RAZ
+	CKR = STR * AT * RAZ
+	CKI = STI * AT * RAZ
+	ACK = AT * RAZ
+	TST = dsqrt(ACK / TOL)
+	ITIME = 1
+	for K = 1; K <= 80; K++ {
+		PTR = P2R
+		PTI = P2I
+		P2R = P1R - (CKR*PTR - CKI*PTI)
+		P2I = P1I - (CKR*PTI + CKI*PTR)
+		P1R = PTR
+		P1I = PTI
+		CKR = CKR + RZR
+		CKI = CKI + RZI
+		AP = zabs(complex(P2R, P2I))
+		if AP < TST {
+			continue
+		}
+		if ITIME == 2 {
+			goto Forty
+		}
+		ACK = zabs(complex(CKR, CKI))
+		FLAM = ACK + dsqrt(ACK*ACK-1.0E0)
+		FKAP = AP / zabs(complex(P1R, P1I))
+		RHO = dmin(FLAM, FKAP)
+		TST = TST * dsqrt(RHO/(RHO*RHO-1.0E0))
+		ITIME = 2
+	}
+	goto OneTen
+Forty:
+	// BACKWARD RECURRENCE AND SUM NORMALIZING RELATION.
+	K = K + 1
+	KK = max0(I+IAZ, K+INU)
+	FKK = float64(float32(KK))
+	P1R = ZEROR
+	P1I = ZEROI
+
+	// SCALE P2 AND SUM BY SCLE.
+	P2R = SCLE
+	P2I = ZEROI
+	FNF = FNU - float64(float32(IFNU))
+	TFNF = FNF + FNF
+	BK = dgamln(FKK+TFNF+1.0E0, IDUM) - dgamln(FKK+1.0E0, IDUM) - dgamln(TFNF+1.0E0, IDUM)
+	BK = dexp(BK)
+	SUMR = ZEROR
+	SUMI = ZEROI
+	KM = KK - INU
+	for I = 1; I <= KM; I++ {
+		PTR = P2R
+		PTI = P2I
+		P2R = P1R + (FKK+FNF)*(RZR*PTR-RZI*PTI)
+		P2I = P1I + (FKK+FNF)*(RZI*PTR+RZR*PTI)
+		P1R = PTR
+		P1I = PTI
+		AK = 1.0E0 - TFNF/(FKK+TFNF)
+		ACK = BK * AK
+		SUMR = SUMR + (ACK+BK)*P1R
+		SUMI = SUMI + (ACK+BK)*P1I
+		BK = ACK
+		FKK = FKK - 1.0E0
+	}
+	YR[N] = P2R
+	YI[N] = P2I
+	if N == 1 {
+		goto Seventy
+	}
+	for I = 2; I <= N; I++ {
+		PTR = P2R
+		PTI = P2I
+		P2R = P1R + (FKK+FNF)*(RZR*PTR-RZI*PTI)
+		P2I = P1I + (FKK+FNF)*(RZI*PTR+RZR*PTI)
+		P1R = PTR
+		P1I = PTI
+		AK = 1.0E0 - TFNF/(FKK+TFNF)
+		ACK = BK * AK
+		SUMR = SUMR + (ACK+BK)*P1R
+		SUMI = SUMI + (ACK+BK)*P1I
+		BK = ACK
+		FKK = FKK - 1.0E0
+		M = N - I + 1
+		YR[M] = P2R
+		YI[M] = P2I
+	}
+Seventy:
+	if IFNU <= 0 {
+		goto Ninety
+	}
+	for I = 1; I <= IFNU; I++ {
+		PTR = P2R
+		PTI = P2I
+		P2R = P1R + (FKK+FNF)*(RZR*PTR-RZI*PTI)
+		P2I = P1I + (FKK+FNF)*(RZR*PTI+RZI*PTR)
+		P1R = PTR
+		P1I = PTI
+		AK = 1.0E0 - TFNF/(FKK+TFNF)
+		ACK = BK * AK
+		SUMR = SUMR + (ACK+BK)*P1R
+		SUMI = SUMI + (ACK+BK)*P1I
+		BK = ACK
+		FKK = FKK - 1.0E0
+	}
+Ninety:
+	PTR = ZR
+	PTI = ZI
+	if KODE == 2 {
+		PTR = ZEROR
+	}
+	tmp = zlog(complex(RZR, RZI))
+	STR = real(tmp)
+	STI = imag(tmp)
+	P1R = -FNF*STR + PTR
+	P1I = -FNF*STI + PTI
+	AP = dgamln(1.0E0+FNF, IDUM)
+	PTR = P1R - AP
+	PTI = P1I
+
+	// THE DIVISION CEXP(PT)/(SUM+P2) IS ALTERED TO AVOID OVERFLOW
+	// IN THE DENOMINATOR BY SQUARING LARGE QUANTITIES.
+	P2R = P2R + SUMR
+	P2I = P2I + SUMI
+	AP = zabs(complex(P2R, P2I))
+	P1R = 1.0E0 / AP
+	tmp = zexp(complex(PTR, PTI))
+	STR = real(tmp)
+	STI = imag(tmp)
+	CKR = STR * P1R
+	CKI = STI * P1R
+	PTR = P2R * P1R
+	PTI = -P2I * P1R
+	tmp = zmlt(complex(CKR, CKI), complex(PTR, PTI))
+	CNORMR = real(tmp)
+	CNORMI = imag(tmp)
+	for I = 1; I <= N; I++ {
+		STR = YR[I]*CNORMR - YI[I]*CNORMI
+		YI[I] = YR[I]*CNORMI + YI[I]*CNORMR
+		YR[I] = STR
+	}
+	return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL
+OneTen:
+	NZ = -2
+	return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL
+}
+
+// ZSERI COMPUTES THE I BESSEL FUNCTION FOR REAL(Z)>=0.0 BY
+// MEANS OF THE POWER SERIES FOR LARGE CABS(Z) IN THE
+// REGION CABS(Z)<=2*SQRT(FNU+1). NZ=0 IS A NORMAL return.
+// NZ>0 MEANS THAT THE LAST NZ COMPONENTS WERE SET TO ZERO
+// DUE TO UNDERFLOW. NZ<0 MEANS UNDERFLOW OCCURRED, BUT THE
+// CONDITION CABS(Z)<=2*SQRT(FNU+1) WAS VIOLATED AND THE
+// COMPUTATION MUST BE COMPLETED IN ANOTHER ROUTINE WITH N=N-ABS(NZ).
+func zseriOrig(ZR, ZI, FNU float64, KODE, N int, YR, YI []float64, NZ int, TOL, ELIM, ALIM float64) (
+	ZRout, ZIout, FNUout float64, KODEout, Nout int, YRout, YIout []float64, NZout int, TOLout, ELIMout, ALIMout float64) {
+	var AA, ACZ, AK, AK1I, AK1R, ARM, ASCLE, ATOL,
+		AZ, CKI, CKR, COEFI, COEFR, CONEI, CONER, CRSCR, CZI, CZR, DFNU,
+		FNUP, HZI, HZR, RAZ, RS, RTR1, RZI, RZR, S, SS, STI,
+		STR, S1I, S1R, S2I, S2R, ZEROI, ZEROR float64
+	var I, IB, IDUM, IFLAG, IL, K, L, M, NN, NW int
+	var WR, WI [3]float64
+	var tmp complex128
+
+	CONER = 1.0
+	NZ = 0
+	AZ = zabs(complex(ZR, ZI))
+	if AZ == 0.0E0 {
+		goto OneSixty
+	}
+	// TODO(btracey)
+	// The original fortran line is "ARM = 1.0D+3*D1MACH(1)". Evidently, in Fortran
+	// this is interpreted as one to the power of +3*D1MACH(1). While it is possible
+	// this was intentional, it seems unlikely.
+	//ARM = 1.0E0 + 3*dmach[1]
+	//math.Pow(1, 3*dmach[1])
+	ARM = 1000 * dmach[1]
+	RTR1 = dsqrt(ARM)
+	CRSCR = 1.0E0
+	IFLAG = 0
+	if AZ < ARM {
+		goto OneFifty
+	}
+	HZR = 0.5E0 * ZR
+	HZI = 0.5E0 * ZI
+	CZR = ZEROR
+	CZI = ZEROI
+	if AZ <= RTR1 {
+		goto Ten
+	}
+	tmp = zmlt(complex(HZR, HZI), complex(HZR, HZI))
+	CZR = real(tmp)
+	CZI = imag(tmp)
+Ten:
+	ACZ = zabs(complex(CZR, CZI))
+	NN = N
+	tmp = zlog(complex(HZR, HZI))
+	CKR = real(tmp)
+	CKI = imag(tmp)
+Twenty:
+	DFNU = FNU + float64(float32(NN-1))
+	FNUP = DFNU + 1.0E0
+
+	// UNDERFLOW TEST.
+	AK1R = CKR * DFNU
+	AK1I = CKI * DFNU
+	AK = dgamln(FNUP, IDUM)
+	AK1R = AK1R - AK
+	if KODE == 2 {
+		AK1R = AK1R - ZR
+	}
+	if AK1R > (-ELIM) {
+		goto Forty
+	}
+Thirty:
+	NZ = NZ + 1
+	YR[NN] = ZEROR
+	YI[NN] = ZEROI
+	if ACZ > DFNU {
+		goto OneNinety
+	}
+	NN = NN - 1
+	if NN == 0 {
+		return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+	}
+	goto Twenty
+Forty:
+	if AK1R > (-ALIM) {
+		goto Fifty
+	}
+	IFLAG = 1
+	SS = 1.0E0 / TOL
+	CRSCR = TOL
+	ASCLE = ARM * SS
+Fifty:
+	AA = dexp(AK1R)
+	if IFLAG == 1 {
+		AA = AA * SS
+	}
+	COEFR = AA * dcos(AK1I)
+	COEFI = AA * dsin(AK1I)
+	ATOL = TOL * ACZ / FNUP
+	IL = min0(2, NN)
+	for I = 1; I <= IL; I++ {
+		DFNU = FNU + float64(float32(NN-I))
+		FNUP = DFNU + 1.0E0
+		S1R = CONER
+		S1I = CONEI
+		if ACZ < TOL*FNUP {
+			goto Seventy
+		}
+		AK1R = CONER
+		AK1I = CONEI
+		AK = FNUP + 2.0E0
+		S = FNUP
+		AA = 2.0E0
+	Sixty:
+		RS = 1.0E0 / S
+		STR = AK1R*CZR - AK1I*CZI
+		STI = AK1R*CZI + AK1I*CZR
+		AK1R = STR * RS
+		AK1I = STI * RS
+		S1R = S1R + AK1R
+		S1I = S1I + AK1I
+		S = S + AK
+		AK = AK + 2.0E0
+		AA = AA * ACZ * RS
+		if AA > ATOL {
+			goto Sixty
+		}
+	Seventy:
+		S2R = S1R*COEFR - S1I*COEFI
+		S2I = S1R*COEFI + S1I*COEFR
+		WR[I] = S2R
+		WI[I] = S2I
+		if IFLAG == 0 {
+			goto Eighty
+		}
+		S2R, S2I, NW, ASCLE, TOL = zuchkOrig(S2R, S2I, NW, ASCLE, TOL)
+		if NW != 0 {
+			goto Thirty
+		}
+	Eighty:
+		M = NN - I + 1
+		YR[M] = S2R * CRSCR
+		YI[M] = S2I * CRSCR
+		if I == IL {
+			continue
+		}
+		tmp = zdiv(complex(COEFR, COEFI), complex(HZR, HZI))
+		STR = real(tmp)
+		STI = imag(tmp)
+		COEFR = STR * DFNU
+		COEFI = STI * DFNU
+	}
+	if NN <= 2 {
+		return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+	}
+	K = NN - 2
+	AK = float64(float32(K))
+	RAZ = 1.0E0 / AZ
+	STR = ZR * RAZ
+	STI = -ZI * RAZ
+	RZR = (STR + STR) * RAZ
+	RZI = (STI + STI) * RAZ
+	if IFLAG == 1 {
+		goto OneTwenty
+	}
+	IB = 3
+OneHundred:
+	for I = IB; I <= NN; I++ {
+		YR[K] = (AK+FNU)*(RZR*YR[K+1]-RZI*YI[K+1]) + YR[K+2]
+		YI[K] = (AK+FNU)*(RZR*YI[K+1]+RZI*YR[K+1]) + YI[K+2]
+		AK = AK - 1.0E0
+		K = K - 1
+	}
+	return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+
+	// RECUR BACKWARD WITH SCALED VALUES.
+OneTwenty:
+	// EXP(-ALIM)=EXP(-ELIM)/TOL=APPROX. ONE PRECISION ABOVE THE
+	// UNDERFLOW LIMIT = ASCLE = dmach[1)*SS*1.0D+3.
+	S1R = WR[1]
+	S1I = WI[1]
+	S2R = WR[2]
+	S2I = WI[2]
+	for L = 3; L <= NN; L++ {
+		CKR = S2R
+		CKI = S2I
+		S2R = S1R + (AK+FNU)*(RZR*CKR-RZI*CKI)
+		S2I = S1I + (AK+FNU)*(RZR*CKI+RZI*CKR)
+		S1R = CKR
+		S1I = CKI
+		CKR = S2R * CRSCR
+		CKI = S2I * CRSCR
+		YR[K] = CKR
+		YI[K] = CKI
+		AK = AK - 1.0E0
+		K = K - 1
+		if zabs(complex(CKR, CKI)) > ASCLE {
+			goto OneFourty
+		}
+	}
+	return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+OneFourty:
+	IB = L + 1
+	if IB > NN {
+		return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+	}
+	goto OneHundred
+OneFifty:
+	NZ = N
+	if FNU == 0.0E0 {
+		NZ = NZ - 1
+	}
+OneSixty:
+	YR[1] = ZEROR
+	YI[1] = ZEROI
+	if FNU != 0.0E0 {
+		goto OneSeventy
+	}
+	YR[1] = CONER
+	YI[1] = CONEI
+OneSeventy:
+	if N == 1 {
+		return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+	}
+	for I = 2; I <= N; I++ {
+		YR[I] = ZEROR
+		YI[I] = ZEROI
+	}
+	return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+
+	// return WITH NZ<0 if CABS(Z*Z/4)>FNU+N-NZ-1 COMPLETE
+	// THE CALCULATION IN CBINU WITH N=N-IABS(NZ)
+
+OneNinety:
+	NZ = -NZ
+	return ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM
+}
+
+// ZS1S2 TESTS FOR A POSSIBLE UNDERFLOW RESULTING FROM THE
+// ADDITION OF THE I AND K FUNCTIONS IN THE ANALYTIC CON-
+// TINUATION FORMULA WHERE S1=K FUNCTION AND S2=I FUNCTION.
+// ON KODE=1 THE I AND K FUNCTIONS ARE DIFFERENT ORDERS OF
+// MAGNITUDE, BUT FOR KODE=2 THEY CAN BE OF THE SAME ORDER
+// OF MAGNITUDE AND THE MAXIMUM MUST BE AT LEAST ONE
+// PRECISION ABOVE THE UNDERFLOW LIMIT.
+func zs1s2Orig(ZRR, ZRI, S1R, S1I, S2R, S2I float64, NZ int, ASCLE, ALIM float64, IUF int) (
+	ZRRout, ZRIout, S1Rout, S1Iout, S2Rout, S2Iout float64, NZout int, ASCLEout, ALIMout float64, IUFout int) {
+	var AA, ALN, AS1, AS2, C1I, C1R, S1DI, S1DR, ZEROI, ZEROR float64
+	var tmp complex128
+
+	ZEROR = 0
+	ZEROI = 0
+	NZ = 0
+	AS1 = zabs(complex(S1R, S1I))
+	AS2 = zabs(complex(S2R, S2I))
+	if S1R == 0.0E0 && S1I == 0.0E0 {
+		goto Ten
+	}
+	if AS1 == 0.0E0 {
+		goto Ten
+	}
+	ALN = -ZRR - ZRR + dlog(AS1)
+	S1DR = S1R
+	S1DI = S1I
+	S1R = ZEROR
+	S1I = ZEROI
+	AS1 = ZEROR
+	if ALN < (-ALIM) {
+		goto Ten
+	}
+	tmp = zlog(complex(S1DR, S1DI))
+	C1R = real(tmp)
+	C1I = imag(tmp)
+
+	C1R = C1R - ZRR - ZRR
+	C1I = C1I - ZRI - ZRI
+	tmp = zexp(complex(C1R, C1I))
+	S1R = real(tmp)
+	S1I = imag(tmp)
+	AS1 = zabs(complex(S1R, S1I))
+	IUF = IUF + 1
+Ten:
+	AA = dmax(AS1, AS2)
+	if AA > ASCLE {
+		return ZRR, ZRI, S1R, S1I, S2R, S2I, NZ, ASCLE, ALIM, IUF
+	}
+	S1R = ZEROR
+	S1I = ZEROI
+	S2R = ZEROR
+	S2I = ZEROI
+	NZ = 1
+	IUF = 0
+	return ZRR, ZRI, S1R, S1I, S2R, S2I, NZ, ASCLE, ALIM, IUF
+}
+
+// ZSHCH COMPUTES THE COMPLEX HYPERBOLIC FUNCTIONS CSH=SINH(X+iY) AND
+// CCH=COSH(X+I*Y), WHERE I**2=-1.
+// TODO(btracey): use cmplx.Sinh and cmplx.Cosh.
+func zshchOrig(ZR, ZI, CSHR, CSHI, CCHR, CCHI float64) (ZRout, ZIout, CSHRout, CSHIout, CCHRout, CCHIout float64) {
+	var CH, CN, SH, SN float64
+	SH = math.Sinh(ZR)
+	CH = math.Cosh(ZR)
+	SN = dsin(ZI)
+	CN = dcos(ZI)
+	CSHR = SH * CN
+	CSHI = CH * SN
+	CCHR = CH * CN
+	CCHI = SH * SN
+	return ZR, ZI, CSHR, CSHI, CCHR, CCHI
+}
+
+func dmax(a, b float64) float64 {
+	return math.Max(a, b)
+}
+
+func dmin(a, b float64) float64 {
+	return math.Min(a, b)
+}
+
+func dabs(a float64) float64 {
+	return math.Abs(a)
+}
+
+func datan(a float64) float64 {
+	return math.Atan(a)
+}
+
+func dtan(a float64) float64 {
+	return math.Tan(a)
+}
+
+func dlog(a float64) float64 {
+	return math.Log(a)
+}
+
+func dsin(a float64) float64 {
+	return math.Sin(a)
+}
+
+func dcos(a float64) float64 {
+	return math.Cos(a)
+}
+
+func dexp(a float64) float64 {
+	return math.Exp(a)
+}
+
+func dsqrt(a float64) float64 {
+	return math.Sqrt(a)
+}
+
+func zmlt(a, b complex128) complex128 {
+	return a * b
+}
+
+func zdiv(a, b complex128) complex128 {
+	return a / b
+}
+
+func zabs(a complex128) float64 {
+	return cmplx.Abs(a)
+}
+
+func zsqrt(a complex128) complex128 {
+	return cmplx.Sqrt(a)
+}
+
+func zexp(a complex128) complex128 {
+	return cmplx.Exp(a)
+}
+
+func zlog(a complex128) complex128 {
+	return cmplx.Log(a)
+}
+
+// Zshch computes the hyperbolic sin and cosine of the input z.
+func Zshch(z complex128) (sinh, cosh complex128) {
+	return cmplx.Sinh(z), cmplx.Cosh(z)
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/cephes/cephes.go b/vendor/gonum.org/v1/gonum/mathext/internal/cephes/cephes.go
new file mode 100644
index 00000000..22d26e87
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/cephes/cephes.go
@@ -0,0 +1,28 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package cephes
+
+import "math"
+
+/*
+Additional copyright information:
+
+Code in this package is adapted from the Cephes library (http://www.netlib.org/cephes/).
+There is no explicit licence on Netlib, but the author has agreed to a BSD release.
+See https://github.com/deepmind/torch-cephes/blob/master/LICENSE.txt and
+https://lists.debian.org/debian-legal/2004/12/msg00295.html
+*/
+
+var (
+	badParamOutOfBounds         = "cephes: parameter out of bounds"
+	badParamFunctionSingularity = "cephes: function singularity"
+)
+
+const (
+	machEp  = 1.0 / (1 << 53)
+	maxLog  = 1024 * math.Ln2
+	minLog  = -1075 * math.Ln2
+	maxIter = 2000
+)
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/cephes/doc.go b/vendor/gonum.org/v1/gonum/mathext/internal/cephes/doc.go
new file mode 100644
index 00000000..4fe18ba6
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/cephes/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package cephes implements functions originally in the Netlib code by Stephen Mosher.
+package cephes // import "gonum.org/v1/gonum/mathext/internal/cephes"
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/cephes/igam.go b/vendor/gonum.org/v1/gonum/mathext/internal/cephes/igam.go
new file mode 100644
index 00000000..0a9732e5
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/cephes/igam.go
@@ -0,0 +1,311 @@
+// Derived from SciPy's special/cephes/igam.c and special/cephes/igam.h
+// https://github.com/scipy/scipy/blob/master/scipy/special/cephes/igam.c
+// https://github.com/scipy/scipy/blob/master/scipy/special/cephes/igam.h
+// Made freely available by Stephen L. Moshier without support or guarantee.
+
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+// Copyright ©1985, ©1987 by Stephen L. Moshier
+// Portions Copyright ©2016 The gonum Authors. All rights reserved.
+
+package cephes
+
+import "math"
+
+const (
+	igamDimK       = 25
+	igamDimN       = 25
+	igam           = 1
+	igamC          = 0
+	igamSmall      = 20
+	igamLarge      = 200
+	igamSmallRatio = 0.3
+	igamLargeRatio = 4.5
+)
+
+var igamCoefs = [igamDimK][igamDimN]float64{
+	{-3.3333333333333333e-1, 8.3333333333333333e-2, -1.4814814814814815e-2, 1.1574074074074074e-3, 3.527336860670194e-4, -1.7875514403292181e-4, 3.9192631785224378e-5, -2.1854485106799922e-6, -1.85406221071516e-6, 8.296711340953086e-7, -1.7665952736826079e-7, 6.7078535434014986e-9, 1.0261809784240308e-8, -4.3820360184533532e-9, 9.1476995822367902e-10, -2.551419399494625e-11, -5.8307721325504251e-11, 2.4361948020667416e-11, -5.0276692801141756e-12, 1.1004392031956135e-13, 3.3717632624009854e-13, -1.3923887224181621e-13, 2.8534893807047443e-14, -5.1391118342425726e-16, -1.9752288294349443e-15},
+	{-1.8518518518518519e-3, -3.4722222222222222e-3, 2.6455026455026455e-3, -9.9022633744855967e-4, 2.0576131687242798e-4, -4.0187757201646091e-7, -1.8098550334489978e-5, 7.6491609160811101e-6, -1.6120900894563446e-6, 4.6471278028074343e-9, 1.378633446915721e-7, -5.752545603517705e-8, 1.1951628599778147e-8, -1.7543241719747648e-11, -1.0091543710600413e-9, 4.1627929918425826e-10, -8.5639070264929806e-11, 6.0672151016047586e-14, 7.1624989648114854e-12, -2.9331866437714371e-12, 5.9966963656836887e-13, -2.1671786527323314e-16, -4.9783399723692616e-14, 2.0291628823713425e-14, -4.13125571381061e-15},
+	{4.1335978835978836e-3, -2.6813271604938272e-3, 7.7160493827160494e-4, 2.0093878600823045e-6, -1.0736653226365161e-4, 5.2923448829120125e-5, -1.2760635188618728e-5, 3.4235787340961381e-8, 1.3721957309062933e-6, -6.298992138380055e-7, 1.4280614206064242e-7, -2.0477098421990866e-10, -1.4092529910867521e-8, 6.228974084922022e-9, -1.3670488396617113e-9, 9.4283561590146782e-13, 1.2872252400089318e-10, -5.5645956134363321e-11, 1.1975935546366981e-11, -4.1689782251838635e-15, -1.0940640427884594e-12, 4.6622399463901357e-13, -9.905105763906906e-14, 1.8931876768373515e-17, 8.8592218725911273e-15},
+	{6.4943415637860082e-4, 2.2947209362139918e-4, -4.6918949439525571e-4, 2.6772063206283885e-4, -7.5618016718839764e-5, -2.3965051138672967e-7, 1.1082654115347302e-5, -5.6749528269915966e-6, 1.4230900732435884e-6, -2.7861080291528142e-11, -1.6958404091930277e-7, 8.0994649053880824e-8, -1.9111168485973654e-8, 2.3928620439808118e-12, 2.0620131815488798e-9, -9.4604966618551322e-10, 2.1541049775774908e-10, -1.388823336813903e-14, -2.1894761681963939e-11, 9.7909989511716851e-12, -2.1782191880180962e-12, 6.2088195734079014e-17, 2.126978363279737e-13, -9.3446887915174333e-14, 2.0453671226782849e-14},
+	{-8.618882909167117e-4, 7.8403922172006663e-4, -2.9907248030319018e-4, -1.4638452578843418e-6, 6.6414982154651222e-5, -3.9683650471794347e-5, 1.1375726970678419e-5, 2.5074972262375328e-10, -1.6954149536558306e-6, 8.9075075322053097e-7, -2.2929348340008049e-7, 2.956794137544049e-11, 2.8865829742708784e-8, -1.4189739437803219e-8, 3.4463580499464897e-9, -2.3024517174528067e-13, -3.9409233028046405e-10, 1.8602338968504502e-10, -4.356323005056618e-11, 1.2786001016296231e-15, 4.6792750266579195e-12, -2.1492464706134829e-12, 4.9088156148096522e-13, -6.3385914848915603e-18, -5.0453320690800944e-14},
+	{-3.3679855336635815e-4, -6.9728137583658578e-5, 2.7727532449593921e-4, -1.9932570516188848e-4, 6.7977804779372078e-5, 1.419062920643967e-7, -1.3594048189768693e-5, 8.0184702563342015e-6, -2.2914811765080952e-6, -3.252473551298454e-10, 3.4652846491085265e-7, -1.8447187191171343e-7, 4.8240967037894181e-8, -1.7989466721743515e-14, -6.3061945000135234e-9, 3.1624176287745679e-9, -7.8409242536974293e-10, 5.1926791652540407e-15, 9.3589442423067836e-11, -4.5134262161632782e-11, 1.0799129993116827e-11, -3.661886712685252e-17, -1.210902069055155e-12, 5.6807435849905643e-13, -1.3249659916340829e-13},
+	{5.3130793646399222e-4, -5.9216643735369388e-4, 2.7087820967180448e-4, 7.9023532326603279e-7, -8.1539693675619688e-5, 5.6116827531062497e-5, -1.8329116582843376e-5, -3.0796134506033048e-9, 3.4651553688036091e-6, -2.0291327396058604e-6, 5.7887928631490037e-7, 2.338630673826657e-13, -8.8286007463304835e-8, 4.7435958880408128e-8, -1.2545415020710382e-8, 8.6496488580102925e-14, 1.6846058979264063e-9, -8.5754928235775947e-10, 2.1598224929232125e-10, -7.6132305204761539e-16, -2.6639822008536144e-11, 1.3065700536611057e-11, -3.1799163902367977e-12, 4.7109761213674315e-18, 3.6902800842763467e-13},
+	{3.4436760689237767e-4, 5.1717909082605922e-5, -3.3493161081142236e-4, 2.812695154763237e-4, -1.0976582244684731e-4, -1.2741009095484485e-7, 2.7744451511563644e-5, -1.8263488805711333e-5, 5.7876949497350524e-6, 4.9387589339362704e-10, -1.0595367014026043e-6, 6.1667143761104075e-7, -1.7562973359060462e-7, -1.2974473287015439e-12, 2.695423606288966e-8, -1.4578352908731271e-8, 3.887645959386175e-9, -3.8810022510194121e-17, -5.3279941738772867e-10, 2.7437977643314845e-10, -6.9957960920705679e-11, 2.5899863874868481e-17, 8.8566890996696381e-12, -4.403168815871311e-12, 1.0865561947091654e-12},
+	{-6.5262391859530942e-4, 8.3949872067208728e-4, -4.3829709854172101e-4, -6.969091458420552e-7, 1.6644846642067548e-4, -1.2783517679769219e-4, 4.6299532636913043e-5, 4.5579098679227077e-9, -1.0595271125805195e-5, 6.7833429048651666e-6, -2.1075476666258804e-6, -1.7213731432817145e-11, 3.7735877416110979e-7, -2.1867506700122867e-7, 6.2202288040189269e-8, 6.5977038267330006e-16, -9.5903864974256858e-9, 5.2132144922808078e-9, -1.3991589583935709e-9, 5.382058999060575e-16, 1.9484714275467745e-10, -1.0127287556389682e-10, 2.6077347197254926e-11, -5.0904186999932993e-18, -3.3721464474854592e-12},
+	{-5.9676129019274625e-4, -7.2048954160200106e-5, 6.7823088376673284e-4, -6.4014752602627585e-4, 2.7750107634328704e-4, 1.8197008380465151e-7, -8.4795071170685032e-5, 6.105192082501531e-5, -2.1073920183404862e-5, -8.8585890141255994e-10, 4.5284535953805377e-6, -2.8427815022504408e-6, 8.7082341778646412e-7, 3.6886101871706965e-12, -1.5344695190702061e-7, 8.862466778790695e-8, -2.5184812301826817e-8, -1.0225912098215092e-14, 3.8969470758154777e-9, -2.1267304792235635e-9, 5.7370135528051385e-10, -1.887749850169741e-19, -8.0931538694657866e-11, 4.2382723283449199e-11, -1.1002224534207726e-11},
+	{1.3324454494800656e-3, -1.9144384985654775e-3, 1.1089369134596637e-3, 9.932404122642299e-7, -5.0874501293093199e-4, 4.2735056665392884e-4, -1.6858853767910799e-4, -8.1301893922784998e-9, 4.5284402370562147e-5, -3.127053674781734e-5, 1.044986828530338e-5, 4.8435226265680926e-11, -2.1482565873456258e-6, 1.329369701097492e-6, -4.0295693092101029e-7, -1.7567877666323291e-13, 7.0145043163668257e-8, -4.040787734999483e-8, 1.1474026743371963e-8, 3.9642746853563325e-18, -1.7804938269892714e-9, 9.7480262548731646e-10, -2.6405338676507616e-10, 5.794875163403742e-18, 3.7647749553543836e-11},
+	{1.579727660730835e-3, 1.6251626278391582e-4, -2.0633421035543276e-3, 2.1389686185689098e-3, -1.0108559391263003e-3, -3.9912705529919201e-7, 3.6235025084764691e-4, -2.8143901463712154e-4, 1.0449513336495887e-4, 2.1211418491830297e-9, -2.5779417251947842e-5, 1.7281818956040463e-5, -5.6413773872904282e-6, -1.1024320105776174e-11, 1.1223224418895175e-6, -6.8693396379526735e-7, 2.0653236975414887e-7, 4.6714772409838506e-14, -3.5609886164949055e-8, 2.0470855345905963e-8, -5.8091738633283358e-9, -1.332821287582869e-16, 9.0354604391335133e-10, -4.9598782517330834e-10, 1.3481607129399749e-10},
+	{-4.0725121195140166e-3, 6.4033628338080698e-3, -4.0410161081676618e-3, -2.183732802866233e-6, 2.1740441801254639e-3, -1.9700440518418892e-3, 8.3595469747962458e-4, 1.9445447567109655e-8, -2.5779387120421696e-4, 1.9009987368139304e-4, -6.7696499937438965e-5, -1.4440629666426572e-10, 1.5712512518742269e-5, -1.0304008744776893e-5, 3.304517767401387e-6, 7.9829760242325709e-13, -6.4097794149313004e-7, 3.8894624761300056e-7, -1.1618347644948869e-7, -2.816808630596451e-15, 1.9878012911297093e-8, -1.1407719956357511e-8, 3.2355857064185555e-9, 4.1759468293455945e-20, -5.0423112718105824e-10},
+	{-5.9475779383993003e-3, -5.4016476789260452e-4, 8.7910413550767898e-3, -9.8576315587856125e-3, 5.0134695031021538e-3, 1.2807521786221875e-6, -2.0626019342754683e-3, 1.7109128573523058e-3, -6.7695312714133799e-4, -6.9011545676562133e-9, 1.8855128143995902e-4, -1.3395215663491969e-4, 4.6263183033528039e-5, 4.0034230613321351e-11, -1.0255652921494033e-5, 6.612086372797651e-6, -2.0913022027253008e-6, -2.0951775649603837e-13, 3.9756029041993247e-7, -2.3956211978815887e-7, 7.1182883382145864e-8, 8.925574873053455e-16, -1.2101547235064676e-8, 6.9350618248334386e-9, -1.9661464453856102e-9},
+	{1.7402027787522711e-2, -2.9527880945699121e-2, 2.0045875571402799e-2, 7.0289515966903407e-6, -1.2375421071343148e-2, 1.1976293444235254e-2, -5.4156038466518525e-3, -6.3290893396418616e-8, 1.8855118129005065e-3, -1.473473274825001e-3, 5.5515810097708387e-4, 5.2406834412550662e-10, -1.4357913535784836e-4, 9.9181293224943297e-5, -3.3460834749478311e-5, -3.5755837291098993e-12, 7.1560851960630076e-6, -4.5516802628155526e-6, 1.4236576649271475e-6, 1.8803149082089664e-14, -2.6623403898929211e-7, 1.5950642189595716e-7, -4.7187514673841102e-8, -6.5107872958755177e-17, 7.9795091026746235e-9},
+	{3.0249124160905891e-2, 2.4817436002649977e-3, -4.9939134373457022e-2, 5.9915643009307869e-2, -3.2483207601623391e-2, -5.7212968652103441e-6, 1.5085251778569354e-2, -1.3261324005088445e-2, 5.5515262632426148e-3, 3.0263182257030016e-8, -1.7229548406756723e-3, 1.2893570099929637e-3, -4.6845138348319876e-4, -1.830259937893045e-10, 1.1449739014822654e-4, -7.7378565221244477e-5, 2.5625836246985201e-5, 1.0766165333192814e-12, -5.3246809282422621e-6, 3.349634863064464e-6, -1.0381253128684018e-6, -5.608909920621128e-15, 1.9150821930676591e-7, -1.1418365800203486e-7, 3.3654425209171788e-8},
+	{-9.9051020880159045e-2, 1.7954011706123486e-1, -1.2989606383463778e-1, -3.1478872752284357e-5, 9.0510635276848131e-2, -9.2828824411184397e-2, 4.4412112839877808e-2, 2.7779236316835888e-7, -1.7229543805449697e-2, 1.4182925050891573e-2, -5.6214161633747336e-3, -2.39598509186381e-9, 1.6029634366079908e-3, -1.1606784674435773e-3, 4.1001337768153873e-4, 1.8365800754090661e-11, -9.5844256563655903e-5, 6.3643062337764708e-5, -2.076250624489065e-5, -1.1806020912804483e-13, 4.2131808239120649e-6, -2.6262241337012467e-6, 8.0770620494930662e-7, 6.0125912123632725e-16, -1.4729737374018841e-7},
+	{-1.9994542198219728e-1, -1.5056113040026424e-2, 3.6470239469348489e-1, -4.6435192311733545e-1, 2.6640934719197893e-1, 3.4038266027147191e-5, -1.3784338709329624e-1, 1.276467178337056e-1, -5.6213828755200985e-2, -1.753150885483011e-7, 1.9235592956768113e-2, -1.5088821281095315e-2, 5.7401854451350123e-3, 1.0622382710310225e-9, -1.5335082692563998e-3, 1.0819320643228214e-3, -3.7372510193945659e-4, -6.6170909729031985e-12, 8.4263617380909628e-5, -5.5150706827483479e-5, 1.7769536448348069e-5, 3.8827923210205533e-14, -3.53513697488768e-6, 2.1865832130045269e-6, -6.6812849447625594e-7},
+	{7.2438608504029431e-1, -1.3918010932653375, 1.0654143352413968, 1.876173868950258e-4, -8.2705501176152696e-1, 8.9352433347828414e-1, -4.4971003995291339e-1, -1.6107401567546652e-6, 1.9235590165271091e-1, -1.6597702160042609e-1, 6.8882222681814333e-2, 1.3910091724608687e-8, -2.146911561508663e-2, 1.6228980898865892e-2, -5.9796016172584256e-3, -1.1287469112826745e-10, 1.5167451119784857e-3, -1.0478634293553899e-3, 3.5539072889126421e-4, 8.1704322111801517e-13, -7.7773013442452395e-5, 5.0291413897007722e-5, -1.6035083867000518e-5, 1.2469354315487605e-14, 3.1369106244517615e-6},
+	{1.6668949727276811, 1.165462765994632e-1, -3.3288393225018906, 4.4692325482864037, -2.6977693045875807, -2.600667859891061e-4, 1.5389017615694539, -1.4937962361134612, 6.8881964633233148e-1, 1.3077482004552385e-6, -2.5762963325596288e-1, 2.1097676102125449e-1, -8.3714408359219882e-2, -7.7920428881354753e-9, 2.4267923064833599e-2, -1.7813678334552311e-2, 6.3970330388900056e-3, 4.9430807090480523e-11, -1.5554602758465635e-3, 1.0561196919903214e-3, -3.5277184460472902e-4, 9.3002334645022459e-14, 7.5285855026557172e-5, -4.8186515569156351e-5, 1.5227271505597605e-5},
+	{-6.6188298861372935, 1.3397985455142589e+1, -1.0789350606845146e+1, -1.4352254537875018e-3, 9.2333694596189809, -1.0456552819547769e+1, 5.5105526029033471, 1.2024439690716742e-5, -2.5762961164755816, 2.3207442745387179, -1.0045728797216284, -1.0207833290021914e-7, 3.3975092171169466e-1, -2.6720517450757468e-1, 1.0235252851562706e-1, 8.4329730484871625e-10, -2.7998284958442595e-2, 2.0066274144976813e-2, -7.0554368915086242e-3, 1.9402238183698188e-12, 1.6562888105449611e-3, -1.1082898580743683e-3, 3.654545161310169e-4, -5.1290032026971794e-11, -7.6340103696869031e-5},
+	{-1.7112706061976095e+1, -1.1208044642899116, 3.7131966511885444e+1, -5.2298271025348962e+1, 3.3058589696624618e+1, 2.4791298976200222e-3, -2.061089403411526e+1, 2.088672775145582e+1, -1.0045703956517752e+1, -1.2238783449063012e-5, 4.0770134274221141, -3.473667358470195, 1.4329352617312006, 7.1359914411879712e-8, -4.4797257159115612e-1, 3.4112666080644461e-1, -1.2699786326594923e-1, -2.8953677269081528e-10, 3.3125776278259863e-2, -2.3274087021036101e-2, 8.0399993503648882e-3, -1.177805216235265e-9, -1.8321624891071668e-3, 1.2108282933588665e-3, -3.9479941246822517e-4},
+	{7.389033153567425e+1, -1.5680141270402273e+2, 1.322177542759164e+2, 1.3692876877324546e-2, -1.2366496885920151e+2, 1.4620689391062729e+2, -8.0365587724865346e+1, -1.1259851148881298e-4, 4.0770132196179938e+1, -3.8210340013273034e+1, 1.719522294277362e+1, 9.3519707955168356e-7, -6.2716159907747034, 5.1168999071852637, -2.0319658112299095, -4.9507215582761543e-9, 5.9626397294332597e-1, -4.4220765337238094e-1, 1.6079998700166273e-1, -2.4733786203223402e-8, -4.0307574759979762e-2, 2.7849050747097869e-2, -9.4751858992054221e-3, 6.419922235909132e-6, 2.1250180774699461e-3},
+	{2.1216837098382522e+2, 1.3107863022633868e+1, -4.9698285932871748e+2, 7.3121595266969204e+2, -4.8213821720890847e+2, -2.8817248692894889e-2, 3.2616720302947102e+2, -3.4389340280087117e+2, 1.7195193870816232e+2, 1.4038077378096158e-4, -7.52594195897599e+1, 6.651969984520934e+1, -2.8447519748152462e+1, -7.613702615875391e-7, 9.5402237105304373, -7.5175301113311376, 2.8943997568871961, -4.6612194999538201e-7, -8.0615149598794088e-1, 5.8483006570631029e-1, -2.0845408972964956e-1, 1.4765818959305817e-4, 5.1000433863753019e-2, -3.3066252141883665e-2, 1.5109265210467774e-2},
+	{-9.8959643098322368e+2, 2.1925555360905233e+3, -1.9283586782723356e+3, -1.5925738122215253e-1, 1.9569985945919857e+3, -2.4072514765081556e+3, 1.3756149959336496e+3, 1.2920735237496668e-3, -7.525941715948055e+2, 7.3171668742208716e+2, -3.4137023466220065e+2, -9.9857390260608043e-6, 1.3356313181291573e+2, -1.1276295161252794e+2, 4.6310396098204458e+1, -7.9237387133614756e-6, -1.4510726927018646e+1, 1.1111771248100563e+1, -4.1690817945270892, 3.1008219800117808e-3, 1.1220095449981468, -7.6052379926149916e-1, 3.6262236505085254e-1, 2.216867741940747e-1, 4.8683443692930507e-1},
+}
+
+// Igam computes the incomplete Gamma integral.
+//  Igam(a,x) = (1/ Γ(a)) \int_0^x e^{-t} t^{a-1} dt
+// The input argument a must be positive and x must be non-negative or Igam
+// will panic.
+func Igam(a, x float64) float64 {
+	// The integral is evaluated by either a power series or continued fraction
+	// expansion, depending on the relative values of a and x.
+	// Sources:
+	// [1] "The Digital Library of Mathematical Functions", dlmf.nist.gov
+	// [2] Maddock et. al., "Incomplete Gamma Functions",
+	// http://www.boost.org/doc/libs/1_61_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html
+
+	// Check zero integration limit first
+	if x == 0 {
+		return 0
+	}
+
+	if x < 0 || a <= 0 {
+		panic(badParamOutOfBounds)
+	}
+
+	// Asymptotic regime where a ~ x; see [2].
+	absxmaA := math.Abs(x-a) / a
+	if (igamSmall < a && a < igamLarge && absxmaA < igamSmallRatio) ||
+		(igamLarge < a && absxmaA < igamLargeRatio/math.Sqrt(a)) {
+		return asymptoticSeries(a, x, igam)
+	}
+
+	if x > 1 && x > a {
+		return 1 - IgamC(a, x)
+	}
+
+	return igamSeries(a, x)
+}
+
+// IgamC computes the complemented incomplete Gamma integral.
+//  IgamC(a,x) = 1 - Igam(a,x)
+//             = (1/ Γ(a)) \int_0^\infty e^{-t} t^{a-1} dt
+// The input argument a must be positive and x must be non-negative or
+// IgamC will panic.
+func IgamC(a, x float64) float64 {
+	// The integral is evaluated by either a power series or continued fraction
+	// expansion, depending on the relative values of a and x.
+	// Sources:
+	// [1] "The Digital Library of Mathematical Functions", dlmf.nist.gov
+	// [2] Maddock et. al., "Incomplete Gamma Functions",
+	// http://www.boost.org/doc/libs/1_61_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html
+
+	switch {
+	case x < 0, a <= 0:
+		panic(badParamOutOfBounds)
+	case x == 0:
+		return 1
+	case math.IsInf(x, 0):
+		return 0
+	}
+
+	// Asymptotic regime where a ~ x; see [2].
+	absxmaA := math.Abs(x-a) / a
+	if (igamSmall < a && a < igamLarge && absxmaA < igamSmallRatio) ||
+		(igamLarge < a && absxmaA < igamLargeRatio/math.Sqrt(a)) {
+		return asymptoticSeries(a, x, igamC)
+	}
+
+	// Everywhere else; see [2].
+	if x > 1.1 {
+		if x < a {
+			return 1 - igamSeries(a, x)
+		}
+		return igamCContinuedFraction(a, x)
+	} else if x <= 0.5 {
+		if -0.4/math.Log(x) < a {
+			return 1 - igamSeries(a, x)
+		}
+		return igamCSeries(a, x)
+	}
+
+	if x*1.1 < a {
+		return 1 - igamSeries(a, x)
+	}
+	return igamCSeries(a, x)
+}
+
+// igamFac computes
+//  x^a * e^{-x} / Γ(a)
+// corrected from (15) and (16) in [2] by replacing
+//  e^{x - a}
+// with
+//  e^{a - x}
+func igamFac(a, x float64) float64 {
+	if math.Abs(a-x) > 0.4*math.Abs(a) {
+		ax := a*math.Log(x) - x - lgam(a)
+		return math.Exp(ax)
+	}
+
+	fac := a + lanczosG - 0.5
+	res := math.Sqrt(fac/math.Exp(1)) / lanczosSumExpgScaled(a)
+
+	if a < 200 && x < 200 {
+		res *= math.Exp(a-x) * math.Pow(x/fac, a)
+	} else {
+		num := x - a - lanczosG + 0.5
+		res *= math.Exp(a*log1pmx(num/fac) + x*(0.5-lanczosG)/fac)
+	}
+
+	return res
+}
+
+// igamCContinuedFraction computes IgamC using DLMF 8.9.2.
+func igamCContinuedFraction(a, x float64) float64 {
+	ax := igamFac(a, x)
+	if ax == 0 {
+		return 0
+	}
+
+	// Continued fraction
+	y := 1 - a
+	z := x + y + 1
+	c := 0.0
+	pkm2 := 1.0
+	qkm2 := x
+	pkm1 := x + 1.0
+	qkm1 := z * x
+	ans := pkm1 / qkm1
+
+	for i := 0; i < maxIter; i++ {
+		c += 1.0
+		y += 1.0
+		z += 2.0
+		yc := y * c
+		pk := pkm1*z - pkm2*yc
+		qk := qkm1*z - qkm2*yc
+		var t float64
+		if qk != 0 {
+			r := pk / qk
+			t = math.Abs((ans - r) / r)
+			ans = r
+		} else {
+			t = 1.0
+		}
+		pkm2 = pkm1
+		pkm1 = pk
+		qkm2 = qkm1
+		qkm1 = qk
+		if math.Abs(pk) > big {
+			pkm2 *= biginv
+			pkm1 *= biginv
+			qkm2 *= biginv
+			qkm1 *= biginv
+		}
+		if t <= machEp {
+			break
+		}
+	}
+
+	return ans * ax
+}
+
+// igamSeries computes Igam using DLMF 8.11.4.
+func igamSeries(a, x float64) float64 {
+	ax := igamFac(a, x)
+	if ax == 0 {
+		return 0
+	}
+
+	// Power series
+	r := a
+	c := 1.0
+	ans := 1.0
+
+	for i := 0; i < maxIter; i++ {
+		r += 1.0
+		c *= x / r
+		ans += c
+		if c <= machEp*ans {
+			break
+		}
+	}
+
+	return ans * ax / a
+}
+
+// igamCSeries computes IgamC using DLMF 8.7.3. This is related to the series
+// in igamSeries but extra care is taken to avoid cancellation.
+func igamCSeries(a, x float64) float64 {
+	fac := 1.0
+	sum := 0.0
+
+	for n := 1; n < maxIter; n++ {
+		fac *= -x / float64(n)
+		term := fac / (a + float64(n))
+		sum += term
+		if math.Abs(term) <= machEp*math.Abs(sum) {
+			break
+		}
+	}
+
+	logx := math.Log(x)
+	term := -expm1(a*logx - lgam1p(a))
+	return term - math.Exp(a*logx-lgam(a))*sum
+}
+
+// asymptoticSeries computes Igam/IgamC using DLMF 8.12.3/8.12.4.
+func asymptoticSeries(a, x float64, fun int) float64 {
+	maxpow := 0
+	lambda := x / a
+	sigma := (x - a) / a
+	absoldterm := math.MaxFloat64
+	etapow := [igamDimN]float64{1}
+	sum := 0.0
+	afac := 1.0
+
+	var sgn float64
+	if fun == igam {
+		sgn = -1
+	} else {
+		sgn = 1
+	}
+
+	var eta float64
+	if lambda > 1 {
+		eta = math.Sqrt(-2 * log1pmx(sigma))
+	} else if lambda < 1 {
+		eta = -math.Sqrt(-2 * log1pmx(sigma))
+	} else {
+		eta = 0
+	}
+	res := 0.5 * math.Erfc(sgn*eta*math.Sqrt(a/2))
+
+	for k := 0; k < igamDimK; k++ {
+		ck := igamCoefs[k][0]
+		for n := 1; n < igamDimN; n++ {
+			if n > maxpow {
+				etapow[n] = eta * etapow[n-1]
+				maxpow++
+			}
+			ckterm := igamCoefs[k][n] * etapow[n]
+			ck += ckterm
+			if math.Abs(ckterm) < machEp*math.Abs(ck) {
+				break
+			}
+		}
+		term := ck * afac
+		absterm := math.Abs(term)
+		if absterm > absoldterm {
+			break
+		}
+		sum += term
+		if absterm < machEp*math.Abs(sum) {
+			break
+		}
+		absoldterm = absterm
+		afac /= a
+	}
+	res += sgn * math.Exp(-0.5*a*eta*eta) * sum / math.Sqrt(2*math.Pi*a)
+
+	return res
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/cephes/igami.go b/vendor/gonum.org/v1/gonum/mathext/internal/cephes/igami.go
new file mode 100644
index 00000000..5a8d9a91
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/cephes/igami.go
@@ -0,0 +1,153 @@
+// Derived from SciPy's special/cephes/igami.c
+// https://github.com/scipy/scipy/blob/master/scipy/special/cephes/igami.c
+// Made freely available by Stephen L. Moshier without support or guarantee.
+
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+// Copyright ©1984, ©1987, ©1995 by Stephen L. Moshier
+// Portions Copyright ©2017 The gonum Authors. All rights reserved.
+
+package cephes
+
+import "math"
+
+// IgamI computes the inverse of the incomplete Gamma function. That is, it
+// returns the x such that:
+//  IgamC(a, x) = p
+// The input argument a must be positive and p must be between 0 and 1
+// inclusive or IgamI will panic. IgamI should return a positive number, but
+// can return 0 even with non-zero y due to underflow.
+func IgamI(a, p float64) float64 {
+	// Bound the solution
+	x0 := math.MaxFloat64
+	yl := 0.0
+	x1 := 0.0
+	yh := 1.0
+	dithresh := 5.0 * machEp
+
+	if p < 0 || p > 1 || a <= 0 {
+		panic(badParamOutOfBounds)
+	}
+
+	if p == 0 {
+		return math.Inf(1)
+	}
+
+	if p == 1 {
+		return 0.0
+	}
+
+	// Starting with the approximate value
+	//  x = a y^3
+	// where
+	//  y = 1 - d - ndtri(p) sqrt(d)
+	// and
+	//  d = 1/9a
+	// the routine performs up to 10 Newton iterations to find the root of
+	//  IgamC(a, x) - p = 0
+	d := 1.0 / (9.0 * a)
+	y := 1.0 - d - Ndtri(p)*math.Sqrt(d)
+	x := a * y * y * y
+
+	lgm := lgam(a)
+
+	for i := 0; i < 10; i++ {
+		if x > x0 || x < x1 {
+			break
+		}
+
+		y = IgamC(a, x)
+
+		if y < yl || y > yh {
+			break
+		}
+
+		if y < p {
+			x0 = x
+			yl = y
+		} else {
+			x1 = x
+			yh = y
+		}
+
+		// Compute the derivative of the function at this point
+		d = (a-1)*math.Log(x) - x - lgm
+		if d < -maxLog {
+			break
+		}
+		d = -math.Exp(d)
+
+		// Compute the step to the next approximation of x
+		d = (y - p) / d
+		if math.Abs(d/x) < machEp {
+			return x
+		}
+		x = x - d
+	}
+
+	d = 0.0625
+	if x0 == math.MaxFloat64 {
+		if x <= 0 {
+			x = 1
+		}
+		for x0 == math.MaxFloat64 {
+			x = (1 + d) * x
+			y = IgamC(a, x)
+			if y < p {
+				x0 = x
+				yl = y
+				break
+			}
+			d = d + d
+		}
+	}
+
+	d = 0.5
+	dir := 0
+	for i := 0; i < 400; i++ {
+		x = x1 + d*(x0-x1)
+		y = IgamC(a, x)
+
+		lgm = (x0 - x1) / (x1 + x0)
+		if math.Abs(lgm) < dithresh {
+			break
+		}
+
+		lgm = (y - p) / p
+		if math.Abs(lgm) < dithresh {
+			break
+		}
+
+		if x <= 0 {
+			break
+		}
+
+		if y >= p {
+			x1 = x
+			yh = y
+			if dir < 0 {
+				dir = 0
+				d = 0.5
+			} else if dir > 1 {
+				d = 0.5*d + 0.5
+			} else {
+				d = (p - yl) / (yh - yl)
+			}
+			dir++
+		} else {
+			x0 = x
+			yl = y
+			if dir > 0 {
+				dir = 0
+				d = 0.5
+			} else if dir < -1 {
+				d = 0.5 * d
+			} else {
+				d = (p - yl) / (yh - yl)
+			}
+			dir--
+		}
+	}
+
+	return x
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/cephes/incbeta.go b/vendor/gonum.org/v1/gonum/mathext/internal/cephes/incbeta.go
new file mode 100644
index 00000000..cbe46c47
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/cephes/incbeta.go
@@ -0,0 +1,312 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+/*
+ * Cephes Math Library, Release 2.3:  March, 1995
+ * Copyright 1984, 1995 by Stephen L. Moshier
+ */
+
+package cephes
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/mathext/internal/gonum"
+)
+
+const (
+	maxGam = 171.624376956302725
+	big    = 4.503599627370496e15
+	biginv = 2.22044604925031308085e-16
+)
+
+// Incbet computes the regularized incomplete beta function.
+func Incbet(aa, bb, xx float64) float64 {
+	if aa <= 0 || bb <= 0 {
+		panic(badParamOutOfBounds)
+	}
+	if xx <= 0 || xx >= 1 {
+		if xx == 0 {
+			return 0
+		}
+		if xx == 1 {
+			return 1
+		}
+		panic(badParamOutOfBounds)
+	}
+
+	var flag int
+	if bb*xx <= 1 && xx <= 0.95 {
+		t := pseries(aa, bb, xx)
+		return transformT(t, flag)
+	}
+
+	w := 1 - xx
+
+	// Reverse a and b if x is greater than the mean.
+	var a, b, xc, x float64
+	if xx > aa/(aa+bb) {
+		flag = 1
+		a = bb
+		b = aa
+		xc = xx
+		x = w
+	} else {
+		a = aa
+		b = bb
+		xc = w
+		x = xx
+	}
+
+	if flag == 1 && (b*x) <= 1.0 && x <= 0.95 {
+		t := pseries(a, b, x)
+		return transformT(t, flag)
+	}
+
+	// Choose expansion for better convergence.
+	y := x*(a+b-2.0) - (a - 1.0)
+	if y < 0.0 {
+		w = incbcf(a, b, x)
+	} else {
+		w = incbd(a, b, x) / xc
+	}
+
+	// Multiply w by the factor
+	// x^a * (1-x)^b * Γ(a+b) / (a*Γ(a)*Γ(b))
+	var t float64
+	y = a * math.Log(x)
+	t = b * math.Log(xc)
+	if (a+b) < maxGam && math.Abs(y) < maxLog && math.Abs(t) < maxLog {
+		t = math.Pow(xc, b)
+		t *= math.Pow(x, a)
+		t /= a
+		t *= w
+		t *= 1.0 / gonum.Beta(a, b)
+		return transformT(t, flag)
+	}
+
+	// Resort to logarithms.
+	y += t - gonum.Lbeta(a, b)
+	y += math.Log(w / a)
+	if y < minLog {
+		t = 0.0
+	} else {
+		t = math.Exp(y)
+	}
+
+	return transformT(t, flag)
+}
+
+func transformT(t float64, flag int) float64 {
+	if flag == 1 {
+		if t <= machEp {
+			t = 1.0 - machEp
+		} else {
+			t = 1.0 - t
+		}
+	}
+	return t
+}
+
+// incbcf returns the incomplete beta integral evaluated by a continued fraction
+// expansion.
+func incbcf(a, b, x float64) float64 {
+	var xk, pk, pkm1, pkm2, qk, qkm1, qkm2 float64
+	var k1, k2, k3, k4, k5, k6, k7, k8 float64
+	var r, t, ans, thresh float64
+	var n int
+
+	k1 = a
+	k2 = a + b
+	k3 = a
+	k4 = a + 1.0
+	k5 = 1.0
+	k6 = b - 1.0
+	k7 = k4
+	k8 = a + 2.0
+
+	pkm2 = 0.0
+	qkm2 = 1.0
+	pkm1 = 1.0
+	qkm1 = 1.0
+	ans = 1.0
+	r = 1.0
+	thresh = 3.0 * machEp
+
+	for n = 0; n <= 300; n++ {
+
+		xk = -(x * k1 * k2) / (k3 * k4)
+		pk = pkm1 + pkm2*xk
+		qk = qkm1 + qkm2*xk
+		pkm2 = pkm1
+		pkm1 = pk
+		qkm2 = qkm1
+		qkm1 = qk
+
+		xk = (x * k5 * k6) / (k7 * k8)
+		pk = pkm1 + pkm2*xk
+		qk = qkm1 + qkm2*xk
+		pkm2 = pkm1
+		pkm1 = pk
+		qkm2 = qkm1
+		qkm1 = qk
+
+		if qk != 0 {
+			r = pk / qk
+		}
+		if r != 0 {
+			t = math.Abs((ans - r) / r)
+			ans = r
+		} else {
+			t = 1.0
+		}
+
+		if t < thresh {
+			return ans
+		}
+
+		k1 += 1.0
+		k2 += 1.0
+		k3 += 2.0
+		k4 += 2.0
+		k5 += 1.0
+		k6 -= 1.0
+		k7 += 2.0
+		k8 += 2.0
+
+		if (math.Abs(qk) + math.Abs(pk)) > big {
+			pkm2 *= biginv
+			pkm1 *= biginv
+			qkm2 *= biginv
+			qkm1 *= biginv
+		}
+		if (math.Abs(qk) < biginv) || (math.Abs(pk) < biginv) {
+			pkm2 *= big
+			pkm1 *= big
+			qkm2 *= big
+			qkm1 *= big
+		}
+	}
+
+	return ans
+}
+
+// incbd returns the incomplete beta integral evaluated by a continued fraction
+// expansion.
+func incbd(a, b, x float64) float64 {
+	var xk, pk, pkm1, pkm2, qk, qkm1, qkm2 float64
+	var k1, k2, k3, k4, k5, k6, k7, k8 float64
+	var r, t, ans, z, thresh float64
+	var n int
+
+	k1 = a
+	k2 = b - 1.0
+	k3 = a
+	k4 = a + 1.0
+	k5 = 1.0
+	k6 = a + b
+	k7 = a + 1.0
+	k8 = a + 2.0
+
+	pkm2 = 0.0
+	qkm2 = 1.0
+	pkm1 = 1.0
+	qkm1 = 1.0
+	z = x / (1.0 - x)
+	ans = 1.0
+	r = 1.0
+	thresh = 3.0 * machEp
+	for n = 0; n <= 300; n++ {
+
+		xk = -(z * k1 * k2) / (k3 * k4)
+		pk = pkm1 + pkm2*xk
+		qk = qkm1 + qkm2*xk
+		pkm2 = pkm1
+		pkm1 = pk
+		qkm2 = qkm1
+		qkm1 = qk
+
+		xk = (z * k5 * k6) / (k7 * k8)
+		pk = pkm1 + pkm2*xk
+		qk = qkm1 + qkm2*xk
+		pkm2 = pkm1
+		pkm1 = pk
+		qkm2 = qkm1
+		qkm1 = qk
+
+		if qk != 0 {
+			r = pk / qk
+		}
+		if r != 0 {
+			t = math.Abs((ans - r) / r)
+			ans = r
+		} else {
+			t = 1.0
+		}
+
+		if t < thresh {
+			return ans
+		}
+
+		k1 += 1.0
+		k2 -= 1.0
+		k3 += 2.0
+		k4 += 2.0
+		k5 += 1.0
+		k6 += 1.0
+		k7 += 2.0
+		k8 += 2.0
+
+		if (math.Abs(qk) + math.Abs(pk)) > big {
+			pkm2 *= biginv
+			pkm1 *= biginv
+			qkm2 *= biginv
+			qkm1 *= biginv
+		}
+		if (math.Abs(qk) < biginv) || (math.Abs(pk) < biginv) {
+			pkm2 *= big
+			pkm1 *= big
+			qkm2 *= big
+			qkm1 *= big
+		}
+	}
+	return ans
+}
+
+// pseries returns the incomplete beta integral evaluated by a power series. Use
+// when b*x is small and x not too close to 1.
+func pseries(a, b, x float64) float64 {
+	var s, t, u, v, n, t1, z, ai float64
+	ai = 1.0 / a
+	u = (1.0 - b) * x
+	v = u / (a + 1.0)
+	t1 = v
+	t = u
+	n = 2.0
+	s = 0.0
+	z = machEp * ai
+	for math.Abs(v) > z {
+		u = (n - b) * x / n
+		t *= u
+		v = t / (a + n)
+		s += v
+		n += 1.0
+	}
+	s += t1
+	s += ai
+
+	u = a * math.Log(x)
+	if (a+b) < maxGam && math.Abs(u) < maxLog {
+		t = 1.0 / gonum.Beta(a, b)
+		s = s * t * math.Pow(x, a)
+	} else {
+		t = -gonum.Lbeta(a, b) + u + math.Log(s)
+		if t < minLog {
+			s = 0.0
+		} else {
+			s = math.Exp(t)
+		}
+	}
+	return (s)
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/cephes/incbi.go b/vendor/gonum.org/v1/gonum/mathext/internal/cephes/incbi.go
new file mode 100644
index 00000000..06037867
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/cephes/incbi.go
@@ -0,0 +1,248 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+/*
+ * Cephes Math Library Release 2.4:  March,1996
+ * Copyright 1984, 1996 by Stephen L. Moshier
+ */
+
+package cephes
+
+import "math"
+
+// Incbi computes the inverse of the regularized incomplete beta integral.
+func Incbi(aa, bb, yy0 float64) float64 {
+	var a, b, y0, d, y, x, x0, x1, lgm, yp, di, dithresh, yl, yh, xt float64
+	var i, rflg, dir, nflg int
+
+	i = 0
+	if yy0 <= 0 {
+		return (0.0)
+	}
+	if yy0 >= 1.0 {
+		return (1.0)
+	}
+	x0 = 0.0
+	yl = 0.0
+	x1 = 1.0
+	yh = 1.0
+	nflg = 0
+
+	if aa <= 1.0 || bb <= 1.0 {
+		dithresh = 1.0e-6
+		rflg = 0
+		a = aa
+		b = bb
+		y0 = yy0
+		x = a / (a + b)
+		y = Incbet(a, b, x)
+		goto ihalve
+	} else {
+		dithresh = 1.0e-4
+	}
+	// Approximation to inverse function
+	yp = -Ndtri(yy0)
+
+	if yy0 > 0.5 {
+		rflg = 1
+		a = bb
+		b = aa
+		y0 = 1.0 - yy0
+		yp = -yp
+	} else {
+		rflg = 0
+		a = aa
+		b = bb
+		y0 = yy0
+	}
+
+	lgm = (yp*yp - 3.0) / 6.0
+	x = 2.0 / (1.0/(2.0*a-1.0) + 1.0/(2.0*b-1.0))
+	d = yp*math.Sqrt(x+lgm)/x - (1.0/(2.0*b-1.0)-1.0/(2.0*a-1.0))*(lgm+5.0/6.0-2.0/(3.0*x))
+	d = 2.0 * d
+	if d < minLog {
+		// mtherr("incbi", UNDERFLOW)
+		x = 0
+		goto done
+	}
+	x = a / (a + b*math.Exp(d))
+	y = Incbet(a, b, x)
+	yp = (y - y0) / y0
+	if math.Abs(yp) < 0.2 {
+		goto newt
+	}
+
+	/* Resort to interval halving if not close enough. */
+ihalve:
+
+	dir = 0
+	di = 0.5
+	for i = 0; i < 100; i++ {
+		if i != 0 {
+			x = x0 + di*(x1-x0)
+			if x == 1.0 {
+				x = 1.0 - machEp
+			}
+			if x == 0.0 {
+				di = 0.5
+				x = x0 + di*(x1-x0)
+				if x == 0.0 {
+					// mtherr("incbi", UNDERFLOW)
+					goto done
+				}
+			}
+			y = Incbet(a, b, x)
+			yp = (x1 - x0) / (x1 + x0)
+			if math.Abs(yp) < dithresh {
+				goto newt
+			}
+			yp = (y - y0) / y0
+			if math.Abs(yp) < dithresh {
+				goto newt
+			}
+		}
+		if y < y0 {
+			x0 = x
+			yl = y
+			if dir < 0 {
+				dir = 0
+				di = 0.5
+			} else if dir > 3 {
+				di = 1.0 - (1.0-di)*(1.0-di)
+			} else if dir > 1 {
+				di = 0.5*di + 0.5
+			} else {
+				di = (y0 - y) / (yh - yl)
+			}
+			dir += 1
+			if x0 > 0.75 {
+				if rflg == 1 {
+					rflg = 0
+					a = aa
+					b = bb
+					y0 = yy0
+				} else {
+					rflg = 1
+					a = bb
+					b = aa
+					y0 = 1.0 - yy0
+				}
+				x = 1.0 - x
+				y = Incbet(a, b, x)
+				x0 = 0.0
+				yl = 0.0
+				x1 = 1.0
+				yh = 1.0
+				goto ihalve
+			}
+		} else {
+			x1 = x
+			if rflg == 1 && x1 < machEp {
+				x = 0.0
+				goto done
+			}
+			yh = y
+			if dir > 0 {
+				dir = 0
+				di = 0.5
+			} else if dir < -3 {
+				di = di * di
+			} else if dir < -1 {
+				di = 0.5 * di
+			} else {
+				di = (y - y0) / (yh - yl)
+			}
+			dir -= 1
+		}
+	}
+	// mtherr("incbi", PLOSS)
+	if x0 >= 1.0 {
+		x = 1.0 - machEp
+		goto done
+	}
+	if x <= 0.0 {
+		// mtherr("incbi", UNDERFLOW)
+		x = 0.0
+		goto done
+	}
+
+newt:
+	if nflg > 0 {
+		goto done
+	}
+	nflg = 1
+	lgm = lgam(a+b) - lgam(a) - lgam(b)
+
+	for i = 0; i < 8; i++ {
+		/* Compute the function at this point. */
+		if i != 0 {
+			y = Incbet(a, b, x)
+		}
+		if y < yl {
+			x = x0
+			y = yl
+		} else if y > yh {
+			x = x1
+			y = yh
+		} else if y < y0 {
+			x0 = x
+			yl = y
+		} else {
+			x1 = x
+			yh = y
+		}
+		if x == 1.0 || x == 0.0 {
+			break
+		}
+		/* Compute the derivative of the function at this point. */
+		d = (a-1.0)*math.Log(x) + (b-1.0)*math.Log(1.0-x) + lgm
+		if d < minLog {
+			goto done
+		}
+		if d > maxLog {
+			break
+		}
+		d = math.Exp(d)
+		/* Compute the step to the next approximation of x. */
+		d = (y - y0) / d
+		xt = x - d
+		if xt <= x0 {
+			y = (x - x0) / (x1 - x0)
+			xt = x0 + 0.5*y*(x-x0)
+			if xt <= 0.0 {
+				break
+			}
+		}
+		if xt >= x1 {
+			y = (x1 - x) / (x1 - x0)
+			xt = x1 - 0.5*y*(x1-x)
+			if xt >= 1.0 {
+				break
+			}
+		}
+		x = xt
+		if math.Abs(d/x) < 128.0*machEp {
+			goto done
+		}
+	}
+	/* Did not converge.  */
+	dithresh = 256.0 * machEp
+	goto ihalve
+
+done:
+
+	if rflg > 0 {
+		if x <= machEp {
+			x = 1.0 - machEp
+		} else {
+			x = 1.0 - x
+		}
+	}
+	return (x)
+}
+
+func lgam(a float64) float64 {
+	lg, _ := math.Lgamma(a)
+	return lg
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/cephes/lanczos.go b/vendor/gonum.org/v1/gonum/mathext/internal/cephes/lanczos.go
new file mode 100644
index 00000000..c32909b5
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/cephes/lanczos.go
@@ -0,0 +1,153 @@
+// Derived from SciPy's special/cephes/lanczos.c
+// https://github.com/scipy/scipy/blob/master/scipy/special/cephes/lanczos.c
+
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+// Copyright ©2006 John Maddock
+// Portions Copyright ©2003 Boost
+// Portions Copyright ©2016 The gonum Authors. All rights reserved.
+
+package cephes
+
+// Optimal values for G for each N are taken from
+// http://web.mala.bc.ca/pughg/phdThesis/phdThesis.pdf,
+// as are the theoretical error bounds.
+
+// Constants calculated using the method described by Godfrey
+// http://my.fit.edu/~gabdo/gamma.txt and elaborated by Toth at
+// http://www.rskey.org/gamma.htm using NTL::RR at 1000 bit precision.
+
+var lanczosNum = [...]float64{
+	2.506628274631000270164908177133837338626,
+	210.8242777515793458725097339207133627117,
+	8071.672002365816210638002902272250613822,
+	186056.2653952234950402949897160456992822,
+	2876370.628935372441225409051620849613599,
+	31426415.58540019438061423162831820536287,
+	248874557.8620541565114603864132294232163,
+	1439720407.311721673663223072794912393972,
+	6039542586.35202800506429164430729792107,
+	17921034426.03720969991975575445893111267,
+	35711959237.35566804944018545154716670596,
+	42919803642.64909876895789904700198885093,
+	23531376880.41075968857200767445163675473,
+}
+
+var lanczosDenom = [...]float64{
+	1,
+	66,
+	1925,
+	32670,
+	357423,
+	2637558,
+	13339535,
+	45995730,
+	105258076,
+	150917976,
+	120543840,
+	39916800,
+	0,
+}
+
+var lanczosSumExpgScaledNum = [...]float64{
+	0.006061842346248906525783753964555936883222,
+	0.5098416655656676188125178644804694509993,
+	19.51992788247617482847860966235652136208,
+	449.9445569063168119446858607650988409623,
+	6955.999602515376140356310115515198987526,
+	75999.29304014542649875303443598909137092,
+	601859.6171681098786670226533699352302507,
+	3481712.15498064590882071018964774556468,
+	14605578.08768506808414169982791359218571,
+	43338889.32467613834773723740590533316085,
+	86363131.28813859145546927288977868422342,
+	103794043.1163445451906271053616070238554,
+	56906521.91347156388090791033559122686859,
+}
+
+var lanczosSumExpgScaledDenom = [...]float64{
+	1,
+	66,
+	1925,
+	32670,
+	357423,
+	2637558,
+	13339535,
+	45995730,
+	105258076,
+	150917976,
+	120543840,
+	39916800,
+	0,
+}
+
+var lanczosSumNear1D = [...]float64{
+	0.3394643171893132535170101292240837927725e-9,
+	-0.2499505151487868335680273909354071938387e-8,
+	0.8690926181038057039526127422002498960172e-8,
+	-0.1933117898880828348692541394841204288047e-7,
+	0.3075580174791348492737947340039992829546e-7,
+	-0.2752907702903126466004207345038327818713e-7,
+	-0.1515973019871092388943437623825208095123e-5,
+	0.004785200610085071473880915854204301886437,
+	-0.1993758927614728757314233026257810172008,
+	1.483082862367253753040442933770164111678,
+	-3.327150580651624233553677113928873034916,
+	2.208709979316623790862569924861841433016,
+}
+
+var lanczosSumNear2D = [...]float64{
+	0.1009141566987569892221439918230042368112e-8,
+	-0.7430396708998719707642735577238449585822e-8,
+	0.2583592566524439230844378948704262291927e-7,
+	-0.5746670642147041587497159649318454348117e-7,
+	0.9142922068165324132060550591210267992072e-7,
+	-0.8183698410724358930823737982119474130069e-7,
+	-0.4506604409707170077136555010018549819192e-5,
+	0.01422519127192419234315002746252160965831,
+	-0.5926941084905061794445733628891024027949,
+	4.408830289125943377923077727900630927902,
+	-9.8907772644920670589288081640128194231,
+	6.565936202082889535528455955485877361223,
+}
+
+const lanczosG = 6.024680040776729583740234375
+
+func lanczosSum(x float64) float64 {
+	return ratevl(x,
+		lanczosNum[:],
+		len(lanczosNum)-1,
+		lanczosDenom[:],
+		len(lanczosDenom)-1)
+}
+
+func lanczosSumExpgScaled(x float64) float64 {
+	return ratevl(x,
+		lanczosSumExpgScaledNum[:],
+		len(lanczosSumExpgScaledNum)-1,
+		lanczosSumExpgScaledDenom[:],
+		len(lanczosSumExpgScaledDenom)-1)
+}
+
+func lanczosSumNear1(dx float64) float64 {
+	var result float64
+
+	for i, val := range lanczosSumNear1D {
+		k := float64(i + 1)
+		result += (-val * dx) / (k*dx + k*k)
+	}
+
+	return result
+}
+
+func lanczosSumNear2(dx float64) float64 {
+	var result float64
+	x := dx + 2
+
+	for i, val := range lanczosSumNear2D {
+		k := float64(i + 1)
+		result += (-val * dx) / (x + k*x + k*k - 1)
+	}
+
+	return result
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/cephes/ndtri.go b/vendor/gonum.org/v1/gonum/mathext/internal/cephes/ndtri.go
new file mode 100644
index 00000000..1b26abdc
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/cephes/ndtri.go
@@ -0,0 +1,150 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+/*
+ * Cephes Math Library Release 2.1:  January, 1989
+ * Copyright 1984, 1987, 1989 by Stephen L. Moshier
+ * Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+ */
+
+package cephes
+
+import "math"
+
+// TODO(btracey): There is currently an implementation of this functionality
+// in gonum/stat/distuv. Find out which implementation is better, and rectify
+// by having distuv call this, or moving this implementation into
+// gonum/mathext/internal/gonum.
+
+// math.Sqrt(2*pi)
+const s2pi = 2.50662827463100050242E0
+
+// approximation for 0 <= |y - 0.5| <= 3/8
+var P0 = [5]float64{
+	-5.99633501014107895267E1,
+	9.80010754185999661536E1,
+	-5.66762857469070293439E1,
+	1.39312609387279679503E1,
+	-1.23916583867381258016E0,
+}
+
+var Q0 = [8]float64{
+	/* 1.00000000000000000000E0, */
+	1.95448858338141759834E0,
+	4.67627912898881538453E0,
+	8.63602421390890590575E1,
+	-2.25462687854119370527E2,
+	2.00260212380060660359E2,
+	-8.20372256168333339912E1,
+	1.59056225126211695515E1,
+	-1.18331621121330003142E0,
+}
+
+// Approximation for interval z = math.Sqrt(-2 log y ) between 2 and 8
+// i.e., y between exp(-2) = .135 and exp(-32) = 1.27e-14.
+var P1 = [9]float64{
+	4.05544892305962419923E0,
+	3.15251094599893866154E1,
+	5.71628192246421288162E1,
+	4.40805073893200834700E1,
+	1.46849561928858024014E1,
+	2.18663306850790267539E0,
+	-1.40256079171354495875E-1,
+	-3.50424626827848203418E-2,
+	-8.57456785154685413611E-4,
+}
+
+var Q1 = [8]float64{
+	/*  1.00000000000000000000E0, */
+	1.57799883256466749731E1,
+	4.53907635128879210584E1,
+	4.13172038254672030440E1,
+	1.50425385692907503408E1,
+	2.50464946208309415979E0,
+	-1.42182922854787788574E-1,
+	-3.80806407691578277194E-2,
+	-9.33259480895457427372E-4,
+}
+
+// Approximation for interval z = math.Sqrt(-2 log y ) between 8 and 64
+// i.e., y between exp(-32) = 1.27e-14 and exp(-2048) = 3.67e-890.
+var P2 = [9]float64{
+	3.23774891776946035970E0,
+	6.91522889068984211695E0,
+	3.93881025292474443415E0,
+	1.33303460815807542389E0,
+	2.01485389549179081538E-1,
+	1.23716634817820021358E-2,
+	3.01581553508235416007E-4,
+	2.65806974686737550832E-6,
+	6.23974539184983293730E-9,
+}
+
+var Q2 = [8]float64{
+	/*  1.00000000000000000000E0, */
+	6.02427039364742014255E0,
+	3.67983563856160859403E0,
+	1.37702099489081330271E0,
+	2.16236993594496635890E-1,
+	1.34204006088543189037E-2,
+	3.28014464682127739104E-4,
+	2.89247864745380683936E-6,
+	6.79019408009981274425E-9,
+}
+
+// Ndtri returns the argument, x, for which the area under the
+// Gaussian probability density function (integrated from
+// minus infinity to x) is equal to y.
+func Ndtri(y0 float64) float64 {
+	// For small arguments 0 < y < exp(-2), the program computes
+	// z = math.Sqrt( -2.0 * math.Log(y) );  then the approximation is
+	// x = z - math.Log(z)/z  - (1/z) P(1/z) / Q(1/z).
+	// There are two rational functions P/Q, one for 0 < y < exp(-32)
+	// and the other for y up to exp(-2).  For larger arguments,
+	// w = y - 0.5, and  x/math.Sqrt(2pi) = w + w**3 R(w**2)/S(w**2)).
+	var x, y, z, y2, x0, x1 float64
+	var code int
+
+	if y0 <= 0.0 {
+		if y0 < 0 {
+			panic(badParamOutOfBounds)
+		}
+		return math.Inf(-1)
+	}
+	if y0 >= 1.0 {
+		if y0 > 1 {
+			panic(badParamOutOfBounds)
+		}
+		return math.Inf(1)
+	}
+	code = 1
+	y = y0
+	if y > (1.0 - 0.13533528323661269189) { /* 0.135... = exp(-2) */
+		y = 1.0 - y
+		code = 0
+	}
+
+	if y > 0.13533528323661269189 {
+		y = y - 0.5
+		y2 = y * y
+		x = y + y*(y2*polevl(y2, P0[:], 4)/p1evl(y2, Q0[:], 8))
+		x = x * s2pi
+		return (x)
+	}
+
+	x = math.Sqrt(-2.0 * math.Log(y))
+	x0 = x - math.Log(x)/x
+
+	z = 1.0 / x
+	if x < 8.0 { /* y > exp(-32) = 1.2664165549e-14 */
+		x1 = z * polevl(z, P1[:], 8) / p1evl(z, Q1[:], 8)
+	} else {
+		x1 = z * polevl(z, P2[:], 8) / p1evl(z, Q2[:], 8)
+	}
+	x = x0 - x1
+	if code != 0 {
+		x = -x
+	}
+	return (x)
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/cephes/polevl.go b/vendor/gonum.org/v1/gonum/mathext/internal/cephes/polevl.go
new file mode 100644
index 00000000..5cbd8cbb
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/cephes/polevl.go
@@ -0,0 +1,82 @@
+// Derived from SciPy's special/cephes/polevl.h
+// https://github.com/scipy/scipy/blob/master/scipy/special/cephes/polevl.h
+// Made freely available by Stephen L. Moshier without support or guarantee.
+
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+// Copyright ©1984, ©1987, ©1988 by Stephen L. Moshier
+// Portions Copyright ©2016 The gonum Authors. All rights reserved.
+
+package cephes
+
+import "math"
+
+// polevl evaluates a polynomial of degree N
+//  y = c_0 + c_1 x_1 + c_2 x_2^2 ...
+// where the coefficients are stored in reverse order, i.e. coef[0] = c_n and
+// coef[n] = c_0.
+func polevl(x float64, coef []float64, n int) float64 {
+	ans := coef[0]
+	for i := 1; i <= n; i++ {
+		ans = ans*x + coef[i]
+	}
+	return ans
+}
+
+// p1evl is the same as polevl, except c_n is assumed to be 1 and is not included
+// in the slice.
+func p1evl(x float64, coef []float64, n int) float64 {
+	ans := x + coef[0]
+	for i := 1; i <= n-1; i++ {
+		ans = ans*x + coef[i]
+	}
+	return ans
+}
+
+// ratevl evaluates a rational function
+func ratevl(x float64, num []float64, m int, denom []float64, n int) float64 {
+	// Source: Holin et. al., "Polynomial and Rational Function Evaluation",
+	// http://www.boost.org/doc/libs/1_61_0/libs/math/doc/html/math_toolkit/roots/rational.html
+	absx := math.Abs(x)
+
+	var dir, idx int
+	var y float64
+	if absx > 1 {
+		// Evaluate as a polynomial in 1/x
+		dir = -1
+		idx = m
+		y = 1 / x
+	} else {
+		dir = 1
+		idx = 0
+		y = x
+	}
+
+	// Evaluate the numerator
+	numAns := num[idx]
+	idx += dir
+	for i := 0; i < m; i++ {
+		numAns = numAns*y + num[idx]
+		idx += dir
+	}
+
+	// Evaluate the denominator
+	if absx > 1 {
+		idx = n
+	} else {
+		idx = 0
+	}
+
+	denomAns := denom[idx]
+	idx += dir
+	for i := 0; i < n; i++ {
+		denomAns = denomAns*y + denom[idx]
+		idx += dir
+	}
+
+	if absx > 1 {
+		pow := float64(n - m)
+		return math.Pow(x, pow) * numAns / denomAns
+	}
+	return numAns / denomAns
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/cephes/unity.go b/vendor/gonum.org/v1/gonum/mathext/internal/cephes/unity.go
new file mode 100644
index 00000000..1333dd1d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/cephes/unity.go
@@ -0,0 +1,170 @@
+// Derived from SciPy's special/cephes/unity.c
+// https://github.com/scipy/scipy/blob/master/scipy/special/cephes/unity.c
+// Made freely available by Stephen L. Moshier without support or guarantee.
+
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+// Copyright ©1984, ©1996 by Stephen L. Moshier
+// Portions Copyright ©2016 The gonum Authors. All rights reserved.
+
+package cephes
+
+import "math"
+
+// Relative error approximations for function arguments near unity.
+//  log1p(x) = log(1+x)
+//  expm1(x) = exp(x) - 1
+//  cosm1(x) = cos(x) - 1
+//  lgam1p(x) = lgam(1+x)
+
+const (
+	invSqrt2 = 1 / math.Sqrt2
+	pi4      = math.Pi / 4
+	euler    = 0.577215664901532860606512090082402431 // Euler constant
+)
+
+// Coefficients for
+//  log(1+x) = x - \frac{x^2}{2} + \frac{x^3 lP(x)}{lQ(x)}
+// for
+//  \frac{1}{\sqrt{2}} <= x < \sqrt{2}
+// Theoretical peak relative error = 2.32e-20
+var lP = [...]float64{
+	4.5270000862445199635215E-5,
+	4.9854102823193375972212E-1,
+	6.5787325942061044846969E0,
+	2.9911919328553073277375E1,
+	6.0949667980987787057556E1,
+	5.7112963590585538103336E1,
+	2.0039553499201281259648E1,
+}
+
+var lQ = [...]float64{
+	1.5062909083469192043167E1,
+	8.3047565967967209469434E1,
+	2.2176239823732856465394E2,
+	3.0909872225312059774938E2,
+	2.1642788614495947685003E2,
+	6.0118660497603843919306E1,
+}
+
+// log1p computes
+//  log(1 + x)
+func log1p(x float64) float64 {
+	z := 1 + x
+	if z < invSqrt2 || z > math.Sqrt2 {
+		return math.Log(z)
+	}
+	z = x * x
+	z = -0.5*z + x*(z*polevl(x, lP[:], 6)/p1evl(x, lQ[:], 6))
+	return x + z
+}
+
+// log1pmx computes
+//  log(1 + x) - x
+func log1pmx(x float64) float64 {
+	if math.Abs(x) < 0.5 {
+		xfac := x
+		res := 0.0
+
+		var term float64
+		for n := 2; n < maxIter; n++ {
+			xfac *= -x
+			term = xfac / float64(n)
+			res += term
+			if math.Abs(term) < machEp*math.Abs(res) {
+				break
+			}
+		}
+		return res
+	}
+	return log1p(x) - x
+}
+
+// Coefficients for
+//  e^x = 1 + \frac{2x eP(x^2)}{eQ(x^2) - eP(x^2)}
+// for
+//  -0.5 <= x <= 0.5
+var eP = [...]float64{
+	1.2617719307481059087798E-4,
+	3.0299440770744196129956E-2,
+	9.9999999999999999991025E-1,
+}
+
+var eQ = [...]float64{
+	3.0019850513866445504159E-6,
+	2.5244834034968410419224E-3,
+	2.2726554820815502876593E-1,
+	2.0000000000000000000897E0,
+}
+
+// expm1 computes
+//  expm1(x) = e^x - 1
+func expm1(x float64) float64 {
+	if math.IsInf(x, 0) {
+		if math.IsNaN(x) || x > 0 {
+			return x
+		}
+		return -1
+	}
+	if x < -0.5 || x > 0.5 {
+		return math.Exp(x) - 1
+	}
+	xx := x * x
+	r := x * polevl(xx, eP[:], 2)
+	r = r / (polevl(xx, eQ[:], 3) - r)
+	return r + r
+}
+
+var coscof = [...]float64{
+	4.7377507964246204691685E-14,
+	-1.1470284843425359765671E-11,
+	2.0876754287081521758361E-9,
+	-2.7557319214999787979814E-7,
+	2.4801587301570552304991E-5,
+	-1.3888888888888872993737E-3,
+	4.1666666666666666609054E-2,
+}
+
+// cosm1 computes
+//  cosm1(x) = cos(x) - 1
+func cosm1(x float64) float64 {
+	if x < -pi4 || x > pi4 {
+		return math.Cos(x) - 1
+	}
+	xx := x * x
+	xx = -0.5*xx + xx*xx*polevl(xx, coscof[:], 6)
+	return xx
+}
+
+// lgam1pTayler computes
+//  lgam(x + 1)
+//around x = 0 using its Taylor series.
+func lgam1pTaylor(x float64) float64 {
+	if x == 0 {
+		return 0
+	}
+	res := -euler * x
+	xfac := -x
+	for n := 2; n < 42; n++ {
+		nf := float64(n)
+		xfac *= -x
+		coeff := Zeta(nf, 1) * xfac / nf
+		res += coeff
+		if math.Abs(coeff) < machEp*math.Abs(res) {
+			break
+		}
+	}
+
+	return res
+}
+
+// lgam1p computes
+//  lgam(x + 1)
+func lgam1p(x float64) float64 {
+	if math.Abs(x) <= 0.5 {
+		return lgam1pTaylor(x)
+	} else if math.Abs(x-1) < 0.5 {
+		return math.Log(x) + lgam1pTaylor(x-1)
+	}
+	return lgam(x + 1)
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/cephes/zeta.go b/vendor/gonum.org/v1/gonum/mathext/internal/cephes/zeta.go
new file mode 100644
index 00000000..14a41b6f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/cephes/zeta.go
@@ -0,0 +1,110 @@
+// Derived from SciPy's special/cephes/zeta.c
+// https://github.com/scipy/scipy/blob/master/scipy/special/cephes/zeta.c
+// Made freely available by Stephen L. Moshier without support or guarantee.
+
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+// Copyright ©1984, ©1987 by Stephen L. Moshier
+// Portions Copyright ©2016 The gonum Authors. All rights reserved.
+
+package cephes
+
+import "math"
+
+// zetaCoegs are the expansion coefficients for Euler-Maclaurin summation
+// formula:
+//  \frac{(2k)!}{B_{2k}}
+// where
+//  B_{2k}
+// are Bernoulli numbers.
+var zetaCoefs = [...]float64{
+	12.0,
+	-720.0,
+	30240.0,
+	-1209600.0,
+	47900160.0,
+	-1.307674368e12 / 691,
+	7.47242496e10,
+	-1.067062284288e16 / 3617,
+	5.109094217170944e18 / 43867,
+	-8.028576626982912e20 / 174611,
+	1.5511210043330985984e23 / 854513,
+	-1.6938241367317436694528e27 / 236364091,
+}
+
+// Zeta computes the Riemann zeta function of two arguments.
+//  Zeta(x,q) = \sum_{k=0}^{\infty} (k+q)^{-x}
+// Note that Zeta returns +Inf if x is 1 and will panic if x is less than 1,
+// q is either zero or a negative integer, or q is negative and x is not an
+// integer.
+//
+// Note that:
+//  zeta(x,1) = zetac(x) + 1
+func Zeta(x, q float64) float64 {
+	// REFERENCE: Gradshteyn, I. S., and I. M. Ryzhik, Tables of Integrals, Series,
+	// and Products, p. 1073; Academic Press, 1980.
+	if x == 1 {
+		return math.Inf(1)
+	}
+
+	if x < 1 {
+		panic(badParamOutOfBounds)
+	}
+
+	if q <= 0 {
+		if q == math.Floor(q) {
+			panic(badParamFunctionSingularity)
+		}
+		if x != math.Floor(x) {
+			panic(badParamOutOfBounds) // Because q^-x not defined
+		}
+	}
+
+	// Asymptotic expansion: http://dlmf.nist.gov/25.11#E43
+	if q > 1e8 {
+		return (1/(x-1) + 1/(2*q)) * math.Pow(q, 1-x)
+	}
+
+	// The Euler-Maclaurin summation formula is used to obtain the expansion:
+	//  Zeta(x,q) = \sum_{k=1}^n (k+q)^{-x} + \frac{(n+q)^{1-x}}{x-1} - \frac{1}{2(n+q)^x} + \sum_{j=1}^{\infty} \frac{B_{2j}x(x+1)...(x+2j)}{(2j)! (n+q)^{x+2j+1}}
+	// where
+	//  B_{2j}
+	// are Bernoulli numbers.
+	// Permit negative q but continue sum until n+q > 9. This case should be
+	// handled by a reflection formula. If q<0 and x is an integer, there is a
+	// relation to the polyGamma function.
+	s := math.Pow(q, -x)
+	a := q
+	i := 0
+	b := 0.0
+	for i < 9 || a <= 9 {
+		i++
+		a += 1.0
+		b = math.Pow(a, -x)
+		s += b
+		if math.Abs(b/s) < machEp {
+			return s
+		}
+	}
+
+	w := a
+	s += b * w / (x - 1)
+	s -= 0.5 * b
+	a = 1.0
+	k := 0.0
+	for _, coef := range zetaCoefs {
+		a *= x + k
+		b /= w
+		t := a * b / coef
+		s = s + t
+		t = math.Abs(t / s)
+		if t < machEp {
+			return s
+		}
+		k += 1.0
+		a *= x + k
+		b /= w
+		k += 1.0
+	}
+	return s
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/gonum/beta.go b/vendor/gonum.org/v1/gonum/mathext/internal/gonum/beta.go
new file mode 100644
index 00000000..7038c08f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/gonum/beta.go
@@ -0,0 +1,52 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import (
+	"math"
+)
+
+// Beta returns the value of the complete beta function B(a, b). It is defined as
+//  Γ(a)Γ(b) / Γ(a+b)
+// Special cases are:
+//  B(a,b) returns NaN if a or b is Inf
+//  B(a,b) returns NaN if a and b are 0
+//  B(a,b) returns NaN if a or b is NaN
+//  B(a,b) returns NaN if a or b is < 0
+//  B(a,b) returns +Inf if a xor b is 0.
+//
+// See http://mathworld.wolfram.com/BetaFunction.html for more detailed information.
+func Beta(a, b float64) float64 {
+	return math.Exp(Lbeta(a, b))
+}
+
+// Lbeta returns the natural logarithm of the complete beta function B(a,b).
+// Lbeta is defined as:
+//  Ln(Γ(a)Γ(b)/Γ(a+b))
+// Special cases are:
+//  Lbeta(a,b) returns NaN if a or b is Inf
+//  Lbeta(a,b) returns NaN if a and b are 0
+//  Lbeta(a,b) returns NaN if a or b is NaN
+//  Lbeta(a,b) returns NaN if a or b is < 0
+//  Lbeta(a,b) returns +Inf if a xor b is 0.
+func Lbeta(a, b float64) float64 {
+	switch {
+	case math.IsInf(a, +1) || math.IsInf(b, +1):
+		return math.NaN()
+	case a == 0 && b == 0:
+		return math.NaN()
+	case a < 0 || b < 0:
+		return math.NaN()
+	case math.IsNaN(a) || math.IsNaN(b):
+		return math.NaN()
+	case a == 0 || b == 0:
+		return math.Inf(+1)
+	}
+
+	la, _ := math.Lgamma(a)
+	lb, _ := math.Lgamma(b)
+	lab, _ := math.Lgamma(a + b)
+	return la + lb - lab
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/gonum/doc.go b/vendor/gonum.org/v1/gonum/mathext/internal/gonum/doc.go
new file mode 100644
index 00000000..a726cfcb
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/gonum/doc.go
@@ -0,0 +1,7 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// package gonum contains functions implemented by the gonum team. It is here to
+// avoid circular imports and/or double coding of functions.
+package gonum // import "gonum.org/v1/gonum/mathext/internal/gonum"
diff --git a/vendor/gonum.org/v1/gonum/mathext/internal/gonum/gonum.go b/vendor/gonum.org/v1/gonum/mathext/internal/gonum/gonum.go
new file mode 100644
index 00000000..eae3e1c4
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/internal/gonum/gonum.go
@@ -0,0 +1,5 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
diff --git a/vendor/gonum.org/v1/gonum/mathext/mvgamma.go b/vendor/gonum.org/v1/gonum/mathext/mvgamma.go
new file mode 100644
index 00000000..c18b37ad
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/mvgamma.go
@@ -0,0 +1,32 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mathext
+
+import "math"
+
+const (
+	logPi = 1.14472988584940017414342735135305871164729481 // http://oeis.org/A053510
+)
+
+// MvLgamma returns the log of the multivariate Gamma function. Dim
+// must be greater than zero, and MvLgamma will return NaN if v < (dim-1)/2.
+//
+// See https://en.wikipedia.org/wiki/Multivariate_gamma_function for more
+// information.
+func MvLgamma(v float64, dim int) float64 {
+	if dim < 1 {
+		panic("mathext: negative dimension")
+	}
+	df := float64(dim)
+	if v < (df-1)*0.5 {
+		return math.NaN()
+	}
+	ans := df * (df - 1) * 0.25 * logPi
+	for i := 1; i <= dim; i++ {
+		lg, _ := math.Lgamma(v + float64(1-i)*0.5)
+		ans += lg
+	}
+	return ans
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/mvgamma_test.go b/vendor/gonum.org/v1/gonum/mathext/mvgamma_test.go
new file mode 100644
index 00000000..f7d309c8
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/mvgamma_test.go
@@ -0,0 +1,27 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mathext
+
+import (
+	"math"
+	"testing"
+)
+
+func TestMvLgamma(t *testing.T) {
+	// Values compared with scipy
+	for i, test := range []struct {
+		v   float64
+		dim int
+		ans float64
+	}{
+		{10, 5, 58.893841851237397},
+		{3, 1, 0.69314718055994529},
+	} {
+		ans := MvLgamma(test.v, test.dim)
+		if math.Abs(test.ans-ans) > 1e-14 {
+			t.Errorf("Case %v. got=%v want=%v.", i, ans, test.ans)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/roots.go b/vendor/gonum.org/v1/gonum/mathext/roots.go
new file mode 100644
index 00000000..61ff12c6
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/roots.go
@@ -0,0 +1,178 @@
+// Derived from SciPy's special/c_misc/fsolve.c and special/c_misc/misc.h
+// https://github.com/scipy/scipy/blob/master/scipy/special/c_misc/fsolve.c
+// https://github.com/scipy/scipy/blob/master/scipy/special/c_misc/misc.h
+
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mathext
+
+import "math"
+
+type objectiveFunc func(float64, []float64) float64
+
+type fSolveResult uint8
+
+const (
+	// An exact solution was found, in which case the first point on the
+	// interval is the value
+	fSolveExact fSolveResult = iota + 1
+	// Interval width is less than the tolerance
+	fSolveConverged
+	// Root-finding didn't converge in a set number of iterations
+	fSolveMaxIterations
+)
+
+const (
+	machEp = 1.0 / (1 << 53)
+)
+
+// falsePosition uses a combination of bisection and false position to find a
+// root of a function within a given interval. This is guaranteed to converge,
+// and always keeps a bounding interval, unlike Newton's method. Inputs are:
+//  x1, x2:   initial bounding interval
+//  f1, f2: value of f() at x1 and x2
+//  absErr, relErr: absolute and relative errors on the bounding interval
+//  bisectTil: if > 0.0, perform bisection until the width of the bounding
+//             interval is less than this
+//  f, fExtra: function to find root of is f(x, fExtra)
+// Returns:
+//  result: whether an exact root was found, the process converged to a
+//          bounding interval small than the required error, or the max number
+//          of iterations was hit
+//  bestX: best root approximation
+//  bestF: function value at bestX
+//  errEst: error estimation
+func falsePosition(x1, x2, f1, f2, absErr, relErr, bisectTil float64, f objectiveFunc, fExtra []float64) (fSolveResult, float64, float64, float64) {
+	// The false position steps are either unmodified, or modified with the
+	// Anderson-Bjorck method as appropriate. Theoretically, this has a "speed of
+	// convergence" of 1.7 (bisection is 1, Newton is 2).
+	// Note that this routine was designed initially to work with gammaincinv, so
+	// it may not be tuned right for other problems. Don't use it blindly.
+
+	if f1*f2 >= 0 {
+		panic("Initial interval is not a bounding interval")
+	}
+
+	const (
+		maxIterations = 100
+		bisectIter    = 4
+		bisectWidth   = 4.0
+	)
+
+	const (
+		bisect = iota + 1
+		falseP
+	)
+
+	var state uint8
+	if bisectTil > 0 {
+		state = bisect
+	} else {
+		state = falseP
+	}
+
+	gamma := 1.0
+
+	w := math.Abs(x2 - x1)
+	lastBisectWidth := w
+
+	var nFalseP int
+	var x3, f3, bestX, bestF float64
+	for i := 0; i < maxIterations; i++ {
+		switch state {
+		case bisect:
+			x3 = 0.5 * (x1 + x2)
+			if x3 == x1 || x3 == x2 {
+				// i.e., x1 and x2 are successive floating-point numbers
+				bestX = x3
+				if x3 == x1 {
+					bestF = f1
+				} else {
+					bestF = f2
+				}
+				return fSolveConverged, bestX, bestF, w
+			}
+
+			f3 = f(x3, fExtra)
+			if f3 == 0 {
+				return fSolveExact, x3, f3, w
+			}
+
+			if f3*f2 < 0 {
+				x1 = x2
+				f1 = f2
+			}
+			x2 = x3
+			f2 = f3
+			w = math.Abs(x2 - x1)
+			lastBisectWidth = w
+			if bisectTil > 0 {
+				if w < bisectTil {
+					bisectTil = -1.0
+					gamma = 1.0
+					nFalseP = 0
+					state = falseP
+				}
+			} else {
+				gamma = 1.0
+				nFalseP = 0
+				state = falseP
+			}
+		case falseP:
+			s12 := (f2 - gamma*f1) / (x2 - x1)
+			x3 = x2 - f2/s12
+			f3 = f(x3, fExtra)
+			if f3 == 0 {
+				return fSolveExact, x3, f3, w
+			}
+
+			nFalseP++
+			if f3*f2 < 0 {
+				gamma = 1.0
+				x1 = x2
+				f1 = f2
+			} else {
+				// Anderson-Bjorck method
+				g := 1.0 - f3/f2
+				if g <= 0 {
+					g = 0.5
+				}
+				gamma *= g
+			}
+			x2 = x3
+			f2 = f3
+			w = math.Abs(x2 - x1)
+
+			// Sanity check. For every 4 false position checks, see if we really are
+			// decreasing the interval by comparing to what bisection would have
+			// achieved (or, rather, a bit more lenient than that -- interval
+			// decreased by 4 instead of by 16, as the fp could be decreasing gamma
+			// for a bit). Note that this should guarantee convergence, as it makes
+			// sure that we always end up decreasing the interval width with a
+			// bisection.
+			if nFalseP > bisectIter {
+				if w*bisectWidth > lastBisectWidth {
+					state = bisect
+				}
+				nFalseP = 0
+				lastBisectWidth = w
+			}
+		}
+
+		tol := absErr + relErr*math.Max(math.Max(math.Abs(x1), math.Abs(x2)), 1.0)
+		if w <= tol {
+			if math.Abs(f1) < math.Abs(f2) {
+				bestX = x1
+				bestF = f1
+			} else {
+				bestX = x2
+				bestF = f2
+			}
+			return fSolveConverged, bestX, bestF, w
+		}
+	}
+
+	return fSolveMaxIterations, x3, f3, w
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/zeta.go b/vendor/gonum.org/v1/gonum/mathext/zeta.go
new file mode 100644
index 00000000..920a7e6e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/zeta.go
@@ -0,0 +1,20 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mathext
+
+import "gonum.org/v1/gonum/mathext/internal/cephes"
+
+// Zeta computes the Riemann zeta function of two arguments.
+//  Zeta(x,q) = \sum_{k=0}^{\infty} (k+q)^{-x}
+// Note that Zeta returns +Inf if x is 1 and will panic if x is less than 1,
+// q is either zero or a negative integer, or q is negative and x is not an
+// integer.
+//
+// See http://mathworld.wolfram.com/HurwitzZetaFunction.html
+// or https://en.wikipedia.org/wiki/Multiple_zeta_function#Two_parameters_case
+// for more detailed information.
+func Zeta(x, q float64) float64 {
+	return cephes.Zeta(x, q)
+}
diff --git a/vendor/gonum.org/v1/gonum/mathext/zeta_test.go b/vendor/gonum.org/v1/gonum/mathext/zeta_test.go
new file mode 100644
index 00000000..e415818f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/mathext/zeta_test.go
@@ -0,0 +1,42 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mathext
+
+import (
+	"math"
+	"testing"
+)
+
+func TestZeta(t *testing.T) {
+	for i, test := range []struct {
+		x, q, want float64
+	}{
+		// Results computed using scipy.special.zeta
+		{1, 1, math.Inf(1)},
+		{1.00001, 0.5, 100001.96352290553},
+		{1.0001, 25, 9996.8017690244506},
+		{1.001, 1, 1000.5772884760117},
+		{1.01, 10, 97.773405639173305},
+		{1.5, 2, 1.6123753486854886},
+		{1.5, 20, 0.45287361712938717},
+		{2, -0.7, 14.28618087263834},
+		{2.5, 0.5, 6.2471106345688137},
+		{5, 2.5, 0.013073166646113805},
+		{7.5, 5, 7.9463377443314306e-06},
+		{10, -0.5, 2048.0174503557578},
+		{10, 0.5, 1024.0174503557578},
+		{10, 7.5, 2.5578265694201971e-9},
+		{12, 2.5, 1.7089167198843551e-5},
+		{17, 0.5, 131072.00101513157},
+		{20, -2.5, 2097152.0006014798},
+		{20, 0.75, 315.3368689825316},
+		{25, 0.25, 1125899906842624.0},
+		{30, 1, 1.0000000009313275},
+	} {
+		if got := Zeta(test.x, test.q); math.Abs(got-test.want) > 1e-10 {
+			t.Errorf("test %d Zeta(%g, %g) failed: got %g want %g", i, test.x, test.q, got, test.want)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/README.md b/vendor/gonum.org/v1/gonum/optimize/README.md
new file mode 100644
index 00000000..0067895c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/README.md
@@ -0,0 +1,3 @@
+# Gonum optimize [![GoDoc](https://godoc.org/gonum.org/v1/gonum/optimize?status.svg)](https://godoc.org/gonum.org/v1/gonum/optimize)
+
+Package optimize is an optimization package for the Go language.
diff --git a/vendor/gonum.org/v1/gonum/optimize/backtracking.go b/vendor/gonum.org/v1/gonum/optimize/backtracking.go
new file mode 100644
index 00000000..313077f3
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/backtracking.go
@@ -0,0 +1,82 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package optimize
+
+const (
+	defaultBacktrackingContraction = 0.5
+	defaultBacktrackingDecrease    = 1e-4
+	minimumBacktrackingStepSize    = 1e-20
+)
+
+// Backtracking is a Linesearcher that uses backtracking to find a point that
+// satisfies the Armijo condition with the given decrease factor. If the Armijo
+// condition has not been met, the step size is decreased by ContractionFactor.
+//
+// The Armijo condition only requires the gradient at the beginning of each
+// major iteration (not at successive step locations), and so Backtracking may
+// be a good linesearch for functions with expensive gradients. Backtracking is
+// not appropriate for optimizers that require the Wolfe conditions to be met,
+// such as BFGS.
+//
+// Both DecreaseFactor and ContractionFactor must be between zero and one, and
+// Backtracking will panic otherwise. If either DecreaseFactor or
+// ContractionFactor are zero, it will be set to a reasonable default.
+type Backtracking struct {
+	DecreaseFactor    float64 // Constant factor in the sufficient decrease (Armijo) condition.
+	ContractionFactor float64 // Step size multiplier at each iteration (step *= ContractionFactor).
+
+	stepSize float64
+	initF    float64
+	initG    float64
+
+	lastOp Operation
+}
+
+func (b *Backtracking) Init(f, g float64, step float64) Operation {
+	if step <= 0 {
+		panic("backtracking: bad step size")
+	}
+	if g >= 0 {
+		panic("backtracking: initial derivative is non-negative")
+	}
+
+	if b.ContractionFactor == 0 {
+		b.ContractionFactor = defaultBacktrackingContraction
+	}
+	if b.DecreaseFactor == 0 {
+		b.DecreaseFactor = defaultBacktrackingDecrease
+	}
+	if b.ContractionFactor <= 0 || b.ContractionFactor >= 1 {
+		panic("backtracking: ContractionFactor must be between 0 and 1")
+	}
+	if b.DecreaseFactor <= 0 || b.DecreaseFactor >= 1 {
+		panic("backtracking: DecreaseFactor must be between 0 and 1")
+	}
+
+	b.stepSize = step
+	b.initF = f
+	b.initG = g
+
+	b.lastOp = FuncEvaluation
+	return b.lastOp
+}
+
+func (b *Backtracking) Iterate(f, _ float64) (Operation, float64, error) {
+	if b.lastOp != FuncEvaluation {
+		panic("backtracking: Init has not been called")
+	}
+
+	if ArmijoConditionMet(f, b.initF, b.initG, b.stepSize, b.DecreaseFactor) {
+		b.lastOp = MajorIteration
+		return b.lastOp, b.stepSize, nil
+	}
+	b.stepSize *= b.ContractionFactor
+	if b.stepSize < minimumBacktrackingStepSize {
+		b.lastOp = NoOperation
+		return b.lastOp, b.stepSize, ErrLinesearcherFailure
+	}
+	b.lastOp = FuncEvaluation
+	return b.lastOp, b.stepSize, nil
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/bfgs.go b/vendor/gonum.org/v1/gonum/optimize/bfgs.go
new file mode 100644
index 00000000..997d991b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/bfgs.go
@@ -0,0 +1,160 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package optimize
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/mat"
+)
+
+// BFGS implements the Broyden–Fletcher–Goldfarb–Shanno optimization method. It
+// is a quasi-Newton method that performs successive rank-one updates to an
+// estimate of the inverse Hessian of the objective function. It exhibits
+// super-linear convergence when in proximity to a local minimum. It has memory
+// cost that is O(n^2) relative to the input dimension.
+type BFGS struct {
+	// Linesearcher selects suitable steps along the descent direction.
+	// Accepted steps should satisfy the strong Wolfe conditions.
+	// If Linesearcher == nil, an appropriate default is chosen.
+	Linesearcher Linesearcher
+
+	ls *LinesearchMethod
+
+	dim  int
+	x    mat.VecDense // Location of the last major iteration.
+	grad mat.VecDense // Gradient at the last major iteration.
+	s    mat.VecDense // Difference between locations in this and the previous iteration.
+	y    mat.VecDense // Difference between gradients in this and the previous iteration.
+	tmp  mat.VecDense
+
+	invHess *mat.SymDense
+
+	first bool // Indicator of the first iteration.
+}
+
+func (b *BFGS) Init(loc *Location) (Operation, error) {
+	if b.Linesearcher == nil {
+		b.Linesearcher = &Bisection{}
+	}
+	if b.ls == nil {
+		b.ls = &LinesearchMethod{}
+	}
+	b.ls.Linesearcher = b.Linesearcher
+	b.ls.NextDirectioner = b
+
+	return b.ls.Init(loc)
+}
+
+func (b *BFGS) Iterate(loc *Location) (Operation, error) {
+	return b.ls.Iterate(loc)
+}
+
+func (b *BFGS) InitDirection(loc *Location, dir []float64) (stepSize float64) {
+	dim := len(loc.X)
+	b.dim = dim
+	b.first = true
+
+	x := mat.NewVecDense(dim, loc.X)
+	grad := mat.NewVecDense(dim, loc.Gradient)
+	b.x.CloneVec(x)
+	b.grad.CloneVec(grad)
+
+	b.y.Reset()
+	b.s.Reset()
+	b.tmp.Reset()
+
+	if b.invHess == nil || cap(b.invHess.RawSymmetric().Data) < dim*dim {
+		b.invHess = mat.NewSymDense(dim, nil)
+	} else {
+		b.invHess = mat.NewSymDense(dim, b.invHess.RawSymmetric().Data[:dim*dim])
+	}
+	// The values of the inverse Hessian are initialized in the first call to
+	// NextDirection.
+
+	// Initial direction is just negative of the gradient because the Hessian
+	// is an identity matrix.
+	d := mat.NewVecDense(dim, dir)
+	d.ScaleVec(-1, grad)
+	return 1 / mat.Norm(d, 2)
+}
+
+func (b *BFGS) NextDirection(loc *Location, dir []float64) (stepSize float64) {
+	dim := b.dim
+	if len(loc.X) != dim {
+		panic("bfgs: unexpected size mismatch")
+	}
+	if len(loc.Gradient) != dim {
+		panic("bfgs: unexpected size mismatch")
+	}
+	if len(dir) != dim {
+		panic("bfgs: unexpected size mismatch")
+	}
+
+	x := mat.NewVecDense(dim, loc.X)
+	grad := mat.NewVecDense(dim, loc.Gradient)
+
+	// s = x_{k+1} - x_{k}
+	b.s.SubVec(x, &b.x)
+	// y = g_{k+1} - g_{k}
+	b.y.SubVec(grad, &b.grad)
+
+	sDotY := mat.Dot(&b.s, &b.y)
+
+	if b.first {
+		// Rescale the initial Hessian.
+		// From: Nocedal, J., Wright, S.: Numerical Optimization (2nd ed).
+		//       Springer (2006), page 143, eq. 6.20.
+		yDotY := mat.Dot(&b.y, &b.y)
+		scale := sDotY / yDotY
+		for i := 0; i < dim; i++ {
+			for j := i; j < dim; j++ {
+				if i == j {
+					b.invHess.SetSym(i, i, scale)
+				} else {
+					b.invHess.SetSym(i, j, 0)
+				}
+			}
+		}
+		b.first = false
+	}
+
+	if math.Abs(sDotY) != 0 {
+		// Update the inverse Hessian according to the formula
+		//
+		//  B_{k+1}^-1 = B_k^-1
+		//             + (s_k^T y_k + y_k^T B_k^-1 y_k) / (s_k^T y_k)^2 * (s_k s_k^T)
+		//             - (B_k^-1 y_k s_k^T + s_k y_k^T B_k^-1) / (s_k^T y_k).
+		//
+		// Note that y_k^T B_k^-1 y_k is a scalar, and that the third term is a
+		// rank-two update where B_k^-1 y_k is one vector and s_k is the other.
+		yBy := mat.Inner(&b.y, b.invHess, &b.y)
+		b.tmp.MulVec(b.invHess, &b.y)
+		scale := (1 + yBy/sDotY) / sDotY
+		b.invHess.SymRankOne(b.invHess, scale, &b.s)
+		b.invHess.RankTwo(b.invHess, -1/sDotY, &b.tmp, &b.s)
+	}
+
+	// Update the stored BFGS data.
+	b.x.CopyVec(x)
+	b.grad.CopyVec(grad)
+
+	// New direction is stored in dir.
+	d := mat.NewVecDense(dim, dir)
+	d.MulVec(b.invHess, grad)
+	d.ScaleVec(-1, d)
+
+	return 1
+}
+
+func (*BFGS) Needs() struct {
+	Gradient bool
+	Hessian  bool
+} {
+	return struct {
+		Gradient bool
+		Hessian  bool
+	}{true, false}
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/bisection.go b/vendor/gonum.org/v1/gonum/optimize/bisection.go
new file mode 100644
index 00000000..6dfe8652
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/bisection.go
@@ -0,0 +1,146 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package optimize
+
+import "math"
+
+const (
+	defaultBisectionCurvature = 0.9
+)
+
+// Bisection is a Linesearcher that uses a bisection to find a point that
+// satisfies the strong Wolfe conditions with the given curvature factor and
+// a decrease factor of zero.
+type Bisection struct {
+	// CurvatureFactor is the constant factor in the curvature condition.
+	// Smaller values result in a more exact line search.
+	// A set value must be in the interval (0, 1), otherwise Init will panic.
+	// If it is zero, it will be defaulted to 0.9.
+	CurvatureFactor float64
+
+	minStep  float64
+	maxStep  float64
+	currStep float64
+
+	initF float64
+	minF  float64
+	maxF  float64
+	lastF float64
+
+	initGrad float64
+
+	lastOp Operation
+}
+
+func (b *Bisection) Init(f, g float64, step float64) Operation {
+	if step <= 0 {
+		panic("bisection: bad step size")
+	}
+	if g >= 0 {
+		panic("bisection: initial derivative is non-negative")
+	}
+
+	if b.CurvatureFactor == 0 {
+		b.CurvatureFactor = defaultBisectionCurvature
+	}
+	if b.CurvatureFactor <= 0 || b.CurvatureFactor >= 1 {
+		panic("bisection: CurvatureFactor not between 0 and 1")
+	}
+
+	b.minStep = 0
+	b.maxStep = math.Inf(1)
+	b.currStep = step
+
+	b.initF = f
+	b.minF = f
+	b.maxF = math.NaN()
+
+	b.initGrad = g
+
+	// Only evaluate the gradient when necessary.
+	b.lastOp = FuncEvaluation
+	return b.lastOp
+}
+
+func (b *Bisection) Iterate(f, g float64) (Operation, float64, error) {
+	if b.lastOp != FuncEvaluation && b.lastOp != GradEvaluation {
+		panic("bisection: Init has not been called")
+	}
+	minF := b.initF
+	if b.maxF < minF {
+		minF = b.maxF
+	}
+	if b.minF < minF {
+		minF = b.minF
+	}
+	if b.lastOp == FuncEvaluation {
+		// See if the function value is good enough to make progress. If it is,
+		// evaluate the gradient. If not, set it to the upper bound if the bound
+		// has not yet been found, otherwise iterate toward the minimum location.
+		if f <= minF {
+			b.lastF = f
+			b.lastOp = GradEvaluation
+			return b.lastOp, b.currStep, nil
+		}
+		if math.IsInf(b.maxStep, 1) {
+			b.maxStep = b.currStep
+			b.maxF = f
+			return b.nextStep((b.minStep + b.maxStep) / 2)
+		}
+		if b.minF <= b.maxF {
+			b.maxStep = b.currStep
+			b.maxF = f
+		} else {
+			b.minStep = b.currStep
+			b.minF = f
+		}
+		return b.nextStep((b.minStep + b.maxStep) / 2)
+	}
+	f = b.lastF
+	// The function value was lower. Check if this location is sufficient to
+	// converge the linesearch, otherwise iterate.
+	if StrongWolfeConditionsMet(f, g, minF, b.initGrad, b.currStep, 0, b.CurvatureFactor) {
+		b.lastOp = MajorIteration
+		return b.lastOp, b.currStep, nil
+	}
+	if math.IsInf(b.maxStep, 1) {
+		// The function value is lower. If the gradient is positive, an upper bound
+		// of the minimum been found. If the gradient is negative, search farther
+		// in that direction.
+		if g > 0 {
+			b.maxStep = b.currStep
+			b.maxF = f
+			return b.nextStep((b.minStep + b.maxStep) / 2)
+		}
+		b.minStep = b.currStep
+		b.minF = f
+		return b.nextStep(b.currStep * 2)
+	}
+	// The interval has been bounded, and we have found a new lowest value. Use
+	// the gradient to decide which direction.
+	if g < 0 {
+		b.minStep = b.currStep
+		b.minF = f
+	} else {
+		b.maxStep = b.currStep
+		b.maxF = f
+	}
+	return b.nextStep((b.minStep + b.maxStep) / 2)
+}
+
+// nextStep checks if the new step is equal to the old step.
+// This can happen if min and max are the same, or if the step size is infinity,
+// both of which indicate the minimization must stop. If the steps are different,
+// it sets the new step size and returns the evaluation type and the step. If the steps
+// are the same, it returns an error.
+func (b *Bisection) nextStep(step float64) (Operation, float64, error) {
+	if b.currStep == step {
+		b.lastOp = NoOperation
+		return b.lastOp, b.currStep, ErrLinesearcherFailure
+	}
+	b.currStep = step
+	b.lastOp = FuncEvaluation
+	return b.lastOp, b.currStep, nil
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/cg.go b/vendor/gonum.org/v1/gonum/optimize/cg.go
new file mode 100644
index 00000000..88612d3f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/cg.go
@@ -0,0 +1,313 @@
+package optimize
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+const (
+	iterationRestartFactor = 6
+	angleRestartThreshold  = -0.9
+)
+
+// CGVariant calculates the scaling parameter, β, used for updating the
+// conjugate direction in the nonlinear conjugate gradient (CG) method.
+type CGVariant interface {
+	// Init is called at the first iteration and provides a way to initialize
+	// any internal state.
+	Init(loc *Location)
+	// Beta returns the value of the scaling parameter that is computed
+	// according to the particular variant of the CG method.
+	Beta(grad, gradPrev, dirPrev []float64) float64
+}
+
+// CG implements the nonlinear conjugate gradient method for solving nonlinear
+// unconstrained optimization problems. It is a line search method that
+// generates the search directions d_k according to the formula
+//  d_{k+1} = -∇f_{k+1} + β_k*d_k,   d_0 = -∇f_0.
+// Variants of the conjugate gradient method differ in the choice of the
+// parameter β_k. The conjugate gradient method usually requires fewer function
+// evaluations than the gradient descent method and no matrix storage, but
+// L-BFGS is usually more efficient.
+//
+// CG implements a restart strategy that takes the steepest descent direction
+// (i.e., d_{k+1} = -∇f_{k+1}) whenever any of the following conditions holds:
+//
+//  - A certain number of iterations has elapsed without a restart. This number
+//    is controllable via IterationRestartFactor and if equal to 0, it is set to
+//    a reasonable default based on the problem dimension.
+//  - The angle between the gradients at two consecutive iterations ∇f_k and
+//    ∇f_{k+1} is too large.
+//  - The direction d_{k+1} is not a descent direction.
+//  - β_k returned from CGVariant.Beta is equal to zero.
+//
+// The line search for CG must yield step sizes that satisfy the strong Wolfe
+// conditions at every iteration, otherwise the generated search direction
+// might fail to be a descent direction. The line search should be more
+// stringent compared with those for Newton-like methods, which can be achieved
+// by setting the gradient constant in the strong Wolfe conditions to a small
+// value.
+//
+// See also William Hager, Hongchao Zhang, A survey of nonlinear conjugate
+// gradient methods. Pacific Journal of Optimization, 2 (2006), pp. 35-58, and
+// references therein.
+type CG struct {
+	// Linesearcher must satisfy the strong Wolfe conditions at every iteration.
+	// If Linesearcher == nil, an appropriate default is chosen.
+	Linesearcher Linesearcher
+	// Variant implements the particular CG formula for computing β_k.
+	// If Variant is nil, an appropriate default is chosen.
+	Variant CGVariant
+	// InitialStep estimates the initial line search step size, because the CG
+	// method does not generate well-scaled search directions.
+	// If InitialStep is nil, an appropriate default is chosen.
+	InitialStep StepSizer
+
+	// IterationRestartFactor determines the frequency of restarts based on the
+	// problem dimension. The negative gradient direction is taken whenever
+	// ceil(IterationRestartFactor*(problem dimension)) iterations have elapsed
+	// without a restart. For medium and large-scale problems
+	// IterationRestartFactor should be set to 1, low-dimensional problems a
+	// larger value should be chosen. Note that if the ceil function returns 1,
+	// CG will be identical to gradient descent.
+	// If IterationRestartFactor is 0, it will be set to 6.
+	// CG will panic if IterationRestartFactor is negative.
+	IterationRestartFactor float64
+	// AngleRestartThreshold sets the threshold angle for restart. The method
+	// is restarted if the cosine of the angle between two consecutive
+	// gradients is smaller than or equal to AngleRestartThreshold, that is, if
+	//  ∇f_k·∇f_{k+1} / (|∇f_k| |∇f_{k+1}|) <= AngleRestartThreshold.
+	// A value of AngleRestartThreshold closer to -1 (successive gradients in
+	// exact opposite directions) will tend to reduce the number of restarts.
+	// If AngleRestartThreshold is 0, it will be set to -0.9.
+	// CG will panic if AngleRestartThreshold is not in the interval [-1, 0].
+	AngleRestartThreshold float64
+
+	ls *LinesearchMethod
+
+	restartAfter    int
+	iterFromRestart int
+
+	dirPrev      []float64
+	gradPrev     []float64
+	gradPrevNorm float64
+}
+
+func (cg *CG) Init(loc *Location) (Operation, error) {
+	if cg.IterationRestartFactor < 0 {
+		panic("cg: IterationRestartFactor is negative")
+	}
+	if cg.AngleRestartThreshold < -1 || cg.AngleRestartThreshold > 0 {
+		panic("cg: AngleRestartThreshold not in [-1, 0]")
+	}
+
+	if cg.Linesearcher == nil {
+		cg.Linesearcher = &MoreThuente{CurvatureFactor: 0.1}
+	}
+	if cg.Variant == nil {
+		cg.Variant = &HestenesStiefel{}
+	}
+	if cg.InitialStep == nil {
+		cg.InitialStep = &FirstOrderStepSize{}
+	}
+
+	if cg.IterationRestartFactor == 0 {
+		cg.IterationRestartFactor = iterationRestartFactor
+	}
+	if cg.AngleRestartThreshold == 0 {
+		cg.AngleRestartThreshold = angleRestartThreshold
+	}
+
+	if cg.ls == nil {
+		cg.ls = &LinesearchMethod{}
+	}
+	cg.ls.Linesearcher = cg.Linesearcher
+	cg.ls.NextDirectioner = cg
+
+	return cg.ls.Init(loc)
+}
+
+func (cg *CG) Iterate(loc *Location) (Operation, error) {
+	return cg.ls.Iterate(loc)
+}
+
+func (cg *CG) InitDirection(loc *Location, dir []float64) (stepSize float64) {
+	dim := len(loc.X)
+
+	cg.restartAfter = int(math.Ceil(cg.IterationRestartFactor * float64(dim)))
+	cg.iterFromRestart = 0
+
+	// The initial direction is always the negative gradient.
+	copy(dir, loc.Gradient)
+	floats.Scale(-1, dir)
+
+	cg.dirPrev = resize(cg.dirPrev, dim)
+	copy(cg.dirPrev, dir)
+	cg.gradPrev = resize(cg.gradPrev, dim)
+	copy(cg.gradPrev, loc.Gradient)
+	cg.gradPrevNorm = floats.Norm(loc.Gradient, 2)
+
+	cg.Variant.Init(loc)
+	return cg.InitialStep.Init(loc, dir)
+}
+
+func (cg *CG) NextDirection(loc *Location, dir []float64) (stepSize float64) {
+	copy(dir, loc.Gradient)
+	floats.Scale(-1, dir)
+
+	cg.iterFromRestart++
+	var restart bool
+	if cg.iterFromRestart == cg.restartAfter {
+		// Restart because too many iterations have been taken without a restart.
+		restart = true
+	}
+
+	gDot := floats.Dot(loc.Gradient, cg.gradPrev)
+	gNorm := floats.Norm(loc.Gradient, 2)
+	if gDot <= cg.AngleRestartThreshold*gNorm*cg.gradPrevNorm {
+		// Restart because the angle between the last two gradients is too large.
+		restart = true
+	}
+
+	// Compute the scaling factor β_k even when restarting, because cg.Variant
+	// may be keeping an inner state that needs to be updated at every iteration.
+	beta := cg.Variant.Beta(loc.Gradient, cg.gradPrev, cg.dirPrev)
+	if beta == 0 {
+		// β_k == 0 means that the steepest descent direction will be taken, so
+		// indicate that the method is in fact being restarted.
+		restart = true
+	}
+	if !restart {
+		// The method is not being restarted, so update the descent direction.
+		floats.AddScaled(dir, beta, cg.dirPrev)
+		if floats.Dot(loc.Gradient, dir) >= 0 {
+			// Restart because the new direction is not a descent direction.
+			restart = true
+			copy(dir, loc.Gradient)
+			floats.Scale(-1, dir)
+		}
+	}
+
+	// Get the initial line search step size from the StepSizer even if the
+	// method was restarted, because StepSizers need to see every iteration.
+	stepSize = cg.InitialStep.StepSize(loc, dir)
+	if restart {
+		// The method was restarted and since the steepest descent direction is
+		// not related to the previous direction, discard the estimated step
+		// size from cg.InitialStep and use step size of 1 instead.
+		stepSize = 1
+		// Reset to 0 the counter of iterations taken since the last restart.
+		cg.iterFromRestart = 0
+	}
+
+	copy(cg.gradPrev, loc.Gradient)
+	copy(cg.dirPrev, dir)
+	cg.gradPrevNorm = gNorm
+	return stepSize
+}
+
+func (*CG) Needs() struct {
+	Gradient bool
+	Hessian  bool
+} {
+	return struct {
+		Gradient bool
+		Hessian  bool
+	}{true, false}
+}
+
+// FletcherReeves implements the Fletcher-Reeves variant of the CG method that
+// computes the scaling parameter β_k according to the formula
+//  β_k = |∇f_{k+1}|^2 / |∇f_k|^2.
+type FletcherReeves struct {
+	prevNorm float64
+}
+
+func (fr *FletcherReeves) Init(loc *Location) {
+	fr.prevNorm = floats.Norm(loc.Gradient, 2)
+}
+
+func (fr *FletcherReeves) Beta(grad, _, _ []float64) (beta float64) {
+	norm := floats.Norm(grad, 2)
+	beta = (norm / fr.prevNorm) * (norm / fr.prevNorm)
+	fr.prevNorm = norm
+	return beta
+}
+
+// PolakRibierePolyak implements the Polak-Ribiere-Polyak variant of the CG
+// method that computes the scaling parameter β_k according to the formula
+//  β_k = max(0, ∇f_{k+1}·y_k / |∇f_k|^2),
+// where y_k = ∇f_{k+1} - ∇f_k.
+type PolakRibierePolyak struct {
+	prevNorm float64
+}
+
+func (pr *PolakRibierePolyak) Init(loc *Location) {
+	pr.prevNorm = floats.Norm(loc.Gradient, 2)
+}
+
+func (pr *PolakRibierePolyak) Beta(grad, gradPrev, _ []float64) (beta float64) {
+	norm := floats.Norm(grad, 2)
+	dot := floats.Dot(grad, gradPrev)
+	beta = (norm*norm - dot) / (pr.prevNorm * pr.prevNorm)
+	pr.prevNorm = norm
+	return math.Max(0, beta)
+}
+
+// HestenesStiefel implements the Hestenes-Stiefel variant of the CG method
+// that computes the scaling parameter β_k according to the formula
+//  β_k = max(0, ∇f_{k+1}·y_k / d_k·y_k),
+// where y_k = ∇f_{k+1} - ∇f_k.
+type HestenesStiefel struct {
+	y []float64
+}
+
+func (hs *HestenesStiefel) Init(loc *Location) {
+	hs.y = resize(hs.y, len(loc.Gradient))
+}
+
+func (hs *HestenesStiefel) Beta(grad, gradPrev, dirPrev []float64) (beta float64) {
+	floats.SubTo(hs.y, grad, gradPrev)
+	beta = floats.Dot(grad, hs.y) / floats.Dot(dirPrev, hs.y)
+	return math.Max(0, beta)
+}
+
+// DaiYuan implements the Dai-Yuan variant of the CG method that computes the
+// scaling parameter β_k according to the formula
+//  β_k = |∇f_{k+1}|^2 / d_k·y_k,
+// where y_k = ∇f_{k+1} - ∇f_k.
+type DaiYuan struct {
+	y []float64
+}
+
+func (dy *DaiYuan) Init(loc *Location) {
+	dy.y = resize(dy.y, len(loc.Gradient))
+}
+
+func (dy *DaiYuan) Beta(grad, gradPrev, dirPrev []float64) (beta float64) {
+	floats.SubTo(dy.y, grad, gradPrev)
+	norm := floats.Norm(grad, 2)
+	return norm * norm / floats.Dot(dirPrev, dy.y)
+}
+
+// HagerZhang implements the Hager-Zhang variant of the CG method that computes the
+// scaling parameter β_k according to the formula
+//  β_k = (y_k - 2 d_k |y_k|^2/(d_k·y_k))·∇f_{k+1} / (d_k·y_k),
+// where y_k = ∇f_{k+1} - ∇f_k.
+type HagerZhang struct {
+	y []float64
+}
+
+func (hz *HagerZhang) Init(loc *Location) {
+	hz.y = resize(hz.y, len(loc.Gradient))
+}
+
+func (hz *HagerZhang) Beta(grad, gradPrev, dirPrev []float64) (beta float64) {
+	floats.SubTo(hz.y, grad, gradPrev)
+	dirDotY := floats.Dot(dirPrev, hz.y)
+	gDotY := floats.Dot(grad, hz.y)
+	gDotDir := floats.Dot(grad, dirPrev)
+	yNorm := floats.Norm(hz.y, 2)
+	return (gDotY - 2*gDotDir*yNorm*yNorm/dirDotY) / dirDotY
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/convex/lp/convert.go b/vendor/gonum.org/v1/gonum/optimize/convex/lp/convert.go
new file mode 100644
index 00000000..66ebe2ea
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/convex/lp/convert.go
@@ -0,0 +1,137 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package lp
+
+import (
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+)
+
+// TODO(btracey): Have some sort of preprocessing step for helping to fix A to make it
+// full rank?
+// TODO(btracey): Reduce rows? Get rid of all zeros, places where only one variable
+// is there, etc. Could be implemented with a Reduce function.
+// TODO(btracey): Provide method of artificial variables for help when problem
+// is infeasible?
+// TODO(btracey): Add an lp.Solve that solves an LP in non-standard form.
+
+// Convert converts a General-form LP into a standard form LP.
+// The general form of an LP is:
+//  minimize c^T * x
+//  s.t      G * x <= h
+//           A * x = b
+// And the standard form is:
+//  minimize cNew^T * x
+//  s.t      aNew * x = bNew
+//           x >= 0
+// If there are no constraints of the given type, the inputs may be nil.
+func Convert(c []float64, g mat.Matrix, h []float64, a mat.Matrix, b []float64) (cNew []float64, aNew *mat.Dense, bNew []float64) {
+	nVar := len(c)
+	nIneq := len(h)
+
+	// Check input sizes.
+	if g == nil {
+		if nIneq != 0 {
+			panic(badShape)
+		}
+	} else {
+		gr, gc := g.Dims()
+		if gr != nIneq {
+			panic(badShape)
+		}
+		if gc != nVar {
+			panic(badShape)
+		}
+	}
+
+	nEq := len(b)
+	if a == nil {
+		if nEq != 0 {
+			panic(badShape)
+		}
+	} else {
+		ar, ac := a.Dims()
+		if ar != nEq {
+			panic(badShape)
+		}
+		if ac != nVar {
+			panic(badShape)
+		}
+	}
+
+	// Convert the general form LP.
+	// Derivation:
+	// 0. Start with general form
+	//  min.	c^T * x
+	//  s.t.	G * x <= h
+	//  		A * x = b
+	// 1. Introduce slack variables for each constraint
+	//  min. 	c^T * x
+	//  s.t.	G * x + s = h
+	//			A * x = b
+	//      	s >= 0
+	// 2. Add non-negativity constraints for x by splitting x
+	// into positive and negative components.
+	//   x = xp - xn
+	//   xp >= 0, xn >= 0
+	// This makes the LP
+	//  min.	c^T * xp - c^T xn
+	//  s.t. 	G * xp - G * xn + s = h
+	//			A * xp  - A * xn = b
+	//			xp >= 0, xn >= 0, s >= 0
+	// 3. Write the above in standard form:
+	//  xt = [xp
+	//	 	  xn
+	//		  s ]
+	//  min.	[c^T, -c^T, 0] xt
+	//  s.t.	[G, -G, I] xt = h
+	//   		[A, -A, 0] xt = b
+	//			x >= 0
+
+	// In summary:
+	// Original LP:
+	//  min.	c^T * x
+	//  s.t.	G * x <= h
+	//  		A * x = b
+	// Standard Form:
+	//  xt = [xp; xn; s]
+	//  min.	[c^T, -c^T, 0] xt
+	//  s.t.	[G, -G, I] xt = h
+	//   		[A, -A, 0] xt = b
+	//			x >= 0
+
+	// New size of x is [xp, xn, s]
+	nNewVar := nVar + nVar + nIneq
+
+	// Construct cNew = [c; -c; 0]
+	cNew = make([]float64, nNewVar)
+	copy(cNew, c)
+	copy(cNew[nVar:], c)
+	floats.Scale(-1, cNew[nVar:2*nVar])
+
+	// New number of equality constraints is the number of total constraints.
+	nNewEq := nIneq + nEq
+
+	// Construct bNew = [h, b].
+	bNew = make([]float64, nNewEq)
+	copy(bNew, h)
+	copy(bNew[nIneq:], b)
+
+	// Construct aNew = [G, -G, I; A, -A, 0].
+	aNew = mat.NewDense(nNewEq, nNewVar, nil)
+	if nIneq != 0 {
+		aNew.Slice(0, nIneq, 0, nVar).(*mat.Dense).Copy(g)
+		aNew.Slice(0, nIneq, nVar, 2*nVar).(*mat.Dense).Scale(-1, g)
+		aView := aNew.Slice(0, nIneq, 2*nVar, 2*nVar+nIneq).(*mat.Dense)
+		for i := 0; i < nIneq; i++ {
+			aView.Set(i, i, 1)
+		}
+	}
+	if nEq != 0 {
+		aNew.Slice(nIneq, nIneq+nEq, 0, nVar).(*mat.Dense).Copy(a)
+		aNew.Slice(nIneq, nIneq+nEq, nVar, 2*nVar).(*mat.Dense).Scale(-1, a)
+	}
+	return cNew, aNew, bNew
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/convex/lp/doc.go b/vendor/gonum.org/v1/gonum/optimize/convex/lp/doc.go
new file mode 100644
index 00000000..7b084247
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/convex/lp/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package lp implements routines to solve linear programming problems.
+package lp // import "gonum.org/v1/gonum/optimize/convex/lp"
diff --git a/vendor/gonum.org/v1/gonum/optimize/convex/lp/simplex.go b/vendor/gonum.org/v1/gonum/optimize/convex/lp/simplex.go
new file mode 100644
index 00000000..eb7757ff
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/convex/lp/simplex.go
@@ -0,0 +1,619 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// package lp implements routines for solving linear programs.
+package lp
+
+import (
+	"errors"
+	"fmt"
+	"math"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+)
+
+// TODO(btracey): Could have a solver structure with an abstract factorizer. With
+// this transformation the same high-level code could handle both Dense and Sparse.
+// TODO(btracey): Need to improve error handling. Only want to panic if condition number inf.
+// TODO(btracey): Performance enhancements. There are currently lots of linear
+// solves that can be improved by doing rank-one updates. For example, the swap
+// step is just a rank-one update.
+// TODO(btracey): Better handling on the linear solve errors. If the condition
+// number is not inf and the equation solved "well", should keep moving.
+
+var (
+	ErrBland      = errors.New("lp: bland: all replacements are negative or cause ill-conditioned ab")
+	ErrInfeasible = errors.New("lp: problem is infeasible")
+	ErrLinSolve   = errors.New("lp: linear solve failure")
+	ErrUnbounded  = errors.New("lp: problem is unbounded")
+	ErrSingular   = errors.New("lp: A is singular")
+	ErrZeroColumn = errors.New("lp: A has a column of all zeros")
+	ErrZeroRow    = errors.New("lp: A has a row of all zeros")
+)
+
+var (
+	badShape = "lp: size mismatch"
+)
+
+// TODO(btracey): Should these tolerances be part of a settings struct?
+
+const (
+	// initPosTol is the tolerance on the initial condition being feasible. Strictly,
+	// the x should be positive, but instead it must be greater than -initPosTol.
+	initPosTol = 1e-13
+	// blandNegTol is the tolerance on the value being greater than 0 in the bland test.
+	blandNegTol = 1e-14
+	// rRoundTol is the tolerance for rounding values to zero when testing if
+	// constraints are met.
+	rRoundTol = 1e-13
+	// dRoundTol is the tolerance for testing if values are zero for the problem
+	// being unbounded.
+	dRoundTol = 1e-13
+	// phaseIZeroTol tests if the Phase I problem returned a feasible solution.
+	phaseIZeroTol = 1e-12
+	// blandZeroTol is the tolerance on testing if the bland solution can move.
+	blandZeroTol = 1e-12
+)
+
+// Simplex solves a linear program in standard form using Danzig's Simplex
+// algorithm. The standard form of a linear program is:
+//  minimize	c^T x
+//  s.t. 		A*x = b
+//  			x >= 0 .
+// The input tol sets how close to the optimal solution is found (specifically,
+// when the maximal reduced cost is below tol). An error will be returned if the
+// problem is infeasible or unbounded. In rare cases, numeric errors can cause
+// the Simplex to fail. In this case, an error will be returned along with the
+// most recently found feasible solution.
+//
+// The Convert function can be used to transform a general LP into standard form.
+//
+// The input matrix A must have full rank and may not contain any columns with
+// all zeros. Furthermore, len(c) must equal the number of columns of A, and len(b)
+// must equal the number of rows of A. Simplex will panic if these conditions are
+// not met.
+//
+// initialBasic can be used to set the initial set of indices for a feasible
+// solution to the LP. If an initial feasible solution is not known, initialBasic
+// may be nil. If initialBasic is non-nil, len(initialBasic) must equal the number
+// of rows of A and must be an actual feasible solution to the LP, otherwise
+// Simplex will panic.
+//
+// A description of the Simplex algorithm can be found in Ch. 8 of
+//  Strang, Gilbert. "Linear Algebra and Applications." Academic, New York (1976).
+// For a detailed video introduction, see lectures 11-13 of UC Math 352
+//  https://www.youtube.com/watch?v=ESzYPFkY3og&index=11&list=PLh464gFUoJWOmBYla3zbZbc4nv2AXez6X.
+func Simplex(c []float64, A mat.Matrix, b []float64, tol float64, initialBasic []int) (optF float64, optX []float64, err error) {
+	ans, x, _, err := simplex(initialBasic, c, A, b, tol)
+	return ans, x, err
+}
+
+func simplex(initialBasic []int, c []float64, A mat.Matrix, b []float64, tol float64) (float64, []float64, []int, error) {
+	err := verifyInputs(initialBasic, c, A, b)
+	if err != nil {
+		if err == ErrUnbounded {
+			return math.Inf(-1), nil, nil, ErrUnbounded
+		}
+		return math.NaN(), nil, nil, err
+	}
+	m, n := A.Dims()
+
+	// There is at least one optimal solution to the LP which is at the intersection
+	// to a set of constraint boundaries. For a standard form LP with m variables
+	// and n equality constraints, at least m-n elements of x must equal zero
+	// at optimality. The Simplex algorithm solves the standard-form LP by starting
+	// at an initial constraint vertex and successively moving to adjacent constraint
+	// vertices. At every vertex, the set of non-zero x values is the "basic
+	// feasible solution". The list of non-zero x's are maintained in basicIdxs,
+	// the respective columns of A are in ab, and the actual non-zero values of
+	// x are in xb.
+	//
+	// The LP is equality constrained such that A * x = b. This can be expanded
+	// to
+	//  ab * xb + an * xn = b
+	// where ab are the columns of a in the basic set, and an are all of the
+	// other columns. Since each element of xn is zero by definition, this means
+	// that for all feasible solutions xb = ab^-1 * b.
+	//
+	// Before the simplex algorithm can start, an initial feasible solution must
+	// be found. If initialBasic is non-nil a feasible solution has been supplied.
+	// Otherwise the "Phase I" problem must be solved to find an initial feasible
+	// solution.
+
+	var basicIdxs []int // The indices of the non-zero x values.
+	var ab *mat.Dense   // The subset of columns of A listed in basicIdxs.
+	var xb []float64    // The non-zero elements of x. xb = ab^-1 b
+
+	if initialBasic != nil {
+		// InitialBasic supplied. Panic if incorrect length or infeasible.
+		if len(initialBasic) != m {
+			panic("lp: incorrect number of initial vectors")
+		}
+		ab = mat.NewDense(m, len(initialBasic), nil)
+		extractColumns(ab, A, initialBasic)
+		xb = make([]float64, m)
+		err = initializeFromBasic(xb, ab, b)
+		if err != nil {
+			panic(err)
+		}
+		basicIdxs = make([]int, len(initialBasic))
+		copy(basicIdxs, initialBasic)
+	} else {
+		// No initial basis supplied. Solve the PhaseI problem.
+		basicIdxs, ab, xb, err = findInitialBasic(A, b)
+		if err != nil {
+			return math.NaN(), nil, nil, err
+		}
+	}
+
+	// basicIdxs contains the indexes for an initial feasible solution,
+	// ab contains the extracted columns of A, and xb contains the feasible
+	// solution. All x not in the basic set are 0 by construction.
+
+	// nonBasicIdx is the set of nonbasic variables.
+	nonBasicIdx := make([]int, 0, n-m)
+	inBasic := make(map[int]struct{})
+	for _, v := range basicIdxs {
+		inBasic[v] = struct{}{}
+	}
+	for i := 0; i < n; i++ {
+		_, ok := inBasic[i]
+		if !ok {
+			nonBasicIdx = append(nonBasicIdx, i)
+		}
+	}
+
+	// cb is the subset of c for the basic variables. an and cn
+	// are the equivalents to ab and cb but for the nonbasic variables.
+	cb := make([]float64, len(basicIdxs))
+	for i, idx := range basicIdxs {
+		cb[i] = c[idx]
+	}
+	cn := make([]float64, len(nonBasicIdx))
+	for i, idx := range nonBasicIdx {
+		cn[i] = c[idx]
+	}
+	an := mat.NewDense(m, len(nonBasicIdx), nil)
+	extractColumns(an, A, nonBasicIdx)
+
+	bVec := mat.NewVecDense(len(b), b)
+	cbVec := mat.NewVecDense(len(cb), cb)
+
+	// Temporary data needed each iteration. (Described later)
+	r := make([]float64, n-m)
+	move := make([]float64, m)
+
+	// Solve the linear program starting from the initial feasible set. This is
+	// the "Phase 2" problem.
+	//
+	// Algorithm:
+	// 1) Compute the "reduced costs" for the non-basic variables. The reduced
+	// costs are the lagrange multipliers of the constraints.
+	// 	 r = cn - an^T * ab^-T * cb
+	// 2) If all of the reduced costs are positive, no improvement is possible,
+	// and the solution is optimal (xn can only increase because of
+	// non-negativity constraints). Otherwise, the solution can be improved and
+	// one element will be exchanged in the basic set.
+	// 3) Choose the x_n with the most negative value of r. Call this value xe.
+	// This variable will be swapped into the basic set.
+	// 4) Increase xe until the next constraint boundary is met. This will happen
+	// when the first element in xb becomes 0. The distance xe can increase before
+	// a given element in xb becomes negative can be found from
+	//	xb = Ab^-1 b - Ab^-1 An xn
+	//     = Ab^-1 b - Ab^-1 Ae xe
+	//     = bhat + d x_e
+	//  xe = bhat_i / - d_i
+	// where Ae is the column of A corresponding to xe.
+	// The constraining basic index is the first index for which this is true,
+	// so remove the element which is min_i (bhat_i / -d_i), assuming d_i is negative.
+	// If no d_i is less than 0, then the problem is unbounded.
+	// 5) If the new xe is 0 (that is, bhat_i == 0), then this location is at
+	// the intersection of several constraints. Use the Bland rule instead
+	// of the rule in step 4 to avoid cycling.
+	for {
+		// Compute reduced costs -- r = cn - an^T ab^-T cb
+		var tmp mat.VecDense
+		err = tmp.SolveVec(ab.T(), cbVec)
+		if err != nil {
+			break
+		}
+		data := make([]float64, n-m)
+		tmp2 := mat.NewVecDense(n-m, data)
+		tmp2.MulVec(an.T(), &tmp)
+		floats.SubTo(r, cn, data)
+
+		// Replace the most negative element in the simplex. If there are no
+		// negative entries then the optimal solution has been found.
+		minIdx := floats.MinIdx(r)
+		if r[minIdx] >= -tol {
+			break
+		}
+
+		for i, v := range r {
+			if math.Abs(v) < rRoundTol {
+				r[i] = 0
+			}
+		}
+
+		// Compute the moving distance.
+		err = computeMove(move, minIdx, A, ab, xb, nonBasicIdx)
+		if err != nil {
+			if err == ErrUnbounded {
+				return math.Inf(-1), nil, nil, ErrUnbounded
+			}
+			break
+		}
+
+		// Replace the basic index along the tightest constraint.
+		replace := floats.MinIdx(move)
+		if move[replace] <= 0 {
+			replace, minIdx, err = replaceBland(A, ab, xb, basicIdxs, nonBasicIdx, r, move)
+			if err != nil {
+				if err == ErrUnbounded {
+					return math.Inf(-1), nil, nil, ErrUnbounded
+				}
+				break
+			}
+		}
+
+		// Replace the constrained basicIdx with the newIdx.
+		basicIdxs[replace], nonBasicIdx[minIdx] = nonBasicIdx[minIdx], basicIdxs[replace]
+		cb[replace], cn[minIdx] = cn[minIdx], cb[replace]
+		tmpCol1 := mat.Col(nil, replace, ab)
+		tmpCol2 := mat.Col(nil, minIdx, an)
+		ab.SetCol(replace, tmpCol2)
+		an.SetCol(minIdx, tmpCol1)
+
+		// Compute the new xb.
+		xbVec := mat.NewVecDense(len(xb), xb)
+		err = xbVec.SolveVec(ab, bVec)
+		if err != nil {
+			break
+		}
+	}
+	// Found the optimum successfully or died trying. The basic variables get
+	// their values, and the non-basic variables are all zero.
+	opt := floats.Dot(cb, xb)
+	xopt := make([]float64, n)
+	for i, v := range basicIdxs {
+		xopt[v] = xb[i]
+	}
+	return opt, xopt, basicIdxs, err
+}
+
+// computeMove computes how far can be moved replacing each index. The results
+// are stored into move.
+func computeMove(move []float64, minIdx int, A mat.Matrix, ab *mat.Dense, xb []float64, nonBasicIdx []int) error {
+	// Find ae.
+	col := mat.Col(nil, nonBasicIdx[minIdx], A)
+	aCol := mat.NewVecDense(len(col), col)
+
+	// d = - Ab^-1 Ae
+	nb, _ := ab.Dims()
+	d := make([]float64, nb)
+	dVec := mat.NewVecDense(nb, d)
+	err := dVec.SolveVec(ab, aCol)
+	if err != nil {
+		return ErrLinSolve
+	}
+	floats.Scale(-1, d)
+
+	for i, v := range d {
+		if math.Abs(v) < dRoundTol {
+			d[i] = 0
+		}
+	}
+
+	// If no di < 0, then problem is unbounded.
+	if floats.Min(d) >= 0 {
+		return ErrUnbounded
+	}
+
+	// move = bhat_i / - d_i, assuming d is negative.
+	bHat := xb // ab^-1 b
+	for i, v := range d {
+		if v >= 0 {
+			move[i] = math.Inf(1)
+		} else {
+			move[i] = bHat[i] / math.Abs(v)
+		}
+	}
+	return nil
+}
+
+// replaceBland uses the Bland rule to find the indices to swap if the minimum
+// move is 0. The indices to be swapped are replace and minIdx (following the
+// nomenclature in the main routine).
+func replaceBland(A mat.Matrix, ab *mat.Dense, xb []float64, basicIdxs, nonBasicIdx []int, r, move []float64) (replace, minIdx int, err error) {
+	m, _ := A.Dims()
+	// Use the traditional bland rule, except don't replace a constraint which
+	// causes the new ab to be singular.
+	for i, v := range r {
+		if v > -blandNegTol {
+			continue
+		}
+		minIdx = i
+		err = computeMove(move, minIdx, A, ab, xb, nonBasicIdx)
+		if err != nil {
+			// Either unbounded or something went wrong.
+			return -1, -1, err
+		}
+		replace = floats.MinIdx(move)
+		if math.Abs(move[replace]) > blandZeroTol {
+			// Large enough that it shouldn't be a problem
+			return replace, minIdx, nil
+		}
+		// Find a zero index where replacement is non-singular.
+		biCopy := make([]int, len(basicIdxs))
+		for replace, v := range move {
+			if v > blandZeroTol {
+				continue
+			}
+			copy(biCopy, basicIdxs)
+			biCopy[replace] = nonBasicIdx[minIdx]
+			abTmp := mat.NewDense(m, len(biCopy), nil)
+			extractColumns(abTmp, A, biCopy)
+			// If the condition number is reasonable, use this index.
+			if mat.Cond(abTmp, 1) < 1e16 {
+				return replace, minIdx, nil
+			}
+		}
+	}
+	return -1, -1, ErrBland
+}
+
+func verifyInputs(initialBasic []int, c []float64, A mat.Matrix, b []float64) error {
+	m, n := A.Dims()
+	if len(c) != n {
+		panic("lp: c vector incorrect length")
+	}
+	if len(b) != m {
+		panic("lp: b vector incorrect length")
+	}
+	if len(c) != n {
+		panic("lp: c vector incorrect length")
+	}
+	if len(initialBasic) != 0 && len(initialBasic) != m {
+		panic("lp: initialBasic incorrect length")
+	}
+
+	// Do some sanity checks so that ab does not become singular during the
+	// simplex solution. If the ZeroRow checks are removed then the code for
+	// finding a set of linearly indepent columns must be improved.
+
+	// Check that if a row of A only has zero elements that corresponding
+	// element in b is zero, otherwise the problem is infeasible.
+	// Otherwise return ErrZeroRow.
+	for i := 0; i < m; i++ {
+		isZero := true
+		for j := 0; j < n; j++ {
+			if A.At(i, j) != 0 {
+				isZero = false
+				break
+			}
+		}
+		if isZero && b[i] != 0 {
+			// Infeasible
+			return ErrInfeasible
+		} else if isZero {
+			return ErrZeroRow
+		}
+	}
+	// Check that if a column only has zero elements that the respective C vector
+	// is positive (otherwise unbounded). Otherwise return ErrZeroColumn.
+	for j := 0; j < n; j++ {
+		isZero := true
+		for i := 0; i < m; i++ {
+			if A.At(i, j) != 0 {
+				isZero = false
+				break
+			}
+		}
+		if isZero && c[j] < 0 {
+			return ErrUnbounded
+		} else if isZero {
+			return ErrZeroColumn
+		}
+	}
+	return nil
+}
+
+// initializeFromBasic initializes the basic feasible solution given a set of
+// basic indices. It extracts the columns of A specified by basicIdxs and finds
+// the x values at that location. These are stored into xb.
+//
+// If the columns of A are not linearly independent or if the initial set is not
+// feasible, an error is returned.
+func initializeFromBasic(xb []float64, ab *mat.Dense, b []float64) error {
+	m, _ := ab.Dims()
+	if len(xb) != m {
+		panic("simplex: bad xb length")
+	}
+	xbMat := mat.NewVecDense(m, xb)
+
+	err := xbMat.SolveVec(ab, mat.NewVecDense(m, b))
+	if err != nil {
+		return errors.New("lp: subcolumns of A for supplied initial basic singular")
+	}
+	// The solve ensures that the equality constraints are met (ab * xb = b).
+	// Thus, the solution is feasible if and only if all of the x's are positive.
+	allPos := true
+	for _, v := range xb {
+		if v < -initPosTol {
+			allPos = false
+			break
+		}
+	}
+	if !allPos {
+		return errors.New("lp: supplied subcolumns not a feasible solution")
+	}
+	return nil
+}
+
+// extractColumns copies the columns specified by cols into the columns of dst.
+func extractColumns(dst *mat.Dense, A mat.Matrix, cols []int) {
+	r, c := dst.Dims()
+	ra, _ := A.Dims()
+	if ra != r {
+		panic("simplex: row mismatch")
+	}
+	if c != len(cols) {
+		panic("simplex: column mismatch")
+	}
+	col := make([]float64, r)
+	for j, idx := range cols {
+		mat.Col(col, idx, A)
+		dst.SetCol(j, col)
+	}
+}
+
+// findInitialBasic finds an initial basic solution, and returns the basic
+// indices, ab, and xb.
+func findInitialBasic(A mat.Matrix, b []float64) ([]int, *mat.Dense, []float64, error) {
+	m, n := A.Dims()
+	basicIdxs := findLinearlyIndependent(A)
+	if len(basicIdxs) != m {
+		return nil, nil, nil, ErrSingular
+	}
+
+	// It may be that this linearly independent basis is also a feasible set. If
+	// so, the Phase I problem can be avoided.
+	ab := mat.NewDense(m, len(basicIdxs), nil)
+	extractColumns(ab, A, basicIdxs)
+	xb := make([]float64, m)
+	err := initializeFromBasic(xb, ab, b)
+	if err == nil {
+		return basicIdxs, ab, xb, nil
+	}
+
+	// This set was not feasible. Instead the "Phase I" problem must be solved
+	// to find an initial feasible set of basis.
+	//
+	// Method: Construct an LP whose optimal solution is a feasible solution
+	// to the original LP.
+	// 1) Introduce an artificial variable x_{n+1}.
+	// 2) Let x_j be the most negative element of x_b (largest constraint violation).
+	// 3) Add the artificial variable to A with:
+	//      a_{n+1} = b - \sum_{i in basicIdxs} a_i + a_j
+	//    swap j with n+1 in the basicIdxs.
+	// 4) Define a new LP:
+	//   minimize  x_{n+1}
+	//   subject to [A A_{n+1}][x_1 ... x_{n+1}] = b
+	//          x, x_{n+1} >= 0
+	// 5) Solve this LP. If x_{n+1} != 0, then the problem is infeasible, otherwise
+	// the found basis can be used as an initial basis for phase II.
+	//
+	// The extra column in Step 3 is defined such that the vector of 1s is an
+	// initial feasible solution.
+
+	// Find the largest constraint violator.
+	// Compute a_{n+1} = b - \sum{i in basicIdxs}a_i + a_j. j is in basicIDx, so
+	// instead just subtract the basicIdx columns that are not minIDx.
+	minIdx := floats.MinIdx(xb)
+	aX1 := make([]float64, m)
+	copy(aX1, b)
+	col := make([]float64, m)
+	for i, v := range basicIdxs {
+		if i == minIdx {
+			continue
+		}
+		mat.Col(col, v, A)
+		floats.Sub(aX1, col)
+	}
+
+	// Construct the new LP.
+	// aNew = [A, a_{n+1}]
+	// bNew = b
+	// cNew = 1 for x_{n+1}
+	aNew := mat.NewDense(m, n+1, nil)
+	aNew.Copy(A)
+	aNew.SetCol(n, aX1)
+	basicIdxs[minIdx] = n // swap minIdx with n in the basic set.
+	c := make([]float64, n+1)
+	c[n] = 1
+
+	// Solve the Phase I linear program.
+	_, xOpt, newBasic, err := simplex(basicIdxs, c, aNew, b, 1e-10)
+	if err != nil {
+		return nil, nil, nil, fmt.Errorf("lp: error finding feasible basis: %s", err)
+	}
+
+	// The original LP is infeasible if the added variable has non-zero value
+	// in the optimal solution to the Phase I problem.
+	if math.Abs(xOpt[n]) > phaseIZeroTol {
+		return nil, nil, nil, ErrInfeasible
+	}
+
+	// The basis found in Phase I is a feasible solution to the original LP if
+	// the added variable is not in the basis.
+	addedIdx := -1
+	for i, v := range newBasic {
+		if v == n {
+			addedIdx = i
+		}
+		xb[i] = xOpt[v]
+	}
+	if addedIdx == -1 {
+		extractColumns(ab, A, newBasic)
+		return newBasic, ab, xb, nil
+	}
+
+	// The value of the added variable is in the basis, but it has a zero value.
+	// See if exchanging another variable into the basic set finds a feasible
+	// solution.
+	basicMap := make(map[int]struct{})
+	for _, v := range newBasic {
+		basicMap[v] = struct{}{}
+	}
+	var set bool
+	for i := range xOpt {
+		if _, inBasic := basicMap[i]; inBasic {
+			continue
+		}
+		newBasic[addedIdx] = i
+		if set {
+			mat.Col(col, i, A)
+			ab.SetCol(addedIdx, col)
+		} else {
+			extractColumns(ab, A, newBasic)
+			set = true
+		}
+		err := initializeFromBasic(xb, ab, b)
+		if err == nil {
+			return newBasic, ab, xb, nil
+		}
+	}
+	return nil, nil, nil, ErrInfeasible
+}
+
+// findLinearlyIndependnt finds a set of linearly independent columns of A, and
+// returns the column indexes of the linearly independent columns.
+func findLinearlyIndependent(A mat.Matrix) []int {
+	m, n := A.Dims()
+	idxs := make([]int, 0, m)
+	columns := mat.NewDense(m, m, nil)
+	newCol := make([]float64, m)
+	// Walk in reverse order because slack variables are typically the last columns
+	// of A.
+	for i := n - 1; i >= 0; i-- {
+		if len(idxs) == m {
+			break
+		}
+		mat.Col(newCol, i, A)
+		columns.SetCol(len(idxs), newCol)
+		if len(idxs) == 0 {
+			// A column is linearly independent from the null set.
+			// If all-zero column of A are allowed, this code needs to be adjusted.
+			idxs = append(idxs, i)
+			continue
+		}
+		if mat.Cond(columns.Slice(0, m, 0, len(idxs)+1), 1) > 1e12 {
+			// Not linearly independent.
+			continue
+		}
+		idxs = append(idxs, i)
+	}
+	return idxs
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/convex/lp/simplex_test.go b/vendor/gonum.org/v1/gonum/optimize/convex/lp/simplex_test.go
new file mode 100644
index 00000000..75c759b5
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/convex/lp/simplex_test.go
@@ -0,0 +1,269 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package lp
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+)
+
+const convergenceTol = 1e-10
+
+func TestSimplex(t *testing.T) {
+	// First test specific inputs. These were collected from failures
+	// during randomized testing.
+	// TODO(btracey): Test specific problems with known solutions.
+	for _, test := range []struct {
+		A            mat.Matrix
+		b            []float64
+		c            []float64
+		tol          float64
+		initialBasic []int
+	}{
+		{
+			// Basic feasible LP
+			A: mat.NewDense(2, 4, []float64{
+				-1, 2, 1, 0,
+				3, 1, 0, 1,
+			}),
+			b: []float64{4, 9},
+			c: []float64{-1, -2, 0, 0},
+			//initialBasic: nil,
+			tol: 0,
+		},
+		{
+			// Zero row that caused linear solver failure
+			A: mat.NewDense(3, 5, []float64{0.09917822373225804, 0, 0, -0.2588175087223661, -0.5935518220870567, 1.301111422556007, 0.12220247487326946, 0, 0, -1.9194869979254463, 0, 0, 0, 0, -0.8588221231396473}),
+			b: []float64{0, 0, 0},
+			c: []float64{0, 0.598992624019304, 0, 0, 0},
+		},
+		{
+			// Case that caused linear solver failure
+			A: mat.NewDense(13, 26, []float64{-0.7001209024399848, -0.7027502615621812, -0, 0.7354444798695736, -0, 0.476457578966189, 0.7001209024399848, 0.7027502615621812, 0, -0.7354444798695736, 0, -0.476457578966189, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1.8446087238391438, -0, -0, 0.7705609478497938, -0, -0, -2.7311218710244463, 0, 0, -0.7705609478497938, 0, 0, 2.7311218710244463, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -0, 0.8332519091897401, 0.7762132098737671, -0, -0, -0.052470638647269585, 0, -0.8332519091897401, -0.7762132098737671, 0, 0, 0.052470638647269585, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.9898577208292023, 0.31653724289408824, -0, -0, 0.17797227766447388, 1.2702427184954932, -0.7998764021535656, -0.31653724289408824, 0, 0, -0.17797227766447388, -1.2702427184954932, 0.7998764021535656, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -0, -0, -0, -0, 0.4206278126213235, -0.7253374879437113, 0, 0, 0, 0, -0.4206278126213235, 0.7253374879437113, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -0, -0.7567988418466963, 0.3304567624749696, 0.8385927625193501, -0.0021606686026376387, -0, 0, 0.7567988418466963, -0.3304567624749696, -0.8385927625193501, 0.0021606686026376387, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2.230107839590404, -0.9897104202085316, -0, 0.24703471683023603, -0, -2.382860345431941, 0.6206871648345162, 0.9897104202085316, 0, -0.24703471683023603, 0, 2.382860345431941, -0.6206871648345162, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 1.4350469221322282, -0.9730343818431852, -0, 2.326429855201535, -0, -0.14347849887004038, -1.4350469221322282, 0.9730343818431852, 0, -2.326429855201535, 0, 0.14347849887004038, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -0.7943912888763849, -0.13735037357335078, -0.5101161104860161, -0, -0, -1.4790634590370297, 0.050911195996747316, 0.13735037357335078, 0.5101161104860161, 0, 0, 1.4790634590370297, -0.050911195996747316, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, -0, -0.2515400440591492, 0.2058339272568599, -0, -0, -1.314023802253438, 0, 0.2515400440591492, -0.2058339272568599, 0, 0, 1.314023802253438, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0.08279503413614919, -0.16669071891829756, -0, -0.6208413721884664, -0, -0.6348258970402827, -0.08279503413614919, 0.16669071891829756, 0, 0.6208413721884664, 0, 0.6348258970402827, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, -0, -0, 0.49634739711260845, -0, -0, -0, 0, 0, -0.49634739711260845, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, -0.2797437186631715, -0.8356683570259136, 1.8970426594969672, -0.4095711945594497, 0.45831284820623924, -0.6109615338552246, 0.2797437186631715, 0.8356683570259136, -1.8970426594969672, 0.4095711945594497, -0.45831284820623924, 0.6109615338552246, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1}),
+			b: []float64{-0.8446087238391436, 0, 1.9898577208292023, 0, 0, -2.230107839590404, 0, 0.20560871112361512, 0, 0, 0, 0, 0},
+			c: []float64{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
+		},
+		{
+			// Phase 1 of the above that panicked
+			A: mat.NewDense(26, 52, []float64{0.7001209024399848, -0, -0, -0.31653724289408824, -0, -0, 0.9897104202085316, -1.4350469221322282, 0.13735037357335078, -0, -0.08279503413614919, -0, 0.2797437186631715, -0.7001209024399848, 0, 0, 0.31653724289408824, 0, 0, -0.9897104202085316, 1.4350469221322282, -0.13735037357335078, 0, 0.08279503413614919, 0, -0.2797437186631715, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.7027502615621812, -0, -0.8332519091897401, -0, -0, 0.7567988418466963, -0, 0.9730343818431852, 0.5101161104860161, 0.2515400440591492, 0.16669071891829756, -0, 0.8356683570259136, -0.7027502615621812, 0, 0.8332519091897401, 0, 0, -0.7567988418466963, 0, -0.9730343818431852, -0.5101161104860161, -0.2515400440591492, -0.16669071891829756, 0, -0.8356683570259136, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0, -0.7705609478497938, -0.7762132098737671, -0, -0, -0.3304567624749696, -0.24703471683023603, -0, -0, -0.2058339272568599, -0, -0.49634739711260845, -1.8970426594969672, 0, 0.7705609478497938, 0.7762132098737671, 0, 0, 0.3304567624749696, 0.24703471683023603, 0, 0, 0.2058339272568599, 0, 0.49634739711260845, 1.8970426594969672, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.7354444798695736, -0, -0, -0.17797227766447388, -0, -0.8385927625193501, -0, -2.326429855201535, -0, -0, 0.6208413721884664, -0, 0.4095711945594497, 0.7354444798695736, 0, 0, 0.17797227766447388, 0, 0.8385927625193501, 0, 2.326429855201535, 0, 0, -0.6208413721884664, 0, -0.4095711945594497, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0, -0, -0, -1.2702427184954932, -0.4206278126213235, 0.0021606686026376387, 2.382860345431941, -0, 1.4790634590370297, -0, -0, -0, -0.45831284820623924, 0, 0, 0, 1.2702427184954932, 0.4206278126213235, -0.0021606686026376387, -2.382860345431941, 0, -1.4790634590370297, 0, 0, 0, 0.45831284820623924, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.476457578966189, 2.7311218710244463, 0.052470638647269585, 0.7998764021535656, 0.7253374879437113, -0, -0.6206871648345162, 0.14347849887004038, -0.050911195996747316, 1.314023802253438, 0.6348258970402827, -0, 0.6109615338552246, 0.476457578966189, -2.7311218710244463, -0.052470638647269585, -0.7998764021535656, -0.7253374879437113, 0, 0.6206871648345162, -0.14347849887004038, 0.050911195996747316, -1.314023802253438, -0.6348258970402827, 0, -0.6109615338552246, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.7001209024399848, -0, -0, 0.31653724289408824, -0, -0, -0.9897104202085316, 1.4350469221322282, -0.13735037357335078, -0, 0.08279503413614919, -0, -0.2797437186631715, 0.7001209024399848, 0, 0, -0.31653724289408824, 0, 0, 0.9897104202085316, -1.4350469221322282, 0.13735037357335078, 0, -0.08279503413614919, 0, 0.2797437186631715, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.7027502615621812, -0, 0.8332519091897401, -0, -0, -0.7567988418466963, -0, -0.9730343818431852, -0.5101161104860161, -0.2515400440591492, -0.16669071891829756, -0, -0.8356683570259136, 0.7027502615621812, 0, -0.8332519091897401, 0, 0, 0.7567988418466963, 0, 0.9730343818431852, 0.5101161104860161, 0.2515400440591492, 0.16669071891829756, 0, 0.8356683570259136, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0, 0.7705609478497938, 0.7762132098737671, -0, -0, 0.3304567624749696, 0.24703471683023603, -0, -0, 0.2058339272568599, -0, 0.49634739711260845, 1.8970426594969672, 0, -0.7705609478497938, -0.7762132098737671, 0, 0, -0.3304567624749696, -0.24703471683023603, 0, 0, -0.2058339272568599, 0, -0.49634739711260845, -1.8970426594969672, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.7354444798695736, -0, -0, 0.17797227766447388, -0, 0.8385927625193501, -0, 2.326429855201535, -0, -0, -0.6208413721884664, -0, -0.4095711945594497, -0.7354444798695736, 0, 0, -0.17797227766447388, 0, -0.8385927625193501, 0, -2.326429855201535, 0, 0, 0.6208413721884664, 0, 0.4095711945594497, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0, -0, -0, 1.2702427184954932, 0.4206278126213235, -0.0021606686026376387, -2.382860345431941, -0, -1.4790634590370297, -0, -0, -0, 0.45831284820623924, 0, 0, 0, -1.2702427184954932, -0.4206278126213235, 0.0021606686026376387, 2.382860345431941, 0, 1.4790634590370297, 0, 0, 0, -0.45831284820623924, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.476457578966189, -2.7311218710244463, -0.052470638647269585, -0.7998764021535656, -0.7253374879437113, -0, 0.6206871648345162, -0.14347849887004038, 0.050911195996747316, -1.314023802253438, -0.6348258970402827, -0, -0.6109615338552246, -0.476457578966189, 2.7311218710244463, 0.052470638647269585, 0.7998764021535656, 0.7253374879437113, 0, -0.6206871648345162, 0.14347849887004038, -0.050911195996747316, 1.314023802253438, 0.6348258970402827, 0, 0.6109615338552246, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0, -1, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0, -0, -1, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0, -0, -0, -1, -0, -0, -0, -0, -0, -0, -0, -0, -0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0, -0, -0, -0, -1, -0, -0, -0, -0, -0, -0, -0, -0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0, -0, -0, -0, -0, -1, -0, -0, -0, -0, -0, -0, -0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -0, -0, -0, -0, -0, -0, -1, -0, -0, -0, -0, -0, -0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -0, -0, -0, -0, -0, -0, -0, -1, -0, -0, -0, -0, -0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -0, -0, -0, -0, -0, -0, -0, -0, -1, -0, -0, -0, -0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -1, -0, -0, -0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -1, -0, -0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -1, -0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1.8446087238391438, 1, -0.9898577208292023, 1, 1, 2.230107839590404, 1, 0.7943912888763849, 1, 1, 1, 1, 1, -1.8446087238391438, -1, 0.9898577208292023, -1, -1, -2.230107839590404, -1, -0.7943912888763849, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}),
+			b: []float64{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
+			c: []float64{-0.8446087238391436, 0, 1.9898577208292023, 0, 0, -2.230107839590404, 0, 0.20560871112361512, 0, 0, 0, 0, 0, 0.8446087238391436, -0, -1.9898577208292023, -0, -0, 2.230107839590404, -0, -0.20560871112361512, -0, -0, -0, -0, -0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+		},
+		{
+			// Dense case that panicked.
+			A: mat.NewDense(6, 15, []float64{0.3279477313560112, 0.04126296122557327, 0.24121743535067522, -0.8676933623438741, -0.3279477313560112, -0.04126296122557327, -0.24121743535067522, 0.8676933623438741, 1, 0, 0, 0, 0, 0, 1.3702148909442915, 0.43713186538468607, 0.8613818492485417, -0.9298615442657688, -0.037784779008231184, -0.43713186538468607, -0.8613818492485417, 0.9298615442657688, 0.037784779008231184, 0, 1, 0, 0, 0, 0, 0.3478112701177931, -0, 0.748352668598051, -0.4294796840343912, -0, 0, -0.748352668598051, 0.4294796840343912, 0, 0, 0, 1, 0, 0, 0, -1, -0, 1.1913912184457485, 1.732132186658447, 0.4026384828544584, 0, -1.1913912184457485, -1.732132186658447, -0.4026384828544584, 0, 0, 0, 1, 0, 0, -0.4598555419763902, -0, 1.2088959976921831, -0.7297794575275871, 1.9835614149566971, 0, -1.2088959976921831, 0.7297794575275871, -1.9835614149566971, 0, 0, 0, 0, 1, 0, 0.5986809560819324, 0.19738159369304414, -1.0647198575836367, -0, -0.7264943883762761, -0.19738159369304414, 1.0647198575836367, 0, 0.7264943883762761, 0, 0, 0, 0, 0, 1, 0.36269644970561576}),
+			b: []float64{2.3702148909442915, 1.3478112701177931, 0, -0.4598555419763902, 1.5986809560819324, 1.3626964497056158},
+			c: []float64{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
+		},
+		{
+			A:            mat.NewDense(6, 11, []float64{-0.036551083288733854, -0.8967234664797694, 0.036551083288733854, 0.8967234664797694, 1, 0, 0, 0, 0, 0, -0.719908817815329, -1.9043311904524263, -0, 1.9043311904524263, 0, 0, 1, 0, 0, 0, 0, -1.142213296802784, -0, 0.17584914855696687, 0, -0.17584914855696687, 0, 0, 1, 0, 0, 0, -0.5423586338987796, -0.21663357118058713, -0.4815354890024489, 0.21663357118058713, 0.4815354890024489, 0, 0, 0, 1, 0, 0, -0.6864090947259134, -0, -0, 0, 0, 0, 0, 0, 0, 1, 0, 0.4091621839837596, -1.1853040616164046, -0.11374085137543871, 1.1853040616164046, 0.11374085137543871, 0, 0, 0, 0, 0, 1, -1.7416078575675549}),
+			b:            []float64{0.28009118218467105, -0.14221329680278405, 0.4576413661012204, 0.3135909052740866, 1.4091621839837596, -1.7416078575675549},
+			c:            []float64{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
+			initialBasic: []int{10, 8, 7, 6, 5, 4},
+		},
+		{
+			A:            mat.NewDense(6, 10, []float64{-0.036551083288733854, -0.8967234664797694, 0.036551083288733854, 0.8967234664797694, 1, 0, 0, 0, 0, 0, -1.9043311904524263, -0, 1.9043311904524263, 0, 0, 1, 0, 0, 0, 0, -0, 0.17584914855696687, 0, -0.17584914855696687, 0, 0, 1, 0, 0, 0, -0.21663357118058713, -0.4815354890024489, 0.21663357118058713, 0.4815354890024489, 0, 0, 0, 1, 0, 0, -0, -0, 0, 0, 0, 0, 0, 0, 1, 0, -1.1853040616164046, -0.11374085137543871, 1.1853040616164046, 0.11374085137543871, 0, 0, 0, 0, 0, 1}),
+			b:            []float64{0.28009118218467105, -0.14221329680278405, 0.4576413661012204, 0.3135909052740866, 1.4091621839837596, -1.7416078575675549},
+			c:            []float64{-1.1951160054922971, -1.354633418345746, 1.1951160054922971, 1.354633418345746, 0, 0, 0, 0, 0, 0},
+			initialBasic: []int{0, 8, 7, 6, 5, 4},
+		},
+		{
+			A:            mat.NewDense(6, 14, []float64{-0.4398035705048233, -0, -1.1190414559968929, -0, 0.4398035705048233, 0, 1.1190414559968929, 0, 1, 0, 0, 0, 0, 0, -0, 0.45892918156139395, -0, -0, 0, -0.45892918156139395, 0, 0, 0, 1, 0, 0, 0, 0, -0, -0, -0.3163051515958635, -0, 0, 0, 0.3163051515958635, 0, 0, 0, 1, 0, 0, 0, -0, -0, -1.8226051692445888, -0.8154477101733032, 0, 0, 1.8226051692445888, 0.8154477101733032, 0, 0, 0, 1, 0, 0, -0, 1.0020104354806922, -2.80863692523519, -0.8493721031516384, 0, -1.0020104354806922, 2.80863692523519, 0.8493721031516384, 0, 0, 0, 0, 1, 0, -0.8292937871394104, -1.4615144665021647, -0, -0, 0.8292937871394104, 1.4615144665021647, 0, 0, 0, 0, 0, 0, 0, 1}),
+			b:            []float64{0, -1.0154749704172474, 0, 0, 0, -1.5002324315812783},
+			c:            []float64{1.0665389045026794, 0.097366273706136, 0, 2.7928153636989954, -1.0665389045026794, -0.097366273706136, -0, -2.7928153636989954, 0, 0, 0, 0, 0, 0},
+			initialBasic: []int{5, 12, 11, 10, 0, 8},
+		},
+		{
+			// Bad Phase I setup.
+			A: mat.NewDense(6, 7, []float64{1.4009742075419371, 0, 0.05737255493210325, -2.5954004393412915, 0, 1.561789236911904, 0, 0.17152506517602673, 0, 0, 0, 0, 0, -0.3458126550149948, 1.900744052464951, -0.32773164134097343, -0.9648201331251137, 0, 0, 0, 0, -1.3229549190526497, 0.0692227703722903, 0, 0, -0.1024297720479933, 0.4550740188869777, 0, 0.013599438965679167, 0, 0, 0, 0, 0, -0.1164365105021209, 0, 0, 0.4077091957443405, 1.5682816151954875, 0.8411734682369051, 0.22379142247562167, 1.2206581060250778}),
+			b: []float64{0.3293809220378252, 0, -0.5688424847664554, 0, 0, 1.4832526082339592},
+			c: []float64{0.5246370956983506, -0.36608819899109946, 1.5854141981237713, 0.5170486527020665, 0, 1.4006819866163691, 0.7733814538809437},
+		},
+		{
+			// The problem is feasible, but the PhaseI problem keeps the last
+			// variable in the basis.
+			A:            mat.NewDense(2, 3, []float64{0.7171320440380402, 0, 0.22818288617480836, 0, -0.10030202006494793, -0.3282372661549324}),
+			b:            []float64{0.8913013436978257, 0},
+			c:            []float64{0, 0, 1.16796158316812},
+			initialBasic: nil,
+		},
+		{
+			// Case where primal was returned as feasible, but the dual was returned
+			// as infeasible. This is the dual.
+			// Here, the phase I problem returns the value in the basis but equal
+			// to epsilon and not 0.
+			A: mat.NewDense(5, 11, []float64{0.48619717875196006, 0.5089083769874058, 1.4064796473022745, -0.48619717875196006, -0.5089083769874058, -1.4064796473022745, 1, 0, 0, 0, 0, 1.5169837857318682, -0, -0, -1.5169837857318682, 0, 0, 0, 1, 0, 0, 0, -1.3096160896447528, 0.12600426735917414, 0.296082394213142, 1.3096160896447528, -0.12600426735917414, -0.296082394213142, 0, 0, 1, 0, 0, -0, -0, 1.9870800277141467, 0, 0, -1.9870800277141467, 0, 0, 0, 1, 0, -0.3822356988571877, -0, -0.1793908926957139, 0.3822356988571877, 0, 0.1793908926957139, 0, 0, 0, 0, 1}),
+			b: []float64{0.6015865977347667, 0, -1.5648780993757594, 0, 0},
+			c: []float64{-0.642801659201449, -0.5412741400343285, -1.4634460998530177, 0.642801659201449, 0.5412741400343285, 1.4634460998530177, 0, 0, 0, 0, 0},
+		},
+		{
+			// Caused linear solve error. The error is because replacing the minimum
+			// index in Bland causes the new basis to be singular. This
+			// necessitates the ending loop in bland over possible moves.
+			A: mat.NewDense(9, 23, []float64{-0.898219823758102, -0, -0, -0, 1.067555075209233, 1.581598470243863, -1.0656096883610071, 0.898219823758102, 0, 0, 0, -1.067555075209233, -1.581598470243863, 1.0656096883610071, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1.5657353278668433, 0.5798888118401012, -0, 0.14560553520321928, -0, -0, -0, 1.5657353278668433, -0.5798888118401012, 0, -0.14560553520321928, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -0, -0, -1.5572250142582087, -0, -0, -0, -0, 0, 0, 1.5572250142582087, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -0, -0, -0, -1.1266215512973428, -0, 1.0661059397023553, -0, 0, 0, 0, 1.1266215512973428, 0, -1.0661059397023553, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -0, -2.060232129551813, 1.756900609902372, -0, -0, -0, -0, 0, 2.060232129551813, -1.756900609902372, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1.0628806512935949, -0, -0, 0.3306985942820342, -0, 0.5013194822231914, -0, -1.0628806512935949, 0, 0, -0.3306985942820342, 0, -0.5013194822231914, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -0.02053916418367785, 2.0967009672108627, -0, 1.276296057052031, -0, -0.8396554873675388, -0, 0.02053916418367785, -2.0967009672108627, 0, -1.276296057052031, 0, 0.8396554873675388, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1.5173172721095745, -0, -0, -0, -0, -0.7781977786718928, -0.08927683907374018, 1.5173172721095745, 0, 0, 0, 0, 0.7781977786718928, 0.08927683907374018, 0, 0, 0, 0, 0, 0, 0, 1, 0, -0, -0, -0, -0, -0, 0.39773149008355624, -0, 0, 0, 0, 0, 0, -0.39773149008355624, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}),
+			b: []float64{0, 0, 0, 0, 0, 0, 0, 0, 0},
+			c: []float64{0.24547850255842107, -0.9373919913433648, 0, 0, 0, 0.2961224049153204, 0, -0.24547850255842107, 0.9373919913433648, -0, -0, -0, -0.2961224049153204, -0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+		},
+		{
+			// Caused error because ALL of the possible replacements in Bland cause.
+			// ab to be singular. This necessitates outer loop in bland over possible
+			// moves.
+			A:            mat.NewDense(9, 23, []float64{0.6595219196440785, -0, -0, -1.8259394918781682, -0, -0, 0.005457361044175046, -0.6595219196440785, 0, 0, 1.8259394918781682, 0, 0, -0.005457361044175046, 1, 0, 0, 0, 0, 0, 0, 0, 0, -0, -0.10352878714214864, -0, -0, -0, -0, 0.5945016966696087, 0, 0.10352878714214864, 0, 0, 0, 0, -0.5945016966696087, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0.31734882842876444, -0, -0, -0, -0, -0, -0.716633126367685, -0.31734882842876444, 0, 0, 0, 0, 0, 0.716633126367685, 0, 0, 1, 0, 0, 0, 0, 0, 0, -0.7769812182932578, -0, -0.17370050158829553, 0.19405062263734607, -0, 1.1472330031002533, -0.6776631768730962, 0.7769812182932578, 0, 0.17370050158829553, -0.19405062263734607, 0, -1.1472330031002533, 0.6776631768730962, 0, 0, 0, 1, 0, 0, 0, 0, 0, -0, 0.8285611486611473, -0, -0, -0, -0, -0, 0, -0.8285611486611473, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2.088953453647358, 1.3286488791152795, -0, -0, -0, -0, 0.9147833235021142, 2.088953453647358, -1.3286488791152795, 0, 0, 0, 0, -0.9147833235021142, 0, 0, 0, 0, 0, 1, 0, 0, 0, -0, -0, -0, -0, 0.6560365621262937, -0, -0, 0, 0, 0, 0, -0.6560365621262937, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0.8957188338098074, -0, -0, -0, -0, -0, -0, -0.8957188338098074, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -0.2761381891117365, -0, -0, -0, 1.1154921426237823, 0.06429872020552618, -0, 0.2761381891117365, 0, 0, 0, -1.1154921426237823, -0.06429872020552618, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}),
+			b:            []float64{0, 0, 0, 0, 0.5046208538522362, 1.0859412982429362, -2.066283584195025, 0, -0.2604305274353169},
+			c:            []float64{0, 0, 0, 0, 0, 0, -0.05793762969330718, -0, -0, -0, -0, -0, -0, 0.05793762969330718, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+			initialBasic: []int{22, 11, 7, 19, 18, 17, 16, 15, 14},
+		},
+		{
+			// Caused initial supplied basis of Phase I to be singular.
+			A: mat.NewDense(7, 11, []float64{0, 0, 0, 0, 0, 0.6667874223914787, -0.04779440888372957, -0.810020924434026, 0, 1.4190243477163373, 0, 0, 1.0452496826112936, 1.1966134226828076, 0, 0, 0, 0, -0.676136041089015, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2.123232807871834, 0.2795467733707712, 0.21997115467272987, 0, -0.1572003980840453, 0, 0, 0, 0, 0.5130196002804861, 0, -0.005957174211761673, 0.3262874931735277, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.5582052881594286, 0, 0.3544026193217651, 0, -1.0761986709145068, 0, 0.2438593072108347, 0, 0, 0, 0, 1.387509848081664, 0, 0, 0.3958750570508226, 1.6281679612990678, 0, 0, -0.24638311667922103, 0, 0, 0, 0, 0, 0, -0.628850893994423}),
+			b: []float64{0.4135281763629115, 0, 0, 0, 0, 0, 0},
+			c: []float64{0.5586772876113472, 0, 0.14261332948424457, 0, -0.016394076753000086, -0.506087285562544, 0, 0.37619482505459145, 1.2943822852419233, 0.5887960293578207, 0},
+		},
+	} {
+		testSimplex(t, test.initialBasic, test.c, test.A, test.b, convergenceTol)
+	}
+
+	rnd := rand.New(rand.NewSource(1))
+	// Randomized tests
+	testRandomSimplex(t, 20000, 0.7, 10, rnd)
+	testRandomSimplex(t, 20000, 0, 10, rnd)
+	testRandomSimplex(t, 200, 0, 100, rnd)
+	testRandomSimplex(t, 2, 0, 400, rnd)
+}
+
+func testRandomSimplex(t *testing.T, nTest int, pZero float64, maxN int, rnd *rand.Rand) {
+	// Try a bunch of random LPs
+	for i := 0; i < nTest; i++ {
+		n := rnd.Intn(maxN) + 2 // n must be at least two.
+		m := rnd.Intn(n-1) + 1  // m must be between 1 and n
+		if m == 0 || n == 0 {
+			continue
+		}
+		randValue := func() float64 {
+			//var pZero float64
+			v := rnd.Float64()
+			if v < pZero {
+				return 0
+			}
+			return rnd.NormFloat64()
+		}
+		a := mat.NewDense(m, n, nil)
+		for i := 0; i < m; i++ {
+			for j := 0; j < n; j++ {
+				a.Set(i, j, randValue())
+			}
+		}
+		b := make([]float64, m)
+		for i := range b {
+			b[i] = randValue()
+		}
+
+		c := make([]float64, n)
+		for i := range c {
+			c[i] = randValue()
+		}
+
+		testSimplex(t, nil, c, a, b, convergenceTol)
+	}
+}
+
+func testSimplex(t *testing.T, initialBasic []int, c []float64, a mat.Matrix, b []float64, convergenceTol float64) error {
+	primalOpt, primalX, _, errPrimal := simplex(initialBasic, c, a, b, convergenceTol)
+	if errPrimal == nil {
+		// No error solving the simplex, check that the solution is feasible.
+		var bCheck mat.VecDense
+		bCheck.MulVec(a, mat.NewVecDense(len(primalX), primalX))
+		if !mat.EqualApprox(&bCheck, mat.NewVecDense(len(b), b), 1e-10) {
+			t.Errorf("No error in primal but solution infeasible")
+		}
+	}
+
+	primalInfeasible := errPrimal == ErrInfeasible
+	primalUnbounded := errPrimal == ErrUnbounded
+	primalBounded := errPrimal == nil
+	primalASingular := errPrimal == ErrSingular
+	primalZeroRow := errPrimal == ErrZeroRow
+	primalZeroCol := errPrimal == ErrZeroColumn
+
+	primalBad := !primalInfeasible && !primalUnbounded && !primalBounded && !primalASingular && !primalZeroRow && !primalZeroCol
+
+	// It's an error if it's not one of the known returned errors. If it's
+	// singular the problem is undefined and so the result cannot be compared
+	// to the dual.
+	if errPrimal == ErrSingular || primalBad {
+		if primalBad {
+			t.Errorf("non-known error returned: %s", errPrimal)
+		}
+		return errPrimal
+	}
+
+	// Compare the result to the answer found from solving the dual LP.
+
+	// Construct and solve the dual LP.
+	// Standard Form:
+	//  minimize c^T * x
+	//    subject to  A * x = b, x >= 0
+	// The dual of this problem is
+	//  maximize -b^T * nu
+	//   subject to A^T * nu + c >= 0
+	// Which is
+	//   minimize b^T * nu
+	//   subject to -A^T * nu <= c
+
+	negAT := &mat.Dense{}
+	negAT.Clone(a.T())
+	negAT.Scale(-1, negAT)
+	cNew, aNew, bNew := Convert(b, negAT, c, nil, nil)
+
+	dualOpt, dualX, _, errDual := simplex(nil, cNew, aNew, bNew, convergenceTol)
+	if errDual == nil {
+		// Check that the dual is feasible
+		var bCheck mat.VecDense
+		bCheck.MulVec(aNew, mat.NewVecDense(len(dualX), dualX))
+		if !mat.EqualApprox(&bCheck, mat.NewVecDense(len(bNew), bNew), 1e-10) {
+			t.Errorf("No error in dual but solution infeasible")
+		}
+	}
+
+	// Check about the zero status.
+	if errPrimal == ErrZeroRow || errPrimal == ErrZeroColumn {
+		return errPrimal
+	}
+
+	// If the primal problem is feasible, then the primal and the dual should
+	// be the same answer. We have flopped the sign in the dual (minimizing
+	// b^T *nu instead of maximizing -b^T*nu), so flip it back.
+	if errPrimal == nil {
+		if errDual != nil {
+			t.Errorf("Primal feasible but dual errored: %s", errDual)
+		}
+		dualOpt *= -1
+		if !floats.EqualWithinAbsOrRel(dualOpt, primalOpt, convergenceTol, convergenceTol) {
+			t.Errorf("Primal and dual value mismatch. Primal %v, dual %v.", primalOpt, dualOpt)
+		}
+	}
+	// If the primal problem is unbounded, then the dual should be infeasible.
+	if errPrimal == ErrUnbounded && errDual != ErrInfeasible {
+		t.Errorf("Primal unbounded but dual not infeasible. ErrDual = %s", errDual)
+	}
+
+	// If the dual is unbounded, then the primal should be infeasible.
+	if errDual == ErrUnbounded && errPrimal != ErrInfeasible {
+		t.Errorf("Dual unbounded but primal not infeasible. ErrDual = %s", errPrimal)
+	}
+
+	// If the primal is infeasible, then the dual should be either infeasible
+	// or unbounded.
+	if errPrimal == ErrInfeasible {
+		if errDual != ErrUnbounded && errDual != ErrInfeasible && errDual != ErrZeroColumn {
+			t.Errorf("Primal infeasible but dual not infeasible or unbounded: %s", errDual)
+		}
+	}
+
+	return errPrimal
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/convex/lp/simplexexample_test.go b/vendor/gonum.org/v1/gonum/optimize/convex/lp/simplexexample_test.go
new file mode 100644
index 00000000..b0daa314
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/convex/lp/simplexexample_test.go
@@ -0,0 +1,29 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package lp_test
+
+import (
+	"fmt"
+	"log"
+
+	"gonum.org/v1/gonum/mat"
+	"gonum.org/v1/gonum/optimize/convex/lp"
+)
+
+func ExampleSimplex() {
+	c := []float64{-1, -2, 0, 0}
+	A := mat.NewDense(2, 4, []float64{-1, 2, 1, 0, 3, 1, 0, 1})
+	b := []float64{4, 9}
+
+	opt, x, err := lp.Simplex(c, A, b, 0, nil)
+	if err != nil {
+		log.Fatal(err)
+	}
+	fmt.Printf("opt: %v\n", opt)
+	fmt.Printf("x: %v\n", x)
+	// Output:
+	// opt: -8
+	// x: [2 3 0 0]
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/doc.go b/vendor/gonum.org/v1/gonum/optimize/doc.go
new file mode 100644
index 00000000..1b05a639
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package optimize implements algorithms for finding the optimum value of functions.
+package optimize // import "gonum.org/v1/gonum/optimize"
diff --git a/vendor/gonum.org/v1/gonum/optimize/errors.go b/vendor/gonum.org/v1/gonum/optimize/errors.go
new file mode 100644
index 00000000..07bf5df9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/errors.go
@@ -0,0 +1,72 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package optimize
+
+import (
+	"errors"
+	"fmt"
+	"math"
+)
+
+var (
+	// ErrZeroDimensional signifies an optimization was called with an input of length 0.
+	ErrZeroDimensional = errors.New("optimize: zero dimensional input")
+
+	// ErrLinesearcherFailure signifies that a Linesearcher has iterated too
+	// many times. This may occur if the gradient tolerance is set too low.
+	ErrLinesearcherFailure = errors.New("linesearch: failed to converge")
+
+	// ErrNonDescentDirection signifies that LinesearchMethod has received a
+	// search direction from a NextDirectioner in which the function is not
+	// decreasing.
+	ErrNonDescentDirection = errors.New("linesearch: non-descent search direction")
+
+	// ErrNoProgress signifies that LinesearchMethod cannot make further
+	// progress because there is no change in location after Linesearcher step
+	// due to floating-point arithmetic.
+	ErrNoProgress = errors.New("linesearch: no change in location after Linesearcher step")
+
+	// ErrLinesearcherBound signifies that a Linesearcher reached a step that
+	// lies out of allowed bounds.
+	ErrLinesearcherBound = errors.New("linesearch: step out of bounds")
+)
+
+// ErrFunc is returned when an initial function value is invalid. The error
+// state may be either +Inf or NaN. ErrFunc satisfies the error interface.
+type ErrFunc float64
+
+func (err ErrFunc) Error() string {
+	switch {
+	case math.IsInf(float64(err), 1):
+		return "optimize: initial function value is infinite"
+	case math.IsNaN(float64(err)):
+		return "optimize: initial function value is NaN"
+	default:
+		panic("optimize: bad ErrFunc")
+	}
+}
+
+// ErrGrad is returned when an initial gradient is invalid. The error gradient
+// may be either ±Inf or NaN. ErrGrad satisfies the error interface.
+type ErrGrad struct {
+	Grad  float64 // Grad is the invalid gradient value.
+	Index int     // Index is the position at which the invalid gradient was found.
+}
+
+func (err ErrGrad) Error() string {
+	switch {
+	case math.IsInf(err.Grad, 0):
+		return fmt.Sprintf("optimize: initial gradient is infinite at position %d", err.Index)
+	case math.IsNaN(err.Grad):
+		return fmt.Sprintf("optimize: initial gradient is NaN at position %d", err.Index)
+	default:
+		panic("optimize: bad ErrGrad")
+	}
+}
+
+// List of shared panic strings
+var (
+	badProblem = "optimize: objective function is undefined"
+)
diff --git a/vendor/gonum.org/v1/gonum/optimize/functionconvergence.go b/vendor/gonum.org/v1/gonum/optimize/functionconvergence.go
new file mode 100644
index 00000000..c532072d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/functionconvergence.go
@@ -0,0 +1,40 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package optimize
+
+import "math"
+
+// FunctionConverge tests for the convergence of function values. See comment
+// in Settings.
+type FunctionConverge struct {
+	Absolute   float64
+	Relative   float64
+	Iterations int
+
+	best float64
+	iter int
+}
+
+func (fc *FunctionConverge) Init(f float64) {
+	fc.best = f
+	fc.iter = 0
+}
+
+func (fc *FunctionConverge) FunctionConverged(f float64) Status {
+	if fc.Iterations == 0 {
+		return NotTerminated
+	}
+	maxAbs := math.Max(math.Abs(f), math.Abs(fc.best))
+	if f < fc.best && fc.best-f > fc.Relative*maxAbs+fc.Absolute {
+		fc.best = f
+		fc.iter = 0
+		return NotTerminated
+	}
+	fc.iter++
+	if fc.iter < fc.Iterations {
+		return NotTerminated
+	}
+	return FunctionConvergence
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/functions/doc.go b/vendor/gonum.org/v1/gonum/optimize/functions/doc.go
new file mode 100644
index 00000000..3bdfe8bf
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/functions/doc.go
@@ -0,0 +1,15 @@
+// Copyright ©2017 The Gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package functions provides objective functions for testing optimization
+// algorithms.
+//
+// We encourage outside contributions of additional test functions that exhibit
+// properties not already covered in the testing suite or that have
+// significance due to prior use as benchmark cases.
+package functions // import "gonum.org/v1/gonum/optimize/functions"
+
+const (
+	badInputDim = "functions: wrong input dimension"
+)
diff --git a/vendor/gonum.org/v1/gonum/optimize/functions/functions.go b/vendor/gonum.org/v1/gonum/optimize/functions/functions.go
new file mode 100644
index 00000000..43a4c948
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/functions/functions.go
@@ -0,0 +1,1818 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package functions
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+)
+
+// Beale implements the Beale's function.
+//
+// Standard starting points:
+//  Easy: [1, 1]
+//  Hard: [1, 4]
+//
+// References:
+//  - Beale, E.: On an Iterative Method for Finding a Local Minimum of a
+//    Function of More than One Variable. Technical Report 25, Statistical
+//    Techniques Research Group, Princeton University (1958)
+//  - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
+//    optimization software. ACM Trans Math Softw 7 (1981), 17-41
+type Beale struct{}
+
+func (Beale) Func(x []float64) float64 {
+	if len(x) != 2 {
+		panic("dimension of the problem must be 2")
+	}
+
+	f1 := 1.5 - x[0]*(1-x[1])
+	f2 := 2.25 - x[0]*(1-x[1]*x[1])
+	f3 := 2.625 - x[0]*(1-x[1]*x[1]*x[1])
+	return f1*f1 + f2*f2 + f3*f3
+}
+
+func (Beale) Grad(grad, x []float64) {
+	if len(x) != 2 {
+		panic("dimension of the problem must be 2")
+	}
+	if len(x) != len(grad) {
+		panic("incorrect size of the gradient")
+	}
+
+	t1 := 1 - x[1]
+	t2 := 1 - x[1]*x[1]
+	t3 := 1 - x[1]*x[1]*x[1]
+
+	f1 := 1.5 - x[0]*t1
+	f2 := 2.25 - x[0]*t2
+	f3 := 2.625 - x[0]*t3
+
+	grad[0] = -2 * (f1*t1 + f2*t2 + f3*t3)
+	grad[1] = 2 * x[0] * (f1 + 2*f2*x[1] + 3*f3*x[1]*x[1])
+}
+
+func (Beale) Hess(hess mat.MutableSymmetric, x []float64) {
+	if len(x) != 2 {
+		panic("dimension of the problem must be 2")
+	}
+	if len(x) != hess.Symmetric() {
+		panic("incorrect size of the Hessian")
+	}
+
+	t1 := 1 - x[1]
+	t2 := 1 - x[1]*x[1]
+	t3 := 1 - x[1]*x[1]*x[1]
+	f1 := 1.5 - x[1]*t1
+	f2 := 2.25 - x[1]*t2
+	f3 := 2.625 - x[1]*t3
+
+	h00 := 2 * (t1*t1 + t2*t2 + t3*t3)
+	h01 := 2 * (f1 + x[1]*(2*f2+3*x[1]*f3) - x[0]*(t1+x[1]*(2*t2+3*x[1]*t3)))
+	h11 := 2 * x[0] * (x[0] + 2*f2 + x[1]*(6*f3+x[0]*x[1]*(4+9*x[1]*x[1])))
+	hess.SetSym(0, 0, h00)
+	hess.SetSym(0, 1, h01)
+	hess.SetSym(1, 1, h11)
+}
+
+func (Beale) Minima() []Minimum {
+	return []Minimum{
+		{
+			X:      []float64{3, 0.5},
+			F:      0,
+			Global: true,
+		},
+	}
+}
+
+// BiggsEXP2 implements the the Biggs' EXP2 function.
+//
+// Standard starting point:
+//  [1, 2]
+//
+// Reference:
+//  Biggs, M.C.: Minimization algorithms making use of non-quadratic properties
+//  of the objective function. IMA J Appl Math 8 (1971), 315-327; doi:10.1093/imamat/8.3.315
+type BiggsEXP2 struct{}
+
+func (BiggsEXP2) Func(x []float64) (sum float64) {
+	if len(x) != 2 {
+		panic("dimension of the problem must be 2")
+	}
+
+	for i := 1; i <= 10; i++ {
+		z := float64(i) / 10
+		y := math.Exp(-z) - 5*math.Exp(-10*z)
+		f := math.Exp(-x[0]*z) - 5*math.Exp(-x[1]*z) - y
+		sum += f * f
+	}
+	return sum
+}
+
+func (BiggsEXP2) Grad(grad, x []float64) {
+	if len(x) != 2 {
+		panic("dimension of the problem must be 2")
+	}
+	if len(x) != len(grad) {
+		panic("incorrect size of the gradient")
+	}
+
+	for i := range grad {
+		grad[i] = 0
+	}
+	for i := 1; i <= 10; i++ {
+		z := float64(i) / 10
+		y := math.Exp(-z) - 5*math.Exp(-10*z)
+		f := math.Exp(-x[0]*z) - 5*math.Exp(-x[1]*z) - y
+
+		dfdx0 := -z * math.Exp(-x[0]*z)
+		dfdx1 := 5 * z * math.Exp(-x[1]*z)
+
+		grad[0] += 2 * f * dfdx0
+		grad[1] += 2 * f * dfdx1
+	}
+}
+
+func (BiggsEXP2) Minima() []Minimum {
+	return []Minimum{
+		{
+			X:      []float64{1, 10},
+			F:      0,
+			Global: true,
+		},
+	}
+}
+
+// BiggsEXP3 implements the the Biggs' EXP3 function.
+//
+// Standard starting point:
+//  [1, 2, 1]
+//
+// Reference:
+//  Biggs, M.C.: Minimization algorithms making use of non-quadratic properties
+//  of the objective function. IMA J Appl Math 8 (1971), 315-327; doi:10.1093/imamat/8.3.315
+type BiggsEXP3 struct{}
+
+func (BiggsEXP3) Func(x []float64) (sum float64) {
+	if len(x) != 3 {
+		panic("dimension of the problem must be 3")
+	}
+
+	for i := 1; i <= 10; i++ {
+		z := float64(i) / 10
+		y := math.Exp(-z) - 5*math.Exp(-10*z)
+		f := math.Exp(-x[0]*z) - x[2]*math.Exp(-x[1]*z) - y
+		sum += f * f
+	}
+	return sum
+}
+
+func (BiggsEXP3) Grad(grad, x []float64) {
+	if len(x) != 3 {
+		panic("dimension of the problem must be 3")
+	}
+	if len(x) != len(grad) {
+		panic("incorrect size of the gradient")
+	}
+
+	for i := range grad {
+		grad[i] = 0
+	}
+	for i := 1; i <= 10; i++ {
+		z := float64(i) / 10
+		y := math.Exp(-z) - 5*math.Exp(-10*z)
+		f := math.Exp(-x[0]*z) - x[2]*math.Exp(-x[1]*z) - y
+
+		dfdx0 := -z * math.Exp(-x[0]*z)
+		dfdx1 := x[2] * z * math.Exp(-x[1]*z)
+		dfdx2 := -math.Exp(-x[1] * z)
+
+		grad[0] += 2 * f * dfdx0
+		grad[1] += 2 * f * dfdx1
+		grad[2] += 2 * f * dfdx2
+	}
+}
+
+func (BiggsEXP3) Minima() []Minimum {
+	return []Minimum{
+		{
+			X:      []float64{1, 10, 5},
+			F:      0,
+			Global: true,
+		},
+	}
+}
+
+// BiggsEXP4 implements the the Biggs' EXP4 function.
+//
+// Standard starting point:
+//  [1, 2, 1, 1]
+//
+// Reference:
+//  Biggs, M.C.: Minimization algorithms making use of non-quadratic properties
+//  of the objective function. IMA J Appl Math 8 (1971), 315-327; doi:10.1093/imamat/8.3.315
+type BiggsEXP4 struct{}
+
+func (BiggsEXP4) Func(x []float64) (sum float64) {
+	if len(x) != 4 {
+		panic("dimension of the problem must be 4")
+	}
+
+	for i := 1; i <= 10; i++ {
+		z := float64(i) / 10
+		y := math.Exp(-z) - 5*math.Exp(-10*z)
+		f := x[2]*math.Exp(-x[0]*z) - x[3]*math.Exp(-x[1]*z) - y
+		sum += f * f
+	}
+	return sum
+}
+
+func (BiggsEXP4) Grad(grad, x []float64) {
+	if len(x) != 4 {
+		panic("dimension of the problem must be 4")
+	}
+	if len(x) != len(grad) {
+		panic("incorrect size of the gradient")
+	}
+
+	for i := range grad {
+		grad[i] = 0
+	}
+	for i := 1; i <= 10; i++ {
+		z := float64(i) / 10
+		y := math.Exp(-z) - 5*math.Exp(-10*z)
+		f := x[2]*math.Exp(-x[0]*z) - x[3]*math.Exp(-x[1]*z) - y
+
+		dfdx0 := -z * x[2] * math.Exp(-x[0]*z)
+		dfdx1 := z * x[3] * math.Exp(-x[1]*z)
+		dfdx2 := math.Exp(-x[0] * z)
+		dfdx3 := -math.Exp(-x[1] * z)
+
+		grad[0] += 2 * f * dfdx0
+		grad[1] += 2 * f * dfdx1
+		grad[2] += 2 * f * dfdx2
+		grad[3] += 2 * f * dfdx3
+	}
+}
+
+func (BiggsEXP4) Minima() []Minimum {
+	return []Minimum{
+		{
+			X:      []float64{1, 10, 1, 5},
+			F:      0,
+			Global: true,
+		},
+	}
+}
+
+// BiggsEXP5 implements the the Biggs' EXP5 function.
+//
+// Standard starting point:
+//  [1, 2, 1, 1, 1]
+//
+// Reference:
+//  Biggs, M.C.: Minimization algorithms making use of non-quadratic properties
+//  of the objective function. IMA J Appl Math 8 (1971), 315-327; doi:10.1093/imamat/8.3.315
+type BiggsEXP5 struct{}
+
+func (BiggsEXP5) Func(x []float64) (sum float64) {
+	if len(x) != 5 {
+		panic("dimension of the problem must be 5")
+	}
+
+	for i := 1; i <= 11; i++ {
+		z := float64(i) / 10
+		y := math.Exp(-z) - 5*math.Exp(-10*z) + 3*math.Exp(-4*z)
+		f := x[2]*math.Exp(-x[0]*z) - x[3]*math.Exp(-x[1]*z) + 3*math.Exp(-x[4]*z) - y
+		sum += f * f
+	}
+	return sum
+}
+
+func (BiggsEXP5) Grad(grad, x []float64) {
+	if len(x) != 5 {
+		panic("dimension of the problem must be 5")
+	}
+	if len(x) != len(grad) {
+		panic("incorrect size of the gradient")
+	}
+
+	for i := range grad {
+		grad[i] = 0
+	}
+	for i := 1; i <= 11; i++ {
+		z := float64(i) / 10
+		y := math.Exp(-z) - 5*math.Exp(-10*z) + 3*math.Exp(-4*z)
+		f := x[2]*math.Exp(-x[0]*z) - x[3]*math.Exp(-x[1]*z) + 3*math.Exp(-x[4]*z) - y
+
+		dfdx0 := -z * x[2] * math.Exp(-x[0]*z)
+		dfdx1 := z * x[3] * math.Exp(-x[1]*z)
+		dfdx2 := math.Exp(-x[0] * z)
+		dfdx3 := -math.Exp(-x[1] * z)
+		dfdx4 := -3 * z * math.Exp(-x[4]*z)
+
+		grad[0] += 2 * f * dfdx0
+		grad[1] += 2 * f * dfdx1
+		grad[2] += 2 * f * dfdx2
+		grad[3] += 2 * f * dfdx3
+		grad[4] += 2 * f * dfdx4
+	}
+}
+
+func (BiggsEXP5) Minima() []Minimum {
+	return []Minimum{
+		{
+			X:      []float64{1, 10, 1, 5, 4},
+			F:      0,
+			Global: true,
+		},
+	}
+}
+
+// BiggsEXP6 implements the the Biggs' EXP6 function.
+//
+// Standard starting point:
+//  [1, 2, 1, 1, 1, 1]
+//
+// References:
+//  - Biggs, M.C.: Minimization algorithms making use of non-quadratic
+//    properties of the objective function. IMA J Appl Math 8 (1971), 315-327;
+//    doi:10.1093/imamat/8.3.315
+//  - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
+//    optimization software. ACM Trans Math Softw 7 (1981), 17-41
+type BiggsEXP6 struct{}
+
+func (BiggsEXP6) Func(x []float64) (sum float64) {
+	if len(x) != 6 {
+		panic("dimension of the problem must be 6")
+	}
+
+	for i := 1; i <= 13; i++ {
+		z := float64(i) / 10
+		y := math.Exp(-z) - 5*math.Exp(-10*z) + 3*math.Exp(-4*z)
+		f := x[2]*math.Exp(-x[0]*z) - x[3]*math.Exp(-x[1]*z) + x[5]*math.Exp(-x[4]*z) - y
+		sum += f * f
+	}
+	return sum
+}
+
+func (BiggsEXP6) Grad(grad, x []float64) {
+	if len(x) != 6 {
+		panic("dimension of the problem must be 6")
+	}
+	if len(x) != len(grad) {
+		panic("incorrect size of the gradient")
+	}
+
+	for i := range grad {
+		grad[i] = 0
+	}
+	for i := 1; i <= 13; i++ {
+		z := float64(i) / 10
+		y := math.Exp(-z) - 5*math.Exp(-10*z) + 3*math.Exp(-4*z)
+		f := x[2]*math.Exp(-x[0]*z) - x[3]*math.Exp(-x[1]*z) + x[5]*math.Exp(-x[4]*z) - y
+
+		dfdx0 := -z * x[2] * math.Exp(-x[0]*z)
+		dfdx1 := z * x[3] * math.Exp(-x[1]*z)
+		dfdx2 := math.Exp(-x[0] * z)
+		dfdx3 := -math.Exp(-x[1] * z)
+		dfdx4 := -z * x[5] * math.Exp(-x[4]*z)
+		dfdx5 := math.Exp(-x[4] * z)
+
+		grad[0] += 2 * f * dfdx0
+		grad[1] += 2 * f * dfdx1
+		grad[2] += 2 * f * dfdx2
+		grad[3] += 2 * f * dfdx3
+		grad[4] += 2 * f * dfdx4
+		grad[5] += 2 * f * dfdx5
+	}
+}
+
+func (BiggsEXP6) Minima() []Minimum {
+	return []Minimum{
+		{
+			X:      []float64{1, 10, 1, 5, 4, 3},
+			F:      0,
+			Global: true,
+		},
+		{
+			X: []float64{1.7114159947956764, 17.68319817846745, 1.1631436609697268,
+				5.1865615510738605, 1.7114159947949301, 1.1631436609697998},
+			F:      0.005655649925499929,
+			Global: false,
+		},
+		{
+			// X: []float64{1.22755594752403, X[1] >> 0, 0.83270306333466, X[3] << 0, X[4] = X[0], X[5] = X[2]},
+			X:      []float64{1.22755594752403, 1000, 0.83270306333466, -1000, 1.22755594752403, 0.83270306333466},
+			F:      0.306366772624790,
+			Global: false,
+		},
+	}
+}
+
+// Box3D implements the Box' three-dimensional function.
+//
+// Standard starting point:
+//  [0, 10, 20]
+//
+// References:
+//  - Box, M.J.: A comparison of several current optimization methods, and the
+//    use of transformations in constrained problems. Comput J 9 (1966), 67-77
+//  - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
+//    optimization software. ACM Trans Math Softw 7 (1981), 17-41
+type Box3D struct{}
+
+func (Box3D) Func(x []float64) (sum float64) {
+	if len(x) != 3 {
+		panic("dimension of the problem must be 3")
+	}
+
+	for i := 1; i <= 10; i++ {
+		c := -float64(i) / 10
+		y := math.Exp(c) - math.Exp(10*c)
+		f := math.Exp(c*x[0]) - math.Exp(c*x[1]) - x[2]*y
+		sum += f * f
+	}
+	return sum
+}
+
+func (Box3D) Grad(grad, x []float64) {
+	if len(x) != 3 {
+		panic("dimension of the problem must be 3")
+	}
+	if len(x) != len(grad) {
+		panic("incorrect size of the gradient")
+	}
+
+	grad[0] = 0
+	grad[1] = 0
+	grad[2] = 0
+	for i := 1; i <= 10; i++ {
+		c := -float64(i) / 10
+		y := math.Exp(c) - math.Exp(10*c)
+		f := math.Exp(c*x[0]) - math.Exp(c*x[1]) - x[2]*y
+		grad[0] += 2 * f * c * math.Exp(c*x[0])
+		grad[1] += -2 * f * c * math.Exp(c*x[1])
+		grad[2] += -2 * f * y
+	}
+}
+
+func (Box3D) Minima() []Minimum {
+	return []Minimum{
+		{
+			X:      []float64{1, 10, 1},
+			F:      0,
+			Global: true,
+		},
+		{
+			X:      []float64{10, 1, -1},
+			F:      0,
+			Global: true,
+		},
+		{
+			// Any point at the line {a, a, 0}.
+			X:      []float64{1, 1, 0},
+			F:      0,
+			Global: true,
+		},
+	}
+}
+
+// BraninHoo implements the Branin-Hoo function. BraninHoo is a 2-dimensional
+// test function with three global minima. It is typically evaluated in the domain
+// x_0 ∈ [-5, 10], x_1 ∈ [0, 15].
+//  f(x) = (x_1 - (5.1/(4π^2))*x_0^2 + (5/π)*x_0 - 6)^2 + 10*(1-1/(8π))cos(x_0) + 10
+// It has a minimum value of 0.397887 at x^* = {(-π, 12.275), (π, 2.275), (9.424778, 2.475)}
+//
+// Reference:
+//  https://www.sfu.ca/~ssurjano/branin.html (obtained June 2017)
+type BraninHoo struct{}
+
+func (BraninHoo) Func(x []float64) float64 {
+	if len(x) != 2 {
+		panic("functions: dimension of the problem must be 2")
+	}
+	a, b, c, r, s, t := 1.0, 5.1/(4*math.Pi*math.Pi), 5/math.Pi, 6.0, 10.0, 1/(8*math.Pi)
+
+	term := x[1] - b*x[0]*x[0] + c*x[0] - r
+	return a*term*term + s*(1-t)*math.Cos(x[0]) + s
+}
+
+func (BraninHoo) Minima() []Minimum {
+	return []Minimum{
+		{
+			X:      []float64{-math.Pi, 12.275},
+			F:      0.397887,
+			Global: true,
+		},
+		{
+			X:      []float64{math.Pi, 2.275},
+			F:      0.397887,
+			Global: true,
+		},
+		{
+			X:      []float64{9.424778, 2.475},
+			F:      0.397887,
+			Global: true,
+		},
+	}
+}
+
+// BrownBadlyScaled implements the Brown's badly scaled function.
+//
+// Standard starting point:
+//  [1, 1]
+//
+// References:
+//  - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
+//    optimization software. ACM Trans Math Softw 7 (1981), 17-41
+type BrownBadlyScaled struct{}
+
+func (BrownBadlyScaled) Func(x []float64) float64 {
+	if len(x) != 2 {
+		panic("dimension of the problem must be 2")
+	}
+
+	f1 := x[0] - 1e6
+	f2 := x[1] - 2e-6
+	f3 := x[0]*x[1] - 2
+	return f1*f1 + f2*f2 + f3*f3
+}
+
+func (BrownBadlyScaled) Grad(grad, x []float64) {
+	if len(x) != 2 {
+		panic("dimension of the problem must be 2")
+	}
+	if len(x) != len(grad) {
+		panic("incorrect size of the gradient")
+	}
+
+	f1 := x[0] - 1e6
+	f2 := x[1] - 2e-6
+	f3 := x[0]*x[1] - 2
+	grad[0] = 2*f1 + 2*f3*x[1]
+	grad[1] = 2*f2 + 2*f3*x[0]
+}
+
+func (BrownBadlyScaled) Hess(hess mat.MutableSymmetric, x []float64) {
+	if len(x) != 2 {
+		panic("dimension of the problem must be 2")
+	}
+	if len(x) != hess.Symmetric() {
+		panic("incorrect size of the Hessian")
+	}
+
+	h00 := 2 + 2*x[1]*x[1]
+	h01 := 4*x[0]*x[1] - 4
+	h11 := 2 + 2*x[0]*x[0]
+	hess.SetSym(0, 0, h00)
+	hess.SetSym(0, 1, h01)
+	hess.SetSym(1, 1, h11)
+}
+
+func (BrownBadlyScaled) Minima() []Minimum {
+	return []Minimum{
+		{
+			X:      []float64{1e6, 2e-6},
+			F:      0,
+			Global: true,
+		},
+	}
+}
+
+// BrownAndDennis implements the Brown and Dennis function.
+//
+// Standard starting point:
+//  [25, 5, -5, -1]
+//
+// References:
+//  - Brown, K.M., Dennis, J.E.: New computational algorithms for minimizing a
+//    sum of squares of nonlinear functions. Research Report Number 71-6, Yale
+//    University (1971)
+//  - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
+//    optimization software. ACM Trans Math Softw 7 (1981), 17-41
+type BrownAndDennis struct{}
+
+func (BrownAndDennis) Func(x []float64) (sum float64) {
+	if len(x) != 4 {
+		panic("dimension of the problem must be 4")
+	}
+
+	for i := 1; i <= 20; i++ {
+		c := float64(i) / 5
+		f1 := x[0] + c*x[1] - math.Exp(c)
+		f2 := x[2] + x[3]*math.Sin(c) - math.Cos(c)
+		f := f1*f1 + f2*f2
+		sum += f * f
+	}
+	return sum
+}
+
+func (BrownAndDennis) Grad(grad, x []float64) {
+	if len(x) != 4 {
+		panic("dimension of the problem must be 4")
+	}
+	if len(x) != len(grad) {
+		panic("incorrect size of the gradient")
+	}
+
+	for i := range grad {
+		grad[i] = 0
+	}
+	for i := 1; i <= 20; i++ {
+		c := float64(i) / 5
+		f1 := x[0] + c*x[1] - math.Exp(c)
+		f2 := x[2] + x[3]*math.Sin(c) - math.Cos(c)
+		f := f1*f1 + f2*f2
+		grad[0] += 4 * f * f1
+		grad[1] += 4 * f * f1 * c
+		grad[2] += 4 * f * f2
+		grad[3] += 4 * f * f2 * math.Sin(c)
+	}
+}
+
+func (BrownAndDennis) Hess(hess mat.MutableSymmetric, x []float64) {
+	if len(x) != 4 {
+		panic("dimension of the problem must be 4")
+	}
+	if len(x) != hess.Symmetric() {
+		panic("incorrect size of the Hessian")
+	}
+
+	for i := 0; i < 4; i++ {
+		for j := i; j < 4; j++ {
+			hess.SetSym(i, j, 0)
+		}
+	}
+	for i := 1; i <= 20; i++ {
+		d1 := float64(i) / 5
+		d2 := math.Sin(d1)
+		t1 := x[0] + d1*x[1] - math.Exp(d1)
+		t2 := x[2] + d2*x[3] - math.Cos(d1)
+		t := t1*t1 + t2*t2
+		s3 := 2 * t1 * t2
+		r1 := t + 2*t1*t1
+		r2 := t + 2*t2*t2
+		hess.SetSym(0, 0, hess.At(0, 0)+r1)
+		hess.SetSym(0, 1, hess.At(0, 1)+d1*r1)
+		hess.SetSym(1, 1, hess.At(1, 1)+d1*d1*r1)
+		hess.SetSym(0, 2, hess.At(0, 2)+s3)
+		hess.SetSym(1, 2, hess.At(1, 2)+d1*s3)
+		hess.SetSym(2, 2, hess.At(2, 2)+r2)
+		hess.SetSym(0, 3, hess.At(0, 3)+d2*s3)
+		hess.SetSym(1, 3, hess.At(1, 3)+d1*d2*s3)
+		hess.SetSym(2, 3, hess.At(2, 3)+d2*r2)
+		hess.SetSym(3, 3, hess.At(3, 3)+d2*d2*r2)
+	}
+	for i := 0; i < 4; i++ {
+		for j := i; j < 4; j++ {
+			hess.SetSym(i, j, 4*hess.At(i, j))
+		}
+	}
+}
+
+func (BrownAndDennis) Minima() []Minimum {
+	return []Minimum{
+		{
+			X:      []float64{-11.594439904762162, 13.203630051207202, -0.4034394881768612, 0.2367787744557347},
+			F:      85822.20162635634,
+			Global: true,
+		},
+	}
+}
+
+// ExtendedPowellSingular implements the extended Powell's function.
+// Its Hessian matrix is singular at the minimizer.
+//
+// Standard starting point:
+//  [3, -1, 0, 3, 3, -1, 0, 3, ..., 3, -1, 0, 3]
+//
+// References:
+//  - Spedicato E.: Computational experience with quasi-Newton algorithms for
+//    minimization problems of moderatly large size. Towards Global
+//    Optimization 2 (1978), 209-219
+//  - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
+//    optimization software. ACM Trans Math Softw 7 (1981), 17-41
+type ExtendedPowellSingular struct{}
+
+func (ExtendedPowellSingular) Func(x []float64) (sum float64) {
+	if len(x)%4 != 0 {
+		panic("dimension of the problem must be a multiple of 4")
+	}
+
+	for i := 0; i < len(x); i += 4 {
+		f1 := x[i] + 10*x[i+1]
+		f2 := x[i+2] - x[i+3]
+		t := x[i+1] - 2*x[i+2]
+		f3 := t * t
+		t = x[i] - x[i+3]
+		f4 := t * t
+		sum += f1*f1 + 5*f2*f2 + f3*f3 + 10*f4*f4
+	}
+	return sum
+}
+
+func (ExtendedPowellSingular) Grad(grad, x []float64) {
+	if len(x)%4 != 0 {
+		panic("dimension of the problem must be a multiple of 4")
+	}
+	if len(x) != len(grad) {
+		panic("incorrect size of the gradient")
+	}
+
+	for i := 0; i < len(x); i += 4 {
+		f1 := x[i] + 10*x[i+1]
+		f2 := x[i+2] - x[i+3]
+		t1 := x[i+1] - 2*x[i+2]
+		f3 := t1 * t1
+		t2 := x[i] - x[i+3]
+		f4 := t2 * t2
+		grad[i] = 2*f1 + 40*f4*t2
+		grad[i+1] = 20*f1 + 4*f3*t1
+		grad[i+2] = 10*f2 - 8*f3*t1
+		grad[i+3] = -10*f2 - 40*f4*t2
+	}
+}
+
+func (ExtendedPowellSingular) Minima() []Minimum {
+	return []Minimum{
+		{
+			X:      []float64{0, 0, 0, 0},
+			F:      0,
+			Global: true,
+		},
+		{
+			X:      []float64{0, 0, 0, 0, 0, 0, 0, 0},
+			F:      0,
+			Global: true,
+		},
+		{
+			X:      []float64{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+			F:      0,
+			Global: true,
+		},
+	}
+}
+
+// ExtendedRosenbrock implements the extended, multidimensional Rosenbrock
+// function.
+//
+// Standard starting point:
+//  Easy: [-1.2, 1, -1.2, 1, ...]
+//  Hard: any point far from the minimum
+//
+// References:
+//  - Rosenbrock, H.H.: An Automatic Method for Finding the Greatest or Least
+//    Value of a Function. Computer J 3 (1960), 175-184
+//  - http://en.wikipedia.org/wiki/Rosenbrock_function
+type ExtendedRosenbrock struct{}
+
+func (ExtendedRosenbrock) Func(x []float64) (sum float64) {
+	for i := 0; i < len(x)-1; i++ {
+		a := 1 - x[i]
+		b := x[i+1] - x[i]*x[i]
+		sum += a*a + 100*b*b
+	}
+	return sum
+}
+
+func (ExtendedRosenbrock) Grad(grad, x []float64) {
+	if len(x) != len(grad) {
+		panic("incorrect size of the gradient")
+	}
+
+	dim := len(x)
+	for i := range grad {
+		grad[i] = 0
+	}
+	for i := 0; i < dim-1; i++ {
+		grad[i] -= 2 * (1 - x[i])
+		grad[i] -= 400 * (x[i+1] - x[i]*x[i]) * x[i]
+	}
+	for i := 1; i < dim; i++ {
+		grad[i] += 200 * (x[i] - x[i-1]*x[i-1])
+	}
+}
+
+func (ExtendedRosenbrock) Minima() []Minimum {
+	return []Minimum{
+		{
+			X:      []float64{1, 1},
+			F:      0,
+			Global: true,
+		},
+		{
+			X:      []float64{1, 1, 1},
+			F:      0,
+			Global: true,
+		},
+		{
+			X:      []float64{1, 1, 1, 1},
+			F:      0,
+			Global: true,
+		},
+		{
+			X: []float64{-0.7756592265653526, 0.6130933654850433,
+				0.38206284633839305, 0.14597201855219452},
+			F:      3.701428610430017,
+			Global: false,
+		},
+		{
+			X:      []float64{1, 1, 1, 1, 1},
+			F:      0,
+			Global: true,
+		},
+		{
+			X: []float64{-0.9620510206947502, 0.9357393959767103,
+				0.8807136041943204, 0.7778776758544063, 0.6050936785926526},
+			F:      3.930839434133027,
+			Global: false,
+		},
+		{
+			X: []float64{-0.9865749795709938, 0.9833982288361819, 0.972106670053092,
+				0.9474374368264362, 0.8986511848517299, 0.8075739520354182},
+			F:      3.973940500930295,
+			Global: false,
+		},
+		{
+			X: []float64{-0.9917225725614055, 0.9935553935033712, 0.992173321594692,
+				0.9868987626903134, 0.975164756608872, 0.9514319827049906, 0.9052228177139495},
+			F:      3.9836005364248543,
+			Global: false,
+		},
+		{
+			X:      []float64{1, 1, 1, 1, 1, 1, 1, 1, 1, 1},
+			F:      0,
+			Global: true,
+		},
+	}
+}
+
+// Gaussian implements the Gaussian function.
+// The function has one global minimum and a number of false local minima
+// caused by the finite floating point precision.
+//
+// Standard starting point:
+//  [0.4, 1, 0]
+//
+// Reference:
+//  More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained optimization
+//  software. ACM Trans Math Softw 7 (1981), 17-41
+type Gaussian struct{}
+
+func (Gaussian) y(i int) (yi float64) {
+	switch i {
+	case 1, 15:
+		yi = 0.0009
+	case 2, 14:
+		yi = 0.0044
+	case 3, 13:
+		yi = 0.0175
+	case 4, 12:
+		yi = 0.0540
+	case 5, 11:
+		yi = 0.1295
+	case 6, 10:
+		yi = 0.2420
+	case 7, 9:
+		yi = 0.3521
+	case 8:
+		yi = 0.3989
+	}
+	return yi
+}
+
+func (g Gaussian) Func(x []float64) (sum float64) {
+	if len(x) != 3 {
+		panic("dimension of the problem must be 3")
+	}
+
+	for i := 1; i <= 15; i++ {
+		c := 0.5 * float64(8-i)
+		b := c - x[2]
+		d := b * b
+		e := math.Exp(-0.5 * x[1] * d)
+		f := x[0]*e - g.y(i)
+		sum += f * f
+	}
+	return sum
+}
+
+func (g Gaussian) Grad(grad, x []float64) {
+	if len(x) != 3 {
+		panic("dimension of the problem must be 3")
+	}
+	if len(x) != len(grad) {
+		panic("incorrect size of the gradient")
+	}
+
+	grad[0] = 0
+	grad[1] = 0
+	grad[2] = 0
+	for i := 1; i <= 15; i++ {
+		c := 0.5 * float64(8-i)
+		b := c - x[2]
+		d := b * b
+		e := math.Exp(-0.5 * x[1] * d)
+		f := x[0]*e - g.y(i)
+		grad[0] += 2 * f * e
+		grad[1] -= f * e * d * x[0]
+		grad[2] += 2 * f * e * x[0] * x[1] * b
+	}
+}
+
+func (Gaussian) Minima() []Minimum {
+	return []Minimum{
+		{
+			X:      []float64{0.398956137837997, 1.0000190844805048, 0},
+			F:      1.12793276961912e-08,
+			Global: true,
+		},
+	}
+}
+
+// GulfResearchAndDevelopment implements the Gulf Research and Development function.
+//
+// Standard starting point:
+//  [5, 2.5, 0.15]
+//
+// References:
+//  - Cox, R.A.: Comparison of the performance of seven optimization algorithms
+//    on twelve unconstrained minimization problems. Ref. 1335CNO4, Gulf
+//    Research and Development Company, Pittsburg (1969)
+//  - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
+//    optimization software. ACM Trans Math Softw 7 (1981), 17-41
+type GulfResearchAndDevelopment struct{}
+
+func (GulfResearchAndDevelopment) Func(x []float64) (sum float64) {
+	if len(x) != 3 {
+		panic("dimension of the problem must be 3")
+	}
+
+	for i := 1; i <= 99; i++ {
+		arg := float64(i) / 100
+		r := math.Pow(-50*math.Log(arg), 2.0/3.0) + 25 - x[1]
+		t1 := math.Pow(math.Abs(r), x[2]) / x[0]
+		t2 := math.Exp(-t1)
+		t := t2 - arg
+		sum += t * t
+	}
+	return sum
+}
+
+func (GulfResearchAndDevelopment) Grad(grad, x []float64) {
+	if len(x) != 3 {
+		panic("dimension of the problem must be 3")
+	}
+	if len(x) != len(grad) {
+		panic("incorrect size of the gradient")
+	}
+
+	for i := range grad {
+		grad[i] = 0
+	}
+	for i := 1; i <= 99; i++ {
+		arg := float64(i) / 100
+		r := math.Pow(-50*math.Log(arg), 2.0/3.0) + 25 - x[1]
+		t1 := math.Pow(math.Abs(r), x[2]) / x[0]
+		t2 := math.Exp(-t1)
+		t := t2 - arg
+		s1 := t1 * t2 * t
+		grad[0] += s1
+		grad[1] += s1 / r
+		grad[2] -= s1 * math.Log(math.Abs(r))
+	}
+	grad[0] *= 2 / x[0]
+	grad[1] *= 2 * x[2]
+	grad[2] *= 2
+}
+
+func (GulfResearchAndDevelopment) Minima() []Minimum {
+	return []Minimum{
+		{
+			X:      []float64{50, 25, 1.5},
+			F:      0,
+			Global: true,
+		},
+		{
+			X:      []float64{99.89529935174151, 60.61453902799833, 9.161242695144592},
+			F:      32.8345,
+			Global: false,
+		},
+		{
+			X:      []float64{201.662589489426, 60.61633150468155, 10.224891158488965},
+			F:      32.8345,
+			Global: false,
+		},
+	}
+}
+
+// HelicalValley implements the helical valley function of Fletcher and Powell.
+// Function is not defined at x[0] = 0.
+//
+// Standard starting point:
+//  [-1, 0, 0]
+//
+// References:
+//  - Fletcher, R., Powell, M.J.D.: A rapidly convergent descent method for
+//    minimization. Comput J 6 (1963), 163-168
+//  - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
+//    optimization software. ACM Trans Math Softw 7 (1981), 17-41
+type HelicalValley struct{}
+
+func (HelicalValley) Func(x []float64) float64 {
+	if len(x) != 3 {
+		panic("dimension of the problem must be 3")
+	}
+	if x[0] == 0 {
+		panic("function not defined at x[0] = 0")
+	}
+
+	theta := 0.5 * math.Atan(x[1]/x[0]) / math.Pi
+	if x[0] < 0 {
+		theta += 0.5
+	}
+	f1 := 10 * (x[2] - 10*theta)
+	f2 := 10 * (math.Hypot(x[0], x[1]) - 1)
+	f3 := x[2]
+	return f1*f1 + f2*f2 + f3*f3
+}
+
+func (HelicalValley) Grad(grad, x []float64) {
+	if len(x) != 3 {
+		panic("dimension of the problem must be 3")
+	}
+	if len(x) != len(grad) {
+		panic("incorrect size of the gradient")
+	}
+	if x[0] == 0 {
+		panic("function not defined at x[0] = 0")
+	}
+
+	theta := 0.5 * math.Atan(x[1]/x[0]) / math.Pi
+	if x[0] < 0 {
+		theta += 0.5
+	}
+	h := math.Hypot(x[0], x[1])
+	r := 1 / h
+	q := r * r / math.Pi
+	s := x[2] - 10*theta
+	grad[0] = 200 * (5*s*q*x[1] + (h-1)*r*x[0])
+	grad[1] = 200 * (-5*s*q*x[0] + (h-1)*r*x[1])
+	grad[2] = 2 * (100*s + x[2])
+}
+
+func (HelicalValley) Minima() []Minimum {
+	return []Minimum{
+		{
+			X:      []float64{1, 0, 0},
+			F:      0,
+			Global: true,
+		},
+	}
+}
+
+// Linear implements a linear function.
+type Linear struct{}
+
+func (Linear) Func(x []float64) float64 {
+	return floats.Sum(x)
+}
+
+func (Linear) Grad(grad, x []float64) {
+	if len(x) != len(grad) {
+		panic("incorrect size of the gradient")
+	}
+
+	for i := range grad {
+		grad[i] = 1
+	}
+}
+
+// PenaltyI implements the first penalty function by Gill, Murray and Pitfield.
+//
+// Standard starting point:
+//  [1, ..., n]
+//
+// References:
+//  - Gill, P.E., Murray, W., Pitfield, R.A.: The implementation of two revised
+//    quasi-Newton algorithms for unconstrained optimization. Report NAC 11,
+//    National Phys Lab (1972), 82-83
+//  - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
+//    optimization software. ACM Trans Math Softw 7 (1981), 17-41
+type PenaltyI struct{}
+
+func (PenaltyI) Func(x []float64) (sum float64) {
+	for _, v := range x {
+		sum += (v - 1) * (v - 1)
+	}
+	sum *= 1e-5
+
+	var s float64
+	for _, v := range x {
+		s += v * v
+	}
+	sum += (s - 0.25) * (s - 0.25)
+	return sum
+}
+
+func (PenaltyI) Grad(grad, x []float64) {
+	if len(x) != len(grad) {
+		panic("incorrect size of the gradient")
+	}
+
+	s := -0.25
+	for _, v := range x {
+		s += v * v
+	}
+	for i, v := range x {
+		grad[i] = 2 * (2*s*v + 1e-5*(v-1))
+	}
+}
+
+func (PenaltyI) Minima() []Minimum {
+	return []Minimum{
+		{
+			X:      []float64{0.2500074995875379, 0.2500074995875379, 0.2500074995875379, 0.2500074995875379},
+			F:      2.2499775008999372e-05,
+			Global: true,
+		},
+		{
+			X: []float64{0.15812230111311634, 0.15812230111311634, 0.15812230111311634,
+				0.15812230111311634, 0.15812230111311634, 0.15812230111311634,
+				0.15812230111311634, 0.15812230111311634, 0.15812230111311634, 0.15812230111311634},
+			F:      7.087651467090369e-05,
+			Global: true,
+		},
+	}
+}
+
+// PenaltyII implements the second penalty function by Gill, Murray and Pitfield.
+//
+// Standard starting point:
+//  [0.5, ..., 0.5]
+//
+// References:
+//  - Gill, P.E., Murray, W., Pitfield, R.A.: The implementation of two revised
+//    quasi-Newton algorithms for unconstrained optimization. Report NAC 11,
+//    National Phys Lab (1972), 82-83
+//  - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
+//    optimization software. ACM Trans Math Softw 7 (1981), 17-41
+type PenaltyII struct{}
+
+func (PenaltyII) Func(x []float64) (sum float64) {
+	dim := len(x)
+	s := -1.0
+	for i, v := range x {
+		s += float64(dim-i) * v * v
+	}
+	for i := 1; i < dim; i++ {
+		yi := math.Exp(float64(i+1)/10) + math.Exp(float64(i)/10)
+		f := math.Exp(x[i]/10) + math.Exp(x[i-1]/10) - yi
+		sum += f * f
+	}
+	for i := 1; i < dim; i++ {
+		f := math.Exp(x[i]/10) - math.Exp(-1.0/10)
+		sum += f * f
+	}
+	sum *= 1e-5
+	sum += (x[0] - 0.2) * (x[0] - 0.2)
+	sum += s * s
+	return sum
+}
+
+func (PenaltyII) Grad(grad, x []float64) {
+	if len(x) != len(grad) {
+		panic("incorrect size of the gradient")
+	}
+
+	dim := len(x)
+	s := -1.0
+	for i, v := range x {
+		s += float64(dim-i) * v * v
+	}
+	for i, v := range x {
+		grad[i] = 4 * s * float64(dim-i) * v
+	}
+	for i := 1; i < dim; i++ {
+		yi := math.Exp(float64(i+1)/10) + math.Exp(float64(i)/10)
+		f := math.Exp(x[i]/10) + math.Exp(x[i-1]/10) - yi
+		grad[i] += 1e-5 * f * math.Exp(x[i]/10) / 5
+		grad[i-1] += 1e-5 * f * math.Exp(x[i-1]/10) / 5
+	}
+	for i := 1; i < dim; i++ {
+		f := math.Exp(x[i]/10) - math.Exp(-1.0/10)
+		grad[i] += 1e-5 * f * math.Exp(x[i]/10) / 5
+	}
+	grad[0] += 2 * (x[0] - 0.2)
+}
+
+func (PenaltyII) Minima() []Minimum {
+	return []Minimum{
+		{
+			X:      []float64{0.19999933335, 0.19131670128566283, 0.4801014860897, 0.5188454026659},
+			F:      9.376293007355449e-06,
+			Global: true,
+		},
+		{
+			X: []float64{0.19998360520892217, 0.010350644318663525,
+				0.01960493546891094, 0.03208906550305253, 0.04993267593895693,
+				0.07651399534454084, 0.11862407118600789, 0.1921448731780023,
+				0.3473205862372022, 0.36916437893066273},
+			F:      0.00029366053745674594,
+			Global: true,
+		},
+	}
+}
+
+// PowellBadlyScaled implements the Powell's badly scaled function.
+// The function is very flat near the minimum. A satisfactory solution is one
+// that gives f(x) ≅ 1e-13.
+//
+// Standard starting point:
+//  [0, 1]
+//
+// References:
+//  - Powell, M.J.D.: A Hybrid Method for Nonlinear Equations. Numerical
+//    Methods for Nonlinear Algebraic Equations, P. Rabinowitz (ed.), Gordon
+//    and Breach (1970)
+//  - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
+//    optimization software. ACM Trans Math Softw 7 (1981), 17-41
+type PowellBadlyScaled struct{}
+
+func (PowellBadlyScaled) Func(x []float64) float64 {
+	if len(x) != 2 {
+		panic("dimension of the problem must be 2")
+	}
+
+	f1 := 1e4*x[0]*x[1] - 1
+	f2 := math.Exp(-x[0]) + math.Exp(-x[1]) - 1.0001
+	return f1*f1 + f2*f2
+}
+
+func (PowellBadlyScaled) Grad(grad, x []float64) {
+	if len(x) != 2 {
+		panic("dimension of the problem must be 2")
+	}
+	if len(x) != len(grad) {
+		panic("incorrect size of the gradient")
+	}
+
+	f1 := 1e4*x[0]*x[1] - 1
+	f2 := math.Exp(-x[0]) + math.Exp(-x[1]) - 1.0001
+	grad[0] = 2 * (1e4*f1*x[1] - f2*math.Exp(-x[0]))
+	grad[1] = 2 * (1e4*f1*x[0] - f2*math.Exp(-x[1]))
+}
+
+func (PowellBadlyScaled) Hess(hess mat.MutableSymmetric, x []float64) {
+	if len(x) != 2 {
+		panic("dimension of the problem must be 2")
+	}
+	if len(x) != hess.Symmetric() {
+		panic("incorrect size of the Hessian")
+	}
+
+	t1 := 1e4*x[0]*x[1] - 1
+	s1 := math.Exp(-x[0])
+	s2 := math.Exp(-x[1])
+	t2 := s1 + s2 - 1.0001
+
+	h00 := 2 * (1e8*x[1]*x[1] + s1*(s1+t2))
+	h01 := 2 * (1e4*(1+2*t1) + s1*s2)
+	h11 := 2 * (1e8*x[0]*x[0] + s2*(s2+t2))
+	hess.SetSym(0, 0, h00)
+	hess.SetSym(0, 1, h01)
+	hess.SetSym(1, 1, h11)
+}
+
+func (PowellBadlyScaled) Minima() []Minimum {
+	return []Minimum{
+		{
+			X:      []float64{1.0981593296997149e-05, 9.106146739867375},
+			F:      0,
+			Global: true,
+		},
+	}
+}
+
+// Trigonometric implements the trigonometric function.
+//
+// Standard starting point:
+//  [1/dim, ..., 1/dim]
+//
+// References:
+//  - Spedicato E.: Computational experience with quasi-Newton algorithms for
+//    minimization problems of moderatly large size. Towards Global
+//    Optimization 2 (1978), 209-219
+//  - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
+//    optimization software. ACM Trans Math Softw 7 (1981), 17-41
+type Trigonometric struct{}
+
+func (Trigonometric) Func(x []float64) (sum float64) {
+	var s1 float64
+	for _, v := range x {
+		s1 += math.Cos(v)
+	}
+	for i, v := range x {
+		f := float64(len(x)+i+1) - float64(i+1)*math.Cos(v) - math.Sin(v) - s1
+		sum += f * f
+	}
+	return sum
+}
+
+func (Trigonometric) Grad(grad, x []float64) {
+	if len(x) != len(grad) {
+		panic("incorrect size of the gradient")
+	}
+
+	var s1 float64
+	for _, v := range x {
+		s1 += math.Cos(v)
+	}
+
+	var s2 float64
+	for i, v := range x {
+		f := float64(len(x)+i+1) - float64(i+1)*math.Cos(v) - math.Sin(v) - s1
+		s2 += f
+		grad[i] = 2 * f * (float64(i+1)*math.Sin(v) - math.Cos(v))
+	}
+
+	for i, v := range x {
+		grad[i] += 2 * s2 * math.Sin(v)
+	}
+}
+
+func (Trigonometric) Minima() []Minimum {
+	return []Minimum{
+		{
+			X: []float64{0.04296456438227447, 0.043976287478192246,
+				0.045093397949095684, 0.04633891624617569, 0.047744381782831,
+				0.04935473251330618, 0.05123734850076505, 0.19520946391410446,
+				0.1649776652761741, 0.06014857783799575},
+			F:      0,
+			Global: true,
+		},
+		{
+			// TODO(vladimir-ch): If we knew the location of this minimum more
+			// accurately, we could decrease defaultGradTol.
+			X: []float64{0.05515090434047145, 0.05684061730812344,
+				0.05876400231100774, 0.060990608903034337, 0.06362621381044778,
+				0.06684318087364617, 0.2081615177172172, 0.16436309604419047,
+				0.08500689695564931, 0.09143145386293675},
+			F:      2.795056121876575e-05,
+			Global: false,
+		},
+	}
+}
+
+// VariablyDimensioned implements a variably dimensioned function.
+//
+// Standard starting point:
+//  [..., (dim-i)/dim, ...], i=1,...,dim
+//
+// References:
+//  More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained optimization
+//  software. ACM Trans Math Softw 7 (1981), 17-41
+type VariablyDimensioned struct{}
+
+func (VariablyDimensioned) Func(x []float64) (sum float64) {
+	for _, v := range x {
+		t := v - 1
+		sum += t * t
+	}
+
+	var s float64
+	for i, v := range x {
+		s += float64(i+1) * (v - 1)
+	}
+	s *= s
+	sum += s
+	s *= s
+	sum += s
+	return sum
+}
+
+func (VariablyDimensioned) Grad(grad, x []float64) {
+	if len(x) != len(grad) {
+		panic("incorrect size of the gradient")
+	}
+
+	var s float64
+	for i, v := range x {
+		s += float64(i+1) * (v - 1)
+	}
+	for i, v := range x {
+		grad[i] = 2 * (v - 1 + s*float64(i+1)*(1+2*s*s))
+	}
+}
+
+func (VariablyDimensioned) Minima() []Minimum {
+	return []Minimum{
+		{
+			X:      []float64{1, 1},
+			F:      0,
+			Global: true,
+		},
+		{
+			X:      []float64{1, 1, 1},
+			F:      0,
+			Global: true,
+		},
+		{
+			X:      []float64{1, 1, 1, 1},
+			F:      0,
+			Global: true,
+		},
+		{
+			X:      []float64{1, 1, 1, 1, 1},
+			F:      0,
+			Global: true,
+		},
+		{
+			X:      []float64{1, 1, 1, 1, 1, 1, 1, 1, 1, 1},
+			F:      0,
+			Global: true,
+		},
+	}
+}
+
+// Watson implements the Watson's function.
+// Dimension of the problem should be 2 <= dim <= 31. For dim == 9, the problem
+// of minimizing the function is very ill conditioned.
+//
+// Standard starting point:
+//  [0, ..., 0]
+//
+// References:
+//  - Kowalik, J.S., Osborne, M.R.: Methods for Unconstrained Optimization
+//    Problems. Elsevier North-Holland, New York, 1968
+//  - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
+//    optimization software. ACM Trans Math Softw 7 (1981), 17-41
+type Watson struct{}
+
+func (Watson) Func(x []float64) (sum float64) {
+	for i := 1; i <= 29; i++ {
+		d1 := float64(i) / 29
+
+		d2 := 1.0
+		var s1 float64
+		for j := 1; j < len(x); j++ {
+			s1 += float64(j) * d2 * x[j]
+			d2 *= d1
+		}
+
+		d2 = 1.0
+		var s2 float64
+		for _, v := range x {
+			s2 += d2 * v
+			d2 *= d1
+		}
+
+		t := s1 - s2*s2 - 1
+		sum += t * t
+	}
+	t := x[1] - x[0]*x[0] - 1
+	sum += x[0]*x[0] + t*t
+	return sum
+}
+
+func (Watson) Grad(grad, x []float64) {
+	if len(x) != len(grad) {
+		panic("incorrect size of the gradient")
+	}
+
+	for i := range grad {
+		grad[i] = 0
+	}
+	for i := 1; i <= 29; i++ {
+		d1 := float64(i) / 29
+
+		d2 := 1.0
+		var s1 float64
+		for j := 1; j < len(x); j++ {
+			s1 += float64(j) * d2 * x[j]
+			d2 *= d1
+		}
+
+		d2 = 1.0
+		var s2 float64
+		for _, v := range x {
+			s2 += d2 * v
+			d2 *= d1
+		}
+
+		t := s1 - s2*s2 - 1
+		s3 := 2 * d1 * s2
+		d2 = 2 / d1
+		for j := range x {
+			grad[j] += d2 * (float64(j) - s3) * t
+			d2 *= d1
+		}
+	}
+	t := x[1] - x[0]*x[0] - 1
+	grad[0] += x[0] * (2 - 4*t)
+	grad[1] += 2 * t
+}
+
+func (Watson) Hess(hess mat.MutableSymmetric, x []float64) {
+	dim := len(x)
+	if dim != hess.Symmetric() {
+		panic("incorrect size of the Hessian")
+	}
+
+	for j := 0; j < dim; j++ {
+		for k := j; k < dim; k++ {
+			hess.SetSym(j, k, 0)
+		}
+	}
+	for i := 1; i <= 29; i++ {
+		d1 := float64(i) / 29
+		d2 := 1.0
+		var s1 float64
+		for j := 1; j < dim; j++ {
+			s1 += float64(j) * d2 * x[j]
+			d2 *= d1
+		}
+
+		d2 = 1.0
+		var s2 float64
+		for _, v := range x {
+			s2 += d2 * v
+			d2 *= d1
+		}
+
+		t := s1 - s2*s2 - 1
+		s3 := 2 * d1 * s2
+		d2 = 2 / d1
+		th := 2 * d1 * d1 * t
+		for j := 0; j < dim; j++ {
+			v := float64(j) - s3
+			d3 := 1 / d1
+			for k := 0; k <= j; k++ {
+				hess.SetSym(k, j, hess.At(k, j)+d2*d3*(v*(float64(k)-s3)-th))
+				d3 *= d1
+			}
+			d2 *= d1
+		}
+	}
+	t1 := x[1] - x[0]*x[0] - 1
+	hess.SetSym(0, 0, hess.At(0, 0)+8*x[0]*x[0]+2-4*t1)
+	hess.SetSym(0, 1, hess.At(0, 1)-4*x[0])
+	hess.SetSym(1, 1, hess.At(1, 1)+2)
+}
+
+func (Watson) Minima() []Minimum {
+	return []Minimum{
+		{
+			X: []float64{-0.01572508644590686, 1.012434869244884, -0.23299162372002916,
+				1.2604300800978554, -1.51372891341701, 0.9929964286340117},
+			F:      0.0022876700535523838,
+			Global: true,
+		},
+		{
+			X: []float64{-1.5307036521992127e-05, 0.9997897039319495, 0.01476396369355022,
+				0.14634232829939883, 1.0008211030046426, -2.617731140519101, 4.104403164479245,
+				-3.1436122785568514, 1.0526264080103074},
+			F:      1.399760138096796e-06,
+			Global: true,
+		},
+		// TODO(vladimir-ch): More, Garbow, Hillstrom list just the value, but
+		// not the location. Our minimizers find a minimum, but the value is
+		// different.
+		// {
+		// 	// For dim == 12
+		// 	F:      4.72238e-10,
+		// 	Global: true,
+		// },
+		// TODO(vladimir-ch): netlib/uncon report a value of 2.48631d-20 for dim == 20.
+	}
+}
+
+// Wood implements the Wood's function.
+//
+// Standard starting point:
+//  [-3, -1, -3, -1]
+//
+// References:
+//  - Colville, A.R.: A comparative study of nonlinear programming codes.
+//    Report 320-2949, IBM New York Scientific Center (1968)
+//  - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
+//    optimization software. ACM Trans Math Softw 7 (1981), 17-41
+type Wood struct{}
+
+func (Wood) Func(x []float64) (sum float64) {
+	if len(x) != 4 {
+		panic("dimension of the problem must be 4")
+	}
+
+	f1 := x[1] - x[0]*x[0]
+	f2 := 1 - x[0]
+	f3 := x[3] - x[2]*x[2]
+	f4 := 1 - x[2]
+	f5 := x[1] + x[3] - 2
+	f6 := x[1] - x[3]
+	return 100*f1*f1 + f2*f2 + 90*f3*f3 + f4*f4 + 10*f5*f5 + 0.1*f6*f6
+}
+
+func (Wood) Grad(grad, x []float64) {
+	if len(x) != 4 {
+		panic("dimension of the problem must be 4")
+	}
+	if len(x) != len(grad) {
+		panic("incorrect size of the gradient")
+	}
+
+	f1 := x[1] - x[0]*x[0]
+	f2 := 1 - x[0]
+	f3 := x[3] - x[2]*x[2]
+	f4 := 1 - x[2]
+	f5 := x[1] + x[3] - 2
+	f6 := x[1] - x[3]
+	grad[0] = -2 * (200*f1*x[0] + f2)
+	grad[1] = 2 * (100*f1 + 10*f5 + 0.1*f6)
+	grad[2] = -2 * (180*f3*x[2] + f4)
+	grad[3] = 2 * (90*f3 + 10*f5 - 0.1*f6)
+}
+
+func (Wood) Hess(hess mat.MutableSymmetric, x []float64) {
+	if len(x) != 4 {
+		panic("dimension of the problem must be 4")
+	}
+	if len(x) != hess.Symmetric() {
+		panic("incorrect size of the Hessian")
+	}
+
+	hess.SetSym(0, 0, 400*(3*x[0]*x[0]-x[1])+2)
+	hess.SetSym(0, 1, -400*x[0])
+	hess.SetSym(1, 1, 220.2)
+	hess.SetSym(0, 2, 0)
+	hess.SetSym(1, 2, 0)
+	hess.SetSym(2, 2, 360*(3*x[2]*x[2]-x[3])+2)
+	hess.SetSym(0, 3, 0)
+	hess.SetSym(1, 3, 19.8)
+	hess.SetSym(2, 3, -360*x[2])
+	hess.SetSym(3, 3, 200.2)
+}
+
+func (Wood) Minima() []Minimum {
+	return []Minimum{
+		{
+			X:      []float64{1, 1, 1, 1},
+			F:      0,
+			Global: true,
+		},
+	}
+}
+
+// ConcaveRight implements an univariate function that is concave to the right
+// of the minimizer which is located at x=sqrt(2).
+//
+// References:
+//  More, J.J., and Thuente, D.J.: Line Search Algorithms with Guaranteed Sufficient Decrease.
+//  ACM Transactions on Mathematical Software 20(3) (1994), 286–307, eq. (5.1)
+type ConcaveRight struct{}
+
+func (ConcaveRight) Func(x []float64) float64 {
+	if len(x) != 1 {
+		panic("dimension of the problem must be 1")
+	}
+	return -x[0] / (x[0]*x[0] + 2)
+}
+
+func (ConcaveRight) Grad(grad, x []float64) {
+	if len(x) != 1 {
+		panic("dimension of the problem must be 1")
+	}
+	if len(x) != len(grad) {
+		panic("incorrect size of the gradient")
+	}
+	xSqr := x[0] * x[0]
+	grad[0] = (xSqr - 2) / (xSqr + 2) / (xSqr + 2)
+}
+
+// ConcaveLeft implements an univariate function that is concave to the left of
+// the minimizer which is located at x=399/250=1.596.
+//
+// References:
+//  More, J.J., and Thuente, D.J.: Line Search Algorithms with Guaranteed Sufficient Decrease.
+//  ACM Transactions on Mathematical Software 20(3) (1994), 286–307, eq. (5.2)
+type ConcaveLeft struct{}
+
+func (ConcaveLeft) Func(x []float64) float64 {
+	if len(x) != 1 {
+		panic("dimension of the problem must be 1")
+	}
+	return math.Pow(x[0]+0.004, 4) * (x[0] - 1.996)
+}
+
+func (ConcaveLeft) Grad(grad, x []float64) {
+	if len(x) != 1 {
+		panic("dimension of the problem must be 1")
+	}
+	if len(x) != len(grad) {
+		panic("incorrect size of the gradient")
+	}
+	grad[0] = math.Pow(x[0]+0.004, 3) * (5*x[0] - 7.98)
+}
+
+// Plassmann implements an univariate oscillatory function where the value of L
+// controls the number of oscillations. The value of Beta controls the size of
+// the derivative at zero and the size of the interval where the strong Wolfe
+// conditions can hold. For small values of Beta this function represents a
+// difficult test problem for linesearchers also because the information based
+// on the derivative is unreliable due to the oscillations.
+//
+// References:
+//  More, J.J., and Thuente, D.J.: Line Search Algorithms with Guaranteed Sufficient Decrease.
+//  ACM Transactions on Mathematical Software 20(3) (1994), 286–307, eq. (5.3)
+type Plassmann struct {
+	L    float64 // Number of oscillations for |x-1| ≥ Beta.
+	Beta float64 // Size of the derivative at zero, f'(0) = -Beta.
+}
+
+func (f Plassmann) Func(x []float64) float64 {
+	if len(x) != 1 {
+		panic("dimension of the problem must be 1")
+	}
+	a := x[0]
+	b := f.Beta
+	l := f.L
+	r := 2 * (1 - b) / l / math.Pi * math.Sin(l*math.Pi/2*a)
+	switch {
+	case a <= 1-b:
+		r += 1 - a
+	case 1-b < a && a <= 1+b:
+		r += 0.5 * ((a-1)*(a-1)/b + b)
+	default: // a > 1+b
+		r += a - 1
+	}
+	return r
+}
+
+func (f Plassmann) Grad(grad, x []float64) {
+	if len(x) != 1 {
+		panic("dimension of the problem must be 1")
+	}
+	if len(x) != len(grad) {
+		panic("incorrect size of the gradient")
+	}
+	a := x[0]
+	b := f.Beta
+	l := f.L
+	grad[0] = (1 - b) * math.Cos(l*math.Pi/2*a)
+	switch {
+	case a <= 1-b:
+		grad[0]--
+	case 1-b < a && a <= 1+b:
+		grad[0] += (a - 1) / b
+	default: // a > 1+b
+		grad[0]++
+	}
+}
+
+// YanaiOzawaKaneko is an univariate convex function where the values of Beta1
+// and Beta2 control the curvature around the minimum. Far away from the
+// minimum the function approximates an absolute value function. Near the
+// minimum, the function can either be sharply curved or flat, controlled by
+// the parameter values.
+//
+// References:
+//  - More, J.J., and Thuente, D.J.: Line Search Algorithms with Guaranteed Sufficient Decrease.
+//    ACM Transactions on Mathematical Software 20(3) (1994), 286–307, eq. (5.4)
+//  - Yanai, H., Ozawa, M., and Kaneko, S.: Interpolation methods in one dimensional
+//    optimization. Computing 27 (1981), 155–163
+type YanaiOzawaKaneko struct {
+	Beta1 float64
+	Beta2 float64
+}
+
+func (f YanaiOzawaKaneko) Func(x []float64) float64 {
+	if len(x) != 1 {
+		panic("dimension of the problem must be 1")
+	}
+	a := x[0]
+	b1 := f.Beta1
+	b2 := f.Beta2
+	g1 := math.Sqrt(1+b1*b1) - b1
+	g2 := math.Sqrt(1+b2*b2) - b2
+	return g1*math.Sqrt((a-1)*(a-1)+b2*b2) + g2*math.Sqrt(a*a+b1*b1)
+}
+
+func (f YanaiOzawaKaneko) Grad(grad, x []float64) {
+	if len(x) != 1 {
+		panic("dimension of the problem must be 1")
+	}
+	if len(x) != len(grad) {
+		panic("incorrect size of the gradient")
+	}
+	a := x[0]
+	b1 := f.Beta1
+	b2 := f.Beta2
+	g1 := math.Sqrt(1+b1*b1) - b1
+	g2 := math.Sqrt(1+b2*b2) - b2
+	grad[0] = g1*(a-1)/math.Sqrt(b2*b2+(a-1)*(a-1)) + g2*a/math.Sqrt(b1*b1+a*a)
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/functions/functions_test.go b/vendor/gonum.org/v1/gonum/optimize/functions/functions_test.go
new file mode 100644
index 00000000..0912ab96
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/functions/functions_test.go
@@ -0,0 +1,326 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package functions
+
+import "testing"
+
+func TestBeale(t *testing.T) {
+	tests := []funcTest{
+		{
+			X:        []float64{1, 1},
+			F:        14.203125,
+			Gradient: []float64{0, 27.75},
+		},
+		{
+			X:        []float64{1, 4},
+			F:        4624.453125,
+			Gradient: []float64{8813.25, 6585},
+		},
+	}
+	testFunction(Beale{}, tests, t)
+}
+
+func TestBiggsEXP2(t *testing.T) {
+	tests := []funcTest{
+		{
+			X:        []float64{1, 2},
+			F:        32.26255055084012,
+			Gradient: []float64{8.308203800550878, -25.32607145221645},
+		},
+	}
+	testFunction(BiggsEXP2{}, tests, t)
+}
+
+func TestBiggsEXP3(t *testing.T) {
+	tests := []funcTest{
+		{
+			X:        []float64{1, 2, 1},
+			F:        1.598844540607779,
+			Gradient: []float64{1.0633795027631927, -0.5196392672262664, -0.3180919155433357},
+		},
+	}
+	testFunction(BiggsEXP3{}, tests, t)
+}
+
+func TestBiggsEXP4(t *testing.T) {
+	tests := []funcTest{
+		{
+			X: []float64{1, 2, 1, 1},
+			F: 1.598844540607779,
+			Gradient: []float64{1.0633795027631927, -0.5196392672262664,
+				-0.44245622408151464, -0.3180919155433357},
+		},
+	}
+	testFunction(BiggsEXP4{}, tests, t)
+}
+
+func TestBiggsEXP5(t *testing.T) {
+	tests := []funcTest{
+		{
+			X: []float64{1, 2, 1, 1, 1},
+			F: 13.386420552801937,
+			Gradient: []float64{-6.54665204477596, 3.5259856535515293,
+				14.36984212995392, -9.522506150695783, -19.639956134327882},
+		},
+	}
+	testFunction(BiggsEXP5{}, tests, t)
+}
+
+func TestBiggsEXP6(t *testing.T) {
+	tests := []funcTest{
+		{
+			X: []float64{1, 2, 1, 1, 1, 1},
+			F: 0.77907007565597,
+			Gradient: []float64{-0.149371887533426, -0.183163468182936,
+				-1.483958013575642, 1.428277503849742, -0.149371887533426,
+				-1.483958013575642},
+		},
+	}
+	testFunction(BiggsEXP6{}, tests, t)
+}
+
+func TestBox3D(t *testing.T) {
+	tests := []funcTest{
+		{
+			X:        []float64{0, 10, 20},
+			F:        1031.1538106093985,
+			Gradient: []float64{98.22343149849218, -2.11937420675874, 112.38817362220350},
+		},
+	}
+	testFunction(Box3D{}, tests, t)
+}
+
+func TestBrownBadlyScaled(t *testing.T) {
+	tests := []funcTest{
+		{
+			X:        []float64{1, 1},
+			F:        999998000003,
+			Gradient: []float64{-2e+6, -4e-6},
+		},
+	}
+	testFunction(BrownBadlyScaled{}, tests, t)
+}
+
+// TODO(vladimir-ch): The minimum of BrownAndDennis is not known accurately
+// enough, which would force defaultGradTol to be unnecessarily large for the
+// tests to pass. This is the only function that causes problems, so disable
+// this test until the minimum is more accurate.
+// func TestBrownAndDennis(t *testing.T) {
+// 	tests := []funcTest{
+// 		{
+// 			X:        []float64{25, 5, -5, -1},
+// 			F:        7926693.33699744,
+// 			Gradient: []float64{1149322.836365895, 1779291.674339785, -254579.585463521, -173400.429253115},
+// 		},
+// 	}
+// 	testFunction(BrownAndDennis{}, tests, t)
+// }
+
+func TestExtendedPowellSingular(t *testing.T) {
+	tests := []funcTest{
+		{
+			X:        []float64{3, -1, 0, 3},
+			F:        95,
+			Gradient: []float64{-14, -144, -22, 30},
+		},
+		{
+			X:        []float64{3, -1, 0, 3, 3, -1, 0, 3},
+			F:        190,
+			Gradient: []float64{-14, -144, -22, 30, -14, -144, -22, 30},
+		},
+	}
+	testFunction(ExtendedPowellSingular{}, tests, t)
+}
+
+func TestExtendedRosenbrock(t *testing.T) {
+	tests := []funcTest{
+		{
+			X:        []float64{-1.2, 1},
+			F:        24.2,
+			Gradient: []float64{-215.6, -88},
+		},
+		{
+			X:        []float64{-1.2, 1, -1.2},
+			F:        508.2,
+			Gradient: []float64{-215.6, 792, -440},
+		},
+		{
+			X:        []float64{-1.2, 1, -1.2, 1},
+			F:        532.4,
+			Gradient: []float64{-215.6, 792, -655.6, -88},
+		},
+	}
+	testFunction(ExtendedRosenbrock{}, tests, t)
+}
+
+func TestGaussian(t *testing.T) {
+	tests := []funcTest{
+		{
+			X:        []float64{0.4, 1, 0},
+			F:        3.88810699116688e-06,
+			Gradient: []float64{7.41428466839991e-03, -7.44126392165149e-04, -5.30189685421989e-20},
+		},
+	}
+	testFunction(Gaussian{}, tests, t)
+}
+
+func TestGulfResearchAndDevelopment(t *testing.T) {
+	tests := []funcTest{
+		{
+			X:        []float64{5, 2.5, 0.15},
+			F:        12.11070582556949,
+			Gradient: []float64{2.0879783574289799, 0.0345792619697154, -39.6766801029386400},
+		},
+	}
+	testFunction(GulfResearchAndDevelopment{}, tests, t)
+}
+
+func TestHelicalValley(t *testing.T) {
+	tests := []funcTest{
+		{
+			X:        []float64{-1, 0, 0},
+			F:        2500,
+			Gradient: []float64{0, -1.59154943091895e+03, -1e+03},
+		},
+	}
+	testFunction(HelicalValley{}, tests, t)
+}
+
+func TestPenaltyI(t *testing.T) {
+	tests := []funcTest{
+		{
+			X:        []float64{1, 2, 3, 4},
+			F:        885.06264,
+			Gradient: []float64{119, 238.00002, 357.00004, 476.00006},
+		},
+		{
+			X: []float64{1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
+			F: 148032.56535,
+			Gradient: []float64{1539, 3078.00002, 4617.00004, 6156.00006,
+				7695.00008, 9234.0001, 10773.00012, 12312.00014, 13851.00016, 15390.00018},
+		},
+	}
+	testFunction(PenaltyI{}, tests, t)
+}
+
+func TestPenaltyII(t *testing.T) {
+	tests := []funcTest{
+		{
+			X: []float64{0.5, 0.5, 0.5, 0.5},
+			F: 2.34000880546302,
+			Gradient: []float64{12.59999952896435, 8.99999885134508,
+				5.99999776830493, 2.99999875380719},
+		},
+		{
+			X: []float64{0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5},
+			F: 162.65277656596712,
+			Gradient: []float64{255.5999995289644, 229.4999988513451,
+				203.9999977683049, 178.4999965713605, 152.9999952485322,
+				127.4999937865809, 101.9999921708749, 76.4999903852436,
+				50.9999884118158, 25.4999938418451},
+		},
+	}
+	testFunction(PenaltyII{}, tests, t)
+}
+
+func TestPowelBadlyScaled(t *testing.T) {
+	tests := []funcTest{
+		{
+			X:        []float64{0, 1},
+			F:        1.13526171734838,
+			Gradient: []float64{-2.00007355588823e+04, -2.70596990584991e-01},
+		},
+	}
+	testFunction(PowellBadlyScaled{}, tests, t)
+}
+
+func TestTrigonometric(t *testing.T) {
+	tests := []funcTest{
+		{
+			X:        []float64{0.5, 0.5},
+			F:        0.0126877761614045,
+			Gradient: []float64{-0.00840962732040673, -0.09606967736232540},
+		},
+		{
+			X: []float64{0.2, 0.2, 0.2, 0.2, 0.2},
+			F: 0.0116573789904718,
+			Gradient: []float64{0.04568602319608119, -0.00896259022885634,
+				-0.04777056509084983, -0.07073790138989976, -0.07786459912600564},
+		},
+		{
+			X: []float64{0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1},
+			F: 0.00707575946622261,
+			Gradient: []float64{0.03562782195259399, 0.01872017956076182,
+				0.00380754216611998, -0.00911009023133202, -0.02003271763159338,
+				-0.02896034003466506, -0.03589295744054654, -0.04083056984923782,
+				-0.04377317726073873, -0.04472077967504980},
+		},
+	}
+	testFunction(Trigonometric{}, tests, t)
+}
+
+func TestVariablyDimensioned(t *testing.T) {
+	tests := []funcTest{
+		{
+			X:        []float64{0.5, 0},
+			F:        46.5625,
+			Gradient: []float64{-68.5, -137},
+		},
+		{
+			X:        []float64{2.0 / 3, 1.0 / 3, 0},
+			F:        497.60493827160514,
+			Gradient: []float64{-416.518518518519, -833.037037037037, -1249.555555555556},
+		},
+		{
+			X:        []float64{0.75, 0.5, 0.25, 0},
+			F:        3222.1875,
+			Gradient: []float64{-1703, -3406, -5109, -6812},
+		},
+	}
+	testFunction(VariablyDimensioned{}, tests, t)
+}
+
+func TestWatson(t *testing.T) {
+	tests := []funcTest{
+		{
+			X:        []float64{0, 0},
+			F:        30,
+			Gradient: []float64{0, -60},
+		},
+		{
+			X: []float64{0, 0, 0, 0, 0, 0},
+			F: 30,
+			Gradient: []float64{0, -60, -60, -61.034482758620697,
+				-62.068965517241381, -63.114928861371936},
+		},
+		{
+			X: []float64{0, 0, 0, 0, 0, 0, 0, 0, 0},
+			F: 30,
+			Gradient: []float64{0, -60, -60, -61.034482758620697,
+				-62.068965517241381, -63.114928861371936, -64.172372791012350,
+				-65.241283655050239, -66.321647802373235},
+		},
+		{
+			X: []float64{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+			F: 30,
+			Gradient: []float64{0, -60, -60, -61.034482758620697,
+				-62.068965517241381, -63.114928861371936, -64.172372791012350,
+				-65.241283655050239, -66.321647802373235, -67.413448880864095,
+				-68.516667837400661, -69.631282933991471},
+		},
+	}
+	testFunction(Watson{}, tests, t)
+}
+
+func TestWood(t *testing.T) {
+	tests := []funcTest{
+		{
+			X:        []float64{-3, -1, -3, -1},
+			F:        19192,
+			Gradient: []float64{-12008, -2080, -10808, -1880},
+		},
+	}
+	testFunction(Wood{}, tests, t)
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/functions/minsurf.go b/vendor/gonum.org/v1/gonum/optimize/functions/minsurf.go
new file mode 100644
index 00000000..d975bfdb
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/functions/minsurf.go
@@ -0,0 +1,252 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package functions
+
+import (
+	"fmt"
+	"math"
+)
+
+// MinimalSurface implements a finite element approximation to a minimal
+// surface problem: determine the surface with minimal area and given boundary
+// values in a unit square centered at the origin.
+//
+// References:
+//  Averick, M.B., Carter, R.G., Moré, J.J., Xue, G.-L.: The Minpack-2 Test
+//  Problem Collection. Preprint MCS-P153-0692, Argonne National Laboratory (1992)
+type MinimalSurface struct {
+	bottom, top  []float64
+	left, right  []float64
+	origin, step [2]float64
+}
+
+// NewMinimalSurface creates a new discrete minimal surface problem and
+// precomputes its boundary values. The problem is discretized on a rectilinear
+// grid with nx×ny nodes which means that the problem dimension is (nx-2)(ny-2).
+func NewMinimalSurface(nx, ny int) *MinimalSurface {
+	ms := &MinimalSurface{
+		bottom: make([]float64, nx),
+		top:    make([]float64, nx),
+		left:   make([]float64, ny),
+		right:  make([]float64, ny),
+		origin: [2]float64{-0.5, -0.5},
+		step:   [2]float64{1 / float64(nx-1), 1 / float64(ny-1)},
+	}
+
+	ms.initBoundary(ms.bottom, ms.origin[0], ms.origin[1], ms.step[0], 0)
+	startY := ms.origin[1] + float64(ny-1)*ms.step[1]
+	ms.initBoundary(ms.top, ms.origin[0], startY, ms.step[0], 0)
+	ms.initBoundary(ms.left, ms.origin[0], ms.origin[1], 0, ms.step[1])
+	startX := ms.origin[0] + float64(nx-1)*ms.step[0]
+	ms.initBoundary(ms.right, startX, ms.origin[1], 0, ms.step[1])
+
+	return ms
+}
+
+// Func returns the area of the surface represented by the vector x.
+func (ms *MinimalSurface) Func(x []float64) (area float64) {
+	nx, ny := ms.Dims()
+	if len(x) != (nx-2)*(ny-2) {
+		panic("functions: problem size mismatch")
+	}
+
+	hx, hy := ms.Steps()
+	for j := 0; j < ny-1; j++ {
+		for i := 0; i < nx-1; i++ {
+			vLL := ms.at(i, j, x)
+			vLR := ms.at(i+1, j, x)
+			vUL := ms.at(i, j+1, x)
+			vUR := ms.at(i+1, j+1, x)
+
+			dvLdx := (vLR - vLL) / hx
+			dvLdy := (vUL - vLL) / hy
+			dvUdx := (vUR - vUL) / hx
+			dvUdy := (vUR - vLR) / hy
+
+			fL := math.Sqrt(1 + dvLdx*dvLdx + dvLdy*dvLdy)
+			fU := math.Sqrt(1 + dvUdx*dvUdx + dvUdy*dvUdy)
+			area += fL + fU
+		}
+	}
+	area *= 0.5 * hx * hy
+	return area
+}
+
+// Grad evaluates the area gradient of the surface represented by the vector.
+func (ms *MinimalSurface) Grad(grad, x []float64) {
+	nx, ny := ms.Dims()
+	if len(x) != (nx-2)*(ny-2) {
+		panic("functions: problem size mismatch")
+	}
+	if grad != nil && len(x) != len(grad) {
+		panic("functions: unexpected size mismatch")
+	}
+
+	for i := range grad {
+		grad[i] = 0
+	}
+	hx, hy := ms.Steps()
+	for j := 0; j < ny-1; j++ {
+		for i := 0; i < nx-1; i++ {
+			vLL := ms.at(i, j, x)
+			vLR := ms.at(i+1, j, x)
+			vUL := ms.at(i, j+1, x)
+			vUR := ms.at(i+1, j+1, x)
+
+			dvLdx := (vLR - vLL) / hx
+			dvLdy := (vUL - vLL) / hy
+			dvUdx := (vUR - vUL) / hx
+			dvUdy := (vUR - vLR) / hy
+
+			fL := math.Sqrt(1 + dvLdx*dvLdx + dvLdy*dvLdy)
+			fU := math.Sqrt(1 + dvUdx*dvUdx + dvUdy*dvUdy)
+
+			if grad != nil {
+				if i > 0 {
+					if j > 0 {
+						grad[ms.index(i, j)] -= (dvLdx/hx + dvLdy/hy) / fL
+					}
+					if j < ny-2 {
+						grad[ms.index(i, j+1)] += (dvLdy/hy)/fL - (dvUdx/hx)/fU
+					}
+				}
+				if i < nx-2 {
+					if j > 0 {
+						grad[ms.index(i+1, j)] += (dvLdx/hx)/fL - (dvUdy/hy)/fU
+					}
+					if j < ny-2 {
+						grad[ms.index(i+1, j+1)] += (dvUdx/hx + dvUdy/hy) / fU
+					}
+				}
+			}
+		}
+
+	}
+	cellSize := 0.5 * hx * hy
+	for i := range grad {
+		grad[i] *= cellSize
+	}
+}
+
+// InitX returns a starting location for the minimization problem. Length of
+// the returned slice is (nx-2)(ny-2).
+func (ms *MinimalSurface) InitX() []float64 {
+	nx, ny := ms.Dims()
+	x := make([]float64, (nx-2)*(ny-2))
+	for j := 1; j < ny-1; j++ {
+		for i := 1; i < nx-1; i++ {
+			x[ms.index(i, j)] = (ms.left[j] + ms.bottom[i]) / 2
+		}
+	}
+	return x
+}
+
+// ExactX returns the exact solution to the _continuous_ minimization problem
+// projected on the interior nodes of the grid. Length of the returned slice is
+// (nx-2)(ny-2).
+func (ms *MinimalSurface) ExactX() []float64 {
+	nx, ny := ms.Dims()
+	v := make([]float64, (nx-2)*(ny-2))
+	for j := 1; j < ny-1; j++ {
+		for i := 1; i < nx-1; i++ {
+			v[ms.index(i, j)] = ms.ExactSolution(ms.x(i), ms.y(j))
+		}
+	}
+	return v
+}
+
+// ExactSolution returns the value of the exact solution to the minimal surface
+// problem at (x,y). The exact solution is
+//  F_exact(x,y) = U^2(x,y) - V^2(x,y),
+// where U and V are the unique solutions to the equations
+//  x =  u + uv^2 - u^3/3,
+//  y = -v - u^2v + v^3/3.
+func (ms *MinimalSurface) ExactSolution(x, y float64) float64 {
+	var u = [2]float64{x, -y}
+	var f [2]float64
+	var jac [2][2]float64
+	for k := 0; k < 100; k++ {
+		f[0] = u[0] + u[0]*u[1]*u[1] - u[0]*u[0]*u[0]/3 - x
+		f[1] = -u[1] - u[0]*u[0]*u[1] + u[1]*u[1]*u[1]/3 - y
+		fNorm := math.Hypot(f[0], f[1])
+		if fNorm < 1e-13 {
+			break
+		}
+		jac[0][0] = 1 + u[1]*u[1] - u[0]*u[0]
+		jac[0][1] = 2 * u[0] * u[1]
+		jac[1][0] = -2 * u[0] * u[1]
+		jac[1][1] = -1 - u[0]*u[0] + u[1]*u[1]
+		det := jac[0][0]*jac[1][1] - jac[0][1]*jac[1][0]
+		u[0] -= (jac[1][1]*f[0] - jac[0][1]*f[1]) / det
+		u[1] -= (jac[0][0]*f[1] - jac[1][0]*f[0]) / det
+	}
+	return u[0]*u[0] - u[1]*u[1]
+}
+
+// Dims returns the size of the underlying rectilinear grid.
+func (ms *MinimalSurface) Dims() (nx, ny int) {
+	return len(ms.bottom), len(ms.left)
+}
+
+// Steps returns the spatial step sizes of the underlying rectilinear grid.
+func (ms *MinimalSurface) Steps() (hx, hy float64) {
+	return ms.step[0], ms.step[1]
+}
+
+func (ms *MinimalSurface) x(i int) float64 {
+	return ms.origin[0] + float64(i)*ms.step[0]
+}
+
+func (ms *MinimalSurface) y(j int) float64 {
+	return ms.origin[1] + float64(j)*ms.step[1]
+}
+
+func (ms *MinimalSurface) at(i, j int, x []float64) float64 {
+	nx, ny := ms.Dims()
+	if i < 0 || i >= nx {
+		panic(fmt.Sprintf("node [%v,%v] not on grid", i, j))
+	}
+	if j < 0 || j >= ny {
+		panic(fmt.Sprintf("node [%v,%v] not on grid", i, j))
+	}
+
+	if i == 0 {
+		return ms.left[j]
+	}
+	if j == 0 {
+		return ms.bottom[i]
+	}
+	if i == nx-1 {
+		return ms.right[j]
+	}
+	if j == ny-1 {
+		return ms.top[i]
+	}
+	return x[ms.index(i, j)]
+}
+
+// index maps an interior grid node (i, j) to a one-dimensional index and
+// returns it.
+func (ms *MinimalSurface) index(i, j int) int {
+	nx, ny := ms.Dims()
+	if i <= 0 || i >= nx-1 {
+		panic(fmt.Sprintf("[%v,%v] is not an interior node", i, j))
+	}
+	if j <= 0 || j >= ny-1 {
+		panic(fmt.Sprintf("[%v,%v] is not an interior node", i, j))
+	}
+
+	return i - 1 + (j-1)*(nx-2)
+}
+
+// initBoundary initializes with the exact solution the boundary b whose i-th
+// element b[i] is located at [startX+i×hx, startY+i×hy].
+func (ms *MinimalSurface) initBoundary(b []float64, startX, startY, hx, hy float64) {
+	for i := range b {
+		x := startX + float64(i)*hx
+		y := startY + float64(i)*hy
+		b[i] = ms.ExactSolution(x, y)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/functions/minsurf_test.go b/vendor/gonum.org/v1/gonum/optimize/functions/minsurf_test.go
new file mode 100644
index 00000000..2f123545
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/functions/minsurf_test.go
@@ -0,0 +1,48 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package functions
+
+import (
+	"math"
+	"testing"
+
+	"gonum.org/v1/gonum/diff/fd"
+	"gonum.org/v1/gonum/floats"
+)
+
+func TestMinimalSurface(t *testing.T) {
+	for _, size := range [][2]int{
+		{20, 30},
+		{30, 30},
+		{50, 40},
+	} {
+		f := NewMinimalSurface(size[0], size[1])
+		x0 := f.InitX()
+		grad := make([]float64, len(x0))
+		f.Grad(grad, x0)
+		fdGrad := fd.Gradient(nil, f.Func, x0, &fd.Settings{Formula: fd.Central})
+
+		// Test that the numerical and analytical gradients agree.
+		dist := floats.Distance(grad, fdGrad, math.Inf(1))
+		if dist > 1e-9 {
+			t.Errorf("grid %v x %v: numerical and analytical gradient do not match. |fdGrad - grad|_∞ = %v",
+				size[0], size[1], dist)
+		}
+
+		// Test that the gradient at the minimum is small enough.
+		// In some sense this test is not completely correct because ExactX
+		// returns the exact solution to the continuous problem projected on the
+		// grid, not the exact solution to the discrete problem which we are
+		// solving. This is the reason why a relatively loose tolerance 1e-4
+		// must be used.
+		xSol := f.ExactX()
+		f.Grad(grad, xSol)
+		norm := floats.Norm(grad, math.Inf(1))
+		if norm > 1e-4 {
+			t.Errorf("grid %v x %v: gradient at the minimum not small enough. |grad|_∞ = %v",
+				size[0], size[1], norm)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/functions/validate.go b/vendor/gonum.org/v1/gonum/optimize/functions/validate.go
new file mode 100644
index 00000000..e7c5fee7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/functions/validate.go
@@ -0,0 +1,127 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package functions
+
+import (
+	"math"
+	"testing"
+
+	"gonum.org/v1/gonum/diff/fd"
+	"gonum.org/v1/gonum/floats"
+)
+
+// function represents an objective function.
+type function interface {
+	Func(x []float64) float64
+}
+
+type gradient interface {
+	Grad(grad, x []float64)
+}
+
+// minimumer is an objective function that can also provide information about
+// its minima.
+type minimumer interface {
+	function
+
+	// Minima returns _known_ minima of the function.
+	Minima() []Minimum
+}
+
+// Minimum represents information about an optimal location of a function.
+type Minimum struct {
+	// X is the location of the minimum. X may not be nil.
+	X []float64
+	// F is the value of the objective function at X.
+	F float64
+	// Global indicates if the location is a global minimum.
+	Global bool
+}
+
+type funcTest struct {
+	X []float64
+
+	// F is the expected function value at X.
+	F float64
+	// Gradient is the expected gradient at X. If nil, it is not evaluated.
+	Gradient []float64
+}
+
+// TODO(vladimir-ch): Decide and implement an exported testing function:
+// func Test(f Function, ??? ) ??? {
+// }
+
+const (
+	defaultTol       = 1e-12
+	defaultGradTol   = 1e-9
+	defaultFDGradTol = 1e-5
+)
+
+// testFunction checks that the function can evaluate itself (and its gradient)
+// correctly.
+func testFunction(f function, ftests []funcTest, t *testing.T) {
+	// Make a copy of tests because we may append to the slice.
+	tests := make([]funcTest, len(ftests))
+	copy(tests, ftests)
+
+	// Get information about the function.
+	fMinima, isMinimumer := f.(minimumer)
+	fGradient, isGradient := f.(gradient)
+
+	// If the function is a Minimumer, append its minima to the tests.
+	if isMinimumer {
+		for _, minimum := range fMinima.Minima() {
+			// Allocate gradient only if the function can evaluate it.
+			var grad []float64
+			if isGradient {
+				grad = make([]float64, len(minimum.X))
+			}
+			tests = append(tests, funcTest{
+				X:        minimum.X,
+				F:        minimum.F,
+				Gradient: grad,
+			})
+		}
+	}
+
+	for i, test := range tests {
+		F := f.Func(test.X)
+
+		// Check that the function value is as expected.
+		if math.Abs(F-test.F) > defaultTol {
+			t.Errorf("Test #%d: function value given by Func is incorrect. Want: %v, Got: %v",
+				i, test.F, F)
+		}
+
+		if test.Gradient == nil {
+			continue
+		}
+
+		// Evaluate the finite difference gradient.
+		fdGrad := fd.Gradient(nil, f.Func, test.X, &fd.Settings{
+			Formula: fd.Central,
+			Step:    1e-6,
+		})
+
+		// Check that the finite difference and expected gradients match.
+		if !floats.EqualApprox(fdGrad, test.Gradient, defaultFDGradTol) {
+			dist := floats.Distance(fdGrad, test.Gradient, math.Inf(1))
+			t.Errorf("Test #%d: numerical and expected gradients do not match. |fdGrad - WantGrad|_∞ = %v",
+				i, dist)
+		}
+
+		// If the function is a Gradient, check that it computes the gradient correctly.
+		if isGradient {
+			grad := make([]float64, len(test.Gradient))
+			fGradient.Grad(grad, test.X)
+
+			if !floats.EqualApprox(grad, test.Gradient, defaultGradTol) {
+				dist := floats.Distance(grad, test.Gradient, math.Inf(1))
+				t.Errorf("Test #%d: gradient given by Grad is incorrect. |grad - WantGrad|_∞ = %v",
+					i, dist)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/functions/vlse.go b/vendor/gonum.org/v1/gonum/optimize/functions/vlse.go
new file mode 100644
index 00000000..83fab95f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/functions/vlse.go
@@ -0,0 +1,325 @@
+// Copyright ©2017 The Gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package functions
+
+import "math"
+
+// This file implements functions from the Virtual Library of Simulation Experiments.
+//  https://www.sfu.ca/~ssurjano/optimization.html
+// In many cases gradients and Hessians have been added. In some cases, these
+// are not defined at certain points or manifolds. The gradient in these locations
+// has been set to 0.
+
+// Ackley implements the Ackley function, a function of arbitrary dimension that
+// has many local minima. It has a single global minimum of 0 at 0. Its typical
+// domain is the hypercube of [-32.768, 32.768]^d.
+//  f(x) = -20 * exp(-0.2 sqrt(1/d sum_i x_i^2)) - exp(1/d sum_i cos(2π x_i)) + 20 + exp(1)
+// where d is the input dimension.
+//
+// Reference:
+//  https://www.sfu.ca/~ssurjano/ackley.html (obtained June 2017)
+type Ackley struct{}
+
+func (Ackley) Func(x []float64) float64 {
+	var ss, sc float64
+	for _, v := range x {
+		ss += v * v
+		sc += math.Cos(2 * math.Pi * v)
+	}
+	id := 1 / float64(len(x))
+	return -20*math.Exp(-0.2*math.Sqrt(id*ss)) - math.Exp(id*sc) + 20 + math.E
+}
+
+// Bukin6 implements Bukin's 6th function. The function is two-dimensional, with
+// the typical domain as x_0 ∈ [-15, -5], x_1 ∈ [-3, 3]. The function has a unique
+// global minimum at [-10, 1], and many local minima.
+//  f(x) = 100 * sqrt(|x_1 - 0.01*x_0^2|) + 0.01*|x_0+10|
+// Reference:
+//  https://www.sfu.ca/~ssurjano/bukin6.html (obtained June 2017)
+type Bukin6 struct{}
+
+func (Bukin6) Func(x []float64) float64 {
+	if len(x) != 2 {
+		panic(badInputDim)
+	}
+	return 100*math.Sqrt(math.Abs(x[1]-0.01*x[0]*x[0])) + 0.01*math.Abs(x[0]+10)
+}
+
+// CrossInTray implements the cross-in-tray function. The cross-in-tray function
+// is a two-dimensional function with many local minima, and four global minima
+// at (±1.3491, ±1.3491). The function is typically evaluated in the square
+// [-10,10]^2.
+//  f(x) = -0.001(|sin(x_0)sin(x_1)exp(|100-sqrt((x_0^2+x_1^2)/π)|)|+1)^0.1
+// Reference:
+//  https://www.sfu.ca/~ssurjano/crossit.html (obtained June 2017)
+type CrossInTray struct{}
+
+func (CrossInTray) Func(x []float64) float64 {
+	if len(x) != 2 {
+		panic(badInputDim)
+	}
+	x0 := x[0]
+	x1 := x[1]
+	exp := math.Abs(100 - math.Sqrt((x0*x0+x1*x1)/math.Pi))
+	return -0.0001 * math.Pow(math.Abs(math.Sin(x0)*math.Sin(x1)*math.Exp(exp))+1, 0.1)
+}
+
+// DropWave implements the drop-wave function, a two-dimensional function with
+// many local minima and one global minimum at 0. The function is typically evaluated
+// in the square [-5.12, 5.12]^2.
+//  f(x) = - (1+cos(12*sqrt(x0^2+x1^2))) / (0.5*(x0^2+x1^2)+2)
+// Reference:
+//  https://www.sfu.ca/~ssurjano/drop.html (obtained June 2017)
+type DropWave struct{}
+
+func (DropWave) Func(x []float64) float64 {
+	if len(x) != 2 {
+		panic(badInputDim)
+	}
+	x0 := x[0]
+	x1 := x[1]
+	num := 1 + math.Cos(12*math.Sqrt(x0*x0+x1*x1))
+	den := 0.5*(x0*x0+x1*x1) + 2
+	return -num / den
+}
+
+// Eggholder implements the Eggholder function, a two-dimensional function with
+// many local minima and one global minimum at [512, 404.2319]. The function
+// is typically evaluated in the square [-512, 512]^2.
+//  f(x) = -(x_1+47)*sin(sqrt(|x_1+x_0/2+47|))-x_1*sin(sqrt(|x_0-(x_1+47)|))
+// Reference:
+//  https://www.sfu.ca/~ssurjano/egg.html (obtained June 2017)
+type Eggholder struct{}
+
+func (Eggholder) Func(x []float64) float64 {
+	if len(x) != 2 {
+		panic(badInputDim)
+	}
+	x0 := x[0]
+	x1 := x[1]
+	return -(x1+47)*math.Sin(math.Sqrt(math.Abs(x1+x0/2+47))) -
+		x0*math.Sin(math.Sqrt(math.Abs(x0-x1-47)))
+}
+
+// GramacyLee implements the Gramacy-Lee function, a one-dimensional function
+// with many local minima. The function is typically evaluated on the domain [0.5, 2.5].
+//  f(x) = sin(10πx)/(2x) + (x-1)^4
+// Reference:
+//  https://www.sfu.ca/~ssurjano/grlee12.html (obtained June 2017)
+type GramacyLee struct{}
+
+func (GramacyLee) Func(x []float64) float64 {
+	if len(x) != 1 {
+		panic(badInputDim)
+	}
+	x0 := x[0]
+	return math.Sin(10*math.Pi*x0)/(2*x0) + math.Pow(x0-1, 4)
+}
+
+// Griewank implements the Griewank function, a function of arbitrary dimension that
+// has many local minima. It has a single global minimum of 0 at 0. Its typical
+// domain is the hypercube of [-600, 600]^d.
+//  f(x) = \sum_i x_i^2/4000 - \prod_i cos(x_i/sqrt(i)) + 1
+// where d is the input dimension.
+//
+// Reference:
+//  https://www.sfu.ca/~ssurjano/griewank.html (obtained June 2017)
+type Griewank struct{}
+
+func (Griewank) Func(x []float64) float64 {
+	var ss float64
+	pc := 1.0
+	for i, v := range x {
+		ss += v * v
+		pc *= math.Cos(v / math.Sqrt(float64(i+1)))
+	}
+	return ss/4000 - pc + 1
+}
+
+// HolderTable implements the Holder table function. The Holder table function
+// is a two-dimensional function with many local minima, and four global minima
+// at (±8.05502, ±9.66459). The function is typically evaluated in the square [-10,10]^2.
+//  f(x) = -|sin(x_0)cos(x1)exp(|1-sqrt(x_0^2+x1^2)/π|)|
+// Reference:
+//  https://www.sfu.ca/~ssurjano/holder.html (obtained June 2017)
+type HolderTable struct{}
+
+func (HolderTable) Func(x []float64) float64 {
+	if len(x) != 2 {
+		panic(badInputDim)
+	}
+	x0 := x[0]
+	x1 := x[1]
+	return -math.Abs(math.Sin(x0) * math.Cos(x1) * math.Exp(math.Abs(1-math.Sqrt(x0*x0+x1*x1)/math.Pi)))
+}
+
+// Langermann2 implements the two-dimensional version of the Langermann function.
+// The Langermann function has many local minima. The function is typically
+// evaluated in the square [0,10]^2.
+//  f(x) = \sum_1^5 c_i exp(-(1/π)\sum_{j=1}^2(x_j-A_{ij})^2) * cos(π\sum_{j=1}^2 (x_j - A_{ij})^2)
+//  c = [5]float64{1,2,5,2,3}
+//  A = [5][2]float64{{3,5},{5,2},{2,1},{1,4},{7,9}}
+// Reference:
+//  https://www.sfu.ca/~ssurjano/langer.html (obtained June 2017)
+type Langermann2 struct{}
+
+func (Langermann2) Func(x []float64) float64 {
+	if len(x) != 2 {
+		panic(badInputDim)
+	}
+	var (
+		c = [5]float64{1, 2, 5, 2, 3}
+		A = [5][2]float64{{3, 5}, {5, 2}, {2, 1}, {1, 4}, {7, 9}}
+	)
+	var f float64
+	for i, cv := range c {
+		var ss float64
+		for j, av := range A[i] {
+			xja := x[j] - av
+			ss += xja * xja
+		}
+		f += cv * math.Exp(-(1/math.Pi)*ss) * math.Cos(math.Pi*ss)
+	}
+	return f
+}
+
+// Levy implements the Levy function, a function of arbitrary dimension that
+// has many local minima. It has a single global minimum of 0 at 1. Its typical
+// domain is the hypercube of [-10, 10]^d.
+//  f(x) = sin^2(π*w_0) + \sum_{i=0}^{d-2}(w_i-1)^2*[1+10sin^2(π*w_i+1)] +
+//            (w_{d-1}-1)^2*[1+sin^2(2π*w_{d-1})]
+//   w_i = 1 + (x_i-1)/4
+// where d is the input dimension.
+//
+// Reference:
+//  https://www.sfu.ca/~ssurjano/levy.html (obtained June 2017)
+type Levy struct{}
+
+func (Levy) Func(x []float64) float64 {
+	w1 := 1 + (x[0]-1)/4
+	s1 := math.Sin(math.Pi * w1)
+	sum := s1 * s1
+	for i := 0; i < len(x)-1; i++ {
+		wi := 1 + (x[i]-1)/4
+		s := math.Sin(math.Pi*wi + 1)
+		sum += (wi - 1) * (wi - 1) * (1 + 10*s*s)
+	}
+	wd := 1 + (x[len(x)-1]-1)/4
+	sd := math.Sin(2 * math.Pi * wd)
+	return sum + (wd-1)*(wd-1)*(1+sd*sd)
+}
+
+// Levy13 implements the Levy-13 function, a two-dimensional function
+// with many local minima. It has a single global minimum of 0 at 1. Its typical
+// domain is the square [-10, 10]^2.
+//  f(x) = sin^2(3π*x_0) + (x_0-1)^2*[1+sin^2(3π*x_1)] + (x_1-1)^2*[1+sin^2(2π*x_1)]
+// Reference:
+//  https://www.sfu.ca/~ssurjano/levy13.html (obtained June 2017)
+type Levy13 struct{}
+
+func (Levy13) Func(x []float64) float64 {
+	if len(x) != 2 {
+		panic(badInputDim)
+	}
+	x0 := x[0]
+	x1 := x[1]
+	s0 := math.Sin(3 * math.Pi * x0)
+	s1 := math.Sin(3 * math.Pi * x1)
+	s2 := math.Sin(2 * math.Pi * x1)
+	return s0*s0 + (x0-1)*(x0-1)*(1+s1*s1) + (x1-1)*(x1-1)*(1+s2*s2)
+}
+
+// Rastrigin implements the Rastrigen function, a function of arbitrary dimension
+// that has many local minima. It has a single global minimum of 0 at 0. Its typical
+// domain is the hypercube of [-5.12, 5.12]^d.
+//  f(x) = 10d + \sum_i [x_i^2 - 10cos(2π*x_i)]
+// where d is the input dimension.
+//
+// Reference:
+//  https://www.sfu.ca/~ssurjano/rastr.html (obtained June 2017)
+type Rastrigin struct{}
+
+func (Rastrigin) Func(x []float64) float64 {
+	sum := 10 * float64(len(x))
+	for _, v := range x {
+		sum += v*v - 10*math.Cos(2*math.Pi*v)
+	}
+	return sum
+}
+
+// Schaffer2 implements the second Schaffer function, a two-dimensional function
+// with many local minima. It has a single global minimum of 0 at 0. Its typical
+// domain is the square [-100, 100]^2.
+//  f(x) = 0.5 + (sin^2(x_0^2-x_1^2)-0.5) / (1+0.001*(x_0^2+x_1^2))^2
+// Reference:
+//  https://www.sfu.ca/~ssurjano/schaffer2.html (obtained June 2017)
+type Schaffer2 struct{}
+
+func (Schaffer2) Func(x []float64) float64 {
+	if len(x) != 2 {
+		panic(badInputDim)
+	}
+	x0 := x[0]
+	x1 := x[1]
+	s := math.Sin(x0*x0 - x1*x1)
+	den := 1 + 0.001*(x0*x0+x1*x1)
+	return 0.5 + (s*s-0.5)/(den*den)
+}
+
+// Schaffer4 implements the fourth Schaffer function, a two-dimensional function
+// with many local minima. Its typical domain is the square [-100, 100]^2.
+//  f(x) = 0.5 + (cos(sin(|x_0^2-x_1^2|))-0.5) / (1+0.001*(x_0^2+x_1^2))^2
+// Reference:
+//  https://www.sfu.ca/~ssurjano/schaffer4.html (obtained June 2017)
+type Schaffer4 struct{}
+
+func (Schaffer4) Func(x []float64) float64 {
+	if len(x) != 2 {
+		panic(badInputDim)
+	}
+	x0 := x[0]
+	x1 := x[1]
+	den := 1 + 0.001*(x0*x0+x1*x1)
+	return 0.5 + (math.Cos(math.Sin(math.Abs(x0*x0-x1*x1)))-0.5)/(den*den)
+}
+
+// Schwefel implements the Schwefel function, a function of arbitrary dimension
+// that has many local minima. Its typical domain is the hypercube of [-500, 500]^d.
+//  f(x) = 418.9829*d - \sum_i x_i*sin(sqrt(|x_i|))
+// where d is the input dimension.
+//
+// Reference:
+//  https://www.sfu.ca/~ssurjano/schwef.html (obtained June 2017)
+type Schwefel struct{}
+
+func (Schwefel) Func(x []float64) float64 {
+	var sum float64
+	for _, v := range x {
+		sum += v * math.Sin(math.Sqrt(math.Abs(v)))
+	}
+	return 418.9829*float64(len(x)) - sum
+}
+
+// Shubert implements the Shubert function, a two-dimensional function
+// with many local minima and many global minima. Its typical domain is the
+// square [-10, 10]^2.
+//  f(x) = (sum_{i=1}^5 i cos((i+1)*x_0+i)) * (\sum_{i=1}^5 i cos((i+1)*x_1+i))
+// Reference:
+//  https://www.sfu.ca/~ssurjano/shubert.html (obtained June 2017)
+type Shubert struct{}
+
+func (Shubert) Func(x []float64) float64 {
+	if len(x) != 2 {
+		panic(badInputDim)
+	}
+	x0 := x[0]
+	x1 := x[1]
+	var s0, s1 float64
+	for i := 1.0; i <= 5.0; i++ {
+		s0 += i * math.Cos((i+1)*x0+i)
+		s1 += i * math.Cos((i+1)*x1+i)
+	}
+	return s0 * s1
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/global.go b/vendor/gonum.org/v1/gonum/optimize/global.go
new file mode 100644
index 00000000..9f73b753
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/global.go
@@ -0,0 +1,239 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package optimize
+
+import (
+	"math"
+	"sync"
+	"time"
+)
+
+// GlobalMethod is a global optimizer. Typically will require more function
+// evaluations and no sense of local convergence
+type GlobalMethod interface {
+	// Global tells method the max number of tasks, method returns how many it wants.
+	// This is needed to sync the Global goroutines and inside goroutines.
+	InitGlobal(dim, tasks int) int
+	// Global method may assume that the same task id always has the same pointer with it.
+	IterateGlobal(task int, loc *Location) (Operation, error)
+	Needser
+	// Done communicates to the optimization method that the optimization has
+	// concluded to allow for shutdown.
+	Done()
+}
+
+// Global uses a global optimizer to search for the global minimum of a
+// function. A maximization problem can be transformed into a
+// minimization problem by multiplying the function by -1.
+//
+// The first argument represents the problem to be minimized. Its fields are
+// routines that evaluate the objective function, gradient, and other
+// quantities related to the problem. The objective function, p.Func, must not
+// be nil. The optimization method used may require other fields to be non-nil
+// as specified by method.Needs. Global will panic if these are not met. The
+// method can be determined automatically from the supplied problem which is
+// described below.
+//
+// If p.Status is not nil, it is called before every evaluation. If the
+// returned Status is not NotTerminated or the error is not nil, the
+// optimization run is terminated.
+//
+// The third argument contains the settings for the minimization. The
+// DefaultGlobalSettings function can be called for a Settings struct with the
+// default values initialized. If settings == nil, the default settings are used.
+// Global optimization methods typically do not make assumptions about the number
+// and location of local minima. Thus, the only convergence metric used is the
+// function values found at major iterations of the optimization. Bounds on the
+// length of optimization are obeyed, such as the number of allowed function
+// evaluations.
+//
+// The final argument is the optimization method to use. If method == nil, then
+// an appropriate default is chosen based on the properties of the other arguments
+// (dimension, gradient-free or gradient-based, etc.).
+//
+// If method implements Statuser, method.Status is called before every call
+// to method.Iterate. If the returned Status is not NotTerminated or the
+// error is non-nil, the optimization run is terminated.
+//
+// Global returns a Result struct and any error that occurred. See the
+// documentation of Result for more information.
+//
+// Be aware that the default behavior of Global is to find the minimum.
+// For certain functions and optimization methods, this process can take many
+// function evaluations. If you would like to put limits on this, for example
+// maximum runtime or maximum function evaluations, modify the Settings
+// input struct.
+//
+// Something about Global cannot guarantee strict bounds on function evaluations,
+// iterations, etc. in the precense of concurrency.
+func Global(p Problem, dim int, settings *Settings, method GlobalMethod) (*Result, error) {
+	startTime := time.Now()
+	if method == nil {
+		method = &GuessAndCheck{}
+	}
+	if settings == nil {
+		settings = DefaultSettingsGlobal()
+	}
+	stats := &Stats{}
+	err := checkOptimization(p, dim, method, settings.Recorder)
+	if err != nil {
+		return nil, err
+	}
+
+	optLoc := newLocation(dim, method)
+	optLoc.F = math.Inf(1)
+
+	if settings.FunctionConverge != nil {
+		settings.FunctionConverge.Init(optLoc.F)
+	}
+
+	stats.Runtime = time.Since(startTime)
+
+	// Send initial location to Recorder
+	if settings.Recorder != nil {
+		err = settings.Recorder.Record(optLoc, InitIteration, stats)
+		if err != nil {
+			return nil, err
+		}
+	}
+
+	// Run optimization
+	var status Status
+	status, err = minimizeGlobal(&p, method, settings, stats, optLoc, startTime)
+
+	// Cleanup and collect results
+	if settings.Recorder != nil && err == nil {
+		err = settings.Recorder.Record(optLoc, PostIteration, stats)
+	}
+	stats.Runtime = time.Since(startTime)
+	return &Result{
+		Location: *optLoc,
+		Stats:    *stats,
+		Status:   status,
+	}, err
+}
+
+func minimizeGlobal(p *Problem, method GlobalMethod, settings *Settings, stats *Stats, optLoc *Location, startTime time.Time) (status Status, err error) {
+	dim := len(optLoc.X)
+	statuser, _ := method.(Statuser)
+	gs := &globalStatus{
+		mux:       &sync.RWMutex{},
+		stats:     stats,
+		status:    NotTerminated,
+		p:         p,
+		startTime: startTime,
+		optLoc:    optLoc,
+		settings:  settings,
+		statuser:  statuser,
+	}
+
+	nTasks := settings.Concurrent
+	nTasks = method.InitGlobal(dim, nTasks)
+
+	// Launch optimization workers
+	var wg sync.WaitGroup
+	for task := 0; task < nTasks; task++ {
+		wg.Add(1)
+		go func(task int) {
+			defer wg.Done()
+			loc := newLocation(dim, method)
+			x := make([]float64, dim)
+			globalWorker(task, method, gs, loc, x)
+		}(task)
+	}
+	wg.Wait()
+	method.Done()
+	return gs.status, gs.err
+}
+
+type globalStatus struct {
+	mux       *sync.RWMutex
+	stats     *Stats
+	status    Status
+	p         *Problem
+	startTime time.Time
+	optLoc    *Location
+	settings  *Settings
+	statuser  Statuser
+	err       error
+}
+
+func globalWorker(task int, m GlobalMethod, g *globalStatus, loc *Location, x []float64) {
+	for {
+		// Find Evaluation location
+		op, err := m.IterateGlobal(task, loc)
+		if err != nil {
+			// TODO(btracey): Figure out how to handle errors properly. Shut
+			// everything down? Pass to globalStatus so it can shut everything down?
+			g.mux.Lock()
+			g.err = err
+			g.status = Failure
+			g.mux.Unlock()
+			break
+		}
+
+		// Evaluate location and/or update stats.
+		status := g.globalOperation(op, loc, x)
+		if status != NotTerminated {
+			break
+		}
+	}
+}
+
+// globalOperation updates handles the status received by an individual worker.
+// It uses a mutex to protect updates where necessary.
+func (g *globalStatus) globalOperation(op Operation, loc *Location, x []float64) Status {
+	// Do a quick check to see if one of the other workers converged in the meantime.
+	var status Status
+	var err error
+	g.mux.RLock()
+	status = g.status
+	g.mux.RUnlock()
+	if status != NotTerminated {
+		return status
+	}
+	switch op {
+	case NoOperation:
+	case InitIteration:
+		panic("optimize: Method returned InitIteration")
+	case PostIteration:
+		panic("optimize: Method returned PostIteration")
+	case MajorIteration:
+		g.mux.Lock()
+		g.stats.MajorIterations++
+		copyLocation(g.optLoc, loc)
+		g.mux.Unlock()
+
+		g.mux.RLock()
+		status = checkConvergence(g.optLoc, g.settings, false)
+		g.mux.RUnlock()
+	default: // Any of the Evaluation operations.
+		status, err = evaluate(g.p, loc, op, x)
+		g.mux.Lock()
+		updateStats(g.stats, op)
+		g.mux.Unlock()
+	}
+
+	g.mux.Lock()
+	status, err = iterCleanup(status, err, g.stats, g.settings, g.statuser, g.startTime, loc, op)
+	// Update the termination status if it hasn't already terminated.
+	if g.status == NotTerminated {
+		g.status = status
+		g.err = err
+	}
+	g.mux.Unlock()
+
+	return status
+}
+
+func DefaultSettingsGlobal() *Settings {
+	return &Settings{
+		FunctionThreshold: math.Inf(-1),
+		FunctionConverge: &FunctionConverge{
+			Absolute:   1e-10,
+			Iterations: 100,
+		},
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/gradientdescent.go b/vendor/gonum.org/v1/gonum/optimize/gradientdescent.go
new file mode 100644
index 00000000..292bf5c9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/gradientdescent.go
@@ -0,0 +1,63 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package optimize
+
+import "gonum.org/v1/gonum/floats"
+
+// GradientDescent implements the steepest descent optimization method that
+// performs successive steps along the direction of the negative gradient.
+type GradientDescent struct {
+	// Linesearcher selects suitable steps along the descent direction.
+	// If Linesearcher is nil, a reasonable default will be chosen.
+	Linesearcher Linesearcher
+	// StepSizer determines the initial step size along each direction.
+	// If StepSizer is nil, a reasonable default will be chosen.
+	StepSizer StepSizer
+
+	ls *LinesearchMethod
+}
+
+func (g *GradientDescent) Init(loc *Location) (Operation, error) {
+	if g.Linesearcher == nil {
+		g.Linesearcher = &Backtracking{}
+	}
+	if g.StepSizer == nil {
+		g.StepSizer = &QuadraticStepSize{}
+	}
+
+	if g.ls == nil {
+		g.ls = &LinesearchMethod{}
+	}
+	g.ls.Linesearcher = g.Linesearcher
+	g.ls.NextDirectioner = g
+
+	return g.ls.Init(loc)
+}
+
+func (g *GradientDescent) Iterate(loc *Location) (Operation, error) {
+	return g.ls.Iterate(loc)
+}
+
+func (g *GradientDescent) InitDirection(loc *Location, dir []float64) (stepSize float64) {
+	copy(dir, loc.Gradient)
+	floats.Scale(-1, dir)
+	return g.StepSizer.Init(loc, dir)
+}
+
+func (g *GradientDescent) NextDirection(loc *Location, dir []float64) (stepSize float64) {
+	copy(dir, loc.Gradient)
+	floats.Scale(-1, dir)
+	return g.StepSizer.StepSize(loc, dir)
+}
+
+func (*GradientDescent) Needs() struct {
+	Gradient bool
+	Hessian  bool
+} {
+	return struct {
+		Gradient bool
+		Hessian  bool
+	}{true, false}
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/guessandcheck.go b/vendor/gonum.org/v1/gonum/optimize/guessandcheck.go
new file mode 100644
index 00000000..e08fc4c6
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/guessandcheck.go
@@ -0,0 +1,60 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package optimize
+
+import (
+	"math"
+	"sync"
+
+	"gonum.org/v1/gonum/stat/distmv"
+)
+
+// GuessAndCheck is a global optimizer that evaluates the function at random
+// locations. Not a good optimizer, but useful for comparison and debugging.
+type GuessAndCheck struct {
+	Rander distmv.Rander
+
+	eval []bool
+
+	mux   *sync.Mutex
+	bestF float64
+	bestX []float64
+}
+
+func (g *GuessAndCheck) Needs() struct{ Gradient, Hessian bool } {
+	return struct{ Gradient, Hessian bool }{false, false}
+}
+
+func (g *GuessAndCheck) Done() {
+	// No cleanup needed
+}
+
+func (g *GuessAndCheck) InitGlobal(dim, tasks int) int {
+	g.eval = make([]bool, tasks)
+	g.bestF = math.Inf(1)
+	g.bestX = resize(g.bestX, dim)
+	g.mux = &sync.Mutex{}
+	return tasks
+}
+
+func (g *GuessAndCheck) IterateGlobal(task int, loc *Location) (Operation, error) {
+	// Task is true if it contains a new function evaluation.
+	if g.eval[task] {
+		g.eval[task] = false
+		g.mux.Lock()
+		if loc.F < g.bestF {
+			g.bestF = loc.F
+			copy(g.bestX, loc.X)
+		} else {
+			loc.F = g.bestF
+			copy(loc.X, g.bestX)
+		}
+		g.mux.Unlock()
+		return MajorIteration, nil
+	}
+	g.eval[task] = true
+	g.Rander.Rand(loc.X)
+	return FuncEvaluation, nil
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/guessandcheck_test.go b/vendor/gonum.org/v1/gonum/optimize/guessandcheck_test.go
new file mode 100644
index 00000000..d906f907
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/guessandcheck_test.go
@@ -0,0 +1,34 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package optimize
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/mat"
+	"gonum.org/v1/gonum/optimize/functions"
+	"gonum.org/v1/gonum/stat/distmv"
+)
+
+func TestGuessAndCheck(t *testing.T) {
+	dim := 3000
+	problem := Problem{
+		Func: functions.ExtendedRosenbrock{}.Func,
+	}
+	mu := make([]float64, dim)
+	sigma := mat.NewSymDense(dim, nil)
+	for i := 0; i < dim; i++ {
+		sigma.SetSym(i, i, 1)
+	}
+	d, ok := distmv.NewNormal(mu, sigma, nil)
+	if !ok {
+		panic("bad test")
+	}
+	Global(problem, dim, nil, &GuessAndCheck{Rander: d})
+	settings := DefaultSettingsGlobal()
+	settings.Concurrent = 5
+	settings.MajorIterations = 15
+	Global(problem, dim, settings, &GuessAndCheck{Rander: d})
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/interfaces.go b/vendor/gonum.org/v1/gonum/optimize/interfaces.go
new file mode 100644
index 00000000..12544610
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/interfaces.go
@@ -0,0 +1,130 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package optimize
+
+// A Method can optimize an objective function.
+//
+// It uses a reverse-communication interface between the optimization method
+// and the caller. Method acts as a client that asks the caller to perform
+// needed operations via Operation returned from Init and Iterate methods.
+// This provides independence of the optimization algorithm on user-supplied
+// data and their representation, and enables automation of common operations
+// like checking for (various types of) convergence and maintaining statistics.
+//
+// A Method can command an Evaluation, a MajorIteration or NoOperation operations.
+//
+// An evaluation operation is one or more of the Evaluation operations
+// (FuncEvaluation, GradEvaluation, etc.) which can be combined with
+// the bitwise or operator. In an evaluation operation, the requested fields of
+// Problem will be evaluated at the point specified in Location.X.
+// The corresponding fields of Location will be filled with the results that
+// can be retrieved upon the next call to Iterate. The Method interface
+// requires that entries of Location are not modified aside from the commanded
+// evaluations. Thus, the type implementing Method may use multiple Operations
+// to set the Location fields at a particular x value.
+//
+// Instead of an Evaluation, a Method may declare MajorIteration. In
+// a MajorIteration, the values in the fields of Location are treated as
+// a potential optimizer. The convergence of the optimization routine
+// (GradientThreshold, etc.) is checked at this new best point. In
+// a MajorIteration, the fields of Location must be valid and consistent.
+//
+// A Method must not return InitIteration and PostIteration operations. These are
+// reserved for the clients to be passed to Recorders. A Method must also not
+// combine the Evaluation operations with the Iteration operations.
+type Method interface {
+	// Init initializes the method based on the initial data in loc, updates it
+	// and returns the first operation to be carried out by the caller.
+	// The initial location must be valid as specified by Needs.
+	Init(loc *Location) (Operation, error)
+
+	// Iterate retrieves data from loc, performs one iteration of the method,
+	// updates loc and returns the next operation.
+	Iterate(loc *Location) (Operation, error)
+
+	Needser
+}
+
+type Needser interface {
+	// Needs specifies information about the objective function needed by the
+	// optimizer beyond just the function value. The information is used
+	// internally for initialization and must match evaluation types returned
+	// by Init and Iterate during the optimization process.
+	Needs() struct {
+		Gradient bool
+		Hessian  bool
+	}
+}
+
+// Statuser can report the status and any error. It is intended for methods as
+// an additional error reporting mechanism apart from the errors returned from
+// Init and Iterate.
+type Statuser interface {
+	Status() (Status, error)
+}
+
+// Linesearcher is a type that can perform a line search. It tries to find an
+// (approximate) minimum of the objective function along the search direction
+// dir_k starting at the most recent location x_k, i.e., it tries to minimize
+// the function
+//  φ(step) := f(x_k + step * dir_k) where step > 0.
+// Typically, a Linesearcher will be used in conjunction with LinesearchMethod
+// for performing gradient-based optimization through sequential line searches.
+type Linesearcher interface {
+	// Init initializes the Linesearcher and a new line search. Value and
+	// derivative contain φ(0) and φ'(0), respectively, and step contains the
+	// first trial step length. It returns an Operation that must be one of
+	// FuncEvaluation, GradEvaluation, FuncEvaluation|GradEvaluation. The
+	// caller must evaluate φ(step), φ'(step), or both, respectively, and pass
+	// the result to Linesearcher in value and derivative arguments to Iterate.
+	Init(value, derivative float64, step float64) Operation
+
+	// Iterate takes in the values of φ and φ' evaluated at the previous step
+	// and returns the next operation.
+	//
+	// If op is one of FuncEvaluation, GradEvaluation,
+	// FuncEvaluation|GradEvaluation, the caller must evaluate φ(step),
+	// φ'(step), or both, respectively, and pass the result to Linesearcher in
+	// value and derivative arguments on the next call to Iterate.
+	//
+	// If op is MajorIteration, a sufficiently accurate minimum of φ has been
+	// found at the previous step and the line search has concluded. Init must
+	// be called again to initialize a new line search.
+	//
+	// If err is nil, op must not specify another operation. If err is not nil,
+	// the values of op and step are undefined.
+	Iterate(value, derivative float64) (op Operation, step float64, err error)
+}
+
+// NextDirectioner implements a strategy for computing a new line search
+// direction at each major iteration. Typically, a NextDirectioner will be
+// used in conjunction with LinesearchMethod for performing gradient-based
+// optimization through sequential line searches.
+type NextDirectioner interface {
+	// InitDirection initializes the NextDirectioner at the given starting location,
+	// putting the initial direction in place into dir, and returning the initial
+	// step size. InitDirection must not modify Location.
+	InitDirection(loc *Location, dir []float64) (step float64)
+
+	// NextDirection updates the search direction and step size. Location is
+	// the location seen at the conclusion of the most recent linesearch. The
+	// next search direction is put in place into dir, and the next step size
+	// is returned. NextDirection must not modify Location.
+	NextDirection(loc *Location, dir []float64) (step float64)
+}
+
+// StepSizer can set the next step size of the optimization given the last Location.
+// Returned step size must be positive.
+type StepSizer interface {
+	Init(loc *Location, dir []float64) float64
+	StepSize(loc *Location, dir []float64) float64
+}
+
+// A Recorder can record the progress of the optimization, for example to print
+// the progress to StdOut or to a log file. A Recorder must not modify any data.
+type Recorder interface {
+	Init() error
+	Record(*Location, Operation, *Stats) error
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/lbfgs.go b/vendor/gonum.org/v1/gonum/optimize/lbfgs.go
new file mode 100644
index 00000000..5c549377
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/lbfgs.go
@@ -0,0 +1,167 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package optimize
+
+import (
+	"gonum.org/v1/gonum/floats"
+)
+
+// LBFGS implements the limited-memory BFGS method for gradient-based
+// unconstrained minimization.
+//
+// It stores a modified version of the inverse Hessian approximation H
+// implicitly from the last Store iterations while the normal BFGS method
+// stores and manipulates H directly as a dense matrix. Therefore LBFGS is more
+// appropriate than BFGS for large problems as the cost of LBFGS scales as
+// O(Store * dim) while BFGS scales as O(dim^2). The "forgetful" nature of
+// LBFGS may also make it perform better than BFGS for functions with Hessians
+// that vary rapidly spatially.
+type LBFGS struct {
+	// Linesearcher selects suitable steps along the descent direction.
+	// Accepted steps should satisfy the strong Wolfe conditions.
+	// If Linesearcher is nil, a reasonable default will be chosen.
+	Linesearcher Linesearcher
+	// Store is the size of the limited-memory storage.
+	// If Store is 0, it will be defaulted to 15.
+	Store int
+
+	ls *LinesearchMethod
+
+	dim  int       // Dimension of the problem
+	x    []float64 // Location at the last major iteration
+	grad []float64 // Gradient at the last major iteration
+
+	// History
+	oldest int         // Index of the oldest element of the history
+	y      [][]float64 // Last Store values of y
+	s      [][]float64 // Last Store values of s
+	rho    []float64   // Last Store values of rho
+	a      []float64   // Cache of Hessian updates
+}
+
+func (l *LBFGS) Init(loc *Location) (Operation, error) {
+	if l.Linesearcher == nil {
+		l.Linesearcher = &Bisection{}
+	}
+	if l.Store == 0 {
+		l.Store = 15
+	}
+
+	if l.ls == nil {
+		l.ls = &LinesearchMethod{}
+	}
+	l.ls.Linesearcher = l.Linesearcher
+	l.ls.NextDirectioner = l
+
+	return l.ls.Init(loc)
+}
+
+func (l *LBFGS) Iterate(loc *Location) (Operation, error) {
+	return l.ls.Iterate(loc)
+}
+
+func (l *LBFGS) InitDirection(loc *Location, dir []float64) (stepSize float64) {
+	dim := len(loc.X)
+	l.dim = dim
+	l.oldest = 0
+
+	l.a = resize(l.a, l.Store)
+	l.rho = resize(l.rho, l.Store)
+	l.y = l.initHistory(l.y)
+	l.s = l.initHistory(l.s)
+
+	l.x = resize(l.x, dim)
+	copy(l.x, loc.X)
+
+	l.grad = resize(l.grad, dim)
+	copy(l.grad, loc.Gradient)
+
+	copy(dir, loc.Gradient)
+	floats.Scale(-1, dir)
+	return 1 / floats.Norm(dir, 2)
+}
+
+func (l *LBFGS) initHistory(hist [][]float64) [][]float64 {
+	c := cap(hist)
+	if c < l.Store {
+		n := make([][]float64, l.Store-c)
+		hist = append(hist[:c], n...)
+	}
+	hist = hist[:l.Store]
+	for i := range hist {
+		hist[i] = resize(hist[i], l.dim)
+		for j := range hist[i] {
+			hist[i][j] = 0
+		}
+	}
+	return hist
+}
+
+func (l *LBFGS) NextDirection(loc *Location, dir []float64) (stepSize float64) {
+	// Uses two-loop correction as described in
+	// Nocedal, J., Wright, S.: Numerical Optimization (2nd ed). Springer (2006), chapter 7, page 178.
+
+	if len(loc.X) != l.dim {
+		panic("lbfgs: unexpected size mismatch")
+	}
+	if len(loc.Gradient) != l.dim {
+		panic("lbfgs: unexpected size mismatch")
+	}
+	if len(dir) != l.dim {
+		panic("lbfgs: unexpected size mismatch")
+	}
+
+	y := l.y[l.oldest]
+	floats.SubTo(y, loc.Gradient, l.grad)
+	s := l.s[l.oldest]
+	floats.SubTo(s, loc.X, l.x)
+	sDotY := floats.Dot(s, y)
+	l.rho[l.oldest] = 1 / sDotY
+
+	l.oldest = (l.oldest + 1) % l.Store
+
+	copy(l.x, loc.X)
+	copy(l.grad, loc.Gradient)
+	copy(dir, loc.Gradient)
+
+	// Start with the most recent element and go backward,
+	for i := 0; i < l.Store; i++ {
+		idx := l.oldest - i - 1
+		if idx < 0 {
+			idx += l.Store
+		}
+		l.a[idx] = l.rho[idx] * floats.Dot(l.s[idx], dir)
+		floats.AddScaled(dir, -l.a[idx], l.y[idx])
+	}
+
+	// Scale the initial Hessian.
+	gamma := sDotY / floats.Dot(y, y)
+	floats.Scale(gamma, dir)
+
+	// Start with the oldest element and go forward.
+	for i := 0; i < l.Store; i++ {
+		idx := i + l.oldest
+		if idx >= l.Store {
+			idx -= l.Store
+		}
+		beta := l.rho[idx] * floats.Dot(l.y[idx], dir)
+		floats.AddScaled(dir, l.a[idx]-beta, l.s[idx])
+	}
+
+	// dir contains H^{-1} * g, so flip the direction for minimization.
+	floats.Scale(-1, dir)
+
+	return 1
+}
+
+func (*LBFGS) Needs() struct {
+	Gradient bool
+	Hessian  bool
+} {
+	return struct {
+		Gradient bool
+		Hessian  bool
+	}{true, false}
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/linesearch.go b/vendor/gonum.org/v1/gonum/optimize/linesearch.go
new file mode 100644
index 00000000..37ccb90e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/linesearch.go
@@ -0,0 +1,218 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package optimize
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+// LinesearchMethod represents an abstract optimization method in which a
+// function is optimized through successive line search optimizations.
+type LinesearchMethod struct {
+	// NextDirectioner specifies the search direction of each linesearch.
+	NextDirectioner NextDirectioner
+	// Linesearcher performs a linesearch along the search direction.
+	Linesearcher Linesearcher
+
+	x   []float64 // Starting point for the current iteration.
+	dir []float64 // Search direction for the current iteration.
+
+	first     bool      // Indicator of the first iteration.
+	nextMajor bool      // Indicates that MajorIteration must be commanded at the next call to Iterate.
+	eval      Operation // Indicator of valid fields in Location.
+
+	lastStep float64   // Step taken from x in the previous call to Iterate.
+	lastOp   Operation // Operation returned from the previous call to Iterate.
+}
+
+func (ls *LinesearchMethod) Init(loc *Location) (Operation, error) {
+	if loc.Gradient == nil {
+		panic("linesearch: gradient is nil")
+	}
+
+	dim := len(loc.X)
+	ls.x = resize(ls.x, dim)
+	ls.dir = resize(ls.dir, dim)
+
+	ls.first = true
+	ls.nextMajor = false
+
+	// Indicate that all fields of loc are valid.
+	ls.eval = FuncEvaluation | GradEvaluation
+	if loc.Hessian != nil {
+		ls.eval |= HessEvaluation
+	}
+
+	ls.lastStep = math.NaN()
+	ls.lastOp = NoOperation
+
+	return ls.initNextLinesearch(loc)
+}
+
+func (ls *LinesearchMethod) Iterate(loc *Location) (Operation, error) {
+	switch ls.lastOp {
+	case NoOperation:
+		// TODO(vladimir-ch): Either Init has not been called, or the caller is
+		// trying to resume the optimization run after Iterate previously
+		// returned with an error. Decide what is the proper thing to do. See also #125.
+
+	case MajorIteration:
+		// The previous updated location did not converge the full
+		// optimization. Initialize a new Linesearch.
+		return ls.initNextLinesearch(loc)
+
+	default:
+		// Update the indicator of valid fields of loc.
+		ls.eval |= ls.lastOp
+
+		if ls.nextMajor {
+			ls.nextMajor = false
+
+			// Linesearcher previously finished, and the invalid fields of loc
+			// have now been validated. Announce MajorIteration.
+			ls.lastOp = MajorIteration
+			return ls.lastOp, nil
+		}
+	}
+
+	// Continue the linesearch.
+
+	f := math.NaN()
+	if ls.eval&FuncEvaluation != 0 {
+		f = loc.F
+	}
+	projGrad := math.NaN()
+	if ls.eval&GradEvaluation != 0 {
+		projGrad = floats.Dot(loc.Gradient, ls.dir)
+	}
+	op, step, err := ls.Linesearcher.Iterate(f, projGrad)
+	if err != nil {
+		return ls.error(err)
+	}
+
+	switch op {
+	case MajorIteration:
+		// Linesearch has been finished.
+
+		ls.lastOp = complementEval(loc, ls.eval)
+		if ls.lastOp == NoOperation {
+			// loc is complete, MajorIteration can be declared directly.
+			ls.lastOp = MajorIteration
+		} else {
+			// Declare MajorIteration on the next call to Iterate.
+			ls.nextMajor = true
+		}
+
+	case FuncEvaluation, GradEvaluation, FuncEvaluation | GradEvaluation:
+		if step != ls.lastStep {
+			// We are moving to a new location, and not, say, evaluating extra
+			// information at the current location.
+
+			// Compute the next evaluation point and store it in loc.X.
+			floats.AddScaledTo(loc.X, ls.x, step, ls.dir)
+			if floats.Equal(ls.x, loc.X) {
+				// Step size has become so small that the next evaluation point is
+				// indistinguishable from the starting point for the current
+				// iteration due to rounding errors.
+				return ls.error(ErrNoProgress)
+			}
+			ls.lastStep = step
+			ls.eval = NoOperation // Indicate all invalid fields of loc.
+		}
+		ls.lastOp = op
+
+	default:
+		panic("linesearch: Linesearcher returned invalid operation")
+	}
+
+	return ls.lastOp, nil
+}
+
+func (ls *LinesearchMethod) error(err error) (Operation, error) {
+	ls.lastOp = NoOperation
+	return ls.lastOp, err
+}
+
+// initNextLinesearch initializes the next linesearch using the previous
+// complete location stored in loc. It fills loc.X and returns an evaluation
+// to be performed at loc.X.
+func (ls *LinesearchMethod) initNextLinesearch(loc *Location) (Operation, error) {
+	copy(ls.x, loc.X)
+
+	var step float64
+	if ls.first {
+		ls.first = false
+		step = ls.NextDirectioner.InitDirection(loc, ls.dir)
+	} else {
+		step = ls.NextDirectioner.NextDirection(loc, ls.dir)
+	}
+
+	projGrad := floats.Dot(loc.Gradient, ls.dir)
+	if projGrad >= 0 {
+		return ls.error(ErrNonDescentDirection)
+	}
+
+	op := ls.Linesearcher.Init(loc.F, projGrad, step)
+	switch op {
+	case FuncEvaluation, GradEvaluation, FuncEvaluation | GradEvaluation:
+	default:
+		panic("linesearch: Linesearcher returned invalid operation")
+	}
+
+	floats.AddScaledTo(loc.X, ls.x, step, ls.dir)
+	if floats.Equal(ls.x, loc.X) {
+		// Step size is so small that the next evaluation point is
+		// indistinguishable from the starting point for the current iteration
+		// due to rounding errors.
+		return ls.error(ErrNoProgress)
+	}
+
+	ls.lastStep = step
+	ls.eval = NoOperation // Invalidate all fields of loc.
+
+	ls.lastOp = op
+	return ls.lastOp, nil
+}
+
+// ArmijoConditionMet returns true if the Armijo condition (aka sufficient
+// decrease) has been met. Under normal conditions, the following should be
+// true, though this is not enforced:
+//  - initGrad < 0
+//  - step > 0
+//  - 0 < decrease < 1
+func ArmijoConditionMet(currObj, initObj, initGrad, step, decrease float64) bool {
+	return currObj <= initObj+decrease*step*initGrad
+}
+
+// StrongWolfeConditionsMet returns true if the strong Wolfe conditions have been met.
+// The strong Wolfe conditions ensure sufficient decrease in the function
+// value, and sufficient decrease in the magnitude of the projected gradient.
+// Under normal conditions, the following should be true, though this is not
+// enforced:
+//  - initGrad < 0
+//  - step > 0
+//  - 0 <= decrease < curvature < 1
+func StrongWolfeConditionsMet(currObj, currGrad, initObj, initGrad, step, decrease, curvature float64) bool {
+	if currObj > initObj+decrease*step*initGrad {
+		return false
+	}
+	return math.Abs(currGrad) < curvature*math.Abs(initGrad)
+}
+
+// WeakWolfeConditionsMet returns true if the weak Wolfe conditions have been met.
+// The weak Wolfe conditions ensure sufficient decrease in the function value,
+// and sufficient decrease in the value of the projected gradient. Under normal
+// conditions, the following should be true, though this is not enforced:
+//  - initGrad < 0
+//  - step > 0
+//  - 0 <= decrease < curvature< 1
+func WeakWolfeConditionsMet(currObj, currGrad, initObj, initGrad, step, decrease, curvature float64) bool {
+	if currObj > initObj+decrease*step*initGrad {
+		return false
+	}
+	return currGrad >= curvature*initGrad
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/linesearcher_test.go b/vendor/gonum.org/v1/gonum/optimize/linesearcher_test.go
new file mode 100644
index 00000000..f1def408
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/linesearcher_test.go
@@ -0,0 +1,136 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package optimize
+
+import (
+	"fmt"
+	"math"
+	"reflect"
+	"testing"
+
+	"gonum.org/v1/gonum/optimize/functions"
+)
+
+func TestMoreThuente(t *testing.T) {
+	d := 0.001
+	c := 0.001
+	ls := &MoreThuente{
+		DecreaseFactor:  d,
+		CurvatureFactor: c,
+	}
+	testLinesearcher(t, ls, d, c, true)
+}
+
+func TestBisection(t *testing.T) {
+	c := 0.1
+	ls := &Bisection{
+		CurvatureFactor: c,
+	}
+	testLinesearcher(t, ls, 0, c, true)
+}
+
+func TestBacktracking(t *testing.T) {
+	d := 0.001
+	ls := &Backtracking{
+		DecreaseFactor: d,
+	}
+	testLinesearcher(t, ls, d, 0, false)
+}
+
+type funcGrader interface {
+	Func([]float64) float64
+	Grad([]float64, []float64)
+}
+
+type linesearcherTest struct {
+	name string
+	f    func(float64) float64
+	g    func(float64) float64
+}
+
+func newLinesearcherTest(name string, fg funcGrader) linesearcherTest {
+	grad := make([]float64, 1)
+	return linesearcherTest{
+		name: name,
+		f: func(x float64) float64 {
+			return fg.Func([]float64{x})
+		},
+		g: func(x float64) float64 {
+			fg.Grad(grad, []float64{x})
+			return grad[0]
+		},
+	}
+}
+
+func testLinesearcher(t *testing.T, ls Linesearcher, decrease, curvature float64, strongWolfe bool) {
+	for i, prob := range []linesearcherTest{
+		newLinesearcherTest("Concave-to-the-right function", functions.ConcaveRight{}),
+		newLinesearcherTest("Concave-to-the-left function", functions.ConcaveLeft{}),
+		newLinesearcherTest("Plassmann wiggly function (l=39, beta=0.01)", functions.Plassmann{39, 0.01}),
+		newLinesearcherTest("Yanai-Ozawa-Kaneko function (beta1=0.001, beta2=0.001)", functions.YanaiOzawaKaneko{0.001, 0.001}),
+		newLinesearcherTest("Yanai-Ozawa-Kaneko function (beta1=0.01, beta2=0.001)", functions.YanaiOzawaKaneko{0.01, 0.001}),
+		newLinesearcherTest("Yanai-Ozawa-Kaneko function (beta1=0.001, beta2=0.01)", functions.YanaiOzawaKaneko{0.001, 0.01}),
+	} {
+		for _, initStep := range []float64{0.001, 0.1, 1, 10, 1000} {
+			prefix := fmt.Sprintf("test %d (%v started from %v)", i, prob.name, initStep)
+
+			f0 := prob.f(0)
+			g0 := prob.g(0)
+			if g0 >= 0 {
+				panic("bad test function")
+			}
+
+			op := ls.Init(f0, g0, initStep)
+			if !op.isEvaluation() {
+				t.Errorf("%v: Linesearcher.Init returned non-evaluating operation %v", prefix, op)
+				continue
+			}
+
+			var (
+				err  error
+				k    int
+				f, g float64
+				step float64
+			)
+		loop:
+			for {
+				switch op {
+				case MajorIteration:
+					if f > f0+step*decrease*g0 {
+						t.Errorf("%v: %v found step %v that does not satisfy the sufficient decrease condition",
+							prefix, reflect.TypeOf(ls), step)
+					}
+					if strongWolfe && math.Abs(g) > curvature*(-g0) {
+						t.Errorf("%v: %v found step %v that does not satisfy the curvature condition",
+							prefix, reflect.TypeOf(ls), step)
+					}
+					break loop
+				case FuncEvaluation:
+					f = prob.f(step)
+				case GradEvaluation:
+					g = prob.g(step)
+				case FuncEvaluation | GradEvaluation:
+					f = prob.f(step)
+					g = prob.g(step)
+				default:
+					t.Errorf("%v: Linesearcher returned an invalid operation %v", prefix, op)
+					break loop
+				}
+
+				k++
+				if k == 1000 {
+					t.Errorf("%v: %v did not finish", prefix, reflect.TypeOf(ls))
+					break
+				}
+
+				op, step, err = ls.Iterate(f, g)
+				if err != nil {
+					t.Errorf("%v: %v failed at step %v with %v", prefix, reflect.TypeOf(ls), step, err)
+					break
+				}
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/local.go b/vendor/gonum.org/v1/gonum/optimize/local.go
new file mode 100644
index 00000000..241e80fe
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/local.go
@@ -0,0 +1,225 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package optimize
+
+import (
+	"math"
+	"time"
+)
+
+// Local finds a local minimum of a minimization problem using a sequential
+// algorithm. A maximization problem can be transformed into a minimization
+// problem by multiplying the function by -1.
+//
+// The first argument represents the problem to be minimized. Its fields are
+// routines that evaluate the objective function, gradient, and other
+// quantities related to the problem. The objective function, p.Func, must not
+// be nil. The optimization method used may require other fields to be non-nil
+// as specified by method.Needs. Local will panic if these are not met. The
+// method can be determined automatically from the supplied problem which is
+// described below.
+//
+// If p.Status is not nil, it is called before every evaluation. If the
+// returned Status is not NotTerminated or the error is not nil, the
+// optimization run is terminated.
+//
+// The second argument is the initial location at which to start the minimization.
+// The initial location must be supplied, and must have a length equal to the
+// problem dimension.
+//
+// The third argument contains the settings for the minimization. It is here that
+// gradient tolerance, etc. are specified. The DefaultSettings function
+// can be called for a Settings struct with the default values initialized.
+// If settings == nil, the default settings are used. See the documentation
+// for the Settings structure for more information. The optimization Method used
+// may also contain settings, see documentation for the appropriate optimizer.
+//
+// The final argument is the optimization method to use. If method == nil, then
+// an appropriate default is chosen based on the properties of the other arguments
+// (dimension, gradient-free or gradient-based, etc.). The optimization
+// methods in this package are designed such that reasonable defaults occur
+// if options are not specified explicitly. For example, the code
+//  method := &optimize.BFGS{}
+// creates a pointer to a new BFGS struct. When Local is called, the settings
+// in the method will be populated with default values. The methods are also
+// designed such that they can be reused in future calls to Local.
+//
+// If method implements Statuser, method.Status is called before every call
+// to method.Iterate. If the returned Status is not NotTerminated or the
+// error is non-nil, the optimization run is terminated.
+//
+// Local returns a Result struct and any error that occurred. See the
+// documentation of Result for more information.
+//
+// Be aware that the default behavior of Local is to find the minimum.
+// For certain functions and optimization methods, this process can take many
+// function evaluations. If you would like to put limits on this, for example
+// maximum runtime or maximum function evaluations, modify the Settings
+// input struct.
+func Local(p Problem, initX []float64, settings *Settings, method Method) (*Result, error) {
+	startTime := time.Now()
+	dim := len(initX)
+	if method == nil {
+		method = getDefaultMethod(&p)
+	}
+	if settings == nil {
+		settings = DefaultSettings()
+	}
+
+	stats := &Stats{}
+
+	err := checkOptimization(p, dim, method, settings.Recorder)
+	if err != nil {
+		return nil, err
+	}
+
+	optLoc, err := getStartingLocation(&p, method, initX, stats, settings)
+	if err != nil {
+		return nil, err
+	}
+
+	if settings.FunctionConverge != nil {
+		settings.FunctionConverge.Init(optLoc.F)
+	}
+
+	stats.Runtime = time.Since(startTime)
+
+	// Send initial location to Recorder
+	if settings.Recorder != nil {
+		err = settings.Recorder.Record(optLoc, InitIteration, stats)
+		if err != nil {
+			return nil, err
+		}
+	}
+
+	// Check if the starting location satisfies the convergence criteria.
+	status := checkConvergence(optLoc, settings, true)
+
+	// Run optimization
+	if status == NotTerminated && err == nil {
+		// The starting location is not good enough, we need to perform a
+		// minimization. The optimal location will be stored in-place in
+		// optLoc.
+		status, err = minimize(&p, method, settings, stats, optLoc, startTime)
+	}
+
+	// Cleanup and collect results
+	if settings.Recorder != nil && err == nil {
+		// Send the optimal location to Recorder.
+		err = settings.Recorder.Record(optLoc, PostIteration, stats)
+	}
+	stats.Runtime = time.Since(startTime)
+	return &Result{
+		Location: *optLoc,
+		Stats:    *stats,
+		Status:   status,
+	}, err
+}
+
+func minimize(p *Problem, method Method, settings *Settings, stats *Stats, optLoc *Location, startTime time.Time) (status Status, err error) {
+	loc := &Location{}
+	copyLocation(loc, optLoc)
+	x := make([]float64, len(loc.X))
+
+	statuser, _ := method.(Statuser)
+
+	var op Operation
+	op, err = method.Init(loc)
+	if err != nil {
+		status = Failure
+		return
+	}
+
+	for {
+		// Sequentially call method.Iterate, performing the operations it has
+		// commanded, until convergence.
+
+		switch op {
+		case NoOperation:
+		case InitIteration:
+			panic("optimize: Method returned InitIteration")
+		case PostIteration:
+			panic("optimize: Method returned PostIteration")
+		case MajorIteration:
+			copyLocation(optLoc, loc)
+			stats.MajorIterations++
+			status = checkConvergence(optLoc, settings, true)
+		default: // Any of the Evaluation operations.
+			status, err = evaluate(p, loc, op, x)
+			updateStats(stats, op)
+		}
+
+		status, err = iterCleanup(status, err, stats, settings, statuser, startTime, loc, op)
+		if status != NotTerminated || err != nil {
+			return
+		}
+
+		op, err = method.Iterate(loc)
+		if err != nil {
+			status = Failure
+			return
+		}
+	}
+}
+
+func getDefaultMethod(p *Problem) Method {
+	if p.Grad != nil {
+		return &BFGS{}
+	}
+	return &NelderMead{}
+}
+
+// getStartingLocation allocates and initializes the starting location for the minimization.
+func getStartingLocation(p *Problem, method Method, initX []float64, stats *Stats, settings *Settings) (*Location, error) {
+	dim := len(initX)
+	loc := newLocation(dim, method)
+	copy(loc.X, initX)
+
+	if settings.UseInitialData {
+		loc.F = settings.InitialValue
+		if loc.Gradient != nil {
+			initG := settings.InitialGradient
+			if initG == nil {
+				panic("optimize: initial gradient is nil")
+			}
+			if len(initG) != dim {
+				panic("optimize: initial gradient size mismatch")
+			}
+			copy(loc.Gradient, initG)
+		}
+		if loc.Hessian != nil {
+			initH := settings.InitialHessian
+			if initH == nil {
+				panic("optimize: initial Hessian is nil")
+			}
+			if initH.Symmetric() != dim {
+				panic("optimize: initial Hessian size mismatch")
+			}
+			loc.Hessian.CopySym(initH)
+		}
+	} else {
+		eval := FuncEvaluation
+		if loc.Gradient != nil {
+			eval |= GradEvaluation
+		}
+		if loc.Hessian != nil {
+			eval |= HessEvaluation
+		}
+		x := make([]float64, len(loc.X))
+		evaluate(p, loc, eval, x)
+		updateStats(stats, eval)
+	}
+
+	if math.IsInf(loc.F, 1) || math.IsNaN(loc.F) {
+		return loc, ErrFunc(loc.F)
+	}
+	for i, v := range loc.Gradient {
+		if math.IsInf(v, 0) || math.IsNaN(v) {
+			return loc, ErrGrad{Grad: v, Index: i}
+		}
+	}
+
+	return loc, nil
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/local_example_test.go b/vendor/gonum.org/v1/gonum/optimize/local_example_test.go
new file mode 100644
index 00000000..64940388
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/local_example_test.go
@@ -0,0 +1,43 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package optimize_test
+
+import (
+	"fmt"
+	"log"
+
+	"gonum.org/v1/gonum/optimize"
+	"gonum.org/v1/gonum/optimize/functions"
+)
+
+func ExampleLocal() {
+	p := optimize.Problem{
+		Func: functions.ExtendedRosenbrock{}.Func,
+		Grad: functions.ExtendedRosenbrock{}.Grad,
+	}
+
+	x := []float64{1.3, 0.7, 0.8, 1.9, 1.2}
+	settings := optimize.DefaultSettings()
+	settings.Recorder = nil
+	settings.GradientThreshold = 1e-12
+	settings.FunctionConverge = nil
+
+	result, err := optimize.Local(p, x, settings, &optimize.BFGS{})
+	if err != nil {
+		log.Fatal(err)
+	}
+	if err = result.Status.Err(); err != nil {
+		log.Fatal(err)
+	}
+	fmt.Printf("result.Status: %v\n", result.Status)
+	fmt.Printf("result.X: %v\n", result.X)
+	fmt.Printf("result.F: %v\n", result.F)
+	fmt.Printf("result.Stats.FuncEvaluations: %d\n", result.Stats.FuncEvaluations)
+	// Output:
+	// result.Status: GradientThreshold
+	// result.X: [1 1 1 1 1]
+	// result.F: 0
+	// result.Stats.FuncEvaluations: 35
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/minimize.go b/vendor/gonum.org/v1/gonum/optimize/minimize.go
new file mode 100644
index 00000000..b5373e72
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/minimize.go
@@ -0,0 +1,202 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package optimize
+
+import (
+	"fmt"
+	"math"
+	"time"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+)
+
+// newLocation allocates a new locatian structure of the appropriate size. It
+// allocates memory based on the dimension and the values in Needs. The initial
+// function value is set to math.Inf(1).
+func newLocation(dim int, method Needser) *Location {
+	// TODO(btracey): combine this with Local.
+	loc := &Location{
+		X: make([]float64, dim),
+	}
+	loc.F = math.Inf(1)
+	if method.Needs().Gradient {
+		loc.Gradient = make([]float64, dim)
+	}
+	if method.Needs().Hessian {
+		loc.Hessian = mat.NewSymDense(dim, nil)
+	}
+	return loc
+}
+
+func copyLocation(dst, src *Location) {
+	dst.X = resize(dst.X, len(src.X))
+	copy(dst.X, src.X)
+
+	dst.F = src.F
+
+	dst.Gradient = resize(dst.Gradient, len(src.Gradient))
+	copy(dst.Gradient, src.Gradient)
+
+	if src.Hessian != nil {
+		if dst.Hessian == nil || dst.Hessian.Symmetric() != len(src.X) {
+			dst.Hessian = mat.NewSymDense(len(src.X), nil)
+		}
+		dst.Hessian.CopySym(src.Hessian)
+	}
+}
+
+func checkOptimization(p Problem, dim int, method Needser, recorder Recorder) error {
+	if p.Func == nil {
+		panic(badProblem)
+	}
+	if dim <= 0 {
+		panic("optimize: impossible problem dimension")
+	}
+	if err := p.satisfies(method); err != nil {
+		return err
+	}
+	if p.Status != nil {
+		_, err := p.Status()
+		if err != nil {
+			return err
+		}
+	}
+	if recorder != nil {
+		err := recorder.Init()
+		if err != nil {
+			return err
+		}
+	}
+	return nil
+}
+
+// evaluate evaluates the routines specified by the Operation at loc.X, and stores
+// the answer into loc. loc.X is copied into x before
+// evaluating in order to prevent the routines from modifying it.
+func evaluate(p *Problem, loc *Location, op Operation, x []float64) (Status, error) {
+	if !op.isEvaluation() {
+		panic(fmt.Sprintf("optimize: invalid evaluation %v", op))
+	}
+	if p.Status != nil {
+		status, err := p.Status()
+		if err != nil || status != NotTerminated {
+			return status, err
+		}
+	}
+	copy(x, loc.X)
+	if op&FuncEvaluation != 0 {
+		loc.F = p.Func(x)
+	}
+	if op&GradEvaluation != 0 {
+		p.Grad(loc.Gradient, x)
+	}
+	if op&HessEvaluation != 0 {
+		p.Hess(loc.Hessian, x)
+	}
+	return NotTerminated, nil
+}
+
+// checkConvergence returns NotTerminated if the Location does not satisfy the
+// convergence criteria given by settings. Otherwise a corresponding status is
+// returned.
+// Unlike checkLimits, checkConvergence is called only at MajorIterations.
+//
+// If local is true, gradient convergence is also checked.
+func checkConvergence(loc *Location, settings *Settings, local bool) Status {
+	if local && loc.Gradient != nil {
+		norm := floats.Norm(loc.Gradient, math.Inf(1))
+		if norm < settings.GradientThreshold {
+			return GradientThreshold
+		}
+	}
+	if loc.F < settings.FunctionThreshold {
+		return FunctionThreshold
+	}
+	if settings.FunctionConverge != nil {
+		return settings.FunctionConverge.FunctionConverged(loc.F)
+	}
+	return NotTerminated
+}
+
+// updateStats updates the statistics based on the operation.
+func updateStats(stats *Stats, op Operation) {
+	if op&FuncEvaluation != 0 {
+		stats.FuncEvaluations++
+	}
+	if op&GradEvaluation != 0 {
+		stats.GradEvaluations++
+	}
+	if op&HessEvaluation != 0 {
+		stats.HessEvaluations++
+	}
+}
+
+// checkLimits returns NotTerminated status if the various limits given by
+// settings have not been reached. Otherwise it returns a corresponding status.
+// Unlike checkConvergence, checkLimits is called by Local and Global at _every_
+// iteration.
+func checkLimits(loc *Location, stats *Stats, settings *Settings) Status {
+	// Check the objective function value for negative infinity because it
+	// could break the linesearches and -inf is the best we can do anyway.
+	if math.IsInf(loc.F, -1) {
+		return FunctionNegativeInfinity
+	}
+
+	if settings.MajorIterations > 0 && stats.MajorIterations >= settings.MajorIterations {
+		return IterationLimit
+	}
+
+	if settings.FuncEvaluations > 0 && stats.FuncEvaluations >= settings.FuncEvaluations {
+		return FunctionEvaluationLimit
+	}
+
+	if settings.GradEvaluations > 0 && stats.GradEvaluations >= settings.GradEvaluations {
+		return GradientEvaluationLimit
+	}
+
+	if settings.HessEvaluations > 0 && stats.HessEvaluations >= settings.HessEvaluations {
+		return HessianEvaluationLimit
+	}
+
+	// TODO(vladimir-ch): It would be nice to update Runtime here.
+	if settings.Runtime > 0 && stats.Runtime >= settings.Runtime {
+		return RuntimeLimit
+	}
+
+	return NotTerminated
+}
+
+// TODO(btracey): better name
+func iterCleanup(status Status, err error, stats *Stats, settings *Settings, statuser Statuser, startTime time.Time, loc *Location, op Operation) (Status, error) {
+	if status != NotTerminated || err != nil {
+		return status, err
+	}
+
+	if settings.Recorder != nil {
+		stats.Runtime = time.Since(startTime)
+		err = settings.Recorder.Record(loc, op, stats)
+		if err != nil {
+			if status == NotTerminated {
+				status = Failure
+			}
+			return status, err
+		}
+	}
+
+	stats.Runtime = time.Since(startTime)
+	status = checkLimits(loc, stats, settings)
+	if status != NotTerminated {
+		return status, nil
+	}
+
+	if statuser != nil {
+		status, err = statuser.Status()
+		if err != nil || status != NotTerminated {
+			return status, err
+		}
+	}
+	return status, nil
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/morethuente.go b/vendor/gonum.org/v1/gonum/optimize/morethuente.go
new file mode 100644
index 00000000..ec23167b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/morethuente.go
@@ -0,0 +1,385 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package optimize
+
+import "math"
+
+// MoreThuente is a Linesearcher that finds steps that satisfy both the
+// sufficient decrease and curvature conditions (the strong Wolfe conditions).
+//
+// References:
+//  - More, J.J. and D.J. Thuente: Line Search Algorithms with Guaranteed Sufficient
+//    Decrease. ACM Transactions on Mathematical Software 20(3) (1994), 286-307
+type MoreThuente struct {
+	// DecreaseFactor is the constant factor in the sufficient decrease
+	// (Armijo) condition.
+	// It must be in the interval [0, 1). The default value is 0.
+	DecreaseFactor float64
+	// CurvatureFactor is the constant factor in the Wolfe conditions. Smaller
+	// values result in a more exact line search.
+	// A set value must be in the interval (0, 1). If it is zero, it will be
+	// defaulted to 0.9.
+	CurvatureFactor float64
+	// StepTolerance sets the minimum acceptable width for the linesearch
+	// interval. If the relative interval length is less than this value,
+	// ErrLinesearcherFailure is returned.
+	// It must be non-negative. If it is zero, it will be defaulted to 1e-10.
+	StepTolerance float64
+
+	// MinimumStep is the minimum step that the linesearcher will take.
+	// It must be non-negative and less than MaximumStep. Defaults to no
+	// minimum (a value of 0).
+	MinimumStep float64
+	// MaximumStep is the maximum step that the linesearcher will take.
+	// It must be greater than MinimumStep. If it is zero, it will be defaulted
+	// to 1e20.
+	MaximumStep float64
+
+	bracketed bool    // Indicates if a minimum has been bracketed.
+	fInit     float64 // Function value at step = 0.
+	gInit     float64 // Derivative value at step = 0.
+
+	// When stage is 1, the algorithm updates the interval given by x and y
+	// so that it contains a minimizer of the modified function
+	//  psi(step) = f(step) - f(0) - DecreaseFactor * step * f'(0).
+	// When stage is 2, the interval is updated so that it contains a minimizer
+	// of f.
+	stage int
+
+	step         float64    // Current step.
+	lower, upper float64    // Lower and upper bounds on the next step.
+	x            float64    // Endpoint of the interval with a lower function value.
+	fx, gx       float64    // Data at x.
+	y            float64    // The other endpoint.
+	fy, gy       float64    // Data at y.
+	width        [2]float64 // Width of the interval at two previous iterations.
+}
+
+const (
+	mtMinGrowthFactor float64 = 1.1
+	mtMaxGrowthFactor float64 = 4
+)
+
+func (mt *MoreThuente) Init(f, g float64, step float64) Operation {
+	// Based on the original Fortran code that is available, for example, from
+	//  http://ftp.mcs.anl.gov/pub/MINPACK-2/csrch/
+	// as part of
+	//  MINPACK-2 Project. November 1993.
+	//  Argonne National Laboratory and University of Minnesota.
+	//  Brett M. Averick, Richard G. Carter, and Jorge J. Moré.
+
+	if g >= 0 {
+		panic("morethuente: initial derivative is non-negative")
+	}
+	if step <= 0 {
+		panic("morethuente: invalid initial step")
+	}
+
+	if mt.CurvatureFactor == 0 {
+		mt.CurvatureFactor = 0.9
+	}
+	if mt.StepTolerance == 0 {
+		mt.StepTolerance = 1e-10
+	}
+	if mt.MaximumStep == 0 {
+		mt.MaximumStep = 1e20
+	}
+
+	if mt.MinimumStep < 0 {
+		panic("morethuente: minimum step is negative")
+	}
+	if mt.MaximumStep <= mt.MinimumStep {
+		panic("morethuente: maximum step is not greater than minimum step")
+	}
+	if mt.DecreaseFactor < 0 || mt.DecreaseFactor >= 1 {
+		panic("morethuente: invalid decrease factor")
+	}
+	if mt.CurvatureFactor <= 0 || mt.CurvatureFactor >= 1 {
+		panic("morethuente: invalid curvature factor")
+	}
+	if mt.StepTolerance <= 0 {
+		panic("morethuente: step tolerance is not positive")
+	}
+
+	if step < mt.MinimumStep {
+		step = mt.MinimumStep
+	}
+	if step > mt.MaximumStep {
+		step = mt.MaximumStep
+	}
+
+	mt.bracketed = false
+	mt.stage = 1
+	mt.fInit = f
+	mt.gInit = g
+
+	mt.x, mt.fx, mt.gx = 0, f, g
+	mt.y, mt.fy, mt.gy = 0, f, g
+
+	mt.lower = 0
+	mt.upper = step + mtMaxGrowthFactor*step
+
+	mt.width[0] = mt.MaximumStep - mt.MinimumStep
+	mt.width[1] = 2 * mt.width[0]
+
+	mt.step = step
+	return FuncEvaluation | GradEvaluation
+}
+
+func (mt *MoreThuente) Iterate(f, g float64) (Operation, float64, error) {
+	if mt.stage == 0 {
+		panic("morethuente: Init has not been called")
+	}
+
+	gTest := mt.DecreaseFactor * mt.gInit
+	fTest := mt.fInit + mt.step*gTest
+
+	if mt.bracketed {
+		if mt.step <= mt.lower || mt.step >= mt.upper || mt.upper-mt.lower <= mt.StepTolerance*mt.upper {
+			// step contains the best step found (see below).
+			return NoOperation, mt.step, ErrLinesearcherFailure
+		}
+	}
+	if mt.step == mt.MaximumStep && f <= fTest && g <= gTest {
+		return NoOperation, mt.step, ErrLinesearcherBound
+	}
+	if mt.step == mt.MinimumStep && (f > fTest || g >= gTest) {
+		return NoOperation, mt.step, ErrLinesearcherFailure
+	}
+
+	// Test for convergence.
+	if f <= fTest && math.Abs(g) <= mt.CurvatureFactor*(-mt.gInit) {
+		mt.stage = 0
+		return MajorIteration, mt.step, nil
+	}
+
+	if mt.stage == 1 && f <= fTest && g >= 0 {
+		mt.stage = 2
+	}
+
+	if mt.stage == 1 && f <= mt.fx && f > fTest {
+		// Lower function value but the decrease is not sufficient .
+
+		// Compute values and derivatives of the modified function at step, x, y.
+		fm := f - mt.step*gTest
+		fxm := mt.fx - mt.x*gTest
+		fym := mt.fy - mt.y*gTest
+		gm := g - gTest
+		gxm := mt.gx - gTest
+		gym := mt.gy - gTest
+		// Update x, y and step.
+		mt.nextStep(fxm, gxm, fym, gym, fm, gm)
+		// Recover values and derivates of the non-modified function at x and y.
+		mt.fx = fxm + mt.x*gTest
+		mt.fy = fym + mt.y*gTest
+		mt.gx = gxm + gTest
+		mt.gy = gym + gTest
+	} else {
+		// Update x, y and step.
+		mt.nextStep(mt.fx, mt.gx, mt.fy, mt.gy, f, g)
+	}
+
+	if mt.bracketed {
+		// Monitor the length of the bracketing interval. If the interval has
+		// not been reduced sufficiently after two steps, use bisection to
+		// force its length to zero.
+		width := mt.y - mt.x
+		if math.Abs(width) >= 2.0/3*mt.width[1] {
+			mt.step = mt.x + 0.5*width
+		}
+		mt.width[0], mt.width[1] = math.Abs(width), mt.width[0]
+	}
+
+	if mt.bracketed {
+		mt.lower = math.Min(mt.x, mt.y)
+		mt.upper = math.Max(mt.x, mt.y)
+	} else {
+		mt.lower = mt.step + mtMinGrowthFactor*(mt.step-mt.x)
+		mt.upper = mt.step + mtMaxGrowthFactor*(mt.step-mt.x)
+	}
+
+	// Force the step to be in [MinimumStep, MaximumStep].
+	mt.step = math.Max(mt.MinimumStep, math.Min(mt.step, mt.MaximumStep))
+
+	if mt.bracketed {
+		if mt.step <= mt.lower || mt.step >= mt.upper || mt.upper-mt.lower <= mt.StepTolerance*mt.upper {
+			// If further progress is not possible, set step to the best step
+			// obtained during the search.
+			mt.step = mt.x
+		}
+	}
+
+	return FuncEvaluation | GradEvaluation, mt.step, nil
+}
+
+// nextStep computes the next safeguarded step and updates the interval that
+// contains a step that satisfies the sufficient decrease and curvature
+// conditions.
+func (mt *MoreThuente) nextStep(fx, gx, fy, gy, f, g float64) {
+	x := mt.x
+	y := mt.y
+	step := mt.step
+
+	gNeg := g < 0
+	if gx < 0 {
+		gNeg = !gNeg
+	}
+
+	var next float64
+	var bracketed bool
+	switch {
+	case f > fx:
+		// A higher function value. The minimum is bracketed between x and step.
+		// We want the next step to be closer to x because the function value
+		// there is lower.
+
+		theta := 3*(fx-f)/(step-x) + gx + g
+		s := math.Max(math.Abs(gx), math.Abs(g))
+		s = math.Max(s, math.Abs(theta))
+		gamma := s * math.Sqrt((theta/s)*(theta/s)-(gx/s)*(g/s))
+		if step < x {
+			gamma *= -1
+		}
+		p := gamma - gx + theta
+		q := gamma - gx + gamma + g
+		r := p / q
+		stpc := x + r*(step-x)
+		stpq := x + gx/((fx-f)/(step-x)+gx)/2*(step-x)
+
+		if math.Abs(stpc-x) < math.Abs(stpq-x) {
+			// The cubic step is closer to x than the quadratic step.
+			// Take the cubic step.
+			next = stpc
+		} else {
+			// If f is much larger than fx, then the quadratic step may be too
+			// close to x. Therefore heuristically take the average of the
+			// cubic and quadratic steps.
+			next = stpc + (stpq-stpc)/2
+		}
+		bracketed = true
+
+	case gNeg:
+		// A lower function value and derivatives of opposite sign. The minimum
+		// is bracketed between x and step. If we choose a step that is far
+		// from step, the next iteration will also likely fall in this case.
+
+		theta := 3*(fx-f)/(step-x) + gx + g
+		s := math.Max(math.Abs(gx), math.Abs(g))
+		s = math.Max(s, math.Abs(theta))
+		gamma := s * math.Sqrt((theta/s)*(theta/s)-(gx/s)*(g/s))
+		if step > x {
+			gamma *= -1
+		}
+		p := gamma - g + theta
+		q := gamma - g + gamma + gx
+		r := p / q
+		stpc := step + r*(x-step)
+		stpq := step + g/(g-gx)*(x-step)
+
+		if math.Abs(stpc-step) > math.Abs(stpq-step) {
+			// The cubic step is farther from x than the quadratic step.
+			// Take the cubic step.
+			next = stpc
+		} else {
+			// Take the quadratic step.
+			next = stpq
+		}
+		bracketed = true
+
+	case math.Abs(g) < math.Abs(gx):
+		// A lower function value, derivatives of the same sign, and the
+		// magnitude of the derivative decreases. Extrapolate function values
+		// at x and step so that the next step lies between step and y.
+
+		theta := 3*(fx-f)/(step-x) + gx + g
+		s := math.Max(math.Abs(gx), math.Abs(g))
+		s = math.Max(s, math.Abs(theta))
+		gamma := s * math.Sqrt(math.Max(0, (theta/s)*(theta/s)-(gx/s)*(g/s)))
+		if step > x {
+			gamma *= -1
+		}
+		p := gamma - g + theta
+		q := gamma + gx - g + gamma
+		r := p / q
+		var stpc float64
+		switch {
+		case r < 0 && gamma != 0:
+			stpc = step + r*(x-step)
+		case step > x:
+			stpc = mt.upper
+		default:
+			stpc = mt.lower
+		}
+		stpq := step + g/(g-gx)*(x-step)
+
+		if mt.bracketed {
+			// We are extrapolating so be cautious and take the step that
+			// is closer to step.
+			if math.Abs(stpc-step) < math.Abs(stpq-step) {
+				next = stpc
+			} else {
+				next = stpq
+			}
+			// Modify next if it is close to or beyond y.
+			if step > x {
+				next = math.Min(step+2.0/3*(y-step), next)
+			} else {
+				next = math.Max(step+2.0/3*(y-step), next)
+			}
+		} else {
+			// Minimum has not been bracketed so take the larger step...
+			if math.Abs(stpc-step) > math.Abs(stpq-step) {
+				next = stpc
+			} else {
+				next = stpq
+			}
+			// ...but within reason.
+			next = math.Max(mt.lower, math.Min(next, mt.upper))
+		}
+
+	default:
+		// A lower function value, derivatives of the same sign, and the
+		// magnitude of the derivative does not decrease. The function seems to
+		// decrease rapidly in the direction of the step.
+
+		switch {
+		case mt.bracketed:
+			theta := 3*(f-fy)/(y-step) + gy + g
+			s := math.Max(math.Abs(gy), math.Abs(g))
+			s = math.Max(s, math.Abs(theta))
+			gamma := s * math.Sqrt((theta/s)*(theta/s)-(gy/s)*(g/s))
+			if step > y {
+				gamma *= -1
+			}
+			p := gamma - g + theta
+			q := gamma - g + gamma + gy
+			r := p / q
+			next = step + r*(y-step)
+		case step > x:
+			next = mt.upper
+		default:
+			next = mt.lower
+		}
+	}
+
+	if f > fx {
+		// x is still the best step.
+		mt.y = step
+		mt.fy = f
+		mt.gy = g
+	} else {
+		// step is the new best step.
+		if gNeg {
+			mt.y = x
+			mt.fy = fx
+			mt.gy = gx
+		}
+		mt.x = step
+		mt.fx = f
+		mt.gx = g
+	}
+	mt.bracketed = bracketed
+	mt.step = next
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/neldermead.go b/vendor/gonum.org/v1/gonum/optimize/neldermead.go
new file mode 100644
index 00000000..18964773
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/neldermead.go
@@ -0,0 +1,314 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package optimize
+
+import (
+	"sort"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+// nmIterType is a Nelder-Mead evaluation kind
+type nmIterType int
+
+const (
+	nmReflected = iota
+	nmExpanded
+	nmContractedInside
+	nmContractedOutside
+	nmInitialize
+	nmShrink
+	nmMajor
+)
+
+type nmVertexSorter struct {
+	vertices [][]float64
+	values   []float64
+}
+
+func (n nmVertexSorter) Len() int {
+	return len(n.values)
+}
+
+func (n nmVertexSorter) Less(i, j int) bool {
+	return n.values[i] < n.values[j]
+}
+
+func (n nmVertexSorter) Swap(i, j int) {
+	n.values[i], n.values[j] = n.values[j], n.values[i]
+	n.vertices[i], n.vertices[j] = n.vertices[j], n.vertices[i]
+}
+
+// NelderMead is an implementation of the Nelder-Mead simplex algorithm for
+// gradient-free nonlinear optimization (not to be confused with Danzig's
+// simplex algorithm for linear programming). The implementation follows the
+// algorithm described in
+//
+//  http://epubs.siam.org/doi/pdf/10.1137/S1052623496303470
+//
+// If an initial simplex is provided, it is used and initLoc is ignored. If
+// InitialVertices and InitialValues are both nil, an initial simplex will be
+// generated automatically using the initial location as one vertex, and each
+// additional vertex as SimplexSize away in one dimension.
+//
+// If the simplex update parameters (Reflection, etc.)
+// are zero, they will be set automatically based on the dimension according to
+// the recommendations in
+//
+//  http://www.webpages.uidaho.edu/~fuchang/res/ANMS.pdf
+type NelderMead struct {
+	InitialVertices [][]float64
+	InitialValues   []float64
+	Reflection      float64 // Reflection parameter (>0)
+	Expansion       float64 // Expansion parameter (>1)
+	Contraction     float64 // Contraction parameter (>0, <1)
+	Shrink          float64 // Shrink parameter (>0, <1)
+	SimplexSize     float64 // size of auto-constructed initial simplex
+
+	reflection  float64
+	expansion   float64
+	contraction float64
+	shrink      float64
+
+	vertices [][]float64 // location of the vertices sorted in ascending f
+	values   []float64   // function values at the vertices sorted in ascending f
+	centroid []float64   // centroid of all but the worst vertex
+
+	fillIdx        int        // index for filling the simplex during initialization and shrinking
+	lastIter       nmIterType // Last iteration
+	reflectedPoint []float64  // Storage of the reflected point location
+	reflectedValue float64    // Value at the last reflection point
+}
+
+func (n *NelderMead) Init(loc *Location) (Operation, error) {
+	dim := len(loc.X)
+	if cap(n.vertices) < dim+1 {
+		n.vertices = make([][]float64, dim+1)
+	}
+	n.vertices = n.vertices[:dim+1]
+	for i := range n.vertices {
+		n.vertices[i] = resize(n.vertices[i], dim)
+	}
+	n.values = resize(n.values, dim+1)
+	n.centroid = resize(n.centroid, dim)
+	n.reflectedPoint = resize(n.reflectedPoint, dim)
+
+	if n.SimplexSize == 0 {
+		n.SimplexSize = 0.05
+	}
+
+	// Default parameter choices are chosen in a dimension-dependent way
+	// from http://www.webpages.uidaho.edu/~fuchang/res/ANMS.pdf
+	n.reflection = n.Reflection
+	if n.reflection == 0 {
+		n.reflection = 1
+	}
+	n.expansion = n.Expansion
+	if n.expansion == 0 {
+		n.expansion = 1 + 2/float64(dim)
+	}
+	n.contraction = n.Contraction
+	if n.contraction == 0 {
+		n.contraction = 0.75 - 1/(2*float64(dim))
+	}
+	n.shrink = n.Shrink
+	if n.shrink == 0 {
+		n.shrink = 1 - 1/float64(dim)
+	}
+
+	if n.InitialVertices != nil {
+		// Initial simplex provided. Copy the locations and values, and sort them.
+		if len(n.InitialVertices) != dim+1 {
+			panic("neldermead: incorrect number of vertices in initial simplex")
+		}
+		if len(n.InitialValues) != dim+1 {
+			panic("neldermead: incorrect number of values in initial simplex")
+		}
+		for i := range n.InitialVertices {
+			if len(n.InitialVertices[i]) != dim {
+				panic("neldermead: vertex size mismatch")
+			}
+			copy(n.vertices[i], n.InitialVertices[i])
+		}
+		copy(n.values, n.InitialValues)
+		sort.Sort(nmVertexSorter{n.vertices, n.values})
+		computeCentroid(n.vertices, n.centroid)
+		return n.returnNext(nmMajor, loc)
+	}
+
+	// No simplex provided. Begin initializing initial simplex. First simplex
+	// entry is the initial location, then step 1 in every direction.
+	copy(n.vertices[dim], loc.X)
+	n.values[dim] = loc.F
+	n.fillIdx = 0
+	loc.X[n.fillIdx] += n.SimplexSize
+	n.lastIter = nmInitialize
+	return FuncEvaluation, nil
+}
+
+// computeCentroid computes the centroid of all the simplex vertices except the
+// final one
+func computeCentroid(vertices [][]float64, centroid []float64) {
+	dim := len(centroid)
+	for i := range centroid {
+		centroid[i] = 0
+	}
+	for i := 0; i < dim; i++ {
+		vertex := vertices[i]
+		for j, v := range vertex {
+			centroid[j] += v
+		}
+	}
+	for i := range centroid {
+		centroid[i] /= float64(dim)
+	}
+}
+
+func (n *NelderMead) Iterate(loc *Location) (Operation, error) {
+	dim := len(loc.X)
+	switch n.lastIter {
+	case nmInitialize:
+		n.values[n.fillIdx] = loc.F
+		copy(n.vertices[n.fillIdx], loc.X)
+		n.fillIdx++
+		if n.fillIdx == dim {
+			// Successfully finished building initial simplex.
+			sort.Sort(nmVertexSorter{n.vertices, n.values})
+			computeCentroid(n.vertices, n.centroid)
+			return n.returnNext(nmMajor, loc)
+		}
+		copy(loc.X, n.vertices[dim])
+		loc.X[n.fillIdx] += n.SimplexSize
+		return FuncEvaluation, nil
+	case nmMajor:
+		// Nelder Mead iterations start with Reflection step
+		return n.returnNext(nmReflected, loc)
+	case nmReflected:
+		n.reflectedValue = loc.F
+		switch {
+		case loc.F >= n.values[0] && loc.F < n.values[dim-1]:
+			n.replaceWorst(loc.X, loc.F)
+			return n.returnNext(nmMajor, loc)
+		case loc.F < n.values[0]:
+			return n.returnNext(nmExpanded, loc)
+		default:
+			if loc.F < n.values[dim] {
+				return n.returnNext(nmContractedOutside, loc)
+			}
+			return n.returnNext(nmContractedInside, loc)
+		}
+	case nmExpanded:
+		if loc.F < n.reflectedValue {
+			n.replaceWorst(loc.X, loc.F)
+		} else {
+			n.replaceWorst(n.reflectedPoint, n.reflectedValue)
+		}
+		return n.returnNext(nmMajor, loc)
+	case nmContractedOutside:
+		if loc.F <= n.reflectedValue {
+			n.replaceWorst(loc.X, loc.F)
+			return n.returnNext(nmMajor, loc)
+		}
+		n.fillIdx = 1
+		return n.returnNext(nmShrink, loc)
+	case nmContractedInside:
+		if loc.F < n.values[dim] {
+			n.replaceWorst(loc.X, loc.F)
+			return n.returnNext(nmMajor, loc)
+		}
+		n.fillIdx = 1
+		return n.returnNext(nmShrink, loc)
+	case nmShrink:
+		copy(n.vertices[n.fillIdx], loc.X)
+		n.values[n.fillIdx] = loc.F
+		n.fillIdx++
+		if n.fillIdx != dim+1 {
+			return n.returnNext(nmShrink, loc)
+		}
+		sort.Sort(nmVertexSorter{n.vertices, n.values})
+		computeCentroid(n.vertices, n.centroid)
+		return n.returnNext(nmMajor, loc)
+	default:
+		panic("unreachable")
+	}
+}
+
+// returnNext updates the location based on the iteration type and the current
+// simplex, and returns the next operation.
+func (n *NelderMead) returnNext(iter nmIterType, loc *Location) (Operation, error) {
+	n.lastIter = iter
+	switch iter {
+	case nmMajor:
+		// Fill loc with the current best point and value,
+		// and command a convergence check.
+		copy(loc.X, n.vertices[0])
+		loc.F = n.values[0]
+		return MajorIteration, nil
+	case nmReflected, nmExpanded, nmContractedOutside, nmContractedInside:
+		// x_new = x_centroid + scale * (x_centroid - x_worst)
+		var scale float64
+		switch iter {
+		case nmReflected:
+			scale = n.reflection
+		case nmExpanded:
+			scale = n.reflection * n.expansion
+		case nmContractedOutside:
+			scale = n.reflection * n.contraction
+		case nmContractedInside:
+			scale = -n.contraction
+		}
+		dim := len(loc.X)
+		floats.SubTo(loc.X, n.centroid, n.vertices[dim])
+		floats.Scale(scale, loc.X)
+		floats.Add(loc.X, n.centroid)
+		if iter == nmReflected {
+			copy(n.reflectedPoint, loc.X)
+		}
+		return FuncEvaluation, nil
+	case nmShrink:
+		// x_shrink = x_best + delta * (x_i + x_best)
+		floats.SubTo(loc.X, n.vertices[n.fillIdx], n.vertices[0])
+		floats.Scale(n.shrink, loc.X)
+		floats.Add(loc.X, n.vertices[0])
+		return FuncEvaluation, nil
+	default:
+		panic("unreachable")
+	}
+}
+
+// replaceWorst removes the worst location in the simplex and adds the new
+// {x, f} pair maintaining sorting.
+func (n *NelderMead) replaceWorst(x []float64, f float64) {
+	dim := len(x)
+	if f >= n.values[dim] {
+		panic("increase in simplex value")
+	}
+	copy(n.vertices[dim], x)
+	n.values[dim] = f
+
+	// Sort the newly-added value.
+	for i := dim - 1; i >= 0; i-- {
+		if n.values[i] < f {
+			break
+		}
+		n.vertices[i], n.vertices[i+1] = n.vertices[i+1], n.vertices[i]
+		n.values[i], n.values[i+1] = n.values[i+1], n.values[i]
+	}
+
+	// Update the location of the centroid. Only one point has been replaced, so
+	// subtract the worst point and add the new one.
+	floats.AddScaled(n.centroid, -1/float64(dim), n.vertices[dim])
+	floats.AddScaled(n.centroid, 1/float64(dim), x)
+}
+
+func (*NelderMead) Needs() struct {
+	Gradient bool
+	Hessian  bool
+} {
+	return struct {
+		Gradient bool
+		Hessian  bool
+	}{false, false}
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/newton.go b/vendor/gonum.org/v1/gonum/optimize/newton.go
new file mode 100644
index 00000000..e87c269f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/newton.go
@@ -0,0 +1,147 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package optimize
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/mat"
+)
+
+const maxNewtonModifications = 20
+
+// Newton implements a modified Newton's method for Hessian-based unconstrained
+// minimization. It applies regularization when the Hessian is not positive
+// definite, and it can converge to a local minimum from any starting point.
+//
+// Newton iteratively forms a quadratic model to the objective function f and
+// tries to minimize this approximate model. It generates a sequence of
+// locations x_k by means of
+//  solve H_k d_k = -∇f_k for d_k,
+//  x_{k+1} = x_k + α_k d_k,
+// where H_k is the Hessian matrix of f at x_k and α_k is a step size found by
+// a line search.
+//
+// Away from a minimizer H_k may not be positive definite and d_k may not be a
+// descent direction. Newton implements a Hessian modification strategy that
+// adds successively larger multiples of identity to H_k until it becomes
+// positive definite. Note that the repeated trial factorization of the
+// modified Hessian involved in this process can be computationally expensive.
+//
+// If the Hessian matrix cannot be formed explicitly or if the computational
+// cost of its factorization is prohibitive, BFGS or L-BFGS quasi-Newton method
+// can be used instead.
+type Newton struct {
+	// Linesearcher is used for selecting suitable steps along the descent
+	// direction d. Accepted steps should satisfy at least one of the Wolfe,
+	// Goldstein or Armijo conditions.
+	// If Linesearcher == nil, an appropriate default is chosen.
+	Linesearcher Linesearcher
+	// Increase is the factor by which a scalar tau is successively increased
+	// so that (H + tau*I) is positive definite. Larger values reduce the
+	// number of trial Hessian factorizations, but also reduce the second-order
+	// information in H.
+	// Increase must be greater than 1. If Increase is 0, it is defaulted to 5.
+	Increase float64
+
+	ls *LinesearchMethod
+
+	hess *mat.SymDense // Storage for a copy of the Hessian matrix.
+	chol mat.Cholesky  // Storage for the Cholesky factorization.
+	tau  float64
+}
+
+func (n *Newton) Init(loc *Location) (Operation, error) {
+	if n.Increase == 0 {
+		n.Increase = 5
+	}
+	if n.Increase <= 1 {
+		panic("optimize: Newton.Increase must be greater than 1")
+	}
+	if n.Linesearcher == nil {
+		n.Linesearcher = &Bisection{}
+	}
+	if n.ls == nil {
+		n.ls = &LinesearchMethod{}
+	}
+	n.ls.Linesearcher = n.Linesearcher
+	n.ls.NextDirectioner = n
+
+	return n.ls.Init(loc)
+}
+
+func (n *Newton) Iterate(loc *Location) (Operation, error) {
+	return n.ls.Iterate(loc)
+}
+
+func (n *Newton) InitDirection(loc *Location, dir []float64) (stepSize float64) {
+	dim := len(loc.X)
+	n.hess = resizeSymDense(n.hess, dim)
+	n.tau = 0
+	return n.NextDirection(loc, dir)
+}
+
+func (n *Newton) NextDirection(loc *Location, dir []float64) (stepSize float64) {
+	// This method implements Algorithm 3.3 (Cholesky with Added Multiple of
+	// the Identity) from Nocedal, Wright (2006), 2nd edition.
+
+	dim := len(loc.X)
+	d := mat.NewVecDense(dim, dir)
+	grad := mat.NewVecDense(dim, loc.Gradient)
+	n.hess.CopySym(loc.Hessian)
+
+	// Find the smallest diagonal entry of the Hessian.
+	minA := n.hess.At(0, 0)
+	for i := 1; i < dim; i++ {
+		a := n.hess.At(i, i)
+		if a < minA {
+			minA = a
+		}
+	}
+	// If the smallest diagonal entry is positive, the Hessian may be positive
+	// definite, and so first attempt to apply the Cholesky factorization to
+	// the un-modified Hessian. If the smallest entry is negative, use the
+	// final tau from the last iteration if regularization was needed,
+	// otherwise guess an appropriate value for tau.
+	if minA > 0 {
+		n.tau = 0
+	} else if n.tau == 0 {
+		n.tau = -minA + 0.001
+	}
+
+	for k := 0; k < maxNewtonModifications; k++ {
+		if n.tau != 0 {
+			// Add a multiple of identity to the Hessian.
+			for i := 0; i < dim; i++ {
+				n.hess.SetSym(i, i, loc.Hessian.At(i, i)+n.tau)
+			}
+		}
+		// Try to apply the Cholesky factorization.
+		pd := n.chol.Factorize(n.hess)
+		if pd {
+			// Store the solution in d's backing array, dir.
+			n.chol.SolveVec(d, grad)
+			d.ScaleVec(-1, d)
+			return 1
+		}
+		// Modified Hessian is not PD, so increase tau.
+		n.tau = math.Max(n.Increase*n.tau, 0.001)
+	}
+
+	// Hessian modification failed to get a PD matrix. Return the negative
+	// gradient as the descent direction.
+	d.ScaleVec(-1, grad)
+	return 1
+}
+
+func (n *Newton) Needs() struct {
+	Gradient bool
+	Hessian  bool
+} {
+	return struct {
+		Gradient bool
+		Hessian  bool
+	}{true, true}
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/printer.go b/vendor/gonum.org/v1/gonum/optimize/printer.go
new file mode 100644
index 00000000..56800f3c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/printer.go
@@ -0,0 +1,106 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package optimize
+
+import (
+	"fmt"
+	"io"
+	"math"
+	"os"
+	"time"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+var printerHeadings = [...]string{
+	"Iter",
+	"Runtime",
+	"FuncEvals",
+	"Func",
+	"GradEvals",
+	"|Gradient|∞",
+	"HessEvals",
+}
+
+const (
+	printerBaseTmpl = "%9v  %16v  %9v  %22v" // Base template for headings and values that are always printed.
+	printerGradTmpl = "  %9v  %22v"          // Appended to base template when loc.Gradient != nil.
+	printerHessTmpl = "  %9v"                // Appended to base template when loc.Hessian != nil.
+)
+
+// Printer writes column-format output to the specified writer as the optimization
+// progresses. By default, it writes to os.Stdout.
+type Printer struct {
+	Writer          io.Writer
+	HeadingInterval int
+	ValueInterval   time.Duration
+
+	lastHeading int
+	lastValue   time.Time
+}
+
+func NewPrinter() *Printer {
+	return &Printer{
+		Writer:          os.Stdout,
+		HeadingInterval: 30,
+		ValueInterval:   500 * time.Millisecond,
+	}
+}
+
+func (p *Printer) Init() error {
+	p.lastHeading = p.HeadingInterval              // So the headings are printed the first time.
+	p.lastValue = time.Now().Add(-p.ValueInterval) // So the values are printed the first time.
+	return nil
+}
+
+func (p *Printer) Record(loc *Location, op Operation, stats *Stats) error {
+	if op != MajorIteration && op != InitIteration && op != PostIteration {
+		return nil
+	}
+
+	// Print values always on PostIteration or when ValueInterval has elapsed.
+	printValues := time.Since(p.lastValue) > p.ValueInterval || op == PostIteration
+	if !printValues {
+		// Return early if not printing anything.
+		return nil
+	}
+
+	// Print heading when HeadingInterval lines have been printed, but never on PostIteration.
+	printHeading := p.lastHeading >= p.HeadingInterval && op != PostIteration
+	if printHeading {
+		p.lastHeading = 1
+	} else {
+		p.lastHeading++
+	}
+
+	if printHeading {
+		headings := "\n" + fmt.Sprintf(printerBaseTmpl, printerHeadings[0], printerHeadings[1], printerHeadings[2], printerHeadings[3])
+		if loc.Gradient != nil {
+			headings += fmt.Sprintf(printerGradTmpl, printerHeadings[4], printerHeadings[5])
+		}
+		if loc.Hessian != nil {
+			headings += fmt.Sprintf(printerHessTmpl, printerHeadings[6])
+		}
+		_, err := fmt.Fprintln(p.Writer, headings)
+		if err != nil {
+			return err
+		}
+	}
+
+	values := fmt.Sprintf(printerBaseTmpl, stats.MajorIterations, stats.Runtime, stats.FuncEvaluations, loc.F)
+	if loc.Gradient != nil {
+		values += fmt.Sprintf(printerGradTmpl, stats.GradEvaluations, floats.Norm(loc.Gradient, math.Inf(1)))
+	}
+	if loc.Hessian != nil {
+		values += fmt.Sprintf(printerHessTmpl, stats.HessEvaluations)
+	}
+	_, err := fmt.Fprintln(p.Writer, values)
+	if err != nil {
+		return err
+	}
+
+	p.lastValue = time.Now()
+	return nil
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/stepsizers.go b/vendor/gonum.org/v1/gonum/optimize/stepsizers.go
new file mode 100644
index 00000000..487c158c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/stepsizers.go
@@ -0,0 +1,185 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package optimize
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+const (
+	initialStepFactor = 1
+
+	quadraticMinimumStepSize = 1e-3
+	quadraticMaximumStepSize = 1
+	quadraticThreshold       = 1e-12
+
+	firstOrderMinimumStepSize = quadraticMinimumStepSize
+	firstOrderMaximumStepSize = quadraticMaximumStepSize
+)
+
+// ConstantStepSize is a StepSizer that returns the same step size for
+// every iteration.
+type ConstantStepSize struct {
+	Size float64
+}
+
+func (c ConstantStepSize) Init(_ *Location, _ []float64) float64 {
+	return c.Size
+}
+
+func (c ConstantStepSize) StepSize(_ *Location, _ []float64) float64 {
+	return c.Size
+}
+
+// QuadraticStepSize estimates the initial line search step size as the minimum
+// of a quadratic that interpolates f(x_{k-1}), f(x_k) and ∇f_k⋅p_k.
+// This is useful for line search methods that do not produce well-scaled
+// descent directions, such as gradient descent or conjugate gradient methods.
+// The step size is bounded away from zero.
+type QuadraticStepSize struct {
+	// Threshold determines that the initial step size should be estimated by
+	// quadratic interpolation when the relative change in the objective
+	// function is larger than Threshold.  Otherwise the initial step size is
+	// set to 2*previous step size.
+	// If Threshold is zero, it will be set to 1e-12.
+	Threshold float64
+	// InitialStepFactor sets the step size for the first iteration to be InitialStepFactor / |g|_∞.
+	// If InitialStepFactor is zero, it will be set to one.
+	InitialStepFactor float64
+	// MinStepSize is the lower bound on the estimated step size.
+	// MinStepSize times GradientAbsTol should always be greater than machine epsilon.
+	// If MinStepSize is zero, it will be set to 1e-3.
+	MinStepSize float64
+	// MaxStepSize is the upper bound on the estimated step size.
+	// If MaxStepSize is zero, it will be set to 1.
+	MaxStepSize float64
+
+	fPrev        float64
+	dirPrevNorm  float64
+	projGradPrev float64
+	xPrev        []float64
+}
+
+func (q *QuadraticStepSize) Init(loc *Location, dir []float64) (stepSize float64) {
+	if q.Threshold == 0 {
+		q.Threshold = quadraticThreshold
+	}
+	if q.InitialStepFactor == 0 {
+		q.InitialStepFactor = initialStepFactor
+	}
+	if q.MinStepSize == 0 {
+		q.MinStepSize = quadraticMinimumStepSize
+	}
+	if q.MaxStepSize == 0 {
+		q.MaxStepSize = quadraticMaximumStepSize
+	}
+	if q.MaxStepSize <= q.MinStepSize {
+		panic("optimize: MinStepSize not smaller than MaxStepSize")
+	}
+
+	gNorm := floats.Norm(loc.Gradient, math.Inf(1))
+	stepSize = math.Max(q.MinStepSize, math.Min(q.InitialStepFactor/gNorm, q.MaxStepSize))
+
+	q.fPrev = loc.F
+	q.dirPrevNorm = floats.Norm(dir, 2)
+	q.projGradPrev = floats.Dot(loc.Gradient, dir)
+	q.xPrev = resize(q.xPrev, len(loc.X))
+	copy(q.xPrev, loc.X)
+	return stepSize
+}
+
+func (q *QuadraticStepSize) StepSize(loc *Location, dir []float64) (stepSize float64) {
+	stepSizePrev := floats.Distance(loc.X, q.xPrev, 2) / q.dirPrevNorm
+	projGrad := floats.Dot(loc.Gradient, dir)
+
+	stepSize = 2 * stepSizePrev
+	if !floats.EqualWithinRel(q.fPrev, loc.F, q.Threshold) {
+		// Two consecutive function values are not relatively equal, so
+		// computing the minimum of a quadratic interpolant might make sense
+
+		df := (loc.F - q.fPrev) / stepSizePrev
+		quadTest := df - q.projGradPrev
+		if quadTest > 0 {
+			// There is a chance of approximating the function well by a
+			// quadratic only if the finite difference (f_k-f_{k-1})/stepSizePrev
+			// is larger than ∇f_{k-1}⋅p_{k-1}
+
+			// Set the step size to the minimizer of the quadratic function that
+			// interpolates f_{k-1}, ∇f_{k-1}⋅p_{k-1} and f_k
+			stepSize = -q.projGradPrev * stepSizePrev / quadTest / 2
+		}
+	}
+	// Bound the step size to lie in [MinStepSize, MaxStepSize]
+	stepSize = math.Max(q.MinStepSize, math.Min(stepSize, q.MaxStepSize))
+
+	q.fPrev = loc.F
+	q.dirPrevNorm = floats.Norm(dir, 2)
+	q.projGradPrev = projGrad
+	copy(q.xPrev, loc.X)
+	return stepSize
+}
+
+// FirstOrderStepSize estimates the initial line search step size based on the
+// assumption that the first-order change in the function will be the same as
+// that obtained at the previous iteration. That is, the initial step size s^0_k
+// is chosen so that
+//   s^0_k ∇f_k⋅p_k = s_{k-1} ∇f_{k-1}⋅p_{k-1}
+// This is useful for line search methods that do not produce well-scaled
+// descent directions, such as gradient descent or conjugate gradient methods.
+type FirstOrderStepSize struct {
+	// InitialStepFactor sets the step size for the first iteration to be InitialStepFactor / |g|_∞.
+	// If InitialStepFactor is zero, it will be set to one.
+	InitialStepFactor float64
+	// MinStepSize is the lower bound on the estimated step size.
+	// MinStepSize times GradientAbsTol should always be greater than machine epsilon.
+	// If MinStepSize is zero, it will be set to 1e-3.
+	MinStepSize float64
+	// MaxStepSize is the upper bound on the estimated step size.
+	// If MaxStepSize is zero, it will be set to 1.
+	MaxStepSize float64
+
+	dirPrevNorm  float64
+	projGradPrev float64
+	xPrev        []float64
+}
+
+func (fo *FirstOrderStepSize) Init(loc *Location, dir []float64) (stepSize float64) {
+	if fo.InitialStepFactor == 0 {
+		fo.InitialStepFactor = initialStepFactor
+	}
+	if fo.MinStepSize == 0 {
+		fo.MinStepSize = firstOrderMinimumStepSize
+	}
+	if fo.MaxStepSize == 0 {
+		fo.MaxStepSize = firstOrderMaximumStepSize
+	}
+	if fo.MaxStepSize <= fo.MinStepSize {
+		panic("optimize: MinStepSize not smaller than MaxStepSize")
+	}
+
+	gNorm := floats.Norm(loc.Gradient, math.Inf(1))
+	stepSize = math.Max(fo.MinStepSize, math.Min(fo.InitialStepFactor/gNorm, fo.MaxStepSize))
+
+	fo.dirPrevNorm = floats.Norm(dir, 2)
+	fo.projGradPrev = floats.Dot(loc.Gradient, dir)
+	fo.xPrev = resize(fo.xPrev, len(loc.X))
+	copy(fo.xPrev, loc.X)
+	return stepSize
+}
+
+func (fo *FirstOrderStepSize) StepSize(loc *Location, dir []float64) (stepSize float64) {
+	stepSizePrev := floats.Distance(loc.X, fo.xPrev, 2) / fo.dirPrevNorm
+	projGrad := floats.Dot(loc.Gradient, dir)
+
+	stepSize = stepSizePrev * fo.projGradPrev / projGrad
+	stepSize = math.Max(fo.MinStepSize, math.Min(stepSize, fo.MaxStepSize))
+
+	fo.dirPrevNorm = floats.Norm(dir, 2)
+	fo.projGradPrev = floats.Dot(loc.Gradient, dir)
+	copy(fo.xPrev, loc.X)
+	return stepSize
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/termination.go b/vendor/gonum.org/v1/gonum/optimize/termination.go
new file mode 100644
index 00000000..43c2df68
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/termination.go
@@ -0,0 +1,119 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package optimize
+
+import "errors"
+
+// Status represents the status of the optimization. Programs
+// should not rely on the underlying numeric value of the Status being constant.
+type Status int
+
+const (
+	NotTerminated Status = iota
+	Success
+	FunctionThreshold
+	FunctionConvergence
+	GradientThreshold
+	StepConvergence
+	FunctionNegativeInfinity
+	Failure
+	IterationLimit
+	RuntimeLimit
+	FunctionEvaluationLimit
+	GradientEvaluationLimit
+	HessianEvaluationLimit
+)
+
+func (s Status) String() string {
+	return statuses[s].name
+}
+
+// Early returns true if the status indicates the optimization ended before a
+// minimum was found. As an example, if the maximum iterations was reached, a
+// minimum was not found, but if the gradient norm was reached then a minimum
+// was found.
+func (s Status) Early() bool {
+	return statuses[s].early
+}
+
+// Err returns the error associated with an early ending to the minimization. If
+// Early returns false, Err will return nil.
+func (s Status) Err() error {
+	return statuses[s].err
+}
+
+var statuses = []struct {
+	name  string
+	early bool
+	err   error
+}{
+	{
+		name: "NotTerminated",
+	},
+	{
+		name: "Success",
+	},
+	{
+		name: "FunctionThreshold",
+	},
+	{
+		name: "FunctionConvergence",
+	},
+	{
+		name: "GradientThreshold",
+	},
+	{
+		name: "StepConvergence",
+	},
+	{
+		name: "FunctionNegativeInfinity",
+	},
+	{
+		name:  "Failure",
+		early: true,
+		err:   errors.New("optimize: termination ended in failure"),
+	},
+	{
+		name:  "IterationLimit",
+		early: true,
+		err:   errors.New("optimize: maximum number of major iterations reached"),
+	},
+	{
+		name:  "RuntimeLimit",
+		early: true,
+		err:   errors.New("optimize: maximum runtime reached"),
+	},
+	{
+		name:  "FunctionEvaluationLimit",
+		early: true,
+		err:   errors.New("optimize: maximum number of function evaluations reached"),
+	},
+	{
+		name:  "GradientEvaluationLimit",
+		early: true,
+		err:   errors.New("optimize: maximum number of gradient evaluations reached"),
+	},
+	{
+		name:  "HessianEvaluationLimit",
+		early: true,
+		err:   errors.New("optimize: maximum number of Hessian evaluations reached"),
+	},
+}
+
+// NewStatus returns a unique Status variable to represent a custom status.
+// NewStatus is intended to be called only during package initialization, and
+// calls to NewStatus are not thread safe.
+//
+// NewStatus takes in three arguments, the string that should be output from
+// Status.String, a boolean if the status indicates early optimization conclusion,
+// and the error to return from Err (if any).
+func NewStatus(name string, early bool, err error) Status {
+	statuses = append(statuses, struct {
+		name  string
+		early bool
+		err   error
+	}{name, early, err})
+	return Status(len(statuses) - 1)
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/types.go b/vendor/gonum.org/v1/gonum/optimize/types.go
new file mode 100644
index 00000000..461693ff
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/types.go
@@ -0,0 +1,262 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package optimize
+
+import (
+	"errors"
+	"fmt"
+	"math"
+	"time"
+
+	"gonum.org/v1/gonum/mat"
+)
+
+const defaultGradientAbsTol = 1e-6
+
+// Operation represents the set of operations commanded by Method at each
+// iteration. It is a bitmap of various Iteration and Evaluation constants.
+// Individual constants must NOT be combined together by the binary OR operator
+// except for the Evaluation operations.
+type Operation uint64
+
+// Supported Operations.
+const (
+	// NoOperation specifies that no evaluation or convergence check should
+	// take place.
+	NoOperation Operation = 0
+	// InitIteration is sent to Recorder to indicate the initial location.
+	// All fields of the location to record must be valid.
+	// Method must not return it.
+	InitIteration Operation = 1 << (iota - 1)
+	// PostIteration is sent to Recorder to indicate the final location
+	// reached during an optimization run.
+	// All fields of the location to record must be valid.
+	// Method must not return it.
+	PostIteration
+	// MajorIteration indicates that the next candidate location for
+	// an optimum has been found and convergence should be checked.
+	MajorIteration
+	// FuncEvaluation specifies that the objective function
+	// should be evaluated.
+	FuncEvaluation
+	// GradEvaluation specifies that the gradient
+	// of the objective function should be evaluated.
+	GradEvaluation
+	// HessEvaluation specifies that the Hessian
+	// of the objective function should be evaluated.
+	HessEvaluation
+
+	// Mask for the evaluating operations.
+	evalMask = FuncEvaluation | GradEvaluation | HessEvaluation
+)
+
+func (op Operation) isEvaluation() bool {
+	return op&evalMask != 0 && op&^evalMask == 0
+}
+
+func (op Operation) String() string {
+	if op&evalMask != 0 {
+		return fmt.Sprintf("Evaluation(Func: %t, Grad: %t, Hess: %t, Extra: 0b%b)",
+			op&FuncEvaluation != 0,
+			op&GradEvaluation != 0,
+			op&HessEvaluation != 0,
+			op&^(evalMask))
+	}
+	s, ok := operationNames[op]
+	if ok {
+		return s
+	}
+	return fmt.Sprintf("Operation(%d)", op)
+}
+
+var operationNames = map[Operation]string{
+	NoOperation:    "NoOperation",
+	InitIteration:  "InitIteration",
+	MajorIteration: "MajorIteration",
+	PostIteration:  "PostIteration",
+}
+
+// Location represents a location in the optimization procedure.
+type Location struct {
+	X        []float64
+	F        float64
+	Gradient []float64
+	Hessian  *mat.SymDense
+}
+
+// Result represents the answer of an optimization run. It contains the optimum
+// location as well as the Status at convergence and Statistics taken during the
+// run.
+type Result struct {
+	Location
+	Stats
+	Status Status
+}
+
+// Stats contains the statistics of the run.
+type Stats struct {
+	MajorIterations int           // Total number of major iterations
+	FuncEvaluations int           // Number of evaluations of Func
+	GradEvaluations int           // Number of evaluations of Grad
+	HessEvaluations int           // Number of evaluations of Hess
+	Runtime         time.Duration // Total runtime of the optimization
+}
+
+// complementEval returns an evaluating operation that evaluates fields of loc
+// not evaluated by eval.
+func complementEval(loc *Location, eval Operation) (complEval Operation) {
+	if eval&FuncEvaluation == 0 {
+		complEval = FuncEvaluation
+	}
+	if loc.Gradient != nil && eval&GradEvaluation == 0 {
+		complEval |= GradEvaluation
+	}
+	if loc.Hessian != nil && eval&HessEvaluation == 0 {
+		complEval |= HessEvaluation
+	}
+	return complEval
+}
+
+// Problem describes the optimization problem to be solved.
+type Problem struct {
+	// Func evaluates the objective function at the given location. Func
+	// must not modify x.
+	Func func(x []float64) float64
+
+	// Grad evaluates the gradient at x and stores the result in-place in grad.
+	// Grad must not modify x.
+	Grad func(grad []float64, x []float64)
+
+	// Hess evaluates the Hessian at x and stores the result in-place in hess.
+	// Hess must not modify x.
+	Hess func(hess mat.MutableSymmetric, x []float64)
+
+	// Status reports the status of the objective function being optimized and any
+	// error. This can be used to terminate early, for example when the function is
+	// not able to evaluate itself. The user can use one of the pre-provided Status
+	// constants, or may call NewStatus to create a custom Status value.
+	Status func() (Status, error)
+}
+
+// TODO(btracey): Think about making this an exported function when the
+// constraint interface is designed.
+func (p Problem) satisfies(method Needser) error {
+	if method.Needs().Gradient && p.Grad == nil {
+		return errors.New("optimize: problem does not provide needed Grad function")
+	}
+	if method.Needs().Hessian && p.Hess == nil {
+		return errors.New("optimize: problem does not provide needed Hess function")
+	}
+	return nil
+}
+
+// Settings represents settings of the optimization run. It contains initial
+// settings, convergence information, and Recorder information. In general, users
+// should use DefaultSettings rather than constructing a Settings literal.
+//
+// If UseInitData is true, InitialValue, InitialGradient and InitialHessian
+// specify function information at the initial location.
+//
+// If Recorder is nil, no information will be recorded.
+type Settings struct {
+	UseInitialData  bool          // Use supplied information about the conditions at the initial x.
+	InitialValue    float64       // Function value at the initial x.
+	InitialGradient []float64     // Gradient at the initial x.
+	InitialHessian  *mat.SymDense // Hessian at the initial x.
+
+	// FunctionThreshold is the threshold for acceptably small values of the
+	// objective function. FunctionThreshold status is returned if
+	// the objective function is less than this value.
+	// The default value is -inf.
+	FunctionThreshold float64
+
+	// GradientThreshold determines the accuracy to which the minimum is found.
+	// GradientThreshold status is returned if the infinity norm of
+	// the gradient is less than this value.
+	// Has no effect if gradient information is not used.
+	// The default value is 1e-6.
+	GradientThreshold float64
+
+	// FunctionConverge tests that the function value decreases by a
+	// significant amount over the specified number of iterations.
+	//
+	// If f < f_best and
+	//  f_best - f > FunctionConverge.Relative * maxabs(f, f_best) + FunctionConverge.Absolute
+	// then a significant decrease has occurred, and f_best is updated.
+	//
+	// If there is no significant decrease for FunctionConverge.Iterations
+	// major iterations, FunctionConvergence status is returned.
+	//
+	// If this is nil or if FunctionConverge.Iterations == 0, it has no effect.
+	FunctionConverge *FunctionConverge
+
+	// MajorIterations is the maximum number of iterations allowed.
+	// IterationLimit status is returned if the number of major iterations
+	// equals or exceeds this value.
+	// If it equals zero, this setting has no effect.
+	// The default value is 0.
+	MajorIterations int
+
+	// Runtime is the maximum runtime allowed. RuntimeLimit status is returned
+	// if the duration of the run is longer than this value. Runtime is only
+	// checked at iterations of the Method.
+	// If it equals zero, this setting has no effect.
+	// The default value is 0.
+	Runtime time.Duration
+
+	// FuncEvaluations is the maximum allowed number of function evaluations.
+	// FunctionEvaluationLimit status is returned if the total number of calls
+	// to Func equals or exceeds this number.
+	// If it equals zero, this setting has no effect.
+	// The default value is 0.
+	FuncEvaluations int
+
+	// GradEvaluations is the maximum allowed number of gradient evaluations.
+	// GradientEvaluationLimit status is returned if the total number of calls
+	// to Grad equals or exceeds this number.
+	// If it equals zero, this setting has no effect.
+	// The default value is 0.
+	GradEvaluations int
+
+	// HessEvaluations is the maximum allowed number of Hessian evaluations.
+	// HessianEvaluationLimit status is returned if the total number of calls
+	// to Hess equals or exceeds this number.
+	// If it equals zero, this setting has no effect.
+	// The default value is 0.
+	HessEvaluations int
+
+	Recorder Recorder
+
+	// Concurrent represents how many concurrent evaluations are possible.
+	Concurrent int
+}
+
+// DefaultSettings returns a new Settings struct containing the default settings.
+func DefaultSettings() *Settings {
+	return &Settings{
+		GradientThreshold: defaultGradientAbsTol,
+		FunctionThreshold: math.Inf(-1),
+		FunctionConverge: &FunctionConverge{
+			Absolute:   1e-10,
+			Iterations: 20,
+		},
+	}
+}
+
+// resize takes x and returns a slice of length dim. It returns a resliced x
+// if cap(x) >= dim, and a new slice otherwise.
+func resize(x []float64, dim int) []float64 {
+	if dim > cap(x) {
+		return make([]float64, dim)
+	}
+	return x[:dim]
+}
+
+func resizeSymDense(m *mat.SymDense, dim int) *mat.SymDense {
+	if m == nil || cap(m.RawSymmetric().Data) < dim*dim {
+		return mat.NewSymDense(dim, nil)
+	}
+	return mat.NewSymDense(dim, m.RawSymmetric().Data[:dim*dim])
+}
diff --git a/vendor/gonum.org/v1/gonum/optimize/unconstrained_test.go b/vendor/gonum.org/v1/gonum/optimize/unconstrained_test.go
new file mode 100644
index 00000000..a8cb373f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/optimize/unconstrained_test.go
@@ -0,0 +1,1305 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package optimize
+
+import (
+	"fmt"
+	"math"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+	"gonum.org/v1/gonum/optimize/functions"
+)
+
+type unconstrainedTest struct {
+	// name is the name of the test.
+	name string
+	// p is the optimization problem to be solved.
+	p Problem
+	// x is the initial guess.
+	x []float64
+	// gradTol is the absolute gradient tolerance for the test. If gradTol == 0,
+	// the default value of 1e-12 will be used.
+	gradTol float64
+	// fAbsTol is the absolute function convergence for the test. If fAbsTol == 0,
+	// the default value of 1e-12 will be used.
+	fAbsTol float64
+	// fIter is the number of iterations for function convergence. If fIter == 0,
+	// the default value of 20 will be used.
+	fIter int
+	// long indicates that the test takes long time to finish and will be
+	// excluded if testing.Short returns true.
+	long bool
+}
+
+func (t unconstrainedTest) String() string {
+	dim := len(t.x)
+	if dim <= 10 {
+		// Print the initial X only for small-dimensional problems.
+		return fmt.Sprintf("F: %v\nDim: %v\nInitial X: %v\nGradientThreshold: %v",
+			t.name, dim, t.x, t.gradTol)
+	}
+	return fmt.Sprintf("F: %v\nDim: %v\nGradientThreshold: %v",
+		t.name, dim, t.gradTol)
+}
+
+var gradFreeTests = []unconstrainedTest{
+	{
+		name: "Beale",
+		p: Problem{
+			Func: functions.Beale{}.Func,
+		},
+		x: []float64{1, 1},
+	},
+	{
+		name: "BiggsEXP6",
+		p: Problem{
+			Func: functions.BiggsEXP6{}.Func,
+		},
+		x: []float64{1, 2, 1, 1, 1, 1},
+	},
+	{
+		name: "BrownAndDennis",
+		p: Problem{
+			Func: functions.BrownAndDennis{}.Func,
+		},
+		x: []float64{25, 5, -5, -1},
+	},
+	{
+		name: "ExtendedRosenbrock",
+		p: Problem{
+			Func: functions.ExtendedRosenbrock{}.Func,
+		},
+		x: []float64{-10, 10},
+	},
+	{
+		name: "ExtendedRosenbrock",
+		p: Problem{
+			Func: functions.ExtendedRosenbrock{}.Func,
+		},
+		x: []float64{-5, 4, 16, 3},
+	},
+}
+
+var gradientDescentTests = []unconstrainedTest{
+	{
+		name: "Beale",
+		p: Problem{
+			Func: functions.Beale{}.Func,
+			Grad: functions.Beale{}.Grad,
+		},
+		x: []float64{1, 1},
+	},
+	{
+		name: "Beale",
+		p: Problem{
+			Func: functions.Beale{}.Func,
+			Grad: functions.Beale{}.Grad,
+		},
+		x: []float64{3.00001, 0.50001},
+	},
+	{
+		name: "BiggsEXP2",
+		p: Problem{
+			Func: functions.BiggsEXP2{}.Func,
+			Grad: functions.BiggsEXP2{}.Grad,
+		},
+		x: []float64{1, 2},
+	},
+	{
+		name: "BiggsEXP2",
+		p: Problem{
+			Func: functions.BiggsEXP2{}.Func,
+			Grad: functions.BiggsEXP2{}.Grad,
+		},
+		x: []float64{1.00001, 10.00001},
+	},
+	{
+		name: "BiggsEXP3",
+		p: Problem{
+			Func: functions.BiggsEXP3{}.Func,
+			Grad: functions.BiggsEXP3{}.Grad,
+		},
+		x: []float64{1, 2, 1},
+	},
+	{
+		name: "BiggsEXP3",
+		p: Problem{
+			Func: functions.BiggsEXP3{}.Func,
+			Grad: functions.BiggsEXP3{}.Grad,
+		},
+		x: []float64{1.00001, 10.00001, 3.00001},
+	},
+	{
+		name: "ExtendedRosenbrock",
+		p: Problem{
+			Func: functions.ExtendedRosenbrock{}.Func,
+			Grad: functions.ExtendedRosenbrock{}.Grad,
+		},
+		x:       []float64{-1.2, 1},
+		gradTol: 1e-10,
+	},
+	{
+		name: "ExtendedRosenbrock",
+		p: Problem{
+			Func: functions.ExtendedRosenbrock{}.Func,
+			Grad: functions.ExtendedRosenbrock{}.Grad,
+		},
+		x:       []float64{1.00001, 1.00001},
+		gradTol: 1e-10,
+	},
+	{
+		name: "ExtendedRosenbrock",
+		p: Problem{
+			Func: functions.ExtendedRosenbrock{}.Func,
+			Grad: functions.ExtendedRosenbrock{}.Grad,
+		},
+		x:       []float64{-1.2, 1, -1.2},
+		gradTol: 1e-10,
+	},
+	{
+		name: "ExtendedRosenbrock",
+		p: Problem{
+			Func: functions.ExtendedRosenbrock{}.Func,
+			Grad: functions.ExtendedRosenbrock{}.Grad,
+		},
+		x:    []float64{-120, 100, 50},
+		long: true,
+	},
+	{
+		name: "ExtendedRosenbrock",
+		p: Problem{
+			Func: functions.ExtendedRosenbrock{}.Func,
+			Grad: functions.ExtendedRosenbrock{}.Grad,
+		},
+		x: []float64{1, 1, 1},
+	},
+	{
+		name: "ExtendedRosenbrock",
+		p: Problem{
+			Func: functions.ExtendedRosenbrock{}.Func,
+			Grad: functions.ExtendedRosenbrock{}.Grad,
+		},
+		x:       []float64{1.00001, 1.00001, 1.00001},
+		gradTol: 1e-8,
+	},
+	{
+		name: "Gaussian",
+		p: Problem{
+			Func: functions.Gaussian{}.Func,
+			Grad: functions.Gaussian{}.Grad,
+		},
+		x:       []float64{0.4, 1, 0},
+		gradTol: 1e-9,
+	},
+	{
+		name: "Gaussian",
+		p: Problem{
+			Func: functions.Gaussian{}.Func,
+			Grad: functions.Gaussian{}.Grad,
+		},
+		x:       []float64{0.3989561, 1.0000191, 0},
+		gradTol: 1e-9,
+	},
+	{
+		name: "HelicalValley",
+		p: Problem{
+			Func: functions.HelicalValley{}.Func,
+			Grad: functions.HelicalValley{}.Grad,
+		},
+		x: []float64{-1, 0, 0},
+	},
+	{
+		name: "HelicalValley",
+		p: Problem{
+			Func: functions.HelicalValley{}.Func,
+			Grad: functions.HelicalValley{}.Grad,
+		},
+		x: []float64{1.00001, 0.00001, 0.00001},
+	},
+	{
+		name: "Trigonometric",
+		p: Problem{
+			Func: functions.Trigonometric{}.Func,
+			Grad: functions.Trigonometric{}.Grad,
+		},
+		x:       []float64{0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1},
+		gradTol: 1e-7,
+	},
+	{
+		name: "Trigonometric",
+		p: Problem{
+			Func: functions.Trigonometric{}.Func,
+			Grad: functions.Trigonometric{}.Grad,
+		},
+		x: []float64{0.042964, 0.043976, 0.045093, 0.046338, 0.047744,
+			0.049354, 0.051237, 0.195209, 0.164977, 0.060148},
+		gradTol: 1e-8,
+	},
+	newVariablyDimensioned(2, 0),
+	{
+		name: "VariablyDimensioned",
+		p: Problem{
+			Func: functions.VariablyDimensioned{}.Func,
+			Grad: functions.VariablyDimensioned{}.Grad,
+		},
+		x: []float64{1.00001, 1.00001},
+	},
+	newVariablyDimensioned(10, 0),
+	{
+		name: "VariablyDimensioned",
+		p: Problem{
+			Func: functions.VariablyDimensioned{}.Func,
+			Grad: functions.VariablyDimensioned{}.Grad,
+		},
+		x: []float64{1.00001, 1.00001, 1.00001, 1.00001, 1.00001, 1.00001, 1.00001, 1.00001, 1.00001, 1.00001},
+	},
+}
+
+var cgTests = []unconstrainedTest{
+	{
+		name: "BiggsEXP4",
+		p: Problem{
+			Func: functions.BiggsEXP4{}.Func,
+			Grad: functions.BiggsEXP4{}.Grad,
+		},
+		x: []float64{1, 2, 1, 1},
+	},
+	{
+		name: "BiggsEXP4",
+		p: Problem{
+			Func: functions.BiggsEXP4{}.Func,
+			Grad: functions.BiggsEXP4{}.Grad,
+		},
+		x: []float64{1.00001, 10.00001, 1.00001, 5.00001},
+	},
+	{
+		name: "BiggsEXP5",
+		p: Problem{
+			Func: functions.BiggsEXP5{}.Func,
+			Grad: functions.BiggsEXP5{}.Grad,
+		},
+		x:       []float64{1, 2, 1, 1, 1},
+		gradTol: 1e-7,
+	},
+	{
+		name: "BiggsEXP5",
+		p: Problem{
+			Func: functions.BiggsEXP5{}.Func,
+			Grad: functions.BiggsEXP5{}.Grad,
+		},
+		x: []float64{1.00001, 10.00001, 1.00001, 5.00001, 4.00001},
+	},
+	{
+		name: "BiggsEXP6",
+		p: Problem{
+			Func: functions.BiggsEXP6{}.Func,
+			Grad: functions.BiggsEXP6{}.Grad,
+		},
+		x:       []float64{1, 2, 1, 1, 1, 1},
+		gradTol: 1e-7,
+	},
+	{
+		name: "BiggsEXP6",
+		p: Problem{
+			Func: functions.BiggsEXP6{}.Func,
+			Grad: functions.BiggsEXP6{}.Grad,
+		},
+		x:       []float64{1.00001, 10.00001, 1.00001, 5.00001, 4.00001, 3.00001},
+		gradTol: 1e-8,
+	},
+	{
+		name: "Box3D",
+		p: Problem{
+			Func: functions.Box3D{}.Func,
+			Grad: functions.Box3D{}.Grad,
+		},
+		x: []float64{0, 10, 20},
+	},
+	{
+		name: "Box3D",
+		p: Problem{
+			Func: functions.Box3D{}.Func,
+			Grad: functions.Box3D{}.Grad,
+		},
+		x: []float64{1.00001, 10.00001, 1.00001},
+	},
+	{
+		name: "Box3D",
+		p: Problem{
+			Func: functions.Box3D{}.Func,
+			Grad: functions.Box3D{}.Grad,
+		},
+		x: []float64{100.00001, 100.00001, 0.00001},
+	},
+	{
+		name: "ExtendedPowellSingular",
+		p: Problem{
+			Func: functions.ExtendedPowellSingular{}.Func,
+			Grad: functions.ExtendedPowellSingular{}.Grad,
+		},
+		x: []float64{3, -1, 0, 3},
+	},
+	{
+		name: "ExtendedPowellSingular",
+		p: Problem{
+			Func: functions.ExtendedPowellSingular{}.Func,
+			Grad: functions.ExtendedPowellSingular{}.Grad,
+		},
+		x: []float64{0.00001, 0.00001, 0.00001, 0.00001},
+	},
+	{
+		name: "ExtendedPowellSingular",
+		p: Problem{
+			Func: functions.ExtendedPowellSingular{}.Func,
+			Grad: functions.ExtendedPowellSingular{}.Grad,
+		},
+		x:       []float64{3, -1, 0, 3, 3, -1, 0, 3},
+		gradTol: 1e-8,
+	},
+	{
+		name: "ExtendedPowellSingular",
+		p: Problem{
+			Func: functions.ExtendedPowellSingular{}.Func,
+			Grad: functions.ExtendedPowellSingular{}.Grad,
+		},
+		x: []float64{0.00001, 0.00001, 0.00001, 0.00001, 0.00001, 0.00001, 0.00001, 0.00001},
+	},
+	{
+		name: "ExtendedRosenbrock",
+		p: Problem{
+			Func: functions.ExtendedRosenbrock{}.Func,
+			Grad: functions.ExtendedRosenbrock{}.Grad,
+		},
+		x: []float64{-1.2, 1, -1.2, 1},
+	},
+	{
+		name: "ExtendedRosenbrock",
+		p: Problem{
+			Func: functions.ExtendedRosenbrock{}.Func,
+			Grad: functions.ExtendedRosenbrock{}.Grad,
+		},
+		x:       []float64{1e4, 1e4},
+		gradTol: 1e-10,
+	},
+	{
+		name: "ExtendedRosenbrock",
+		p: Problem{
+			Func: functions.ExtendedRosenbrock{}.Func,
+			Grad: functions.ExtendedRosenbrock{}.Grad,
+		},
+		x:       []float64{1.00001, 1.00001, 1.00001, 1.00001},
+		gradTol: 1e-10,
+	},
+	{
+		name: "PenaltyI",
+		p: Problem{
+			Func: functions.PenaltyI{}.Func,
+			Grad: functions.PenaltyI{}.Grad,
+		},
+		x:       []float64{1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
+		gradTol: 1e-9,
+	},
+	{
+		name: "PenaltyI",
+		p: Problem{
+			Func: functions.PenaltyI{}.Func,
+			Grad: functions.PenaltyI{}.Grad,
+		},
+		x:       []float64{0.250007, 0.250007, 0.250007, 0.250007},
+		gradTol: 1e-10,
+	},
+	{
+		name: "PenaltyI",
+		p: Problem{
+			Func: functions.PenaltyI{}.Func,
+			Grad: functions.PenaltyI{}.Grad,
+		},
+		x: []float64{0.1581, 0.1581, 0.1581, 0.1581, 0.1581, 0.1581,
+			0.1581, 0.1581, 0.1581, 0.1581},
+		gradTol: 1e-10,
+	},
+	{
+		name: "PenaltyII",
+		p: Problem{
+			Func: functions.PenaltyII{}.Func,
+			Grad: functions.PenaltyII{}.Grad,
+		},
+		x:       []float64{0.5, 0.5, 0.5, 0.5},
+		gradTol: 1e-8,
+	},
+	{
+		name: "PenaltyII",
+		p: Problem{
+			Func: functions.PenaltyII{}.Func,
+			Grad: functions.PenaltyII{}.Grad,
+		},
+		x:       []float64{0.19999, 0.19131, 0.4801, 0.51884},
+		gradTol: 1e-8,
+	},
+	{
+		name: "PenaltyII",
+		p: Problem{
+			Func: functions.PenaltyII{}.Func,
+			Grad: functions.PenaltyII{}.Grad,
+		},
+		x: []float64{0.19998, 0.01035, 0.01960, 0.03208, 0.04993, 0.07651,
+			0.11862, 0.19214, 0.34732, 0.36916},
+		gradTol: 1e-6,
+	},
+	{
+		name: "PowellBadlyScaled",
+		p: Problem{
+			Func: functions.PowellBadlyScaled{}.Func,
+			Grad: functions.PowellBadlyScaled{}.Grad,
+		},
+		x:       []float64{1.09815e-05, 9.10614},
+		gradTol: 1e-8,
+	},
+	newVariablyDimensioned(100, 1e-10),
+	newVariablyDimensioned(1000, 1e-7),
+	newVariablyDimensioned(10000, 1e-4),
+	{
+		name: "Watson",
+		p: Problem{
+			Func: functions.Watson{}.Func,
+			Grad: functions.Watson{}.Grad,
+		},
+		x:       []float64{0, 0, 0, 0, 0, 0},
+		gradTol: 1e-6,
+	},
+	{
+		name: "Watson",
+		p: Problem{
+			Func: functions.Watson{}.Func,
+			Grad: functions.Watson{}.Grad,
+		},
+		x:       []float64{-0.01572, 1.01243, -0.23299, 1.26043, -1.51372, 0.99299},
+		gradTol: 1e-6,
+	},
+	{
+		name: "Watson",
+		p: Problem{
+			Func: functions.Watson{}.Func,
+			Grad: functions.Watson{}.Grad,
+		},
+		x:       []float64{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+		gradTol: 1e-6,
+		long:    true,
+	},
+	{
+		name: "Watson",
+		p: Problem{
+			Func: functions.Watson{}.Func,
+			Grad: functions.Watson{}.Grad,
+		},
+		x: []float64{-1.53070e-05, 0.99978, 0.01476, 0.14634, 1.00082,
+			-2.61773, 4.10440, -3.14361, 1.05262},
+		gradTol: 1e-6,
+	},
+	{
+		name: "Wood",
+		p: Problem{
+			Func: functions.Wood{}.Func,
+			Grad: functions.Wood{}.Grad,
+		},
+		x:       []float64{-3, -1, -3, -1},
+		gradTol: 1e-6,
+	},
+}
+
+var quasiNewtonTests = []unconstrainedTest{
+	{
+		name: "BiggsEXP4",
+		p: Problem{
+			Func: functions.BiggsEXP4{}.Func,
+			Grad: functions.BiggsEXP4{}.Grad,
+		},
+		x: []float64{1, 2, 1, 1},
+	},
+	{
+		name: "BiggsEXP4",
+		p: Problem{
+			Func: functions.BiggsEXP4{}.Func,
+			Grad: functions.BiggsEXP4{}.Grad,
+		},
+		x: []float64{1.00001, 10.00001, 1.00001, 5.00001},
+	},
+	{
+		name: "BiggsEXP5",
+		p: Problem{
+			Func: functions.BiggsEXP5{}.Func,
+			Grad: functions.BiggsEXP5{}.Grad,
+		},
+		x:       []float64{1, 2, 1, 1, 1},
+		gradTol: 1e-10,
+	},
+	{
+		name: "BiggsEXP5",
+		p: Problem{
+			Func: functions.BiggsEXP5{}.Func,
+			Grad: functions.BiggsEXP5{}.Grad,
+		},
+		x: []float64{1.00001, 10.00001, 1.00001, 5.00001, 4.00001},
+	},
+	{
+		name: "BiggsEXP6",
+		p: Problem{
+			Func: functions.BiggsEXP6{}.Func,
+			Grad: functions.BiggsEXP6{}.Grad,
+		},
+		x:       []float64{1, 2, 1, 1, 1, 1},
+		gradTol: 1e-8,
+	},
+	{
+		name: "BiggsEXP6",
+		p: Problem{
+			Func: functions.BiggsEXP6{}.Func,
+			Grad: functions.BiggsEXP6{}.Grad,
+		},
+		x:       []float64{1.00001, 10.00001, 1.00001, 5.00001, 4.00001, 3.00001},
+		gradTol: 1e-8,
+	},
+	{
+		name: "Box3D",
+		p: Problem{
+			Func: functions.Box3D{}.Func,
+			Grad: functions.Box3D{}.Grad,
+		},
+		x: []float64{0, 10, 20},
+	},
+	{
+		name: "Box3D",
+		p: Problem{
+			Func: functions.Box3D{}.Func,
+			Grad: functions.Box3D{}.Grad,
+		},
+		x: []float64{1.00001, 10.00001, 1.00001},
+	},
+	{
+		name: "Box3D",
+		p: Problem{
+			Func: functions.Box3D{}.Func,
+			Grad: functions.Box3D{}.Grad,
+		},
+		x: []float64{100.00001, 100.00001, 0.00001},
+	},
+	{
+		name: "BrownBadlyScaled",
+		p: Problem{
+			Func: functions.BrownBadlyScaled{}.Func,
+			Grad: functions.BrownBadlyScaled{}.Grad,
+		},
+		x: []float64{1, 1},
+	},
+	{
+		name: "BrownBadlyScaled",
+		p: Problem{
+			Func: functions.BrownBadlyScaled{}.Func,
+			Grad: functions.BrownBadlyScaled{}.Grad,
+		},
+		x: []float64{1.000001e6, 2.01e-6},
+	},
+	{
+		name: "ExtendedPowellSingular",
+		p: Problem{
+			Func: functions.ExtendedPowellSingular{}.Func,
+			Grad: functions.ExtendedPowellSingular{}.Grad,
+		},
+		x: []float64{3, -1, 0, 3},
+	},
+	{
+		name: "ExtendedPowellSingular",
+		p: Problem{
+			Func: functions.ExtendedPowellSingular{}.Func,
+			Grad: functions.ExtendedPowellSingular{}.Grad,
+		},
+		x: []float64{0.00001, 0.00001, 0.00001, 0.00001},
+	},
+	{
+		name: "ExtendedPowellSingular",
+		p: Problem{
+			Func: functions.ExtendedPowellSingular{}.Func,
+			Grad: functions.ExtendedPowellSingular{}.Grad,
+		},
+		x: []float64{3, -1, 0, 3, 3, -1, 0, 3},
+	},
+	{
+		name: "ExtendedPowellSingular",
+		p: Problem{
+			Func: functions.ExtendedPowellSingular{}.Func,
+			Grad: functions.ExtendedPowellSingular{}.Grad,
+		},
+		x: []float64{0.00001, 0.00001, 0.00001, 0.00001, 0.00001, 0.00001, 0.00001, 0.00001},
+	},
+	{
+		name: "ExtendedRosenbrock",
+		p: Problem{
+			Func: functions.ExtendedRosenbrock{}.Func,
+			Grad: functions.ExtendedRosenbrock{}.Grad,
+		},
+		x: []float64{-1.2, 1, -1.2, 1},
+	},
+	{
+		name: "ExtendedRosenbrock",
+		p: Problem{
+			Func: functions.ExtendedRosenbrock{}.Func,
+			Grad: functions.ExtendedRosenbrock{}.Grad,
+		},
+		x: []float64{1.00001, 1.00001, 1.00001, 1.00001},
+	},
+	{
+		name: "Gaussian",
+		p: Problem{
+			Func: functions.Gaussian{}.Func,
+			Grad: functions.Gaussian{}.Grad,
+		},
+		x:       []float64{0.4, 1, 0},
+		gradTol: 1e-11,
+	},
+	{
+		name: "GulfResearchAndDevelopment",
+		p: Problem{
+			Func: functions.GulfResearchAndDevelopment{}.Func,
+			Grad: functions.GulfResearchAndDevelopment{}.Grad,
+		},
+		x: []float64{5, 2.5, 0.15},
+	},
+	{
+		name: "GulfResearchAndDevelopment",
+		p: Problem{
+			Func: functions.GulfResearchAndDevelopment{}.Func,
+			Grad: functions.GulfResearchAndDevelopment{}.Grad,
+		},
+		x: []float64{50.00001, 25.00001, 1.50001},
+	},
+	{
+		name: "GulfResearchAndDevelopment",
+		p: Problem{
+			Func: functions.GulfResearchAndDevelopment{}.Func,
+			Grad: functions.GulfResearchAndDevelopment{}.Grad,
+		},
+		x: []float64{99.89529, 60.61453, 9.16124},
+	},
+	{
+		name: "GulfResearchAndDevelopment",
+		p: Problem{
+			Func: functions.GulfResearchAndDevelopment{}.Func,
+			Grad: functions.GulfResearchAndDevelopment{}.Grad,
+		},
+		x: []float64{201.66258, 60.61633, 10.22489},
+	},
+	{
+		name: "PenaltyI",
+		p: Problem{
+			Func: functions.PenaltyI{}.Func,
+			Grad: functions.PenaltyI{}.Grad,
+		},
+		x: []float64{1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
+	},
+	{
+		name: "PenaltyI",
+		p: Problem{
+			Func: functions.PenaltyI{}.Func,
+			Grad: functions.PenaltyI{}.Grad,
+		},
+		x:       []float64{0.250007, 0.250007, 0.250007, 0.250007},
+		gradTol: 1e-9,
+	},
+	{
+		name: "PenaltyI",
+		p: Problem{
+			Func: functions.PenaltyI{}.Func,
+			Grad: functions.PenaltyI{}.Grad,
+		},
+		x: []float64{0.1581, 0.1581, 0.1581, 0.1581, 0.1581, 0.1581,
+			0.1581, 0.1581, 0.1581, 0.1581},
+	},
+	{
+		name: "PenaltyII",
+		p: Problem{
+			Func: functions.PenaltyII{}.Func,
+			Grad: functions.PenaltyII{}.Grad,
+		},
+		x:       []float64{0.5, 0.5, 0.5, 0.5},
+		gradTol: 1e-10,
+	},
+	{
+		name: "PenaltyII",
+		p: Problem{
+			Func: functions.PenaltyII{}.Func,
+			Grad: functions.PenaltyII{}.Grad,
+		},
+		x:       []float64{0.19999, 0.19131, 0.4801, 0.51884},
+		gradTol: 1e-10,
+	},
+	{
+		name: "PenaltyII",
+		p: Problem{
+			Func: functions.PenaltyII{}.Func,
+			Grad: functions.PenaltyII{}.Grad,
+		},
+		x:       []float64{0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5},
+		gradTol: 1e-9,
+	},
+	{
+		name: "PenaltyII",
+		p: Problem{
+			Func: functions.PenaltyII{}.Func,
+			Grad: functions.PenaltyII{}.Grad,
+		},
+		x: []float64{0.19998, 0.01035, 0.01960, 0.03208, 0.04993, 0.07651,
+			0.11862, 0.19214, 0.34732, 0.36916},
+		gradTol: 1e-9,
+	},
+	{
+		name: "PowellBadlyScaled",
+		p: Problem{
+			Func: functions.PowellBadlyScaled{}.Func,
+			Grad: functions.PowellBadlyScaled{}.Grad,
+		},
+		x: []float64{0, 1},
+	},
+	{
+		name: "PowellBadlyScaled",
+		p: Problem{
+			Func: functions.PowellBadlyScaled{}.Func,
+			Grad: functions.PowellBadlyScaled{}.Grad,
+		},
+		x:       []float64{1.09815e-05, 9.10614},
+		gradTol: 1e-10,
+	},
+	newVariablyDimensioned(100, 1e-10),
+	{
+		name: "Watson",
+		p: Problem{
+			Func: functions.Watson{}.Func,
+			Grad: functions.Watson{}.Grad,
+		},
+		x:       []float64{0, 0, 0, 0, 0, 0},
+		gradTol: 1e-7,
+	},
+	{
+		name: "Watson",
+		p: Problem{
+			Func: functions.Watson{}.Func,
+			Grad: functions.Watson{}.Grad,
+		},
+		x:       []float64{-0.01572, 1.01243, -0.23299, 1.26043, -1.51372, 0.99299},
+		gradTol: 1e-7,
+	},
+	{
+		name: "Watson",
+		p: Problem{
+			Func: functions.Watson{}.Func,
+			Grad: functions.Watson{}.Grad,
+		},
+		x:       []float64{0, 0, 0, 0, 0, 0, 0, 0, 0},
+		gradTol: 1e-8,
+	},
+	{
+		name: "Watson",
+		p: Problem{
+			Func: functions.Watson{}.Func,
+			Grad: functions.Watson{}.Grad,
+		},
+		x: []float64{-1.53070e-05, 0.99978, 0.01476, 0.14634, 1.00082,
+			-2.61773, 4.10440, -3.14361, 1.05262},
+		gradTol: 1e-8,
+	},
+}
+
+var bfgsTests = []unconstrainedTest{
+	{
+		name: "BiggsEXP6",
+		p: Problem{
+			Func: functions.BiggsEXP6{}.Func,
+			Grad: functions.BiggsEXP6{}.Grad,
+		},
+		x:       []float64{1, 2, 1, 1, 1, 1},
+		gradTol: 1e-10,
+	},
+	{
+		name: "BiggsEXP6",
+		p: Problem{
+			Func: functions.BiggsEXP6{}.Func,
+			Grad: functions.BiggsEXP6{}.Grad,
+		},
+		x:       []float64{1.00001, 10.00001, 1.00001, 5.00001, 4.00001, 3.00001},
+		gradTol: 1e-10,
+	},
+	{
+		name: "BrownAndDennis",
+		p: Problem{
+			Func: functions.BrownAndDennis{}.Func,
+			Grad: functions.BrownAndDennis{}.Grad,
+		},
+		x:       []float64{25, 5, -5, -1},
+		gradTol: 1e-5,
+	},
+	{
+		name: "ExtendedRosenbrock",
+		p: Problem{
+			Func: functions.ExtendedRosenbrock{}.Func,
+			Grad: functions.ExtendedRosenbrock{}.Grad,
+		},
+		x:       []float64{1e5, 1e5},
+		gradTol: 1e-10,
+	},
+	{
+		name: "Gaussian",
+		p: Problem{
+			Func: functions.Gaussian{}.Func,
+			Grad: functions.Gaussian{}.Grad,
+		},
+		x:       []float64{0.398, 1, 0},
+		gradTol: 1e-11,
+	},
+	{
+		name: "Wood",
+		p: Problem{
+			Func: functions.Wood{}.Func,
+			Grad: functions.Wood{}.Grad,
+		},
+		x: []float64{-3, -1, -3, -1},
+	},
+}
+
+var lbfgsTests = []unconstrainedTest{
+	{
+		name: "BiggsEXP6",
+		p: Problem{
+			Func: functions.BiggsEXP6{}.Func,
+			Grad: functions.BiggsEXP6{}.Grad,
+		},
+		x:       []float64{1, 2, 1, 1, 1, 1},
+		gradTol: 1e-8,
+	},
+	{
+		name: "BiggsEXP6",
+		p: Problem{
+			Func: functions.BiggsEXP6{}.Func,
+			Grad: functions.BiggsEXP6{}.Grad,
+		},
+		x:       []float64{1.00001, 10.00001, 1.00001, 5.00001, 4.00001, 3.00001},
+		gradTol: 1e-8,
+	},
+	{
+		name: "ExtendedRosenbrock",
+		p: Problem{
+			Func: functions.ExtendedRosenbrock{}.Func,
+			Grad: functions.ExtendedRosenbrock{}.Grad,
+		},
+		x:       []float64{1e7, 1e6},
+		gradTol: 1e-10,
+	},
+	{
+		name: "Gaussian",
+		p: Problem{
+			Func: functions.Gaussian{}.Func,
+			Grad: functions.Gaussian{}.Grad,
+		},
+		x:       []float64{0.398, 1, 0},
+		gradTol: 1e-10,
+	},
+	newVariablyDimensioned(1000, 1e-8),
+	newVariablyDimensioned(10000, 1e-5),
+}
+
+var newtonTests = []unconstrainedTest{
+	{
+		name: "Beale",
+		p: Problem{
+			Func: functions.Beale{}.Func,
+			Grad: functions.Beale{}.Grad,
+			Hess: functions.Beale{}.Hess,
+		},
+		x: []float64{1, 1},
+	},
+	{
+		name: "BrownAndDennis",
+		p: Problem{
+			Func: functions.BrownAndDennis{}.Func,
+			Grad: functions.BrownAndDennis{}.Grad,
+			Hess: functions.BrownAndDennis{}.Hess,
+		},
+		x:       []float64{25, 5, -5, -1},
+		gradTol: 1e-10,
+	},
+	{
+		name: "BrownBadlyScaled",
+		p: Problem{
+			Func: functions.BrownBadlyScaled{}.Func,
+			Grad: functions.BrownBadlyScaled{}.Grad,
+			Hess: functions.BrownBadlyScaled{}.Hess,
+		},
+		x: []float64{1, 1},
+	},
+	{
+		name: "PowellBadlyScaled",
+		p: Problem{
+			Func: functions.PowellBadlyScaled{}.Func,
+			Grad: functions.PowellBadlyScaled{}.Grad,
+			Hess: functions.PowellBadlyScaled{}.Hess,
+		},
+		x:       []float64{0, 1},
+		gradTol: 1e-10,
+	},
+	{
+		name: "Watson",
+		p: Problem{
+			Func: functions.Watson{}.Func,
+			Grad: functions.Watson{}.Grad,
+			Hess: functions.Watson{}.Hess,
+		},
+		x: []float64{0, 0, 0, 0, 0, 0},
+	},
+	{
+		name: "Watson",
+		p: Problem{
+			Func: functions.Watson{}.Func,
+			Grad: functions.Watson{}.Grad,
+			Hess: functions.Watson{}.Hess,
+		},
+		x: []float64{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+	},
+	{
+		name: "Wood",
+		p: Problem{
+			Func: functions.Wood{}.Func,
+			Grad: functions.Wood{}.Grad,
+			Hess: functions.Wood{}.Hess,
+		},
+		x: []float64{-3, -1, -3, -1},
+	},
+}
+
+func newVariablyDimensioned(dim int, gradTol float64) unconstrainedTest {
+	x := make([]float64, dim)
+	for i := range x {
+		x[i] = float64(dim-i-1) / float64(dim)
+	}
+	return unconstrainedTest{
+		name: "VariablyDimensioned",
+		p: Problem{
+			Func: functions.VariablyDimensioned{}.Func,
+			Grad: functions.VariablyDimensioned{}.Grad,
+		},
+		x:       x,
+		gradTol: gradTol,
+	}
+}
+
+func TestLocal(t *testing.T) {
+	var tests []unconstrainedTest
+	// Mix of functions with and without Grad method.
+	tests = append(tests, gradFreeTests...)
+	tests = append(tests, gradientDescentTests...)
+	testLocal(t, tests, nil)
+}
+
+func TestNelderMead(t *testing.T) {
+	var tests []unconstrainedTest
+	// Mix of functions with and without Grad method.
+	tests = append(tests, gradFreeTests...)
+	tests = append(tests, gradientDescentTests...)
+	testLocal(t, tests, &NelderMead{})
+}
+
+func TestGradientDescent(t *testing.T) {
+	testLocal(t, gradientDescentTests, &GradientDescent{})
+}
+
+func TestGradientDescentBacktracking(t *testing.T) {
+	testLocal(t, gradientDescentTests, &GradientDescent{
+		Linesearcher: &Backtracking{
+			DecreaseFactor: 0.1,
+		},
+	})
+}
+
+func TestGradientDescentBisection(t *testing.T) {
+	testLocal(t, gradientDescentTests, &GradientDescent{
+		Linesearcher: &Bisection{},
+	})
+}
+
+func TestCG(t *testing.T) {
+	var tests []unconstrainedTest
+	tests = append(tests, gradientDescentTests...)
+	tests = append(tests, cgTests...)
+	testLocal(t, tests, &CG{})
+}
+
+func TestFletcherReevesQuadStep(t *testing.T) {
+	var tests []unconstrainedTest
+	tests = append(tests, gradientDescentTests...)
+	tests = append(tests, cgTests...)
+	testLocal(t, tests, &CG{
+		Variant:     &FletcherReeves{},
+		InitialStep: &QuadraticStepSize{},
+	})
+}
+
+func TestFletcherReevesFirstOrderStep(t *testing.T) {
+	var tests []unconstrainedTest
+	tests = append(tests, gradientDescentTests...)
+	tests = append(tests, cgTests...)
+	testLocal(t, tests, &CG{
+		Variant:     &FletcherReeves{},
+		InitialStep: &FirstOrderStepSize{},
+	})
+}
+
+func TestHestenesStiefelQuadStep(t *testing.T) {
+	var tests []unconstrainedTest
+	tests = append(tests, gradientDescentTests...)
+	tests = append(tests, cgTests...)
+	testLocal(t, tests, &CG{
+		Variant:     &HestenesStiefel{},
+		InitialStep: &QuadraticStepSize{},
+	})
+}
+
+func TestHestenesStiefelFirstOrderStep(t *testing.T) {
+	var tests []unconstrainedTest
+	tests = append(tests, gradientDescentTests...)
+	tests = append(tests, cgTests...)
+	testLocal(t, tests, &CG{
+		Variant:     &HestenesStiefel{},
+		InitialStep: &FirstOrderStepSize{},
+	})
+}
+
+func TestPolakRibiereQuadStep(t *testing.T) {
+	var tests []unconstrainedTest
+	tests = append(tests, gradientDescentTests...)
+	tests = append(tests, cgTests...)
+	testLocal(t, tests, &CG{
+		Variant:     &PolakRibierePolyak{},
+		InitialStep: &QuadraticStepSize{},
+	})
+}
+
+func TestPolakRibiereFirstOrderStep(t *testing.T) {
+	var tests []unconstrainedTest
+	tests = append(tests, gradientDescentTests...)
+	tests = append(tests, cgTests...)
+	testLocal(t, tests, &CG{
+		Variant:     &PolakRibierePolyak{},
+		InitialStep: &FirstOrderStepSize{},
+	})
+}
+
+func TestDaiYuanQuadStep(t *testing.T) {
+	var tests []unconstrainedTest
+	tests = append(tests, gradientDescentTests...)
+	tests = append(tests, cgTests...)
+	testLocal(t, tests, &CG{
+		Variant:     &DaiYuan{},
+		InitialStep: &QuadraticStepSize{},
+	})
+}
+
+func TestDaiYuanFirstOrderStep(t *testing.T) {
+	var tests []unconstrainedTest
+	tests = append(tests, gradientDescentTests...)
+	tests = append(tests, cgTests...)
+	testLocal(t, tests, &CG{
+		Variant:     &DaiYuan{},
+		InitialStep: &FirstOrderStepSize{},
+	})
+}
+
+func TestHagerZhangQuadStep(t *testing.T) {
+	var tests []unconstrainedTest
+	tests = append(tests, gradientDescentTests...)
+	tests = append(tests, cgTests...)
+	testLocal(t, tests, &CG{
+		Variant:     &HagerZhang{},
+		InitialStep: &QuadraticStepSize{},
+	})
+}
+
+func TestHagerZhangFirstOrderStep(t *testing.T) {
+	var tests []unconstrainedTest
+	tests = append(tests, gradientDescentTests...)
+	tests = append(tests, cgTests...)
+	testLocal(t, tests, &CG{
+		Variant:     &HagerZhang{},
+		InitialStep: &FirstOrderStepSize{},
+	})
+}
+
+func TestBFGS(t *testing.T) {
+	var tests []unconstrainedTest
+	tests = append(tests, gradientDescentTests...)
+	tests = append(tests, quasiNewtonTests...)
+	tests = append(tests, bfgsTests...)
+	testLocal(t, tests, &BFGS{})
+}
+
+func TestLBFGS(t *testing.T) {
+	var tests []unconstrainedTest
+	tests = append(tests, gradientDescentTests...)
+	tests = append(tests, quasiNewtonTests...)
+	tests = append(tests, lbfgsTests...)
+	testLocal(t, tests, &LBFGS{})
+}
+
+func TestNewton(t *testing.T) {
+	testLocal(t, newtonTests, &Newton{})
+}
+
+func testLocal(t *testing.T, tests []unconstrainedTest, method Method) {
+	for _, test := range tests {
+		if test.long && testing.Short() {
+			continue
+		}
+
+		settings := DefaultSettings()
+		settings.Recorder = nil
+		if method != nil && method.Needs().Gradient {
+			// Turn off function convergence checks for gradient-based methods.
+			settings.FunctionConverge = nil
+		} else {
+			if test.fIter == 0 {
+				test.fIter = 20
+			}
+			settings.FunctionConverge.Iterations = test.fIter
+			if test.fAbsTol == 0 {
+				test.fAbsTol = 1e-12
+			}
+			settings.FunctionConverge.Absolute = test.fAbsTol
+		}
+		if test.gradTol == 0 {
+			test.gradTol = 1e-12
+		}
+		settings.GradientThreshold = test.gradTol
+
+		result, err := Local(test.p, test.x, settings, method)
+		if err != nil {
+			t.Errorf("error finding minimum (%v) for:\n%v", err, test)
+			continue
+		}
+		if result == nil {
+			t.Errorf("nil result without error for:\n%v", test)
+			continue
+		}
+
+		// Check that the function value at the found optimum location is
+		// equal to result.F.
+		optF := test.p.Func(result.X)
+		if optF != result.F {
+			t.Errorf("Function value at the optimum location %v not equal to the returned value %v for:\n%v",
+				optF, result.F, test)
+		}
+		if result.Gradient != nil {
+			// Evaluate the norm of the gradient at the found optimum location.
+			g := make([]float64, len(test.x))
+			test.p.Grad(g, result.X)
+
+			if !floats.Equal(result.Gradient, g) {
+				t.Errorf("Gradient at the optimum location not equal to the returned value for:\n%v", test)
+			}
+
+			optNorm := floats.Norm(g, math.Inf(1))
+			// Check that the norm of the gradient at the found optimum location is
+			// smaller than the tolerance.
+			if optNorm >= settings.GradientThreshold {
+				t.Errorf("Norm of the gradient at the optimum location %v not smaller than tolerance %v for:\n%v",
+					optNorm, settings.GradientThreshold, test)
+			}
+		}
+
+		if method == nil {
+			// The tests below make sense only if the method used is known.
+			continue
+		}
+
+		if !method.Needs().Gradient && !method.Needs().Hessian {
+			// Gradient-free tests can correctly terminate only with
+			// FunctionConvergence status.
+			if result.Status != FunctionConvergence {
+				t.Errorf("Status not %v, %v instead", FunctionConvergence, result.Status)
+			}
+		}
+
+		// We are going to restart the solution using known initial data, so
+		// evaluate them.
+		settings.UseInitialData = true
+		settings.InitialValue = test.p.Func(test.x)
+		if method.Needs().Gradient {
+			settings.InitialGradient = resize(settings.InitialGradient, len(test.x))
+			test.p.Grad(settings.InitialGradient, test.x)
+		}
+		if method.Needs().Hessian {
+			settings.InitialHessian = mat.NewSymDense(len(test.x), nil)
+			test.p.Hess(settings.InitialHessian, test.x)
+		}
+
+		// Rerun the test again to make sure that it gets the same answer with
+		// the same starting condition. Moreover, we are using the initial data.
+		result2, err2 := Local(test.p, test.x, settings, method)
+		if err2 != nil {
+			t.Errorf("error finding minimum second time (%v) for:\n%v", err2, test)
+			continue
+		}
+		if result2 == nil {
+			t.Errorf("second time nil result without error for:\n%v", test)
+			continue
+		}
+
+		// At the moment all the optimizers are deterministic, so check that we
+		// get _exactly_ the same answer second time as well.
+		if result.F != result2.F || !floats.Equal(result.X, result2.X) {
+			t.Errorf("Different minimum second time for:\n%v", test)
+		}
+
+		// Check that providing initial data reduces the number of evaluations exactly by one.
+		if result.FuncEvaluations != result2.FuncEvaluations+1 {
+			t.Errorf("Providing initial data does not reduce the number of Func calls for:\n%v", test)
+			continue
+		}
+		if method.Needs().Gradient {
+			if result.GradEvaluations != result2.GradEvaluations+1 {
+				t.Errorf("Providing initial data does not reduce the number of Grad calls for:\n%v", test)
+				continue
+			}
+		}
+		if method.Needs().Hessian {
+			if result.HessEvaluations != result2.HessEvaluations+1 {
+				t.Errorf("Providing initial data does not reduce the number of Hess calls for:\n%v", test)
+				continue
+			}
+		}
+	}
+}
+
+func TestIssue76(t *testing.T) {
+	p := Problem{
+		Func: functions.BrownAndDennis{}.Func,
+		Grad: functions.BrownAndDennis{}.Grad,
+	}
+	// Location very close to the minimum.
+	x := []float64{-11.594439904886773, 13.203630051265385, -0.40343948776868443, 0.2367787746745986}
+	s := &Settings{
+		FunctionThreshold: math.Inf(-1),
+		GradientThreshold: 1e-14,
+		MajorIterations:   1000000,
+	}
+	m := &GradientDescent{
+		Linesearcher: &Backtracking{},
+	}
+	// We are not interested in the error, only in the returned status.
+	r, _ := Local(p, x, s, m)
+	// With the above stringent tolerance, the optimizer will never
+	// successfully reach the minimum. Check if it terminated in a finite
+	// number of steps.
+	if r.Status == IterationLimit {
+		t.Error("Issue https://github.com/gonum/optimize/issues/76 not fixed")
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/appengine_test.go b/vendor/gonum.org/v1/gonum/stat/appengine_test.go
new file mode 100644
index 00000000..bb2b93c7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/appengine_test.go
@@ -0,0 +1,9 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build noasm appengine
+
+package stat
+
+func init() { appengine = true }
diff --git a/vendor/gonum.org/v1/gonum/stat/boston_data_test.go b/vendor/gonum.org/v1/gonum/stat/boston_data_test.go
new file mode 100644
index 00000000..e85a505f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/boston_data_test.go
@@ -0,0 +1,531 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package stat_test
+
+import "gonum.org/v1/gonum/mat"
+
+// Boston Housing Data of Harrison and Rubinfeld (1978)
+// http://dx.doi.org/10.1016/0095-0696(78)90006-2
+// http://lib.stat.cmu.edu/datasets/boston
+// Columns are;
+//  per capita crime rate by town,
+//  proportion of non-retail business acres per town,
+//  nitric oxide concentration (parts per 10 million),
+//  weighted distances to Boston employment centers,
+//  index of accessibility to radial highways,
+//  pupil-teacher ratio by town,
+//  proportion of blacks by town,
+//  average number of rooms per dwelling,
+//  proportion of owner-occupied units built prior to 1940,
+//  full-value property-tax rate per $10000,
+//  median value of owner-occupied homes in $1000s.
+var bostonData = mat.NewDense(506, 11, []float64{
+	0.00632, 2.31000, 0.53800, 4.09000, 1.00000, 15.30000, 396.90000, 6.57500, 65.20000, 296.00000, 24.00000,
+	0.02731, 7.07000, 0.46900, 4.96710, 2.00000, 17.80000, 396.90000, 6.42100, 78.90000, 242.00000, 21.60000,
+	0.02729, 7.07000, 0.46900, 4.96710, 2.00000, 17.80000, 392.83000, 7.18500, 61.10000, 242.00000, 34.70000,
+	0.03237, 2.18000, 0.45800, 6.06220, 3.00000, 18.70000, 394.63000, 6.99800, 45.80000, 222.00000, 33.40000,
+	0.06905, 2.18000, 0.45800, 6.06220, 3.00000, 18.70000, 396.90000, 7.14700, 54.20000, 222.00000, 36.20000,
+	0.02985, 2.18000, 0.45800, 6.06220, 3.00000, 18.70000, 394.12000, 6.43000, 58.70000, 222.00000, 28.70000,
+	0.08829, 7.87000, 0.52400, 5.56050, 5.00000, 15.20000, 395.60000, 6.01200, 66.60000, 311.00000, 22.90000,
+	0.14455, 7.87000, 0.52400, 5.95050, 5.00000, 15.20000, 396.90000, 6.17200, 96.10000, 311.00000, 27.10000,
+	0.21124, 7.87000, 0.52400, 6.08210, 5.00000, 15.20000, 386.63000, 5.63100, 100.00000, 311.00000, 16.50000,
+	0.17004, 7.87000, 0.52400, 6.59210, 5.00000, 15.20000, 386.71000, 6.00400, 85.90000, 311.00000, 18.90000,
+	0.22489, 7.87000, 0.52400, 6.34670, 5.00000, 15.20000, 392.52000, 6.37700, 94.30000, 311.00000, 15.00000,
+	0.11747, 7.87000, 0.52400, 6.22670, 5.00000, 15.20000, 396.90000, 6.00900, 82.90000, 311.00000, 18.90000,
+	0.09378, 7.87000, 0.52400, 5.45090, 5.00000, 15.20000, 390.50000, 5.88900, 39.00000, 311.00000, 21.70000,
+	0.62976, 8.14000, 0.53800, 4.70750, 4.00000, 21.00000, 396.90000, 5.94900, 61.80000, 307.00000, 20.40000,
+	0.63796, 8.14000, 0.53800, 4.46190, 4.00000, 21.00000, 380.02000, 6.09600, 84.50000, 307.00000, 18.20000,
+	0.62739, 8.14000, 0.53800, 4.49860, 4.00000, 21.00000, 395.62000, 5.83400, 56.50000, 307.00000, 19.90000,
+	1.05393, 8.14000, 0.53800, 4.49860, 4.00000, 21.00000, 386.85000, 5.93500, 29.30000, 307.00000, 23.10000,
+	0.78420, 8.14000, 0.53800, 4.25790, 4.00000, 21.00000, 386.75000, 5.99000, 81.70000, 307.00000, 17.50000,
+	0.80271, 8.14000, 0.53800, 3.79650, 4.00000, 21.00000, 288.99000, 5.45600, 36.60000, 307.00000, 20.20000,
+	0.72580, 8.14000, 0.53800, 3.79650, 4.00000, 21.00000, 390.95000, 5.72700, 69.50000, 307.00000, 18.20000,
+	1.25179, 8.14000, 0.53800, 3.79790, 4.00000, 21.00000, 376.57000, 5.57000, 98.10000, 307.00000, 13.60000,
+	0.85204, 8.14000, 0.53800, 4.01230, 4.00000, 21.00000, 392.53000, 5.96500, 89.20000, 307.00000, 19.60000,
+	1.23247, 8.14000, 0.53800, 3.97690, 4.00000, 21.00000, 396.90000, 6.14200, 91.70000, 307.00000, 15.20000,
+	0.98843, 8.14000, 0.53800, 4.09520, 4.00000, 21.00000, 394.54000, 5.81300, 100.00000, 307.00000, 14.50000,
+	0.75026, 8.14000, 0.53800, 4.39960, 4.00000, 21.00000, 394.33000, 5.92400, 94.10000, 307.00000, 15.60000,
+	0.84054, 8.14000, 0.53800, 4.45460, 4.00000, 21.00000, 303.42000, 5.59900, 85.70000, 307.00000, 13.90000,
+	0.67191, 8.14000, 0.53800, 4.68200, 4.00000, 21.00000, 376.88000, 5.81300, 90.30000, 307.00000, 16.60000,
+	0.95577, 8.14000, 0.53800, 4.45340, 4.00000, 21.00000, 306.38000, 6.04700, 88.80000, 307.00000, 14.80000,
+	0.77299, 8.14000, 0.53800, 4.45470, 4.00000, 21.00000, 387.94000, 6.49500, 94.40000, 307.00000, 18.40000,
+	1.00245, 8.14000, 0.53800, 4.23900, 4.00000, 21.00000, 380.23000, 6.67400, 87.30000, 307.00000, 21.00000,
+	1.13081, 8.14000, 0.53800, 4.23300, 4.00000, 21.00000, 360.17000, 5.71300, 94.10000, 307.00000, 12.70000,
+	1.35472, 8.14000, 0.53800, 4.17500, 4.00000, 21.00000, 376.73000, 6.07200, 100.00000, 307.00000, 14.50000,
+	1.38799, 8.14000, 0.53800, 3.99000, 4.00000, 21.00000, 232.60000, 5.95000, 82.00000, 307.00000, 13.20000,
+	1.15172, 8.14000, 0.53800, 3.78720, 4.00000, 21.00000, 358.77000, 5.70100, 95.00000, 307.00000, 13.10000,
+	1.61282, 8.14000, 0.53800, 3.75980, 4.00000, 21.00000, 248.31000, 6.09600, 96.90000, 307.00000, 13.50000,
+	0.06417, 5.96000, 0.49900, 3.36030, 5.00000, 19.20000, 396.90000, 5.93300, 68.20000, 279.00000, 18.90000,
+	0.09744, 5.96000, 0.49900, 3.37790, 5.00000, 19.20000, 377.56000, 5.84100, 61.40000, 279.00000, 20.00000,
+	0.08014, 5.96000, 0.49900, 3.93420, 5.00000, 19.20000, 396.90000, 5.85000, 41.50000, 279.00000, 21.00000,
+	0.17505, 5.96000, 0.49900, 3.84730, 5.00000, 19.20000, 393.43000, 5.96600, 30.20000, 279.00000, 24.70000,
+	0.02763, 2.95000, 0.42800, 5.40110, 3.00000, 18.30000, 395.63000, 6.59500, 21.80000, 252.00000, 30.80000,
+	0.03359, 2.95000, 0.42800, 5.40110, 3.00000, 18.30000, 395.62000, 7.02400, 15.80000, 252.00000, 34.90000,
+	0.12744, 6.91000, 0.44800, 5.72090, 3.00000, 17.90000, 385.41000, 6.77000, 2.90000, 233.00000, 26.60000,
+	0.14150, 6.91000, 0.44800, 5.72090, 3.00000, 17.90000, 383.37000, 6.16900, 6.60000, 233.00000, 25.30000,
+	0.15936, 6.91000, 0.44800, 5.72090, 3.00000, 17.90000, 394.46000, 6.21100, 6.50000, 233.00000, 24.70000,
+	0.12269, 6.91000, 0.44800, 5.72090, 3.00000, 17.90000, 389.39000, 6.06900, 40.00000, 233.00000, 21.20000,
+	0.17142, 6.91000, 0.44800, 5.10040, 3.00000, 17.90000, 396.90000, 5.68200, 33.80000, 233.00000, 19.30000,
+	0.18836, 6.91000, 0.44800, 5.10040, 3.00000, 17.90000, 396.90000, 5.78600, 33.30000, 233.00000, 20.00000,
+	0.22927, 6.91000, 0.44800, 5.68940, 3.00000, 17.90000, 392.74000, 6.03000, 85.50000, 233.00000, 16.60000,
+	0.25387, 6.91000, 0.44800, 5.87000, 3.00000, 17.90000, 396.90000, 5.39900, 95.30000, 233.00000, 14.40000,
+	0.21977, 6.91000, 0.44800, 6.08770, 3.00000, 17.90000, 396.90000, 5.60200, 62.00000, 233.00000, 19.40000,
+	0.08873, 5.64000, 0.43900, 6.81470, 4.00000, 16.80000, 395.56000, 5.96300, 45.70000, 243.00000, 19.70000,
+	0.04337, 5.64000, 0.43900, 6.81470, 4.00000, 16.80000, 393.97000, 6.11500, 63.00000, 243.00000, 20.50000,
+	0.05360, 5.64000, 0.43900, 6.81470, 4.00000, 16.80000, 396.90000, 6.51100, 21.10000, 243.00000, 25.00000,
+	0.04981, 5.64000, 0.43900, 6.81470, 4.00000, 16.80000, 396.90000, 5.99800, 21.40000, 243.00000, 23.40000,
+	0.01360, 4.00000, 0.41000, 7.31970, 3.00000, 21.10000, 396.90000, 5.88800, 47.60000, 469.00000, 18.90000,
+	0.01311, 1.22000, 0.40300, 8.69660, 5.00000, 17.90000, 395.93000, 7.24900, 21.90000, 226.00000, 35.40000,
+	0.02055, 0.74000, 0.41000, 9.18760, 2.00000, 17.30000, 396.90000, 6.38300, 35.70000, 313.00000, 24.70000,
+	0.01432, 1.32000, 0.41100, 8.32480, 5.00000, 15.10000, 392.90000, 6.81600, 40.50000, 256.00000, 31.60000,
+	0.15445, 5.13000, 0.45300, 7.81480, 8.00000, 19.70000, 390.68000, 6.14500, 29.20000, 284.00000, 23.30000,
+	0.10328, 5.13000, 0.45300, 6.93200, 8.00000, 19.70000, 396.90000, 5.92700, 47.20000, 284.00000, 19.60000,
+	0.14932, 5.13000, 0.45300, 7.22540, 8.00000, 19.70000, 395.11000, 5.74100, 66.20000, 284.00000, 18.70000,
+	0.17171, 5.13000, 0.45300, 6.81850, 8.00000, 19.70000, 378.08000, 5.96600, 93.40000, 284.00000, 16.00000,
+	0.11027, 5.13000, 0.45300, 7.22550, 8.00000, 19.70000, 396.90000, 6.45600, 67.80000, 284.00000, 22.20000,
+	0.12650, 5.13000, 0.45300, 7.98090, 8.00000, 19.70000, 395.58000, 6.76200, 43.40000, 284.00000, 25.00000,
+	0.01951, 1.38000, 0.41610, 9.22290, 3.00000, 18.60000, 393.24000, 7.10400, 59.50000, 216.00000, 33.00000,
+	0.03584, 3.37000, 0.39800, 6.61150, 4.00000, 16.10000, 396.90000, 6.29000, 17.80000, 337.00000, 23.50000,
+	0.04379, 3.37000, 0.39800, 6.61150, 4.00000, 16.10000, 396.90000, 5.78700, 31.10000, 337.00000, 19.40000,
+	0.05789, 6.07000, 0.40900, 6.49800, 4.00000, 18.90000, 396.21000, 5.87800, 21.40000, 345.00000, 22.00000,
+	0.13554, 6.07000, 0.40900, 6.49800, 4.00000, 18.90000, 396.90000, 5.59400, 36.80000, 345.00000, 17.40000,
+	0.12816, 6.07000, 0.40900, 6.49800, 4.00000, 18.90000, 396.90000, 5.88500, 33.00000, 345.00000, 20.90000,
+	0.08826, 10.81000, 0.41300, 5.28730, 4.00000, 19.20000, 383.73000, 6.41700, 6.60000, 305.00000, 24.20000,
+	0.15876, 10.81000, 0.41300, 5.28730, 4.00000, 19.20000, 376.94000, 5.96100, 17.50000, 305.00000, 21.70000,
+	0.09164, 10.81000, 0.41300, 5.28730, 4.00000, 19.20000, 390.91000, 6.06500, 7.80000, 305.00000, 22.80000,
+	0.19539, 10.81000, 0.41300, 5.28730, 4.00000, 19.20000, 377.17000, 6.24500, 6.20000, 305.00000, 23.40000,
+	0.07896, 12.83000, 0.43700, 4.25150, 5.00000, 18.70000, 394.92000, 6.27300, 6.00000, 398.00000, 24.10000,
+	0.09512, 12.83000, 0.43700, 4.50260, 5.00000, 18.70000, 383.23000, 6.28600, 45.00000, 398.00000, 21.40000,
+	0.10153, 12.83000, 0.43700, 4.05220, 5.00000, 18.70000, 373.66000, 6.27900, 74.50000, 398.00000, 20.00000,
+	0.08707, 12.83000, 0.43700, 4.09050, 5.00000, 18.70000, 386.96000, 6.14000, 45.80000, 398.00000, 20.80000,
+	0.05646, 12.83000, 0.43700, 5.01410, 5.00000, 18.70000, 386.40000, 6.23200, 53.70000, 398.00000, 21.20000,
+	0.08387, 12.83000, 0.43700, 4.50260, 5.00000, 18.70000, 396.06000, 5.87400, 36.60000, 398.00000, 20.30000,
+	0.04113, 4.86000, 0.42600, 5.40070, 4.00000, 19.00000, 396.90000, 6.72700, 33.50000, 281.00000, 28.00000,
+	0.04462, 4.86000, 0.42600, 5.40070, 4.00000, 19.00000, 395.63000, 6.61900, 70.40000, 281.00000, 23.90000,
+	0.03659, 4.86000, 0.42600, 5.40070, 4.00000, 19.00000, 396.90000, 6.30200, 32.20000, 281.00000, 24.80000,
+	0.03551, 4.86000, 0.42600, 5.40070, 4.00000, 19.00000, 390.64000, 6.16700, 46.70000, 281.00000, 22.90000,
+	0.05059, 4.49000, 0.44900, 4.77940, 3.00000, 18.50000, 396.90000, 6.38900, 48.00000, 247.00000, 23.90000,
+	0.05735, 4.49000, 0.44900, 4.43770, 3.00000, 18.50000, 392.30000, 6.63000, 56.10000, 247.00000, 26.60000,
+	0.05188, 4.49000, 0.44900, 4.42720, 3.00000, 18.50000, 395.99000, 6.01500, 45.10000, 247.00000, 22.50000,
+	0.07151, 4.49000, 0.44900, 3.74760, 3.00000, 18.50000, 395.15000, 6.12100, 56.80000, 247.00000, 22.20000,
+	0.05660, 3.41000, 0.48900, 3.42170, 2.00000, 17.80000, 396.90000, 7.00700, 86.30000, 270.00000, 23.60000,
+	0.05302, 3.41000, 0.48900, 3.41450, 2.00000, 17.80000, 396.06000, 7.07900, 63.10000, 270.00000, 28.70000,
+	0.04684, 3.41000, 0.48900, 3.09230, 2.00000, 17.80000, 392.18000, 6.41700, 66.10000, 270.00000, 22.60000,
+	0.03932, 3.41000, 0.48900, 3.09210, 2.00000, 17.80000, 393.55000, 6.40500, 73.90000, 270.00000, 22.00000,
+	0.04203, 15.04000, 0.46400, 3.66590, 4.00000, 18.20000, 395.01000, 6.44200, 53.60000, 270.00000, 22.90000,
+	0.02875, 15.04000, 0.46400, 3.66590, 4.00000, 18.20000, 396.33000, 6.21100, 28.90000, 270.00000, 25.00000,
+	0.04294, 15.04000, 0.46400, 3.61500, 4.00000, 18.20000, 396.90000, 6.24900, 77.30000, 270.00000, 20.60000,
+	0.12204, 2.89000, 0.44500, 3.49520, 2.00000, 18.00000, 357.98000, 6.62500, 57.80000, 276.00000, 28.40000,
+	0.11504, 2.89000, 0.44500, 3.49520, 2.00000, 18.00000, 391.83000, 6.16300, 69.60000, 276.00000, 21.40000,
+	0.12083, 2.89000, 0.44500, 3.49520, 2.00000, 18.00000, 396.90000, 8.06900, 76.00000, 276.00000, 38.70000,
+	0.08187, 2.89000, 0.44500, 3.49520, 2.00000, 18.00000, 393.53000, 7.82000, 36.90000, 276.00000, 43.80000,
+	0.06860, 2.89000, 0.44500, 3.49520, 2.00000, 18.00000, 396.90000, 7.41600, 62.50000, 276.00000, 33.20000,
+	0.14866, 8.56000, 0.52000, 2.77780, 5.00000, 20.90000, 394.76000, 6.72700, 79.90000, 384.00000, 27.50000,
+	0.11432, 8.56000, 0.52000, 2.85610, 5.00000, 20.90000, 395.58000, 6.78100, 71.30000, 384.00000, 26.50000,
+	0.22876, 8.56000, 0.52000, 2.71470, 5.00000, 20.90000, 70.80000, 6.40500, 85.40000, 384.00000, 18.60000,
+	0.21161, 8.56000, 0.52000, 2.71470, 5.00000, 20.90000, 394.47000, 6.13700, 87.40000, 384.00000, 19.30000,
+	0.13960, 8.56000, 0.52000, 2.42100, 5.00000, 20.90000, 392.69000, 6.16700, 90.00000, 384.00000, 20.10000,
+	0.13262, 8.56000, 0.52000, 2.10690, 5.00000, 20.90000, 394.05000, 5.85100, 96.70000, 384.00000, 19.50000,
+	0.17120, 8.56000, 0.52000, 2.21100, 5.00000, 20.90000, 395.67000, 5.83600, 91.90000, 384.00000, 19.50000,
+	0.13117, 8.56000, 0.52000, 2.12240, 5.00000, 20.90000, 387.69000, 6.12700, 85.20000, 384.00000, 20.40000,
+	0.12802, 8.56000, 0.52000, 2.43290, 5.00000, 20.90000, 395.24000, 6.47400, 97.10000, 384.00000, 19.80000,
+	0.26363, 8.56000, 0.52000, 2.54510, 5.00000, 20.90000, 391.23000, 6.22900, 91.20000, 384.00000, 19.40000,
+	0.10793, 8.56000, 0.52000, 2.77780, 5.00000, 20.90000, 393.49000, 6.19500, 54.40000, 384.00000, 21.70000,
+	0.10084, 10.01000, 0.54700, 2.67750, 6.00000, 17.80000, 395.59000, 6.71500, 81.60000, 432.00000, 22.80000,
+	0.12329, 10.01000, 0.54700, 2.35340, 6.00000, 17.80000, 394.95000, 5.91300, 92.90000, 432.00000, 18.80000,
+	0.22212, 10.01000, 0.54700, 2.54800, 6.00000, 17.80000, 396.90000, 6.09200, 95.40000, 432.00000, 18.70000,
+	0.14231, 10.01000, 0.54700, 2.25650, 6.00000, 17.80000, 388.74000, 6.25400, 84.20000, 432.00000, 18.50000,
+	0.17134, 10.01000, 0.54700, 2.46310, 6.00000, 17.80000, 344.91000, 5.92800, 88.20000, 432.00000, 18.30000,
+	0.13158, 10.01000, 0.54700, 2.73010, 6.00000, 17.80000, 393.30000, 6.17600, 72.50000, 432.00000, 21.20000,
+	0.15098, 10.01000, 0.54700, 2.74740, 6.00000, 17.80000, 394.51000, 6.02100, 82.60000, 432.00000, 19.20000,
+	0.13058, 10.01000, 0.54700, 2.47750, 6.00000, 17.80000, 338.63000, 5.87200, 73.10000, 432.00000, 20.40000,
+	0.14476, 10.01000, 0.54700, 2.75920, 6.00000, 17.80000, 391.50000, 5.73100, 65.20000, 432.00000, 19.30000,
+	0.06899, 25.65000, 0.58100, 2.25770, 2.00000, 19.10000, 389.15000, 5.87000, 69.70000, 188.00000, 22.00000,
+	0.07165, 25.65000, 0.58100, 2.19740, 2.00000, 19.10000, 377.67000, 6.00400, 84.10000, 188.00000, 20.30000,
+	0.09299, 25.65000, 0.58100, 2.08690, 2.00000, 19.10000, 378.09000, 5.96100, 92.90000, 188.00000, 20.50000,
+	0.15038, 25.65000, 0.58100, 1.94440, 2.00000, 19.10000, 370.31000, 5.85600, 97.00000, 188.00000, 17.30000,
+	0.09849, 25.65000, 0.58100, 2.00630, 2.00000, 19.10000, 379.38000, 5.87900, 95.80000, 188.00000, 18.80000,
+	0.16902, 25.65000, 0.58100, 1.99290, 2.00000, 19.10000, 385.02000, 5.98600, 88.40000, 188.00000, 21.40000,
+	0.38735, 25.65000, 0.58100, 1.75720, 2.00000, 19.10000, 359.29000, 5.61300, 95.60000, 188.00000, 15.70000,
+	0.25915, 21.89000, 0.62400, 1.78830, 4.00000, 21.20000, 392.11000, 5.69300, 96.00000, 437.00000, 16.20000,
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+	45.74610, 18.10000, 0.69300, 1.65820, 24.00000, 20.20000, 88.27000, 4.51900, 100.00000, 666.00000, 7.00000,
+	18.08460, 18.10000, 0.67900, 1.83470, 24.00000, 20.20000, 27.25000, 6.43400, 100.00000, 666.00000, 7.20000,
+	10.83420, 18.10000, 0.67900, 1.81950, 24.00000, 20.20000, 21.57000, 6.78200, 90.80000, 666.00000, 7.50000,
+	25.94060, 18.10000, 0.67900, 1.64750, 24.00000, 20.20000, 127.36000, 5.30400, 89.10000, 666.00000, 10.40000,
+	73.53410, 18.10000, 0.67900, 1.80260, 24.00000, 20.20000, 16.45000, 5.95700, 100.00000, 666.00000, 8.80000,
+	11.81230, 18.10000, 0.71800, 1.79400, 24.00000, 20.20000, 48.45000, 6.82400, 76.50000, 666.00000, 8.40000,
+	11.08740, 18.10000, 0.71800, 1.85890, 24.00000, 20.20000, 318.75000, 6.41100, 100.00000, 666.00000, 16.70000,
+	7.02259, 18.10000, 0.71800, 1.87460, 24.00000, 20.20000, 319.98000, 6.00600, 95.30000, 666.00000, 14.20000,
+	12.04820, 18.10000, 0.61400, 1.95120, 24.00000, 20.20000, 291.55000, 5.64800, 87.60000, 666.00000, 20.80000,
+	7.05042, 18.10000, 0.61400, 2.02180, 24.00000, 20.20000, 2.52000, 6.10300, 85.10000, 666.00000, 13.40000,
+	8.79212, 18.10000, 0.58400, 2.06350, 24.00000, 20.20000, 3.65000, 5.56500, 70.60000, 666.00000, 11.70000,
+	15.86030, 18.10000, 0.67900, 1.90960, 24.00000, 20.20000, 7.68000, 5.89600, 95.40000, 666.00000, 8.30000,
+	12.24720, 18.10000, 0.58400, 1.99760, 24.00000, 20.20000, 24.65000, 5.83700, 59.70000, 666.00000, 10.20000,
+	37.66190, 18.10000, 0.67900, 1.86290, 24.00000, 20.20000, 18.82000, 6.20200, 78.70000, 666.00000, 10.90000,
+	7.36711, 18.10000, 0.67900, 1.93560, 24.00000, 20.20000, 96.73000, 6.19300, 78.10000, 666.00000, 11.00000,
+	9.33889, 18.10000, 0.67900, 1.96820, 24.00000, 20.20000, 60.72000, 6.38000, 95.60000, 666.00000, 9.50000,
+	8.49213, 18.10000, 0.58400, 2.05270, 24.00000, 20.20000, 83.45000, 6.34800, 86.10000, 666.00000, 14.50000,
+	10.06230, 18.10000, 0.58400, 2.08820, 24.00000, 20.20000, 81.33000, 6.83300, 94.30000, 666.00000, 14.10000,
+	6.44405, 18.10000, 0.58400, 2.20040, 24.00000, 20.20000, 97.95000, 6.42500, 74.80000, 666.00000, 16.10000,
+	5.58107, 18.10000, 0.71300, 2.31580, 24.00000, 20.20000, 100.19000, 6.43600, 87.90000, 666.00000, 14.30000,
+	13.91340, 18.10000, 0.71300, 2.22220, 24.00000, 20.20000, 100.63000, 6.20800, 95.00000, 666.00000, 11.70000,
+	11.16040, 18.10000, 0.74000, 2.12470, 24.00000, 20.20000, 109.85000, 6.62900, 94.60000, 666.00000, 13.40000,
+	14.42080, 18.10000, 0.74000, 2.00260, 24.00000, 20.20000, 27.49000, 6.46100, 93.30000, 666.00000, 9.60000,
+	15.17720, 18.10000, 0.74000, 1.91420, 24.00000, 20.20000, 9.32000, 6.15200, 100.00000, 666.00000, 8.70000,
+	13.67810, 18.10000, 0.74000, 1.82060, 24.00000, 20.20000, 68.95000, 5.93500, 87.90000, 666.00000, 8.40000,
+	9.39063, 18.10000, 0.74000, 1.81720, 24.00000, 20.20000, 396.90000, 5.62700, 93.90000, 666.00000, 12.80000,
+	22.05110, 18.10000, 0.74000, 1.86620, 24.00000, 20.20000, 391.45000, 5.81800, 92.40000, 666.00000, 10.50000,
+	9.72418, 18.10000, 0.74000, 2.06510, 24.00000, 20.20000, 385.96000, 6.40600, 97.20000, 666.00000, 17.10000,
+	5.66637, 18.10000, 0.74000, 2.00480, 24.00000, 20.20000, 395.69000, 6.21900, 100.00000, 666.00000, 18.40000,
+	9.96654, 18.10000, 0.74000, 1.97840, 24.00000, 20.20000, 386.73000, 6.48500, 100.00000, 666.00000, 15.40000,
+	12.80230, 18.10000, 0.74000, 1.89560, 24.00000, 20.20000, 240.52000, 5.85400, 96.60000, 666.00000, 10.80000,
+	10.67180, 18.10000, 0.74000, 1.98790, 24.00000, 20.20000, 43.06000, 6.45900, 94.80000, 666.00000, 11.80000,
+	6.28807, 18.10000, 0.74000, 2.07200, 24.00000, 20.20000, 318.01000, 6.34100, 96.40000, 666.00000, 14.90000,
+	9.92485, 18.10000, 0.74000, 2.19800, 24.00000, 20.20000, 388.52000, 6.25100, 96.60000, 666.00000, 12.60000,
+	9.32909, 18.10000, 0.71300, 2.26160, 24.00000, 20.20000, 396.90000, 6.18500, 98.70000, 666.00000, 14.10000,
+	7.52601, 18.10000, 0.71300, 2.18500, 24.00000, 20.20000, 304.21000, 6.41700, 98.30000, 666.00000, 13.00000,
+	6.71772, 18.10000, 0.71300, 2.32360, 24.00000, 20.20000, 0.32000, 6.74900, 92.60000, 666.00000, 13.40000,
+	5.44114, 18.10000, 0.71300, 2.35520, 24.00000, 20.20000, 355.29000, 6.65500, 98.20000, 666.00000, 15.20000,
+	5.09017, 18.10000, 0.71300, 2.36820, 24.00000, 20.20000, 385.09000, 6.29700, 91.80000, 666.00000, 16.10000,
+	8.24809, 18.10000, 0.71300, 2.45270, 24.00000, 20.20000, 375.87000, 7.39300, 99.30000, 666.00000, 17.80000,
+	9.51363, 18.10000, 0.71300, 2.49610, 24.00000, 20.20000, 6.68000, 6.72800, 94.10000, 666.00000, 14.90000,
+	4.75237, 18.10000, 0.71300, 2.43580, 24.00000, 20.20000, 50.92000, 6.52500, 86.50000, 666.00000, 14.10000,
+	4.66883, 18.10000, 0.71300, 2.58060, 24.00000, 20.20000, 10.48000, 5.97600, 87.90000, 666.00000, 12.70000,
+	8.20058, 18.10000, 0.71300, 2.77920, 24.00000, 20.20000, 3.50000, 5.93600, 80.30000, 666.00000, 13.50000,
+	7.75223, 18.10000, 0.71300, 2.78310, 24.00000, 20.20000, 272.21000, 6.30100, 83.70000, 666.00000, 14.90000,
+	6.80117, 18.10000, 0.71300, 2.71750, 24.00000, 20.20000, 396.90000, 6.08100, 84.40000, 666.00000, 20.00000,
+	4.81213, 18.10000, 0.71300, 2.59750, 24.00000, 20.20000, 255.23000, 6.70100, 90.00000, 666.00000, 16.40000,
+	3.69311, 18.10000, 0.71300, 2.56710, 24.00000, 20.20000, 391.43000, 6.37600, 88.40000, 666.00000, 17.70000,
+	6.65492, 18.10000, 0.71300, 2.73440, 24.00000, 20.20000, 396.90000, 6.31700, 83.00000, 666.00000, 19.50000,
+	5.82115, 18.10000, 0.71300, 2.80160, 24.00000, 20.20000, 393.82000, 6.51300, 89.90000, 666.00000, 20.20000,
+	7.83932, 18.10000, 0.65500, 2.96340, 24.00000, 20.20000, 396.90000, 6.20900, 65.40000, 666.00000, 21.40000,
+	3.16360, 18.10000, 0.65500, 3.06650, 24.00000, 20.20000, 334.40000, 5.75900, 48.20000, 666.00000, 19.90000,
+	3.77498, 18.10000, 0.65500, 2.87150, 24.00000, 20.20000, 22.01000, 5.95200, 84.70000, 666.00000, 19.00000,
+	4.42228, 18.10000, 0.58400, 2.54030, 24.00000, 20.20000, 331.29000, 6.00300, 94.50000, 666.00000, 19.10000,
+	15.57570, 18.10000, 0.58000, 2.90840, 24.00000, 20.20000, 368.74000, 5.92600, 71.00000, 666.00000, 19.10000,
+	13.07510, 18.10000, 0.58000, 2.82370, 24.00000, 20.20000, 396.90000, 5.71300, 56.70000, 666.00000, 20.10000,
+	4.34879, 18.10000, 0.58000, 3.03340, 24.00000, 20.20000, 396.90000, 6.16700, 84.00000, 666.00000, 19.90000,
+	4.03841, 18.10000, 0.53200, 3.09930, 24.00000, 20.20000, 395.33000, 6.22900, 90.70000, 666.00000, 19.60000,
+	3.56868, 18.10000, 0.58000, 2.89650, 24.00000, 20.20000, 393.37000, 6.43700, 75.00000, 666.00000, 23.20000,
+	4.64689, 18.10000, 0.61400, 2.53290, 24.00000, 20.20000, 374.68000, 6.98000, 67.60000, 666.00000, 29.80000,
+	8.05579, 18.10000, 0.58400, 2.42980, 24.00000, 20.20000, 352.58000, 5.42700, 95.40000, 666.00000, 13.80000,
+	6.39312, 18.10000, 0.58400, 2.20600, 24.00000, 20.20000, 302.76000, 6.16200, 97.40000, 666.00000, 13.30000,
+	4.87141, 18.10000, 0.61400, 2.30530, 24.00000, 20.20000, 396.21000, 6.48400, 93.60000, 666.00000, 16.70000,
+	15.02340, 18.10000, 0.61400, 2.10070, 24.00000, 20.20000, 349.48000, 5.30400, 97.30000, 666.00000, 12.00000,
+	10.23300, 18.10000, 0.61400, 2.17050, 24.00000, 20.20000, 379.70000, 6.18500, 96.70000, 666.00000, 14.60000,
+	14.33370, 18.10000, 0.61400, 1.95120, 24.00000, 20.20000, 383.32000, 6.22900, 88.00000, 666.00000, 21.40000,
+	5.82401, 18.10000, 0.53200, 3.42420, 24.00000, 20.20000, 396.90000, 6.24200, 64.70000, 666.00000, 23.00000,
+	5.70818, 18.10000, 0.53200, 3.33170, 24.00000, 20.20000, 393.07000, 6.75000, 74.90000, 666.00000, 23.70000,
+	5.73116, 18.10000, 0.53200, 3.41060, 24.00000, 20.20000, 395.28000, 7.06100, 77.00000, 666.00000, 25.00000,
+	2.81838, 18.10000, 0.53200, 4.09830, 24.00000, 20.20000, 392.92000, 5.76200, 40.30000, 666.00000, 21.80000,
+	2.37857, 18.10000, 0.58300, 3.72400, 24.00000, 20.20000, 370.73000, 5.87100, 41.90000, 666.00000, 20.60000,
+	3.67367, 18.10000, 0.58300, 3.99170, 24.00000, 20.20000, 388.62000, 6.31200, 51.90000, 666.00000, 21.20000,
+	5.69175, 18.10000, 0.58300, 3.54590, 24.00000, 20.20000, 392.68000, 6.11400, 79.80000, 666.00000, 19.10000,
+	4.83567, 18.10000, 0.58300, 3.15230, 24.00000, 20.20000, 388.22000, 5.90500, 53.20000, 666.00000, 20.60000,
+	0.15086, 27.74000, 0.60900, 1.82090, 4.00000, 20.10000, 395.09000, 5.45400, 92.70000, 711.00000, 15.20000,
+	0.18337, 27.74000, 0.60900, 1.75540, 4.00000, 20.10000, 344.05000, 5.41400, 98.30000, 711.00000, 7.00000,
+	0.20746, 27.74000, 0.60900, 1.82260, 4.00000, 20.10000, 318.43000, 5.09300, 98.00000, 711.00000, 8.10000,
+	0.10574, 27.74000, 0.60900, 1.86810, 4.00000, 20.10000, 390.11000, 5.98300, 98.80000, 711.00000, 13.60000,
+	0.11132, 27.74000, 0.60900, 2.10990, 4.00000, 20.10000, 396.90000, 5.98300, 83.50000, 711.00000, 20.10000,
+	0.17331, 9.69000, 0.58500, 2.38170, 6.00000, 19.20000, 396.90000, 5.70700, 54.00000, 391.00000, 21.80000,
+	0.27957, 9.69000, 0.58500, 2.38170, 6.00000, 19.20000, 396.90000, 5.92600, 42.60000, 391.00000, 24.50000,
+	0.17899, 9.69000, 0.58500, 2.79860, 6.00000, 19.20000, 393.29000, 5.67000, 28.80000, 391.00000, 23.10000,
+	0.28960, 9.69000, 0.58500, 2.79860, 6.00000, 19.20000, 396.90000, 5.39000, 72.90000, 391.00000, 19.70000,
+	0.26838, 9.69000, 0.58500, 2.89270, 6.00000, 19.20000, 396.90000, 5.79400, 70.60000, 391.00000, 18.30000,
+	0.23912, 9.69000, 0.58500, 2.40910, 6.00000, 19.20000, 396.90000, 6.01900, 65.30000, 391.00000, 21.20000,
+	0.17783, 9.69000, 0.58500, 2.39990, 6.00000, 19.20000, 395.77000, 5.56900, 73.50000, 391.00000, 17.50000,
+	0.22438, 9.69000, 0.58500, 2.49820, 6.00000, 19.20000, 396.90000, 6.02700, 79.70000, 391.00000, 16.80000,
+	0.06263, 11.93000, 0.57300, 2.47860, 1.00000, 21.00000, 391.99000, 6.59300, 69.10000, 273.00000, 22.40000,
+	0.04527, 11.93000, 0.57300, 2.28750, 1.00000, 21.00000, 396.90000, 6.12000, 76.70000, 273.00000, 20.60000,
+	0.06076, 11.93000, 0.57300, 2.16750, 1.00000, 21.00000, 396.90000, 6.97600, 91.00000, 273.00000, 23.90000,
+	0.10959, 11.93000, 0.57300, 2.38890, 1.00000, 21.00000, 393.45000, 6.79400, 89.30000, 273.00000, 22.00000,
+	0.04741, 11.93000, 0.57300, 2.50500, 1.00000, 21.00000, 396.90000, 6.03000, 80.80000, 273.00000, 11.90000,
+})
diff --git a/vendor/gonum.org/v1/gonum/stat/car_data_test.go b/vendor/gonum.org/v1/gonum/stat/car_data_test.go
new file mode 100644
index 00000000..a3cdabb2
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/car_data_test.go
@@ -0,0 +1,406 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package stat_test
+
+import "gonum.org/v1/gonum/mat"
+
+// ASA Car Exposition Data of Ramos and Donoho (1983)
+// http://lib.stat.cmu.edu/datasets/cars.desc
+// http://lib.stat.cmu.edu/datasets/cars.data
+// Columns are: displacement, horsepower, weight, acceleration, MPG.
+var carData = mat.NewDense(392, 5, []float64{
+	307.0, 130.0, 3504.0, 12.0, 18.0,
+	350.0, 165.0, 3693.0, 11.5, 15.0,
+	318.0, 150.0, 3436.0, 11.0, 18.0,
+	304.0, 150.0, 3433.0, 12.0, 16.0,
+	302.0, 140.0, 3449.0, 10.5, 17.0,
+	429.0, 198.0, 4341.0, 10.0, 15.0,
+	454.0, 220.0, 4354.0, 9.0, 14.0,
+	440.0, 215.0, 4312.0, 8.5, 14.0,
+	455.0, 225.0, 4425.0, 10.0, 14.0,
+	390.0, 190.0, 3850.0, 8.5, 15.0,
+	383.0, 170.0, 3563.0, 10.0, 15.0,
+	340.0, 160.0, 3609.0, 8.0, 14.0,
+	400.0, 150.0, 3761.0, 9.5, 15.0,
+	455.0, 225.0, 3086.0, 10.0, 14.0,
+	113.0, 95.0, 2372.0, 15.0, 24.0,
+	198.0, 95.0, 2833.0, 15.5, 22.0,
+	199.0, 97.0, 2774.0, 15.5, 18.0,
+	200.0, 85.0, 2587.0, 16.0, 21.0,
+	97.0, 88.0, 2130.0, 14.5, 27.0,
+	97.0, 46.0, 1835.0, 20.5, 26.0,
+	110.0, 87.0, 2672.0, 17.5, 25.0,
+	107.0, 90.0, 2430.0, 14.5, 24.0,
+	104.0, 95.0, 2375.0, 17.5, 25.0,
+	121.0, 113.0, 2234.0, 12.5, 26.0,
+	199.0, 90.0, 2648.0, 15.0, 21.0,
+	360.0, 215.0, 4615.0, 14.0, 10.0,
+	307.0, 200.0, 4376.0, 15.0, 10.0,
+	318.0, 210.0, 4382.0, 13.5, 11.0,
+	304.0, 193.0, 4732.0, 18.5, 9.0,
+	97.0, 88.0, 2130.0, 14.5, 27.0,
+	140.0, 90.0, 2264.0, 15.5, 28.0,
+	113.0, 95.0, 2228.0, 14.0, 25.0,
+	232.0, 100.0, 2634.0, 13.0, 19.0,
+	225.0, 105.0, 3439.0, 15.5, 16.0,
+	250.0, 100.0, 3329.0, 15.5, 17.0,
+	250.0, 88.0, 3302.0, 15.5, 19.0,
+	232.0, 100.0, 3288.0, 15.5, 18.0,
+	350.0, 165.0, 4209.0, 12.0, 14.0,
+	400.0, 175.0, 4464.0, 11.5, 14.0,
+	351.0, 153.0, 4154.0, 13.5, 14.0,
+	318.0, 150.0, 4096.0, 13.0, 14.0,
+	383.0, 180.0, 4955.0, 11.5, 12.0,
+	400.0, 170.0, 4746.0, 12.0, 13.0,
+	400.0, 175.0, 5140.0, 12.0, 13.0,
+	258.0, 110.0, 2962.0, 13.5, 18.0,
+	140.0, 72.0, 2408.0, 19.0, 22.0,
+	250.0, 100.0, 3282.0, 15.0, 19.0,
+	250.0, 88.0, 3139.0, 14.5, 18.0,
+	122.0, 86.0, 2220.0, 14.0, 23.0,
+	116.0, 90.0, 2123.0, 14.0, 28.0,
+	79.0, 70.0, 2074.0, 19.5, 30.0,
+	88.0, 76.0, 2065.0, 14.5, 30.0,
+	71.0, 65.0, 1773.0, 19.0, 31.0,
+	72.0, 69.0, 1613.0, 18.0, 35.0,
+	97.0, 60.0, 1834.0, 19.0, 27.0,
+	91.0, 70.0, 1955.0, 20.5, 26.0,
+	113.0, 95.0, 2278.0, 15.5, 24.0,
+	97.5, 80.0, 2126.0, 17.0, 25.0,
+	97.0, 54.0, 2254.0, 23.5, 23.0,
+	140.0, 90.0, 2408.0, 19.5, 20.0,
+	122.0, 86.0, 2226.0, 16.5, 21.0,
+	350.0, 165.0, 4274.0, 12.0, 13.0,
+	400.0, 175.0, 4385.0, 12.0, 14.0,
+	318.0, 150.0, 4135.0, 13.5, 15.0,
+	351.0, 153.0, 4129.0, 13.0, 14.0,
+	304.0, 150.0, 3672.0, 11.5, 17.0,
+	429.0, 208.0, 4633.0, 11.0, 11.0,
+	350.0, 155.0, 4502.0, 13.5, 13.0,
+	350.0, 160.0, 4456.0, 13.5, 12.0,
+	400.0, 190.0, 4422.0, 12.5, 13.0,
+	70.0, 97.0, 2330.0, 13.5, 19.0,
+	304.0, 150.0, 3892.0, 12.5, 15.0,
+	307.0, 130.0, 4098.0, 14.0, 13.0,
+	302.0, 140.0, 4294.0, 16.0, 13.0,
+	318.0, 150.0, 4077.0, 14.0, 14.0,
+	121.0, 112.0, 2933.0, 14.5, 18.0,
+	121.0, 76.0, 2511.0, 18.0, 22.0,
+	120.0, 87.0, 2979.0, 19.5, 21.0,
+	96.0, 69.0, 2189.0, 18.0, 26.0,
+	122.0, 86.0, 2395.0, 16.0, 22.0,
+	97.0, 92.0, 2288.0, 17.0, 28.0,
+	120.0, 97.0, 2506.0, 14.5, 23.0,
+	98.0, 80.0, 2164.0, 15.0, 28.0,
+	97.0, 88.0, 2100.0, 16.5, 27.0,
+	350.0, 175.0, 4100.0, 13.0, 13.0,
+	304.0, 150.0, 3672.0, 11.5, 14.0,
+	350.0, 145.0, 3988.0, 13.0, 13.0,
+	302.0, 137.0, 4042.0, 14.5, 14.0,
+	318.0, 150.0, 3777.0, 12.5, 15.0,
+	429.0, 198.0, 4952.0, 11.5, 12.0,
+	400.0, 150.0, 4464.0, 12.0, 13.0,
+	351.0, 158.0, 4363.0, 13.0, 13.0,
+	318.0, 150.0, 4237.0, 14.5, 14.0,
+	440.0, 215.0, 4735.0, 11.0, 13.0,
+	455.0, 225.0, 4951.0, 11.0, 12.0,
+	360.0, 175.0, 3821.0, 11.0, 13.0,
+	225.0, 105.0, 3121.0, 16.5, 18.0,
+	250.0, 100.0, 3278.0, 18.0, 16.0,
+	232.0, 100.0, 2945.0, 16.0, 18.0,
+	250.0, 88.0, 3021.0, 16.5, 18.0,
+	198.0, 95.0, 2904.0, 16.0, 23.0,
+	97.0, 46.0, 1950.0, 21.0, 26.0,
+	400.0, 150.0, 4997.0, 14.0, 11.0,
+	400.0, 167.0, 4906.0, 12.5, 12.0,
+	360.0, 170.0, 4654.0, 13.0, 13.0,
+	350.0, 180.0, 4499.0, 12.5, 12.0,
+	232.0, 100.0, 2789.0, 15.0, 18.0,
+	97.0, 88.0, 2279.0, 19.0, 20.0,
+	140.0, 72.0, 2401.0, 19.5, 21.0,
+	108.0, 94.0, 2379.0, 16.5, 22.0,
+	70.0, 90.0, 2124.0, 13.5, 18.0,
+	122.0, 85.0, 2310.0, 18.5, 19.0,
+	155.0, 107.0, 2472.0, 14.0, 21.0,
+	98.0, 90.0, 2265.0, 15.5, 26.0,
+	350.0, 145.0, 4082.0, 13.0, 15.0,
+	400.0, 230.0, 4278.0, 9.5, 16.0,
+	68.0, 49.0, 1867.0, 19.5, 29.0,
+	116.0, 75.0, 2158.0, 15.5, 24.0,
+	114.0, 91.0, 2582.0, 14.0, 20.0,
+	121.0, 112.0, 2868.0, 15.5, 19.0,
+	318.0, 150.0, 3399.0, 11.0, 15.0,
+	121.0, 110.0, 2660.0, 14.0, 24.0,
+	156.0, 122.0, 2807.0, 13.5, 20.0,
+	350.0, 180.0, 3664.0, 11.0, 11.0,
+	198.0, 95.0, 3102.0, 16.5, 20.0,
+	232.0, 100.0, 2901.0, 16.0, 19.0,
+	250.0, 100.0, 3336.0, 17.0, 15.0,
+	79.0, 67.0, 1950.0, 19.0, 31.0,
+	122.0, 80.0, 2451.0, 16.5, 26.0,
+	71.0, 65.0, 1836.0, 21.0, 32.0,
+	140.0, 75.0, 2542.0, 17.0, 25.0,
+	250.0, 100.0, 3781.0, 17.0, 16.0,
+	258.0, 110.0, 3632.0, 18.0, 16.0,
+	225.0, 105.0, 3613.0, 16.5, 18.0,
+	302.0, 140.0, 4141.0, 14.0, 16.0,
+	350.0, 150.0, 4699.0, 14.5, 13.0,
+	318.0, 150.0, 4457.0, 13.5, 14.0,
+	302.0, 140.0, 4638.0, 16.0, 14.0,
+	304.0, 150.0, 4257.0, 15.5, 14.0,
+	98.0, 83.0, 2219.0, 16.5, 29.0,
+	79.0, 67.0, 1963.0, 15.5, 26.0,
+	97.0, 78.0, 2300.0, 14.5, 26.0,
+	76.0, 52.0, 1649.0, 16.5, 31.0,
+	83.0, 61.0, 2003.0, 19.0, 32.0,
+	90.0, 75.0, 2125.0, 14.5, 28.0,
+	90.0, 75.0, 2108.0, 15.5, 24.0,
+	116.0, 75.0, 2246.0, 14.0, 26.0,
+	120.0, 97.0, 2489.0, 15.0, 24.0,
+	108.0, 93.0, 2391.0, 15.5, 26.0,
+	79.0, 67.0, 2000.0, 16.0, 31.0,
+	225.0, 95.0, 3264.0, 16.0, 19.0,
+	250.0, 105.0, 3459.0, 16.0, 18.0,
+	250.0, 72.0, 3432.0, 21.0, 15.0,
+	250.0, 72.0, 3158.0, 19.5, 15.0,
+	400.0, 170.0, 4668.0, 11.5, 16.0,
+	350.0, 145.0, 4440.0, 14.0, 15.0,
+	318.0, 150.0, 4498.0, 14.5, 16.0,
+	351.0, 148.0, 4657.0, 13.5, 14.0,
+	231.0, 110.0, 3907.0, 21.0, 17.0,
+	250.0, 105.0, 3897.0, 18.5, 16.0,
+	258.0, 110.0, 3730.0, 19.0, 15.0,
+	225.0, 95.0, 3785.0, 19.0, 18.0,
+	231.0, 110.0, 3039.0, 15.0, 21.0,
+	262.0, 110.0, 3221.0, 13.5, 20.0,
+	302.0, 129.0, 3169.0, 12.0, 13.0,
+	97.0, 75.0, 2171.0, 16.0, 29.0,
+	140.0, 83.0, 2639.0, 17.0, 23.0,
+	232.0, 100.0, 2914.0, 16.0, 20.0,
+	140.0, 78.0, 2592.0, 18.5, 23.0,
+	134.0, 96.0, 2702.0, 13.5, 24.0,
+	90.0, 71.0, 2223.0, 16.5, 25.0,
+	119.0, 97.0, 2545.0, 17.0, 24.0,
+	171.0, 97.0, 2984.0, 14.5, 18.0,
+	90.0, 70.0, 1937.0, 14.0, 29.0,
+	232.0, 90.0, 3211.0, 17.0, 19.0,
+	115.0, 95.0, 2694.0, 15.0, 23.0,
+	120.0, 88.0, 2957.0, 17.0, 23.0,
+	121.0, 98.0, 2945.0, 14.5, 22.0,
+	121.0, 115.0, 2671.0, 13.5, 25.0,
+	91.0, 53.0, 1795.0, 17.5, 33.0,
+	107.0, 86.0, 2464.0, 15.5, 28.0,
+	116.0, 81.0, 2220.0, 16.9, 25.0,
+	140.0, 92.0, 2572.0, 14.9, 25.0,
+	98.0, 79.0, 2255.0, 17.7, 26.0,
+	101.0, 83.0, 2202.0, 15.3, 27.0,
+	305.0, 140.0, 4215.0, 13.0, 17.5,
+	318.0, 150.0, 4190.0, 13.0, 16.0,
+	304.0, 120.0, 3962.0, 13.9, 15.5,
+	351.0, 152.0, 4215.0, 12.8, 14.5,
+	225.0, 100.0, 3233.0, 15.4, 22.0,
+	250.0, 105.0, 3353.0, 14.5, 22.0,
+	200.0, 81.0, 3012.0, 17.6, 24.0,
+	232.0, 90.0, 3085.0, 17.6, 22.5,
+	85.0, 52.0, 2035.0, 22.2, 29.0,
+	98.0, 60.0, 2164.0, 22.1, 24.5,
+	90.0, 70.0, 1937.0, 14.2, 29.0,
+	91.0, 53.0, 1795.0, 17.4, 33.0,
+	225.0, 100.0, 3651.0, 17.7, 20.0,
+	250.0, 78.0, 3574.0, 21.0, 18.0,
+	250.0, 110.0, 3645.0, 16.2, 18.5,
+	258.0, 95.0, 3193.0, 17.8, 17.5,
+	97.0, 71.0, 1825.0, 12.2, 29.5,
+	85.0, 70.0, 1990.0, 17.0, 32.0,
+	97.0, 75.0, 2155.0, 16.4, 28.0,
+	140.0, 72.0, 2565.0, 13.6, 26.5,
+	130.0, 102.0, 3150.0, 15.7, 20.0,
+	318.0, 150.0, 3940.0, 13.2, 13.0,
+	120.0, 88.0, 3270.0, 21.9, 19.0,
+	156.0, 108.0, 2930.0, 15.5, 19.0,
+	168.0, 120.0, 3820.0, 16.7, 16.5,
+	350.0, 180.0, 4380.0, 12.1, 16.5,
+	350.0, 145.0, 4055.0, 12.0, 13.0,
+	302.0, 130.0, 3870.0, 15.0, 13.0,
+	318.0, 150.0, 3755.0, 14.0, 13.0,
+	98.0, 68.0, 2045.0, 18.5, 31.5,
+	111.0, 80.0, 2155.0, 14.8, 30.0,
+	79.0, 58.0, 1825.0, 18.6, 36.0,
+	122.0, 96.0, 2300.0, 15.5, 25.5,
+	85.0, 70.0, 1945.0, 16.8, 33.5,
+	305.0, 145.0, 3880.0, 12.5, 17.5,
+	260.0, 110.0, 4060.0, 19.0, 17.0,
+	318.0, 145.0, 4140.0, 13.7, 15.5,
+	302.0, 130.0, 4295.0, 14.9, 15.0,
+	250.0, 110.0, 3520.0, 16.4, 17.5,
+	231.0, 105.0, 3425.0, 16.9, 20.5,
+	225.0, 100.0, 3630.0, 17.7, 19.0,
+	250.0, 98.0, 3525.0, 19.0, 18.5,
+	400.0, 180.0, 4220.0, 11.1, 16.0,
+	350.0, 170.0, 4165.0, 11.4, 15.5,
+	400.0, 190.0, 4325.0, 12.2, 15.5,
+	351.0, 149.0, 4335.0, 14.5, 16.0,
+	97.0, 78.0, 1940.0, 14.5, 29.0,
+	151.0, 88.0, 2740.0, 16.0, 24.5,
+	97.0, 75.0, 2265.0, 18.2, 26.0,
+	140.0, 89.0, 2755.0, 15.8, 25.5,
+	98.0, 63.0, 2051.0, 17.0, 30.5,
+	98.0, 83.0, 2075.0, 15.9, 33.5,
+	97.0, 67.0, 1985.0, 16.4, 30.0,
+	97.0, 78.0, 2190.0, 14.1, 30.5,
+	146.0, 97.0, 2815.0, 14.5, 22.0,
+	121.0, 110.0, 2600.0, 12.8, 21.5,
+	80.0, 110.0, 2720.0, 13.5, 21.5,
+	90.0, 48.0, 1985.0, 21.5, 43.1,
+	98.0, 66.0, 1800.0, 14.4, 36.1,
+	78.0, 52.0, 1985.0, 19.4, 32.8,
+	85.0, 70.0, 2070.0, 18.6, 39.4,
+	91.0, 60.0, 1800.0, 16.4, 36.1,
+	260.0, 110.0, 3365.0, 15.5, 19.9,
+	318.0, 140.0, 3735.0, 13.2, 19.4,
+	302.0, 139.0, 3570.0, 12.8, 20.2,
+	231.0, 105.0, 3535.0, 19.2, 19.2,
+	200.0, 95.0, 3155.0, 18.2, 20.5,
+	200.0, 85.0, 2965.0, 15.8, 20.2,
+	140.0, 88.0, 2720.0, 15.4, 25.1,
+	225.0, 100.0, 3430.0, 17.2, 20.5,
+	232.0, 90.0, 3210.0, 17.2, 19.4,
+	231.0, 105.0, 3380.0, 15.8, 20.6,
+	200.0, 85.0, 3070.0, 16.7, 20.8,
+	225.0, 110.0, 3620.0, 18.7, 18.6,
+	258.0, 120.0, 3410.0, 15.1, 18.1,
+	305.0, 145.0, 3425.0, 13.2, 19.2,
+	231.0, 165.0, 3445.0, 13.4, 17.7,
+	302.0, 139.0, 3205.0, 11.2, 18.1,
+	318.0, 140.0, 4080.0, 13.7, 17.5,
+	98.0, 68.0, 2155.0, 16.5, 30.0,
+	134.0, 95.0, 2560.0, 14.2, 27.5,
+	119.0, 97.0, 2300.0, 14.7, 27.2,
+	105.0, 75.0, 2230.0, 14.5, 30.9,
+	134.0, 95.0, 2515.0, 14.8, 21.1,
+	156.0, 105.0, 2745.0, 16.7, 23.2,
+	151.0, 85.0, 2855.0, 17.6, 23.8,
+	119.0, 97.0, 2405.0, 14.9, 23.9,
+	131.0, 103.0, 2830.0, 15.9, 20.3,
+	163.0, 125.0, 3140.0, 13.6, 17.0,
+	121.0, 115.0, 2795.0, 15.7, 21.6,
+	163.0, 133.0, 3410.0, 15.8, 16.2,
+	89.0, 71.0, 1990.0, 14.9, 31.5,
+	98.0, 68.0, 2135.0, 16.6, 29.5,
+	231.0, 115.0, 3245.0, 15.4, 21.5,
+	200.0, 85.0, 2990.0, 18.2, 19.8,
+	140.0, 88.0, 2890.0, 17.3, 22.3,
+	232.0, 90.0, 3265.0, 18.2, 20.2,
+	225.0, 110.0, 3360.0, 16.6, 20.6,
+	305.0, 130.0, 3840.0, 15.4, 17.0,
+	302.0, 129.0, 3725.0, 13.4, 17.6,
+	351.0, 138.0, 3955.0, 13.2, 16.5,
+	318.0, 135.0, 3830.0, 15.2, 18.2,
+	350.0, 155.0, 4360.0, 14.9, 16.9,
+	351.0, 142.0, 4054.0, 14.3, 15.5,
+	267.0, 125.0, 3605.0, 15.0, 19.2,
+	360.0, 150.0, 3940.0, 13.0, 18.5,
+	89.0, 71.0, 1925.0, 14.0, 31.9,
+	86.0, 65.0, 1975.0, 15.2, 34.1,
+	98.0, 80.0, 1915.0, 14.4, 35.7,
+	121.0, 80.0, 2670.0, 15.0, 27.4,
+	183.0, 77.0, 3530.0, 20.1, 25.4,
+	350.0, 125.0, 3900.0, 17.4, 23.0,
+	141.0, 71.0, 3190.0, 24.8, 27.2,
+	260.0, 90.0, 3420.0, 22.2, 23.9,
+	105.0, 70.0, 2200.0, 13.2, 34.2,
+	105.0, 70.0, 2150.0, 14.9, 34.5,
+	85.0, 65.0, 2020.0, 19.2, 31.8,
+	91.0, 69.0, 2130.0, 14.7, 37.3,
+	151.0, 90.0, 2670.0, 16.0, 28.4,
+	173.0, 115.0, 2595.0, 11.3, 28.8,
+	173.0, 115.0, 2700.0, 12.9, 26.8,
+	151.0, 90.0, 2556.0, 13.2, 33.5,
+	98.0, 76.0, 2144.0, 14.7, 41.5,
+	89.0, 60.0, 1968.0, 18.8, 38.1,
+	98.0, 70.0, 2120.0, 15.5, 32.1,
+	86.0, 65.0, 2019.0, 16.4, 37.2,
+	151.0, 90.0, 2678.0, 16.5, 28.0,
+	140.0, 88.0, 2870.0, 18.1, 26.4,
+	151.0, 90.0, 3003.0, 20.1, 24.3,
+	225.0, 90.0, 3381.0, 18.7, 19.1,
+	97.0, 78.0, 2188.0, 15.8, 34.3,
+	134.0, 90.0, 2711.0, 15.5, 29.8,
+	120.0, 75.0, 2542.0, 17.5, 31.3,
+	119.0, 92.0, 2434.0, 15.0, 37.0,
+	108.0, 75.0, 2265.0, 15.2, 32.2,
+	86.0, 65.0, 2110.0, 17.9, 46.6,
+	156.0, 105.0, 2800.0, 14.4, 27.9,
+	85.0, 65.0, 2110.0, 19.2, 40.8,
+	90.0, 48.0, 2085.0, 21.7, 44.3,
+	90.0, 48.0, 2335.0, 23.7, 43.4,
+	121.0, 67.0, 2950.0, 19.9, 36.4,
+	146.0, 67.0, 3250.0, 21.8, 30.0,
+	91.0, 67.0, 1850.0, 13.8, 44.6,
+	97.0, 67.0, 2145.0, 18.0, 33.8,
+	89.0, 62.0, 1845.0, 15.3, 29.8,
+	168.0, 132.0, 2910.0, 11.4, 32.7,
+	70.0, 100.0, 2420.0, 12.5, 23.7,
+	122.0, 88.0, 2500.0, 15.1, 35.0,
+	107.0, 72.0, 2290.0, 17.0, 32.4,
+	135.0, 84.0, 2490.0, 15.7, 27.2,
+	151.0, 84.0, 2635.0, 16.4, 26.6,
+	156.0, 92.0, 2620.0, 14.4, 25.8,
+	173.0, 110.0, 2725.0, 12.6, 23.5,
+	135.0, 84.0, 2385.0, 12.9, 30.0,
+	79.0, 58.0, 1755.0, 16.9, 39.1,
+	86.0, 64.0, 1875.0, 16.4, 39.0,
+	81.0, 60.0, 1760.0, 16.1, 35.1,
+	97.0, 67.0, 2065.0, 17.8, 32.3,
+	85.0, 65.0, 1975.0, 19.4, 37.0,
+	89.0, 62.0, 2050.0, 17.3, 37.7,
+	91.0, 68.0, 1985.0, 16.0, 34.1,
+	105.0, 63.0, 2215.0, 14.9, 34.7,
+	98.0, 65.0, 2045.0, 16.2, 34.4,
+	98.0, 65.0, 2380.0, 20.7, 29.9,
+	105.0, 74.0, 2190.0, 14.2, 33.0,
+	107.0, 75.0, 2210.0, 14.4, 33.7,
+	108.0, 75.0, 2350.0, 16.8, 32.4,
+	119.0, 100.0, 2615.0, 14.8, 32.9,
+	120.0, 74.0, 2635.0, 18.3, 31.6,
+	141.0, 80.0, 3230.0, 20.4, 28.1,
+	145.0, 76.0, 3160.0, 19.6, 30.7,
+	168.0, 116.0, 2900.0, 12.6, 25.4,
+	146.0, 120.0, 2930.0, 13.8, 24.2,
+	231.0, 110.0, 3415.0, 15.8, 22.4,
+	350.0, 105.0, 3725.0, 19.0, 26.6,
+	200.0, 88.0, 3060.0, 17.1, 20.2,
+	225.0, 85.0, 3465.0, 16.6, 17.6,
+	112.0, 88.0, 2605.0, 19.6, 28.0,
+	112.0, 88.0, 2640.0, 18.6, 27.0,
+	112.0, 88.0, 2395.0, 18.0, 34.0,
+	112.0, 85.0, 2575.0, 16.2, 31.0,
+	135.0, 84.0, 2525.0, 16.0, 29.0,
+	151.0, 90.0, 2735.0, 18.0, 27.0,
+	140.0, 92.0, 2865.0, 16.4, 24.0,
+	105.0, 74.0, 1980.0, 15.3, 36.0,
+	91.0, 68.0, 2025.0, 18.2, 37.0,
+	91.0, 68.0, 1970.0, 17.6, 31.0,
+	105.0, 63.0, 2125.0, 14.7, 38.0,
+	98.0, 70.0, 2125.0, 17.3, 36.0,
+	120.0, 88.0, 2160.0, 14.5, 36.0,
+	107.0, 75.0, 2205.0, 14.5, 36.0,
+	108.0, 70.0, 2245.0, 16.9, 34.0,
+	91.0, 67.0, 1965.0, 15.0, 38.0,
+	91.0, 67.0, 1965.0, 15.7, 32.0,
+	91.0, 67.0, 1995.0, 16.2, 38.0,
+	181.0, 110.0, 2945.0, 16.4, 25.0,
+	262.0, 85.0, 3015.0, 17.0, 38.0,
+	156.0, 92.0, 2585.0, 14.5, 26.0,
+	232.0, 112.0, 2835.0, 14.7, 22.0,
+	144.0, 96.0, 2665.0, 13.9, 32.0,
+	135.0, 84.0, 2370.0, 13.0, 36.0,
+	151.0, 90.0, 2950.0, 17.3, 27.0,
+	140.0, 86.0, 2790.0, 15.6, 27.0,
+	97.0, 52.0, 2130.0, 24.6, 44.0,
+	135.0, 84.0, 2295.0, 11.6, 32.0,
+	120.0, 79.0, 2625.0, 18.6, 28.0,
+	119.0, 82.0, 2720.0, 19.4, 31.0,
+})
diff --git a/vendor/gonum.org/v1/gonum/stat/cca_example_test.go b/vendor/gonum.org/v1/gonum/stat/cca_example_test.go
new file mode 100644
index 00000000..f053e5ad
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/cca_example_test.go
@@ -0,0 +1,165 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package stat_test
+
+import (
+	"fmt"
+	"log"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+	"gonum.org/v1/gonum/stat"
+)
+
+// symView is a helper for getting a View of a SymDense.
+type symView struct {
+	sym *mat.SymDense
+
+	i, j, r, c int
+}
+
+func (s symView) Dims() (r, c int) { return s.r, s.c }
+
+func (s symView) At(i, j int) float64 {
+	if i < 0 || s.r <= i {
+		panic("i out of bounds")
+	}
+	if j < 0 || s.c <= j {
+		panic("j out of bounds")
+	}
+	return s.sym.At(s.i+i, s.j+j)
+}
+
+func (s symView) T() mat.Matrix { return mat.Transpose{s} }
+
+func ExampleCC() {
+	// This example is directly analogous to Example 3.5 on page 87 of
+	// Koch, Inge. Analysis of multivariate and high-dimensional data.
+	// Vol. 32. Cambridge University Press, 2013. ISBN: 9780521887939
+
+	// bostonData is the Boston Housing Data of Harrison and Rubinfeld (1978)
+	n, _ := bostonData.Dims()
+	var xd, yd = 7, 4
+	// The variables (columns) of bostonData can be partitioned into two sets:
+	// those that deal with environmental/social variables (xdata), and those
+	// that contain information regarding the individual (ydata). Because the
+	// variables can be naturally partitioned in this way, these data are
+	// appropriate for canonical correlation analysis. The columns (variables)
+	// of xdata are, in order:
+	//  per capita crime rate by town,
+	//  proportion of non-retail business acres per town,
+	//  nitric oxide concentration (parts per 10 million),
+	//  weighted distances to Boston employment centres,
+	//  index of accessibility to radial highways,
+	//  pupil-teacher ratio by town, and
+	//  proportion of blacks by town.
+	xdata := bostonData.Slice(0, n, 0, xd)
+
+	// The columns (variables) of ydata are, in order:
+	//  average number of rooms per dwelling,
+	//  proportion of owner-occupied units built prior to 1940,
+	//  full-value property-tax rate per $10000, and
+	//  median value of owner-occupied homes in $1000s.
+	ydata := bostonData.Slice(0, n, xd, xd+yd)
+
+	// For comparison, calculate the correlation matrix for the original data.
+	var cor mat.SymDense
+	stat.CorrelationMatrix(&cor, bostonData, nil)
+
+	// Extract just those correlations that are between xdata and ydata.
+	var corRaw = symView{sym: &cor, i: 0, j: xd, r: xd, c: yd}
+
+	// Note that the strongest correlation between individual variables is 0.91
+	// between the 5th variable of xdata (index of accessibility to radial
+	// highways) and the 3rd variable of ydata (full-value property-tax rate per
+	// $10000).
+	fmt.Printf("corRaw = %.4f", mat.Formatted(corRaw, mat.Prefix("         ")))
+
+	// Calculate the canonical correlations.
+	var cc stat.CC
+	err := cc.CanonicalCorrelations(xdata, ydata, nil)
+	if err != nil {
+		log.Fatal(err)
+	}
+
+	// Unpack cc.
+	ccors := cc.CorrsTo(nil)
+	pVecs := cc.LeftTo(nil, true)
+	qVecs := cc.RightTo(nil, true)
+	phiVs := cc.LeftTo(nil, false)
+	psiVs := cc.RightTo(nil, false)
+
+	// Canonical Correlation Matrix, or the correlations between the sphered
+	// data.
+	var corSph mat.Dense
+	corSph.Clone(pVecs)
+	col := make([]float64, xd)
+	for j := 0; j < yd; j++ {
+		mat.Col(col, j, &corSph)
+		floats.Scale(ccors[j], col)
+		corSph.SetCol(j, col)
+	}
+	corSph.Product(&corSph, qVecs.T())
+	fmt.Printf("\n\ncorSph = %.4f", mat.Formatted(&corSph, mat.Prefix("         ")))
+
+	// Canonical Correlations. Note that the first canonical correlation is
+	// 0.95, stronger than the greatest correlation in the original data, and
+	// much stronger than the greatest correlation in the sphered data.
+	fmt.Printf("\n\nccors = %.4f", ccors)
+
+	// Left and right eigenvectors of the canonical correlation matrix.
+	fmt.Printf("\n\npVecs = %.4f", mat.Formatted(pVecs, mat.Prefix("        ")))
+	fmt.Printf("\n\nqVecs = %.4f", mat.Formatted(qVecs, mat.Prefix("        ")))
+
+	// Canonical Correlation Transforms. These can be useful as they represent
+	// the canonical variables as linear combinations of the original variables.
+	fmt.Printf("\n\nphiVs = %.4f", mat.Formatted(phiVs, mat.Prefix("        ")))
+	fmt.Printf("\n\npsiVs = %.4f", mat.Formatted(psiVs, mat.Prefix("        ")))
+
+	// Output:
+	// corRaw = ⎡-0.2192   0.3527   0.5828  -0.3883⎤
+	//          ⎢-0.3917   0.6448   0.7208  -0.4837⎥
+	//          ⎢-0.3022   0.7315   0.6680  -0.4273⎥
+	//          ⎢ 0.2052  -0.7479  -0.5344   0.2499⎥
+	//          ⎢-0.2098   0.4560   0.9102  -0.3816⎥
+	//          ⎢-0.3555   0.2615   0.4609  -0.5078⎥
+	//          ⎣ 0.1281  -0.2735  -0.4418   0.3335⎦
+	//
+	// corSph = ⎡ 0.0118   0.0525   0.2300  -0.1363⎤
+	//          ⎢-0.1810   0.3213   0.3814  -0.1412⎥
+	//          ⎢ 0.0166   0.2241   0.0104  -0.2235⎥
+	//          ⎢ 0.0346  -0.5481  -0.0034  -0.1994⎥
+	//          ⎢ 0.0303  -0.0956   0.7152   0.2039⎥
+	//          ⎢-0.0298  -0.0022   0.0739  -0.3703⎥
+	//          ⎣-0.1226  -0.0746  -0.3899   0.1541⎦
+	//
+	// ccors = [0.9451 0.6787 0.5714 0.2010]
+	//
+	// pVecs = ⎡-0.2574   0.0158   0.2122  -0.0946⎤
+	//         ⎢-0.4837   0.3837   0.1474   0.6597⎥
+	//         ⎢-0.0801   0.3494   0.3287  -0.2862⎥
+	//         ⎢ 0.1278  -0.7337   0.4851   0.2248⎥
+	//         ⎢-0.6969  -0.4342  -0.3603   0.0291⎥
+	//         ⎢-0.0991   0.0503   0.6384   0.1022⎥
+	//         ⎣ 0.4260   0.0323  -0.2290   0.6419⎦
+	//
+	// qVecs = ⎡ 0.0182  -0.1583  -0.0067  -0.9872⎤
+	//         ⎢-0.2348   0.9483  -0.1462  -0.1554⎥
+	//         ⎢-0.9701  -0.2406  -0.0252   0.0209⎥
+	//         ⎣ 0.0593  -0.1330  -0.9889   0.0291⎦
+	//
+	// phiVs = ⎡-0.0027   0.0093   0.0490  -0.0155⎤
+	//         ⎢-0.0429  -0.0242   0.0361   0.1839⎥
+	//         ⎢-1.2248   5.6031   5.8094  -4.7927⎥
+	//         ⎢-0.0044  -0.3424   0.4470   0.1150⎥
+	//         ⎢-0.0742  -0.1193  -0.1116   0.0022⎥
+	//         ⎢-0.0233   0.1046   0.3853  -0.0161⎥
+	//         ⎣ 0.0001   0.0005  -0.0030   0.0082⎦
+	//
+	// psiVs = ⎡ 0.0302  -0.3002   0.0878  -1.9583⎤
+	//         ⎢-0.0065   0.0392  -0.0118  -0.0061⎥
+	//         ⎢-0.0052  -0.0046  -0.0023   0.0008⎥
+	//         ⎣ 0.0020   0.0037  -0.1293   0.1038⎦
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/cca_test.go b/vendor/gonum.org/v1/gonum/stat/cca_test.go
new file mode 100644
index 00000000..117ae5f2
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/cca_test.go
@@ -0,0 +1,191 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package stat_test
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+	"gonum.org/v1/gonum/stat"
+)
+
+func TestCanonicalCorrelations(t *testing.T) {
+tests:
+	for i, test := range []struct {
+		xdata     mat.Matrix
+		ydata     mat.Matrix
+		weights   []float64
+		wantCorrs []float64
+		wantpVecs *mat.Dense
+		wantqVecs *mat.Dense
+		wantphiVs *mat.Dense
+		wantpsiVs *mat.Dense
+		epsilon   float64
+	}{
+		// Test results verified using R.
+		{ // Truncated iris data, Sepal vs Petal measurements.
+			xdata: mat.NewDense(10, 2, []float64{
+				5.1, 3.5,
+				4.9, 3.0,
+				4.7, 3.2,
+				4.6, 3.1,
+				5.0, 3.6,
+				5.4, 3.9,
+				4.6, 3.4,
+				5.0, 3.4,
+				4.4, 2.9,
+				4.9, 3.1,
+			}),
+			ydata: mat.NewDense(10, 2, []float64{
+				1.4, 0.2,
+				1.4, 0.2,
+				1.3, 0.2,
+				1.5, 0.2,
+				1.4, 0.2,
+				1.7, 0.4,
+				1.4, 0.3,
+				1.5, 0.2,
+				1.4, 0.2,
+				1.5, 0.1,
+			}),
+			wantCorrs: []float64{0.7250624174504773, 0.5547679185730191},
+			wantpVecs: mat.NewDense(2, 2, []float64{
+				0.0765914610875867, 0.9970625597666721,
+				0.9970625597666721, -0.0765914610875868,
+			}),
+			wantqVecs: mat.NewDense(2, 2, []float64{
+				0.3075184850910837, 0.9515421069649439,
+				0.9515421069649439, -0.3075184850910837,
+			}),
+			wantphiVs: mat.NewDense(2, 2, []float64{
+				-1.9794877596804641, 5.2016325219025124,
+				4.5211829944066553, -2.7263663170835697,
+			}),
+			wantpsiVs: mat.NewDense(2, 2, []float64{
+				-0.0613084818030103, 10.8514169865438941,
+				12.7209032660734298, -7.6793888180353775,
+			}),
+			epsilon: 1e-12,
+		},
+		// Test results compared to those results presented in examples by
+		// Koch, Inge. Analysis of multivariate and high-dimensional data.
+		// Vol. 32. Cambridge University Press, 2013. ISBN: 9780521887939
+		{ // ASA Car Exposition Data of Ramos and Donoho (1983)
+			// Displacement, Horsepower, Weight
+			xdata: carData.Slice(0, 392, 0, 3),
+			// Acceleration, MPG
+			ydata:     carData.Slice(0, 392, 3, 5),
+			wantCorrs: []float64{0.8782187384352336, 0.6328187219216761},
+			wantpVecs: mat.NewDense(3, 2, []float64{
+				0.3218296374829181, 0.3947540257657075,
+				0.4162807660635797, 0.7573719053303306,
+				0.8503740401982725, -0.5201509936144236,
+			}),
+			wantqVecs: mat.NewDense(2, 2, []float64{
+				-0.5161984172278830, -0.8564690269072364,
+				-0.8564690269072364, 0.5161984172278830,
+			}),
+			wantphiVs: mat.NewDense(3, 2, []float64{
+				0.0025033152994308, 0.0047795464118615,
+				0.0201923608080173, 0.0409150208725958,
+				-0.0000247374128745, -0.0026766435161875,
+			}),
+			wantpsiVs: mat.NewDense(2, 2, []float64{
+				-0.1666196759760772, -0.3637393866139658,
+				-0.0915512109649727, 0.1077863777929168,
+			}),
+			epsilon: 1e-12,
+		},
+		// Test results compared to those results presented in examples by
+		// Koch, Inge. Analysis of multivariate and high-dimensional data.
+		// Vol. 32. Cambridge University Press, 2013. ISBN: 9780521887939
+		{ // Boston Housing Data of Harrison and Rubinfeld (1978)
+			// Per capita crime rate by town,
+			// Proportion of non-retail business acres per town,
+			// Nitric oxide concentration (parts per 10 million),
+			// Weighted distances to Boston employment centres,
+			// Index of accessibility to radial highways,
+			// Pupil-teacher ratio by town, Proportion of blacks by town
+			xdata: bostonData.Slice(0, 506, 0, 7),
+			// Average number of rooms per dwelling,
+			// Proportion of owner-occupied units built prior to 1940,
+			// Full-value property-tax rate per $10000,
+			// Median value of owner-occupied homes in $1000s
+			ydata:     bostonData.Slice(0, 506, 7, 11),
+			wantCorrs: []float64{0.9451239443886021, 0.6786622733370654, 0.5714338361583764, 0.2009739704710440},
+			wantpVecs: mat.NewDense(7, 4, []float64{
+				-0.2574391924541903, 0.0158477516621194, 0.2122169934631024, -0.0945733803894706,
+				-0.4836594430018478, 0.3837101908138468, 0.1474448317415911, 0.6597324886718275,
+				-0.0800776365873296, 0.3493556742809252, 0.3287336458109373, -0.2862040444334655,
+				0.1277586360386374, -0.7337427663667596, 0.4851134819037011, 0.2247964865970192,
+				-0.6969432006136684, -0.4341748776002893, -0.3602872887636357, 0.0290661608626292,
+				-0.0990903250057199, 0.0503411215453873, 0.6384330631742202, 0.1022367136218303,
+				0.4260459963765036, 0.0323334351308141, -0.2289527516030810, 0.6419232947608805,
+			}),
+			wantqVecs: mat.NewDense(4, 4, []float64{
+				0.0181660502363264, -0.1583489460479038, -0.0066723577642883, -0.9871935400650649,
+				-0.2347699045986119, 0.9483314614936594, -0.1462420505631345, -0.1554470767919033,
+				-0.9700704038477141, -0.2406071741000039, -0.0251838984227037, 0.0209134074358349,
+				0.0593000682318482, -0.1330460003097728, -0.9889057151969489, 0.0291161494720761,
+			}),
+			wantphiVs: mat.NewDense(7, 4, []float64{
+				-0.0027462234108197, 0.0093444513500898, 0.0489643932714296, -0.0154967189805819,
+				-0.0428564455279537, -0.0241708702119420, 0.0360723472093996, 0.1838983230588095,
+				-1.2248435648802380, 5.6030921364723980, 5.8094144583797025, -4.7926812190419676,
+				-0.0043684825094649, -0.3424101164977618, 0.4469961215717917, 0.1150161814353696,
+				-0.0741534069521954, -0.1193135794923700, -0.1115518305471460, 0.0021638758323088,
+				-0.0233270323101624, 0.1046330818178399, 0.3853045975077387, -0.0160927870102877,
+				0.0001293051387859, 0.0004540746921446, -0.0030296315865440, 0.0081895477974654,
+			}),
+			wantpsiVs: mat.NewDense(4, 4, []float64{
+				0.0301593362017375, -0.3002219289647127, 0.0878217377593682, -1.9583226531517062,
+				-0.0065483104073892, 0.0392212086716247, -0.0117570776209991, -0.0061113064481860,
+				-0.0052075523350125, -0.0045770200452960, -0.0022762313289592, 0.0008441873006821,
+				0.0020111735096327, 0.0037352799829930, -0.1292578071621794, 0.1037709056329765,
+			}),
+			epsilon: 1e-12,
+		},
+	} {
+		var cc stat.CC
+		var corrs []float64
+		var pVecs, qVecs *mat.Dense
+		var phiVs, psiVs *mat.Dense
+		for j := 0; j < 2; j++ {
+			err := cc.CanonicalCorrelations(test.xdata, test.ydata, test.weights)
+			if err != nil {
+				t.Errorf("%d use %d: unexpected error: %v", i, j, err)
+				continue tests
+			}
+
+			corrs = cc.CorrsTo(corrs)
+			pVecs = cc.LeftTo(pVecs, true)
+			qVecs = cc.RightTo(qVecs, true)
+			phiVs = cc.LeftTo(phiVs, false)
+			psiVs = cc.RightTo(psiVs, false)
+
+			if !floats.EqualApprox(corrs, test.wantCorrs, test.epsilon) {
+				t.Errorf("%d use %d: unexpected variance result got:%v, want:%v",
+					i, j, corrs, test.wantCorrs)
+			}
+			if !mat.EqualApprox(pVecs, test.wantpVecs, test.epsilon) {
+				t.Errorf("%d use %d: unexpected CCA result got:\n%v\nwant:\n%v",
+					i, j, mat.Formatted(pVecs), mat.Formatted(test.wantpVecs))
+			}
+			if !mat.EqualApprox(qVecs, test.wantqVecs, test.epsilon) {
+				t.Errorf("%d use %d: unexpected CCA result got:\n%v\nwant:\n%v",
+					i, j, mat.Formatted(qVecs), mat.Formatted(test.wantqVecs))
+			}
+			if !mat.EqualApprox(phiVs, test.wantphiVs, test.epsilon) {
+				t.Errorf("%d use %d: unexpected CCA result got:\n%v\nwant:\n%v",
+					i, j, mat.Formatted(phiVs), mat.Formatted(test.wantphiVs))
+			}
+			if !mat.EqualApprox(psiVs, test.wantpsiVs, test.epsilon) {
+				t.Errorf("%d use %d: unexpected CCA result got:\n%v\nwant:\n%v",
+					i, j, mat.Formatted(psiVs), mat.Formatted(test.wantpsiVs))
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/combin/combin.go b/vendor/gonum.org/v1/gonum/stat/combin/combin.go
new file mode 100644
index 00000000..d4e1f6e6
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/combin/combin.go
@@ -0,0 +1,181 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package combin
+
+import "math"
+
+const (
+	badNegInput = "combin: negative input"
+	badSetSize  = "combin: n < k"
+	badInput    = "combin: wrong input slice length"
+)
+
+// Binomial returns the binomial coefficient of (n,k), also commonly referred to
+// as "n choose k".
+//
+// The binomial coefficient, C(n,k), is the number of unordered combinations of
+// k elements in a set that is n elements big, and is defined as
+//
+//  C(n,k) = n!/((n-k)!k!)
+//
+// n and k must be non-negative with n >= k, otherwise Binomial will panic.
+// No check is made for overflow.
+func Binomial(n, k int) int {
+	if n < 0 || k < 0 {
+		panic(badNegInput)
+	}
+	if n < k {
+		panic(badSetSize)
+	}
+	// (n,k) = (n, n-k)
+	if k > n/2 {
+		k = n - k
+	}
+	b := 1
+	for i := 1; i <= k; i++ {
+		b = (n - k + i) * b / i
+	}
+	return b
+}
+
+// GeneralizedBinomial returns the generalized binomial coefficient of (n, k),
+// defined as
+//  Γ(n+1) / (Γ(k+1) Γ(n-k+1))
+// where Γ is the Gamma function. GeneralizedBinomial is useful for continuous
+// relaxations of the binomial coefficient, or when the binomial coefficient value
+// may overflow int. In the latter case, one may use math/big for an exact
+// computation.
+//
+// n and k must be non-negative with n >= k, otherwise GeneralizedBinomial will panic.
+func GeneralizedBinomial(n, k float64) float64 {
+	return math.Exp(LogGeneralizedBinomial(n, k))
+}
+
+// LogGeneralizedBinomial returns the log of the generalized binomial coefficient.
+// See GeneralizedBinomial for more information.
+func LogGeneralizedBinomial(n, k float64) float64 {
+	if n < 0 || k < 0 {
+		panic(badNegInput)
+	}
+	if n < k {
+		panic(badSetSize)
+	}
+	a, _ := math.Lgamma(n + 1)
+	b, _ := math.Lgamma(k + 1)
+	c, _ := math.Lgamma(n - k + 1)
+	return a - b - c
+}
+
+// CombinationGenerator generates combinations iteratively. Combinations may be
+// called to generate all combinations collectively.
+type CombinationGenerator struct {
+	n         int
+	k         int
+	previous  []int
+	remaining int
+}
+
+// NewCombinationGenerator returns a CombinationGenerator for generating the
+// combinations of k elements from a set of size n.
+//
+// n and k must be non-negative with n >= k, otherwise NewCombinationGenerator
+// will panic.
+func NewCombinationGenerator(n, k int) *CombinationGenerator {
+	return &CombinationGenerator{
+		n:         n,
+		k:         k,
+		remaining: Binomial(n, k),
+	}
+}
+
+// Next advances the iterator if there are combinations remaining to be generated,
+// and returns false if all combinations have been generated. Next must be called
+// to initialize the first value before calling Combination or Combination will
+// panic. The value returned by Combination is only changed during calls to Next.
+func (c *CombinationGenerator) Next() bool {
+	if c.remaining <= 0 {
+		// Next is called before combination, so c.remaining is set to zero before
+		// Combination is called. Thus, Combination cannot panic on zero, and a
+		// second sentinel value is needed.
+		c.remaining = -1
+		return false
+	}
+	if c.previous == nil {
+		c.previous = make([]int, c.k)
+		for i := range c.previous {
+			c.previous[i] = i
+		}
+	} else {
+		nextCombination(c.previous, c.n, c.k)
+	}
+	c.remaining--
+	return true
+}
+
+// Combination generates the next combination. If next is non-nil, it must have
+// length k and the result will be stored in-place into combination. If combination
+// is nil a new slice will be allocated and returned. If all of the combinations
+// have already been constructed (Next() returns false), Combination will panic.
+//
+// Next must be called to initialize the first value before calling Combination
+// or Combination will panic. The value returned by Combination is only changed
+// during calls to Next.
+func (c *CombinationGenerator) Combination(combination []int) []int {
+	if c.remaining == -1 {
+		panic("combin: all combinations have been generated")
+	}
+	if c.previous == nil {
+		panic("combin: Combination called before Next")
+	}
+	if combination == nil {
+		combination = make([]int, c.k)
+	}
+	if len(combination) != c.k {
+		panic(badInput)
+	}
+	copy(combination, c.previous)
+	return combination
+}
+
+// Combinations generates all of the combinations of k elements from a
+// set of size n. The returned slice has length Binomial(n,k) and each inner slice
+// has length k.
+//
+// n and k must be non-negative with n >= k, otherwise Combinations will panic.
+//
+// CombinationGenerator may alternatively be used to generate the combinations
+// iteratively instead of collectively.
+func Combinations(n, k int) [][]int {
+	combins := Binomial(n, k)
+	data := make([][]int, combins)
+	if len(data) == 0 {
+		return data
+	}
+	data[0] = make([]int, k)
+	for i := range data[0] {
+		data[0][i] = i
+	}
+	for i := 1; i < combins; i++ {
+		next := make([]int, k)
+		copy(next, data[i-1])
+		nextCombination(next, n, k)
+		data[i] = next
+	}
+	return data
+}
+
+// nextCombination generates the combination after s, overwriting the input value.
+func nextCombination(s []int, n, k int) {
+	for j := k - 1; j >= 0; j-- {
+		if s[j] == n+j-k {
+			continue
+		}
+		s[j]++
+		for l := j + 1; l < k; l++ {
+			s[l] = s[j] + l - j
+		}
+		break
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/combin/combin_test.go b/vendor/gonum.org/v1/gonum/stat/combin/combin_test.go
new file mode 100644
index 00000000..8226a675
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/combin/combin_test.go
@@ -0,0 +1,181 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package combin
+
+import (
+	"math/big"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+// intSosMatch returns true if the two slices of slices are equal.
+func intSosMatch(a, b [][]int) bool {
+	if len(a) != len(b) {
+		return false
+	}
+	for i, s := range a {
+		if len(s) != len(b[i]) {
+			return false
+		}
+		for j, v := range s {
+			if v != b[i][j] {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+var binomialTests = []struct {
+	n, k, ans int
+}{
+	{0, 0, 1},
+	{5, 0, 1},
+	{5, 1, 5},
+	{5, 2, 10},
+	{5, 3, 10},
+	{5, 4, 5},
+	{5, 5, 1},
+
+	{6, 0, 1},
+	{6, 1, 6},
+	{6, 2, 15},
+	{6, 3, 20},
+	{6, 4, 15},
+	{6, 5, 6},
+	{6, 6, 1},
+
+	{20, 0, 1},
+	{20, 1, 20},
+	{20, 2, 190},
+	{20, 3, 1140},
+	{20, 4, 4845},
+	{20, 5, 15504},
+	{20, 6, 38760},
+	{20, 7, 77520},
+	{20, 8, 125970},
+	{20, 9, 167960},
+	{20, 10, 184756},
+	{20, 11, 167960},
+	{20, 12, 125970},
+	{20, 13, 77520},
+	{20, 14, 38760},
+	{20, 15, 15504},
+	{20, 16, 4845},
+	{20, 17, 1140},
+	{20, 18, 190},
+	{20, 19, 20},
+	{20, 20, 1},
+}
+
+func TestBinomial(t *testing.T) {
+	for cas, test := range binomialTests {
+		ans := Binomial(test.n, test.k)
+		if ans != test.ans {
+			t.Errorf("Case %v: Binomial mismatch. Got %v, want %v.", cas, ans, test.ans)
+		}
+	}
+	var (
+		n    = 61
+		want big.Int
+		got  big.Int
+	)
+	for k := 0; k <= n; k++ {
+		want.Binomial(int64(n), int64(k))
+		got.SetInt64(int64(Binomial(n, k)))
+		if want.Cmp(&got) != 0 {
+			t.Errorf("Case n=%v,k=%v: Binomial mismatch for large n. Got %v, want %v.", n, k, got, want)
+		}
+	}
+}
+
+func TestGeneralizedBinomial(t *testing.T) {
+	for cas, test := range binomialTests {
+		ans := GeneralizedBinomial(float64(test.n), float64(test.k))
+		if !floats.EqualWithinAbsOrRel(ans, float64(test.ans), 1e-14, 1e-14) {
+			t.Errorf("Case %v: Binomial mismatch. Got %v, want %v.", cas, ans, test.ans)
+		}
+	}
+}
+
+func TestCombinations(t *testing.T) {
+	for cas, test := range []struct {
+		n, k int
+		data [][]int
+	}{
+		{
+			n:    1,
+			k:    1,
+			data: [][]int{{0}},
+		},
+		{
+			n:    2,
+			k:    1,
+			data: [][]int{{0}, {1}},
+		},
+		{
+			n:    2,
+			k:    2,
+			data: [][]int{{0, 1}},
+		},
+		{
+			n:    3,
+			k:    1,
+			data: [][]int{{0}, {1}, {2}},
+		},
+		{
+			n:    3,
+			k:    2,
+			data: [][]int{{0, 1}, {0, 2}, {1, 2}},
+		},
+		{
+			n:    3,
+			k:    3,
+			data: [][]int{{0, 1, 2}},
+		},
+		{
+			n:    4,
+			k:    1,
+			data: [][]int{{0}, {1}, {2}, {3}},
+		},
+		{
+			n:    4,
+			k:    2,
+			data: [][]int{{0, 1}, {0, 2}, {0, 3}, {1, 2}, {1, 3}, {2, 3}},
+		},
+		{
+			n:    4,
+			k:    3,
+			data: [][]int{{0, 1, 2}, {0, 1, 3}, {0, 2, 3}, {1, 2, 3}},
+		},
+		{
+			n:    4,
+			k:    4,
+			data: [][]int{{0, 1, 2, 3}},
+		},
+	} {
+		data := Combinations(test.n, test.k)
+		if !intSosMatch(data, test.data) {
+			t.Errorf("Cas %v: Generated combinations mismatch. Got %v, want %v.", cas, data, test.data)
+		}
+	}
+}
+
+func TestCombinationGenerator(t *testing.T) {
+	for n := 0; n <= 10; n++ {
+		for k := 1; k <= n; k++ {
+			combinations := Combinations(n, k)
+			cg := NewCombinationGenerator(n, k)
+			genCombs := make([][]int, 0, len(combinations))
+			for cg.Next() {
+				genCombs = append(genCombs, cg.Combination(nil))
+			}
+			if !intSosMatch(combinations, genCombs) {
+				t.Errorf("Combinations and generated combinations do not match. n = %v, k = %v", n, k)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/combin/doc.go b/vendor/gonum.org/v1/gonum/stat/combin/doc.go
new file mode 100644
index 00000000..935ccdb8
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/combin/doc.go
@@ -0,0 +1,7 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package combin implements routines involving combinatorics (permutations,
+// combinations, etc.).
+package combin // import "gonum.org/v1/gonum/stat/combin"
diff --git a/vendor/gonum.org/v1/gonum/stat/distmat/doc.go b/vendor/gonum.org/v1/gonum/stat/distmat/doc.go
new file mode 100644
index 00000000..baca067d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distmat/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package distmat provides probability distributions over matrices.
+package distmat // import "gonum.org/v1/gonum/stat/distmat"
diff --git a/vendor/gonum.org/v1/gonum/stat/distmat/general.go b/vendor/gonum.org/v1/gonum/stat/distmat/general.go
new file mode 100644
index 00000000..21bbc95d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distmat/general.go
@@ -0,0 +1,7 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distmat
+
+var badDim = "distmat: dimension mismatch"
diff --git a/vendor/gonum.org/v1/gonum/stat/distmat/wishart.go b/vendor/gonum.org/v1/gonum/stat/distmat/wishart.go
new file mode 100644
index 00000000..97992ce0
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distmat/wishart.go
@@ -0,0 +1,209 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distmat
+
+import (
+	"math"
+	"math/rand"
+	"sync"
+
+	"gonum.org/v1/gonum/mat"
+	"gonum.org/v1/gonum/mathext"
+	"gonum.org/v1/gonum/stat/distuv"
+)
+
+// Wishart is a distribution over d×d positive symmetric definite matrices. It
+// is parametrized by a scalar degrees of freedom parameter ν and a d×d positive
+// definite matrix V.
+//
+// The Wishart PDF is given by
+//  p(X) = [|X|^((ν-d-1)/2) * exp(-tr(V^-1 * X)/2)] / [2^(ν*d/2) * |V|^(ν/2) * Γ_d(ν/2)]
+// where X is a d×d PSD matrix, ν > d-1, |·| denotes the determinant, tr is the
+// trace and Γ_d is the multivariate gamma function.
+//
+// See https://en.wikipedia.org/wiki/Wishart_distribution for more information.
+type Wishart struct {
+	nu  float64
+	src *rand.Rand
+
+	dim     int
+	cholv   mat.Cholesky
+	logdetv float64
+	upper   mat.TriDense
+
+	once sync.Once
+	v    *mat.SymDense // only stored if needed
+}
+
+// NewWishart returns a new Wishart distribution with the given shape matrix and
+// degrees of freedom parameter. NewWishart returns whether the creation was
+// successful.
+//
+// NewWishart panics if nu <= d - 1 where d is the order of v.
+func NewWishart(v mat.Symmetric, nu float64, src *rand.Rand) (*Wishart, bool) {
+	dim := v.Symmetric()
+	if nu <= float64(dim-1) {
+		panic("wishart: nu must be greater than dim-1")
+	}
+	var chol mat.Cholesky
+	ok := chol.Factorize(v)
+	if !ok {
+		return nil, false
+	}
+
+	var u mat.TriDense
+	chol.UTo(&u)
+
+	w := &Wishart{
+		nu:  nu,
+		src: src,
+
+		dim:     dim,
+		cholv:   chol,
+		logdetv: chol.LogDet(),
+		upper:   u,
+	}
+	return w, true
+}
+
+// MeanSym returns the mean matrix of the distribution as a symmetric matrix.
+// If x is nil, a new matrix is allocated and returned. If x is not nil, the
+// result is stored in-place into x and MeanSym will panic if the order of x
+// is not equal to the order of the receiver.
+func (w *Wishart) MeanSym(x *mat.SymDense) *mat.SymDense {
+	if x == nil {
+		x = mat.NewSymDense(w.dim, nil)
+	}
+	d := x.Symmetric()
+	if d != w.dim {
+		panic(badDim)
+	}
+	w.setV()
+	x.CopySym(w.v)
+	x.ScaleSym(w.nu, x)
+	return x
+}
+
+// ProbSym returns the probability of the symmetric matrix x. If x is not positive
+// definite (the Cholesky decomposition fails), it has 0 probability.
+func (w *Wishart) ProbSym(x mat.Symmetric) float64 {
+	return math.Exp(w.LogProbSym(x))
+}
+
+// LogProbSym returns the log of the probability of the input symmetric matrix.
+//
+// LogProbSym returns -∞ if the input matrix is not positive definite (the Cholesky
+// decomposition fails).
+func (w *Wishart) LogProbSym(x mat.Symmetric) float64 {
+	dim := x.Symmetric()
+	if dim != w.dim {
+		panic(badDim)
+	}
+	var chol mat.Cholesky
+	ok := chol.Factorize(x)
+	if !ok {
+		return math.Inf(-1)
+	}
+	return w.logProbSymChol(&chol)
+}
+
+// LogProbSymChol returns the log of the probability of the input symmetric matrix
+// given its Cholesky decomposition.
+func (w *Wishart) LogProbSymChol(cholX *mat.Cholesky) float64 {
+	dim := cholX.Size()
+	if dim != w.dim {
+		panic(badDim)
+	}
+	return w.logProbSymChol(cholX)
+}
+
+func (w *Wishart) logProbSymChol(cholX *mat.Cholesky) float64 {
+	// The PDF is
+	//  p(X) = [|X|^((ν-d-1)/2) * exp(-tr(V^-1 * X)/2)] / [2^(ν*d/2) * |V|^(ν/2) * Γ_d(ν/2)]
+	// The LogPDF is thus
+	//  (ν-d-1)/2 * log(|X|) - tr(V^-1 * X)/2  - (ν*d/2)*log(2) - ν/2 * log(|V|) - log(Γ_d(ν/2))
+	logdetx := cholX.LogDet()
+
+	// Compute tr(V^-1 * X), using the fact that X = U^T * U.
+	var u mat.TriDense
+	cholX.UTo(&u)
+
+	var vinvx mat.Dense
+	err := w.cholv.Solve(&vinvx, u.T())
+	if err != nil {
+		return math.Inf(-1)
+	}
+	vinvx.Mul(&vinvx, &u)
+	tr := mat.Trace(&vinvx)
+
+	fnu := float64(w.nu)
+	fdim := float64(w.dim)
+
+	return 0.5*((fnu-fdim-1)*logdetx-tr-fnu*fdim*math.Ln2-fnu*w.logdetv) - mathext.MvLgamma(0.5*fnu, w.dim)
+}
+
+// RandSym generates a random symmetric matrix from the distribution.
+func (w *Wishart) RandSym(x *mat.SymDense) *mat.SymDense {
+	if x == nil {
+		x = &mat.SymDense{}
+	}
+	var c mat.Cholesky
+	w.RandChol(&c)
+	c.To(x)
+	return x
+}
+
+// RandChol generates the Cholesky decomposition of a random matrix from the distribution.
+func (w *Wishart) RandChol(c *mat.Cholesky) *mat.Cholesky {
+	// TODO(btracey): Modify the code if the underlying data from c is exposed
+	// to avoid the dim^2 allocation here.
+
+	// Use the Bartlett Decomposition, which says that
+	//  X ~ L A A^T L^T
+	// Where A is a lower triangular matrix in which the diagonal of A is
+	// generated from the square roots of χ^2 random variables, and the
+	// off-diagonals are generated from standard normal variables.
+	// The above gives the cholesky decomposition of X, where L_x = L A.
+	//
+	// mat64 works with the upper triagular decomposition, so we would like to do
+	// the same. We can instead say that
+	//  U_x = L_x^T = (L * A)^T = A^T * L^T = A^T * U
+	// Instead, generate A^T, by using the procedure above, except as an upper
+	// triangular matrix.
+	norm := distuv.Normal{
+		Mu:     0,
+		Sigma:  1,
+		Source: w.src,
+	}
+
+	t := mat.NewTriDense(w.dim, mat.Upper, nil)
+	for i := 0; i < w.dim; i++ {
+		v := distuv.ChiSquared{
+			K:   w.nu - float64(i),
+			Src: w.src,
+		}.Rand()
+		t.SetTri(i, i, math.Sqrt(v))
+	}
+	for i := 0; i < w.dim; i++ {
+		for j := i + 1; j < w.dim; j++ {
+			t.SetTri(i, j, norm.Rand())
+		}
+	}
+
+	t.MulTri(t, &w.upper)
+	if c == nil {
+		c = &mat.Cholesky{}
+	}
+	c.SetFromU(t)
+	return c
+}
+
+// setV computes and stores the covariance matrix of the distribution.
+func (w *Wishart) setV() {
+	w.once.Do(func() {
+		w.v = mat.NewSymDense(w.dim, nil)
+		w.cholv.To(w.v)
+	})
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distmat/wishart_test.go b/vendor/gonum.org/v1/gonum/stat/distmat/wishart_test.go
new file mode 100644
index 00000000..96350c64
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distmat/wishart_test.go
@@ -0,0 +1,129 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distmat
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+)
+
+func TestWishart(t *testing.T) {
+	for c, test := range []struct {
+		v   *mat.SymDense
+		nu  float64
+		xs  []*mat.SymDense
+		lps []float64
+	}{
+		// Logprob data compared with scipy.
+		{
+			v:  mat.NewSymDense(2, []float64{1, 0, 0, 1}),
+			nu: 4,
+			xs: []*mat.SymDense{
+				mat.NewSymDense(2, []float64{0.9, 0.1, 0.1, 0.9}),
+			},
+			lps: []float64{-4.2357432031863409},
+		},
+		{
+			v:  mat.NewSymDense(2, []float64{0.8, -0.2, -0.2, 0.7}),
+			nu: 5,
+			xs: []*mat.SymDense{
+				mat.NewSymDense(2, []float64{0.9, 0.1, 0.1, 0.9}),
+				mat.NewSymDense(2, []float64{0.3, -0.1, -0.1, 0.7}),
+			},
+			lps: []float64{-4.2476495605333575, -4.9993285370378633},
+		},
+		{
+			v:  mat.NewSymDense(3, []float64{0.8, 0.3, 0.1, 0.3, 0.7, -0.1, 0.1, -0.1, 7}),
+			nu: 5,
+			xs: []*mat.SymDense{
+				mat.NewSymDense(3, []float64{1, 0.2, -0.3, 0.2, 0.6, -0.2, -0.3, -0.2, 6}),
+			},
+			lps: []float64{-11.010982249229421},
+		},
+	} {
+		w, ok := NewWishart(test.v, test.nu, nil)
+		if !ok {
+			panic("bad test")
+		}
+		for i, x := range test.xs {
+			lp := w.LogProbSym(x)
+
+			var chol mat.Cholesky
+			ok := chol.Factorize(x)
+			if !ok {
+				panic("bad test")
+			}
+			lpc := w.LogProbSymChol(&chol)
+
+			if math.Abs(lp-lpc) > 1e-14 {
+				t.Errorf("Case %d, test %d: probability mismatch between chol and not", c, i)
+			}
+			if !floats.EqualWithinAbsOrRel(lp, test.lps[i], 1e-14, 1e-14) {
+				t.Errorf("Case %d, test %d: got %v, want %v", c, i, lp, test.lps[i])
+			}
+		}
+
+		ch := w.RandChol(nil)
+		w.RandChol(ch)
+
+		s := w.RandSym(nil)
+		w.RandSym(s)
+
+	}
+}
+
+func TestWishartRand(t *testing.T) {
+	for c, test := range []struct {
+		v       *mat.SymDense
+		nu      float64
+		samples int
+		tol     float64
+	}{
+		{
+			v:       mat.NewSymDense(2, []float64{0.8, -0.2, -0.2, 0.7}),
+			nu:      5,
+			samples: 30000,
+			tol:     3e-2,
+		},
+		{
+			v:       mat.NewSymDense(3, []float64{0.8, 0.3, 0.1, 0.3, 0.7, -0.1, 0.1, -0.1, 7}),
+			nu:      5,
+			samples: 30000,
+			tol:     3e-2,
+		},
+		{
+			v: mat.NewSymDense(4, []float64{
+				0.8, 0.3, 0.1, -0.2,
+				0.3, 0.7, -0.1, 0.4,
+				0.1, -0.1, 7, 1,
+				-0.2, -0.1, 1, 6}),
+			nu:      6,
+			samples: 30000,
+			tol:     1e-1,
+		},
+	} {
+		rnd := rand.New(rand.NewSource(1))
+		dim := test.v.Symmetric()
+		w, ok := NewWishart(test.v, test.nu, rnd)
+		if !ok {
+			panic("bad test")
+		}
+		mean := mat.NewSymDense(dim, nil)
+		x := mat.NewSymDense(dim, nil)
+		for i := 0; i < test.samples; i++ {
+			w.RandSym(x)
+			x.ScaleSym(1/float64(test.samples), x)
+			mean.AddSym(mean, x)
+		}
+		trueMean := w.MeanSym(nil)
+		if !mat.EqualApprox(trueMean, mean, test.tol) {
+			t.Errorf("Case %d: Mismatch between estimated and true mean. Got\n%0.4v\nWant\n%0.4v\n", c, mat.Formatted(mean), mat.Formatted(trueMean))
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distmv/dirichlet.go b/vendor/gonum.org/v1/gonum/stat/distmv/dirichlet.go
new file mode 100644
index 00000000..fbf2128f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distmv/dirichlet.go
@@ -0,0 +1,144 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distmv
+
+import (
+	"math"
+	"math/rand"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+	"gonum.org/v1/gonum/stat/distuv"
+)
+
+// Dirichlet implements the Dirichlet probability distribution.
+//
+// The Dirichlet distribution is a continuous probability distribution that
+// generates elements over the probability simplex, i.e. ||x||_1 = 1. The Dirichlet
+// distribution is the conjugate prior to the categorical distribution and the
+// multivariate version of the beta distribution. The probability of a point x is
+//  1/Beta(α) \prod_i x_i^(α_i - 1)
+// where Beta(α) is the multivariate Beta function (see the mathext package).
+//
+// For more information see https://en.wikipedia.org/wiki/Dirichlet_distribution
+type Dirichlet struct {
+	alpha []float64
+	dim   int
+	src   *rand.Rand
+
+	lbeta    float64
+	sumAlpha float64
+}
+
+// NewDirichlet creates a new dirichlet distribution with the given parameters alpha.
+// NewDirichlet will panic if len(alpha) == 0, or if any alpha is <= 0.
+func NewDirichlet(alpha []float64, src *rand.Rand) *Dirichlet {
+	dim := len(alpha)
+	if dim == 0 {
+		panic(badZeroDimension)
+	}
+	for _, v := range alpha {
+		if v <= 0 {
+			panic("dirichlet: non-positive alpha")
+		}
+	}
+	a := make([]float64, len(alpha))
+	copy(a, alpha)
+	d := &Dirichlet{
+		alpha: a,
+		dim:   dim,
+		src:   src,
+	}
+	d.lbeta, d.sumAlpha = d.genLBeta(a)
+	return d
+}
+
+// CovarianceMatrix returns the covariance matrix of the distribution. Upon
+// return, the value at element {i, j} of the covariance matrix is equal to
+// the covariance of the i^th and j^th variables.
+//  covariance(i, j) = E[(x_i - E[x_i])(x_j - E[x_j])]
+// If the input matrix is nil a new matrix is allocated, otherwise the result
+// is stored in-place into the input.
+func (d *Dirichlet) CovarianceMatrix(cov *mat.SymDense) *mat.SymDense {
+	if cov == nil {
+		cov = mat.NewSymDense(d.Dim(), nil)
+	} else if cov.Symmetric() == 0 {
+		*cov = *(cov.GrowSquare(d.dim).(*mat.SymDense))
+	} else if cov.Symmetric() != d.dim {
+		panic("normal: input matrix size mismatch")
+	}
+	scale := 1 / (d.sumAlpha * d.sumAlpha * (d.sumAlpha + 1))
+	for i := 0; i < d.dim; i++ {
+		ai := d.alpha[i]
+		v := ai * (d.sumAlpha - ai) * scale
+		cov.SetSym(i, i, v)
+		for j := i + 1; j < d.dim; j++ {
+			aj := d.alpha[j]
+			v := -ai * aj * scale
+			cov.SetSym(i, j, v)
+		}
+	}
+	return cov
+}
+
+// genLBeta computes the generalized LBeta function.
+func (d *Dirichlet) genLBeta(alpha []float64) (lbeta, sumAlpha float64) {
+	for _, alpha := range d.alpha {
+		lg, _ := math.Lgamma(alpha)
+		lbeta += lg
+		sumAlpha += alpha
+	}
+	lg, _ := math.Lgamma(sumAlpha)
+	return lbeta - lg, sumAlpha
+}
+
+// Dim returns the dimension of the distribution.
+func (d *Dirichlet) Dim() int {
+	return d.dim
+}
+
+// LogProb computes the log of the pdf of the point x.
+//
+// It does not check that ||x||_1 = 1.
+func (d *Dirichlet) LogProb(x []float64) float64 {
+	dim := d.dim
+	if len(x) != dim {
+		panic(badSizeMismatch)
+	}
+	var lprob float64
+	for i, x := range x {
+		lprob += (d.alpha[i] - 1) * math.Log(x)
+	}
+	lprob -= d.lbeta
+	return lprob
+}
+
+// Mean returns the mean of the probability distribution at x. If the
+// input argument is nil, a new slice will be allocated, otherwise the result
+// will be put in-place into the receiver.
+func (d *Dirichlet) Mean(x []float64) []float64 {
+	x = reuseAs(x, d.dim)
+	copy(x, d.alpha)
+	floats.Scale(1/d.sumAlpha, x)
+	return x
+}
+
+// Prob computes the value of the probability density function at x.
+func (d *Dirichlet) Prob(x []float64) float64 {
+	return math.Exp(d.LogProb(x))
+}
+
+// Rand generates a random number according to the distributon.
+// If the input slice is nil, new memory is allocated, otherwise the result is stored
+// in place.
+func (d *Dirichlet) Rand(x []float64) []float64 {
+	x = reuseAs(x, d.dim)
+	for i := range x {
+		x[i] = distuv.Gamma{Alpha: d.alpha[i], Beta: 1, Source: d.src}.Rand()
+	}
+	sum := floats.Sum(x)
+	floats.Scale(1/sum, x)
+	return x
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distmv/dirichlet_test.go b/vendor/gonum.org/v1/gonum/stat/distmv/dirichlet_test.go
new file mode 100644
index 00000000..43f77007
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distmv/dirichlet_test.go
@@ -0,0 +1,67 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distmv
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/mat"
+)
+
+func TestDirichlet(t *testing.T) {
+	// Data from Scipy.
+	for cas, test := range []struct {
+		Dir  *Dirichlet
+		x    []float64
+		prob float64
+	}{
+		{
+			NewDirichlet([]float64{1, 1, 1}, nil),
+			[]float64{0.2, 0.3, 0.5},
+			2.0,
+		},
+		{
+			NewDirichlet([]float64{0.6, 10, 8.7}, nil),
+			[]float64{0.2, 0.3, 0.5},
+			0.24079612737071665,
+		},
+	} {
+		p := test.Dir.Prob(test.x)
+		if math.Abs(p-test.prob) > 1e-14 {
+			t.Errorf("Probablility mismatch. Case %v. Got %v, want %v", cas, p, test.prob)
+		}
+	}
+
+	rnd := rand.New(rand.NewSource(1))
+	for cas, test := range []struct {
+		Dir *Dirichlet
+	}{
+		{
+			NewDirichlet([]float64{1, 1, 1}, rnd),
+		},
+		{
+			NewDirichlet([]float64{2, 3}, rnd),
+		},
+		{
+			NewDirichlet([]float64{0.2, 0.3}, rnd),
+		},
+		{
+			NewDirichlet([]float64{0.2, 4}, rnd),
+		},
+		{
+			NewDirichlet([]float64{0.1, 4, 20}, rnd),
+		},
+	} {
+		const n = 1e5
+		d := test.Dir
+		dim := d.Dim()
+		x := mat.NewDense(n, dim, nil)
+		generateSamples(x, d)
+		checkMean(t, cas, x, d, 1e-2)
+		checkCov(t, cas, x, d, 1e-2)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distmv/doc.go b/vendor/gonum.org/v1/gonum/stat/distmv/doc.go
new file mode 100644
index 00000000..c126be97
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distmv/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package distmv provides multivariate random distribution types.
+package distmv // import "gonum.org/v1/gonum/stat/distmv"
diff --git a/vendor/gonum.org/v1/gonum/stat/distmv/general.go b/vendor/gonum.org/v1/gonum/stat/distmv/general.go
new file mode 100644
index 00000000..f473efdf
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distmv/general.go
@@ -0,0 +1,30 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distmv
+
+var (
+	badQuantile      = "distmv: quantile not between 0 and 1"
+	badReceiver      = "distmv: input slice is not nil or the correct length"
+	badSizeMismatch  = "distmv: size mismatch"
+	badZeroDimension = "distmv: zero dimensional input"
+	nonPosDimension  = "distmv: non-positive dimension input"
+)
+
+const logTwoPi = 1.8378770664093454835606594728112352797227949472755668
+
+// useAs gets a slice of size n. If len(x) == n, x is returned, if len(x) == 0
+// then a slice is returned of length n.
+func reuseAs(x []float64, n int) []float64 {
+	if len(x) == n {
+		return x
+	}
+	if len(x) == 0 {
+		if cap(x) >= n {
+			return x[:n]
+		}
+		return make([]float64, n)
+	}
+	panic(badReceiver)
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distmv/general_test.go b/vendor/gonum.org/v1/gonum/stat/distmv/general_test.go
new file mode 100644
index 00000000..05e65f7b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distmv/general_test.go
@@ -0,0 +1,96 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distmv
+
+import (
+	"math"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+	"gonum.org/v1/gonum/stat"
+)
+
+type prober interface {
+	Prob(x []float64) float64
+	LogProb(x []float64) float64
+}
+
+type probCase struct {
+	dist    prober
+	loc     []float64
+	logProb float64
+}
+
+func testProbability(t *testing.T, cases []probCase) {
+	for _, test := range cases {
+		logProb := test.dist.LogProb(test.loc)
+		if math.Abs(logProb-test.logProb) > 1e-14 {
+			t.Errorf("LogProb mismatch: want: %v, got: %v", test.logProb, logProb)
+		}
+		prob := test.dist.Prob(test.loc)
+		if math.Abs(prob-math.Exp(test.logProb)) > 1e-14 {
+			t.Errorf("Prob mismatch: want: %v, got: %v", math.Exp(test.logProb), prob)
+		}
+	}
+}
+
+func generateSamples(x *mat.Dense, r Rander) {
+	n, _ := x.Dims()
+	for i := 0; i < n; i++ {
+		r.Rand(x.RawRowView(i))
+	}
+}
+
+type Meaner interface {
+	Mean([]float64) []float64
+}
+
+func checkMean(t *testing.T, cas int, x *mat.Dense, m Meaner, tol float64) {
+	mean := m.Mean(nil)
+
+	// Check that the answer is identical when using nil or non-nil.
+	mean2 := make([]float64, len(mean))
+	m.Mean(mean2)
+	if !floats.Equal(mean, mean2) {
+		t.Errorf("Mean mismatch when providing nil and slice. Case %v", cas)
+	}
+
+	// Check that the mean matches the samples.
+	r, _ := x.Dims()
+	col := make([]float64, r)
+	meanEst := make([]float64, len(mean))
+	for i := range meanEst {
+		meanEst[i] = stat.Mean(mat.Col(col, i, x), nil)
+	}
+	if !floats.EqualApprox(mean, meanEst, tol) {
+		t.Errorf("Returned mean and sample mean mismatch. Case %v. Empirical %v, returned %v", cas, meanEst, mean)
+	}
+}
+
+type Cover interface {
+	CovarianceMatrix(*mat.SymDense) *mat.SymDense
+}
+
+func checkCov(t *testing.T, cas int, x *mat.Dense, c Cover, tol float64) {
+	cov := c.CovarianceMatrix(nil)
+	n := cov.Symmetric()
+	cov2 := mat.NewSymDense(n, nil)
+	c.CovarianceMatrix(cov2)
+	if !mat.Equal(cov, cov2) {
+		t.Errorf("Cov mismatch when providing nil and matrix. Case %v", cas)
+	}
+	var cov3 mat.SymDense
+	c.CovarianceMatrix(&cov3)
+	if !mat.Equal(cov, &cov3) {
+		t.Errorf("Cov mismatch when providing zero matrix. Case %v", cas)
+	}
+
+	// Check that the covariance matrix matches the samples
+	covEst := stat.CovarianceMatrix(nil, x, nil)
+	if !mat.EqualApprox(covEst, cov, tol) {
+		t.Errorf("Return cov and sample cov mismatch. Cas %v.\nGot:\n%0.4v\nWant:\n%0.4v", cas, mat.Formatted(cov), mat.Formatted(covEst))
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distmv/interfaces.go b/vendor/gonum.org/v1/gonum/stat/distmv/interfaces.go
new file mode 100644
index 00000000..57411933
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distmv/interfaces.go
@@ -0,0 +1,33 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distmv
+
+// Quantiler returns the multi-dimensional inverse cumulative distribution function.
+// len(x) must equal len(p), and if x is non-nil, len(x) must also equal len(p).
+// If x is nil, a new slice will be allocated and returned, otherwise the quantile
+// will be stored in-place into x. All of the values of p must be between 0 and 1,
+// or Quantile will panic.
+type Quantiler interface {
+	Quantile(x, p []float64) []float64
+}
+
+// LogProber computes the log of the probability of the point x.
+type LogProber interface {
+	LogProb(x []float64) float64
+}
+
+// Rander generates a random number according to the distributon.
+// If the input is non-nil, len(x) must equal len(p) and the dimension of the distribution,
+// otherwise Quantile will panic.
+// If the input is nil, a new slice will be allocated and returned.
+type Rander interface {
+	Rand(x []float64) []float64
+}
+
+// RandLogProber is both a Rander and a LogProber.
+type RandLogProber interface {
+	Rander
+	LogProber
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distmv/normal.go b/vendor/gonum.org/v1/gonum/stat/distmv/normal.go
new file mode 100644
index 00000000..1d5098fd
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distmv/normal.go
@@ -0,0 +1,345 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distmv
+
+import (
+	"math"
+	"math/rand"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+	"gonum.org/v1/gonum/stat"
+	"gonum.org/v1/gonum/stat/distuv"
+)
+
+var (
+	badInputLength = "distmv: input slice length mismatch"
+)
+
+// Normal is a multivariate normal distribution (also known as the multivariate
+// Gaussian distribution). Its pdf in k dimensions is given by
+//  (2 π)^(-k/2) |Σ|^(-1/2) exp(-1/2 (x-μ)'Σ^-1(x-μ))
+// where μ is the mean vector and Σ the covariance matrix. Σ must be symmetric
+// and positive definite. Use NewNormal to construct.
+type Normal struct {
+	mu []float64
+
+	sigma mat.SymDense
+
+	chol       mat.Cholesky
+	lower      mat.TriDense
+	logSqrtDet float64
+	dim        int
+
+	src *rand.Rand
+}
+
+// NewNormal creates a new Normal with the given mean and covariance matrix.
+// NewNormal panics if len(mu) == 0, or if len(mu) != sigma.N. If the covariance
+// matrix is not positive-definite, the returned boolean is false.
+func NewNormal(mu []float64, sigma mat.Symmetric, src *rand.Rand) (*Normal, bool) {
+	if len(mu) == 0 {
+		panic(badZeroDimension)
+	}
+	dim := sigma.Symmetric()
+	if dim != len(mu) {
+		panic(badSizeMismatch)
+	}
+	n := &Normal{
+		src: src,
+		dim: dim,
+		mu:  make([]float64, dim),
+	}
+	copy(n.mu, mu)
+	ok := n.chol.Factorize(sigma)
+	if !ok {
+		return nil, false
+	}
+	n.sigma = *mat.NewSymDense(dim, nil)
+	n.sigma.CopySym(sigma)
+	n.chol.LTo(&n.lower)
+	n.logSqrtDet = 0.5 * n.chol.LogDet()
+	return n, true
+}
+
+// NewNormalChol creates a new Normal distribution with the given mean and
+// covariance matrix represented by its Cholesky decomposition. NewNormalChol
+// panics if len(mu) is not equal to chol.Size().
+func NewNormalChol(mu []float64, chol *mat.Cholesky, src *rand.Rand) *Normal {
+	dim := len(mu)
+	if dim != chol.Size() {
+		panic(badSizeMismatch)
+	}
+	n := &Normal{
+		src: src,
+		dim: dim,
+		mu:  make([]float64, dim),
+	}
+	n.chol.Clone(chol)
+	copy(n.mu, mu)
+	chol.LTo(&n.lower)
+	n.logSqrtDet = 0.5 * n.chol.LogDet()
+	return n
+}
+
+// NewNormalPrecision creates a new Normal distribution with the given mean and
+// precision matrix (inverse of the covariance matrix). NewNormalPrecision
+// panics if len(mu) is not equal to prec.Symmetric(). If the precision matrix
+// is not positive-definite, NewNormalPrecision returns nil for norm and false
+// for ok.
+func NewNormalPrecision(mu []float64, prec *mat.SymDense, src *rand.Rand) (norm *Normal, ok bool) {
+	if len(mu) == 0 {
+		panic(badZeroDimension)
+	}
+	dim := prec.Symmetric()
+	if dim != len(mu) {
+		panic(badSizeMismatch)
+	}
+	// TODO(btracey): Computing a matrix inverse is generally numerically instable.
+	// This only has to compute the inverse of a positive definite matrix, which
+	// is much better, but this still loses precision. It is worth considering if
+	// instead the precision matrix should be stored explicitly and used instead
+	// of the Cholesky decomposition of the covariance matrix where appropriate.
+	var chol mat.Cholesky
+	ok = chol.Factorize(prec)
+	if !ok {
+		return nil, false
+	}
+	var sigma mat.SymDense
+	chol.InverseTo(&sigma)
+	return NewNormal(mu, &sigma, src)
+}
+
+// ConditionNormal returns the Normal distribution that is the receiver conditioned
+// on the input evidence. The returned multivariate normal has dimension
+// n - len(observed), where n is the dimension of the original receiver. The updated
+// mean and covariance are
+//  mu = mu_un + sigma_{ob,un}^T * sigma_{ob,ob}^-1 (v - mu_ob)
+//  sigma = sigma_{un,un} - sigma_{ob,un}^T * sigma_{ob,ob}^-1 * sigma_{ob,un}
+// where mu_un and mu_ob are the original means of the unobserved and observed
+// variables respectively, sigma_{un,un} is the unobserved subset of the covariance
+// matrix, sigma_{ob,ob} is the observed subset of the covariance matrix, and
+// sigma_{un,ob} are the cross terms. The elements of x_2 have been observed with
+// values v. The dimension order is preserved during conditioning, so if the value
+// of dimension 1 is observed, the returned normal represents dimensions {0, 2, ...}
+// of the original Normal distribution.
+//
+// ConditionNormal returns {nil, false} if there is a failure during the update.
+// Mathematically this is impossible, but can occur with finite precision arithmetic.
+func (n *Normal) ConditionNormal(observed []int, values []float64, src *rand.Rand) (*Normal, bool) {
+	if len(observed) == 0 {
+		panic("normal: no observed value")
+	}
+	if len(observed) != len(values) {
+		panic(badInputLength)
+	}
+	for _, v := range observed {
+		if v < 0 || v >= n.Dim() {
+			panic("normal: observed value out of bounds")
+		}
+	}
+
+	_, mu1, sigma11 := studentsTConditional(observed, values, math.Inf(1), n.mu, &n.sigma)
+	if mu1 == nil {
+		return nil, false
+	}
+	return NewNormal(mu1, sigma11, src)
+}
+
+// CovarianceMatrix returns the covariance matrix of the distribution. Upon
+// return, the value at element {i, j} of the covariance matrix is equal to
+// the covariance of the i^th and j^th variables.
+//  covariance(i, j) = E[(x_i - E[x_i])(x_j - E[x_j])]
+// If the input matrix is nil a new matrix is allocated, otherwise the result
+// is stored in-place into the input.
+func (n *Normal) CovarianceMatrix(s *mat.SymDense) *mat.SymDense {
+	if s == nil {
+		s = mat.NewSymDense(n.Dim(), nil)
+	}
+	sn := s.Symmetric()
+	if sn != n.Dim() {
+		panic("normal: input matrix size mismatch")
+	}
+	s.CopySym(&n.sigma)
+	return s
+}
+
+// Dim returns the dimension of the distribution.
+func (n *Normal) Dim() int {
+	return n.dim
+}
+
+// Entropy returns the differential entropy of the distribution.
+func (n *Normal) Entropy() float64 {
+	return float64(n.dim)/2*(1+logTwoPi) + n.logSqrtDet
+}
+
+// LogProb computes the log of the pdf of the point x.
+func (n *Normal) LogProb(x []float64) float64 {
+	dim := n.dim
+	if len(x) != dim {
+		panic(badSizeMismatch)
+	}
+	c := -0.5*float64(dim)*logTwoPi - n.logSqrtDet
+	dst := stat.Mahalanobis(mat.NewVecDense(dim, x), mat.NewVecDense(dim, n.mu), &n.chol)
+	return c - 0.5*dst*dst
+}
+
+// MarginalNormal returns the marginal distribution of the given input variables.
+// That is, MarginalNormal returns
+//  p(x_i) = \int_{x_o} p(x_i | x_o) p(x_o) dx_o
+// where x_i are the dimensions in the input, and x_o are the remaining dimensions.
+// See https://en.wikipedia.org/wiki/Marginal_distribution for more information.
+//
+// The input src is passed to the call to NewNormal.
+func (n *Normal) MarginalNormal(vars []int, src *rand.Rand) (*Normal, bool) {
+	newMean := make([]float64, len(vars))
+	for i, v := range vars {
+		newMean[i] = n.mu[v]
+	}
+	var s mat.SymDense
+	s.SubsetSym(&n.sigma, vars)
+	return NewNormal(newMean, &s, src)
+}
+
+// MarginalNormalSingle returns the marginal of the given input variable.
+// That is, MarginalNormal returns
+//  p(x_i) = \int_{x_¬i} p(x_i | x_¬i) p(x_¬i) dx_¬i
+// where i is the input index.
+// See https://en.wikipedia.org/wiki/Marginal_distribution for more information.
+//
+// The input src is passed to the constructed distuv.Normal.
+func (n *Normal) MarginalNormalSingle(i int, src *rand.Rand) distuv.Normal {
+	return distuv.Normal{
+		Mu:     n.mu[i],
+		Sigma:  math.Sqrt(n.sigma.At(i, i)),
+		Source: src,
+	}
+}
+
+// Mean returns the mean of the probability distribution at x. If the
+// input argument is nil, a new slice will be allocated, otherwise the result
+// will be put in-place into the receiver.
+func (n *Normal) Mean(x []float64) []float64 {
+	x = reuseAs(x, n.dim)
+	copy(x, n.mu)
+	return x
+}
+
+// Prob computes the value of the probability density function at x.
+func (n *Normal) Prob(x []float64) float64 {
+	return math.Exp(n.LogProb(x))
+}
+
+// Quantile returns the multi-dimensional inverse cumulative distribution function.
+// If x is nil, a new slice will be allocated and returned. If x is non-nil,
+// len(x) must equal len(p) and the quantile will be stored in-place into x.
+// All of the values of p must be between 0 and 1, inclusive, or Quantile will panic.
+func (n *Normal) Quantile(x, p []float64) []float64 {
+	dim := n.Dim()
+	if len(p) != dim {
+		panic(badInputLength)
+	}
+	if x == nil {
+		x = make([]float64, dim)
+	}
+	if len(x) != len(p) {
+		panic(badInputLength)
+	}
+
+	// Transform to a standard normal and then transform to a multivariate Gaussian.
+	tmp := make([]float64, len(x))
+	for i, v := range p {
+		tmp[i] = distuv.UnitNormal.Quantile(v)
+	}
+	n.TransformNormal(x, tmp)
+	return x
+}
+
+// Rand generates a random number according to the distributon.
+// If the input slice is nil, new memory is allocated, otherwise the result is stored
+// in place.
+func (n *Normal) Rand(x []float64) []float64 {
+	x = reuseAs(x, n.dim)
+	tmp := make([]float64, n.dim)
+	if n.src == nil {
+		for i := range x {
+			tmp[i] = rand.NormFloat64()
+		}
+	} else {
+		for i := range x {
+			tmp[i] = n.src.NormFloat64()
+		}
+	}
+	n.transformNormal(x, tmp)
+	return x
+}
+
+// ScoreInput returns the gradient of the log-probability with respect to the
+// input x. That is, ScoreInput computes
+//  ∇_x log(p(x))
+// If score is nil, a new slice will be allocated and returned. If score is of
+// length the dimension of Normal, then the result will be put in-place into score.
+// If neither of these is true, ScoreInput will panic.
+func (n *Normal) ScoreInput(score, x []float64) []float64 {
+	// Normal log probability is
+	//  c - 0.5*(x-μ)' Σ^-1 (x-μ).
+	// So the derivative is just
+	//  -Σ^-1 (x-μ).
+	if len(x) != n.Dim() {
+		panic(badInputLength)
+	}
+	if score == nil {
+		score = make([]float64, len(x))
+	}
+	if len(score) != len(x) {
+		panic(badSizeMismatch)
+	}
+	tmp := make([]float64, len(x))
+	copy(tmp, x)
+	floats.Sub(tmp, n.mu)
+
+	n.chol.SolveVec(mat.NewVecDense(len(score), score), mat.NewVecDense(len(tmp), tmp))
+	floats.Scale(-1, score)
+	return score
+}
+
+// SetMean changes the mean of the normal distribution. SetMean panics if len(mu)
+// does not equal the dimension of the normal distribution.
+func (n *Normal) SetMean(mu []float64) {
+	if len(mu) != n.Dim() {
+		panic(badSizeMismatch)
+	}
+	copy(n.mu, mu)
+}
+
+// TransformNormal transforms the vector, normal, generated from a standard
+// multidimensional normal into a vector that has been generated under the
+// distribution of the receiver.
+//
+// If dst is non-nil, the result will be stored into dst, otherwise a new slice
+// will be allocated. TransformNormal will panic if the length of normal is not
+// the dimension of the receiver, or if dst is non-nil and len(dist) != len(normal).
+func (n *Normal) TransformNormal(dst, normal []float64) []float64 {
+	if len(normal) != n.dim {
+		panic(badInputLength)
+	}
+	dst = reuseAs(dst, n.dim)
+	if len(dst) != len(normal) {
+		panic(badInputLength)
+	}
+	n.transformNormal(dst, normal)
+	return dst
+}
+
+// transformNormal performs the same operation as TransformNormal except no
+// safety checks are performed and both input slices must be non-nil.
+func (n *Normal) transformNormal(dst, normal []float64) []float64 {
+	srcVec := mat.NewVecDense(n.dim, normal)
+	dstVec := mat.NewVecDense(n.dim, dst)
+	dstVec.MulVec(&n.lower, srcVec)
+	floats.Add(dst, n.mu)
+	return dst
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distmv/normal_test.go b/vendor/gonum.org/v1/gonum/stat/distmv/normal_test.go
new file mode 100644
index 00000000..88ac12b9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distmv/normal_test.go
@@ -0,0 +1,573 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distmv
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/diff/fd"
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+	"gonum.org/v1/gonum/stat"
+)
+
+type mvTest struct {
+	Mu      []float64
+	Sigma   *mat.SymDense
+	Loc     []float64
+	Logprob float64
+	Prob    float64
+}
+
+func TestNormProbs(t *testing.T) {
+	dist1, ok := NewNormal([]float64{0, 0}, mat.NewSymDense(2, []float64{1, 0, 0, 1}), nil)
+	if !ok {
+		t.Errorf("bad test")
+	}
+	dist2, ok := NewNormal([]float64{6, 7}, mat.NewSymDense(2, []float64{8, 2, 0, 4}), nil)
+	if !ok {
+		t.Errorf("bad test")
+	}
+	testProbability(t, []probCase{
+		{
+			dist:    dist1,
+			loc:     []float64{0, 0},
+			logProb: -1.837877066409345,
+		},
+		{
+			dist:    dist2,
+			loc:     []float64{6, 7},
+			logProb: -3.503979321496947,
+		},
+		{
+			dist:    dist2,
+			loc:     []float64{1, 2},
+			logProb: -7.075407892925519,
+		},
+	})
+}
+
+func TestNewNormalChol(t *testing.T) {
+	for _, test := range []struct {
+		mean []float64
+		cov  *mat.SymDense
+	}{
+		{
+			mean: []float64{2, 3},
+			cov:  mat.NewSymDense(2, []float64{1, 0.1, 0.1, 1}),
+		},
+	} {
+		var chol mat.Cholesky
+		ok := chol.Factorize(test.cov)
+		if !ok {
+			panic("bad test")
+		}
+		n := NewNormalChol(test.mean, &chol, nil)
+		// Generate a random number and calculate probability to ensure things
+		// have been set properly. See issue #426.
+		x := n.Rand(nil)
+		_ = n.Prob(x)
+	}
+}
+
+func TestNormRand(t *testing.T) {
+	for _, test := range []struct {
+		mean []float64
+		cov  []float64
+	}{
+		{
+			mean: []float64{0, 0},
+			cov: []float64{
+				1, 0,
+				0, 1,
+			},
+		},
+		{
+			mean: []float64{0, 0},
+			cov: []float64{
+				1, 0.9,
+				0.9, 1,
+			},
+		},
+		{
+			mean: []float64{6, 7},
+			cov: []float64{
+				5, 0.9,
+				0.9, 2,
+			},
+		},
+	} {
+		dim := len(test.mean)
+		cov := mat.NewSymDense(dim, test.cov)
+		n, ok := NewNormal(test.mean, cov, nil)
+		if !ok {
+			t.Errorf("bad covariance matrix")
+		}
+
+		nSamples := 1000000
+		samps := mat.NewDense(nSamples, dim, nil)
+		for i := 0; i < nSamples; i++ {
+			n.Rand(samps.RawRowView(i))
+		}
+		estMean := make([]float64, dim)
+		for i := range estMean {
+			estMean[i] = stat.Mean(mat.Col(nil, i, samps), nil)
+		}
+		if !floats.EqualApprox(estMean, test.mean, 1e-2) {
+			t.Errorf("Mean mismatch: want: %v, got %v", test.mean, estMean)
+		}
+		estCov := stat.CovarianceMatrix(nil, samps, nil)
+		if !mat.EqualApprox(estCov, cov, 1e-2) {
+			t.Errorf("Cov mismatch: want: %v, got %v", cov, estCov)
+		}
+	}
+}
+
+func TestNormalQuantile(t *testing.T) {
+	for _, test := range []struct {
+		mean []float64
+		cov  []float64
+	}{
+		{
+			mean: []float64{6, 7},
+			cov: []float64{
+				5, 0.9,
+				0.9, 2,
+			},
+		},
+	} {
+		dim := len(test.mean)
+		cov := mat.NewSymDense(dim, test.cov)
+		n, ok := NewNormal(test.mean, cov, nil)
+		if !ok {
+			t.Errorf("bad covariance matrix")
+		}
+
+		nSamples := 1000000
+		rnd := rand.New(rand.NewSource(1))
+		samps := mat.NewDense(nSamples, dim, nil)
+		tmp := make([]float64, dim)
+		for i := 0; i < nSamples; i++ {
+			for j := range tmp {
+				tmp[j] = rnd.Float64()
+			}
+			n.Quantile(samps.RawRowView(i), tmp)
+		}
+		estMean := make([]float64, dim)
+		for i := range estMean {
+			estMean[i] = stat.Mean(mat.Col(nil, i, samps), nil)
+		}
+		if !floats.EqualApprox(estMean, test.mean, 1e-2) {
+			t.Errorf("Mean mismatch: want: %v, got %v", test.mean, estMean)
+		}
+		estCov := stat.CovarianceMatrix(nil, samps, nil)
+		if !mat.EqualApprox(estCov, cov, 1e-2) {
+			t.Errorf("Cov mismatch: want: %v, got %v", cov, estCov)
+		}
+	}
+}
+
+func TestConditionNormal(t *testing.T) {
+	// Uncorrelated values shouldn't influence the updated values.
+	for _, test := range []struct {
+		mu       []float64
+		sigma    *mat.SymDense
+		observed []int
+		values   []float64
+
+		newMu    []float64
+		newSigma *mat.SymDense
+	}{
+		{
+			mu:       []float64{2, 3},
+			sigma:    mat.NewSymDense(2, []float64{2, 0, 0, 5}),
+			observed: []int{0},
+			values:   []float64{10},
+
+			newMu:    []float64{3},
+			newSigma: mat.NewSymDense(1, []float64{5}),
+		},
+		{
+			mu:       []float64{2, 3},
+			sigma:    mat.NewSymDense(2, []float64{2, 0, 0, 5}),
+			observed: []int{1},
+			values:   []float64{10},
+
+			newMu:    []float64{2},
+			newSigma: mat.NewSymDense(1, []float64{2}),
+		},
+		{
+			mu:       []float64{2, 3, 4},
+			sigma:    mat.NewSymDense(3, []float64{2, 0, 0, 0, 5, 0, 0, 0, 10}),
+			observed: []int{1},
+			values:   []float64{10},
+
+			newMu:    []float64{2, 4},
+			newSigma: mat.NewSymDense(2, []float64{2, 0, 0, 10}),
+		},
+		{
+			mu:       []float64{2, 3, 4},
+			sigma:    mat.NewSymDense(3, []float64{2, 0, 0, 0, 5, 0, 0, 0, 10}),
+			observed: []int{0, 1},
+			values:   []float64{10, 15},
+
+			newMu:    []float64{4},
+			newSigma: mat.NewSymDense(1, []float64{10}),
+		},
+		{
+			mu:       []float64{2, 3, 4, 5},
+			sigma:    mat.NewSymDense(4, []float64{2, 0.5, 0, 0, 0.5, 5, 0, 0, 0, 0, 10, 2, 0, 0, 2, 3}),
+			observed: []int{0, 1},
+			values:   []float64{10, 15},
+
+			newMu:    []float64{4, 5},
+			newSigma: mat.NewSymDense(2, []float64{10, 2, 2, 3}),
+		},
+	} {
+		normal, ok := NewNormal(test.mu, test.sigma, nil)
+		if !ok {
+			t.Fatalf("Bad test, original sigma not positive definite")
+		}
+		newNormal, ok := normal.ConditionNormal(test.observed, test.values, nil)
+		if !ok {
+			t.Fatalf("Bad test, update failure")
+		}
+
+		if !floats.EqualApprox(test.newMu, newNormal.mu, 1e-12) {
+			t.Errorf("Updated mean mismatch. Want %v, got %v.", test.newMu, newNormal.mu)
+		}
+
+		var sigma mat.SymDense
+		newNormal.chol.To(&sigma)
+		if !mat.EqualApprox(test.newSigma, &sigma, 1e-12) {
+			t.Errorf("Updated sigma mismatch\n.Want:\n% v\nGot:\n% v\n", test.newSigma, sigma)
+		}
+	}
+
+	// Test bivariate case where the update rule is analytic
+	for _, test := range []struct {
+		mu    []float64
+		std   []float64
+		rho   float64
+		value float64
+	}{
+		{
+			mu:    []float64{2, 3},
+			std:   []float64{3, 5},
+			rho:   0.9,
+			value: 1000,
+		},
+		{
+			mu:    []float64{2, 3},
+			std:   []float64{3, 5},
+			rho:   -0.9,
+			value: 1000,
+		},
+	} {
+		std := test.std
+		rho := test.rho
+		sigma := mat.NewSymDense(2, []float64{std[0] * std[0], std[0] * std[1] * rho, std[0] * std[1] * rho, std[1] * std[1]})
+		normal, ok := NewNormal(test.mu, sigma, nil)
+		if !ok {
+			t.Fatalf("Bad test, original sigma not positive definite")
+		}
+		newNormal, ok := normal.ConditionNormal([]int{1}, []float64{test.value}, nil)
+		if !ok {
+			t.Fatalf("Bad test, update failed")
+		}
+		var newSigma mat.SymDense
+		newNormal.chol.To(&newSigma)
+		trueMean := test.mu[0] + rho*(std[0]/std[1])*(test.value-test.mu[1])
+		if math.Abs(trueMean-newNormal.mu[0]) > 1e-14 {
+			t.Errorf("Mean mismatch. Want %v, got %v", trueMean, newNormal.mu[0])
+		}
+		trueVar := (1 - rho*rho) * std[0] * std[0]
+		if math.Abs(trueVar-newSigma.At(0, 0)) > 1e-14 {
+			t.Errorf("Std mismatch. Want %v, got %v", trueMean, newNormal.mu[0])
+		}
+	}
+
+	// Test via sampling.
+	for _, test := range []struct {
+		mu         []float64
+		sigma      *mat.SymDense
+		observed   []int
+		unobserved []int
+		value      []float64
+	}{
+		// The indices in unobserved must be in ascending order for this test.
+		{
+			mu:    []float64{2, 3, 4},
+			sigma: mat.NewSymDense(3, []float64{2, 0.5, 3, 0.5, 1, 0.6, 3, 0.6, 10}),
+
+			observed:   []int{0},
+			unobserved: []int{1, 2},
+			value:      []float64{1.9},
+		},
+		{
+			mu:    []float64{2, 3, 4, 5},
+			sigma: mat.NewSymDense(4, []float64{2, 0.5, 3, 0.1, 0.5, 1, 0.6, 0.2, 3, 0.6, 10, 0.3, 0.1, 0.2, 0.3, 3}),
+
+			observed:   []int{0, 3},
+			unobserved: []int{1, 2},
+			value:      []float64{1.9, 2.9},
+		},
+	} {
+		totalSamp := 4000000
+		var nSamp int
+		samples := mat.NewDense(totalSamp, len(test.mu), nil)
+		normal, ok := NewNormal(test.mu, test.sigma, nil)
+		if !ok {
+			t.Errorf("bad test")
+		}
+		sample := make([]float64, len(test.mu))
+		for i := 0; i < totalSamp; i++ {
+			normal.Rand(sample)
+			isClose := true
+			for i, v := range test.observed {
+				if math.Abs(sample[v]-test.value[i]) > 1e-1 {
+					isClose = false
+					break
+				}
+			}
+			if isClose {
+				samples.SetRow(nSamp, sample)
+				nSamp++
+			}
+		}
+
+		if nSamp < 100 {
+			t.Errorf("bad test, not enough samples")
+			continue
+		}
+		samples = samples.Slice(0, nSamp, 0, len(test.mu)).(*mat.Dense)
+
+		// Compute mean and covariance matrix.
+		estMean := make([]float64, len(test.mu))
+		for i := range estMean {
+			estMean[i] = stat.Mean(mat.Col(nil, i, samples), nil)
+		}
+		estCov := stat.CovarianceMatrix(nil, samples, nil)
+
+		// Compute update rule.
+		newNormal, ok := normal.ConditionNormal(test.observed, test.value, nil)
+		if !ok {
+			t.Fatalf("Bad test, update failure")
+		}
+
+		var subEstMean []float64
+		for _, v := range test.unobserved {
+
+			subEstMean = append(subEstMean, estMean[v])
+		}
+		subEstCov := mat.NewSymDense(len(test.unobserved), nil)
+		for i := 0; i < len(test.unobserved); i++ {
+			for j := i; j < len(test.unobserved); j++ {
+				subEstCov.SetSym(i, j, estCov.At(test.unobserved[i], test.unobserved[j]))
+			}
+		}
+
+		for i, v := range subEstMean {
+			if math.Abs(newNormal.mu[i]-v) > 5e-2 {
+				t.Errorf("Mean mismatch. Want %v, got %v.", newNormal.mu[i], v)
+			}
+		}
+		var sigma mat.SymDense
+		newNormal.chol.To(&sigma)
+		if !mat.EqualApprox(&sigma, subEstCov, 1e-1) {
+			t.Errorf("Covariance mismatch. Want:\n%0.8v\nGot:\n%0.8v\n", subEstCov, sigma)
+		}
+	}
+}
+
+func TestCovarianceMatrix(t *testing.T) {
+	for _, test := range []struct {
+		mu    []float64
+		sigma *mat.SymDense
+	}{
+		{
+			mu:    []float64{2, 3, 4},
+			sigma: mat.NewSymDense(3, []float64{1, 0.5, 3, 0.5, 8, -1, 3, -1, 15}),
+		},
+	} {
+		normal, ok := NewNormal(test.mu, test.sigma, nil)
+		if !ok {
+			t.Fatalf("Bad test, covariance matrix not positive definite")
+		}
+		cov := normal.CovarianceMatrix(nil)
+		if !mat.EqualApprox(cov, test.sigma, 1e-14) {
+			t.Errorf("Covariance mismatch with nil input")
+		}
+		dim := test.sigma.Symmetric()
+		cov = mat.NewSymDense(dim, nil)
+		normal.CovarianceMatrix(cov)
+		if !mat.EqualApprox(cov, test.sigma, 1e-14) {
+			t.Errorf("Covariance mismatch with supplied input")
+		}
+	}
+}
+
+func TestMarginal(t *testing.T) {
+	for _, test := range []struct {
+		mu       []float64
+		sigma    *mat.SymDense
+		marginal []int
+	}{
+		{
+			mu:       []float64{2, 3, 4},
+			sigma:    mat.NewSymDense(3, []float64{2, 0.5, 3, 0.5, 1, 0.6, 3, 0.6, 10}),
+			marginal: []int{0},
+		},
+		{
+			mu:       []float64{2, 3, 4},
+			sigma:    mat.NewSymDense(3, []float64{2, 0.5, 3, 0.5, 1, 0.6, 3, 0.6, 10}),
+			marginal: []int{0, 2},
+		},
+		{
+			mu:    []float64{2, 3, 4, 5},
+			sigma: mat.NewSymDense(4, []float64{2, 0.5, 3, 0.1, 0.5, 1, 0.6, 0.2, 3, 0.6, 10, 0.3, 0.1, 0.2, 0.3, 3}),
+
+			marginal: []int{0, 3},
+		},
+	} {
+		normal, ok := NewNormal(test.mu, test.sigma, nil)
+		if !ok {
+			t.Fatalf("Bad test, covariance matrix not positive definite")
+		}
+		marginal, ok := normal.MarginalNormal(test.marginal, nil)
+		if !ok {
+			t.Fatalf("Bad test, marginal matrix not positive definite")
+		}
+		dim := normal.Dim()
+		nSamples := 1000000
+		samps := mat.NewDense(nSamples, dim, nil)
+		for i := 0; i < nSamples; i++ {
+			normal.Rand(samps.RawRowView(i))
+		}
+		estMean := make([]float64, dim)
+		for i := range estMean {
+			estMean[i] = stat.Mean(mat.Col(nil, i, samps), nil)
+		}
+		for i, v := range test.marginal {
+			if math.Abs(marginal.mu[i]-estMean[v]) > 1e-2 {
+				t.Errorf("Mean mismatch: want: %v, got %v", estMean[v], marginal.mu[i])
+			}
+		}
+
+		marginalCov := marginal.CovarianceMatrix(nil)
+		estCov := stat.CovarianceMatrix(nil, samps, nil)
+		for i, v1 := range test.marginal {
+			for j, v2 := range test.marginal {
+				c := marginalCov.At(i, j)
+				ec := estCov.At(v1, v2)
+				if math.Abs(c-ec) > 5e-2 {
+					t.Errorf("Cov mismatch element i = %d, j = %d: want: %v, got %v", i, j, c, ec)
+				}
+			}
+		}
+	}
+}
+
+func TestMarginalSingle(t *testing.T) {
+	for _, test := range []struct {
+		mu    []float64
+		sigma *mat.SymDense
+	}{
+		{
+			mu:    []float64{2, 3, 4},
+			sigma: mat.NewSymDense(3, []float64{2, 0.5, 3, 0.5, 1, 0.6, 3, 0.6, 10}),
+		},
+		{
+			mu:    []float64{2, 3, 4, 5},
+			sigma: mat.NewSymDense(4, []float64{2, 0.5, 3, 0.1, 0.5, 1, 0.6, 0.2, 3, 0.6, 10, 0.3, 0.1, 0.2, 0.3, 3}),
+		},
+	} {
+		normal, ok := NewNormal(test.mu, test.sigma, nil)
+		if !ok {
+			t.Fatalf("Bad test, covariance matrix not positive definite")
+		}
+		for i, mean := range test.mu {
+			norm := normal.MarginalNormalSingle(i, nil)
+			if norm.Mean() != mean {
+				t.Errorf("Mean mismatch nil Sigma, idx %v: want %v, got %v.", i, mean, norm.Mean())
+			}
+			std := math.Sqrt(test.sigma.At(i, i))
+			if math.Abs(norm.StdDev()-std) > 1e-14 {
+				t.Errorf("StdDev mismatch nil Sigma, idx %v: want %v, got %v.", i, std, norm.StdDev())
+			}
+		}
+	}
+
+	// Test matching with TestMarginal.
+	rnd := rand.New(rand.NewSource(1))
+	for cas := 0; cas < 10; cas++ {
+		dim := rnd.Intn(10) + 1
+		mu := make([]float64, dim)
+		for i := range mu {
+			mu[i] = rnd.Float64()
+		}
+		x := make([]float64, dim*dim)
+		for i := range x {
+			x[i] = rnd.Float64()
+		}
+		matrix := mat.NewDense(dim, dim, x)
+		var sigma mat.SymDense
+		sigma.SymOuterK(1, matrix)
+
+		normal, ok := NewNormal(mu, &sigma, nil)
+		if !ok {
+			t.Fatal("bad test")
+		}
+		for i := 0; i < dim; i++ {
+			single := normal.MarginalNormalSingle(i, nil)
+			mult, ok := normal.MarginalNormal([]int{i}, nil)
+			if !ok {
+				t.Fatal("bad test")
+			}
+			if math.Abs(single.Mean()-mult.Mean(nil)[0]) > 1e-14 {
+				t.Errorf("Mean mismatch")
+			}
+			if math.Abs(single.Variance()-mult.CovarianceMatrix(nil).At(0, 0)) > 1e-14 {
+				t.Errorf("Variance mismatch")
+			}
+		}
+	}
+}
+
+func TestNormalScoreInput(t *testing.T) {
+	for cas, test := range []struct {
+		mu    []float64
+		sigma *mat.SymDense
+		x     []float64
+	}{
+		{
+			mu:    []float64{2, 3, 4},
+			sigma: mat.NewSymDense(3, []float64{2, 0.5, 3, 0.5, 1, 0.6, 3, 0.6, 10}),
+			x:     []float64{1, 3.1, -2},
+		},
+		{
+			mu:    []float64{2, 3, 4, 5},
+			sigma: mat.NewSymDense(4, []float64{2, 0.5, 3, 0.1, 0.5, 1, 0.6, 0.2, 3, 0.6, 10, 0.3, 0.1, 0.2, 0.3, 3}),
+			x:     []float64{1, 3.1, -2, 5},
+		},
+	} {
+		normal, ok := NewNormal(test.mu, test.sigma, nil)
+		if !ok {
+			t.Fatalf("Bad test, covariance matrix not positive definite")
+		}
+		x := make([]float64, len(test.x))
+		copy(x, test.x)
+		score := normal.ScoreInput(nil, x)
+		if !floats.Equal(x, test.x) {
+			t.Errorf("x modified during call to ScoreInput")
+		}
+		scoreFD := fd.Gradient(nil, normal.LogProb, x, nil)
+		if !floats.EqualApprox(score, scoreFD, 1e-4) {
+			t.Errorf("Case %d: derivative mismatch. Got %v, want %v", cas, score, scoreFD)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distmv/normalbench_test.go b/vendor/gonum.org/v1/gonum/stat/distmv/normalbench_test.go
new file mode 100644
index 00000000..a8890439
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distmv/normalbench_test.go
@@ -0,0 +1,73 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distmv
+
+import (
+	"log"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/mat"
+)
+
+func BenchmarkMarginalNormal10(b *testing.B) {
+	sz := 10
+	rnd := rand.New(rand.NewSource(1))
+	normal := randomNormal(sz, rnd)
+	_ = normal.CovarianceMatrix(nil) // pre-compute sigma
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		marg, ok := normal.MarginalNormal([]int{1}, nil)
+		if !ok {
+			b.Error("bad test")
+		}
+		_ = marg
+	}
+}
+
+func BenchmarkMarginalNormalReset10(b *testing.B) {
+	sz := 10
+	rnd := rand.New(rand.NewSource(1))
+	normal := randomNormal(sz, rnd)
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		marg, ok := normal.MarginalNormal([]int{1}, nil)
+		if !ok {
+			b.Error("bad test")
+		}
+		_ = marg
+	}
+}
+
+func BenchmarkMarginalNormalSingle10(b *testing.B) {
+	sz := 10
+	rnd := rand.New(rand.NewSource(1))
+	normal := randomNormal(sz, rnd)
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		marg := normal.MarginalNormalSingle(1, nil)
+		_ = marg
+	}
+}
+
+func randomNormal(sz int, rnd *rand.Rand) *Normal {
+	mu := make([]float64, sz)
+	for i := range mu {
+		mu[i] = rnd.Float64()
+	}
+	data := make([]float64, sz*sz)
+	for i := range data {
+		data[i] = rnd.Float64()
+	}
+	dM := mat.NewDense(sz, sz, data)
+	var sigma mat.SymDense
+	sigma.SymOuterK(1, dM)
+
+	normal, ok := NewNormal(mu, &sigma, nil)
+	if !ok {
+		log.Fatal("bad test, not pos def")
+	}
+	return normal
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distmv/statdist.go b/vendor/gonum.org/v1/gonum/stat/distmv/statdist.go
new file mode 100644
index 00000000..9a2f3bd7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distmv/statdist.go
@@ -0,0 +1,320 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distmv
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+	"gonum.org/v1/gonum/stat"
+)
+
+// Bhattacharyya is a type for computing the Bhattacharyya distance between
+// probability distributions.
+//
+// The Bhattacharyya distance is defined as
+//  D_B = -ln(BC(l,r))
+//  BC = \int_-∞^∞ (p(x)q(x))^(1/2) dx
+// Where BC is known as the Bhattacharyya coefficient.
+// The Bhattacharyya distance is related to the Hellinger distance by
+//  H = sqrt(1-BC)
+// For more information, see
+//  https://en.wikipedia.org/wiki/Bhattacharyya_distance
+type Bhattacharyya struct{}
+
+// DistNormal computes the Bhattacharyya distance between normal distributions l and r.
+// The dimensions of the input distributions must match or DistNormal will panic.
+//
+// For Normal distributions, the Bhattacharyya distance is
+//  Σ = (Σ_l + Σ_r)/2
+//  D_B = (1/8)*(μ_l - μ_r)^T*Σ^-1*(μ_l - μ_r) + (1/2)*ln(det(Σ)/(det(Σ_l)*det(Σ_r))^(1/2))
+func (Bhattacharyya) DistNormal(l, r *Normal) float64 {
+	dim := l.Dim()
+	if dim != r.Dim() {
+		panic(badSizeMismatch)
+	}
+
+	var sigma mat.SymDense
+	sigma.AddSym(&l.sigma, &r.sigma)
+	sigma.ScaleSym(0.5, &sigma)
+
+	var chol mat.Cholesky
+	chol.Factorize(&sigma)
+
+	mahalanobis := stat.Mahalanobis(mat.NewVecDense(dim, l.mu), mat.NewVecDense(dim, r.mu), &chol)
+	mahalanobisSq := mahalanobis * mahalanobis
+
+	dl := l.chol.LogDet()
+	dr := r.chol.LogDet()
+	ds := chol.LogDet()
+
+	return 0.125*mahalanobisSq + 0.5*ds - 0.25*dl - 0.25*dr
+}
+
+// DistUniform computes the Bhattacharyya distance between uniform distributions l and r.
+// The dimensions of the input distributions must match or DistUniform will panic.
+func (Bhattacharyya) DistUniform(l, r *Uniform) float64 {
+	if len(l.bounds) != len(r.bounds) {
+		panic(badSizeMismatch)
+	}
+	// BC = \int \sqrt(p(x)q(x)), which for uniform distributions is a constant
+	// over the volume where both distributions have positive probability.
+	// Compute the overlap and the value of sqrt(p(x)q(x)). The entropy is the
+	// negative log probability of the distribution (use instead of LogProb so
+	// it is not necessary to construct an x value).
+	//
+	// BC = volume * sqrt(p(x)q(x))
+	// logBC = log(volume) + 0.5*(logP + logQ)
+	// D_B = -logBC
+	return -unifLogVolOverlap(l.bounds, r.bounds) + 0.5*(l.Entropy()+r.Entropy())
+}
+
+// unifLogVolOverlap computes the log of the volume of the hyper-rectangle where
+// both uniform distributions have positive probability.
+func unifLogVolOverlap(b1, b2 []Bound) float64 {
+	var logVolOverlap float64
+	for dim, v1 := range b1 {
+		v2 := b2[dim]
+		// If the surfaces don't overlap, then the volume is 0
+		if v1.Max <= v2.Min || v2.Max <= v1.Min {
+			return math.Inf(-1)
+		}
+		vol := math.Min(v1.Max, v2.Max) - math.Max(v1.Min, v2.Min)
+		logVolOverlap += math.Log(vol)
+	}
+	return logVolOverlap
+}
+
+// CrossEntropy is a type for computing the cross-entropy between probability
+// distributions.
+//
+// The cross-entropy is defined as
+//  - \int_x l(x) log(r(x)) dx = KL(l || r) + H(l)
+// where KL is the Kullback-Leibler divergence and H is the entropy.
+// For more information, see
+//  https://en.wikipedia.org/wiki/Cross_entropy
+type CrossEntropy struct{}
+
+// DistNormal returns the cross-entropy between normal distributions l and r.
+// The dimensions of the input distributions must match or DistNormal will panic.
+func (CrossEntropy) DistNormal(l, r *Normal) float64 {
+	if l.Dim() != r.Dim() {
+		panic(badSizeMismatch)
+	}
+	kl := KullbackLeibler{}.DistNormal(l, r)
+	return kl + l.Entropy()
+}
+
+// Hellinger is a type for computing the Hellinger distance between probability
+// distributions.
+//
+// The Hellinger distance is defined as
+//  H^2(l,r) = 1/2 * int_x (\sqrt(l(x)) - \sqrt(r(x)))^2 dx
+// and is bounded between 0 and 1.
+// The Hellinger distance is related to the Bhattacharyya distance by
+//  H^2 = 1 - exp(-Db)
+// For more information, see
+//  https://en.wikipedia.org/wiki/Hellinger_distance
+type Hellinger struct{}
+
+// DistNormal returns the Hellinger distance between normal distributions l and r.
+// The dimensions of the input distributions must match or DistNormal will panic.
+//
+// See the documentation of Bhattacharyya.DistNormal for the formula for Normal
+// distributions.
+func (Hellinger) DistNormal(l, r *Normal) float64 {
+	if l.Dim() != r.Dim() {
+		panic(badSizeMismatch)
+	}
+	db := Bhattacharyya{}.DistNormal(l, r)
+	bc := math.Exp(-db)
+	return math.Sqrt(1 - bc)
+}
+
+// KullbackLiebler is a type for computing the Kullback-Leibler divergence from l to r.
+//
+// The Kullback-Liebler divergence is defined as
+//  D_KL(l || r ) = \int_x p(x) log(p(x)/q(x)) dx
+// Note that the Kullback-Liebler divergence is not symmetric with respect to
+// the order of the input arguments.
+type KullbackLeibler struct{}
+
+// DistNormal returns the KullbackLeibler distance between normal distributions l and r.
+// The dimensions of the input distributions must match or DistNormal will panic.
+//
+// For two normal distributions, the KL divergence is computed as
+//   D_KL(l || r) = 0.5*[ln(|Σ_r|) - ln(|Σ_l|) + (μ_l - μ_r)^T*Σ_r^-1*(μ_l - μ_r) + tr(Σ_r^-1*Σ_l)-d]
+func (KullbackLeibler) DistNormal(l, r *Normal) float64 {
+	dim := l.Dim()
+	if dim != r.Dim() {
+		panic(badSizeMismatch)
+	}
+
+	mahalanobis := stat.Mahalanobis(mat.NewVecDense(dim, l.mu), mat.NewVecDense(dim, r.mu), &r.chol)
+	mahalanobisSq := mahalanobis * mahalanobis
+
+	// TODO(btracey): Optimize where there is a SolveCholeskySym
+	// TODO(btracey): There may be a more efficient way to just compute the trace
+	// Compute tr(Σ_r^-1*Σ_l) using the fact that Σ_l = U^T * U
+	var u mat.TriDense
+	l.chol.UTo(&u)
+	var m mat.Dense
+	err := r.chol.Solve(&m, u.T())
+	if err != nil {
+		return math.NaN()
+	}
+	m.Mul(&m, &u)
+	tr := mat.Trace(&m)
+
+	return r.logSqrtDet - l.logSqrtDet + 0.5*(mahalanobisSq+tr-float64(l.dim))
+}
+
+// DistUniform returns the KullbackLeibler distance between uniform distributions
+// l and r. The dimensions of the input distributions must match or DistUniform
+// will panic.
+func (KullbackLeibler) DistUniform(l, r *Uniform) float64 {
+	bl := l.Bounds(nil)
+	br := r.Bounds(nil)
+	if len(bl) != len(br) {
+		panic(badSizeMismatch)
+	}
+
+	// The KL is ∞ if l is not completely contained within r, because then
+	// r(x) is zero when l(x) is non-zero for some x.
+	contained := true
+	for i, v := range bl {
+		if v.Min < br[i].Min || br[i].Max < v.Max {
+			contained = false
+			break
+		}
+	}
+	if !contained {
+		return math.Inf(1)
+	}
+
+	// The KL divergence is finite.
+	//
+	// KL defines 0*ln(0) = 0, so there is no contribution to KL where l(x) = 0.
+	// Inside the region, l(x) and r(x) are constant (uniform distribution), and
+	// this constant is integrated over l(x), which integrates out to one.
+	// The entropy is -log(p(x)).
+	logPx := -l.Entropy()
+	logQx := -r.Entropy()
+	return logPx - logQx
+}
+
+// Renyi is a type for computing the Rényi divergence of order α from l to r.
+//
+// The Rényi divergence with α > 0, α ≠ 1 is defined as
+//  D_α(l || r) = 1/(α-1) log(\int_-∞^∞ l(x)^α r(x)^(1-α)dx)
+// The Rényi divergence has special forms for α = 0 and α = 1. This type does
+// not implement α = ∞. For α = 0,
+//  D_0(l || r) = -log \int_-∞^∞ r(x)1{p(x)>0} dx
+// that is, the negative log probability under r(x) that l(x) > 0.
+// When α = 1, the Rényi divergence is equal to the Kullback-Leibler divergence.
+// The Rényi divergence is also equal to half the Bhattacharyya distance when α = 0.5.
+//
+// The parameter α must be in 0 ≤ α < ∞ or the distance functions will panic.
+type Renyi struct {
+	Alpha float64
+}
+
+// DistNormal returns the Rényi divergence between normal distributions l and r.
+// The dimensions of the input distributions must match or DistNormal will panic.
+//
+// For two normal distributions, the Rényi divergence is computed as
+//  Σ_α = (1-α) Σ_l + αΣ_r
+//  D_α(l||r) = α/2 * (μ_l - μ_r)'*Σ_α^-1*(μ_l - μ_r) + 1/(2(α-1))*ln(|Σ_λ|/(|Σ_l|^(1-α)*|Σ_r|^α))
+//
+// For a more nicely formatted version of the formula, see Eq. 15 of
+//  Kolchinsky, Artemy, and Brendan D. Tracey. "Estimating Mixture Entropy
+//  with Pairwise Distances." arXiv preprint arXiv:1706.02419 (2017).
+// Note that the this formula is for Chernoff divergence, which differs from
+// Rényi divergence by a factor of 1-α. Also be aware that most sources in
+// the literature report this formula incorrectly.
+func (renyi Renyi) DistNormal(l, r *Normal) float64 {
+	if renyi.Alpha < 0 {
+		panic("renyi: alpha < 0")
+	}
+	dim := l.Dim()
+	if dim != r.Dim() {
+		panic(badSizeMismatch)
+	}
+	if renyi.Alpha == 0 {
+		return 0
+	}
+	if renyi.Alpha == 1 {
+		return KullbackLeibler{}.DistNormal(l, r)
+	}
+
+	logDetL := l.chol.LogDet()
+	logDetR := r.chol.LogDet()
+
+	// Σ_α = (1-α)Σ_l + αΣ_r.
+	sigA := mat.NewSymDense(dim, nil)
+	for i := 0; i < dim; i++ {
+		for j := i; j < dim; j++ {
+			v := (1-renyi.Alpha)*l.sigma.At(i, j) + renyi.Alpha*r.sigma.At(i, j)
+			sigA.SetSym(i, j, v)
+		}
+	}
+
+	var chol mat.Cholesky
+	ok := chol.Factorize(sigA)
+	if !ok {
+		return math.NaN()
+	}
+	logDetA := chol.LogDet()
+
+	mahalanobis := stat.Mahalanobis(mat.NewVecDense(dim, l.mu), mat.NewVecDense(dim, r.mu), &chol)
+	mahalanobisSq := mahalanobis * mahalanobis
+
+	return (renyi.Alpha/2)*mahalanobisSq + 1/(2*(1-renyi.Alpha))*(logDetA-(1-renyi.Alpha)*logDetL-renyi.Alpha*logDetR)
+}
+
+// Wasserstein is a type for computing the Wasserstein distance between two
+// probability distributions.
+//
+// The Wasserstein distance is defined as
+//  W(l,r) := inf 𝔼(||X-Y||_2^2)^1/2
+// For more information, see
+//  https://en.wikipedia.org/wiki/Wasserstein_metric
+type Wasserstein struct{}
+
+// DistNormal returns the Wasserstein distance between normal distributions l and r.
+// The dimensions of the input distributions must match or DistNormal will panic.
+//
+// The Wasserstein distance for Normal distributions is
+//  d^2 = ||m_l - m_r||_2^2 + Tr(Σ_l + Σ_r - 2(Σ_l^(1/2)*Σ_r*Σ_l^(1/2))^(1/2))
+// For more information, see
+//  http://djalil.chafai.net/blog/2010/04/30/wasserstein-distance-between-two-gaussians/
+func (Wasserstein) DistNormal(l, r *Normal) float64 {
+	dim := l.Dim()
+	if dim != r.Dim() {
+		panic(badSizeMismatch)
+	}
+
+	d := floats.Distance(l.mu, r.mu, 2)
+	d = d * d
+
+	// Compute Σ_l^(1/2)
+	var ssl mat.SymDense
+	ssl.PowPSD(&l.sigma, 0.5)
+	// Compute Σ_l^(1/2)*Σ_r*Σ_l^(1/2)
+	var mean mat.Dense
+	mean.Mul(&ssl, &r.sigma)
+	mean.Mul(&mean, &ssl)
+
+	// Reinterpret as symdense, and take Σ^(1/2)
+	meanSym := mat.NewSymDense(dim, mean.RawMatrix().Data)
+	ssl.PowPSD(meanSym, 0.5)
+
+	tr := mat.Trace(&r.sigma)
+	tl := mat.Trace(&l.sigma)
+	tm := mat.Trace(&ssl)
+
+	return d + tl + tr - 2*tm
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distmv/statdist_test.go b/vendor/gonum.org/v1/gonum/stat/distmv/statdist_test.go
new file mode 100644
index 00000000..a3d1d9c2
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distmv/statdist_test.go
@@ -0,0 +1,329 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distmv
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+)
+
+func TestBhattacharyyaNormal(t *testing.T) {
+	for cas, test := range []struct {
+		am, bm  []float64
+		ac, bc  *mat.SymDense
+		samples int
+		tol     float64
+	}{
+		{
+			am:      []float64{2, 3},
+			ac:      mat.NewSymDense(2, []float64{3, -1, -1, 2}),
+			bm:      []float64{-1, 1},
+			bc:      mat.NewSymDense(2, []float64{1.5, 0.2, 0.2, 0.9}),
+			samples: 100000,
+			tol:     1e-2,
+		},
+	} {
+		rnd := rand.New(rand.NewSource(1))
+		a, ok := NewNormal(test.am, test.ac, rnd)
+		if !ok {
+			panic("bad test")
+		}
+		b, ok := NewNormal(test.bm, test.bc, rnd)
+		if !ok {
+			panic("bad test")
+		}
+		want := bhattacharyyaSample(a.Dim(), test.samples, a, b)
+		got := Bhattacharyya{}.DistNormal(a, b)
+		if math.Abs(want-got) > test.tol {
+			t.Errorf("Bhattacharyya mismatch, case %d: got %v, want %v", cas, got, want)
+		}
+
+		// Bhattacharyya should by symmetric
+		got2 := Bhattacharyya{}.DistNormal(b, a)
+		if math.Abs(got-got2) > 1e-14 {
+			t.Errorf("Bhattacharyya distance not symmetric")
+		}
+	}
+}
+
+func TestBhattacharyyaUniform(t *testing.T) {
+	rnd := rand.New(rand.NewSource(1))
+	for cas, test := range []struct {
+		a, b    *Uniform
+		samples int
+		tol     float64
+	}{
+		{
+			a:       NewUniform([]Bound{{-3, 2}, {-5, 8}}, rnd),
+			b:       NewUniform([]Bound{{-4, 1}, {-7, 10}}, rnd),
+			samples: 100000,
+			tol:     1e-2,
+		},
+		{
+			a:       NewUniform([]Bound{{-3, 2}, {-5, 8}}, rnd),
+			b:       NewUniform([]Bound{{-5, -4}, {-7, 10}}, rnd),
+			samples: 100000,
+			tol:     1e-2,
+		},
+	} {
+		a, b := test.a, test.b
+		want := bhattacharyyaSample(a.Dim(), test.samples, a, b)
+		got := Bhattacharyya{}.DistUniform(a, b)
+		if math.Abs(want-got) > test.tol {
+			t.Errorf("Bhattacharyya mismatch, case %d: got %v, want %v", cas, got, want)
+		}
+		// Bhattacharyya should by symmetric
+		got2 := Bhattacharyya{}.DistUniform(b, a)
+		if math.Abs(got-got2) > 1e-14 {
+			t.Errorf("Bhattacharyya distance not symmetric")
+		}
+	}
+}
+
+// bhattacharyyaSample finds an estimate of the Bhattacharyya coefficient through
+// sampling.
+func bhattacharyyaSample(dim, samples int, l RandLogProber, r LogProber) float64 {
+	lBhatt := make([]float64, samples)
+	x := make([]float64, dim)
+	for i := 0; i < samples; i++ {
+		// Do importance sampling over a: \int sqrt(a*b)/a * a dx
+		l.Rand(x)
+		pa := l.LogProb(x)
+		pb := r.LogProb(x)
+		lBhatt[i] = 0.5*pb - 0.5*pa
+	}
+	logBc := floats.LogSumExp(lBhatt) - math.Log(float64(samples))
+	return -logBc
+}
+
+func TestCrossEntropyNormal(t *testing.T) {
+	for cas, test := range []struct {
+		am, bm  []float64
+		ac, bc  *mat.SymDense
+		samples int
+		tol     float64
+	}{
+		{
+			am:      []float64{2, 3},
+			ac:      mat.NewSymDense(2, []float64{3, -1, -1, 2}),
+			bm:      []float64{-1, 1},
+			bc:      mat.NewSymDense(2, []float64{1.5, 0.2, 0.2, 0.9}),
+			samples: 100000,
+			tol:     1e-2,
+		},
+	} {
+		rnd := rand.New(rand.NewSource(1))
+		a, ok := NewNormal(test.am, test.ac, rnd)
+		if !ok {
+			panic("bad test")
+		}
+		b, ok := NewNormal(test.bm, test.bc, rnd)
+		if !ok {
+			panic("bad test")
+		}
+		var ce float64
+		x := make([]float64, a.Dim())
+		for i := 0; i < test.samples; i++ {
+			a.Rand(x)
+			ce -= b.LogProb(x)
+		}
+		ce /= float64(test.samples)
+		got := CrossEntropy{}.DistNormal(a, b)
+		if math.Abs(ce-got) > test.tol {
+			t.Errorf("CrossEntropy mismatch, case %d: got %v, want %v", cas, got, ce)
+		}
+	}
+}
+
+func TestHellingerNormal(t *testing.T) {
+	for cas, test := range []struct {
+		am, bm  []float64
+		ac, bc  *mat.SymDense
+		samples int
+		tol     float64
+	}{
+		{
+			am:      []float64{2, 3},
+			ac:      mat.NewSymDense(2, []float64{3, -1, -1, 2}),
+			bm:      []float64{-1, 1},
+			bc:      mat.NewSymDense(2, []float64{1.5, 0.2, 0.2, 0.9}),
+			samples: 100000,
+			tol:     5e-1,
+		},
+	} {
+		rnd := rand.New(rand.NewSource(1))
+		a, ok := NewNormal(test.am, test.ac, rnd)
+		if !ok {
+			panic("bad test")
+		}
+		b, ok := NewNormal(test.bm, test.bc, rnd)
+		if !ok {
+			panic("bad test")
+		}
+		lAitchEDoubleHockeySticks := make([]float64, test.samples)
+		x := make([]float64, a.Dim())
+		for i := 0; i < test.samples; i++ {
+			// Do importance sampling over a: \int (\sqrt(a)-\sqrt(b))^2/a * a dx
+			a.Rand(x)
+			pa := a.LogProb(x)
+			pb := b.LogProb(x)
+			d := math.Exp(0.5*pa) - math.Exp(0.5*pb)
+			d = d * d
+			lAitchEDoubleHockeySticks[i] = math.Log(d) - pa
+		}
+		want := math.Sqrt(0.5 * math.Exp(floats.LogSumExp(lAitchEDoubleHockeySticks)-math.Log(float64(test.samples))))
+		got := Hellinger{}.DistNormal(a, b)
+		if math.Abs(want-got) > test.tol {
+			t.Errorf("Hellinger mismatch, case %d: got %v, want %v", cas, got, want)
+		}
+	}
+}
+
+func TestKullbackLeiblerNormal(t *testing.T) {
+	for cas, test := range []struct {
+		am, bm  []float64
+		ac, bc  *mat.SymDense
+		samples int
+		tol     float64
+	}{
+		{
+			am:      []float64{2, 3},
+			ac:      mat.NewSymDense(2, []float64{3, -1, -1, 2}),
+			bm:      []float64{-1, 1},
+			bc:      mat.NewSymDense(2, []float64{1.5, 0.2, 0.2, 0.9}),
+			samples: 10000,
+			tol:     1e-2,
+		},
+	} {
+		rnd := rand.New(rand.NewSource(1))
+		a, ok := NewNormal(test.am, test.ac, rnd)
+		if !ok {
+			panic("bad test")
+		}
+		b, ok := NewNormal(test.bm, test.bc, rnd)
+		if !ok {
+			panic("bad test")
+		}
+		want := klSample(a.Dim(), test.samples, a, b)
+		got := KullbackLeibler{}.DistNormal(a, b)
+		if !floats.EqualWithinAbsOrRel(want, got, test.tol, test.tol) {
+			t.Errorf("Case %d, KL mismatch: got %v, want %v", cas, got, want)
+		}
+	}
+}
+
+func TestKullbackLeiblerUniform(t *testing.T) {
+	rnd := rand.New(rand.NewSource(1))
+	for cas, test := range []struct {
+		a, b    *Uniform
+		samples int
+		tol     float64
+	}{
+		{
+			a:       NewUniform([]Bound{{-5, 2}, {-7, 12}}, rnd),
+			b:       NewUniform([]Bound{{-4, 1}, {-7, 10}}, rnd),
+			samples: 100000,
+			tol:     1e-2,
+		},
+		{
+			a:       NewUniform([]Bound{{-5, 2}, {-7, 12}}, rnd),
+			b:       NewUniform([]Bound{{-9, -6}, {-7, 10}}, rnd),
+			samples: 100000,
+			tol:     1e-2,
+		},
+	} {
+		a, b := test.a, test.b
+		want := klSample(a.Dim(), test.samples, a, b)
+		got := KullbackLeibler{}.DistUniform(a, b)
+		if math.Abs(want-got) > test.tol {
+			t.Errorf("Kullback-Leibler mismatch, case %d: got %v, want %v", cas, got, want)
+		}
+	}
+}
+
+// klSample finds an estimate of the Kullback-Leibler divergence through sampling.
+func klSample(dim, samples int, l RandLogProber, r LogProber) float64 {
+	var klmc float64
+	x := make([]float64, dim)
+	for i := 0; i < samples; i++ {
+		l.Rand(x)
+		pa := l.LogProb(x)
+		pb := r.LogProb(x)
+		klmc += pa - pb
+	}
+	return klmc / float64(samples)
+}
+
+func TestRenyiNormal(t *testing.T) {
+	for cas, test := range []struct {
+		am, bm  []float64
+		ac, bc  *mat.SymDense
+		alpha   float64
+		samples int
+		tol     float64
+	}{
+		{
+			am:      []float64{2, 3},
+			ac:      mat.NewSymDense(2, []float64{3, -1, -1, 2}),
+			bm:      []float64{-1, 1},
+			bc:      mat.NewSymDense(2, []float64{1.5, 0.2, 0.2, 0.9}),
+			alpha:   0.3,
+			samples: 10000,
+			tol:     1e-2,
+		},
+	} {
+		rnd := rand.New(rand.NewSource(1))
+		a, ok := NewNormal(test.am, test.ac, rnd)
+		if !ok {
+			panic("bad test")
+		}
+		b, ok := NewNormal(test.bm, test.bc, rnd)
+		if !ok {
+			panic("bad test")
+		}
+		want := renyiSample(a.Dim(), test.samples, test.alpha, a, b)
+		got := Renyi{Alpha: test.alpha}.DistNormal(a, b)
+		if !floats.EqualWithinAbsOrRel(want, got, test.tol, test.tol) {
+			t.Errorf("Case %d: Renyi sampling mismatch: got %v, want %v", cas, got, want)
+		}
+
+		// Compare with Bhattacharyya.
+		want = 2 * Bhattacharyya{}.DistNormal(a, b)
+		got = Renyi{Alpha: 0.5}.DistNormal(a, b)
+		if math.Abs(want-got) > 1e-10 {
+			t.Errorf("Case %d: Renyi mismatch with Bhattacharyya: got %v, want %v", cas, got, want)
+		}
+
+		// Compare with KL in both directions.
+		want = KullbackLeibler{}.DistNormal(a, b)
+		got = Renyi{Alpha: 0.9999999}.DistNormal(a, b) // very close to 1 but not equal to 1.
+		if math.Abs(want-got) > 1e-6 {
+			t.Errorf("Case %d: Renyi mismatch with KL(a||b): got %v, want %v", cas, got, want)
+		}
+		want = KullbackLeibler{}.DistNormal(b, a)
+		got = Renyi{Alpha: 0.9999999}.DistNormal(b, a) // very close to 1 but not equal to 1.
+		if math.Abs(want-got) > 1e-6 {
+			t.Errorf("Case %d: Renyi mismatch with KL(b||a): got %v, want %v", cas, got, want)
+		}
+	}
+}
+
+// renyiSample finds an estimate of the Rényi divergence through sampling.
+// Note that this sampling procedure only works if l has broader support than r.
+func renyiSample(dim, samples int, alpha float64, l RandLogProber, r LogProber) float64 {
+	rmcs := make([]float64, samples)
+	x := make([]float64, dim)
+	for i := 0; i < samples; i++ {
+		l.Rand(x)
+		pa := l.LogProb(x)
+		pb := r.LogProb(x)
+		rmcs[i] = (alpha-1)*pa + (1-alpha)*pb
+	}
+	return 1 / (alpha - 1) * (floats.LogSumExp(rmcs) - math.Log(float64(samples)))
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distmv/studentst.go b/vendor/gonum.org/v1/gonum/stat/distmv/studentst.go
new file mode 100644
index 00000000..041b1369
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distmv/studentst.go
@@ -0,0 +1,354 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distmv
+
+import (
+	"math"
+	"math/rand"
+	"sort"
+
+	"golang.org/x/tools/container/intsets"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+	"gonum.org/v1/gonum/stat/distuv"
+)
+
+// StudentsT is a multivariate Student's T distribution. It is a distribution over
+// ℝ^n with the probability density
+//  p(y) = (Γ((ν+n)/2) / Γ(ν/2)) * (νπ)^(-n/2) * |Ʃ|^(-1/2) *
+//             (1 + 1/ν * (y-μ)^T * Ʃ^-1 * (y-μ))^(-(ν+n)/2)
+// where ν is a scalar greater than 2, μ is a vector in ℝ^n, and Ʃ is an n×n
+// symmetric positive definite matrix.
+//
+// In this distribution, ν sets the spread of the distribution, similar to
+// the degrees of freedom in a univariate Student's T distribution. As ν → ∞,
+// the distribution approaches a multi-variate normal distribution.
+// μ is the mean of the distribution, and the covariance is  ν/(ν-2)*Ʃ.
+//
+// See https://en.wikipedia.org/wiki/Student%27s_t-distribution and
+// http://users.isy.liu.se/en/rt/roth/student.pdf for more information.
+type StudentsT struct {
+	nu  float64
+	mu  []float64
+	src *rand.Rand
+
+	sigma mat.SymDense // only stored if needed
+
+	chol       mat.Cholesky
+	lower      mat.TriDense
+	logSqrtDet float64
+	dim        int
+}
+
+// NewStudentsT creates a new StudentsT with the given nu, mu, and sigma
+// parameters.
+//
+// NewStudentsT panics if len(mu) == 0, or if len(mu) != sigma.Symmetric(). If
+// the covariance matrix is not positive-definite, nil is returned and ok is false.
+func NewStudentsT(mu []float64, sigma mat.Symmetric, nu float64, src *rand.Rand) (dist *StudentsT, ok bool) {
+	if len(mu) == 0 {
+		panic(badZeroDimension)
+	}
+	dim := sigma.Symmetric()
+	if dim != len(mu) {
+		panic(badSizeMismatch)
+	}
+
+	s := &StudentsT{
+		nu:  nu,
+		mu:  make([]float64, dim),
+		dim: dim,
+		src: src,
+	}
+	copy(s.mu, mu)
+
+	ok = s.chol.Factorize(sigma)
+	if !ok {
+		return nil, false
+	}
+	s.sigma = *mat.NewSymDense(dim, nil)
+	s.sigma.CopySym(sigma)
+	s.chol.LTo(&s.lower)
+	s.logSqrtDet = 0.5 * s.chol.LogDet()
+	return s, true
+}
+
+// ConditionStudentsT returns the Student's T distribution that is the receiver
+// conditioned on the input evidence, and the success of the operation.
+// The returned Student's T has dimension
+// n - len(observed), where n is the dimension of the original receiver.
+// The dimension order is preserved during conditioning, so if the value
+// of dimension 1 is observed, the returned normal represents dimensions {0, 2, ...}
+// of the original Student's T distribution.
+//
+// ok indicates whether there was a failure during the update. If ok is false
+// the operation failed and dist is not usable.
+// Mathematically this is impossible, but can occur with finite precision arithmetic.
+func (s *StudentsT) ConditionStudentsT(observed []int, values []float64, src *rand.Rand) (dist *StudentsT, ok bool) {
+	if len(observed) == 0 {
+		panic("studentst: no observed value")
+	}
+	if len(observed) != len(values) {
+		panic(badInputLength)
+	}
+
+	for _, v := range observed {
+		if v < 0 || v >= s.dim {
+			panic("studentst: observed value out of bounds")
+		}
+	}
+
+	newNu, newMean, newSigma := studentsTConditional(observed, values, s.nu, s.mu, &s.sigma)
+	if newMean == nil {
+		return nil, false
+	}
+
+	return NewStudentsT(newMean, newSigma, newNu, src)
+
+}
+
+// studentsTConditional updates a Student's T distribution based on the observed samples
+// (see documentation for the public function). The Gaussian conditional update
+// is treated as a special case when  nu == math.Inf(1).
+func studentsTConditional(observed []int, values []float64, nu float64, mu []float64, sigma mat.Symmetric) (newNu float64, newMean []float64, newSigma *mat.SymDense) {
+	dim := len(mu)
+	ob := len(observed)
+
+	unobserved := findUnob(observed, dim)
+
+	unob := len(unobserved)
+	if unob == 0 {
+		panic("stat: all dimensions observed")
+	}
+
+	mu1 := make([]float64, unob)
+	for i, v := range unobserved {
+		mu1[i] = mu[v]
+	}
+	mu2 := make([]float64, ob) // really v - mu2
+	for i, v := range observed {
+		mu2[i] = values[i] - mu[v]
+	}
+
+	var sigma11, sigma22 mat.SymDense
+	sigma11.SubsetSym(sigma, unobserved)
+	sigma22.SubsetSym(sigma, observed)
+
+	sigma21 := mat.NewDense(ob, unob, nil)
+	for i, r := range observed {
+		for j, c := range unobserved {
+			v := sigma.At(r, c)
+			sigma21.Set(i, j, v)
+		}
+	}
+
+	var chol mat.Cholesky
+	ok := chol.Factorize(&sigma22)
+	if !ok {
+		return math.NaN(), nil, nil
+	}
+
+	// Compute mu_1 + sigma_{2,1}^T * sigma_{2,2}^-1 (v - mu_2).
+	v := mat.NewVecDense(ob, mu2)
+	var tmp, tmp2 mat.VecDense
+	err := chol.SolveVec(&tmp, v)
+	if err != nil {
+		return math.NaN(), nil, nil
+	}
+	tmp2.MulVec(sigma21.T(), &tmp)
+
+	for i := range mu1 {
+		mu1[i] += tmp2.At(i, 0)
+	}
+
+	// Compute tmp4 = sigma_{2,1}^T * sigma_{2,2}^-1 * sigma_{2,1}.
+	// TODO(btracey): Should this be a method of SymDense?
+	var tmp3, tmp4 mat.Dense
+	err = chol.Solve(&tmp3, sigma21)
+	if err != nil {
+		return math.NaN(), nil, nil
+	}
+	tmp4.Mul(sigma21.T(), &tmp3)
+
+	// Compute sigma_{1,1} - tmp4
+	// TODO(btracey): If tmp4 can constructed with a method, then this can be
+	// replaced with SubSym.
+	for i := 0; i < len(unobserved); i++ {
+		for j := i; j < len(unobserved); j++ {
+			v := sigma11.At(i, j)
+			sigma11.SetSym(i, j, v-tmp4.At(i, j))
+		}
+	}
+
+	// The computed variables are accurate for a Normal.
+	if math.IsInf(nu, 1) {
+		return nu, mu1, &sigma11
+	}
+
+	// Compute beta = (v - mu_2)^T * sigma_{2,2}^-1 * (v - mu_2)^T
+	beta := mat.Dot(v, &tmp)
+
+	// Scale the covariance matrix
+	sigma11.ScaleSym((nu+beta)/(nu+float64(ob)), &sigma11)
+
+	return nu + float64(ob), mu1, &sigma11
+}
+
+// findUnob returns the unobserved variables (the complementary set to observed).
+// findUnob panics if any value repeated in observed.
+func findUnob(observed []int, dim int) (unobserved []int) {
+	var setOb intsets.Sparse
+	for _, v := range observed {
+		setOb.Insert(v)
+	}
+	var setAll intsets.Sparse
+	for i := 0; i < dim; i++ {
+		setAll.Insert(i)
+	}
+	var setUnob intsets.Sparse
+	setUnob.Difference(&setAll, &setOb)
+	unobserved = setUnob.AppendTo(nil)
+	sort.Ints(unobserved)
+	return unobserved
+}
+
+// CovarianceMatrix returns the covariance matrix of the distribution. Upon
+// return, the value at element {i, j} of the covariance matrix is equal to
+// the covariance of the i^th and j^th variables.
+//  covariance(i, j) = E[(x_i - E[x_i])(x_j - E[x_j])]
+// If the input matrix is nil a new matrix is allocated, otherwise the result
+// is stored in-place into the input.
+func (st *StudentsT) CovarianceMatrix(s *mat.SymDense) *mat.SymDense {
+	if s == nil {
+		s = mat.NewSymDense(st.dim, nil)
+	}
+	sn := s.Symmetric()
+	if sn != st.dim {
+		panic("normal: input matrix size mismatch")
+	}
+	s.CopySym(&st.sigma)
+	s.ScaleSym(st.nu/(st.nu-2), s)
+	return s
+}
+
+// Dim returns the dimension of the distribution.
+func (s *StudentsT) Dim() int {
+	return s.dim
+}
+
+// LogProb computes the log of the pdf of the point x.
+func (s *StudentsT) LogProb(y []float64) float64 {
+	if len(y) != s.dim {
+		panic(badInputLength)
+	}
+
+	nu := s.nu
+	n := float64(s.dim)
+	lg1, _ := math.Lgamma((nu + n) / 2)
+	lg2, _ := math.Lgamma(nu / 2)
+
+	t1 := lg1 - lg2 - n/2*math.Log(nu*math.Pi) - s.logSqrtDet
+
+	shift := make([]float64, len(y))
+	copy(shift, y)
+	floats.Sub(shift, s.mu)
+
+	x := mat.NewVecDense(s.dim, shift)
+
+	var tmp mat.VecDense
+	s.chol.SolveVec(&tmp, x)
+
+	dot := mat.Dot(&tmp, x)
+
+	return t1 - ((nu+n)/2)*math.Log(1+dot/nu)
+}
+
+// MarginalStudentsT returns the marginal distribution of the given input variables,
+// and the success of the operation.
+// That is, MarginalStudentsT returns
+//  p(x_i) = \int_{x_o} p(x_i | x_o) p(x_o) dx_o
+// where x_i are the dimensions in the input, and x_o are the remaining dimensions.
+// See https://en.wikipedia.org/wiki/Marginal_distribution for more information.
+//
+// The input src is passed to the created StudentsT.
+//
+// ok indicates whether there was a failure during the marginalization. If ok is false
+// the operation failed and dist is not usable.
+// Mathematically this is impossible, but can occur with finite precision arithmetic.
+func (s *StudentsT) MarginalStudentsT(vars []int, src *rand.Rand) (dist *StudentsT, ok bool) {
+	newMean := make([]float64, len(vars))
+	for i, v := range vars {
+		newMean[i] = s.mu[v]
+	}
+	var newSigma mat.SymDense
+	newSigma.SubsetSym(&s.sigma, vars)
+	return NewStudentsT(newMean, &newSigma, s.nu, src)
+}
+
+// MarginalStudentsT returns the marginal distribution of the given input variable.
+// That is, MarginalStudentsT returns
+//  p(x_i) = \int_{x_o} p(x_i | x_o) p(x_o) dx_o
+// where i is the input index, and x_o are the remaining dimensions.
+// See https://en.wikipedia.org/wiki/Marginal_distribution for more information.
+//
+// The input src is passed to the call to NewStudentsT.
+func (s *StudentsT) MarginalStudentsTSingle(i int, src *rand.Rand) distuv.StudentsT {
+	return distuv.StudentsT{
+		Mu:    s.mu[i],
+		Sigma: math.Sqrt(s.sigma.At(i, i)),
+		Nu:    s.nu,
+		Src:   src,
+	}
+}
+
+// TODO(btracey): Implement marginal single. Need to modify univariate StudentsT
+// to be three-parameter.
+
+// Mean returns the mean of the probability distribution at x. If the
+// input argument is nil, a new slice will be allocated, otherwise the result
+// will be put in-place into the receiver.
+func (s *StudentsT) Mean(x []float64) []float64 {
+	x = reuseAs(x, s.dim)
+	copy(x, s.mu)
+	return x
+}
+
+// Prob computes the value of the probability density function at x.
+func (s *StudentsT) Prob(y []float64) float64 {
+	return math.Exp(s.LogProb(y))
+}
+
+// Rand generates a random number according to the distributon.
+// If the input slice is nil, new memory is allocated, otherwise the result is stored
+// in place.
+func (s *StudentsT) Rand(x []float64) []float64 {
+	// If Y is distributed according to N(0,Sigma), and U is chi^2 with
+	// parameter ν, then
+	//  X = mu + Y * sqrt(nu / U)
+	// X is distributed according to this distribution.
+
+	// Generate Y.
+	x = reuseAs(x, s.dim)
+	tmp := make([]float64, s.dim)
+	if s.src == nil {
+		for i := range x {
+			tmp[i] = rand.NormFloat64()
+		}
+	} else {
+		for i := range x {
+			tmp[i] = s.src.NormFloat64()
+		}
+	}
+	xVec := mat.NewVecDense(s.dim, x)
+	tmpVec := mat.NewVecDense(s.dim, tmp)
+	xVec.MulVec(&s.lower, tmpVec)
+
+	u := distuv.ChiSquared{K: s.nu, Src: s.src}.Rand()
+	floats.Scale(math.Sqrt(s.nu/u), x)
+
+	floats.Add(x, s.mu)
+	return x
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distmv/studentst_test.go b/vendor/gonum.org/v1/gonum/stat/distmv/studentst_test.go
new file mode 100644
index 00000000..b21a07f8
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distmv/studentst_test.go
@@ -0,0 +1,265 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distmv
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+	"gonum.org/v1/gonum/stat"
+)
+
+func TestStudentTProbs(t *testing.T) {
+	src := rand.New(rand.NewSource(1))
+	for _, test := range []struct {
+		nu    float64
+		mu    []float64
+		sigma *mat.SymDense
+
+		x     [][]float64
+		probs []float64
+	}{
+		{
+			nu:    3,
+			mu:    []float64{0, 0},
+			sigma: mat.NewSymDense(2, []float64{1, 0, 0, 1}),
+
+			x: [][]float64{
+				{0, 0},
+				{1, -1},
+				{3, 4},
+				{-1, -2},
+			},
+			// Outputs compared with WolframAlpha.
+			probs: []float64{
+				0.159154943091895335768883,
+				0.0443811199724279860006777747927,
+				0.0005980371870904696541052658,
+				0.01370560783418571283428283,
+			},
+		},
+		{
+			nu:    4,
+			mu:    []float64{2, -3},
+			sigma: mat.NewSymDense(2, []float64{8, -1, -1, 5}),
+
+			x: [][]float64{
+				{0, 0},
+				{1, -1},
+				{3, 4},
+				{-1, -2},
+				{2, -3},
+			},
+			// Outputs compared with WolframAlpha.
+			probs: []float64{
+				0.007360810111491788657953608191001,
+				0.0143309905845607117740440592999,
+				0.0005307774290578041397794096037035009801668903,
+				0.0115657422475668739943625904793879,
+				0.0254851872062589062995305736215,
+			},
+		},
+	} {
+		s, ok := NewStudentsT(test.mu, test.sigma, test.nu, src)
+		if !ok {
+			t.Fatal("bad test")
+		}
+		for i, x := range test.x {
+			xcpy := make([]float64, len(x))
+			copy(xcpy, x)
+			p := s.Prob(x)
+			if !floats.Same(x, xcpy) {
+				t.Errorf("X modified during call to prob, %v, %v", x, xcpy)
+			}
+			if !floats.EqualWithinAbsOrRel(p, test.probs[i], 1e-10, 1e-10) {
+				t.Errorf("Probability mismatch. X = %v. Got %v, want %v.", x, p, test.probs[i])
+			}
+		}
+	}
+}
+
+func TestStudentsTRand(t *testing.T) {
+	src := rand.New(rand.NewSource(1))
+	for cas, test := range []struct {
+		mean   []float64
+		cov    *mat.SymDense
+		nu     float64
+		tolcov float64
+	}{
+		{
+			mean:   []float64{0, 0},
+			cov:    mat.NewSymDense(2, []float64{1, 0, 0, 1}),
+			nu:     4,
+			tolcov: 1e-2,
+		},
+		{
+			mean:   []float64{3, 4},
+			cov:    mat.NewSymDense(2, []float64{5, 1.2, 1.2, 6}),
+			nu:     8,
+			tolcov: 1e-2,
+		},
+		{
+			mean:   []float64{3, 4, -2},
+			cov:    mat.NewSymDense(3, []float64{5, 1.2, -0.8, 1.2, 6, 0.4, -0.8, 0.4, 2}),
+			nu:     8,
+			tolcov: 1e-2,
+		},
+	} {
+		s, ok := NewStudentsT(test.mean, test.cov, test.nu, src)
+		if !ok {
+			t.Fatal("bad test")
+		}
+		const nSamples = 1e6
+		dim := len(test.mean)
+		samps := mat.NewDense(nSamples, dim, nil)
+		for i := 0; i < nSamples; i++ {
+			s.Rand(samps.RawRowView(i))
+		}
+		estMean := make([]float64, dim)
+		for i := range estMean {
+			estMean[i] = stat.Mean(mat.Col(nil, i, samps), nil)
+		}
+		mean := s.Mean(nil)
+		if !floats.EqualApprox(estMean, mean, 1e-2) {
+			t.Errorf("Mean mismatch: want: %v, got %v", test.mean, estMean)
+		}
+		cov := s.CovarianceMatrix(nil)
+		estCov := stat.CovarianceMatrix(nil, samps, nil)
+		if !mat.EqualApprox(estCov, cov, test.tolcov) {
+			t.Errorf("Case %d: Cov mismatch: want: %v, got %v", cas, cov, estCov)
+		}
+	}
+}
+
+func TestStudentsTConditional(t *testing.T) {
+	src := rand.New(rand.NewSource(1))
+	for _, test := range []struct {
+		mean []float64
+		cov  *mat.SymDense
+		nu   float64
+
+		idx    []int
+		value  []float64
+		tolcov float64
+	}{
+		{
+			mean:  []float64{3, 4, -2},
+			cov:   mat.NewSymDense(3, []float64{5, 1.2, -0.8, 1.2, 6, 0.4, -0.8, 0.4, 2}),
+			nu:    8,
+			idx:   []int{0},
+			value: []float64{6},
+
+			tolcov: 1e-2,
+		},
+	} {
+		s, ok := NewStudentsT(test.mean, test.cov, test.nu, src)
+		if !ok {
+			t.Fatal("bad test")
+		}
+
+		sUp, ok := s.ConditionStudentsT(test.idx, test.value, src)
+		if !ok {
+			t.Error("unexpected failure of ConditionStudentsT")
+		}
+
+		// Compute the other values by hand the inefficient way to compare
+		newNu := test.nu + float64(len(test.idx))
+		if newNu != sUp.nu {
+			t.Errorf("Updated nu mismatch. Got %v, want %v", s.nu, newNu)
+		}
+		dim := len(test.mean)
+		unob := findUnob(test.idx, dim)
+		ob := test.idx
+
+		muUnob := make([]float64, len(unob))
+		for i, v := range unob {
+			muUnob[i] = test.mean[v]
+		}
+		muOb := make([]float64, len(ob))
+		for i, v := range ob {
+			muOb[i] = test.mean[v]
+		}
+
+		var sig11, sig22 mat.SymDense
+		sig11.SubsetSym(&s.sigma, unob)
+		sig22.SubsetSym(&s.sigma, ob)
+
+		sig12 := mat.NewDense(len(unob), len(ob), nil)
+		for i := range unob {
+			for j := range ob {
+				sig12.Set(i, j, s.sigma.At(unob[i], ob[j]))
+			}
+		}
+
+		shift := make([]float64, len(ob))
+		copy(shift, test.value)
+		floats.Sub(shift, muOb)
+
+		newMu := make([]float64, len(muUnob))
+		newMuVec := mat.NewVecDense(len(muUnob), newMu)
+		shiftVec := mat.NewVecDense(len(shift), shift)
+		var tmp mat.VecDense
+		tmp.SolveVec(&sig22, shiftVec)
+		newMuVec.MulVec(sig12, &tmp)
+		floats.Add(newMu, muUnob)
+
+		if !floats.EqualApprox(newMu, sUp.mu, 1e-10) {
+			t.Errorf("Mu mismatch. Got %v, want %v", sUp.mu, newMu)
+		}
+
+		var tmp2 mat.Dense
+		tmp2.Solve(&sig22, sig12.T())
+
+		var tmp3 mat.Dense
+		tmp3.Mul(sig12, &tmp2)
+		tmp3.Sub(&sig11, &tmp3)
+
+		dot := mat.Dot(shiftVec, &tmp)
+		tmp3.Scale((test.nu+dot)/(test.nu+float64(len(ob))), &tmp3)
+		if !mat.EqualApprox(&tmp3, &sUp.sigma, 1e-10) {
+			t.Errorf("Sigma mismatch")
+		}
+	}
+}
+
+func TestStudentsTMarginalSingle(t *testing.T) {
+	for _, test := range []struct {
+		mu    []float64
+		sigma *mat.SymDense
+		nu    float64
+	}{
+		{
+			mu:    []float64{2, 3, 4},
+			sigma: mat.NewSymDense(3, []float64{2, 0.5, 3, 0.5, 1, 0.6, 3, 0.6, 10}),
+			nu:    5,
+		},
+		{
+			mu:    []float64{2, 3, 4, 5},
+			sigma: mat.NewSymDense(4, []float64{2, 0.5, 3, 0.1, 0.5, 1, 0.6, 0.2, 3, 0.6, 10, 0.3, 0.1, 0.2, 0.3, 3}),
+			nu:    6,
+		},
+	} {
+		studentst, ok := NewStudentsT(test.mu, test.sigma, test.nu, nil)
+		if !ok {
+			t.Fatalf("Bad test, covariance matrix not positive definite")
+		}
+		for i, mean := range test.mu {
+			st := studentst.MarginalStudentsTSingle(i, nil)
+			if st.Mean() != mean {
+				t.Errorf("Mean mismatch nil Sigma, idx %v: want %v, got %v.", i, mean, st.Mean())
+			}
+			std := math.Sqrt(test.sigma.At(i, i))
+			if math.Abs(st.Sigma-std) > 1e-14 {
+				t.Errorf("StdDev mismatch nil Sigma, idx %v: want %v, got %v.", i, std, st.StdDev())
+			}
+			if st.Nu != test.nu {
+				t.Errorf("Nu mismatch nil Sigma, idx %v: want %v, got %v ", i, test.nu, st.Nu)
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distmv/uniform.go b/vendor/gonum.org/v1/gonum/stat/distmv/uniform.go
new file mode 100644
index 00000000..c28a0232
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distmv/uniform.go
@@ -0,0 +1,196 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distmv
+
+import (
+	"math"
+	"math/rand"
+)
+
+type Bound struct {
+	Min float64
+	Max float64
+}
+
+// Uniform represents a multivariate uniform distribution.
+type Uniform struct {
+	bounds []Bound
+	dim    int
+	src    *rand.Rand
+}
+
+// NewUniform creates a new uniform distribution with the given bounds.
+func NewUniform(bnds []Bound, src *rand.Rand) *Uniform {
+	dim := len(bnds)
+	if dim == 0 {
+		panic(badZeroDimension)
+	}
+	for _, b := range bnds {
+		if b.Max < b.Min {
+			panic("uniform: maximum less than minimum")
+		}
+	}
+	u := &Uniform{
+		bounds: make([]Bound, dim),
+		dim:    dim,
+		src:    src,
+	}
+	for i, b := range bnds {
+		u.bounds[i].Min = b.Min
+		u.bounds[i].Max = b.Max
+	}
+	return u
+}
+
+// NewUnitUniform creates a new Uniform distribution over the dim-dimensional
+// unit hypercube. That is, a uniform distribution where each dimension has
+// Min = 0 and Max = 1.
+func NewUnitUniform(dim int, src *rand.Rand) *Uniform {
+	if dim <= 0 {
+		panic(nonPosDimension)
+	}
+	bounds := make([]Bound, dim)
+	for i := range bounds {
+		bounds[i].Min = 0
+		bounds[i].Max = 1
+	}
+	return &Uniform{
+		bounds: bounds,
+		dim:    dim,
+		src:    src,
+	}
+}
+
+// Bounds returns the bounds on the variables of the distribution. If the input
+// is nil, a new slice is allocated and returned. If the input is non-nil, then
+// the bounds are stored in-place into the input argument, and Bounds will panic
+// if len(bounds) != u.Dim().
+func (u *Uniform) Bounds(bounds []Bound) []Bound {
+	if bounds == nil {
+		bounds = make([]Bound, u.Dim())
+	}
+	if len(bounds) != u.Dim() {
+		panic(badInputLength)
+	}
+	copy(bounds, u.bounds)
+	return bounds
+}
+
+// CDF returns the multidimensional cumulative distribution function of the
+// probability distribution at the point x. If p is non-nil, the CDF is stored
+// in-place into the first argument, otherwise a new slice is allocated and
+// returned.
+//
+// CDF will panic if len(x) is not equal to the dimension of the distribution,
+// or if p is non-nil and len(p) is not equal to the dimension of the distribution.
+func (u *Uniform) CDF(p, x []float64) []float64 {
+	if len(x) != u.dim {
+		panic(badSizeMismatch)
+	}
+	if p == nil {
+		p = make([]float64, u.dim)
+	}
+	if len(p) != u.dim {
+		panic(badSizeMismatch)
+	}
+	for i, v := range x {
+		if v < u.bounds[i].Min {
+			p[i] = 0
+		} else if v > u.bounds[i].Max {
+			p[i] = 1
+		} else {
+			p[i] = (v - u.bounds[i].Min) / (u.bounds[i].Max - u.bounds[i].Min)
+		}
+	}
+	return p
+}
+
+// Dim returns the dimension of the distribution.
+func (u *Uniform) Dim() int {
+	return u.dim
+}
+
+// Entropy returns the differential entropy of the distribution.
+func (u *Uniform) Entropy() float64 {
+	// Entropy is log of the volume.
+	var logVol float64
+	for _, b := range u.bounds {
+		logVol += math.Log(b.Max - b.Min)
+	}
+	return logVol
+}
+
+// LogProb computes the log of the pdf of the point x.
+func (u *Uniform) LogProb(x []float64) float64 {
+	dim := u.dim
+	if len(x) != dim {
+		panic(badSizeMismatch)
+	}
+	var logprob float64
+	for i, b := range u.bounds {
+		if x[i] < b.Min || x[i] > b.Max {
+			return math.Inf(-1)
+		}
+		logprob -= math.Log(b.Max - b.Min)
+	}
+	return logprob
+}
+
+// Mean returns the mean of the probability distribution at x. If the
+// input argument is nil, a new slice will be allocated, otherwise the result
+// will be put in-place into the receiver.
+func (u *Uniform) Mean(x []float64) []float64 {
+	x = reuseAs(x, u.dim)
+	for i, b := range u.bounds {
+		x[i] = (b.Max + b.Min) / 2
+	}
+	return x
+}
+
+// Prob computes the value of the probability density function at x.
+func (u *Uniform) Prob(x []float64) float64 {
+	return math.Exp(u.LogProb(x))
+}
+
+// Rand generates a random number according to the distributon.
+// If the input slice is nil, new memory is allocated, otherwise the result is stored
+// in place.
+func (u *Uniform) Rand(x []float64) []float64 {
+	x = reuseAs(x, u.dim)
+	if u.src == nil {
+		for i, b := range u.bounds {
+			x[i] = rand.Float64()*(b.Max-b.Min) + b.Min
+		}
+		return x
+	}
+	for i, b := range u.bounds {
+		x[i] = rand.Float64()*(b.Max-b.Min) + b.Min
+	}
+	return x
+}
+
+// Quantile returns the multi-dimensional inverse cumulative distribution function.
+// len(x) must equal len(p), and if x is non-nil, len(x) must also equal len(p).
+// If x is nil, a new slice will be allocated and returned, otherwise the quantile
+// will be stored in-place into x. All of the values of p must be between 0 and 1,
+// or Quantile will panic.
+func (u *Uniform) Quantile(x, p []float64) []float64 {
+	if len(p) != u.dim {
+		panic(badSizeMismatch)
+	}
+	if x == nil {
+		x = make([]float64, u.dim)
+	}
+	if len(x) != u.dim {
+		panic(badSizeMismatch)
+	}
+	for i, v := range p {
+		if v < 0 || v > 1 {
+			panic(badQuantile)
+		}
+		x[i] = v*(u.bounds[i].Max-u.bounds[i].Min) + u.bounds[i].Min
+	}
+	return x
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distmv/uniform_test.go b/vendor/gonum.org/v1/gonum/stat/distmv/uniform_test.go
new file mode 100644
index 00000000..c52e09a9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distmv/uniform_test.go
@@ -0,0 +1,31 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distmv
+
+import (
+	"math"
+	"testing"
+)
+
+func TestUniformEntropy(t *testing.T) {
+	for _, test := range []struct {
+		Uniform *Uniform
+		Entropy float64
+	}{
+		{
+			NewUniform([]Bound{{0, 1}, {0, 1}}, nil),
+			0,
+		},
+		{
+			NewUniform([]Bound{{-1, 3}, {2, 8}, {-5, -3}}, nil),
+			math.Log(48),
+		},
+	} {
+		ent := test.Uniform.Entropy()
+		if math.Abs(ent-test.Entropy) > 1e-14 {
+			t.Errorf("Entropy mismatch. Got %v, want %v", ent, test.Entropy)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/bernoulli.go b/vendor/gonum.org/v1/gonum/stat/distuv/bernoulli.go
new file mode 100644
index 00000000..c03578f1
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/bernoulli.go
@@ -0,0 +1,131 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"math"
+	"math/rand"
+)
+
+// Bernoulli represents a random variable whose value is 1 with probability p and
+// value of zero with probability 1-P. The value of P must be between 0 and 1.
+// More information at https://en.wikipedia.org/wiki/Bernoulli_distribution.
+type Bernoulli struct {
+	P      float64
+	Source *rand.Rand
+}
+
+// CDF computes the value of the cumulative density function at x.
+func (b Bernoulli) CDF(x float64) float64 {
+	if x < 0 {
+		return 0
+	}
+	if x < 1 {
+		return 1 - b.P
+	}
+	return 1
+}
+
+// Entropy returns the entropy of the distribution.
+func (b Bernoulli) Entropy() float64 {
+	if b.P == 0 {
+		return 0
+	}
+	if b.P == 1 {
+		return 1
+	}
+	q := 1 - b.P
+	return -b.P*math.Log(b.P) - q*math.Log(q)
+}
+
+// ExKurtosis returns the excess kurtosis of the distribution.
+func (b Bernoulli) ExKurtosis() float64 {
+	pq := b.P * (1 - b.P)
+	return (1 - 6*pq) / pq
+}
+
+// LogProb computes the natural logarithm of the value of the probability density function at x.
+func (b Bernoulli) LogProb(x float64) float64 {
+	if x == 0 {
+		return math.Log(1 - b.P)
+	}
+	if x == 1 {
+		return math.Log(b.P)
+	}
+	return math.Inf(-1)
+}
+
+// Mean returns the mean of the probability distribution.
+func (b Bernoulli) Mean() float64 {
+	return b.P
+}
+
+// Median returns the median of the probability distribution.
+func (b Bernoulli) Median() float64 {
+	p := b.P
+	switch {
+	case p < 0.5:
+		return 0
+	case p > 0.5:
+		return 1
+	default:
+		return 0.5
+	}
+}
+
+// NumParameters returns the number of parameters in the distribution.
+func (Bernoulli) NumParameters() int {
+	return 1
+}
+
+// Prob computes the value of the probability distribution at x.
+func (b Bernoulli) Prob(x float64) float64 {
+	return math.Exp(b.LogProb(x))
+}
+
+// Quantile returns the inverse of the cumulative probability distribution.
+func (b Bernoulli) Quantile(p float64) float64 {
+	if p < 0 || 1 < p {
+		panic(badPercentile)
+	}
+	if p < 1-b.P {
+		return 0
+	}
+	return 1
+}
+
+// Rand returns a random sample drawn from the distribution.
+func (b Bernoulli) Rand() float64 {
+	var rnd float64
+	if b.Source == nil {
+		rnd = rand.Float64()
+	} else {
+		rnd = b.Source.Float64()
+	}
+	if rnd < b.P {
+		return 1
+	}
+	return 0
+}
+
+// Skewness returns the skewness of the distribution.
+func (b Bernoulli) Skewness() float64 {
+	return (1 - 2*b.P) / math.Sqrt(b.P*(1-b.P))
+}
+
+// StdDev returns the standard deviation of the probability distribution.
+func (b Bernoulli) StdDev() float64 {
+	return math.Sqrt(b.Variance())
+}
+
+// Survival returns the survival function (complementary CDF) at x.
+func (b Bernoulli) Survival(x float64) float64 {
+	return 1 - b.CDF(x)
+}
+
+// Variance returns the variance of the probability distribution.
+func (b Bernoulli) Variance() float64 {
+	return b.P * (1 - b.P)
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/bernoulli_test.go b/vendor/gonum.org/v1/gonum/stat/distuv/bernoulli_test.go
new file mode 100644
index 00000000..107135ec
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/bernoulli_test.go
@@ -0,0 +1,23 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import "testing"
+
+func TestBernoulli(t *testing.T) {
+	for i, dist := range []Bernoulli{
+		{
+			P: 0.5,
+		},
+		{
+			P: 0.9,
+		},
+		{
+			P: 0.2,
+		},
+	} {
+		testFullDist(t, dist, i, false)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/beta.go b/vendor/gonum.org/v1/gonum/stat/distuv/beta.go
new file mode 100644
index 00000000..7c456009
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/beta.go
@@ -0,0 +1,126 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"math"
+	"math/rand"
+
+	"gonum.org/v1/gonum/mathext"
+)
+
+// Beta implements the Beta distribution, a two-parameter continuous distribution
+// with support between 0 and 1.
+//
+// The beta distribution has density function
+//  x^(α-1) * (1-x)^(β-1) * Γ(α+β) / (Γ(α)*Γ(β))
+//
+// For more information, see https://en.wikipedia.org/wiki/Beta_distribution
+type Beta struct {
+	// Alpha is the left shape parameter of the distribution. Alpha must be greater
+	// than 0.
+	Alpha float64
+	// Beta is the right shape parameter of the distribution. Beta must be greater
+	// than 0.
+	Beta float64
+
+	Source *rand.Rand
+}
+
+// CDF computes the value of the cumulative distribution function at x.
+func (b Beta) CDF(x float64) float64 {
+	if x <= 0 {
+		return 0
+	}
+	if x >= 1 {
+		return 1
+	}
+	return mathext.RegIncBeta(b.Alpha, b.Beta, x)
+}
+
+// ExKurtosis returns the excess kurtosis of the distribution.
+func (b Beta) ExKurtosis() float64 {
+	num := 6 * ((b.Alpha-b.Beta)*(b.Alpha-b.Beta)*(b.Alpha+b.Beta+1) - b.Alpha*b.Beta*(b.Alpha+b.Beta+2))
+	den := b.Alpha * b.Beta * (b.Alpha + b.Beta + 2) * (b.Alpha + b.Beta + 3)
+	return num / den
+}
+
+// LogProb computes the natural logarithm of the value of the probability
+// density function at x.
+func (b Beta) LogProb(x float64) float64 {
+	if x < 0 || x > 1 {
+		return math.Inf(-1)
+	}
+
+	if b.Alpha <= 0 || b.Beta <= 0 {
+		panic("beta: negative parameters")
+	}
+
+	lab, _ := math.Lgamma(b.Alpha + b.Beta)
+	la, _ := math.Lgamma(b.Alpha)
+	lb, _ := math.Lgamma(b.Beta)
+	return lab - la - lb + (b.Alpha-1)*math.Log(x) + (b.Beta-1)*math.Log(1-x)
+}
+
+// Mean returns the mean of the probability distribution.
+func (b Beta) Mean() float64 {
+	return b.Alpha / (b.Alpha + b.Beta)
+}
+
+// Mode returns the mode of the distribution.
+//
+// Mode returns NaN if either parameter is less than or equal to 1 as a special case.
+func (b Beta) Mode() float64 {
+	if b.Alpha <= 1 || b.Beta <= 1 {
+		return math.NaN()
+	}
+	return (b.Alpha - 1) / (b.Alpha + b.Beta - 2)
+}
+
+// NumParameters returns the number of parameters in the distribution.
+func (b Beta) NumParameters() int {
+	return 2
+}
+
+// Prob computes the value of the probability density function at x.
+func (b Beta) Prob(x float64) float64 {
+	return math.Exp(b.LogProb(x))
+}
+
+// Quantile returns the inverse of the cumulative distribution function.
+func (b Beta) Quantile(p float64) float64 {
+	if p < 0 || p > 1 {
+		panic(badPercentile)
+	}
+	return mathext.InvRegIncBeta(b.Alpha, b.Beta, p)
+}
+
+// Rand returns a random sample drawn from the distribution.
+func (b Beta) Rand() float64 {
+	ga := Gamma{Alpha: b.Alpha, Beta: 1, Source: b.Source}.Rand()
+	gb := Gamma{Alpha: b.Beta, Beta: 1, Source: b.Source}.Rand()
+	return ga / (ga + gb)
+}
+
+// StdDev returns the standard deviation of the probability distribution.
+func (b Beta) StdDev() float64 {
+	return math.Sqrt(b.Variance())
+}
+
+// Survival returns the survival function (complementary CDF) at x.
+func (b Beta) Survival(x float64) float64 {
+	switch {
+	case x <= 0:
+		return 1
+	case x >= 1:
+		return 0
+	}
+	return mathext.RegIncBeta(b.Beta, b.Alpha, 1-x)
+}
+
+// Variance returns the variance of the probability distribution.
+func (b Beta) Variance() float64 {
+	return b.Alpha * b.Beta / ((b.Alpha + b.Beta) * (b.Alpha + b.Beta) * (b.Alpha + b.Beta + 1))
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/beta_test.go b/vendor/gonum.org/v1/gonum/stat/distuv/beta_test.go
new file mode 100644
index 00000000..ffa1c25b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/beta_test.go
@@ -0,0 +1,61 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"math"
+	"math/rand"
+	"sort"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+func TestBetaProb(t *testing.T) {
+	// Values a comparison with scipy
+	for _, test := range []struct {
+		x, alpha, beta, want float64
+	}{
+		{0.1, 2, 0.5, 0.079056941504209499},
+		{0.5, 1, 5.1, 0.29740426605235754},
+		{0.1, 0.5, 0.5, 1.0610329539459691},
+		{1, 0.5, 0.5, math.Inf(1)},
+		{-1, 0.5, 0.5, 0},
+	} {
+		pdf := Beta{Alpha: test.alpha, Beta: test.beta}.Prob(test.x)
+		if !floats.EqualWithinAbsOrRel(pdf, test.want, 1e-10, 1e-10) {
+			t.Errorf("Pdf mismatch. Got %v, want %v", pdf, test.want)
+		}
+	}
+}
+
+func TestBetaRand(t *testing.T) {
+	src := rand.New(rand.NewSource(1))
+	for i, b := range []Beta{
+		{Alpha: 0.5, Beta: 0.5, Source: src},
+		{Alpha: 5, Beta: 1, Source: src},
+		{Alpha: 2, Beta: 2, Source: src},
+		{Alpha: 2, Beta: 5, Source: src},
+	} {
+		testBeta(t, b, i)
+	}
+}
+
+func testBeta(t *testing.T, b Beta, i int) {
+	tol := 1e-2
+	const n = 5e4
+	const bins = 10
+	x := make([]float64, n)
+	generateSamples(x, b)
+	sort.Float64s(x)
+
+	testRandLogProbContinuous(t, i, 0, x, b, tol, bins)
+	checkMean(t, i, x, b, tol)
+	checkVarAndStd(t, i, x, b, tol)
+	checkExKurtosis(t, i, x, b, 5e-2)
+	checkProbContinuous(t, i, x, b, 1e-3)
+	checkQuantileCDFSurvival(t, i, x, b, tol)
+	checkProbQuantContinuous(t, i, x, b, tol)
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/categorical.go b/vendor/gonum.org/v1/gonum/stat/distuv/categorical.go
new file mode 100644
index 00000000..d2053e93
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/categorical.go
@@ -0,0 +1,184 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"math"
+	"math/rand"
+)
+
+// Categorical is an extension of the Bernoulli distribution where x takes
+// values {0, 1, ..., len(w)-1} where w is the weight vector. Categorical must
+// be initialized with NewCategorical.
+type Categorical struct {
+	weights []float64
+
+	// heap is a weight heap.
+	//
+	// It keeps a heap-organised sum of remaining
+	// index weights that are available to be taken
+	// from.
+	//
+	// Each element holds the sum of weights for
+	// the corresponding index, plus the sum of
+	// of its children's weights; the children
+	// of an element i can be found at positions
+	// 2*(i+1)-1 and 2*(i+1). The root of the
+	// weight heap is at element 0.
+	//
+	// See comments in container/heap for an
+	// explanation of the layout of a heap.
+	heap []float64
+
+	src *rand.Rand
+}
+
+// NewCategorical constructs a new categorical distribution where the probability
+// that x equals i is proportional to w[i]. All of the weights must be
+// nonnegative, and at least one of the weights must be positive.
+func NewCategorical(w []float64, src *rand.Rand) Categorical {
+	c := Categorical{
+		weights: make([]float64, len(w)),
+		heap:    make([]float64, len(w)),
+		src:     src,
+	}
+	c.ReweightAll(w)
+	return c
+}
+
+// CDF computes the value of the cumulative density function at x.
+func (c Categorical) CDF(x float64) float64 {
+	var cdf float64
+	for i, w := range c.weights {
+		if x < float64(i) {
+			break
+		}
+		cdf += w
+	}
+	return cdf / c.heap[0]
+}
+
+// Entropy returns the entropy of the distribution.
+func (c Categorical) Entropy() float64 {
+	var ent float64
+	for _, w := range c.weights {
+		if w == 0 {
+			continue
+		}
+		p := w / c.heap[0]
+		ent += p * math.Log(p)
+	}
+	return -ent
+}
+
+// Len returns the number of values x could possibly take (the length of the
+// initial supplied weight vector).
+func (c Categorical) Len() int {
+	return len(c.weights)
+}
+
+// Mean returns the mean of the probability distribution.
+func (c Categorical) Mean() float64 {
+	var mean float64
+	for i, v := range c.weights {
+		mean += float64(i) * v
+	}
+	return mean / c.heap[0]
+}
+
+// Prob computes the value of the probability density function at x.
+func (c Categorical) Prob(x float64) float64 {
+	xi := int(x)
+	if float64(xi) != x {
+		return 0
+	}
+	if xi < 0 || xi > len(c.weights)-1 {
+		return 0
+	}
+	return c.weights[xi] / c.heap[0]
+}
+
+// LogProb computes the natural logarithm of the value of the probability density function at x.
+func (c Categorical) LogProb(x float64) float64 {
+	return math.Log(c.Prob(x))
+}
+
+// Rand returns a random draw from the categorical distribution.
+func (c Categorical) Rand() float64 {
+	var r float64
+	if c.src == nil {
+		r = c.heap[0] * rand.Float64()
+	} else {
+		r = c.heap[0] * c.src.Float64()
+	}
+	i := 1
+	last := -1
+	left := len(c.weights)
+	for {
+		if r -= c.weights[i-1]; r <= 0 {
+			break // Fall within item i-1.
+		}
+		i <<= 1 // Move to left child.
+		if d := c.heap[i-1]; r > d {
+			r -= d
+			// If enough r to pass left child,
+			// move to right child state will
+			// be caught at break above.
+			i++
+		}
+		if i == last || left < 0 {
+			panic("categorical: bad sample")
+		}
+		last = i
+		left--
+	}
+	return float64(i - 1)
+}
+
+// Reweight sets the weight of item idx to w. The input weight must be
+// non-negative, and after reweighting at least one of the weights must be
+// positive.
+func (c Categorical) Reweight(idx int, w float64) {
+	if w < 0 {
+		panic("categorical: negative weight")
+	}
+	w, c.weights[idx] = c.weights[idx]-w, w
+	idx++
+	for idx > 0 {
+		c.heap[idx-1] -= w
+		idx >>= 1
+	}
+	if c.heap[0] <= 0 {
+		panic("categorical: sum of the weights non-positive")
+	}
+}
+
+// ReweightAll resets the weights of the distribution. ReweightAll panics if
+// len(w) != c.Len. All of the weights must be nonnegative, and at least one of
+// the weights must be positive.
+func (c Categorical) ReweightAll(w []float64) {
+	if len(w) != c.Len() {
+		panic("categorical: length of the slices do not match")
+	}
+	for _, v := range w {
+		if v < 0 {
+			panic("categorical: negative weight")
+		}
+	}
+	copy(c.weights, w)
+	c.reset()
+}
+
+func (c Categorical) reset() {
+	copy(c.heap, c.weights)
+	for i := len(c.heap) - 1; i > 0; i-- {
+		// Sometimes 1-based counting makes sense.
+		c.heap[((i+1)>>1)-1] += c.heap[i]
+	}
+	// TODO(btracey): Renormalization for weird weights?
+	if c.heap[0] <= 0 {
+		panic("categorical: sum of the weights non-positive")
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/categorical_test.go b/vendor/gonum.org/v1/gonum/stat/distuv/categorical_test.go
new file mode 100644
index 00000000..decd181d
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/categorical_test.go
@@ -0,0 +1,196 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+func TestCategoricalProb(t *testing.T) {
+	for _, test := range [][]float64{
+		{1, 2, 3, 0},
+	} {
+		dist := NewCategorical(test, nil)
+		norm := make([]float64, len(test))
+		floats.Scale(1/floats.Sum(norm), norm)
+		for i, v := range norm {
+			p := dist.Prob(float64(i))
+			if math.Abs(p-v) > 1e-14 {
+				t.Errorf("Probability mismatch element %d", i)
+			}
+			p = dist.Prob(float64(i) + 0.5)
+			if p != 0 {
+				t.Errorf("Non-zero probability for non-integer x")
+			}
+		}
+		p := dist.Prob(-1)
+		if p != 0 {
+			t.Errorf("Non-zero probability for -1")
+		}
+		p = dist.Prob(float64(len(test)))
+		if p != 0 {
+			t.Errorf("Non-zero probability for len(test)")
+		}
+	}
+}
+
+func TestCategoricalRand(t *testing.T) {
+	for _, test := range [][]float64{
+		{1, 2, 3, 0},
+	} {
+		dist := NewCategorical(test, nil)
+		nSamples := 2000000
+		counts := sampleCategorical(t, dist, nSamples)
+
+		probs := make([]float64, len(test))
+		for i := range probs {
+			probs[i] = dist.Prob(float64(i))
+		}
+		same := samedDistCategorical(dist, counts, probs, 1e-2)
+		if !same {
+			t.Errorf("Probability mismatch. Want %v, got %v", probs, counts)
+		}
+
+		dist.Reweight(len(test)-1, 10)
+		counts = sampleCategorical(t, dist, nSamples)
+		probs = make([]float64, len(test))
+		for i := range probs {
+			probs[i] = dist.Prob(float64(i))
+		}
+		same = samedDistCategorical(dist, counts, probs, 1e-2)
+		if !same {
+			t.Errorf("Probability mismatch after Reweight. Want %v, got %v", probs, counts)
+		}
+
+		w := make([]float64, len(test))
+		for i := range w {
+			w[i] = rand.Float64()
+		}
+
+		dist.ReweightAll(w)
+		counts = sampleCategorical(t, dist, nSamples)
+		probs = make([]float64, len(test))
+		for i := range probs {
+			probs[i] = dist.Prob(float64(i))
+		}
+		same = samedDistCategorical(dist, counts, probs, 1e-2)
+		if !same {
+			t.Errorf("Probability mismatch after ReweightAll. Want %v, got %v", probs, counts)
+		}
+	}
+}
+
+func sampleCategorical(t *testing.T, dist Categorical, nSamples int) []float64 {
+	counts := make([]float64, dist.Len())
+	for i := 0; i < nSamples; i++ {
+		v := dist.Rand()
+		if float64(int(v)) != v {
+			t.Fatalf("Random number is not an integer")
+		}
+		counts[int(v)]++
+	}
+	sum := floats.Sum(counts)
+	floats.Scale(1/sum, counts)
+	return counts
+}
+
+func samedDistCategorical(dist Categorical, counts, probs []float64, tol float64) bool {
+	same := true
+	for i, prob := range probs {
+		if prob == 0 && counts[i] != 0 {
+			same = false
+			break
+		}
+		if !floats.EqualWithinAbsOrRel(prob, counts[i], tol, tol) {
+			same = false
+			break
+		}
+	}
+	return same
+}
+
+func TestCategoricalCDF(t *testing.T) {
+	for _, test := range [][]float64{
+		{1, 2, 3, 0, 4},
+	} {
+		c := make([]float64, len(test))
+		copy(c, test)
+		floats.Scale(1/floats.Sum(c), c)
+		sum := make([]float64, len(test))
+		floats.CumSum(sum, c)
+
+		dist := NewCategorical(test, nil)
+		cdf := dist.CDF(-0.5)
+		if cdf != 0 {
+			t.Errorf("CDF of negative number not zero")
+		}
+		for i := range c {
+			cdf := dist.CDF(float64(i))
+			if math.Abs(cdf-sum[i]) > 1e-14 {
+				t.Errorf("CDF mismatch %v. Want %v, got %v.", float64(i), sum[i], cdf)
+			}
+			cdfp := dist.CDF(float64(i) + 0.5)
+			if cdfp != cdf {
+				t.Errorf("CDF mismatch for non-integer input")
+			}
+		}
+	}
+}
+
+func TestCategoricalEntropy(t *testing.T) {
+	for _, test := range []struct {
+		weights []float64
+		entropy float64
+	}{
+		{
+			weights: []float64{1, 1},
+			entropy: math.Ln2,
+		},
+		{
+			weights: []float64{1, 1, 1, 1},
+			entropy: math.Log(4),
+		},
+		{
+			weights: []float64{0, 0, 1, 1, 0, 0},
+			entropy: math.Ln2,
+		},
+	} {
+		dist := NewCategorical(test.weights, nil)
+		entropy := dist.Entropy()
+		if math.IsNaN(entropy) || math.Abs(entropy-test.entropy) > 1e-14 {
+			t.Errorf("Entropy mismatch. Want %v, got %v.", test.entropy, entropy)
+		}
+	}
+}
+
+func TestCategoricalMean(t *testing.T) {
+	for _, test := range []struct {
+		weights []float64
+		mean    float64
+	}{
+		{
+			weights: []float64{10, 0, 0, 0},
+			mean:    0,
+		},
+		{
+			weights: []float64{0, 10, 0, 0},
+			mean:    1,
+		},
+		{
+			weights: []float64{1, 2, 3, 4},
+			mean:    2,
+		},
+	} {
+		dist := NewCategorical(test.weights, nil)
+		mean := dist.Mean()
+		if math.IsNaN(mean) || math.Abs(mean-test.mean) > 1e-14 {
+			t.Errorf("Entropy mismatch. Want %v, got %v.", test.mean, mean)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/chisquared.go b/vendor/gonum.org/v1/gonum/stat/distuv/chisquared.go
new file mode 100644
index 00000000..2c9827b7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/chisquared.go
@@ -0,0 +1,99 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"math"
+	"math/rand"
+
+	"gonum.org/v1/gonum/mathext"
+)
+
+// ChiSquared implements the χ² distribution, a one parameter distribution
+// with support on the positive numbers.
+//
+// The density function is given by
+//  1/(2^{k/2} * Γ(k/2)) * x^{k/2 - 1} * e^{-x/2}
+// It is a special case of the Gamma distribution, Γ(k/2, 1/2).
+//
+// For more information, see https://en.wikipedia.org/wiki/Chi-squared_distribution.
+type ChiSquared struct {
+	// K is the shape parameter, corresponding to the degrees of freedom. Must
+	// be greater than 0.
+	K float64
+
+	Src *rand.Rand
+}
+
+// CDF computes the value of the cumulative density function at x.
+func (c ChiSquared) CDF(x float64) float64 {
+	return mathext.GammaInc(c.K/2, x/2)
+}
+
+// ExKurtosis returns the excess kurtosis of the distribution.
+func (c ChiSquared) ExKurtosis() float64 {
+	return 12 / c.K
+}
+
+// LogProb computes the natural logarithm of the value of the probability
+// density function at x.
+func (c ChiSquared) LogProb(x float64) float64 {
+	if x < 0 {
+		return math.Inf(-1)
+	}
+	lg, _ := math.Lgamma(c.K / 2)
+	return (c.K/2-1)*math.Log(x) - x/2 - (c.K/2)*math.Ln2 - lg
+}
+
+// Mean returns the mean of the probability distribution.
+func (c ChiSquared) Mean() float64 {
+	return c.K
+}
+
+// Mode returns the mode of the distribution.
+func (c ChiSquared) Mode() float64 {
+	return math.Min(c.K-2, 0)
+}
+
+// NumParameters returns the number of parameters in the distribution.
+func (c ChiSquared) NumParameters() int {
+	return 1
+}
+
+// Prob computes the value of the probability density function at x.
+func (c ChiSquared) Prob(x float64) float64 {
+	return math.Exp(c.LogProb(x))
+}
+
+// Rand returns a random sample drawn from the distribution.
+func (c ChiSquared) Rand() float64 {
+	return Gamma{c.K / 2, 0.5, c.Src}.Rand()
+}
+
+// Quantile returns the inverse of the cumulative distribution function.
+func (c ChiSquared) Quantile(p float64) float64 {
+	if p < 0 || p > 1 {
+		panic(badPercentile)
+	}
+	return mathext.GammaIncInv(0.5*c.K, p) * 2
+}
+
+// StdDev returns the standard deviation of the probability distribution.
+func (c ChiSquared) StdDev() float64 {
+	return math.Sqrt(c.Variance())
+}
+
+// Survival returns the survival function (complementary CDF) at x.
+func (c ChiSquared) Survival(x float64) float64 {
+	if x < 0 {
+		return 1
+	}
+	return mathext.GammaIncComp(0.5*c.K, 0.5*x)
+}
+
+// Variance returns the variance of the probability distribution.
+func (c ChiSquared) Variance() float64 {
+	return 2 * c.K
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/chisquared_test.go b/vendor/gonum.org/v1/gonum/stat/distuv/chisquared_test.go
new file mode 100644
index 00000000..56941cd0
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/chisquared_test.go
@@ -0,0 +1,78 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"math/rand"
+	"sort"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+func TestChiSquaredProb(t *testing.T) {
+	for _, test := range []struct {
+		x, k, want float64
+	}{
+		{10, 3, 0.0085003666025203432},
+		{2.3, 3, 0.19157345407042367},
+		{0.8, 0.2, 0.080363259903912673},
+	} {
+		pdf := ChiSquared{test.k, nil}.Prob(test.x)
+		if !floats.EqualWithinAbsOrRel(pdf, test.want, 1e-10, 1e-10) {
+			t.Errorf("Pdf mismatch, x = %v, K = %v. Got %v, want %v", test.x, test.k, pdf, test.want)
+		}
+	}
+}
+
+func TestChiSquaredCDF(t *testing.T) {
+	for _, test := range []struct {
+		x, k, want float64
+	}{
+		// Values calculated with scipy.stats.chi2.cdf
+		{0, 1, 0},
+		{0.01, 5, 5.3002700426865167e-07},
+		{0.05, 3, 0.002929332764619924},
+		{0.5, 2, 0.22119921692859512},
+		{0.95, 3, 0.1866520918701263},
+		{0.99, 5, 0.036631697220869196},
+		{1, 1, 0.68268949213708596},
+		{1.5, 4, 0.17335853270322427},
+		{10, 10, 0.55950671493478743},
+		{25, 15, 0.95005656637357172},
+	} {
+		cdf := ChiSquared{test.k, nil}.CDF(test.x)
+		if !floats.EqualWithinAbsOrRel(cdf, test.want, 1e-10, 1e-10) {
+			t.Errorf("CDF mismatch, x = %v, K = %v. Got %v, want %v", test.x, test.k, cdf, test.want)
+		}
+	}
+}
+
+func TestChiSquared(t *testing.T) {
+	src := rand.New(rand.NewSource(1))
+	for i, b := range []ChiSquared{
+		{3, src},
+		{1.5, src},
+		{0.9, src},
+	} {
+		testChiSquared(t, b, i)
+	}
+}
+
+func testChiSquared(t *testing.T, c ChiSquared, i int) {
+	tol := 1e-2
+	const n = 1e5
+	const bins = 50
+	x := make([]float64, n)
+	generateSamples(x, c)
+	sort.Float64s(x)
+
+	testRandLogProbContinuous(t, i, 0, x, c, tol, bins)
+	checkMean(t, i, x, c, tol)
+	checkVarAndStd(t, i, x, c, tol)
+	checkExKurtosis(t, i, x, c, 7e-2)
+	checkProbContinuous(t, i, x, c, 1e-3)
+	checkQuantileCDFSurvival(t, i, x, c, 1e-2)
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/constants.go b/vendor/gonum.org/v1/gonum/stat/distuv/constants.go
new file mode 100644
index 00000000..9de7d4dc
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/constants.go
@@ -0,0 +1,24 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+const (
+	// oneOverRoot2Pi is the value of 1/(2Pi)^(1/2)
+	// http://www.wolframalpha.com/input/?i=1%2F%282+*+pi%29%5E%281%2F2%29
+	oneOverRoot2Pi = 0.39894228040143267793994605993438186847585863116493465766592582967065792589930183850125233390730693643030255886263518268
+
+	//LogRoot2Pi is the value of log(sqrt(2*Pi))
+	logRoot2Pi    = 0.91893853320467274178032973640561763986139747363778341281715154048276569592726039769474329863595419762200564662463433744
+	negLogRoot2Pi = -logRoot2Pi
+	log2Pi        = 1.8378770664093454835606594728112352797227949472755668
+	ln2           = 0.69314718055994530941723212145817656807550013436025525412068000949339362196969471560586332699641868754200148102057068573368552023
+
+	// Euler–Mascheroni constant.
+	eulerGamma = 0.5772156649015328606065120900824024310421593359399235988057672348848677267776646709369470632917467495146314472498070824809605
+)
+
+const (
+	panicNameMismatch = "parameter name mismatch"
+)
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/distribution_test.go b/vendor/gonum.org/v1/gonum/stat/distuv/distribution_test.go
new file mode 100644
index 00000000..722c438a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/distribution_test.go
@@ -0,0 +1,293 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"math"
+	"sort"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/integrate/quad"
+	"gonum.org/v1/gonum/stat"
+)
+
+type meaner interface {
+	Mean() float64
+}
+
+type quantiler interface {
+	Quantile(float64) float64
+}
+
+type medianer interface {
+	quantiler
+	Median() float64
+}
+
+type varStder interface {
+	StdDev() float64
+	Variance() float64
+}
+
+type entropyer interface {
+	LogProber
+	Entropy() float64
+}
+
+type exKurtosiser interface {
+	ExKurtosis() float64
+	Mean() float64
+}
+
+type skewnesser interface {
+	StdDev() float64
+	Mean() float64
+	Skewness() float64
+}
+
+type cumulanter interface {
+	Quantiler
+	CDF(x float64) float64
+	Survival(x float64) float64
+}
+
+func generateSamples(x []float64, r Rander) {
+	for i := range x {
+		x[i] = r.Rand()
+	}
+}
+
+type probLogprober interface {
+	Prob(x float64) float64
+	LogProb(x float64) float64
+}
+
+type cumulantProber interface {
+	cumulanter
+	probLogprober
+}
+
+func checkMean(t *testing.T, i int, x []float64, m meaner, tol float64) {
+	mean := stat.Mean(x, nil)
+	if !floats.EqualWithinAbsOrRel(mean, m.Mean(), tol, tol) {
+		t.Errorf("Mean mismatch case %v: want: %v, got: %v", i, mean, m.Mean())
+	}
+}
+
+func checkMedian(t *testing.T, i int, x []float64, m medianer, tol float64) {
+	median := stat.Quantile(0.5, stat.Empirical, x, nil)
+	if !floats.EqualWithinAbsOrRel(median, m.Median(), tol, tol) {
+		t.Errorf("Median mismatch case %v: want: %v, got: %v", i, median, m.Median())
+	}
+}
+
+func checkVarAndStd(t *testing.T, i int, x []float64, v varStder, tol float64) {
+	variance := stat.Variance(x, nil)
+	if !floats.EqualWithinAbsOrRel(variance, v.Variance(), tol, tol) {
+		t.Errorf("Variance mismatch case %v: want: %v, got: %v", i, variance, v.Variance())
+	}
+	std := math.Sqrt(variance)
+	if !floats.EqualWithinAbsOrRel(std, v.StdDev(), tol, tol) {
+		t.Errorf("StdDev mismatch case %v: want: %v, got: %v", i, std, v.StdDev())
+	}
+}
+
+func checkEntropy(t *testing.T, i int, x []float64, e entropyer, tol float64) {
+	tmp := make([]float64, len(x))
+	for i, v := range x {
+		tmp[i] = -e.LogProb(v)
+	}
+	entropy := stat.Mean(tmp, nil)
+	if !floats.EqualWithinAbsOrRel(entropy, e.Entropy(), tol, tol) {
+		t.Errorf("Entropy mismatch case %v: want: %v, got: %v", i, entropy, e.Entropy())
+	}
+}
+
+func checkExKurtosis(t *testing.T, i int, x []float64, e exKurtosiser, tol float64) {
+	mean := e.Mean()
+	tmp := make([]float64, len(x))
+	for i, x := range x {
+		tmp[i] = math.Pow(x-mean, 4)
+	}
+	variance := stat.Variance(x, nil)
+	mu4 := stat.Mean(tmp, nil)
+	kurtosis := mu4/(variance*variance) - 3
+	if !floats.EqualWithinAbsOrRel(kurtosis, e.ExKurtosis(), tol, tol) {
+		t.Errorf("ExKurtosis mismatch case %v: want: %v, got: %v", i, kurtosis, e.ExKurtosis())
+	}
+}
+
+func checkSkewness(t *testing.T, i int, x []float64, s skewnesser, tol float64) {
+	mean := s.Mean()
+	std := s.StdDev()
+	tmp := make([]float64, len(x))
+	for i, v := range x {
+		tmp[i] = math.Pow(v-mean, 3)
+	}
+	mu3 := stat.Mean(tmp, nil)
+	skewness := mu3 / math.Pow(std, 3)
+	if !floats.EqualWithinAbsOrRel(skewness, s.Skewness(), tol, tol) {
+		t.Errorf("Skewness mismatch case %v: want: %v, got: %v", i, skewness, s.Skewness())
+	}
+}
+
+func checkQuantileCDFSurvival(t *testing.T, i int, xs []float64, c cumulanter, tol float64) {
+	// Quantile, CDF, and survival check.
+	for i, p := range []float64{0.1, 0.25, 0.5, 0.75, 0.9} {
+		x := c.Quantile(p)
+		cdf := c.CDF(x)
+		estCDF := stat.CDF(x, stat.Empirical, xs, nil)
+		if !floats.EqualWithinAbsOrRel(cdf, estCDF, tol, tol) {
+			t.Errorf("CDF mismatch case %v: want: %v, got: %v", i, estCDF, cdf)
+		}
+		if !floats.EqualWithinAbsOrRel(cdf, p, tol, tol) {
+			t.Errorf("Quantile/CDF mismatch case %v: want: %v, got: %v", i, p, cdf)
+		}
+		if math.Abs(1-cdf-c.Survival(x)) > 1e-14 {
+			t.Errorf("Survival/CDF mismatch case %v: want: %v, got: %v", i, 1-cdf, c.Survival(x))
+		}
+	}
+}
+
+func checkProbContinuous(t *testing.T, i int, x []float64, p probLogprober, tol float64) {
+	// Check that the PDF is consistent (integrates to 1).
+	q := quad.Fixed(p.Prob, math.Inf(-1), math.Inf(1), 1000000, nil, 0)
+	if math.Abs(q-1) > tol {
+		t.Errorf("Probability distribution doesn't integrate to 1. Case %v: Got %v", i, q)
+	}
+
+	// Check that PDF and LogPDF are consistent.
+	for i, v := range x {
+		if math.Abs(math.Log(p.Prob(v))-p.LogProb(v)) > 1e-14 {
+			t.Errorf("Prob and LogProb mismatch case %v at %v: want %v, got %v", i, v, math.Log(v), p.LogProb(v))
+			break
+		}
+	}
+}
+
+// checkProbQuantContinuous checks that the Prob, Rand, and Quantile are all consistent.
+// checkProbContinuous only checks that Prob is a valid distribution (integrates
+// to 1 and greater than 0). However, this is also true if the PDF of a different
+// distribution is used. This checks that PDF is also consistent with the
+// CDF implementation and the random samples.
+func checkProbQuantContinuous(t *testing.T, i int, xs []float64, c cumulantProber, tol float64) {
+	ps := make([]float64, 101)
+	floats.Span(ps, 0, 1)
+
+	var xp, x float64
+	for i, p := range ps {
+		x = c.Quantile(p)
+		if p == 0 {
+			xp = x
+			if floats.Min(xs) < x {
+				t.Errorf("Sample of x less than Quantile(0). Case %v.", i)
+				break
+			}
+			continue
+		}
+		if p == 1 {
+			if floats.Max(xs) > x {
+				t.Errorf("Sample of x greater than Quantile(1). Case %v.", i)
+				break
+			}
+		}
+
+		// The integral of the PDF between xp and x should be the difference in
+		// the quantiles.
+		q := quad.Fixed(c.Prob, xp, x, 1000, nil, 0)
+		if math.Abs(q-(p-ps[i-1])) > 1e-5 {
+			t.Errorf("Integral of PDF doesn't match quantile. Case %v. Want %v, got %v.", i, p-ps[i-1], q)
+			break
+		}
+
+		pEst := stat.CDF(x, stat.Empirical, xs, nil)
+		if math.Abs(pEst-p) > tol {
+			t.Errorf("Empirical CDF doesn't match quantile. Case %v.", i)
+		}
+		xp = x
+	}
+}
+
+// checkProbDiscrete confirms that PDF and Rand are consistent for discrete distributions.
+func checkProbDiscrete(t *testing.T, i int, xs []float64, p probLogprober, tol float64) {
+	// Make a map of all of the unique samples.
+	m := make(map[float64]int)
+	for _, v := range xs {
+		m[v]++
+	}
+	for x, count := range m {
+		prob := float64(count) / float64(len(xs))
+		if math.Abs(prob-p.Prob(x)) > tol {
+			t.Errorf("PDF mismatch case %v at %v: want %v, got %v", i, x, prob, p.Prob(x))
+		}
+		if math.Abs(math.Log(p.Prob(x))-p.LogProb(x)) > 1e-14 {
+			t.Errorf("Prob and LogProb mismatch case %v at %v: want %v, got %v", i, x, math.Log(x), p.LogProb(x))
+		}
+	}
+}
+
+// dist is a type that implements the standard set of routines.
+type fullDist interface {
+	CDF(x float64) float64
+	Entropy() float64
+	ExKurtosis() float64
+	LogProb(x float64) float64
+	Mean() float64
+	Median() float64
+	NumParameters() int
+	Prob(x float64) float64
+	Quantile(p float64) float64
+	Rand() float64
+	Skewness() float64
+	StdDev() float64
+	Survival(x float64) float64
+	Variance() float64
+}
+
+// testFullDist tests all of the functions of a fullDist.
+func testFullDist(t *testing.T, f fullDist, i int, continuous bool) {
+	tol := 1e-2
+	const n = 1e6
+	x := make([]float64, n)
+	generateSamples(x, f)
+	sort.Float64s(x)
+
+	checkMean(t, i, x, f, tol)
+	checkVarAndStd(t, i, x, f, tol)
+	checkEntropy(t, i, x, f, tol)
+	checkExKurtosis(t, i, x, f, tol)
+	checkSkewness(t, i, x, f, tol)
+	if continuous {
+		// In a discrete distribution, the median may not have positive probability.
+		checkMedian(t, i, x, f, tol)
+		// In a discrete distribution, the CDF and Quantile may not be perfect mappings.
+		checkQuantileCDFSurvival(t, i, x, f, tol)
+		// Integrate over the PDF
+		checkProbContinuous(t, i, x, f, 1e-10)
+		checkProbQuantContinuous(t, i, x, f, tol)
+	} else {
+		// Check against empirical PDF.
+		checkProbDiscrete(t, i, x, f, tol)
+	}
+}
+
+// testRandLogProb tests that LogProb and Rand give consistent results. This
+// can be used when the distribution does not implement CDF.
+func testRandLogProbContinuous(t *testing.T, i int, min float64, x []float64, f LogProber, tol float64, bins int) {
+	for cdf := 1 / float64(bins); cdf <= 1-1/float64(bins); cdf += 1 / float64(bins) {
+		// Get the estimated CDF from the samples
+		pt := stat.Quantile(cdf, stat.Empirical, x, nil)
+
+		prob := func(x float64) float64 {
+			return math.Exp(f.LogProb(x))
+		}
+		// Integrate the PDF to find the CDF
+		estCDF := quad.Fixed(prob, min, pt, 1000, nil, 0)
+		if !floats.EqualWithinAbsOrRel(cdf, estCDF, tol, tol) {
+			t.Errorf("Mismatch between integral of PDF and empirical CDF. Case %v. Want %v, got %v", i, cdf, estCDF)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/doc.go b/vendor/gonum.org/v1/gonum/stat/distuv/doc.go
new file mode 100644
index 00000000..bdf073f5
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package distuv provides univariate random distribution types.
+package distuv // import "gonum.org/v1/gonum/stat/distuv"
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/exponential.go b/vendor/gonum.org/v1/gonum/stat/distuv/exponential.go
new file mode 100644
index 00000000..c29f9fef
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/exponential.go
@@ -0,0 +1,259 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"math"
+	"math/rand"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/stat"
+)
+
+// Exponential represents the exponential distribution (https://en.wikipedia.org/wiki/Exponential_distribution).
+type Exponential struct {
+	Rate   float64
+	Source *rand.Rand
+}
+
+// CDF computes the value of the cumulative density function at x.
+func (e Exponential) CDF(x float64) float64 {
+	if x < 0 {
+		return 0
+	}
+	return 1 - math.Exp(-e.Rate*x)
+}
+
+// ConjugateUpdate updates the parameters of the distribution from the sufficient
+// statistics of a set of samples. The sufficient statistics, suffStat, have been
+// observed with nSamples observations. The prior values of the distribution are those
+// currently in the distribution, and have been observed with priorStrength samples.
+//
+// For the exponential distribution, the sufficient statistic is the inverse of
+// the mean of the samples.
+// The prior is having seen priorStrength[0] samples with inverse mean Exponential.Rate
+// As a result of this function, Exponential.Rate is updated based on the weighted
+// samples, and priorStrength is modified to include the new number of samples observed.
+//
+// This function panics if len(suffStat) != 1 or len(priorStrength) != 1.
+func (e *Exponential) ConjugateUpdate(suffStat []float64, nSamples float64, priorStrength []float64) {
+	if len(suffStat) != 1 {
+		panic("exponential: incorrect suffStat length")
+	}
+	if len(priorStrength) != 1 {
+		panic("exponential: incorrect priorStrength length")
+	}
+
+	totalSamples := nSamples + priorStrength[0]
+
+	totalSum := nSamples / suffStat[0]
+	if !(priorStrength[0] == 0) {
+		totalSum += priorStrength[0] / e.Rate
+	}
+	e.Rate = totalSamples / totalSum
+	priorStrength[0] = totalSamples
+}
+
+// Entropy returns the entropy of the distribution.
+func (e Exponential) Entropy() float64 {
+	return 1 - math.Log(e.Rate)
+}
+
+// ExKurtosis returns the excess kurtosis of the distribution.
+func (Exponential) ExKurtosis() float64 {
+	return 6
+}
+
+// Fit sets the parameters of the probability distribution from the
+// data samples x with relative weights w.
+// If weights is nil, then all the weights are 1.
+// If weights is not nil, then the len(weights) must equal len(samples).
+func (e *Exponential) Fit(samples, weights []float64) {
+	suffStat := make([]float64, e.NumSuffStat())
+	nSamples := e.SuffStat(suffStat, samples, weights)
+	e.ConjugateUpdate(suffStat, nSamples, make([]float64, e.NumSuffStat()))
+}
+
+// LogProb computes the natural logarithm of the value of the probability density function at x.
+func (e Exponential) LogProb(x float64) float64 {
+	if x < 0 {
+		return math.Inf(-1)
+	}
+	return math.Log(e.Rate) - e.Rate*x
+}
+
+// Mean returns the mean of the probability distribution.
+func (e Exponential) Mean() float64 {
+	return 1 / e.Rate
+}
+
+// Median returns the median of the probability distribution.
+func (e Exponential) Median() float64 {
+	return math.Ln2 / e.Rate
+}
+
+// Mode returns the mode of the probability distribution.
+func (Exponential) Mode() float64 {
+	return 0
+}
+
+// NumParameters returns the number of parameters in the distribution.
+func (Exponential) NumParameters() int {
+	return 1
+}
+
+// NumSuffStat returns the number of sufficient statistics for the distribution.
+func (Exponential) NumSuffStat() int {
+	return 1
+}
+
+// Prob computes the value of the probability density function at x.
+func (e Exponential) Prob(x float64) float64 {
+	return math.Exp(e.LogProb(x))
+}
+
+// Quantile returns the inverse of the cumulative probability distribution.
+func (e Exponential) Quantile(p float64) float64 {
+	if p < 0 || p > 1 {
+		panic(badPercentile)
+	}
+	return -math.Log(1-p) / e.Rate
+}
+
+// Rand returns a random sample drawn from the distribution.
+func (e Exponential) Rand() float64 {
+	var rnd float64
+	if e.Source == nil {
+		rnd = rand.ExpFloat64()
+	} else {
+		rnd = e.Source.ExpFloat64()
+	}
+	return rnd / e.Rate
+}
+
+// Score returns the score function with respect to the parameters of the
+// distribution at the input location x. The score function is the derivative
+// of the log-likelihood at x with respect to the parameters
+//  (∂/∂θ) log(p(x;θ))
+// If deriv is non-nil, len(deriv) must equal the number of parameters otherwise
+// Score will panic, and the derivative is stored in-place into deriv. If deriv
+// is nil a new slice will be allocated and returned.
+//
+// The order is [∂LogProb / ∂Rate].
+//
+// For more information, see https://en.wikipedia.org/wiki/Score_%28statistics%29.
+//
+// Special cases:
+//  Score(0) = [NaN]
+func (e Exponential) Score(deriv []float64, x float64) []float64 {
+	if deriv == nil {
+		deriv = make([]float64, e.NumParameters())
+	}
+	if len(deriv) != e.NumParameters() {
+		panic(badLength)
+	}
+	if x > 0 {
+		deriv[0] = 1/e.Rate - x
+		return deriv
+	}
+	if x < 0 {
+		deriv[0] = 0
+		return deriv
+	}
+	deriv[0] = math.NaN()
+	return deriv
+}
+
+// ScoreInput returns the score function with respect to the input of the
+// distribution at the input location specified by x. The score function is the
+// derivative of the log-likelihood
+//  (d/dx) log(p(x)) .
+// Special cases:
+//  ScoreInput(0) = NaN
+func (e Exponential) ScoreInput(x float64) float64 {
+	if x > 0 {
+		return -e.Rate
+	}
+	if x < 0 {
+		return 0
+	}
+	return math.NaN()
+}
+
+// Skewness returns the skewness of the distribution.
+func (Exponential) Skewness() float64 {
+	return 2
+}
+
+// StdDev returns the standard deviation of the probability distribution.
+func (e Exponential) StdDev() float64 {
+	return 1 / e.Rate
+}
+
+// SuffStat computes the sufficient statistics of set of samples to update
+// the distribution. The sufficient statistics are stored in place, and the
+// effective number of samples are returned.
+//
+// The exponential distribution has one sufficient statistic, the average rate
+// of the samples.
+//
+// If weights is nil, the weights are assumed to be 1, otherwise panics if
+// len(samples) != len(weights). Panics if len(suffStat) != NumSuffStat().
+func (Exponential) SuffStat(suffStat, samples, weights []float64) (nSamples float64) {
+	if len(weights) != 0 && len(samples) != len(weights) {
+		panic(badLength)
+	}
+
+	if len(suffStat) != (Exponential{}).NumSuffStat() {
+		panic(badSuffStat)
+	}
+
+	if len(weights) == 0 {
+		nSamples = float64(len(samples))
+	} else {
+		nSamples = floats.Sum(weights)
+	}
+
+	mean := stat.Mean(samples, weights)
+	suffStat[0] = 1 / mean
+	return nSamples
+}
+
+// Survival returns the survival function (complementary CDF) at x.
+func (e Exponential) Survival(x float64) float64 {
+	if x < 0 {
+		return 1
+	}
+	return math.Exp(-e.Rate * x)
+}
+
+// setParameters modifies the parameters of the distribution.
+func (e *Exponential) setParameters(p []Parameter) {
+	if len(p) != e.NumParameters() {
+		panic("exponential: incorrect number of parameters to set")
+	}
+	if p[0].Name != "Rate" {
+		panic("exponential: " + panicNameMismatch)
+	}
+	e.Rate = p[0].Value
+}
+
+// Variance returns the variance of the probability distribution.
+func (e Exponential) Variance() float64 {
+	return 1 / (e.Rate * e.Rate)
+}
+
+// parameters returns the parameters of the distribution.
+func (e Exponential) parameters(p []Parameter) []Parameter {
+	nParam := e.NumParameters()
+	if p == nil {
+		p = make([]Parameter, nParam)
+	} else if len(p) != nParam {
+		panic("exponential: improper parameter length")
+	}
+	p[0].Name = "Rate"
+	p[0].Value = e.Rate
+	return p
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/exponential_test.go b/vendor/gonum.org/v1/gonum/stat/distuv/exponential_test.go
new file mode 100644
index 00000000..9c389702
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/exponential_test.go
@@ -0,0 +1,71 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"math"
+	"testing"
+)
+
+func TestExponentialProb(t *testing.T) {
+	pts := []univariateProbPoint{
+		{
+			loc:     0,
+			prob:    1,
+			cumProb: 0,
+			logProb: 0,
+		},
+		{
+			loc:     -1,
+			prob:    0,
+			cumProb: 0,
+			logProb: math.Inf(-1),
+		},
+		{
+			loc:     1,
+			prob:    1 / (math.E),
+			cumProb: 0.6321205588285576784044762298385391325541888689682321654921631983025385042551001966428527256540803563,
+			logProb: -1,
+		},
+		{
+			loc:     20,
+			prob:    math.Exp(-20),
+			cumProb: 0.999999997938846377561442172034059619844179023624192724400896307027755338370835976215440646720089072,
+			logProb: -20,
+		},
+	}
+	testDistributionProbs(t, Exponential{Rate: 1}, "Exponential", pts)
+}
+
+func TestExponentialFitPrior(t *testing.T) {
+	testConjugateUpdate(t, func() ConjugateUpdater { return &Exponential{Rate: 13.7} })
+}
+
+func TestExponentialScore(t *testing.T) {
+	for _, test := range []*Exponential{
+		{
+			Rate: 1,
+		},
+		{
+			Rate: 0.35,
+		},
+		{
+			Rate: 4.6,
+		},
+	} {
+		testDerivParam(t, test)
+	}
+}
+
+func TestExponentialFitPanic(t *testing.T) {
+	e := Exponential{Rate: 2}
+	defer func() {
+		r := recover()
+		if r != nil {
+			t.Errorf("unexpected panic for Fit call: %v", r)
+		}
+	}()
+	e.Fit(make([]float64, 10), nil)
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/f.go b/vendor/gonum.org/v1/gonum/stat/distuv/f.go
new file mode 100644
index 00000000..6e689e6e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/f.go
@@ -0,0 +1,132 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"math"
+	"math/rand"
+
+	"gonum.org/v1/gonum/mathext"
+)
+
+// F implements the F-distribution, a two-parameter continuous distribution
+// with support over the positive real numbers.
+//
+// The F-distribution has density function
+//  sqrt(((d1*x)^d1) * d2^d2 / ((d1*x+d2)^(d1+d2))) / (x * B(d1/2,d2/2))
+// where B is the beta function.
+//
+// For more information, see https://en.wikipedia.org/wiki/F-distribution
+type F struct {
+	D1     float64 // Degrees of freedom for the numerator
+	D2     float64 // Degrees of freedom for the denominator
+	Source *rand.Rand
+}
+
+// CDF computes the value of the cumulative density function at x.
+func (f F) CDF(x float64) float64 {
+	return mathext.RegIncBeta(f.D1/2, f.D2/2, f.D1*x/(f.D1*x+f.D2))
+}
+
+// ExKurtosis returns the excess kurtosis of the distribution.
+//
+// ExKurtosis returns NaN if the D2 parameter is less or equal to 8.
+func (f F) ExKurtosis() float64 {
+	if f.D2 <= 8 {
+		return math.NaN()
+	}
+	return (12 / (f.D2 - 6)) * ((5*f.D2-22)/(f.D2-8) + ((f.D2-4)/f.D1)*((f.D2-2)/(f.D2-8))*((f.D2-2)/(f.D1+f.D2-2)))
+}
+
+// LogProb computes the natural logarithm of the value of the probability
+// density function at x.
+func (f F) LogProb(x float64) float64 {
+	return 0.5*(f.D1*math.Log(f.D1*x)+f.D2*math.Log(f.D2)-(f.D1+f.D2)*math.Log(f.D1*x+f.D2)) - math.Log(x) - mathext.Lbeta(f.D1/2, f.D2/2)
+}
+
+// Mean returns the mean of the probability distribution.
+//
+// Mean returns NaN if the D2 parameter is less than or equal to 2.
+func (f F) Mean() float64 {
+	if f.D2 <= 2 {
+		return math.NaN()
+	}
+	return f.D2 / (f.D2 - 2)
+}
+
+// Mode returns the mode of the distribution.
+//
+// Mode returns NaN if the D1 parameter is less than or equal to 2.
+func (f F) Mode() float64 {
+	if f.D1 <= 2 {
+		return math.NaN()
+	}
+	return ((f.D1 - 2) / f.D1) * (f.D2 / (f.D2 + 2))
+}
+
+// NumParameters returns the number of parameters in the distribution.
+func (f F) NumParameters() int {
+	return 2
+}
+
+// Prob computes the value of the probability density function at x.
+func (f F) Prob(x float64) float64 {
+	return math.Exp(f.LogProb(x))
+}
+
+// Quantile returns the inverse of the cumulative distribution function.
+func (f F) Quantile(p float64) float64 {
+	if p < 0 || p > 1 {
+		panic(badPercentile)
+	}
+	y := mathext.InvRegIncBeta(0.5*f.D1, 0.5*f.D2, p)
+	return f.D2 * y / (f.D1 * (1 - y))
+}
+
+// Rand returns a random sample drawn from the distribution.
+func (f F) Rand() float64 {
+	u1 := ChiSquared{f.D1, f.Source}.Rand()
+	u2 := ChiSquared{f.D2, f.Source}.Rand()
+	return (u1 / f.D1) / (u2 / f.D2)
+}
+
+// Skewness returns the skewness of the distribution.
+//
+// Skewness returns NaN if the D2 parameter is less than or equal to 6.
+func (f F) Skewness() float64 {
+	if f.D2 <= 6 {
+		return math.NaN()
+	}
+	num := (2*f.D1 + f.D2 - 2) * math.Sqrt(8*(f.D2-4))
+	den := (f.D2 - 6) * math.Sqrt(f.D1*(f.D1+f.D2-2))
+	return num / den
+}
+
+// StdDev returns the standard deviation of the probability distribution.
+//
+// StdDev returns NaN if the D2 parameter is less than or equal to 4.
+func (f F) StdDev() float64 {
+	if f.D2 <= 4 {
+		return math.NaN()
+	}
+	return math.Sqrt(f.Variance())
+}
+
+// Survival returns the survival function (complementary CDF) at x.
+func (f F) Survival(x float64) float64 {
+	return 1 - f.CDF(x)
+}
+
+// Variance returns the variance of the probability distribution.
+//
+// Variance returns NaN if the D2 parameter is less than or equal to 4.
+func (f F) Variance() float64 {
+	if f.D2 <= 4 {
+		return math.NaN()
+	}
+	num := 2 * f.D2 * f.D2 * (f.D1 + f.D2 - 2)
+	den := f.D1 * (f.D2 - 2) * (f.D2 - 2) * (f.D2 - 4)
+	return num / den
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/f_test.go b/vendor/gonum.org/v1/gonum/stat/distuv/f_test.go
new file mode 100644
index 00000000..7e5dfbea
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/f_test.go
@@ -0,0 +1,89 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"math/rand"
+	"sort"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+func TestFProb(t *testing.T) {
+	for _, test := range []struct {
+		x, d1, d2, want float64
+	}{
+		// Values calculated with scipy.stats.f
+		{0.0001, 4, 6, 0.00053315559110558126},
+		{0.1, 1, 1, 0.91507658371794609},
+		{0.5, 11, 7, 0.66644660411410883},
+		{0.9, 20, 15, 0.88293424959522437},
+		{1, 1, 1, 0.15915494309189535},
+		{2, 15, 12, 0.16611971273429088},
+		{5, 4, 8, 0.013599775603702537},
+		{10, 12, 9, 0.00032922887567957289},
+		{100, 7, 7, 6.08037637806889e-08},
+		{1000, 2, 1, 1.1171959870312232e-05},
+	} {
+		pdf := F{test.d1, test.d2, nil}.Prob(test.x)
+		if !floats.EqualWithinAbsOrRel(pdf, test.want, 1e-10, 1e-10) {
+			t.Errorf("Prob mismatch, x = %v, d1 = %v, d2 = %v. Got %v, want %v", test.x, test.d1, test.d2, pdf, test.want)
+		}
+	}
+}
+
+func TestFCDF(t *testing.T) {
+	for _, test := range []struct {
+		x, d1, d2, want float64
+	}{
+		// Values calculated with scipy.stats.f
+		{0.0001, 4, 6, 2.6660741629519019e-08},
+		{0.1, 1, 1, 0.19498222904213672},
+		{0.5, 11, 7, 0.14625028471336987},
+		{0.9, 20, 15, 0.40567939897287852},
+		{1, 1, 1, 0.50000000000000011},
+		{2, 15, 12, 0.8839384428956264},
+		{5, 4, 8, 0.97429642410900219},
+		{10, 12, 9, 0.99915733385467187},
+		{100, 7, 7, 0.99999823560259171},
+		{1000, 2, 1, 0.97764490829950534},
+	} {
+		cdf := F{test.d1, test.d2, nil}.CDF(test.x)
+		if !floats.EqualWithinAbsOrRel(cdf, test.want, 1e-10, 1e-10) {
+			t.Errorf("CDF mismatch, x = %v, d1 = %v, d2 = %v. Got %v, want %v", test.x, test.d1, test.d2, cdf, test.want)
+		}
+	}
+}
+
+func TestF(t *testing.T) {
+	src := rand.New(rand.NewSource(1))
+	for i, b := range []F{
+		{13, 16, src},
+		{42, 31, src},
+		{77, 92, src},
+	} {
+		testF(t, b, i)
+	}
+}
+
+func testF(t *testing.T, f F, i int) {
+	const (
+		tol  = 1e-2
+		n    = 1e5
+		bins = 50
+	)
+	x := make([]float64, n)
+	generateSamples(x, f)
+	sort.Float64s(x)
+
+	testRandLogProbContinuous(t, i, 0, x, f, tol, bins)
+	checkProbContinuous(t, i, x, f, 1e-3)
+	checkMean(t, i, x, f, tol)
+	checkVarAndStd(t, i, x, f, tol)
+	checkExKurtosis(t, i, x, f, 1e-1)
+	checkSkewness(t, i, x, f, 5e-2)
+	checkQuantileCDFSurvival(t, i, x, f, 5e-3)
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/gamma.go b/vendor/gonum.org/v1/gonum/stat/distuv/gamma.go
new file mode 100644
index 00000000..650ad6c8
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/gamma.go
@@ -0,0 +1,244 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"math"
+	"math/rand"
+
+	"gonum.org/v1/gonum/mathext"
+)
+
+// Gamma implements the Gamma distribution, a two-parameter continuous distribution
+// with support over the positive real numbers.
+//
+// The gamma distribution has density function
+//  β^α / Γ(α) x^(α-1)e^(-βx)
+//
+// For more information, see https://en.wikipedia.org/wiki/Gamma_distribution
+type Gamma struct {
+	// Alpha is the shape parameter of the distribution. Alpha must be greater
+	// than 0. If Alpha == 1, this is equivalent to an exponential distribution.
+	Alpha float64
+	// Beta is the rate parameter of the distribution. Beta must be greater than 0.
+	// If Beta == 2, this is equivalent to a Chi-Squared distribution.
+	Beta float64
+
+	Source *rand.Rand
+}
+
+// CDF computes the value of the cumulative distribution function at x.
+func (g Gamma) CDF(x float64) float64 {
+	if x < 0 {
+		return 0
+	}
+	return mathext.GammaInc(g.Alpha, g.Beta*x)
+}
+
+// ExKurtosis returns the excess kurtosis of the distribution.
+func (g Gamma) ExKurtosis() float64 {
+	return 6 / g.Alpha
+}
+
+// LogProb computes the natural logarithm of the value of the probability
+// density function at x.
+func (g Gamma) LogProb(x float64) float64 {
+	if x <= 0 {
+		return math.Inf(-1)
+	}
+	a := g.Alpha
+	b := g.Beta
+	lg, _ := math.Lgamma(a)
+	return a*math.Log(b) - lg + (a-1)*math.Log(x) - b*x
+}
+
+// Mean returns the mean of the probability distribution.
+func (g Gamma) Mean() float64 {
+	return g.Alpha / g.Beta
+}
+
+// Mode returns the mode of the normal distribution.
+//
+// The mode is NaN in the special case where the Alpha (shape) parameter
+// is less than 1.
+func (g Gamma) Mode() float64 {
+	if g.Alpha < 1 {
+		return math.NaN()
+	}
+	return (g.Alpha - 1) / g.Beta
+}
+
+// NumParameters returns the number of parameters in the distribution.
+func (Gamma) NumParameters() int {
+	return 2
+}
+
+// Prob computes the value of the probability density function at x.
+func (g Gamma) Prob(x float64) float64 {
+	return math.Exp(g.LogProb(x))
+}
+
+// Quantile returns the inverse of the cumulative distribution function.
+func (g Gamma) Quantile(p float64) float64 {
+	if p < 0 || p > 1 {
+		panic(badPercentile)
+	}
+	return mathext.GammaIncInv(g.Alpha, p) / g.Beta
+}
+
+// Rand returns a random sample drawn from the distribution.
+//
+// Rand panics if either alpha or beta is <= 0.
+func (g Gamma) Rand() float64 {
+	if g.Beta <= 0 {
+		panic("gamma: beta <= 0")
+	}
+
+	unifrnd := rand.Float64
+	exprnd := rand.ExpFloat64
+	normrnd := rand.NormFloat64
+	if g.Source != nil {
+		unifrnd = g.Source.Float64
+		exprnd = g.Source.ExpFloat64
+		normrnd = g.Source.NormFloat64
+	}
+
+	a := g.Alpha
+	b := g.Beta
+	switch {
+	case a <= 0:
+		panic("gamma: alpha < 0")
+	case a == 1:
+		// Generate from exponential
+		return exprnd() / b
+	case a < 0.3:
+		// Generate using
+		//  Liu, Chuanhai, Martin, Ryan and Syring, Nick. "Simulating from a
+		//  gamma distribution with small shape parameter"
+		//  https://arxiv.org/abs/1302.1884
+		//   use this reference: http://link.springer.com/article/10.1007/s00180-016-0692-0
+
+		// Algorithm adjusted to work in log space as much as possible.
+		lambda := 1/a - 1
+		lw := math.Log(a) - 1 - math.Log(1-a)
+		lr := -math.Log(1 + math.Exp(lw))
+		lc, _ := math.Lgamma(a + 1)
+		for {
+			e := exprnd()
+			var z float64
+			if e >= -lr {
+				z = e + lr
+			} else {
+				z = -exprnd() / lambda
+			}
+			lh := lc - z - math.Exp(-z/a)
+			var lEta float64
+			if z >= 0 {
+				lEta = lc - z
+			} else {
+				lEta = lc + lw + math.Log(lambda) + lambda*z
+			}
+			if lh-lEta > -exprnd() {
+				return math.Exp(-z/a) / b
+			}
+		}
+	case a >= 0.3 && a < 1:
+		// Generate using:
+		//  Kundu, Debasis, and Rameshwar D. Gupta. "A convenient way of generating
+		//  gamma random variables using generalized exponential distribution."
+		//  Computational Statistics & Data Analysis 51.6 (2007): 2796-2802.
+
+		// TODO(btracey): Change to using Algorithm 3 if we can find the bug in
+		// the implementation below.
+
+		// Algorithm 2.
+		alpha := g.Alpha
+		a := math.Pow(1-expNegOneHalf, alpha) / (math.Pow(1-expNegOneHalf, alpha) + alpha*math.Exp(-1)/math.Pow(2, alpha))
+		b := math.Pow(1-expNegOneHalf, alpha) + alpha/math.E/math.Pow(2, alpha)
+		var x float64
+		for {
+			u := unifrnd()
+			if u <= a {
+				x = -2 * math.Log(1-math.Pow(u*b, 1/alpha))
+			} else {
+				x = -math.Log(math.Pow(2, alpha) / alpha * b * (1 - u))
+			}
+			v := unifrnd()
+			if x <= 1 {
+				if v <= math.Pow(x, alpha-1)*math.Exp(-x/2)/(math.Pow(2, alpha-1)*math.Pow(1-math.Exp(-x/2), alpha-1)) {
+					break
+				}
+			} else {
+				if v <= math.Pow(x, alpha-1) {
+					break
+				}
+			}
+		}
+		return x / g.Beta
+
+		/*
+			//  Algorithm 3.
+			d := 1.0334 - 0.0766*math.Exp(2.2942*alpha)
+			a := math.Pow(2, alpha) * math.Pow(1-math.Exp(-d/2), alpha)
+			b := alpha * math.Pow(d, alpha-1) * math.Exp(-d)
+			c := a + b
+			var x float64
+			for {
+				u := unifrnd()
+				if u <= a/(a+b) {
+					x = -2 * math.Log(1-math.Pow(c*u, 1/a)/2)
+				} else {
+					x = -math.Log(c * (1 - u) / (alpha * math.Pow(d, alpha-1)))
+				}
+				v := unifrnd()
+				if x <= d {
+					if v <= (math.Pow(x, alpha-1)*math.Exp(-x/2))/(math.Pow(2, alpha-1)*math.Pow(1-math.Exp(-x/2), alpha-1)) {
+						break
+					}
+				} else {
+					if v <= math.Pow(d/x, 1-alpha) {
+						break
+					}
+				}
+			}
+			return x / g.Beta
+		*/
+	case a > 1:
+		// Generate using:
+		//  Marsaglia, George, and Wai Wan Tsang. "A simple method for generating
+		//  gamma variables." ACM Transactions on Mathematical Software (TOMS)
+		//  26.3 (2000): 363-372.
+		d := a - 1.0/3
+		c := 1 / (3 * math.Sqrt(d))
+		for {
+			u := -exprnd()
+			x := normrnd()
+			v := 1 + x*c
+			v = v * v * v
+			if u < 0.5*x*x+d*(1-v+math.Log(v)) {
+				return d * v / b
+			}
+		}
+	}
+	panic("unreachable")
+}
+
+// Survival returns the survival function (complementary CDF) at x.
+func (g Gamma) Survival(x float64) float64 {
+	if x < 0 {
+		return 1
+	}
+	return mathext.GammaIncComp(g.Alpha, g.Beta*x)
+}
+
+// StdDev returns the standard deviation of the probability distribution.
+func (g Gamma) StdDev() float64 {
+	return math.Sqrt(g.Variance())
+}
+
+// Variance returns the variance of the probability distribution.
+func (g Gamma) Variance() float64 {
+	return g.Alpha / g.Beta / g.Beta
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/gamma_test.go b/vendor/gonum.org/v1/gonum/stat/distuv/gamma_test.go
new file mode 100644
index 00000000..6a1a9bf7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/gamma_test.go
@@ -0,0 +1,63 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"math/rand"
+	"sort"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+func TestGamma(t *testing.T) {
+	// Values a comparison with scipy
+	for _, test := range []struct {
+		x, alpha, want float64
+	}{
+		{0.9, 0.1, 0.046986817861555757},
+		{0.9, 0.01, 0.0045384353289090401},
+		{0.45, 0.01, 0.014137035997241795},
+	} {
+		pdf := Gamma{Alpha: test.alpha, Beta: 1}.Prob(test.x)
+		if !floats.EqualWithinAbsOrRel(pdf, test.want, 1e-10, 1e-10) {
+			t.Errorf("Pdf mismatch. Got %v, want %v", pdf, test.want)
+		}
+	}
+	src := rand.New(rand.NewSource(1))
+	for i, g := range []Gamma{
+
+		{Alpha: 0.5, Beta: 0.8, Source: src},
+		{Alpha: 0.9, Beta: 6, Source: src},
+		{Alpha: 0.9, Beta: 500, Source: src},
+
+		{Alpha: 1, Beta: 1, Source: src},
+
+		{Alpha: 1.6, Beta: 0.4, Source: src},
+		{Alpha: 2.6, Beta: 1.5, Source: src},
+		{Alpha: 5.6, Beta: 0.5, Source: src},
+		{Alpha: 30, Beta: 1.7, Source: src},
+		{Alpha: 30.2, Beta: 1.7, Source: src},
+	} {
+		testGamma(t, g, i)
+	}
+}
+
+func testGamma(t *testing.T, f Gamma, i int) {
+	// TODO(btracey): Replace this when Gamma implements FullDist.
+	tol := 1e-2
+	const n = 1e5
+	const bins = 50
+	x := make([]float64, n)
+	generateSamples(x, f)
+	sort.Float64s(x)
+
+	testRandLogProbContinuous(t, i, 0, x, f, tol, bins)
+	checkMean(t, i, x, f, tol)
+	checkVarAndStd(t, i, x, f, 2e-2)
+	checkExKurtosis(t, i, x, f, 2e-1)
+	checkProbContinuous(t, i, x, f, 1e-3)
+	checkQuantileCDFSurvival(t, i, x, f, 5e-2)
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/general.go b/vendor/gonum.org/v1/gonum/stat/distuv/general.go
new file mode 100644
index 00000000..3d9cb865
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/general.go
@@ -0,0 +1,24 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import "math"
+
+// Parameter represents a parameter of a probability distribution
+type Parameter struct {
+	Name  string
+	Value float64
+}
+
+var (
+	badPercentile = "distuv: percentile out of bounds"
+	badLength     = "distuv: slice length mismatch"
+	badSuffStat   = "distuv: wrong suffStat length"
+	badNoSamples  = "distuv: must have at least one sample"
+)
+
+var (
+	expNegOneHalf = math.Exp(-0.5)
+)
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/general_test.go b/vendor/gonum.org/v1/gonum/stat/distuv/general_test.go
new file mode 100644
index 00000000..63a89dd0
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/general_test.go
@@ -0,0 +1,204 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"fmt"
+	"math"
+	"testing"
+
+	"gonum.org/v1/gonum/diff/fd"
+	"gonum.org/v1/gonum/floats"
+)
+
+type univariateProbPoint struct {
+	loc     float64
+	logProb float64
+	cumProb float64
+	prob    float64
+}
+
+type UniProbDist interface {
+	Prob(float64) float64
+	CDF(float64) float64
+	LogProb(float64) float64
+	Quantile(float64) float64
+	Survival(float64) float64
+}
+
+func absEq(a, b float64) bool {
+	// This is expressed as the inverse to catch the
+	// case a = Inf and b = Inf of the same sign.
+	return !(math.Abs(a-b) > 1e-14)
+}
+
+// TODO: Implement a better test for Quantile
+func testDistributionProbs(t *testing.T, dist UniProbDist, name string, pts []univariateProbPoint) {
+	for _, pt := range pts {
+		logProb := dist.LogProb(pt.loc)
+		if !absEq(logProb, pt.logProb) {
+			t.Errorf("Log probability doesnt match for "+name+". Expected %v. Found %v", pt.logProb, logProb)
+		}
+		prob := dist.Prob(pt.loc)
+		if !absEq(prob, pt.prob) {
+			t.Errorf("Probability doesn't match for "+name+". Expected %v. Found %v", pt.prob, prob)
+		}
+		cumProb := dist.CDF(pt.loc)
+		if !absEq(cumProb, pt.cumProb) {
+			t.Errorf("Cumulative Probability doesn't match for "+name+". Expected %v. Found %v", pt.cumProb, cumProb)
+		}
+		if !absEq(dist.Survival(pt.loc), 1-pt.cumProb) {
+			t.Errorf("Survival doesn't match for %v. Expected %v, Found %v", name, 1-pt.cumProb, dist.Survival(pt.loc))
+		}
+		if pt.prob != 0 {
+			if math.Abs(dist.Quantile(pt.cumProb)-pt.loc) > 1e-4 {
+				fmt.Println("true =", pt.loc)
+				fmt.Println("calculated=", dist.Quantile(pt.cumProb))
+				t.Errorf("Quantile doesn't match for "+name+", loc =  %v", pt.loc)
+			}
+		}
+	}
+}
+
+type ConjugateUpdater interface {
+	NumParameters() int
+	parameters([]Parameter) []Parameter
+
+	NumSuffStat() int
+	SuffStat([]float64, []float64, []float64) float64
+	ConjugateUpdate([]float64, float64, []float64)
+
+	Rand() float64
+}
+
+func testConjugateUpdate(t *testing.T, newFittable func() ConjugateUpdater) {
+	for i, test := range []struct {
+		samps   []float64
+		weights []float64
+	}{
+		{
+			samps:   randn(newFittable(), 10),
+			weights: nil,
+		},
+		{
+			samps:   randn(newFittable(), 10),
+			weights: ones(10),
+		},
+		{
+			samps:   randn(newFittable(), 10),
+			weights: randn(&Exponential{Rate: 1}, 10),
+		},
+	} {
+		// ensure that conjugate produces the same result both incrementally and all at once
+		incDist := newFittable()
+		stats := make([]float64, incDist.NumSuffStat())
+		prior := make([]float64, incDist.NumParameters())
+		for j := range test.samps {
+			var incWeights, allWeights []float64
+			if test.weights != nil {
+				incWeights = test.weights[j : j+1]
+				allWeights = test.weights[0 : j+1]
+			}
+			nsInc := incDist.SuffStat(stats, test.samps[j:j+1], incWeights)
+			incDist.ConjugateUpdate(stats, nsInc, prior)
+
+			allDist := newFittable()
+			nsAll := allDist.SuffStat(stats, test.samps[0:j+1], allWeights)
+			allDist.ConjugateUpdate(stats, nsAll, make([]float64, allDist.NumParameters()))
+			if !parametersEqual(incDist.parameters(nil), allDist.parameters(nil), 1e-12) {
+				t.Errorf("prior doesn't match after incremental update for (%d, %d). Incremental is %v, all at once is %v", i, j, incDist, allDist)
+			}
+
+			if test.weights == nil {
+				onesDist := newFittable()
+				nsOnes := onesDist.SuffStat(stats, test.samps[0:j+1], ones(j+1))
+				onesDist.ConjugateUpdate(stats, nsOnes, make([]float64, onesDist.NumParameters()))
+				if !parametersEqual(onesDist.parameters(nil), incDist.parameters(nil), 1e-14) {
+					t.Errorf("nil and uniform weighted prior doesn't match for incremental update for (%d, %d). Uniform weighted is %v, nil is %v", i, j, onesDist, incDist)
+				}
+				if !parametersEqual(onesDist.parameters(nil), allDist.parameters(nil), 1e-14) {
+					t.Errorf("nil and uniform weighted prior doesn't match for all at once update for (%d, %d). Uniform weighted is %v, nil is %v", i, j, onesDist, incDist)
+				}
+			}
+		}
+	}
+}
+
+// randn generates a specified number of random samples
+func randn(dist Rander, n int) []float64 {
+	x := make([]float64, n)
+	for i := range x {
+		x[i] = dist.Rand()
+	}
+	return x
+}
+
+func ones(n int) []float64 {
+	x := make([]float64, n)
+	for i := range x {
+		x[i] = 1
+	}
+	return x
+}
+
+func parametersEqual(p1, p2 []Parameter, tol float64) bool {
+	for i, p := range p1 {
+		if p.Name != p2[i].Name {
+			return false
+		}
+		if math.Abs(p.Value-p2[i].Value) > tol {
+			return false
+		}
+	}
+	return true
+}
+
+type derivParamTester interface {
+	LogProb(x float64) float64
+	Score(deriv []float64, x float64) []float64
+	Quantile(p float64) float64
+	NumParameters() int
+	parameters([]Parameter) []Parameter
+	setParameters([]Parameter)
+}
+
+func testDerivParam(t *testing.T, d derivParamTester) {
+	// Tests that the derivative matches for a number of different quantiles
+	// along the distribution.
+	nTest := 10
+	quantiles := make([]float64, nTest)
+	floats.Span(quantiles, 0.1, 0.9)
+
+	deriv := make([]float64, d.NumParameters())
+	fdDeriv := make([]float64, d.NumParameters())
+
+	initParams := d.parameters(nil)
+	init := make([]float64, d.NumParameters())
+	for i, v := range initParams {
+		init[i] = v.Value
+	}
+	for _, v := range quantiles {
+		d.setParameters(initParams)
+		x := d.Quantile(v)
+		d.Score(deriv, x)
+		f := func(p []float64) float64 {
+			params := d.parameters(nil)
+			for i, v := range p {
+				params[i].Value = v
+			}
+			d.setParameters(params)
+			return d.LogProb(x)
+		}
+		fd.Gradient(fdDeriv, f, init, nil)
+		if !floats.EqualApprox(deriv, fdDeriv, 1e-6) {
+			t.Fatal("Derivative mismatch. Want", fdDeriv, ", got", deriv, ".")
+		}
+		d.setParameters(initParams)
+		d2 := d.Score(nil, x)
+		if !floats.EqualApprox(d2, deriv, 1e-14) {
+			t.Errorf("Derivative mismatch when input nil Want %v, got %v", d2, deriv)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/interfaces.go b/vendor/gonum.org/v1/gonum/stat/distuv/interfaces.go
new file mode 100644
index 00000000..b2eb80ba
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/interfaces.go
@@ -0,0 +1,22 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+type LogProber interface {
+	LogProb(float64) float64
+}
+
+type Rander interface {
+	Rand() float64
+}
+
+type RandLogProber interface {
+	Rander
+	LogProber
+}
+
+type Quantiler interface {
+	Quantile(p float64) float64
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/laplace.go b/vendor/gonum.org/v1/gonum/stat/distuv/laplace.go
new file mode 100644
index 00000000..716d79f6
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/laplace.go
@@ -0,0 +1,251 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"math"
+	"math/rand"
+	"sort"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/stat"
+)
+
+// Laplace represents the Laplace distribution (https://en.wikipedia.org/wiki/Laplace_distribution).
+type Laplace struct {
+	Mu     float64 // Mean of the Laplace distribution
+	Scale  float64 // Scale of the Laplace distribution
+	Source *rand.Rand
+}
+
+// CDF computes the value of the cumulative density function at x.
+func (l Laplace) CDF(x float64) float64 {
+	if x < l.Mu {
+		return 0.5 * math.Exp((x-l.Mu)/l.Scale)
+	}
+	return 1 - 0.5*math.Exp(-(x-l.Mu)/l.Scale)
+}
+
+// Entropy returns the entropy of the distribution.
+func (l Laplace) Entropy() float64 {
+	return 1 + math.Log(2*l.Scale)
+}
+
+// ExKurtosis returns the excess kurtosis of the distribution.
+func (l Laplace) ExKurtosis() float64 {
+	return 3
+}
+
+// Fit sets the parameters of the probability distribution from the
+// data samples x with relative weights w.
+// If weights is nil, then all the weights are 1.
+// If weights is not nil, then the len(weights) must equal len(samples).
+//
+// Note: Laplace distribution has no FitPrior because it has no sufficient
+// statistics.
+func (l *Laplace) Fit(samples, weights []float64) {
+	if len(samples) != len(weights) {
+		panic(badLength)
+	}
+
+	if len(samples) == 0 {
+		panic(badNoSamples)
+	}
+	if len(samples) == 1 {
+		l.Mu = samples[0]
+		l.Scale = 0
+		return
+	}
+
+	var (
+		sortedSamples []float64
+		sortedWeights []float64
+	)
+	if sort.Float64sAreSorted(samples) {
+		sortedSamples = samples
+		sortedWeights = weights
+	} else {
+		// Need to copy variables so the input variables aren't effected by the sorting
+		sortedSamples = make([]float64, len(samples))
+		copy(sortedSamples, samples)
+		sortedWeights := make([]float64, len(samples))
+		copy(sortedWeights, weights)
+
+		stat.SortWeighted(sortedSamples, sortedWeights)
+	}
+
+	// The (weighted) median of the samples is the maximum likelihood estimate
+	// of the mean parameter
+	// TODO: Rethink quantile type when stat has more options
+	l.Mu = stat.Quantile(0.5, stat.Empirical, sortedSamples, sortedWeights)
+
+	sumWeights := floats.Sum(weights)
+
+	// The scale parameter is the average absolute distance
+	// between the sample and the mean
+	absError := stat.MomentAbout(1, samples, l.Mu, weights)
+
+	l.Scale = absError / sumWeights
+}
+
+// LogProb computes the natural logarithm of the value of the probability density
+// function at x.
+func (l Laplace) LogProb(x float64) float64 {
+	return -math.Ln2 - math.Log(l.Scale) - math.Abs(x-l.Mu)/l.Scale
+}
+
+// MarshalParameters implements the ParameterMarshaler interface
+func (l Laplace) MarshalParameters(p []Parameter) {
+	if len(p) != l.NumParameters() {
+		panic(badLength)
+	}
+	p[0].Name = "Mu"
+	p[0].Value = l.Mu
+	p[1].Name = "Scale"
+	p[1].Value = l.Scale
+}
+
+// Mean returns the mean of the probability distribution.
+func (l Laplace) Mean() float64 {
+	return l.Mu
+}
+
+// Median returns the median of the LaPlace distribution.
+func (l Laplace) Median() float64 {
+	return l.Mu
+}
+
+// Mode returns the mode of the LaPlace distribution.
+func (l Laplace) Mode() float64 {
+	return l.Mu
+}
+
+// NumParameters returns the number of parameters in the distribution.
+func (l Laplace) NumParameters() int {
+	return 2
+}
+
+// Quantile returns the inverse of the cumulative probability distribution.
+func (l Laplace) Quantile(p float64) float64 {
+	if p < 0 || p > 1 {
+		panic(badPercentile)
+	}
+	if p < 0.5 {
+		return l.Mu + l.Scale*math.Log(1+2*(p-0.5))
+	}
+	return l.Mu - l.Scale*math.Log(1-2*(p-0.5))
+}
+
+// Prob computes the value of the probability density function at x.
+func (l Laplace) Prob(x float64) float64 {
+	return math.Exp(l.LogProb(x))
+}
+
+// Rand returns a random sample drawn from the distribution.
+func (l Laplace) Rand() float64 {
+	var rnd float64
+	if l.Source == nil {
+		rnd = rand.Float64()
+	} else {
+		rnd = l.Source.Float64()
+	}
+	u := rnd - 0.5
+	if u < 0 {
+		return l.Mu + l.Scale*math.Log(1+2*u)
+	}
+	return l.Mu - l.Scale*math.Log(1-2*u)
+}
+
+// Score returns the score function with respect to the parameters of the
+// distribution at the input location x. The score function is the derivative
+// of the log-likelihood at x with respect to the parameters
+//  (∂/∂θ) log(p(x;θ))
+// If deriv is non-nil, len(deriv) must equal the number of parameters otherwise
+// Score will panic, and the derivative is stored in-place into deriv. If deriv
+// is nil a new slice will be allocated and returned.
+//
+// The order is [∂LogProb / ∂Mu, ∂LogProb / ∂Scale].
+//
+// For more information, see https://en.wikipedia.org/wiki/Score_%28statistics%29.
+//
+// Special cases:
+//  Score(0) = [0, -0.5/l.Scale]
+func (l Laplace) Score(deriv []float64, x float64) []float64 {
+	if deriv == nil {
+		deriv = make([]float64, l.NumParameters())
+	}
+	if len(deriv) != l.NumParameters() {
+		panic(badLength)
+	}
+	diff := x - l.Mu
+	if diff > 0 {
+		deriv[0] = 1 / l.Scale
+	} else if diff < 0 {
+		deriv[0] = -1 / l.Scale
+	} else if diff == 0 {
+		deriv[0] = 0
+	} else {
+		// must be NaN
+		deriv[0] = math.NaN()
+	}
+
+	deriv[1] = math.Abs(diff)/(l.Scale*l.Scale) - 0.5/(l.Scale)
+	return deriv
+}
+
+// ScoreInput returns the score function with respect to the input of the
+// distribution at the input location specified by x. The score function is the
+// derivative of the log-likelihood
+//  (d/dx) log(p(x)) .
+// Special cases:
+//  ScoreInput(l.Mu) = 0
+func (l Laplace) ScoreInput(x float64) float64 {
+	diff := x - l.Mu
+	if diff == 0 {
+		return 0
+	}
+	if diff > 0 {
+		return -1 / l.Scale
+	}
+	return 1 / l.Scale
+}
+
+// Skewness returns the skewness of the distribution.
+func (Laplace) Skewness() float64 {
+	return 0
+}
+
+// StdDev returns the standard deviation of the distribution.
+func (l Laplace) StdDev() float64 {
+	return math.Sqrt2 * l.Scale
+}
+
+// Survival returns the survival function (complementary CDF) at x.
+func (l Laplace) Survival(x float64) float64 {
+	if x < l.Mu {
+		return 1 - 0.5*math.Exp((x-l.Mu)/l.Scale)
+	}
+	return 0.5 * math.Exp(-(x-l.Mu)/l.Scale)
+}
+
+// UnmarshalParameters implements the ParameterMarshaler interface
+func (l *Laplace) UnmarshalParameters(p []Parameter) {
+	if len(p) != l.NumParameters() {
+		panic(badLength)
+	}
+	if p[0].Name != "Mu" {
+		panic("laplace: " + panicNameMismatch)
+	}
+	if p[1].Name != "Scale" {
+		panic("laplace: " + panicNameMismatch)
+	}
+	l.Mu = p[0].Value
+	l.Scale = p[1].Value
+}
+
+// Variance returns the variance of the probability distribution.
+func (l Laplace) Variance() float64 {
+	return 2 * l.Scale * l.Scale
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/laplace_test.go b/vendor/gonum.org/v1/gonum/stat/distuv/laplace_test.go
new file mode 100644
index 00000000..0cbb2594
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/laplace_test.go
@@ -0,0 +1,58 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"math"
+	"testing"
+)
+
+func TestLaplaceProb(t *testing.T) {
+	pts := []univariateProbPoint{
+		{
+			loc:     0,
+			prob:    0.5,
+			cumProb: 0.5,
+			logProb: math.Log(0.5),
+		},
+		{
+			loc:     -1,
+			prob:    1 / (2 * math.E),
+			cumProb: 0.1839397205857211607977618850807304337229055655158839172539184008487307478724499016785736371729598219,
+			logProb: math.Log(1 / (2 * math.E)),
+		},
+		{
+			loc:     1,
+			prob:    1 / (2 * math.E),
+			cumProb: 0.8160602794142788392022381149192695662770944344841160827460815991512692521275500983214263628270401781,
+			logProb: math.Log(1 / (2 * math.E)),
+		},
+		{
+			loc:     -7,
+			prob:    1 / (2 * math.Pow(math.E, 7)),
+			cumProb: 0.0004559409827772581040015680422046413132368622637180269204080667109447399446551532646631395032324502210,
+			logProb: math.Log(1 / (2 * math.Pow(math.E, 7))),
+		},
+		{
+			loc:     7,
+			prob:    1 / (2 * math.Pow(math.E, 7)),
+			cumProb: 0.9995440590172227418959984319577953586867631377362819730795919332890552600553448467353368604967675498,
+			logProb: math.Log(1 / (2 * math.Pow(math.E, 7))),
+		},
+		{
+			loc:     -20,
+			prob:    math.Exp(-20.69314718055994530941723212145817656807550013436025525412068000949339362196969471560586332699641869),
+			cumProb: 1.030576811219278913982970190077910488187903637799551846486122330814582011892279676639955463952790684 * 1e-9,
+			logProb: -20.69314718055994530941723212145817656807550013436025525412068000949339362196969471560586332699641869,
+		},
+		{
+			loc:     20,
+			prob:    math.Exp(-20.69314718055994530941723212145817656807550013436025525412068000949339362196969471560586332699641869),
+			cumProb: 0.999999998969423188780721086017029809922089511812096362200448153513877669185417988107720323360044536,
+			logProb: -20.69314718055994530941723212145817656807550013436025525412068000949339362196969471560586332699641869,
+		},
+	}
+	testDistributionProbs(t, Laplace{Mu: 0, Scale: 1}, "Laplace", pts)
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/lognormal.go b/vendor/gonum.org/v1/gonum/stat/distuv/lognormal.go
new file mode 100644
index 00000000..e13afce5
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/lognormal.go
@@ -0,0 +1,112 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"math"
+	"math/rand"
+)
+
+// LogNormal represents a random variable whose log is normally distributed.
+// The probability density function is given by
+//  1/(x σ √2π) exp(-(ln(x)-μ)^2)/(2σ^2))
+type LogNormal struct {
+	Mu     float64
+	Sigma  float64
+	Source *rand.Rand
+}
+
+// CDF computes the value of the cumulative density function at x.
+func (l LogNormal) CDF(x float64) float64 {
+	return 0.5 + 0.5*math.Erf((math.Log(x)-l.Mu)/(math.Sqrt2*l.Sigma))
+}
+
+// Entropy returns the differential entropy of the distribution.
+func (l LogNormal) Entropy() float64 {
+	return 0.5 + 0.5*math.Log(2*math.Pi*l.Sigma*l.Sigma) + l.Mu
+}
+
+// ExKurtosis returns the excess kurtosis of the distribution.
+func (l LogNormal) ExKurtosis() float64 {
+	s2 := l.Sigma * l.Sigma
+	return math.Exp(4*s2) + 2*math.Exp(3*s2) + 3*math.Exp(2*s2) - 6
+}
+
+// LogProb computes the natural logarithm of the value of the probability density function at x.
+func (l LogNormal) LogProb(x float64) float64 {
+	if x < 0 {
+		return math.Inf(-1)
+	}
+	logx := math.Log(x)
+	normdiff := (logx - l.Mu) / l.Sigma
+	return -0.5*normdiff*normdiff - logx - math.Log(l.Sigma) - logRoot2Pi
+}
+
+// Mean returns the mean of the probability distribution.
+func (l LogNormal) Mean() float64 {
+	return math.Exp(l.Mu + 0.5*l.Sigma*l.Sigma)
+}
+
+// Median returns the median of the probability distribution.
+func (l LogNormal) Median() float64 {
+	return math.Exp(l.Mu)
+}
+
+// Mode returns the mode of the probability distribution.
+func (l LogNormal) Mode() float64 {
+	return l.Mu
+}
+
+// NumParameters returns the number of parameters in the distribution.
+func (LogNormal) NumParameters() int {
+	return 2
+}
+
+// Prob computes the value of the probability density function at x.
+func (l LogNormal) Prob(x float64) float64 {
+	return math.Exp(l.LogProb(x))
+}
+
+// Quantile returns the inverse of the cumulative probability distribution.
+func (l LogNormal) Quantile(p float64) float64 {
+	if p < 0 || p > 1 {
+		panic(badPercentile)
+	}
+	// Formula from http://www.math.uah.edu/stat/special/LogNormal.html.
+	return math.Exp(l.Mu + l.Sigma*UnitNormal.Quantile(p))
+}
+
+// Rand returns a random sample drawn from the distribution.
+func (l LogNormal) Rand() float64 {
+	var rnd float64
+	if l.Source == nil {
+		rnd = rand.NormFloat64()
+	} else {
+		rnd = l.Source.NormFloat64()
+	}
+	return math.Exp(rnd*l.Sigma + l.Mu)
+}
+
+// Skewness returns the skewness of the distribution.
+func (l LogNormal) Skewness() float64 {
+	s2 := l.Sigma * l.Sigma
+	return (math.Exp(s2) + 2) * math.Sqrt(math.Exp(s2)-1)
+}
+
+// StdDev returns the standard deviation of the probability distribution.
+func (l LogNormal) StdDev() float64 {
+	return math.Sqrt(l.Variance())
+}
+
+// Survival returns the survival function (complementary CDF) at x.
+func (l LogNormal) Survival(x float64) float64 {
+	return 0.5 * (1 - math.Erf((math.Log(x)-l.Mu)/(math.Sqrt2*l.Sigma)))
+}
+
+// Variance returns the variance of the probability distribution.
+func (l LogNormal) Variance() float64 {
+	s2 := l.Sigma * l.Sigma
+	return (math.Exp(s2) - 1) * math.Exp(2*l.Mu+s2)
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/lognormal_test.go b/vendor/gonum.org/v1/gonum/stat/distuv/lognormal_test.go
new file mode 100644
index 00000000..a4dc19ad
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/lognormal_test.go
@@ -0,0 +1,44 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"sort"
+	"testing"
+)
+
+func TestLognormal(t *testing.T) {
+	for i, dist := range []LogNormal{
+		{
+			Mu:    0.1,
+			Sigma: 0.3,
+		},
+		{
+			Mu:    0.01,
+			Sigma: 0.01,
+		},
+		{
+			Mu:    2,
+			Sigma: 0.01,
+		},
+	} {
+		f := dist
+		tol := 1e-2
+		const n = 1e5
+		x := make([]float64, n)
+		generateSamples(x, f)
+		sort.Float64s(x)
+
+		checkMean(t, i, x, f, tol)
+		checkVarAndStd(t, i, x, f, tol)
+		checkEntropy(t, i, x, f, tol)
+		checkExKurtosis(t, i, x, f, 2e-1)
+		checkSkewness(t, i, x, f, 5e-2)
+		checkMedian(t, i, x, f, tol)
+		checkQuantileCDFSurvival(t, i, x, f, tol)
+		checkProbContinuous(t, i, x, f, 1e-10)
+		checkProbQuantContinuous(t, i, x, f, tol)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/norm.go b/vendor/gonum.org/v1/gonum/stat/distuv/norm.go
new file mode 100644
index 00000000..05b86bdd
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/norm.go
@@ -0,0 +1,254 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"math"
+	"math/rand"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mathext"
+	"gonum.org/v1/gonum/stat"
+)
+
+// UnitNormal is an instantiation of the normal distribution with Mu = 0 and Sigma = 1.
+var UnitNormal = Normal{Mu: 0, Sigma: 1}
+
+// Normal respresents a normal (Gaussian) distribution (https://en.wikipedia.org/wiki/Normal_distribution).
+type Normal struct {
+	Mu     float64 // Mean of the normal distribution
+	Sigma  float64 // Standard deviation of the normal distribution
+	Source *rand.Rand
+
+	// Needs to be Mu and Sigma and not Mean and StdDev because Normal has functions
+	// Mean and StdDev
+}
+
+// CDF computes the value of the cumulative density function at x.
+func (n Normal) CDF(x float64) float64 {
+	return 0.5 * (1 + math.Erf((x-n.Mu)/(n.Sigma*math.Sqrt2)))
+}
+
+// ConjugateUpdate updates the parameters of the distribution from the sufficient
+// statistics of a set of samples. The sufficient statistics, suffStat, have been
+// observed with nSamples observations. The prior values of the distribution are those
+// currently in the distribution, and have been observed with priorStrength samples.
+//
+// For the normal distribution, the sufficient statistics are the mean and
+// uncorrected standard deviation of the samples.
+// The prior is having seen strength[0] samples with mean Normal.Mu
+// and strength[1] samples with standard deviation Normal.Sigma. As a result of
+// this function, Normal.Mu and Normal.Sigma are updated based on the weighted
+// samples, and strength is modified to include the new number of samples observed.
+//
+// This function panics if len(suffStat) != 2 or len(priorStrength) != 2.
+func (n *Normal) ConjugateUpdate(suffStat []float64, nSamples float64, priorStrength []float64) {
+
+	// TODO: Support prior strength with math.Inf(1) to allow updating with
+	// a known mean/standard deviation
+
+	totalMeanSamples := nSamples + priorStrength[0]
+	totalSum := suffStat[0]*nSamples + n.Mu*priorStrength[0]
+
+	totalVarianceSamples := nSamples + priorStrength[1]
+	// sample variance
+	totalVariance := nSamples * suffStat[1] * suffStat[1]
+	// add prior variance
+	totalVariance += priorStrength[1] * n.Sigma * n.Sigma
+	// add cross variance from the difference of the means
+	meanDiff := (suffStat[0] - n.Mu)
+	totalVariance += priorStrength[0] * nSamples * meanDiff * meanDiff / totalMeanSamples
+
+	n.Mu = totalSum / totalMeanSamples
+	n.Sigma = math.Sqrt(totalVariance / totalVarianceSamples)
+	floats.AddConst(nSamples, priorStrength)
+}
+
+// Entropy returns the differential entropy of the distribution.
+func (n Normal) Entropy() float64 {
+	return 0.5 * (log2Pi + 1 + 2*math.Log(n.Sigma))
+}
+
+// ExKurtosis returns the excess kurtosis of the distribution.
+func (Normal) ExKurtosis() float64 {
+	return 0
+}
+
+// Fit sets the parameters of the probability distribution from the
+// data samples x with relative weights w. If weights is nil, then all the weights
+// are 1. If weights is not nil, then the len(weights) must equal len(samples).
+func (n *Normal) Fit(samples, weights []float64) {
+	suffStat := make([]float64, n.NumSuffStat())
+	nSamples := n.SuffStat(suffStat, samples, weights)
+	n.ConjugateUpdate(suffStat, nSamples, make([]float64, n.NumSuffStat()))
+}
+
+// LogProb computes the natural logarithm of the value of the probability density function at x.
+func (n Normal) LogProb(x float64) float64 {
+	return negLogRoot2Pi - math.Log(n.Sigma) - (x-n.Mu)*(x-n.Mu)/(2*n.Sigma*n.Sigma)
+}
+
+// Mean returns the mean of the probability distribution.
+func (n Normal) Mean() float64 {
+	return n.Mu
+}
+
+// Median returns the median of the normal distribution.
+func (n Normal) Median() float64 {
+	return n.Mu
+}
+
+// Mode returns the mode of the normal distribution.
+func (n Normal) Mode() float64 {
+	return n.Mu
+}
+
+// NumParameters returns the number of parameters in the distribution.
+func (Normal) NumParameters() int {
+	return 2
+}
+
+// NumSuffStat returns the number of sufficient statistics for the distribution.
+func (Normal) NumSuffStat() int {
+	return 2
+}
+
+// Prob computes the value of the probability density function at x.
+func (n Normal) Prob(x float64) float64 {
+	return math.Exp(n.LogProb(x))
+}
+
+// Quantile returns the inverse of the cumulative probability distribution.
+func (n Normal) Quantile(p float64) float64 {
+	if p < 0 || p > 1 {
+		panic(badPercentile)
+	}
+	return n.Mu + n.Sigma*mathext.NormalQuantile(p)
+}
+
+// Rand returns a random sample drawn from the distribution.
+func (n Normal) Rand() float64 {
+	var rnd float64
+	if n.Source == nil {
+		rnd = rand.NormFloat64()
+	} else {
+		rnd = n.Source.NormFloat64()
+	}
+	return rnd*n.Sigma + n.Mu
+}
+
+// Score returns the score function with respect to the parameters of the
+// distribution at the input location x. The score function is the derivative
+// of the log-likelihood at x with respect to the parameters
+//  (∂/∂θ) log(p(x;θ))
+// If deriv is non-nil, len(deriv) must equal the number of parameters otherwise
+// Score will panic, and the derivative is stored in-place into deriv. If deriv
+// is nil a new slice will be allocated and returned.
+//
+// The order is [∂LogProb / ∂Mu, ∂LogProb / ∂Sigma].
+//
+// For more information, see https://en.wikipedia.org/wiki/Score_%28statistics%29.
+func (n Normal) Score(deriv []float64, x float64) []float64 {
+	if deriv == nil {
+		deriv = make([]float64, n.NumParameters())
+	}
+	if len(deriv) != n.NumParameters() {
+		panic(badLength)
+	}
+	deriv[0] = (x - n.Mu) / (n.Sigma * n.Sigma)
+	deriv[1] = 1 / n.Sigma * (-1 + ((x-n.Mu)/n.Sigma)*((x-n.Mu)/n.Sigma))
+	return deriv
+}
+
+// ScoreInput returns the score function with respect to the input of the
+// distribution at the input location specified by x. The score function is the
+// derivative of the log-likelihood
+//  (d/dx) log(p(x)) .
+func (n Normal) ScoreInput(x float64) float64 {
+	return -(1 / (2 * n.Sigma * n.Sigma)) * 2 * (x - n.Mu)
+}
+
+// Skewness returns the skewness of the distribution.
+func (Normal) Skewness() float64 {
+	return 0
+}
+
+// StdDev returns the standard deviation of the probability distribution.
+func (n Normal) StdDev() float64 {
+	return n.Sigma
+}
+
+// SuffStat computes the sufficient statistics of a set of samples to update
+// the distribution. The sufficient statistics are stored in place, and the
+// effective number of samples are returned.
+//
+// The normal distribution has two sufficient statistics, the mean of the samples
+// and the standard deviation of the samples.
+//
+// If weights is nil, the weights are assumed to be 1, otherwise panics if
+// len(samples) != len(weights). Panics if len(suffStat) != NumSuffStat().
+func (Normal) SuffStat(suffStat, samples, weights []float64) (nSamples float64) {
+	lenSamp := len(samples)
+	if len(weights) != 0 && len(samples) != len(weights) {
+		panic(badLength)
+	}
+	if len(suffStat) != (Normal{}).NumSuffStat() {
+		panic(badSuffStat)
+	}
+
+	if len(weights) == 0 {
+		nSamples = float64(lenSamp)
+	} else {
+		nSamples = floats.Sum(weights)
+	}
+
+	mean := stat.Mean(samples, weights)
+	suffStat[0] = mean
+
+	// Use Moment and not StdDev because we want it to be uncorrected
+	variance := stat.MomentAbout(2, samples, mean, weights)
+	suffStat[1] = math.Sqrt(variance)
+	return nSamples
+}
+
+// Survival returns the survival function (complementary CDF) at x.
+func (n Normal) Survival(x float64) float64 {
+	return 0.5 * (1 - math.Erf((x-n.Mu)/(n.Sigma*math.Sqrt2)))
+}
+
+// setParameters modifies the parameters of the distribution.
+func (n *Normal) setParameters(p []Parameter) {
+	if len(p) != n.NumParameters() {
+		panic("normal: incorrect number of parameters to set")
+	}
+	if p[0].Name != "Mu" {
+		panic("normal: " + panicNameMismatch)
+	}
+	if p[1].Name != "Sigma" {
+		panic("normal: " + panicNameMismatch)
+	}
+	n.Mu = p[0].Value
+	n.Sigma = p[1].Value
+}
+
+// Variance returns the variance of the probability distribution.
+func (n Normal) Variance() float64 {
+	return n.Sigma * n.Sigma
+}
+
+// parameters returns the parameters of the distribution.
+func (n Normal) parameters(p []Parameter) []Parameter {
+	nParam := n.NumParameters()
+	if p == nil {
+		p = make([]Parameter, nParam)
+	} else if len(p) != nParam {
+		panic("normal: improper parameter length")
+	}
+	p[0].Name = "Mu"
+	p[0].Value = n.Mu
+	p[1].Name = "Sigma"
+	p[1].Value = n.Sigma
+	return p
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/norm_example_test.go b/vendor/gonum.org/v1/gonum/stat/distuv/norm_example_test.go
new file mode 100644
index 00000000..b913282f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/norm_example_test.go
@@ -0,0 +1,35 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv_test
+
+import (
+	"fmt"
+
+	"gonum.org/v1/gonum/stat"
+	"gonum.org/v1/gonum/stat/distuv"
+)
+
+func ExampleNormal() {
+	// Create a normal distribution
+	dist := distuv.Normal{
+		Mu:    2,
+		Sigma: 5,
+	}
+
+	data := make([]float64, 1e5)
+
+	// Draw some random values from the standard normal distribution
+	for i := range data {
+		data[i] = dist.Rand()
+	}
+
+	mean, std := stat.MeanStdDev(data, nil)
+	meanErr := stat.StdErr(std, float64(len(data)))
+
+	fmt.Printf("mean= %1.1f ± %0.1v\n", mean, meanErr)
+
+	// Output:
+	// mean= 2.0 ± 0.02
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/norm_test.go b/vendor/gonum.org/v1/gonum/stat/distuv/norm_test.go
new file mode 100644
index 00000000..0179e173
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/norm_test.go
@@ -0,0 +1,171 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"math"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+// TestNormalProbs tests LogProb, Prob, CumProb, and Quantile
+func TestNormalProbs(t *testing.T) {
+	pts := []univariateProbPoint{
+		{
+			loc:     0,
+			prob:    oneOverRoot2Pi,
+			cumProb: 0.5,
+			logProb: -0.91893853320467274178032973640561763986139747363778341281715,
+		},
+		{
+			loc:     -1,
+			prob:    0.2419707245191433497978301929355606548286719707374350254875550842811000635700832945083112946939424047,
+			cumProb: 0.158655253931457051414767454367962077522087033273395609012605,
+			logProb: math.Log(0.2419707245191433497978301929355606548286719707374350254875550842811000635700832945083112946939424047),
+		},
+		{
+			loc:     1,
+			prob:    0.2419707245191433497978301929355606548286719707374350254875550842811000635700832945083112946939424047,
+			cumProb: 0.841344746068542948585232545632037922477912966726604390987394,
+			logProb: math.Log(0.2419707245191433497978301929355606548286719707374350254875550842811000635700832945083112946939424047),
+		},
+		{
+			loc:     -7,
+			prob:    9.134720408364593342868613916794233023000190834851937054490546361277622761970225469305158915808284566e-12,
+			cumProb: 1.279812543885835004383623690780832998032844154198717929e-12,
+			logProb: math.Log(9.134720408364593342868613916794233023000190834851937054490546361277622761970225469305158915808284566e-12),
+		},
+		{
+			loc:     7,
+			prob:    9.134720408364593342868613916794233023000190834851937054490546361277622761970225469305158915808284566e-12,
+			cumProb: 0.99999999999872018745611416499561637630921916700196715584580,
+			logProb: math.Log(9.134720408364593342868613916794233023000190834851937054490546361277622761970225469305158915808284566e-12),
+		},
+	}
+	testDistributionProbs(t, Normal{Mu: 0, Sigma: 1}, "normal", pts)
+
+	pts = []univariateProbPoint{
+		{
+			loc:     2,
+			prob:    0.07978845608028653558798921198687637369517172623298693153318516593413158517986036770025046678146138729,
+			cumProb: 0.5,
+			logProb: math.Log(0.07978845608028653558798921198687637369517172623298693153318516593413158517986036770025046678146138729),
+		},
+		{
+			loc:     -3,
+			prob:    0.04839414490382866995956603858711213096573439414748700509751101685622001271401665890166225893878848095,
+			cumProb: 0.158655253931457051414767454367962077522087033273395609012605,
+			logProb: math.Log(0.04839414490382866995956603858711213096573439414748700509751101685622001271401665890166225893878848095),
+		},
+		{
+			loc:     7,
+			prob:    0.04839414490382866995956603858711213096573439414748700509751101685622001271401665890166225893878848095,
+			cumProb: 0.841344746068542948585232545632037922477912966726604390987394,
+			logProb: math.Log(0.04839414490382866995956603858711213096573439414748700509751101685622001271401665890166225893878848095),
+		},
+		{
+			loc:     -33,
+			prob:    1.826944081672918668573722783358846604600038166970387410898109272255524552394045093861031783161656913e-12,
+			cumProb: 1.279812543885835004383623690780832998032844154198717929e-12,
+			logProb: math.Log(1.826944081672918668573722783358846604600038166970387410898109272255524552394045093861031783161656913e-12),
+		},
+		{
+			loc:     37,
+			prob:    1.826944081672918668573722783358846604600038166970387410898109272255524552394045093861031783161656913e-12,
+			cumProb: 0.99999999999872018745611416499561637630921916700196715584580,
+			logProb: math.Log(1.826944081672918668573722783358846604600038166970387410898109272255524552394045093861031783161656913e-12),
+		},
+	}
+	testDistributionProbs(t, Normal{Mu: 2, Sigma: 5}, "normal", pts)
+}
+
+func TestNormFitPrior(t *testing.T) {
+	testConjugateUpdate(t, func() ConjugateUpdater { return &Normal{Mu: -10, Sigma: 6} })
+}
+
+func TestNormScore(t *testing.T) {
+	for _, test := range []*Normal{
+		{
+			Mu:    0,
+			Sigma: 1,
+		},
+		{
+			Mu:    0.32238,
+			Sigma: 13.69,
+		},
+	} {
+		testDerivParam(t, test)
+	}
+}
+
+func TestNormalQuantile(t *testing.T) {
+	// Values from https://www.johndcook.com/blog/normal_cdf_inverse/
+	p := []float64{
+		0.0000001,
+		0.00001,
+		0.001,
+		0.05,
+		0.15,
+		0.25,
+		0.35,
+		0.45,
+		0.55,
+		0.65,
+		0.75,
+		0.85,
+		0.95,
+		0.999,
+		0.99999,
+		0.9999999,
+	}
+	ans := []float64{
+		-5.199337582187471,
+		-4.264890793922602,
+		-3.090232306167813,
+		-1.6448536269514729,
+		-1.0364333894937896,
+		-0.6744897501960817,
+		-0.38532046640756773,
+		-0.12566134685507402,
+		0.12566134685507402,
+		0.38532046640756773,
+		0.6744897501960817,
+		1.0364333894937896,
+		1.6448536269514729,
+		3.090232306167813,
+		4.264890793922602,
+		5.199337582187471,
+	}
+	for i, v := range p {
+		got := UnitNormal.Quantile(v)
+		if !floats.EqualWithinAbsOrRel(got, ans[i], 1e-10, 1e-10) {
+			t.Errorf("Quantile mismatch. Case %d, want: %v, got: %v", i, ans[i], got)
+		}
+	}
+}
+
+func TestNormFitPanic(t *testing.T) {
+	n := Normal{Mu: 0, Sigma: 1}
+	defer func() {
+		r := recover()
+		if r != nil {
+			t.Errorf("unexpected panic for Fit call: %v", r)
+		}
+	}()
+	n.Fit(make([]float64, 10), nil)
+}
+
+func BenchmarkNormalQuantile(b *testing.B) {
+	n := Normal{Mu: 2, Sigma: 3.1}
+	ps := make([]float64, 1000) // ensure there are small values
+	floats.Span(ps, 0, 1)
+	for i := 0; i < b.N; i++ {
+		for _, v := range ps {
+			x := n.Quantile(v)
+			_ = x
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/studentst.go b/vendor/gonum.org/v1/gonum/stat/distuv/studentst.go
new file mode 100644
index 00000000..84b6b6e2
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/studentst.go
@@ -0,0 +1,160 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"math"
+	"math/rand"
+
+	"gonum.org/v1/gonum/mathext"
+)
+
+const logPi = 1.1447298858494001741 // http://oeis.org/A053510
+
+// StudentsT implements the three-parameter Student's T distribution, a distribution
+// over the real numbers.
+//
+// The Student's T distribution has density function
+//  Γ((ν+1)/2) / (sqrt(νπ) Γ(ν/2) σ) (1 + 1/ν * ((x-μ)/σ)^2)^(-(ν+1)/2)
+//
+// The Student's T distribution approaches the normal distribution as ν → ∞.
+//
+// For more information, see https://en.wikipedia.org/wiki/Student%27s_t-distribution,
+// specifically https://en.wikipedia.org/wiki/Student%27s_t-distribution#Non-standardized_Student.27s_t-distribution .
+//
+// The standard Student's T distribution is with Mu = 0, and Sigma = 1.
+type StudentsT struct {
+	// Mu is the location parameter of the distribution, and the mean of the
+	// distribution
+	Mu float64
+
+	// Sigma is the scale parameter of the distribution. It is related to the
+	// standard deviation by std = Sigma * sqrt(Nu/(Nu-2))
+	Sigma float64
+
+	// Nu is the shape prameter of the distribution, representing the number of
+	// degrees of the distribution, and one less than the number of observations
+	// from a Normal distribution.
+	Nu float64
+
+	Src *rand.Rand
+}
+
+// CDF computes the value of the cumulative distribution function at x.
+func (s StudentsT) CDF(x float64) float64 {
+	// transform to standard normal
+	y := (x - s.Mu) / s.Sigma
+	if y == 0 {
+		return 0.5
+	}
+	// For t > 0
+	// F(y) = 1 - 0.5 * I_t(y)(nu/2, 1/2)
+	// t(y) = nu/(y^2 + nu)
+	// and 1 - F(y) for t < 0
+	t := s.Nu / (y*y + s.Nu)
+	if y > 0 {
+		return 1 - 0.5*mathext.RegIncBeta(0.5*s.Nu, 0.5, t)
+	}
+	return 0.5 * mathext.RegIncBeta(s.Nu/2, 0.5, t)
+}
+
+// LogProb computes the natural logarithm of the value of the probability
+// density function at x.
+func (s StudentsT) LogProb(x float64) float64 {
+	g1, _ := math.Lgamma((s.Nu + 1) / 2)
+	g2, _ := math.Lgamma(s.Nu / 2)
+	z := (x - s.Mu) / s.Sigma
+	return g1 - g2 - 0.5*math.Log(s.Nu) - 0.5*logPi - math.Log(s.Sigma) - ((s.Nu+1)/2)*math.Log(1+z*z/s.Nu)
+}
+
+// Mean returns the mean of the probability distribution.
+func (s StudentsT) Mean() float64 {
+	return s.Mu
+}
+
+// Mode returns the mode of the distribution.
+func (s StudentsT) Mode() float64 {
+	return s.Mu
+}
+
+// NumParameters returns the number of parameters in the distribution.
+func (StudentsT) NumParameters() int {
+	return 3
+}
+
+// Prob computes the value of the probability density function at x.
+func (s StudentsT) Prob(x float64) float64 {
+	return math.Exp(s.LogProb(x))
+}
+
+// Quantile returns the inverse of the cumulative distribution function.
+func (s StudentsT) Quantile(p float64) float64 {
+	if p < 0 || p > 1 {
+		panic(badPercentile)
+	}
+	// F(x) = 1 - 0.5 * I_t(x)(nu/2, 1/2)
+	// t(x) = nu/(t^2 + nu)
+	if p == 0.5 {
+		return s.Mu
+	}
+	var y float64
+	if p > 0.5 {
+		// Know t > 0
+		t := mathext.InvRegIncBeta(s.Nu/2, 0.5, 2*(1-p))
+		y = math.Sqrt(s.Nu * (1 - t) / t)
+	} else {
+		t := mathext.InvRegIncBeta(s.Nu/2, 0.5, 2*p)
+		y = -math.Sqrt(s.Nu * (1 - t) / t)
+	}
+	// Convert out of standard normal
+	return y*s.Sigma + s.Mu
+}
+
+// Rand returns a random sample drawn from the distribution.
+func (s StudentsT) Rand() float64 {
+	// http://www.math.uah.edu/stat/special/Student.html
+	n := Normal{0, 1, s.Src}.Rand()
+	c := Gamma{s.Nu / 2, 0.5, s.Src}.Rand()
+	z := n / math.Sqrt(c/s.Nu)
+	return z*s.Sigma + s.Mu
+}
+
+// StdDev returns the standard deviation of the probability distribution.
+//
+// The standard deviation is undefined for ν <= 1, and this returns math.NaN().
+func (s StudentsT) StdDev() float64 {
+	return math.Sqrt(s.Variance())
+}
+
+// Survival returns the survival function (complementary CDF) at x.
+func (s StudentsT) Survival(x float64) float64 {
+	// transform to standard normal
+	y := (x - s.Mu) / s.Sigma
+	if y == 0 {
+		return 0.5
+	}
+	// For t > 0
+	// F(y) = 1 - 0.5 * I_t(y)(nu/2, 1/2)
+	// t(y) = nu/(y^2 + nu)
+	// and 1 - F(y) for t < 0
+	t := s.Nu / (y*y + s.Nu)
+	if y > 0 {
+		return 0.5 * mathext.RegIncBeta(s.Nu/2, 0.5, t)
+	}
+	return 1 - 0.5*mathext.RegIncBeta(s.Nu/2, 0.5, t)
+}
+
+// Variance returns the variance of the probability distribution.
+//
+// The variance is undefined for ν <= 1, and this returns math.NaN().
+func (s StudentsT) Variance() float64 {
+	if s.Nu < 1 {
+		return math.NaN()
+	}
+	if s.Nu <= 2 {
+		return math.Inf(1)
+	}
+	return s.Sigma * s.Sigma * s.Nu / (s.Nu - 2)
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/studentst_test.go b/vendor/gonum.org/v1/gonum/stat/distuv/studentst_test.go
new file mode 100644
index 00000000..d3ad225b
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/studentst_test.go
@@ -0,0 +1,83 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"math"
+	"math/rand"
+	"sort"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+func TestStudentsTProb(t *testing.T) {
+	for _, test := range []struct {
+		x, mu, sigma, nu, want float64
+	}{
+		// Values comparison with scipy.
+		{0.01, 0, 1, 2.74, 0.364778548181318},
+		{-0.01, 0, 1, 2.74, 0.364778548181318},
+		{0.4, 0, 1, 1.6, 0.30376391362582678},
+		{-0.4, 0, 1, 1.6, 0.30376391362582678},
+		{0.2, 15, 5, 10, 0.0024440848858034393},
+	} {
+		pdf := StudentsT{test.mu, test.sigma, test.nu, nil}.Prob(test.x)
+		if !floats.EqualWithinAbsOrRel(pdf, test.want, 1e-10, 1e-10) {
+			t.Errorf("Pdf mismatch, x = %v, Nu = %v. Got %v, want %v", test.x, test.nu, pdf, test.want)
+		}
+	}
+}
+
+func TestStudentsT(t *testing.T) {
+	src := rand.New(rand.NewSource(1))
+	for i, b := range []StudentsT{
+		{0, 1, 3.3, src},
+		{0, 1, 7.2, src},
+		{0, 1, 12, src},
+		{0.9, 0.8, 6, src},
+	} {
+		testStudentsT(t, b, i)
+	}
+}
+
+func testStudentsT(t *testing.T, c StudentsT, i int) {
+	tol := 1e-2
+	const n = 1e5
+	const bins = 50
+	x := make([]float64, n)
+	generateSamples(x, c)
+	sort.Float64s(x)
+
+	testRandLogProbContinuous(t, i, math.Inf(-1), x, c, tol, bins)
+	checkMean(t, i, x, c, tol)
+	if c.Nu > 2 {
+		checkVarAndStd(t, i, x, c, 5e-2)
+	}
+	checkProbContinuous(t, i, x, c, 1e-3)
+	checkQuantileCDFSurvival(t, i, x, c, tol)
+	checkProbQuantContinuous(t, i, x, c, tol)
+}
+
+func TestStudentsTQuantile(t *testing.T) {
+	nSteps := 101
+	probs := make([]float64, nSteps)
+	floats.Span(probs, 0, 1)
+	for i, b := range []StudentsT{
+		{0, 1, 3.3, nil},
+		{0, 1, 7.2, nil},
+		{0, 1, 12, nil},
+		{0.9, 0.8, 6, nil},
+	} {
+		for _, p := range probs {
+			x := b.Quantile(p)
+			p2 := b.CDF(x)
+			if !floats.EqualWithinAbsOrRel(p, p2, 1e-10, 1e-10) {
+				t.Errorf("mismatch between CDF and Quantile. Case %v. Want %v, got %v", i, p, p2)
+				break
+			}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/triangle.go b/vendor/gonum.org/v1/gonum/stat/distuv/triangle.go
new file mode 100644
index 00000000..157b9ea1
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/triangle.go
@@ -0,0 +1,192 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"math"
+	"math/rand"
+)
+
+// Triangle represents a triangle distribution (https://en.wikipedia.org/wiki/Triangular_distribution).
+type Triangle struct {
+	a, b, c float64
+	Source  *rand.Rand
+}
+
+// NewTriangle constructs a new triangle distribution with lower limit a, upper limit b, and mode c.
+// Constraints are a < b and a ≤ c ≤ b.
+// This distribution is uncommon in nature, but may be useful for simulation.
+func NewTriangle(a, b, c float64) Triangle {
+	checkTriangleParameters(a, b, c)
+	return Triangle{a, b, c, nil}
+}
+
+func checkTriangleParameters(a, b, c float64) {
+	if a >= b {
+		panic("triangle: constraint of a < b violated")
+	}
+	if a > c {
+		panic("triangle: constraint of a <= c violated")
+	}
+	if c > b {
+		panic("triangle: constraint of c <= b violated")
+	}
+}
+
+// CDF computes the value of the cumulative density function at x.
+func (t Triangle) CDF(x float64) float64 {
+	switch {
+	case x <= t.a:
+		return 0
+	case x <= t.c:
+		d := x - t.a
+		return (d * d) / ((t.b - t.a) * (t.c - t.a))
+	case x < t.b:
+		d := t.b - x
+		return 1 - (d*d)/((t.b-t.a)*(t.b-t.c))
+	default:
+		return 1
+	}
+}
+
+// Entropy returns the entropy of the distribution.
+func (t Triangle) Entropy() float64 {
+	return 0.5 + math.Log(t.b-t.a) - math.Ln2
+}
+
+// ExKurtosis returns the excess kurtosis of the distribution.
+func (Triangle) ExKurtosis() float64 {
+	return -3.0 / 5.0
+}
+
+// Fit is not appropriate for Triangle, because the distribution is generally used when there is little data.
+
+// LogProb computes the natural logarithm of the value of the probability density function at x.
+func (t Triangle) LogProb(x float64) float64 {
+	return math.Log(t.Prob(x))
+}
+
+// Mean returns the mean of the probability distribution.
+func (t Triangle) Mean() float64 {
+	return (t.a + t.b + t.c) / 3
+}
+
+// Median returns the median of the probability distribution.
+func (t Triangle) Median() float64 {
+	if t.c >= (t.a+t.b)/2 {
+		return t.a + math.Sqrt((t.b-t.a)*(t.c-t.a)/2)
+	}
+	return t.b - math.Sqrt((t.b-t.a)*(t.b-t.c)/2)
+}
+
+// Mode returns the mode of the probability distribution.
+func (t Triangle) Mode() float64 {
+	return t.c
+}
+
+// NumParameters returns the number of parameters in the distribution.
+func (Triangle) NumParameters() int {
+	return 3
+}
+
+// Prob computes the value of the probability density function at x.
+func (t Triangle) Prob(x float64) float64 {
+	switch {
+	case x < t.a:
+		return 0
+	case x < t.c:
+		return 2 * (x - t.a) / ((t.b - t.a) * (t.c - t.a))
+	case x == t.c:
+		return 2 / (t.b - t.a)
+	case x <= t.b:
+		return 2 * (t.b - x) / ((t.b - t.a) * (t.b - t.c))
+	default:
+		return 0
+	}
+}
+
+// Quantile returns the inverse of the cumulative probability distribution.
+func (t Triangle) Quantile(p float64) float64 {
+	if p < 0 || p > 1 {
+		panic(badPercentile)
+	}
+
+	f := (t.c - t.a) / (t.b - t.a)
+
+	if p < f {
+		return t.a + math.Sqrt(p*(t.b-t.a)*(t.c-t.a))
+	}
+	return t.b - math.Sqrt((1-p)*(t.b-t.a)*(t.b-t.c))
+}
+
+// Rand returns a random sample drawn from the distribution.
+func (t Triangle) Rand() float64 {
+	var rnd float64
+	if t.Source == nil {
+		rnd = rand.Float64()
+	} else {
+		rnd = t.Source.Float64()
+	}
+
+	return t.Quantile(rnd)
+}
+
+// Skewness returns the skewness of the distribution.
+func (t Triangle) Skewness() float64 {
+	n := math.Sqrt2 * (t.a + t.b - 2*t.c) * (2*t.a - t.b - t.c) * (t.a - 2*t.b + t.c)
+	d := 5 * math.Pow(t.a*t.a+t.b*t.b+t.c*t.c-t.a*t.b-t.a*t.c-t.b*t.c, 3.0/2.0)
+
+	return n / d
+}
+
+// StdDev returns the standard deviation of the probability distribution.
+func (t Triangle) StdDev() float64 {
+	return math.Sqrt(t.Variance())
+}
+
+// Survival returns the survival function (complementary CDF) at x.
+func (t Triangle) Survival(x float64) float64 {
+	return 1 - t.CDF(x)
+}
+
+// MarshalParameters implements the ParameterMarshaler interface
+func (t Triangle) MarshalParameters(p []Parameter) {
+	if len(p) != t.NumParameters() {
+		panic("triangle: improper parameter length")
+	}
+	p[0].Name = "A"
+	p[0].Value = t.a
+	p[1].Name = "B"
+	p[1].Value = t.b
+	p[2].Name = "C"
+	p[2].Value = t.c
+}
+
+// UnmarshalParameters implements the ParameterMarshaler interface
+func (t *Triangle) UnmarshalParameters(p []Parameter) {
+	if len(p) != t.NumParameters() {
+		panic("triangle: incorrect number of parameters to set")
+	}
+	if p[0].Name != "A" {
+		panic("triangle: " + panicNameMismatch)
+	}
+	if p[1].Name != "B" {
+		panic("triangle: " + panicNameMismatch)
+	}
+	if p[2].Name != "C" {
+		panic("triangle: " + panicNameMismatch)
+	}
+
+	checkTriangleParameters(p[0].Value, p[1].Value, p[2].Value)
+
+	t.a = p[0].Value
+	t.b = p[1].Value
+	t.c = p[2].Value
+}
+
+// Variance returns the variance of the probability distribution.
+func (t Triangle) Variance() float64 {
+	return (t.a*t.a + t.b*t.b + t.c*t.c - t.a*t.b - t.a*t.c - t.b*t.c) / 18
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/triangle_test.go b/vendor/gonum.org/v1/gonum/stat/distuv/triangle_test.go
new file mode 100644
index 00000000..c18ea939
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/triangle_test.go
@@ -0,0 +1,101 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"math"
+	"math/rand"
+	"sort"
+	"testing"
+)
+
+func TestTriangleConstraint(t *testing.T) {
+	defer func() {
+		if r := recover(); r == nil {
+			t.Errorf("The constraints were violated, but not caught")
+		}
+	}()
+
+	// test b < a
+	NewTriangle(3, 1, 2)
+	// test c > b
+	NewTriangle(1, 2, 3)
+}
+
+func TestTriangle(t *testing.T) {
+	src := rand.New(rand.NewSource(1))
+	for i, test := range []struct {
+		a, b, c float64
+	}{
+		{
+			a: 0.0,
+			b: 1.0,
+			c: 0.5,
+		},
+		{
+			a: 0.1,
+			b: 0.3,
+			c: 0.2,
+		},
+		{
+			a: 1.0,
+			b: 2.0,
+			c: 1.5,
+		},
+		{
+			a: 0.0,
+			b: 1.0,
+			c: 0.0,
+		},
+	} {
+		f := NewTriangle(test.a, test.b, test.c)
+		f.Source = src
+		tol := 1e-2
+		const n = 1e5
+		x := make([]float64, n)
+		generateSamples(x, f)
+		sort.Float64s(x)
+
+		checkMean(t, i, x, f, tol)
+		checkVarAndStd(t, i, x, f, tol)
+		checkEntropy(t, i, x, f, tol)
+		checkExKurtosis(t, i, x, f, tol)
+		checkSkewness(t, i, x, f, 5e-2)
+		checkMedian(t, i, x, f, tol)
+		checkQuantileCDFSurvival(t, i, x, f, tol)
+		checkProbContinuous(t, i, x, f, 1e-10)
+		checkProbQuantContinuous(t, i, x, f, tol)
+	}
+}
+
+func TestTriangleProb(t *testing.T) {
+	pts := []univariateProbPoint{
+		{
+			loc:     0.5,
+			prob:    0,
+			cumProb: 0,
+			logProb: math.Inf(-1),
+		},
+		{
+			loc:     1,
+			prob:    0,
+			cumProb: 0,
+			logProb: math.Inf(-1),
+		},
+		{
+			loc:     2,
+			prob:    1.0,
+			cumProb: 0.5,
+			logProb: 0,
+		},
+		{
+			loc:     3,
+			prob:    0,
+			cumProb: 1,
+			logProb: math.Inf(-1),
+		},
+	}
+	testDistributionProbs(t, NewTriangle(1, 3, 2), "Standard 1,2,3 Triangle", pts)
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/uniform.go b/vendor/gonum.org/v1/gonum/stat/distuv/uniform.go
new file mode 100644
index 00000000..0c6c41b7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/uniform.go
@@ -0,0 +1,158 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"math"
+	"math/rand"
+)
+
+// UnitUniform is an instantiation of the uniform distribution with Min = 0
+// and Max = 1.
+var UnitUniform = Uniform{Min: 0, Max: 1}
+
+// Uniform represents a continuous uniform distribution (https://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29).
+type Uniform struct {
+	Min    float64
+	Max    float64
+	Source *rand.Rand
+}
+
+// CDF computes the value of the cumulative density function at x.
+func (u Uniform) CDF(x float64) float64 {
+	if x < u.Min {
+		return 0
+	}
+	if x > u.Max {
+		return 1
+	}
+	return (x - u.Min) / (u.Max - u.Min)
+}
+
+// Uniform doesn't have any of the DLogProbD? because the derivative is 0 everywhere
+// except where it's undefined
+
+// Entropy returns the entropy of the distribution.
+func (u Uniform) Entropy() float64 {
+	return math.Log(u.Max - u.Min)
+}
+
+// ExKurtosis returns the excess kurtosis of the distribution.
+func (Uniform) ExKurtosis() float64 {
+	return -6.0 / 5.0
+}
+
+// Uniform doesn't have Fit because it's a bad idea to fit a uniform from data.
+
+// LogProb computes the natural logarithm of the value of the probability density function at x.
+func (u Uniform) LogProb(x float64) float64 {
+	if x < u.Min {
+		return math.Inf(-1)
+	}
+	if x > u.Max {
+		return math.Inf(-1)
+	}
+	return -math.Log(u.Max - u.Min)
+}
+
+// MarshalParameters implements the ParameterMarshaler interface
+func (u Uniform) MarshalParameters(p []Parameter) {
+	if len(p) != u.NumParameters() {
+		panic("uniform: improper parameter length")
+	}
+	p[0].Name = "Min"
+	p[0].Value = u.Min
+	p[1].Name = "Max"
+	p[1].Value = u.Max
+}
+
+// Mean returns the mean of the probability distribution.
+func (u Uniform) Mean() float64 {
+	return (u.Max + u.Min) / 2
+}
+
+// Median returns the median of the probability distribution.
+func (u Uniform) Median() float64 {
+	return (u.Max + u.Min) / 2
+}
+
+// Uniform doesn't have a mode because it's any value in the distribution
+
+// NumParameters returns the number of parameters in the distribution.
+func (Uniform) NumParameters() int {
+	return 2
+}
+
+// Prob computes the value of the probability density function at x.
+func (u Uniform) Prob(x float64) float64 {
+	if x < u.Min {
+		return 0
+	}
+	if x > u.Max {
+		return 0
+	}
+	return 1 / (u.Max - u.Min)
+}
+
+// Quantile returns the inverse of the cumulative probability distribution.
+func (u Uniform) Quantile(p float64) float64 {
+	if p < 0 || p > 1 {
+		panic(badPercentile)
+	}
+	return p*(u.Max-u.Min) + u.Min
+}
+
+// Rand returns a random sample drawn from the distribution.
+func (u Uniform) Rand() float64 {
+	var rnd float64
+	if u.Source == nil {
+		rnd = rand.Float64()
+	} else {
+		rnd = u.Source.Float64()
+	}
+	return rnd*(u.Max-u.Min) + u.Min
+}
+
+// Skewness returns the skewness of the distribution.
+func (Uniform) Skewness() float64 {
+	return 0
+}
+
+// StdDev returns the standard deviation of the probability distribution.
+func (u Uniform) StdDev() float64 {
+	return math.Sqrt(u.Variance())
+}
+
+// Survival returns the survival function (complementary CDF) at x.
+func (u Uniform) Survival(x float64) float64 {
+	if x < u.Min {
+		return 1
+	}
+	if x > u.Max {
+		return 0
+	}
+	return (u.Max - x) / (u.Max - u.Min)
+}
+
+// UnmarshalParameters implements the ParameterMarshaler interface
+func (u *Uniform) UnmarshalParameters(p []Parameter) {
+	if len(p) != u.NumParameters() {
+		panic("uniform: incorrect number of parameters to set")
+	}
+	if p[0].Name != "Min" {
+		panic("uniform: " + panicNameMismatch)
+	}
+	if p[1].Name != "Max" {
+		panic("uniform: " + panicNameMismatch)
+	}
+
+	u.Min = p[0].Value
+	u.Max = p[1].Value
+}
+
+// Variance returns the variance of the probability distribution.
+func (u Uniform) Variance() float64 {
+	return 1.0 / 12.0 * (u.Max - u.Min) * (u.Max - u.Min)
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/weibull.go b/vendor/gonum.org/v1/gonum/stat/distuv/weibull.go
new file mode 100644
index 00000000..72f7f97a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/weibull.go
@@ -0,0 +1,247 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"math"
+	"math/cmplx"
+	"math/rand"
+)
+
+// Weibull distribution. Valid range for x is [0,+∞).
+type Weibull struct {
+	// Shape parameter of the distribution. A value of 1 represents
+	// the exponential distribution. A value of 2 represents the
+	// Rayleigh distribution. Valid range is (0,+∞).
+	K float64
+	// Scale parameter of the distribution. Valid range is (0,+∞).
+	Lambda float64
+	// Source of random numbers
+	Source *rand.Rand
+}
+
+// CDF computes the value of the cumulative density function at x.
+func (w Weibull) CDF(x float64) float64 {
+	if x < 0 {
+		return 0
+	} else {
+		return 1 - cmplx.Abs(cmplx.Exp(w.LogCDF(x)))
+	}
+}
+
+// Entropy returns the entropy of the distribution.
+func (w Weibull) Entropy() float64 {
+	return eulerGamma*(1-1/w.K) + math.Log(w.Lambda/w.K) + 1
+}
+
+// ExKurtosis returns the excess kurtosis of the distribution.
+func (w Weibull) ExKurtosis() float64 {
+	return (-6*w.gammaIPow(1, 4) + 12*w.gammaIPow(1, 2)*math.Gamma(1+2/w.K) - 3*w.gammaIPow(2, 2) - 4*math.Gamma(1+1/w.K)*math.Gamma(1+3/w.K) + math.Gamma(1+4/w.K)) / math.Pow(math.Gamma(1+2/w.K)-w.gammaIPow(1, 2), 2)
+}
+
+// gammIPow is a shortcut for computing the gamma function to a power.
+func (w Weibull) gammaIPow(i, pow float64) float64 {
+	return math.Pow(math.Gamma(1+i/w.K), pow)
+}
+
+// LogCDF computes the value of the log of the cumulative density function at x.
+func (w Weibull) LogCDF(x float64) complex128 {
+	if x < 0 {
+		return 0
+	} else {
+		return cmplx.Log(-1) + complex(-math.Pow(x/w.Lambda, w.K), 0)
+	}
+}
+
+// LogProb computes the natural logarithm of the value of the probability
+// density function at x. Zero is returned if x is less than zero.
+//
+// Special cases occur when x == 0, and the result depends on the shape
+// parameter as follows:
+//  If 0 < K < 1, LogProb returns +Inf.
+//  If K == 1, LogProb returns 0.
+//  If K > 1, LogProb returns -Inf.
+func (w Weibull) LogProb(x float64) float64 {
+	if x < 0 {
+		return 0
+	} else {
+		return math.Log(w.K) - math.Log(w.Lambda) + (w.K-1)*(math.Log(x)-math.Log(w.Lambda)) - math.Pow(x/w.Lambda, w.K)
+	}
+}
+
+// Survival returns the log of the survival function (complementary CDF) at x.
+func (w Weibull) LogSurvival(x float64) float64 {
+	if x < 0 {
+		return 0
+	} else {
+		return -math.Pow(x/w.Lambda, w.K)
+	}
+}
+
+// Mean returns the mean of the probability distribution.
+func (w Weibull) Mean() float64 {
+	return w.Lambda * math.Gamma(1+1/w.K)
+}
+
+// Median returns the median of the normal distribution.
+func (w Weibull) Median() float64 {
+	return w.Lambda * math.Pow(ln2, 1/w.K)
+}
+
+// Mode returns the mode of the normal distribution.
+//
+// The mode is NaN in the special case where the K (shape) parameter
+// is less than 1.
+func (w Weibull) Mode() float64 {
+	if w.K > 1 {
+		return w.Lambda * math.Pow((w.K-1)/w.K, 1/w.K)
+	} else if w.K == 1 {
+		return 0
+	} else {
+		return math.NaN()
+	}
+}
+
+// NumParameters returns the number of parameters in the distribution.
+func (Weibull) NumParameters() int {
+	return 2
+}
+
+// Prob computes the value of the probability density function at x.
+func (w Weibull) Prob(x float64) float64 {
+	if x < 0 {
+		return 0
+	} else {
+		return math.Exp(w.LogProb(x))
+	}
+}
+
+// Quantile returns the inverse of the cumulative probability distribution.
+func (w Weibull) Quantile(p float64) float64 {
+	if p < 0 || p > 1 {
+		panic(badPercentile)
+	}
+	return w.Lambda * math.Pow(-math.Log(1-p), 1/w.K)
+}
+
+// Rand returns a random sample drawn from the distribution.
+func (w Weibull) Rand() float64 {
+	var rnd float64
+	if w.Source == nil {
+		rnd = rand.Float64()
+	} else {
+		rnd = w.Source.Float64()
+	}
+	return w.Quantile(rnd)
+}
+
+// Score returns the score function with respect to the parameters of the
+// distribution at the input location x. The score function is the derivative
+// of the log-likelihood at x with respect to the parameters
+//  (∂/∂θ) log(p(x;θ))
+// If deriv is non-nil, len(deriv) must equal the number of parameters otherwise
+// Score will panic, and the derivative is stored in-place into deriv. If deriv
+// is nil a new slice will be allocated and returned.
+//
+// The order is [∂LogProb / ∂K, ∂LogProb / ∂λ].
+//
+// For more information, see https://en.wikipedia.org/wiki/Score_%28statistics%29.
+//
+// Special cases:
+//  Score(0) = [NaN, NaN]
+func (w Weibull) Score(deriv []float64, x float64) []float64 {
+	if deriv == nil {
+		deriv = make([]float64, w.NumParameters())
+	}
+	if len(deriv) != w.NumParameters() {
+		panic(badLength)
+	}
+	if x > 0 {
+		deriv[0] = 1/w.K + math.Log(x) - math.Log(w.Lambda) - (math.Log(x)-math.Log(w.Lambda))*math.Pow(x/w.Lambda, w.K)
+		deriv[1] = (w.K * (math.Pow(x/w.Lambda, w.K) - 1)) / w.Lambda
+		return deriv
+	}
+	if x < 0 {
+		deriv[0] = 0
+		deriv[1] = 0
+		return deriv
+	}
+	deriv[0] = math.NaN()
+	deriv[0] = math.NaN()
+	return deriv
+}
+
+// ScoreInput returns the score function with respect to the input of the
+// distribution at the input location specified by x. The score function is the
+// derivative of the log-likelihood
+//  (d/dx) log(p(x)) .
+//
+// Special cases:
+//  ScoreInput(0) = NaN
+func (w Weibull) ScoreInput(x float64) float64 {
+	if x > 0 {
+		return (-w.K*math.Pow(x/w.Lambda, w.K) + w.K - 1) / x
+	}
+	if x < 0 {
+		return 0
+	}
+	return math.NaN()
+}
+
+// Skewness returns the skewness of the distribution.
+func (w Weibull) Skewness() float64 {
+	stdDev := w.StdDev()
+	firstGamma, firstGammaSign := math.Lgamma(1 + 3/w.K)
+	logFirst := firstGamma + 3*(math.Log(w.Lambda)-math.Log(stdDev))
+	logSecond := math.Log(3) + math.Log(w.Mean()) + 2*math.Log(stdDev) - 3*math.Log(stdDev)
+	logThird := 3 * (math.Log(w.Mean()) - math.Log(stdDev))
+	return float64(firstGammaSign)*math.Exp(logFirst) - math.Exp(logSecond) - math.Exp(logThird)
+}
+
+// StdDev returns the standard deviation of the probability distribution.
+func (w Weibull) StdDev() float64 {
+	return math.Sqrt(w.Variance())
+}
+
+// Survival returns the survival function (complementary CDF) at x.
+func (w Weibull) Survival(x float64) float64 {
+	return math.Exp(w.LogSurvival(x))
+}
+
+// setParameters modifies the parameters of the distribution.
+func (w *Weibull) setParameters(p []Parameter) {
+	if len(p) != w.NumParameters() {
+		panic("weibull: incorrect number of parameters to set")
+	}
+	if p[0].Name != "K" {
+		panic("weibull: " + panicNameMismatch)
+	}
+	if p[1].Name != "λ" {
+		panic("weibull: " + panicNameMismatch)
+	}
+	w.K = p[0].Value
+	w.Lambda = p[1].Value
+}
+
+// Variance returns the variance of the probability distribution.
+func (w Weibull) Variance() float64 {
+	return math.Pow(w.Lambda, 2) * (math.Gamma(1+2/w.K) - w.gammaIPow(1, 2))
+}
+
+// parameters returns the parameters of the distribution.
+func (w Weibull) parameters(p []Parameter) []Parameter {
+	nParam := w.NumParameters()
+	if p == nil {
+		p = make([]Parameter, nParam)
+	} else if len(p) != nParam {
+		panic("weibull: improper parameter length")
+	}
+	p[0].Name = "K"
+	p[0].Value = w.K
+	p[1].Name = "λ"
+	p[1].Value = w.Lambda
+	return p
+
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/distuv/weibull_test.go b/vendor/gonum.org/v1/gonum/stat/distuv/weibull_test.go
new file mode 100644
index 00000000..cd78f49f
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/distuv/weibull_test.go
@@ -0,0 +1,209 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"math"
+	"testing"
+)
+
+func TestHalfKStandardWeibullProb(t *testing.T) {
+	pts := []univariateProbPoint{
+		{
+			loc:     0,
+			prob:    math.Inf(1),
+			cumProb: 0,
+			logProb: math.Inf(1),
+		},
+		{
+			loc:     -1,
+			prob:    0,
+			cumProb: 0,
+			logProb: 0,
+		},
+		{
+			loc:     1,
+			prob:    0.183939720585721,
+			cumProb: 0.632120558828558,
+			logProb: -1.693147180559950,
+		},
+		{
+			loc:     20,
+			prob:    0.001277118038048,
+			cumProb: 0.988577109006533,
+			logProb: -6.663149272336520,
+		},
+	}
+	testDistributionProbs(t, Weibull{K: 0.5, Lambda: 1}, "0.5K Standard Weibull", pts)
+}
+
+func TestExponentialStandardWeibullProb(t *testing.T) {
+	pts := []univariateProbPoint{
+		{
+			loc:     0,
+			prob:    1,
+			cumProb: 0,
+			logProb: math.Inf(1),
+		},
+		{
+			loc:     -1,
+			prob:    0,
+			cumProb: 0,
+			logProb: 0,
+		},
+		{
+			loc:     1,
+			prob:    0.367879441171442,
+			cumProb: 0.632120558828558,
+			logProb: -1.0,
+		},
+		{
+			loc:     20,
+			prob:    0.000000002061154,
+			cumProb: 0.999999997938846,
+			logProb: -20.0,
+		},
+	}
+	testDistributionProbs(t, Weibull{K: 1, Lambda: 1}, "1K (Exponential) Standard Weibull", pts)
+}
+
+func TestRayleighStandardWeibullProb(t *testing.T) {
+	pts := []univariateProbPoint{
+		{
+			loc:     0,
+			prob:    0,
+			cumProb: 0,
+			logProb: math.Inf(-1),
+		},
+		{
+			loc:     -1,
+			prob:    0,
+			cumProb: 0,
+			logProb: 0,
+		},
+		{
+			loc:     1,
+			prob:    0.735758882342885,
+			cumProb: 0.632120558828558,
+			logProb: -0.306852819440055,
+		},
+		{
+			loc:     20,
+			prob:    0,
+			cumProb: 1,
+			logProb: -396.31112054588607,
+		},
+	}
+	testDistributionProbs(t, Weibull{K: 2, Lambda: 1}, "2K (Rayleigh) Standard Weibull", pts)
+}
+
+func TestFiveKStandardWeibullProb(t *testing.T) {
+	pts := []univariateProbPoint{
+		{
+			loc:     0,
+			prob:    0,
+			cumProb: 0,
+			logProb: math.Inf(-1),
+		},
+		{
+			loc:     -1,
+			prob:    0,
+			cumProb: 0,
+			logProb: 0,
+		},
+		{
+			loc:     1,
+			prob:    1.839397205857210,
+			cumProb: 0.632120558828558,
+			logProb: 0.609437912434100,
+		},
+		{
+			loc:     20,
+			prob:    0,
+			cumProb: 1,
+			logProb: -3199986.4076329935,
+		},
+	}
+	testDistributionProbs(t, Weibull{K: 5, Lambda: 1}, "5K Standard Weibull", pts)
+}
+
+func TestScaledUpHalfKStandardWeibullProb(t *testing.T) {
+	pts := []univariateProbPoint{
+		{
+			loc:     0,
+			prob:    math.Inf(1),
+			cumProb: 0,
+			logProb: math.Inf(1),
+		},
+		{
+			loc:     -1,
+			prob:    0,
+			cumProb: 0,
+			logProb: 0,
+		},
+		{
+			loc:     1,
+			prob:    0.180436508682207,
+			cumProb: 0.558022622759326,
+			logProb: -1.712376315541750,
+		},
+		{
+			loc:     20,
+			prob:    0.002369136850928,
+			cumProb: 0.974047406098605,
+			logProb: -6.045229588092130,
+		},
+	}
+	testDistributionProbs(t, Weibull{K: 0.5, Lambda: 1.5}, "0.5K 1.5λ Weibull", pts)
+}
+
+func TestScaledDownHalfKStandardWeibullProb(t *testing.T) {
+	pts := []univariateProbPoint{
+		{
+			loc:     0,
+			prob:    math.Inf(1),
+			cumProb: 0,
+			logProb: math.Inf(1),
+		},
+		{
+			loc:     -1,
+			prob:    0,
+			cumProb: 0,
+			logProb: 0,
+		},
+		{
+			loc:     1,
+			prob:    0.171909491538362,
+			cumProb: 0.756883265565786,
+			logProb: -1.760787152653070,
+		},
+		{
+			loc:     20,
+			prob:    0.000283302579100,
+			cumProb: 0.998208237166091,
+			logProb: -8.168995047393730,
+		},
+	}
+	testDistributionProbs(t, Weibull{K: 0.5, Lambda: 0.5}, "0.5K 0.5λ Weibull", pts)
+}
+
+func TestWeibullScore(t *testing.T) {
+	for _, test := range []*Weibull{
+		{
+			K:      1,
+			Lambda: 1,
+		},
+		{
+			K:      2,
+			Lambda: 3.6,
+		},
+		{
+			K:      3.4,
+			Lambda: 8,
+		},
+	} {
+		testDerivParam(t, test)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/faithful_test.go b/vendor/gonum.org/v1/gonum/stat/faithful_test.go
new file mode 100644
index 00000000..981eff1c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/faithful_test.go
@@ -0,0 +1,81 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package stat
+
+// faithful is the faithful data set from R.
+var faithful = struct{ waiting, eruptions []float64 }{
+	waiting: []float64{
+		79, 54, 74, 62, 85, 55, 88, 85,
+		51, 85, 54, 84, 78, 47, 83, 52,
+		62, 84, 52, 79, 51, 47, 78, 69,
+		74, 83, 55, 76, 78, 79, 73, 77,
+		66, 80, 74, 52, 48, 80, 59, 90,
+		80, 58, 84, 58, 73, 83, 64, 53,
+		82, 59, 75, 90, 54, 80, 54, 83,
+		71, 64, 77, 81, 59, 84, 48, 82,
+		60, 92, 78, 78, 65, 73, 82, 56,
+		79, 71, 62, 76, 60, 78, 76, 83,
+		75, 82, 70, 65, 73, 88, 76, 80,
+		48, 86, 60, 90, 50, 78, 63, 72,
+		84, 75, 51, 82, 62, 88, 49, 83,
+		81, 47, 84, 52, 86, 81, 75, 59,
+		89, 79, 59, 81, 50, 85, 59, 87,
+		53, 69, 77, 56, 88, 81, 45, 82,
+		55, 90, 45, 83, 56, 89, 46, 82,
+		51, 86, 53, 79, 81, 60, 82, 77,
+		76, 59, 80, 49, 96, 53, 77, 77,
+		65, 81, 71, 70, 81, 93, 53, 89,
+		45, 86, 58, 78, 66, 76, 63, 88,
+		52, 93, 49, 57, 77, 68, 81, 81,
+		73, 50, 85, 74, 55, 77, 83, 83,
+		51, 78, 84, 46, 83, 55, 81, 57,
+		76, 84, 77, 81, 87, 77, 51, 78,
+		60, 82, 91, 53, 78, 46, 77, 84,
+		49, 83, 71, 80, 49, 75, 64, 76,
+		53, 94, 55, 76, 50, 82, 54, 75,
+		78, 79, 78, 78, 70, 79, 70, 54,
+		86, 50, 90, 54, 54, 77, 79, 64,
+		75, 47, 86, 63, 85, 82, 57, 82,
+		67, 74, 54, 83, 73, 73, 88, 80,
+		71, 83, 56, 79, 78, 84, 58, 83,
+		43, 60, 75, 81, 46, 90, 46, 74,
+	},
+	eruptions: []float64{
+		3.600, 1.800, 3.333, 2.283, 4.533, 2.883, 4.700, 3.600,
+		1.950, 4.350, 1.833, 3.917, 4.200, 1.750, 4.700, 2.167,
+		1.750, 4.800, 1.600, 4.250, 1.800, 1.750, 3.450, 3.067,
+		4.533, 3.600, 1.967, 4.083, 3.850, 4.433, 4.300, 4.467,
+		3.367, 4.033, 3.833, 2.017, 1.867, 4.833, 1.833, 4.783,
+		4.350, 1.883, 4.567, 1.750, 4.533, 3.317, 3.833, 2.100,
+		4.633, 2.000, 4.800, 4.716, 1.833, 4.833, 1.733, 4.883,
+		3.717, 1.667, 4.567, 4.317, 2.233, 4.500, 1.750, 4.800,
+		1.817, 4.400, 4.167, 4.700, 2.067, 4.700, 4.033, 1.967,
+		4.500, 4.000, 1.983, 5.067, 2.017, 4.567, 3.883, 3.600,
+		4.133, 4.333, 4.100, 2.633, 4.067, 4.933, 3.950, 4.517,
+		2.167, 4.000, 2.200, 4.333, 1.867, 4.817, 1.833, 4.300,
+		4.667, 3.750, 1.867, 4.900, 2.483, 4.367, 2.100, 4.500,
+		4.050, 1.867, 4.700, 1.783, 4.850, 3.683, 4.733, 2.300,
+		4.900, 4.417, 1.700, 4.633, 2.317, 4.600, 1.817, 4.417,
+		2.617, 4.067, 4.250, 1.967, 4.600, 3.767, 1.917, 4.500,
+		2.267, 4.650, 1.867, 4.167, 2.800, 4.333, 1.833, 4.383,
+		1.883, 4.933, 2.033, 3.733, 4.233, 2.233, 4.533, 4.817,
+		4.333, 1.983, 4.633, 2.017, 5.100, 1.800, 5.033, 4.000,
+		2.400, 4.600, 3.567, 4.000, 4.500, 4.083, 1.800, 3.967,
+		2.200, 4.150, 2.000, 3.833, 3.500, 4.583, 2.367, 5.000,
+		1.933, 4.617, 1.917, 2.083, 4.583, 3.333, 4.167, 4.333,
+		4.500, 2.417, 4.000, 4.167, 1.883, 4.583, 4.250, 3.767,
+		2.033, 4.433, 4.083, 1.833, 4.417, 2.183, 4.800, 1.833,
+		4.800, 4.100, 3.966, 4.233, 3.500, 4.366, 2.250, 4.667,
+		2.100, 4.350, 4.133, 1.867, 4.600, 1.783, 4.367, 3.850,
+		1.933, 4.500, 2.383, 4.700, 1.867, 3.833, 3.417, 4.233,
+		2.400, 4.800, 2.000, 4.150, 1.867, 4.267, 1.750, 4.483,
+		4.000, 4.117, 4.083, 4.267, 3.917, 4.550, 4.083, 2.417,
+		4.183, 2.217, 4.450, 1.883, 1.850, 4.283, 3.950, 2.333,
+		4.150, 2.350, 4.933, 2.900, 4.583, 3.833, 2.083, 4.367,
+		2.133, 4.350, 2.200, 4.450, 3.567, 4.500, 4.150, 3.817,
+		3.917, 4.450, 2.000, 4.283, 4.767, 4.533, 1.850, 4.250,
+		1.983, 2.250, 4.750, 4.117, 2.150, 4.417, 1.817, 4.467,
+	},
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/moments_bench_test.go b/vendor/gonum.org/v1/gonum/stat/moments_bench_test.go
new file mode 100644
index 00000000..6df41394
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/moments_bench_test.go
@@ -0,0 +1,611 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// a set of benchmarks to evaluate the performance of the various
+// moment statistics: Mean, Variance, StdDev, MeanVariance, MeanStdDev,
+// Covariance, Correlation, Skew, ExKurtosis, Moment, MomentAbout, ...
+//
+// It tests both weighted and unweighted versions by using a slice of
+// all ones.
+
+package stat
+
+import (
+	"math/rand"
+	"testing"
+)
+
+const (
+	small  = 10
+	medium = 1000
+	large  = 100000
+	huge   = 10000000
+)
+
+// tests for unweighted versions
+
+func RandomSlice(l int) []float64 {
+	s := make([]float64, l)
+	for i := range s {
+		s[i] = rand.Float64()
+	}
+	return s
+}
+
+func benchmarkMean(b *testing.B, s, wts []float64) {
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		Mean(s, wts)
+	}
+}
+
+func BenchmarkMeanSmall(b *testing.B) {
+	s := RandomSlice(small)
+	benchmarkMean(b, s, nil)
+}
+
+func BenchmarkMeanMedium(b *testing.B) {
+	s := RandomSlice(medium)
+	benchmarkMean(b, s, nil)
+}
+
+func BenchmarkMeanLarge(b *testing.B) {
+	s := RandomSlice(large)
+	benchmarkMean(b, s, nil)
+}
+
+func BenchmarkMeanHuge(b *testing.B) {
+	s := RandomSlice(huge)
+	benchmarkMean(b, s, nil)
+}
+
+func BenchmarkMeanSmallWeighted(b *testing.B) {
+	s := RandomSlice(small)
+	wts := RandomSlice(small)
+	benchmarkMean(b, s, wts)
+}
+
+func BenchmarkMeanMediumWeighted(b *testing.B) {
+	s := RandomSlice(medium)
+	wts := RandomSlice(medium)
+	benchmarkMean(b, s, wts)
+}
+
+func BenchmarkMeanLargeWeighted(b *testing.B) {
+	s := RandomSlice(large)
+	wts := RandomSlice(large)
+	benchmarkMean(b, s, wts)
+}
+
+func BenchmarkMeanHugeWeighted(b *testing.B) {
+	s := RandomSlice(huge)
+	wts := RandomSlice(huge)
+	benchmarkMean(b, s, wts)
+}
+
+func benchmarkVariance(b *testing.B, s, wts []float64) {
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		Variance(s, wts)
+	}
+}
+
+func BenchmarkVarianceSmall(b *testing.B) {
+	s := RandomSlice(small)
+	benchmarkVariance(b, s, nil)
+}
+
+func BenchmarkVarianceMedium(b *testing.B) {
+	s := RandomSlice(medium)
+	benchmarkVariance(b, s, nil)
+}
+
+func BenchmarkVarianceLarge(b *testing.B) {
+	s := RandomSlice(large)
+	benchmarkVariance(b, s, nil)
+}
+
+func BenchmarkVarianceHuge(b *testing.B) {
+	s := RandomSlice(huge)
+	benchmarkVariance(b, s, nil)
+}
+
+func BenchmarkVarianceSmallWeighted(b *testing.B) {
+	s := RandomSlice(small)
+	wts := RandomSlice(small)
+	benchmarkVariance(b, s, wts)
+}
+
+func BenchmarkVarianceMediumWeighted(b *testing.B) {
+	s := RandomSlice(medium)
+	wts := RandomSlice(medium)
+	benchmarkVariance(b, s, wts)
+}
+
+func BenchmarkVarianceLargeWeighted(b *testing.B) {
+	s := RandomSlice(large)
+	wts := RandomSlice(large)
+	benchmarkVariance(b, s, wts)
+}
+
+func BenchmarkVarianceHugeWeighted(b *testing.B) {
+	s := RandomSlice(huge)
+	wts := RandomSlice(huge)
+	benchmarkVariance(b, s, wts)
+}
+
+func benchmarkStdDev(b *testing.B, s, wts []float64) {
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		StdDev(s, wts)
+	}
+}
+
+func BenchmarkStdDevSmall(b *testing.B) {
+	s := RandomSlice(small)
+	benchmarkStdDev(b, s, nil)
+}
+
+func BenchmarkStdDevMedium(b *testing.B) {
+	s := RandomSlice(medium)
+	benchmarkStdDev(b, s, nil)
+}
+
+func BenchmarkStdDevLarge(b *testing.B) {
+	s := RandomSlice(large)
+	benchmarkStdDev(b, s, nil)
+}
+
+func BenchmarkStdDevHuge(b *testing.B) {
+	s := RandomSlice(huge)
+	benchmarkStdDev(b, s, nil)
+}
+
+func BenchmarkStdDevSmallWeighted(b *testing.B) {
+	s := RandomSlice(small)
+	wts := RandomSlice(small)
+	benchmarkStdDev(b, s, wts)
+}
+
+func BenchmarkStdDevMediumWeighted(b *testing.B) {
+	s := RandomSlice(medium)
+	wts := RandomSlice(medium)
+	benchmarkStdDev(b, s, wts)
+}
+
+func BenchmarkStdDevLargeWeighted(b *testing.B) {
+	s := RandomSlice(large)
+	wts := RandomSlice(large)
+	benchmarkStdDev(b, s, wts)
+}
+
+func BenchmarkStdDevHugeWeighted(b *testing.B) {
+	s := RandomSlice(huge)
+	wts := RandomSlice(huge)
+	benchmarkStdDev(b, s, wts)
+}
+
+func benchmarkMeanVariance(b *testing.B, s, wts []float64) {
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		MeanVariance(s, wts)
+	}
+}
+
+func BenchmarkMeanVarianceSmall(b *testing.B) {
+	s := RandomSlice(small)
+	benchmarkMeanVariance(b, s, nil)
+}
+
+func BenchmarkMeanVarianceMedium(b *testing.B) {
+	s := RandomSlice(medium)
+	benchmarkMeanVariance(b, s, nil)
+}
+
+func BenchmarkMeanVarianceLarge(b *testing.B) {
+	s := RandomSlice(large)
+	benchmarkMeanVariance(b, s, nil)
+}
+
+func BenchmarkMeanVarianceHuge(b *testing.B) {
+	s := RandomSlice(huge)
+	benchmarkMeanVariance(b, s, nil)
+}
+
+func BenchmarkMeanVarianceSmallWeighted(b *testing.B) {
+	s := RandomSlice(small)
+	wts := RandomSlice(small)
+	benchmarkMeanVariance(b, s, wts)
+}
+
+func BenchmarkMeanVarianceMediumWeighted(b *testing.B) {
+	s := RandomSlice(medium)
+	wts := RandomSlice(medium)
+	benchmarkMeanVariance(b, s, wts)
+}
+
+func BenchmarkMeanVarianceLargeWeighted(b *testing.B) {
+	s := RandomSlice(large)
+	wts := RandomSlice(large)
+	benchmarkMeanVariance(b, s, wts)
+}
+
+func BenchmarkMeanVarianceHugeWeighted(b *testing.B) {
+	s := RandomSlice(huge)
+	wts := RandomSlice(huge)
+	benchmarkMeanVariance(b, s, wts)
+}
+
+func benchmarkMeanStdDev(b *testing.B, s, wts []float64) {
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		MeanStdDev(s, wts)
+	}
+}
+
+func BenchmarkMeanStdDevSmall(b *testing.B) {
+	s := RandomSlice(small)
+	benchmarkMeanStdDev(b, s, nil)
+}
+
+func BenchmarkMeanStdDevMedium(b *testing.B) {
+	s := RandomSlice(medium)
+	benchmarkMeanStdDev(b, s, nil)
+}
+
+func BenchmarkMeanStdDevLarge(b *testing.B) {
+	s := RandomSlice(large)
+	benchmarkMeanStdDev(b, s, nil)
+}
+
+func BenchmarkMeanStdDevHuge(b *testing.B) {
+	s := RandomSlice(huge)
+	benchmarkMeanStdDev(b, s, nil)
+}
+
+func BenchmarkMeanStdDevSmallWeighted(b *testing.B) {
+	s := RandomSlice(small)
+	wts := RandomSlice(small)
+	benchmarkMeanStdDev(b, s, wts)
+}
+
+func BenchmarkMeanStdDevMediumWeighted(b *testing.B) {
+	s := RandomSlice(medium)
+	wts := RandomSlice(medium)
+	benchmarkMeanStdDev(b, s, wts)
+}
+
+func BenchmarkMeanStdDevLargeWeighted(b *testing.B) {
+	s := RandomSlice(large)
+	wts := RandomSlice(large)
+	benchmarkMeanStdDev(b, s, wts)
+}
+
+func BenchmarkMeanStdDevHugeWeighted(b *testing.B) {
+	s := RandomSlice(huge)
+	wts := RandomSlice(huge)
+	benchmarkMeanStdDev(b, s, wts)
+}
+
+func benchmarkCovariance(b *testing.B, s1, s2, wts []float64) {
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		Covariance(s1, s2, wts)
+	}
+}
+
+func BenchmarkCovarianceSmall(b *testing.B) {
+	s1 := RandomSlice(small)
+	s2 := RandomSlice(small)
+	benchmarkCovariance(b, s1, s2, nil)
+}
+
+func BenchmarkCovarianceMedium(b *testing.B) {
+	s1 := RandomSlice(medium)
+	s2 := RandomSlice(medium)
+	benchmarkCovariance(b, s1, s2, nil)
+}
+
+func BenchmarkCovarianceLarge(b *testing.B) {
+	s1 := RandomSlice(large)
+	s2 := RandomSlice(large)
+	benchmarkCovariance(b, s1, s2, nil)
+}
+
+func BenchmarkCovarianceHuge(b *testing.B) {
+	s1 := RandomSlice(huge)
+	s2 := RandomSlice(huge)
+	benchmarkCovariance(b, s1, s2, nil)
+}
+
+func BenchmarkCovarianceSmallWeighted(b *testing.B) {
+	s1 := RandomSlice(small)
+	s2 := RandomSlice(small)
+	wts := RandomSlice(small)
+	benchmarkCovariance(b, s1, s2, wts)
+}
+
+func BenchmarkCovarianceMediumWeighted(b *testing.B) {
+	s1 := RandomSlice(medium)
+	s2 := RandomSlice(medium)
+	wts := RandomSlice(medium)
+	benchmarkCovariance(b, s1, s2, wts)
+}
+
+func BenchmarkCovarianceLargeWeighted(b *testing.B) {
+	s1 := RandomSlice(large)
+	s2 := RandomSlice(large)
+	wts := RandomSlice(large)
+	benchmarkCovariance(b, s1, s2, wts)
+}
+
+func BenchmarkCovarianceHugeWeighted(b *testing.B) {
+	s1 := RandomSlice(huge)
+	s2 := RandomSlice(huge)
+	wts := RandomSlice(huge)
+	benchmarkCovariance(b, s1, s2, wts)
+}
+
+func benchmarkCorrelation(b *testing.B, s1, s2, wts []float64) {
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		Correlation(s1, s2, wts)
+	}
+}
+
+func BenchmarkCorrelationSmall(b *testing.B) {
+	s1 := RandomSlice(small)
+	s2 := RandomSlice(small)
+	benchmarkCorrelation(b, s1, s2, nil)
+}
+
+func BenchmarkCorrelationMedium(b *testing.B) {
+	s1 := RandomSlice(medium)
+	s2 := RandomSlice(medium)
+	benchmarkCorrelation(b, s1, s2, nil)
+}
+
+func BenchmarkCorrelationLarge(b *testing.B) {
+	s1 := RandomSlice(large)
+	s2 := RandomSlice(large)
+	benchmarkCorrelation(b, s1, s2, nil)
+}
+
+func BenchmarkCorrelationHuge(b *testing.B) {
+	s1 := RandomSlice(huge)
+	s2 := RandomSlice(huge)
+	benchmarkCorrelation(b, s1, s2, nil)
+}
+
+func BenchmarkCorrelationSmallWeighted(b *testing.B) {
+	s1 := RandomSlice(small)
+	s2 := RandomSlice(small)
+	wts := RandomSlice(small)
+	benchmarkCorrelation(b, s1, s2, wts)
+}
+
+func BenchmarkCorrelationMediumWeighted(b *testing.B) {
+	s1 := RandomSlice(medium)
+	s2 := RandomSlice(medium)
+	wts := RandomSlice(medium)
+	benchmarkCorrelation(b, s1, s2, wts)
+}
+
+func BenchmarkCorrelationLargeWeighted(b *testing.B) {
+	s1 := RandomSlice(large)
+	s2 := RandomSlice(large)
+	wts := RandomSlice(large)
+	benchmarkCorrelation(b, s1, s2, wts)
+}
+
+func BenchmarkCorrelationHugeWeighted(b *testing.B) {
+	s1 := RandomSlice(huge)
+	s2 := RandomSlice(huge)
+	wts := RandomSlice(huge)
+	benchmarkCorrelation(b, s1, s2, wts)
+}
+
+func benchmarkSkew(b *testing.B, s, wts []float64) {
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		Skew(s, wts)
+	}
+}
+
+func BenchmarkSkewSmall(b *testing.B) {
+	s := RandomSlice(small)
+	benchmarkSkew(b, s, nil)
+}
+
+func BenchmarkSkewMedium(b *testing.B) {
+	s := RandomSlice(medium)
+	benchmarkSkew(b, s, nil)
+}
+
+func BenchmarkSkewLarge(b *testing.B) {
+	s := RandomSlice(large)
+	benchmarkSkew(b, s, nil)
+}
+
+func BenchmarkSkewHuge(b *testing.B) {
+	s := RandomSlice(huge)
+	benchmarkSkew(b, s, nil)
+}
+
+func BenchmarkSkewSmallWeighted(b *testing.B) {
+	s := RandomSlice(small)
+	wts := RandomSlice(small)
+	benchmarkSkew(b, s, wts)
+}
+
+func BenchmarkSkewMediumWeighted(b *testing.B) {
+	s := RandomSlice(medium)
+	wts := RandomSlice(medium)
+	benchmarkSkew(b, s, wts)
+}
+
+func BenchmarkSkewLargeWeighted(b *testing.B) {
+	s := RandomSlice(large)
+	wts := RandomSlice(large)
+	benchmarkSkew(b, s, wts)
+}
+
+func BenchmarkSkewHugeWeighted(b *testing.B) {
+	s := RandomSlice(huge)
+	wts := RandomSlice(huge)
+	benchmarkSkew(b, s, wts)
+}
+
+func benchmarkExKurtosis(b *testing.B, s, wts []float64) {
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		ExKurtosis(s, wts)
+	}
+}
+
+func BenchmarkExKurtosisSmall(b *testing.B) {
+	s := RandomSlice(small)
+	benchmarkExKurtosis(b, s, nil)
+}
+
+func BenchmarkExKurtosisMedium(b *testing.B) {
+	s := RandomSlice(medium)
+	benchmarkExKurtosis(b, s, nil)
+}
+
+func BenchmarkExKurtosisLarge(b *testing.B) {
+	s := RandomSlice(large)
+	benchmarkExKurtosis(b, s, nil)
+}
+
+func BenchmarkExKurtosisHuge(b *testing.B) {
+	s := RandomSlice(huge)
+	benchmarkExKurtosis(b, s, nil)
+}
+
+func BenchmarkExKurtosisSmallWeighted(b *testing.B) {
+	s := RandomSlice(small)
+	wts := RandomSlice(small)
+	benchmarkExKurtosis(b, s, wts)
+}
+
+func BenchmarkExKurtosisMediumWeighted(b *testing.B) {
+	s := RandomSlice(medium)
+	wts := RandomSlice(medium)
+	benchmarkExKurtosis(b, s, wts)
+}
+
+func BenchmarkExKurtosisLargeWeighted(b *testing.B) {
+	s := RandomSlice(large)
+	wts := RandomSlice(large)
+	benchmarkExKurtosis(b, s, wts)
+}
+
+func BenchmarkExKurtosisHugeWeighted(b *testing.B) {
+	s := RandomSlice(huge)
+	wts := RandomSlice(huge)
+	benchmarkExKurtosis(b, s, wts)
+}
+
+func benchmarkMoment(b *testing.B, n float64, s, wts []float64) {
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		Moment(n, s, wts)
+	}
+}
+
+func BenchmarkMomentSmall(b *testing.B) {
+	s := RandomSlice(small)
+	benchmarkMoment(b, 5, s, nil)
+}
+
+func BenchmarkMomentMedium(b *testing.B) {
+	s := RandomSlice(medium)
+	benchmarkMoment(b, 5, s, nil)
+}
+
+func BenchmarkMomentLarge(b *testing.B) {
+	s := RandomSlice(large)
+	benchmarkMoment(b, 5, s, nil)
+}
+
+func BenchmarkMomentHuge(b *testing.B) {
+	s := RandomSlice(huge)
+	benchmarkMoment(b, 5, s, nil)
+}
+
+func BenchmarkMomentSmallWeighted(b *testing.B) {
+	s := RandomSlice(small)
+	wts := RandomSlice(small)
+	benchmarkMoment(b, 5, s, wts)
+}
+
+func BenchmarkMomentMediumWeighted(b *testing.B) {
+	s := RandomSlice(medium)
+	wts := RandomSlice(medium)
+	benchmarkMoment(b, 5, s, wts)
+}
+
+func BenchmarkMomentLargeWeighted(b *testing.B) {
+	s := RandomSlice(large)
+	wts := RandomSlice(large)
+	benchmarkMoment(b, 5, s, wts)
+}
+
+func BenchmarkMomentHugeWeighted(b *testing.B) {
+	s := RandomSlice(huge)
+	wts := RandomSlice(huge)
+	benchmarkMoment(b, 5, s, wts)
+}
+
+func benchmarkMomentAbout(b *testing.B, n float64, s []float64, mean float64, wts []float64) {
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		MomentAbout(n, s, mean, wts)
+	}
+}
+
+func BenchmarkMomentAboutSmall(b *testing.B) {
+	s := RandomSlice(small)
+	benchmarkMomentAbout(b, 5, s, 0, nil)
+}
+
+func BenchmarkMomentAboutMedium(b *testing.B) {
+	s := RandomSlice(medium)
+	benchmarkMomentAbout(b, 5, s, 0, nil)
+}
+
+func BenchmarkMomentAboutLarge(b *testing.B) {
+	s := RandomSlice(large)
+	benchmarkMomentAbout(b, 5, s, 0, nil)
+}
+
+func BenchmarkMomentAboutHuge(b *testing.B) {
+	s := RandomSlice(huge)
+	benchmarkMomentAbout(b, 5, s, 0, nil)
+}
+
+func BenchmarkMomentAboutSmallWeighted(b *testing.B) {
+	s := RandomSlice(small)
+	wts := RandomSlice(small)
+	benchmarkMomentAbout(b, 5, s, 0, wts)
+}
+
+func BenchmarkMomentAboutMediumWeighted(b *testing.B) {
+	s := RandomSlice(medium)
+	wts := RandomSlice(medium)
+	benchmarkMomentAbout(b, 5, s, 0, wts)
+}
+
+func BenchmarkMomentAboutLargeWeighted(b *testing.B) {
+	s := RandomSlice(large)
+	wts := RandomSlice(large)
+	benchmarkMomentAbout(b, 5, s, 0, wts)
+}
+
+func BenchmarkMomentAboutHugeWeighted(b *testing.B) {
+	s := RandomSlice(huge)
+	wts := RandomSlice(huge)
+	benchmarkMomentAbout(b, 5, s, 0, wts)
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/pca_example_test.go b/vendor/gonum.org/v1/gonum/stat/pca_example_test.go
new file mode 100644
index 00000000..b434a91a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/pca_example_test.go
@@ -0,0 +1,60 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package stat_test
+
+import (
+	"fmt"
+
+	"gonum.org/v1/gonum/mat"
+	"gonum.org/v1/gonum/stat"
+)
+
+func ExamplePC() {
+	// iris is a truncated sample of the Fisher's Iris dataset.
+	n := 10
+	d := 4
+	iris := mat.NewDense(n, d, []float64{
+		5.1, 3.5, 1.4, 0.2,
+		4.9, 3.0, 1.4, 0.2,
+		4.7, 3.2, 1.3, 0.2,
+		4.6, 3.1, 1.5, 0.2,
+		5.0, 3.6, 1.4, 0.2,
+		5.4, 3.9, 1.7, 0.4,
+		4.6, 3.4, 1.4, 0.3,
+		5.0, 3.4, 1.5, 0.2,
+		4.4, 2.9, 1.4, 0.2,
+		4.9, 3.1, 1.5, 0.1,
+	})
+
+	// Calculate the principal component direction vectors
+	// and variances.
+	var pc stat.PC
+	ok := pc.PrincipalComponents(iris, nil)
+	if !ok {
+		return
+	}
+	fmt.Printf("variances = %.4f\n\n", pc.VarsTo(nil))
+
+	// Project the data onto the first 2 principal components.
+	k := 2
+	var proj mat.Dense
+	proj.Mul(iris, pc.VectorsTo(nil).Slice(0, d, 0, k))
+
+	fmt.Printf("proj = %.4f", mat.Formatted(&proj, mat.Prefix("       ")))
+
+	// Output:
+	// variances = [0.1666 0.0207 0.0079 0.0019]
+	//
+	// proj = ⎡-6.1686   1.4659⎤
+	//        ⎢-5.6767   1.6459⎥
+	//        ⎢-5.6699   1.3642⎥
+	//        ⎢-5.5643   1.3816⎥
+	//        ⎢-6.1734   1.3309⎥
+	//        ⎢-6.7278   1.4021⎥
+	//        ⎢-5.7743   1.1498⎥
+	//        ⎢-6.0466   1.4714⎥
+	//        ⎢-5.2709   1.3570⎥
+	//        ⎣-5.7533   1.6207⎦
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/pca_test.go b/vendor/gonum.org/v1/gonum/stat/pca_test.go
new file mode 100644
index 00000000..6af1b8c0
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/pca_test.go
@@ -0,0 +1,188 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package stat
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+)
+
+var appengine bool
+
+func TestPrincipalComponents(t *testing.T) {
+	if appengine {
+		t.Skip("non-asm implementation fails test")
+	}
+tests:
+	for i, test := range []struct {
+		data     mat.Matrix
+		weights  []float64
+		wantVecs *mat.Dense
+		wantVars []float64
+		epsilon  float64
+	}{
+		// Test results verified using R.
+		{
+			data: mat.NewDense(3, 3, []float64{
+				1, 2, 3,
+				4, 5, 6,
+				7, 8, 9,
+			}),
+			wantVecs: mat.NewDense(3, 3, []float64{
+				0.5773502691896258, 0.8164965809277261, 0,
+				0.577350269189626, -0.4082482904638632, -0.7071067811865476,
+				0.5773502691896258, -0.4082482904638631, 0.7071067811865475,
+			}),
+			wantVars: []float64{27, 0, 0},
+			epsilon:  1e-12,
+		},
+		{ // Truncated iris data.
+			data: mat.NewDense(10, 4, []float64{
+				5.1, 3.5, 1.4, 0.2,
+				4.9, 3.0, 1.4, 0.2,
+				4.7, 3.2, 1.3, 0.2,
+				4.6, 3.1, 1.5, 0.2,
+				5.0, 3.6, 1.4, 0.2,
+				5.4, 3.9, 1.7, 0.4,
+				4.6, 3.4, 1.4, 0.3,
+				5.0, 3.4, 1.5, 0.2,
+				4.4, 2.9, 1.4, 0.2,
+				4.9, 3.1, 1.5, 0.1,
+			}),
+			wantVecs: mat.NewDense(4, 4, []float64{
+				-0.6681110197952722, 0.7064764857539533, -0.14026590216895132, -0.18666578956412125,
+				-0.7166344774801547, -0.6427036135482664, -0.135650285905254, 0.23444848208629923,
+				-0.164411275166307, 0.11898477441068218, 0.9136367900709548, 0.35224901970831746,
+				-0.11415613655453069, -0.2714141920887426, 0.35664028439226514, -0.8866286823515034,
+			}),
+			wantVars: []float64{0.1665786313282786, 0.02065509475412993, 0.007944620317765855, 0.0019327647109368329},
+			epsilon:  1e-12,
+		},
+		{ // Truncated iris data to form wide matrix.
+			data: mat.NewDense(3, 4, []float64{
+				5.1, 3.5, 1.4, 0.2,
+				4.9, 3.0, 1.4, 0.2,
+				4.7, 3.2, 1.3, 0.2,
+			}),
+			wantVecs: mat.NewDense(4, 3, []float64{
+				-0.5705187254552365, -0.7505979435049239, 0.08084520834544455,
+				-0.8166537769529318, 0.5615147645527523, -0.032338083338177705,
+				-0.08709186238359454, -0.3482870890450082, -0.22636658336724505,
+				0, 0, -0.9701425001453315,
+			}),
+			wantVars: []float64{0.0844692361537822, 0.022197430512884326, 0},
+			epsilon:  1e-12,
+		},
+		{ // Truncated iris data transposed to check for operation on fat input.
+			data: mat.NewDense(10, 4, []float64{
+				5.1, 3.5, 1.4, 0.2,
+				4.9, 3.0, 1.4, 0.2,
+				4.7, 3.2, 1.3, 0.2,
+				4.6, 3.1, 1.5, 0.2,
+				5.0, 3.6, 1.4, 0.2,
+				5.4, 3.9, 1.7, 0.4,
+				4.6, 3.4, 1.4, 0.3,
+				5.0, 3.4, 1.5, 0.2,
+				4.4, 2.9, 1.4, 0.2,
+				4.9, 3.1, 1.5, 0.1,
+			}).T(),
+			wantVecs: mat.NewDense(10, 4, []float64{
+				-0.3366602459946619, -0.1373634006401213, 0.3465102523547623, -0.10290179303893479,
+				-0.31381852053861975, 0.5197145790632827, 0.5567296129086686, -0.15923062170153618,
+				-0.30857197637565165, -0.07670930360819002, 0.36159923003337235, 0.3342301027853355,
+				-0.29527124351656137, 0.16885455995353074, -0.5056204762881208, 0.32580913261444344,
+				-0.3327611073694004, -0.39365834489416474, 0.04900050959307464, 0.46812879383236555,
+				-0.34445484362044815, -0.2985206914561878, -0.1009714701361799, -0.16803618186050803,
+				-0.2986246350957691, -0.4222037823717799, -0.11838613462182519, -0.580283530375069,
+				-0.325911246223126, 0.024366468758217238, -0.12082035131864265, 0.16756027181337868,
+				-0.2814284432361538, 0.240812316260054, -0.24061437569068145, -0.365034616264623,
+				-0.31906138507685167, 0.4423912824105986, -0.2906412122303604, 0.027551046870337714,
+			}),
+			wantVars: []float64{41.8851906634233, 0.07762619213464989, 0.010516477775373585, 0},
+			epsilon:  1e-12,
+		},
+		{ // Truncated iris data unitary weights.
+			data: mat.NewDense(10, 4, []float64{
+				5.1, 3.5, 1.4, 0.2,
+				4.9, 3.0, 1.4, 0.2,
+				4.7, 3.2, 1.3, 0.2,
+				4.6, 3.1, 1.5, 0.2,
+				5.0, 3.6, 1.4, 0.2,
+				5.4, 3.9, 1.7, 0.4,
+				4.6, 3.4, 1.4, 0.3,
+				5.0, 3.4, 1.5, 0.2,
+				4.4, 2.9, 1.4, 0.2,
+				4.9, 3.1, 1.5, 0.1,
+			}),
+			weights: []float64{1, 1, 1, 1, 1, 1, 1, 1, 1, 1},
+			wantVecs: mat.NewDense(4, 4, []float64{
+				-0.6681110197952722, 0.7064764857539533, -0.14026590216895132, -0.18666578956412125,
+				-0.7166344774801547, -0.6427036135482664, -0.135650285905254, 0.23444848208629923,
+				-0.164411275166307, 0.11898477441068218, 0.9136367900709548, 0.35224901970831746,
+				-0.11415613655453069, -0.2714141920887426, 0.35664028439226514, -0.8866286823515034,
+			}),
+			wantVars: []float64{0.1665786313282786, 0.02065509475412993, 0.007944620317765855, 0.0019327647109368329},
+			epsilon:  1e-12,
+		},
+		{ // Truncated iris data non-unitary weights.
+			data: mat.NewDense(10, 4, []float64{
+				5.1, 3.5, 1.4, 0.2,
+				4.9, 3.0, 1.4, 0.2,
+				4.7, 3.2, 1.3, 0.2,
+				4.6, 3.1, 1.5, 0.2,
+				5.0, 3.6, 1.4, 0.2,
+				5.4, 3.9, 1.7, 0.4,
+				4.6, 3.4, 1.4, 0.3,
+				5.0, 3.4, 1.5, 0.2,
+				4.4, 2.9, 1.4, 0.2,
+				4.9, 3.1, 1.5, 0.1,
+			}),
+			weights: []float64{2, 3, 1, 1, 1, 1, 1, 1, 1, 2},
+			wantVecs: mat.NewDense(4, 4, []float64{
+				-0.618936145422414, 0.763069301531647, 0.124857741232537, 0.138035623677211,
+				-0.763958271606519, -0.603881770702898, 0.118267155321333, -0.194184052457746,
+				-0.143552119754944, 0.090014599564871, -0.942209377020044, -0.289018426115945,
+				-0.112599271966947, -0.212012782487076, -0.287515067921680, 0.927203898682805,
+			}),
+			wantVars: []float64{0.129621985550623, 0.022417487771598, 0.006454461065715, 0.002495076601075},
+			epsilon:  1e-12,
+		},
+	} {
+		var pc PC
+		var vecs *mat.Dense
+		var vars []float64
+		for j := 0; j < 2; j++ {
+			ok := pc.PrincipalComponents(test.data, test.weights)
+			vecs = pc.VectorsTo(vecs)
+			vars = pc.VarsTo(vars)
+			if !ok {
+				t.Errorf("unexpected SVD failure for test %d use %d", i, j)
+				continue tests
+			}
+			if !mat.EqualApprox(vecs, test.wantVecs, test.epsilon) {
+				t.Errorf("%d use %d: unexpected PCA result got:\n%v\nwant:\n%v",
+					i, j, mat.Formatted(vecs), mat.Formatted(test.wantVecs))
+			}
+			if !approxEqual(vars, test.wantVars, test.epsilon) {
+				t.Errorf("%d use %d: unexpected variance result got:%v, want:%v",
+					i, j, vars, test.wantVars)
+			}
+		}
+	}
+}
+
+func approxEqual(a, b []float64, epsilon float64) bool {
+	if len(a) != len(b) {
+		return false
+	}
+	for i, v := range a {
+		if !floats.EqualWithinAbsOrRel(v, b[i], epsilon, epsilon) {
+			return false
+		}
+	}
+	return true
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/roc_example_test.go b/vendor/gonum.org/v1/gonum/stat/roc_example_test.go
new file mode 100644
index 00000000..9dce80b1
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/roc_example_test.go
@@ -0,0 +1,56 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package stat_test
+
+import (
+	"fmt"
+
+	"gonum.org/v1/gonum/integrate"
+	"gonum.org/v1/gonum/stat"
+)
+
+func ExampleROC_weighted() {
+	y := []float64{0, 3, 5, 6, 7.5, 8}
+	classes := []bool{true, false, true, false, false, false}
+	weights := []float64{4, 1, 6, 3, 2, 2}
+
+	tpr, fpr := stat.ROC(0, y, classes, weights)
+	fmt.Printf("true  positive rate: %v\n", tpr)
+	fmt.Printf("false positive rate: %v\n", fpr)
+
+	// Output:
+	// true  positive rate: [0 0.4 0.4 1 1 1 1]
+	// false positive rate: [0 0 0.125 0.125 0.5 0.75 1]
+}
+
+func ExampleROC_unweighted() {
+	y := []float64{0, 3, 5, 6, 7.5, 8}
+	classes := []bool{true, false, true, false, false, false}
+
+	tpr, fpr := stat.ROC(0, y, classes, nil)
+	fmt.Printf("true  positive rate: %v\n", tpr)
+	fmt.Printf("false positive rate: %v\n", fpr)
+
+	// Output:
+	// true  positive rate: [0 0.5 0.5 1 1 1 1]
+	// false positive rate: [0 0 0.25 0.25 0.5 0.75 1]
+}
+
+func ExampleROC_aUC() {
+	y := []float64{0.1, 0.35, 0.4, 0.8}
+	classes := []bool{true, false, true, false}
+
+	tpr, fpr := stat.ROC(0, y, classes, nil)
+	// compute Area Under Curve
+	auc := integrate.Trapezoidal(fpr, tpr)
+	fmt.Printf("true  positive rate: %v\n", tpr)
+	fmt.Printf("false positive rate: %v\n", fpr)
+	fmt.Printf("auc: %v\n", auc)
+
+	// Output:
+	// true  positive rate: [0 0.5 0.5 1 1]
+	// false positive rate: [0 0 0.5 0.5 1]
+	// auc: 0.75
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/roc_test.go b/vendor/gonum.org/v1/gonum/stat/roc_test.go
new file mode 100644
index 00000000..99fdae13
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/roc_test.go
@@ -0,0 +1,178 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package stat
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+// Test cases where calculated manually.
+func TestROC(t *testing.T) {
+	cases := []struct {
+		y       []float64
+		c       []bool
+		w       []float64
+		n       int
+		wantTPR []float64
+		wantFPR []float64
+	}{
+		{
+			y:       []float64{0, 3, 5, 6, 7.5, 8},
+			c:       []bool{true, false, true, false, false, false},
+			wantTPR: []float64{0, 0.5, 0.5, 1, 1, 1, 1},
+			wantFPR: []float64{0, 0, 0.25, 0.25, 0.5, 0.75, 1},
+		},
+		{
+			y:       []float64{0, 3, 5, 6, 7.5, 8},
+			c:       []bool{true, false, true, false, false, false},
+			w:       []float64{4, 1, 6, 3, 2, 2},
+			wantTPR: []float64{0, 0.4, 0.4, 1, 1, 1, 1},
+			wantFPR: []float64{0, 0, 0.125, 0.125, 0.5, 0.75, 1},
+		},
+		{
+			y:       []float64{0, 3, 5, 6, 7.5, 8},
+			c:       []bool{true, false, true, false, false, false},
+			n:       int(5),
+			wantTPR: []float64{0, 0.5, 0.5, 1, 1},
+			wantFPR: []float64{0, 0, 0.25, 0.5, 1},
+		},
+		{
+			y:       []float64{0, 3, 5, 6, 7.5, 8},
+			c:       []bool{true, false, true, false, false, false},
+			n:       int(9),
+			wantTPR: []float64{0, 0.5, 0.5, 0.5, 0.5, 1, 1, 1, 1},
+			wantFPR: []float64{0, 0, 0, 0.25, 0.25, 0.25, 0.5, 0.5, 1},
+		},
+		{
+			y:       []float64{0, 3, 5, 6, 7.5, 8},
+			c:       []bool{true, false, true, false, false, false},
+			w:       []float64{4, 1, 6, 3, 2, 2},
+			n:       int(5),
+			wantTPR: []float64{0, 0.4, 0.4, 1, 1},
+			wantFPR: []float64{0, 0, 0.125, 0.5, 1},
+		},
+		{
+			y:       []float64{0, 3, 5, 6, 7.5, 8},
+			c:       []bool{true, false, true, false, false, false},
+			w:       []float64{4, 1, 6, 3, 2, 2},
+			n:       int(9),
+			wantTPR: []float64{0, 0.4, 0.4, 0.4, 0.4, 1, 1, 1, 1},
+			wantFPR: []float64{0, 0, 0, 0.125, 0.125, 0.125, 0.5, 0.5, 1},
+		},
+		{
+			y:       []float64{0, 3, 6, 6, 6, 8},
+			c:       []bool{true, false, true, false, false, false},
+			wantTPR: []float64{0, 0.5, 0.5, 1, 1},
+			wantFPR: []float64{0, 0, 0.25, 0.75, 1},
+		},
+		{
+			y:       []float64{0, 3, 6, 6, 6, 8},
+			c:       []bool{true, false, true, false, false, false},
+			w:       []float64{4, 1, 6, 3, 2, 2},
+			wantTPR: []float64{0, 0.4, 0.4, 1, 1},
+			wantFPR: []float64{0, 0, 0.125, 0.75, 1},
+		},
+		{
+			y:       []float64{0, 3, 6, 6, 6, 8},
+			c:       []bool{true, false, true, false, false, false},
+			n:       int(5),
+			wantTPR: []float64{0, 0.5, 0.5, 1, 1},
+			wantFPR: []float64{0, 0, 0.25, 0.75, 1},
+		},
+		{
+			y:       []float64{0, 3, 6, 6, 6, 8},
+			c:       []bool{true, false, true, false, false, false},
+			n:       int(9),
+			wantTPR: []float64{0, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 1, 1},
+			wantFPR: []float64{0, 0, 0, 0.25, 0.25, 0.25, 0.75, 0.75, 1},
+		},
+		{
+			y:       []float64{0, 3, 6, 6, 6, 8},
+			c:       []bool{true, false, true, false, false, false},
+			w:       []float64{4, 1, 6, 3, 2, 2},
+			n:       int(5),
+			wantTPR: []float64{0, 0.4, 0.4, 1, 1},
+			wantFPR: []float64{0, 0, 0.125, 0.75, 1},
+		},
+		{
+			y:       []float64{0, 3, 6, 6, 6, 8},
+			c:       []bool{true, false, true, false, false, false},
+			w:       []float64{4, 1, 6, 3, 2, 2},
+			n:       int(9),
+			wantTPR: []float64{0, 0.4, 0.4, 0.4, 0.4, 0.4, 1, 1, 1},
+			wantFPR: []float64{0, 0, 0, 0.125, 0.125, 0.125, 0.75, 0.75, 1},
+		},
+		{
+			y:       []float64{1, 2},
+			c:       []bool{true, true},
+			wantTPR: []float64{0, 0.5, 1},
+			wantFPR: []float64{0, 0, 1},
+		},
+		{
+			y:       []float64{1, 2},
+			c:       []bool{true, true},
+			n:       int(2),
+			wantTPR: []float64{0, 1},
+			wantFPR: []float64{0, 1},
+		},
+		{
+			y:       []float64{1, 2},
+			c:       []bool{true, true},
+			n:       int(7),
+			wantTPR: []float64{0, 0.5, 0.5, 0.5, 0.5, 0.5, 1},
+			wantFPR: []float64{0, 0, 0, 0, 0, 0, 1},
+		},
+		{
+			y:       []float64{1},
+			c:       []bool{true},
+			wantTPR: []float64{0, 1},
+			wantFPR: []float64{0, 1},
+		},
+		{
+			y:       []float64{1},
+			c:       []bool{true},
+			n:       int(2),
+			wantTPR: []float64{0, 1},
+			wantFPR: []float64{0, 1},
+		},
+		{
+			y:       []float64{1},
+			c:       []bool{false},
+			wantTPR: []float64{0, 1},
+			wantFPR: []float64{0, 1},
+		},
+		{
+			y:       []float64{0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 10},
+			c:       []bool{true, false, true, true, false, false, true},
+			n:       int(5),
+			wantTPR: []float64{0, 0.75, 0.75, 0.75, 1},
+			wantFPR: []float64{0, 1, 1, 1, 1},
+		},
+		{
+			y:       []float64{},
+			c:       []bool{},
+			wantTPR: nil,
+			wantFPR: nil,
+		},
+		{
+			y:       []float64{},
+			c:       []bool{},
+			n:       int(5),
+			wantTPR: nil,
+			wantFPR: nil,
+		},
+	}
+	for i, test := range cases {
+		gotTPR, gotFPR := ROC(test.n, test.y, test.c, test.w)
+		if !floats.Same(gotTPR, test.wantTPR) {
+			t.Errorf("%d: unexpected TPR got:%v want:%v", i, gotTPR, test.wantTPR)
+		}
+		if !floats.Same(gotFPR, test.wantFPR) {
+			t.Errorf("%d: unexpected FPR got:%v want:%v", i, gotFPR, test.wantFPR)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/samplemv/doc.go b/vendor/gonum.org/v1/gonum/stat/samplemv/doc.go
new file mode 100644
index 00000000..ab4f37cc
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/samplemv/doc.go
@@ -0,0 +1,11 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package samplemv implements advanced sampling routines from explicit and implicit
+// probability distributions.
+//
+// Each sampling routine is implemented as a stateless function with a
+// complementary wrapper type. The wrapper types allow the sampling routines
+// to implement interfaces.
+package samplemv // import "gonum.org/v1/gonum/stat/samplemv"
diff --git a/vendor/gonum.org/v1/gonum/stat/samplemv/metropolishastings.go b/vendor/gonum.org/v1/gonum/stat/samplemv/metropolishastings.go
new file mode 100644
index 00000000..d4d210e8
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/samplemv/metropolishastings.go
@@ -0,0 +1,221 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package samplemv
+
+import (
+	"math"
+	"math/rand"
+
+	"gonum.org/v1/gonum/mat"
+	"gonum.org/v1/gonum/stat/distmv"
+)
+
+var _ Sampler = MetropolisHastingser{}
+
+// MHProposal defines a proposal distribution for Metropolis Hastings.
+type MHProposal interface {
+	// ConditionalLogProb returns the probability of the first argument
+	// conditioned on being at the second argument.
+	//  p(x|y)
+	// ConditionalLogProb panics if the input slices are not the same length.
+	ConditionalLogProb(x, y []float64) (prob float64)
+
+	// ConditionalRand generates a new random location conditioned being at the
+	// location y. If the first argument is nil, a new slice is allocated and
+	// returned. Otherwise, the random location is stored in-place into the first
+	// argument, and ConditionalRand will panic if the input slice lengths differ.
+	ConditionalRand(x, y []float64) []float64
+}
+
+// MetropolisHastingser is a wrapper around the MetropolisHastings sampling type.
+//
+// BurnIn sets the number of samples to discard before keeping the first sample.
+// A properly set BurnIn rate will decorrelate the sampling chain from the initial
+// location. The proper BurnIn value will depend on the mixing time of the
+// Markov chain defined by the target and proposal distributions.
+//
+// Rate sets the number of samples to discard in between each kept sample. A
+// higher rate will better approximate independently and identically distributed
+// samples, while a lower rate will keep more information (at the cost of
+// higher correlation between samples). If Rate is 0 it is defaulted to 1.
+//
+// The initial value is NOT changed during calls to Sample.
+type MetropolisHastingser struct {
+	Initial  []float64
+	Target   distmv.LogProber
+	Proposal MHProposal
+	Src      *rand.Rand
+
+	BurnIn int
+	Rate   int
+}
+
+// Sample generates rows(batch) samples using the Metropolis Hastings sample
+// generation method. The initial location is NOT updated during the call to Sample.
+//
+// The number of columns in batch must equal len(m.Initial), otherwise Sample
+// will panic.
+func (m MetropolisHastingser) Sample(batch *mat.Dense) {
+	burnIn := m.BurnIn
+	rate := m.Rate
+	if rate == 0 {
+		rate = 1
+	}
+	r, c := batch.Dims()
+	if len(m.Initial) != c {
+		panic("metropolishastings: length mismatch")
+	}
+
+	// Use the optimal size for the temporary memory to allow the fewest calls
+	// to MetropolisHastings. The case where tmp shadows samples must be
+	// aligned with the logic after burn-in so that tmp does not shadow samples
+	// during the rate portion.
+	tmp := batch
+	if rate > r {
+		tmp = mat.NewDense(rate, c, nil)
+	}
+	rTmp, _ := tmp.Dims()
+
+	// Perform burn-in.
+	remaining := burnIn
+	initial := make([]float64, c)
+	copy(initial, m.Initial)
+	for remaining != 0 {
+		newSamp := min(rTmp, remaining)
+		MetropolisHastings(tmp.Slice(0, newSamp, 0, c).(*mat.Dense), initial, m.Target, m.Proposal, m.Src)
+		copy(initial, tmp.RawRowView(newSamp-1))
+		remaining -= newSamp
+	}
+
+	if rate == 1 {
+		MetropolisHastings(batch, initial, m.Target, m.Proposal, m.Src)
+		return
+	}
+
+	if rTmp <= r {
+		tmp = mat.NewDense(rate, c, nil)
+	}
+
+	// Take a single sample from the chain.
+	MetropolisHastings(batch.Slice(0, 1, 0, c).(*mat.Dense), initial, m.Target, m.Proposal, m.Src)
+
+	copy(initial, batch.RawRowView(0))
+	// For all of the other samples, first generate Rate samples and then actually
+	// accept the last one.
+	for i := 1; i < r; i++ {
+		MetropolisHastings(tmp, initial, m.Target, m.Proposal, m.Src)
+		v := tmp.RawRowView(rate - 1)
+		batch.SetRow(i, v)
+		copy(initial, v)
+	}
+}
+
+// MetropolisHastings generates rows(batch) samples using the Metropolis Hastings
+// algorithm (http://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm),
+// with the given target and proposal distributions, starting at the initial location
+// and storing the results in-place into samples. If src != nil, it will be used to generate random
+// numbers, otherwise rand.Float64 will be used.
+//
+// Metropolis-Hastings is a Markov-chain Monte Carlo algorithm that generates
+// samples according to the distribution specified by target by using the Markov
+// chain implicitly defined by the proposal distribution. At each
+// iteration, a proposal point is generated randomly from the current location.
+// This proposal point is accepted with probability
+//  p = min(1, (target(new) * proposal(current|new)) / (target(current) * proposal(new|current)))
+// If the new location is accepted, it is stored into batch and becomes the
+// new current location. If it is rejected, the current location remains and
+// is stored into samples. Thus, a location is stored into batch at every iteration.
+//
+// The samples in Metropolis Hastings are correlated with one another through the
+// Markov chain. As a result, the initial value can have a significant influence
+// on the early samples, and so, typically, the first samples generated by the chain
+// are ignored. This is known as "burn-in", and can be accomplished with slicing.
+// The best choice for burn-in length will depend on the sampling and target
+// distributions.
+//
+// Many choose to have a sampling "rate" where a number of samples
+// are ignored in between each kept sample. This helps decorrelate
+// the samples from one another, but also reduces the number of available samples.
+// A sampling rate can be implemented with successive calls to MetropolisHastings.
+func MetropolisHastings(batch *mat.Dense, initial []float64, target distmv.LogProber, proposal MHProposal, src *rand.Rand) {
+	f64 := rand.Float64
+	if src != nil {
+		f64 = src.Float64
+	}
+	if len(initial) == 0 {
+		panic("metropolishastings: zero length initial")
+	}
+	r, _ := batch.Dims()
+	current := make([]float64, len(initial))
+	copy(current, initial)
+	proposed := make([]float64, len(initial))
+	currentLogProb := target.LogProb(initial)
+	for i := 0; i < r; i++ {
+		proposal.ConditionalRand(proposed, current)
+		proposedLogProb := target.LogProb(proposed)
+		probTo := proposal.ConditionalLogProb(proposed, current)
+		probBack := proposal.ConditionalLogProb(current, proposed)
+
+		accept := math.Exp(proposedLogProb + probBack - probTo - currentLogProb)
+		if accept > f64() {
+			copy(current, proposed)
+			currentLogProb = proposedLogProb
+		}
+		batch.SetRow(i, current)
+	}
+}
+
+// ProposalNormal is a sampling distribution for Metropolis-Hastings. It has a
+// fixed covariance matrix and changes the mean based on the current sampling
+// location.
+type ProposalNormal struct {
+	normal *distmv.Normal
+}
+
+// NewProposalNormal constructs a new ProposalNormal for use as a proposal
+// distribution for Metropolis-Hastings. ProposalNormal is a multivariate normal
+// distribution (implemented by distmv.Normal) where the covariance matrix is fixed
+// and the mean of the distribution changes.
+//
+// NewProposalNormal returns {nil, false} if the covariance matrix is not positive-definite.
+func NewProposalNormal(sigma *mat.SymDense, src *rand.Rand) (*ProposalNormal, bool) {
+	mu := make([]float64, sigma.Symmetric())
+	normal, ok := distmv.NewNormal(mu, sigma, src)
+	if !ok {
+		return nil, false
+	}
+	p := &ProposalNormal{
+		normal: normal,
+	}
+	return p, true
+}
+
+// ConditionalLogProb returns the probability of the first argument conditioned on
+// being at the second argument.
+//  p(x|y)
+// ConditionalLogProb panics if the input slices are not the same length or
+// are not equal to the dimension of the covariance matrix.
+func (p *ProposalNormal) ConditionalLogProb(x, y []float64) (prob float64) {
+	// Either SetMean or LogProb will panic if the slice lengths are innaccurate.
+	p.normal.SetMean(y)
+	return p.normal.LogProb(x)
+}
+
+// ConditionalRand generates a new random location conditioned being at the
+// location y. If the first argument is nil, a new slice is allocated and
+// returned. Otherwise, the random location is stored in-place into the first
+// argument, and ConditionalRand will panic if the input slice lengths differ or
+// if they are not equal to the dimension of the covariance matrix.
+func (p *ProposalNormal) ConditionalRand(x, y []float64) []float64 {
+	if x == nil {
+		x = make([]float64, p.normal.Dim())
+	}
+	if len(x) != len(y) {
+		panic(badLengthMismatch)
+	}
+	p.normal.SetMean(y)
+	p.normal.Rand(x)
+	return x
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/samplemv/sample_test.go b/vendor/gonum.org/v1/gonum/stat/samplemv/sample_test.go
new file mode 100644
index 00000000..9a3764de
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/samplemv/sample_test.go
@@ -0,0 +1,280 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+package samplemv
+
+import (
+	"fmt"
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+	"gonum.org/v1/gonum/stat"
+	"gonum.org/v1/gonum/stat/distmv"
+)
+
+type lhDist interface {
+	Quantile(x, p []float64) []float64
+	CDF(p, x []float64) []float64
+	Dim() int
+}
+
+func TestLatinHypercube(t *testing.T) {
+	for _, nSamples := range []int{1, 2, 5, 10, 20} {
+		for _, dist := range []lhDist{
+			distmv.NewUniform([]distmv.Bound{{0, 3}}, nil),
+			distmv.NewUniform([]distmv.Bound{{0, 3}, {-1, 5}, {-4, -1}}, nil),
+		} {
+			dim := dist.Dim()
+			batch := mat.NewDense(nSamples, dim, nil)
+			LatinHypercube(batch, dist, nil)
+			// Latin hypercube should have one entry per hyperrow.
+			present := make([][]bool, nSamples)
+			for i := range present {
+				present[i] = make([]bool, dim)
+			}
+			cdf := make([]float64, dim)
+			for i := 0; i < nSamples; i++ {
+				dist.CDF(cdf, batch.RawRowView(i))
+				for j := 0; j < dim; j++ {
+					p := cdf[j]
+					quadrant := int(math.Floor(p * float64(nSamples)))
+					present[quadrant][j] = true
+				}
+			}
+			allPresent := true
+			for i := 0; i < nSamples; i++ {
+				for j := 0; j < dim; j++ {
+					if !present[i][j] {
+						allPresent = false
+					}
+				}
+			}
+			if !allPresent {
+				t.Errorf("All quadrants not present")
+			}
+		}
+	}
+}
+
+func TestImportance(t *testing.T) {
+	// Test by finding the expected value of a multi-variate normal.
+	dim := 3
+	target, ok := randomNormal(dim)
+	if !ok {
+		t.Fatal("bad test, sigma not pos def")
+	}
+
+	muImp := make([]float64, dim)
+	sigmaImp := mat.NewSymDense(dim, nil)
+	for i := 0; i < dim; i++ {
+		sigmaImp.SetSym(i, i, 3)
+	}
+	proposal, ok := distmv.NewNormal(muImp, sigmaImp, nil)
+	if !ok {
+		t.Fatal("bad test, sigma not pos def")
+	}
+
+	nSamples := 100000
+	batch := mat.NewDense(nSamples, dim, nil)
+	weights := make([]float64, nSamples)
+	Importance(batch, weights, target, proposal)
+
+	compareNormal(t, target, batch, weights, 5e-2, 5e-2)
+}
+
+func TestRejection(t *testing.T) {
+	// Test by finding the expected value of a uniform.
+	dim := 3
+	bounds := make([]distmv.Bound, dim)
+	for i := 0; i < dim; i++ {
+		min := rand.NormFloat64()
+		max := rand.NormFloat64()
+		if min > max {
+			min, max = max, min
+		}
+		bounds[i].Min = min
+		bounds[i].Max = max
+	}
+	target := distmv.NewUniform(bounds, nil)
+	mu := target.Mean(nil)
+
+	muImp := make([]float64, dim)
+	sigmaImp := mat.NewSymDense(dim, nil)
+	for i := 0; i < dim; i++ {
+		sigmaImp.SetSym(i, i, 6)
+	}
+	proposal, ok := distmv.NewNormal(muImp, sigmaImp, nil)
+	if !ok {
+		t.Fatal("bad test, sigma not pos def")
+	}
+
+	nSamples := 1000
+	batch := mat.NewDense(nSamples, dim, nil)
+	weights := make([]float64, nSamples)
+	_, ok = Rejection(batch, target, proposal, 1000, nil)
+	if !ok {
+		t.Error("Bad test, nan samples")
+	}
+
+	for i := 0; i < dim; i++ {
+		col := mat.Col(nil, i, batch)
+		ev := stat.Mean(col, weights)
+		if math.Abs(ev-mu[i]) > 1e-2 {
+			t.Errorf("Mean mismatch: Want %v, got %v", mu[i], ev)
+		}
+	}
+}
+
+func TestMetropolisHastings(t *testing.T) {
+	// Test by finding the expected value of a normal distribution.
+	dim := 3
+	target, ok := randomNormal(dim)
+	if !ok {
+		t.Fatal("bad test, sigma not pos def")
+	}
+
+	sigmaImp := mat.NewSymDense(dim, nil)
+	for i := 0; i < dim; i++ {
+		sigmaImp.SetSym(i, i, 0.25)
+	}
+	proposal, ok := NewProposalNormal(sigmaImp, nil)
+	if !ok {
+		t.Fatal("bad test, sigma not pos def")
+	}
+
+	nSamples := 100000
+	burnin := 5000
+	batch := mat.NewDense(nSamples, dim, nil)
+	initial := make([]float64, dim)
+	MetropolisHastings(batch, initial, target, proposal, nil)
+	batch = batch.Slice(burnin, nSamples, 0, dim).(*mat.Dense)
+
+	compareNormal(t, target, batch, nil, 5e-1, 5e-1)
+}
+
+// randomNormal constructs a random Normal distribution.
+func randomNormal(dim int) (*distmv.Normal, bool) {
+	data := make([]float64, dim*dim)
+	for i := range data {
+		data[i] = rand.Float64()
+	}
+	a := mat.NewDense(dim, dim, data)
+	var sigma mat.SymDense
+	sigma.SymOuterK(1, a)
+	mu := make([]float64, dim)
+	for i := range mu {
+		mu[i] = rand.NormFloat64()
+	}
+	return distmv.NewNormal(mu, &sigma, nil)
+}
+
+func compareNormal(t *testing.T, want *distmv.Normal, batch *mat.Dense, weights []float64, meanTol, covTol float64) {
+	dim := want.Dim()
+	mu := want.Mean(nil)
+	sigma := want.CovarianceMatrix(nil)
+	n, _ := batch.Dims()
+	if weights == nil {
+		weights = make([]float64, n)
+		for i := range weights {
+			weights[i] = 1
+		}
+	}
+	for i := 0; i < dim; i++ {
+		col := mat.Col(nil, i, batch)
+		ev := stat.Mean(col, weights)
+		if math.Abs(ev-mu[i]) > meanTol {
+			t.Errorf("Mean mismatch: Want %v, got %v", mu[i], ev)
+		}
+	}
+
+	cov := stat.CovarianceMatrix(nil, batch, weights)
+	if !mat.EqualApprox(cov, sigma, covTol) {
+		t.Errorf("Covariance matrix mismatch")
+	}
+}
+
+func TestMetropolisHastingser(t *testing.T) {
+	for seed, test := range []struct {
+		dim, burnin, rate, samples int
+	}{
+		{3, 10, 1, 1},
+		{3, 10, 2, 1},
+		{3, 10, 1, 2},
+		{3, 10, 3, 2},
+		{3, 10, 7, 4},
+		{3, 10, 7, 4},
+
+		{3, 11, 51, 103},
+		{3, 11, 103, 51},
+		{3, 51, 11, 103},
+		{3, 51, 103, 11},
+		{3, 103, 11, 51},
+		{3, 103, 51, 11},
+	} {
+		dim := test.dim
+
+		initial := make([]float64, dim)
+		target, ok := randomNormal(dim)
+		if !ok {
+			t.Fatal("bad test, sigma not pos def")
+		}
+
+		sigmaImp := mat.NewSymDense(dim, nil)
+		for i := 0; i < dim; i++ {
+			sigmaImp.SetSym(i, i, 0.25)
+		}
+		proposal, ok := NewProposalNormal(sigmaImp, nil)
+		if !ok {
+			t.Fatal("bad test, sigma not pos def")
+		}
+
+		// Test the Metropolis Hastingser by generating all the samples, then generating
+		// the same samples with a burnin and rate.
+		rand.Seed(int64(seed))
+		mh := MetropolisHastingser{
+			Initial:  initial,
+			Target:   target,
+			Proposal: proposal,
+			Src:      nil,
+			BurnIn:   0,
+			Rate:     0,
+		}
+		samples := test.samples
+		burnin := test.burnin
+		rate := test.rate
+		fullBatch := mat.NewDense(1+burnin+rate*(samples-1), dim, nil)
+		mh.Sample(fullBatch)
+		mh = MetropolisHastingser{
+			Initial:  initial,
+			Target:   target,
+			Proposal: proposal,
+			Src:      nil,
+			BurnIn:   burnin,
+			Rate:     rate,
+		}
+		rand.Seed(int64(seed))
+		batch := mat.NewDense(samples, dim, nil)
+		mh.Sample(batch)
+
+		same := true
+		count := burnin
+		for i := 0; i < samples; i++ {
+			if !floats.Equal(batch.RawRowView(i), fullBatch.RawRowView(count)) {
+				fmt.Println("sample ", i, "is different")
+				same = false
+				break
+			}
+			count += rate
+		}
+
+		if !same {
+			fmt.Printf("%v\n", mat.Formatted(batch))
+			fmt.Printf("%v\n", mat.Formatted(fullBatch))
+
+			t.Errorf("sampling mismatch: dim = %v, burnin = %v, rate = %v, samples = %v", dim, burnin, rate, samples)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/samplemv/samplemv.go b/vendor/gonum.org/v1/gonum/stat/samplemv/samplemv.go
new file mode 100644
index 00000000..5b72ca3c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/samplemv/samplemv.go
@@ -0,0 +1,274 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package samplemv
+
+import (
+	"errors"
+	"math"
+	"math/rand"
+
+	"gonum.org/v1/gonum/mat"
+	"gonum.org/v1/gonum/stat/distmv"
+)
+
+var (
+	badLengthMismatch = "samplemv: slice length mismatch"
+)
+
+var (
+	_ Sampler = LatinHypercuber{}
+	_ Sampler = (*Rejectioner)(nil)
+	_ Sampler = IIDer{}
+
+	_ WeightedSampler = SampleUniformWeighted{}
+	_ WeightedSampler = Importancer{}
+)
+
+func min(a, b int) int {
+	if a < b {
+		return a
+	}
+	return b
+}
+
+// Sampler generates a batch of samples according to the rule specified by the
+// implementing type. The number of samples generated is equal to rows(batch),
+// and the samples are stored in-place into the input.
+type Sampler interface {
+	Sample(batch *mat.Dense)
+}
+
+// WeightedSampler generates a batch of samples and their relative weights
+// according to the rule specified by the implementing type. The number of samples
+// generated is equal to rows(batch), and the samples and weights
+// are stored in-place into the inputs. The length of weights must equal
+// rows(batch), otherwise SampleWeighted will panic.
+type WeightedSampler interface {
+	SampleWeighted(batch *mat.Dense, weights []float64)
+}
+
+// SampleUniformWeighted wraps a Sampler type to create a WeightedSampler where all
+// weights are equal.
+type SampleUniformWeighted struct {
+	Sampler
+}
+
+// SampleWeighted generates rows(batch) samples from the embedded Sampler type
+// and sets all of the weights equal to 1. If rows(batch) and len(weights)
+// of weights are not equal, SampleWeighted will panic.
+func (w SampleUniformWeighted) SampleWeighted(batch *mat.Dense, weights []float64) {
+	r, _ := batch.Dims()
+	if r != len(weights) {
+		panic(badLengthMismatch)
+	}
+	w.Sample(batch)
+	for i := range weights {
+		weights[i] = 1
+	}
+}
+
+// LatinHypercuber is a wrapper around the LatinHypercube sampling generation
+// method.
+type LatinHypercuber struct {
+	Q   distmv.Quantiler
+	Src *rand.Rand
+}
+
+// Sample generates rows(batch) samples using the LatinHypercube generation
+// procedure.
+func (l LatinHypercuber) Sample(batch *mat.Dense) {
+	LatinHypercube(batch, l.Q, l.Src)
+}
+
+// LatinHypercube generates rows(batch) samples using Latin hypercube sampling
+// from the given distribution. If src is not nil, it will be used to generate
+// random numbers, otherwise rand.Float64 will be used.
+//
+// Latin hypercube sampling divides the cumulative distribution function into equally
+// spaced bins and guarantees that one sample is generated per bin. Within each bin,
+// the location is randomly sampled. The distmv.NewUnitUniform function can be used
+// for easy sampling from the unit hypercube.
+func LatinHypercube(batch *mat.Dense, q distmv.Quantiler, src *rand.Rand) {
+	r, c := batch.Dims()
+	var f64 func() float64
+	var perm func(int) []int
+	if src != nil {
+		f64 = src.Float64
+		perm = src.Perm
+	} else {
+		f64 = rand.Float64
+		perm = rand.Perm
+	}
+	r64 := float64(r)
+	for i := 0; i < c; i++ {
+		p := perm(r)
+		for j := 0; j < r; j++ {
+			v := f64()/r64 + float64(j)/r64
+			batch.Set(p[j], i, v)
+		}
+	}
+	p := make([]float64, c)
+	for i := 0; i < r; i++ {
+		copy(p, batch.RawRowView(i))
+		q.Quantile(batch.RawRowView(i), p)
+	}
+}
+
+// Importancer is a wrapper around the Importance sampling generation method.
+type Importancer struct {
+	Target   distmv.LogProber
+	Proposal distmv.RandLogProber
+}
+
+// SampleWeighted generates rows(batch) samples using the Importance sampling
+// generation procedure.
+func (l Importancer) SampleWeighted(batch *mat.Dense, weights []float64) {
+	Importance(batch, weights, l.Target, l.Proposal)
+}
+
+// Importance sampling generates rows(batch) samples from the proposal distribution,
+// and stores the locations and importance sampling weights in place.
+//
+// Importance sampling is a variance reduction technique where samples are
+// generated from a proposal distribution, q(x), instead of the target distribution
+// p(x). This allows relatively unlikely samples in p(x) to be generated more frequently.
+//
+// The importance sampling weight at x is given by p(x)/q(x). To reduce variance,
+// a good proposal distribution will bound this sampling weight. This implies the
+// support of q(x) should be at least as broad as p(x), and q(x) should be "fatter tailed"
+// than p(x).
+//
+// If weights is nil, the weights are not stored. The length of weights must equal
+// the length of batch, otherwise Importance will panic.
+func Importance(batch *mat.Dense, weights []float64, target distmv.LogProber, proposal distmv.RandLogProber) {
+	r, _ := batch.Dims()
+	if r != len(weights) {
+		panic(badLengthMismatch)
+	}
+	for i := 0; i < r; i++ {
+		v := batch.RawRowView(i)
+		proposal.Rand(v)
+		weights[i] = math.Exp(target.LogProb(v) - proposal.LogProb(v))
+	}
+}
+
+// ErrRejection is returned when the constant in Rejection is not sufficiently high.
+var ErrRejection = errors.New("rejection: acceptance ratio above 1")
+
+// Rejectioner is a wrapper around the Rejection sampling generation procedure.
+// If the rejection sampling fails during the call to Sample, all samples will
+// be set to math.NaN() and a call to Err will return a non-nil value.
+type Rejectioner struct {
+	C        float64
+	Target   distmv.LogProber
+	Proposal distmv.RandLogProber
+	Src      *rand.Rand
+
+	err      error
+	proposed int
+}
+
+// Err returns nil if the most recent call to sample was successful, and returns
+// ErrRejection if it was not.
+func (r *Rejectioner) Err() error {
+	return r.err
+}
+
+// Proposed returns the number of samples proposed during the most recent call to
+// Sample.
+func (r *Rejectioner) Proposed() int {
+	return r.proposed
+}
+
+// Sample generates rows(batch) using the Rejection sampling generation procedure.
+// Rejection sampling may fail if the constant is insufficiently high, as described
+// in the function comment for Rejection. If the generation fails, the samples
+// are set to math.NaN(), and a call to Err will return a non-nil value.
+func (r *Rejectioner) Sample(batch *mat.Dense) {
+	r.err = nil
+	r.proposed = 0
+	proposed, ok := Rejection(batch, r.Target, r.Proposal, r.C, r.Src)
+	if !ok {
+		r.err = ErrRejection
+	}
+	r.proposed = proposed
+}
+
+// Rejection generates rows(batch) samples using the rejection sampling algorithm and
+// stores them in place into samples.
+// Sampling continues until batch is filled. Rejection returns the total number of proposed
+// locations and a boolean indicating if the rejection sampling assumption is
+// violated (see details below). If the returned boolean is false, all elements
+// of samples are set to NaN. If src != nil, it will be used to generate random
+// numbers, otherwise rand.Float64 will be used.
+//
+// Rejection sampling generates points from the target distribution by using
+// the proposal distribution. At each step of the algorithm, the proposaed point
+// is accepted with probability
+//  p = target(x) / (proposal(x) * c)
+// where target(x) is the probability of the point according to the target distribution
+// and proposal(x) is the probability according to the proposal distribution.
+// The constant c must be chosen such that target(x) < proposal(x) * c for all x.
+// The expected number of proposed samples is len(samples) * c.
+//
+// Target may return the true (log of) the probablity of the location, or it may return
+// a value that is proportional to the probability (logprob + constant). This is
+// useful for cases where the probability distribution is only known up to a normalization
+// constant.
+func Rejection(batch *mat.Dense, target distmv.LogProber, proposal distmv.RandLogProber, c float64, src *rand.Rand) (nProposed int, ok bool) {
+	if c < 1 {
+		panic("rejection: acceptance constant must be greater than 1")
+	}
+	f64 := rand.Float64
+	if src != nil {
+		f64 = src.Float64
+	}
+	r, dim := batch.Dims()
+	v := make([]float64, dim)
+	var idx int
+	for {
+		nProposed++
+		proposal.Rand(v)
+		qx := proposal.LogProb(v)
+		px := target.LogProb(v)
+		accept := math.Exp(px-qx) / c
+		if accept > 1 {
+			// Invalidate the whole result and return a failure.
+			for i := 0; i < r; i++ {
+				for j := 0; j < dim; j++ {
+					batch.Set(i, j, math.NaN())
+				}
+			}
+			return nProposed, false
+		}
+		if accept > f64() {
+			batch.SetRow(idx, v)
+			idx++
+			if idx == r {
+				break
+			}
+		}
+	}
+	return nProposed, true
+}
+
+// IIDer is a wrapper around the IID sample generation method.
+type IIDer struct {
+	Dist distmv.Rander
+}
+
+// Sample generates a set of identically and independently distributed samples.
+func (iid IIDer) Sample(batch *mat.Dense) {
+	IID(batch, iid.Dist)
+}
+
+// IID generates a set of independently and identically distributed samples from
+// the input distribution.
+func IID(batch *mat.Dense, d distmv.Rander) {
+	r, _ := batch.Dims()
+	for i := 0; i < r; i++ {
+		d.Rand(batch.RawRowView(i))
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/sampleuv/doc.go b/vendor/gonum.org/v1/gonum/stat/sampleuv/doc.go
new file mode 100644
index 00000000..9beb4ddc
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/sampleuv/doc.go
@@ -0,0 +1,11 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package sampleuv implements advanced sampling routines from explicit and implicit
+// probability distributions.
+//
+// Each sampling routine is implemented as a stateless function with a
+// complementary wrapper type. The wrapper types allow the sampling routines
+// to implement interfaces.
+package sampleuv // import "gonum.org/v1/gonum/stat/sampleuv"
diff --git a/vendor/gonum.org/v1/gonum/stat/sampleuv/example_burnin_test.go b/vendor/gonum.org/v1/gonum/stat/sampleuv/example_burnin_test.go
new file mode 100644
index 00000000..db1d1c31
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/sampleuv/example_burnin_test.go
@@ -0,0 +1,39 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package sampleuv
+
+import "gonum.org/v1/gonum/stat/distuv"
+
+type ProposalDist struct {
+	Sigma float64
+}
+
+func (p ProposalDist) ConditionalRand(y float64) float64 {
+	return distuv.Normal{Mu: y, Sigma: p.Sigma}.Rand()
+}
+
+func (p ProposalDist) ConditionalLogProb(x, y float64) float64 {
+	return distuv.Normal{Mu: y, Sigma: p.Sigma}.LogProb(x)
+}
+
+func ExampleMetropolisHastings_burnin() {
+	n := 1000    // The number of samples to generate.
+	burnin := 50 // Number of samples to ignore at the start.
+	var initial float64
+	// target is the distribution from which we would like to sample.
+	target := distuv.Weibull{K: 5, Lambda: 0.5}
+	// proposal is the proposal distribution. Here, we are choosing
+	// a tight Gaussian distribution around the current location. In
+	// typical problems, if Sigma is too small, it takes a lot of samples
+	// to move around the distribution. If Sigma is too large, it can be hard
+	// to find acceptable samples.
+	proposal := ProposalDist{Sigma: 0.2}
+
+	samples := make([]float64, n+burnin)
+	MetropolisHastings(samples, initial, target, proposal, nil)
+
+	// Remove the initial samples through slicing.
+	samples = samples[burnin:]
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/sampleuv/example_rate_test.go b/vendor/gonum.org/v1/gonum/stat/sampleuv/example_rate_test.go
new file mode 100644
index 00000000..86917998
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/sampleuv/example_rate_test.go
@@ -0,0 +1,49 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package sampleuv
+
+import "gonum.org/v1/gonum/stat/distuv"
+
+func max(a, b int) int {
+	if a < b {
+		return b
+	}
+	return a
+}
+
+func ExampleMetropolisHastings_samplingRate() {
+	// See Burnin example for a description of these quantities.
+	n := 1000
+	burnin := 300
+	var initial float64
+	target := distuv.Weibull{K: 5, Lambda: 0.5}
+	proposal := ProposalDist{Sigma: 0.2}
+
+	// Successive samples are correlated with one another through the
+	// Markov Chain defined by the proposal distribution. To get less
+	// correlated samples, one may use a sampling rate, in which only
+	// one sample from every few is accepted from the chain. This can
+	// be accomplished through a for loop.
+	rate := 50
+
+	tmp := make([]float64, max(rate, burnin))
+
+	// First deal with burnin.
+	tmp = tmp[:burnin]
+	MetropolisHastings(tmp, initial, target, proposal, nil)
+	// The final sample in tmp in the final point in the chain.
+	// Use it as the new initial location.
+	initial = tmp[len(tmp)-1]
+
+	// Now, generate samples by using one every rate samples.
+	tmp = tmp[:rate]
+	samples := make([]float64, n)
+	samples[0] = initial
+	for i := 1; i < len(samples); i++ {
+		MetropolisHastings(tmp, initial, target, proposal, nil)
+		initial = tmp[len(tmp)-1]
+		samples[i] = initial
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/sampleuv/sample.go b/vendor/gonum.org/v1/gonum/stat/sampleuv/sample.go
new file mode 100644
index 00000000..1d836390
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/sampleuv/sample.go
@@ -0,0 +1,393 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package sampleuv
+
+import (
+	"errors"
+	"math"
+	"math/rand"
+
+	"gonum.org/v1/gonum/stat/distuv"
+)
+
+var (
+	badLengthMismatch = "sample: slice length mismatch"
+)
+
+var (
+	_ Sampler = LatinHypercuber{}
+	_ Sampler = MetropolisHastingser{}
+	_ Sampler = (*Rejectioner)(nil)
+	_ Sampler = IIDer{}
+
+	_ WeightedSampler = SampleUniformWeighted{}
+	_ WeightedSampler = Importancer{}
+)
+
+func min(a, b int) int {
+	if a < b {
+		return a
+	}
+	return b
+}
+
+// Sampler generates a batch of samples according to the rule specified by the
+// implementing type. The number of samples generated is equal to len(batch),
+// and the samples are stored in-place into the input.
+type Sampler interface {
+	Sample(batch []float64)
+}
+
+// WeightedSampler generates a batch of samples and their relative weights
+// according to the rule specified by the implementing type. The number of samples
+// generated is equal to len(batch), and the samples and weights
+// are stored in-place into the inputs. The length of weights must equal
+// len(batch), otherwise SampleWeighted will panic.
+type WeightedSampler interface {
+	SampleWeighted(batch, weights []float64)
+}
+
+// SampleUniformWeighted wraps a Sampler type to create a WeightedSampler where all
+// weights are equal.
+type SampleUniformWeighted struct {
+	Sampler
+}
+
+// SampleWeighted generates len(batch) samples from the embedded Sampler type
+// and sets all of the weights equal to 1. If len(batch) and len(weights)
+// are not equal, SampleWeighted will panic.
+func (w SampleUniformWeighted) SampleWeighted(batch, weights []float64) {
+	if len(batch) != len(weights) {
+		panic(badLengthMismatch)
+	}
+	w.Sample(batch)
+	for i := range weights {
+		weights[i] = 1
+	}
+}
+
+// LatinHypercuber is a wrapper around the LatinHypercube sampling generation
+// method.
+type LatinHypercuber struct {
+	Q   distuv.Quantiler
+	Src *rand.Rand
+}
+
+// Sample generates len(batch) samples using the LatinHypercube generation
+// procedure.
+func (l LatinHypercuber) Sample(batch []float64) {
+	LatinHypercube(batch, l.Q, l.Src)
+}
+
+// LatinHypercube generates len(batch) samples using Latin hypercube sampling
+// from the given distribution. If src != nil, it will be used to generate
+// random numbers, otherwise rand.Float64 will be used.
+//
+// Latin hypercube sampling divides the cumulative distribution function into equally
+// spaced bins and guarantees that one sample is generated per bin. Within each bin,
+// the location is randomly sampled. The distuv.UnitUniform variable can be used
+// for easy generation from the unit interval.
+func LatinHypercube(batch []float64, q distuv.Quantiler, src *rand.Rand) {
+	n := len(batch)
+	var perm []int
+	var f64 func() float64
+	if src != nil {
+		f64 = src.Float64
+		perm = src.Perm(n)
+	} else {
+		f64 = rand.Float64
+		perm = rand.Perm(n)
+	}
+	for i := range batch {
+		v := f64()/float64(n) + float64(i)/float64(n)
+		batch[perm[i]] = q.Quantile(v)
+	}
+}
+
+// Importancer is a wrapper around the Importance sampling generation method.
+type Importancer struct {
+	Target   distuv.LogProber
+	Proposal distuv.RandLogProber
+}
+
+// Sample generates len(batch) samples using the Importance sampling generation
+// procedure.
+func (l Importancer) SampleWeighted(batch, weights []float64) {
+	Importance(batch, weights, l.Target, l.Proposal)
+}
+
+// Importance sampling generates len(batch) samples from the proposal distribution,
+// and stores the locations and importance sampling weights in place.
+//
+// Importance sampling is a variance reduction technique where samples are
+// generated from a proposal distribution, q(x), instead of the target distribution
+// p(x). This allows relatively unlikely samples in p(x) to be generated more frequently.
+//
+// The importance sampling weight at x is given by p(x)/q(x). To reduce variance,
+// a good proposal distribution will bound this sampling weight. This implies the
+// support of q(x) should be at least as broad as p(x), and q(x) should be "fatter tailed"
+// than p(x).
+//
+// If weights is nil, the weights are not stored. The length of weights must equal
+// the length of batch, otherwise Importance will panic.
+func Importance(batch, weights []float64, target distuv.LogProber, proposal distuv.RandLogProber) {
+	if len(batch) != len(weights) {
+		panic(badLengthMismatch)
+	}
+	for i := range batch {
+		v := proposal.Rand()
+		batch[i] = v
+		weights[i] = math.Exp(target.LogProb(v) - proposal.LogProb(v))
+	}
+}
+
+// ErrRejection is returned when the constant in Rejection is not sufficiently high.
+var ErrRejection = errors.New("rejection: acceptance ratio above 1")
+
+// Rejectioner is a wrapper around the Rejection sampling generation procedure.
+// If the rejection sampling fails during the call to Sample, all samples will
+// be set to math.NaN() and a call to Err will return a non-nil value.
+type Rejectioner struct {
+	C        float64
+	Target   distuv.LogProber
+	Proposal distuv.RandLogProber
+	Src      *rand.Rand
+
+	err      error
+	proposed int
+}
+
+// Err returns nil if the most recent call to sample was successful, and returns
+// ErrRejection if it was not.
+func (r *Rejectioner) Err() error {
+	return r.err
+}
+
+// Proposed returns the number of samples proposed during the most recent call to
+// Sample.
+func (r *Rejectioner) Proposed() int {
+	return r.proposed
+}
+
+// Sample generates len(batch) using the Rejection sampling generation procedure.
+// Rejection sampling may fail if the constant is insufficiently high, as described
+// in the function comment for Rejection. If the generation fails, the samples
+// are set to math.NaN(), and a call to Err will return a non-nil value.
+func (r *Rejectioner) Sample(batch []float64) {
+	r.err = nil
+	r.proposed = 0
+	proposed, ok := Rejection(batch, r.Target, r.Proposal, r.C, r.Src)
+	if !ok {
+		r.err = ErrRejection
+	}
+	r.proposed = proposed
+}
+
+// Rejection generates len(batch) samples using the rejection sampling algorithm
+// and stores them in place into samples. Sampling continues until batch is
+// filled. Rejection returns the total number of proposed locations and a boolean
+// indicating if the rejection sampling assumption is violated (see details
+// below). If the returned boolean is false, all elements of samples are set to
+// NaN. If src is not nil, it will be used to generate random numbers, otherwise
+// rand.Float64 will be used.
+//
+// Rejection sampling generates points from the target distribution by using
+// the proposal distribution. At each step of the algorithm, the proposed point
+// is accepted with probability
+//  p = target(x) / (proposal(x) * c)
+// where target(x) is the probability of the point according to the target distribution
+// and proposal(x) is the probability according to the proposal distribution.
+// The constant c must be chosen such that target(x) < proposal(x) * c for all x.
+// The expected number of proposed samples is len(samples) * c.
+//
+// Target may return the true (log of) the probablity of the location, or it may return
+// a value that is proportional to the probability (logprob + constant). This is
+// useful for cases where the probability distribution is only known up to a normalization
+// constant.
+func Rejection(batch []float64, target distuv.LogProber, proposal distuv.RandLogProber, c float64, src *rand.Rand) (nProposed int, ok bool) {
+	if c < 1 {
+		panic("rejection: acceptance constant must be greater than 1")
+	}
+	f64 := rand.Float64
+	if src != nil {
+		f64 = src.Float64
+	}
+	var idx int
+	for {
+		nProposed++
+		v := proposal.Rand()
+		qx := proposal.LogProb(v)
+		px := target.LogProb(v)
+		accept := math.Exp(px-qx) / c
+		if accept > 1 {
+			// Invalidate the whole result and return a failure.
+			for i := range batch {
+				batch[i] = math.NaN()
+			}
+			return nProposed, false
+		}
+		if accept > f64() {
+			batch[idx] = v
+			idx++
+			if idx == len(batch) {
+				break
+			}
+		}
+	}
+	return nProposed, true
+}
+
+// MHProposal defines a proposal distribution for Metropolis Hastings.
+type MHProposal interface {
+	// ConditionalDist returns the probability of the first argument conditioned on
+	// being at the second argument
+	//  p(x|y)
+	ConditionalLogProb(x, y float64) (prob float64)
+
+	// ConditionalRand generates a new random location conditioned being at the
+	// location y.
+	ConditionalRand(y float64) (x float64)
+}
+
+// MetropolisHastingser is a wrapper around the MetropolisHastings sampling type.
+//
+// BurnIn sets the number of samples to discard before keeping the first sample.
+// A properly set BurnIn rate will decorrelate the sampling chain from the initial
+// location. The proper BurnIn value will depend on the mixing time of the
+// Markov chain defined by the target and proposal distributions.
+//
+// Rate sets the number of samples to discard in between each kept sample. A
+// higher rate will better approximate independently and identically distributed
+// samples, while a lower rate will keep more information (at the cost of
+// higher correlation between samples). If Rate is 0 it is defaulted to 1.
+//
+// The initial value is NOT changed during calls to Sample.
+type MetropolisHastingser struct {
+	Initial  float64
+	Target   distuv.LogProber
+	Proposal MHProposal
+	Src      *rand.Rand
+
+	BurnIn int
+	Rate   int
+}
+
+// Sample generates len(batch) samples using the Metropolis Hastings sample
+// generation method. The initial location is NOT updated during the call to Sample.
+func (m MetropolisHastingser) Sample(batch []float64) {
+	burnIn := m.BurnIn
+	rate := m.Rate
+	if rate == 0 {
+		rate = 1
+	}
+
+	// Use the optimal size for the temporary memory to allow the fewest calls
+	// to MetropolisHastings. The case where tmp shadows samples must be
+	// aligned with the logic after burn-in so that tmp does not shadow samples
+	// during the rate portion.
+	tmp := batch
+	if rate > len(batch) {
+		tmp = make([]float64, rate)
+	}
+
+	// Perform burn-in.
+	remaining := burnIn
+	initial := m.Initial
+	for remaining != 0 {
+		newSamp := min(len(tmp), remaining)
+		MetropolisHastings(tmp[newSamp:], initial, m.Target, m.Proposal, m.Src)
+		initial = tmp[newSamp-1]
+		remaining -= newSamp
+	}
+
+	if rate == 1 {
+		MetropolisHastings(batch, initial, m.Target, m.Proposal, m.Src)
+		return
+	}
+
+	if len(tmp) <= len(batch) {
+		tmp = make([]float64, rate)
+	}
+
+	// Take a single sample from the chain
+	MetropolisHastings(batch[0:1], initial, m.Target, m.Proposal, m.Src)
+	initial = batch[0]
+
+	// For all of the other samples, first generate Rate samples and then actually
+	// accept the last one.
+	for i := 1; i < len(batch); i++ {
+		MetropolisHastings(tmp, initial, m.Target, m.Proposal, m.Src)
+		v := tmp[rate-1]
+		batch[i] = v
+		initial = v
+	}
+}
+
+// MetropolisHastings generates len(batch) samples using the Metropolis Hastings
+// algorithm (http://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm),
+// with the given target and proposal distributions, starting at the initial location
+// and storing the results in-place into samples. If src != nil, it will be used to generate random
+// numbers, otherwise rand.Float64 will be used.
+//
+// Metropolis-Hastings is a Markov-chain Monte Carlo algorithm that generates
+// samples according to the distribution specified by target by using the Markov
+// chain implicitly defined by the proposal distribution. At each
+// iteration, a proposal point is generated randomly from the current location.
+// This proposal point is accepted with probability
+//  p = min(1, (target(new) * proposal(current|new)) / (target(current) * proposal(new|current)))
+// If the new location is accepted, it is stored into batch and becomes the
+// new current location. If it is rejected, the current location remains and
+// is stored into samples. Thus, a location is stored into batch at every iteration.
+//
+// The samples in Metropolis Hastings are correlated with one another through the
+// Markov chain. As a result, the initial value can have a significant influence
+// on the early samples, and so, typically, the first samples generated by the chain
+// are ignored. This is known as "burn-in", and can be accomplished with slicing.
+// The best choice for burn-in length will depend on the sampling and target
+// distributions.
+//
+// Many choose to have a sampling "rate" where a number of samples
+// are ignored in between each kept sample. This helps decorrelate
+// the samples from one another, but also reduces the number of available samples.
+// A sampling rate can be implemented with successive calls to MetropolisHastings.
+func MetropolisHastings(batch []float64, initial float64, target distuv.LogProber, proposal MHProposal, src *rand.Rand) {
+	f64 := rand.Float64
+	if src != nil {
+		f64 = src.Float64
+	}
+	current := initial
+	currentLogProb := target.LogProb(initial)
+	for i := range batch {
+		proposed := proposal.ConditionalRand(current)
+		proposedLogProb := target.LogProb(proposed)
+		probTo := proposal.ConditionalLogProb(proposed, current)
+		probBack := proposal.ConditionalLogProb(current, proposed)
+
+		accept := math.Exp(proposedLogProb + probBack - probTo - currentLogProb)
+		if accept > f64() {
+			current = proposed
+			currentLogProb = proposedLogProb
+		}
+		batch[i] = current
+	}
+}
+
+// IIDer is a wrapper around the IID sample generation method.
+type IIDer struct {
+	Dist distuv.Rander
+}
+
+// Sample generates a set of identically and independently distributed samples.
+func (iid IIDer) Sample(batch []float64) {
+	IID(batch, iid.Dist)
+}
+
+// IID generates a set of independently and identically distributed samples from
+// the input distribution.
+func IID(batch []float64, d distuv.Rander) {
+	for i := range batch {
+		batch[i] = d.Rand()
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/sampleuv/sample_test.go b/vendor/gonum.org/v1/gonum/stat/sampleuv/sample_test.go
new file mode 100644
index 00000000..49965ec0
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/sampleuv/sample_test.go
@@ -0,0 +1,99 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package sampleuv
+
+import (
+	"math"
+	"sort"
+	"testing"
+
+	"gonum.org/v1/gonum/stat"
+	"gonum.org/v1/gonum/stat/distuv"
+)
+
+type lhDist interface {
+	Quantile(float64) float64
+	CDF(float64) float64
+}
+
+func TestLatinHypercube(t *testing.T) {
+	for _, nSamples := range []int{1, 2, 5, 10, 20} {
+		samples := make([]float64, nSamples)
+		for _, dist := range []lhDist{
+			distuv.Uniform{Min: 0, Max: 1},
+			distuv.Uniform{Min: 0, Max: 10},
+			distuv.Normal{Mu: 5, Sigma: 3},
+		} {
+			LatinHypercube(samples, dist, nil)
+			sort.Float64s(samples)
+			for i, v := range samples {
+				p := dist.CDF(v)
+				if p < float64(i)/float64(nSamples) || p > float64(i+1)/float64(nSamples) {
+					t.Errorf("probability out of bounds")
+				}
+			}
+		}
+	}
+}
+
+func TestImportance(t *testing.T) {
+	// Test by finding the expected value of a Normal.
+	trueMean := 3.0
+	target := distuv.Normal{Mu: trueMean, Sigma: 2}
+	proposal := distuv.Normal{Mu: 0, Sigma: 5}
+	nSamples := 100000
+	x := make([]float64, nSamples)
+	weights := make([]float64, nSamples)
+	Importance(x, weights, target, proposal)
+	ev := stat.Mean(x, weights)
+	if math.Abs(ev-trueMean) > 1e-2 {
+		t.Errorf("Mean mismatch: Want %v, got %v", trueMean, ev)
+	}
+}
+
+func TestRejection(t *testing.T) {
+	// Test by finding the expected value of a Normal.
+	trueMean := 3.0
+	target := distuv.Normal{Mu: trueMean, Sigma: 2}
+	proposal := distuv.Normal{Mu: 0, Sigma: 5}
+
+	nSamples := 20000
+	x := make([]float64, nSamples)
+	Rejection(x, target, proposal, 100, nil)
+	ev := stat.Mean(x, nil)
+	if math.Abs(ev-trueMean) > 2e-2 {
+		t.Errorf("Mean mismatch: Want %v, got %v", trueMean, ev)
+	}
+}
+
+type condNorm struct {
+	Sigma float64
+}
+
+func (c condNorm) ConditionalRand(y float64) float64 {
+	return distuv.Normal{Mu: y, Sigma: c.Sigma}.Rand()
+}
+
+func (c condNorm) ConditionalLogProb(x, y float64) float64 {
+	return distuv.Normal{Mu: y, Sigma: c.Sigma}.LogProb(x)
+}
+
+func TestMetropolisHastings(t *testing.T) {
+	// Test by finding the expected value of a Normal.
+	trueMean := 3.0
+	target := distuv.Normal{Mu: trueMean, Sigma: 2}
+	proposal := condNorm{Sigma: 5}
+
+	burnin := 500
+	nSamples := 100000 + burnin
+	x := make([]float64, nSamples)
+	MetropolisHastings(x, 100, target, proposal, nil)
+	// Remove burnin
+	x = x[burnin:]
+	ev := stat.Mean(x, nil)
+	if math.Abs(ev-trueMean) > 1e-2 {
+		t.Errorf("Mean mismatch: Want %v, got %v", trueMean, ev)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/sampleuv/weighted.go b/vendor/gonum.org/v1/gonum/stat/sampleuv/weighted.go
new file mode 100644
index 00000000..006cafdd
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/sampleuv/weighted.go
@@ -0,0 +1,138 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this code is governed by a BSD-style
+// license that can be found in the LICENSE file
+
+package sampleuv
+
+import (
+	"math/rand"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+// Weighted provides sampling without replacement from a collection of items with
+// non-uniform probability.
+type Weighted struct {
+	weights []float64
+	// heap is a weight heap.
+	//
+	// It keeps a heap-organised sum of remaining
+	// index weights that are available to be taken
+	// from.
+	//
+	// Each element holds the sum of weights for
+	// the corresponding index, plus the sum of
+	// of its children's weights; the children
+	// of an element i can be found at positions
+	// 2*(i+1)-1 and 2*(i+1). The root of the
+	// weight heap is at element 0.
+	//
+	// See comments in container/heap for an
+	// explanation of the layout of a heap.
+	heap []float64
+	src  *rand.Rand
+}
+
+// NewWeighted returns a Weighted for the weights w. If src is nil, rand.Rand is
+// used as the random source.
+//
+// Note that sampling from weights with a high variance or overall low absolute
+// value sum may result in problems with numerical stability.
+func NewWeighted(w []float64, src *rand.Rand) Weighted {
+	s := Weighted{
+		weights: make([]float64, len(w)),
+		heap:    make([]float64, len(w)),
+		src:     src,
+	}
+	s.ReweightAll(w)
+	return s
+}
+
+// Len returns the number of items held by the Weighted, including items
+// already taken.
+func (s Weighted) Len() int { return len(s.weights) }
+
+// Take returns an index from the Weighted with probability proportional
+// to the weight of the item. The weight of the item is then set to zero.
+// Take returns false if there are no items remaining.
+func (s Weighted) Take() (idx int, ok bool) {
+	const small = 1e-12
+	if floats.EqualWithinAbsOrRel(s.heap[0], 0, small, small) {
+		return -1, false
+	}
+
+	var r float64
+	if s.src == nil {
+		r = s.heap[0] * rand.Float64()
+	} else {
+		r = s.heap[0] * s.src.Float64()
+	}
+	i := 1
+	last := -1
+	left := len(s.weights)
+	for {
+		if r -= s.weights[i-1]; r <= 0 {
+			break // Fall within item i-1.
+		}
+		i <<= 1 // Move to left child.
+		if d := s.heap[i-1]; r > d {
+			r -= d
+			// If enough r to pass left child
+			// move to right child state will
+			// be caught at break above.
+			i++
+		}
+		if i == last || left < 0 {
+			// No progression.
+			return -1, false
+		}
+		last = i
+		left--
+	}
+
+	w, idx := s.weights[i-1], i-1
+
+	s.weights[i-1] = 0
+	for i > 0 {
+		s.heap[i-1] -= w
+		// The following condition is necessary to
+		// handle floating point error. If we see
+		// a heap value below zero, we know we need
+		// to rebuild it.
+		if s.heap[i-1] < 0 {
+			s.reset()
+			return idx, true
+		}
+		i >>= 1
+	}
+
+	return idx, true
+}
+
+// Reweight sets the weight of item idx to w.
+func (s Weighted) Reweight(idx int, w float64) {
+	w, s.weights[idx] = s.weights[idx]-w, w
+	idx++
+	for idx > 0 {
+		s.heap[idx-1] -= w
+		idx >>= 1
+	}
+}
+
+// ReweightAll sets the weight of all items in the Weighted. ReweightAll
+// panics if len(w) != s.Len.
+func (s Weighted) ReweightAll(w []float64) {
+	if len(w) != s.Len() {
+		panic("floats: length of the slices do not match")
+	}
+	copy(s.weights, w)
+	s.reset()
+}
+
+func (s Weighted) reset() {
+	copy(s.heap, s.weights)
+	for i := len(s.heap) - 1; i > 0; i-- {
+		// Sometimes 1-based counting makes sense.
+		s.heap[((i+1)>>1)-1] += s.heap[i]
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/sampleuv/weighted_test.go b/vendor/gonum.org/v1/gonum/stat/sampleuv/weighted_test.go
new file mode 100644
index 00000000..ad2799f9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/sampleuv/weighted_test.go
@@ -0,0 +1,267 @@
+// Copyright ©2015 The gonum Authors. All rights reserved.
+// Use of this code is governed by a BSD-style
+// license that can be found in the LICENSE file
+
+package sampleuv
+
+import (
+	"flag"
+	"math/rand"
+	"reflect"
+	"testing"
+	"time"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+var prob = flag.Bool("prob", false, "enables probabilistic testing of the random weighted sampler")
+
+const sigChi2 = 16.92 // p = 0.05 df = 9
+
+var (
+	newExp = func() []float64 {
+		return []float64{1 << 0, 1 << 1, 1 << 2, 1 << 3, 1 << 4, 1 << 5, 1 << 6, 1 << 7, 1 << 8, 1 << 9}
+	}
+	exp = newExp()
+
+	obt = []float64{973, 1937, 3898, 7897, 15769, 31284, 62176, 125408, 250295, 500363}
+)
+
+func newTestWeighted() Weighted {
+	weights := make([]float64, len(obt))
+	for i := range weights {
+		weights[i] = float64(int(1) << uint(i))
+	}
+	return NewWeighted(weights, nil)
+}
+
+func TestWeightedUnseeded(t *testing.T) {
+	rand.Seed(0)
+
+	want := Weighted{
+		weights: []float64{1 << 0, 1 << 1, 1 << 2, 1 << 3, 1 << 4, 1 << 5, 1 << 6, 1 << 7, 1 << 8, 1 << 9},
+		heap: []float64{
+			exp[0] + exp[1] + exp[3] + exp[4] + exp[7] + exp[8] + exp[9] + exp[2] + exp[5] + exp[6],
+			exp[1] + exp[3] + exp[4] + exp[7] + exp[8] + exp[9],
+			exp[2] + exp[5] + exp[6],
+			exp[3] + exp[7] + exp[8],
+			exp[4] + exp[9],
+			exp[5],
+			exp[6],
+			exp[7],
+			exp[8],
+			exp[9],
+		},
+	}
+
+	ts := newTestWeighted()
+	if !reflect.DeepEqual(ts, want) {
+		t.Fatalf("unexpected new Weighted value:\ngot: %#v\nwant:%#v", ts, want)
+	}
+
+	f := make([]float64, len(obt))
+	for i := 0; i < 1e6; i++ {
+		item, ok := newTestWeighted().Take()
+		if !ok {
+			t.Fatal("Weighted unexpectedly empty")
+		}
+		f[item]++
+	}
+
+	exp := newExp()
+	fac := floats.Sum(f) / floats.Sum(exp)
+	for i := range f {
+		exp[i] *= fac
+	}
+
+	if !reflect.DeepEqual(f, obt) {
+		t.Fatalf("unexpected selection:\ngot: %#v\nwant:%#v", f, obt)
+	}
+
+	// Check that this is within statistical expectations - we know this is true for this set.
+	X := chi2(f, exp)
+	if X >= sigChi2 {
+		t.Errorf("H₀: d(Sample) = d(Expect), H₁: d(S) ≠ d(Expect). df = %d, p = 0.05, X² threshold = %.2f, X² = %f", len(f)-1, sigChi2, X)
+	}
+}
+
+func TestWeightedTimeSeeded(t *testing.T) {
+	if !*prob {
+		t.Skip("probabilistic testing not requested")
+	}
+	t.Log("Note: This test is stochastic and is expected to fail with probability ≈ 0.05.")
+
+	rand.Seed(time.Now().Unix())
+
+	f := make([]float64, len(obt))
+	for i := 0; i < 1e6; i++ {
+		item, ok := newTestWeighted().Take()
+		if !ok {
+			t.Fatal("Weighted unexpectedly empty")
+		}
+		f[item]++
+	}
+
+	exp := newExp()
+	fac := floats.Sum(f) / floats.Sum(exp)
+	for i := range f {
+		exp[i] *= fac
+	}
+
+	// Check that our obtained values are within statistical expectations for p = 0.05.
+	// This will not be true approximately 1 in 20 tests.
+	X := chi2(f, exp)
+	if X >= sigChi2 {
+		t.Errorf("H₀: d(Sample) = d(Expect), H₁: d(S) ≠ d(Expect). df = %d, p = 0.05, X² threshold = %.2f, X² = %f", len(f)-1, sigChi2, X)
+	}
+}
+
+func TestWeightZero(t *testing.T) {
+	rand.Seed(0)
+
+	want := Weighted{
+		weights: []float64{1 << 0, 1 << 1, 1 << 2, 1 << 3, 1 << 4, 1 << 5, 0, 1 << 7, 1 << 8, 1 << 9},
+		heap: []float64{
+			exp[0] + exp[1] + exp[3] + exp[4] + exp[7] + exp[8] + exp[9] + exp[2] + exp[5],
+			exp[1] + exp[3] + exp[4] + exp[7] + exp[8] + exp[9],
+			exp[2] + exp[5],
+			exp[3] + exp[7] + exp[8],
+			exp[4] + exp[9],
+			exp[5],
+			0,
+			exp[7],
+			exp[8],
+			exp[9],
+		},
+	}
+
+	ts := newTestWeighted()
+	ts.Reweight(6, 0)
+	if !reflect.DeepEqual(ts, want) {
+		t.Fatalf("unexpected new Weighted value:\ngot: %#v\nwant:%#v", ts, want)
+	}
+
+	f := make([]float64, len(obt))
+	for i := 0; i < 1e6; i++ {
+		ts := newTestWeighted()
+		ts.Reweight(6, 0)
+		item, ok := ts.Take()
+		if !ok {
+			t.Fatal("Weighted unexpectedly empty")
+		}
+		f[item]++
+	}
+
+	exp := newExp()
+	fac := floats.Sum(f) / floats.Sum(exp)
+	for i := range f {
+		exp[i] *= fac
+	}
+
+	if f[6] != 0 {
+		t.Errorf("unexpected selection rate for zero-weighted item: got: %v want:%v", f[6], 0)
+	}
+	if reflect.DeepEqual(f[:6], obt[:6]) {
+		t.Fatalf("unexpected selection: too few elements chosen in range:\ngot: %v\nwant:%v",
+			f[:6], obt[:6])
+	}
+	if reflect.DeepEqual(f[7:], obt[7:]) {
+		t.Fatalf("unexpected selection: too few elements chosen in range:\ngot: %v\nwant:%v",
+			f[7:], obt[7:])
+	}
+}
+
+func TestWeightIncrease(t *testing.T) {
+	rand.Seed(0)
+
+	want := Weighted{
+		weights: []float64{1 << 0, 1 << 1, 1 << 2, 1 << 3, 1 << 4, 1 << 5, 1 << 9 * 2, 1 << 7, 1 << 8, 1 << 9},
+		heap: []float64{
+			exp[0] + exp[1] + exp[3] + exp[4] + exp[7] + exp[8] + exp[9] + exp[2] + exp[5] + exp[9]*2,
+			exp[1] + exp[3] + exp[4] + exp[7] + exp[8] + exp[9],
+			exp[2] + exp[5] + exp[9]*2,
+			exp[3] + exp[7] + exp[8],
+			exp[4] + exp[9],
+			exp[5],
+			exp[9] * 2,
+			exp[7],
+			exp[8],
+			exp[9],
+		},
+	}
+
+	ts := newTestWeighted()
+	ts.Reweight(6, ts.weights[len(ts.weights)-1]*2)
+	if !reflect.DeepEqual(ts, want) {
+		t.Fatalf("unexpected new Weighted value:\ngot: %#v\nwant:%#v", ts, want)
+	}
+
+	f := make([]float64, len(obt))
+	for i := 0; i < 1e6; i++ {
+		ts := newTestWeighted()
+		ts.Reweight(6, ts.weights[len(ts.weights)-1]*2)
+		item, ok := ts.Take()
+		if !ok {
+			t.Fatal("Weighted unexpectedly empty")
+		}
+		f[item]++
+	}
+
+	exp := newExp()
+	fac := floats.Sum(f) / floats.Sum(exp)
+	for i := range f {
+		exp[i] *= fac
+	}
+
+	if f[6] < f[9] {
+		t.Errorf("unexpected selection rate for re-weighted item: got: %v want:%v", f[6], f[9])
+	}
+	if reflect.DeepEqual(f[:6], obt[:6]) {
+		t.Fatalf("unexpected selection: too many elements chosen in range:\ngot: %v\nwant:%v",
+			f[:6], obt[:6])
+	}
+	if reflect.DeepEqual(f[7:], obt[7:]) {
+		t.Fatalf("unexpected selection: too many elements chosen in range:\ngot: %v\nwant:%v",
+			f[7:], obt[7:])
+	}
+}
+
+func chi2(ob, ex []float64) (sum float64) {
+	for i := range ob {
+		x := ob[i] - ex[i]
+		sum += (x * x) / ex[i]
+	}
+
+	return sum
+}
+
+func TestWeightedNoResample(t *testing.T) {
+	const (
+		tries = 10
+		n     = 10e4
+	)
+	ts := NewWeighted(make([]float64, n), nil)
+	w := make([]float64, n)
+	for i := 0; i < tries; i++ {
+		for j := range w {
+			w[j] = rand.Float64() * n
+		}
+		ts.ReweightAll(w)
+		taken := make(map[int]struct{})
+		var c int
+		for {
+			item, ok := ts.Take()
+			if !ok {
+				if c != n {
+					t.Errorf("unexpected number of items: got: %d want: %d", c, int(n))
+				}
+				break
+			}
+			c++
+			if _, exists := taken[item]; exists {
+				t.Errorf("unexpected duplicate sample for item: %d", item)
+			}
+			taken[item] = struct{}{}
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/sampleuv/withoutreplacement.go b/vendor/gonum.org/v1/gonum/stat/sampleuv/withoutreplacement.go
new file mode 100644
index 00000000..9fbc543c
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/sampleuv/withoutreplacement.go
@@ -0,0 +1,59 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package sampleuv
+
+import (
+	"math/rand"
+	"sort"
+)
+
+// WithoutReplacement samples len(idxs) integers from [0, n) without replacement.
+// That is, upon return the elements of idxs will be unique integers. If source
+// is non-nil it will be used to generate random numbers, otherwise the default
+// source from the math/rand package will be used.
+//
+// WithoutReplacement will panic if len(idxs) > n.
+func WithoutReplacement(idxs []int, n int, src *rand.Rand) {
+	if len(idxs) == 0 {
+		panic("withoutreplacement: zero length input")
+	}
+	if len(idxs) > n {
+		panic("withoutreplacement: impossible size inputs")
+	}
+
+	// There are two algorithms. One is to generate a random permutation
+	// and take the first len(idxs) elements. The second is to generate
+	// individual random numbers for each element and check uniqueness. The first
+	// method scales as O(n), and the second scales as O(len(idxs)^2). Choose
+	// the algorithm accordingly.
+	if n < len(idxs)*len(idxs) {
+		var perm []int
+		if src != nil {
+			perm = src.Perm(n)
+		} else {
+			perm = rand.Perm(n)
+		}
+		copy(idxs, perm)
+	}
+
+	// Instead, generate the random numbers directly.
+	sorted := make([]int, 0, len(idxs))
+	for i := range idxs {
+		var r int
+		if src != nil {
+			r = src.Intn(n - i)
+		} else {
+			r = rand.Intn(n - i)
+		}
+		for _, v := range sorted {
+			if r >= v {
+				r++
+			}
+		}
+		idxs[i] = r
+		sorted = append(sorted, r)
+		sort.Ints(sorted)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/sampleuv/withoutreplacement_test.go b/vendor/gonum.org/v1/gonum/stat/sampleuv/withoutreplacement_test.go
new file mode 100644
index 00000000..fca5d7d3
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/sampleuv/withoutreplacement_test.go
@@ -0,0 +1,65 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package sampleuv
+
+import (
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+func TestWithoutReplacement(t *testing.T) {
+	for cas, test := range []struct {
+		N      int
+		K      int
+		Src    *rand.Rand
+		Trials int
+		Tol    float64
+	}{
+		{
+			// Test with perm and source.
+			N: 10, K: 5, Src: rand.New(rand.NewSource(1)),
+			Trials: 100000, Tol: 1e-3,
+		},
+		{
+			// Test without perm and with source.
+			N: 10, K: 3, Src: rand.New(rand.NewSource(1)),
+			Trials: 100000, Tol: 1e-3,
+		},
+	} {
+		dist := make([]float64, test.N)
+		for trial := 0; trial < test.Trials; trial++ {
+			idxs := make([]int, test.K)
+			WithoutReplacement(idxs, test.N, test.Src)
+
+			allDiff := true
+			for i := 0; i < len(idxs); i++ {
+				v := idxs[i]
+				for j := i + 1; j < len(idxs); j++ {
+					if v == idxs[j] {
+						allDiff = false
+						break
+					}
+				}
+			}
+			if !allDiff {
+				t.Errorf("Cas %d: Repeat in sampling. Idxs =%v", cas, idxs)
+			}
+			for _, v := range idxs {
+				dist[v]++
+			}
+		}
+		div := 1 / (float64(test.Trials) * float64(test.K))
+		floats.Scale(div, dist)
+		want := make([]float64, test.N)
+		for i := range want {
+			want[i] = 1 / float64(test.N)
+		}
+		if !floats.EqualApprox(want, dist, test.Tol) {
+			t.Errorf("Cas %d: biased sampling. Want = %v, got = %v", cas, want, dist)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/spatial/doc.go b/vendor/gonum.org/v1/gonum/stat/spatial/doc.go
new file mode 100644
index 00000000..139d22d9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/spatial/doc.go
@@ -0,0 +1,6 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package spatial provides spatial statistical functions.
+package spatial // import "gonum.org/v1/gonum/stat/spatial"
diff --git a/vendor/gonum.org/v1/gonum/stat/spatial/spatial.go b/vendor/gonum.org/v1/gonum/stat/spatial/spatial.go
new file mode 100644
index 00000000..a45fe422
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/spatial/spatial.go
@@ -0,0 +1,162 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package spatial
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/mat"
+	"gonum.org/v1/gonum/stat"
+)
+
+// TODO(kortschak): Implement weighted routines.
+
+// GetisOrdGStar returns the Local Getis-Ord G*i statistic for element of of the
+// weighted data using the provided locality matrix. The returned value is a z-score.
+//
+//  G^*_i = num_i / den_i
+//
+//  num_i = \sum_j (w_{ij} x_j) - \bar X \sum_j w_{ij}
+//  den_i = S \sqrt(((n \sum_j w_{ij}^2 - (\sum_j w_{ij})^2))/(n - 1))
+//  \bar X = (\sum_j x_j) / n
+//  S = \sqrt((\sum_j x_j^2)/n - (\bar X)^2)
+//
+// GetisOrdGStar will panic if locality is not a square matrix with dimensions the
+// same as the length of data or if i is not a valid index into data.
+//
+// See doi.org/10.1111%2Fj.1538-4632.1995.tb00912.x.
+//
+// Weighted Getis-Ord G*i is not currently implemented and GetisOrdGStar will
+// panic if weights is not nil.
+func GetisOrdGStar(i int, data, weights []float64, locality mat.Matrix) float64 {
+	if weights != nil {
+		panic("spatial: weighted data not yet implemented")
+	}
+	r, c := locality.Dims()
+	if r != len(data) || c != len(data) {
+		panic("spatial: data length mismatch")
+	}
+
+	n := float64(len(data))
+	mean, std := stat.MeanStdDev(data, weights)
+	var dwd, dww, sw float64
+	if doer, ok := locality.(mat.RowNonZeroDoer); ok {
+		doer.DoRowNonZero(i, func(_, j int, w float64) {
+			sw += w
+			dwd += w * data[j]
+			dww += w * w
+		})
+	} else {
+		for j, v := range data {
+			w := locality.At(i, j)
+			sw += w
+			dwd += w * v
+			dww += w * w
+		}
+	}
+	s := std * math.Sqrt((n-1)/n)
+
+	return (dwd - mean*sw) / (s * math.Sqrt((n*dww-sw*sw)/(n-1)))
+}
+
+// GlobalMoransI performs Global Moran's I calculation of spatial autocorrelation
+// for the given data using the provided locality matrix. GlobalMoransI returns
+// Moran's I, Var(I) and the z-score associated with those values.
+// GlobalMoransI will panic if locality is not a square matrix with dimensions the
+// same as the length of data.
+//
+// See https://doi.org/10.1111%2Fj.1538-4632.2007.00708.x.
+//
+// Weighted Global Moran's I is not currently implemented and GlobalMoransI will
+// panic if weights is not nil.
+func GlobalMoransI(data, weights []float64, locality mat.Matrix) (i, v, z float64) {
+	if weights != nil {
+		panic("spatial: weighted data not yet implemented")
+	}
+	if r, c := locality.Dims(); r != len(data) || c != len(data) {
+		panic("spatial: data length mismatch")
+	}
+	mean := stat.Mean(data, nil)
+
+	doer, isDoer := locality.(mat.RowNonZeroDoer)
+
+	// Calculate Moran's I for the data.
+	var num, den, sum float64
+	for i, xi := range data {
+		zi := xi - mean
+		den += zi * zi
+		if isDoer {
+			doer.DoRowNonZero(i, func(_, j int, w float64) {
+				sum += w
+				zj := data[j] - mean
+				num += w * zi * zj
+			})
+		} else {
+			for j, xj := range data {
+				w := locality.At(i, j)
+				sum += w
+				zj := xj - mean
+				num += w * zi * zj
+			}
+		}
+	}
+	i = (float64(len(data)) / sum) * (num / den)
+
+	// Calculate Moran's E(I) for the data.
+	e := -1 / float64(len(data)-1)
+
+	// Calculate Moran's Var(I) for the data.
+	//  http://pro.arcgis.com/en/pro-app/tool-reference/spatial-statistics/h-how-spatial-autocorrelation-moran-s-i-spatial-st.htm
+	//  http://pro.arcgis.com/en/pro-app/tool-reference/spatial-statistics/h-global-morans-i-additional-math.htm
+	var s0, s1, s2 float64
+	var var2, var4 float64
+	for i, v := range data {
+		v -= mean
+		v *= v
+		var2 += v
+		var4 += v * v
+
+		var p2 float64
+		if isDoer {
+			doer.DoRowNonZero(i, func(i, j int, wij float64) {
+				wji := locality.At(j, i)
+
+				s0 += wij
+
+				v := wij + wji
+				s1 += v * v
+
+				p2 += v
+			})
+		} else {
+			for j := range data {
+				wij := locality.At(i, j)
+				wji := locality.At(j, i)
+
+				s0 += wij
+
+				v := wij + wji
+				s1 += v * v
+
+				p2 += v
+			}
+		}
+		s2 += p2 * p2
+	}
+	s1 *= 0.5
+
+	n := float64(len(data))
+	a := n * ((n*n-3*n+3)*s1 - n*s2 + 3*s0*s0)
+	c := (n - 1) * (n - 2) * (n - 3) * s0 * s0
+	d := var4 / (var2 * var2)
+	b := d * ((n*n-n)*s1 - 2*n*s2 + 6*s0*s0)
+
+	v = (a-b)/c - e*e
+
+	// Calculate z-score associated with Moran's I for the data.
+	z = (i - e) / math.Sqrt(v)
+
+	return i, v, z
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/spatial/spatial_areal_example_test.go b/vendor/gonum.org/v1/gonum/stat/spatial/spatial_areal_example_test.go
new file mode 100644
index 00000000..1f849292
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/spatial/spatial_areal_example_test.go
@@ -0,0 +1,74 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package spatial_test
+
+import (
+	"fmt"
+	"math"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+	"gonum.org/v1/gonum/stat/spatial"
+)
+
+// Euclid is a mat.Matrix whose elements refects the Euclidean
+// distance between a series of unit-separated points strided
+// to be arranged in an x by y grid.
+type Euclid struct{ x, y int }
+
+func (e Euclid) Dims() (r, c int) { return e.x * e.y, e.x * e.y }
+func (e Euclid) At(i, j int) float64 {
+	d := e.x * e.y
+	if i < 0 || d <= i || j < 0 || d <= j {
+		panic("bounds error")
+	}
+	if i == j {
+		return 0
+	}
+	x := float64(j%e.x - i%e.x)
+	y := float64(j/e.x - i/e.x)
+	return 1 / math.Hypot(x, y)
+}
+func (e Euclid) T() mat.Matrix { return mat.Transpose{e} }
+
+func ExampleGlobalMoransI_areal() {
+	locality := Euclid{10, 10}
+
+	data1 := []float64{
+		1, 0, 0, 1, 0, 0, 1, 0, 0, 0,
+		0, 1, 1, 0, 0, 1, 0, 0, 0, 0,
+		1, 0, 0, 1, 0, 0, 0, 0, 1, 0,
+		0, 0, 1, 0, 1, 0, 1, 0, 0, 0,
+		1, 0, 0, 0, 0, 0, 0, 1, 0, 0,
+		0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
+		0, 0, 1, 0, 0, 0, 1, 0, 1, 0,
+		1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+		0, 0, 1, 0, 1, 0, 1, 0, 0, 0,
+		1, 0, 0, 0, 0, 0, 0, 0, 1, 0,
+	}
+	i1, _, z1 := spatial.GlobalMoransI(data1, nil, locality)
+
+	data2 := []float64{
+		0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+		0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+		0, 0, 0, 1, 1, 0, 0, 0, 0, 0,
+		0, 0, 1, 1, 1, 1, 0, 0, 0, 0,
+		0, 0, 1, 1, 1, 1, 0, 0, 0, 0,
+		0, 0, 0, 1, 1, 1, 0, 0, 0, 0,
+		0, 0, 0, 0, 1, 0, 0, 0, 1, 0,
+		0, 0, 0, 0, 0, 0, 0, 1, 1, 1,
+		0, 0, 0, 0, 0, 0, 0, 1, 1, 1,
+		0, 0, 0, 0, 0, 0, 0, 1, 1, 1,
+	}
+	i2, _, z2 := spatial.GlobalMoransI(data2, nil, locality)
+
+	fmt.Printf("%v scattered points Moran's I=%.4v z-score=%.4v\n", floats.Sum(data1), i1, z1)
+	fmt.Printf("%v clustered points Moran's I=%.4v z-score=%.4v\n", floats.Sum(data2), i2, z2)
+
+	// Output:
+	//
+	// 24 scattered points Moran's I=-0.02999 z-score=-1.913
+	// 24 clustered points Moran's I=0.09922 z-score=10.52
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/spatial/spatial_example_test.go b/vendor/gonum.org/v1/gonum/stat/spatial/spatial_example_test.go
new file mode 100644
index 00000000..e5281a7e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/spatial/spatial_example_test.go
@@ -0,0 +1,142 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package spatial_test
+
+import (
+	"fmt"
+
+	"gonum.org/v1/gonum/mat"
+	"gonum.org/v1/gonum/stat/spatial"
+)
+
+func ExampleGlobalMoransI_linear() {
+	data := []float64{0, 0, 0, 1, 1, 1, 0, 1, 0, 0}
+
+	// The locality here describes spatial neighbor
+	// relationships.
+	locality := mat.NewDense(10, 10, []float64{
+		0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
+		1, 0, 1, 0, 0, 0, 0, 0, 0, 0,
+		0, 1, 0, 1, 0, 0, 0, 0, 0, 0,
+		0, 0, 1, 0, 1, 0, 0, 0, 0, 0,
+		0, 0, 0, 1, 0, 1, 0, 0, 0, 0,
+		0, 0, 0, 0, 1, 0, 1, 0, 0, 0,
+		0, 0, 0, 0, 0, 1, 0, 1, 0, 0,
+		0, 0, 0, 0, 0, 0, 1, 0, 1, 0,
+		0, 0, 0, 0, 0, 0, 0, 1, 0, 1,
+		0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
+	})
+
+	i, _, z := spatial.GlobalMoransI(data, nil, locality)
+
+	fmt.Printf("Moran's I=%.4v z-score=%.4v\n", i, z)
+
+	// Output:
+	//
+	// Moran's I=0.1111 z-score=0.6335
+}
+
+func ExampleGlobalMoransI_banded() {
+	data := []float64{0, 0, 0, 1, 1, 1, 0, 1, 0, 0}
+
+	// The locality here describes spatial neighbor
+	// relationships.
+	// This example uses the band matrix representation
+	// to improve time and space efficiency.
+	locality := mat.NewBandDense(10, 10, 1, 1, []float64{
+		0, 0, 1,
+		1, 0, 1,
+		1, 0, 1,
+		1, 0, 1,
+		1, 0, 1,
+		1, 0, 1,
+		1, 0, 1,
+		1, 0, 1,
+		1, 0, 1,
+		1, 0, 0,
+	})
+
+	i, _, z := spatial.GlobalMoransI(data, nil, locality)
+
+	fmt.Printf("Moran's I=%.4v z-score=%.4v\n", i, z)
+
+	// Output:
+	//
+	// Moran's I=0.1111 z-score=0.6335
+}
+
+func ExampleGetisOrdGStar() {
+	data := []float64{0, 0, 0, 1, 1, 1, 0, 1, 0, 0}
+
+	// The locality here describes spatial neighbor
+	// relationships including self.
+	locality := mat.NewDense(10, 10, []float64{
+		1, 1, 0, 0, 0, 0, 0, 0, 0, 0,
+		1, 1, 1, 0, 0, 0, 0, 0, 0, 0,
+		0, 1, 1, 1, 0, 0, 0, 0, 0, 0,
+		0, 0, 1, 1, 1, 0, 0, 0, 0, 0,
+		0, 0, 0, 1, 1, 1, 0, 0, 0, 0,
+		0, 0, 0, 0, 1, 1, 1, 0, 0, 0,
+		0, 0, 0, 0, 0, 1, 1, 1, 0, 0,
+		0, 0, 0, 0, 0, 0, 1, 1, 1, 0,
+		0, 0, 0, 0, 0, 0, 0, 1, 1, 1,
+		0, 0, 0, 0, 0, 0, 0, 0, 1, 1,
+	})
+
+	for i, v := range data {
+		fmt.Printf("v=%v G*i=% .4v\n", v, spatial.GetisOrdGStar(i, data, nil, locality))
+	}
+
+	// Output:
+	//
+	// v=0 G*i=-1.225
+	// v=0 G*i=-1.604
+	// v=0 G*i=-0.2673
+	// v=1 G*i= 1.069
+	// v=1 G*i= 2.405
+	// v=1 G*i= 1.069
+	// v=0 G*i= 1.069
+	// v=1 G*i=-0.2673
+	// v=0 G*i=-0.2673
+	// v=0 G*i=-1.225
+}
+
+func ExampleGetisOrd_band() {
+	data := []float64{0, 0, 0, 1, 1, 1, 0, 1, 0, 0}
+
+	// The locality here describes spatial neighbor
+	// relationships including self.
+	// This example uses the band matrix representation
+	// to improve time and space efficiency.
+	locality := mat.NewBandDense(10, 10, 1, 1, []float64{
+		0, 1, 1,
+		1, 1, 1,
+		1, 1, 1,
+		1, 1, 1,
+		1, 1, 1,
+		1, 1, 1,
+		1, 1, 1,
+		1, 1, 1,
+		1, 1, 1,
+		1, 1, 0,
+	})
+
+	for i, v := range data {
+		fmt.Printf("v=%v G*i=% .4v\n", v, spatial.GetisOrdGStar(i, data, nil, locality))
+	}
+
+	// Output:
+	//
+	// v=0 G*i=-1.225
+	// v=0 G*i=-1.604
+	// v=0 G*i=-0.2673
+	// v=1 G*i= 1.069
+	// v=1 G*i= 2.405
+	// v=1 G*i= 1.069
+	// v=0 G*i= 1.069
+	// v=1 G*i=-0.2673
+	// v=0 G*i=-0.2673
+	// v=0 G*i=-1.225
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/spatial/spatial_test.go b/vendor/gonum.org/v1/gonum/stat/spatial/spatial_test.go
new file mode 100644
index 00000000..f91edfdf
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/spatial/spatial_test.go
@@ -0,0 +1,293 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package spatial
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+)
+
+func simpleAdjacency(n, wide int, diag bool) mat.Matrix {
+	m := mat.NewDense(n, n, nil)
+	for i := 0; i < n; i++ {
+		for j := 1; j <= wide; j++ {
+			if j > i {
+				continue
+			}
+			m.Set(i-j, i, 1)
+			m.Set(i, i-j, 1)
+		}
+		if diag {
+			m.Set(i, i, 1)
+		}
+	}
+	return m
+}
+
+func simpleAdjacencyBand(n, wide int, diag bool) mat.Matrix {
+	m := mat.NewBandDense(n, n, wide, wide, nil)
+	for i := 0; i < n; i++ {
+		for j := 1; j <= wide; j++ {
+			if j > i {
+				continue
+			}
+			m.SetBand(i-j, i, 1)
+			m.SetBand(i, i-j, 1)
+		}
+		if diag {
+			m.SetBand(i, i, 1)
+		}
+	}
+	return m
+}
+
+var spatialTests = []struct {
+	from, to float64
+	n, wide  int
+	fn       func(float64, int, *rand.Rand) float64
+	locality func(n, wide int, diag bool) mat.Matrix
+
+	// Values for MoranI and z-score are obtained from
+	// an R reference implementation.
+	wantMoranI float64
+	wantZ      float64
+
+	// The value for expected number of significant
+	// segments is obtained from visual inspection
+	// of the plotted data.
+	wantSegs int
+}{
+	// Dense matrix locality.
+	{
+		from: 0, to: 1, n: 1000, wide: 1,
+		fn: func(_ float64, _ int, rnd *rand.Rand) float64 {
+			return rnd.Float64()
+		},
+		locality: simpleAdjacency,
+
+		wantMoranI: -0.0019631298955953233,
+		wantZ:      -0.03039477405151108,
+		wantSegs:   0,
+	},
+	{
+		from: -math.Pi / 2, to: 3 * math.Pi / 2, n: 1000, wide: 1,
+		fn: func(x float64, _ int, _ *rand.Rand) float64 {
+			y := math.Sin(x)
+			if math.Abs(y) > 0.5 {
+				y *= 1/math.Abs(y) - 1
+			}
+			return y * math.Sin(x*2)
+		},
+		locality: simpleAdjacency,
+
+		wantMoranI: 1.0008149537991464,
+		wantZ:      31.648547078779092,
+		wantSegs:   4,
+	},
+	{
+		from: 0, to: 1, n: 1000, wide: 1,
+		fn: func(_ float64, _ int, rnd *rand.Rand) float64 {
+			return rnd.NormFloat64()
+		},
+		locality: simpleAdjacency,
+
+		wantMoranI: 0.031195199553564902,
+		wantZ:      1.0171161514080056,
+		wantSegs:   0,
+	},
+	{
+		from: 0, to: 1, n: 1000, wide: 1,
+		fn: func(x float64, _ int, rnd *rand.Rand) float64 {
+			if rnd.Float64() < 0.5 {
+				return rnd.NormFloat64() + 5
+			}
+			return rnd.NormFloat64()
+		},
+		locality: simpleAdjacency,
+
+		wantMoranI: -0.016245135637562223,
+		wantZ:      -0.48157993864993476,
+		wantSegs:   0,
+	},
+	{
+		from: 0, to: 1, n: 1000, wide: 1,
+		fn: func(x float64, i int, rnd *rand.Rand) float64 {
+			if i%2 == 0 {
+				return rnd.NormFloat64() + 5
+			}
+			return rnd.NormFloat64()
+		},
+		locality: simpleAdjacency,
+
+		wantMoranI: -0.8565268969272998,
+		wantZ:      -27.027057520918113,
+		wantSegs:   0,
+	},
+	{
+		from: 0, to: 1, n: 1000, wide: 1,
+		fn: func(_ float64, i int, _ *rand.Rand) float64 {
+			return float64(i % 2)
+		},
+		locality: simpleAdjacency,
+
+		wantMoranI: -1,
+		wantZ:      -31.559531064275987,
+		wantSegs:   0,
+	},
+
+	// Band matrix locality.
+	{
+		from: 0, to: 1, n: 1000, wide: 1,
+		fn: func(_ float64, _ int, rnd *rand.Rand) float64 {
+			return rnd.Float64()
+		},
+		locality: simpleAdjacencyBand,
+
+		wantMoranI: -0.0019631298955953233,
+		wantZ:      -0.03039477405151108,
+		wantSegs:   0,
+	},
+	{
+		from: -math.Pi / 2, to: 3 * math.Pi / 2, n: 1000, wide: 1,
+		fn: func(x float64, _ int, _ *rand.Rand) float64 {
+			y := math.Sin(x)
+			if math.Abs(y) > 0.5 {
+				y *= 1/math.Abs(y) - 1
+			}
+			return y * math.Sin(x*2)
+		},
+		locality: simpleAdjacencyBand,
+
+		wantMoranI: 1.0008149537991464,
+		wantZ:      31.648547078779092,
+		wantSegs:   4,
+	},
+	{
+		from: 0, to: 1, n: 1000, wide: 1,
+		fn: func(_ float64, _ int, rnd *rand.Rand) float64 {
+			return rnd.NormFloat64()
+		},
+		locality: simpleAdjacencyBand,
+
+		wantMoranI: 0.031195199553564902,
+		wantZ:      1.0171161514080056,
+		wantSegs:   0,
+	},
+	{
+		from: 0, to: 1, n: 1000, wide: 1,
+		fn: func(x float64, _ int, rnd *rand.Rand) float64 {
+			if rnd.Float64() < 0.5 {
+				return rnd.NormFloat64() + 5
+			}
+			return rnd.NormFloat64()
+		},
+		locality: simpleAdjacencyBand,
+
+		wantMoranI: -0.016245135637562223,
+		wantZ:      -0.48157993864993476,
+		wantSegs:   0,
+	},
+	{
+		from: 0, to: 1, n: 1000, wide: 1,
+		fn: func(x float64, i int, rnd *rand.Rand) float64 {
+			if i%2 == 0 {
+				return rnd.NormFloat64() + 5
+			}
+			return rnd.NormFloat64()
+		},
+		locality: simpleAdjacencyBand,
+
+		wantMoranI: -0.8565268969272998,
+		wantZ:      -27.027057520918113,
+		wantSegs:   0,
+	},
+	{
+		from: 0, to: 1, n: 1000, wide: 1,
+		fn: func(_ float64, i int, _ *rand.Rand) float64 {
+			return float64(i % 2)
+		},
+		locality: simpleAdjacencyBand,
+
+		wantMoranI: -1,
+		wantZ:      -31.559531064275987,
+		wantSegs:   0,
+	},
+}
+
+func TestGetisOrd(t *testing.T) {
+	for ti, test := range spatialTests {
+		rnd := rand.New(rand.NewSource(1))
+		data := make([]float64, test.n)
+		step := (test.to - test.from) / float64(test.n)
+		for i := range data {
+			data[i] = test.fn(test.from+step*float64(i), i, rnd)
+		}
+		locality := test.locality(test.n, test.wide, true)
+
+		nseg := getisOrdSegments(data, nil, locality)
+		if nseg != test.wantSegs {
+			t.Errorf("unexpected number of significant segments for test %d: got:%d want:%d",
+				ti, nseg, test.wantSegs)
+		}
+	}
+}
+
+// getisOrdSegments returns the number of contiguously significant G*i segemtns in
+// data. This allows an intuitive validation of the function in lieu of a reference
+// implementation.
+func getisOrdSegments(data, weight []float64, locality mat.Matrix) int {
+	const thresh = 2
+	var nseg int
+	segstart := -1
+	for i := range data {
+		gi := GetisOrdGStar(i, data, weight, locality)
+		if segstart != -1 {
+			if math.Abs(gi) < thresh {
+				// Filter short segments.
+				if i-segstart < 5 {
+					segstart = -1
+					continue
+				}
+
+				segstart = -1
+				nseg++
+			}
+			continue
+		}
+		if math.Abs(gi) >= thresh {
+			segstart = i
+		}
+	}
+	if segstart != -1 && len(data)-segstart >= 5 {
+		nseg++
+	}
+	return nseg
+}
+
+func TestGlobalMoransI(t *testing.T) {
+	const tol = 1e-14
+	for ti, test := range spatialTests {
+		rnd := rand.New(rand.NewSource(1))
+		data := make([]float64, test.n)
+		step := (test.to - test.from) / float64(test.n)
+		for i := range data {
+			data[i] = test.fn(test.from+step*float64(i), i, rnd)
+		}
+		locality := test.locality(test.n, test.wide, false)
+
+		gotI, _, gotZ := GlobalMoransI(data, nil, locality)
+
+		if !floats.EqualWithinAbsOrRel(gotI, test.wantMoranI, tol, tol) {
+			t.Errorf("unexpected Moran's I value for test %d: got:%v want:%v", ti, gotI, test.wantMoranI)
+		}
+		if !floats.EqualWithinAbsOrRel(gotZ, test.wantZ, tol, tol) {
+			t.Errorf("unexpected Moran's I z-score for test %d: got:%v want:%v", ti, gotZ, test.wantZ)
+		}
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/stat_test.go b/vendor/gonum.org/v1/gonum/stat/stat_test.go
new file mode 100644
index 00000000..bdb24dd3
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/stat_test.go
@@ -0,0 +1,1569 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package stat
+
+import (
+	"fmt"
+	"math"
+	"reflect"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+func ExampleCircularMean() {
+	x := []float64{0, 0.25 * math.Pi, 0.75 * math.Pi}
+	weights := []float64{1, 2, 2.5}
+	cmean := CircularMean(x, weights)
+
+	fmt.Printf("The circular mean is %.5f.\n", cmean)
+	// Output:
+	// The circular mean is 1.37037.
+}
+
+func TestCircularMean(t *testing.T) {
+	for i, test := range []struct {
+		x   []float64
+		wts []float64
+		ans float64
+	}{
+		// Values compared against scipy.
+		{
+			x:   []float64{0, 2 * math.Pi},
+			ans: 0,
+		},
+		{
+			x:   []float64{0, 0.5 * math.Pi},
+			ans: 0.78539816339744,
+		},
+		{
+			x:   []float64{-1.5 * math.Pi, 0.5 * math.Pi, 2.5 * math.Pi},
+			wts: []float64{1, 2, 3},
+			ans: 0.5 * math.Pi,
+		},
+		{
+			x:   []float64{0, 0.5 * math.Pi},
+			wts: []float64{1, 2},
+			ans: 1.10714871779409,
+		},
+	} {
+		c := CircularMean(test.x, test.wts)
+		if math.Abs(c-test.ans) > 1e-14 {
+			t.Errorf("Circular mean mismatch case %d: Expected %v, Found %v", i, test.ans, c)
+		}
+	}
+	if !Panics(func() { CircularMean(make([]float64, 3), make([]float64, 2)) }) {
+		t.Errorf("CircularMean did not panic with x, wts length mismatch")
+	}
+}
+
+func ExampleCorrelation() {
+	x := []float64{8, -3, 7, 8, -4}
+	y := []float64{10, 5, 6, 3, -1}
+	w := []float64{2, 1.5, 3, 3, 2}
+
+	fmt.Println("Correlation computes the degree to which two datasets move together")
+	fmt.Println("about their mean. For example, x and y above move similarly.")
+
+	c := Correlation(x, y, w)
+	fmt.Printf("Correlation is %.5f\n", c)
+
+	// Output:
+	// Correlation computes the degree to which two datasets move together
+	// about their mean. For example, x and y above move similarly.
+	// Correlation is 0.59915
+}
+
+func TestCorrelation(t *testing.T) {
+	for i, test := range []struct {
+		x   []float64
+		y   []float64
+		w   []float64
+		ans float64
+	}{
+		{
+			x:   []float64{8, -3, 7, 8, -4},
+			y:   []float64{8, -3, 7, 8, -4},
+			w:   nil,
+			ans: 1,
+		},
+		{
+			x:   []float64{8, -3, 7, 8, -4},
+			y:   []float64{8, -3, 7, 8, -4},
+			w:   []float64{1, 1, 1, 1, 1},
+			ans: 1,
+		},
+		{
+			x:   []float64{8, -3, 7, 8, -4},
+			y:   []float64{8, -3, 7, 8, -4},
+			w:   []float64{1, 6, 7, 0.8, 2.1},
+			ans: 1,
+		},
+		{
+			x:   []float64{8, -3, 7, 8, -4},
+			y:   []float64{10, 15, 4, 5, -1},
+			w:   nil,
+			ans: 0.0093334660769059,
+		},
+		{
+			x:   []float64{8, -3, 7, 8, -4},
+			y:   []float64{10, 15, 4, 5, -1},
+			w:   nil,
+			ans: 0.0093334660769059,
+		},
+		{
+			x:   []float64{8, -3, 7, 8, -4},
+			y:   []float64{10, 15, 4, 5, -1},
+			w:   []float64{1, 3, 1, 2, 2},
+			ans: -0.13966633352689,
+		},
+	} {
+		c := Correlation(test.x, test.y, test.w)
+		if math.Abs(test.ans-c) > 1e-14 {
+			t.Errorf("Correlation mismatch case %d. Expected %v, Found %v", i, test.ans, c)
+		}
+	}
+	if !Panics(func() { Correlation(make([]float64, 2), make([]float64, 3), make([]float64, 3)) }) {
+		t.Errorf("Correlation did not panic with length mismatch")
+	}
+	if !Panics(func() { Correlation(make([]float64, 2), make([]float64, 3), nil) }) {
+		t.Errorf("Correlation did not panic with length mismatch")
+	}
+	if !Panics(func() { Correlation(make([]float64, 3), make([]float64, 3), make([]float64, 2)) }) {
+		t.Errorf("Correlation did not panic with weights length mismatch")
+	}
+}
+
+func ExampleCovariance() {
+	fmt.Println("Covariance computes the degree to which datasets move together")
+	fmt.Println("about their mean.")
+	x := []float64{8, -3, 7, 8, -4}
+	y := []float64{10, 2, 2, 4, 1}
+	cov := Covariance(x, y, nil)
+	fmt.Printf("Cov = %.4f\n", cov)
+	fmt.Println("If datasets move perfectly together, the variance equals the covariance")
+	y2 := []float64{12, 1, 11, 12, 0}
+	cov2 := Covariance(x, y2, nil)
+	varX := Variance(x, nil)
+	fmt.Printf("Cov2 is %.4f, VarX is %.4f", cov2, varX)
+	// Output:
+	// Covariance computes the degree to which datasets move together
+	// about their mean.
+	// Cov = 13.8000
+	// If datasets move perfectly together, the variance equals the covariance
+	// Cov2 is 37.7000, VarX is 37.7000
+}
+
+func TestCovariance(t *testing.T) {
+	for i, test := range []struct {
+		p       []float64
+		q       []float64
+		weights []float64
+		ans     float64
+	}{
+		{
+			p:   []float64{0.75, 0.1, 0.05},
+			q:   []float64{0.5, 0.25, 0.25},
+			ans: 0.05625,
+		},
+		{
+			p:   []float64{1, 2, 3},
+			q:   []float64{2, 4, 6},
+			ans: 2,
+		},
+		{
+			p:   []float64{1, 2, 3},
+			q:   []float64{1, 4, 9},
+			ans: 4,
+		},
+		{
+			p:       []float64{1, 2, 3},
+			q:       []float64{1, 4, 9},
+			weights: []float64{1, 1.5, 1},
+			ans:     3.2,
+		},
+		{
+			p:       []float64{1, 4, 9},
+			q:       []float64{1, 4, 9},
+			weights: []float64{1, 1.5, 1},
+			ans:     13.142857142857146,
+		},
+	} {
+		c := Covariance(test.p, test.q, test.weights)
+		if math.Abs(c-test.ans) > 1e-14 {
+			t.Errorf("Covariance mismatch case %d: Expected %v, Found %v", i, test.ans, c)
+		}
+	}
+
+	// test the panic states
+	if !Panics(func() { Covariance(make([]float64, 2), make([]float64, 3), nil) }) {
+		t.Errorf("Covariance did not panic with x, y length mismatch")
+	}
+	if !Panics(func() { Covariance(make([]float64, 3), make([]float64, 3), make([]float64, 2)) }) {
+		t.Errorf("Covariance did not panic with x, weights length mismatch")
+	}
+
+}
+
+func TestCrossEntropy(t *testing.T) {
+	for i, test := range []struct {
+		p   []float64
+		q   []float64
+		ans float64
+	}{
+		{
+			p:   []float64{0.75, 0.1, 0.05},
+			q:   []float64{0.5, 0.25, 0.25},
+			ans: 0.7278045395879426,
+		},
+		{
+			p:   []float64{0.75, 0.1, 0.05, 0, 0, 0},
+			q:   []float64{0.5, 0.25, 0.25, 0, 0, 0},
+			ans: 0.7278045395879426,
+		},
+		{
+			p:   []float64{0.75, 0.1, 0.05, 0, 0, 0.1},
+			q:   []float64{0.5, 0.25, 0.25, 0, 0, 0},
+			ans: math.Inf(1),
+		},
+		{
+			p:   nil,
+			q:   nil,
+			ans: 0,
+		},
+	} {
+		c := CrossEntropy(test.p, test.q)
+		if math.Abs(c-test.ans) > 1e-14 {
+			t.Errorf("Cross entropy mismatch case %d: Expected %v, Found %v", i, test.ans, c)
+		}
+	}
+	if !Panics(func() { CrossEntropy(make([]float64, 3), make([]float64, 2)) }) {
+		t.Errorf("CrossEntropy did not panic with p, q length mismatch")
+	}
+}
+
+func ExampleEntropy() {
+
+	p := []float64{0.05, 0.1, 0.9, 0.05}
+	entP := Entropy(p)
+
+	q := []float64{0.2, 0.4, 0.25, 0.15}
+	entQ := Entropy(q)
+
+	r := []float64{0.2, 0, 0, 0.5, 0, 0.2, 0.1, 0, 0, 0}
+	entR := Entropy(r)
+
+	s := []float64{0, 0, 1, 0}
+	entS := Entropy(s)
+
+	fmt.Println("Entropy is a measure of the amount of uncertainty in a distribution")
+	fmt.Printf("The second bin of p is very likely to occur. It's entropy is %.4f\n", entP)
+	fmt.Printf("The distribution of q is more spread out. It's entropy is %.4f\n", entQ)
+	fmt.Println("Adding buckets with zero probability does not change the entropy.")
+	fmt.Printf("The entropy of r is: %.4f\n", entR)
+	fmt.Printf("A distribution with no uncertainty has entropy %.4f\n", entS)
+	// Output:
+	// Entropy is a measure of the amount of uncertainty in a distribution
+	// The second bin of p is very likely to occur. It's entropy is 0.6247
+	// The distribution of q is more spread out. It's entropy is 1.3195
+	// Adding buckets with zero probability does not change the entropy.
+	// The entropy of r is: 1.2206
+	// A distribution with no uncertainty has entropy 0.0000
+}
+
+func ExampleExKurtosis() {
+	fmt.Println(`Kurtosis is a measure of the 'peakedness' of a distribution, and the
+excess kurtosis is the kurtosis above or below that of the standard normal
+distribution`)
+	x := []float64{5, 4, -3, -2}
+	kurt := ExKurtosis(x, nil)
+	fmt.Printf("ExKurtosis = %.5f\n", kurt)
+	weights := []float64{1, 2, 3, 5}
+	wKurt := ExKurtosis(x, weights)
+	fmt.Printf("Weighted ExKurtosis is %.4f", wKurt)
+	// Output:
+	// Kurtosis is a measure of the 'peakedness' of a distribution, and the
+	// excess kurtosis is the kurtosis above or below that of the standard normal
+	// distribution
+	// ExKurtosis = -5.41200
+	// Weighted ExKurtosis is -0.6779
+}
+
+func TestExKurtosis(t *testing.T) {
+	// the example does a good job, this just has to cover the panic
+	if !Panics(func() { ExKurtosis(make([]float64, 3), make([]float64, 2)) }) {
+		t.Errorf("ExKurtosis did not panic with x, weights length mismatch")
+	}
+}
+
+func ExampleGeometricMean() {
+	x := []float64{8, 2, 9, 15, 4}
+	weights := []float64{2, 2, 6, 7, 1}
+	mean := Mean(x, weights)
+	gmean := GeometricMean(x, weights)
+
+	logx := make([]float64, len(x))
+	for i, v := range x {
+		logx[i] = math.Log(v)
+	}
+	expMeanLog := math.Exp(Mean(logx, weights))
+	fmt.Printf("The arithmetic mean is %.4f, but the geometric mean is %.4f.\n", mean, gmean)
+	fmt.Printf("The exponential of the mean of the logs is %.4f\n", expMeanLog)
+	// Output:
+	// The arithmetic mean is 10.1667, but the geometric mean is 8.7637.
+	// The exponential of the mean of the logs is 8.7637
+}
+
+func TestGeometricMean(t *testing.T) {
+	for i, test := range []struct {
+		x   []float64
+		wts []float64
+		ans float64
+	}{
+		{
+			x:   []float64{2, 8},
+			ans: 4,
+		},
+		{
+			x:   []float64{3, 81},
+			wts: []float64{2, 1},
+			ans: 9,
+		},
+	} {
+		c := GeometricMean(test.x, test.wts)
+		if math.Abs(c-test.ans) > 1e-14 {
+			t.Errorf("Geometric mean mismatch case %d: Expected %v, Found %v", i, test.ans, c)
+		}
+	}
+	if !Panics(func() { GeometricMean(make([]float64, 3), make([]float64, 2)) }) {
+		t.Errorf("GeometricMean did not panic with x, wts length mismatch")
+	}
+}
+
+func ExampleHarmonicMean() {
+	x := []float64{8, 2, 9, 15, 4}
+	weights := []float64{2, 2, 6, 7, 1}
+	mean := Mean(x, weights)
+	hmean := HarmonicMean(x, weights)
+
+	fmt.Printf("The arithmetic mean is %.5f, but the harmonic mean is %.4f.\n", mean, hmean)
+	// Output:
+	// The arithmetic mean is 10.16667, but the harmonic mean is 6.8354.
+}
+
+func TestHarmonicMean(t *testing.T) {
+	for i, test := range []struct {
+		x   []float64
+		wts []float64
+		ans float64
+	}{
+		{
+			x:   []float64{.5, .125},
+			ans: .2,
+		},
+		{
+			x:   []float64{.5, .125},
+			wts: []float64{2, 1},
+			ans: .25,
+		},
+	} {
+		c := HarmonicMean(test.x, test.wts)
+		if math.Abs(c-test.ans) > 1e-14 {
+			t.Errorf("Harmonic mean mismatch case %d: Expected %v, Found %v", i, test.ans, c)
+		}
+	}
+	if !Panics(func() { HarmonicMean(make([]float64, 3), make([]float64, 2)) }) {
+		t.Errorf("HarmonicMean did not panic with x, wts length mismatch")
+	}
+}
+
+func TestHistogram(t *testing.T) {
+	for i, test := range []struct {
+		x        []float64
+		weights  []float64
+		dividers []float64
+		ans      []float64
+	}{
+		{
+			x:        []float64{1, 3, 5, 6, 7, 8},
+			dividers: []float64{0, 2, 4, 6, 7, 9},
+			ans:      []float64{1, 1, 1, 1, 2},
+		},
+		{
+			x:        []float64{1, 3, 5, 6, 7, 8},
+			dividers: []float64{1, 2, 4, 6, 7, 9},
+			weights:  []float64{1, 2, 1, 1, 1, 2},
+			ans:      []float64{1, 2, 1, 1, 3},
+		},
+		{
+			x:        []float64{1, 8},
+			dividers: []float64{0, 2, 4, 6, 7, 9},
+			weights:  []float64{1, 2},
+			ans:      []float64{1, 0, 0, 0, 2},
+		},
+		{
+			x:        []float64{1, 8},
+			dividers: []float64{0, 2, 4, 6, 7, 9},
+			ans:      []float64{1, 0, 0, 0, 1},
+		},
+		{
+			x:        []float64{},
+			dividers: []float64{1, 3},
+			ans:      []float64{0},
+		},
+	} {
+		hist := Histogram(nil, test.dividers, test.x, test.weights)
+		if !floats.Equal(hist, test.ans) {
+			t.Errorf("Hist mismatch case %d. Expected %v, Found %v", i, test.ans, hist)
+		}
+		// Test with non-zero values
+		Histogram(hist, test.dividers, test.x, test.weights)
+		if !floats.Equal(hist, test.ans) {
+			t.Errorf("Hist mismatch case %d. Expected %v, Found %v", i, test.ans, hist)
+		}
+	}
+	// panic cases
+	for _, test := range []struct {
+		name     string
+		x        []float64
+		weights  []float64
+		dividers []float64
+		count    []float64
+	}{
+		{
+			name:    "len(x) != len(weights)",
+			x:       []float64{1, 3, 5, 6, 7, 8},
+			weights: []float64{1, 1, 1, 1},
+		},
+		{
+			name:     "len(count) != len(dividers) - 1",
+			x:        []float64{1, 3, 5, 6, 7, 8},
+			dividers: []float64{1, 4, 9},
+			count:    make([]float64, 6),
+		},
+		{
+			name:     "dividers not sorted",
+			x:        []float64{1, 3, 5, 6, 7, 8},
+			dividers: []float64{0, -1, 0},
+		},
+		{
+			name:     "x not sorted",
+			x:        []float64{1, 5, 2, 9, 7, 8},
+			dividers: []float64{1, 4, 9},
+		},
+		{
+			name:     "fewer than 2 dividers",
+			x:        []float64{1, 2, 3},
+			dividers: []float64{5},
+		},
+		{
+			name:     "x too large",
+			x:        []float64{1, 2, 3},
+			dividers: []float64{1, 3},
+		},
+		{
+			name:     "x too small",
+			x:        []float64{1, 2, 3},
+			dividers: []float64{2, 3},
+		},
+	} {
+		if !Panics(func() { Histogram(test.count, test.dividers, test.x, test.weights) }) {
+			t.Errorf("Histogram did not panic when %s", test.name)
+		}
+	}
+}
+
+func ExampleHistogram() {
+	x := make([]float64, 101)
+	for i := range x {
+		x[i] = 1.1 * float64(i) // x data ranges from 0 to 110
+	}
+	dividers := []float64{0, 7, 20, 100, 1000}
+	fmt.Println(`Histogram counts the amount of data in the bins specified by
+the dividers. In this data set, there are 7 data points less than 7 (between dividers[0]
+and dividers[1]), 12 data points between 7 and 20 (dividers[1] and dividers[2]),
+and 0 data points above 1000. Since dividers has length 5, there will be 4 bins.`)
+	hist := Histogram(nil, dividers, x, nil)
+	fmt.Printf("Hist = %v\n", hist)
+
+	fmt.Println()
+	fmt.Println("For ease, the floats Span function can be used to set the dividers")
+	nBins := 10
+	dividers = make([]float64, nBins+1)
+	min := floats.Min(x)
+	max := floats.Max(x)
+	// Increase the maximum divider so that the maximum value of x is contained
+	// within the last bucket.
+	max += 1
+	floats.Span(dividers, min, max)
+	// Span includes the min and the max. Trim the dividers to create 10 buckets
+	hist = Histogram(nil, dividers, x, nil)
+	fmt.Printf("Hist = %v\n", hist)
+	fmt.Println()
+	fmt.Println(`Histogram also works with weighted data, and allows reusing of
+the count field in order to avoid extra garbage`)
+	weights := make([]float64, len(x))
+	for i := range weights {
+		weights[i] = float64(i + 1)
+	}
+	Histogram(hist, dividers, x, weights)
+	fmt.Printf("Weighted Hist = %v\n", hist)
+
+	// Output:
+	// Histogram counts the amount of data in the bins specified by
+	// the dividers. In this data set, there are 7 data points less than 7 (between dividers[0]
+	// and dividers[1]), 12 data points between 7 and 20 (dividers[1] and dividers[2]),
+	// and 0 data points above 1000. Since dividers has length 5, there will be 4 bins.
+	// Hist = [7 12 72 10]
+	//
+	// For ease, the floats Span function can be used to set the dividers
+	// Hist = [11 10 10 10 10 10 10 10 10 10]
+	//
+	// Histogram also works with weighted data, and allows reusing of
+	// the count field in order to avoid extra garbage
+	// Weighted Hist = [66 165 265 365 465 565 665 765 865 965]
+}
+
+func TestJensenShannon(t *testing.T) {
+	for i, test := range []struct {
+		p []float64
+		q []float64
+	}{
+		{
+			p: []float64{0.5, 0.1, 0.3, 0.1},
+			q: []float64{0.1, 0.4, 0.25, 0.25},
+		},
+		{
+			p: []float64{0.4, 0.6, 0.0},
+			q: []float64{0.2, 0.2, 0.6},
+		},
+		{
+			p: []float64{0.1, 0.1, 0.0, 0.8},
+			q: []float64{0.6, 0.3, 0.0, 0.1},
+		},
+		{
+			p: []float64{0.5, 0.1, 0.3, 0.1},
+			q: []float64{0.5, 0, 0.25, 0.25},
+		},
+		{
+			p: []float64{0.5, 0.1, 0, 0.4},
+			q: []float64{0.1, 0.4, 0.25, 0.25},
+		},
+	} {
+
+		m := make([]float64, len(test.p))
+		p := test.p
+		q := test.q
+		floats.Add(m, p)
+		floats.Add(m, q)
+		floats.Scale(0.5, m)
+
+		js1 := 0.5*KullbackLeibler(p, m) + 0.5*KullbackLeibler(q, m)
+		js2 := JensenShannon(p, q)
+
+		if math.IsNaN(js2) {
+			t.Errorf("In case %v, JS distance is NaN", i)
+		}
+
+		if math.Abs(js1-js2) > 1e-14 {
+			t.Errorf("JS mismatch case %v. Expected %v, found %v.", i, js1, js2)
+		}
+	}
+	if !Panics(func() { JensenShannon(make([]float64, 3), make([]float64, 2)) }) {
+		t.Errorf("JensenShannon did not panic with p, q length mismatch")
+	}
+}
+
+func TestKolmogorovSmirnov(t *testing.T) {
+	for i, test := range []struct {
+		x        []float64
+		xWeights []float64
+		y        []float64
+		yWeights []float64
+		dist     float64
+	}{
+
+		{
+			dist: 0,
+		},
+		{
+			x:    []float64{1},
+			dist: 1,
+		},
+		{
+			y:    []float64{1},
+			dist: 1,
+		},
+		{
+			x:        []float64{1},
+			xWeights: []float64{8},
+			dist:     1,
+		},
+		{
+			y:        []float64{1},
+			yWeights: []float64{8},
+			dist:     1,
+		},
+		{
+			x:        []float64{1},
+			xWeights: []float64{8},
+			y:        []float64{1},
+			yWeights: []float64{8},
+			dist:     0,
+		},
+		{
+			x:        []float64{1, 1, 1},
+			xWeights: []float64{2, 3, 7},
+			y:        []float64{1},
+			yWeights: []float64{8},
+			dist:     0,
+		},
+		{
+			x:        []float64{1, 1, 1, 1, 1},
+			y:        []float64{1, 1, 1},
+			yWeights: []float64{2, 5, 2},
+			dist:     0,
+		},
+
+		{
+			x:    []float64{1, 2, 3},
+			y:    []float64{1, 2, 3},
+			dist: 0,
+		},
+		{
+			x:        []float64{1, 2, 3},
+			y:        []float64{1, 2, 3},
+			yWeights: []float64{1, 1, 1},
+			dist:     0,
+		},
+
+		{
+			x:        []float64{1, 2, 3},
+			xWeights: []float64{1, 1, 1},
+			y:        []float64{1, 2, 3},
+			yWeights: []float64{1, 1, 1},
+			dist:     0,
+		},
+		{
+			x:        []float64{1, 2},
+			xWeights: []float64{2, 5},
+			y:        []float64{1, 1, 2, 2, 2, 2, 2},
+			dist:     0,
+		},
+		{
+			x:        []float64{1, 1, 2, 2, 2, 2, 2},
+			y:        []float64{1, 2},
+			yWeights: []float64{2, 5},
+			dist:     0,
+		},
+		{
+			x:        []float64{1, 1, 2, 2, 2},
+			xWeights: []float64{0.5, 1.5, 1, 2, 2},
+			y:        []float64{1, 2},
+			yWeights: []float64{2, 5},
+			dist:     0,
+		},
+		{
+			x:    []float64{1, 2, 3, 4},
+			y:    []float64{5, 6},
+			dist: 1,
+		},
+		{
+			x:    []float64{5, 6},
+			y:    []float64{1, 2, 3, 4},
+			dist: 1,
+		},
+		{
+			x:        []float64{5, 6},
+			xWeights: []float64{8, 7},
+			y:        []float64{1, 2, 3, 4},
+			dist:     1,
+		},
+		{
+			x:        []float64{5, 6},
+			xWeights: []float64{8, 7},
+			y:        []float64{1, 2, 3, 4},
+			yWeights: []float64{9, 2, 1, 6},
+			dist:     1,
+		},
+		{
+			x:        []float64{-4, 5, 6},
+			xWeights: []float64{0, 8, 7},
+			y:        []float64{1, 2, 3, 4},
+			yWeights: []float64{9, 2, 1, 6},
+			dist:     1,
+		},
+		{
+			x:        []float64{-4, -2, -2, 5, 6},
+			xWeights: []float64{0, 0, 0, 8, 7},
+			y:        []float64{1, 2, 3, 4},
+			yWeights: []float64{9, 2, 1, 6},
+			dist:     1,
+		},
+		{
+			x:    []float64{1, 2, 3},
+			y:    []float64{1, 1, 3},
+			dist: 1.0 / 3.0,
+		},
+		{
+			x:        []float64{1, 2, 3},
+			y:        []float64{1, 3},
+			yWeights: []float64{2, 1},
+			dist:     1.0 / 3.0,
+		},
+		{
+			x:        []float64{1, 2, 3},
+			xWeights: []float64{2, 2, 2},
+			y:        []float64{1, 3},
+			yWeights: []float64{2, 1},
+			dist:     1.0 / 3.0,
+		},
+		{
+			x:    []float64{2, 3, 4},
+			y:    []float64{1, 5},
+			dist: 1.0 / 2.0,
+		},
+		{
+			x:    []float64{1, 2, math.NaN()},
+			y:    []float64{1, 1, 3},
+			dist: math.NaN(),
+		},
+		{
+			x:    []float64{1, 2, 3},
+			y:    []float64{1, 1, math.NaN()},
+			dist: math.NaN(),
+		},
+	} {
+		dist := KolmogorovSmirnov(test.x, test.xWeights, test.y, test.yWeights)
+		if math.Abs(dist-test.dist) > 1e-14 && !(math.IsNaN(test.dist) && math.IsNaN(dist)) {
+			t.Errorf("Distance mismatch case %v: Expected: %v, Found: %v", i, test.dist, dist)
+		}
+	}
+	// panic cases
+	for _, test := range []struct {
+		name     string
+		x        []float64
+		xWeights []float64
+		y        []float64
+		yWeights []float64
+	}{
+		{
+			name:     "len(x) != len(xWeights)",
+			x:        []float64{1, 3, 5, 6, 7, 8},
+			xWeights: []float64{1, 1, 1, 1},
+		},
+		{
+			name:     "len(y) != len(yWeights)",
+			x:        []float64{1, 3, 5, 6, 7, 8},
+			y:        []float64{1, 3, 5, 6, 7, 8},
+			yWeights: []float64{1, 1, 1, 1},
+		},
+		{
+			name: "x not sorted",
+			x:    []float64{10, 3, 5, 6, 7, 8},
+			y:    []float64{1, 3, 5, 6, 7, 8},
+		},
+		{
+			name: "y not sorted",
+			x:    []float64{1, 3, 5, 6, 7, 8},
+			y:    []float64{10, 3, 5, 6, 7, 8},
+		},
+	} {
+		if !Panics(func() { KolmogorovSmirnov(test.x, test.xWeights, test.y, test.yWeights) }) {
+			t.Errorf("KolmogorovSmirnov did not panic when %s", test.name)
+		}
+	}
+}
+
+func ExampleKullbackLeibler() {
+
+	p := []float64{0.05, 0.1, 0.9, 0.05}
+	q := []float64{0.2, 0.4, 0.25, 0.15}
+	s := []float64{0, 0, 1, 0}
+
+	klPQ := KullbackLeibler(p, q)
+	klPS := KullbackLeibler(p, s)
+	klPP := KullbackLeibler(p, p)
+
+	fmt.Println("Kullback-Leibler is one measure of the difference between two distributions")
+	fmt.Printf("The K-L distance between p and q is %.4f\n", klPQ)
+	fmt.Println("It is impossible for s and p to be the same distribution, because")
+	fmt.Println("the first bucket has zero probability in s and non-zero in p. Thus,")
+	fmt.Printf("the K-L distance between them is %.4f\n", klPS)
+	fmt.Printf("The K-L distance between identical distributions is %.4f\n", klPP)
+
+	// Kullback-Leibler is one measure of the difference between two distributions
+	// The K-L distance between p and q is 0.8900
+	// It is impossible for s and p to be the same distribution, because
+	// the first bucket has zero probability in s and non-zero in p. Thus,
+	// the K-L distance between them is +Inf
+	// The K-L distance between identical distributions is 0.0000
+}
+
+func TestKullbackLeibler(t *testing.T) {
+	if !Panics(func() { KullbackLeibler(make([]float64, 3), make([]float64, 2)) }) {
+		t.Errorf("KullbackLeibler did not panic with p, q length mismatch")
+	}
+}
+
+var linearRegressionTests = []struct {
+	name string
+
+	x, y    []float64
+	weights []float64
+	origin  bool
+
+	alpha float64
+	beta  float64
+	r     float64
+
+	tol float64
+}{
+	{
+		name: "faithful",
+
+		x: faithful.waiting,
+		y: faithful.eruptions,
+
+		// Values calculated by R using lm(eruptions ~ waiting, data=faithful).
+		alpha: -1.87402,
+		beta:  0.07563,
+		r:     0.8114608,
+
+		tol: 1e-5,
+	},
+	{
+		name: "faithful through origin",
+
+		x:      faithful.waiting,
+		y:      faithful.eruptions,
+		origin: true,
+
+		// Values calculated by R using lm(eruptions ~ waiting - 1, data=faithful).
+		alpha: 0,
+		beta:  0.05013,
+		r:     0.9726036,
+
+		tol: 1e-5,
+	},
+	{
+		name: "faithful explicit weights",
+
+		x: faithful.waiting,
+		y: faithful.eruptions,
+		weights: func() []float64 {
+			w := make([]float64, len(faithful.eruptions))
+			for i := range w {
+				w[i] = 1
+			}
+			return w
+		}(),
+
+		// Values calculated by R using lm(eruptions ~ waiting, data=faithful).
+		alpha: -1.87402,
+		beta:  0.07563,
+		r:     0.8114608,
+
+		tol: 1e-5,
+	},
+	{
+		name: "faithful non-uniform weights",
+
+		x:       faithful.waiting,
+		y:       faithful.eruptions,
+		weights: faithful.waiting, // Just an arbitrary set of non-uniform weights.
+
+		// Values calculated by R using lm(eruptions ~ waiting, data=faithful, weights=faithful$waiting).
+		alpha: -1.79268,
+		beta:  0.07452,
+		r:     0.7840372,
+
+		tol: 1e-5,
+	},
+}
+
+func TestLinearRegression(t *testing.T) {
+	for _, test := range linearRegressionTests {
+		alpha, beta := LinearRegression(test.x, test.y, test.weights, test.origin)
+		var r float64
+		if test.origin {
+			r = RNoughtSquared(test.x, test.y, test.weights, beta)
+		} else {
+			r = RSquared(test.x, test.y, test.weights, alpha, beta)
+			ests := make([]float64, len(test.y))
+			for i, x := range test.x {
+				ests[i] = alpha + beta*x
+			}
+			rvals := RSquaredFrom(ests, test.y, test.weights)
+			if r != rvals {
+				t.Errorf("%s: RSquared and RSquaredFrom mismatch: %v != %v", test.name, r, rvals)
+			}
+		}
+		if !floats.EqualWithinAbsOrRel(alpha, test.alpha, test.tol, test.tol) {
+			t.Errorf("%s: unexpected alpha estimate: want:%v got:%v", test.name, test.alpha, alpha)
+		}
+		if !floats.EqualWithinAbsOrRel(beta, test.beta, test.tol, test.tol) {
+			t.Errorf("%s: unexpected beta estimate: want:%v got:%v", test.name, test.beta, beta)
+		}
+		if !floats.EqualWithinAbsOrRel(r, test.r, test.tol, test.tol) {
+			t.Errorf("%s: unexpected r estimate: want:%v got:%v", test.name, test.r, r)
+		}
+	}
+}
+
+func TestChiSquare(t *testing.T) {
+	for i, test := range []struct {
+		p   []float64
+		q   []float64
+		res float64
+	}{
+		{
+			p:   []float64{16, 18, 16, 14, 12, 12},
+			q:   []float64{16, 16, 16, 16, 16, 8},
+			res: 3.5,
+		},
+		{
+			p:   []float64{16, 18, 16, 14, 12, 12},
+			q:   []float64{8, 20, 20, 16, 12, 12},
+			res: 9.25,
+		},
+		{
+			p:   []float64{40, 60, 30, 45},
+			q:   []float64{50, 50, 50, 50},
+			res: 12.5,
+		},
+		{
+			p:   []float64{40, 60, 30, 45, 0, 0},
+			q:   []float64{50, 50, 50, 50, 0, 0},
+			res: 12.5,
+		},
+	} {
+		resultpq := ChiSquare(test.p, test.q)
+
+		if math.Abs(resultpq-test.res) > 1e-10 {
+			t.Errorf("ChiSquare distance mismatch in case %d. Expected %v, Found %v", i, test.res, resultpq)
+		}
+	}
+	if !Panics(func() { ChiSquare(make([]float64, 2), make([]float64, 3)) }) {
+		t.Errorf("ChiSquare did not panic with length mismatch")
+	}
+}
+
+// Panics returns true if the called function panics during evaluation.
+func Panics(fun func()) (b bool) {
+	defer func() {
+		err := recover()
+		if err != nil {
+			b = true
+		}
+	}()
+	fun()
+	return
+}
+
+func TestBhattacharyya(t *testing.T) {
+	for i, test := range []struct {
+		p   []float64
+		q   []float64
+		res float64
+	}{
+		{
+			p:   []float64{0.5, 0.1, 0.3, 0.1},
+			q:   []float64{0.1, 0.4, 0.25, 0.25},
+			res: 0.15597338718671386,
+		},
+		{
+			p:   []float64{0.4, 0.6, 0.0},
+			q:   []float64{0.2, 0.2, 0.6},
+			res: 0.46322207765351153,
+		},
+		{
+			p:   []float64{0.1, 0.1, 0.0, 0.8},
+			q:   []float64{0.6, 0.3, 0.0, 0.1},
+			res: 0.3552520032137785,
+		},
+	} {
+		resultpq := Bhattacharyya(test.p, test.q)
+		resultqp := Bhattacharyya(test.q, test.p)
+
+		if math.Abs(resultpq-test.res) > 1e-10 {
+			t.Errorf("Bhattacharyya distance mismatch in case %d. Expected %v, Found %v", i, test.res, resultpq)
+		}
+		if math.Abs(resultpq-resultqp) > 1e-10 {
+			t.Errorf("Bhattacharyya distance is assymmetric in case %d.", i)
+		}
+	}
+	// Bhattacharyya should panic if the inputs have different length
+	if !Panics(func() { Bhattacharyya(make([]float64, 2), make([]float64, 3)) }) {
+		t.Errorf("Bhattacharyya did not panic with length mismatch")
+	}
+}
+
+func TestHellinger(t *testing.T) {
+	for i, test := range []struct {
+		p   []float64
+		q   []float64
+		res float64
+	}{
+		{
+			p:   []float64{0.5, 0.1, 0.3, 0.1},
+			q:   []float64{0.1, 0.4, 0.25, 0.25},
+			res: 0.3800237367441919,
+		},
+		{
+			p:   []float64{0.4, 0.6, 0.0},
+			q:   []float64{0.2, 0.2, 0.6},
+			res: 0.6088900771170487,
+		},
+		{
+			p:   []float64{0.1, 0.1, 0.0, 0.8},
+			q:   []float64{0.6, 0.3, 0.0, 0.1},
+			res: 0.5468118803484205,
+		},
+	} {
+		resultpq := Hellinger(test.p, test.q)
+		resultqp := Hellinger(test.q, test.p)
+
+		if math.Abs(resultpq-test.res) > 1e-10 {
+			t.Errorf("Hellinger distance mismatch in case %d. Expected %v, Found %v", i, test.res, resultpq)
+		}
+		if math.Abs(resultpq-resultqp) > 1e-10 {
+			t.Errorf("Hellinger distance is assymmetric in case %d.", i)
+		}
+	}
+	if !Panics(func() { Hellinger(make([]float64, 2), make([]float64, 3)) }) {
+		t.Errorf("Hellinger did not panic with length mismatch")
+	}
+}
+
+func ExampleMean() {
+	x := []float64{8.2, -6, 5, 7}
+	mean := Mean(x, nil)
+	fmt.Printf("The mean of the samples is %.4f\n", mean)
+	w := []float64{2, 6, 3, 5}
+	weightedMean := Mean(x, w)
+	fmt.Printf("The weighted mean of the samples is %.4f\n", weightedMean)
+	x2 := []float64{8.2, 8.2, -6, -6, -6, -6, -6, -6, 5, 5, 5, 7, 7, 7, 7, 7}
+	mean2 := Mean(x2, nil)
+	fmt.Printf("The mean of x2 is %.4f\n", mean2)
+	fmt.Println("The weights act as if there were more samples of that number")
+	// Output:
+	// The mean of the samples is 3.5500
+	// The weighted mean of the samples is 1.9000
+	// The mean of x2 is 1.9000
+	// The weights act as if there were more samples of that number
+}
+func TestMean(t *testing.T) {
+	if !Panics(func() { Mean(make([]float64, 3), make([]float64, 2)) }) {
+		t.Errorf("Mean did not panic with x, weights length mismatch")
+	}
+}
+
+func TestMode(t *testing.T) {
+	for i, test := range []struct {
+		x       []float64
+		weights []float64
+		ans     float64
+		count   float64
+	}{
+		{},
+		{
+			x:     []float64{1, 6, 1, 9, -2},
+			ans:   1,
+			count: 2,
+		},
+		{
+			x:       []float64{1, 6, 1, 9, -2},
+			weights: []float64{1, 7, 3, 5, 0},
+			ans:     6,
+			count:   7,
+		},
+	} {
+		m, count := Mode(test.x, test.weights)
+		if test.ans != m {
+			t.Errorf("Mode mismatch case %d. Expected %v, found %v", i, test.ans, m)
+		}
+		if test.count != count {
+			t.Errorf("Mode count mismatch case %d. Expected %v, found %v", i, test.count, count)
+		}
+	}
+	if !Panics(func() { Mode(make([]float64, 3), make([]float64, 2)) }) {
+		t.Errorf("Mode did not panic with x, weights length mismatch")
+	}
+}
+
+func TestMoment(t *testing.T) {
+	for i, test := range []struct {
+		x       []float64
+		weights []float64
+		moment  float64
+		ans     float64
+	}{
+		{
+			x:      []float64{6, 2, 4, 8, 10},
+			moment: 5,
+			ans:    0,
+		},
+		{
+			x:       []float64{6, 2, 4, 8, 10},
+			weights: []float64{1, 2, 2, 2, 1},
+			moment:  5,
+			ans:     121.875,
+		},
+	} {
+		m := Moment(test.moment, test.x, test.weights)
+		if math.Abs(test.ans-m) > 1e-14 {
+			t.Errorf("Moment mismatch case %d. Expected %v, found %v", i, test.ans, m)
+		}
+	}
+	if !Panics(func() { Moment(1, make([]float64, 3), make([]float64, 2)) }) {
+		t.Errorf("Moment did not panic with x, weights length mismatch")
+	}
+}
+
+func TestMomentAbout(t *testing.T) {
+	for i, test := range []struct {
+		x       []float64
+		weights []float64
+		moment  float64
+		mean    float64
+		ans     float64
+	}{
+		{
+			x:      []float64{6, 2, 4, 8, 9},
+			mean:   3,
+			moment: 5,
+			ans:    2.2288e3,
+		},
+		{
+			x:       []float64{6, 2, 4, 8, 9},
+			weights: []float64{1, 2, 2, 2, 1},
+			mean:    3,
+			moment:  5,
+			ans:     1.783625e3,
+		},
+	} {
+		m := MomentAbout(test.moment, test.x, test.mean, test.weights)
+		if math.Abs(test.ans-m) > 1e-14 {
+			t.Errorf("MomentAbout mismatch case %d. Expected %v, found %v", i, test.ans, m)
+		}
+	}
+	if !Panics(func() { MomentAbout(1, make([]float64, 3), 0, make([]float64, 2)) }) {
+		t.Errorf("MomentAbout did not panic with x, weights length mismatch")
+	}
+}
+
+func TestCDF(t *testing.T) {
+	cumulantKinds := []CumulantKind{Empirical}
+	for i, test := range []struct {
+		q       []float64
+		x       []float64
+		weights []float64
+		ans     [][]float64
+	}{
+		{},
+		{
+			q:   []float64{0, 0.9, 1, 1.1, 2.9, 3, 3.1, 4.9, 5, 5.1},
+			x:   []float64{1, 2, 3, 4, 5},
+			ans: [][]float64{{0, 0, 0.2, 0.2, 0.4, 0.6, 0.6, 0.8, 1, 1}},
+		},
+		{
+			q:       []float64{0, 0.9, 1, 1.1, 2.9, 3, 3.1, 4.9, 5, 5.1},
+			x:       []float64{1, 2, 3, 4, 5},
+			weights: []float64{1, 1, 1, 1, 1},
+			ans:     [][]float64{{0, 0, 0.2, 0.2, 0.4, 0.6, 0.6, 0.8, 1, 1}},
+		},
+		{
+			q:   []float64{0, 0.9, 1},
+			x:   []float64{math.NaN()},
+			ans: [][]float64{{math.NaN(), math.NaN(), math.NaN()}},
+		},
+	} {
+		copyX := make([]float64, len(test.x))
+		copy(copyX, test.x)
+		var copyW []float64
+		if test.weights != nil {
+			copyW = make([]float64, len(test.weights))
+			copy(copyW, test.weights)
+		}
+		for j, q := range test.q {
+			for k, kind := range cumulantKinds {
+				v := CDF(q, kind, test.x, test.weights)
+				if !floats.Equal(copyX, test.x) && !math.IsNaN(v) {
+					t.Errorf("x changed for case %d kind %d percentile %v", i, k, q)
+				}
+				if !floats.Equal(copyW, test.weights) {
+					t.Errorf("x changed for case %d kind %d percentile %v", i, k, q)
+				}
+				if v != test.ans[k][j] && !(math.IsNaN(v) && math.IsNaN(test.ans[k][j])) {
+					t.Errorf("mismatch case %d kind %d percentile %v. Expected: %v, found: %v", i, k, q, test.ans[k][j], v)
+				}
+			}
+		}
+	}
+
+	// these test cases should all result in a panic
+	for i, test := range []struct {
+		name    string
+		q       float64
+		kind    CumulantKind
+		x       []float64
+		weights []float64
+	}{
+		{
+			name:    "len(x) != len(weights)",
+			q:       1.5,
+			kind:    Empirical,
+			x:       []float64{1, 2, 3, 4, 5},
+			weights: []float64{1, 2, 3},
+		},
+		{
+			name: "unsorted x",
+			q:    1.5,
+			kind: Empirical,
+			x:    []float64{3, 2, 1},
+		},
+		{
+			name: "unknown CumulantKind",
+			q:    1.5,
+			kind: CumulantKind(1000), // bogus
+			x:    []float64{1, 2, 3},
+		},
+	} {
+		if !Panics(func() { CDF(test.q, test.kind, test.x, test.weights) }) {
+			t.Errorf("did not panic as expected with %s for case %d kind %d percentile %v x %v weights %v", test.name, i, test.kind, test.q, test.x, test.weights)
+		}
+	}
+
+}
+
+func TestQuantile(t *testing.T) {
+	cumulantKinds := []CumulantKind{Empirical}
+	for i, test := range []struct {
+		p   []float64
+		x   []float64
+		w   []float64
+		ans [][]float64
+	}{
+		{
+			p:   []float64{0, 0.05, 0.1, 0.15, 0.45, 0.5, 0.55, 0.85, 0.9, 0.95, 1},
+			x:   []float64{1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
+			w:   nil,
+			ans: [][]float64{{1, 1, 1, 2, 5, 5, 6, 9, 9, 10, 10}},
+		},
+		{
+			p:   []float64{0, 0.05, 0.1, 0.15, 0.45, 0.5, 0.55, 0.85, 0.9, 0.95, 1},
+			x:   []float64{1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
+			w:   []float64{3, 3, 3, 3, 3, 3, 3, 3, 3, 3},
+			ans: [][]float64{{1, 1, 1, 2, 5, 5, 6, 9, 9, 10, 10}},
+		},
+		{
+			p:   []float64{0.5},
+			x:   []float64{1, 2, 3, 4, 5, 6, 7, 8, math.NaN(), 10},
+			ans: [][]float64{{math.NaN()}},
+		},
+	} {
+		copyX := make([]float64, len(test.x))
+		copy(copyX, test.x)
+		var copyW []float64
+		if test.w != nil {
+			copyW = make([]float64, len(test.w))
+			copy(copyW, test.w)
+		}
+		for j, p := range test.p {
+			for k, kind := range cumulantKinds {
+				v := Quantile(p, kind, test.x, test.w)
+				if !floats.Same(copyX, test.x) {
+					t.Errorf("x changed for case %d kind %d percentile %v", i, k, p)
+				}
+				if !floats.Same(copyW, test.w) {
+					t.Errorf("x changed for case %d kind %d percentile %v", i, k, p)
+				}
+				if v != test.ans[k][j] && !(math.IsNaN(v) && math.IsNaN(test.ans[k][j])) {
+					t.Errorf("mismatch case %d kind %d percentile %v. Expected: %v, found: %v", i, k, p, test.ans[k][j], v)
+				}
+			}
+		}
+	}
+	// panic cases
+	for _, test := range []struct {
+		name string
+		p    float64
+		c    CumulantKind
+		x    []float64
+		w    []float64
+	}{
+		{
+			name: "p < 0",
+			c:    Empirical,
+			p:    -1,
+		},
+		{
+			name: "p > 1",
+			c:    Empirical,
+			p:    2,
+		},
+		{
+			name: "p is NaN",
+			c:    Empirical,
+			p:    math.NaN(),
+		},
+		{
+			name: "len(x) != len(weights)",
+			c:    Empirical,
+			p:    .5,
+			x:    make([]float64, 4),
+			w:    make([]float64, 2),
+		},
+		{
+			name: "x not sorted",
+			c:    Empirical,
+			p:    .5,
+			x:    []float64{3, 2, 1},
+		},
+		{
+			name: "CumulantKind is unknown",
+			c:    CumulantKind(1000),
+			p:    .5,
+			x:    []float64{1, 2, 3},
+		},
+	} {
+		if !Panics(func() { Quantile(test.p, test.c, test.x, test.w) }) {
+			t.Errorf("Quantile did not panic when %s", test.name)
+		}
+	}
+}
+
+func ExampleStdDev() {
+	x := []float64{8, 2, -9, 15, 4}
+	stdev := StdDev(x, nil)
+	fmt.Printf("The standard deviation of the samples is %.4f\n", stdev)
+
+	weights := []float64{2, 2, 6, 7, 1}
+	weightedStdev := StdDev(x, weights)
+	fmt.Printf("The weighted standard deviation of the samples is %.4f\n", weightedStdev)
+	// Output:
+	// The standard deviation of the samples is 8.8034
+	// The weighted standard deviation of the samples is 10.5733
+}
+
+func ExampleStdErr() {
+	x := []float64{8, 2, -9, 15, 4}
+	weights := []float64{2, 2, 6, 7, 1}
+	mean := Mean(x, weights)
+	stdev := StdDev(x, weights)
+	nSamples := floats.Sum(weights)
+	stdErr := StdErr(stdev, nSamples)
+	fmt.Printf("The standard deviation is %.4f and there are %g samples, so the mean\nis likely %.4f ± %.4f.", stdev, nSamples, mean, stdErr)
+	// Output:
+	// The standard deviation is 10.5733 and there are 18 samples, so the mean
+	// is likely 4.1667 ± 2.4921.
+}
+
+func TestSkew(t *testing.T) {
+	for i, test := range []struct {
+		x       []float64
+		weights []float64
+		ans     float64
+	}{
+		{
+			x:       []float64{8, 3, 7, 8, 4},
+			weights: nil,
+			ans:     -0.581456499151665,
+		},
+		{
+			x:       []float64{8, 3, 7, 8, 4},
+			weights: []float64{1, 1, 1, 1, 1},
+			ans:     -0.581456499151665,
+		},
+		{
+			x:       []float64{8, 3, 7, 8, 4},
+			weights: []float64{2, 1, 2, 1, 1},
+			ans:     -1.12066646837198,
+		},
+	} {
+		skew := Skew(test.x, test.weights)
+		if math.Abs(skew-test.ans) > 1e-14 {
+			t.Errorf("Skew mismatch case %d. Expected %v, Found %v", i, test.ans, skew)
+		}
+	}
+	if !Panics(func() { Skew(make([]float64, 3), make([]float64, 2)) }) {
+		t.Errorf("Skew did not panic with x, weights length mismatch")
+	}
+}
+
+func TestSortWeighted(t *testing.T) {
+	for i, test := range []struct {
+		x    []float64
+		w    []float64
+		ansx []float64
+		answ []float64
+	}{
+		{
+			x:    []float64{8, 3, 7, 8, 4},
+			ansx: []float64{3, 4, 7, 8, 8},
+		},
+		{
+			x:    []float64{8, 3, 7, 8, 4},
+			w:    []float64{.5, 1, 1, .5, 1},
+			ansx: []float64{3, 4, 7, 8, 8},
+			answ: []float64{1, 1, 1, .5, .5},
+		},
+	} {
+		SortWeighted(test.x, test.w)
+		if !floats.Same(test.x, test.ansx) {
+			t.Errorf("SortWeighted mismatch case %d. Expected x %v, Found x %v", i, test.ansx, test.x)
+		}
+		if !(test.w == nil) && !floats.Same(test.w, test.answ) {
+			t.Errorf("SortWeighted mismatch case %d. Expected w %v, Found w %v", i, test.answ, test.w)
+		}
+	}
+	if !Panics(func() { SortWeighted(make([]float64, 3), make([]float64, 2)) }) {
+		t.Errorf("SortWeighted did not panic with x, weights length mismatch")
+	}
+}
+
+func TestSortWeightedLabeled(t *testing.T) {
+	for i, test := range []struct {
+		x    []float64
+		l    []bool
+		w    []float64
+		ansx []float64
+		ansl []bool
+		answ []float64
+	}{
+		{
+			x:    []float64{8, 3, 7, 8, 4},
+			ansx: []float64{3, 4, 7, 8, 8},
+		},
+		{
+			x:    []float64{8, 3, 7, 8, 4},
+			w:    []float64{.5, 1, 1, .5, 1},
+			ansx: []float64{3, 4, 7, 8, 8},
+			answ: []float64{1, 1, 1, .5, .5},
+		},
+		{
+			x:    []float64{8, 3, 7, 8, 4},
+			l:    []bool{false, false, true, false, true},
+			ansx: []float64{3, 4, 7, 8, 8},
+			ansl: []bool{false, true, true, false, false},
+		},
+		{
+			x:    []float64{8, 3, 7, 8, 4},
+			l:    []bool{false, false, true, false, true},
+			w:    []float64{.5, 1, 1, .5, 1},
+			ansx: []float64{3, 4, 7, 8, 8},
+			ansl: []bool{false, true, true, false, false},
+			answ: []float64{1, 1, 1, .5, .5},
+		},
+	} {
+		SortWeightedLabeled(test.x, test.l, test.w)
+		if !floats.Same(test.x, test.ansx) {
+			t.Errorf("SortWeightedLabelled mismatch case %d. Expected x %v, Found x %v", i, test.ansx, test.x)
+		}
+		if (test.l != nil) && !reflect.DeepEqual(test.l, test.ansl) {
+			t.Errorf("SortWeightedLabelled mismatch case %d. Expected l %v, Found l %v", i, test.ansl, test.l)
+		}
+		if (test.w != nil) && !floats.Same(test.w, test.answ) {
+			t.Errorf("SortWeightedLabelled mismatch case %d. Expected w %v, Found w %v", i, test.answ, test.w)
+		}
+	}
+	if !Panics(func() { SortWeightedLabeled(make([]float64, 3), make([]bool, 2), make([]float64, 3)) }) {
+		t.Errorf("SortWeighted did not panic with x, labels length mismatch")
+	}
+	if !Panics(func() { SortWeightedLabeled(make([]float64, 3), make([]bool, 2), nil) }) {
+		t.Errorf("SortWeighted did not panic with x, labels length mismatch")
+	}
+	if !Panics(func() { SortWeightedLabeled(make([]float64, 3), make([]bool, 3), make([]float64, 2)) }) {
+		t.Errorf("SortWeighted did not panic with x, weights length mismatch")
+	}
+	if !Panics(func() { SortWeightedLabeled(make([]float64, 3), nil, make([]float64, 2)) }) {
+		t.Errorf("SortWeighted did not panic with x, weights length mismatch")
+	}
+}
+
+func TestVariance(t *testing.T) {
+	for i, test := range []struct {
+		x       []float64
+		weights []float64
+		ans     float64
+	}{
+		{
+			x:       []float64{8, -3, 7, 8, -4},
+			weights: nil,
+			ans:     37.7,
+		},
+		{
+			x:       []float64{8, -3, 7, 8, -4},
+			weights: []float64{1, 1, 1, 1, 1},
+			ans:     37.7,
+		},
+		{
+			x:       []float64{8, 3, 7, 8, 4},
+			weights: []float64{2, 1, 2, 1, 1},
+			ans:     4.2857142857142865,
+		},
+		{
+			x:       []float64{1, 4, 9},
+			weights: []float64{1, 1.5, 1},
+			ans:     13.142857142857146,
+		},
+		{
+			x:       []float64{1, 2, 3},
+			weights: []float64{1, 1.5, 1},
+			ans:     .8,
+		},
+	} {
+		variance := Variance(test.x, test.weights)
+		if math.Abs(variance-test.ans) > 1e-14 {
+			t.Errorf("Variance mismatch case %d. Expected %v, Found %v", i, test.ans, variance)
+		}
+	}
+	if !Panics(func() { Variance(make([]float64, 3), make([]float64, 2)) }) {
+		t.Errorf("Variance did not panic with x, weights length mismatch")
+	}
+
+}
+
+func ExampleVariance() {
+	x := []float64{8, 2, -9, 15, 4}
+	variance := Variance(x, nil)
+	fmt.Printf("The variance of the samples is %.4f\n", variance)
+
+	weights := []float64{2, 2, 6, 7, 1}
+	weightedVariance := Variance(x, weights)
+	fmt.Printf("The weighted variance of the samples is %.4f\n", weightedVariance)
+	// Output:
+	// The variance of the samples is 77.5000
+	// The weighted variance of the samples is 111.7941
+}
+
+func TestStdScore(t *testing.T) {
+	for i, test := range []struct {
+		x float64
+		u float64
+		s float64
+		z float64
+	}{
+		{
+			x: 4,
+			u: -6,
+			s: 5,
+			z: 2,
+		},
+		{
+			x: 1,
+			u: 0,
+			s: 1,
+			z: 1,
+		},
+	} {
+		z := StdScore(test.x, test.u, test.s)
+		if math.Abs(z-test.z) > 1e-14 {
+			t.Errorf("StdScore mismatch case %d. Expected %v, Found %v", i, test.z, z)
+		}
+	}
+
+}
diff --git a/vendor/gonum.org/v1/gonum/stat/statmat_test.go b/vendor/gonum.org/v1/gonum/stat/statmat_test.go
new file mode 100644
index 00000000..5ac809ef
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/stat/statmat_test.go
@@ -0,0 +1,463 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package stat
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+)
+
+func TestCovarianceMatrix(t *testing.T) {
+	// An alternative way to test this is to call the Variance and
+	// Covariance functions and ensure that the results are identical.
+	for i, test := range []struct {
+		data    *mat.Dense
+		weights []float64
+		ans     *mat.Dense
+	}{
+		{
+			data: mat.NewDense(5, 2, []float64{
+				-2, -4,
+				-1, 2,
+				0, 0,
+				1, -2,
+				2, 4,
+			}),
+			weights: nil,
+			ans: mat.NewDense(2, 2, []float64{
+				2.5, 3,
+				3, 10,
+			}),
+		}, {
+			data: mat.NewDense(3, 2, []float64{
+				1, 1,
+				2, 4,
+				3, 9,
+			}),
+			weights: []float64{
+				1,
+				1.5,
+				1,
+			},
+			ans: mat.NewDense(2, 2, []float64{
+				.8, 3.2,
+				3.2, 13.142857142857146,
+			}),
+		},
+	} {
+		// Make a copy of the data to check that it isn't changing.
+		r := test.data.RawMatrix()
+		d := make([]float64, len(r.Data))
+		copy(d, r.Data)
+
+		w := make([]float64, len(test.weights))
+		if test.weights != nil {
+			copy(w, test.weights)
+		}
+		for _, cov := range []*mat.SymDense{nil, {}} {
+			c := CovarianceMatrix(cov, test.data, test.weights)
+			if !mat.Equal(c, test.ans) {
+				t.Errorf("%d: expected cov %v, found %v", i, test.ans, c)
+			}
+			if !floats.Equal(d, r.Data) {
+				t.Errorf("%d: data was modified during execution", i)
+			}
+			if !floats.Equal(w, test.weights) {
+				t.Errorf("%d: weights was modified during execution", i)
+			}
+
+			// compare with call to Covariance
+			_, cols := c.Dims()
+			for ci := 0; ci < cols; ci++ {
+				for cj := 0; cj < cols; cj++ {
+					x := mat.Col(nil, ci, test.data)
+					y := mat.Col(nil, cj, test.data)
+					cov := Covariance(x, y, test.weights)
+					if math.Abs(cov-c.At(ci, cj)) > 1e-14 {
+						t.Errorf("CovMat does not match at (%v, %v). Want %v, got %v.", ci, cj, cov, c.At(ci, cj))
+					}
+				}
+			}
+		}
+
+	}
+	if !Panics(func() { CovarianceMatrix(nil, mat.NewDense(5, 2, nil), []float64{}) }) {
+		t.Errorf("CovarianceMatrix did not panic with weight size mismatch")
+	}
+	if !Panics(func() { CovarianceMatrix(mat.NewSymDense(1, nil), mat.NewDense(5, 2, nil), nil) }) {
+		t.Errorf("CovarianceMatrix did not panic with preallocation size mismatch")
+	}
+	if !Panics(func() { CovarianceMatrix(nil, mat.NewDense(2, 2, []float64{1, 2, 3, 4}), []float64{1, -1}) }) {
+		t.Errorf("CovarianceMatrix did not panic with negative weights")
+	}
+}
+
+func TestCorrelationMatrix(t *testing.T) {
+	for i, test := range []struct {
+		data    *mat.Dense
+		weights []float64
+		ans     *mat.Dense
+	}{
+		{
+			data: mat.NewDense(3, 3, []float64{
+				1, 2, 3,
+				3, 4, 5,
+				5, 6, 7,
+			}),
+			weights: nil,
+			ans: mat.NewDense(3, 3, []float64{
+				1, 1, 1,
+				1, 1, 1,
+				1, 1, 1,
+			}),
+		},
+		{
+			data: mat.NewDense(5, 2, []float64{
+				-2, -4,
+				-1, 2,
+				0, 0,
+				1, -2,
+				2, 4,
+			}),
+			weights: nil,
+			ans: mat.NewDense(2, 2, []float64{
+				1, 0.6,
+				0.6, 1,
+			}),
+		}, {
+			data: mat.NewDense(3, 2, []float64{
+				1, 1,
+				2, 4,
+				3, 9,
+			}),
+			weights: []float64{
+				1,
+				1.5,
+				1,
+			},
+			ans: mat.NewDense(2, 2, []float64{
+				1, 0.9868703275903379,
+				0.9868703275903379, 1,
+			}),
+		},
+	} {
+		// Make a copy of the data to check that it isn't changing.
+		r := test.data.RawMatrix()
+		d := make([]float64, len(r.Data))
+		copy(d, r.Data)
+
+		w := make([]float64, len(test.weights))
+		if test.weights != nil {
+			copy(w, test.weights)
+		}
+		for _, corr := range []*mat.SymDense{nil, {}} {
+			c := CorrelationMatrix(corr, test.data, test.weights)
+			if !mat.Equal(c, test.ans) {
+				t.Errorf("%d: expected corr %v, found %v", i, test.ans, c)
+			}
+			if !floats.Equal(d, r.Data) {
+				t.Errorf("%d: data was modified during execution", i)
+			}
+			if !floats.Equal(w, test.weights) {
+				t.Errorf("%d: weights was modified during execution", i)
+			}
+
+			// compare with call to Covariance
+			_, cols := c.Dims()
+			for ci := 0; ci < cols; ci++ {
+				for cj := 0; cj < cols; cj++ {
+					x := mat.Col(nil, ci, test.data)
+					y := mat.Col(nil, cj, test.data)
+					corr := Correlation(x, y, test.weights)
+					if math.Abs(corr-c.At(ci, cj)) > 1e-14 {
+						t.Errorf("CorrMat does not match at (%v, %v). Want %v, got %v.", ci, cj, corr, c.At(ci, cj))
+					}
+				}
+			}
+		}
+
+	}
+	if !Panics(func() { CorrelationMatrix(nil, mat.NewDense(5, 2, nil), []float64{}) }) {
+		t.Errorf("CorrelationMatrix did not panic with weight size mismatch")
+	}
+	if !Panics(func() { CorrelationMatrix(mat.NewSymDense(1, nil), mat.NewDense(5, 2, nil), nil) }) {
+		t.Errorf("CorrelationMatrix did not panic with preallocation size mismatch")
+	}
+	if !Panics(func() { CorrelationMatrix(nil, mat.NewDense(2, 2, []float64{1, 2, 3, 4}), []float64{1, -1}) }) {
+		t.Errorf("CorrelationMatrix did not panic with negative weights")
+	}
+}
+
+func TestCorrCov(t *testing.T) {
+	// test both Cov2Corr and Cov2Corr
+	for i, test := range []struct {
+		data    *mat.Dense
+		weights []float64
+	}{
+		{
+			data: mat.NewDense(3, 3, []float64{
+				1, 2, 3,
+				3, 4, 5,
+				5, 6, 7,
+			}),
+			weights: nil,
+		},
+		{
+			data: mat.NewDense(5, 2, []float64{
+				-2, -4,
+				-1, 2,
+				0, 0,
+				1, -2,
+				2, 4,
+			}),
+			weights: nil,
+		}, {
+			data: mat.NewDense(3, 2, []float64{
+				1, 1,
+				2, 4,
+				3, 9,
+			}),
+			weights: []float64{
+				1,
+				1.5,
+				1,
+			},
+		},
+	} {
+		corr := CorrelationMatrix(nil, test.data, test.weights)
+		cov := CovarianceMatrix(nil, test.data, test.weights)
+
+		r := cov.Symmetric()
+
+		// Get the diagonal elements from cov to determine the sigmas.
+		sigmas := make([]float64, r)
+		for i := range sigmas {
+			sigmas[i] = math.Sqrt(cov.At(i, i))
+		}
+
+		covFromCorr := mat.NewSymDense(corr.Symmetric(), nil)
+		covFromCorr.CopySym(corr)
+		corrToCov(covFromCorr, sigmas)
+
+		corrFromCov := mat.NewSymDense(cov.Symmetric(), nil)
+		corrFromCov.CopySym(cov)
+		covToCorr(corrFromCov)
+
+		if !mat.EqualApprox(corr, corrFromCov, 1e-14) {
+			t.Errorf("%d: corrToCov did not match direct Correlation calculation.  Want: %v, got: %v. ", i, corr, corrFromCov)
+		}
+		if !mat.EqualApprox(cov, covFromCorr, 1e-14) {
+			t.Errorf("%d: covToCorr did not match direct Covariance calculation.  Want: %v, got: %v. ", i, cov, covFromCorr)
+		}
+
+		if !Panics(func() { corrToCov(mat.NewSymDense(2, nil), []float64{}) }) {
+			t.Errorf("CorrelationMatrix did not panic with sigma size mismatch")
+		}
+	}
+}
+
+func TestMahalanobis(t *testing.T) {
+	// Comparison with scipy.
+	for cas, test := range []struct {
+		x, y  *mat.VecDense
+		Sigma *mat.SymDense
+		ans   float64
+	}{
+		{
+			x: mat.NewVecDense(3, []float64{1, 2, 3}),
+			y: mat.NewVecDense(3, []float64{0.8, 1.1, -1}),
+			Sigma: mat.NewSymDense(3,
+				[]float64{
+					0.8, 0.3, 0.1,
+					0.3, 0.7, -0.1,
+					0.1, -0.1, 7}),
+			ans: 1.9251757377680914,
+		},
+	} {
+		var chol mat.Cholesky
+		ok := chol.Factorize(test.Sigma)
+		if !ok {
+			panic("bad test")
+		}
+		ans := Mahalanobis(test.x, test.y, &chol)
+		if math.Abs(ans-test.ans) > 1e-14 {
+			t.Errorf("Cas %d: got %v, want %v", cas, ans, test.ans)
+		}
+	}
+}
+
+// benchmarks
+
+func randMat(r, c int) mat.Matrix {
+	x := make([]float64, r*c)
+	for i := range x {
+		x[i] = rand.Float64()
+	}
+	return mat.NewDense(r, c, x)
+}
+
+func benchmarkCovarianceMatrix(b *testing.B, m mat.Matrix) {
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		CovarianceMatrix(nil, m, nil)
+	}
+}
+func benchmarkCovarianceMatrixWeighted(b *testing.B, m mat.Matrix) {
+	r, _ := m.Dims()
+	wts := make([]float64, r)
+	for i := range wts {
+		wts[i] = 0.5
+	}
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		CovarianceMatrix(nil, m, wts)
+	}
+}
+func benchmarkCovarianceMatrixInPlace(b *testing.B, m mat.Matrix) {
+	_, c := m.Dims()
+	res := mat.NewSymDense(c, nil)
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		CovarianceMatrix(res, m, nil)
+	}
+}
+
+func BenchmarkCovarianceMatrixSmallxSmall(b *testing.B) {
+	// 10 * 10 elements
+	x := randMat(small, small)
+	benchmarkCovarianceMatrix(b, x)
+}
+func BenchmarkCovarianceMatrixSmallxMedium(b *testing.B) {
+	// 10 * 1000 elements
+	x := randMat(small, medium)
+	benchmarkCovarianceMatrix(b, x)
+}
+
+func BenchmarkCovarianceMatrixMediumxSmall(b *testing.B) {
+	// 1000 * 10 elements
+	x := randMat(medium, small)
+	benchmarkCovarianceMatrix(b, x)
+}
+func BenchmarkCovarianceMatrixMediumxMedium(b *testing.B) {
+	// 1000 * 1000 elements
+	x := randMat(medium, medium)
+	benchmarkCovarianceMatrix(b, x)
+}
+
+func BenchmarkCovarianceMatrixLargexSmall(b *testing.B) {
+	// 1e5 * 10 elements
+	x := randMat(large, small)
+	benchmarkCovarianceMatrix(b, x)
+}
+
+func BenchmarkCovarianceMatrixHugexSmall(b *testing.B) {
+	// 1e7 * 10 elements
+	x := randMat(huge, small)
+	benchmarkCovarianceMatrix(b, x)
+}
+
+func BenchmarkCovarianceMatrixSmallxSmallWeighted(b *testing.B) {
+	// 10 * 10 elements
+	x := randMat(small, small)
+	benchmarkCovarianceMatrixWeighted(b, x)
+}
+func BenchmarkCovarianceMatrixSmallxMediumWeighted(b *testing.B) {
+	// 10 * 1000 elements
+	x := randMat(small, medium)
+	benchmarkCovarianceMatrixWeighted(b, x)
+}
+
+func BenchmarkCovarianceMatrixMediumxSmallWeighted(b *testing.B) {
+	// 1000 * 10 elements
+	x := randMat(medium, small)
+	benchmarkCovarianceMatrixWeighted(b, x)
+}
+func BenchmarkCovarianceMatrixMediumxMediumWeighted(b *testing.B) {
+	// 1000 * 1000 elements
+	x := randMat(medium, medium)
+	benchmarkCovarianceMatrixWeighted(b, x)
+}
+
+func BenchmarkCovarianceMatrixLargexSmallWeighted(b *testing.B) {
+	// 1e5 * 10 elements
+	x := randMat(large, small)
+	benchmarkCovarianceMatrixWeighted(b, x)
+}
+
+func BenchmarkCovarianceMatrixHugexSmallWeighted(b *testing.B) {
+	// 1e7 * 10 elements
+	x := randMat(huge, small)
+	benchmarkCovarianceMatrixWeighted(b, x)
+}
+
+func BenchmarkCovarianceMatrixSmallxSmallInPlace(b *testing.B) {
+	// 10 * 10 elements
+	x := randMat(small, small)
+	benchmarkCovarianceMatrixInPlace(b, x)
+}
+func BenchmarkCovarianceMatrixSmallxMediumInPlace(b *testing.B) {
+	// 10 * 1000 elements
+	x := randMat(small, medium)
+	benchmarkCovarianceMatrixInPlace(b, x)
+}
+
+func BenchmarkCovarianceMatrixMediumxSmallInPlace(b *testing.B) {
+	// 1000 * 10 elements
+	x := randMat(medium, small)
+	benchmarkCovarianceMatrixInPlace(b, x)
+}
+func BenchmarkCovarianceMatrixMediumxMediumInPlace(b *testing.B) {
+	// 1000 * 1000 elements
+	x := randMat(medium, medium)
+	benchmarkCovarianceMatrixInPlace(b, x)
+}
+
+func BenchmarkCovarianceMatrixLargexSmallInPlace(b *testing.B) {
+	// 1e5 * 10 elements
+	x := randMat(large, small)
+	benchmarkCovarianceMatrixInPlace(b, x)
+}
+
+func BenchmarkCovarianceMatrixHugexSmallInPlace(b *testing.B) {
+	// 1e7 * 10 elements
+	x := randMat(huge, small)
+	benchmarkCovarianceMatrixInPlace(b, x)
+}
+
+func BenchmarkCovToCorr(b *testing.B) {
+	// generate a 10x10 covariance matrix
+	m := randMat(small, small)
+	c := CovarianceMatrix(nil, m, nil)
+	cc := mat.NewSymDense(c.Symmetric(), nil)
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		b.StopTimer()
+		cc.CopySym(c)
+		b.StartTimer()
+		covToCorr(cc)
+	}
+}
+
+func BenchmarkCorrToCov(b *testing.B) {
+	// generate a 10x10 correlation matrix
+	m := randMat(small, small)
+	c := CorrelationMatrix(nil, m, nil)
+	cc := mat.NewSymDense(c.Symmetric(), nil)
+	sigma := make([]float64, small)
+	for i := range sigma {
+		sigma[i] = 2
+	}
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		b.StopTimer()
+		cc.CopySym(c)
+		b.StartTimer()
+		corrToCov(cc, sigma)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/unit/autogen.go b/vendor/gonum.org/v1/gonum/unit/autogen.go
new file mode 100644
index 00000000..829c7318
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/unit/autogen.go
@@ -0,0 +1,363 @@
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build ignore
+
+package main
+
+import (
+	"bytes"
+	"go/format"
+	"log"
+	"os"
+	"path/filepath"
+	"strings"
+	"text/template"
+)
+
+type Unit struct {
+	Name          string
+	Receiver      string
+	Offset        int    // From normal (for example, mass base unit is kg, not kg)
+	PrintString   string // print string for the unit (kg for mass)
+	ExtraConstant []Constant
+	Suffix        string
+	Singular      string
+	TypeComment   string // Text to comment the type
+	Dimensions    []Dimension
+	ErForm        string //For Xxxer interface
+}
+
+type Dimension struct {
+	Name  string
+	Power int
+}
+
+const (
+	TimeName   string = "TimeDim"
+	LengthName string = "LengthDim"
+	MassName   string = "MassDim"
+)
+
+type Constant struct {
+	Name  string
+	Value string
+}
+
+type Prefix struct {
+	Name  string
+	Power int
+}
+
+var Prefixes = []Prefix{
+	{
+		Name:  "Yotta",
+		Power: 24,
+	},
+	{
+		Name:  "Zetta",
+		Power: 21,
+	},
+	{
+		Name:  "Exa",
+		Power: 18,
+	},
+	{
+		Name:  "Peta",
+		Power: 15,
+	},
+	{
+		Name:  "Tera",
+		Power: 12,
+	},
+	{
+		Name:  "Giga",
+		Power: 9,
+	},
+	{
+		Name:  "Mega",
+		Power: 6,
+	},
+	{
+		Name:  "Kilo",
+		Power: 3,
+	},
+	{
+		Name:  "Hecto",
+		Power: 2,
+	},
+	{
+		Name:  "Deca",
+		Power: 1,
+	},
+	{
+		Name:  "",
+		Power: 0,
+	},
+	{
+		Name:  "Deci",
+		Power: -1,
+	},
+	{
+		Name:  "Centi",
+		Power: -2,
+	},
+	{
+		Name:  "Milli",
+		Power: -3,
+	},
+	{
+		Name:  "Micro",
+		Power: -6,
+	},
+	{
+		Name:  "Nano",
+		Power: -9,
+	},
+	{
+		Name:  "Pico",
+		Power: -12,
+	},
+	{
+		Name:  "Femto",
+		Power: -15,
+	},
+	{
+		Name:  "Atto",
+		Power: -18,
+	},
+	{
+		Name:  "Zepto",
+		Power: -21,
+	},
+	{
+		Name:  "Yocto",
+		Power: -24,
+	},
+}
+
+var Units = []Unit{
+	{
+		Name:        "Mass",
+		Receiver:    "m",
+		Offset:      -3,
+		PrintString: "kg",
+		Suffix:      "gram",
+		Singular:    "Gram",
+		TypeComment: "Mass represents a mass in kilograms",
+		Dimensions: []Dimension{
+			{
+				Name:  MassName,
+				Power: 1,
+			},
+		},
+	},
+	{
+		Name:        "Length",
+		Receiver:    "l",
+		PrintString: "m",
+		Suffix:      "meter",
+		Singular:    "Meter",
+		TypeComment: "Length represents a length in meters",
+		Dimensions: []Dimension{
+			{
+				Name:  LengthName,
+				Power: 1,
+			},
+		},
+	},
+	{
+		Name:        "Time",
+		Receiver:    "t",
+		PrintString: "s",
+		Suffix:      "second",
+		Singular:    "Second",
+		TypeComment: "Time represents a time in seconds",
+		ExtraConstant: []Constant{
+			{
+				Name:  "Hour",
+				Value: "3600",
+			},
+			{
+				Name:  "Minute",
+				Value: "60",
+			},
+		},
+		Dimensions: []Dimension{
+			{
+				Name:  TimeName,
+				Power: 1,
+			},
+		},
+		ErForm: "Timer",
+	},
+}
+
+var gopath string
+var unitPkgPath string
+
+func init() {
+	gopath = os.Getenv("GOPATH")
+	if gopath == "" {
+		log.Fatal("no gopath")
+	}
+
+	unitPkgPath = filepath.Join(gopath, "src", "gonum.org", "v1", "gonum", "unit")
+}
+
+// Generate generates a file for each of the units
+func main() {
+	for _, unit := range Units {
+		generate(unit)
+	}
+}
+
+const headerTemplate = `// Code generated by "go generate gonum.org/v1/gonum/unit”; DO NOT EDIT.
+
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package unit
+
+import (
+	"errors"
+	"fmt"
+	"math"
+)
+
+// {{.TypeComment}}
+type {{.Name}} float64
+`
+
+var header = template.Must(template.New("header").Parse(headerTemplate))
+
+const constTemplate = `
+const(
+	{{$unit := .Unit}}
+	{{range $unit.ExtraConstant}} {{.Name}} {{$unit.Name}} = {{.Value}}
+	{{end}}
+	{{$prefixes := .Prefixes}}
+	{{range $prefixes}} {{if .Name}} {{.Name}}{{$unit.Suffix}} {{else}} {{$unit.Singular}} {{end}} {{$unit.Name}} = {{if .Power}} 1e{{.Power}} {{else}} 1.0 {{end}}
+	{{end}}
+)
+`
+
+var prefix = template.Must(template.New("prefix").Parse(constTemplate))
+
+const methodTemplate = `
+// Unit converts the {{.Name}} to a *Unit
+func ({{.Receiver}} {{.Name}}) Unit() *Unit {
+	return New(float64({{.Receiver}}), Dimensions{
+		{{range .Dimensions}} {{.Name}}: {{.Power}},
+		{{end}}
+		})
+}
+
+// {{.Name}} allows {{.Name}} to implement a {{if .ErForm}}{{.ErForm}}{{else}}{{.Name}}er{{end}} interface
+func ({{.Receiver}} {{.Name}}) {{.Name}}() {{.Name}} {
+	return {{.Receiver}}
+}
+
+// From converts the unit into the receiver. From returns an
+// error if there is a mismatch in dimension
+func ({{.Receiver}} *{{.Name}}) From(u Uniter) error {
+	if !DimensionsMatch(u, {{.Singular}}){
+		*{{.Receiver}} = {{.Name}}(math.NaN())
+		return errors.New("Dimension mismatch")
+	}
+	*{{.Receiver}} = {{.Name}}(u.Unit().Value())
+	return nil
+}
+`
+
+var methods = template.Must(template.New("methods").Parse(methodTemplate))
+
+const formatTemplate = `
+func ({{.Receiver}} {{.Name}}) Format(fs fmt.State, c rune) {
+	switch c {
+	case 'v':
+		if fs.Flag('#') {
+			fmt.Fprintf(fs, "%T(%v)", {{.Receiver}}, float64({{.Receiver}}))
+			return
+		}
+		fallthrough
+	case 'e', 'E', 'f', 'F', 'g', 'G':
+		p, pOk := fs.Precision()
+		w, wOk := fs.Width()
+		switch {
+		case pOk && wOk:
+			fmt.Fprintf(fs, "%*.*"+string(c), w, p, float64({{.Receiver}}))
+		case pOk:
+			fmt.Fprintf(fs, "%.*"+string(c), p, float64({{.Receiver}}))
+		case wOk:
+			fmt.Fprintf(fs, "%*"+string(c), w, float64({{.Receiver}}))
+		default:
+			fmt.Fprintf(fs, "%"+string(c), float64({{.Receiver}}))
+		}
+		fmt.Fprint(fs, " {{.PrintString}}")
+	default:
+		fmt.Fprintf(fs, "%%!%c(%T=%g {{.PrintString}})", c, {{.Receiver}}, float64({{.Receiver}}))
+	}
+}
+`
+
+var form = template.Must(template.New("format").Parse(formatTemplate))
+
+func generate(unit Unit) {
+	lowerName := strings.ToLower(unit.Name)
+	filename := filepath.Join(unitPkgPath, lowerName+".go")
+	f, err := os.Create(filename)
+	if err != nil {
+		log.Fatal(err)
+	}
+	defer f.Close()
+
+	// Need to define new prefixes because text/template can't do math.
+	// Need to do math because kilogram = 1 not 10^3
+
+	prefixes := make([]Prefix, len(Prefixes))
+	for i, p := range Prefixes {
+		prefixes[i].Name = p.Name
+		prefixes[i].Power = p.Power + unit.Offset
+	}
+
+	data := struct {
+		Prefixes []Prefix
+		Unit     Unit
+	}{
+		prefixes,
+		unit,
+	}
+
+	buf := bytes.NewBuffer(make([]byte, 0))
+
+	err = header.Execute(buf, unit)
+	if err != nil {
+		log.Fatal(err)
+	}
+
+	err = prefix.Execute(buf, data)
+	if err != nil {
+		log.Fatal(err)
+	}
+
+	err = methods.Execute(buf, unit)
+	if err != nil {
+		log.Fatal(err)
+	}
+
+	err = form.Execute(buf, unit)
+	if err != nil {
+		log.Fatal(err)
+	}
+
+	b, err := format.Source(buf.Bytes())
+	if err != nil {
+		f.Write(buf.Bytes()) // This is here to debug bad format
+		log.Fatalf("error formatting: %s", err)
+	}
+
+	f.Write(b)
+}
diff --git a/vendor/gonum.org/v1/gonum/unit/consts.go b/vendor/gonum.org/v1/gonum/unit/consts.go
new file mode 100644
index 00000000..908d478e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/unit/consts.go
@@ -0,0 +1,29 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package unit
+
+const (
+	Yotta = 1e24
+	Zetta = 1e21
+	Exa   = 1e18
+	Peta  = 1e15
+	Tera  = 1e12
+	Giga  = 1e9
+	Mega  = 1e6
+	Kilo  = 1e3
+	Hecto = 1e2
+	Deca  = 1e1
+
+	Deci  = 1e-1
+	Centi = 1e-2
+	Milli = 1e-3
+	Micro = 1e-6
+	Nano  = 1e-9
+	Pico  = 1e-12
+	Femto = 1e-15
+	Atto  = 1e-18
+	Zepto = 1e-21
+	Yocto = 1e-24
+)
diff --git a/vendor/gonum.org/v1/gonum/unit/dimless.go b/vendor/gonum.org/v1/gonum/unit/dimless.go
new file mode 100644
index 00000000..5c6ce36e
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/unit/dimless.go
@@ -0,0 +1,66 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package unit
+
+import (
+	"errors"
+	"fmt"
+	"math"
+)
+
+// Dimless represents a dimensionless constant
+type Dimless float64
+
+const (
+	One Dimless = 1.0
+)
+
+// Unit converts the Dimless to a unit
+func (d Dimless) Unit() *Unit {
+	return New(float64(d), Dimensions{})
+}
+
+// Dimless allows Dimless to implement a Dimlesser interface
+func (d Dimless) Dimless() Dimless {
+	return d
+}
+
+// From converts the unit to a dimless. Returns an error if there
+// is a mismatch in dimension
+func (d *Dimless) From(u *Unit) error {
+	if !DimensionsMatch(u, One) {
+		(*d) = Dimless(math.NaN())
+		return errors.New("Dimension mismatch")
+	}
+	(*d) = Dimless(u.Unit().Value())
+	return nil
+}
+
+func (d Dimless) Format(fs fmt.State, c rune) {
+	switch c {
+	case 'v':
+		if fs.Flag('#') {
+			fmt.Fprintf(fs, "%T(%v)", d, float64(d))
+			return
+		}
+		fallthrough
+	case 'e', 'E', 'f', 'F', 'g', 'G':
+		p, pOk := fs.Precision()
+		w, wOk := fs.Width()
+		switch {
+		case pOk && wOk:
+			fmt.Fprintf(fs, "%*.*"+string(c), w, p, float64(d))
+		case pOk:
+			fmt.Fprintf(fs, "%.*"+string(c), p, float64(d))
+		case wOk:
+			fmt.Fprintf(fs, "%*"+string(c), w, float64(d))
+		default:
+			fmt.Fprintf(fs, "%"+string(c), float64(d))
+		}
+	default:
+		fmt.Fprintf(fs, "%%!%c(%T=%g)", c, d, float64(d))
+		return
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/unit/doc.go b/vendor/gonum.org/v1/gonum/unit/doc.go
new file mode 100644
index 00000000..97ca4386
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/unit/doc.go
@@ -0,0 +1,83 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//go:generate go run autogen.go
+
+// Package unit provides a set of types and constants that facilitate
+// the use of the International System of Units (SI).
+//
+// Unit provides two main functionalities.
+//
+// 1)
+// It provides a number of types representing either an SI base unit
+// or a common combination of base units, named for the unit it
+// represents (Length, Mass, Pressure, etc.). Each type has
+// a float64 as the underlying unit, and its value represents the
+// number of that underlying unit (Kilogram, Meter, Pascal, etc.).
+// For example,
+//		height := 1.6 * unit.Meter
+//		acc := unit.Acceleration(9.8)
+// creates a variable named 'height' with a value of 1.6 meters, and
+// a variable named 'acc' with a value of 9.8 meters per second squared.
+// These types can be used to add compile-time safety to code. For
+// example,
+//		func UnitDensity(t unit.Temperature, pressure unit.Pressure) (unit.Density){
+//			...
+//		}
+//		func main(){
+//			t := 300 * unit.Kelvin
+//			p := 5 * unit.Bar
+//			rho := UnitDensity(p, t) // compile-time error
+//		}
+// gives a compile-time error (temperature type does not match pressure type)
+// while the corresponding code using float64 runs without error.
+//		func Float64Density(temperature, pressure float64) (float64){
+//			...
+//		}
+//		func main(){
+//			t := 300.0 // degrees kelvin
+//			p := 50000.0 // Pascals
+//			rho := Float64Density(p, t) // no error
+//		}
+// Many types have constants defined representing named SI units (Meter,
+// Kilogram, etc. ) or SI derived units (Bar, Hz, etc.). The Unit package
+// additionally provides untyped constants for SI prefixes, so the following
+// are all equivalent.
+//		l := 0.001 * unit.Meter
+//		k := 1 * unit.Milli * unit.Meter
+//		j := unit.Length(0.001)
+//
+// 2)
+// Unit provides the type "Unit", meant to represent a general dimensional
+// value. unit.Unit can be used to help prevent errors of dimensionality
+// when multiplying or dividing dimensional numbers. This package also
+// provides the "Uniter" interface which is satisfied by any type which can
+// be converted to a unit. New varibles of type Unit can be created with
+// the New function and the Dimensions map. For example, the code
+//		acc := New(9.81, Dimensions{LengthDim:1, TimeDim: -2})
+// creates a variable "acc" which has a value of 9.81 m/s^2. Methods of
+// unit can be used to modify this value, for example:
+// 		acc.Mul(1.0 * unit.Kilogram).Mul(1 * unit.Meter)
+// To convert the unit back into a typed float64 value, the From methods
+// of the dimensional types should be used. From will return an error if the
+// dimensions do not match.
+// 		var energy unit.Energy
+//		err := (*energy).From(acc)
+// Domain-specific problems may need custom dimensions, and for this purpose
+// NewDimension should be used to help avoid accidental overlap between
+// packages. For example, results from a blood test may be measured in
+// "White blood cells per slide". In this case, NewDimension should be
+// used to create a 'WhiteBloodCell' dimension. NewDimension takes in a
+// string which will be used for printing that dimension, and will return
+// a unique dimension number. NewDimension should not be
+// used, however, to create the unit of 'Slide', because in this case slide
+// is just a measurement of area. Instead, a constant could be defined.
+//		const Slide unit.Area =  0.001875 // m^2
+// Please note that Unit cannot catch all errors related to dimensionality.
+// Different physical ideas are sometimes expressed with the same dimensions
+// and Unit is incapable of catching these mismatches. For example, energy and
+// torque are both expressed as force times distance (Newton-meters in SI),
+// but it is wrong to say that a torque of 10 N-m is the same as 10 J, even
+// though the dimensions agree.
+package unit // import "gonum.org/v1/gonum/unit"
diff --git a/vendor/gonum.org/v1/gonum/unit/length.go b/vendor/gonum.org/v1/gonum/unit/length.go
new file mode 100644
index 00000000..f7ffde23
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/unit/length.go
@@ -0,0 +1,90 @@
+// Code generated by "go generate gonum.org/v1/gonum/unit”; DO NOT EDIT.
+
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package unit
+
+import (
+	"errors"
+	"fmt"
+	"math"
+)
+
+// Length represents a length in meters
+type Length float64
+
+const (
+	Yottameter Length = 1e24
+	Zettameter Length = 1e21
+	Exameter   Length = 1e18
+	Petameter  Length = 1e15
+	Terameter  Length = 1e12
+	Gigameter  Length = 1e9
+	Megameter  Length = 1e6
+	Kilometer  Length = 1e3
+	Hectometer Length = 1e2
+	Decameter  Length = 1e1
+	Meter      Length = 1.0
+	Decimeter  Length = 1e-1
+	Centimeter Length = 1e-2
+	Millimeter Length = 1e-3
+	Micrometer Length = 1e-6
+	Nanometer  Length = 1e-9
+	Picometer  Length = 1e-12
+	Femtometer Length = 1e-15
+	Attometer  Length = 1e-18
+	Zeptometer Length = 1e-21
+	Yoctometer Length = 1e-24
+)
+
+// Unit converts the Length to a *Unit
+func (l Length) Unit() *Unit {
+	return New(float64(l), Dimensions{
+		LengthDim: 1,
+	})
+}
+
+// Length allows Length to implement a Lengther interface
+func (l Length) Length() Length {
+	return l
+}
+
+// From converts the unit into the receiver. From returns an
+// error if there is a mismatch in dimension
+func (l *Length) From(u Uniter) error {
+	if !DimensionsMatch(u, Meter) {
+		*l = Length(math.NaN())
+		return errors.New("Dimension mismatch")
+	}
+	*l = Length(u.Unit().Value())
+	return nil
+}
+
+func (l Length) Format(fs fmt.State, c rune) {
+	switch c {
+	case 'v':
+		if fs.Flag('#') {
+			fmt.Fprintf(fs, "%T(%v)", l, float64(l))
+			return
+		}
+		fallthrough
+	case 'e', 'E', 'f', 'F', 'g', 'G':
+		p, pOk := fs.Precision()
+		w, wOk := fs.Width()
+		switch {
+		case pOk && wOk:
+			fmt.Fprintf(fs, "%*.*"+string(c), w, p, float64(l))
+		case pOk:
+			fmt.Fprintf(fs, "%.*"+string(c), p, float64(l))
+		case wOk:
+			fmt.Fprintf(fs, "%*"+string(c), w, float64(l))
+		default:
+			fmt.Fprintf(fs, "%"+string(c), float64(l))
+		}
+		fmt.Fprint(fs, " m")
+	default:
+		fmt.Fprintf(fs, "%%!%c(%T=%g m)", c, l, float64(l))
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/unit/mass.go b/vendor/gonum.org/v1/gonum/unit/mass.go
new file mode 100644
index 00000000..2b127046
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/unit/mass.go
@@ -0,0 +1,90 @@
+// Code generated by "go generate gonum.org/v1/gonum/unit”; DO NOT EDIT.
+
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package unit
+
+import (
+	"errors"
+	"fmt"
+	"math"
+)
+
+// Mass represents a mass in kilograms
+type Mass float64
+
+const (
+	Yottagram Mass = 1e21
+	Zettagram Mass = 1e18
+	Exagram   Mass = 1e15
+	Petagram  Mass = 1e12
+	Teragram  Mass = 1e9
+	Gigagram  Mass = 1e6
+	Megagram  Mass = 1e3
+	Kilogram  Mass = 1.0
+	Hectogram Mass = 1e-1
+	Decagram  Mass = 1e-2
+	Gram      Mass = 1e-3
+	Decigram  Mass = 1e-4
+	Centigram Mass = 1e-5
+	Milligram Mass = 1e-6
+	Microgram Mass = 1e-9
+	Nanogram  Mass = 1e-12
+	Picogram  Mass = 1e-15
+	Femtogram Mass = 1e-18
+	Attogram  Mass = 1e-21
+	Zeptogram Mass = 1e-24
+	Yoctogram Mass = 1e-27
+)
+
+// Unit converts the Mass to a *Unit
+func (m Mass) Unit() *Unit {
+	return New(float64(m), Dimensions{
+		MassDim: 1,
+	})
+}
+
+// Mass allows Mass to implement a Masser interface
+func (m Mass) Mass() Mass {
+	return m
+}
+
+// From converts the unit into the receiver. From returns an
+// error if there is a mismatch in dimension
+func (m *Mass) From(u Uniter) error {
+	if !DimensionsMatch(u, Gram) {
+		*m = Mass(math.NaN())
+		return errors.New("Dimension mismatch")
+	}
+	*m = Mass(u.Unit().Value())
+	return nil
+}
+
+func (m Mass) Format(fs fmt.State, c rune) {
+	switch c {
+	case 'v':
+		if fs.Flag('#') {
+			fmt.Fprintf(fs, "%T(%v)", m, float64(m))
+			return
+		}
+		fallthrough
+	case 'e', 'E', 'f', 'F', 'g', 'G':
+		p, pOk := fs.Precision()
+		w, wOk := fs.Width()
+		switch {
+		case pOk && wOk:
+			fmt.Fprintf(fs, "%*.*"+string(c), w, p, float64(m))
+		case pOk:
+			fmt.Fprintf(fs, "%.*"+string(c), p, float64(m))
+		case wOk:
+			fmt.Fprintf(fs, "%*"+string(c), w, float64(m))
+		default:
+			fmt.Fprintf(fs, "%"+string(c), float64(m))
+		}
+		fmt.Fprint(fs, " kg")
+	default:
+		fmt.Fprintf(fs, "%%!%c(%T=%g kg)", c, m, float64(m))
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/unit/time.go b/vendor/gonum.org/v1/gonum/unit/time.go
new file mode 100644
index 00000000..ef70fb8a
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/unit/time.go
@@ -0,0 +1,93 @@
+// Code generated by "go generate gonum.org/v1/gonum/unit”; DO NOT EDIT.
+
+// Copyright ©2014 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package unit
+
+import (
+	"errors"
+	"fmt"
+	"math"
+)
+
+// Time represents a time in seconds
+type Time float64
+
+const (
+	Hour   Time = 3600
+	Minute Time = 60
+
+	Yottasecond Time = 1e24
+	Zettasecond Time = 1e21
+	Exasecond   Time = 1e18
+	Petasecond  Time = 1e15
+	Terasecond  Time = 1e12
+	Gigasecond  Time = 1e9
+	Megasecond  Time = 1e6
+	Kilosecond  Time = 1e3
+	Hectosecond Time = 1e2
+	Decasecond  Time = 1e1
+	Second      Time = 1.0
+	Decisecond  Time = 1e-1
+	Centisecond Time = 1e-2
+	Millisecond Time = 1e-3
+	Microsecond Time = 1e-6
+	Nanosecond  Time = 1e-9
+	Picosecond  Time = 1e-12
+	Femtosecond Time = 1e-15
+	Attosecond  Time = 1e-18
+	Zeptosecond Time = 1e-21
+	Yoctosecond Time = 1e-24
+)
+
+// Unit converts the Time to a *Unit
+func (t Time) Unit() *Unit {
+	return New(float64(t), Dimensions{
+		TimeDim: 1,
+	})
+}
+
+// Time allows Time to implement a Timer interface
+func (t Time) Time() Time {
+	return t
+}
+
+// From converts the unit into the receiver. From returns an
+// error if there is a mismatch in dimension
+func (t *Time) From(u Uniter) error {
+	if !DimensionsMatch(u, Second) {
+		*t = Time(math.NaN())
+		return errors.New("Dimension mismatch")
+	}
+	*t = Time(u.Unit().Value())
+	return nil
+}
+
+func (t Time) Format(fs fmt.State, c rune) {
+	switch c {
+	case 'v':
+		if fs.Flag('#') {
+			fmt.Fprintf(fs, "%T(%v)", t, float64(t))
+			return
+		}
+		fallthrough
+	case 'e', 'E', 'f', 'F', 'g', 'G':
+		p, pOk := fs.Precision()
+		w, wOk := fs.Width()
+		switch {
+		case pOk && wOk:
+			fmt.Fprintf(fs, "%*.*"+string(c), w, p, float64(t))
+		case pOk:
+			fmt.Fprintf(fs, "%.*"+string(c), p, float64(t))
+		case wOk:
+			fmt.Fprintf(fs, "%*"+string(c), w, float64(t))
+		default:
+			fmt.Fprintf(fs, "%"+string(c), float64(t))
+		}
+		fmt.Fprint(fs, " s")
+	default:
+		fmt.Fprintf(fs, "%%!%c(%T=%g s)", c, t, float64(t))
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/unit/unit_test.go b/vendor/gonum.org/v1/gonum/unit/unit_test.go
new file mode 100644
index 00000000..258df365
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/unit/unit_test.go
@@ -0,0 +1,352 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package unit
+
+import (
+	"fmt"
+	"math"
+	"testing"
+)
+
+var formatTests = []struct {
+	unit   Uniter
+	format string
+	expect string
+}{
+	{New(9.81, Dimensions{MassDim: 1, TimeDim: -2}), "%f", "9.810000 kg s^-2"},
+	{New(9.81, Dimensions{MassDim: 1, TimeDim: -2}), "%1.f", "10 kg s^-2"},
+	{New(9.81, Dimensions{MassDim: 1, TimeDim: -2}), "%.1f", "9.8 kg s^-2"},
+	{New(9.81, Dimensions{MassDim: 1, TimeDim: -2, LengthDim: 0}), "%f", "9.810000 kg s^-2"},
+	{New(6.62606957e-34, Dimensions{MassDim: 2, TimeDim: -1}), "%e", "6.626070e-34 kg^2 s^-1"},
+	{New(6.62606957e-34, Dimensions{MassDim: 2, TimeDim: -1}), "%.3e", "6.626e-34 kg^2 s^-1"},
+	{New(6.62606957e-34, Dimensions{MassDim: 2, TimeDim: -1}), "%v", "6.62606957e-34 kg^2 s^-1"},
+	{New(6.62606957e-34, Dimensions{MassDim: 2, TimeDim: -1}), "%s", "%!s(*Unit=6.62606957e-34 kg^2 s^-1)"},
+	{Dimless(math.E), "%v", "2.718281828459045"},
+	{Dimless(math.E), "%#v", "unit.Dimless(2.718281828459045)"},
+	{Dimless(math.E), "%s", "%!s(unit.Dimless=2.718281828459045)"},
+	{Mass(1), "%v", "1 kg"},
+	{Mass(1), "%#v", "unit.Mass(1)"},
+	{Mass(1), "%s", "%!s(unit.Mass=1 kg)"},
+	{Length(1.61619926e-35), "%v", "1.61619926e-35 m"},
+	{Length(1.61619926e-35), "%#v", "unit.Length(1.61619926e-35)"},
+	{Length(1.61619926e-35), "%s", "%!s(unit.Length=1.61619926e-35 m)"},
+	{Time(15.2), "%v", "15.2 s"},
+	{Time(15.2), "%#v", "unit.Time(15.2)"},
+	{Time(15.2), "%s", "%!s(unit.Time=15.2 s)"},
+}
+
+func TestFormat(t *testing.T) {
+	for _, ts := range formatTests {
+		if r := fmt.Sprintf(ts.format, ts.unit); r != ts.expect {
+			t.Errorf("Format %q: got: %q expected: %q", ts.format, r, ts.expect)
+		}
+	}
+}
+
+func TestGoStringFormat(t *testing.T) {
+	expect1 := `&unit.Unit{dimensions:unit.Dimensions{4:2, 6:-1}, formatted:"", value:6.62606957e-34}`
+	expect2 := `&unit.Unit{dimensions:unit.Dimensions{6:-1, 4:2}, formatted:"", value:6.62606957e-34}`
+	if r := fmt.Sprintf("%#v", New(6.62606957e-34, Dimensions{MassDim: 2, TimeDim: -1})); r != expect1 && r != expect2 {
+		t.Errorf("Format %q: got: %q expected: %q", "%#v", r, expect1)
+	}
+}
+
+var initializationTests = []struct {
+	unit     *Unit
+	expValue float64
+	expMap   map[Dimension]int
+}{
+	{New(9.81, Dimensions{MassDim: 1, TimeDim: -2}), 9.81, Dimensions{MassDim: 1, TimeDim: -2}},
+	{New(9.81, Dimensions{MassDim: 1, TimeDim: -2, LengthDim: 0, CurrentDim: 0}), 9.81, Dimensions{MassDim: 1, TimeDim: -2}},
+}
+
+func TestInitialization(t *testing.T) {
+	for _, ts := range initializationTests {
+		if ts.expValue != ts.unit.value {
+			t.Errorf("Value wrong on initialization: got: %v expected: %v", ts.unit.value, ts.expValue)
+		}
+		if len(ts.expMap) != len(ts.unit.dimensions) {
+			t.Errorf("Map mismatch: got: %#v expected: %#v", ts.unit.dimensions, ts.expMap)
+		}
+		for key, val := range ts.expMap {
+			if ts.unit.dimensions[key] != val {
+				t.Errorf("Map mismatch: got: %#v expected: %#v", ts.unit.dimensions, ts.expMap)
+			}
+		}
+	}
+}
+
+var dimensionEqualityTests = []struct {
+	name        string
+	a           Uniter
+	b           Uniter
+	shouldMatch bool
+}{
+	{"same_empty", New(1.0, Dimensions{}), New(1.0, Dimensions{}), true},
+	{"same_one", New(1.0, Dimensions{TimeDim: 1}), New(1.0, Dimensions{TimeDim: 1}), true},
+	{"same_mult", New(1.0, Dimensions{TimeDim: 1, LengthDim: -2}), New(1.0, Dimensions{TimeDim: 1, LengthDim: -2}), true},
+	{"diff_one_empty", New(1.0, Dimensions{}), New(1.0, Dimensions{TimeDim: 1, LengthDim: -2}), false},
+	{"diff_same_dim", New(1.0, Dimensions{TimeDim: 1}), New(1.0, Dimensions{TimeDim: 2}), false},
+	{"diff_same_pow", New(1.0, Dimensions{LengthDim: 1}), New(1.0, Dimensions{TimeDim: 1}), false},
+	{"diff_numdim", New(1.0, Dimensions{TimeDim: 1, LengthDim: 2}), New(1.0, Dimensions{TimeDim: 2}), false},
+	{"diff_one_same_dim", New(1.0, Dimensions{LengthDim: 1, TimeDim: 1}), New(1.0, Dimensions{LengthDim: 1, TimeDim: 2}), false},
+}
+
+func TestDimensionEquality(t *testing.T) {
+	for _, ts := range dimensionEqualityTests {
+		if DimensionsMatch(ts.a, ts.b) != ts.shouldMatch {
+			t.Errorf("Dimension comparison incorrect for case %s. got: %v, expected: %v", ts.name, !ts.shouldMatch, ts.shouldMatch)
+		}
+	}
+}
+
+type UnitStructer interface {
+	UnitStruct() *UnitStruct
+}
+
+type UnitStruct struct {
+	current     int
+	length      int
+	luminosity  int
+	mass        int
+	temperature int
+	time        int
+	chemamt     int // For mol
+	value       float64
+}
+
+// Check if the dimensions of two units are the same
+func DimensionsMatchStruct(aU, bU UnitStructer) bool {
+	a := aU.UnitStruct()
+	b := bU.UnitStruct()
+	if a.length != b.length {
+		return false
+	}
+	if a.time != b.time {
+		return false
+	}
+	if a.mass != b.mass {
+		return false
+	}
+	if a.current != b.current {
+		return false
+	}
+	if a.temperature != b.temperature {
+		return false
+	}
+	if a.luminosity != b.luminosity {
+		return false
+	}
+	if a.chemamt != b.chemamt {
+		return false
+	}
+	return true
+}
+
+func (u *UnitStruct) UnitStruct() *UnitStruct {
+	return u
+}
+
+func (u *UnitStruct) Add(aU UnitStructer) *UnitStruct {
+	a := aU.UnitStruct()
+	if !DimensionsMatchStruct(a, u) {
+		panic("dimension mismatch")
+	}
+	u.value += a.value
+	return u
+}
+
+func (u *UnitStruct) Mul(aU UnitStructer) *UnitStruct {
+	a := aU.UnitStruct()
+	u.length += a.length
+	u.time += a.time
+	u.mass += a.mass
+	u.current += a.current
+	u.temperature += a.temperature
+	u.luminosity += a.luminosity
+	u.chemamt += a.chemamt
+	u.value *= a.value
+	return u
+}
+
+var u3 *UnitStruct
+
+func BenchmarkAddStruct(b *testing.B) {
+	u1 := &UnitStruct{current: 1, chemamt: 5, value: 10}
+	u2 := &UnitStruct{current: 1, chemamt: 5, value: 100}
+	for i := 0; i < b.N; i++ {
+		u2.Add(u1)
+	}
+}
+
+func BenchmarkMulStruct(b *testing.B) {
+	u1 := &UnitStruct{current: 1, chemamt: 5, value: 10}
+	u2 := &UnitStruct{mass: 1, time: 1, value: 100}
+	for i := 0; i < b.N; i++ {
+		u2.Mul(u1)
+	}
+}
+
+type UnitMapper interface {
+	UnitMap() *UnitMap
+}
+
+type dimensionMap int
+
+const (
+	LengthB dimensionMap = iota
+	TimeB
+	MassB
+	CurrentB
+	TemperatureB
+	LuminosityB
+	ChemAmtB
+)
+
+type UnitMap struct {
+	dimension map[dimensionMap]int
+	value     float64
+}
+
+// Check if the dimensions of two units are the same
+func DimensionsMatchMap(aU, bU UnitMapper) bool {
+	a := aU.UnitMap()
+	b := bU.UnitMap()
+	if len(a.dimension) != len(b.dimension) {
+		panic("Unequal dimension")
+	}
+	for key, dimA := range a.dimension {
+		dimB, ok := b.dimension[key]
+		if !ok || dimA != dimB {
+			panic("Unequal dimension")
+		}
+	}
+	return true
+}
+
+func (u *UnitMap) UnitMap() *UnitMap {
+	return u
+}
+
+func (u *UnitMap) Add(aU UnitMapper) *UnitMap {
+	a := aU.UnitMap()
+	if !DimensionsMatchMap(a, u) {
+		panic("dimension mismatch")
+	}
+	u.value += a.value
+	return u
+}
+
+func (u *UnitMap) Mul(aU UnitMapper) *UnitMap {
+	a := aU.UnitMap()
+	for key, val := range a.dimension {
+		u.dimension[key] += val
+	}
+	u.value *= a.value
+	return u
+}
+
+var sink float64
+
+func BenchmarkAddFloat(b *testing.B) {
+	sink = 0
+	c := 10.0
+	for i := 0; i < b.N; i++ {
+		sink += c
+	}
+}
+
+func BenchmarkMulFloat(b *testing.B) {
+	sink = 0
+	c := 10.0
+	for i := 0; i < b.N; i++ {
+		sink *= c
+	}
+}
+
+func BenchmarkAddMapSmall(b *testing.B) {
+	u1 := &UnitMap{value: 10}
+	u1.dimension = make(map[dimensionMap]int)
+	u1.dimension[CurrentB] = 1
+	u1.dimension[ChemAmtB] = 5
+
+	u2 := &UnitMap{value: 10}
+	u2.dimension = make(map[dimensionMap]int)
+	u2.dimension[CurrentB] = 1
+	u2.dimension[ChemAmtB] = 5
+	for i := 0; i < b.N; i++ {
+		u2.Add(u1)
+	}
+}
+
+func BenchmarkMulMapSmallDiff(b *testing.B) {
+	u1 := &UnitMap{value: 10}
+	u1.dimension = make(map[dimensionMap]int)
+	u1.dimension[LengthB] = 1
+
+	u2 := &UnitMap{value: 10}
+	u2.dimension = make(map[dimensionMap]int)
+	u2.dimension[MassB] = 1
+	for i := 0; i < b.N; i++ {
+		u2.Mul(u1)
+	}
+}
+
+func BenchmarkMulMapSmallSame(b *testing.B) {
+	u1 := &UnitMap{value: 10}
+	u1.dimension = make(map[dimensionMap]int)
+	u1.dimension[LengthB] = 1
+
+	u2 := &UnitMap{value: 10}
+	u2.dimension = make(map[dimensionMap]int)
+	u2.dimension[LengthB] = 2
+	for i := 0; i < b.N; i++ {
+		u2.Mul(u1)
+	}
+}
+
+func BenchmarkMulMapLargeDiff(b *testing.B) {
+	u1 := &UnitMap{value: 10}
+	u1.dimension = make(map[dimensionMap]int)
+	u1.dimension[LengthB] = 1
+	u1.dimension[MassB] = 1
+	u1.dimension[ChemAmtB] = 1
+	u1.dimension[TemperatureB] = 1
+	u1.dimension[LuminosityB] = 1
+	u1.dimension[TimeB] = 1
+	u1.dimension[CurrentB] = 1
+
+	u2 := &UnitMap{value: 10}
+	u2.dimension = make(map[dimensionMap]int)
+	u2.dimension[MassB] = 1
+	for i := 0; i < b.N; i++ {
+		u2.Mul(u1)
+	}
+}
+
+func BenchmarkMulMapLargeSame(b *testing.B) {
+	u1 := &UnitMap{value: 10}
+	u1.dimension = make(map[dimensionMap]int)
+	u1.dimension[LengthB] = 2
+	u1.dimension[MassB] = 2
+	u1.dimension[ChemAmtB] = 2
+	u1.dimension[TemperatureB] = 2
+	u1.dimension[LuminosityB] = 2
+	u1.dimension[TimeB] = 2
+	u1.dimension[CurrentB] = 2
+
+	u2 := &UnitMap{value: 10}
+	u2.dimension = make(map[dimensionMap]int)
+	u2.dimension[LengthB] = 3
+	u2.dimension[MassB] = 3
+	u2.dimension[ChemAmtB] = 3
+	u2.dimension[TemperatureB] = 3
+	u2.dimension[LuminosityB] = 3
+	u2.dimension[TimeB] = 3
+	u2.dimension[CurrentB] = 3
+	for i := 0; i < b.N; i++ {
+		u2.Mul(u1)
+	}
+}
diff --git a/vendor/gonum.org/v1/gonum/unit/unitexample_test.go b/vendor/gonum.org/v1/gonum/unit/unitexample_test.go
new file mode 100644
index 00000000..d81faae7
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/unit/unitexample_test.go
@@ -0,0 +1,29 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package unit_test
+
+import (
+	"fmt"
+
+	"gonum.org/v1/gonum/unit"
+)
+
+func ExampleNew() {
+	// Create an acceleration of 3 m/s^2
+	accel := unit.New(3.0, unit.Dimensions{unit.LengthDim: 1, unit.TimeDim: -2})
+	fmt.Println(accel)
+
+	// Output: 3 m s^-2
+}
+
+func ExampleNewDimension() {
+	// Create a "trees" dimension
+	// Typically, this should be used within an init function
+	treeDim := unit.NewDimension("tree")
+	countPerArea := unit.New(0.1, unit.Dimensions{treeDim: 1, unit.LengthDim: -2})
+	fmt.Println(countPerArea)
+
+	// Output: 0.1 tree m^-2
+}
diff --git a/vendor/gonum.org/v1/gonum/unit/unittype.go b/vendor/gonum.org/v1/gonum/unit/unittype.go
new file mode 100644
index 00000000..21311fd9
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/unit/unittype.go
@@ -0,0 +1,342 @@
+// Copyright ©2013 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package unit
+
+import (
+	"bytes"
+	"fmt"
+	"sort"
+)
+
+// Uniter is a type that can be converted to a Unit.
+type Uniter interface {
+	Unit() *Unit
+}
+
+// Dimension is a type representing an SI base dimension or a distinct
+// orthogonal dimension. Non-SI dimensions can be created using the NewDimension
+// function, typically within an init function.
+type Dimension int
+
+// String returns the string for the dimension.
+func (d Dimension) String() string {
+	switch {
+	case d == reserved:
+		return "reserved"
+	case d < Dimension(len(symbols)):
+		return symbols[d]
+	default:
+		panic("unit: illegal dimension")
+	}
+}
+
+const (
+	// SI Base Units
+	reserved Dimension = iota
+	CurrentDim
+	LengthDim
+	LuminousIntensityDim
+	MassDim
+	TemperatureDim
+	TimeDim
+	// Other common SI Dimensions
+	AngleDim // e.g. radians
+)
+
+var (
+	symbols = []string{
+		CurrentDim:           "A",
+		LengthDim:            "m",
+		LuminousIntensityDim: "cd",
+		MassDim:              "kg",
+		TemperatureDim:       "K",
+		TimeDim:              "s",
+		AngleDim:             "rad",
+	}
+
+	// dimensions guarantees there aren't two identical symbols
+	// SI symbol list from http://lamar.colostate.edu/~hillger/basic.htm
+	dimensions = map[string]Dimension{
+		"A":   CurrentDim,
+		"m":   LengthDim,
+		"cd":  LuminousIntensityDim,
+		"kg":  MassDim,
+		"K":   TemperatureDim,
+		"s":   TimeDim,
+		"rad": AngleDim,
+
+		// Reserve common SI symbols
+		// base units
+		"mol": reserved,
+		// prefixes
+		"Y":  reserved,
+		"Z":  reserved,
+		"E":  reserved,
+		"P":  reserved,
+		"T":  reserved,
+		"G":  reserved,
+		"M":  reserved,
+		"k":  reserved,
+		"h":  reserved,
+		"da": reserved,
+		"d":  reserved,
+		"c":  reserved,
+		"μ":  reserved,
+		"n":  reserved,
+		"p":  reserved,
+		"f":  reserved,
+		"a":  reserved,
+		"z":  reserved,
+		"y":  reserved,
+		// SI Derived units with special symbols
+		"sr":  reserved,
+		"F":   reserved,
+		"C":   reserved,
+		"S":   reserved,
+		"H":   reserved,
+		"V":   reserved,
+		"Ω":   reserved,
+		"J":   reserved,
+		"N":   reserved,
+		"Hz":  reserved,
+		"lx":  reserved,
+		"lm":  reserved,
+		"Wb":  reserved,
+		"W":   reserved,
+		"Pa":  reserved,
+		"Bq":  reserved,
+		"Gy":  reserved,
+		"Sv":  reserved,
+		"kat": reserved,
+		// Units in use with SI
+		"ha": reserved,
+		"L":  reserved,
+		"l":  reserved,
+		// Units in Use Temporarily with SI
+		"bar": reserved,
+		"b":   reserved,
+		"Ci":  reserved,
+		"R":   reserved,
+		"rd":  reserved,
+		"rem": reserved,
+	}
+)
+
+// Dimensions represent the dimensionality of the unit in powers
+// of that dimension. If a key is not present, the power of that
+// dimension is zero. Dimensions is used in conjunction with New.
+type Dimensions map[Dimension]int
+
+func (d Dimensions) String() string {
+	// Map iterates randomly, but print should be in a fixed order. Can't use
+	// dimension number, because for user-defined dimension that number may
+	// not be fixed from run to run.
+	atoms := make(unitPrinters, 0, len(d))
+	for dimension, power := range d {
+		if power != 0 {
+			atoms = append(atoms, atom{dimension, power})
+		}
+	}
+	sort.Sort(atoms)
+	var b bytes.Buffer
+	for i, a := range atoms {
+		if i > 0 {
+			b.WriteByte(' ')
+		}
+		fmt.Fprintf(&b, "%s", a.Dimension)
+		if a.pow != 1 {
+			fmt.Fprintf(&b, "^%d", a.pow)
+		}
+	}
+
+	return b.String()
+}
+
+type atom struct {
+	Dimension
+	pow int
+}
+
+type unitPrinters []atom
+
+func (u unitPrinters) Len() int {
+	return len(u)
+}
+
+func (u unitPrinters) Less(i, j int) bool {
+	// Order first by positive powers, then by name.
+	if u[i].pow*u[j].pow < 0 {
+		return u[i].pow > 0
+	}
+	return u[i].String() < u[j].String()
+}
+
+func (u unitPrinters) Swap(i, j int) {
+	u[i], u[j] = u[j], u[i]
+}
+
+// NewDimension creates a new orthogonal dimension with the given symbol, and
+// returns the value of that dimension. The input symbol must not overlap with
+// any of the any of the SI base units or other symbols of common use in SI ("kg",
+// "J", etc.), and must not overlap with any other dimensions created by calls
+// to NewDimension. The SymbolExists function can check if the symbol exists.
+// NewDimension will panic if the input symbol matches an existing symbol.
+//
+// NewDimension should only be called for unit types that are actually orthogonal
+// to the base dimensions defined in this package. Please see the package-level
+// documentation for further explanation.
+func NewDimension(symbol string) Dimension {
+	_, ok := dimensions[symbol]
+	if ok {
+		panic("unit: dimension string \"" + symbol + "\" already used")
+	}
+	d := Dimension(len(symbols))
+	symbols = append(symbols, symbol)
+	dimensions[symbol] = d
+	return d
+}
+
+// SymoblExists returns whether the given symbol is already in use.
+func SymbolExists(symbol string) bool {
+	_, ok := dimensions[symbol]
+	return ok
+}
+
+// Unit represents a dimensional value. The dimensions will typically be in SI
+// units, but can also include dimensions created with NewDimension. The Unit type
+// is most useful for ensuring dimensional consistency when manipulating types
+// with different units, for example, by multiplying  an acceleration with a
+// mass to get a force. Please see the package documentation for further explanation.
+type Unit struct {
+	dimensions Dimensions
+	formatted  string
+	value      float64
+}
+
+// New creates a new variable of type Unit which has the value and dimensions
+// specified by the inputs. The built-in dimensions are always in SI units
+// (meters, kilograms, etc.).
+func New(value float64, d Dimensions) *Unit {
+	u := &Unit{
+		dimensions: make(map[Dimension]int),
+		value:      value,
+	}
+	for key, val := range d {
+		if val != 0 {
+			u.dimensions[key] = val
+		}
+	}
+	return u
+}
+
+// DimensionsMatch checks if the dimensions of two Uniters are the same.
+func DimensionsMatch(a, b Uniter) bool {
+	aUnit := a.Unit()
+	bUnit := b.Unit()
+	if len(aUnit.dimensions) != len(bUnit.dimensions) {
+		return false
+	}
+	for key, val := range aUnit.dimensions {
+		if bUnit.dimensions[key] != val {
+			return false
+		}
+	}
+	return true
+}
+
+// Add adds the function argument to the receiver. Panics if the units of
+// the receiver and the argument don't match.
+func (u *Unit) Add(uniter Uniter) *Unit {
+	a := uniter.Unit()
+	if !DimensionsMatch(u, a) {
+		panic("unit: mismatched dimensions in addition")
+	}
+	u.value += a.value
+	return u
+}
+
+// Unit implements the Uniter interface
+func (u *Unit) Unit() *Unit {
+	return u
+}
+
+// Mul multiply the receiver by the input changing the dimensions
+// of the receiver as appropriate. The input is not changed.
+func (u *Unit) Mul(uniter Uniter) *Unit {
+	a := uniter.Unit()
+	for key, val := range a.dimensions {
+		if d := u.dimensions[key]; d == -val {
+			delete(u.dimensions, key)
+		} else {
+			u.dimensions[key] = d + val
+		}
+	}
+	u.formatted = ""
+	u.value *= a.value
+	return u
+}
+
+// Div divides the receiver by the argument changing the
+// dimensions of the receiver as appropriate.
+func (u *Unit) Div(uniter Uniter) *Unit {
+	a := uniter.Unit()
+	u.value /= a.value
+	for key, val := range a.dimensions {
+		if d := u.dimensions[key]; d == val {
+			delete(u.dimensions, key)
+		} else {
+			u.dimensions[key] = d - val
+		}
+	}
+	u.formatted = ""
+	return u
+}
+
+// Value return the raw value of the unit as a float64. Use of this
+// method is, in general, not recommended, though it can be useful
+// for printing. Instead, the From type of a specific dimension
+// should be used to guarantee dimension consistency.
+func (u *Unit) Value() float64 {
+	return u.value
+}
+
+// Format makes Unit satisfy the fmt.Formatter interface. The unit is formatted
+// with dimensions appended. If the power if the dimension is not zero or one,
+// symbol^power is appended, if the power is one, just the symbol is appended
+// and if the power is zero, nothing is appended. Dimensions are appended
+// in order by symbol name with positive powers ahead of negative powers.
+func (u *Unit) Format(fs fmt.State, c rune) {
+	if u == nil {
+		fmt.Fprint(fs, "<nil>")
+	}
+	switch c {
+	case 'v':
+		if fs.Flag('#') {
+			fmt.Fprintf(fs, "&%#v", *u)
+			return
+		}
+		fallthrough
+	case 'e', 'E', 'f', 'F', 'g', 'G':
+		p, pOk := fs.Precision()
+		w, wOk := fs.Width()
+		switch {
+		case pOk && wOk:
+			fmt.Fprintf(fs, "%*.*"+string(c), w, p, u.value)
+		case pOk:
+			fmt.Fprintf(fs, "%.*"+string(c), p, u.value)
+		case wOk:
+			fmt.Fprintf(fs, "%*"+string(c), w, u.value)
+		default:
+			fmt.Fprintf(fs, "%"+string(c), u.value)
+		}
+	default:
+		fmt.Fprintf(fs, "%%!%c(*Unit=%g)", c, u)
+		return
+	}
+	if u.formatted == "" && len(u.dimensions) > 0 {
+		u.formatted = u.dimensions.String()
+	}
+	fmt.Fprintf(fs, " %s", u.formatted)
+}

From a74edc5121a05347df9a782119403cc42c5cda38 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E4=BA=8E=E7=BA=A2=E9=9B=A8?= <yuhongyu04@126.com>
Date: Fri, 21 Sep 2018 16:22:15 +0800
Subject: [PATCH 6/8] test order difficulty

---
 gateway/wallet_service.go | 5 +----
 1 file changed, 1 insertion(+), 4 deletions(-)

diff --git a/gateway/wallet_service.go b/gateway/wallet_service.go
index efd2bfdb..91892a21 100644
--- a/gateway/wallet_service.go
+++ b/gateway/wallet_service.go
@@ -412,9 +412,6 @@ type AddTokenReq struct {
 	Decimals             string `json:"decimals"`
 }
 
-type OrderDifficultyReq struct {
-}
-
 type OrderDifficultyRes struct {
 	Difficulty common.Hash `json:"difficulty"`
 }
@@ -554,7 +551,7 @@ func (w *WalletServiceImpl) GetPriceQuote(query PriceQuoteQuery) (result PriceQu
 	return rst, nil
 }
 
-func (w *WalletServiceImpl) GetOrderDifficulty(req OrderDifficultyReq) (result OrderDifficultyRes, err error) {
+func (w *WalletServiceImpl) GetOrderDifficulty() (result OrderDifficultyRes, err error) {
 	diff, err1 := order_difficulty.GetDifficulty()
 	return OrderDifficultyRes{Difficulty: diff}, err1
 }

From 29242a64695078f63bc0bf472801c3557716954e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E4=BA=8E=E7=BA=A2=E9=9B=A8?= <yuhongyu04@126.com>
Date: Fri, 21 Sep 2018 16:59:21 +0800
Subject: [PATCH 7/8] test order difficulty

---
 config/relay.toml                           |  6 ++++
 gateway/gateway.go                          | 14 +++++----
 gateway/order_difficulty/difficulty.go      | 32 ++++++++++-----------
 gateway/order_difficulty/difficulty_test.go | 14 ++++-----
 4 files changed, 35 insertions(+), 31 deletions(-)

diff --git a/config/relay.toml b/config/relay.toml
index 05c0f98c..e45392ca 100644
--- a/config/relay.toml
+++ b/config/relay.toml
@@ -132,3 +132,9 @@ title = "miner"
 [cloud_watch]
     enabled = false
     region = ""
+
+[order_difficulty]
+    base_difficulty = "0x0000000000000000000000000000000000000000000000000000000000000010"
+    threshold = 20
+    cal_count = 100
+    duration = 2
\ No newline at end of file
diff --git a/gateway/gateway.go b/gateway/gateway.go
index f1e3f4ff..73e865ce 100644
--- a/gateway/gateway.go
+++ b/gateway/gateway.go
@@ -24,6 +24,7 @@ import (
 	"errors"
 	"fmt"
 	"github.com/Loopring/relay-cluster/accountmanager"
+	"github.com/Loopring/relay-cluster/gateway/order_difficulty"
 	"github.com/Loopring/relay-cluster/ordermanager/manager"
 	"github.com/Loopring/relay-cluster/ordermanager/viewer"
 	"github.com/Loopring/relay-lib/broadcast"
@@ -36,8 +37,8 @@ import (
 	"github.com/Loopring/relay-lib/types"
 	"github.com/ethereum/go-ethereum/common"
 	"math/big"
-	"time"
 	"strings"
+	"time"
 )
 
 type Gateway struct {
@@ -85,7 +86,7 @@ func Initialize(filterOptions *GatewayFiltersOptions, options *GateWayOptions, o
 	gateway.marketCap = marketCap
 
 	// new pow filter
-	powFilter := &PowFilter{Difficulty: types.HexToBigint(filterOptions.PowFilter.Difficulty)}
+	powFilter := &PowFilter{}
 
 	// new base filter
 	baseFilter := &BaseFilter{
@@ -400,7 +401,6 @@ func (f *CutoffFilter) filter(o *types.Order) (bool, error) {
 }
 
 type PowFilter struct {
-	Difficulty *big.Int
 }
 
 func (f *PowFilter) filter(o *types.Order) (bool, error) {
@@ -410,9 +410,11 @@ func (f *PowFilter) filter(o *types.Order) (bool, error) {
 	}
 
 	pow := GetPow(o.V, o.R, o.S, o.PowNonce)
-
-	if pow.Cmp(f.Difficulty) < 0 {
-		return false, fmt.Errorf("invalid pow")
+	if diffHex, err := order_difficulty.GetDifficulty(); nil == err {
+		diff := types.HexToBigint(diffHex)
+		if pow.Cmp(diff) < 0 {
+			return false, fmt.Errorf("invalid pow")
+		}
 	}
 	return true, nil
 }
diff --git a/gateway/order_difficulty/difficulty.go b/gateway/order_difficulty/difficulty.go
index 08c42f6a..50f508dd 100644
--- a/gateway/order_difficulty/difficulty.go
+++ b/gateway/order_difficulty/difficulty.go
@@ -48,7 +48,7 @@ type OrderDifficultyEvaluator struct {
 }
 
 type OrderDifficulty struct {
-	Difficulty common.Hash
+	Difficulty string
 	OrdersNum  int64
 	TimeStamp  int64
 }
@@ -68,8 +68,8 @@ func (evaluator *OrderDifficultyEvaluator) getDiffCacheKey(createTime int64) (ke
 }
 
 func NewOrderDifficultyEvaluator(config OrderDifficultyConfig) *OrderDifficultyEvaluator {
-	if nil == config.BaseDifficulty {
-		config.BaseDifficulty = big.NewInt(0)
+	if "" == config.BaseDifficulty {
+		config.BaseDifficulty = "0x10"
 	}
 	if 0 == config.CalCount {
 		config.CalCount = 1000
@@ -81,12 +81,13 @@ func NewOrderDifficultyEvaluator(config OrderDifficultyConfig) *OrderDifficultyE
 		config.Threshold = 10
 	}
 	evaluator := &OrderDifficultyEvaluator{calCount: config.CalCount, duration: config.Duration}
-	evaluator.evaluator = &LinearEvaluator{baseDifficulty: config.BaseDifficulty, threshold: config.Threshold}
+	baseDifficulty := types.HexToBigint(config.BaseDifficulty)
+	evaluator.evaluator = &LinearEvaluator{baseDifficulty: baseDifficulty, threshold: config.Threshold}
 	return evaluator
 }
 
 type OrderDifficultyConfig struct {
-	BaseDifficulty *big.Int
+	BaseDifficulty string
 	Threshold      int64
 	CalCount       int64
 	Duration       int64
@@ -99,9 +100,8 @@ func (evaluator *OrderDifficultyEvaluator) Start() {
 			log.Errorf("erro:%s", err.Error())
 		} else {
 			if _, err1 := GetDifficulty(); nil != err1 {
-				println("##########")
-				diff := common.BytesToHash(evaluator.evaluator.getBaseDifficulty().Bytes())
-				cache.Set(OrderDifficultyKey, []byte(diff.Hex()), int64(10000))
+				diffHex := types.BigintToHex(evaluator.evaluator.getBaseDifficulty())
+				cache.Set(OrderDifficultyKey, []byte(diffHex), int64(10000))
 			}
 			//now := time.Now().Unix()
 			//orderCntList := []*OrderDifficulty{}
@@ -118,8 +118,8 @@ func (evaluator *OrderDifficultyEvaluator) Start() {
 				select {
 				case <-time.After(time.Duration(evaluator.duration) * time.Second):
 					now := time.Now().Unix()
-					if diffHash, err := GetDifficulty(); nil == err {
-						currentDiff := diffHash
+					if diffHex, err := GetDifficulty(); nil == err {
+						currentDiff := diffHex
 						orderDiff := &OrderDifficulty{}
 						cacheKey, _ := evaluator.getOrderCacheKey(now)
 						orderDiff.OrdersNum = 0
@@ -215,7 +215,7 @@ func (evaluator *LinearEvaluator) CalcAndSaveDifficulty(orderCntList []*OrderDif
 	return evaluator.nextDifficulty(orderList)
 }
 
-func NewOrderDiff(ordersNum int64, diff common.Hash) *OrderDifficulty {
+func NewOrderDiff(ordersNum int64, diff string) *OrderDifficulty {
 	return &OrderDifficulty{OrdersNum: ordersNum, Difficulty: diff}
 }
 
@@ -229,8 +229,8 @@ func (evaluator *LinearEvaluator) nextDifficulty(orderCntList []*OrderDifficulty
 		return evaluator.baseDifficulty
 	} else {
 		currentDiff := new(big.Int).Set(evaluator.baseDifficulty)
-		if currentDiffBytes, err := GetDifficulty(); nil == err {
-			currentDiff = new(big.Int).SetBytes(currentDiffBytes.Bytes())
+		if currentDiffHex, err := GetDifficulty(); nil == err {
+			currentDiff = types.HexToBigint(currentDiffHex)
 		}
 		addRatio := big.NewInt(3)
 		if nextOrderDiff.OrdersNum > int64(float64(evaluator.threshold)*1.5) {
@@ -242,10 +242,10 @@ func (evaluator *LinearEvaluator) nextDifficulty(orderCntList []*OrderDifficulty
 	}
 }
 
-func GetDifficulty() (common.Hash, error) {
+func GetDifficulty() (string, error) {
 	if data, err := cache.Get(OrderDifficultyKey); nil == err {
-		return common.HexToHash(string(data)), nil
+		return string(data), nil
 	} else {
-		return common.Hash{}, err
+		return "0x0", err
 	}
 }
diff --git a/gateway/order_difficulty/difficulty_test.go b/gateway/order_difficulty/difficulty_test.go
index 9dd69d6d..defff98c 100644
--- a/gateway/order_difficulty/difficulty_test.go
+++ b/gateway/order_difficulty/difficulty_test.go
@@ -24,8 +24,8 @@ import (
 	"github.com/Loopring/relay-lib/cache"
 	"github.com/Loopring/relay-lib/cache/redis"
 	"github.com/Loopring/relay-lib/log"
+	"github.com/Loopring/relay-lib/types"
 	"github.com/Loopring/relay-lib/zklock"
-	"github.com/ethereum/go-ethereum/common"
 	"go.uber.org/zap"
 	"math/big"
 	"testing"
@@ -70,14 +70,10 @@ func TestEvaluator(t *testing.T) {
 func TestLinearEvaluator_CalcAndSaveDifficulty(t *testing.T) {
 	evaluator := order_difficulty.NewLinearEvaluator(big.NewInt(100), 200)
 	cntList := make([]*order_difficulty.OrderDifficulty, 0)
-	cntList = append(cntList, order_difficulty.NewOrderDiff(100, common.BytesToHash(big.NewInt(100).Bytes())))
-	cntList = append(cntList, order_difficulty.NewOrderDiff(900, common.BytesToHash(big.NewInt(200).Bytes())))
-	cntList = append(cntList, order_difficulty.NewOrderDiff(900, common.BytesToHash(big.NewInt(200).Bytes())))
-	cntList = append(cntList, order_difficulty.NewOrderDiff(400, common.BytesToHash(big.NewInt(200).Bytes())))
-	cntList = append(cntList, order_difficulty.NewOrderDiff(400, common.BytesToHash(big.NewInt(200).Bytes())))
-	cntList = append(cntList, order_difficulty.NewOrderDiff(400, common.BytesToHash(big.NewInt(200).Bytes())))
-	cntList = append(cntList, order_difficulty.NewOrderDiff(400, common.BytesToHash(big.NewInt(200).Bytes())))
-	cntList = append(cntList, order_difficulty.NewOrderDiff(600, common.BytesToHash(big.NewInt(200).Bytes())))
+	cntList = append(cntList, order_difficulty.NewOrderDiff(100, types.BigintToHex(big.NewInt(100))))
+	cntList = append(cntList, order_difficulty.NewOrderDiff(900, types.BigintToHex(big.NewInt(200))))
+	cntList = append(cntList, order_difficulty.NewOrderDiff(900, types.BigintToHex(big.NewInt(200))))
+	cntList = append(cntList, order_difficulty.NewOrderDiff(400, types.BigintToHex(big.NewInt(200))))
 	//cntList = append(cntList, order_difficulty.NewOrderDiff(700, common.BytesToHash(big.NewInt(200).Bytes())))
 	//cntList = append(cntList, order_difficulty.NewOrderDiff(700, common.BytesToHash(big.NewInt(200).Bytes())))
 	println(evaluator.CalcAndSaveDifficulty(cntList, 10).String())

From 3d8f95539ab19a8a606c83395e0188ca877a863d Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E4=BA=8E=E7=BA=A2=E9=9B=A8?= <yuhongyu04@126.com>
Date: Fri, 21 Sep 2018 17:07:41 +0800
Subject: [PATCH 8/8] fix compile bug

---
 gateway/wallet_service.go | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/gateway/wallet_service.go b/gateway/wallet_service.go
index 91892a21..77803e10 100644
--- a/gateway/wallet_service.go
+++ b/gateway/wallet_service.go
@@ -413,7 +413,7 @@ type AddTokenReq struct {
 }
 
 type OrderDifficultyRes struct {
-	Difficulty common.Hash `json:"difficulty"`
+	Difficulty string `json:"difficulty"`
 }
 
 type WalletServiceImpl struct {